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A NOVEL PROCESS FOR FABRICATING
MEMBRANE-ELECTRODE ASSEMBLIES
WITH LOW PLATINUM LOADING FOR USE
IN PROTON EXCHANGE MEMBRANE FUEL
CELLS
by
Shahram Karimi
A thesis submitted in conformity with the requirements for the
degree of Doctor of Philosophy
Graduate Department of Chemical Engineering and Applied
Chemistry
University of Toronto
Copyright by Shahram Karimi (2011)
ii
A NOVEL PROCESS FOR FABRICATING MEMBRANE-ELECTRODE
ASSEMBLIES WITH LOW PLATINUM LOADING FOR USE IN PROTON
EXCHANGE MEMBRANE FUEL CELLS
Shahram Karimi
Doctor of Philosophy
Department of Chemical Engineering & Applied Chemistry
University of Toronto (2011)
ABSTRACT
A novel method based on pulse current electrodeposition (PCE) employing four different
waveforms was developed and utilized for fabricating membrane-electrode assemblies
(MEAs) with low platinum loading for use in low-temperature proton exchange
membrane fuel cells. It was found that both peak deposition current density and duty
cycle control the nucleation rate and the growth of platinum crystallites. Based on the
combination of parameters used in this study, the optimum conditions for PCE were
found to be a peak deposition current density of 400 mA cm-2
, a duty cycle of 4%, and a
pulse generated and delivered in the microsecond range utilizing a ramp-down waveform.
MEAs prepared by PCE using the ramp-down waveform show performance comparable
with commercial MEAs that employ ten times the loading of platinum catalyst. The
thickness of the pulse electrodeposited catalyst layer is about 5-7 µm, which is ten times
thinner than that of commercial state-of-the-art electrodes.
MEAs prepared by PCE outperformed commercial MEAs when subjected to a series of
steady-state and transient lifetime tests. In steady-state lifetime tests, the average cell
voltage over a 3000-h period at a constant current density of 619 mA cm-2
for the in-
house and the state-of-the-art MEAs were 564 mV and 505 mV, respectively. In
addition, the influence of substrate and carbon powder type, hydrophobic polymer
content in the gas diffusion layer, microporous layer loading, and the through-plane gas
permeability of different gas diffusion layers on fuel cell performance were investigated
and optimized.
iii
Finally, two mathematical models based on the microhardness model developed by
Molina et al. [J. Molina, B. A. Hoyos, Electrochim. Acta, 54 (2009) 1784-1790] and
Milchev [A. Milchev, ―Electrocrystallization: Fundamentals of Nucleation And Growth‖
2002, Kluwer Academic Publishers, 189-215] were refined and further developed, one
based on pure diffusion control and another based on joint diffusion, ohmic and charge
transfer control developed by Milchev [A. Milchev, J. Electroanal. Chem., 312 (1991)
267-275 & A. Milchev, Electrochim. Acta, 37 (12) (1992) 2229-2232]. Experimental
results validated the above models and a strong correlation between the microhardness
and the particle size of the deposited layer was established.
iv
ACKNOWLEDGEMENTS
I would like to take this opportunity to express my most heartfelt gratitude and deepest
appreciation to my supervisor, Professor Frank Foulkes, first for the immeasurable
amount of support, encouragement, and guidance he has provided throughout this
research and second, and equally important, for all the invaluable life lessons and
sometimes short but often long discussions on anything and everything. Professor
Foulkes’ insights and, more importantly, patience throughout this research have been
enlivening. I would also like to extend my sincerest thanks to my committee members
Professor Charles Mims and Professor Donald Kirk for their continued support and
guidance and, at times, a much-needed push to put me back on the right track.
Last, but not least, I am greatly indebted to my wife, Shahin, for her unending love,
unlimited patience and support, and for giving me the opportunity to follow my dreams.
Her unselfish character, kind nature, and constant encouragement have made a world of
difference and words cannot express my deepest feelings and appreciations. This is hers
as much as it is mine.
v
TABLE OF CONTENTS PAGE NO.
ABSTRACT……………………………………………………………….... ii
ACKNOWLEDGMENTS………………………………………………... ….. iv
TABLE OF CONTENTS………………………………………………… ….. v
LIST OF FIGURES………………………………………………………. ….. x
LIST OF TABLES………………………………………………………... ….. xviii
NOMENCLATURE………………………………………………………. ….. xx
1 INTRODUCTION
1.1 Rationale…………………………………………………… ….. 1
1.2 Catalyst Layer……………………………………………… ….. 2
1.3 Pulse Electroplating………………………………………... ….. 3
1.4 Thesis Objectives…………………………………………... ….. 5
2 BACKGROUND
2.1 Hydrogen Fuel Cells……………………………………….. ….. 6
2.1.1 A Condensed History………………………………. ….. 6
2.1.2 How Fuel Cells Work…………………………........ ….. 7
2.1.3 Different Types of Fuel Cells……………………… ….. 8
2.2 Main Components of a Fuel Cell………………………… ….. 9
2.2.1 Polymer Electrolyte Membrane……………………. ….. 9
2.2.2 Catalyst Layer……………………………………… ….. 13
2.2.3 Gas Diffusion Layer………………………………. ….. 16
2.2.4 Bipolar Plates……………………………………… ….. 20
3 FUEL CELL THERMODYNAMICS
3.1 Introduction………………………………………………… ….. 38
3.2 Reversible Cell Voltage under Non-Standard Conditions…. ….. 38
3.2.1 Introduction………………………………………… ….. 38
3.2.2 Reversible Cell Voltage as a Function of
Temperature……………………………………… ….. 38
3.2.3 Reversible Cell Voltage as a Function of
Pressure…………………………………………… ….. 40
3.5.4 Reversible Cell Voltage as a Function of
Concentration……………………………………… ….. 42
3.3 Fuel Cell Efficiency……………………………………… ….. 43
vi
4 FUEL CELL ELECTROCHEMISTRY
4.1 Introduction………………………………………………… ….. 45
4.2 Electrode Kinetics………………………………………… ….. 45
4.3 The Butler-Volmer Equation……………………………… ….. 47
4.4 Overvoltage and Current Density………………………… ….. 49
4.5 Fuel Cell Losses…………………………………………… ….. 51
4.5.1 Introduction……………………………………..… ….. 51
4.5.2 Activation Overvoltage…………………………… ….. 52
4.5.3 Ohmic Overvoltage………………………………… ….. 54
4.5.4 Concentration Overvoltage ...……………………… ….. 55
4.5.5 Mixed Potential at Electrodes……………………… ….. 56
5 CATALYST LOADING 5.1 Introduction…………………………………………………... 57
5.2 Catalyst Loading Methods………………………………… …... 58
5.2.1 Application of Catalyst to Gas Diffusion Layers ..... …... 59
5.2.1.1 Application of Catalyst by Spreading ………. 60
5.2.1.2 Application of Catalyst by Spraying……….... 61
5.2.1.3 Application of Catalyst by Painting………….. 62
5.2.1.4 Application of Catalyst by Powder
Deposition ……………………………………. 63
5.2.1.5 Application of Catalyst by Ionomer
Impregnation …………………………………. 63
5.2.1.6 Application of Catalyst by Electrodeposition. 65
5.2.2 Application of Catalyst to Membrane………………… 65
5.2.2.1 Application of Catalyst by Painting …………. 66
5.2.2.2 Application of Catalyst by Dry Spraying……. 67
5.2.2.3 Application of Catalyst by Sputtering ……….. 68
5.2.2.4 Application of Catalyst by Impregnation
Reduction …………………………………….. 72
5.2.2.5 Application of Catalyst by Evaporative
Deposition ……………………………………. 73
6 ELECTRODEPOSITION 6.1 Introduction ………………………………………………….. 75
6.2 Electroless Deposition ……………………………………….. 75
6.2.1 Electroless Palladium Deposition ……………………. 79
6.2.2 Electroless Platinum Deposition ……………………… 80
6.3 Pulse and Direct Current Electrodeposition………………….. 81
6.3.1 Introduction …………………………………………… 81
6.3.2 Direct Current Electrodeposition …………………….. 82
6.3.3 Pulse Current Electrodeposition………………………. 86
6.3.3.1 Introduction …………………………………… 86
6.3.3.2 Factors Influencing PC Electrodeposition……. 88
6.3.3.3 Major Types of Pulse Waveforms …………… 92
6.3.4 Nucleation and Growth during Electrocatalyzation….. 94
vii
6.3.4.1 Nucleation Rate ……………………………… 97
6.3.5 Electrodeposition of Metals and Alloys…………… ….. 98
6.3.5.1 Introduction………………………………….. 98
6.3.5.2 Copper and its Alloys………………………….. 98
6.3.5.3 Nickel and its Alloys………………………. ….. 103
6.3.5.4 Platinum and its Alloys……………………. ….. 106
6.3.5.5 Other Metals and Alloys…………………….. 115
7 EXPERIMENTAL PROCEDURES 7.1 Hydrophobic Polymer Coating……………………………..... 118
7.2 Sintering of Treated Carbon Substrates…………………….... 119
7.3 Carbon Ink Preparation: Microporous Layer Application…. …… 119
7.4 Nafion Impregnation………………………………………..... 120
7.5 Catalyst Electrodeposition………………………………….... 121
7.5.1 Platinum Electrodeposition…………………………… 121
7.5.2 Copper Electrodeposition…………………………….. 124
7.5.3 Nickel Electrodeposition……………………………… 124
7.6 MEA Fabrication and Testing……………………………….... 125
7.6.1 MEA Preparation……………………………………..... 125
7.6.2 Electrochemical Measurements……………………….. 125
7.6.2.1 Single Fuel Cell Tests………………………….. 125
7.6.2.2 Life Test and Durability Assessment of MEAs:
Static Testing…………………………………. 127
7.6.2.3 Life Test and Durability Assessment of MEAs:
Dynamic Testing………………………………. 128
7.6.2.4 X-Ray Diffraction…………………………….. 130
7.6.2.5 Scanning Electron Microscopy……………….. 130
7.6.2.6 Transmission Electron Microscopy…………... 131
7.7 Porosity Measurements of Gas Diffusion Layer………….... ….... 131
7.8 Through-Plane Gas Permeability……………………………... 132
8 RESULTS AND DISCUSSION 8.1 Influence of Hydrophobic Polymer (PTFE) Content in GDL 134
8.1.1 Influence of PTFE Loading on Cell Performance…… 135
8.1.2 Influence of PTFE Loading in Microporous Layer on
Cell Performance……………..……………………….. 138
8.1.3 Influence of MPL Loading on Cell Performance……. 141
8.2 Effects of Carbon Powder Characteristics on Cell
Performance…………………………………………………... 144
8.3 Nafion Impregnation…………………………………………….. 155
8.3.1 Impregnation Time……………………………………… 155
8.3.2 Nafion®
Ion-Exchange Capacity………………………… 160
8.4 Effect of Substrate Type on Cell Performance………………….. 161
8.4.1 Influence of Substrate Thickness and Other Physical
Parameters……………………………………………….. 161
8.4.2. Porosity Measurements………………………………….. 170
viii
8.4.3 Through-Plane Gas Permeability………………………. 171
8.5 Catalyst Electrodeposition……………………………………… 181
8.5.1 Copper Electrodeposition………………………………. 181
8.5.2 Elemental Analysis using EDX………………………. 184
8.5.3 Platinum Electrodeposition…………………………... 187
8.5.3.1 Direct Current Electrodeposition…………..... 187
8.5.3.2 Pulse Current Electrodeposition……………... 190
8.5.3.2.1 Influence of Cathodic Peak Current
Density……………………………… 190
8.5.3.2.2 Influence of Duty Cycle…………… 194
8.5.3.2.2.1 Regular Duty Cycles:
10%-100%...................... 194
8.5.3.2.2.2 Low Duty Cycles:
2%-10%......................... 196
8.5.3.2.3 Influence of Pulse Duration……….. 199
8.5.3.3 Influence of Plating Bath Concentration on
MEA Performance………………………….... 202
8.5.3.4 Platinum Distribution in Carbon Substrates
Fabricated by Pulse Electrodeposition………. 206
8.5.4 Effect of Pulse Current Waveform on
Electrodeposited Catalyst Layer Properties……..…… 209
8.5.5 Effect of Plating Solution Flow Rate on MEA
Performance……………………………………………. 213
8.5.6 Anode Platinum Loading………………………………. 215
8.5.7 Lifetime Behaviour of MEAs Prepared by Pulse
Electrodeposition and Conventional Techniques:
Static Testing…………………………………………. 217
8.5.8 Lifetime Behaviour of MEAs Prepared by Pulse
Electrodeposition and Conventional Techniques:
Dynamic Testing……………………………………... 221
9 MATHEMATICAL MODEL
9.1 Introduction………………………………………………….. 227
9.2 Mathematical Model Development…………………………. 227
9.2.1 Concentration and Overvoltage Profiles of
Different Current Waveforms……………………….. 227
9.2.2 Electrochemical Nucleation and Critical Nucleus…... 233
9.2.3 Different Types of Crystal Growth…… …... 238
9.2.3.1 Electrochemical Crystal Growth under Pure
Charge Transfer Control……………………… 239
9.2.3.2 Electrochemical Crystal Growth under Combined
Charge Transfer and Diffusion Control………… 240
9.2.3.3 Electrochemical Crystal Growth under Pure
Diffusion Control……………………………….. 242
9.2.3.4 Electrochemical Crystal Growth under
Ohmic Control……………………………….. 242
ix
9.2.3.5 Electrochemical Crystal Growth under
Combined Charge Transfer and Ohmic Control 243
9.3 Model Validation…………………………………………….. 245
9.3.1. Nickel Electrodeposition…………………………….. 245
9.3.2 Model Predictions for Nickel Concentration
Overvoltage for Various Waveforms………………. ….. 251
9.3.3 Platinum Electrodeposition………………………….. 261
9.3.3.1 Modification of the Mathematical Model for
Platinum Electrodeposition………………….. 262
9.3.3.1.1 Effect of Supporting Electrolyte….. 263
9.3.3.2 Comparison of Experimental and Model
Platinum Microhardness Data……………….. 280
9.3.3.3 Platinum Concentration Variation in the
Cathode Diffusion Layer……………………. 283
9.3.3.4 Concentration Overvoltage and Pulse Current
Waveforms…………………………………… 285
9.3.3.5 Nucleation Rate and Pulse Current
Waveforms…………………………………… 286
9.3.3.6 Duty Cycle and Pulse Current Waveforms… ….. 288
9.3.3.7 Influence of Waveform on Critical Nucleus
Size………………………………………….... 293
9.3.3.8 Influence of Cathodic Peak Deposition
Current Density on Nucleation Rate of
Platinum for Various Waveforms………….... 295
9.3.3.9 Comparison of Commercial and In-House
MEAs…………………………………………. 302
10 CONCLUSIONS……….................................................................. …... 305
11 RECOMMENDATIONS AND FUTURE WORK……………….. 309
12 REFERENCES………………………………………………………. 310
13 APPENDICES……………………………………………………….. 334
Appendix A: Physical data for platinum group metals……… 334
Appendix B: The electrical double layer…………………….. 335
Appendix C: Pump calibration data………………………….. 341
Appendix D: Derivation of equations……………………….. 344
Appendix E: Microhardness test.…………………………….. 382
x
LIST OF FIGURES
Figure 1-1 Schematic diagram of a square pulse current waveform
Figure 2-1 A simple proton exchange membrane fuel cell
Figure 2-2 Nafion® perfluorinated ionomer
Figure 2-3 (a) Toray carbon paper and (b) Toray carbon cloth
Figure 2-4 Classification of materials for bipolar plates in PEMFCs
Figure 2-5 Different flow field configurations: (a) parallel, (b) serpentine, (c) parallel-
serpentine, (d) interdigitated, and (e) pin or grid type
Figure 3-1 Reversible cell potential as a function of pressure for PEMFCs at 25 °C
Figure 4-1 A typical performance curve for a hydrogen fuel cell operated at STP
Figure 5-1 A simple schematic of a five-layer membrane-electrode assembly
Figure 5-2 Catalyst loading methods
Figure 6-1 A simplified equivalent circuit for single-electrode reaction
Figure 6-2 Actual and Nernst diffusion layers during non-steady-state electrolysis
Figure 6-3 Free energy of formation of a cluster as a function of size N
Figure 7-1 Drying of substrates in an oven
Figure 7-2 Electrodeposition flow cell
Figure 7-3 Different types of waveform
Figure 7-4 A simple representation of MEA fabrication process
Figure 7-5 A simple schematic of the experimental setup for MEA characterization
Figure 7-6 Schematic representation of a 200-W PEMFC system used in a tricycle
Figure 7-7 Fuel cell bicycle (direct drive)
Figure 7-8 Laboratory apparatus for through-plane permeability measurement of GDLs
Figure 8-1 Surface Morphology of Carbon Paper Substrates before (a) and after (b)
PTFE application (60 wt%)
Figure8-2(a) Impact of PTFE loading on through-plane resistivity of PTFE-treated
Toray TGP-H-090 carbon papers at various pressures (sintering
temperature: 360 °C; surface area: 10 cm2)
Figure 8-2(b) Impact of PTFE loading on through-plane resistivity of PTFE-treated
Toray TGP-H-090 carbon papers at various pressures (sintering
temperature: 360 °C; surface area: 10 cm2)
Figure 8-3 Influence of sintering temperature on through-plane resistivity of PTFE-
treated carbon papers subjected to varying pressures (PTFE loading: 110%;
surface area: 10 cm2)
xi
Figure 8-4 Influence of PTFE content on fuel cell performance operated at a cell
temperature of 50 °C in H2/Air with a platinum loading of 0.3 mg cm-2
per
electrode
Figure 8-5 Fuel cell potential with varying PTFE content at different current densities
operated at a cell temperature of 50 °C in H2/Air with a platinum loading of
0.3 mg cm-2
per electrode
Figure 8-6 Influence of diffusion layer loading on cell performance operated at a
cell temperature of 50 °C in H2/Air with a platinum loading of 0.3 mg
cm-2
per electrode
Figure 8-7 Surface morphology of diffusion layers containing Vulcan XC-72 and (a)
no PTFE; (b) 10 wt% PTFE; (c) 30 wt% PTFE; (d) 50 wt% PTFE
Figure 8-8 Pore volume distribution of several GDLs prepared using five different
types of carbon and graphite
Figure 8-9 Influence of carbon type in the MPL on cell performance of a H2/Air fuel
cell operated at a cell temperature of 50 °C with a platinum loading of 0.3
mg cm-2
per electrode
Figure 8-10 Cell performance as a function of MPL macropore volume at four different
current densities (hydrogen-air fuel cell with a cell temperature of 50 °C)
Figure 8-11 SEM images of microporous layers of a number of MEAs prepared by (a)
SAB, (b) Vulcan Xc-72, (c) Asbury 850
Figure 8-12 The impact of impregnation time on Nafion® loading
Figure 8-13 Effect of number of Nafion® applications on total Nafion
® loading
Figure 8-14(a) Untreated carbon electrode, ×130; (b) one Nafion® application, ×130 ;
(c) five Nafion® applications, ×153; (d) 10 Nafion
® applications, ×130;
all micrographs show the top surface of the GDE; floating method used
to load Nafion®
Figure 8-15(a) Micrograph of the surface of a carbon electrode with 14 Nafion®
applications, ×130; (b) cross section, ×130
Figure 8-16 Polarization curves for different substrates in H2/O2 with a platinum
loading of 0.3 mg cm-2
per electrode and a cell temperature of 50 °C
Figure 8-17 Polarization curves for different Substrates in H2/Air with a platinum
loading of 0.3 mg cm-2
per electrode and a cell temperature of 50 °C
Figure 8-18(a) Cell voltage as a function of original GDL thickness with a platinum
loading of 0.3 mg cm-2
for a H2/Air fuel cell at a cell temperatutre of
50 °C
Figure 8-18(b) A simple representation of compressed and uncompressed GDL
Figure 8-19 Illustration of various random fiber orientation distribution in 1, 2 and 3
dimensions
xii
Figure 8-20 Comparison of experimental and theoretical variations in through-plane
permeability as a function of medium porosity for carbon papers under
investigation
Figure 8-21 Influence of PTFE on the porosity of Toray TGPH 090 carbon paper
Figure 8-22 Effect of PTFE content on porosity and average pore diameter of Toray
TGPH 090 carbon paper
Figure 8-23 Differential pore volume for Toray TGPH 090 carbon paper substrates with
different PTFE loadings
Figure 8-24 Cumulative pore volume of Toray TGPH 090 carbon paper substrates with
different amounts of hydrophobic polymer
Figure 8-25 Percent of substrate pore volume with pore diameters of at least 7 m as a
function of permeability coefficient
Figure 8-26 Influence of pulse period on current efficiency of copper electrodeposition
Figure 8-27 Influence of duty cycle on current efficiency of copper electrodeposition
Figure 8-28 Influence of the number of applications on carbon electrode coverage
Figure 8-29 EDX spectrum of a carbon electrode cross section impregnated with 14
coatings and electroplated with copper
Figure 8-30 An EDX spectrum analysis of a carbon electrode cross section
impregnated with Nafion® and electroplated with copper
Figure 8-31 Effect of electrodeposition current density on cell performance in DC
electrodeposition (H2/Air; 20 wt% PTFE; 0.30 mg Pt/cm2; cell
temperature = 50 °C)
Figure 8-32 Effect of electrodeposition current density on cell performance in DC
electrodeposition (H2/Air; 20 wt% PTFE; 0.30 mg Pt/cm2; cell
temperature = 50 °C)
Figure 8-33 SEM cross-sectional micrographs of electrodes prepared by pulse
electrodeposition at peak current densities of a) 50 mA cm-2
and b)70 mA
cm-2
Figure 8-34 Effect of electrodeposition peak current density in square pulse
electrodeposition on fuel cell performance (H2/Air; 20 wt% PTFE;
0.30 mg Pt/cm2; cell temperature = 50 °C; TGPH-090 carbon paper)
Figure 8-35 Effect of electrodeposition peak current density on fuel cell performance in
square pulse electrodeposition (H2/Air; 20 wt% PTFE; pulse period = 750
ms; 0.30 mg Pt/cm2; cell temperature = 50 °C; TGPH-090 carbon paper)
Figure 8-36 Effect of PC and DC electrodeposition on fuel cell performance (H2/Air;
20 wt% PTFE; 0.30 mg Pt/cm2; cell temperature = 50 °C)
Figure 8-37 Effect of PC duty cycle on fuel cell performance (H2/Air; 20 wt% PTFE;
0.30 mg Pt/cm2; cell temperature = 50 °C; TGPH-090 carbon paper)
xiii
Figure 8-38 The relationship between duty cycle and cell voltage for different fuel cell
output current densities in fuel cells utilizing PC-electrodeposited catalysts
(H2/Air; 20 wt% PTFE; 0.30 mg Pt/cm2; cell temperature = 50 °C; TGPH-
090 carbon paper)
Figure 8-39 Effect of electrodeposition peak current density with low duty cycles (ф) (4% and 20%) in square pulse electrodeposition on fuel cell performance
(H2/Air; 20 wt% 20 wt% PTFE; 0.30 mg Pt/cm2; cell temperature = 50 °C)
Figure 8-40 Effect of square pulse electrodeposition peak current density with 4% duty
cycle (ф) on fuel cell voltage for fuel cell output current densities of 200-
1000 mA cm-2
(H2/Air; 20 wt% PTFE; 0.30 mg Pt/cm2; cell temperature =
50 °C)
Figure 8-41 Effects of duty cycle and pulse current density on fuel cell performance
(square pulse; H2/Air; 20 wt% PTFE; 0.30 mg Pt/cm2 per electrode; cell
temperature = 50 °C)
Figure 8-42 Effects of pulse frequency (on-time/off-time) on cell performance (square
pulse; H2/Air; 20 wt% PTFE; 25% duty cycle; 0.30 mg Pt/cm2; cell
temperature = 50 °C)
Figure 8-43 The relationship between pulse frequency and cell voltage for fuel cell
output current densities of 200-1000 mA cm-2
using PC electrodeposition
(square pulse; H2/Air; PTFE = 20 wt%; 20% duty cycle; 0.30 mg Pt/cm2;
cell temperature = 50 °C)
Figure 8-44 Effects of plating bath Pt(NH3)4Cl2 concentration on MEA performance
(square pulse; H2/Air; 20 wt% PTFE; 20% duty cycle; 0.35 mg Pt/cm2 per
electrode; cell temperature = 50 °C)
Figure 8-45 Cross-sectional platinum line scans for MEAs prepared from plating baths
with different platinum concentrations: (a) 1.0 mM; (b) 50 mM; (c) 100
mM; (d) 500 mM and (e) 1000 mM
Figure 8-46 Carbon substrate impregnated with platinum
Figure 8-47 Platinum distribution on a carbon substrate as a function of distance from
the centre of the substrate
Figure 8-48 An electron micrograph of a composite fuel cell MEA
Figure 8-49 Cell performance as a function of electrodeposition waveform (H2/O2; 20
wt% PTFE; 4% duty cycle; 0.35 mg Pt/cm2; cell temperature = 50 °C)
Figure 8-50 TEM images of platinum catalyst electrodeposited employing different
pulse waveforms: (a) ramp-down (b) triangular and (c) rectangular (peak
deposition current density = 400 mA cm-2
; 4% duty cycle; 0.35 mg Pt
cm-2
)
xiv
Figure 8-51 Size distribution of platinum nanoparticles according to the type of
waveform: (a) ramp-down (b) triangular and (c) rectangular waveforms
(peak deposition current density = 400 mA cm-2
; 4% duty cycle; 0.35 mg
Pt cm-2
per electrode)
Figure 8-52 Influence of plating solution flow rate on MEA performance (square pulse;
H2/Air; 20 wt% PTFE; 20% duty cycle; 0.35 mg Pt/cm2 per electrode;
cell temperature = 50 °C)
Figure 8-53 Influence of plating bath flow rate on fuel cell voltage at four different
current densities (H2/Air; 20 wt% PTFE; 20% duty cycle; 0.35 mg
Pt/cm2 per electrode; cell temperature = 50 °C)
Figure 8-54 Influence of anode platinum loading on fuel cell performance (square
pulse; H2/Air; 20 wt% PTFE; cathode = 0.35 mg Pt cm-2
; 20% duty cycle;
cell temperature = 50 °C)
Figure 8-55 Influence of anode Pt loading on electrode performance at four different
current densities (square pulse; H2/Air; 20 wt% PTFE; cathode = 0.35 mg
Pt cm-2
; 20% duty cycle; cell temperature = 50 °C)
Figure 8-56 Durability of single commercial and in-house MEAs with apparent areas
of 5 cm2 and platinum loadings of 0.5 mg cm
-2 on both anode and cathode
operated at a cell temperature of 60 °C and ambient pressure. Hydrogen
and air are used as fuel and oxidant, respectively, entering the cell at 100%
RH. The operation time is 4100 h.
Figure 8-57 Durability of single commercial and in-house MEAs with apparent areas
of 5 cm2 and platinum loadings of 0.5 mg cm
-2 on both anode and cathode
operated at a cell temperature of 60 °C and ambient pressure. Hydrogen
and air are used as fuel and oxidant, respectively, entering the cell at 100%
RH. The operation time is 280 h.
Figure 8-58 SEM images of the cross section of the in-house MEA showing
delamination at different magnifications (top) 125 (bottom) 200
Figure 8-59 Durability of single in-house MEA with apparent area of 5 cm2 and a
platinum loading of 0.5 mg cm-2
on both anode and cathode operated at a
cell temperature of 60 °C and ambient pressure. Hydrogen and air are used
as fuel and oxidant, respectively, entering the cell at 100% RH. The
operation time is 3000 h.
Figure 8-60 Open circuit voltage (OCV) data obtained at different time intervals for an
in-house and a commercial MEA
Figure 8-61 Power output of 200-W PEM fuel cell stacks containing in-house and
commercial MEAs running on hydrogen and air at ambient temperature
and pressure
xv
Figure 8-62 Initial OCV of in-house and commercial (E-TEK) MEAs in PEM fuel cell
stack in a dynamic system running on H2/Air at ambient temperature and
pressure (0.35 mg Pt/cm2 for anode and cathode of both MEAs)
Figure 8-63 Final OCV of in-house and commercial (E-TEK) MEAs in PEM fuel cell
stack in a dynamic system running on H2/Air at ambient temperature and
pressure (0.35 mg Pt/cm2 for anode and cathode of both MEAs)
Figure 8-64 Maximum power output of 42-cell fuel cell stacks containing in-house and
commercial (E-TEK) MEAs tested in a dynamic system running on H2/Air
at ambient temperature and pressure (0.35 mg Pt/cm2 for anode and
cathode of both MEAs)
Figure 9-1 A liquid droplet formed on (a) a flat solid surface and (b) its cross section
Figure 9-2 Comparison between the experimental and various models for Ni coating
hardness using rectangular waveform
Figure 9-3 Comparison between the experimental and various models for Ni coating
hardness using ramp-up waveform
Figure 9-4 Comparison between the experimental and various models for Ni coating
hardness using ramp-down waveform
Figure 9-5 Comparison between the experimental and various models for Ni coating
hardness using triangular waveform
Figure 9-6 Concentration overvoltage for various waveforms with a peak current
density of 400 mA cm-2
, on-time & off-time of 5 ms (50% duty cycle) and
100 Hz (showing the first full cycle)
Figure 9-7 Nickel concentration in the cathode diffusion layer for various waveforms
with a peak current density of 400 mA cm-2
, on-time and off-time of 5 ms
each (50% duty cycle) and 100 Hz (showing the first full cycle , on-time
and off-time)
Figure 9-8 Nickel concentration in the cathode diffusion layer for various waveforms
with a peak current density of 40 mA cm-2
, on time of 0.1 ms, 1000 pulse
cycles and duty cycles of 10% - 100%. The initial bulk nickel
concentration is 1.427 mol L-1
.
Figure 9-9 Nucleation rate for a single cycle (on-time only is shown) for all
waveforms with a peak deposition current density of 400 mA cm-2
and
50% duty cycle
Figure 9-10 Calculated critical nucleus size for a single cycle (on-time only is shown)
for all waveforms with a peak deposition current density of 400 mA cm-2
and 50% duty cycle
Figure 9-11 XRD patterns exhibiting the influence of pulse duty cycle on crystal
orientation of nickel deposits with a constant peak current density of 400
mA cm-2
xvi
Figure 9-12 Surface morphology of electrodeposited nickel at a constant deposition
current density of 400 mA cm-2
and various duty cycles: (a) 20% and (b)
80%
Figure 9-13 Comparison of experimental and model microhardness data for various
pulse waveforms: a) Ramp-down, b) Triangular, c) Ramp-up and d)
Rectangular, deposited at different peak current densities (4% duty cycle;
50 mM Pt concentration)
Figure 9-14 Influence of different waveforms on platinum microhardness deposited at
various peak deposition current densities
Figure 9-15 Platinum concentration in the cathode diffusion layer for various
waveforms with a peak deposition current density of 400 mA cm-2
, on-
time and off-time of 5.0 ms each (50% duty cycle) and 100 Hz (showing
the first full cycle)
Figure 9-16 Concentration overvoltage for various waveforms with a peak deposition
current density of 400 mA cm-2
, on-time & off-time of 5 ms (50% duty
cycle) and 100 Hz (showing the first fuel cycle)
Figure 9-17 Nucleation rate for various waveforms with a peak deposition current
density of 400 mA cm-2
, on-time of 5 ms and 100 Hz (showing the first
half-cycle)
Figure 9-18 Platinum ion concentration in the cathode diffusion layer as a function of
duty cycle in the Millisecond Range for all four waveforms with a peak
deposition current density of 400 mA cm-2
, on-time of 0.002 s and 100
pulse cycles
Figure 9-19 Platinum ion concentration in the cathode diffusion layer as a function of
duty cycle in the Microsecond Range for all four waveforms with a peak
deposition current density of 400 mA cm-2
, on-time of 0.0002 s and 1000
pulse cycles
Figure 9-20 Platinum ion concentration in the cathode diffusion layer as a function of
duty cycle in the Millisecond Range for all four waveforms with a peak
deposition current density of 50 mA cm-2
, on-time of 0.02 s and 50 pulse
cycles
Figure 9-21 Platinum ion concentration in the cathode diffusion layer as a function of
duty cycle in the Microsecond Range for all four waveforms with a peak
deposition current density of 50 mA cm-2
, on-time of 0.0002 s and 5000
pulse cycles
Figure 9-22 Critical nucleus size of platinum as a function of time for various
waveforms with a peak deposition current density of 400 mA cm-2
, on-
time of 5 ms and 100 Hz (showing the first half-cycle)
Figure 9-23 Nucleation rate for various waveforms with an on-time of 1.0 ms, off-time
of 49 ms, 2% duty cycle, and 100 pulse cycles at different peak current
densities
xvii
Figure 9-24 Nucleation rate for various waveforms with an on-time of 100 ms, off-
time of 400 ms, 20% duty cycle, and 100 pulse cycles at different peak
current densities
Figure 9-25 Concentration overvoltage as a function of peak deposition current density
for all waveforms with a pulse on-time of 1.0 ms, pulse off-time of 49 ms,
2% duty cycle, and 100 pulse cycles
Figure 9-26 Platinum concentration as a function of peak deposition current density for
all waveforms with a pulse on-time of 1.0 ms, pulse off-time of 49.0 ms,
2% duty cycle, and 100 pulse cycles
Figure 9-27 Platinum concentration as a function of peak deposition current density for
all waveforms with a pulse on-time of 1.0 ms, pulse off-time of 4.0 ms,
20% duty cycle, and 100 pulse cycles
Figure 9-28 Nucleation as a function of peak deposition current density for all
waveforms with a duty cycle of 2%, pulse on-time of 2 ms, pulse off-time
of 98 ms and 1000 pulse cycles: (a) 50 mA cm-2
(b) 100 mA cm-2
, (c) 200
mA cm-2
, (d) 300 mA cm-2
, (e) 400 mA cm-2
, (f) 500 mA cm-2
, and (g) 600
mA cm-2
Figure 9-29 Influence of peak deposition current density on microhardness and grain
diamter of a Pt electrodeposited layer (ramp-down waveform; 2% duty
cycle; microsecond pulses)
Figure 9-30 Influence of average grain diameter on microhardness of an
electrodeposited layer (ramp-down waveform; 2% duty cycle;
microsecond pulses)
Figure 9-31 Influence of catalyst deposition method and loading on fuel cell
performance (ramp-down waveform; H2/Air; 20 wt% PTFE; operating
pressure = 1.0 bar; cell temperature = 40 °C)
Figure B-1 A parallel-plate capacitor
Figure B-2 Helmholtz compact double-layer model
Figure B-3 Gouy-Chapman model of electrical double layer
Figure B-4 Stern model of electrical double layer
Figure B-5 Grahame’s triple-layer model
Figure C-1 Electroplating bath flow rate as a function of pump speed and temperature
Figure E-1 Vickers indenter
xviii
LIST OF TABLES
Table 2-1 Potential coating materials for metallic bipolar plates
Table 2-2 Chemical composition of several stainless steels
Table 2-3 Primary coating materials and methods for 316 and 316L SS bipolar plates
Table 2-4 Chemical and physical properties of graphite and 316L SS
Table 3-1 Influence of temperature on reversible cell voltage at 1.0 bar pressure
Table 3-2 Influence of pressure on reversible cell voltage at a fixed temperature of
25 °C
Table 5-1 Effective surface area of several commercial carbon black powders
Table 6-1 Main characteristics of electrochemical and chemical deposition methods
Table 6-2 Chemical properties of several reducing agents
Table 7-1 Bath composition and electroplating conditions for Ni plating
Table 8-1 Manufacturers’ data: characteristics of different carbon powders in GDLs
Table 8-2 Diffusion coefficient of oxygen in water at different temperatures
Table 8-3 Diffusion coefficient of oxygen (as a binary mixture) in air at atmospheric
pressure
Table 8-4 Influence of carbon / graphite loading in MPLs on fuel cell performance
Table 8-5 Effects of impregnation time on Nafion® loading utilizing the floating
Method
Table 8-6 Nafion® impregnation of GDEs utilizing floating and brushing techniques
Table 8-7 Nafion® impregnation with 1 to 14 applications
Table 8-8 Ion exchange capacity data for different samples
Table 8-9 Physical properties of a number of different gas diffusion layers
Table 8-10 Porosity data for untreated GDLs
Table 8-11 Through-plane permeability values of untreated substrates
Table 8-12 Archie’s law parameters used to calculate absolute permeability using the
model of Tomakakis et al [634]
Table 8-13 Comparison of experimental and theoretical absolute permeability values of
different carbon substrates
Table 8-14 Influence of pulse period on current efficiency of copper electrodeposition
Table 8-15 Influence of duty cycle on current efficiency of copper electrodeposition
Table 8-16 EDX analysis of carbon substrates
xix
Table 8-17 Effect of plating bath flow rate on MEA performance
Table 9-1 Experimental and model hardness data for nickel (rectangular waveform)
Table 9-2 Experimental and model hardness data for nickel (ramp-up waveform)
Table 9-3 Experimental and model hardness data for nickel (ramp-down waveform)
Table 9-4 Experimental and model hardness data for nickel (triangular waveform)
Table 9-5 Physical constants and variables used for determining nickel-coating
microhardness and other characteristics
Table 9-6 Physical constants and variables used for determining the platinum-coating
microhardness and other characteristics
Table 9-7 Nucleation rate for all waveforms for the first pulse cycle with a pulse on-
time of 5.0 ms and a peak deposition current density of 400 mA cm-2
Table 9-8 Platinum ion concentration in the cathode diffusion layer as a function of
duty cycle in the Millisecond Range for all four waveforms with a peak
deposition current density of 400 mA cm-2
Table 9-9 Platinum ion concentration in the cathode diffusion layer as a function of duty
cycle in the Microsecond Range for all four waveforms with a peak
deposition current density of 400 mA cm-2
Table 9-10 Performance comparison of conventional and PC electrodeposited MEAs
Table A-1 Physical data for Platinum Group Metals
Table C-1 Pump calibration, Tygon L/S 16 Tubing, 25 °C
Table C-2 Pump calibration, Tygon L/S 16 Tubing, 50 °C
Table C-3 Pump calibration, Tygon L/S 25 Tubing, 25 °C
Table C-4 Pump calibration, Tygon L/S 25 Tubing, 50 °C
xx
NOMENCLATURE
Symbol Quantity [units]
aH2 activity of hydrogen [unitless]
aO2 activity of oxygen [unitless]
aH2O activity of water [unitless]
A area [m2]
A active area of the electrode [cm-2
] A nucleation rate constant atm standard atmospheric pressure [=101325 Pa]
B constant of proportionality
c0 initial bulk concentration [mol L-1
]
cs surface concentration [mol L-1
]
C Celsius [C]
Cb bulk concentration [mol L-1
]
Cdl capacitance of the double layer [F·cm-2
]
CGC Gouy-Chapman capacitance [F·cm-2
]
CH Helmholtz capacitance [F·cm-2]
Cj concentration of species j [mol m-3
]
Ddl thickness of the double layer [cm]
Dj diffusion coefficient or diffusivity of species j [m2 s
-1]
partial differential operator
Ecell cell voltage [V]
Erev reversible cell voltage [V]
Eeqm equilibrium cell voltage [V]
E change in total energy of a system [J]
ƒ frequency [s-1
]
F Faraday’s constant [C mol-1
]
(FD)per mole driving force for diffusion [N mol-1
]
F’D driving force acting on one liter of solution [mol L-1
]
)( 0F wetting angle function [unitless]
G reactant consumption rate [mol s-1
]
G Gibbs free energy [J]
G standard Gibbs free energy [J]
G activation Gibbs function [J]
GC activation Gibbs function, chemical component [J]
G(N) Gibbs free energy of formation of a cluster [J]
GT,P change in Gibbs free energy at constant temperature and pressure [J]
h Planck’s constant [J s]
H enthalpy [J]
H microhardness [kg mm-2
]
H hydrogen atom
H+ hydrogen ion (proton)
H2 hydrogen gas
xxi
H(x) Heaviside function
H change in enthalpy [J mol-1
]
ia average current density [mA cm-2
]
iC capacitive current [mA cm-2
]
iF Faradic current [mA cm-2
]
iP peak current density [mA cm-2
]
itot or iT total galvanostatic current density [mA cm-2
]
iN nucleation current [mA cm-2
]
iG growth current [mA cm-2
]
i exchange current density [mA cm-2
]
i,a anode exchange current density [mA cm-2
]
i,c cathode exchange current density [mA cm-2
]
I current [A]
I1 single cluster growth current [mA cm-2
]
J(u) nucleation rate at time t = u [nuclei s-1
]
j flux of reactants reaching the surface of the electrode [mol s-1
cm-2
]
jb backward reactant concentration flux [mol s-1
cm-2
]
jf forward reactant concentration flux [mol s-1
cm-2
]
kb backward rate constant [L s-1
]
kB Boltzmann’s constant [J K-1
]
kf forward rate constant [L s-1
]
kCK Carman-Kozeny constant
K1 penetrability of the moving dislocation boundary [MPa m1/2
]
K0 value determined by dislocation boundary [MPa]
L length [m] (also a unit for volume, litre)
m mass of the system [kg]
m mass flux of a fluid [kg s-1
m-2
]
M metal
MA metal salt
n number of moles of gas [mol]
n number of moles of electrons transferred per mole of reaction [unitless]
ni number of moles of species i [mol]
nj molar flow rate of ion or species j through the electrolyte [mol s-1
]
jn molar flux of the ion through the electrolyte [mol s-1
cm-2
]
N number of pulse cycles
NC or nc critical radius of the cluster [m]
N maximum possible number of sites of nuclei on the substrate surface per
unit area
O2 oxygen gas
Ox oxidized species in a half-cell electrochemical reaction
P perimeter [m]
P pressure [Pa]
Pi partial pressure of species i [Pa]
P standard pressure [1 bar]
PH2 partial pressure of hydrogen gas [Pa]
xxii
PO2 partial pressure of oxygen gas [Pa]
q heat per mole [J mol-1
]
qGC Gouy-Chapman excess charge [C]
qH Helmholtz excess charge [C]
qS total charge on the solution side [C]
Q heat [J]
Qrev reversible heat [J]
r area-specific resistance [k cm2]
r radial distance from the centre of the cluster [m]
rC critical radius of the surface nucleus [m]
R resistance []
R radius of a cluster [m]
R’ universal gas constant [J mol-1
K-1
]
R average radius of the formed grains [m]
Rg radius of a growing nucleus [nm]
Red reduced species in a half-cell electrochemical reaction
s area occupied by one atom on the surface of the nucleus [m2]
s molar entropy [J K-1
mol-1
]
S entropy [J K-1
]
Sh Heaviside function
Sk Heaviside function
Sw Heaviside function
S surface area of a nucleus [m2]
S change in entropy [J K-1
]
S standard change in entropy [J K-1
]
t time [s]
tC charge time [µs]
tD discharge time [µs]
toff time the pulse is off [ms]
ton time the pulse is on [ms]
T temperature [K]
TH high temperature for a heat engine [K]
TL low temperature for a heat engine [K]
v velocity of the system [m s-1
]
v superficial velocity [m s-1
]
vM molar volume [m3 mol
-1]
vP specific molar volume of gas products [m3 mol
-1]
vR specific molar volume of gas reactants [m3 mol
-1]
V volume [m3]
V1 initial volume [m3]
V2 final volume [m3]
Vp pore volume [m3]
Vb bulk volume [m3]
Vs solid volume [m3]
V change in volume of a system [m3]
W work [J]
xxiii
W small change in work [J]
W1 mass of the membrane (SPE) before drying [g]
W2 mass of the membrane (SPE) after drying [g]
Wnet mechanical work delivered by a heat engine [J]
Greek Letters
α transfer coefficient [unitless]
σ specific free surface energy [J m-2
]
Forchheimer or inertial coefficient [m-1
]
ratio of the bulk concentration of supporting electrolyte to the bulk
concentration of the depositing electrolyte
dielectric constant [unitless]
edge energy [J cm-1
]
porosity
el specific conductivity of the solution [-1
cm-1
]
double-layer thickness [cm]
infinitesimal incremental amount of a path function
distance between two plates in a capacitor [m]
(x) Dirac delta distribution
change in a property
z change in elevation [m]
duty cycle [unitless]
membrane water content [g]
µ chemical potential [J mol-1
]
µ* chemical potential in the reference state [J mol-1
]
kinematic viscosity [Pa s]
toruosity
pulse period [ms]
number of states available to a molecule
overvoltage [V]
ohmic overvoltage [V]
act activation overvoltage [V]
C concentration overvoltage [V]
s overvoltage at the surface of the cluster [V]
energy conversion efficiency of a fuel cell [unitless]
j effective diffusivity [cm2 s
-1]
(N) surface potential [V]
electrical potential difference [V]
(0) potential at the electrode surface [V]
(x) local potential at a distance x from the electrode surface [V]
xxiv
Subscripts
atm of the atmosphere
eqm equilibrium value
ext ―external‖ value of a property
f final state of a system or process
f process of formation
g gas
i initial state of a system or process
irrev an irreversible process
L liquid
max maximum value
min minimum value
P at constant pressure
rev reversible process
s solid
soln solution phase
STP standard temperature and pressure (0 C and 1.0 atm pressure)
surr the surroundings
T at constant temperature
univ universe (defined as system plus surroundings)
v vapour
V at constant volume
x in the x-direction
y in the y-direction
z in the z-direction
Superscripts
dot (e.g., m ) denotes a rate (e.g., m is the rate of mass flowing through the system)
macron (e.g., g ) denotes the specific value of a property (e.g., g is the specific Gibbs
free energy in J kg-1
)
degrees Celsius
denotes standard conditions
Physical Constants
Symbol Quantity Value units
eo elementary charge 1.6022 10-19
C
F Faraday’s constant 96 487 C mol-1
g acceleration due to gravity 9.806 m s-2
kB Boltzmann’s constant 1.381 10-23
J K-1
NA Avogadro’s number 6.022 1023
mol-1
R’ Universal gas constant 8.3145 J mol-1
K-1
xxv
Glossary of Abbreviations
AES Auger Electron Spectroscopy
ASR Area-Specific Resistance
AST Accelerated Stress Test
BMC Bulk-Molding Compound
CE Current Efficiency
CL Catalyst Layer
CVD Chemical Vapour Deposition
DC Direct Current
DMFC Direct Methanol Fuel Cell
EDS Energy Dispersive Spectroscopy
FEP Fluorinated Ethylene Propylene
GDE Gas Diffusion Electrode
GDL Gas Diffusion Layer
HOPG Highly Ordered Pyrolytic Graphite
IC Integrated Circuit
ICP-OES Inductively Coupled Plasma-Optical Emission Spectroscopy
IEC Ion Exchange Capacity
IEM Ion Exchange Membrane
MEA Membrane-Electrode Assembly
OCV Open Circuit Voltage
ORR Oxygen Reduction Reaction
PANI Polyaniline
PC Pulse Current
PCE Pulse Current Electrodeposition
PCB Printed Circuit Board
PEM Proton Exchange Membrane or Polymer Electrolyte Membrane
PEMFC Proton Exchange Membrane Fuel Cell
PFSA Perfluorosulfonic Acid
PGMs Platinum-Group Metals
PPS Polyphenylene Sulfide
PRC Pulse Reverse Current
PSSA Polystyrene Divinylbenzene Sulfonic Acid
PTFE Polytetrafluoroethylene
PVD Physical Vapour Deposition
RDE Rotating Disk Electrode
RDS Rate-Determining Step
SEM Scanning Electron Microscopy
SPE Solid Polymer Electrolyte
TEM Transmission Electron Microscopy
US DOE United States Department of Energy
XPS X-ray Photoelectron Spectroscopy
XRD X-Ray Diffraction
1
1.0 INTRODUCTION
1.1 Rationale
Today, the burning of fossil fuels is closely associated with climate change, acid rain and
global warming. Furthermore, the prospect of finding significant new oil and gas fields is
slim. Even if significant new reserves of fossil fuels are discovered, will we be willing to
live with the consequences of ―burning‖ them? Anthropogenic carbon dioxide poses a
serious threat to our environment, economy and, more importantly, to our social well-
being. Energy issues such as resource depletion, energy security, end-use efficiency, and
climate change require deep thinking and timely solutions. Fuel cells can play a vital role
in alleviating some of the aforementioned problems and challenges facing humanity [1].
Proton exchange membrane fuel cells (PEMFCs) are electrochemical devices that convert
the chemical energy of the reactants (a fuel and an oxidant) directly to electrical energy in
the form of low voltage direct current (DC) and heat, without combustion. They have
been receiving significant attention due to their high power density, energy efficiency and
environmentally friendly characteristics [2-11]. However, one of the major impediments
in making them a viable power source is the high manufacturing cost due to the low
activity of the catalyst and hence, high platinum content [12-29] and the prohibitively
high cost of solid polymer electrolytes such as Nafion® [30-36 ]. In order to increase
platinum utilization, various methods have been developed to increase the effective
surface area of platinum through a particle size reduction and/or increase of the interface
between the catalyst, electrolyte and reactants [9, 25, 37-42]. A significant number of
patents also have been filed and granted over the past few decades underlying the
importance of such methods and processes in the PEMFC field [43-104].
Platinum deposition methods generally can be categorized in two different groups:
powder type and non-powder type. In a powder type process a platinum salt is first
chemically reduced by a reducing agent that leaves the platinum in a colloidal form.
Platinum particles in solution then are adsorbed on high surface area carbon to make
carbon-supported platinum. This is a simple and cost-effective process in which the final
amount of platinum on carbon can easily be controlled through the initial concentration
of the platinum salt. However, it is very difficult to increase the platinum-carbon ratio in
2
carbon-supported platinum beyond 40% without increasing platinum particle size [17].
The oxidation of hydrogen at the anode and, more importantly, the reduction of oxygen at
the cathode are directly dependent on the effective surface area of the electrocatalyst in
the catalyst layer and, therefore on the platinum particle size. As a result, maintaining
small catalyst particle size is paramount in fuel cell design. In addition, since increasing
the platinum ratio in the carbon-supported platinum is limited, this would hinder the
efforts to decrease the catalyst layer thickness with the result that a better mass transport
of reactants and products cannot be achieved [105].
On the other hand, in non-powder type processes the platinum particles are directly
deposited onto the surface of the carbon electrode or membrane. Sputter deposition is a
well-known process and several researchers have shown that it can be utilized to prepare
MEAs with high platinum utilization [105, 106]. However, this method requires high
initial investment due to the prohibitively high cost of vacuum equipment. Maintenance
costs are also high and extra care must be exercised to minimize contamination [106].
Another method is based on a two-step process in which a membrane such as Nafion®
initially undergoes an ion exchange reaction with metal salt of the catalyst to be deposited
and then reduced to the metal catalyst by a reducing agent. Although this process ensures
a good contact between the membrane and the metal catalyst, the electronic pathway
through the carbon particles is missing. A new approach based on pulse electrodeposition
to fabricate MEAs has exhibited promising results in laboratories [9, 107, 108].
1.2 Catalyst Layer
The fuel cell half reactions taking place on the surface of uncatalyzed electrodes are too
slow for practical applications, the oxygen reaction being especially problematic.
Accordingly, a catalyst layer is provided to increase the reaction rates. The electrodes are
made porous to facilitate the diffusion of the gases—both fuel and oxidant. Each
electrode has a carbon backbone in which are bonded small particles of platinum, about 2
nanometers in diameter [108]. This greatly increases the available surface area for the
half reactions to occur, thereby increasing their reaction rates. In addition, both platinum
3
and carbon are good electronic conductors, which facilitate the movement of electrons
through the electrodes to the external circuit.
Platinum, on account of its unique properties, has become an integral part of the proton
exchange membrane (PEM) fuel cell. The original membrane-electrode assemblies
(MEAs) were made in the 1960s for the Gemini space program and utilized about 4
milligrams of platinum per square centimeter of membrane area [108]. Although the
amount of platinum used in today’s PEM fuel cells has decreased to about 0.1-1.0
mg/cm2, this is still too high to support significant market penetration. It is essential,
therefore, to further lower catalyst loading without significant loss in catalytic activity.
Recent efforts to increase the platinum utilization without loss in performance have
resulted in the development of new methods for fabricating gas diffusion electrodes
(GDEs) with low or modest loadings of expensive platinum that provide unusually highly
efficient utilization of platinum metal. One such method was developed by Reddy et al.
[107] and was patented in 1992.
1.3 Pulse Electroplating
Electroplating with pulse current (PC) is becoming increasingly popular because it offers
several advantages over direct current plating, such as mass transfer enhancement and the
availability of additional process parameters—on-time, off-time and pulse current
density—which can be varied independently to influence deposit properties [9].
In PC electrodeposition, the current density or the applied potential is alternated rapidly
between two different values. This is done with a series of pulses of equal amplitude,
duration and polarity, separated by periods of zero current [6]. Each pulse consists of two
periods: an ―on-time‖ period in which the current is applied and an ―off-time‖ period
during which no current is applied. It is during the latter period when metal ions from the
bulk solution diffuse into the layer next to the working electrode; i.e., carbon paper or
carbon cloth in our experiments. When the current is applied during the on-time, more
evenly distributed ions are available for electrodeposition. A pulsing scheme is shown in
Figure 1-1.
4
Figure 1-1 Schematic Diagram of a Square Pulse Current Wavefor
It is evident from the above discussion and Figure 1-1 that in order to characterize a
simple direct current, it is sufficient to know the current density; however, the
characterization of a square pulse current waveform requires three parameters to be
known. These are cathodic current density, the cathodic pulse length (on-time) and the
interval between the pulses (off-time). A very useful term frequently encountered is the
duty cycle,
, representing the portion of the time when the current is on. It may be
defined as follows:
offon
on
tt
t
(1-1)
The average current density, ia, can be defined by the following equation:
pa ii (1-2)
ton toff
Pulse
Period
iP
Figure 1-1 Schematic diagram of a square pulse current waveform
Average current, ia
Peak current, ip
Time
5
1.4 Thesis Objectives
The primary objective of this work is to develop a novel PEM fuel cell catalyzation
technique to selectively deposit catalyst nanoparticles on carbon-based substrates where
both electronic and ionic pathways exist. This will ensure not only the existence, but also
the expansion of the three-phase interface leading to lower precious metal loadings.
Conventional deposition techniques, including spraying, brushing and rolling have been
proven to be unsuitable for attaining high catalyst utilization. Consequently,
unconventional methods have been employed to attain better results. One such method is
pulse current electrodeposition, which has shown great promise to selectively deposit
nanocatalysts where they are needed. Although the superiority of pulse electrodeposition
has been established in other applications, such as nickel electroforming and
semiconductors, its use in platinum electrodeposition has been limited to square-pulse
waveforms for fuel cell use. The influence of other types of waveform on the quality of
the electrodeposits has not been reported in the literature. Therefore, another objective of
this thesis is to evaluate the suitability and influence of other waveforms, specifically
triangular, ramp up and ramp down, on the quality of a number of metal deposits,
including platinum.
One of the main advantages of such methods cited by many researchers is the number of
independent variables that can potentially be optimized to improve deposit properties and
qualities. This can readily be done by employing parametric studies where the number of
variables is small—one or two. However, when the number of variables increase, it
becomes very difficult to optimize the process in a timely fashion. As a result, utilization
of more sophisticated techniques and strategies become essential. Consequently, another
objective of this thesis is to develop a modeling tool and optimization technique to
provide an accurate prediction of the influence of all these variables—pulse on-time,
pulse off-time, pulse frequency, duty cycle, type of waveform, peak current density and
total charge—on catalyst layer properties and, ultimately, on fuel cell performance.
6
1.0 BACKGROUND
1.1 Hydrogen Fuel Cells
2.1.1 A Condensed History
At first, fuel cells might seem to be a marvel of the 20th
and 21st centuries; however, they
have been around since 1839, when William Grove, a professor of experimental
philosophy at the London Royal Institution and a friend of Michael Faraday, first
discovered the principle of the device [109]. Thirty-seven years earlier, in 1802, British
chemist Sir Humphrey Davy discovered that water can be decomposed into its
constituents—hydrogen and oxygen—when an electric current is passed through it. This
process was later called electrolysis. Grove successfully demonstrated that the process of
electrochemical decomposition can be reversed, and that hydrogen and oxygen may be
combined to form water and energy in the form of heat and electricity [109]. Grove
realized both the simplicity of the process and its applications; however, he soon
abandoned his work on the fuel cell because he was not able to generate useful amounts
of energy. A few years later, when carbon-based fuels were used in an attempt to
eliminate the need for pure hydrogen with no success, efforts were abandoned until 1889
when Ludwig Mond and Charles Langer repeated the work of Grove and managed to
produce 1.5 W with 50% efficiency while replacing oxygen with air, and pure hydrogen
with impure industrial gas obtained from coal [2, 110]. This was a great achievement, and
for the first time the device was called a hydrogen fuel cell. But, once again, the project
stalled owing to the high cost of the platinum catalyst that was being poisoned by traces
of carbon monoxide present in the gas. Attempts were made to improve the device
without much success until 1932, when Francis Bacon developed the first modern
hydrogen fuel cell in the United States. For the next 20 years, much effort was expended
to increase the power output and efficiency of such devices until finally, in 1952, a 5-kW
fuel cell system was successfully tested [109]. The next push came from an unfamiliar
source—the U.S. space program. The appeal of the hydrogen fuel cell was apparent to
many scientists and engineers working for NASA; it was less dangerous than any nuclear
device, and much simpler to deal with in terms of installation, maintenance, and repair on
board shuttles. In addition, hydrogen fuel cells were more compact and lighter than any
7
other energy-producing device and storage medium, including state-of-the-art batteries
[109].
The transfer of hydrogen fuel cell technology to extraterrestrial applications proved to be
an easy task for two reasons: first, a large amount of fuel, pure hydrogen, was not needed,
and second, economics played a minuscule role. On the other hand, such a technology
transfer to terrestrial applications has been proven to be difficult. One of the main reasons
is the need for significant amounts of pure hydrogen. Another obvious reason is the cost
of such systems.
2.1.2 How Proton Exchange Membrane Fuel Cells Work
A fuel cell is an electrochemical device that converts the energy associated with the
combination of a hydrogen-rich fuel with an oxidant such as oxygen directly to electrical
energy without the need for the intermediate combustion steps found in internal
combustion engines. A fuel cell, in its simplest form, consists of a cathode, an anode, a
membrane electrolyte capable of conducting ionic current but not electrons, and an
external circuit connecting the two electrodes together to provide a path for the flow of
electronic current.
As hydrogen flows into the fuel cell on the anode side, a platinum catalyst promotes the
dissociation of hydrogen gas into hydrogen ions and electrons. The hydrogen ions pass
through the membrane from the anode compartment and migrate toward the cathode,
while the electrons that are released flow through the external circuit to the cathode.
Oxygen, on the other hand, flows into the fuel cell on the cathode side, where it combines
with the incoming hydrogen ions and electrons with the help of a noble metal catalyst to
produce electricity, water and heat. The electrons flow through an electric load (such as
an electric motor) located in the external circuit and generate low-voltage electricity, as
shown in Figure 2-1. The following are the electrochemical reactions taking place at both
the anode and the cathode:
Anode: H2 (g) 2H+
+ 2e- (2-1)
Cathode: ½O2 (g) + 2H+ + 2e
- H2O (liq) (2-2)
Overall: H2 (g) + ½O2 (g) H2O(liq) (2-3)
8
Figure 2-1 A simple proton exchange membrane fuel cell
The practical operating voltage from a single cell is about 0.7 V. Desired voltages of any
value can be obtained by connecting a predetermined number of cells in series. Although
the underlying electrochemical principles are similar to those of a battery, unlike
batteries, fuel cells are, in theory, capable of producing electricity indefinitely as long as
fuel and oxidant are supplied to them.
2.1.3 Different Types of Fuel Cell
Fuel cell design varies according to several parameters, including the power demands of a
given system and the operating temperature that is best suited to that particular
application [2, 109]. At present, there are five main types of fuel cell that are either under
development or commercially available. Because the electrolyte defines the key
properties, including the operating temperature, fuel cells are often named by the
electrolyte they employ. However, one also can classify fuel cells based on their
operating temperature or the state of the fuel used. The five main fuel cell technologies
are proton exchange membrane, alkaline, phosphoric acid, molten carbonate, and solid
H2 (g) 2H+
+ 2e-
½O2 (g) + 2H+ + 2e
- H2O (liq)
Solid Polymer Electrolyte
Load
FUEL
OXIDANT
9
oxide. Proton exchange membrane fuel cells are the smallest and lightest of the designs,
making them the best candidate for both transportation and portable applications. They
exhibit an overall maximum energy conversion efficiency of 40% to 60% and operate at a
temperature of about 80 °C [109, 111]. The applications, properties, advantages, and
disadvantages of these and other types of fuel cells have been fully discussed elsewhere
[2, 112-115].
2.2 Main Components of a PEM Fuel Cell
2.2.1 Polymer Electrolyte Membrane
Fuel cell design has gone through major changes with the advent of solid polymer
electrolytes (SPEs). Proton exchange membrane fuel cells employ a membrane electrode
assembly (MEA), which comprises an ion-exchange membrane sandwiched between the
two electrodes. Solid polymer electrolytes, also known as ion exchange membranes
(IEMs), were originally used as separators in electrochemical cells containing two
different electrolytes. Meyer [117] employed an IEM to separate the electrolytes of a
concentration battery. Jude et al. [118] presented a method in which the electrolytes of a
Daniell cell were separated with the help of an IEM. Pitzer [119] and Morehouse [120]
utilized IEMs to depolarize cells by removing reaction products. IEMs also have been
used to supply a cell with required reactants. This was shown by Robinson [121], who
employed a permanganate anion exchange resin in the cathode of a Leclanché cell.
The first use of an IEM as an electrolyte in an electrochemical cell was successfully
demonstrated by Grubb [121] where the current was entirely conducted through and by
the IEM. He used two different types of commercial membrane, namely Amberplex C-1
(a sulfonated polystyrene resin) and Nepton CR-51 (a sulfonated phenol formaldehyde
polymer formed into a homogenous sheet), to conduct battery experiments [121].
Significant progress and exposure were achieved when General Electric used
hydrocarbon-type polymers such as cross-linked polystyrene divinylbenzene sulfonic
acid (PSSA) and sulfonated phenol-formaldehyde to launch the first hydrogen fuel cell
aboard a space shuttle in the 1960s [112]. This gave a much needed impetus to further the
R&D activities in the field of SPEs. However, soon it was realized that the useful life of
hydrocarbon-based polymers are short due to the presence of C-H bonds, which
10
contribute to the instability of the complete chain via C-H bond cleavage. Research
continued and promising results were obtained when all the hydrogen atoms in carbon-
hydrogen bonds were replaced with fluorine atoms through a perfluorination process.
Carbon-fluorine bonds exhibit stronger affinity for each other, resulting in a much
stronger bond than a C-H bond. This translates into a rigid and long lasting structure,
prolonging its useful life.
All these led to the development and synthesis of a family of fluorocarbon copolymers
such as Nafion®. Nafion
® is a sulfonated tetrafluoroethylene copolymer discovered in
1962 by Walther Grot while working at DuPont de Nemours [122]. It all began when one
of DuPont’s scientific groups, known as the Plastics Exploration Research Group, was
persistently working on fluorine technology to develop monomers for copolymerization
with tetrafluoroethylene (TFE) [123]. The goal of the study was to manufacture a
material with exceptional dielectric and antistick properties as well as having a low
coefficient of friction. Such material would mirror the properties of another important
class of materials, Teflon. However, the product of the reaction between TFE and sulfur
trioxide exhibited some interesting properties that were initially considered to be inferior
to Teflon. The striking difference between the two was the inactivity of Teflon with
regards to its environment, while the new material showed a great tendency to interact
with its local surrounding. It was not until 1964 that DuPont realized some of the
desirable properties of Nafion®. It became apparent that this new material could be used
as a membrane separator in several industries, including chloralkali cells for production
of chlorine and sodium hydroxide. However, the above industries were in no rush to
adopt the new technology, since energy was considered to be abundant and relatively
cheap and there were no stringent environmental regulations. The push came from
General Electric while working on PEM fuel cell development for the U.S. space
program, where their state-of-the-art fuel cells were failing prematurely due to the
instability of the polystyrene sulfonic acid polymer membranes employed in oxidative
environments [123]. This provided the impetus for PEM fuel cells to gain acceptance in
the scientific community and arose interest and curiosity to further develop such fuel
cells.
11
Nafion®
membrane consists of a tetrafluoroethylene (Teflon) backbone with side chains
terminating in sulfonic acid groups. The Teflon backbone is strongly hydrophobic,
alleviating flooding problems, while the sulfonic acid groups are highly hydrophilic,
helping to retain enough water to keep the membrane hydrated during operation. The
strong nature of the C-F bonds ensures thermal and chemical stability in an acidic
environment. The protons on the sulfonic acid (SO3H) groups become mobile when
hydrated and can be transported from one side to another, traversing the whole membrane
structure in the form of hydronium ions. In hydrogen fuel cells, hydronium ions move
through the hydrophilic membrane structure from anode to cathode while sulfonate
groups are fixed. The chemical structure of Nafion® is shown in Figure 2-2.
Figure 2-2 Nafion® perfluorinated ionomer
There has been a considerable interest in SPEs, including Nafion®, over the past several
decades. This is mainly due to their desirable characteristics and their wide range of
applications in many industrial processes, including electrolytic cells used to produce
chlorine and sodium hydroxide, batteries, and fuel cells [124-128].
Perfluorosulfonic acid (PFSA) membranes must exhibit several key characteristics to be
successfully incorporated into PEM fuel cells. These include, but are not limited to, good
protonic conductivity, no electronic conductivity, stability in acidic environments,
impermeable to gases (i.e., hydrogen and oxygen), and both thermal and mechanical
stability. Much effort has been expended on the development of PFSAs for use in PEM
fuel cells over the years. Early work examined the water content of PSFAs, since it was
known that this would have a profound effect on proton conductivity. This kind of
research is still on-going. Koptizke et al. [128] studied the relationship between the water
O-----H
+
12
uptake and proton conductivity of several different PSFAs, including Nafion® 117, as a
function of temperature. Cappadonia et al. [129] also investigated the conductance of
Nafion®
membranes as a function of temperature utilizing impedance spectroscopy to
establish a link. In an early paper, Uosaki et al. [130] using Nafion® 117 and, employing
impedance spectroscopy and differential scanning calorimetry between 180 K and room
temperature, showed that the conductivity of Nafion® can be linked to the structure of
water in the membrane. Zawodzinski and co-workers [131] at Los Alamos National
Laboratory compared the intrinsic water uptake and water transport properties of
different membranes including Nafion® 117 and Dow’s XUS13204.10 developmental
fuel cell membrane, under conditions similar to operating PEM fuel cells. They
concluded that the higher density of ionic groups combined with higher water content per
sulfonic acid group gives rise to increased protonic conductivity. Earlier, Zawodzinski et
al. [132] reported water uptake and transport properties of Nafion® 117 membrane when
immersed in liquid water and exposed to water vapour of varying activities at 30 °C.
As mentioned above, the conductivity, and hence the performance, of SPEs depends on
the amount of free water within the membrane. Accordingly, diffusion of water within
such structures is crucial. Motupally et al. [133] reported experimental and simulated data
for the diffusion of water across Nafion® 115 membranes as a function of the water
activity gradient. The activity gradient was varied by changing the nitrogen flow rate into
the cell or by varying the cell pressure. Others have also reported different values for the
diffusion coefficient of water through Nafion®. Fuller [134] determined the diffusion
coefficient of water across Nafion® by measuring the water flux across membranes
having water on one side and nitrogen gas on the other. Zawodzinski et al. [135]
accomplished the task by employing a nuclear magnetic resonance technique. Many other
groups also have studied the conductivity of Nafion® membranes using diverse methods
such as ac impedance spectroscopy [136-140] and dc techniques [141, 142]. Furthermore,
a wide variety of environments also has been employed and reported, including water,
water vapour, 1.0 molar sulfuric acid, and humidified gases at various temperatures [132,
135, 140, 141, 143]. It is not surprising that different values have been reported in the
literature depending on the methods and test conditions used.
13
Membrane water content () can be defined as the number of moles of water divided by
the number of moles of ion exchange site:
2
21
02.18
)(
W
WWM (2-4)
Where M is the equivalent weight of the membrane, and W1 and W2 are the weights of the
membrane before and after drying, respectively.
Another important characteristic of Nafion® membranes is their ion exchange capacity
(IEC). The ion exchange capacity of a material may be defined as ―a reversible exchange
of ions between a solid and liquid in which there is no substantial change in the structure
of the solid‖ [144]. The total ion exchange capacity of an ion exchange material is the
number of ionic sites per unit weight or volume of resin. The dry weight total capacity is
usually expressed in milliequivalents per gram of dry resin in the H+ form. Ion exchange
capacity of Nafion® and Nafion
® composites have been extensively reported [145-153].
2.2.2 Catalyst Layer
Proton exchange membrane fuel cells utilize a solid polymer electrolyte membrane
disposed between two porous electrodes, often made of treated carbon paper or cloth.
This structure constitutes the MEA. Each electrode contains a catalyst layer, and,
depending on the required power output and operating conditions, in addition, also may
have an admixture of selected catalysts, an ionomer similar to that used for the ion
exchange membrane, and a binder such as polytetrafluoroethylene (PTFE). Furthermore,
the catalyst can be a metal black, an alloy (Pt/Ni or Pt/Ru for the anode of PEMFCs) or
an unsupported or supported metal catalyst (platinum supported on carbon being a prime
example). Regardless of the catalyst layer composition, it is strategically located next to
the solid polymer electrolyte; e.g., Nafion®.
The catalyst layer in conjunction with the SPE plays a vital role in the operation of
PEMFCs. It is here where electrochemical reactions (i.e., hydrogen oxidation and oxygen
reduction) take place. In order to catalyze these reactions, catalyst particles must establish
both electronic and ionic contacts. The former are achieved through the continuous
14
contact between catalyst particles and the highly conductive carbon substrate, while the
latter are accomplished through intimate contact with the ion-conducting membrane. The
contact point between catalysts, reactant gases and membrane is referred to as the three-
phase interface. The effective area of active catalyst sites must be several times greater
than the geometric area of the electrode in order to achieve reasonable reaction rates. One
method to accomplish this is by making the electrodes reasonably thin to create a three-
dimensional structure, where enough sites are available for catalyst particles to be
deposited [154].
Electrocatalyst can be deposited at the membrane-electrode interface in two different
ways to achieve the goal of catalyzing hydrogen oxidation and oxygen reduction. It can
either be applied as a thin layer on the solid polymer electrolyte or on the carbon
substrate (carbon cloth or carbon paper). In the former case, a thin layer of the
electrocatalyst is directly applied onto the solid membrane using various methods. In the
latter case, a catalyst ink is applied onto the electrode substrate by brushing, spraying,
rolling and other methods. Direct application on the solid membrane creates a thin
electrocatalyst layer resulting in a low catalyst loading and good mass transport
properties. In contrast, the application of the catalyst ink on the substrate may require a
higher catalyst loading since the catalyst ink tends to penetrate into the substrate,
resulting in inactive sites where no ionic contact is established. This issue, however, has
been resolved by impregnating a perfluorosulfonate ionomer into the substrate. Ticianelli
et al. [155] successfully demonstrated this method and lowered the platinum loading
without adverse impacts on fuel cell performance. Several years later, Wilson et al. [41,
156] proposed a method in which carbon-supported platinum particles were ultrasonically
mixed with Nafion® to make a catalyst ink and then applied onto a substrate. It should be
noted that the previous catalyst ink also can be applied directly onto the solid polymer
and then bonded, on both sides, to appropriate gas diffusion layers; i.e., carbon substrates,
to fabricate MEAs.
Recent efforts to decrease platinum loading through increased platinum utilization have
resulted in the development of a number of novel methods. These can be broadly
categorized into two groups: one is to use new materials to construct the catalyst layer
15
and the other is to optimize the structure of the catalyst layer to increase utility and
minimize irreversible losses. The former can be accomplished by modification of the
carbon-supported platinum. The latter is achieved by optimizing the structure of the
catalyst layer using different fabrication methods and materials. Uchida et al. [157]
examined the effects of the microstructure of the carbon support in conjunction with
PFSA distribution in the catalyst layer on the overall performance of a PEM fuel cell.
Their method was based on the process of PFSA colloid formation [17] and it was
concluded that fuel cell performance was directly affected by the PFSA and carbon
support content. Shin et al. [158] reported on the effects of the preparation method of the
catalyst ink on electrode structure and, ultimately, on fuel cell performance. It was
reported that the electrodes prepared by a colloidal method exhibited better results than
those prepared by a method in which the catalyst ink was a solution. Organic solvents
also have been used in the fabrication of thin catalyst layers. In a study published by
Yang et al. [159], five different organic solvents—butyl acetate, iso-amyl alcohol, diethyl
oxalate, ethylene glycol and ethylene glycol dimethyl ether—were used to prepare MEAs
using a transfer method. The MEAs prepared using ethylene glycol showed the best
results. It was, however, observed that the micropores in the MEAs showed partial
blockage by remaining solvent even after heat treatment. Increased porosity in the
catalyst layer also has been exploited by several researchers. Fisher et al. [160]
investigated the influence of pore-forming additives on overall cell performance.
Additional coarse porosity was obtained by adding pore formers to the catalyst ink.
The structure, properties and factors influencing the performance of catalyst layers in
PEM fuel cells have been extensively studied and reported in the literature. The cathode
catalyst layer has attracted much of the attention due to the greatest irreversible losses in
cell voltage occurring in this layer, compared with loses in the anode catalyst layer [161-
163]. Yoon et al. [164] examined the influence of the pore structure of the cathode
catalyst layer on overall cell performance. They utilized a spray-drying method to prepare
MEAs with varying degrees of porosity and pore structure and reported that the addition
of thermoplastic agents enhances structural stability and, consequently, overall cell
performance, concluding that pore-forming agents facilitate the transport of oxygen gas
through the catalyst layer. Yang et al. [165] studied the effects of ethylene glycol addition
16
to the catalyst slurry and observed an improved performance. They hypothesized that
propylene glycol acts as a pore-forming agent facilitating the transport of gas through the
catalyst layer. Chisaka et al. [166] investigated the effect of glycerol on the catalyst layer
when added to the catalyst ink. A decal method was employed to fabricate catalyst layers
with various mass ratios of glycerol to carbon in the catalyst ink, ranging from 0.0 to
20.0. Jia et al. [167] conducted research on the effect of surface oxidation of the carbon
support with nitric acid before platinum deposition, and reported an increase in cell
performance due to Pt particle size reduction. Mukerjee et al. [168] reported the result of
an in situ X-ray absorption study on several well-defined carbon-supported platinum
electrocatalysts with particle sizes in the neighbourhood of 25 to 90 Å.
2.2.3 Gas Diffusion Layer
In almost all PEM fuel cells, a reinforced material, often made of carbon paper or cloth
(Figure 2-3), is inserted between the bipolar plate and the catalyst layer. It is commonly
referred to as the gas diffusion layer (GDL). GDLs are porous in structure to allow the
passage of reactants to the catalyst layers on both sides of the cell and to ease the removal
of excess water from the cathode catalyst layer to avoid ―flooding‖. Flooding becomes a
major limiting factor in PEMFC performance when both cathode catalyst layer and GDL
become saturated with water. This fills the micropores inside the cathode GDL reducing
the paths for oxygen transport, contributing to the overall irreversible losses [112, 169].
Figure 2-3 (a) Toray Carbon Paper [116] (b) Toray Carbon Cloth [116]
17
In addition, GDLs must collect the current generated inside the fuel cell at the catalyst
layer and direct it to the external circuit while minimizing losses during transport. This is
accomplished by incorporating materials that are highly conductive into the structure;
carbon powder is a good example. Furthermore, the GDL needs to remove heat from
inside the cell and provide the MEA with stability and integrity. Some of the desired
characteristics are in contrast to each other; for example, water and heat removal from
inside the MEA is enhanced by increasing the porosity of the GDL, but this inherently
reduces mechanical strength as well as ionic and electrical conductivities of GDLs.
Hydrophobic agents such as PTFE are used to enhance water repellent and removal
characteristics of GDLs [17, 170-173]. However, it is well established now that as the
amount of hydrophobic polymer in the GDL increases, the conductivity and porosity will
decrease [174]. From the above discussion, it becomes clear that a well-balanced
approach is needed to successfully design an effective GDL.
Until recently, less attention had been devoted to the study, design, and fabrication of
GDLs. Instead, much time and effort has been spent on examining and optimizing the
membrane and the catalyst layer. The main reason for this has been economic, since both
the membrane and the catalyst layer are by far the most expensive components of an
MEA. However, it has been realized that an effective and reliable path between the
bipolar plates and the MEA of a PEM fuel cell is critical to overall cell performance. As a
result, systematic studies on various aspects of GDLs now have been carried out and
reported in the literature. De Sena et al. [175] studied the limiting structural effects of
porous GDLs on the oxygen reduction reaction (ORR) in 0.5 M sulfuric acid solution.
They reported that for an MEA with 10 wt% Pt/C, a PTFE content of 35 wt% results in
superior cell performance. Lee et al. [176] presented changes in the performance of a
PEM fuel cell as a function of the compression pressure from the bolts that clamp the fuel
cell. They utilized three different types of GDLs—Toray™, ELAT®, and CARBEL
®
combined with Toray™—to study the impact on the overall cell performance. The
performance changes are related to changes in porosity, the electrical contact resistance,
and the water management in the GDL. Carbon black and similar materials are routinely
used in GDLs to increase their electrical conductivities and pore-forming capabilities.
Passalacqua and coworkers [177] investigated the influence of several carbon blacks and
18
graphite on cell performance. Shawinigan Acetylene Black (SAB) was found to produce
the best results when compared with Vulcan XC-72, Mogul L, and Asbury 850 graphite.
This was attributed to improvements in gas diffusion characteristics, including better
water management properties in such GDLs. Antolini et al. [178] reported the effects of
two different carbon powders—Shawinigan and Vulcan XC-72—as materials for both
carbon cloth and carbon paper-based cathode GDLs on the performance of PEM fuel
cells. Cathode electrodes having Shawinigan carbon incorporated into their GDLs
exhibited better performance than electrodes prepared using Vulcan XC-72 carbon.
However, at high operating pressures, the best results were obtained when Vulcan carbon
was used in the catalyst side and Shawinigan in the gas side of cathode GDLs. It is worth
noting that the surface area of Vulcan XC-72 (around 250 m2 g
-1) is much greater than
Shawinigan carbon (about 70 m2 g
-1). Similar results also have been reported by other
workers [179-181].
It is generally agreed that the cathode of a PEMFC is its most important component,
controlling the overall cell performance. Much of the irreversible losses in a PEMFC
during operation are attributed to the losses due to an ineffective cathode electrode. The
oxygen reduction reaction is often the limiting kinetic step determining the overall cell
performance, and its rate is directly proportional to the rate of oxygen transport from the
flow field through the GDL and into the catalyst layer. There are several factors
hindering this diffusion process with accumulation of water inside the pores of both the
catalyst and gas diffusion layers considered to be the most serious. It is, therefore,
imperative to fabricate MEAs with adequate water management capabilities. To avoid
flooding the catalyst layer and enhance cell performance, a hydrophobic polymer such as
PTFE is often mixed with carbon powder and other materials and pasted onto a substrate
to prepare a GDL. Such a layer exhibits superior water repellent properties if proper care
is exercised during preparation and application. It is worth noting that PTFE (and all
hydrophobic polymers) cannot conduct electrons, therefore, its proportion to carbon
powder must be carefully determined to enhance its water impedance characteristics
while minimizing ohmic losses.
19
Numerous reports have been published on the appropriate use of such polymers in fuel
cells. Bevers et al. [182] examined the influence of various PTFE loadings and sintering
times on carbon papers. They highlighted the tradeoff between PTFE content (i.e.,
hydrophobicity) and conductivity of GDLs. The same authors [183] also presented their
findings on the influence of PTFE coating and sintering time on different paper
properties. Giorgi et al. [184] investigated the influence of the diffusion layer porosity as
well as the PTFE content and structure of the GDL on the performance of low platinum
electrodes in PEMFCs. Best performance was reported at low PTFE contents (less than
20 wt%) for the cathode electrode. Paganin et al. [185] studied the influence of PTFE
content for a three-layer structure with 20 wt% Pt/C and 0.4 mg Pt/cm2 and found that a
PTFE loading of 15 wt% produces the best result. Moreira and co-workers [186]
determined the optimum PTFE loading for both the anode and the cathode of a PEFMC.
They proposed a 10% and a 30% PTFE content (by mass) for the cathode and anode,
respectively. Lim and Wang [187] reported the impact of fluorinated ethylene propylene
(FEP) content in GDLs, ranging from 10% to 40% by weight, on the performance of
PEMFCs. A GDL impregnated with 10% FEP was recommended.
Several models also have been proposed to describe the microstructure of various
electrodes, and PTFE in GDLs has been reported to be present in different structural
forms [188-192]. Watanabe et al. [189] presented a model in which the PTFE present in a
GDL has an irregular shape, and, while binding the various components together,
including carbon black, it may prevent the latter from mixing with the electrolyte. Later,
Passalacqua et al. [193] introduced a set of parameters to characterize GDLs, using the
model presented by Watanabe et al. [189]. As mentioned earlier, PTFE is known to be
present in various forms, including agglomerate, films, and fibrils, when bonded to other
components of an MEA. Pebler [194] proposed a network of thin films of fibers during
various stages of electrode fabrication and Holze and Mass [195] reported both
agglomerate and fiber forms of Teflon in electrodes. Other workers [190, 196] have also
validated the models presented by Pebler and Holze by utilizing scanning electron
microscopy (SEM) to show a hydrophobic polymer layer as segregated regions in
different electrodes.
20
It has been reported that the addition of a microporous layer (MPL) between the GDL
and the catalyst layer of an MEA can improve the cell performance [178, 185, 200]. The
effects of various substrates, carbon powder, composition, and thickness of such a layer
have extensively been studied and reported [178, 184, 185, 197-200]. A series of
mathematical models also has been developed to explain the functions of such layers.
Martys [201] developed a numerical method to study the effect of water saturation in a
porous medium with spherical incursions. Nam et al. [202] employed a network model
for anisotropic solid structure and water to show the dependence of the effective
diffusivity of fibrous diffusion media on the porosity and saturation of such media. The
above model also has been used to show the increase in cell performance when a two-
layer diffusion medium is utilized.
2.2.4 Bipolar Plates
The practical operating voltage from a single cell is about 0.7 V. Desired voltages are
obtained by connecting a predetermined number of cells in series; this is accomplished by
inserting a highly conductive material—known as a bipolar plate—between two parallel
MEAs. Such plates are by volume, weight and cost the most critical component of a fuel
cell stack [203, 204]. They account for more than 40% of the total stack cost and about
80% of the total weight [205-211]. As a result, there have been significant R&D activities
in the past few years to lower their cost and reduce their size.
Bipolar plates perform a number of critical functions simultaneously in a fuel cell stack to
ensure acceptable levels of power output and a long stack lifetime. They act as a current
conductor between adjacent MEAs, provide pathways for reactant gases (hydrogen and
oxygen or air), facilitate water and heat management throughout the stack, and provide
structural support for the whole stack. Accordingly, they must exhibit excellent electrical
and thermal conductivity, corrosion resistance, mechanical and chemical stability, and
low gas permeability. Furthermore, raw materials must be widely available at reasonable
cost and be amenable to rapid and cost-effective fabrication methods and processes [203].
Due to the multifaceted characteristics of bipolar plates and a wide combination of
physical and chemical properties that are often contradictory, a large number of
21
candidates has been proposed and investigated over the years. As a result, a set of targets
and requirements has been established to develop suitable material for the fabrication of
bipolar plates. A summary of such requirements and targets is presented below [203,
204]:
Bulk electrical conductivity: > 100 S cm-1
Hydrogen permeability: < 2 × 10-6
cm3 cm
-2 s
-1
Corrosion rate: < 16 µA cm-2
Tensile strength: > 41 MPa
Flexural strength: > 59 MPa
Thermal conductivity: > 10 W m-1
K-1
Thermal stability: up to 120 °C
Chemical and electrochemical stability in acidic environments
Low thermal expansion
Acceptable hydrophobicity (or hydrophilicity)
Bipolar plates are commonly made of graphite for its corrosion resistance characteristics
as well as its low surface contact resistance. However, graphite is brittle, permeable to
gases, and exhibits poor mechanical properties. Furthermore, it is not suitable for mass
production, since the fabrication of channels in the plate surfaces requires machining, a
very time-consuming and costly process [204, 211-213]. Additionally, post processing
such as resin impregnation is often required to ensure the impermeability of graphite
plates to reactant gases. Other materials have been considered as replacements for
graphite plates; a break down of such materials is given in Figure 2-4 [210].
Polymer composites—both polymer-carbon and polymer-metal—offer alternative paths
for fabricating bipolar plates. Bin et al. [211] examined the conductivity and flexural
strength of polyvinylidene fluoride (PVDF)/titanium silicon carbide (Ti3SiC2) composite
bipolar plates prepared by compression molding. The effects of Ti3SiC2 content, particle
size, mould pressure and mould pressing time were investigated. Adequate electrical
conductivity and flexural strength were achieved by optimizing the above parameters.
22
Figure 2-4 Classification of materials for bipolar plates in PEMFCs [210]
Composites fabricated with 80 wt% Ti3SiC2, mould pressure of 10 MPa and a mould
pressing time of 10 minutes exhibited the best results. Kirchain et al. [214] reported that
significant cost reductions can be achieved when graphite-based material is replaced with
composites or metal alloys. Based on their cost model approximation, with composites,
the cost of bipolar plates is reduced to 15-29% of the stack cost. Polymer composites
exhibit all the desired characteristics of graphite plates, but also are amenable to easy and
cost effective high-volume processing methodologies. They can be molded into various
shapes and sizes in a cost-effective manner. It is, however, difficult to meet the required
thickness and resistance targets, because such polymers are inherently insulating. One
solution is to fill them with corrosion-resistant conductive particles such as graphite or
carbon black. In order to meet the resistance targets, however, high loadings of
conductive particles must be applied (greater than 50 v/o), which exceeds the percolation
METALS NON-METALS
s COMPOSITES
Coated Non-Coated
Bases:
-Al
-Ti
-Ni
-SS
Stainless steel
-Austenitic
-Ferric
Non-porous graphite Metal Based Carbon Based
Resin:
-Thermoplastics
-PVF
-Polypropylene
-Polyethylene
-Thermosets
-Epoxy resin
-Phenoic resin
-Furan resin
-Vinyl ester
-Graphite
-Polycarbonate
-SS
Filler:
-Graphite
-Carbon black
-Coke-graphite
Fibre:
-Graphite
-Cellulose
-Cotton flock
23
threshold concentration of 5-20 v/o and approaches, and in some cases surpasses, the
critical pigment volume concentration of 50-70 v/o [215]. At such concentrations,
conductive particles would form a long and continuous path for electrons to travel
through the whole thickness of the plate with ease, lowering the resistance by several
orders of magnitude. But, this insulator-conductor transition takes place at the expense of
the mechanical properties of the plate, since there will not be enough polymer binder to
hold everything together. This also will lead to the formation of more ―holes‖ or ―gaps‖
between various particles in the matrix, making the plate more brittle. Blunk et al. [215]
studied high-graphite-filled composites to find out if such plates can meet plate
resistance, thickness, and permeation rate targets simultaneously. In such plates, the
insulating polymer is mixed with high loadings of corrosion-resistant graphite particles to
meet the resistance target. However, at high graphite loadings (>50 v/o) not enough
polymer resin is present to fill the gaps between graphite particles, hence more pathways
for electron conduction are formed, increasing the conductivity of such plates. This,
however, is achieved at the expense of a porous and weaker plate. It is reported that this
also will increase H2 permeation rates when the plates are made thin enough to meet the
required high stack volumetric and gravimetric power densities.
Kuan et al. [216] investigated the impact of graphite content on the physical properties of
composite bipolar plates composed of vinyl ester resin prepared by a bulk-moulding
compound (BMC) process. They reported an increase in the porosity of the composite
bipolar plates from 0.06 to 2.64% as the graphite content increased from 60 to 80 wt%,
while the electrical resistance and flexural strength of the bipolar plates decreased from
20,000 to 5.8 mΩ and 38.47 MPa (60 wt% graphite) to 27.3 MPa (80 wt% graphite),
respectively. It is apparent that great care must be exercised when designing such plates.
Huang et al. [217] developed a method to fabricate bipolar plates using thermoplastic
composite materials consisting of graphite, thermoplastic fibers and glass or carbon
fibers. A wet-lay (paper-making) process was utilized to fabricate highly formable sheets
that were then stacked and compression molded to make bipolar plates with gas flow
channels. Graphite content was varied between 50 – 70 wt% and in-plane and through-
plane conductivity ranges of 140-310 S cm-1
and 15-50 S m-1
, respectively, were
24
reported. Yin et al. [218] studied the effects of resin content, molding temperature and
time on conductivity and bending strength of the composite materials made from phenol
formaldehyde resin powder and graphite using hot-pressure molding. Some interesting
results are reported: the conductivity decreases and bending strength increases with the
increase of resin content, while conductivity varies non-linearly (wave-like) with an
increase in temperature. Other workers have reported similar findings on resin-graphite
composites for bipolar plates [219-224].
Middleman et al. [225] proposed a process for large-scale production of composite
bipolar plates in which excellent physical and chemical properties are observed. Cho et
al. [226] demonstrated the viability of composite bipolar plates by developing plates with
performances comparable to that of graphite plates. Kuan et al. [227] utilized a bulk-
molding compound process to fabricate vinyl ester-graphite composite bipolar plates.
Such plates exhibited properties similar to those of graphite plates. Chun-hui et al. [228]
examined the flexural strength, pore size distribution, resistance to acid corrosion and
thermal properties of sodium silicate/graphite composite bipolar plates. A flexural
strength of 15 MPa was reported when the graphite content was about 40 wt% and it was
claimed that the plates withstood the force of machining flow fields. However, significant
amounts of pores have been reported and attributed to the formation of silica gel due to
solidification of sodium silicate. Furthermore, a corrosion current of 32 µA cm-2
has been
reported for bipolar plates with a 60 wt% graphite content in 1.0 M H2SO4 solution at
room temperature, showing their acid-resistant properties (the US Department of Energy
requires a corrosion rate of 10-5
A cm-2
for bipolar plates). Finally, it was claimed that the
water content of the above plates can reach 9 wt%, and that this water may be used to
humidify the incoming gases during operation. Xia et al. [229] determined the effects of
resin content, molding temperature and holding time on the conductivity and bending
strength of polyphenylene sulfide (PPS) resin/graphite bipolar plates fabricated using a
simple hot pressing technique. They reported a decrease in the electrical conductivity of
the composite with increase in the resin content, while the bending strength exhibited a
cyclic trend with an increase at very low and very high resin content and a gradual
decrease between the two extremes. An optimum resin content of 20 wt% was suggested.
25
An electrical conductivity of 118.9 S cm-1
and bending strength of 52.4 MPa are reported
for composite bipolar plates with 20% PPS resin content when molded at 380 °C for 30
min. Radhakrishnan et al. [230] also used PPS resin in conjunction with graphite to
fabricate bipolar plates by high-pressure compaction. Resistance values of 0.1 Ω were
achieved and reported. Huang et al. [231] utilized a wet-lay process to fabricate bipolar
plates from a mixture of PPS resin, graphite and glass or carbon fibers. In-plane
conductivities of 200-300 S cm-1
, tensile strength of 57 MPa, flexural strength of 96 MPa,
and impact strength of 81 J m-1
were achieved in their studies.
Bipolar plate manufacturers and suppliers rely heavily on the high concentration of
conductive graphite or carbon particles in composite bipolar plates to meet conductivity
targets set by various organizations such as the US DOE. Although such high loadings
yield composite plates that meet or surpass such targets, they become brittle, leading to
high scrap rates during plate manufacturing, adhesive bonding and stack assembly [232].
This becomes critical when thin plates are required to achieve high stack volumetric
power densities. It is expected that PEM fuel cells used for transportation applications
must possess a stack volumetric power density of at least 2 kW L-1
. This translates into
bipolar plates with thicknesses of 1.5 mm or less. As a result, extensive research has been
conducted with the aim of reducing graphite or carbon content while maintaining an
acceptable level of conductivity. Malliaris and Turner [233] studied the influence of
several parameters including binder type, filler particle size, and filler distribution.
Tchoudakow et al. [234] reported their findings on various polymer blends with lower
graphite content; and Sichel [235] investigated the impact of degree of mixing of low-
concentration polymer blends. Grunlan et al. [236] determined the impact of particulate
polymer microstructure, while Zhang et al. [237] examined the influence of polymer
crystallinity on the percolation threshold of conductive material (graphite or carbon
black).
Metals, on the other hand, offer better mechanical properties, higher electrical
conductivity, gas impermeability, and manufacturability; but suffer from corrosion and
are denser than graphite-based materials, thereby adding to the weight of the stack.
26
Considerable efforts have been expended to use noble metals, stainless steel, aluminum
and titanium as the material of choice for fabricating bipolar plates.
Metals such as titanium and stainless steel exhibit excellent mechanical properties and
have very low gas permeation rates. They are also suitable for mass production with low
scrap rates and are stable in a PEM fuel cell environment where low pH values are
common. The good corrosion characteristics of stainless steels and titanium are attributed
to the passivation of such metals in the presence of oxygen, where a protective oxide
metal film is formed on their surface. Such an advantage comes at the expense of metal
conductivity, which is hindered by the presence of such insulating protective layers. In
order to make these metallic plates conductive, it becomes necessary to remove such
oxide films or reduce their thickness to an acceptable level and apply a conductive and
corrosion-resistant film to retard the further formation of oxide films and decrease their
interfacial contact resistance. There are several concerns with such conductive layer
coatings. First, there is always the possibility of imperfections such as pinholes and micro
and macro cracks, which can lead to localized corrosion. This undermines the integrity of
the plates and, most importantly, poisons the membrane when dissolved ions diffuse into
the membrane and occupy the exchange sites, thereby lowering the ionic conductivity
and the overall performance of the stack [238]. Second, the cost and durability of such
conductive layers become an issue, since both are the main impediments to the
commercialization of fuel cells. Several fuel cell manufacturers have developed both
organic and inorganic protective and conductive coatings for metallic bipolar plates
[232]. A number of coating materials for metallic bipolar plates is presented in Table 2-1
[210]. Coating materials also have been classified as carbon- and metal-based. The
former includes conductive polymers, graphite, diamond-like carbon and organic self-
assembled monopolymers, while the latter utilizes noble metals, metal carbides and metal
nitrides. Extensive research on both carbon- and metal-based coatings has been
conducted and reported in the literature. It is generally agreed that such coatings must be
conductive and adhere to the substrate; i.e., metallic bipolar plates [238, 239, 246].
Proper adherence to the substrate is achieved by careful selection of coating materials
with similar thermal expansion coefficient as the substrate to minimize micro and macro-
27
Table 2-1 Potential coating materials for metallic bipolar plates [210]
Coatings Base Plate Materials
Aluminum Stainless Steel Titanium Nickel
Conductive Polymer [239] ×
Diamond-like Carbon [239] ×
Gold [240, 241] ×
Graphite Foil [242] × × ×
Graphite Topcoat [242] × × × ×
Indium Tin Oxide [243] ×
Lead Oxide [243] ×
Organic Monopolymer [239] ×
Silicon Carbide [243] ×
Titanium-Aluminum [243] ×
Titanium Nitride [243] ×
Oxides [244] ×
Chromium Nitride [245] Ni/Cr
crack formation. Woodman et al. [240] investigated the roles of thermal expansion
coefficient and corrosion resistance of a number of different bipolar plates on stack
performance. Li et al. [247] examined the corrosion behavior and conductivity of 316 SS
coated with TiN. It is reported that both corrosion resistance and electrical conductivity
of such plates are improved in simulated conditions similar to those of a real PEMFC.
Long-term studies on the stability of such plates have yet to be performed.
Cho et al. [208] conducted long-term studies on the corrosion behavior of TiN-coated 316
SS and reported significant improvement when compared with uncoated 316 SS. The
authors also have reported their findings in terms of surface energy, water contact angle
and surface wetability. Water contact angles of 90° and 60° are reported for TiN-coated
316 SS and 316 SS with no coatings. It is interesting to note that the water contact angle
of TiN-coated 316 SS is similar to that of graphite. This has been confirmed by Taniguchi
and Yasuda [248] who observed an increase in power output of a PEM fuel cell stack
when gas flow channels showed low water wetability.
A wide variety of coatings (see Table 2-1) and processes have been developed to address
the concerns associated with metallic bipolar plates. Joseph et al. [249] investigated the
viability of conductive polymer coatings such as polyaniline (PANI) and polypyrrole
28
(PPY) on 304 SS. They reported superior corrosion behavior and acceptable interfacial
contact resistance. Once again, long-term, economical viability and durability studies are
absent from this report.
Brady et al. [250] developed a preferential thermal nitridation process in which a nickel-
chromium alloy was coated with a thin layer of CrN/Ce2N. Based on their observations,
defect- and pinhole-free can be achieved with excellent corrosion resistance and
negligible interfacial contact resistance. Another substrate, 446 SS, also has been tested
with positive outcomes in terms of corrosion and contact resistance. But, admittedly such
coatings and processes are not cost effective. Physical vapor deposition (PVD) was
employed by Lee et al. [244] on two base metals, namely 316L SS and 5052 aluminum
alloy, with a YZU001-like diamond film. Tafel extrapolations from polarization curves
were used to compare the corrosion rates of the above metal plates with that of graphite.
Surprisingly, metallic plates outperformed graphite plates when placed in a single cell to
measure interfacial contact resistance and performance. According to the authors, 316L
SS plates exhibited better corrosion resistance with the above coating when compared
with aluminum plates. However, aluminum plates proved to be superior compared with
SS when interfacial contact resistance was concerned, although they had a shorter life
when tested in a single cell. There has been a great interest in carbon composite materials
for bipolar plates.
Due to their low cost, high strength and ease of machining, metallic bipolar plates have
attracted the attention of the research community. Stainless steel, by far, has been the
focus of on-going research over the past several years. The selection criteria for SS
bipolar plates is primarily the Cr, N, Mo content in accordance with the pitting resistance
equivalent [251, 252]. Stainless steels come in different compositions and, accordingly,
behave differently in various environments. Chemical compositions of some of the most
widely used SS are shown in Table 2-2 [251]. Stainless steel bipolar plates with different
compositions have been used extensively by different workers [253-258]. Davies et al.
[256] conducted a series of experiments on three types of stainless steel bipolar plates,
namely 310L, 316L and 904L. They reported that 904L performed the best while 316L
exhibited the worst result in an environment similar to that of a PEM fuel cell.
29
Table 2-2 Chemical composition of several stainless steels [252]
Material 316L 317L 904L 349TM
C ≤ 0.028 ≤ 0.028 0.011 0.05
Cr 16.20-16.80 18.10-18.60 20.48 23
Ni 10.10-10.30 12.45-12.75 24.59 14.5
Mn 1.70-1.95 1.60-1.90 1.53 1.5
Mo 2.03-2.25 3.05-3.35 4.5
Si 0.45-0.65 0.25-0.55 0.46 1.4
N 0.020-0.040 0.045-0.070 0.13
Cu ≤ 0.50 ≤ 0.50 1.4
Cb 0.4
Co ≤ 0.50
Fe Balance Balance Balance Balance
In another published paper, the same authors [257] utilized Auger Electron Spectroscopy
(AES) to determine the thickness of the passive film on the surface of various SS bipolar
plates. It was reported that the thickness of the passive layer decreases with the alloying
element content, and often varies between 3 to 5 nm. It was concluded that higher
alloying content promotes lower interfacial contact resistance. There have been some
disagreements amongst various groups on the relationship between alloying content and
corrosion and contact resistance behaviour of various stainless steel bipolar plates [253,
254, 257]. Such disagreements are, however, due to the pretreatment and the surface
conditions of such bipolar plates.
316 stainless steel has been receiving increasing attention as a replacement for non-
porous graphite in bipolar plates. Wang et al. [205] investigated the influence of oxygen
and hydrogen-containing environments on the corrosion behaviour of such bipolar plates.
Intergranular and pitting corrosion in both the oxygen and hydrogen-containing
environments were reported with a greater corrosion resistance shown by 316L SS
bipolar plates in simulated cathodes. This has been attributed to the cathodic protection
ability of the oxygen-containing environments. In addition, metal ion concentrations of
about 25 and 42 ppm at the anode and cathode, respectively, after 5000 h of operation are
reported utilizing potentiostatic tests (using ICP-OES). It was concluded that 316L SS
bipolar plates must be coated, since such levels of ion concentrations can adversely affect
30
the membrane. The above finding also was confirmed by another group, Ma et al. [259]
studied the corrosion behaviour of 316L SS bipolar plates and concluded that 316L SS
must be coated since it can be corroded in both anode and cathode environments. It is
common practice to coat 316L and 316 stainless steel bipolar plates for use in PEM fuel
cells [260-263]. Table 2-3 summarizes several coating methods and materials used on
316L and 316 SS for use in bipolar plates [205].
Wang et al. [264] developed a method to electro-polymerize polypyrrole films on 316L
stainless steel using both galvanostatic and cyclic voltammometric methods. The
aforementioned electrochemical methods yielded two different films with marked
differences in morphology. Optical microscopy revealed less intergranular corrosion for
plates covered with a dense coat of polypyrrole when compared with untreated 316L SS
plates. Feng et al. [265] investigated the impact of a nickel-rich layer with a thickness of
about 100 µm deposited on 316L SS by ion implantation. All tests showed higher
chemical stability of such plates in accelerated cathode environments containing 0.5 M
H2SO4 with 2 ppm HF at 80 °C. The superiority of Ni-coated plates is attributed to the
reduction in passive layer thickness caused by the Ni implantation. In recent years,
chromium-nitrogen films as a coating material for stainless steel plates have received
some attention. According to Fu et al. [266] 316L SS plates coated with Cr0.49 N0.51
delivered the best result in terms of interfacial conductivity, corrosion resistance, and
high surface energy. Cho et al. [267] applied a dense layer of chromium on 316L
austenitic stainless steel by pack cementation at 1100 °C for several time periods, ranging
from 2.5 to 10 hours. At short time periods; i.e., less than 5 hours, improvements in
Table 2-3 Primary coating materials and methods for 316 and 316L SS bipolar plates
[205]
Coating Material Coating Method
TiN Hollow Cathode Discharge Ion Plating
TiN PVD
PPY and PANI Electrochemical Method
Nitride Plasma Nitriding
No Coating Material Electrochemical Surface Process to Form Passive Film
31
corrosion resistance was reported. However, for longer running times; i.e., greater than 5
hours, no significant improvements were found.
Composite films also have been developed and applied on stainless steel bipolar plates to
improve their corrosion resistance and interfacial contact resistance. Fu et al. [268]
electrodeposited an Ag-polytetrafluoroethylene composite layer on 316L SS bipolar
plates and reported that the above plates exhibit lower interfacial contact resistance,
higher corrosion resistance and better hydrophobic characteristics. Novel composite
bipolar plates based on 316L SS also have been investigated. Kuo et al. [269] fabricated
bipolar plates using 316L SS and Nylon-6 polymer thermoplastic matrix using an
injection molding process. It was claimed that such bipolar plates are relatively light
weight, easy to process, inexpensive and exhibit favorable gas tightness, hardness and
corrosion resistance. However, they failed to match graphite bipolar plates as far as the
stack performance was concerned. Table 2-4 compares graphite and 316L SS in terms of
their chemical and physical properties [269].
Other types of stainless steel such as 304 SS also have been widely used as bipolar plates.
Chung et al. [270] and Fukutsuka et al. [271] both utilized carbon-coated 304 SS in
single-cell and three-cell PEM fuel cells, respectively. The first group employed thermal
chemical vapor deposition (CVD) to deposit a carbon film on Ni-coated 304 SS plates.
Table 2-4 Chemical and physical properties of graphite and 316L SS [269]
Property Graphite 316L SS
Cost (US $ kg -1
) 75 15
Density (g cm-3
) 2.25 8.02
Thickness of bipolar plate (mm) 2.5-4 1-2
Modulus of elasticity (Gpa) 10 193
Tesnile strength (Mpa) 15.85 515
Corrosion current (mA cm-2
) <0.1 <0.1
Electrical resistivity (Ω cm х 10-6
) 6000 73
Thermal conductivity (W m-1
K-1
) 23.9 16.3
Permeability (cm s-1
) 10-2
- 10-6
<10-12
32
Chemical stabilities comparable to PocoTM graphite were reported. The second group used
plasma-assisted CVD to deposit a carbon layer on 304 SS. It was reported that carbon-
coated 304 SS exhibited higher electrical conductivity compared with uncoated 304 SS,
while maintaining an acceptable level of corrosion resistance. As both studies were
carried out for relatively short times, long-term experiments are required to justify the use
of such materials as bipolar plates in PEM fuel cells. Noble metals such as gold also
have been used to coat stainless steel to improve its chemical and other properties in
harsh environments similar to that of PEM fuel cells [238, 241]. However, such metals
are prohibitively expensive and often thicker layers are needed to provide adequate
corrosion resistance of the base metal in acidic environments [271]. But, the greatest
level of success that has been reported on metal bipolar plates has been achieved with
noble metal coatings. Wang et al. [272] examined gold-plated titanium bipolar plates in a
single cell of 25 cm2 active area. A proprietary method was used to deposit gold coatings
of 2.5 μm thickness onto titanium plates. Polarization curves for graphite, pure titanium
and titanium coated with gold were presented at several different cell temperatures,
ranging from 40 to 80 °C. Gold-plated titanium plates performed poorly when the cell
temperature increased from 40 to 60 °C. However, a significant improvement was
reported at higher cell temperatures of 80 – 90 °C. In a paper published earlier by the
same group [273], three different types of metallic bipolar plates were examined: pure
titanium, titanium sintered with iridium oxide and titanium coated with platinum.
Titanium plates coated with platinum delivered the best result when tested in a single
PEM fuel cell operated at cell temperatures of 50 - 65 °C.
Copper alloys also have been studied as a potential candidate for bipolar plates in fuel
cells. Good corrosion resistance of copper and its alloys in weakly corroding
environments has been reported in the literature [274-276]. Nikam et al. [277] examined
the corrosion behaviour of copper-beryllium alloy C-17200 using a Tafel extrapolation
technique. It was noted that true corrosion representation can not be achieved from such
plots. As a result, chroamperometry was utilized to gain a better understanding by
analyzing the corrosion products by employing SEM, EDS and XPS. In an earlier work
[274], the authors presented their findings on the resistivity of the corrosion layer of the
above alloy using a four point probe apparatus in 0.5 M H2SO4 solution.
33
A large number of coating processes and techniques has been employed both in the
research community and in industry to deposit a wide array of coating materials on
different base materials. Pulse current electrodeposition has been successfully used to
apply a thin layer of gold over aluminum bipolar plates [278, 279]. Painting and pressing
have been employed to apply a graphite layer onto aluminum, titanium and nickel bipolar
plates [242], while electron beam evaporation can place a thin layer of indium-doped tin
oxide on a number of base metals, including stainless steel [243]. Physical vapor
deposition has been employed to deposit a number of coating materials such as chromium
or nickel-phosphorus alloy onto aluminum, stainless steel and titanium [280]. Vapor
deposition and sputtering has been reported to deliver excellent results when lead oxide
was deposited onto stainless steel bipolar plates [281].
As mentioned earlier, one of the primary functions of bipolar plates is to provide a path
for reactant gases to be homogeneously distributed over the surface of the catalyzed
electrodes. Accordingly, a number of different geometries are used and referred to as
flow fields. Figure 2-5 shows some of the most widely used flow-field configurations.
The proper design of such flow fields is not only critical in fuel and oxidant delivery, but
also in efficient heat and water management inside the stack. An extensive body of
research has been generated over the past few decades dealing with this special issue
[282-289].
Carrette et al. [282], Hertwig et al. [283] and Costamagna and Srinivasan [284] presented
detailed reviews of most of the flow-field designs and configurations and listed their
advantages and disadvantages. In a US patent filed and granted in 1992, Watkins et al.
[286] claimed as much as a 50% increase in overall cell performance by optimizing the
distribution of reactant gases via proper flow-field design. In another US patent, Reiser
and Sawyer [287] presented a flow-field network of many cubical or circular pins
arranged in a consistent pattern. In an interesting design, Pollegri and Spaziante [288]
showed a straight flow-field pattern in which an array of independent parallel flow
channels is connected to gas inlet and outlet. It was noted that the stack did not perform
very well when air was used as the oxidant after extended periods of operation. This drop
34
(a) (b) (c)
(d) (e)
Figure 2-5 Different flow field configurations: (a) parallel, (b) serpentine, (c) parallel-
serpentine, (d) interdigitated, and (e) pine or grid type
in performance was attributed to the inability of the bipolar plates to effectively transport
water out of the cell.
Two particular flow-field designs have been widely used in research and the fuel cell
industry: parallel and serpentine. The former configuration is often used because of its
simplicity, lower pressure drop between inlet and outlet of the gas channels and uniform
distribution of the reactant gases over the surface of the both electrodes. However, the
channels in a parallel flow field can easily be blocked by liquid water. This becomes
critical at the cathode where water is the byproduct and can easily lead to flooding and a
lowering of fuel cell performance. In addition, once a channel is clogged, the active area
of the electrode that is in direct contact with the bipolar plate becomes inactive as long as
the pathway is restricted to the flow of the reactant gas. As a result, the use of parallel
flow fields is restrictive in PEM fuel cells. On the other hand, the serpentine flow fields
35
can readily push the liquid water out of the channel due to high gas flow rate. The flow
field channels are often rectangular in cross section; however, other geometries such as
triangular, semi-circular and trapezoidal also have been reported in the literature [206,
290, 291]. The three critical variables in flow field design are channel depth, width and
land (rib) with average values of 1.5, 1.5, and 0.5 mm, respectively [206]. These
dimensions are always optimized to create a uniform gas distribution inside the cell or
stack with a reasonable pressure drop as the gases traverse the whole length of the
electrode, as well as providing a high contact area between the bipolar plate and the
electrodes for effective current collection. Watkins et al. [292] optimized the dimensions
of a bipolar plate for the cathode side of a PEM fuel cell. They reported that the optimal
ranges for the channel width, length and the land (rib) are 1.14-1.4 mm, 0.89-1.4 mm, and
1.02-2.04 mm, respectively.
Over the past few decades, in an attempt to improve fuel cell performance many studies
have been carried out to optimize all types of flow patterns. Mathematical models and
numerical simulations also have played a key role in gaining a better understanding of
how different flow-field configurations function in both a single cell and in stacks [293-
301]. Springer et al. [293] developed a one-dimensional steady state model that was
based on experimentally-derived parameters for PEM fuel cells. Another one-
dimensional model was presented by Gurau et al. [294] in which a cathode gas channel, a
gas diffusion layer and a membrane were all considered. A number of equations for
oxygen mass transport inside the cell and proton migration inside the membrane were
used and analytical solutions were derived. Two dimensional models were proposed by
Fuller and Newman [295] and Nguyen and White [296]. Numerical simulations were
presented to examine both water and heat management in PEM fuel cells. Ge and Yi
[297] also presented a two-dimensional model that highlighted the dependence of water
movement inside the cell on operating conditions and membrane thickness. Wang et al.
[298] studied the two-phased flow transport of air inside the cathode of a PEM fuel cell.
Their two-dimensional model was successful in predicting the transition between single
and two-phase regimes.
36
Yan et al. [299] developed a three-dimensional model to analyze the effects of the
contraction ratios of height and length on cell performance of PEM fuel cells. Their
model revealed that the reductions of the outlet channel flow areas increase the reactant
gas velocities in these regions and reactant transport and utilization as well as liquid
water removal. Recently, Cho et al. [300] proposed a three-dimensional, non-isothermal,
and steady state model to underline the heat transport characteristics of flow fields in
PEM fuel cells. According to this model, the maximum temperature occurs at the
cathode. This is primarily attributed to the formation of water at the cathode. Sinha et al.
[301] also developed a three-dimensional, non-isothermal PEM fuel cell model based on
serpentine and parallel flow-field designs operated at 95 °C and operating under different
inlet humidity conditions. It was noted that parallel flow fields outperformed the other
configuration at elevated cell temperatures and low inlet relative humidity.
The importance of bipolar plates as an integral component of PEM fuel cells becomes
clear when one looks at the large number of patents that have been filed and granted in
recent years [302-324]. Rock [302] proposed a design where serpentine flow channels are
arranged in a mirror-image fashion. According to this design, the inlet legs of each
channel border the inlet legs of the next adjacent channels in the same flow field. It is
claimed that in such arrangements the serpentine flow channels can be made longer and
may contain more medial legs than conventional serpentine flow channels. Low pressure
drops between adjacent legs also are claimed. In another patent [303] Rock presented a
serpentine flow field with a number of serially-linked serpentine segments extending
between inlet and outlet openings. Griffith [304] developed a serpentine flow design for
which each channel has an inlet, outlet, and at least one medial leg with hairpin curves
connecting the legs to each other. All legs extend in the same direction from the inlet to
the outlet with varying length. It was reported that this achieved better water
management. Rock [305] devised bipolar plates in which serpentine flow fields are
formed on one side and interdigitated flow fields on the opposite side. Furthermore, a
staggering seal arrangement was employed to direct gaseous reactant flow through the
stack in such a way that the seal thickness was maximized while the distance between
adjacent cells was minimized. A layered design was reported by Carlstrom [306] by
mating two interlocking layers that form an internal fluid channel between these two
37
layers, where a cooling fluid was circulated throughout the stack. One advantage of this
design is claimed to be its ability to be fabricated from a wide variety of materials,
including carbon, metals and composites. Boff and Turpin [307] believe that in most
cases, GDLs do not perform very well because the incoming gas appears to be unable to
access the whole area between the channels, but reaches only the area above the channel
and a small margin surrounding the channels. This is supported by the observation that
interdigitated channels achieve higher electrical efficiencies since the gas is forced into
the areas above the lands. It has been realized that by forming sufficiently fine channels
on the face of the flow fields (less than 0.2 mm in width) the aforementioned problem can
be curtailed without the use of separate GDLs. It also has been noted that narrow tracks
result in a reduction in resistive electrical losses.
In an interesting design, Trabold and Owejan [308] proposed a flow-field design in which
the channels include a number of side walls formed in different orientations. In addition,
an electrically-conductive member is incorporated at the surface of the plate to serve as
gas diffusion media. It is claimed that a better water transport is achieved. Rock et al.
[309] presented a serpentine flow design, where efficient thermal management is
obtained by creating coolant pathway between the two exposed faces of a single plate.
Mercuri [310] developed a fabrication method to manufacture graphite bipolar plates
from flexible graphite and preferably from uncured resin-impregnated graphite. Two
separate components; i.e., faces, one with a protrusion and another with a recession are
separately fabricated. The two pieces are then pressed together in such a way that the
protrusion of the first component is received in the recess of the second component and
finally heated to cure the resin and bond the components together.
There also have been significant activities in fabricating bipolar plates from a different
number of candidate materials with no winner to date. Metallic plates have been
fabricated and tested for their corrosion resistance and interfacial contact resistance
properties [311-316]. Composite materials also have been widely used in both fuel cells
and electrolyzers [317-324].
38
2.0 FUEL CELL THERMODYNAMICS
3.1 Introduction
Classical thermodynamics deals with transformation of energy from one form to another.
Since fuel cells convert the chemical energy of a fuel into electrical energy, it would be
beneficial to understand how such conversions take place. Thermodynamics can predict if
a particular reaction is energetically spontaneous. In addition, it will place an upper limit
on the quantity of the electrical energy that may be generated through the half-cell
reactions inside a fuel cell. This is referred to as ―ideal‖ work output and it should be
realized that real fuel cells operate below such limits due to a number of losses associated
with various cell components. These losses will be discussed in more detail in subsequent
chapters.
3.2 Reversible Cell Voltage Under Non-Standard Conditions
3.2.1 Introduction
It is often necessary to predict the reversible voltage of a fuel cell under non-standard
conditions. Fuel cells are usually run at temperatures higher than room temperature; even
PEM fuel cells are generally operated at 60 °C or higher to increase their efficiency.
Furthermore, it is often a requirement to pressurize the incoming gases (fuel and oxidant)
to increase the efficiency of the fuel cell. Lastly, the concentration (activity) of reactant
species can vary. It is important to be able to predict the voltage of a fuel cell at any
arbitrary temperature, pressure and fuel and oxidant concentrations. In the following
section, the influences of the above variables on the cell voltage will be explored.
3.2.2 Reversible Cell Voltage as a Function of Temperature
The cell voltage can be expressed in terms of Gibbs free energy formation at constant
temperature and pressure, ΔGT,P:
nF
GE
PT , (3-1)
The variation in cell voltage as a function of temperature at constant pressure can be
expressed as:
39
nF
S
dT
dE
P
(3-2)
where ΔS is the entropy change for the reaction, and
)()( TnF
SETE
(3-3)
For the reaction: H2 (g) + ½O2 (g) H2O (liq) (3-4)
The entropy change at 25 °C and one bar pressure is given by
)(2)(2)(2 21
ggliq OSHSOHSS (3-5)
= 69.91 – 130.684 – ½ [205.138]
= -163.343 J K-1
mol-1
This yields: 14104645.8)96487)(2(
343.163
KV
dT
dE
P
(3-6)
Over the narrow temperature range of 0 °C to 100 °C, ΔS will not vary significantly;
therefore the reversible voltage for the reaction will decrease with increasing temperature
by about 8.46 mV K-1
. When the reaction proceeds to water in the vapour state,
11
)(2 825.188 molKJOHS v
and .10303.2 14
KV
dT
dE
P
Table 3-1 shows values of E° at one bar pressure and various temperatures.
Table 3-1 Influence of temperature on reversible cell voltage at 1.0 bar pressure
Temperature (°C) Reversible Cell Voltage (V) Reversible Cell Voltage (V)
Liquid Water Water Vapour
25 1.229 1.184
40 1.216 1.181
50 1.208 1.179
80 1.182 1.172
100 1.165 1.167
40
Since S for a fuel cells is usually negative, the reversible voltage of a hydrogen fuel cell
will decrease as the cell temperature increases. Thus, for a reversible hydrogen-oxygen
fuel cell with water vapour as the by-product, there will be an approximate 23 mV
decrease in cell voltage for every 100 degree increase in cell temperature [113]. This
may not have a significant impact on PEM fuel cells, but will certainly manifest itself in
high-temperature fuel cells. This, however, does not mean that fuel cells must be operated
at low temperatures to increase their efficiency. Fuel cell kinetics dictates higher
temperature, since kinetic losses usually decrease with increasing temperature.
3.2.3 Reversible Cell Voltage as a Function of Pressure
Reactant pressure and concentration also can influence the reversible voltage of a fuel
cell. The pressure effects on reversible cell voltage are discussed here and concentration
impacts will be discussed in a later section.
Consider reaction (3-4), from thermodynamics
2222 2
1
2
1OHOHliq
T
vvvvv
VdP
G
(3-7)
Assuming ideal gas behaviour and :22 OH PP
P
TR
P
TR
P
TR
dP
G
OHT
5.1
2
1
22 (3-8)
but: EFnG PT , (3-9)
therefore: P
TRV
P
EFn
P
G
5.1 (3-10)
and: PFn
TR
P
E
5.1 (3-11)
41
Integrating equation (3-11) from standard pressure (P° = 1.0 bar) to an arbitrary pressure,
P, while keeping temperature constant yields,
P
P
Fn
TREET ln
5.1 (3-12)
The influence of pressure, like temperature, on reversible cell voltage is minimal. For a
PEM fuel cell operating at 25 °C, the reversible cell voltage as a function of pressure, for
both liquid water and water vapour as products, is shown in Table 3-2 and Figure 3-1.
Table 3-2 Influence of pressure on reversible cell voltage at a fixed temperature of 25 °C
Pressure (bar) Reversible Cell Potential (V) Reversible Cell Potential (V)
Liquid Water Water Vapour
1.0 1.229 1.185
2.0 1.242 1.189
3.0 1.250 1.192
4.0 1.256 1.194
5.0 1.260 1.195
6.0 1.264 1.196
7.0 1.266 1.197
8.0 1.269 1.198
9.0 1.271 1.199
10.0 1.273 1.200
When liquid water is the product of the above PEM fuel cell, increasing the pressure of
the incoming gases from 1.0 bar to 5.0 bar and then to 10.0 bar increases the reversible
cell potential by only 2.5% and 3.6%, respectively. The influence of the pressure is
clearly minimal. In practice, high gas pressures may not be desirable owing to
mechanical issues. However, the pressure effects on real fuel cells can be significantly
higher than those predicted by thermodynamics, owing to enhanced kinetics and mass
transport [112].
42
1.18
1.19
1.20
1.21
1.22
1.23
1.24
1.25
1.26
1.27
1.28
0.0 2.0 4.0 6.0 8.0 10.0 12.0
Gas Pressure (atm)
Revers
ible
Cell
Po
ten
tial
(V)
Liquid Water
Water Vapour
Figure 3-1 Reversible cell potential as a function of pressure for PEMFCs at 25 °C
3.2.4 Reversible Cell Voltage as a Function of Concentration
Pure hydrogen and oxygen are seldom used in practice. Hydrogen fuel is usually
extracted from hydrocarbon fuels via reformation or partial oxidation processes.
Accordingly, the fuel stream consists of a mixture of hydrogen (about 50% - 70%), inerts
(water vapour, carbon dioxide, etc.), and active species (carbon monoxide).
The oxidant is generally taken from air, hence contains a large number of both inert and
active species. Even pure hydrogen and oxygen need to be humidified before entering the
fuel cell to ensure that the solid electrolyte membrane is adequately hydrated. Chemically
inert species such as water vapour influence the reversible cell voltage of PEMFCs by
lowering the concentrations of both fuel and oxidant, which, in turn, increase mass
transport resistance to the active sites on both the anode and cathode. Chemically active
species such as carbon monoxide have a more marked impact on the reversible cell
potential, the most important of which is poisoning of the noble metal catalyst.
43
Applying the Nernst equation to the PEM fuel cell reaction gives:
2
21
2
2ln2 OH
OH
aa
a
F
TREE
(3-13)
At the relatively low pressures found in PEM fuel cells the gas activities can be replaced
with their partial pressures. Furthermore, if the fuel cell is operated below 100 °C so that
liquid water is generated, the activity of water may be assumed to be close to unity.
Thus 2/1
22ln
2OH PP
F
TREE
(3-14)
The above expression confirms that pressurizing the incoming gases will result in a slight
increase in the reversible cell voltage. Compared with pure gases at 1.0 bar pressure, with
fuel and oxidant streams of 0.5 and 0.21 (mole fraction), respectively, the reversible
voltage will only decrease by 0.0189 V. This reveals that losses due to other
irreversibilities are much greater. Such irreversibilities include slow oxygen reduction at
the cathode and slow rates of mass and charge transfer. These irreversibilities are
discussed in the next section.
3.3 Fuel Cell Efficiency
The maximum thermal efficiency ε of a heat engine is defined as the maximum amount
of work that it can deliver with the thermal energy supplied to the engine. For a
combustion engine, this is simply the fraction of the enthalpy of combustion of the fuel
that can be delivered as work:
HI
LO
combust
net
in
net
T
T
H
W
Q
W
1max (3-15)
where THI is the temperature at which the combustion takes place and TLO is the
temperature of the heat sink (usually that of the surroundings).
Fuel cells, on the other hand, operate at constant temperature and both reactants and
products can enter and exit the system at similar temperatures. The following expression
is based on the fact that fuel cells are not subject to the above Carnot cycle limitation:
44
Thus combust
PT
H
G
,
fuel theof combustion ofenthalpy
producedenergy electrical (3-16)
Equation (3-16) is often referred to as the thermodynamic efficiency. It is also helpful to
express the efficiency of a fuel cell in terms of its output voltage. The voltage efficiency,
εv, of a fuel cell is largely determined by the cell voltage, Vc, divided by the reversible
OCV:
%100E
VC
v (3-17)
However, not all the fuel fed to a fuel cell participates in the electrochemical reaction
taking place at the anode. Some fuel will simply pass through the membrane and react
with the oxygen on the other side or leaves the cell unreacted. This lowers the overall
efficiency of the cell, as a result, a coefficient, known as the fuel utilization coefficient, εf,
is often introduced to account for such losses. This is just the fraction of the fuel that
reacts to generate electrical output. Thus the overall energy conversion efficiency of the
fuel cell is given by:
fv
combust
PT
H
G
, (3-18)
Although the ideal (maximum) efficiency of a fuel cell depends on thermodynamics, the
real (actual) efficiency depends on electrode kinetics. Electrode kinetics and fuel cell
electrochemistry are briefly discussed in the next section to present a simple overview of
electrode kinetics and further elucidate the problem of efficiency as related to
electrochemical conversion devices such as fuel cells.
45
3.0 FUEL CELL ELECTROCHEMISTRY
3.1 Introduction
A brief overview of fuel cell thermodynamics was presented in the preceding section.
Thermodynamic analysis provides us with necessary information to predict the
performance of a particular fuel cell based on a set of variables and state functions. The
main goal of thermodynamic calculations is to determine whether a particular process
proceeds to completion without help from external means; i.e., predicts the spontaneity of
a particular process. However, it cannot predict the rate of the electrochemical reactions
taking place on the surface of the electrodes or the mechanism of the reactions occurring
inside the cell. Furthermore, thermodynamic analysis is unable to tell us how much
energy is lost under real conditions; i.e., irreversible losses. To deal with these aspects we
must examine the electrochemical kinetics of the process.
4.2 Electrode Kinetics
Electrochemical reactions are defined as chemical reactions in which electrons are
transferred between an electrode—a metal or a semiconductor—and an electrolyte—a
solid polymer electrolyte, a molten salt or an aqueous electrolyte solution [331]. It is
apparent that both a transfer of electrical charge and a change in Gibbs free energy
accompany all electrochemical reactions. The primary function of electrode kinetics is to
investigate the sequence of partial reactions taking place on the surface of electrodes and
explain the mechanism of such reactions to determine the overall electrode reaction. This
information is then utilized to determine the rate-determining steps for the overall
electrode reaction. The overall rate of the reaction is evaluated by the rate of the slowest
step—the rate-determining step (RDS) [331].
The general half-cell reactions can be expressed as follows:
RedneOx (4-1)
The forward reaction presents a reduction reaction, where reactant ―Ox‖ undergoes a
reduction process by gaining ―n‖ electrons to form ―Red‖. For the opposite direction,
reactant ―Red‖ participates in an oxidation reaction and loses ―n‖ electrons to from ―Ox‖.
At equilibrium both processes take place at an equal rate resulting in no net electrode
46
current. In other words, for an electrode-electrolyte system at equilibrium, the rate of
electron generation equals the rate of electron consumption. When only one direction of
equation (4-1) is considered, the rate of electron consumption or generation—the current
that is produced—can be expressed as follows [330]:
jFAnI (4-2)
where I ≡ current in amperes
n ≡ number of electrons transferred
A ≡ the active area of the electrode in cm2
F ≡ Faraday’s constant (96487 C mol-1
e-)
j ≡ flux of reactants reaching the surface of the electrode in mol s-1
cm-2
Equation (4-2) can be expressed in terms of current density, i (A cm-2
), which makes
comparison of different electrodes easier and more manageable by eliminating the need
to account for the surface area of each electrode.
jFni (4-3)
The current that is produced as a result of the electrode processes can be determined by
the rate of the reactant conversion at the surface of the electrode, which, in turn, is a
function of surface concentration of the reactant(s). Considering equation (4-1), for the
reduction process (forward reaction), the flux is given by [330]:
sff Oxkj ][ (4-4)
Similarly, for the oxidation half reaction (backward reaction) the flux is:
sbb Redkj ][ (4-5)
where jf ≡ forward reaction flux in mol s-1
cm-2
jb ≡ backward reaction flux in mol s-1
cm-2
kf ≡ forward rate coefficient in L s-1
cm-2
kb ≡ backward rate coefficient in L s-1
cm-2
[—]s ≡ reactant concentration at surface in mol L-1
The net current density is the difference between the forward current density and the
backward current density:
47
)][Re][( sbsf dkFOxkFni (4-6)
As mentioned above, at equilibrium, the rate of forward reaction equals the rate of
backward reaction; accordingly, the net current is zero since the reaction will proceed at
the same rate in both directions. This rate, expressed as a current density, is known as
exchange current density, i₀.
4.3 The Butler-Volmer Equation
For an electrochemical process to proceed there must be a charge transfer across the
electrode/electrolyte interface. In moving from the electrolyte to the electrode or vice
versa, the charge must overcome an activation energy barrier [154, 330], the magnitude
of which is directly proportional to the change in Gibbs free energy of the products and
the reactants. The rate constant for each charge transfer process (in s-1
) can be written as:
TR
G
h
Tkk B exp (4-7)
where ΔG# = the activation energy barrier in J mol
-1
kB = Boltzmann’s constant in J K-1
h = Planck’s constant in J s
T = Temperature in K
Since electrochemical reactions involve the transfer of charge and are accompanied by a
change in the energy state of the system, the Gibbs activation energy may be thought of
as containing both electrical and chemical components. For the cathodic direction:
FnGG C (4-8)
For the anodic direction:
FnGG C )1( (4-9)
where
CG chemical component (subscript ―c‖ indicates the chemical
component)
potential difference component
charge transfer coefficient
48
Thus the heterogeneous rate constant for the forward direction, kf, can be expressed by
substituting equation (4-8) into (4-7) to give:
TR
Fn
TR
G
h
Tkk
fcBf
expexp
, (4-10)
The overvoltage or overpotential (also known as polarization) for an electrochemical
reaction is defined as:
revEE (4-11)
where E is the electrode potential and Erev is the reversible or equilibrium voltage for the
reaction. It is also customary to define the overvoltage as:
rev (4-12)
For a fuel cell, by convention, the overvoltage of the anode is positive, while that for the
cathode is negative. Equation (4-10) can be expressed for each direction in terms of the
overvoltage to give:
TR
Fn
TR
Fn
TR
G
h
Tkk revfcB
f
expexpexp
, (4-13)
TR
Fn
TR
Fn
TR
G
h
Tkk revbcB
b
]1[exp
]1[expexp
,(4-14)
All the terms in equations (4-13) and (4-14) with the exception of the last term, can be
gathered into a constant term k₀:
TR
Fnkk ff
exp,0 (4-15)
TR
Fnkk bb
]1[exp,0 (4-16)
Substitution of (4-15) and (4-16) into (4-6) gives the net electrode current density as a
function of the electrode overvoltage:
49
TR
FnkdFn
TR
FnkOxFni bsfs
]1[exp][Reexp][ ,0,0 (4-17)
The exchange current density, i0, was defined in section 4.2; a more comprehensive form
of exchange current density can be derived from equation (4-17) by noting that both the
overvoltage and external current are zero when the electrode is in equilibrium [330]:
0,00,00 ][Re][ ikdFnkOxFn bf (4-18)
An expression that relates overvoltage to current density can be derived by substituting
equation (4-18) into equation (4-17):
TR
Fn
TR
Fnii
]1[expexp0 (4-19)
The above equation is known as the Butler-Volmer equation and is a general expression
for an electrochemical reaction incorporating both reduction (left expression) and
oxidation (right expression) components. In an operating fuel cell, if the overvoltage of
an electrode is significantly positive, then the oxidation term (right side) becomes bigger,
while the reduction term (left side) becomes smaller resulting in a net current density that
is negative. This corresponds to an oxidation reaction, where electrons leave the
electrode, similar to the oxidation of hydrogen at the anode in PEM fuel cells. If the
overvoltage is, however, significantly negative the reduction term in equation (4-19)
becomes dominant, as is the case with the reduction of oxygen at the cathode in a PEM
fuel cell [330].
4.4 Overvoltage and Current Density
An important relationship between overvoltage and current density can be established by
examining the limiting form of the Butler-Volmer equation when the overvoltage is very
small. Consider equation (4-19), when the overvoltage is very small; i.e., 1TR
F, and
generally around 0.01 V or smaller, the expression can be expanded and written as [332]:
50
TR
FiTRFTRFii
0
0 ])/(1[/)1(1 (4-20)
This is based on the expansion of the exponential using xe x 1
Equation (4-20) shows that at low overvoltage the current density is directly proportional
to the overvoltage. Under these conditions, the interface between the electrode and the
electrolyte behaves similar to an ohmic conductor. If the overvoltage is slightly positive,
an anodic (positive) current will be generated, and when the overvoltage is small and
negative, a cathodic (negative) current will be generated. That is:
0i
iF
TR
(4-21)
Another limiting form of the Butler-Volmer equation arises when the overvoltage is
large—larger than 0.1 V. When the overvoltage is positive and greater than 0.1 V, the
first term in the Butler-Volmer equation becomes negligible so that:
TR
Fnii
)1(exp0 (4-22)
Similarly when the overvoltage is more negative than 0.1 V, the second term of equation
(4-19) becomes negligible:
TR
Fnii
exp0 (4-23)
And iFn
TRi
Fn
TRlnln
(4-24)
51
4.5 Fuel Cell Losses
4.5.1 Introduction
The ideal cell voltage for a PEM fuel cell can readily be evaluated. Under standard
conditions with water as the byproduct, at 25 °C the ideal cell voltage for a PEM fuel cell
is 1.229 V. In practice, however, the real cell voltage is usually considerably less than
this, even at open-circuit voltage, when no net current flows. This is attributed to a
number of irreversibilities associated with all types of fuel cells. The typical performance
of a hydrogen fuel cell—a polarization curve—operated under standard conditions is
shown in Figure 4-1, where three distinct regions can be observed.
It should be noted that even at the open-circuit voltage the actual cell voltage is less than
the reversible value. In addition to the three distinctive regions where voltage losses are
manifested, fuel crossover also can lower the actual cell voltage. The causes of voltage
losses for each of these regions are discussed and ways to minimize them are presented
below.
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0 200 400 600 800 1000 1200 1400 1600 1800 2000
Current Density (mA cm-2
)
Ce
ll V
olt
ag
e (
V)
Ideal Voltage = 1.229 V at STD
Ohmic Polarization Concentration
Polarization
Activation
Polarization
Figure 4-1 A typical performance curve for a hydrogen fuel cell operated at 1.0 bar
pressure and 25 °C
Reversible Cell Voltage = 1.229 V at STP
52
4.5.2 Activation Overvoltage
The first part of a polarization curve for hydrogen fuel cells operating at temperatures
lower than 100 °C shows a sharp drop in cell voltage as it begins to move away from the
open circuit voltage. This drop is highly non-linear and is attributed to the slowness of
the charge transfer reactions occurring on the surface of both anode and cathode. It is
understood that for electrons to be transferred to or from an electrode in electrochemical
systems, a driving force must exist to attract or repel electrons through the external
circuit. This motive force is provided by a portion of the voltage that is initially generated
within the cell as it moves away from equilibrium. As a result, this portion of the voltage
will not be available to do useful work. In this region the difference between the open
circuit voltage and the actual voltage is called activation overvoltage or activation
polarization, act [328]:
0
logi
iaact (4-25)
Upon a closer examination, it becomes apparent that this is just another form of the Tafel
equation. It is also common practice to present the above equation in terms of natural
logarithms:
0
lni
iAact (4-26)
It is noted that the activation overvoltage can be lowered either by decreasing the
constant, A, or by increasing the exchange current density, i0. Accordingly, the exchange
current density is higher for faster reactions manifesting a more active electrode surface
while a smaller exchange current density translates into a slower reaction and a less
active electrode surface. It is, therefore, desirable to increase i0 at both the anode and the
cathode. This is especially critical for the cathode of a fuel cell where oxygen reduction
takes place and the exchange current density is much smaller compared with that of the
anode where hydrogen oxidation occurs. The difference in exchange current density can
sometimes be as high as 5 orders of magnitude. Consequently, activation overvoltage at
the anode usually can be ignored. For instance, for hydrogen fuel cells operated at low
temperatures, typical values for the exchange current density at the anode and the cathode
53
are 200 mA cm-2
and 0.1 mA cm-2
, respectively. A complete expression for the activation
overvoltage of a hydrogen fuel cell can be derived by taking into account both the anode
and the cathode overvoltages:
c
c
a
aacti
iA
i
iA
,0,0
lnln (4-27)
This can be rearranged and expressed as [328]:
b
iAact ln (4-28)
where A = Aa + Ac and )()( ,0,0A
A
cA
A
a
ca
iib
The constant A is found to be a function of temperature and a constant known as the
charge transfer coefficient, . Charge transfer coefficient values range from 0.0 to 1.0
with a value of about 0.5 for the anode and 0.1 to 0.5 for the cathode of a hydrogen fuel
cell. The constant A is known to be a function of temperature and electrode material. A
simple relationship between constant A, temperature and charge transfer coefficient has
been reported in the literature [328]:
F
TRA
2
(4-29)
It should be noted that the Tafel equation can be expressed in terms of current density
instead of overvoltage.
Aii act
exp0 (4-30)
Substituting equation (4-29) into equation (4-30) yields:
TR
Fii act2
exp0 (4-31)
The above equation is another way of expressing the Bulter-Volmer equation.
For a PEM fuel cell with no losses other than activation polarization at both anode and
cathode, the real cell voltage is given by:
54
c
c
a
ai
iA
i
iAEE
,0,0
lnln (4-32)
or simply,
actEE (4-33)
As mentioned previously, there are two ways of lowering the activation overvoltage for a
hydrogen fuel cell, and thereby increasing the cell voltage. First approach involves
lowering the constant A, while the second approach requires increasing the exchange
current density. The latter can be attained by increasing the cell temperature, utilizing
better catalysts, increasing reactant pressure, maximizing the true surface area of the
electrodes, and increasing reactant concentration.
4.5.3 Ohmic Overvoltage
The second region of a polarization curve for a low-temperature hydrogen fuel cell shows
a linear drop in cell voltage as more current is drawn. This is the simplest cause of
potential loss in hydrogen fuel cells and arises primarily because of the ohmic resistance
to the flow of electrons and ions. Electronic resistances appear in the catalyst and gas
diffusion layers, bipolar plates, and cell interconnects, while ionic resistance manifests
itself primarily in the electrolyte; i.e., Nafion®
. Ohm’s law can be used to approximate
this relationship; however, in order to compare the results with other losses, the equation
must be expressed in terms of current density. Starting with Ohm’s law:
RIV (4-34)
In equation (4-34), the current, I, in amperes, is readily converted to current density, i, in
mA cm-2
, but the resistance, R, has to be expressed in terms of resistance per unit cell
surface area; i.e., per cm2. This quantity is known as the area-specific resistance (ASR)
and is represented by the symbol r given in kΩ cm2. Equation (4-34) can be expressed in
terms of this new quantity:
riohmic (4-35)
The most effective way to reduce ohmic overvoltage is to make the membrane
electrolyte, the electrodes, and the MEAs as thin as possible. Making the electrolyte too
55
thin, however, may permit fuel crossover to become an issue. Furthermore, the integrity
of the whole MEA can become compromised if it is not thick enough to prevent short-
circuiting with the adjacent electrode. Equally important is the incorporation of a good
design and use of appropriate materials for the fabrication of the bipolar plates and other
cell interconnects.
4.5.4 Concentration Overvoltage
At the anode it is evident that the voltage depends on the partial pressure of the hydrogen
gas in the fuel mixture, and, as the hydrogen partial pressure decreases, the cell potential
also will decrease. Even using pure hydrogen as fuel, a pressure drop will exist between
the consumption site at the three-phase interface and the supply container, the magnitude
of which depends on the current being drawn from the cell and the design of the gas
delivery system [328].
A similar problem exists at the cathode. Although it is a well-established fact that
reduction in fuel and oxidant pressures will lead to lower cell voltages, it is not easy to
model such changes with certainty. A simple equation commonly used to express the
relationship between concentration polarization and reactant pressure is:
1
2lnP
P
Fn
TRconc (4-36)
where n is the number of electrons per mole of the reactant for the half-cell reaction
under investigation (2 for hydrogen oxidation and 4 for oxygen reduction in PEM fuel
cells), P1 is the pressure at zero current density, and P2 is the pressure at any current
density. Unlike the previous expressions for activation and ohmic polarizations, equation
(4-36) must be used with caution, since it is only approximate. This has been confirmed
by comparison with experimental values [328]. An empirical expression that is often
used in the fuel cell literature is:
ni
conc em (4-37)
m and n are fitted empirical constants. In practice, m and n are often taken as 3 × 10-5
V
and 8 × 10-3
cm2 m A
-1, respectively [328].
56
4.5.5 Mixed Potential at Electrodes
This type of voltage loss arises predominantly by the occurrence of undesired reactions
both at the cathode and the anode resulting in a lowering of the equilibrium potential. The
primary source of such losses is the crossover of the fuel through the electrolyte from the
anode to the cathode resulting in direct mixing with the oxidant and subsequent parasitic
consumption of reactants.
Electrolytes in general and solid polymer electrolytes in particular, are selected based on
their ionic conductivities, their inability to transport electrons, and their impermeability to
hydrogen fuel and oxidants. Selecting SPEs of higher thickness alleviates the fuel
crossover problem at the expense of ionic conductivity. Fortunately such flows of
electrons and fuels are often insignificant and can be ignored in PEM fuel cells. Such
losses are not easy to quantify, but can be measured indirectly by determining the rate of
fuel use at the anode or of oxidant at the cathode. The relationship between hydrogen use,
G in mol s-1
, and the generated current as a result of parasitic consumption is:
FGI 2 (4-38)
The small current, ir that would result from this parasitic reaction can be added to
equation (4-26) to take into account the above losses [328]:
0
lni
iiA r
act (4-39)
57
4.0 CATALYST LOADING
5.1 Introduction
The MEA of a hydrogen fuel cell is considered to be its most critical component. It
consists of two pretreated carbon substrates—either paper or cloth—known as gas
diffusion layers (GDLs), a membrane to separate the anode and the cathode, and two
catalyst layers, each strategically placed between the last two layers (see Figure 5-1). The
roles of both solid polymer electrolyte membranes and GDLs in PEM fuel cells were
discussed earlier (see sections 2.2.1 and 2.2.3). The catalyst layer is, by far, the most-
studied component of an MEA. It is the locus of all electrochemical reactions taking
place inside the cell and its primary function is to facilitate these reactions both at the
cathode and the anode. This is of special importance for the cathodic oxygen reduction
reaction (ORR), the rate of which can be lower by several orders of magnitude than that
of the anodic hydrogen oxidation reaction. One of the major requirements for the
cathodic reduction of oxygen in hydrogen fuel cells is that the reaction proceeds at low
overvoltages. Platinum and platinum-group metals (PGMs) satisfy this requirement, and,
in addition, are stable in the acidic environment of the fuel cell. However, they are
prohibitively expensive, and significant reduction in their loading without compromising
cell performance is required to ensure their feasibility in low-temperature fuel cells.
Figure 5-1 A simple schematic of a five-layer membrane-electrode assembly
Carbon
Substrate
Carbon
Substrate
Solid
Polymer
Electrolyte
Anode
Catalyst
Layer
Cathode
Catalyst
Layer
58
Electrocatalysts were originally made from pure platinum black crystallites with average
particle diameters in the range of 10 – 20 nm. The effective surface area of such
electrocatalysts is relatively small, owing to their large diameters, resulting in high
loadings to deliver an acceptable cell performance. By the late 1980s and early 1990s, a
ten-fold reduction in noble catalyst loading had been achieved, and the performance of
such cells was comparable, and in some cases, even better than, PEMFCs with higher
catalyst loadings [335]. Two innovations played critical roles in achieving this; first was
the replacement of platinum black with platinum supported on high surface-area carbon.
This not only created platinum catalysts that were smaller in size—2-5 nm diameter—but
also created a viable and extensive pathway for electrons to move away from the catalyst
layer, where they are generated, towards the external circuit, where they perform useful
work. Raistrick et al. [340] replaced platinum black with 10% carbon-supported platinum
particles in the range of 2-3 nm in diameter by preparing a catalyst ink containing carbon-
supported platinum, polytetrafluoroethylene, and solubilized Nafion®. Other workers,
including Ticianelli et al. [341] and Gottesfeld and Zawodzinski [342], further improved
cell performance by increasing the amount of Pt/C from 10% to 20% and optimizing the
amount of solubilized Nafion® in the catalyst ink. Second, it was realized that in order to
extend the three-phase interface, SPE must be able to penetrate inside the substrate, even
into the micropores, to come into full contact with the electrocatalyst and gas phases
during operation. Accordingly, a solubilized form of a SPE (e.g., 5% Nafion® in an
alcoholic solution) was impregnated into the catalyst side of a GDL. This had a positive
impact on cell performance, primarily by extending the three phase interface. However,
not all the methods commonly used today use ionomer impregnation.
5.2 Catalyst Layer Application Methods
Catalysts can be applied directly onto either two GDLs (e.g., carbon substrates) followed
by hot pressing of a SPE in the middle, or they can be loaded onto both sides of a solid
polymer electrolyte and then sandwiched between two GDLs. Regardless of the addition
sequence, there are several methods that are used for catalyst loading. These are grouped
and presented in Figure 5-2.
59
5.2.1 Application of Catalyst to Gas Diffusion Layers
There are many methods for catalyst application, but seven different techniques are
widely used to apply a thin layer of catalyst on carbon paper or cloth GDLs. Most of
these methods employ a two-step process to deposit noble metals onto the surface of a
GDL, consisting of a catalyst ink preparation step followed by an application phase.
However, a single sputtering process also can be used to perform this task with
comparable results. These methods are briefly discussed in the following subsections.
Figure 5-2 Catalyst loading methods
Catalyst Loading
Application to SPE Application to GDL
Spreading
Spraying
Painting
Sputtering
Powder Deposition
Ionomer Impregnation
Electrodeposition
DC Electrodeposition
Pulse Electrodeposition
Painting
Dry Spraying
Sputtering
Decaling
Evaporative Deposition
Impregnation-Reduction
60
5.2.1.1 Application of Catalyst by Spreading
Catalyst deposition by spreading is one of the earliest methods utilized to provide a
relatively consistent layer on various GDLs. The first step involves the preparation of a
catalyst ink that generally consists of carbon powder, PTFE and catalyst. The above ink is
mixed using mechanical agitators, and often ultrasonic mixers, to ensure a well-mixed
dough. The above catalyst ink then is applied onto a pre-treated carbon substrate using a
heavy metallic cylindrical roller on a flat surface.
Srinivasan et al. [343] utilized this method and reported a thin and uniform catalyst layer
on wet-proofed carbon cloth. With this technique the catalyst loading is directly
proportional to the thickness of the catalyst layer. Consequently, the amount of platinum
per unit area can readily be controlled during deposition by monitoring the catalyst layer.
Higher loadings can be easily obtained by repeating the second step (application phase).
This simple control comes at the expense of catalyst particle size (bigger particles result),
which can adversely influence cell performance, since increasing catalyst size decreases
catalyst activity. This becomes noticeable when the catalyst-to-carbon ratio increases to
40 wt% or greater. Catalyst layer cracking is another shortfall associated with this
method; however, several workers [344-346] have reported catalyst layers having cracks
whose area is less than 10% of the total area of the catalyst layer, and even crack-free
catalyst layers with acceptable performance. Ueyama [344] examined the impact of
several factors—including the thickness of the catalyst layer, the type of carbon support,
and the drying rate of the solvent used for making the catalyst ink—on the properties of
the catalyst layer in general, and catalyst consistency and freedom from cracks in
particular. In another patent, Sompalli et al. [345] presented an invention in which
significant reductions in ―mud-cracking‖ of catalyst layers is obtained either by pre-
treating the substrate with a wetting solvent prior to MEA fabrication or by utilizing a
post-treatment approach, in which the catalyst ink contains a solvent that is wetting to the
substrate. But, upon drying of the catalyst layer, it then is coated with a solution of an
ionomer and a solvent that is non-wetting to the substrate. It is claimed that both methods
control the drying rate to form a more uniform and robust electrode by preventing
electrode shrinkage and subsequent cracking of the catalyst layer. Iwasaki et al. [346]
61
proposed a method in which it is claimed that catalyst layers with less than 10% cracking
(compared with the whole catalyst layer area) can be formed. According to their method
a substrate—carbon paper or cloth—is coated with a slurry containing only carbon
powder and PTFE. This is followed by drying the previous coat under pressure to form a
hydrophobic layer. Carbon powder, PTFE and a suitable catalyst then are mixed and the
electrode is coated with this new paste. The amount of catalyst loading is simply
controlled by carefully monitoring the catalyst layer thickness. The electrode is once
again pressurized to dry the last coating. They suggested heating the MEA to remove any
remaining solvent in the hydrophobic layer before using it in a fuel cell. Uchida et al.
[347] developed a method for fabricating MEAs by first creating a paste containing
carbon-supported platinum, Nafion® solution, and a solvent. This paste was then spread
on a pre-treated carbon electrode. A significant improvement in cell performance was
reported and attributed to an increase in contact between the catalyst particles and the
electrolyte in the MEA.
The spreading method is popular because of its simplicity and cost effectiveness.
However, it suffers from lack of adequate control in terms of catalyst particle size when
higher catalyst loadings are desired. For higher catalyst loadings it is often necessary to
apply several coatings, and, to avoid re-dissolving of catalyst ink components in the
previous layer, the electrode generally is sintered between each application.
5.2.1.2 Application of Catalyst by Spraying
In this method, similar to the previous one, catalyst ink is prepared by mixing carbon
powder, PTFE, water, alcohol and a catalyst. The main difference between this catalyst
ink and that presented in the previous method is the respective viscosity. In the spreading
method, a rather thick and viscous ink is desirable, while in the spraying method, due to
the nature of the application process, the catalyst ink must be thin with a low viscosity to
ensure an adequate flow.
The ink then is simply sprayed onto a wet-proofed substrate. The amount of catalyst
loading is optimized by controlling the thickness of the catalyst layer. Higher catalyst
loadings are attained by repeatedly spraying the ink onto the electrode. The electrode is
62
always sintered between each application to prevent various components of the previous
layer from re-dissolving in the next layer [335]. It is a common practice to roll the
electrode to produce a catalyst layer that is thin, homogenous and of uniform thickness.
In addition, rolling has been found to produce layers with low porosity. Srinivasan et al.
[343] proposed a method in which the electrolyte is suspended in a mixture containing
alcohol, water and PTFE. They reported comparable performance when compared with
MEAs fabricated via the spreading method. Tanaka et al. [348] developed a method for
fabricating multi-layered gas diffusion electrodes in which both layers—a water repellent
layer and an electrocatalyst layer—are formed via spraying. A wide range of catalyst
particle size (2 to 100 nm diameter) was reported.
The spraying method has gained popularity amongst some workers owing to its ease of
use, scalability, and minimal equipment requirements. However, similar to the spreading
method, at higher catalyst loadings the catalyst particle size increases, consequently
decreasing its activity and lowering cell performance.
5.2.1.3 Application of Catalyst by Painting
This is one of the oldest and most cost-effective methods to deposit a noble metal catalyst
onto an electrode. Similar to the spray method, the catalyst ink must be thin with low
viscosity to ensure that a uniform layer is applied to the electrode with each application.
An artist’s paintbrush generally is used to transfer the catalyst from the mixing container
onto the electrode. Electrodes with carbon substrates are always wet-proofed to control
the depth of the catalyst ink penetration inside the electrode. This method is not intended
for mass production of GDLs or substrates with large surface areas; however, although it
can produce MEAs with acceptable results in a lab setting, it does require extra care and
effort to ensure reproducibility. Catalyst loading is optimized simply by controlling the
catalyst layer thickness. And, as is the case with the first two methods, the electrode is
sintered between each application to avoid dissolution of the components of the previous
layer into the next layer. This method suffers from the same shortcomings of the first two
methods.
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5.2.1.4 Application of Catalyst by Powder Deposition
In catalyst powder deposition, a mixture of carbon powder, carbon-supported platinum
and PTFE is vigorously mixed in a fast running knife mill under forced cooling [335].
The mixture then is applied onto a wet-proofed carbon paper, carbon cloth or other
suitable substrate. Bevers et al. [349] reported significant improvements in both gas and
water transport properties of MEAs fabricated using this method, which differs from the
previous two in terms of catalyst ink preparation. While both spreading and spraying rely
on mechanical and ultrasonic mixers, catalyst powder deposition takes advantage of a
mill to produce a well-mixed and homogeneous mixture. Although the need for special
equipment is somewhat greater than for the previously-discussed methods, the catalyst
application step has many similarities with both spraying and spreading. As a result, most
catalyst layers produced via this method exhibit similar properties to those of catalyst
layers prepared by spraying or spreading techniques.
5.2.1.5 Application of Catalyst by Ionomer Impregnation
In most methods discussed so far, a layer of solubilized electrolyte (e.g., Nafion®) is
applied to the catalyst side of the electrode after catalyzation. This is believed to extend
the three-phase interface by maximizing the contact points between the electrolyte and
the catalyst particles (and of course, the reactants when the cell is in operation). Although
this will create more contact points between the electrolyte and the catalyst, the extent of
these contact points depends upon the depth of penetration of the electrolyte into the
catalyst layer. Some of the micropores in the catalyst layer can be as small as 5-20 nm in
diameter and, as a result, ionomer molecules cannot reach them. Gottesfeld and
Zawodzinski [342] reported a significant improvement in cell performance when a
solubilized electrolyte is added to the catalyst ink prior to application rather than after
catalyzation. This will further increase the protonic access to the majority of the catalyst
sites not in intimate contact with the solid electrolyte after hot pressing. Ionomer
impregnation is particularly effective in liquid-fed fuel cells such as direct methanol fuel
cells (DMFCs).
64
Zhang et al. [350] reported a technique in which the catalyst side of each electrode of a
DMFC was impregnated with a 1% solution of Nafion® before and after catalyzation.
They claim that the initial ionomer impregnation covers a significant surface area of the
substrate with a thin layer of the ionomer, resulting in a reduction of pore sizes inside the
substrate. This can lower the tendency of electrocatalyst to penetrate too deeply into the
substrate, and consequently become isolated and inactive. If this holds true, then catalyst
particles will remain very close to the substrate-membrane interface, and the likelihood of
them becoming active increases significantly. The second ionomer impregnation—after
catalyzation—further brings the deposited catalyst particles into contact with the
electrolyte, and hence increases cell performance. However, one must carefully optimize
the amount of solubilized electrolyte loading since it tends to alter the wetability
characteristics of the substrate, as pointed out by the authors. It is also worth investigating
the influence of an additional ionomer layer between the GDL and the catalyst layer on
the transport of electrons from the three-phase interface to the outside circuit. It is well-
known that one of the selection criteria for electrolyte membranes in fuel cells is their
inability to conduct electrons. An additional layer of Nafion®, for instance, between the
GDL and the catalyst layer will hinder the transport of electrons, resulting in inferior
performance if not designed and applied properly.
In another patent [351] by the same inventors (reference 350), the anode of a fuel cell
containing a solid polymer electrolyte is first oxidized in a simple electrochemical cell
comprising the electrode (working electrode) and a counter electrode both immersed in
an appropriate, preferably acidic, aqueous solution. A d.c. power supply is connected
across the electrodes (positive terminal connected to the working electrode) and electric
current allowed to pass through the solution. It is reported that by passing 20-80 C cm-2
of charge for about 5 to 10 minutes at a cell voltage of 4.0 V, the working electrode can
effectively be oxidized. The treated substrate is then impregnated with about 0.3 mg cm-2
of 1% Nafion® solution in isopropanol. This is followed by catalyzation and MEA
fabrication. It is reported that the above MEA performed better than other MEAs—both
oxidatively treated and non-treated MEAs with no ionomer impregnation. However, no
improvement in cell performance is reported for oxidatively-treated MEAs compared
with conventional MEAs.
65
In yet another patent, Wilson [352], argues that it is difficult to obtain high ionomer
loadings to maximize the contact between the catalyst particles and the ionomer if an
ionomer impregnation method is utilized. He points out that the differential swelling
between the SPE and the catalyst layers—arising from differing hydration
characteristics—leads to delamination between these two layers. This can not only
interrupt the ionic path and consequently lower cell efficiency, but also compromise the
integrity of the cell or the whole stack. This subject area is covered in detail elsewhere
[353-355].
5.2.1.6 Application of Catalyst by Electrodeposition
Considerable attention has been given to electrodeposition of metals from both acidic and
non-acidic solutions, primarily because of ease of use and relatively low-cost
requirements. In its most basic form, a porous carbon electrode—either carbon paper or
cloth—is first impregnated by a liquid ionomer followed by electrodeposition of platinum
from a suitable platinum complex. It is claimed that this technique deposits platinum only
at sites where both electronic and ionic pathways are present [38, 105, 335], thereby
ensuring higher-than-normal catalyst utilization rates.
Reddy et al. [107] developed an electrochemical catalyzation technique in which
platinum was electrodeposited from a commercial platinum complex solution onto an
uncatalyzed carbon electrode previously impregnated with a Nafion® solution. Due to the
affinity of Nafion® for cations, platinum ions readily diffuse through the Nafion
® layer
and are electrodeposited only in places where both ionic and electronic pathways exist. A
detailed discussion on electrodeposition of metals in general, and noble metals in
particular, is given in section 5.3.
5.2.2 Application of Catalyst to Membrane
Catalysts also can be deposited onto solid polymer electrolytes and then bonded to two
GDLs—one on each side—prior to hot pressing. There are several methods that can be
used to accomplish this task, which are briefly discussed in the following sections.
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5.2.2.1 Application of Catalyst by Painting
This is a two-step technique in which, similar to many other methods, a catalyst ink is
prepared, followed by applying the ink onto both sides of the SPE using an artist’s brush.
The platinum ink is prepared by carefully mixing predetermined amounts of carbon-
supported platinum and solubilized Nafion®. The ink is thoroughly mixed using both
mechanical and ultrasonic mixers. Gottesfeld and Wilson [36, 156] examined this
technique by painting a layer of this ink directly onto a dry membrane in the Na+ form.
The ink consisted of 20 wt% carbon-supported platinum, 5 wt% Nafion® solution, water
and glycerol. A three-to-one ratio for the carbon-supported platinum and Nafion® was
reported, and NaOH was added after the catalyst, Nafion® and water were well mixed to
avoid gelling of the solution. A thin layer of this ink then was painted onto both sides of a
dry solid Nafion®
membrane and baked at about 160-190 C. A certain amount of
distortion was reported due to the swelling effect of the solvents; consequently, it was
recommended—especially for thinner membranes or heavy-ink applications—that the
painted electrode be dried on a special heated vacuum table. The authors suggested
baking the painted electrodes at temperatures relatively lower than the final curing
temperature, followed by rapid heating to the desired temperature. It was claimed that
this minimized the amount of distortion and cracking that is often associated with high-
temperature baking.
The last step involved the conversion of the membrane from the Na+ form to the H
+ form.
This was accomplished by immersing the membrane in lightly boiling 0.1 M aqueous
sulfuric acid for about 2 hours, followed by successive rinsing in lightly boiling deionized
water. Finally, the sample was air-dried for several hours and two GDLs hot pressed onto
each side to form an MEA. This is a simple and cost-effective technique for deposition of
platinum onto membranes, but it has several drawbacks. Although the catalyst layer
exhibits a uniform catalyst concentration profile, it is difficult to control the catalyst
particle size at high catalyst-to-carbon ratios; i.e.; platinum-to-carbon ratios of more than
40 wt%. Furthermore, this method is not suited for mass production of MEAs, where
robustness and reproducibility are of great importance.
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5.2.2.2 Application of Catalyst by Dry Spraying
This is another two-step technique in which a catalyst ink is first prepared and then
sprayed onto a dry solid electrolyte. The catalyst ink is prepared by careful mixing of
carbon-supported platinum, electrolyte membrane in powder form, PTFE and filler
materials in a knife mill. The mixture is then atomized and sprayed through a slit nozzle
directly onto a dried solid membrane [335, 356]. The catalyst layer is air-dried and hot-
pressed or hot-rolled to ensure adequate electronic and ionic contact.
This technique can produce catalyst layers as thin as 5 m, if the degree of atomization is
optimized [335]. The platinum-to-carbon ratio can readily be controlled by monitoring
the initial concentration of the platinum salt; and consequently, the level of platinum
loading can be optimized. As is the case with many powder type deposition techniques, a
uniform catalyst distribution inside the catalyst layer is easily achieved; however, it is
very difficult to keep the catalyst size under 5 nm in diameter when the initial platinum-
to-carbon ratio exceeds 40 wt%.
Benitez et al. [357] developed a two-step method based on an electrospray technique. The
first phase involved the preparation of a catalyst ink by thoroughly mixing carbon-
supported platinum (20 wt%), Nafion® solution (5 wt%) and different solvents, including
ethanol, glycerol and n-butyl acetate. Three different methods for catalytic ink dispersion
onto a carbon cloth substrate were used and compared: normal spray, impregnation and
electrospray. For deposition based on the electrospray technique, a high electric field was
applied between the catalyst ink and the substrate. The catalyst ink was forced to flow
inside a capillary tube in which a 3300 to 4000 V was applied between this tube and the
carbon substrate. A resulting mist of highly charged droplets emerged from the apparatus
and deposited onto the surface of the carbon paper. All the MEAs were characterized by
means of scanning electron microscopy with EDAX-system, X-ray photoelectron
spectroscopy (XPS), and X-ray diffraction (XRD). Morphological and structural
information were obtained for all MEAs and it was claimed that MEAs fabricated by this
technique exhibited three times higher power density than those fabricated by the
impregnation method and eight times higher than those prepared using a conventional
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spray technique. It also was claimed that this method is suitable for large-scale operations
using low-cost processes.
5.2.2.3 Application of Catalyst by Sputtering
Most of the research conducted to date on reducing the amount of noble metal catalyst in
fuel cells has focused either on lowering the size of the catalyst particles [106, 155, 341,
358-362] or localizing the catalyst in the close proximity of the electrolyte, where both
ionic and electronic pathways exist [115, 363]. The latter can be achieved by sputter
depositing a thin layer of catalyst close to or on the membrane. Conventional electrodes
have platinum loadings of about 0.4 mg cm-2
, while a normal sputtered platinum film of
about 5 nm in thickness has a Pt loading of around 0.014 mg cm-2
[362]. To achieve good
cell performance, an MEA with sputter-deposited platinum must satisfy several
requirements. First, it needs to maximize the three-phase interface to enhance the half-
cell reactions taking place on both anode and cathode. Second, the layer must be as thin
as possible to minimize ohmic losses, maximize gas transport within the layer, and
optimize water removal capabilities of the cell. Last, the sputtered layer must strongly
adhere to the membrane to function properly and effectively and to prolong its useful life
[362].
Hirano et al. [106] studied the performance of several MEAs prepared by a sputter
deposition technique. The sputter deposition was carried out on uncatalyzed and wet-
proofed (50 wt%) E-TEK electrodes in an argon atmosphere and a low pressure of
210-2
Torr. Furthermore, an accelerating potential of 470 V, a plate-current of 500 mA,
and a sputter-deposition rate of 0.039 mg cm-2
were utilized. The electrocatalyst layers of
both anode (conventional E-TEK electrode) and cathode (sputter-deposited catalyst layer)
were impregnated with Nafion®
solution. It was claimed that MEAs with a sputtered
platinum layer of only 0.1 mg cm-2
performed as well as state-of-the-art MEAs, with the
exception of high current density regions, where they were outperformed by conventional
E-TEK electrodes.
69
O’Hayre et al. [362] demonstrated the viability of the direct sputter deposition technique
by depositing platinum on Nafion®
117. It was claimed that MEAs prepared by this
method and having a platinum thickness of only 5-10 µm had a power output that was
several orders of magnitude greater than MEAs fabricated using conventional methods of
platinum deposition. Membrane-electrode assemblies with platinum loadings of 0.04 mg
cm-2
fabricated by the above method were compared with conventional MEAs having
platinum loadings of around 0.4 mg cm-2
. The power output of the sputter-deposited
MEAs was reported to be about 60% of that obtained from conventional state-of-the-art
MEAs. The authors emphasized the importance of carrying out the experiments at high
temperature and humidity to ensure the superiority of sputtered-platinum layers, since
almost all lab trials are performed under ideal lab conditions.
Gruber et al. [364] examined the influence of sputter-deposited catalyst layers on two
different types of GDL—SIGRACET GDL-HM (SGL Technologies, SGL Carbon
Group) and uncatalyzed ELAT (E-TEK Div., De Nora). Platinum catalyst layers were
deposited from a Pt diode target at 50 W rf (radio frequency) power and a pressure of 2.0
Pa at room temperature. The sputtered catalyst layers were characterized by SEM, EDX
and XRD techniques, and their performance was evaluated in a single cell (2.25 cm2
electrode area) and compared with state-of-the-art E-TEK electrodes (ELAT electrodes
with 1.0 mg cm-2
Pt loading). It was reported that although the performance of electrodes
with sputter-deposited platinum was lower than that of catalyzed ELAT electrodes, the
loadings of the former were lower than the latter by about one order of magnitude. E-
TEK electrodes with a loading of only 0.005 mg cm-2
of sputtered platinum delivered 124
mW cm-2
, compared with 203 mW cm-2
for ELAT’s state-of-the-art electrodes with as
much as 0.107 mg cm-2
of platinum. It also was stated that the inclusion of a small
amount of chromium can improve cell performance, as can the addition of two ―ultra-thin
Cr layers into a 25 nm Pt catalyst layer‖ [362] with platinum loading of 0.054 mg cm-2
. A
maximum power density of 200 mW cm-2
was reported, but the amount of chromium that
was added to the catalyst layer was not disclosed.
In a somewhat different approach, Nakakubo et al. [365] proposed a method in which a
thin platinum layer was sputter deposited onto a 50-m-thick PTFE sheet in air at low
70
pressure. This layer then was transferred to a solid polymer electrolyte membrane
(Nafion® 112) by hot pressing. A thin layer of gold also was sputter deposited to function
as a conductive layer. The sputtering process was conducted under a vacuum pressure of
6 Pa, a discharge current of 15 mA, a working distance of 30 mm, and an operating
temperature of 15 C. The sputtering process was performed under a nitrogen or air
atmosphere with a sputter-deposition rate of 0.0077 mg cm-2
min-1
. An additional layer of
ionomer (0.0 to 2.5 wt% Nafion®) was applied to the surface of the catalyst layer to
increase the three-phase interface. The influence of sputter-deposition time on single cell
performance was reported to be the highest for samples with the longest deposition time
of 90 minutes (deposition times of 15, 30, 60 and 90 minutes were reported). Cyclic
voltammograms (CV) in addition to polarization curves were provided to substantiate the
above claim. The high performance of the above MEAs was attributed to the high
catalyst activity and sufficient mass transport of such MEAs due to their ultra thin porous
and continuous catalyst layers.
Cha et al. [366] developed a multiple plasma-sputtering technique in which several
ultrathin layers of the catalyst were applied as opposed to a single layer. In their study,
Nafion® 115 in Na
+ form was used as the substrate and the sputtering system utilized a
radio frequency (rf) or direct current power source to form the plasma flame, with a basic
vacuum pressure of 1.33 mPa or less. The delivered power for the rf power source was
reported to be 50 W, while that for the d.c. source was 30 W. After each sputtering, air
was used to dry the catalyst layer. To further improve catalyst utilization, two additional
steps were implemented. First, a 5 wt% solution of Nafion® was brushed on the sputtered
catalyst layer to enhance the contact points between catalyst particles and the ionomer.
Second, a mixture of Nafion® solution (5 wt%), carbon powder and isopropyl alcohol
was simply brushed onto the catalyst layer. The substrate/catalyst layer structure was air
dried for an hour before being converted to the H+ form. Toray carbon papers with an
average thickness of 0.17 mm were placed on each side of the membrane/catalyst
assembly without hot pressing. The authors reported catalyst utilization efficiencies ten
times higher than those obtained from electrodes fabricated by conventional methods. It
71
is worth mentioning that these assemblies are not true MEAs, the latter usually being
prepared by hot pressing.
As stated earlier and reported by several workers [115, 363], at high current densities, a
large fraction of the current is generated near the front surface of the electrode, where the
catalyst layer is in close contact with the SPE. To ensure high efficiency and greater cell
output at higher current densities, both mass transport and ohmic limitations must be
minimized. Hence, depositing the catalyst particles near the front surface of the electrode,
where intimate contact between catalyst particles and the ionomer is maximized, is highly
desired. One of the earliest studies was conducted and reported by Ticianelli et al. [363]
in which three different methods were employed to fabricate MEAs: use of a higher wt%
Pt/C in the carbon-supported catalyst, use of a thin sputtered catalyst layer on Prototech
electrodes, and a combination of the two. Significant improvements in power output for
all three methods were reported. For the first method, in which electrodes were prepared
with 20 and 40 wt% Pt/C rather than with the standard 10 wt% Pt/C, the increase in
performance was attributed to the reduction in the thickness of the active layer from
about 100 m in the conventional electrodes to around 50 m and 25 m for electrodes
with 20 and 40 wt% Pt/C, respectively. This reduction in thickness provides for a better
supply of reactant gases to the catalyst sites and lowers the ohmic overvoltage since the
path traveled by reactant gases is considerably shortened. The authors claim that a
combination of higher Pt/C loading (20 wt%) and an ultrathin sputtered film of platinum
on the surface of the electrode delivered the best results in terms of cell voltage. This was
explained in terms of a reduction in the catalyst layer thickness and a higher
concentration of electrocatalyst particles near the front surface of the electrode, where
they come in direct contact with the solid polymer electrolyte, ensuring an ionic pathway.
Electrodes with 40 wt% Pt/C plus a sputtered film of platinum with an approximate
thickness of 50 nm were reported to be inferior to similar electrodes with 20 wt% Pt/C in
the catalyst layer. This was attributed to the larger catalyst particles, and hence lower
effective platinum surface area, in the layer with 40 wt% Pt/C.
Huang et al. [367] examined the impact of input power and sputtering-gas pressure on the
performance of PEMFC electrodes. A radio frequency magnetron sputter deposition
72
process was employed to prepare electrodes for MEA fabrication with three input power
levels of 50, 100, and 150 W. It was reported that at a Pt loading of 0.1 mg cm-2
and a
sputtering-gas pressure of 0.001 Torr, the electrodes prepared at 100 W delivered the best
performance when compared with electrodes fabricated at 50 and 150 W. The authors
also report a marked increase in the Pt sputter deposition rate with increasing rf power at
0.001 Torr. Average Pt sputter deposition rates of 22, 39, and 50 nm min-1
(corresponding
to 0.047, 0.084, and 0.107 mg cm-2
min-1
) for the rf powers of 50, 100, and 150 W,
respectively, were reported. These findings have been confirmed by other researchers
[368, 369]. Kawamura et al. [368] reported a similar trend in which the Pt deposition rate
on a glass substrate was observed to increase from 25 to 41 nm min-1
when the rf power
was increased from 25 to 40 W. Chapman et al. [369] attributed this increase in Pt
deposition rate to an increase in the plasma density at elevated RF values, which arises
from an increase in the plasma if Ar+.
Despite producing MEAs with excellent performance in terms of cell output, this method
has not gained any more ground than other methods discussed earlier. The main reason
for this is the need for expensive equipment, as well as the inability of this method to
effectively deposit catalyst particles on the surface of electrodes with unconventional
shapes.
5.2.2.4 Application of Catalyst by Impregnation Reduction
In this method a solid polymer electrolyte membrane in Na+ form is exposed to a
platinum salt solution such as (NH3)4PtCl2. This is generally followed by converting the
PFSA from its original Na+ form to the more useful H
+ form. The last step involves the
reduction of catalyst particles by exposing the membrane to an aqueous solution
containing a reducing agent such as NaBH4 [335]. Foster et al. [370] and Fedkiw and Her
[371] have independently reported significant improvements in the cell output obtained
from MEAs fabricated via this method with metal loadings in the order of 2 – 6 mg Pt
cm-2
.
In a similar fashion, surface ion-exchange can be employed to deposit noble metal
catalysts onto carbon black without using reducing agents or precursor salts. Yasuda et
73
al. [372], investigated the deposition of ultrafine platinum particles on carbon black by a
surface ion exchange method using several different carbon black powders, including
Vulcan XC-72R, Black Perals 2000, Denka Black and two trial samples from Denka:
ONB-250 and FX-35. The effective surface areas per unit weight of the first three
commercially available carbon black powders are tabulated in Table 5-1.
Table 5-1 Effective surface area of several commercial carbon black powders [372]
Carbon Black Powder Vulcan XC-72R Black Pearls Denka Black ONB-250 FX-35
Effective Surface Area (m2 g
-1) 257 1475 61 N/A N/A
5.2.2.5 Application of Catalyst by Evaporative Deposition
This technique involves a two-step process in which a catalyst salt is first deposited onto
a dry solid polymer membrane through evaporation followed by catalyst reduction. Foster
et al. [370] reported the evaporative deposition of a platinum salt—(NH3)4PtCl2—onto
dry Nafion® followed by the reduction of the platinum by exposing the treated Nafion®
to a solution of NaBH4. It has been claimed that platinum loadings of 0.1 mg Pt cm-2
or
less are achievable [335].
5.2.2.5 Application of Catalyst by Catalyst Decaling
This is another example of a multi-step process to deposit a highly dispersed catalyst
layer onto a dry solid polymer electrolyte membrane. Similar to many of the previously-
discussed techniques, the first step involves the preparation of catalyst ink. Carbon-
supported platinum, solubilized Nafion®, and a carefully selected solvent are thoroughly
mixed using both mechanical agitation and ultrasonic mixing. This ink is then applied,
often using a paintbrush or a spray gun, onto a Teflon blank and heated until dry.
Additional layers of the catalyst ink are added until the desired catalyst loading is
achieved. It is crucial, however, to dry each layer before the application of the next to
avoid the dissolution of the top layer into the previous layer. Catalyst loading and, more
importantly, catalyst layer thickness, also can be controlled by the initial concentration of
the Pt catalyst in the carbon-supported platinum. As is the case with many powder type
74
deposition techniques, a uniform catalyst distribution inside the catalyst layer is easily
achieved; however, it is very difficult to keep the catalyst size under 5 nm in diameter
when the initial platinum-to-carbon ratio exceeds 40 wt%. The next step involves hot
pressing the coated Teflon blanks to both sides of a dry solid Nafion® membrane. When
the PTFE layers—Teflon—are peeled away, a thin layer of catalyst is left on each side of
the Nafion® membrane. It is common practice to use Nafion
® membranes in the Na
+ form
and then convert them to the more useful H+
form after the addition of catalyst layers.
Gottesfeld and Wilson [41, 156] presented a decaling method where the protonated form
of the solubilized Nafion® is first converted to the TBA
+ (tetrabutylammonium) form by
mixing it with an alcoholic solution of TBAOH. Glycerol also is added to enhance the
paintability and the stability of the catalyst ink [335].
75
5.0 ELECTRODEPOSITION
6.1 Introduction
Electrochemical deposition of precious metals and their alloys from a number of media,
including aqueous and fused-salt electrolytes, involves the reduction of the desired metal
ions from the solution to the metallic state onto the surface of a substrate. The platinum
group metals (PGM)—Ru, Rh, Pd, Os, Ir, and Pt—are inert by nature and are placed at
the bottom of the emf (electromotive force) series. Physical properties of precious metals
are shown in Appendix A, Table 1. These metals in solution (ionic form) have a great
affinity for electrons and can readily be reduced and remain in the metallic state for as
long as is needed.
The reduction of a metal ion, Mz+
, from an aqueous solution can simply be represented
by:
Mz+
(solution) + ze- M(lattice) (6-1)
The above cathodic (reduction) reaction can proceed via two different processes:
electrodeposition or electroless deposition. Although both processes create nano- or
micro-metallic particles on the substrate, they follow two different paths to acquire the
electrons needed to reduce the metal ions. In the electrochemical method, the required
electrons are supplied via an external source such as a d.c. power supply. In addition, two
separate electrodes are needed for both cathodic and anodic reactions to proceed. In the
chemical or electroless deposition method—also known as the autocatalytic technique—
the need for an external electron source is eliminated since electrons are provided by a
reducing agent in the solution. A number of different characteristics and parameters of
electrochemical and chemical deposition methods are summarized in Table 6-1 [373].
6.2 Electroless Deposition
Interest and activity in electroless deposition has been on the rise since its disclosure by
Brenner and Riddell [374, 375] in 1946. In an electroless deposition, the basic
components include an electrolyte containing the desired cation, a substrate and a
reducing agent to act the electron source (electron donor).
76
Table 6-1 Main characteristics of electrochemical and chemical deposition methods [337]
Property Electrochemical Deposition Chemical Deposition
Driving Force External Power Supply Reducing Agent (RA)
Cathodic Reaction Mz+ + ze- → M Mz+ + RA + ze- → M
Anodic Reaction M → Mz+ + ze- RA → [RA]ox + ze-
Overall Reaction Manode → Mcathode Mz+ + RA → M + [RA]ox
Anodic Site Anode itself Work piece
Cathodic Site Work piece Work piece
The overall cell reaction for an electroless deposition can be expressed as follows:
Metal Ion (solution) + Reducing Agent (solution) M (lattice) + Oxidation Product (solution) (6-2)
It is noted that both electron transfer reactions take place at the same electrode having the
same electrolyte-electrode interface. It is evident that the electrode surface is divided into
two catalytic sites, namely anodic and cathodic sites, to initiate and promote both the
oxidation and reduction processes. A flow of electrons will take place between such sites
on the same substrate since both reactions are occurring on the same electrode [333].
Several electrochemical models have been proposed for electroless deposition processes.
One particular theory—the mixed-potential theory of corrosion processes—has been used
by several workers to describe the various processes taking place during electroless
plating [376, 377]. This theory, originally developed and presented by Wagner and Traud
[378] in 1938, treats the overall cell reaction for an electroless process as two partial
reactions: a reduction and an oxidation reaction as presented in equations (6-3) and (6-4).
Reduction: Mz+
(solution) + ze- M(lattice) (6-3)
Oxidation: Red (solution) Ox(solution) + ze- (6-4)
This theory explains the overall reaction in terms of three current-potential (i-v) curves:
two i-v curves for the partial reactions and another for the overall reaction. A thorough
discussion of this theory and its use in electroless deposition is given elsewhere [333,
379].
77
Electroless deposition is often selected over other plating and deposition processes for its
simplicity in terms of equipment selection and setup and/or for the production of deposits
with unique chemical, mechanical and magnetic properties. In addition, electroless
deposition generates deposits that are uniform, less porous, and can be formed directly on
non-conductive substrates. Since the mid 20th
century, a significant number of metals and
alloys have been employed as candidates for electroless deposition on a wide variety of
substrates. Copper and nickel deposits have been extensively studied using this method
with other metals such as cobalt, gold and silver being deposited and examined during the
past decades. More recently, platinum group metals, especially palladium, have been
deposited using electroless deposition techniques in the area of corrosion protection and
jewelry making. However, for fuel cell applications, there have been no significant
activities in employing this method for depositing catalysts on GDLs or PFSAs. This is
primarily attributed to the lack of control that such a technique provides in terms of the
catalyst layer deposition. One of the main reasons that this method has been gaining
acceptance both in the industry and in academia since its inception about 60 years ago is
its ability to produce ―uniform‖ deposits. This, however, may not be desirable when thin
catalyst layers with high catalytic activities are required.
Regardless of the above issues, PGM—especially platinum and palladium—have been
plated and examined using a number of different solution baths containing different
reducing agents. Hypophosphite, borohydride, alkylamine boranres, and hydrazine have
been extensively used as reducing agents in electroless plating of PGMs. Some of the
properties of the above chemicals are summarized in Table 6-2 [373, 380]. Borohydrides
such as sodium borohydride are mainly used in highly alkaline media, while for slightly
alkaline, neutral, and slightly acidic solutions, boro-amines are widely employed.
Substrates that do not exhibit catalytic activities in some deposition solution baths—such
as silver or copper in hypophosphite-containing baths—become catalytically active in
other plating baths—silver or copper in dimethyl amine borane-containing solution baths
[373].
78
Table 6-2 Chemical properties of several reducing agents [373]
Reducing Agent No. of Available
Electrons
Redox Potential (vs SHE) (V)
at 25 °C
Sodium hypophosphite
(NaPO2H2)
2 -1.40
Hydrazine
(N2H4)
4 -1.16
Dimethylamine borane
(CH3)2NH:BH3
6 -1.20
Diethylamine borane
(CH3CH2)2NH:BH3
6 -1.10
Sodium borohydride
(NaBH4)
8 -1.20
The catalytic activity of several metals, including platinum and palladium in a number of
plating baths with different compositions was investigated by Ohno et al. [381]. Several
reducing agents including formaldehyde, borohydride, hypophosphite, dimethyl amine
borane, and hydrazine were used to prepare the various baths. The authors reported
marked differences in the properties of the deposited layers depending on the reducing
agents used in the plating baths. Boron and phosphorus-based reducing agents created
amorphous deposits with addition of elemental boron and phosphorus to the layer. In
applications where a pure metallic layer such as platinum or palladium is desired, and
impurities cannot be tolerated, the use of hydrazine as the reducing agent is
recommended. In such cases purity levels of 97% or greater are reported with the balance
consisting of nitrogen and/or oxygen and small traces of other elements [382]. Hydrazine
has become a popular reducing agent in electroless plating, not only for its ability to
produce relatively pure deposit layers, but also for its wide range of applications in both
acidic and basic plating environments. Furthermore, hydrazine can reduce multi-valent
metals either to a lower valent state or to the metallic form (zero valent state). This is
simply accomplished by close monitoring and control of the plating environments [383].
Hydrazine, which is a stronger reducing agent in alkaline media than in acidic media,
functions according to the following reactions [373, 383, 384].
79
)66(7.8845 :Acid
)56(7.447444 :Alkaline
1298252
12982242
molkJGeHNHN
molkJGeOHNOHHN
In applications where the acidity or the alkalinity of the plating bath is critical, extra care
must be exercised when hydrazine is used as a reducing agent since some of it can be
oxidized to ammonia, changing the pH of the plating bath as deposition progresses. The
oxidation of hydrazine to ammonia occurs according to [373]:
)76(2222 3242 OHNHeOHHN
Hypophosphite also is used as the electron donor in some applications when utilization
efficiency is not the determining factor. As with most reducing agents, side reactions are
a common concern with hypophosphite complexes. Elemental phosphorus and hydrogen
are the main side products and can have significant impacts on the properties of the
deposited layers. In applications, such as medical applications, where impurities in the
deposited layer cannot be tolerated, other reducing agents must be considered. The
deposited layer also can adversely be affected if the rate of hydrogen evolution is above a
critical limit. The above reactions are shown below [373]:
)106(222
)96(
)86(224222
22
222
3222
OHHeOH
OHOHPPOHH
eHHHPOOHPOH
ads
ads
Borohydride and dimethyl amine borane complexes generate elemental boron as an
undesired by-product according to the following reactions [373]:
)136(653
)126(43)(
)116(84)(8
3322232
4
244
eHBOHNHROHBHNHR
OHBeOHB
eOHOHBOHBH
6.2.1 Electroless Palladium Deposition
Palladium is the most widely used noble metal that has been plated onto a number of
different substrates via electroless deposition. This can be attributed to the many
applications that palladium has found over the last several decades, especially in the
electronics industry, where it has been extensively used as a barrier layer or conductive
80
film on a number of electronics components to enhance their performance. In addition,
inorganic membranes covered with a layer of palladium metal have been utilized to
promote hydrogenation and dehydrogenation reactions [373]. Since the advent of fuel
cells, and especially after the oil crisis of 1973, palladium also has been used as a catalyst
along with platinum and ruthenium.
A number of different solution baths have been used for electroless palladium deposition,
with hydrazine and hypophosphite in alkaline media being the most widely utilized
reducing agents. In fact, hypophosphite was the first reducing agent used to deposit
palladium via an electroless process in 1969 [373, 385]. The main source of palladium
metal is palladium tetrammine chloride (II)—Pd(NH3)4Cl2—with the corresponding
reaction in an electroless deposition bath with hydrazine as the electron donor being
[373]:
2Pd(NH3)4
2 N2H4 4OH 2Pd0 8NH3 N2 4H2O (614)
It has been reported that the rate of electroless palladium deposition increases with
increasing operating temperature, palladium concentration and reducing agent
concentration in the plating bath [373]. It also has been reported that the deposition rates
decrease as deposition progresses in plating baths where hydrazine is used as a reducing
agent [373, 386]. This is primarily attributed to the breakdown of hydrazine to ammonia
by the freshly deposited palladium layer according to equation (6-7). Several solutions
have been proposed to rectify this problem, including the addition of a fresh supply of
hydrazine to the plating bath during the plating process [386, 387]. Palladium complexes
also have been reported to retard the breakdown of hydrazine in a number of plating
baths when coupled with a stabilizer such as ammonium chloride [388].
6.2.2 Electroless Platinum Deposition
Platinum, on account of its unique properties, also has found many applications,
including the medical field as well as catalysis. The first cases of electroless platinum
deposition on catalytic surfaces were reported in 1969 by Oster et al. [389] and Rhoda
and Vines [390]. The former used a combination of platinum sulfate and borohydride,
while the latter employed sodium hexahydroxy platinate in conjunction with hydrazine.
81
Rhoda and Vines [390] reported a deposition rate of 12 m h-1
at room temperature while
continuously supplying hydrazine to the plating bath. Both these processes were known
to be inefficient. Consequently, Leeman et al. [391] proposed a plating bath containing
hexachloroplatinic salts and hydrazine as the source of platinum and reducing agent.
Different hexachloroplatinic salts were suggested for alkaline and acidic plating baths.
Hexachloroplatinic acid (H2PtCl6) and hydrochloric acid in conjunction with a reducing
agent such as hydrazine is often used in acidic media with the following reduction
process:
H2PtCl6 2HClN2H4 8HClPtN2 (615)
In alkaline plating baths, another platinum salt, (NH4)2PtCl6, is used with hydrazine as the
reducing agent, often in the presence of ammonium hydroxide. The reduction of platinum
takes place according to:
(NH4 )PtCl6 4e 2NH4Cl Pt 4Cl (616)
One of the main uses of electroless platinum deposition is in the medical field, where
biologically inert materials are required for coating implantable electrodes. Platinum and
PGM electroless deposition methods are rarely used in manufacturing fuel cell
components, including the catalyst layers in MEAs. This is mainly because of the lack of
control provided by this method during the deposition process.
6.3 Pulse and Direct Current Electrodeposition
6.3.1 Introduction
Today’s state-of-the-art catalyst deposition techniques can be divided broadly into two
groups: powder and non-powder. In powder type techniques, the catalyst is often
deposited first on high-surface-area carbon (known as carbon-supported platinum, if
platinum is used as the catalyst). A slurry or ink then is prepared by ultrasonically mixing
the above carbon-supported catalyst with a hydrophobic polymer and often a lower
aliphatic alcohol and pre-determined amounts of solubilized Nafion® (or other liquid
SPEs). The last step involves the addition of this ―ink‖ onto the solid polymer electrolyte
membrane or onto the GDL by one of the methods discussed earlier in section 5. MEAs
then are fabricated by the addition of GDLs, if the ink was applied onto a SPE, or by the
82
addition of SPE, if the ink was applied to a GDL. MEAs fabricated according to such
techniques exhibit a uniform catalyst concentration profile, owing to the high degree of
catalyst dispersion and mixing with the binder. In addition, the thickness of the catalyst
layer can effectively be reduced by increasing the catalyst content in the Pt/C powder
without impacting the catalyst loading per unit area of electrode [38]. However, at high
catalyst-to-carbon ratios; i.e., greater than 40%, the catalyst particle size will inevitably
increase, resulting in a decrease in its effective surface area which, in turn, lowers the
oxygen reduction activity of the catalyst.
A number of non-powder type techniques have been developed and experimented with
over the past two decades [370, 371]. Such methods have attracted attention due to their
reproducibility, relative ease of use, and the ability to create very small catalyst particles
(less than 5 nm in diameter) and generate a high Pt/C ratio at the membrane-electrode
interface [371]. As previously mentioned, one of the most promising catalyst deposition
methods is electrodeposition, in which a direct current is passed through a solution
containing the desired electrocatalyst metal ions that is in contact with the substrate.
Metal ions first reach the deposition sites via surface diffusion on the substrate, where
they subsequently are reduced to metals by gaining electrons from an external power
supply or from an electron-donor compound in the solution.
6.3.2 Direct Current Electrodeposition
Direct current (DC) electrodeposition has been widely used in the plating industry, where
a number of metals are plated onto different substrates for various reasons, including
corrosion and wear protection, hardness improvement, and aesthetic enhancement. DC
electrodeposition can be carried out utilizing both batch and continuous flow processes;
however, the former are more prevalent. According to this method, the substrate is
immersed into a plating solution, where it comes into direct contact with the dissolved
metal ions (or alloys) of interest that will be deposited on its surface. A counter electrode
also is placed in the plating cell in close proximity to the substrate (the working
electrode) to complete the cell. A reference electrode often is placed near the working
electrode to take measurements during the electroplating process for future optimization.
83
An interface between the working electrode and the plating solution will be established as
soon as they come into contact. The thickness of this interface varies from several m to
several mm depending on the nature of the solvent, solute, the substrate, and the degree
of mechanical agitation. The interface on the solution side contains the metal ions of
interest, which will begin to migrate towards the electrode when the working electrode is
made more negative. The ions are first adsorbed on the surface of the electrode and then
reduced to metal adatoms in a single or multi-step process, depending on the cation type.
This involves one or several charge transfer steps in which the cation receives one or
more electrons to be reduced and finally incorporated into the substrate matrix. In theory,
this process will continue as long as sufficient metal ions are present in the interface close
to the substrate and electrons are supplied to the working electrode by an external power
supply. In reality, as the deposition process progresses, the metal ions in the interface
close to the working electrode become exhausted and the ion concentration near the
surface of the cathode approaches zero. As the ion concentration in this region
diminishes, new catalyst nuclei cease to be formed on the surface of the cathode; instead
the existing crystals begin to grow and dendrites are formed. The ―limiting current
density‖ is reached when the ion concentration near the surface of the cathode reaches
zero and dendritic crystals start to form via growth of the existing crystals.
The properties of the metal deposits can seldom be controlled by the current density,
which is the usual variable in DC electrodeposition. In a plating system, because the
concentration of ions near the surface of the substrate will gradually decrease as the
plating progresses, the ions must be replenished from the bulk solution for the process to
continue. Short of adding more salts to the bath, this can be accomplished by convection,
ionic migration and diffusion. Since ions carry charge, one-dimensional ion transport in
an electrolyte can be expressed as a current density, from:
)176( Fzni jj
where, jn is the molar flux of the ion through the electrolyte in mol s-1
cm-2
; zj is the
charge number on the ion in eq mol-1
; and F is Faraday’s constant in C eq-1
. Mass
diffusion occurs as a result of an ion concentration gradient in the electrolyte, and is
described mathematically by Fick’s law as:
84
x
cDn
j
jj
(6-18)
where, Dj is the diffusion coefficient or diffusivity of species j in cm2 s
-1, cj is the
concentration of the same species in mol cm-3
, and x is the position in cm.
Convection, on the other hand, is affected by net motion of the electrolyte:
xjj vcn (6-19)
where vx is the velocity of species j in cm s-1
and other symbols have their usual
meanings.
Lastly, ionic migration is driven by an electrical potential difference between two points.
In an electrolyte containing a conducting ion the molar flow rate of the ion can be
calculated according to the following expression,
x
cDTR
Fzn jj
j
j
(6-20)
where, is the electrical potential difference in V and other symbols have their usual
meanings. The total ion transport flux can be approximated by combining equations (6-
18) to (6-20) if the usual assumption is made that the three fluxes are mutually
independent:
x
cDTR
Fzvc
x
cDn jj
j
xj
j
jj
(6-21)
Equations (6-19) to (6-21) represent one-dimensional ion transport in an electrolyte. For
three dimensional transport the corresponding expressions based on the Nernst-Plank
equation are:
x
cDTR
Fzvc
x
cDn jxj
j
xj
j
xjxj
,,,
(6-22)
y
cDTR
Fzvc
y
cDn jyj
j
yj
j
yjyj
,,,
(6-23)
z
cDTR
Fzvc
z
cDn jzj
j
zj
j
zjzj
,,,
(6-24)
85
The net current density for one-dimensional ion transport, i, now can be represented by
substituting equation (6-21) into equation (6-17) to give:
]][[ Fzx
cDTR
Fzvc
x
cDi jjj
j
xj
j
j
(6-25)
The mobility of an ion, uj, is given by:
TR
DFzu
jj
j
2
(6-26)
where, uj is the mobility of the ion in m s-1
(V m-1
)-1
and other symbols have their usual
meanings. The mobility is a measure of how fast an ion moves under the influence of a
unit potential difference, and is a function of the ionic charge, operating temperature and
pressure, ionic concentration, and ionic size.
The relationship between ionic conductivity, mobility, and concentration can be
expressed as
jjjj cuzF (6-27)
It can be seen that as the charge of the ion, zj, is increased, the total current carried per ion
is increased proportionally, increasing, in turn, the effective conductivity, (in S m2
mol-1
). In addition, an increase in the mobility of the charge carriers also will increase the
ionic conductivity. The same holds true for the ionic concentration. Equation (6-27) also
can be written as
jjjj cDzTR
F 22
(6-28)
However, such processes cannot normally keep up with the electrodeposition rate and the
metal ion concentration drops as electrodeposition continues. This is even more
detrimental when the current density increases. As the deposition current density
increases, the metal ions close to the cathode will be consumed at a faster rate, which is
directly proportional to the magnitude of the applied current density (set and controlled
by the external power supply). As the metal ion concentration drops and the existing
crystals begin to grow, the catalytic activity of the deposited catalyst layer is adversely
affected. This problem can readily be rectified by the addition of relaxation times during
86
the electrodeposition; that is, by the inclusion of ―no current‖ times, when the external
power supply is turned off. This results in an ion replenishment in which metal ions are
transported from the bulk to the interface by diffusion and natural or forced convection.
This is the basis for pulsed current (PC) electrodeposition.
6.3.3 Pulsed Current Electrodeposition
6.3.3.1 Introduction
In DC and PC electrodeposition processes, metal ions are transported from the bulk to the
interface near the working electrode (the cathode of the electrochemical-plating cell).
One or all three transport modes discussed in the previous section contribute to this
transport. This is, however, accomplished more effectively in PC electrodeposition owing
to the use of relaxation times, which allow fresh ions to enter the interphase at the
electrode surface. In PC electrodeposition, either the current density or the applied
potential is alternated rapidly between two different values. This is done with a series of
pulses of equal amplitude, duration and polarity, separated by periods of zero current [6].
Each pulse consists of two periods: an ―on-time‖ in which the current is applied and an
―off-time‖ during which no current is applied. It is during the latter period that metal
ions from the bulk solution diffuse into the layer next to the working electrode; i.e.,
carbon paper or carbon cloth in our experiments. When the current is applied during the
on-time, more evenly distributed ions are available for electrodeposition.
It is well known that, compared with conventional DC electrodeposition, PC
electrodeposition exhibits many advantages in terms of deposited particle size, stronger
adhesion, and better hardness [9]. In addition, PC electrodeposition can positively affect
several key properties of the deposited metals, including their size, morphology, degree
of porosity, and even crystal orientation, by enhancing mass transfer. Thus it is possible
to effectively control a number of physical, chemical, and electrochemical properties of
the deposited layer by changing and controlling the PC electroplating parameters,
including pulse amplitude, width, and frequency. PC electrodeposition generally favours
finer and smaller grain sizes and increases the number of nuclei per unit area of substrate.
87
An external DC power supply provides the cathode with the flow of electrons needed for
the reduction of the metal ion. As a result, an electrical double layer is formed at the
electrode-electrolyte interface on the solution side (see Appendix B). The thickness of
this layer is dependant on several parameters, including the type of electrolyte, the degree
of agitation present, and plating parameters such as the applied current density, duty
cycle, etc. In DC electrodeposition, at the onset of deposition this layer begins to appear
and grows as plating continues until it reaches a defined thickness. After this critical
thickness has been reached, it remains relatively constant as long as no significant
changes are introduced to the plating cell. Due to the existence of opposite charges on
both sides of such a layer, it is inevitably charged and remains in this state as long as two
conditions are met: a steady flow of electrons continues to reach the cathode and there is
a sufficient amount of metal ions in the electrolyte. The former condition is easily met as
long as the power supply is operational and the resistance to the flow of electronic current
from the external source to the cathode is minimal. However, as the plating continues,
ions in the bulk solution will experience a resistance as they try to diffuse into this layer
and be reduced on the surface of the cathode. The concentration of metal ions in this
layer, known as the diffuse double layer, will decrease until it reaches a critical value at
which there will not be enough metal ions in the vicinity of the cathode to initiate the
formation of new nuclei. As a result, existing crystals will begin to grow and dendrites
will start to form. At this point, the system is in a mass-transport-limited mode and,
unless fresh metal ions are allowed to enter the diffuse layer, the formation of new nuclei
ceases and the deposited layer will lose some of its ductility and electrical conductivity,
amongst other important and desired characteristics.
As previously mentioned, PC electrodeposition can readily rectify the above problem by
significantly raising the limiting current density by replenishing the metal ions in the
diffuse layer during the time when the current (or potential) is interrupted; i.e., during
off-time [391]. It is important to recall that DC electrodeposition has only one parameter,
namely applied current density (or applied voltage). These can be varied, but there are
limitations, the most important of which is the limiting current density. The applied
current density in DC electrodeposition must be closely regulated and always be kept at
values lower than the limiting current density to avoid dendrite formation and, in more
88
severe cases, the loss of the deposition layer. But, in PC electrodeposition, there are three
parameters that can be independently varied: on-time (ton), off-time (toff), and peak
current density (iP). The first two variables—on-time and off-time—can be related
through another variable known as the duty cycle, γ, which is the percentage of the cycle
time during which the current (or potential) is on. This was previously defined in section
1.3 as
%100
offon
on
tt
t (1-1)
The frequency of a waveform is defined as the reciprocal of the cycle time (t):
ttt
foffon
11
(6-29)
Thus the duty cycle also can be defined in terms of cycle frequency:
)()( fton (6-30)
The average current density, iA, is defined as
)()( PA ii (6-31)
In practice, PC electrodeposition often involves a duty cycle of 5%-50% and on-times
and off-times from s to ms, depending on the application and desired characteristics of
the deposited layer [391].
6.3.3.2 Factors Influencing PC Electrodeposition
Electrical double layer – the nature and the thickness of this layer is critical in the
outcome of the deposited layer in terms of its morphology, hardness, and grain size. This
layer has been described in Appendix B. A constant current must be supplied to the above
layer to increase its potential to a level that is sufficient for metal deposition. When a
constant current is applied to a plating system, it is used to perform two varying tasks:
first, it must charge the double layer and, second, it needs to sustain the desired electrode
reaction that reduces metal from solution and leads to the incorporation of adatoms into
the substrate. Accordingly, the total galvanostatic current density supplied to the
electrode, itot, consists of two parts, a capacitive current, iC, that charges the double layer
89
and a Faradic current, iF, that corresponds to the rate of metal deposition. This can be
written as:
FCtot iii (6-32)
The first step after a galvanostatic current is supplied to the plating cell involves charging
the double-layer capacitance, Cdl, from the reversible potential, E, to a higher potential,
Ei, where the electrode reaction (reduction of the metal) begins to take place at a
measurable rate [333, 391]. Paunovic & Schlesinger have presented a simplified
equivalent circuit for a single-electrode reaction as shown in Figure 6-1, where RCT is the
charge-transfer resistance of the electrode reaction [333].
Figure 6-1 A simplified equivalent circuit for single-electrode reaction [333]
The time, t, needed to charge capacitor C in a resistance-capacitance circuit to 99% of the
imposed voltage is given by [333]:
RCCt VV 6.4)(99.0 (6-33)
where R is the resistance in Ω and C is the capacitance in µF. The time required to charge
the electrical double layer is referred to as the charge time, tC, defined as the time
required for the Faradic current, iF, to reach 99% of the peak current density, iP. The
discharge time, tD, is the time needed to decrease the Faradic current, iF, to 1% of the
peak current density, iP. Two simple formulae for selection of charge and discharge times
have been given by Chandrasekar and Pushpavanam [391] and Puippe and Leaman [392]:
P
Ci
t17
(6-34)
Cdl
itot
iC
iF
RCT
90
P
Di
t120
(6-35)
where tD (and tC) is in µs and ip is in A cm-2
.
Mass Transport – for the simple reduction of a metal ion, Mz+
, in an aqueous solution,
Mz+
(solution) + ze- M(lattice) (6-1)
the electrode reaction rate (or the current) is governed by the rates of several processes
[393]:
1. Mass transfer of reactant to the electrode from the bulk solution.
2. Electron transfer at the electrode surface.
3. Chemical reactions before and after the electron transfer step. These can be either
homogenous or heterogeneous processes taking place on the surface of the
electrode.
4. Physical processes, mostly in the form of surface reactions such as adsorption,
desorption, and crystallization.
The simplest reactions involve only mass transfer of the reactants from the bulk solution
to the surface of the electrode. However, this plays a critical role in limiting or enhancing
the deposition rate and, consequently, influences some of the key properties of the
deposited layer, including its grain size, hardness, and morphology. One of the most
important parameters for mass transport in both DC and PC electrodeposition is the
limiting current density, iL.
The concept of limiting current density can be better understood by considering the
Nernst Diffusion-Layer Model. According to this model, the concentration of the metal
ion in the bulk solution up to a distance from the surface of the cathode is cb and falls
linearly to cx as it approaches the working-electrode surface. The model assumes that the
contribution of the double-layer effect is negligible and that this diffuse layer—known as
the Nernst diffusion layer—is for all purposes stagnant. This stipulates that the existence
of any stirring has practically no impact on the diffuse layer, but will be effective beyond
this layer, at distances x > , as shown in Figure 6-2.
91
Figure 6-2 Actual and Nernst diffusion layers during non-steady-state electrolysis [333]
Based on this model the concentration gradient of the metal ion at the cathode is given
by:
0
0
xb
x
cc
x
c (6-36)
Furthermore, the rate of reaction based on the current density can be calculated as
follows:
0xb
j
ccDFni (6-37)
where Dj is the diffusion coefficient of the plating species j. For constant current
polarization, the diffusion-layer thickness increases with the square root of time
according to [333]:
tD j2 (6-38)
x = 0
Nernst Diffusion Layer - Model
Actual Concentration
Distance from Electrode, x
Concentration, C(x)
cb
Nernst Diffusion Layer Thickness
92
From Eq. (6-37) it is apparent that the maximum current density is obtained when the
term cx=0 is zero, giving rise to the maximum concentration gradient. At this current
density, known as the limiting current density, iL, the metal ions are reduced as soon as
they reach the electrode surface. This implies that the concentration of metal ion at the
electrode surface is practically zero and that the rate-limiting step is the transfer of metal
ions to the surface of the electrode.
In PC electrodeposition, the magnitude of the limiting current density is strongly
dependent on the pulse parameters, particularly, on the pulse on-time, ton. A primary
objective in all plating systems is to increase the magnitude of iL so higher peak current
densities (iP) and, consequently, greater average current densities (iA) can be applied. As
ton increases, the corresponding iL will decrease. Consequently, ton must be as short as
possible—low duty cycle—to stay below the corresponding limiting current density, but
sufficiently long to fully charge the electrical double layer [391]. In DC electroplating,
the properties of the deposited layers will be adversely affected if the applied current
density is close to the limiting current density. In practice, the allowed applied current
density is often 10%-20% of the corresponding limiting current density [391].
Conversely, in PC electrodeposition, smooth, crack-free, and uniform deposit layers are
obtained even when the applied current density approaches the limiting current density,
provided that the diffusion layer is relatively thin.
6.3.3.3 Major Types of Pulse Waveforms
A wide variety of waveforms has been used in a number of industries utilizing PC
electrodeposition, including printed circuit board (PCB) and integrated circuit (IC)
manufacturing. This has been accelerated over the past two decades owing to significant
improvements in modern electronics and microprocessor capabilities. Simple computer
programs and codes can easily be written to generate complex waveforms that previously
were either very tedious or almost impossible to achieve. Applied current waveforms are
broadly divided into two groups: (1) unipolar, where all the pulses have similar polarities
(unidirectional pulses) and (2) bipolar, where both anodic and cathodic pulses are
applied.
93
A large number of different waveforms has been created and experimented with for a
wide array of applications. Some of the most important waveforms, as well DC
electrodeposition, are briefly discussed below with reference to noble metal catalyst
deposition.
Direct Current Electrodeposition—conventional DC electrodeposition has been
extensively used and reported in the literature [9, 12, 394-399]. Lin-Cai and Pletcher
[394], who examined the activity per surface metal atom for hydrogen evolution on
electrodeposited platinum, observed that clusters less than 20 nm in diameter were
inactive and that a minimum of twenty platinum monolayers was required to achieve
normal activity. Itaya et al. [395] reported good catalytic activity of a platinum catalyst
layer electrodeposited through a PFSA membrane onto a glassy carbon electrode. A study
reported by Jannakoudakis et al. [396] outlined the electrodeposition of platinum from a
number of different plating baths, including Pt(NH3)64+
complex onto polyacrylonitrile
fiber supports. Srinivasan et al. [397] carried out a series of experiments to deposit
platinum onto Prototech GDLs using a chloroplatinic acid electrolyte. They reported that
the performance of MEAs fabricated by electrodeposition were comparable to MEAs
made using other methods. Shimazu et al. [398] and Kanevskii et al. [399] studied the
electrodeposition of platinum from chloride anion complexes onto more easily
characterized surfaces such as glassy carbon.
Cathodic Pulse followed by a Period of Zero Current (or Potential)—according to this
technique the current (or potential) is alternated between a maximum and a minimum
value with relaxation periods in between. A main feature of such waveforms is their
identical amplitude during the whole plating process. They may include anodic currents,
in which the current is intentionally reversed to create deposits with unique properties;
this is known as pulse reverse current (PRC), and has been widely used in the electronics
industry for the deposition of copper onto a number of substrates. There are many types
of waveforms that can be generated using a function generator and/or a galvanostat.
These include square pulse, ramp-up, ramp-down, and triangular, to name but a few.
94
Duplex Pulses—this type of waveform contains a series of pulses at one level followed
by another series of pulses at another level, all in one direction. The sudden variation in
the current or potential level of the pulses results in changes in the dynamics of the
plating bath, particularly in the vicinity of the working electrode, where metal ions must
be present at all times and, preferably, uniformly along the deposition surface.
Pulse-on-Pulse Waveform—these waveforms consist of pulses at specific amplitudes
followed by another set at higher or lower amplitudes. Similar to duplex pulses, pulse-on-
pulse waveforms offer complex waveforms that can effectively change the dynamics of
the plating bath to create deposits with specific properties. Such waveforms, however, are
not easy to generate and require more expensive equipment.
Superimposing Periodic Reverse on High Frequency Pulse—this type is characterized by
a series of pulses with controllable pulse parameters, including amplitude, frequency and
duration. The waveform is often sinusoidal with fast turn-ton and a slow turn-toff [391].
One of the main advantages of complicated waveforms over both DC and simple
waveforms is the increased number of variables at the researcher’s disposal, which
provide workers with tools to create deposits with unique properties. However, as the
number of variables increases, it becomes more difficult to fully understand the influence
of each variable on deposit properties [391].
6.3.4 Nucleation and Growth during Electrocatalyzation1
A good understanding of the processes involved in electrodeposition, from the
transportation of ions from the bulk solution to the reduction and incorporation of
adatoms into the crystal matrix, is invaluable in creating deposits with unique properties.
This is particularly important in the early stages of phase transition comprising nucleation
and crystal growth [400]. In the case of noble metals, a good understanding of the early
stages of electrocrystallization is critical in creating highly dispersed metal phases with
good catalytic activity. It is generally agreed that the primary processes leading to
1 Many of the formulas presented in this section are derived in Ref. 333.
95
nucleation and growth during the initial stages of electrocrystallization on a substrate are
now well understood [401-403].
The first atomic model of electrochemical crystal growth was developed by Erdey-Gruz
and Volmer [404, 405] in the early 1930s, and treated the substrate as a perfect crystal
surface. One of the main implications of perfect crystals with no imperfections is that
there is no site for crystal growth and the first step of the process must be nucleation. By
the mid 1950s, it was realized that real substrates contain imperfections, and
consequently, have many growth sites. This realization created a different way of
thinking with respect to crystallization and introduced several new models. These new
models were strengthened and validated by the results of in situ surface analytical
methods, including scanning tunnel microscopy (STM) and atomic force microscopy
(AFM).
Electrocrystallization involves the incorporation of adatoms (or adions) into the substrate
crystal lattice by two different, but interdependent processes: (1) nucleation, and (2)
crystal growth. The first process—nucleation—becomes dominant with high adatom
population, high overvoltage, and low surface diffusion. By reversing the above factors,
the second process—crystal growth—becomes the dominant process. In PC
electrodeposition, a high population of adatoms and high overvoltage can readily be
achieved through high peak current density [391].
From a molecular point of view, a nucleus—a cluster of atoms—is only stable when it
reaches and then exceeds a critical size. Two processes play important roles in the
formation and growth of these clusters: (1) the arrival and adsorption of ions at the
surface of the substrate and (2) the movement of adsorbed ions across the surface. The
instability of these adsorbed ions stems from the fact that their binding energy to the
crystal is relatively low; as a result, they will stay on the surface as an adion only for a
very short time. However, their stability is significantly increased through formation of
clusters with other incoming and adsorbed adions. The free energy of formation of a
cluster containing N ions is given by:
)()( NezNNG (6-39)
96
where the first term refers to the energy that is required to bring N ions from the solution
to the surface of the substrate and the second term signifies the increase in the surface
energy as the cluster grows. It is apparent that both terms are functions of N, the first term
increases linearly with N, while the second term increases as N2/3
. The Gibbs free energy
of formation of a 2-dimensional cluster as a function of size is shown in Figure 6-3,
which shows that the free energy of formation of a cluster initially increases with N until
it reaches a critical value and then begins to drop sharply as N further increases [333].
Figure 6-3 Free energy of formation of a cluster as a function of size N [333]
The critical cluster size, NC, can be calculated from the following expression:
2
2
ez
sbNC (6-40)
where b is defined as
P 2
4S (P and S are the perimeter and the surface area of the nucleus,
respectively) and s is the area occupied by one atom on the surface of the nucleus,
is
the edge energy, e is the charge of a single electron, and
is the corresponding
overvoltage. Another important parameter, the critical radius of the surface nucleus, rc,
can be evaluated from:
ze
src (6-41)
It is seen that both NC and rc are strong functions of overvoltage.
G
N
NC
GC
97
6.3.4.1 Nucleation Rate
The rate of nucleation for conversion of a site on a real substrate into nuclei is given by:
ANNdt
dN)( (6-42)
where A is the nucleation rate constant and N₀ is the maximum possible number of
nucleus sites on the substrate surface per unit area. N₀ often depends on the applied
potential, but is always smaller than the atomic density. A wide range of values from 104
cm-2
to 1010
cm-2
has been reported for N₀ [401, 406]. Equation (6-42) can be rearranged
and integrated to obtain equation (6-43), which is easier to work with:
AteNN
1 (6-43)
There are two limiting cases for equation (6-43) at the start of the nucleation process; i.e.,
when time (t) is small:
Limiting case1: large nucleation constant, A:
NN (6-44)
This indicates that almost all the sites on the substrate surface are converted to nuclei
immediately after a potential change in the plating system is detected. This is known as
instantaneous nucleation and refers to the case in which the maximum number of nuclei
is formed. However, it is well known and widely reported in the literature that there is
actually a delay time between the first potential perturbation and the time the first nucleus
is formed. This has been mainly attributed to the build-up of the critical nuclei that must
be present at the beginning of the process before nucleation can be initiated [401, 407].
For all practical purposes, such a time delay can be ignored without severe implications
on experimental outcomes [401, 408-412].
Limiting case 2: small nucleation constant, A:
When 1At equation (6-43) reduces to:
tANN (6-45)
98
In this case the number of nuclei increase as plating progresses; i.e., N is a function of
time. This is referred to as ―progressive nucleation‖.
The nucleation rate, J, for 2-dimensional nucleation is given by:
Tkez
bskJ
2
1 exp (6-46)
where k1 is the rate constant, S
Pb4
2
is a geometric factor relating the perimeter of the
nucleus to its surface area (equal to for a spherical nucleus), is the edge energy in J
cm-1
, z is the charge of the ion, e is the electronic charge, k is Boltzmann’s constant, T is
the system temperature, and is the overvoltage.
From the above equation it can be seen that as the overvoltage increases, the nucleation
rate also will increase. The system temperature, T, will have the same effect, but its
impact will not be as significant as the change in overvoltage (for instance, it will be
easier to increase the overvoltage by a factor of 2 or 3 than to increase the system
temperature by the same magnitude; recall that the temperature is in kelvin).
6.3.5 Electrodeposition of Metals and Alloys
6.3.5.1 Introduction
The recent upsurge of interest in the electrodeposition of individual metals and their
alloys on various substrates has its roots in:
The electronics and microprocessor industries for the manufacture of PCBs and
ICs,
Metal deposition for magnetic devices such as disks and,
Deposition of single and multilayer structures for a number of chemical and
electrochemical processes, including the deposition of catalyst layers—mostly
noble metals—on GDLs for use in PEM fuel cells and electrolyzers.
6.3.5.2 Copper and its Alloys
The electrochemical deposition of copper has been studied extensively for two reasons:
(1) its technological use in the manufacture of ICs for the production of interconnection
99
lines, and (2) its scientific use as a base system to study the nucleation and growth of
metals under different conditions. Copper, by far, has been the most studied deposited
metal under different experimental conditions. Initial and advanced stages of copper
deposition in a large number of plating baths with different compositions have been
extensively examined and reported in the literature [413-424]. One of the unique
characteristics of any copper system is its relatively low exchange current density [413].
This results in charge transfer across the electrical double layer being the dominant force
in copper deposition, particularly when the deposition times are relatively short [413-415,
417]. It is customary to neglect the contribution of the charge transfer resistance when
dealing with dilute copper solutions. It is, however, beneficial to consider the
contributions of both charge transfer and diffusion limitations during the nucleation and
growth of copper crystals in all plating solutions. One of the few studies considering both
contributions has been reported by Melchev and Sapryanova [413], who examined the
nucleation and growth of copper crystals on an easily characterizeable substrate (glassy
carbon) under potentiostatic conditions. Current transients under different overvoltages
were employed to generate data to support the theory of progressive nucleation and
growth under combined charge transfer and diffusion limitations. It was concluded that
the progressive nucleation of copper on a glassy carbon electrode is dependent upon both
charge transfer and the diffusion mechanism of the copper ions.
One of the first investigations on the PC electrodeposition of copper was reported in 1979
by Cheh et al. [425]. This study was particularly concerned with the current efficiency
(CE) of copper electrodeposition under pulsed current conditions. It was reported that the
current efficiency of copper plating from an acidic plating bath was lower than a similar
system under DC conditions, and continued to drop below 100% as the off-time was
increased or the pulse duration was shortened. A mathematical model was formulated to
simulate a Cu/CuSO4 system under pulsed current conditions using a rotating disk
electrode (RDE) to explain the above observations. The effects of electrical double-layer
charging were ignored. Another study on the mechanism of copper electrodeposition by
PC electrodeposition and its impact on the current efficiency of the plating process was
made by Tsai et al. [426], who examined the effects of pulse period and duty cycle on the
CE of copper plating from an acidic bath under a wide range of pulse periods from 200 to
100
0.02 ms. A mathematical model based on an equivalent circuit was developed to simulate
the potential responses. It was reported that the current efficiency decreased with
shortening pulse period in the millisecond range, while it increased in the microsecond
range. These marked differences were explained in terms of dominant rate-determining
steps in both ranges.
More recently, Zhang et al. [427] reported the generation of 10 m copper films prepared
by pulse electrodeposition with different peak current densities and pulse on-times. These
authors reported that higher pulses lead to a stronger self-annealing effect on grain
recrystallization and growth. Similar findings also have been reported by Shen et al.
[428] and Ma et al. [429]. Furthermore, films electroplated at higher current densities
have been reported to take less time to complete the self-annealing process compared
with those electroplated at lower current densities [430-434].
Numerous studies have been carried out and reported on copper nucleation mechanisms
via electrodeposition on a number of substrates, including vitreous carbon [435-438],
sputtered TiN [439], and copper [440]. Grujicic and Pesic [435] studied the reaction and
nucleation mechanism of copper electrodeposition from plating solutions containing
ammonia. The effects of applied potential, copper concentration in the plating bath, and
substrate surface morphology were investigated. It was concluded that the copper
concentration is not an effective parameter to consider, and closer attention must be paid
to the pH of the plating bath during electrodeposition.
Alloy deposition techniques are as old as the electrodeposition methods employed for
individual metals; for instance, the deposition of brass was first carried out in 1840. The
electrodeposition of alloys is subject to the same principles as single metals, but when
deposited, may not exhibit the same properties as the individual metals present in the
alloy. In most cases, the deposits show superior and unique properties that are highly
desirable. Nickel-copper alloys have been extensively studied and used in the industry in
microsystems due to their superior corrosion resistance and magnetic and thermophysical
properties [441]. Other properties of great interest are wear resistance and magnetic and
optical characteristics.
101
Electrodeposition of nickel-copper alloys has been carried out employing galvanostatic
[442], potentiostatic [443], pulsed current [444] and pulse-reverse current [445, 446]
techniques from a number of different plating baths, including sulfamate [447], cyanide
[448], citrate [449], sulfate-oxalate [450], and pyrophosphate [451]. The Ni-Cu alloy
plating process is a codeposition process in which the more noble metal, copper, is
preferentially deposited first followed by nickel. As with many alloys, the standard
reduction potentials of copper and nickel, +0.337 V and -0.25 V, respectively, vs. SHE at
25 °C, are quite far apart in the standard emf series. The difference can be narrowed or
eliminated by including a significant change in ionic concentration through complex ion
formation, such as by the addition of a complexing agent like citrate. Roos et al. [452]
studied the electrodeposition of Ni-Cu alloys from plating baths with varying
compositions and citrate as a complexing agent on RDEs and Hull cell electrodes. The
former substrate was replaced with rotating cylinders, since the current distribution on
RDEs was observed to be non-uniform. Quang et al. [453] also utilized a number of
different citrate baths and reported crack-free deposits with thicknesses in excess of 100
microns. Later, in 1997, Bonhote et al. [444] showed that the microstructure of a Ni-Cu
deposited multilayer could effectively be controlled by controlling the applied current
density. It also was reported that when the applied current density used for copper
deposition was lower than its limiting current density, the multilayer structure was
oriented along the (110) direction.
In addition to citrate, other complexing agents such as sulfamate also have been utilized
in Ni-Cu electrodeposition. Tench et al. [454] examined the influence of Ni-Cu plating
baths on the quality of multilayers containing sulfamates. Plating baths with low
concentrations of copper were recommended. Furthermore, Ni-Cu multilayers
electrodeposited by PC electrodeposition techniques were found to be superior in terms
of tensile strength, compared with multilayers obtained by DC plating with identical
plating bath compositions. Bradley et al. [447] and Menezes et al. [455] studied the pulse
plating of Ni-Cu alloys from plating baths containing sulfamates. They both suggested
the use of citrate baths for thick Ni-Cu multilayers. Lin et al. [456] investigated the
influence of ammonium ions in sulfamate electrolytes on deposited nickel layer. It was
102
reported that ammonium ions increased the internal stress by greatly refining the grain
structure and increasing the defect density. However, an increase in hardness also was
observed. The influence of ammonium on Ni-Cu systems was reported by Chassaing et
al. [457, 458]. The influence of other compounds on the dynamics of copper, nickel, and
copper-nickel systems has been periodically reported in the literature; these include
tartrate and ammonium chloride [459], chloride and nitrate ions [460] and ammonia-
based media [461].
The influence of other important plating parameters such as plating bath pH also has been
widely studied. However, the majority of the plating baths have their pH in the acidic
region, where sulfuric acid is often used to maintain a constant pH during electroplating.
Green et al. [462] experimented with citrate electrolytes with two different pH values: 4.1
and 6.0. They found that the plating bath with pH 6.0 was more stable than that with pH
4.1. Arvinda et al. [463] investigated the deposition of copper from two different alkaline
solutions—hydroxide and triethanolamine—with citrate as the complexing agent.
Mathematical models have been developed by many researchers to describe and predict
the codeposition of nickel and copper from various plating baths. One of the first
mathematical models was formulated by Guglelmi [464] in the early 1970s. This model is
based on a two-step adsorption, one weak (physical in nature) and the other rather strong
(electrochemical in nature). According to this model, particle concentration in the deposit
increases with increasing electrolyte concentration and decreases with increasing current
density. Mass transport and convective flows are ignored since the model predictions are
based on the assumption that adequate mixing is provided throughout the deposition
process. Roos et al. [465] verified the validity of the above model by examining the
codeposition of alumina and copper from a sulfate electrolyte. Later in the year, Celis et
al. [466] carried out similar experiments on the codeposition of alumina and copper from
a copper sulfate electrolyte. Their results were in good agreement with Guglelmi’s model.
Several years later, in 1987, Celis et al. [467] developed a new model based on
Guglelmi’s original model, but proposed a five-step adsorption model as opposed to
Guglelmi’s original two-step model. The validity of this new model was tested and
verified by a series of experiments on the codeposition of alumina with copper from a
103
copper sulfate plating bath. Another model by Valdes et al. [468] attempted to explain the
codeposition process by considering the electrochemical and hydrodynamic forces acting
on particles in the plating bath. This model was based on very fast kinetics leading to the
capture of all particles approaching within a certain critical distance of the substrate. A
new concept—―perfect sink‖—was introduced that would predict an increase in the
deposition rate with increasing current density.
The development of a significant number of mathematical models since the early 1980s
has paved the way to a better understanding of the electrodeposition process with its
many variables. Fransaer et al. [469] proposed a trajectory model for large particles (> 1
micron) and later developed another model to describe the influence of various particles
in the plating bath on the applied current [470]. Wang et al. [471] introduced a model
based on adsorption strength, postulating that particles adsorbed on the surface of the
electrode can detach themselves depending on the deposition conditions. Vereecken et al.
[472] formulated a model by considering the convective diffusion of particles to the
electrode surface. They were successful in describing the kinetics of nanoparticles during
electrodeposition. A model based on primary current distribution and ohmic resistance in
the plating bath was introduced by West et al. [473]. A one-dimensional diffusion model
was postulated by Bade et al. [474], who investigated the deposition of Ni in microholes
using micro RDEs. Griffith et al. [475] proposed both one- and two-dimensional models,
where the 2-D model was limited to the deposition of a single species. Another one-
dimensional model was proposed by West et al. [476] for electrodeposition of copper
using pulse and pulse-reverse plating methods. Andricacos et al. [477] proposed another
model for the deposition of copper for chip interconnects. The validity of the above
model was later verified through experimental work carried out by the authors [478].
Other models by West et al. [479], Gill et al. [480], and Panda [441] have shed more light
on these interesting but not fully-understood phenomena.
6.3.5.3 Nickel and its Alloys
Nanocrystalline materials have found many uses due to their unique mechanical,
chemical, and electrochemical properties [481-483], and nickel coatings are amongst the
104
earliest commercially-available electrodeposited thin films [484-486]. One of the
simplest baths, developed by Watts in 1916, is still in use today owing to its low cost,
ease of preparation, and simple control [484-487]. As with other metals, nickel can be
deposited on many different substrates using various techniques, including DC and Pulse
electrodeposition.
The synthesis of nanocrystalline nickel by electrodeposition has been widely reported in
the literature. Direct current electrodeposition has been successfully used to produce
nanocrystalline materials, including nickel and its alloys. Ebrahimi et al. [488] have
produced nanocrystalline nickel layers from a nickel sulphamate bath. They reported thin
layers of electrodeposited Ni with grain sizes ranging from 35 to 97 nm. Bakonyi et al.
[489] synthesized nanocrystalline nickel by DC electrodeposition using a plating bath
containing Na2SO4, NiSO4, and HCOOH.
For reasons previously discussed, PC electrodeposition has become the method of choice
for creating nanocrystalline materials. It is well known and well documented in the
literature that the properties of metals and alloys can readily be altered and improved by
modifying their microstructures by controlling the pulse parameters, including applied
peak current density, on-time, and off-time [490, 491]. Erb et al. [492], Klement et al.
[493], and Brooks et al. [494] studied the impact of various electroplating parameters on
the structure and properties of pulse electroplated nickel. They all reported the synthesis
of nickel nanoparticles with grain sizes in the range of 6-100 nm, utilizing a Watts bath
with small amounts of saccharin. Pulse electrodeposition was carried out with on-time
and off-time of 2.5 ms and 45 ms, respectively. Natter et al. [495-497] in a series of
papers reported the creation of nanocrystalline nickel with grain sizes of less than 50 nm
using pulse electrodeposition with on-time and off-time ranging from 1-5 ms and 50-100
ms, respectively. The plating bath was reported to contain NiSO4, H3PO4, NH4Cl, and
Na-K tartarate. Jeong et al. [498] investigated the influence of pulse parameters on the
grain size reduction of nanocrystalline nickel deposits and correlated and reported
superior wear resistance compared with similar pure nickel layers deposited by
conventional methods. In a similar study, Chen et al. [499] examined the influence of
pulse frequency on the microstructure of Ni-Al2O3 composite coating. They also studied
105
the impact of pulse frequency on the hardness and wear resistance of the above
composite, and found that the pulse frequency significantly influenced the preferred
orientation of the composite coatings; as the pulse frequency increased, the texture of the
coatings changed from a preferred and strong (111) to a more random orientation. Yang
et al. [500] examined the influence of pulse parameters on the corrosion resistance and
porosity of electrodeposited nickel coatings. Direct current electrodeposition was also
employed and it was observed that the porosity of nickel deposits created by PC
electrodeposition significantly decreased, resulting in better corrosion-resistant properties
compared with DC electrodeposition. Qu et al. [501] experimented with ultra narrow
pulse width and high peak current density to produce nanocrystalline nickel coatings with
low porosity, small grain size, and minimal internal stress. It was claimed that grain sizes
ranging from 50 to 200 nm were obtained when the current density changed from 300 to
60 A dm-2
. The hardness of the nickel deposits also was reported to increase with
increasing current density in the range of 20 to 150 A dm-2
; however, it decreased at
current densities greater that 150 A dm-2
.
Much of the published work on pulse electrodeposition has focused on a rectangular
waveform. Accordingly, most of the comparative studies between pulse electrodeposition
and other methods are based on this waveform. Several workers, however, have shifted
their focus to different types of waveforms. Wong et al. [502] presented their
experimental and theoretical works on the surface finish of nickel electroforms prepared
by using five different waveforms: rectangular, triangular, ramp-up, and ramp-down, all
with relaxation times (off-times) and a ramp sawtooth waveform without any relaxation
period. They claimed that at constant electrodeposition parameters—peak current density,
pulse period, electrodeposition thickness—ramp waveforms produced the best results in
terms of surface roughness, followed by triangular and rectangular waveforms. It was
noted that surface roughness could readily be reduced by as much as two to three times
when ramp (both up and down) and triangular waveforms were utilized. In a similar
study, Chan et al. [503] investigated the influence of rectangular, triangular, and
sinusoidal waveforms on crystallographic texture, microstructure, and the surface
finishing of electroformed nickel, and reported that smaller grain size and a better surface
finish were obtained by employing a triangular waveform. In another study conducted
106
and reported by Wong et al. [504], the highest hardness and the smallest grain size of
nickel electroforms were obtained when a ramp-down waveform with relaxation times
was used. Analytical equations for overvoltage and nucleation rates at a constant current
density and deposition thickness were also derived.
6.3.5.4 Platinum and its Alloys
In recent years, there has been a growing interest in the development of highly dispersed
catalyst layers containing Pt and PGMs with high catalytic activity for use in low-
temperature hydrogen fuel cells [505-508].
A number of different methods have been devised to deposit a predetermined amount of
catalyst on GDLs or SPEs. Chemical reduction of commercially available platinum salts
such as H2PtCl6 and Pt(NH3)4Cl2 by a reducing agent such as NaBH4 is one of the most
commonly used methods [509]. The impregnation-reduction method also is widely used
to deposit Pt onto different types of SPEs [510-512]. A combination of reduction and
decal transfer processes also has been explored, in which the reduced platinum alloy
particles are first precipitated out of solution and made into an electrode by the decal
transfer technique [41, 509]. However, the utilization of catalyst particles prepared using
the above methods normally is less than 20%, primarily due to their relatively large size
or lack of ionic and/or electronic contacts. Another common technique to prepare carbon-
supported platinum is to employ a ―sulphito route‖, where chloride is first removed from
H2PtCl6 by converting it into Na6Pt(SO3)4 and then precipitating platinum oxide colloids
onto suspended carbon-black particles, and finally producing Pt/C by a simple chemical
reduction process [509, 513]. An average platinum particle diameter of 1.5-1.8 nm has
been reported using this technique [509, 513]; however, due to the nature of this method,
more than half the deposited electrocatalyst may not be available to participate in the
redox reactions inside the fuel cell [513, 514].
As a result, there has been a significant level of activity in the field of electrocatalyst
deposition for use in sensors, medical devices, and fuel cells, particularly proton
exchange membrane and direct methanol fuel cells. To ensure high utilization of
deposited catalyst particles, two conditions must be met: small particle size—often less
107
than 5 nm in diameter—and the presence of the catalyst in the three-phase interface,
where both the reduction and oxidation reactions take place. The former can be
accomplished by many of the methods explained in this section as well as in section 5.2.
The latter is more difficult to achieve, since most of the conventional deposition
techniques cannot ensure contact between the polymer electrolyte membrane and all—or
even most—of the deposited catalyst particles. Of the various deposition techniques
available today, pulse electrodeposition has received much attention for a number of
reasons [12, 107]. It provides the worker with more control over the deposition process,
where, at least in theory, catalyst particles can selectively be deposited in places where
both ionic—via the polymer electrolyte—and electronic—through the carbon network—
pathways are readily available. The creation of nanoparticles in the range of 1.5-3.0 nm is
ensured by controlling and optimizing the electrodeposition parameters, such as the
applied cathodic current density, pulse on-time, and pulse off-time. However,
maintaining small particle size during electrodeposition is challenging, since after the
initial phase of nucleation, when small catalyst crystals are formed, these crystals have a
tendency to grow by incorporating future incoming platinum particles. Accordingly,
major studies have been conducted to gain a better understanding of the electrodeposition
process from a number of different plating bath solutions and under varying experimental
conditions. A brief review of some of the published work is given here.
In order to understand the influence of various plating parameters, such as applied current
density and pulse period, on the properties of the electrodeposited catalyst layer, it is
imperative to be able to characterize this layer with ease and certainty. A number of
studies have been conducted on the electrodeposition of platinum from different solutions
onto glassy carbon substrates [13, 394, 398, 509, 515-518]. Such substrates are easy to
prepare and work with and, more importantly, they can easily be characterized.
In 1986, Itaya et al. [517] reported the electrodeposition of platinum into Nafion® on
glassy carbon substrates. A solution of potassium hexachloroplatinate (K2PtCl6) in 1.0 M
H2SO4 was used as the electrolyte, while a 3 wt% Nafion®
solution in ethanol was
utilized to prepare the electrode coatings. Cyclic voltammetry (CV) was employed to
deposit platinum into the Nafion® film. The average size of the electrodeposited platinum
108
crystals was reported to be in the range of 10-20 nm. Ye et al. [518] also electrodeposited
Pt within a Nafion® film coated on glassy carbon electrodes. Two potential-control
methods—cyclic and constant potential—were employed to form an electrodeposited Pt
layer on the working electrode in a three-electrode cell with a Pt foil and a mercurous
sulfate electrode as the counter and reference electrodes, respectively. It was claimed
that the Pt particles prepared by the cyclic-potential method were smaller than those
prepared by the fixed-potential technique. Thompson et al. [509] investigated the
electroreduction of platinum from a solution of H3Pt(SO3)2OH onto glassy carbon as a
base material and then onto carbon black (CB) based electrodes. A three-cell electrode
containing a platinum wire as the counter electrode, a saturated calomel electrode as the
reference electrode, and glassy carbon and CB-based substrates as the working electrode
was used. All the experiments were carried out at room temperature. The electroreduction
of H3Pt(SO3)2OH to form platinum nanoparticles is considered to take place according to
the following reaction:
2
3
02
23 22)( SOPteSOPt (6-47)
It is noted that the production of sulphite ions (SO32-
) or other sulphur-containing
compounds can potentially lead to the poisoning of the platinum electrocatalysts by
sulphide ions (S2-
). A possible pathway for the formation of sulphide ions from sulphite
ions is
2
2
2
3 366 SOHHeSO (6-48)
The authors argued that the poisoning effect of sulphide ions during the electroreduction
may actually be beneficial in inhibiting the growth of platinum crystals, leading to very
small catalyst particles on the substrate. No concrete evidence was provided, but the use
of surface techniques such as X-ray photoelectron spectroscopy (XPS) was suggested to
verify the above claim.
In the early 1990s, Taylor et al. [107, 519] described and patented an electrochemical
catalyzation technique in which it was claimed platinum particles in the range of 25 to 35
Å can selectively be deposited in places where both ionic and electronic pathways exist.
Electrodes fabricated via the above process exhibited higher catalytic activities compared
109
with other state-of-the-art electrodes prepared utilizing powder-type techniques. This was
attributed to the enhancement of the three-phase interface by extending it beyond what
was possible with conventional methods. This was in agreement with McBreen’s [520]
findings that platinum particles not in contact with the solid polymer electrolyte will not
be utilized in either the hydrogen oxidation or oxygen reduction reactions in PEMFCs.
Zubimendi et al. [521] examined the early stages of platinum electrodeposition on highly
ordered pyrolytic graphite (HOPG) from a H2PtCl6 solution, and reported that the initial
stages of platinum electrodeposition involve nucleation and growth at surface defects on
the above substrate. Low cathodic potentials and low charge densities produced rounded
platinum clusters of about 2 nm in diameter, while compact platinum crystals with flat
terraces were formed as the applied cathodic potential and charge density were increased.
Hogarth et al. [522] presented a simple technique to electrodeposit platinum on pre-
treated carbon cloth for use in electrooxidation of methanol in sulphuric acid electrolytes.
A three-electrode cell fitted with the pre-treated carbon cloth as the working electrode, a
platinum gauze as the counter electrode, and a Hg/Hg2SO4 reference electrode were used
to carry out the electrodeposition. A 0.02 M solution of chloroplatinic acid was used as
the electrolyte and the platinum was electrodeposited onto the working electrode under
potentiostatic conditions (-0.30 V vs. Hg/Hg2SO4). The performance of the above
electrode was compared with that of conventional electrodes (chemically-deposited Pt)
for the oxidation of methanol in 2.5 M H2SO4 at 60 ºC. Similar performances were
reported, although the platinum crystals obtained by electrodeposition were twice the size
of those deposited using chemical methods. This was attributed to the higher catalytic
activity of platinum particles deposited by the electrodeposit technique.
Mechanistic investigations of electrochemical nucleation and growth of platinum clusters
on various substrates and under different experimental conditions are of great importance
in understanding the influence of various plating parameters on the deposit properties,
including crystal size, geometry, effective surface area, and the thickness of the deposited
layer. Kelaidopolou et al. [523] studied the kinetics of nucleation and growth of platinum
clusters on a tungsten substrate from an aqueous solution of 0.002 M K2PtCl6 and 0.1 M
HClO4. Milchev et al. [400] performed a series of experiments under the same
experimental conditions and electrolyte solution as in the previous study by
110
Kelaidopolou, but replaced the working electrode with titanium. It was reported that, as
was the case with tungsten, the nucleation and growth of platinum clusters on an oxidized
titanium surface is controlled by kinetic factors. The cathodic current transients under
potentiostatic conditions were recorded and analyzed with respect to the theory of
progressive nucleation with overlap of diffusion zones and limited number of active sites.
As previously discussed, the electrodeposition of platinum on HOPG can provide useful
information about the early stages of the nucleation process; however, the deposition
process must be halted at a very early stage of nuclei growth to avoid overlap of the
diffusion zone with the crystal growth [521, 524-526]. In addition, the electrodes
fabricated by this method contain very small amounts of catalyst, which falls short of the
critical minimum needed for use in PEM fuel cells. It is believed that not only the small
size of platinum particles, but also the distance between adjacent Pt clusters can impact
their catalytic activity in fuel cells [524, 527-530]. The latter is known to be related to the
platinum loading that, in turn, depends on the deposition time. As the deposition time is
lengthened, the amount of the deposited catalyst is increased; however, this also
encourages crystal growth and will adversely affect cell performance by lowering the
effective surface area of catalyst nanoparticles. Chen et al. [524] investigated the
nucleation and growth mechanism of Pt on microelectrodes less than 10 nm in diameter.
The extremely small surface area of such substrates allows for single nuclei to form,
making the investigation easier and more manageable. Single nucleation and growth can
be achieved at either low or high overvoltages, nucleation being controlled by the rate of
charge transfer, while growth is predominantly under diffusion control. Larger electrodes
(up to 100 nm in size) can effectively be used for single-nuclei deposition when the
overvoltage is maximized; i.e., diffusion-controlled deposition. The diffusion coefficient
of the PtCl62-
anion and the exchange current density for the reduction reaction of the
above anion to metallic Pt were reported to be (1.2 ± 0.1) 10-5
cm2 s
-1 and (8 ± 1) 10
-6
A cm-2
, respectively.
The electrodeposition of platinum often proceeds via the reduction of Pt(II) or Pt(IV)
complexes with a number of complexing ligands, including Cl, NO2, and NH3 [531]. The
first attempt to electrodeposit platinum from an aqueous solution dates back to the
111
beginning of the 19th
century in which an acidic solution based on [PtCl6]-2
was employed
[532]. Platinum has been electroreduced from a number of different aqueous solutions
such as H2PtCl6 [9, 513, 524, 533-541], K2PtCl6 [400, 509, 510, 542], K2PtCl4 [543],
K2Pt(NO2)4 [544], H3Pt(SO3)2OH [509], Pt(NH4)2Cl6 [531], Pt(NH3)4HPO4 [545], and
Pt(NH3)4Cl2 [12, 107, 519, 533]. The resulting platinum solutions are classified as acidic
or basic. In acidic solutions, in the presence of chloride ions and Pt(0), the reaction
proceeds according to:
ClPtPtClPtCl 22
2
6
2
4 (6-49)
In acidic media (HCl), the formation of (PtCl4)2-
is dominant, since the equilibrium is
shifted to the left [531]. The current efficiency of such plating baths is relatively high, but
the films deposited from such solutions contain small grain sizes and large internal
stresses, which result in cracking of films thicker than about 1m [531]. However, this
does not pose a problem in fabricating MEAs, since the goal is not to deposit thick layers
on substrates, but to electrodeposit well dispersed nano-particles at the three-phase
interface. Nevertheless, acidic solutions are not compatible with most of the existing
SPEs, almost none of which transport anions, because in electrodeposition, the catalyst
compounds must traverse the SPE layer to reach the carbon network on the other side to
be reduced. As a result, most researchers have tried to perform the catalyst
electrodeposition prior to SPE addition [9, 105, 536]. Another solution sought by several
workers has been the inclusion of a supporting salt in the aqueous electrolyte to enhance
the diffusion of anions across the membrane [535, 546].
Alkaline plating baths, on the other hand, contain the cationic form of platinum
compounds and do not suffer from the mobility restrictions inside the SPE layer like
acidic deposition solutions. Alkaline baths consist mainly of solutions of [Pt(NH3)4]2+
and
Pt(NH3)2(NO2)2, but Pt deposition from other plating baths such as [Pt(OH)6]2-
also has
been reported [531, 532]. Although platinum-containing cations can readily diffuse
through the solid polymer electrolyte, the current efficiency of such solutions is very low
at room temperature. Accordingly, the temperature of the plating bath must be increased
to enhance the current efficiency. The current efficiency of Pt(NH3)2(NO2)2 is a strong
function of temperature and increases from less than 10% at room temperature to over
112
50% at 60 C. Tetrammineplatinum (II)—[Pt(NH3)4]2+
—behaves in a similar manner, but
in order to achieve current efficiencies in excess of 50%, the plating bath temperature
must be raised to 90 C [531]. It is also common practice to maintain the pH of the
plating bath in the narrow range of 10.0-10.5 using a buffer solution such as a dilute
solution of sodium phosphate [544, 547-549]. However, deposition solutions at other pH
values also have been reported. Whalen et al. [531] investigated the deposition of
platinum film from a plating solution containing 17 mM (NH4)2PtCl6 and 250 mM
Na2HPO4 at pH 7.8.
Pulse electrodeposition of metals on conductive surfaces can be performed either in
galvanostatic or potentiostatic modes. The former can simply be carried out in a two-
electrode cell, a current source, and an arbitrary waveform generator. The potentiostatic
technique, on the other hand, requires a three-electrode cell and is not convenient for
electrodes having a geometric surface area greater than 10 cm2 [542]. Gloaguean et al.
[550] and Thomson et al. [551] evaluated the performance of PEM fuel cell MEAs
fabricated using potentiostatic pulse electrodeposition, while Choi et al. [9], Kim et al.
[105], and Coutanceau et al. [542] evaluated the performance of MEAs prepared by
galvanostatic pulse electrodeposition.
Several researchers have examined the influence of various pulse parameters on the
properties of the deposited catalyst layers for use in hydrogen fuel cells. Choi et al. [9]
investigated the effects of pulse duty cycle and applied cathodic current density on the
activity of the deposited layer and compared it with electrodes fabricated by DC
electrodeposition. With DC electrodeposition, the best electrodes are reported to be
prepared at a current density of 25 mA cm-2
. It is claimed that at higher current densities,
electrode performance drops sharply, possibly due to the growth of dendritic crystals and
the loss of the deposition layer, as a result of hydrogen evolution. However, in PC
electrodeposition, the peak current density can be significantly higher than the DC
electrodeposition and the best performance is reported with electrodes prepared at a
deposition current density of 50 mA cm-2
. The optimum pulse conditions for the above
electrodes are reported to be an on-time of 100 ms and an off-time of 300 ms for a duty
cycle of 25%. The conditions of PC electrodeposition in terms of off- and on-times and
113
the peak current density were given as 10 to 100 ms and 10 to 50 mA cm-2
, respectively.
The total amount of charge for fabrication of a single electrode through both DC and PC
electrodeposition techniques is reported to be 4 C cm-2
. The effect of electrode roughness
on the electrodeposition also was briefly discussed. The preparation of carbon electrodes
(application of the carbon ink prior to Pt electrodeposition) by brushing was suggested,
since smaller platinum particles in the neighborhood of 150 nm in diameter were
observed after the completion of the pulse electrodeposition. In contrast, the size of the
platinum deposits on electrodes prepared by the rolling method was reported to be around
250 nm in diameter.
Kim et al. [536] described a pulse electrodeposition technique in which platinum particles
smaller than 5 nm in diameter were claimed to be deposited directly on the surface of
carbon electrodes. Using an acidic plating bath containing H2PtCl6, SPE impregnation
was performed after catalyzation. It was claimed that the Pt-to-carbon ratio at a distance
of 1m from the membrane was about 75 wt% and was lowered to almost zero at a
distance of about 7 m from the membrane; therefore, it was possible to deposit a very
thin (about 5 m) layer of platinum close to the membrane, where both ionic and
electronic contacts could be secured. The authors reported that MEAs fabricated using
this technique exhibited a current density of 0.33 A cm-2
at 0.8 V with a platinum loading
of 0.25 mg cm-2
. The electrodeposition parameters for electrodes with the best fuel cell
performance were an applied peak current density of 200 mA cm-2
, a duty cycle of 4.6%,
and a total charge density of 11 C cm-2
. In a later study [105] the same authors reported a
different set of PC electrodeposition conditions under which the best electrodes were
prepared using a peak current density of 400 mA cm-2
, a duty cycle of 2.9%, and a total
charge density of 8 C cm-2
. These electrodes exhibited a high catalyst performance of 380
mA cm-2
at 0.8 V. Any increase in total charge density above 8 C cm-2
was claimed only
to increase the catalyst loading and its thickness without enhancing catalytic activity. A
range of 6 to 16 C m-2
was reported with 8 C cm-2
being the optimum charge density
under the above conditions (peak current density of 200 mA cm-2
and duty cycle 4.6%).
Ye et al. [541] studied the influence of shape control agents such as polyethylene glycol
(PEG-10000) and lead (II) acetate on the performance of electrodes prepared by pulse
114
electrodeposition. The morphology and microstructure of the platinum deposits were
reported to change from spherical clusters to clump-like crystal aggregations and finally
to elongated leaf-like flake clusters for no additives, PEG-10000 and lead (II) acetate,
respectively. It was claimed that the addition of PEG-10000 to the catalyst ink can
significantly improve the catalytic activity of the electrode towards oxygen reduction in
fuel cells. The pulse electrodeposition parameters under which the electrodes were
prepared were not clearly stated. Chen et al. [552] examined the influence of plating bath
viscosity on the performance of pulse electrodeposited platinum nanoclusters on carbon
nanotubes. Pulse electrodeposition of Pt nanocrystals from plating baths of increased
viscosity containing H2PtCl6 and glycerol was claimed to improve their activity towards
oxygen reduction. This higher catalytic activity was attributed to the ability to control the
size of the deposited Pt particles by optimizing the viscosity of the plating bath. It was
claimed that the addition of glycerol can significantly lower the diffusional mass
transport of the metal ions and, consequently, inhibit the growth of the deposited metal
crystals. Verbrugge [12] further researched the Electrocatalyzation technique first
proposed by Taylor et al. [107, 519] using two different plating baths, one containing
copper sulfate and the other tetrammine platinum (II) chloride. A Pt(NH3)4Cl2 threshold
concentration of 10 mM was recommended to ensure an acceptable current efficiency for
platinum deposition and inhibit hydrogen evolution that becomes the dominant reaction
at the cathode. Furthermore, a potential range of 0.0 V to -0.8 V (vs. Ag/AgCl) was
suggested for platinum deposition from a 10 mM Pt(NH3)4Cl2 plating bath.
Electrodeposition of bimetallic Pt alloy systems under both potentiostatic [553, 554-558]
and galvanostatic [542, 559, 560] control also has been reported. Coutanceau et al. [542]
investigated the influence of the relaxation time on the electrocatalyst particle size and
performance of anodes fabricated by galvanostatic pulse electrodeposition of Pt-Ru on
carbon electrodes for use in DMFCs. It was claimed that shorter off-times produced
smaller particle size with higher performance. This is in sharp contrast with other
workers’ findings using Pt alone [9, 107, 519]. It was reported that at loadings of 2 mg
cm-2
of Pt-Ru alloy, most catalyst particles range from 5 to 8 nm in size, with the best
performance delivered by MEAs containing a Pt-Ru atomic ratio of 80:20 in the
operating temperature range 50-110 C. Fujita et al. [555] also studied the influence of
115
pulse off-time on the properties of Co-Pt thick film magnets, including current efficiency,
internal stress, and film composition. The pulse on-time and current density were
constant at 2.0 ms and 50 mA cm-2
, respectively, while the pulse off-time was varied
between 0.0 and 58.0 ms. The current efficiency was observed to increase from 5% to
50% as the pulse off-time was increased from 0.0 to 30.0 ms, and then stayed constant at
pulse off-times greater than 30 ms. The observed improvement in the current efficiency
was attributed to the retardation of hydrogen evolution.
Wei et al. [553] pulse electrodeposited a thin layer of Pt-Ru catalyst on a glassy carbon
rotating disk electrode on which a layer of Nafion® had previously been applied. All
electrodepositions were performed under potentiostatic conditions and it was claimed that
the performance of electrodes fabricated via the above method with an estimated loading
of 77 g Pt-Ru/cm2 was superior to that of conventional electrodes with loadings of 100
g Pt-Ru/cm2. Nishimura et al. [558] developed a method for the electrodeposition of Pt-
based nanoparticles in conjunction with Ni by means of double potential step electrolysis.
Platinum-nickel alloy was deposited at the first step, followed by the dissolution of Ni
during the second step. It was reported that Pt-Ni nanoparticles in the order of 5.4 ± 1.5
nm could be formed. It was further claimed that the oxygen reduction electrocatalytic
activity of electrodes fabricated by the above technique was twice that of electrodes
containing pure platinum. Leistner et al. [560] developed a pulse electrodeposition
method for preparing Fe/Pt multilayers with low oxygen content for use in micromagnets
and high density magnetic data storage systems. The pulse electrodeposition was carried
out under potential control using a single bath technique. Pulse durations ranging from 25
s to 20 min were studied; however, other pulse parameters were not stated. It was claimed
that Fe/Pt bilayers as thin as 40 nm with low oxygen content can be achieved using the
above method.
6.3.5.5 Other Metals and Alloys
The electrodeposition of metallic alloys has been extensively studied for decades [561,
562]. These alloys have been found to be very useful in a number of industries, including
microelectronics for high density magnetic recording devices, high-end tool
116
manufacturers for corrosion and wear protection, and biomedical applications in which
there is an ever-growing demand for precision devices such as implants.
Zinc alloys have been investigated by several workers because of their superior protective
properties [563-565] and their observed catalytic activity [566-569]. Zn-Ni alloy has been
the alloy of choice for many reasons, the most important of which is its superior
corrosion resistance. It is widely reported that pulse electrodeposited Zn-Ni layers exhibit
better corrosion resistance than similar layers deposited using conventional methods. This
has been attributed primarily to the existence of a -phase and a more compact and
relatively homogeneous layer [391, 570-573]. The use of Zn-Co alloys also has been
investigated by several workers for their anti-corrosion characteristics [574] as well as for
their promising catalytic activity [575, 576]. Fei et al. [577] studied the influence of
pulse-reverse parameters on the properties of electrodeposited Zn-Co layers of varying
cobalt content prepared under different plating conditions. Most studies have reported a
maximum Co content of 6-7 wt% due to limitations arising from anomalous co-
deposition [577, 578-580]. Fei et al. [577] showed that the cobalt content in Zn-Co alloy
deposits is a strong function of both the average current density and the fraction of the
pulse reverse in square pulse reverse electrodeposition. The frequency of the pulse was
reported to have little impact on the outcomes, but does influence the microstructure of
the resulting Zn-Co layer. High cobalt content (greater than 90 wt%) was achieved at
average current densities of 10 mA cm-2
or lower, with a sharp decrease when the current
density was increased from 10 to 20 mA cm-2
, followed by a gradual increase beyond 20
mA cm-2
. Zn-Mn alloys have been studied mainly for their exceptional protective
properties [564, 581], with alloys having a Mn content of 30-40% exhibiting the highest
corrosion resistance [565, 582]. Müller et al. [565] examined the influence of pulse,
pulse reverse, and superimposed current modulations on the properties of Zn-Mn
deposits. The alloys were characterized by their composition, structure, thickness, and
morphology. It was reported that all the pulse forms employed having the same average
current density created deposits with higher manganese content compared with deposits
prepared using direct current electrodeposition, but that the current efficiencies were
lower. Deposits created by pulse reverse electrodeposition are reported to exhibit the best
117
results in terms of thickness and composition. Pulse electrodeposition of pure zinc as
protective layers also has been studied. Youssef et al. [583] conducted a series of
corrosion experiments on electrodeposited zinc and electrogalvanized steel in de-aerated
0.50 M NaOH solution. It was claimed that the estimated corrosion rate (90 A cm-2
) of
the electrodeposited zinc specimen was about 60% lower than that of the
electrogalvanized steel (229 A cm-2
).
In recent years, the electrodeposition of metal oxide films has attracted the attention of
many researchers in a number of different fields, including electronic, catalytic, and
biomedical. Of special interest is the electrodeposition of manganese dioxides for use in
lithium batteries [584], sensors [585], and supercapacitors [586]. Moses et al. [587]
investigated the microstructure and properties of manganese dioxide films prepared by
galvanostatic, pulse, and pulse reverse electrodeposition techniques using KMnO4
solutions of various concentrations, ranging from 0.01 to 0.10 M. Oxide films prepared
by pulse-reverse electrodeposition exhibited higher specific capacitance than those
generated by other techniques, including galvanostatic methods. The plating conditions in
pulse reverse were a constant cathodic current density of 1-2 mA cm-2
for a period of 2-5
min followed by a reverse current density (i.e., opposite polarity) of 0.5-1 mA cm-2
for
0.5-1 min. Wu et al. [588], who examined the influence of PC electrodeposition on the
properties of deposited Mn-Co films for in SOFCs as interconnects, found that the Mn
content decreased with increasing off-time and that the surface morphologies changed
from flake-like particles to crystalline structures.
Other metals and alloys that have benefited from pulse electrodeposition—both under
potentiostatic and galvanostatic control—are gold [589, 590], Au-Co [591], Au-Ni [592],
chromium [593, 595], Cr-Ni [596], silver [597], Ag-Sn [392], and Ag-Pd [598]. In fact,
the benefits of PC electrodeposition became apparent in the early 1950s when it was
originally employed to deposit gold from a number of acidic electrolyte solutions onto
different substrates, where it had been tried unsuccessfully in the past using DC
electrodeposition [599, 600].
118
6.0 EXPERIMENTAL PROCEDURE
7.1 Hydrophobic Polymer Coating
Commercial carbon papers (Toray TGPH-030, 060, 090, 120; E-TEK) and cloths (ELAT,
E-TEK) were made hydrophobic by treating with PTFE (60 wt% solid, Alfa Aesar)
according to the following procedure. Substrates were first cut into desired shapes
(circles of 3.5 cm in diameter, in most cases) and immersed in acetone (ACS reagent
grade) for 1 h to remove any dust and foreign matter from the carbon fibers. The
substrates were rinsed for 5 minutes with fresh acetone and then dried in an oven at 80 C
for several hours. The carbon papers/cloths were slowly lowered into a PTFE suspension
and left for 5 minutes before they were removed and placed in an oven to dry. To ensure
a uniform drying and to avoid the migration of PTFE to only small areas on the
substrates, they were placed on six long needles (with pointed ends up) inside an oven
and dried for several hours at 80-90 C as shown in Figure 7-1. PTFE loadings were
determined by gravimetric analysis and the above procedure was repeated until the
desired loading was achieved. A brushing method also was employed, in which PTFE
was applied using an artist’s paint brush. Extra care was exercised to ensure uniform
PTFE distribution by applying constant paintbrush strokes. Samples were finally placed
in an oven and sintered at 360 C for 20 min. A number of MEAs were fabricated using
pre-treated carbon substrates (treated with FEP or PTFE by the manufacturer); such
samples are clearly identified in this study.
Figure 7-1 Drying of substrates in an oven
119
7.2 Sintering of Treated Carbon Substrates
The impact of sintering temperature and duration on the through-plane electrical
resistance of PTFE-treated carbon substrates was determined by evaluating through-plane
electrical resistance as a function of PTFE content and applied contact pressure, ranging
from 100 to 500 bars. After PTFE application, each sample was placed in an oven and
rapidly heated up to a pre-set temperature, ranging from 100 C to 430 C. For various
sintering temperatures, the sintering time was kept constant at 30 minutes and was
recorded from the time the oven reached the desired temperature. The oven then was
quickly turned off and the samples removed several minutes after being cooled down; the
oven temperature was in the neighbourhood of 50-60 C at the time of sample removal.
The samples were then transferred into a moisture-free environment for future analysis.
The influence of sintering duration on through-plane electrical resistance of treated-
carbon substrates was determined by keeping the sintering temperature constant at 360
C for all samples, while varying the sintering time from 10 to 50 minutes. The oven
temperature was 360 C at the time of sample placement and maintained at this
temperature for the duration of the experiment. The PTFE-to-substrate ratio (based on
mass) was around 1.0-1.1 for all samples.
The through-plane electrical resistance of each sample was measured by placing it
between two polished copper plates each with a contact surface area of 25 cm2 and
connected by wires to a milliohm meter (Chroma 16502, four terminal test cable with
temperature compensation card, at 1 kHz).
7.3 Carbon Ink Preparation: Microporous Layer Application
Membrane-electrode assemblies were first fabricated by preparing a homogeneous
suspension referred to as ―carbon ink‖. The first step involved the treatment of carbon
black (Vulcan XC-72 or another carbon/graphite powder) at 600 C for 3 hours to remove
any trace organic matter. Pretreated carbon black, PTFE, and isopropyl alcohol (HPLC
grade) then were mixed in an ultrasonic bath and/or ultrasonic homogenizer. Electrodes
with various diffusion layer loadings (0.5-2.0 mg cm-2
) were prepared by brushing the
120
prepared paste onto one side of a wet-proofed carbon cloth or paper and then dried in an
oven at 200 C for 6 hours. This layer is known as the micro-porous layer (MPL). This
diffusion layer or MPL is strategically placed between the catalyst and gas diffusion
layers to remove water from inside the catalyst layer via capillary action, to enhance the
electronic conductivity of the MEA, and to prevent the movement of the catalyst layer
further into the GDL. The side with the carbon ink is referred to as the ―carbon side‖,
while the other side with only PTFE is known as the ―gas side‖. Each electrode was
weighed before and after the application of the carbon ink. The resulting carbon substrate
has a strong hydrophobic nature. Several carbon substrates also were treated with a
hydrophilic paste to add a hydrophilic layer on top of the hydrophobic layer. Glycerol
was added to the carbon ink and then homogenized in an ultrasonic bath for at least one
hour before brushing onto the hydrophobic layer. The hydrophilic layer loading was 0.5
or 1.0 mg/cm2 in all cases. Both the anode and cathode were prepared in this manner.
7.4 Nafion® Impregnation
Nafion® impregnation was achieved utilizing two widely used methods: floating and
brushing. In the floating method, a partially fabricated gas diffusion electrode (GDE),
from the previous step, was floated, carbon-face down, on the surface of an alcoholic
solution of 5% Nafion® (by weight) in a shallow beaker. The solid polymer electrolyte
solution was allowed to penetrate part way into the gas permeable face. An impregnation
time of 30 seconds was used, which provided Nafion® loadings of about 1.0 mg cm
-2.
Excess solution was allowed to drain off the electrode surface, which then was dried in
air for 12 hours. In the brushing method, an artist’s brush was used to gently brush
Nafion® solution onto the carbon face of the electrode. Extra care was exercised to
maintain an identical process throughout the experiments by keeping the number of
strokes and soaking time (soaking the brush in the Nafion® solution) constant. The extent
of the impregnation was determined by using scanning electron microscopy.
The ion-exchange capacity (IEC) of a number of samples was determined by placing
them in 250 mL of 2.0 M NaCl solution while purging nitrogen gas through the solution
for one hour to convert the membrane from the H+
form to the Na+ form. The resulting
121
solution then was titrated with standardized 0.05 M NaOH to an end point. The volume
of NaOH consumed was noted and used to calculate the moles of H+ in solution.
Assuming complete conversion of the membrane to the Na+ form, the ion-exchange
capacity was calculated using:
IEC (VNaOH ) (CNaOH ) (1/mass of the sample) (1eq mol1) (1000 meq eq1) (71)
where, VNaOH = volume of NaOH (L)
CNaOH = concentration of NaOH (mol L-1
)
IEC = ion-exchange capacity (meq g-1
)
7.5 Catalyst Electrodeposition
7.5.1 Platinum Electrodeposition
Electrodeposition was primarily carried out at 20 C with several test runs at 50 C in a
flow cell (see Figure 7-2) using a platinum solution containing 0.05 M Pt(NH3)4Cl2. All
solutions were prepared from analytic grade chemicals and deionized water (18 MΩ·cm).
The uncatalyzed carbon substrate was mounted inside the flow cell on a sample holder
coupled with a platinum disk and a platinum wire as current collectors. The substrate size
was kept constant at 3.5 cm diameter throughout the experiments. A platinum disk of 2.5
cm in diameter was used as the anode. A Masterflex peristaltic pump was used to
circulate the electrolyte through the flow cell during electrodeposition. The electrolyte
container was kept in a water bath to ensure a constant temperature during the
electrodeposition process. Two different sizes of tubing—Tygon L/S 16 and L/S 25—
were used with the pump to achieve various flow rates. Also, calibrations were performed
using the copper plating bath solution at two different temperatures, 25 °C and 50 °C.
The solution was run through the pump and into a graduated cylinder where it was
carefully measured. The results are tabulated in Tables C-1 through C-4 and shown
graphically in Figure C-1 in Appendix C.
122
Figure 7-2 Electrodeposition flow cell
Plating Solution
OUT
Plating Solution
IN
Platinum
Disk
(Anode)
Carbon
Substrate
(Cathode)
123
An EG&G (model 371, PARC or model 273, PARC) potentiostat coupled with an EG&G
universal programmer (model 175, PARC) was used to control both the pulse wave and
the deposition current density. An oscilloscope (HP model 54504A) was employed to
monitor the waveform and other parameters such as duty cycle and peak current density
throughout each experiment. The peak deposition current densities, pulse on-time, pulse
off-time and the duty cycles were varied to optimize the deposition process and
consequently, the dispersion and size of the catalyst particles. Catalyst loadings in the
range of 0.05-0.50 mg cm-2
for both anode and cathode were prepared by controlling the
electrodeposition peak current density and total charge density. At the completion of
electrodeposition, each electrode was washed with deionized water (18 MΩ·cm) for at
least 15 minutes to remove any free platinum from the substrate pores. The electrodes
then were heated in air at 300 C for 1 h to remove the solvent in the hydrophobic layer
of the electrode. Four different waveforms—rectangular, triangular, ramp-up and ramp-
down—were employed to perform electrodeposition (Figure 7-3).
Figure 7-3 Different types of waveform
ip
ip
t t
i
i
Rectangular Triangular
Ramp up Ramp down
a b
a a
124
7.5.2 Copper Electrodeposition
Copper electrodeposition on carbon substrates was initially carried out to gain experience
with the proposed technique and to lower cost because of the prohibitive cost of
platinum. Electrodeposition was performed at 20 C using an acidic bath containing 0.05
M CuSO4.5H2O and 0.5 M H2SO4 (all analytic grade chemicals) under both direct current
(DC) and pulse current (PC) electrodeposition. Similar to platinum electrodeposition, pre-
treated carbon papers and cloths were used as the substrates of choice. The equipment
setup and experimental procedure were similar to the method utilized for platinum
electrodeposition—section 7.5.1.
7.5.3 Nickel Electrodeposition
Nickel electrodeposition also was experimented with for the same reasons as copper. A
modified Watts nickel bath and electroplating conditions are presented in Table 7-1. All
solutions were prepared from analytic grade chemicals and deionized water. The
electrolyte bath was agitated by a mechanical stirrer at 500 rpm and the temperature
maintained at 50 °C throughout the plating process. The initial pH of the electrolyte was
4.2, a value commonly used for Ni electroplating. AISI 431 stainless steel (3.5 cm in
diameter) was used as a substrate.
Table 7-1 Bath composition and electroplating conditions for Ni plating
Nickel Sulphamate 330 g L-1
Nickel Chloride 15 g L-1
Boric Acid 30 g L-1
Sodium Dodecyl Sulphate 0.2 g L-1
pH 4.2
Temperature 50 ± 1 °C
Peak Current Density 10 – 1000 mA cm-2
Duty Cycle 2 – 100%
Period of One Cycle µs - ms
125
Prior to placement inside the electroplating cell, the substrate was first ground to a finish
on grade 180 emery paper, rinsed with deionized water, and then scrubbed with alcohol
and acetone and finally rinsed with deionized water. After electrodeposition, the surface
morphology of each specimen was examined and characterized using SEM. The grain
sizes were measured according to ASTM E112-95, while microhardness tests were
performed in accordance with ASTM E384. A brief description of the latter method is
provided in Appendix E.
7.6 MEA Fabrication and Testing
7.6.1 MEA Preparation
The Pt-containing electrodes (both cathode and anode) fabricated according to the
method presented in section 7.5.1 in conjunction with a solid membrane (Nafion® 112,
115 or 117) were bonded to form an MEA by hot pressing at 130 C and 1500 kPa for 2
min for carbon cloth and at 125 C and 1400 kPa for 3 min for carbon paper substrates
(see Figure 7-4). A single 5-cm2 fuel cell with serpentine flow pattern (EFC05-01SP,
Electrochem Inc.) in conjunction with a gas supply and measuring devices was used to
evaluate the performance of all MEAs.
7.6.2 Electrochemical Measurements
7.6.2.1 Single Fuel Cell Tests
Two different experimental set-ups were used to characterize the MEAs in a 5-cm2 fuel
cell. The first set-up included two mass flow meters to accurately and independently
control and monitor the flow rates of reactant gases, two humidifiers to control the
humidity levels of entering gases, several digital multimeters to monitor and record the
cell outputs (Flukes 187 and 189 multimeters, Fluke Corp.), a resistance decade box
(model 1434-N, General Radio CO), and a single 5-cm2 PEM fuel cell with internal
heaters (EFC05-01SP, Electrochem Inc.). A simple schematic of this set-up is shown in
Figure 7-5. A fully automated multi-range fuel cell test station (Series 850e, Scribner
Associates Inc.) and a manual fuel cell test system (Electrochem Inc.) also were
employed to perform some of the tests in the later stages of the research.
126
Figure 7-4 A simple representation of the MEA fabrication process
(1) (2) (3) (4)
(5) (6)
Carbon
Substrate
(untreated)
Microporous
Layer
(PTFE + C)
Nafion®
Layer
(deposited)
Platinum
Nanoparticles
(electrodeposited)
+ +
Anode SPE Cathode
Hot-bonded and
pressed
Complete MEA
127
Figure 7-5 A simple schematic of the experimental setup for MEA characterization
7.6.2.2 Life Test and Durability Assessment of MEAs: Static Testing2
The durability of different MEAs was evaluated using a 5-cm2 single cell with serpentine
flow fields at a constant cell temperature of 60 °C with both reactants being fully
humidified at 65 °C before entering the cell. Hydrogen and air (or pure oxygen with a
stoichiometry of 1.5) were used as fuel and oxidant with stoichiometries of 1.2 and 2.5,
respectively. Polarization and potential-time curves were obtained using a fully
automated fuel cell test station (Series 850e, Scribner Associates Inc.) in a galvanostatic
polarization mode. Potential-time curves were obtained at a constant load; i.e., 619 mA
cm-2
, for a maximum of 4000 h, at specified time intervals. Each MEA was conditioned
with fully-humidified fuel and oxidant at 65 °C and a constant load of 50 mA cm-2
for 24
h prior to testing to ensure the high ionic conductivity of the Nafion® layers in the
MEA—the SPE separating the anode and the cathode and the solubilized Nafion® that
2 These tests were carried out at Lambton College under the supervision of the author
Anode
Cathode
SPE
H2
O2
or
Air
N2
Humidifiers Single-Cell
Fuel Cell
Mass
Flow Meters
Back-Pressure
Regulators
128
was applied onto the GDE before catalyzation. MEAs also were analyzed after the
completion of lifetime tests using SEM to observe any change in their morphology.
7.6.2.3 Life Test and Durability Determination of MEAs: Dynamic Testing3
Two series of experiments were carried out to determine the durability and reliability of
MEAs prepared according to the pulse-electrodeposition technique proposed in this
thesis. In the first series, the behaviour of the MEAs in a real application under constant
load was determined by installing them into a 200-W PEM fuel cell stack (Horizon Fuel
Cell Technologies Pte. Ltd.) running on hydrogen and air without external
humidification. Hydrogen was supplied by a 900-L metal hydride canister (Ovonics,
USA). The fuel cell stack then was used to charge a battery bank containing three 12
VDC lead-acid batteries each with 7.2 A-h capacity. The battery bank, in turn, was used
to power a tricycle with a 350-W electric motor (BionX, Canada). The power output of
the stack was monitored and recorded over a period of twenty-six weeks for a total of 60
individual charges. A schematic representation of the tricycle fuel cell system is shown in
Figure 7-6.
In the second series, the true dynamic behaviour of in-house and commercial MEAs was
assessed in two separate 200-W PEM fuel cell stacks (Horizon Fuel Cell Technologies
Pte. Ltd.), one containing in-house MEAs and another using commercial MEAs. In
contrast to the tricycle fuel cell system, this setup did not have a battery bank. Instead, the
fuel cell stack was used to directly power a bicycle. Real-time data were collected at three
different stages: before the operation of the bicycle, during the operation (when the
bicycle was on the road relying on fuel cell stack power) and after the completion of road
trials. Polarization and open-circuit voltage (OCV) curves at different operating times
were compared. In addition, maximum power outputs from single 200-W PEM fuel cell
stacks at full and partial loads while the bicycle was in operation were recorded. This
system is shown in Figure 7-7. The bicycle was powered by only one of the stacks at any
time during the experimental phase and each stack was operated for three hours per day
for 112 days.
3 These tests were carried out at Lambton College under the supervision of the author
129
Figure 7-6 Schematic representation of a 200-W PEMFC system used in a tricycle
200-W
FUEL CELL
STACK
130
Figure 7-7 Fuel cell bicycle (direct drive)
7.6.2.4 X-Ray Diffraction
Catalyzed substrates were characterized using an X-ray diffractometer (Rigaku MSC,
Woodlands, TX, USA) employing a graphite crystal counter monochromator filtering Cu
Kβ radiation. The operating parameters of the X-ray source were 40 kV and 40 mA with
the patterns recorded in a 2θ, ranging from 20-90° and a step scanning rate of 1° per
minute.
7.6.2.5 Scanning Electron Microscopy
Gas diffusion electrodes and membrane-electrode assemblies were examined by scanning
electron microscopy using a high resolution SEM (S-4700, Hitachi Ltd.) coupled with an
EDX. Incident electron beam energies from 3 – 30 keV were utilized. SEM was used to
study the surface morphology of GDLs before and after the application of PTFE, MPLs
and catalyst layers, as well as to determine the thicknesses of the various MEA
components.
131
7.6.2.6 Transmission Electron Microscopy
Catalysts were characterized by transmission electron microscopy (TEM) using a high-
resolution TEM (JEOLEM-2010EX, Japan) with a spatial resolution of 1.0 nm. Particle
size analysis was performed by digital image processing of bright field transmission
electron micrographs of platinum particles with background correction. The latter was
carried out by digitally reducing the background levels and increasing the global intensity
differences between platinum nanoparticles and the support material.
7.7 Porosity Measurements of Gas Diffusion Layer
The bulk porosity of each untreated GDL was determined using a mercury porosimeter
(Micromeritics Autopore IV 9500, Micromeritics, USA). Mercury Porosimetry requires
the specimen to be completely dry; accordingly, all samples were dried in a vacuum oven
at 200 °C for 12 hours prior to testing. After placing each sample inside the sample
holder, the mercury pressure was gradually increased from 0.003 to 200 MPa and the
corresponding intruded volume measured and recorded. The total pore volume of each
sample was taken as the total cumulative volume of intruded mercury. Pore size
distributions also were estimated by measuring and recording the incremental volume of
mercury at each pressure. A contact angle of 130° and a mercury/vapour surface tension
of 0.485 N m-1
were assumed for calculation purposes.
The bulk porosity of a number of GDLs also was determined by immersing the samples
in decane—a wetting fluid—and utilizing gravimetric analysis. ―Dry‖ samples were first
weighed using a semi-micro balance and then were completely immersed in a shallow
beaker filled with decane and left undisturbed for 20 minutes, after which they were
removed from the beaker and excess solution allowed to drain. Samples were
immediately dried using felt-free papers and their masses measured and recorded. This
method was found to be simple and yielded results in good agreement with those
obtained from porosimetry.
132
7.8 Through-Plane Gas Permeability Measurement
Gas permeability through the plane (along the z direction) of a number of untreated GDLs
was measured using the in-house-fabricated apparatus, similar to the device used by
Gostick et al. [620], shown in Figure 7-8. The size of each sample was 3.3 cm in diameter
and, as can be seen in Figure 7-8, each GDL was compressed and secured between two
plates and a tight gas seal obtained by tightening the eight bolts. Air was fed to the GDL
via the circular channel at the centre of the top plate and the flow rate of the gas (air in
this study) at the outlet was measured using a digital flow meter (Omega FVL-1616A;
with a maximum flow rate of 20 sccm). The pressure change across the GDL was also
measured with a differential pressure transducer (Omega PX653) in conjunction with a
data acquisition system (National Instrument, NI USB-6009).
The pressure drop of each sample for a constant flow rate was measured six times and an
average value was calculated. The thickness of each substrate was measured using a
caliper. The gas permeability of the samples was evaluated by calculating the
corresponding gas permeability coefficients, k, based on the following rearranged form of
Darcy’s law.
)( vP
Lk
(7-2)
where, k is the substrate permeability coefficient, m2; L is the substrate thickness, m;
P is the pressure drop across the substrate, Pa; v is the superficial velocity, calculated
from the air flow rate divided by the substrate area, m s-1
; and
is the fluid viscosity (1.8
10-5
Pas, for air at 25 °C).
133
Figure 7-8 Laboratory apparatus for through-plane permeability measurement of GDLs
ΔP
Air In
Air Out
Data
Logger
Test Sample
134
7.0 RESULTS AND DISCUSSION
8.1 Influence of Hydrophobic Polymer (PTFE) Content in GDL
The original two-layer electrodes of the 1980s have evolved into the more effective three-
layer electrodes of today. Early electrodes comprised a wet-proofed support layer and a
catalyst layer consisting of carbon-supported platinum, solubilized SPE (e.g., Nafion®)
and PTFE. Today’s electrodes have incorporated a microporous layer (MPL) sandwiched
between the catalyst and the gas diffusion layers. The performance of three-layer
electrodes is generally superior to that of dual-layer electrodes. However, the
performance of fuel cell electrodes is influenced by many factors, including (1) type of
support material; i.e., carbon paper or cloth and whether it is woven or non-woven, (2)
the thickness and porosity of the support material, (3) the amount of hydrophobic
polymer, (4) type of electrocatalyst, including size, morphology, loading, type of carbon
support, and presence of other metals (bimetallic electrocatalysts), (5) SPE loading and
type (thickness and equivalent weight), (6) thickness of the GDL, and (7) fabrication
method and thermal treatment [10, 328].
The primary function of a GDL is twofold: to ensure a homogeneous distribution of the
reactant gases towards the catalyst layer and to remove the water generated inside the
catalyst layer by effectively removing it from the interior of the MEA and transporting it
towards the bipolar plates, where it leaves the cell or stack. The latter is achieved by
employing a hydrophobic polymer such as PTFE, which is first applied on both sides of
untreated substrates (carbon paper or cloth) to make them hydrophobic and then, in an
additional step, mixed with carbon powder and applied onto the gas diffusion electrode
(GDE) prior to Nafion®
impregnation and catalyst deposition to form a microporous
layer. Since PTFE is not electrically conductive, its proportion with respect to carbon
powder must be carefully selected and optimized to enhance its water blocking properties
while at the same time minimizing ohmic losses. It is, therefore, critical to determine the
optimum weight ratio between PTFE and the substrate to provide an adequate network of
macropores for fluid transport during fuel cell/stack operation while maintaining high
electronic conductivity. It is also imperative to optimize the ratio of PTFE to carbon
powder in the microporous layer of the GDL to enhance fuel cell performance. In
addition to the above functions, the GDL provides a support for the MEA membrane and
135
catalyst layers, and, more importantly, creates a pathway for the effective transport of
electrons from inside the MEA to the current collectors, and ultimately, to the external
circuit.
8.1.1 Influence of PTFE Loading on Cell Performance
A series of experiments was performed to determine the effect of PTFE loading, ranging
from 20% to 150% (based on the untreated weight of the substrate) on the substrate
through-plane conductivity. The extent of the surface coverage of the carbon fibers by the
hydrophobic polymer can clearly be seen in the SEM images of Figure 8-1, where
untreated (a) and wet-proofed (b) carbon papers are shown. The through-plane
conductivity of all carbon substrates decreased as the level of hydrophobic polymer
increased. This is expected since higher PTFE loadings result in more coverage of the
substrate fibers, which conduct electrons from one side of the GDL to the other.
(a) (b)
Figure 8-1 Surface morphology of carbon paper substrates before (a) and after (b) PTFE
application (60 wt%)
The through-plane resistance of Toray TGPH-090 carbon papers treated with varying
amounts of PTFE and subjected to applied pressures ranging from 50 to 480 bars is
shown in Figures 8-2(a) and (b). Similar results were obtained for other types of carbon
papers and cloths.
136
According to Figure 8-2(a), at all pressures the resistance increases almost linearly with
increased PTFE loading, but drops with increased pressure, especially if the PTFE
loading is high. This can be attributed primarily to the changes in PTFE distribution on
the surface, and ultimately, inside the micro- and macro-pores of the substrate as the
applied pressure is increased. Initially, when the pressure is negligible, most of the PTFE
resides on the surface of the substrate, creating an insulating barrier to the transport of
electrons across the carbon substrate, resulting inevitably in high through-plane electrical
resistance. Also, the applied pressure forces the substrate fibers to come into closer
contact, creating an additional series of pathways for electronic conduction, further
lowering the resistance.
Figure 8-2 (a) Impact of PTFE loading on through-plane resistivity of PTFE-treated
Toray TGP-H-090 carbon papers at various pressures (sintering temperature: 360 °C;
surface area: 25 cm2)
137
Figure 8-2 (b) Impact of PTFE loading on through-plane resistivity of PTFE-treated
Toray TGP-H-090 carbon papers at various pressures (sintering temperature: 360 °C;
surface area: 25 cm2)
As the pressure begins to increase and passes a critical point (around 150 bar for most
samples), the through-plane electrical resistance starts to fall less rapidly with further
increases in pressure. At applied pressures greater than about 350 bar, the change in
through-plane electrical resistance is negligible for most PTFE loadings. At this point, the
PTFE is well distributed both on the substrate surface and inside the pores. Regardless of
the applied pressure, no new contact points are created between the carbon fibers, hence
no more clear pathways for the conduction of electrons, and no further increase in
conductivity.
The influence of sintering temperature on the through-plane electrical resistance of a
number of carbon substrates also was investigated. The result for one of the carbon-paper
substrates—Toray TGPH-090—is presented in Figure 8-3. The first noticeable trend is
the marked increase in the through-plane electrical resistance of substrates sintered at
higher temperatures. This is expected since higher sintering temperatures result in a more
uniform distribution of the hydrophobic polymer both on the substrate surface and within
the micropores, consequently lowering the electronic conductivity by effectively covering
138
Figure 8-3 Influence of sintering temperature on through-plane resistance of PTFE-
treated Toray TGPH-090 carbon papers subjected to varying sressures (PTFE loading:
110%; surface area: 25 cm2)
the carbon substrate fibers. As before, the decrease in through-plane electrical resistance
of all samples with increasing applied pressure is mainly due to the formation of new
carbon networks inside the GDL.
8.1.2 Influence of PTFE Loading in Microporous Layer on Cell Performance
A series of experiments was carried out to examine the influence on fuel cell performance
of hydrophobic polymer content in the MPL of GDEs and to determine the optimal
amount for carbon paper substrates. Both anodes and cathodes were prepared in the same
way. Figure 8-4 shows the polarization curves for MEAs made with Toray TGHP-090
carbon paper and different PTFE loadings, ranging from 10 wt% to 60 wt% (with respect
to the carbon powder in the MPL). Each data point represents an average of at least five
steady-state runs. The amount of PTFE was kept constant in both anode and cathode in
this series of experiments. As can be seen from Figure 8-4, the best result was obtained
with GDLs containing 20 wt% PTFE. This is in agreement with observations reported by
other researchers [426, 601].
139
Figure 8-4 Influence of PTFE content on fuel cell performance operated at a cell
temperature of 50 °C in H2/Air with a platinum loading of 0.3 mg cm-2
per electrode;
fully humidified fuel and oxidant with stoichiometries of 1.2 and 2.5, respectively
The curve for 30 wt% PTFE shows nearly equal performance, especially at higher current
densities. The reason that the 30 wt% PTFE becomes increasingly as effective as the 20
wt% PTFE as the current density increases may be attributed to the better water removal
ability of the GDL with a higher PTFE content. At these high water-producing levels, 30
wt% PTFE is more effective in preventing flooding of the GDL by effectively removing
the excess water away from the catalyst and gas diffusion layers. Overall, however, the
20 wt% PTFE was found to be the best for all practical situations, considering the fact
that PEMFCs are not normally operated at high current densities. At higher PTFE levels
(40 wt% and greater), however, ohmic losses become dominant and the overall cell
performance decreases. In addition, high PTFE levels can influence the pore-forming
capability of GDLs; high PTFE levels in GDLs are known to decrease the porosity of
diffusion layers, which adversely affects the GDL by lowering its ability to remove water
from inside the MEA and transport gases to and from the catalyst layers.
140
Figure 8-5 shows the correlation between PTFE content and the voltage obtained at
several different current densities ranging from 200 to 1000 mA cm-2
. As previously
mentioned, the best result is obtained for electrodes with 20 wt% PTFE. Hydrophobic
polymer contents of greater than 20 wt% (with respect to carbon) would contribute to
ohmic losses caused by the non-conducting PTFE.
On the other hand, PTFE contents less than 20 wt% would allow better electric
conductivity, but may limit the access of reactant gases to the reaction sites, resulting in a
lower performance due to greater diffusion and activation losses. Furthermore,
inadequate PTFE content would allow the retention of water inside the MEA, creating a
barrier, which limits the transport of gases to and products away from the reaction sites
and retarding half-cell reaction rates. In addition, liquid water can cover the surface of
active catalyst sites required for half-cell reactions and hinder hydrogen oxidation at the
anode, and more importantly, oxygen reduction at the cathode.
Figure 8-5 Fuel cell potential with varying PTFE content at different current densities
operated at a cell temperature of 50 °C in H2/Air with a platinum loading of 0.3 mg cm-2
per electrode; fully humidified fuel and oxidant with stoichiometries of 1.2 and 2.5,
respectively
141
As mentioned previously, the slight increase in the voltage at high current densities when
the PTFE content is increased from 20 to 30 wt% occurs in the mass-transport limited
region (i > 0.9 A cm-2
), and is due to better GDL water management at higher PTFE
content. Most fuel cells, however, are operated in the ohmic region, where the operating
voltage for a single cell is about 0.6-0.8 V. Fig. 8-5 clearly shows that for all practical
operating conditions, 20 wt% PTFE content exhibits the best performance.
8.1.3 Influence of MPL Loading on Cell Performance
Extensive experimental work has been performed and reported by many researchers on
the composition of the diffusion layer and the type of carbon powder utilized [9-11].
However, little attention has been directed at the effect of microporous layer (MPL)
loading or thickness on the electrode flooding level and, ultimately, on fuel cell
performance. It is apparent from Fig. 8-6 that thin MPLs (i.e., lower loadings) are very
sensitive to liquid water accumulation. The pore volume that is required to conduct fluid
transport inside the MEA—fuel and oxidant gases to the catalyst layers and liquid water
away from the catalyst layers—is smaller for thinner MPLs. Therefore, when liquid water
enters the GDL at a given rate, a thinner MPL is expected to have a higher liquid water
saturation level than a thicker one, resulting in less available pore volume for fluid
transport. Conversely, a thicker MPL is capable of retaining more liquid water and still
have enough free pores to transport fluids to and from the catalyst layers. However, as
discussed above, excessive PTFE loading, which results in thicker MPLs, reduces the
electronic pathways, making it more difficult for electrons to leave the GDL, thereby
lowering overall cell performance.
Figure 8-6 indicates that the best results are obtained for electrodes with 1.5 mg PTFE-C
cm-2
. Microporous layers with less than 1.0 mg PTFE-C cm-2
exhibit the worst cell
performance due to lack of sufficient hydrophobic polymer in the diffusion layer. This
contributes to diffusion losses since most pores in this layer are filled with liquid water,
thereby impeding gas transport to and from the active sites in the catalyst layer. There
also is the possibility of the catalyst sites themselves being covered with liquid water
since the cell now operates under flooded conditions.
142
Figure 8-6 Influence of diffusion layer loading on cell performance operated at a cell
temperature of 50 °C in H2/Air with a platinum loading of 0.3 mg cm-2
per electrode;
fully humidified fuel and oxidant with stoichiometries of 1.2 and 2.5, respectively
Accordingly, even if the reactants can diffuse through the GDL and reach the catalyst
layer, they will have to dissolve in a water film and diffuse to the catalyst layer; this will
slow down the reaction rates. On the other hand, a thicker MPL may pose other
limitations, such as creating a longer pathway for diffusion of gases to and from the
catalyst layer as well as a higher electrical resistance due to the longer pathways for
electrons to reach the external circuit. It is clear from this series of experiments that the
gas permeability of the MPL is a major factor influencing electrode performance.
Figure 8-7 presents SEM micrographs of the diffusion layers. Examination of these
images, obtained at the same magnification, shows that Vulcan XC-72 particles are
covered by a PTFE film and that some of the macropores are blocked by this film,
especially at higher PTFE content. The extent of this coverage is directly proportional to
the amount of PTFE present in the diffusion layer. At low PTFE content—around 10
wt%—although the diffusion layer shows high electronic conductivity, it is not
sufficiently hydrophobic, and cell performance drops because of mass transport
limitations due to water accumulation inside the MEA. On the other hand, when the
concentration of PTFE in the diffusion layer is increased to 40 wt% or greater, a large
143
percentage of the carbon fibers are covered with a non-conducting material that is
resistant to the flow of electrons, leading to a marked drop in cell performance. Aside
from the apparent surface coverage of the carbon fibers by the hydrophobic polymer,
internal coverage also will be higher due to the migration of PTFE inside the diffusion
layer as the PTFE content increases. Accordingly, a delicate balance must be maintained
to maximize performance.
(a) (b)
(c) (d)
Figure 8-7 Surface morphology of MPLs containing Vulcan XC-72 and (a) No PTFE;
(b) 10 wt% PTFE; (c) 30 wt% PTFE; (d) 50 wt% PFE
144
8.2 Effects of Carbon Powder Characteristics on Cell Performance
It has been reported that the physical properties of the carbon powder in the MEAs of
low-temperature fuel cells can significantly alter the chemical and physical characteristics
of both the gas diffusion and catalyst layers [602]. In the case of the catalyst layers,
carbon has been established as the best support candidate on account of its high effective
surface area, good electrical conductivity, adequate surface hydrophobicity, good
mechanical and chemical stability in harsh environments and relatively low cost [603]. In
addition, the carbon pore structure can be modified to create a wide array of pore size
distributions needed for various applications [604]. Granular, powder-activated carbons
and carbon blacks have been extensively used as catalyst supports; however, there has
been a growing interest in the use of other types of carbon materials such as activated
carbon fibers, nanofibers and nanotubes. A comprehensive review of such materials for
use as catalysts or catalyst supports has recently been published [605].
In this part of the study, a large number of GDEs were prepared using six different
carbon/graphite materials: Vulcan XC-72, Shawinigan Acetylene Black (SAB), Ketjen
Black DJ-600, Black Pearls 2000, Asbury 850, and Mogul L. Important physical
characteristics of the above materials are listed in Table 8-1. It is important to note that
the list of carbon materials used for fabrication of carbon-supported catalyst and MPLs is
long and, in addition to carbon blacks and graphite, includes active carbons and active
carbon fibers, glassy carbon, pyrolytic carbons, fullerenes, and nanotubes [603].
A large number of MEAs were fabricated according to the method explained in section 7.
Both anodes and cathodes of all MEAs were prepared in the same manner with the type
of carbon/graphite used in the diffusion layer being the primary variable. Several MEAs
were fabricated with different carbon loadings to evaluate the impact on fuel cell
performance. All MEAs were tested in a 5-cm2 fuel cell with hydrogen and air supplied
to the cell as fuel and oxidant, respectively.
Porosimetry experiments also were carried out on several electrodes before catalyst
deposition to characterize the diffusion layers based on the type of carbon or graphite
used in the MPL. The pore distribution patterns of several MPLs fabricated using five
145
Table 8-1 Manufacturers’ data: characteristics of different carbon powders in GDLs
Property SAB Vulcan
XC-72
Ketjen Black
DJ-600
Black Pearls
2000
Asbury
850
Mogul L
Source
Acetylene
Oil-furnace
Specific Surface
Area (m2 g
-1)
64
252
1300
1500
13
140
Area of Mesopores
(m2 g
-1)
64
177
1230
1020
Total Pore Volume
(cm3 g
-1)
0.2
0.63
2.68
2.56
Micropore Volume
(cm3 g
-1)
0.0
0.037
0.029
0.208
Avg Pore Diameter
(nm)
14.4
15.9
9.45
20.6
> 30
>45
Primary Particle
Diameter (nm)
42
20 - 30
35 - 40
10 - 15
Projection Area of
Aggregates (m2)
0.52
0.14
Crystallite Size
(nm)
4.1
2.0
1.4
1.1
different carbon and graphite materials are shown in Figure 8-8. Pore distribution curves
are arbitrarily divided into three regions: less than 0.05 m, 0.05 m to 1.00 m and
greater than 1.00 m. It is interesting to note that the pore size distributions in the first
region are similar for almost all types of carbon and graphite. The differences begin to
appear when the pore radii increase and reach the second region—0.05 m to 1.00 m—
and significant differences become apparent when the pore radii enter the third region—
greater than 1.00 m.
146
Figure 8-8 Pore volume distribution of several GDLs prepared using five different types
of carbon and graphite
Figures 8-9 shows the cell performance of a number of MEAs prepared with different
carbon/graphite in the microporous layer with a constant carbon loading of 1.5 mg cm-2
.
The cell temperature was maintained at 50 C, while the temperatures of the incoming
hydrogen gas and air were kept at 5 C higher than the cell temperature. At low current
densities—less than 100 mA cm-2
—the effect of carbon type on fuel cell performance is
negligible. As the current density passes 200 mA cm-2
, marked differences become
noticeable. At current densities higher than 500 mA cm-2
, MEAs with SAB and Vulcan
XC-72 show better performance than the other four, and at current densities higher than
600 mA cm-2
(diffusion-limited region), MEAs with SAB outperform those with Vulcan
XC-72.
One of the primary differences between these carbon and graphite materials is their
specific surface area, ranging from 13 m2 g
-1 for Asbury 850 to 1500 m
2 g
-1 for Black
Pearls 2000. Upon a closer investigation, however, no correspondence between specific
surface area and cell performance is observed. A better correlation, however, is observed
between total macropore volume and cell performance.
147
Figure 8-9 Influence of carbon type in the MPL on cell performance of a H2/Air fuel cell
operated at a cell temperature of 50 °C with a platinum loading of 0.3 mg cm-2
per
electrode; fully humidified fuel and oxidant with stoichiometries of 1.2 and 2.5,
respectively
By examining Table 8-1 and Fig 8-9, a noticeable trend is revealed: at high current
densities the cell voltage increases with increasing macropore (> 1 µm diameter) volume.
In other words, cell performance increases as macropore volume in the MPL increases.
Shawinigan acetylene black has the highest macropore volume of all types of
carbon/graphite investigated in this study and delivered the best performance when tested
in a fuel cell, while Mogul L has the smallest volume of macropores, and, accordingly
exhibited the worst cell performance when tested in the same fuel cell under identical test
conditions. This difference in cell performance is most pronounced at higher current
densities, as can be seen from Figure 8-10. At high current densities (the diffusion-
controlled region) the removal of water from the cell becomes critical, and failure to do
so will result in a sharp decrease in cell performance, primarily due to formation and
stagnation of water inside the pores of the MPL as well as the GDL. This will, in turn,
hinder the transport of gases to and from the catalyst layer, lowering cell performance.
The aforementioned explanation is in agreement with the pore volume distribution of the
various carbon/graphite shown in Figure 8-8.
148
Figure 8-10 Cell performance as a function of MPL macropore volume at four
different current densities (H2/Air fuel cell with a cell temperature of 50 °C; fully
humidified fuel and oxidant with stoichiometries of 1.2 and 2.5, respectively)
As previously mentioned, pore distribution curves are conventionally divided into three
regions: less than 0.05 m, 0.05 m to 1.00 m and greater than 1.00 m, identified as
primary, secondary and tertiary (macro) pores, respectively. SAB has the smallest pore
volume in the primary range (micropores), while possessing the highest pore volume in
the tertiary range (macropores). On the other hand, a significant portion of the pores in
Ketjen Black DJ-600 is in the micro range—primary pores. Such pores are more prone to
flooding since liquid water can easily fill them, blocking the passage of reactants and
products to and from the catalyst layer. This is amplified in the cathode of an MEA at
high current densities, where the rate of water generation is high.
The results also might be explained in terms of capillary condensation theory. It has long
been known that if a capillary is immersed in a liquid capable of wetting its walls, the
liquid rises in the capillary, forming a meniscus that is concave toward the vapour phase
[606]. The vapour pressure over this meniscus is often lower than the vapour pressure of
the liquid by an amount equal to pressure exerted by the liquid in the capillary [606]. A
mathematical expression, known as the Young-Laplace equation, is often used to
149
calculate the vapour pressure over a capillary. The difference in pressure between the two
sides of the (spherical) meniscus is:
r
P2
(8-1)
Where, ΔP is the pressure difference between the two sides of a meniscus in Pa , γ is
surface tension of the liquid in N m-1
, and r is the radius of the capillary in m. Cylindrical
capillaries have been assumed in deriving the above expression. It can readily be seen
that as the radius r of the capillary decreases, the difference between normal and
equilibrium pressure increases, causing the liquid to condense at pressures far below the
normal vapour pressure.
A simple explanation of the capillary condensation theory is necessary to fully
understand the influence of total porosity and micropores in the various carbon and
graphite materials employed to prepare MPLs. In its simplest form, where a flat solid
surface adsorbent is in contact with a gas, monomolecular adsorption is the dominant
process occurring as the pressure of the gas increases. This will continue until the surface
of the adsorbent is covered by a single layer of gas adsorbate. The formation of additional
layers requires an increase in pressure. However, if the adsorbent contains pores that are
at least several times greater in width than the diameter of the adsorbate molecules, even
more layers of adsorbate molecules will be adsorbed on the walls of the adsorbent. This
happens because in such pores under pressure, in addition to multimolecular layer
formation, condensation of the gaseous molecules also will occur. As the gas pressure is
further increased, the thickness of the multimolecular layer also is increased, causing
adjacent multimolecular layers to join and form a meniscus of condensed adsorbate. This
will initially take place inside the pores with the smallest cross-section and then will
move along to other pores forming additional menisci [607]. If the adsorbate molecules
are capable of wetting the adsorbent walls, the resulting meniscus is concave, and
molecules of adsorbate are readily condensed on the meniscus at pressures lower than the
saturation vapor pressure [606, 607]. The molecules in a concave surface are more tightly
held together due to a larger number of neighboring molecules than on a flat surface at
the same temperature. This lowers the equilibrium vapour pressure of a gas over a
150
concave surface, compared with a flat surface, and speeds up the condensation process
[607].
According to this theory, in PEMFCs the condensation of water inside the pores of the
MPLs and GDLs occurs below the actual saturation vapour pressure, and will occur
sooner in smaller pores. On this basis, the superior performance of SAB in MPLs of low-
temperature fuel cells can readily be explained in terms of its pore distribution. SAB
possesses the highest percentage of macropores among all types of carbon and graphite
investigated in this study, while having the least amount of micropores. Equation (8-1)
shows that the difference between the normal and equilibrium vapour pressures is
inversely proportional to the radius of the capillary; consequently, small pores will
experience more adsorbate condensation than large pores. Conversely, higher capillary
radii ensure the availability of free and clear passages inside the MPL for transport of
gases to and from the catalyst layer. Thus carbon materials containing a significant
amount of micro- and meso-pores, such as Ketjen Black and Black Pearls 2000, will
undergo condensation of water sooner, restricting the flow of gases and leading to
inferior cell performance. However, even the most widely used carbon material in
PEMFCs—Vulcan XC-72—also contains a significant number of micropores, which will
adversely influence cell performance at high current densities.
The importance of gas transport inside both the MPL as well as the GDL can be
explained using the standard equation for the diffusion-limited current density:
xx cDAFni lim (8-2)
where n is the number of electrons released by the half-cell reaction, F is Faraday’s
constant, A is the effective area of the microporous or gas diffusion layer, Dx is the
diffusion coefficient of species x inside the GDL or MPL, cx is the concentration of
species x before entering the GDL/MPL and
is the thickness of the GDL/MPL layer.
Thus, for the cathode side of an MEA operating under flooding conditions equation (8-2)
shows that ilim decreases owing to the lower diffusion coefficient of oxygen in water
compared with air. The diffusion coefficient of oxygen in water can be estimated using
151
the following correlation developed by Wilke and Chang [608], which is based on
Stokes-Einstein equation:
))((
104.7
22
22
22
2/1
8
OOH
OHOH
OHOV
MTD
(8-3)
where OHOD22
is the diffusion coefficient of oxygen in water (cm2 s
-1)
T is the absolute temperature of the system (K)
H2O is a parameter used to describe the solvent (= 2.26 for water (ref.
609))
M H2O is the molar mass of water (g mol-1
)
H2O is the viscosity of water (cp)
VO2 is the molar volume of oxygen, which is 25.6 cm
3 mol
-1 at STP (ref.
610)
The diffusion coefficient of oxygen in air can be estimated using the following
expression [609]:
j
i
iTiPjTjP
TD
TD
i
j
j
i
BABAT
T
P
PDD
2
3
)()( ,, (8-4)
where D(A-B) is the diffusion coefficient of the binary pair (cm2 s
-1)
D /T is the collision integral for molecular diffusion
P (Pa) and T (K) are the pressure and temperature of the components,
respectively
i and j are reference and modeled conditions, respectively
It should be noted that
D /T is a function of
T AB , where
is the Boltzmann’s
constant and
AB is the energy of molecular interaction. For binary mixtures of oxygen
with carbon dioxide, nitrogen and water vapour,
T AB varies between 1.3 to 3.5 over
the temperature range of 0 C to 80 C [611].
Based on equations (8-3) and (8-4), the diffusion coefficients of oxygen in water and air
at several temperatures are presented in Tables 8-2 and 8-3 [611, 612]. Tables 8-2 and
8-3 show that the effect of temperature on the diffusion coefficient of oxygen in water is
152
more significant than in air. Increasing the temperature from 20 to 40 C increases the
diffusion coefficient of the former by more than 60% and the latter by only about 25%.
This will have important consequences for PEMFCs containing carbon with significant
amounts of micropores in their GDLs and/or MPLs. At high current densities, where the
rate of water generation at the cathode reaches its peak, the micropores in both GDL and
MPL tend to clog quickly, restricting the flow of gases to and from the catalyst layer. The
problem is amplified if the cell is operated at low temperatures, because of the decrease
in
DO2.
Table 8-2 Diffusion coefficient of oxygen in water at different temperatures [611, 612]
Temperature
(C)
Viscosity of Water
(cp)
DO2
(10-5
cm2 s
-1)
20 1.002 1.97
40 0.653 3.24
50 0.547 3.99
60 0.467 4.82
Table 8-3 Diffusion coefficient of oxygen (as a binary mixture) in air at atmospheric
pressure [613]
Binary Mixture Temperature
(C)
A
DO2
(cm2 s
-1)
O2 – CO2
20
40
146 0.153
0.193
O2 – H2O(v) 20
40
201 0.240
0.339
O2 – N2 20
40
102 0.219
0.274
153
To sum up, equation (8-2) indicates that the limiting current density is directly
proportional to2OD . Furthermore, the oxygen diffusion coefficient in air is three to four
orders of magnitude greater than in water. Consequently, MPLs with a small fraction of
micropores and a large fraction of macropores are best suited for applications requiring
high current densities and lower temperature operation.
A series of experiments was carried out to further determine the influence of carbon
loading in the MPL on cell performance. Different amounts and types of carbon or
graphite were applied to both the anodes and cathodes of a number of MEAs. The
experimental results are presented in Table 8-4, which shows that membrane-electrode
assemblies employing SAB, Vulcan XC-72, Ketjen Black and Black Pearl delivered the
best performance with a carbon loading of 1.5 mg cm-2
in both H2-Air cells as well as
H2-O2 cells. The cell performance fell sharply as the carbon in the microporous layer
further increased to 3.0 mg cm-2
. As previously discussed, increasing the carbon loading
beyond 1.5 mg cm-2
causes cell performance to decrease, primarily because of the
creation of a longer pathway for reactant gases to travel from the GDL to the catalyst
layer via the MPL, and similarly, for products, especially liquid water, to exit the MEA.
However, a somewhat different trend was observed with Asbury 850 and Mogul L, for
which performance slightly improved as the loading was increased from 1.0 to 3.0 mg
cm-2
, but leveled off at loadings greater than 3.0 mg cm-2
. The slight improvement in cell
performance for MEAs with higher-than-normal loadings of Asbury 850 is attributed to a
better coverage of the electrode surface with increased loading. At lower loadings, such
as 1.5 mg cm-2
, SAB shows a homogenous surface with randomly distributed micro
channels. In contrast, large flaky agglomerates and non-homogenous surfaces are
observed from micrographs of MPLs prepared with Asbury 850 and Mogul L at the same
loadings.
154
Table 8-4 – Influence of carbon / graphite loading in MPLs on cell performance
Sample Carbon Type Carbon Loading Oxidant Max. Power
(mg cm-2
) (mW cm-2
)
A01 SAB 1.0 Air 273
A02 SAB 1.0 Oxygen 771
A03 SAB 1.5 Air 286
A04 SAB 1.5 Oxygen 806
A05 SAB 3.0 Air 229
A06 Vulcan XC-72 1.0 Air 251
A07 Vulcan XC-72 1.0 Oxygen 744
A08 Vulcan XC-72 1.5 Air 266
A09 Vulcan XC-72 1.5 Oxygen 782
A10 Vulcan XC-72 3.0 Air 206
A11 Ketjen Black 1.0 Air 213
A12 Ketjen Black 1.5 Air 226
A13 Ketjen Black 1.5 Oxygen 698
A14 Ketjen Black 2.0 Air 225
A15 Ketjen Black 3.0 Air 204
A16 Black Pearl 1.0 Air 200
A17 Black Pearl 1.5 Air 221
A18 Black Pearl 1.5 Oxygen 692
A19 Black Pearl 2.0 Air 225
A20 Black Pearl 3.0 Air 194
A21 Asbury 850 1.0 Air 162
A22 Asbury 850 1.5 Air 169
A23 Asbury 850 2.0 Air 177
A24 Asbury 850 3.0 Air 196
A25 Asbury 850 3.0 Oxygen 554
A26 Asbury 850 5.0 Air 193
A27 Mogul L 1.0 Air 149
A28 Mogul L 1.5 Air 152
A29 Mogul L 2.0 Air 168
A30 Mogul L 3.0 Air 174
A31 Mogul L 3.0 Oxygen 521
A32 Mogul L 5.0 Air 170
It was noted that an increase in MPL carbon loading with Mogul L beyond 3.0 mg cm-2
did not result in better cell performance. The existence of such large flakes is indicative
of incomplete coverage of the carbon fibers of the GDL, which leads to the creation of
non-homogenous surfaces such as those seen in the micrographs of Figure 8-11. This will
155
(a) (b) (c)
Figure 8-11 SEM images of microporous layers of a number of MEAs prepared by (a)
SAB, х 500 (b) Vulcan XC-72, х500 (c) Asbury 850, х500.
adversely influence the movement of reactant gases through the MPL and, equally
important, the transport of product water away from the MEA interior via the MPL.
Increasing of carbon (or graphite) content in the MPL results in a better coverage of the
GDL and, consequently, a better cell performance.
8.3 Nafion® Impregnation
8.3.1 Impregnation Time
Nafion®
impregnation was achieved by either floating or brushing, as described in section
7.3. The Nafion® film should be gas tight and must be non-electron conducting.
Consequently, sufficient Nafion®
must be applied on the carbon electrode surface. First,
a series of experiments was performed to determine the optimum impregnation time
based on the floating method. Table 8-5 shows the difference between 30 s, 60 s, 1 h,
and 24 h Nafion® impregnation times using the above method. The results indicate that
beyond about one minute, longer contact with Nafion®
solution does not significantly
affect the Nafion® loading. The results are also presented graphically in Figure 8-12. To
prepare GDEs with non-electron conducting properties on one side using the brushing
technique, several layers of Nafion® solution, ranging from one to fourteen applications,
were applied to one side of the GDE. The results of these experiments are presented in
Tables 8-6 and 8-7, which show that somewhat higher Nafion® loadings are obtained by
employing the brushing method.
156
Table 8-5 Effects of impregnation time on Nafion® loading utilizing the floating method
Impregnation Mass of the Electrode Nafion Average Literature
Time Before After Difference Loading Nafion Value
Impregnation Impregnation Loading
(g) (g) (g) (mg/cm2) (mg/cm
2) (mg/cm
2)
30 s 0.12695 0.14202 0.01507 1.57
30 s 0.13046 0.14581 0.01535 1.60
30 s 0.12523 0.13976 0.01453 1.51 1.57 1.51*
30s 0.11856 0.13416 0.0156 1.62
60 s 0.12520 0.14426 0.01906 1.98
60 s 0.12464 0.14373 0.01909 1.98
60 s 0.12073 0.13918 0.01845 1.92 1.97
60 s 0.13147 0.15050 0.01903 1.98
1 h 0.1152 0.13641 0.02121 2.20
1 h 0.11957 0.14132 0.02175 2.26
1 h 0.12564 0.14658 0.02094 2.18 2.22
1 h 0.13044 0.15206 0.02162 2.25
24 h 0.12651 0.14973 0.02322 2.41
24 h 0.13147 0.15533 0.02386 2.48
24 h 0.11783 0.14081 0.02298 2.39 2.43 2.5*
24 h 0.12460 0.14815 0.02355 2.45
* N.R.K. Vilambi, E.B. Anderson, and E.J. Taylor, U.S. Patent 508144 (Jan. 28, 1992)
Figure 8-12 The impact of impregnation time on Nafion® loading
157
Table 8-6 Nafion® impregnation of GDEs utilizing floating and brushing techniques
Method Mass (g)
Original 1st
Nafion 2nd
Nafion 3rd
Nafion 4th
Nafion 5th
Nafion
Applic. deposited Applic. deposited Applic. deposited Applic. deposited Applic. deposited
Floating 0.12520 0.14466 0.01946 0.16331 0.01865 0.18010 0.01679 0.19740 0.01730 0.21390 0.01650
Floating 0.12464 0.14373 0.01909 0.16148 0.01775 0.18170 0.02022 0.19505 0.01335 0.20880 0.01375
Floating 0.11856 0.13463 0.01607 0.15371 0.01908 0.17120 0.01749 0.18797 0.01677 0.20030 0.01233
Floating 0.13147 0.15050 0.01903 0.17247 0.02197 0.18634 0.01387 0.20314 0.01680 0.21899 0.01585
Floating 0.12073 0.13918 0.01845 0.15918 0.02000 0.17469 0.01551 0.18992 0.01523 0.20481 0.01489
Floating 0.12033 0.13820 0.01787 0.15389 0.01569 0.17259 0.01870 0.18990 0.01731 0.20002 0.01012
Floating 0.12619 0.15020 0.02401 0.17400 0.02380 0.19429 0.02029 0.21293 0.01864 0.23661 0.02368
Floating 0.11855 0.13920 0.02065 0.15926 0.02006 0.18214 0.02288 0.21010 0.02796 0.23190 0.02180
Brushing 0.11758 0.14349 0.02591 0.17214 0.02865 0.18626 0.01412 0.20136 0.01510 0.21606 0.01470
Brushing 0.12023 0.14349 0.02326 0.16722 0.02373 0.18186 0.01464 0.19708 0.01522 0.21147 0.01439
Brushing 0.11946 0.14225 0.02279 0.16360 0.02135 0.17898 0.01538 0.19474 0.01576 0.21018 0.01544
Brushing 0.12333 0.14494 0.02161 0.16177 0.01683 0.17748 0.01571 0.19445 0.01697 0.21042 0.01597
Table 8-7 Nafion® impregnation with 1 to 14 applications
No of Nafion Cumulative Amount of Nafion Deposited (mg/cm2)
Applications Floating Brushing
1 2.01 (0.06)* 2.43 (0.04)
2 4.05 (0.09) 4.78 (0.07)
3 6.09 (0.08) 7.05 (0.14)
4 7.95 (0.11) 9.17 (0.12)
5 9.63 (0.12) 11.22 (0.11)
6 11.31 (0.19) 13.19 (0.18)
7 12.87 (0.26) 14.89 (0.22)
8 14.22 (0.23) 16.46 (0.24)
9 15.41 (0.25) 17.79 (0.29)
10 16.64 (0.31) 19.05 (0.27)
11 17.71 (0.42) 20.23 (0.38)
12 18.66 (0.39) 21.36 (0.44)
13 19.51 (0.54) 22.45 (0.52)
14 20.28 (0.60) 23.46 (0.63)
* Standard deviations are shown in brackets
As shown in Figure 8-13, for the first 5-6 applications, the amount of deposited Nafion®
increases linearly with the number of applications, after which the slope decreases to a
158
0.00
5.00
10.00
15.00
20.00
25.00
0 5 10 15
Number of Nafion Coatings
Mas
s of
Naf
ion
(mg/
cm2 )
Floating Method
Brushing Method
Figure 8-13 Effect of number of Nafion® applications on total Nafion
® loading
somewhat lower value. This is probably due to the fact that during the first 5-6
applications, the Nafion® solution rapidly penetrates into the region of the carbon
substrate near the surface, effectively sealing it off to further penetration. After the sixth
application, the Nafion® layer begins to build up on the surface and its thickness starts to
grow.
Scanning electron microscopy was used to examine the microstructure of a number of
carbon electrodes. Figure 8-14(a) shows the surface microstructure of untreated carbon
paper, while Figures 8-14(b)-(d) show the surface microstructure of carbon electrodes
treated with 1, 5, and 10 Nafion® applications (using floating method), respectively, in
which the carbon electrodes were air cured for 12 h prior to the next application. From
these micrographs, it is evident that initially Nafion® covers the surface, but there still
remain big channels on the surface even after 5 applications. However, after 10
applications, these channels begin to disappear, and by the 14th
application they are
hardly visible, as seen from Figure 8-15(a), confirming that after the sixth application
Nafion®
starts to build on the surface of the electrode after sealing off most of the gaps.
As the number of applications increases, more Nafion® covers the surface, until finally a
uniform Nafion® film is formed on the carbon electrode. This is confirmed by Fig. 8-
15(b), which is a scanning electron micrograph of the cross-section of a carbon electrode
159
with 14 Nafion®
applications, and indicates that the thickness of the Nafion® film is about
50-60 µm.
Figure 8-14 (a) Untreated carbon electrode, ×130; (b) one Nafion®
application, ×130 ;
(c) five Nafion® applications, ×153; (d) 10 Nafion
® applications, ×130; all micrographs
show the top surface of the GDE; floating method used to load Nafion®
160
Figure 8-15 (a) Micrograph of the surface of a carbon electrode with 14 Nafion®
applications, ×130; (b) cross section, ×130
8.3.2 Nafion® Ion-Exchange Capacity
The total capacity of an ion exchange material is the number of ionic sites per unit weight
or volume of resin. The dry weight total capacity is usually expressed in milliequivalents
per gram of dry resin in the H+ form. Ion-exchange capacities (IECs) of several Nafion
®-
impregnated samples were determined following the procedure outlined in section 7.3. In
addition, the IEC of pure Nafion® film also was determined for comparison purposes.
The IEC of the samples impregnated with Nafion® was found to be lower than both
commercial Nafion® membrane and the Nafion
® solution used for impregnation. This
may partly be attributed to the incomplete conversion of H+
to Na+ form inside the
substrate prior to titration or perhaps to some elements in the carbon binding with some
of the exchange sites. The results are tabulated in Table 8-8.
Carbon Deposited
Nafion®
161
Table 8-8 Ion exchange capacity data for different samples
Sample Dry Mass Titrant Vol. IEC Avg. IEC
(g) 0.05 M NaOH (mL) (meq/g)* (meq/g)
Nafion Membrane (117) 0.37520 6.69 0.910
Nafion Membrane (117) 0.35893 6.43 0.914 0.908
Nafion Membrane (117) 0.36841 6.51 0.902
Air-Dried Nafion Solution 0.19651 3.44 0.893
Air-Dried Nafion Solution 0.21048 3.72 0.902 0.896
Air-Dried Nafion Solution 0.20954 3.67 0.894
Nafion-impregnated Sample 0.12161 1.89 0.793
Nafion-impregnated Sample 0.11340 1.67 0.751
Nafion-impregnated Sample 0.14032 1.63 0.593
Nafion-impregnated Sample 0.14050 1.76 0.639 0.689
Nafion-impregnated Sample 0.13826 1.78 0.657
Nafion-impregnated Sample 0.12173 1.65 0.691
Nafion-impregnated Sample 0.13179 1.80 0.697
* meq per gram of dry H+ form
8.4 Effects of Different Types of Substrates on Cell Performance
8.4.1 Influence of Substrate Thickness and other Physical Parameters
A number of MEAs were fabricated using seven carbon substrates with different physical
properties. All other parameters, including diffusion layer loading, PTFE content and
catalyst and Nafion® loadings were kept constant. In addition, both the anode and cathode
of each MEA were made from the same type of carbon substrate. The physical
characteristics of these substrates are reported in Table 8-9.
Figs. 8-16 and 8-17 show that MEAs prepared with ETEK-Elat from BASF and TGP-H-
090 from Toray Industries, Inc. exhibited the best results when fed with either pure
oxygen or air as oxidant and pure hydrogen as fuel. All experiments were performed in a
single 5-cm2 fuel cell running at atmospheric pressure and a cell temperature of 50 C
without external humidification. MEAs fabricated from Toray’s TGP-H-030 performed
the worst. .
162
Table 8-9 Physical properties of a number of different gas diffusion layers
Property Unit ETEK-Elat Toray Toray Toray Toray Stackpole Ballard Avcarb
LT 1200-W TGP-H-030 TGP-H-060 TGP-H-090 TGP-H-120 PC-206 1071 HCB
Thickness µm 275 110 190 280 370 330 380
Bulk Density* g cm-3
0.727 0.4 0.44 0.44 0.45 0.42 0.31
Porosity*
% 78 80 78 78 78 > 70 > 50
Porosity (experimental, Porosimetry) Surface Roughness*
%
µm
79.9
--
81.6 8
80.4 8
79.5 8
77.1 8
--
--
86.0
--
Gas Permeability* ml min-1
> 900 2500 1900 1700 1500 > 1000 > 700
Electrical Resistivity*
through plane mΩ.cm 410 80 80 80 80 -- 110
in-plane mΩ.cm -- -- 5.8 5.6 4.7 -- 9
Thermal Conductivity*
through plane (room temp) W m-1
K-1
-- -- 1.7 1.7 1.7 -- --
in-plane (room temp) W m-1
K-1
-- -- 21 21 21 -- --
in-plane (100 °C) W m-1
K-1
-- -- 23 23 23 -- --
* Indicates Specification from Manufacturer
163
Figure 8-16 Polarization curves for different substrates in H2/O2 with a platinum loading
of 0.3 mg cm-2
per electrode, Nafion® 112, cell temperature of 50 °C and fully humidified
fuel and oxidant with stoichiometries of 1.2 and 1.5, respectively
Figure 8-17 Polarization curves for different substrates in H2/Air with a platinum loading
of 0.3 mg cm-2
per electrode, Nafion® 112, cell temperature of 50 °C and fully humidified
fuel and oxidant with stoichiometries of 1.2 and 2.5, respectively
164
Figure 8-16 compares the cell performance of MEAs made from different substrates in a
hydrogen-oxygen fuel cell. At low current densities (less than 300 mA cm-2
) all MEAs
perform equally well; however, at current densities higher than 300 mA cm-2
, the thickest
and the thinest GDLs from Toray Industries Inc.—TGP-H-120 (370 µm) and TGP-H-030
(110 µm)—start to lag behind the others. The differences in cell performance become
very apparent when the current density reaches 1500 mA cm-2
. At this current density, the
MEAs containing the above two substrates are operating under flooded conditions. On
the other hand, MEAs fabricated from ETEK-Elat carbon cloth and TGP-H-090 and PC-
206 carbon papers exhibit satisfactory performance even at high current densities. The
MEA fabricated from the carbon paper from Ballard performed equally well until about
1000 mA cm-2
, after which the cell voltage gradually declined followed by a sharp
decrease beyond 1800 mA cm-2
. A similar trend also is observed in Figure 8-17, where
air is employed as the oxidant. However, when air was used as oxidant, the thickest
substrate—TGP-H-120—exhibited a better performance compared with both TGP-H-030
and TGP-H-060. This was surprising since the lower partial pressure of oxygen in air
requires shorter pathways from the bipolar plate to the catalyst layer to minimize pressure
drop within the channels of GDL. Also, a thinner GDL exhibits better electronic
conduction owing to the shorter paths that electrons must traverse from the catalyst layer
to the bipolar plates. On the other hand, a thicker GDL, provided that all other parameters
are unchanged, provides more macropores for diffusion of reactant gases and
transportation of water to and from the catalyst layer. This is undoubtedly important
when the cell is operated at high current densities, where the rates of oxygen
consumption and water generation are high. As expected, the cell voltage for all MEAs
dropped when oxygen was replaced with air, on account of the lower partial pressure of
oxygen in air. The differences in cell performance with respect to the various substrate
materials can be understood by referring to the physical characteristics of each carbon
cloth or paper given in Table 8-9.
It is important to understand the primary functions of the GDL prior to a full discusion of
why and how the differing physical properties of this layer influence the performance of
an MEA. A GDL is a layer of porous, electronically conductive and mechanially and
165
chemically stable material that is strategically placed between the catalyst layer and the
flow field both on the anode and cathode sides of a PEM fuel cell. Although most
attention has been paid to the optimization of the catalyst and electrolyte layers, GDLs
also provide a number of important functions, and their optimization can significantly
improve cell performance.
Thus, they facilitate the transport of reactant gases to the catalyst layers; act as an
electronic conductor between the catalyst layers and biopolar/end plates; serve as a
thermal conductor by effectively removing heat from the inside of MEAs; aid in water
management of the MEA by transporting excess water from the catalyst layers to outside
the cell; provide mechanical supports for electrolyte and catalyst layers; and minimize
electronic contact resistance by ensuring good electrical and physical contact between the
GDL and the catalyst layer on one side, and the GDL and the flow-field plate on the other
side. In some instances, GDLs also act as substrates for the deposition of the
electrocatalyst layer before MEA fabrication.
In view of the above functions, it becomes apparent that a number of the material
properties required are inherently diametrically opposite in nature. For example, the
porosity of the GDL needs to be high enough to ensure effective transport of reactant
gases to the catalyst layers; however, the porosity cannot be so high that the through-
plane electronic conductivity of the material is compromised. Furthermore, GDLs must
be able to withstand compressive forces while maintaining mechanical integrity. This is
especially important in fuel cell stacks where the compression is relatively high to ensure
stack integrity, low electrical contact resistance and adequate gas tightness. However,
porosity levels tend to decrease as compression is increased. Another important function
of the GDL is the effective removal of excess water from inside the MEA; this is
particulary critical at the cathode at high current densities, where the rate of water
generation is high and, if not effectively removed, causes the cell to operate under
flooded conditions, which restrict the flow of reactant gases to the catalyst layers. GDLs
often are treated with a hydrophobic polymer to alleviate this problem; however, all
hydrophobic polymers are non-electronic conductors. Accordingly, their content must be
166
optimized to facilitate the movement of water within the MEA, while maintaining good
electronic conductivity. Additionally, porosity decreases with increasing hydrophobic
content.
The thickness of a typical GDL ranges from 100 to 400 m, with the optimal thickness
being determined by several parameters, including the effective transport of reactants and
products to and from the catalyst layer, through-plane electronic conductivity, and pore
stability under compression. Typical porosity vlaues for GDLs vary from 70% to 90%
(by volume), depending on operational conditions. Pore stability and resilience increase
with GDL thickness, permitting higher compression to be applied; however, the transport
properties of GDLs are often improved when the thickness is decreased, due to shorter
pathways for reactants and products. All these variables must be closely examined and
controlled when optimizing GDLs in fuel cells.
When examining the polarizaton curves shown in Figures 8-16 and 8-17 in conjunction
with the data presented in Table 8-9 (no PTFE or MPL), no apparent correspondence
appears between cell performance and GDL thickness with the exception that GDLs with
medium thickness tend to perform better than very thin or very thick GDLs.
Nevertheless, the use of different carbon substrates with varying thickness reveals a
noticeable influence on cell performance in both H2/O2 and H2/air fuel cells. As
previously discussed, the optimal GDL thickness is a compromise between the number of
pores available for effective gas and water transport within the MEA and resilience of the
substrate to pore destruction under compression. In this study, the thickness of untreated
GDLs varied from 110 to 380 m and the best two performances were observed with
MEAs fabricated from ETEK-Elat and TGP-H-090 with corresponding thicknesses of
275 m and 280 m (untreated state under no compression), respectively. For
comparison purposes, all GDLs in this study were divided into three groups based on
their original thickness: low (less than 200 m), medium (between 200-300 m) and high
(greater than 300 m). As shown in Figure 8-18(a), cell performance is not significantly
influenced by GDL thickness at low current densities (less than 400 mA cm-2
). However,
it improves as GDL thickness increases and reaches a maximum at around 280 m at
167
Figure 8-18(a) Cell voltage as a function of original GDL thickness with a platinum
loading of 0.3 mg cm-2
for a H2/air fuel cell, Nafion® 112, cell temperatutre of 50 °C and
fully humidified fuel and oxidant with stoichiometries of 1.2 and 2.5, respectively
current densities higher than 400 mA cm-2
and then begins to decrease as the thickness is
further increased beyond 300 m. The effect of thickness on cell performance is most
pronounced when the cell is operating at high current densities, which corresponds to the
diffusion-controlled region, where mass transport losses become dominant and reactant
delivery to the catalyst sites and water removal from within the MEA become crucial.
As mentioned above, although thin GDLs reduce mass transport losses and enhance
electronic conduction, they are more prone to flooding than thicker ones, leading to
significant losses when operated at high current densities.
The gas permeability of the GDL plays an important role in gas and water transport and
can significanlty influence cell performance. The porosity, , of a fibrous material,
including carbon-based electrodes, is defined as the ratio of the pore volume to the total
volume of the sample [618]:
sample
pore
V
V (8-5)
168
The porosity of a carbon-based GDL is calculated from its weigth per unit area (W/A),
solid phase density ( real ) and compressed thickness (d):
))()((
1Ad
W
real (8-6)
The solid phase density of carbon-based materials varies from 1.6 to 1.95 g cm-3
[619].
The porosity of a compressed GDL (see Fig 8-18(b)) also can be expressed in terms of its
compressed pore volume (Vp,c) and uncompressed bulk pore volume (Vb,u) [620]:
)( ,,,, cbubupcp VVVV (8-7)
)( ,,, upubcb VVV (8-8a)
)( ,,, ubuubcb VVV (8-8b)
)1(,, uubcb VV (8-9)
Where
u is the bulk porosity of the uncompressed fibrous material. The above equations
assume that the solid fibres are incompressible and that deformation takes place only in
the direction of the compressive force, perpendicular to the fibre orientation in the x-y
plane. The effective diffusion coefficients (Deff) of the hydrogen and oxygen are
influenced by the GDL bulk porosity,
u , according to [621]:
22 NO
effD
D
(8-10)
where
is the tortousity and 22 NOD is the binary diffusion coefficient of oxygen in
nitrogen. The tortousity is estimated using the Bruggeman equation [622]:
1
(8-11)
The relationship between permeability and porosity is often described by the Carman-
Kozeny equation, which relates the absolute permeability Kabs to the porosity
u and grain
size
. In fuel cell studies, the grain size is replaced with the fiber diameter df, and the
generalized form of this equation becomes [623]:
32 fabs dK (8-12)
169
Figure 8-18(b) A simple representation of compressed and uncompressed GDL
More specifically, a fitting parameter known as the Carman-Kozeny parameter, kKC, is
used to determine the permeability of GDLs, yielding [620]:
2
32
)1(16
KC
f
absk
dK (8-13)
Porosity of several untreated carbon substrates were determined using mercury intrusion
porosimetry. The experimental data, shown in Table 8-9, are in good agreement with the
manufacturers’ data.
Both the in-plane and through-plane permeability of different GDLs have been
investigated and reported in the literature. Williams et. al [614] presented a correlation
Pore
Fibre
Uncompressed Fibrous
Material
Compressed Fibrous Material
Uncompressed pore volume = Vp,u = εu Vb,u
170
between the through-plane permeability and the limiting current density. It is well-
established that diffusion is the primary driving force behind the through-plane transport
of fluids within GDLs. However, more recently, a large number of researchers have come
to the conclusion that in-plane permeability is more critical than through-plane
permeability in PEMFCs [615-617]. The primary driving force for in-plane permeability
is convection—forced convection in most cases. It is worth noting that both natural and
forced convection can enhance mass transport within the flow-field channels.
8.4.2 Porosity Measurements
The bulk porosity of each untreated GDL was determined according to the methods
described in section 7.6 and reported in Table 8-10 supplied by the manufacturers. The
greatest significance of the bulk porosity of the GDL is its ability to influence the
effective diffusion coefficient of the porous medium according to equation (8-10). The
relationship between the permeability and porosity of a material, as reported in equation
(8-12), is further developed and discussed in the following section. It suffices to state that
MEAs fabricated from Toray TGP-H-090 and E-TEK LT 1200-W delivered the best
results when used in a single cell. Both have porosities in the neighbourhood of 80%,
which lies in the middle of the porosity spectrum (77% - 86%).
Table 8-10 Porosity data for untreated GDLs
Material Porosity Porosity Porosity
Porosimetry Gravimetric Difference Manufacturer
(%) (%) (%) (%)
Toray TGPH 030 81.6 82.4 0.8 82
Toray TGPH 060 80.4 82.3 1.9 80
Toray TGPH 090 79.5 78.1 -1.4 79
Toray TGPH 120 77.1 78.6 1.5 77
E-TEK LT 1200-W 79.9 79.3 -0.6 79
Ballard Avcarb 1071 HCB 86.0 88.7 2.7 82
171
To sum up, the greatest difference beween the highest and lowest porosity is about 8.9%.
This is a strong indication that other important parameters are involved and that the bulk
porosity of untreated GDLs, although important, does not impart a significant impact on
cell performance.
8.4.3 Through-Plane Gas Permeability
The through-plane permeability of a number of the substrates used in section 8.4.1 to
fabricate MEAs was evaluated using the method described in section 7.7. The
permeability of these GDLs was determined using equations (7-2) and (8-15), based on
the assumption that the Forchheimer effect (see below) does not apply to this series of
substrates.
This assumption is valid since in the creeping flow regime, inertial forces are negligible
in comparison with pressure and viscous forces, of which the latter is the dominant
source of pressure loss. It is only at higher velocities where the former becomes the
dominant source of pressure loss due to acceleration and deceleration of the fluid inside
the porous medium. This is known as the Forchheimer effect, and must be taken into
account when determining the absolute permeability of a porous material in which the
fluid velocity cannot be considered low. This is accomplished by adding the above
contribution to equation (7-2):
vvk
vP
(8-14)
where
is the density of the fluid and
is the inertial coefficient, known also as the
Forchheimer or non-Darcy coefficient.
For a compressible fluid flowing inside a porous medium at a relatively low velocity, the
solution of Darcy’s law has been shown to be [620, 627]:
))(()(2
22
mk
MTRL
PPfluid
outin
(8-15)
where Pin and Pout are the inlet and outlet pressures of the fluid, L is the substrate length,
R’ is the universal gas constant, T the temperature, Mfluid the molecular weight of the
fluid (air in this study), µ is the viscosity of air (1.85 × 10-5
Pa·s) and m is the mass flux
172
through the substrate. It should be noted that equation (8-15) is valid only for one-
dimensional flows.
At higher fluid velocities, the contribution from inertial forces becomes significant and
can no longer be ignored; accordingly, Darcy’s law must be modified to account for such
losses. For a compressible fluid the Forchheimer term must be added to the right-hand
side of equation (8-15) transforming it to the following equation:
2
22
))(())(()(2
mmk
MTRL
PPfluid
outin
(8-16)
Experimental values for the through-plane permeability of a number of untreated
substrates are reported in Table 8-11. These values are the average of at least five
samples taken from the same sheet of material. The through-plane permeability of
Stackpole PC-206 substrate was not determined because of a lack of adequate material.
Comparison of these results with those reported by other researchers shows good
agreement. Mathias et al. [615] reported a range of values for the through-plane
permeability of Toray TGP-H-060, ranging from 5.0 х 10-12
to 10 х 10-12
m2. Gostick et
al. [620] evaluated the through-plane permeability of Toray TGP-H-090 and reported a
value of 8.99 х 10-12
m2. Williams et al. [614] tested the the through-plane permeability of
Toray TGP-H-120 and found it to be 8.69 х 10-12
m2.
Table 8-11 Through-plane permeability values of untreated substrates
Material Permeability Coefficient,
kz × 1012
Number of Replicates
Average Deviation
(m2) (%)
Toray TGPH 030 10.2 5 3.13
Toray TGPH 060 9.41 5 2.71
Toray TGPH 090 8.94 6 1.84
Toray TGPH 120 8.63 5 3.27
E-TEK LT 1200-W 63.9 5 3.46
Ballard Avcarb 1071 HCB
9.88 6 5.07
173
The viscous permeability of fibrous materials has been studied by many workers.
Johnson et al. [628] proposed a transport parameter based on electrical conduction
phenomena that would allow permeability approximations from readily available or
easily measured properties such as porosity, specific surface area and formation factor.
Jackson and James [629] introduced a set of dimensionless viscous permeabilities derived
from earlier experimental measurements to help with theoretical predictions. Fluid
permeability also has been linked to diffusion parameters, including effective diffusivity
and mean survival time [630-633]. More recently, Tomadakis and Robertson [634]
presented a comprehensive model to predict the viscous permeability of different types of
fibers with random structures. They considered structures formed by cylindrical fibers
with random distribution in 1, 2 and 3 directions, as depicted in Figure 8-19. Comparison
with a large number of experimental data has shown good agreement. The strength of this
model is based on several premises: first, the fibers in all dimensions are allowed to
overlap, freely mimicking the fibers of real structures. Second, the model requires only
readily measureable parameters such as fiber diameter and porosity, without relying on
hard-to-obtain fitting parameters. A detalied description of the model is provided
elsewhere [634-637] and the absolute permeability, k, is estimated using the
mathematical expression:
2
2
2
2 ])1[()1(
)(
)(ln8rk
pp
p
(8-17)
where
is the material porosity, r is the average radius of the fibers, and
and
p are
constants that depend on the direction of the flow with respect to the planes of the fibers
as well as the fiber arrangement in 1-, 2-, and 3-dimensions.
The two constants
and p are known as Archie’s law parameters for the bulk diffusion
tortuosity and conduction-based permeability of randomly overlapping fiber structures
[634], and are given in Table 8-12 for the above model.
174
1-D 2-D 3-D
Figure 8-19 Illustration of various random fiber orientation distribution in 1, 2 and 3
dimensions
Table 8-12 Archie’s law parameters used to calculate absolute permeability using the
model of Tomakakis et al [634]
Structure Flow Direction εp α
1-D Parallel 0 0
Perpendicular 0.33 0.707
2-D Parallel 0.11 0.521
Perpendicular 0.11 0.785
3-D All directions 0.037 0.661
The data obtained from the above model are compared with the experimental results of
the present study in Table 8-13. The absolute permeabilities, kz, are calculated for one,
two and three dimensional random fiber structures. The above model predicted the
absolute permeability to flow perpendicular to the planes of the fibers quite well with the
exception of the substrate from Ballard, for which the deviation is attributed primarily to
the presence of considerable quantities of filler inside the matrix.
Comparison of predicted through-plane permeabilities with the corresponding
experimental data show an excellent agreement with 2-D structures with the exception of
carbon substrates from BASF and Ballard (see Table 8-13). A comparison between the
above model in 2-D and the experimental values is indicated in Table 8-13 and presented
graphically in Figure 8-20. An excellent agreement between the experimental through-
175
plane permeability data and the corresponding values predicted by the above model for 2-
D structures is observed. For instance, the through-permeability of Toray TGP-H-060 is
estimated to be 9.65 × 10-12
m2, which is in good agreement with the experimental value
of 9.41× 10-12
m2. It is worth mentioning that Tomadakis and Robertson’s model also
takes into consideration the influence of the anisotrophy of the material. This is important
for materials with highly-aligned fibers, since they exhibit the highest anisotrophy, which
can have a direct impact on the through-plane permeability of a substrate. The
permeability of substrates with high anisotrophy can differ from others by as much as a
factor of 2 [620]. Gas diffusion layers are often treated with a hydrophobic polymer to
ensure sufficient water removal capability, especially when operated at high current
densities. However, the addition of a hydrophobic polymer alters the total porosity and,
consequently, the diffusibility.
Table 8-13 Comparison of experimental and theoretical absolute permeability values of
different carbon substrates
Material Porosity Fiber
Diameter Absolute Permeability, K % Difference
(%) (µm) (×10-12
m2) for 2-D Values
Experimental Mathematical Modeling
1-D 2-D 3-D
Toray TGPH 030 81.6 8.8 10.2 7.96 10.9 14.5 0.7
Toray TGPH 060 80.4 9.0 9.41 12.8 9.65 12.8 0.24
Toray TGPH 090 79.5 9.4 8.94 6.6 9.3 12.4 0.36
Toray TGPH 120 77.1 10.8 8.63 6.18 8.96 12.1 0.33
E-TEK LT 1200-W 79.9 14.9 63.9 17.6 24.7 32.9 -39.2
Ballard Avcarb 86.0 7.1 9.88 10.9 14.4 18.8 4.52
176
Figure 8-20 Comparison of experimental and theoretical variations in through-plane 2-D
permeability as a function of medium porosity for carbon papers under investigation
A number of GDLs were fabricated from Toray TGPH 090 carbon paper pre-treated with
varying amounts of PTFE, ranging from 10 to 50 wt%. As expected, the substrate
porosity decreased with increasing PTFE content in an almost linear fashion, as can be
seen from Figure 8-21. The average pore diameter of the substrate also decreased with
increasing PTFE content; however, the trend was rather non-linear, as shown in
Figure 8-22. To fully understand the effect of PTFE content on pore volume and,
ultimately, on gas diffuseability and cell performance, the pore diameter as a function of
differential pore volume for substrates containing 10-30 wt% PTFE was determined.
177
Figure 8-21 Influence of PTFE on the porosity of Toray TGPH 090 carbon paper
Figure 8-22 Effect of PTFE content on porosity and average pore diameter of Toray
TGPH 090 carbon paper
178
The results (Figure 8-23) show that GDLs containing 10 wt% PTFE exhibit a wider pore
volume distribution than those treated with higher PTFE loadings. This is true for both
small pores (less than 5 µm) and large pores (greater than 100 µm), indicating that the
amount of applied PTFE is not sufficient to cover most of the pores. However, at PTFE
loadings greater than 20 wt%, a rather narrow pore size distribution is observed,
indicating that most pores at both ends of the spectrum are covered by PTFE. It also can
be seen that the total pore volume decreases with increasing PTFE content, in turn,
restricting the flow of gases inside the GDL. These findings are in agreement with those
reported by other researchers [200, 640, 641].
Cumulative pore volumes of substrates treated with varying amounts of PTFE also were
evaluated and are presented in Figure 8-24, which shows that the cumulative pore volume
of all substrates decreases as PTFE content is increased from 10 to 50 wt%. In addition,
when each curve is individually analyzed, it can be seen that regardless of the PTFE
content, pores with diameters of about 4 µm or smaller are not affected by PTFE
treatment, a constant cumulative pore volume being observed for all the examined
substrates in this region. However, a sharp decrease can be seen for pores with diameters
Figure 8-23 Differential pore volume for Toray TGPH 090 carbon paper substrates with
different PTFE loadings
179
Figure 8-24 Cumulative pore volume of Toray TGPH 090 carbon paper substrates with
different amounts of hydrophobic polymer
greater than 4 µm and is amplified for those in the neighborhood of 50 – 300 µm in
diameter. This implies that most of the PTFE infiltrates into pores with diameters of 4 µm
or greater. One of the implications of this is that small pores (less than 4 µm in diameter)
will not be sufficiently hydrophobic, significantly increasing the probability of water
saturation and flooding leading to performance losses. Furthermore, there exist two
different primary types of diffusion in porous media: Knudsen and Maxwellian (bulk
diffusion). The former arises from the continuous collision of gas molecules with the pore
walls and often takes place in long pores with narrow diameters (2 – 50 nm). In other
words, this form of diffusion is dominant when the mean-free path is significantly larger
than the diameter of the pore. It has been reported that Knudsen diffusion is the dominant
mode when the pore diameter is less than 70 nm, which is one-tenth of the mean-free
path of air [614]. Bulk diffusion, on the other hand, dominates when the pore diameter is
at least 100 times greater than the mean-free path of the flowing gas molecules. Williams
et al. [614] also have noted that the effective diffusion coefficient is one order of
magnitude higher for conventional carbon substrates when bulk diffusion is the dominant
mode of diffusion.
180
Figure 8-23 shows that when the PTFE content is greater than 20 wt%, some of the pores
are unnecessarily narrowed or even blocked. This will lower the permeability of the GDL
and, ultimately, lower cell performance. Evidently, there is an optimal PTFE content that
will achieve the two critical objectives of ensuring adequate hydrophobicity to prevent
flooding without restricting the flow paths for mass transport to and from the catalyst
layer.
As stated above, when the pore diameter is greater than the mean-free path of air by a
factor of two, bulk diffusion becomes the dominant form of mass transfer. To illustrate
this, a plot of the pore volume contributed by pores having a minimum diameter of 7.0
m (100 times the mean-free path of air) as a function of the oxygen permeability
coefficient is presented in Figure 8-25, which shows as expected that the permeability
increases with the percentage of large pores. This can be attributed to the enhanced
convection of the oxidant inside the GDL. The ability of the substrate to effectively
remove water also will benefit from larger pores.
Figure 8-25 Percent of substrate pore volume with pore diameters of at least 7 m as a
function of permeability coefficient
181
8.5 Catalyst Electrodeposition
8.5.1 Copper Electrodeposition
For preliminary experiments, platinum was replaced with copper on account of the
prohibitive cost of the former. Copper electrodeposition was carried out following the
procedure outlined in section 7.4.2. The effects of different pulse current
electrodeposition parameters—pulse on-time, pulse off-time and duty cycle—on the
current efficiency of copper electrodeposition from an acidic bath were determined.
Since the properties of an electrodeposit can be influenced by its thickness, this parameter
was held constant at 0.05 mm throughout for each experiment. The parallel plate flow
cell was used with a 3.0-cm-diameter platinum screen as a counter electrode to deposit
copper onto carbon substrates at pulse current densities between 10-50 mA cm-2
. The
current efficiency was calculated by gravimetric analysis. Current efficiencies of copper
electrodeposition with different pulse periods, ranging from 4 to 400 ms, and duty cycles
of 25% and 50% are presented numerically in Tables 8-14 and 8-15 and graphically in
Figures 8-26 and 8-27, respectively.
Figure 8-26 Influence of pulse period on current efficiency of copper electrodeposition
182
Figure 8-27 Influence of duty cycle on current efficiency of copper electrodeposition
As shown in Figure 8-26, the current efficiency decreases with decreasing pulse period in
the millisecond region from about 92% to 76% for pulse periods between 400 ms to 4 ms,
respectively. This can be explained in terms of the dissolution of copper adatoms with
shortening pulses in the millisecond range. The reduction mechanism of copper has been
extensively studied [425, 426, 435, 436, 623]. It is believed that cupric ions are initially
adsorbed onto the surface of the substrate and then reduced to copper in two steps. The
copper adatoms then diffuse to the kink sites and steps, where they are incorporated into
the substrate matrix. However, if the pulse period is too short, the copper adatoms will
not have sufficient time to get into the kink sites and will, during the off period, degrade
as copper atoms suspended in the bulk solution and will re-dissolve into bulk solution.
Steps involved in the copper deposition process are shown below [601]:
Cu+2
(aq) Cu+2
(ad) adsorption (8-18)
Cu+2
(ad) + e- Cu
+1(ad) first charge transfer (8-19)
Cu+1
(ad) + e- Cu(ad) second charge transfer (8-20)
Cu(ad) Cu(cry) surface diffusion (8-21)
Cu(ad) Cu metal degradation (8-22)
2Cu+1
(ad) Cu+2
(aq) + Cu(s) disproportionation (8-23)
183
The decrease in current efficiency corresponding to the shortening of the pulse periods is
gradual from 400 ms to 40 ms; however, a sharp decrease is observed when the pulse
period is further shortened to 4 ms, as seen in Figure 8-26. If the on-time becomes very
short, as is the case for pulse periods less than 40 ms, there will not be sufficient time for
many copper adatoms to reach the kink sites and they may diffuse back into the solution
as suspended solids during the off-time, thereby lowering the current efficiency.
Figure 8-27 shows the influence of the duty cycle on the current efficiency of copper
deposition. The current efficiency decreases from about 99%, for DC electroplating at
100% duty cycle, to about 82% for a duty cycle of 10%. This is reasonable since a 10%
duty cycle corresponds to a longer off-time and, consequently, less time for the copper
adatoms to be incorporated into the substrate matrix, leading naturally to a lowering of
the current efficiency.
Table 8-14 Influence of pulse period on current efficiency of copper electrodeposition
Method Pulse Period Average Current Current Efficiency Average
Density Current Efficiency
(ms) (mA/cm2) (%) (%)
DC 10 98.7
DC 10 99.4 99.1
DC 10 99.1
PC* 400 10 91.6
PC* 400 10 91.0 91.6
PC* 400 10 92.3
PC* 100 10 88.5
PC* 100 10 90.0 88.9
PC* 100 10 88.3
PC* 40 10 87.0
PC* 40 10 86.1 86.3
PC* 40 10 85.7
PC* 4 10 76.2
PC* 4 10 74.5 75.9
PC* 4 10 76.9
* For a duty cycle of 25%
184
Table 8-15 Influence of duty cycle on current efficiency of copper electrodeposition
Method Duty Cycle Average Current Current Efficiency Average
Density Current Efficiency
(%) (mA/cm2) (%) (%)
PC 10 4 83.4
PC 10 4 80.6 81.8
PC 10 4 81.5
PC 25 10 91.6
PC 25 10 91.0 91.6
PC 25 10 92.3
PC 50 20 94.3
PC 50 20 95.1 94.8
PC 50 20 94.9
PC 75 30 96.7
PC 75 30 97.5 97.2
PC 75 30 97.4
DC 100 10 98.7
DC 100 10 99.4 99.1
DC 100 10 99.1
DC 100 20 98.2 98.5
DC 100 20 98.8
8.5.2 Elemental Analysis using EDX
Scanning electron microscopy was used in combination with EDX to determine the
elemental composition of the deposits. The extent of Nafion® coverage was evaluated by
comparing the amount of carbon present on the surface of a carbon electrode after each
Nafion® application. The results are presented numerically and graphically in Table 8-16
and Figure 8-28, respectively. Figure 8-28 shows that the amount of carbon present on
the surface of a carbon electrode decreases sharply from about 100% to only 25% with
the first three Nafion®
applications, and then follows a more gradual decline until the
electrode surface is completely covered with Nafion® after 7 applications. After the 7
th
application, Nafion® begins to build up only on the surface, thickening the Nafion
® coat.
Fig. 8-29 shows the EDX spectrum of a carbon electrode that first had been coated with
185
Nafion®, followed by depositing copper. The spectrum analyzed the cross-sectional
region at the carbon/Nafion® interface and confirms that the copper was deposited at the
correct location (see Figure 8-30).
Table 8-16 EDX analysis of carbon substrates
Number of Nafion % Carbon on
Applications the substrate
0 99.4
1 52.0
2 36.4
3 25.5
4 21.8
5 11.3
6 8.4
7 1.9
8 0
9 0
10 0
Figure 8-28 Influence of the number of applications on carbon electrode coverage
186
Figure 8-29 EDX spectrum of the interfacial cross-section of a carbon electrode
impregnated with 14 coatings of Nafion® and electroplated with copper
Figure 8-30 An EDX spectrum analysis of a carbon electrode cross section
impregnated with Nafion® and electroplated with copper
Carbon
Nafion
®
Cross-sectional
area analyzed
Sample: <Untitled>
Comments:
Acquired: 13-Aug-2004, 17:38
Processed: 13-Aug-2004, 17:41
Standardized: 16-Apr-2002, 10:54
Detector window: Beryllium
Accelerating voltage: 20
Tilt: 15
Elevation: 10
Azimuth: 13
Correction method automatically selected: PAP
Element wt% ZAF factor 3 sigma
C 24.04 0.368 191.9888 !
S 26.70 0.726 11.425 !
O 39.97 0.863 63.542 !
Cu 9.26 2.181 57.1153 !
Total 99.97
187
It is important to note that a correct sulfur-to-oxygen mass ratio of 0.6680 can be
calculated from data in Fig. 8-30, proving the presence of sulfonic groups (-SO3-) on the
substrate surface.
8.5.3 Platinum Electrodeposition
8.5.3.1 Direct Current Electrodeposition
A series of experiments was carried out to study the effects of various electrodeposition
parameters in both Direct Current (DC) and Pulse Current (PC) electrodeposition. In this
section the results for DC electrodeposition are presented. The findings for PC
electrodeposition are discussed in the following section.
Since DC electrodeposition has only one variable, namely, the current density, iDC, only
minimal control is possible in DC systems. As the deposition current density increases,
the metal ion concentration is depleted near the surface of the cathode and dendrites
begin to form. Eventually, the concentration near the surface of the cathode approaches
zero and the ―limiting current density‖, iL, is reached, and crystal growth becomes the
dominant process as opposed to nuclei formation. Mass transport limitations can clearly
be seen in Figure 8-31, where the performance of electrodes fabricated by DC
electrodeposition of Pt at various current densities, ranging from 10 to 50 mA cm-2
, is
shown. The best performance was observed at a plating current density of about 15 mA
cm-2
.
Figure 8-32 presents cross-plots of the same results as a function of the cell voltage vs.
the applied Pt deposition current density at different cell current densities. Again, it is
evident that the best performance was obtained using a deposition current density in the
neighbourhood of 15-20 mA cm-2
. This behaviour can be explained in terms of Pt crystal
growth and nuclei formation. At very low current densities, the rate at which electrons are
supplied to the surface is low compared with the diffusion rate of platinum metal ions.
Consequently, platinum ions will crystallize at stable places on the electrode surface and
the growth of existing crystals will dominate. This increases the particle size of the
deposited catalyst and, at the same time, decreases the available surface area for reaction,
and more importantly, for the reduction of oxygen at the cathode. However, as the
188
Figure 8-31 Effect of Pt electrodeposition current density on cell performance in DC
electrodeposition (H2/Air, 20 wt% PTFE, 0.30 mg Pt cm-2
per electrode, Nafion® 112,
cell temperature of 50 °C, fully humidified fuel and oxidant with stoichiometries of 1.2
and 2.5, respectively)
Figure 8-32 Effect of electrodeposition current density on cell performance in DC
electrodeposition (H2/Air, 20 wt% PTFE, 0.30 mg Pt cm-2
per electrode, Nafion® 112,
cell temperature of 50 °C, fully humidified fuel and oxidant with stoichiometries of 1.2
and 2.5, respectively)
189
deposition current density increases, the rate at which electrons are supplied to the
surface is no longer slower than the metal ion diffusion rate. This increases the rate of
nuclei formation and consequently, decreases the deposited platinum particle size.
As the deposition current density increases beyond 15 mA cm-2
, concentration
polarization becomes increasingly significant and, metal once more moves to the tips of
the existing crystals, which begin to grow. Again, the crystals become dendritic and this
diminishes the surface area of the catalyst necessary for both hydrogen oxidation and
oxygen reduction and decreases electrode performance. As can be seen from Figure 8-31,
at high deposition current densities (40 mA cm-2
and greater) the performance of the
MEA drops sharply. This is primarily attributed to the generation of hydrogen at such
current densities, which adversely affects the deposited catalyst layer. This is confirmed
by examining the cross section SEM images (Fig. 8-33) of two electrodes; one fabricated
at a peak current density of 50 mA cm-2
and the other at a higher peak current density of
70 mA cm-2
. While a strong platinum peak is observed for the electrode prepared at the
lower peak current density (micrograph (a)), no such peak is observed for the higher
current density. At the higher peak current density, the deposited catalyst layer is
removed due to the generation of hydrogen.
Carbon Carbon
Figure 8-33 Enhanced SEM cross-sectional micrographs of electrodes prepared by pulse
electrodeposition at peak current densities of (a) 50 mA cm-2
and (b) 70 mA cm-2
(a) (b)
Nafion®
Nafion®
15 µm 15 µm
190
8.5.3.2 Pulse Current Electrodeposition
8.5.3.2.1 Influence of Cathodic Peak Current Density
It is known that PC electrodeposition has several advantages over DC electrodeposition
in terms of controlled particle size, better adhesion to the substrate and uniform
distribution of deposited metals within the catalyst layer [9]. It has also three independent
variables as opposed to only one with DC electrodeposition. These variables—peak
deposition current density, on-time and off-time—can be manipulated to optimize the
performance of the catalyzed electrode. The effect of peak deposition current density on
fuel cell performance is shown in Figures 8-34 and 8-35.
In this experiment, the peak current density was varied while keeping the duty cycle,
pulse period and charge density constant. As can be seen from Figures 8-34 and 8-35, the
electrodes prepared at a peak current density of 50 mA cm-2
exhibit better performance
than those prepared at either lower or higher peak current densities. This increase in
performance can be attributed to an increase in the active surface area of the deposited
platinum and selective platinum loading in the catalyst layer close to the Nafion®
membrane, leading to the extension of the three-phase interface. In an electroplating
process, metal ions are transferred to the cathode, where adatoms are formed by the
electron transfer process and, consequently, incorporated into the crystal lattice. As
discussed earlier, two competing processes are involved: nucleation and crystal growth.
At low current densities, because the rate of diffusion from solution is higher than the rate
of charge transfer, metal ions have sufficient time to find stable places on existing
crystals to attach themselves and be incorporated into the crystal lattice and the crystal
grows, leading to lower catalyst surface area. As the pulse deposition current density
increases, there is no longer sufficient time for adatoms to diffuse across the surface to be
incorporated into a growing crystal. Instead, as each new adatom is deposited, it becomes
a single nucleus or part of a very small number of nuclei. The result is an increase in the
number, but a decrease in the size, of the Pt crystallites, resulting in a catalyst layer with
superior properties in terms of hydrogen oxidation and oxygen reduction.
191
Figure 8-34 Effect of electrodeposition peak current density in square pulse
electrodeposition on cell performance (H2/Air, 20 wt% PTFE; 0.30 mg Pt cm-2
per
electrode, cell temperature of 50 °C, Nafion® 112, TGPH-090 carbon paper, fully
humidified fuel and oxidant with stoichiometries of 1.2 and 2.5, respectively)
Figure 8-35 Effect of electrodeposition peak current density on fuel cell performance in
square pulse electrodeposition (H2/Air, 20 wt% PTFE, 0.30 mg Pt cm-2
per electrode, cell
temperature of 50 °C, Nafion® 112, TGPH-090 carbon paper, fully humidified fuel and
oxidant with stoichiometries of 1.2 and 2.5, respectively)
192
As the peak deposition current density increases beyond 50 mA cm-2
, surface diffusion
becomes the rate-determining step, the system approaches its ―limiting current density‖,
and dendrites begin to form. Crystal growth then becomes the dominant process and the
size of the catalyst particles starts to increase, resulting in a lower catalyst effective
surface area and, consequently lower performance. At very high peak current densities—
greater than 70 mA cm-2
—hydrogen may be evolved contributing to spalling of the
catalyst layer and a sharp decline in performance.
The rate of nuclei formation can be expressed by [333]:
Tkez
bskJ
2
1 exp (8-24)
where k1 is a rate constant; b is a geometric factor; s is the area occupied by one atom on
the surface of the cluster;
is specific edge energy; and k is Boltzmann’s constant. T, z, e
and
have their usual meanings.
As can be seen from the above equation, the rate of nuclei formation increases as the
reaction overvoltage,
, increases4. Furthermore, under activation control the overvoltage
is given by the Tafel equation:
)(log i (8-25)
Equations (8-24) and (8-25) show that as the applied current density, i, increases the
overvoltage, η, also increases, increasing the nucleation rate and promoting a catalyst
layer with smaller platinum particle size, and hence better performance.
One of the main advantages of pulse electrodeposition is its ability to impede the onset of
crystal growth by increasing the limiting current density. This is achieved by
replenishment of ions in the vicinity of the cathode during pulse off-time, allowing a
higher cathodic current density to be applied at the electrode surface compared with DC
electrodeposition because of the higher concentration of platinum ions near the electrode
surface. On the other hand, the application of a continuous current in DC
4 In this treatment, as explained later (section 9.2.3.1 ), cathodic overvoltages are treated as positive
quantities.
193
electrodeposition leads to a steady decline in the concentration of the electroactive
species in the diffusion layer, eventually to a point where it becomes zero. At this point,
dendrites will start to form and existing crystals will grow, diminishing the effective
surface area of the deposited layer. Figure 8-36 shows the polarization curves of the
MEAs prepared by DC and PC electrodeposition. The pulse-electrodeposited electrode
was prepared under the conditions of 50 mA cm-2
of peak deposition current density,
100 ms on-time and 300 ms off-time. A continuous current density of 15 mA cm-2
was
applied for DC electrodeposition. Total charge density was kept identical in both cases.
The results clearly show the superiority of PC electrodeposition, and are attributed to the
smaller Pt particle size of the electrodes prepared by PC electrodeposition.
Figure 8-36 Effect of PC and DC electrodeposition on fuel cell performance (H2/Air, 20
wt% PTFE, 0.30 mg Pt cm-2
per electrode, cell temperature of 50 °C, Nafion® 112, fully
humidified fuel and oxidant with stoichiometries of 1.2 and 2.5, respectively)
194
8.5.3.2.2 Influence of Duty Cycle
8.5.3.2.2.1 Regular Duty Cycles : 10%-100%
Figure 8-37 shows the polarization curves for a number of MEAs prepared by square
pulse current electrodeposition with a varying duty cycle. The duty cycle was varied by
changing the off-time while the peak current density, on-time and charge density were
fixed at 50 mA cm-2
, 150 ms and 6 C cm-2
, respectively. The results indicate that the
duration of off-time plays an important role in the deposition of platinum since it is
during this period that fresh platinum ions are replenished close to the surface of the
cathode from the bulk solution. It is also during the off-time that platinum ions diffuse to
the surface of the electrode, making it possible to perform electrodeposition at a higher
pulse current density, raising the overvoltage and increasing the rate of nuclei formation.
This trend in Figure 8-38, can be explained in terms of the limiting current density and its
effect on the quality of the deposited platinum. When the pulse off-time is too long with
respect to pulse on-time—low duty cycle—the limiting current density becomes higher
than the applied current density requiring a longer deposition time to achieve the same
platinum loading.
Figure 8-37 Effect of PC duty cycle on fuel cell performance (H2/Air, 20 wt% PTFE,
0.30 mg Pt cm-2
per electrode, cell temperature of 50 °C, Nafion® 112, TGPH-090 carbon
paper, fully humidified fuel and oxidant with stoichiometries of 1.2 and 2.5, respectively)
195
Figure 8-38 The relationship between duty cycle and cell voltage for different fuel cell
output current densities in fuel cells utilizing PC-electrodeposited catalysts (H2/Air, 20
wt% PTFE, 0.30 mg Pt cm-2
per electroede, cell temperature of 50 °C, TGPH-090 carbon
paper, fully humidified fuel and oxidant with stoichiometries of 1.2 and 2.5, respectively)
This is analogous to electrodeposition with a low pulse current density. As mentioned
before, low pulse current densities lower the formation of new nuclei resulting in poor
electrode performance. One approach to rectify this is to raise the peak current density so
charge transfer will no longer be the rate-determining step. This is discussed in the
following section, where low duty cycles and high peak current densities are utilized to
electrodeposit fine catalyst layers. On the other hand, if the off-time is too short—high
duty cycle—there is not enough time for fresh platinum ions to diffuse into the diffusion
layer from the bulk solution and reach the surface of the cathode. Furthermore, the
limiting current density of an electroplating system is inversely proportional to the
applied duty cycle. In other words, as the duty cycle increases, the limiting current
density of the system will inevitably decrease. This will, in turn, impose a limitation on
the size of the applied peak current density that can be used. Generally, a higher peak
current density must be applied to promote nuclei formation and avoid crystal growth.
For a particular electroplating system, if the peak current density is greater than its
corresponding limiting current density, then crystal growth becomes the dominant
process, increasing the size of the deposited catalysts and, consequently, decreasing the
196
effective surface area of the deposited platinum. It is important to note that in this series
of experiments the limit for the applied peak current density is set at 25 mA cm-2
. Higher
peak current densities were found to surpass the limiting current density of the system,
leading to crystal growth and dendrite formation. Electrodes fabricated at higher peak
current densities; i.e., greater than 25 mA cm-2
, exhibit poor single cell performance, as
can be seen in Figure 8-37, where a peak current density of 50 mA cm-2
was employed.
A duty cycle of 10% is not adequate to effectively promote nucleation. In this case,
charge transfer is the rate-limiting step and adatoms will have enough time to reach stable
places—existing crystals—on the surface of the cathode.
Therefore, it is crucial to optimize the duty cycle in order to decrease the platinum
particle size and to increase the fuel cell performance. A duty cycle of 20% was found to
provide the best results under the specified experimental conditions.
8.5.3.2.2.2 Low Duty Cycles: 2%-10%
Membrane-electrode assemblies prepared by square pulse electrodeposition with low
duty cycles, ranging from 2% to 10%, have been reported to perform better than MEAs
fabricated utilizing higher duty cycles [105, 536].
Figures 8-39 and 8-40 show the effect of a very low duty cycle of 4% on electrode
performance in a fuel cell. A slight improvement in the performance of electrodes
fabricated at a low duty cycle (4%) is observed compared with electrodes prepared at
higher duty cycles (greater than 10% with 20% being the best at 50 mA cm-2
). As before,
this can be explained in terms of the nucleation rate and crystal growth of deposited
platinum catalyst. As the duty cycle decreases, the average current density decreases as
well. As a result, higher cathodic peak current densities can be applied, leading to higher
cathodic overvoltages. This promotes the formation of new nuclei, resulting in finer and
smaller platinum particles on the carbon substrate and, ultimately, in better fuel cell
performance. This can clearly be seen in Figure 41 where the electrode prepared with a
duty cycle of 4% and a peak current density of 400 mA cm-2
exhibits better performance
than the electrode fabricated at a duty cycle of 20% and a corresponding cathodic peak
197
Figure 8-39 Effect of electrodeposition peak current density with low duty cycles (ф) (4% and 20%) in square pulse electrodeposition on fuel cell performance (H2/Air, 20
wt% PTFE, 0.30 mg Pt cm-2
per electrode, cell temperature of 50 °C, Nafion® 112, fully
humidified fuel and oxidant with stoichiometries of 1.2 and 2.5, respectively)
Figure 8-40 Effect of square pulse electrodeposition peak current density with 4% duty
cycle (ф) on fuel cell voltage for fuel cell output current densities of 200-1000 mA cm-2
(H2/Air, 20 wt% PTFE, 0.30 mg Pt cm-2
per electrode, cell temperature of 50 °C, Nafion®
112, fully humidified fuel and oxidant with stoichiometries of 1.2 and 2.5, respectively)
198
current density of 50 mA cm-2
. It must be noted that the average current density in both
cases is below the critical limiting current density of 15 mA cm-2
for DC
electrodeposition. This can be further substantiated by considering the electrodes
prepared using a pulse current density of 600 mA cm-2
. In this case, the average current
density is greater than the limiting current density and, consequently, an inferior
performance is observed, probably as a result of dendrite formation and crystal growth.
On the other hand, at a duty cycle of 4% and low cathodic peak current density (50 mA
cm-2
) the average current density is not high enough to support the formation of new
nuclei, and results in the growth of platinum crystals. This lowers the effective surface
area of the platinum for hydrogen oxidation, and more importantly, for oxygen reduction,
leading to a lower-than-expected fuel cell performance.
This can partially be explained by determining ―where‖ electrocatalysts are likely to be
deposited under such electroplating conditions. This requires a good understanding of the
current density distribution throughout the substrate and all the parameters influencing it.
It is known that the current density distribution throughout electronically conductive
carbon substrates is impacted by mass transport limitations, kinetics of the catalyst
deposition process and ohmic drop throughout the substrate [12, 624-626]. Mass
transport limitations are generally reduced by increasing the concentration of the catalyst
ions in the solution. This will result in the deposition of catalyst particles away from the
active layer since platinum ions can now penetrate further into the substrate and then be
reduced, if the cathodic peak current density is relatively low. Although in this study the
concentration of platinum is low to ensure its deposition in regions where both ionic and
electronic pathways exist, the applied cathodic peak current density must be high enough
to inhibit its penetration into the substrate, where it will become inactive. On the other
hand, if the cathodic peak current density is too high, hydrogen evolution becomes the
predominant reaction, destroying the deposited platinum layer. In addition, according to
Equation (8-24) high cathodic peak current densities increase the nucleation rate by
increasing the overvoltage. This will, in turn, improve fuel cell performance.
199
Figure 8-41 compares the performance of electrodes fabricated at various duty cycles,
ranging from 2% to 20% and corresponding average current densities of 6 – 16 mA cm-2
.
Similar trends to the case of 4% duty cycle were observed, and the same argument can be
used to explain these findings.
Figure 8-41 Effects of duty cycle and pulse current density on fuel cell performance
(square pulse, H2/Air, 20 wt% PTFE, 0.30 mg Pt cm-2
per electrode, cell temperature of
50 °C, fully humidified fuel and oxidant with stoichiometries of 1.2 and 2.5, respectively)
8.5.3.2.3 Influence of Pulse Duration
Figure 8-42 presents the performance plots of MEAs fabricated by square-pulse
electrodeposition with varying pulse periods, ranging from 40 to 4000 ms, at a deposition
peak current density of 50 mA cm-2
and a duty cycle of 25%. The results indicate that
pulse frequency plays an important role in the deposition of active catalysts. When the
pulse period is too short (for instance on-time/off-time of 10/30 ms), there is not enough
time for fresh platinum ions in the bulk solution to reach the surface of the electrode
during off-time since the on-time is relatively long. Although the duty cycle is set at
200
25%, a substantial amount of platinum ions will move into the substrate from the
diffusion layer and will be deposited both on the surface and inside of the substrate due to
the relatively long on-time. This will lower the concentration of the platinum ions inside
the diffusion layer, where the onset of limiting current density is inevitable. On the other
hand, if the pulse period is too long, the corresponding on-time will be long as well (1000
ms in the worst case) contributing to the exhaustion of platinum ions near the surface of
the cathode, resulting in the growth of the platinum crystals and a lowering of the
nucleation rate. This contributes to an inferior MEA performance by decreasing the
effective surface area of the platinum for both oxidation and reduction.
An on-time of 150 ms and off-time of 450 ms was found to deliver the best results under
the specified experimental conditions. Figure 8-43 shows the relationship between pulse
frequency and cell performance at five different fuel cell output current densities, ranging
from 200 – 1000 mA cm-2
. It can be seen that electrodes prepared using long pulse
periods; i.e., greater than 1500 ms, deliver the worst results when compared with
electrodes fabricated employing very low pulse frequencies—less than 50 ms. This can
be explained in terms of the available platinum ions close to the cathode during the on-
time of the pulse period. With low pulse frequencies, the on-time is relatively short and
the average current density is often below the limiting current density. This ensures the
presence of an ample supply of platinum ions near the surface of the cathode during the
electrodeposition period. On the other hand, with high pulse frequencies, the on-time is
relatively long and the number of platinum ions in the diffusion layer will diminish
during this period. At this point mass transport will become the rate-determining step and
crystal growth will become the dominant process, leading to a lower catalyst surface area
and, ultimately, lower fuel cell performance. According to Figure 8-43, a pulse frequency
with an on-time of 150 ms and an off-time of 450 ms (for a pulse period of 600 ms)
delivers the best performance at all current densities investigated in this series of
experiments. MEAs fabricated with a pulse frequency of 400 ms performed equally well;
however, a sharp decrease in performance was observed when the pulse frequency was
further decreased to 200 ms.
201
Figure 8-42 Effects of pulse frequency (on-time/off-time) on cell performance (square
pulse, H2/Air, 20 wt% PTFE, 20% duty cycle, 0.30 mg Pt cm-2
per electrode, cell
temperature of 50 °C, Nafion® 112, fully humidified fuel and oxidant with
stoichiometries of 1.2 and 2.5, respectively)
Figure 8-43 The relationship between pulse frequency and cell voltage for fuel cell
output current densities of 200-1000 mA cm-2
using PC electrodeposition (square pulse,
H2/Air, 20 wt% PTFE, 20% duty cycle, 0.30 mg Pt cm-2
per electrode, cell temperature of
50 °C, fully humidified fuel and oxidant with stoichiometries of 1.2 and 2.5, respectively)
202
8.5.3.3 Influence of Plating Bath Concentration on MEA Performance
A series of experiments was conducted to determine the optimal concentration of the
cation in the plating solution. Five plating solutions with Pt(NH3)4Cl2 concentrations,
ranging from 1.00 to 1000 mM were prepared and used to deposit platinum onto identical
carbon (TGPH-090, Toray) substrates using square pulse electrodeposition. All other
parameters, including peak current density, off-time, on-time, duty cycle and platinum
loading were kept constant. Figure 8-44 shows that a plating solution concentration of
50 mM delivered the best results. Platinum line scans of the cross sections of the above
MEAs were obtained to estimate the thickness of the catalyst layers as well as their
distribution inside the GDL using EPMA. Figures 8-45 (a)-(e) compare the Pt content at
the electrode surfaces adjacent to the Nafion® layer as well as the extent of platinum
penetration into the GDL. According to these line scans, the Pt content; i.e., its intensity,
is at its maximum at the interface between the GDL and the Nafion® layer for all cases.
However, the extent of Pt penetration inside the GDL shows the highest level for MEAs
prepared with concentrated plating solutions; i.e., 500 mM and 1000 mM.
Figure 8-44 Effects of plating bath Pt(NH3)4Cl2 concentration on MEA performance
(square pulse, H2/Air, 20 wt% PTFE, 20% duty cycle, 0.35 mg Pt cm-2
per electrode, cell
temperature of 50 °C, Nafion® 112, fully humidified fuel and oxidant with
stoichiometries of 1.2 and 2.5, respectively)
203
Figure 8-45 Cross-sectional platinum line scans for MEAs prepared from plating baths
with different platinum concentrations: (a) 1.0 mM; (b) 50 mM; (c) 100 mM; (d) 500 mM
and (e) 1000 mM
Nafion® GDL
204
On the other hand, MEAs prepared with plating solutions containing 50 mM and 100 mM
of cations show a high Pt intensity at the interface and a fast decline into the GDL and
away from the Nafion®
-GDL interface. Reference to Figure 8-44 shows that the catalyst
deposited from the 50 mM and 100 mM baths delivered the best fuel cell performance.
The MEA made from the least-concentrated bath—1.0 mM—exhibits the worst cell
performance, although the extent of its penetration into the GDL is relatively low.
However, the Pt intensity at the GDL-Nafion®
interface is the lowest amongst all the
examined MEAs.
The primary objective of employing a pulse current electrodeposition technique is to
selectively deposit platinum particles within the active catalyst layers, where both
electronic and ionic pathways exist. To achieve this selective deposition, a number of
parameters must be carefully selected and optimized, including the concentration of the
Pt(NH3)42+
cation in the plating bath.
The cation concentration in the bath must be relatively low for two reasons. First, for the
cation to reach the active layer and then be deposited, it first must pass through the
cation-conducting selective Nafion® membrane adjacent to the active layer. To ensure the
conduction of metal cations through the Nation®
, the concentration of the metal cation
must be lower than the fixed charge of the membrane. The fixed charge concentration of
most SPEs is around 1.0 mol L-1
(based on total membrane volume) [12, 141].
Accordingly, the concentration of the metal cation in the plating bath must be lower than
1.0 mol L-1
. Second, the current density distribution throughout the carbon substrate
dictates the localization of the catalyst particles and, as discussed below, the metal cation
concentration can play a major role.
Two scenarios can be considered: very low and high cation concentrations. For the
former, the current-density distribution throughout the carbon substrate is controlled
primarily by the extent of the cation transport inside the substrate. Although the low
concentration limits the movement of metal ions and ensures their reduction as soon as
they reach the active layer, they can become inactive due to simultaneous side reactions
in the same region of the electrode, such as the reduction of water. Since the Pt ion is
205
dissolved in an aqueous solution, it is possible for the solvent to be reduced before the
platinum. This can take place according to the following reaction:
2H2O + 2e- H2 (g) + 2OH
- (aq) (8-26)
This, of course, depends on the kinetic resistance associated with the reduction of
platinum being minimal [12]. Reaction (8-26) not only retards the reduction of the metal
cations, but also destroys the existing catalyst layer due to evolution of hydrogen. In
addition, owing to the presence of a very small number of metal cations, the deposition of
significant amounts of the catalyst may not be possible.
On the other hand, if the concentration of the cation in the plating solution is too high,
then the current-density distribution throughout the substrate is no longer governed by
ionic mass transport, but rather by deposition kinetics and, more importantly, by the
ohmic drop throughout the substrate. In this case, a large portion of the catalyst ions can
move away from the active layer and be deposited inside the carbon substrate, and,
ultimately, become inactive. In other words, some of the metal ions will have enough
time to move away from the region where both ionic and electronic connections are
available (GDL-Nafion®
interface), and will be reduced in places where only electronic
pathways are present. This can be overcome by providing the metal ions with sufficient
electrons to facilitate the reduction process by increasing the current density. However,
this will inevitably lead to hydrogen generation and the loss of the catalyst layer, as
previously explained.
The reduction of the platinum-complex cation into metallic platinum can be represented
by the following reaction:
Pt(NH3)42+
+ 2e- Pt + 4NH3 (8-27)
Since ammonia is a weak base, the solution in the diffusion layer adjacent to the electrode
surface can become basic as the electroplating progresses. Furthermore, NH3 can react
with Brønsted acids (proton donors) to form ammonium, a relatively strong conjugated
acid, according to the following chemical reaction:
NH3 + H2O ↔ NH4+ + OH
- (8-28)
206
Selective electrodeposition of platinum inside the active layer is a sensitive process and
the inhibition of competing processes is critical. Therefore, it is imperative to maintain an
ammonium concentration that is well below that of the platinum [12]. The extent of
ammonium production in an aqueous solution is a function of pH. If the pH is low, the
equilibrium shifts to the right (according to equation (8-28)) and more ammonium is
produced. On the other hand, if the pH is high, the equilibrium shifts to the left.
Furthermore, high average current densities facilitate the production of ammonium in
aqueous solutions. This was not deemed to be a problem in this series of experiments,
since the applied average current densities were low enough to inhibit the onset of
ammonium production.
8.5.3.4 Platinum Distribution in Carbon Substrates Fabricated by Pulse
Electrodeposition
A series of experiments was performed to determine the platinum distribution in 3.5 cm
diameter carbon substrates (TGPH-090, Toray). Each carbon substrate was cut into 10
equal area annuli (Figure 8-46) and the amount of platinum determined using gravimetric
analysis. Five identical samples were analyzed to ensure the accuracy and reproducibility
of the reported data. The results, presented in Figure 8-47, indicate an almost uniform
platinum distribution in the area used as active electrode (a 2.24 cm 2.24 cm electrode
is cut to make a 5-cm2
MEA). It should be noted that no platinum was found near the
edges of the circular electrodes. This was expected since there was no contact between
this part of the electrode and the plating solution during electrocatalyzation, since the
substrate was sitting inside the sample holder on an o-ring.
Figure 8-48 shows an electron micrograph of a composite fuel cell MEA consisting of a
cathode prepared using our PC electrodeposition technique bonded to a commercial
Nafion®
112 membrane. The Nafion®
membrane in turn is bonded to an anode, which
consists of a commercial E-TEK electrode, prepared using a commercial rolling
technique. All five layers of the MEA are clearly visible and their thicknesses can readily
be determined. The bright portions on either side of the Nafion® membrane indicate the
presence of a heavy metal such as platinum. The thickness of the Nafion® 112 membrane
can readily be confirmed as 50 µm.
207
Figure 8-46 Carbon substrate impregnated with platinum
It is important to note the thickness of the pulse-electrodeposited platinum layer on the
cathode side of the MEA and compare it with the E-TEK electrode on the anode side.
The thickness of the former is about 5 m while the thickness of the latter is almost ten
times higher at about 50 m. The thickness of the catalyst layer can play a vital role in
the distribution of gases and water inside the MEA and hence, can directly influence the
performance of the fuel cell. It is known that thick catalyst layers (greater than 10 m)
lead to lower cell performance due to the longer paths for reactants to reach the three-
phase interface deep inside the MEA, where the redox reactions take place. In addition,
ohmic losses also increase since electrons are forced to take a longer path to reach the
GDL, and, ultimately, the external circuit.
1.75 cm
2.24 cm
Active area
used in fuel
cell
208
Figure 8-47 Platinum distribution on a carbon substrate as a function of distance from
the centre of the substrate
Figure 8-48 An electron micrograph of a composite fuel cell MEA
Cathode
GDL Bonded
Nafion®
Membrane
~ 50 m
E-TEK Pt/C
Layer
~ 40 m
0.3 mgPt/cm2
Anode
GDL
Pt Layer
Deposited
by Pulse Electrod-
eposition
~ 5-7 m
0.3 mgPt/cm
2
E-TEK Electrode
20 m
--------
Pt zone
Pt zone
17.5 13.5 8.8 4.4 0.0 4.4 8.8 13.5 17.5
Distance from the centre of the substrate (mm)
mg Pt cm-2
209
8.5.4 Effect of Pulse Current Waveform on Properties of Electrodeposited
Catalyst Layer
Most of the research carried out globally on electroforming and electrodeposition is
focused on utilizing square-wave pulse current to improve deposit quality. There has
been a limited number of published articles on the use of other types of waveform to
enhance surface finishing and hardness of some deposited metals such as nickel [503]
and nickel alloys [504], but no reports on using different types of waveform to
electrodeposit platinum and platinum-group metals for use as electrocatalysts.
Therefore, a series of experiments was conducted to determine the influence of different
pulse current waveforms on deposit quality, particularly the catalytic activity of platinum
towards hydrogen oxidation and oxygen reduction in a PEM fuel cell. Figure 8-49
compares the performance of electrodes prepared by employing different waveforms—
rectangular, ramp up, triangular and ramp down—with a duty cycle of 4% and a peak
current density of 400 mA cm-2
. The best performance was exhibited by the MEA
prepared with a ramp-down waveform. The MEA fabricated using a triangular waveform
performed equally well, followed by that created using a ramp-up waveform. The MEA
made by employing a rectangular waveform delivered the worst performance. It is
important to note that at low current densities (less than 1000 mA cm-2
), the performance
curves are very similar; and only a slight improvement is achieved; however, at higher
current densities (greater than 1700 mA cm-2
), an almost 20% improvement in fuel cell
current density output is observed, when using waveforms other than the conventional
rectangular one.
The above results can be explained in terms of the size and distribution of the deposited
platinum. When a rectangular waveform is used, the current density is instantaneously
increased to the peak current density and then kept constant for the duration of on-time.
The continuous high cathodic current encourages crystal growth and hence fewer nuclei
are formed, resulting in a decrease in the number and an increase in the size of the Pt
crystallites and, consequently, a decrease in the effective surface area of the deposited
platinum. On the other hand, if the nucleation rate can be increased at the beginning of
the process, the overall crystal growth is retarded as the electrodeposition continues, and
210
Figure 8-49 Cell performance as a function of electrodeposition waveform (H2/O2, 20
wt% PTFE, 4% duty cycle, 0.35 ± 0.02 mg Pt cm-2
per electrode, cell temperature of 50
°C, fully humidified fuel and oxidant with stoichiometries of 1.2 and 1.5, respectively)
well-dispersed and relatively small catalyst particles can be obtained. This takes place
when a ramp-down waveform is employed. To elaborate, a sharp increase in the applied
peak current density at the start of the pulse (similar to a square-pulsed waveform)
establishes a high concentration overvoltage leading to an increase in nucleation rate in
accordance with equation (6-47). If continued; however, the number of electroactive
species in the diffusion layer close to the surface of the cathode diminish faster than they
can reach the substrate surface from the bulk solution. At this point, the nucleation rate
decreases; but, since the cathodic current is still at its maximum, crystal growth becomes
the dominant mode of electrodeposition, leading to inevitable growth of existing crystals.
In other words, when a high peak current density is applied and maintained for an
extended period of time—as is the case for a rectangular pulse waveform—the system is
no longer limited by charge transfer, but by diffusion. In this case, adatoms will have
enough time to find stable places on the surface of the substrate to be reduced; i.e., on the
surface of existing crystals, rather than forming new nuclei. This diminishes the effective
surface area of the deposited catalyst, leading to inferior fuel cell performance. The
aforementioned problem is rectified by limiting the duration of the peak current density
to inhibit crystal growth. A ramp-down waveform is a prime example of such a strategy,
211
in which the peak current density is sharply increased to promote nuclei formation,
followed by a gradual decrease to impede crystal growth (by preventing the onset of a
diffusion-controlled process) while new nuclei can still be formed.
A triangular waveform also is designed to promote nuclei formation, while inhibiting
crystal growth when the pulse current is applied. Similar to a ramp-down waveform, a
rapid increase at the beginning of the pulse ensures the creation of high concentration
overvoltage at the electrolyte-electrode interface, transforming the electrodeposition
process to be dominated by nucleation. As the applied current density increases, the
concentration of the electroactive species at the interface decreases, shifting the system
into one that is dominated by crystal growth. However, as soon as the peak current
density is reached, the pulse current changes direction and starts to decrease as
electrodeposition continues. As a result, the concentration of the electroactive species in
the diffusion layer starts to increase once again, before the limiting current density is
reached. The end result is a well-dispersed catalyst layer with high active surface areas.
A ramp-up waveform is similar to a triangular one, at least at the beginning. A gradual
increase is observed at the start of the pulse promoting nucleation rather than crystal
growth. However, compared with a triangular waveform, it takes twice as long to reach
the designated peak current density. This additional time allows the adatoms to find
stable places on the surface of the electrode to be reduced (i.e., the existing crystals) and
the nucleation rate will decrease as a result. However, a sharp drop in the applied current
density at the conclusion of the on-time (ton) ceases crystal growth, ensuring smaller
particle size compared with a square-pulse waveform, for which the peak current density
is applied for the complete duration of pulse on-time.
Figure 8-50 shows TEM images of platinum particles for electrodes fabricated using (a)
ramp-down, (b) triangular and (c) rectangular waveforms with a peak deposition current
density of 400 mA cm-2
, a duty cycle of 4%, and 0.35 ± 0.02 mg Pt cm-2
. Electrocatalysts
prepared by the ramp-down and triangular waveforms exhibited a more uniform
distribution and smaller particle size than obtained by the conventional rectangular
waveform. These micrographs further validate the superiority of ramp-down and
212
Figure 50 TEM images of platinum catalyst electrodeposited employing different pulse
waveforms: (a) ramp-down (b) triangular and (c) rectangular (peak deposition current
density = 400 mA cm-2
, 4% duty cycle, 0.35 ± 0.02 mg Pt cm-2
per electrode)
Figure 8-51 Size distribution of platinum nanoparticles according to the type of
waveform: (a) ramp-down (b) triangular and (c) rectangular waveforms (peak deposition
current density = 400 mA cm-2
, 4% duty cycle, 0.35 ± 0.02 mg Pt cm-2
per electrode)
(a) (b) (c)
50 nm
50 nm
50 nm
213
triangular waveforms over the rectangular waveform in depositing a more uniform layer
with smaller nanoparticles. Figure 8-51 shows the histograms of the platinum particle
size for all three waveforms, where a significant proportion of the platinum nanoparticles
are in the neighbourhood of 1-3 nm (about 90% for the ramp-down and around 85% for
the triangular waveforms), while for the rectangular waveform, the majority of the
platinum nanoparticles are in the range of 3-5 nm (more than 80%). These clearly prove
the superiority of the ramp-down and triangular waveforms over the conventional
rectangular waveform and validate the experimental fuel cell performance results. They
also are in good agreement with the mathematical modeling predictions presented in
section 9.3.
8.5.5 Effect of Plating Solution Flow Rate on MEA Performance
Figure 8-52 presents the polarization curves for electrodes fabricated with different
electrolyte (platinum plating solution) flow rates in the plating cell. The amount of
platinum loading in the cathode and anode, duty cycle and peak current density were kept
constant at 0.35 ± 0.02 mg cm-2
, 20% and 50 mA cm-2
, respectively. The influence of
flow rate during electrodeposition is minimal; however, marginal improvements in
performance were observed for electrodes fabricated using higher flow rates. An
electrolyte flow rate of 454 mL min-1
was found to provide the best results (see Table 8-
17 and Figure 8-53). This can be attributed to a better mixing during deposition,
especially near the surface of the cathode, where the solution velocity is much lower than
that in the bulk solution. A shift from laminar to turbulent flow at higher flow rates also
may contribute to higher electrode performance, since more platinum ions will be
available near the surface of the cathode, resulting in a more uniform platinum
distribution.
214
Figure 8-52 Influence of plating solution flow rate on MEA performance (square pulse,
H2/Air, 20 wt% PTFE, 20% duty cycle, 0.35 ± 0.02 mg Pt cm-2
per electrode, cell
temperature of 50 °C, Nafion® 112, fully humidified fuel and oxidant with
stoichiometries of 1.2 and 2.5, respectively)
Table 8-17 Effect of plating bath flow rate on MEA performance
Electrolyte Flow Rate
(mL min-1
)
Voltage (V) at
200 mA cm-2
800 mA cm-2
92 0.689 0.314
235 0.690 0.320
454 0.706 0.331
581 0.685 0.327
215
Figure 8-53 Influence of plating bath flow rate on fuel cell voltage at four different
current densities (H2/Air, 20 wt% PTFE, 20% duty cycle, 0.35 ± 0.02 mg Pt cm-2
per
electrode, cell temperature of 50 °C, Nafion® 112, fully humidified fuel and oxidant with
stoichiometries of 1.2 and 2.5, respectively)
8.5.6 Anode Platinum Loading
It is well established that the cathode of a PEM fuel cell is the most influential component
controlling cell performance. In addition, more than half the total voltage loss in a PEM
fuel cell can be attributed to the poor cathode performance. The oxygen reduction
reaction is the rate-limiting reaction and many researchers have tried to optimize its
performance. As a result, the amount, distribution and size of the platinum electrocatalyst
play an important role in fuel cell design and operation. Consequently, the anodic
hydrogen oxidation reaction is fast and may not need as much platinum catalyst as the
cathode.
A series of experiments was performed to examine the effects of anode platinum loading
on fuel cell performance. Figure 8-54 presents the polarization curves of different
electrodes with varying amounts of platinum on the anode. The amount of platinum
loading at the cathode was kept constant at 0.35 mg cm-2
, along with duty cycle (20%)
216
and peak current density (50 mA cm-2
). The results indicate that the lowering of the
platinum loading at the anode from 0.35 to 0.15 ± 0.02 mg cm-2
has only a very minor
effect on fuel cell performance. However, anode loadings less than 0.15 ± 0.02 mg cm-2
result in a sharp decline in performance.
The above finding also is presented in Figure 8-55 in terms of platinum loading and cell
voltage for four different fuel cell output current densities. It is clear that reducing the
platinum loading at the anode from 0.35 to 0.15 ± 0.02 mg cm-2
has a very small impact
on cell performance. However, loadings less than 0.15 ± 0.02 mg cm-2
adversely affect
the performance of the anode, most notably, at high current densities, where a marked
decline is observed.
Figure 8-54 Influence of anode platinum loading on fuel cell performance (square pulse,
H2/Air, 20 wt% PTFE, cathode = 0.35 ± 0.02 mg Pt cm-2
, 20% duty cycle, cell
temperature of 50 °C, Nafion® 112, and fully humidified fuel and oxidant with
stoichiometries of 1.2 and 2.5, respectively)
217
Figure 8-55 Influence of anode Pt loading on electrode performance at four different
current densities (square pulse, H2/Air, 20 wt% PTFE, cathode = 0.35 ± 0.02 mg Pt cm-2
;
20% duty cycle, cell temperature of 50 °C, Nafion® 112, and fully humidified fuel and
oxidant with stoichiometries of 1.2 and 2.5, respectively)
8.5.7 Lifetime Behaviour of MEAs Prepared by Pulse Electrodeposition and
Conventional Techniques: Static Testing
Steady-state lifetime tests were performed on both commercial and in-house MEAs. The
former were obtained from E-TEK (E-TEK Div. of De Nora N.A., Inc., USA) and the
latter were prepared using the catalyzation technique described in this report. The type of
catalyst, gas diffusion layers and SPEs were identical for both MEAs. Although most
researchers prefer to employ accelerated stress tests (AST) to evaluate the durability of
different MEAs in PEM fuel cells, a steady-state lifetime test was utilized here to gain a
better understanding of various failure modes. The emphasis was placed on catalyst
degradation, since this was the primary difference between the two specimens under
investigation.
Catalyst degradation in PEM fuel cells operated for extended periods of time has been
associated with delamination of the catalyst layer, catalyst migration, catalyst ripening,
catalyst washout and carbon corrosion [427]. All these undesirable but inevitable
processes can contribute to apparent activity loss in the catalyst layer, and generally result
from changes in the microstructure of this layer and/or the loss of electronic and ionic
contact with the GDL and/or SPE.
218
A durability test on two different MEAs—E-TEK MEA and in-house MEA—was
performed in accordance with the experimental procedure outlined in section 7.6.2.2.
Figure 8-56 compares the potential-time curves for these MEAs, both of which were
fabricated with similar components, including identical Nafion® layers and catalyst type
on both anode and cathode. The in-house MEA generated a higher cell voltage for the
first 240 hours of operation compared with the commercial MEA from E-TEK, as shown
in Figure 8-57. However, the in-house MEA experienced a sharp decline in cell voltage at
about the 240-h mark, its performance dropping by approximately 10%, from 555 mV to
around 500 mV, after which it maintained a relatively constant output of 495 mV until
the 2800-h mark, when the cell voltage again began to fall. This time, however, it did not
recover and the cell voltage reached zero after 200 hours of operation after the decline at
the 2800-h mark. On the other hand, the commercial MEA performed well until it was
removed from the test cell after 4100 hours of continuous operation.
The sharp decrease in cell voltage after the second decline, indicated that a major failure
inside the MEA had occurred. Subsequent scanning electron microscopy revealed a
significant separation between the SPE and the catalyst layer on the cathode side of the
in-house MEA, as shown in Figure 8-58. Minor separation on the anode side also was
evident. These problems were attributed to an ineffective MEA fabrication process in this
case. Accordingly, another MEA identical to the first in-house MEA was prepared to
prove the above hypothesis. This time extra care was exercised during the fabrication and
testing phases to minimize human and mechanical errors. The durability of this second
MEA was determined according to the experimental procedure given in section 7.6.2.2.
After an operation of nearly 3000 hours, the MEA’s performance was comparable to that
of the commercial MEA without a noticeable decay in cell voltage during the complete
operation cycle. Life test results for this second MEA are presented in Figure 8-59. The
decrease in cell voltage for the in-house and the commercial MEAs for the initial 3000 h
of operation were found to be 2.1% and 2.8%, respectively.
219
Figure 8-56 Durability of single commercial (0.50 mg Pt cm-2
per electrode) and in-house
(0.35 mg Pt cm-2
per electrode) MEAs with apparent areas of 5 cm2 operated at a cell
temperature of 60 °C. Hydrogen and air are used as fuel and oxidant entering the cell at
100% RH with stoichiometries of 1.2 and 2.5, respectively. The operation time is 4100 h.
Figure 8-57 Durability of single commercial (0.50 mg Pt cm-2
per electrode) and in-house
(0.35 mg Pt cm-2
per electrode) MEAs with apparent areas of 5 cm2 operated at a cell
temperature of 60 °C. Hydrogen and air are used as fuel and oxidant entering the cell at
100% RH with stoichiometries of 1.2 and 2.5, respectively. The operation time is 280 h.
220
Figure 8-58 SEM image of the cross section of the in-house MEA showing delamination
on one side of the Nafion® membrane
Figure 8-59 Durability of single commercial (0.50 mg Pt cm-2
per electrode) and in-
house (0.35 mg Pt cm-2
per electrode) MEAs with apparent areas of 5 cm2 operated at a
cell temperature of 60 °C and ambient pressure. Hydrogen and air are used as fuel and
oxidant entering the cell at 100% RH with stoichiometries of 1.2 and 2.5, respectively.
The operation time is 3000 h.
04589 20 kV 50m
Apparent
delamination on
one side of the SPE
Nafion® 112
Cathode catalyst layer
Anode catalyst layer
221
Figure 8-60 shows the open circuit voltage data for the commercial and in-house MEAs
obtained at different time intervals. It can be seen that OCVs initially increase slightly
with time, reach a maximum value at about 2000 h (for both MEAs) and then decrease.
Furthermore, the OCV of the in-house MEA was higher than that of the commercial
MEA for the first 250 hours and between 2000 and 2500 hours after which the OCV of
the commercial MEA was higher for the remainder of the test. The initial rise in OCV of
both MEAs is attributed to the continuous hydration of Nafion®, where ionic conductivity
is improved resulting in a slight increase in cell performance.
Figure 8-60 Open circuit voltage (OCV) data obtained at different time intervals for
an in-house and a commercial MEA
8.5.8 Lifetime Behaviour of MEAs Prepared by Pulse Electrodeposition and
Conventional Techniques: Dynamic Testing
Steady-state lifetime tests reveal important information about the durability of MEAs;
however, such information is only pertinent to systems under a constant load. Real
systems, on the other hand, operate under transient conditions, where the load is
constantly changing in response to real-time variations in operational demands. To gain a
better understanding of the influence of changes in operational conditions on MEAs, a
222
number of dynamic life tests were carried out according to the experimental procedure
outlined in section 7.6.2.3.
Figure 8-61 shows the power output of two 200-W PEM fuel cell stacks, one containing
in-house and the other commercial MEAs. Both stacks were used to charge a battery
bank comprising three 12-V lead acid batteries sixty-three times over a 60 day period.
The initial performance of the stack containing the in-house MEAs was superior to that of
the commercial MEAs. This can clearly be seen in Figure 8-61 for the first 30 charges,
where the average power outputs are 218 W and 214 W for in-house and commercial
MEAs, respectively. The degree of variation in stack output also was lower for the in-
house MEAs for the first 30 charges. The drop in performance, however, was more
pronounced for the in-house MEAs after the 30th
charge. This is most likely due to settled
changes in the morphology and distribution of catalyst particles in the MEAs.
Figure 8-61 Power output of 200-W PEM fuel cell stacks containing in-house and
commercial MEAs running on hydrogen and air at ambient temperature and pressure
223
In another series of experiments, two 200-W PEM fuel cell stacks, each containing 42
cells, were used to directly power an electric bicycle (see Figure 7-6) to assess the
durability and performance of different MEAs operated with changing loads according to
the experimental procedure outlined in section 7.6.2.3. Figure 8-62 shows the OCVs for
both MEAs at the start of each trial run. The initial OCV of the stack containing in-house
MEAs was higher for every run compared with that of the stack utilizing commercial
MEAs. In addition, the variation in OCV throughout the experiment was greater for the
commercial MEAs. At 1.007 V the average initial OCV for the fuel cell stack containing
in-house MEAs was about 6% higher than its commercial counterpart. Since the primary
difference between the above MEAs was the method employed to deposit catalysts, it can
be concluded that the noticeable improvement of in-house MEAs is due to higher catalyst
utilization.
The OCVs of both fuel cell stacks also were recorded at the end of each trial run; the
results are presented graphically in Figure 8-63. Initially, the OCVs of both stacks
increased and then leveled off for the remainder of the experiment. Similar to the
previous series of initial OCVs, the final OCVs of the stack containing in-house MEAs
were higher than those of the stack containing commercial MEAs. The average final
OCV of the fuel cell stack utilizing in-house MEAs was 1.022 V, while that of the
commercial stack was 1.012 V; this is an increase of 10 mV (about 1%). This small
improvement may result from a more effective catalyst layer based on the deposition
method described in this thesis. As can be seen from Figure 8-48, the catalyst layer
deposited by the pulse electrodeposition technique is about 5 m in thickness compared
with the commercial layer that is approximately 10 times thicker at 50 m. The benefits
of a thin catalyst layer are twofold: better water management and lower ohmic losses,
both of which contribute to higher cell/stack performance. Due to shorter pathways from
the catalyst/membrane interface to the GDL, water is more effectively removed from the
interior of the MEA avoiding flooding conditions, where stack performance is
compromised. In addition, elevated hydration levels of the catalyst and electrolyte layers
are possible, which results in higher ionic conductivity of the electrolyte.
224
Figure 8-62 Initial OCV of in-house and commercial (E-TEK) MEAs in PEM fuel cell
stack in a dynamic system running on H2/Air at ambient temperature and pressure (0.50 ±
0.02 mg Pt cm-2
for anode and cathode of the commercial MEAs and 0.35 ± 0.02 mg Pt
cm-2
for the in-house MEAs)
Figure 8-63 Final OCV of in-house and commercial (E-TEK) MEAs in PEM fuel cell
stack in a dynamic system running on H2/Air at ambient temperature and pressure (0.50 ±
0.02 mg Pt cm-2
for anode and cathode of the commercial MEAs and 0.35 ± 0.02 mg Pt
cm-2
for the in-house MEAs)
225
Furthermore, thin catalyst layers lead to a superior cell performance since reactants (and
products) are no longer required to travel through long pathways to reach the three-phase
interface deep inside the MEA, where the electrochemical reactions are taking place.
Lastly, ohmic losses decrease in the presence of a thin catalyst layer, since electrons now
are only required to traverse a shorter distance between the place they are generated (the
catalyst/SPE interface) and the current collectors.
The next series of experiments on MEA durability involved recording and analyzing the
maximum power points for both fuel cell stacks—one containing in-house MEAs and
another employing commercial MEAs—during the operation of the direct-drive bicycle
under real-life conditions in accordance with the method presented in section 7.6.2.3.
Figure 8-63 shows the maximum power points obtained from both fuel cell stacks while
the bicycle was running powered directly by a single stack at any one time. The reported
maximum power points in Figure 8-64 are the single highest recorded power output
during a given run. A similar trend for both fuel cell stacks was observed: a sharp
increase in fuel cell power output for the first 10 runs followed by a more gradual
increase in stack output. Initially, the performance of the fuel cell stack containing the
commercial MEAs was slightly higher than those employing in-house MEAs; however,
this trend was reversed quickly and, after about 15 runs, the latter stack exhibited a
slightly better performance for the remainder of the trial runs. The maximum power
points of in-house and commercial MEAs were 231 W and 222 W, respectively. More
importantly, the average peak power points (the highest recorded power output during a
single run—about 90 minutes) for the stacks utilizing in-house and commercial MEAs for
the complete duration of this series of experiment were 225 W and 217 W, respectively.
The observed 4% increase in the average cell power output is ascribed to a more effective
catalyst layer present in the in-house MEAs compared with commercial MEAs.
226
Figure 8-64 Maximum power output of 42-cell fuel cell stacks containing in-house and
commercial (E-TEK) MEAs tested in a dynamic system running on H2/Air at ambient
temperature and pressure (0.50 ± 0.02 mg Pt cm-2
for anode and cathode of the
commercial MEAs and 0.35 ± 0.02 mg Pt cm-2
for the in-house MEAs)
227
8.0 Mathematical Model
9.1 Introduction
A mathematical model based on the works of Molina et al. [642] and Milchev [643, 652,
653] was further developed and refined to describe the dynamics of the experimental
metal electrodeposition process onto a solid surface. The model predicts and explains a
number of key concepts and variations in such systems, including species concentration
in the vicinity of the working electrode with time, grain size distribution of the
electrodeposited species, the magnitude of the overvoltage during the process, the
nucleation rate, the grain growth and the hardness of the resulting layer using four
different waveforms: rectangular, triangular, ramp down and ramp up, all with relaxation
times. Nickel was initially used to carry out the pulse electrodeposition to show the
generality of the model and to curtail cost.
9.2 Mathematical Model Development
9.2.1 Concentration and Overvoltage Profiles of Different Current Waveforms
It is imperative to understand the mass transfer mechanism during metal deposition.
There are three primary modes of mass transfer: diffusion, convection, and ionic
migration. Diffusion is usually described by Fick’s first law, where the diffusion flux of
a solute in a one-dimensional binary system is given by:
x
CDJ
(9-1)
where J is the diffusion flux of the species (mol cm-2
s-1
), D is the diffusion coefficient or
diffusivity (cm2 s
-1), C is the concentration (mol cm
-3) and x is the direction of the flux
(cm).
The driving force FD for diffusion of any given species is the gradient in its chemical
potential:
1
molper
molNdx
dFD
(9-2)
where (FD)per mol is the driving force per mole.
228
The driving force F'D acting on one liter of solution of concentration c in mol L-1
is
L
N
mol
N
L
mol
DD cFF (9-3)
dx
dc
dx
dcFD
(9-4)
For realistic concentration gradients the diffusion flux JD is directly proportional to the
driving force:
dx
dcB
dx
dcBFBJ DD
(9-5)
where B is a constant of proportionality.
The chemical potential µ of any given species in solution is given by
)(ln cyTR (9-6)
where µ*, a function of temperature only, is the chemical potential in the reference state
(an ideal interaction-free one molar solution) and y is the activity coefficient of the
species. Differentiating (9-6):
dx
dy
ydx
dc
cTR
dx
d 11 (9-7)
If the concentration gradient is not too great, it can be assumed that the activity
coefficient is approximately constant over the gradient, so that dy/dx ≈ 0, and (9-7)
becomes
dx
dc
c
TR
dx
dc
cTR
dx
d 1 (9-8)
dx
d
TR
c
dx
dc (9-9)
Experimentally it is observed that the diffusion flux JD is proportional to the
concentration gradient (Fick’s Diffusion Law):
229
dx
dcDJ D (9-10)
where D is the diffusion coefficient for the species.
Substituting (9-9) into (9-10) gives
dx
d
TR
cD
dx
d
RT
cD
dx
dcDJ D
(9-11)
Fick’s first law assumes that the concentration of the species under investigation is
independent of time. In real systems, however, as electrodeposition progresses, the
concentration of the species in the vicinity of the working electrode will inevitably
change. Fick’s second law takes this into account and predicts how concentration varies
with time as a result of diffusion. Fick’s second law is generally derived from Fick’s first
law:
x
cD
xJ
xt
C
(9-12)
Two cases can be considered:
The diffusion coefficient, D, is independent of the coordinate and/or species
concentration:
2
2
x
cDc
xxD
x
cD
xt
c
(9-13)
The diffusion coefficient, D, is not independent of the coordinate and/or the species
concentration:
cDt
c
(9-14)
Metal deposition or electrodeposition can be described by Fick’s second law of diffusion
with a constant diffusion coefficient, namely
2
2
x
cD
t
c
(9-15)
This equation can readily be solved by assigning an initial condition (9-16) and two
boundary conditions (9-17 and 9-18) [642]:
ocxc ),0( (9-16)
230
octc ),( (9-17)
zFD
ti
x
c
x
)(
0
(9-18)
The current density function, i(t), in expression (9-18) is unique for each type of current
waveform and can be expressed by a unit step function that is discontinuous with a
―zero‖ value for negative argument and a value of ―one‖ for a positive argument. This is
known as a Heaviside function and is routinely used in signal processing to define signals
that switch on and off at specified time intervals. Generally speaking, the Heaviside
function H(x) is the cumulative distribution function of a random variable and can be
expressed as the integral of the Dirac delta distribution,
:
x
dxxxH )()( (9-19)
where the Dirac delta distribution,
(x), is expressed as:
0,0
0,)(
x
xx (9-20)
Based on the above definitions, the Heaviside function is commonly defined as:
0,0
0,1)(
x
xxH (9-21)
Based on the Heaviside function, Molina et al. [642] have defined the mathematical
expressions for four different current waveforms—rectangular, triangular, ramp up and
ramp down—as follows:
Rectangular: )()()( tStSiti kwp (9-22)
Triangular:
)()()()()( tStS
b
thtStS
a
wtiti hkkwp (9-23)
Ramp up: )()()( tStSwta
iti kw
p (9-24)
Ramp down: )()()( tStStka
iti kw
p (9-25)
231
where a and b are defined in Fig. 7-3 and the Heaviside function is defined in terms of
Sk(t):
ktif
ktiftSk
0
1)( (9-26)
In equations (9-22) to (9-25):
Nw (9-27)
aNk (9-28)
baNh (9-29)
where N is the number of pulse cycles (N = 0, 1, 2, ….., n) and
is the pulse period.
To obtain analytical solutions, the partial differential equation (9-15) is solved using
Laplace transforms. The full solution for the rectangular waveform is presented below
and a detailed solution for the ramp-down waveform is provided in Appendix D.
The mass transfer in most electrochemical systems, including electrodeposition processes
employing different waveforms, is customarily described by Fick’s second law of
diffusion—equation (9-15). Taking the Laplace transform of this equation yields:
02
2
ccsdx
cdD (9-30)
According to the initial condition—equation (9-16)—the concentration at the start of the
first pulse (t = 0) is equal to the bulk concentration; the Laplace transform of (9-16)
results in:
s
cxc 0),0( (9-31)
Similarly, the Laplace transform of the boundary condition (9-17) gives:
s
csc 0),( (9-32)
Applying the Laplace transform to the mathematical expression representing the
rectangular waveform, expression (9-22), yields:
232
22)(
s
e
s
eiti
ksws
p (9-33)
Substituting the transformed Heaviside function—(9-33)—into boundary condition
(9-18) results in:
22
0s
e
s
e
DFz
i
x
c kswsp
x
(9-34)
The ordinary differential equation (ODE) that was derived from Fick’s second law of
diffusion (presented in equation (9-30)) can readily be solved using expressions (9-22)
and (9-32) to give
s
ceAc
xD
s
0
(9-35)
The constant A in the above expression can be evaluated by taking its derivative and
putting it into equation (9-34):
s
c
s
D
DFz
i
s
c
e
dx
cdA
p
D
s
001
(9-36)
Simplifying the above equation:
)379(
1
2/32/3
22
s
e
s
e
DzF
i
s
e
s
e
sDzF
iA
kswsp
kswsp
Putting equation (9-37) into (9-35):
s
ce
s
e
s
e
DFz
ixsc
xD
sksws
p 0
2/32/3),(
(9-38)
The surface concentration can be expressed as follow:
233
s
ce
s
e
s
e
DFz
ixsc
D
sksws
p 0)0(
2/32/3),(
(9-39)
2/32/3
0),(s
e
s
e
DFz
i
s
cxsc
kswsp
(9-40)
The solution to the original diffusion equation is obtained by applying the inverse
Laplace transform to equation (9-40):
)419()(
)2/3()(
2/3)0,(
2/12/1
0
tS
kttS
wt
DzF
ictc kw
p
The concentration overvoltage for a diffusion-controlled process is represented by:
0
)0,(ln
c
tc
Fz
TR (9-42)
Substituting equation (9-41) into (9-42) yields the overvoltage equation for a rectangular
waveform:
0
2/12/1
0 )()2/3(
)(2/3
lnc
tSkt
tSwt
DzF
ic
zF
RTkw
p
(9-43)
)(
)2/3()(
2/31ln
2/12/1
0
tSkt
tSwt
DFcz
i
Fz
TRkw
p (9-44)
Equations (9-41) and (9-44) are used to determine the concentration and concentration
overvoltage profiles of electrochemical systems employing square-pulse
electrodeposition.
9.2.2 Electrochemical Nucleation and the Critical Nucleus
Electrochemical nucleation occurs between two different phases: the electrolyte
containing the metal ions and the electron-conducting electrode. Under special
conditions, ions in the electrolyte that are in close proximity to the working electrode
begin to exchange electrons, resulting in an interfacial charge transfer and, ultimately,
234
electrochemical nucleation. For the nucleation and growth of any metal nanocrystallite,
including platinum on a carbon substrate, two limiting cases must be examined:
instantaneous and progressive nucleation. In the case of the former, the number of nuclei
present on the surface of the substrate at any time after the plating current is applied will
remain constant. For the latter; however, the number of nuclei is a function of time; i.e., it
continuously increases as plating progresses.
Earlier theories of electrochemical crystal growth at the atomic level considered the
substrates to be perfect surfaces without growth sites. As a result, nucleation was
perceived as the first step in deposition [333]. Later, researchers realized that ―real‖
surfaces have imperfections and, consequently, an array of growth sites. For progressive
nucleation, the total applied current,
iT (t) , is divided into two parts: a nucleation current,
iN (t) , and a growth current,
iG(t), such that
)()()( tititi GNT (9-45)
The nucleation rate J is related to the nucleation current,
iN (t) [642, 643]:
c
N
nez
tiJ
)(
(9-46)
where nc represents the size of the critical nucleus, which, according to Milchev [643] is
the ―cluster of the new phase that is in unstable equilibrium with the supersaturated
parent phase.‖ Here the ―unstable equilibrium‖ refers to the state of the system, since,
adding more atoms to the cluster from the parent phase will convert the critical nucleus
into a stable cluster leading to its irreversible growth. On the other hand, removal of
atoms from the cluster will lead to its irreversible decay [643].
According to Milchev [643] & Molina et al. [642], the critical nucleus size is defined as:
)(3
3203
23
F
vn M
c
(9-47)
where, is the specific free surface energy (J m-2
), vM is the molecular volume of the
metallic deposit (m3 mol
-1), and
is the electrochemical potential of the building units
or components (J), given by
235
ez (9-48)
and
F(0) is the wetting angle function, defined as:
)(cos4
1)cos(
4
3
2
1)( 0
3
0
0
0
V
VF (9-49)
In the above equation, V is the volume of a spherical segment with radius R formed by a
liquid droplet on a flat solid surface with a cap-shaped form as shown in Figure 9-1(a),
and V0 is the volume of a normal sphere. V and V0 are defined in equations (9-50) and (9-
51), respectively [643]:
0
3
0
3
0 coscos323
1),(
RRV (9-50)
3
03
4RV
(9-51)
(a) (b)
Figure 9-1 A liquid droplet formed on (a) a flat solid surface and (b) its cross section
[643]
In Figure 9-1 (b) and equations (9-49) and (9-50),
0 is the wetting angle (Rad). The
required energy for an accumulation of atoms to form a stable cluster—the critical
nucleus—is given in terms of changes in the electrochemical Gibbs free energy of the
system [642]:
cc nnG
2
1)( (9-52)
Substituting equation (9-47) into (9-52) yields:
236
)(3
16)( 02
23
F
vnG M
c
(9-53)
For the case of progressive and instantaneous nucleation without overlap, the initial
creation of nuclei on the substrate does not influence future nuclei formation or
interaction amongst growing clusters since the actual surface fraction covered by the
growing nuclei is negligible compared with the total surface area of the substrate. The
growth current, iG(t), for an electrochemical system with progressive nucleation is given
by [642, 643]:
t
G duutIuJti0
1 )()()( (9-54)
where, J(u) is the nucleation rate at time t = u and I1(t – u) is the growth current of a
single cluster formed at t = u.
The single cluster growth current, I1, is an important parameter in defining the
crystallization process and is given by the following expression [643]:
)(exp1 2/1
2/3
1 tTR
FzAI
(9-55)
where 2/3
0
2/1
0
2/5 ][][)(][2 cDvFzFA M (9-56)
The radius Rc of a homogeneously formed hemisphere on the surface of a solid substrate
can be calculated using the Gibbs-Thomson equation:
M
c
vR
2 (9-57)
Consider a single nucleus formed on the surface of a substrate at t = u. As
electrodeposition continues, this nucleus will grow and it is necessary to determine its
radius at any point in time during electrodeposition. The radius Rg of a growing nucleus
at time t since its formation on a foreign solid surface is calculated from:
)(
)(
)(4
3)(
0
3
tJ
ti
FzF
vtR
gM
g
(9-58)
237
If a cap-shaped grain is assumed (refer to Figure 9-1, ref. [643]), the final size Rf
distribution can be evaluated knowing Rc, Rg and the wetting angle,
0:
33
0
3 )(sin gcf RRR (9-59)
The average radius of the formed grains can readily be obtained by combining equations
(9-46) and (9-59):
3/1
0
0
3
)(
)()(
2
t
t
f
dttJ
dttJtRd
R (9-60a)
Lastly, the grain average radius R (or diameter d ) obtained from equation (9-60) can be
used to obtain the hardness (H) of the deposited layer using the Hall-Petch equation
[642]:
g
kH
y3 (9-61)
In the above equation, g is the acceleration due to gravity and ky is defined as [642]:
d
kkk l
oy (9-62)
where k0 is a materials constant for the starting stress for dislocation movement; this also
can be thought of as the resistance of the lattice to dislocation motion, and kl is the
strengthening coefficient, which is a constant unique to each material.
Substituting (9-62) into (9-61) and rearranging, gives the average grain diameter d as a
function of the hardness H:
2
3
3
o
l
kgH
kd (9-60b)
In this study, the average particle size of an electrodeposited platinum layer is correlated
with its hardness both experimentally and theoretically. The latter is accomplished
through mathematical modeling of such a layer using the Hall-Petch relationship, based
on the work of Molina et al. [642]. It is well established that material hardness increases
with decreasing particle size as long as the critical grain size has been established. The
238
hardness decreases with decreasing grain size below this critical grain size. It is also
proven that the catalytic activity of any catalyst, including platinum, increases with
increasing effective surface area. In other words, smaller catalyst particles will exhibit a
higher catalytic activity.
9.2.3 Different Types of Crystal Growth5
The catalytic activity of a catalyst layer correlates strongly with its particle size and, in
turn, with its average grain diameter. Hence, it is necessary to calculate the nucleation
rate, J(t), of an electrodeposition process in order to evaluate its average grain diameter
using equation (9-60b). The evaluation of nucleation rate, however, requires prior
knowledge of both nucleation and growth currents in the case of progressive nucleation.
Most published works [502, 540, 642] have assumed that the contribution of one of these
currents—usually the growth current, iG(t)—is negligible compared with the other.
In this study, contributions from both nucleation and growth currents for all waveforms
are considered. Hence the nucleation rate in equation (9-46) is evaluated from equation
(9-45) by considering a number of unique electrochemical growth conditions. The
growth current, iG(t), for any electrodeposition process involving progressive nucleation
can be readily evaluated by solving the convolution integral shown in equation (9-54). A
closer examination of this expression reveals that I1(t)—the current of a hemispherical
cluster growing at a constant electrode potential—must be determined. Based on the
works of Milchev [643], two mathematical expressions for the radius R(t) and the current
I1(t) of a single growing hemispherical cluster will be derived for five unique cases of
electrochemical growth under pure charge transfer control (ionic), pure diffusion control,
pure ohmic control, combined charge transfer and diffusion control and combined charge
transfer and ohmic control.
It is worth noting that the growth of any cluster in this fashion is similar to the growth of
a hemispherical liquid drop on a solid surface. This dictates that the faces of a 3-
dimensional crystal must contain a large number of growth sites [643], and is a frequently
5 These are based on the works of Milchev [643] and full derivations of equations indicated with an asterisk
(*) are given in the appendix.
239
used approximation that is satisfied in this study, owing to the existence of a considerable
number of growth sites on carbon substrates.
9.2.3.1 Electrochemical Crystal Growth under Pure Charge Transfer Control
Consider a single-ion electrochemical system where pulse current electrodeposition is
about to be carried out to deposit a nanocrystallite metallic layer with a cluster of radius R
and a surface area, SR, on a foreign solid substrate. During the very first transient stage of
this process, the double layer is charged, and the overvoltage at time t, t, is given by
[643]:
dlel
tC
texp1 (9-63)
where η is the steady state overvoltage, and el and Cdl are the ohmic resistance of the
electrolyte and the double layer capacitance, respectively. It is evident that after some
time t ≈ 5(el)(Cdl), the double layer is fully charged and the overvoltage becomes .
Beyond this time the kinetics are governed by charge transfer kinetics, with
= Erev – E > 0. From this time onwards, the formation of a new phase—nuclei—on the
electrode surface becomes the dominant process. Initially, the growth of the cluster on the
electrode surface is dominated by the rate of charge transfer across the electrical double
layer at the electrode-electrolyte interface. The growth current, I1(t), is approximated by
the Butler-Volmer equation as [643]:
TR
Fz
TR
FzitStI R
)1(expexp)()( 01 (9-64)
where i0 is the exchange current density (A cm-2
) and SR = 2 R2(t). Substituting for SR
yields
TR
Fz
TR
FzitRtI
)1(expexp)(2)( 0
2
1 (9-65)
It should be noted that in this treatment both cathodic currents and cathodic overvoltages
are treated as positive quantities. This simplifies the logarithmic treatment of negative
numbers.
240
The mass balance during the growth of a single spherical nucleus controlled by ion mass
transfer also can be described by Faraday’s law according to [643]:
dt
dRR
v
FztI
M
2
1
2)(
(9-66)*
It should be noted that this equation describes the mass balance irrespective of the growth
mechanism. Explicit formulae for I1(t) and R(t) can be obtained by combining equations
(9-65) and (9-66) and solving the resulting differential equation with the boundary
condition R(t) = 0 at t = 0. As a result:
tTR
Fz
TR
Fz
Fz
vitR M
)1(expexp)( 0 (9-67)*
2
3
2
3
0
2
1
)1(expexp
)(
2)( t
TR
Fz
TR
Fz
Fz
ivtI M
(9-68)*
Equation (9-68) is used to determine the growth current in the convolution integral
presented in equation (9-54) for cases where crystal growth is controlled by charge
transfer across the electrical double layer.
9.2.3.2 Electrochemical Crystal Growth under Combined Charge Transfer and
Diffusion Control
The previous case is applicable only to systems where the electrodeposition is carried out
in a relatively short time period, the primary assumption being that the concentration of
the electroactive species at the surface of the electrode, cs, is virtually identical to c₀, that
in the bulk solution. However, for longer times when the surface concentration of the
electroactive species is lower than the bulk concentration, in addition to charge transfer,
diffusion also must be considered. For the simple case of steady-state diffusion, the
concentration of the electroactive species around the growing hemispherical cluster is
given by [643]:
c
c
r
Rcc s11 (9-69)*
241
where R is the radius of each cluster and r is the radial distance from the centre of the
cluster. If an instantaneous steady state is assumed, the concentration gradient at the
cluster-electrolyte interface is given by
R
cc
dr
dc s
Rr
)(
(9-70)*
Combining Faraday’s law (equation (9-66)) with equations (9-65) and (9-70) results in:
TR
FziRcDFz
TR
Fz
TR
FzcDiv
dt
dRM
exp
)1(expexp
0
0
(9-71)*
Imposing the initial condition, R(t) =0 at t = 0, gives [643]:
121)(2/1 ntmtR (9-72)*
where Pi
cDFzm
0
(9-73)
TR
FzP
exp (9-74)
cDFz
Qivn M
2
2
0
)(
(9-75)
TR
Fz
TR
FzQ
)12(exp
2exp (9-76)
Substituting equations (9-72) – (9-76) into Faraday’s law (9-65) and solving for the
growth current yields:
1
)21(
1)(
2/11nt
ntptI (9-77)*
where
3
0
24
Pi
QcDFzp
(9-77a)
242
Equations (9-72) and (9-77) are used to calculate R(t) and the growth current, I1(t), in the
convolution integral of equation (9-54) for cases where crystal growth is controlled by a
combination of charge transfer and diffusion.
9.2.3.3 Electrochemical Crystal Growth under Pure Diffusion Control
The electrochemical crystal growth is assumed to be under pure diffusion control when
electrodeposition times are relatively long. The same holds true when the exchange
current density is high provided that nt > 50. In such cases I1(t) and R(t) can be
expressed as [643]:
2/1
2/1
2/1exp12)( t
TR
FzvcDtR M
(9-78)*
2/1
2/3
2/33/1
1 exp12)()( tTR
FzvcDFztI M
(9-79)*
Equations (9-78) and (9-79) can be further simplified, provided that the following
conditions are satisfied:
the surface concentration of the electroactive species approaches zero; i.e., cs 0,
the cathodic overvoltage is greater than FzTR /5 (69.6 mV at 50 °C)
Under these conditions,
2/12/12)( tvcDtR M (9-80)
2/12/33/1
1 2)( tvcDFztI M (9-81)
9.2.3.4 Electrochemical Crystal Growth under Complete Ohmic Control
The concentration of the electroactive species at the surface of the substrate, cs, stays
very close to the bulk concentration, c₀, during pulse electrodeposition if two conditions
are met:
the cluster is growing at a relatively low rate,
the electrolyte is continuously stirred during the electrodeposition process
In this case, the total overvoltage η consists of the overvoltage at the surface of the
cluster, ηs, plus the ohmic drop through the solution:
243
)()(1 RtIs (9-82)
where (R) is the ohmic resistance of the electrolyte around the cluster, calculated from
L
R
RR
el
12
1)(
(9-83)*
where, el (-1
cm-1
) is the specific conductivity of the solution and L is the distance
between the cluster and the counter electrode. Equation (9-83) can be simplified if the
distance between the cluster and the counter electrode is much greater than the radius of a
single cluster formed on the surface of the working electrode; i.e., L >> R. This is
actually the case in this study; hence the following equation has been employed to
calculate (R):
R
Rel2
1)( (9-84)
If the overvoltage at the surface of the cluster is entirely accounted for by the ohmic drop,
then, from equation (9-82), the total overvoltage η reduces to the ohmic drop through the
solution:
)()(1 RtI (9-85)
Substituting equation (9-84) into (9-85) gives:
R
tI
el
2
)(1 (9-86)
From which RtI el2)( (9-86a)
Thus, when the growth kinetics of the cluster is under complete ohmic control, Equations
(9-66) and (9-86a) give the radius of the cluster and its growth current as [643]:
2/1
2/1
2)( t
Fz
vtR Mel
(9-87)*
2/1
2/1
2/32/3
1 2)( tFz
vtI M
el
(9-88)*
244
9.2.3.5 Electrochemical Crystal Growth under Combined Charge Transfer and
Ohmic Control
This case is, by far, the most complicated of those discussed so far. In this case, the
overvoltage at the cluster surface is given by Equation (9-82) and (9-84) as [643]:
)()(1 RtIs
R
tI
el
2
)(1 (9-89)
And the Butler-Volmer equation takes the form:
R
tI
TR
Fz
R
tI
TR
FziRtI
elel
2
)()1(exp
2
)(exp2)( 11
0
2
1 (9-90)
Equating Eqn (9-66) with Eqn (9-90) gives [643]:
dt
dRRPP
dt
dRRPP
dt
dR4321 expexp (9-91)*
where
TR
Fz
Fz
iv oM exp1P (9-92)
MvTR
Fz
2
2P (9-93)
TR
Fz
Fz
iv oM )1(exp3P (9-94)
MvTR
Fz
2)1(
4P (9-95)
Approximate analytical expressions for the above equation are provided for low and high
ohmic drops by Melchev [643], since an exact solution to this equation is not possible.
245
9.3 Model Validation
The proposed electrodeposition technique should work for the deposition of any metal
cation onto a conductive substrate provided that the concentration of the metal in the
plating bath is low. In addition, the mathematical model developed in the previous
section is applicable to any electrodeposition system, irrespective of the type of metal. To
demonstrate the generality of this hypothesis, a series of experiments was carried out
using nickel and copper. The results for copper have been presented in previous sections;
here the findings for nickel are discussed, followed by the findings for platinum. The
validity of the mathematical model developed is verified by comparison with the
experimental results.
9.3.1 Nickel Electrodeposition
Nickel electrodeposition was carried out according to the method described in section
7.5.3. After electrodeposition, the surface morphology of each specimen was examined
and characterized using SEM. The grain sizes were measured according to ASTM E112-
95, while microhardness tests were performed in accordance with ASTM E384 (refer to
Appendix E for a brief description of the latter method). Experimental results—taken
from the present study as well as from published work [504]—then were compared with
hardness results generated by the model developed in this study and a similar model
reported by Molina et al. [642]. Both experimental and model data are presented in
tabulated and graphical formats in Tables 9-1 through 9-4 and Figures 9-2 to 9-5,
respectively.
Experimental and model results for a rectangular waveform are given in Table 9-1. Our
experimental data first are compared with a set reported by Wong et al. [504], who used
identical electrolyte bath composition and electrodeposition parameters. A comparison
between the two experimental sets shows a strong agreement. Mathematical model
hardness data were obtained by considering five different sets of conditions in terms of
nucleation and growth currents as described in sections 9.2.3.1 through 9.2.3.5. It should
be noted that the peak current density of the rectangular waveform must be half that of
the other waveforms to generate the same average current density.
246
Table 9-1 Experimental and model hardness data for nickel (rectangular waveform)
Hardness (kg mm-2)
Average current density (mA cm
-2)
Experimental Mathematical
Wong et al.
This study
Molina et al.
model
Pure diffusion
Pure charge
Transfer (ionic)
Pure ohmic
Combined charge
transfer & diffusion
Combined charge
transfer & ohmic
100 140 136 118 105 148 147 155 155
200 160 157 166 147 208 208 220 220
300 175 173 203 181 255 255 269 269
400 200 202 235 208 295 295 311 311
500 260 254 264 233 331 331 348 349
600 350 347 290 255 363 363 383 383
Table 9-2 Experimental and model hardness data for nickel (ramp-up waveform)
Hardness (kg mm-2)
Average current density (mA cm
-2)
Experimental Mathematical
Wong et al.
This study
Molina et al.
model
Pure diffusion
Pure charge
Transfer (ionic)
Pure ohmic
Combined charge
transfer & diffusion
Combined charge
transfer & ohmic
100 153 155 129 125 125 125 104 104
200 175 173 182 177 177 177 147 147
300 195 199 223 216 216 216 179 179
400 225 229 259 249 249 249 207 207
500 290 286 290 279 279 279 231 231
600 390 388 319 305 305 305 253 253
247
Table 9-3 Experimental and model hardness data for nickel (ramp-down waveform)
Hardness (kg mm-2)
Average current density (mA cm
-2)
Experimental Mathematical
Wong et al.
This study
Molina et al.
model
Pure diffusion
Pure charge transfer (ionic)
Pure ohmic
Combined charge
transfer & diffusion
Combined charge
transfer & ohmic
100 162 166 124 148 148 148 180 180
200 195 196 175 209 209 209 254 254
300 225 228 214 256 256 256 311 311
400 268 272 248 295 295 295 359 359
500 330 334 278 330 330 330 402 402
600 450 447 305 362 362 362 441 441
Table 9-4 Experimental and model hardness data for nickel (triangular waveform)
Hardness (kg mm-2)
Average current density (mA cm
-2)
Experimental Mathematical
Wong et al.
This study
Molina et al.
model
Pure diffusion
Pure charge transfer (ionic)
Pure ohmic
Combined charge
transfer & diffusion
Combined charge
transfer & ohmic
100 158 159 129 140 140 140 141 141
200 180 182 182 198 198 198 199 199
300 210 212 223 242 242 242 243 243
400 245 251 258 280 280 280 281 281
500 310 303 289 313 313 313 314 314
600 410 412 318 343 343 343 344 344
248
Figure 9-2 Comparison between the experimental and various models for Ni coating
hardness using rectangular waveform
Figure 9-3 Comparison between the experimental and various models for Ni coating
hardness using ramp-up waveform
249
Figure 9-4 Comparison between the experimental and various models for Ni coating
hardness using ramp-down waveform
Figure 9-5 Comparison between the experimental and various models for Ni coating
hardness using triangular waveform
250
As can be seen from Table 9-1 and Figure 9-2, the model predictions for pure diffusion
control, pure ohmic control and pure charge transfer control give the best approximation
of hardness values, the only exception being when the system is operated at the lowest
average current density of 100 mA cm-2
. All other models overestimate the hardness
values for average current densities between 200 and 500 mA cm-2
. In general, as the
current density is increased, the microhardness of the deposit layer also increases.
Table 9-2 and Figure 9-3 compare the hardness results generated by a ramp up waveform
with the experimental data. Here the closest fit seems to be obtained for crystal growth
under pure diffusion, ohmic or ionic control. The model based on a combined ion and
diffusion control underestimates the hardness values and deviates significantly from the
experimental ones at higher average current densities—500 mA cm-2
and beyond. The
predictions from our model based on pure diffusion, for example, are very close to those
made by Molina et al. [642] with the former providing a better approximation for peak
current densities, ranging from 200 to 500 mA cm-2
, while the latter gives closer
approximation for low (100 mA cm-2
) and high (500 mA cm-2
) average current densities.
Similar to the rectangular and ramp up waveforms, for the ramp down waveform (Figure
9-4), the model based on pure diffusion control generates the best results for applied
average current densities below 500 mA cm-2
. For the triangular waveform (Figure 9-5),
all models performed equally well. Noticeable changes cannot be observed from Figure
9-5, where all experimental and model values are graphically presented; however, upon
inspection of the data in Table 9-4, a very slight improvement in predicted hardness
values in the neighbourhood of 200 – 500 mA cm-2
can be seen. The model under pure
diffusion control generated data that are in good agreement with the corresponding
experimental values.
In general, the results indicate that the mathematical models based on pure diffusion,
ohmic and charge transfer control generate data which are in reasonably good agreement
with experimental values reported in the literature by Wong et al. [540] and as well as
with those obtained in the present study. As mentioned previously, both model and
experimental data present a clear and consistent trend with respect to applied average
251
current density and nickel-coating microhardness: as the applied average current density
increases, the microhardness increases as well.
The physical constants, variables and electrodeposition parameters that were employed to
solve the mathematical expressions in the models are summarized in Table 9-5.
Table 9-5 Physical constants and variables used for determining nickel-coating
microhardness and other characteristics
Property Symbol Value Unit Reference
Specific edge energy σ 0.255 J m-1 [644]
Diffusion coefficient D 1.329 × 10-9 m2 s-1 [645]
Molecular volume vm 1.1410 х 10-29 m3 mol-1
Dislocation blocking value K0 7 MPa [333, 642]
Penetrability of the moving Kl 0.18 MPa m-1/2 [333, 642]
dislocation boundary
Wetting angle γ0 π/2 Rad [642]
Temperature T 328.15 K
Initial Ni concentration C0 1.472 kmol m-3
Pulse duty cycle θ 0.5
Frequency f 100 Hz
Ionic charge z +2
Electronic charge e 1.602 × 10-19 C
Faraday's constant F 96487 C mol-1
Universal gas constant R 8.314 J mol-1 K-1
Acceleration due to gravity g 9.8 m s-2
9.3.2 Model Predictions for Nickel Concentration Overvoltage for various Waveforms
Figure 9-6 shows the concentration overvoltage predicted by the model developed in the
previous section that is based on the model presented by Molina et al. [642]. As can be
seen from this figure, the ramp-down waveform generates the highest concentration
overvoltage at the beginning of the pulse, and then subsides as electrodeposition
continues. A similar trend can be observed for the rectangular waveform, where the
concentration overvoltage has the second highest value initially. However, for the latter
waveform, the concentration overvoltage continues to rise as long as the current is on.
252
Figure 9-6 Concentration overvoltage for various waveforms with a peak current density
of 400 mA cm-2
, on-time & off-time of 5 ms (50% duty cycle) and 100 Hz (showing the
first full cycle)
These observations can be explained by examining the waveforms and how the current is
initially imposed on the system. In the case of a ramp-down waveform, the peak current
density rises quickly (much more like a step function) resulting in a sharp decrease in the
concentration of the electroactive species (Ni++
ion in this case) in the diffusion layer
leading to a sharp increase in concentration overvoltage. As soon as the maximum peak
current density is reached, however, the applied current density begins to recede, causing
the corresponding concentration overvoltage to gradually decline until the pulse on-time
is complete and the relaxation period (off-time) begins. Similarly, with the onset of a
rectangular waveform, the concentration overvoltage quickly rises; however, contrary to
the ramp-down waveform, the resulting concentration overvoltage continues to rise due
to the rapid depletion of nickel ions close to the cathode as a result of a high and
continuous peak current density. Accordingly, the concentration overvoltage steadily
increases until the pulse on-time period has elapsed and the relaxation period
commences.
According to Figure 9-6, both the ramp-up and triangular waveforms exhibit a slow rise
in concentration overvoltage at the beginning of the pulse on-time. A closer examination
253
of these waveforms shows that the applied current density in both cases does not reach its
highest value (i.e., the peak current density) until the middle or the last part of the pulse
on-time for the triangular and ramp-up waveforms, respectively. Consequently, the
decrease in the concentration of the nickel ions very close to the surface of the cathode is
more gradual than the previous rectangular and ramp-down waveforms. In addition, the
rise in the concentration overvoltage is faster for the triangular waveform than for the
ramp-up waveform. This is anticipated since the peak current density of the former
waveform is reached in half the time as the latter. This, in turn, causes a faster drop in the
concentration of the electroactive species in the cathode diffusion layer, leading to higher
concentration overvoltage in a shorter time period.
Similar to ramp-down waveform, the concentration overvoltage of the triangular
waveform reaches a maximum about 3.5 ms after the pulse on-time is activated (1.0 ms
after it reaches the maximum applied current density) and then begins to decline as the
applied current density starts to decrease. In contrast, the corresponding concentration
overvoltage of the ramp-up waveform continues to rise until the end of the pulse on-time.
Again, this is expected since the applied current density during pulse on-time of a ramp-
up waveform is constantly increasing and reaches its maximum value only at the
completion of the pulse on-time. It can be seen that the highest concentration overvoltage
occurs with the ramp-up waveform. However, this does not translate into a higher
nucleation rate, since the total concentration overvoltage for the entire pulse on-time of
the ramp-up waveform is smaller than the other three, as can be observed by comparing
the corresponding areas under each curve in Figure 9-6.
The above findings are in good agreement with the results reported by other workers
[504, 642]. However, most pulse electrodeposition models, including the two cited in this
study, use a 50% duty cycle with the assumption that the concentration of the
electroactive species in the diffusion layer will recover and reach its initial bulk value
after the completion of each pulse period. In other words, it is assumed that the
concentration of the metal ions in the diffusion layer is replenished during the pulse off-
time, when ions from the bulk solution diffuse into the diffusion layer. Despite this
relaxation time, the ion concentration in the vicinity of the cathode does not regain its
254
initial (bulk) concentration and will always decrease with increasing pulse cycles; this is
especially true for large duty cycles (50% and higher), when the pulse off-time is not long
enough (relative to the on-time) to allow ion recovery in the cathode diffusion layer. This
is predicted by the model developed in this study and presented in Figure 9-7. Figure 9-7
shows the calculated variation in nickel ion concentration in the cathode diffusion layer
during a single 10-ms pulse with a peak current density of 400 mA cm-2
and a duty cycle
of 50% for the four waveforms examined in this study. The concentration profiles are
distinctively characteristic for each waveform. The highest initial decline in nickel
concentration during pulse on-time is observed for rectangular and ramp-down
waveforms. This results from the sharp increase in applied current density at the start of
the pulse, leading to a higher deposition rate and a marked decline in nickel
concentration. For the ramp-down waveform the ion concentration in the diffusion layer
will recover and start to increase as the pulse on-time progresses, unlike the rectangular
waveform for which the concentration decreases throughout the complete pulse on-time.
Figure 9-7 Nickel concentration in the cathode diffusion layer for various waveforms
with a peak current density of 400 mA cm-2
, on-time and off-time of 5 ms each (50%
duty cycle) and 100 Hz (showing the first full cycle , on-time and off-time)
255
For the triangular and ramp-up waveforms, the initial decline in the concentration of
nickel ions in the cathode diffusion layer is more subtle compared with ramp-down and
rectangular waveforms. This is attributed to the gradual increase in the applied current
density during the pulse on-time in contrast to the sharp increase for the other two
waveforms. In addition, the decrease in nickel ion concentration in the diffusion layer
when a triangular waveform is employed is initially more pronounced than with a ramp-
up waveform, since the peak current density of the former is reached in half the time as
that of the latter. Furthermore, in the case of a triangular waveform, the concentration of
the electroactive species in the cathode diffusion layer begins to increase as the applied
current density reaches its maximum and then starts to decline. At this point, the rate of
nickel electrodeposition begins to fall and the diffusion rate from the bulk solution into
the diffusion layer becomes greater, increasing the concentration within the diffusion
layer. The concentration in the diffusion layer for a ramp-up waveform, however,
continues to decrease as the electrodeposition progresses owing to the continuous rise in
applied current density until the completion of the pulse on-time.
The vertical dashed line marks the end of the pulse on-time and the commencement of its
off-time. As expected, the nickel ion concentration decreases during pulse on-time when
the ions migrate from the diffusion layer to the surface of the substrate and are
subsequently reduced. Accordingly, a concentration gradient between the bulk solution
and the cathode diffusion layer is established and nickel ions begin to enter the latter
layer from the bulk solution. However, the rate of nickel electrodeposition is significantly
higher than the diffusion rate resulting in a reduction in nickel ion concentration in the
diffusion layer.
With time, the nickel ion concentration in the diffusion layer continues to decrease until it
approaches zero, when the limiting current density is reached and crystals begin to grow
at a faster rate. However, it is anticipated that nickel ions enter the cathode diffusion
layer when the current is interrupted. This ensures the presence of free metal ions in the
diffusion layer for the next pulse cycle. The extent of nickel ion replenishment in the
diffusion layer depends on several factors, including applied peak current density, pulse
duration, and duty cycle. One of the most important variables is the pulse off-time and if
256
its duration (with respect to on-time) is not long enough, the concentration of the metal
ion in the diffusion layer will not reach its initial value and the concentration in the
cathode diffusion layer will decrease with each pulse cycle. In most studies, a duty cycle
of 50% is employed with the assumption that the concentration of the electroactive
species will reach its original value at the completion of the pulse off-time. According to
the model developed in this study, the concentration of nickel ion in the cathode diffusion
layer does not reach its initial value at the conclusion of the pulse off-time for any of the
waveforms. The difference is most pronounced for the rectangular waveform, where the
difference between the initial and final nickel ion concentrations is twice that of the other
waveforms. It is thus evident that a 50% duty cycle is not sufficient to ensure the return
of the metal ion concentration to its initial level after the conclusion of the pulse off-time.
This is predicted by the model developed in this study and presented in Figure 9-8, where
concentrations at the end of the last pulse cycle (i.e.; 1000th
) for all waveforms at
different duty cycles are shown. The decrease in final concentration with increasing duty
cycle is more gradual for ramp-down and triangular waveforms compared with ramp-up
and rectangular waveforms, where the concentration declines more rapidly at higher duty
cycles.
Figure 9-8 Nickel concentration in the cathode diffusion layer for various waveforms
with a peak current density of 40 mA cm-2
, on-time of 0.1 ms, 1000 pulse cycles and
duty cycles of 10% - 100%. The initial bulk nickel concentration is 1.427 mol L-1
.
257
The nucleation rate and critical nucleus size of the deposited nickel for one pulse cycle
for all four waveforms are presented in Figures 9-9 and 9-10, respectively. According to
Figure 9-9, the ramp-down waveform exhibits the highest nucleation rate at the beginning
of pulse on-time, while the ramp-up waveform shows its highest nucleation rate at the
end of pulse on-time. This is expected since the nucleation rate is directly proportional to
the applied peak current density; as the cathodic peak current density increases, the
nucleation rate also increases. In case of the ramp-down waveform, the highest cathodic
peak current density is applied at the start of the pulse on-time, resulting in an increase in
the formation of new nuclei, which gradually will decrease as the applied current density
subsides with the progression of pulse on-time.
Figure 9-9 Nucleation rate for a single cycle (on-time only is shown) for all waveforms
with a peak deposition current density of 400 mA cm-2
and 50% duty cycle
258
Fig 9-10 Calculated critical nucleus size for a single cycle (on-time only is shown) for all
waveforms with a peak deposition current density of 400 mA cm-2
and 50% duty cycle
In contrast, for the ramp-up waveform, the cathodic current density is at its minimum at
the beginning of the pulse on-time and gradually increases until it reaches its maximum at
the end of the pulse on-time. Accordingly, the nucleation rate is very slow at the start of
the pulse on-time, but exhibits an exponential growth as the applied current density
increases. The rectangular waveform shows a gradual increase in nucleation rate as the
pulse on-time progresses and, similar to the ramp-up waveform, reaches its maximum at
the end of the pulse on-time. The triangular waveform, on the other hand, displays an
initial slow rise in nucleation rate followed by a rapid rise as the current density reaches
its maximum, and subsequently tapers off as the applied current density subsides.
According to Figure 9-9, the highest nucleation rate is attained by the ramp-up waveform;
however, this does not guarantee the generation of the smallest crystallites, as can be
observed from Figure 9-10. The evolution of the critical nucleus size for all waveforms
shown in Figure 9-10 indicates that the ramp-down waveform results in a smaller nucleus
size near the start of the pulse, while larger nuclei are obtained at the end of the
waveform. Interestingly, the nucleus size increases for both ramp-down and triangular
waveforms at the end of the pulse on-time. This is attributed to the lower current density
259
at the end of the pulse on-time, which, in the case of triangular and ramp-down
waveforms, favours the growth of existing nuclei. Overall, however, the smallest critical
nucleus size is attained with the ramp-down waveform.
To verify the model predictions, the influence of pulse duty cycle on deposit quality was
compared with X-ray Diffraction (XRD) spectra obtained according to the method
outlined in section 7.6.2.4. The XRD patterns shown in Figure 9-11 reveal the preferred
orientation of the nickel deposits obtained using the ramp-down waveform with a
constant peak current density of 400 mA cm-2
and varying duty cycles. As can be seen,
the diffraction intensity of the (200) orientation increases with decreasing duty cycle.
This is primarily attributed to the reduction in grain size of the deposited nickel and is
further substantiated by comparing the SEM images of the nickel deposits shown in
Figure 9-12. Figure 9-12 (a) shows the surface morphology of nickel deposits obtained at
a low pulse duty cycle of 20% in which small grains are dominant.
In contrast, when a duty cycle of 80% is employed, the surface morphology is
significantly altered and the nickel deposits contain a large number of crystallites that are
pyramidal in shape and significantly larger than the crystals shown in Figure 9-12 (a),
where a lower duty cycle has been utilized. The necessary condition for creating new
crystalline phase from the electrolyte solution is the presence of nickel ions in the cathode
diffusion layer during the pulse on-time to inhibit crystal growth and promote nucleation.
A lengthy pulse on-time—long duty cycle—results in fast diminution of electroactive
species in the cathode diffusion layer and, consequently, leads to crystal growth.
260
Figure 9-11 XRD patterns exhibiting the influence of pulse duty cycle on crystal
orientation of nickel deposits with a constant peak current density of 400 mA cm-2
Figure 9-12 Surface morphology of electrodeposited nickel at a constant deposition
current density of 400 mA cm-2
and various duty cycles: (a) 20% and (b) 80%
(a) (b) 1 µm
___
1 µm
___
261
9.3.3 Platinum Electrodeposition
Platinum electrodeposition was carried out according to the method outlined in section
7.5.1 with two minor modifications. First, for microhardness tests, the substrate was
changed from carbon paper or cloth to AISI 431 stainless steel, since it is almost
impossible to perform a Vicker’s test on the actual MEA and it has been necessary to
assume that the grains deposited on the AISI 431 stainless steel plates are the same as
those deposited onto the carbon substrates. Second, the exposed surface area of all
stainless steel plates to the plating solution inside the electroplating flow cell was limited
to 1.0 cm2 and the plating bath temperature was maintained at 25 °C throughout the
plating process. Prior to placement inside the electroplating cell, the substrate was first
ground to a finish on grade 180 emery paper, rinsed with deionized water, and then
scrubbed with alcohol and acetone and finally rinsed with deionized water.
After electrodeposition, the surface morphology of each specimen was examined and
characterized using SEM and microhardness, the latter obtained in accordance with the
ASTM E384 method. Experimental findings were subsequently compared with the
hardness results generated by the model developed in this study. Physical constants and
variables used for determining the platinum-coating microhardness and other
characteristics are summarized in Table 9-6. The number of test samples was limited to a
few compared with nickel due to the prohibitive cost of platinum. Based on the findings
in the previous section for nickel electrodeposition modeling, the mathematical model for
platinum electrodeposition is based on crystal growth under pure diffusion control.
However, a number of modifications were made to ensure the validity of the model; these
are discussed in following section (9.3.3.1).
The ―size effect‖ of platinum particle on the electroreduction of oxygen is one of the
most important and widely-studied areas in electrochemical science. As discussed in
previous sections, platinum metals electrodeposited by a pulse current electrodeposition
technique tend to deposit platinum catalyst particles that are smaller in size, selectively
deposited on the carbon substrate, and in direct contact with both carbon support and the
membrane electrolyte, leading to higher fuel cell performance. In addition, certain pulse
waveforms have been shown to create smaller platinum particles, resulting in higher fuel
262
cell performance compared with other type of waveforms. The primary objective of this
part of the study is to use the mathematical model that was refined and developed (based
on the works of Molina et al. [642]) in the preceding section to predict the influence of
different pulse parameters such as peak cathodic current density, duty cycle, pulse
frequency, millisecond and microsecond pulses, and pulse off-time on the microhardness
of platinum deposits and, ultimately, on fuel cell performance. Similar to nickel
electrodeposition, model microhardness data are compared with the experimental values
to validate the mathematical model developed in this study and to gain an understanding
of the influence of electrodeposition parameters on platinum microhardness and,
subsequently, fuel cell performance.
Table 9-6 Physical constants and variables used for determining the platinum-coating
microhardness and other characteristics [646, 647]
Property Symbol Value Unit
Specific edge energy σ 0.240 J m-1
Diffusion coefficient D 1.20 × 10-9 m2 s-1
Molecular volume vm 1.5095 х 10-29 m3 mol-1
Dislocation blocking value K0 7 MPa
Penetrability of the moving Kl 0.168 MPa m-1/2
dislocation boundary
Wetting angle γ0 π/2 Rad
Temperature T 298.15 K
Initial Pt concentration C0 0.05 mol L-1
Pulse duty cycle θ 0.5
Frequency f 100 Hz
Ionic charge z +2
Electronic charge e 1.602 × 10-19 C
Faraday's constant F 96487 C mol-1
Universal gas constant R 8.314 J mol-1 K-1
Acceleration due to gravity g 9.8 m s-2
9.3.3.1 Modification of the Mathematical Model for Platinum Electrodeposition
One of the long standing issues in the theory of crystal growth (and nucleation) is the
prediction of the growth rates of spherical or hemispherical crystals on foreign substrates.
263
Most of the theoretical works have considered three rate-determining cases: (i) slow bulk
diffusion of the electroactive species from the bulk solution to the surface of the growing
crystal, (ii) slow interfacial charge transfer, and (iii) mixed kinetics or rate control by
both bulk diffusion and interfacial ion processes [648-651]. A number of studies also
have considered the more complicated case of joint ohmic, diffusion, and charge transfer
limitations, where the electrochemical nucleation and growth take place in the complete
absence of any supporting electrolyte [652-654]. This was the case in this study where
platinum was electroreduced on different substrates in the absence of a supporting
electrolyte. The model developed and tested in the preceding section (nickel deposition),
however, was based on a plating bath containing supporting electrolyte. In such cases, the
theoretical model only accounts for joint diffusion and charge transfer limitations.
Consequently, the model needs to be modified to account for ohmic limitations, where
platinum electrodeposition is carried out in the complete absence of supporting
electrolyte. In the following section we refine and further develop the model presented in
the preceding sections to include ohmic limitations and validate the model by comparing
it with experimental data obtained for platinum electrodeposition. A detailed treatment of
electroplating systems where a supporting electrolyte is present also is provided.
9.3.3.1.1 Effect of Supporting Electrolyte6
(a) In the Absence of Supporting Electrolyte
The standard form of the Butler-Volmer equation for the metal deposition process
Mzze
M (9-91)
is
TR
Fz
TR
Fzii actact
o
)1(expexp (9-92)
where act is the charge transfer overvoltage (activation overvoltage), is the transfer
coefficient for the charge transfer reaction, and io is the exchange current density. In the
above expression the cathodic contribution to the net current density (the first term in the
brackets) is taken as positive, the anodic contribution (the second term in the brackets) is
6 These are based on the works of Milchev et al. [643, 652, 653] and full derivations of equations indicated
with an asterisk (*) are given in the appendix.
264
taken as negative, and cathodic overvoltages are taken as positive. By denoting cathodic
overvoltages and currents as positive quantities in the following derivations, the
complexities of dealing with the logarithms of negative numbers are avoided. Also, to
avoid confusion between the radius R of the deposited metal cluster and the gas constant,
the gas constant is designated as R .
When the rate of (9-91) is completely controlled by the rate of the charge transfer process
(activation-controlled), the exchange current density io is related to the concentration co
of the metal ion in the bulk solution. However, when the concentration cS of the metal ion
adjacent to the metal surface is different from that in the bulk solution, as is the case
when there are solution mass transport limitations, the exchange current density io must
be replaced with io, S, which is the exchange current density referred to the concentration
cS . The relationship between io, S and io is given by
1
,
o
S
oSoc
cii (9-93)*
Furthermore, in the presence of a concentration gradient in the depositing species, in
addition to the charge transfer overvoltage act, the total cathodic overvoltage will include
a concentration overvoltage C given by
S
o
Cc
c
Fz
RTln (9-94)
such that the total cathodic overvoltage T will be
T = ∆E = act + C (9-95)
where ∆E is the external cathodic voltage applied between the reference electrode and the
metal surface. Rearranging (9-95):
act =
o
S
c
c
Fz
RTE ln (9-96)
Substituting (9-93) and (9-96) into (9-92) rearranges to give
265
i =
TR
EFz
TR
EFz
c
ci
o
S
o
)1(expexp
(9-97)
i.e.,
TR
EFz
TR
EFz
c
ciS
o
S
oR
)1(expexpI
=
TR
EFz
TR
EFz
c
ciR
o
S
o
)1(expexp2 2
(9-98)
where SR 2R2 is the surface area of the hemispherical cluster of radius R. When
cS co , C 0 and Eqn (9-98) reduces to Eqn (8-92). Eqn (9-98) must be used
whenever cS < co.
The external cathodic potential ∆E applied to the working electrode (where the metal
deposition takes place) is measured against a reference potential Eref . For convenience we
take this reference potential as the stable equilibrium potential set up between an
electrode made of the bulk metal M and its
ions Mz
at the concentration of the bulk
solution, where the metal M is the same
metal that is to be deposited on the surface
of the working electrode. We designate this
equilibrium potential as o and the potential
at the surface of the working electrode as
S. The potential o
is taken as the potential
in the solution at the reference point in the
solution that corresponds to the tip of the
Luggin capillary (or the reference
electrode). Thus any applied external potential ∆E applied to the working electrode can
be expressed as
∆E = o S (9-99)
If the cluster is growing at a fixed external applied voltage ∆E, reference to the diagram
shows that
c
x
o
S
solution metal
act
∆E
266
∆E = C + + act (9-100)
where act is the charge transfer overvoltage, is the ohmic overvoltage (the ohmic
drop present in the solution between the reference electrode and the working electrode),
and C is the concentration overvoltage between the reference electrode and the working
electrode. All the quantities in Eqn (9-100) are taken as positive.
In the absence of supporting electrolyte part of the ion transport occurs by ionic migration
of the charged ions under the influence of the applied voltage gradient.
The positive x–direction is taken as away from the electrode surface where the metal
deposition takes place. Taking cathodic currents as positive, the cationic diffusion flux
towards the electrode is given by
xd
dcDJ D
(9-101)
where c+ is the concentration of the cation in solution and D+ is its diffusion coefficient.
Using the selected sign convention, since 0dxdc , the cation diffusion flux JD
is
positive, which means that the cations diffuse from the bulk solution towards the
electrode. The conduction (or ionic migration) flux is given by
xd
dUcJ C
(9-102)
where U+ is the mobility of the cation and d dx is the voltage gradient in the solution.
The mobility, which is the ionic migration velocity per unit field strength, is always
defined as a positive quantity. Since d dx is positive (the voltage becomes less negative
as the distance from the cathode increases), it follows from (9-102) that the cation
conduction flux JC
, like the diffusion flux JD
, also is positive. Therefore both fluxes
move towards the electrode surface and, neglecting convection in the diffusion zone, the
total cationic current density iT
is given by
iT
=
CDCD FJzFJzii
= xx d
dUcFz
d
dcFDz
(9-103)
In dilute solution the Einstein relation links diffusion to conduction by
267
U i | zi | FDi
R T (9-104)
where R is the gas constant and T is the absolute temperature. Substituting (9-104) into
(9-103) gives
iT
=
xx d
d
TR
FDzcFz
d
dcFDz
=
xx d
d
TR
cDFz
d
dcFDz
2
(9-105)
Now consider the anions: For the anions, since the negatively-charged electrode exerts a
repulsive effect, the anionic conduction flux JC
is away from the electrode. This reduces
the anionic concentration S)(c adjacent to the electrode, establishing a positive anionic
concentration gradient that sets up an anionic diffusion flux JD
towards the electrode.
Since it is assumed that no anions are discharged at the electrode and that there is no
convective mass transfer taking place in the diffusion layer, it follows that there is no net
anionic flux JT
in the diffusion layer, and that the anionic diffusion flux towards the
electrode is exactly balanced by the anionic migration flux away from the electrode.
Thus, for the anions in the diffusion layer
iT
=
xx d
dUcFz
d
dcFDzii CD
||||
= xx d
d
TR
FDzcFz
d
dcDFz
|||||| (9-106)
The negative sign in front of the second term indicates that the anionic conduction flux is
in the opposite direction to the (positive) anionic diffusion flux.
But, since iT
= 0, xx d
d
TR
FDzcFz
d
dcFDz
|||||| = 0
Rearranging: d
dx =
xd
dc
TR
FDzcFz
FDz
||||
|| =
xd
dc
cFz
TR
|| (9-107)
But, from charge neutrality, czcz || (9-108)
268
Putting (9-108) into (9-107): xx d
dc
Fcz
TR
d
d
(9-109)
From (9-108),
cz
zc
||
Differentiating: xx d
dc
z
z
d
dc
||
(9-110)
Substituting (9-110) into (9-109): xx d
dc
z
z
Fcz
TR
d
d
||
(9-111)
Putting (9-111) into (9-105): iT
=
xx d
dc
z
z
Fcz
TR
TR
cDFz
d
dcFDz
||
2
= xx d
dc
z
zFDz
d
dcFDz
||
and therefore xd
dc
z
zFDziT
||1 (9-112)
Thus, from Eqn (9-112), when there is transport by both diffusion and ionic migration,
the total cationic current density at the cathode surface (where x = 0) is
0
1
xxd
dcaFDziT (9-113)
where a is defined as a z
| z | (9-114)
From Faraday’s Law the total current is
I 2zF
vM
R2 dR
dt (9-115)
For a hemispherical cluster of radius R the surface area is 12 4R
2 2R2; therefore,
from (9-113), the total current passing through the surface of the cluster is
R
d
dcaFDzRI
xx
12 2 (9-116)
The concentration gradient at the surface of the cluster is
269
o
SoSoSo
Rc
c
R
c
R
c
R
c
R
cc
d
dc1
xx
(9-117)
Substitution of (9-117) into (9-116) gives the total current passing through the surface of
the cluster as
o
S
oc
cCaFDRzI 112 (9-118)
The term (1 + a) accounts for the contribution of ionic migration to the total current.
When diffusion and ionic migration are both present, the charge transfer overvoltage act
that must be used in Eqn (9-92) is a function of the applied cathodic voltage and the
concentration and ohmic overvoltages. This relationship is given by Eqn (9-100) as
act = ∆E – C – (9-119)
The concentration overvoltage C is given by Eqn (9-94). The ohmic overvoltage is
just the voltage drop through the diffusion zone. This is determined as follows:
From Eqns (9-111) and (9-114), xx d
dc
cFz
TRa
d
d
1
from which
c
dc
Fz
TRad
Integrating
1
2
12 lnc
c
Fz
TRa (9-120)
At R = , 2 = o and c2 = co
At R = R, 1 = S
and c1 = cS
Putting these boundary conditions into Eqn (9-120) gives the ohmic overvoltage as
S
o
Soc
c
Fz
aTRln (9-121)
Putting (9-94) and (9-121) into (9-119):
270
act = ∆E –
S
o
c
c
Fz
TRln –
S
o
c
c
Fz
aTRln
= ∆E
S
o
c
ca
Fz
TRln1 (9-122)
As discussed above, when cS < co , the exchange current density io in Eqn (9-92) must be
replaced with iS,o given by Eqn (9-93) to yield
I = SR i
=
TR
Fz
TR
FziR actact
So
)1(expexp2 ,
2
=
TR
Fz
TR
Fz
c
ciR actact
o
S
o
)1(expexp2
1
2 (9-123)
Substituting (9-122) into (9-123):
I =
o
S
o
S
oc
ca
Fz
TR
TR
Fz
TR
EFz
c
ciR ln1exp2
1
2
–
o
S
c
ca
Fz
TR
TR
Fz
TR
EFzln1
)1()1(exp
=
o
S
o
S
oc
ca
TR
EFz
c
ciR ln1exp2
1
2
–
o
S
c
ca
TR
EFzln1)1(
)1(exp
=
)1(1
lnexpexp2 2
a
o
S
o
S
oc
c
TR
EFz
c
ciR
–
)1)(1(
lnexp)1(
exp
a
o
S
c
c
TR
EFz
271
=
a
o
S
o
S
oc
c
TR
EFz
c
ciR
exp2
1
2 –
aa
o
S
c
c
TR
EFz1
)1(exp
=
TR
EFz
c
ciR
a
o
S
o
exp2
1
2 –
TR
EFz
c
ca
o
S )1(exp
)1(
(9-124)
Eqn (9-124) gives the expression for the growth current I of a hemispherical cluster of
radius R in the presence of joint diffusion and ionic migration (ohmic) control in the
absence of any supporting electrolyte.
Equations (9-115) and (9-118) each give expressions for the total current I. Equating
these two equations gives:
o
S
o
M c
ccaFDRz
dt
dRR
v
Fz112
2 2
from which dt
dR
cDva
R
c
c
oMo
S
)1(1 (9-125)
Eqn (9-115) rearranges to
22 FRz
Iv
dt
dR M
(9-126)
Substituting (9-125) into (9-124):
I =
TR
EFz
dt
dR
cDva
RiR
a
oM
o
exp)1(
12
1
2
–
TR
EFz
dt
dR
cDva
Ra
oM
)1(exp
)1(1
)1(
(9-127)
Substituting (9-127) into (9-126):
dR
dt =
TR
EFz
c
c
TR
EFz
c
ciR
FRz
vaa
o
S
o
S
o
M )1(expexp2
2
)1(1
2
2
272
=
TR
EFz
dt
dR
cDva
RiR
FRz
va
oM
o
M
exp)1(
122
1
2
2
–
TR
EFz
dt
dR
cDva
Ra
oM
)1(exp
)1(1
)1(
=
TR
EFz
dt
dR
cDva
R
Fz
iva
oM
oM
exp)1(
1
1
–
TR
EFz
dt
dR
cDva
Ra
oM
)1(exp
)1(1
)1(
(9-128)
In Eqn (9-128) the term exp (1)zFE R T can be expanded to
exp(1 )zFE
R T
= exp
( 1)zFE
R T
=
TR
EFz
TR
EFzexpexp
(9-129)
Substituting (9-129) into (9-128) gives
dR
dt =
TR
EFz
dt
dRR
cDvaFz
iva
oM
oM
exp)1(
11
1
–
TR
EFz
TR
EFz
dt
dRR
cDva
a
oM
expexp)1(
11
)1(
(9-130)
Eqn (9-130) gives the rate of cluster growth as a function of time, and can be expressed
more concisely as [653]:
dR
dt A1F1 A2F2
(9-131)
where F1 = 44AA
3A
o
S
c
c
dt
dRR1 (9-132)
F2 = 55AA
3A
o
S
c
c
dt
dRR1 (9-133)
273
A1 =
TR
EFz
Fz
iv oM exp (9-134)
A2 =
TR
EFzexp1A (9-135)
A3 = TRatv
FzacDv
M
oM
1
1
2
1
(9-136)
A4 = a1 (9-137)
A5 = 1 a (9-138)
where t+ is the transport number of the cation and is the specific conductivity of the
solution.
Although Eqn (9-130) cannot be solved analytically, for short and long periods of time
the following two approximate solutions are valid [652].
Short times and low ohmic and concentration overvoltages
At short times and low current, oS cc 1 and dt)dRR(A3 0, so that the terms F1
and F2 in Eqn (9-131) can be expressed through the first two terms of binomial
expansions, which, for x2 < 1, state that
1 x n 1 nx
(n)(n1)x 2
2!
(n)(n 1)(n 2)x3
3! . . . ≈ 1– nx
and 1 x n 1 nx
(n)(n 1)x2
2!
(n)(n 1)(n 2)x3
3! . . . ≈ 1+nx
Under these conditions and, with the initial conditions that R = 0 at t = 0, Eqn (9-131)
can be solved to give
R R Tt 1 a
zFio B1
2vMio
2 AB t
R Tt 1 a
1/ 2
1
(9-139)
where A = expzFE
R T
exp
(1 )zFE
R T
(9-140)
B = 1 a expzFE
R T
1 a exp
(1 )zFE
R T
(9-141)
274
Using Eqn (9-139) with Eqn (9-124) for the current gives
1)1(21
)1(1142/12
2
2
2
aTtRtvi
aTtRtvi
Fz
aTtRI
Mo
Mo
AB
AB
B
A
oi (9-142)
Equations (9-139) and (9-142) give I and R as a function of time for short times when
I
R 0.1
2t(1 a) R T
zF
(9-143)
Long times and high ohmic and concentration overvoltages
For very high ohmic and concentration overvoltages the charge transfer overvoltage tends
towards zero and the concentration of the cation at the electrode surface will be at the
limiting value cS,m. Under these conditions Eqn (9-122) becomes
act = ∆E
S
o
c
ca
Fz
TRln1 = 0
from which TRa
EFz
c
c
mS
o
)1(ln
,
TRa
EFz
c
c
mS
o
)1(exp
,
(9-144)
Under these conditions the maximum concentration overvoltage C,m will be [653]:
C,m =
mS
o
c
c
Fz
TR
.
ln =
TRa
EFz
Fz
TR
)1(expln
= R T
zF
zFE
1 a R T =
E
1 a (9-145)
and, from Eqn (9-121) the maximum ohmic overvoltage ,m will be
, m = o S,m
=
mS
o
c
c
Fz
TRa
,
ln = a R T
zFln exp
zFE
(1 a) R T
= a R T
zFln exp
zFE
(1 a) R T
=
aE
1 a (9-146)
In this case the functions F1 and F2 in Eqn (9-126) can be approximated by the first two
275
terms of the Taylor expansion around cS,m co to give
R R Tt
iozFP1
2vMio
2(1 a)Qt
R Tt+
1/ 2
1
(9-147)
where P = expzFE
(1 a) R T
(9-148)
Q = exp2zFE
(1 a) R T
exp
(21)zFE
(1 a) R T
(9-149)
Combining Eqn (9-147) with Eqn (9-115) gives [653]:
I 4 R Tt
2(1 a)Q
io zF 2
P3
1 vMio2 (1 a)Q t R Tt
1 2vMio
2(1 a)Q t R Tt
1 / 2 1
(9-150)*
Equations (9-147) and (9-150) give I and R as a function of time for long times when
I
R
2t(1 a) R T
zF1 1
0.2
a
exp
zFE
(1 a) R T
(9-151) I
R
2t(1 a) R T
zF1 1
0.2
a
exp
zFE
(1 a) R T
. . . (61)
(b) In the Presence of Supporting Electrolyte
Milchev’s treatment presented above in part (a) deals with the absence of supporting
electrolyte. The same author also has derived similar equations that take into account the
presence of supporting electrolyte [653]. For this latter case, the rate of cluster growth
with time is given by
a
dt
dRR
acDvTR
EFz
Fz
iv
dt
dR
oM
oM
1
11
11exp
1
a
dt
dRR
acDvTR
EFz
TR
EFz
Fz
iv
oM
oM
)1(
11
11
)1(expexp
. . . (9-152)
where D+ and co are the diffusion coefficient and the bulk concentration of the depositing
cation Mz
, respectively.
276
Eqn (9-152), which gives the rate of cluster growth with time in the presence of
supporting electrolyte, is identical to Eqn (9-130), which gives the rate of cluster growth
with time in the absence of supporting electrolyte, with the exception of the factors
and . In the derivation of Eqn (9-152), Milchev has chosen as supporting
electrolytes salts with the same anion as that of the salt MA from which the desired
metal deposits. Also, the valences of the cations and anions of the supporting electrolytes
BA have been chosen to be the same as those of the depositing salt MA . Thus, if
the metal M is being deposited from its ions Mz
from the salt MA , the supporting
electrolyte will consist of salts of the type BA whose cation Bz
has the same valence
z as that of Mz
. Accordingly, the factor is defined as the ratio of the bulk
concentration of supporting electrolyte to the bulk concentration of the depositing
electrolyte:
oM
oB
o
z
o
z
c
c
M
B
)(
)(
][
][
(9-153)
Thus is a measure of the relative level of supporting electrolyte present. If there is no
supporting electrolyte, = 0 and Eqn (9-152) reduces to Eqn (9-130).
Eqn (9-152) can be expressed more concisely as [653]:
dR
dt A 1 F 1 A 2 F 2 (9-154)
where F 1 = 44AA
3A
oB
SB
c
c
dt
dRR
)(
)(1 (9-155)
F 2 = 55AA
3A
oB
SB
c
c
dt
dRR
)(
)(1 (9-156)
A 1 =
TR
EFz
TR
EFz
Fz
iv oM )1(expexp
(9-157)
A 2 = 111
oM cDv (9-158)
A 3 = 111
oM cDv (9-159)
A 4 = a1 (9-160)
277
A 5 = 1 a (9-161)
In Eqn (9-158) and all those that follow below, D+ and co are, respectively, the diffusion
coefficient and bulk concentration of the depositing cation, Mz
.
As in the case of Eqn (9-130), Eqn (9-152) cannot be solved analytically, although
approximate expressions for R and I as functions of time can be made, as follows:
Short times and low ohmic and concentration overvoltages.
At short times and low current, oBSB )(c)(c 1 and A 3R(dR dt) 0, so that the terms
F 1 and F 2 in Eqn (9-154) can be expressed through the first two terms of binomial
expansions, as shown earlier for the case without supporting electrolyte. When this is
done, Eqn (9-154) reduces to
01 2132413 AAdt
dRRAAAAA (9-162)
With the initial condition that at t = 0 R = 0, Eqn (9-162) can be solved to give R as a
function of time t as
11
21
1
exp
2/1
2
2
tFzc
vi
TREFzi
FzcDR
o
Mo
o
o
BA
B+D
(9-163)*
where A =
TR
EFz
TR
EFz )21(exp
2exp
(9-164)
B =
TR
EFz
a
a
a
aexp
1
1
1
1 (9-165)
Substitution of Eqn (9-163) into Eqn (9-115) gives the current I as the following function
of time:
1)121
)111
3exp
42/122
2222
(Dt)(
(Dt)(
+
+
Fzcvi
Fzcvi
TREFzi
FczDI
oMo
oMo
o
o
BA
BA
B
. . . (9-166)
278
Equations (9-163) and (9-166) satisfactorily describe the growth process if [653]:
ocDFza )1)(1(2.0 R
I
1.0
dt
dRR3A (9-167)
Long times and high ohmic and concentration overvoltages.
In this case the ion transport from the bulk solution to the electrode determines the rate of
the growth process, and the activation overvoltage required to discharge the ions onto the
metal surface becomes negligibly small compared with the magnitude of the
concentration and ohmic overvoltages. This approaches the limiting condition act 0 as
t for which the surface concentration of the anion B attains its limiting
value cB,m S. This permits a determination of the following minimum value of the ratio
oBSB )(c)(c [653]:
)1(1
)(
)( , aM
c
c
oB
SmB (9-168)
where M = exp zFE R T
1 (9-169)
From these relationships it is possible to obtain the maximum possible values of the
concentration overvoltage C,m and ohmic overvoltage ,m for any given values of ,
∆E, and T. The maximum concentration overvoltage is
C,m R T
zFln
Ma
(1 )M1a (9-170)
and the maximum ohmic overvoltage is
, m R T
zF 1 a lnM (9-171)
Under these conditions approximate solutions for R and I as functions of time can be
obtained by expanding the terms F 1 and F 2 as the first two terms of a Taylor’s series to
transform Eqn (9-154) into
279
M(1 A 5) (1a)
A 1 A 4M A 2 A 5 A 3R dR
dt
– A 1M A 4 A 4 1 M1(1a) – A 2 A 5 1 A 5 M1 (1a) = 0 (9-172)
Eqn (9-172) can be solved with the usual boundary conditions that R = 0 at t = 0 to give
1)1)(1(2
1
2/1
2
22
o
oM
o
o
cFzD
taiv
i
FczDR
PQ
Q
(9-173)
where P 1M1 (1a)
(9-174)
TR
EFzM
aa exp
)1(Q (9-175)
Substitution of Eqn (9-173) into Eqn (9-115) gives the current I as a function of time for
long times as
1)1)(1(21
)1)(1(11142/1222
2222
ooM
ooM
o
o
cFzDtaiv
cFzDtaiv
i
aFczDI
PQ
PQ
Q
P
. . . (9-176)
Eqns (9-173) and (9-176) are valid approximations for long times when [653]:
)1(12.011)1)(1(2
M
aaFczD o
R
I (9-177)
The transients evaluated when = 0, correspond to the cluster growth in the absence of
supporting electrolyte under joint ohmic, diffusion, and charge transfer limitations. The
values at, say, = 100, correspond to growth in the presence of a large excess of
supporting electrolyte, for which the cluster growth is controlled only by joint diffusion
and charge transfer limitations. The above theory has been verified for the
electrodeposition of Ag crystals from a solution consisting of 0.5 M AgNO3 in 1.0 M
HNO3 [654]. The results of this latter study show that the presence of even small amounts
of supporting electrolyte can significantly decrease the crystal growth rate.
280
9.3.3.2 Comparison of Experimental and Model Platinum Microhardness Data
Figure 9-13 compares the experimental microhardness results with those of the models
presented in the preceding sections, one based on pure diffusion (see section 9.2) and
another based on ohmic, ionic and diffusion control with no supporting electrolyte
(referred to as modified model; section 9.3.3.1). Figure 9-13(a) shows the experimental
result (dashed line) and compares it with both model predictions for the ramp-down
waveform at different peak deposition current densities. A comparison of the
experimental and model results reveal a strong correlation between the experimental and
the modified model for peak deposition current densities ranging from 200 to 400 mA
cm-2
, while a better agreement is obtained at the lowest and highest peak deposition
current densities when the model is based on pure diffusion control. A similar trend also
is observed for the triangular waveform (Fig. 9-13(b)).
In case of the ramp-up waveform, the modified model underestimates the microhardness
of the deposited platinum layer, while the model based on pure diffusion control
generates data that are in better agreement with the experimental findings. These trends
can be explained by examining the characteristics of all the waveforms examined in this
research. In case of the ramp-down and triangular waveforms, although the rise in
deposition current density is faster than the ramp-up waveform, the decline begins almost
instantaneously in the case of ramp-down waveform and half-way through the pulse on-
time for the triangular waveform. This ensures that diffusion of the electroactive species
from the bulk solution into the diffusion layer is no longer the rate-determining factor
after the deposition current density begins to decline, and other factors become more
dominant. For instance, charge transfer across the deposition layer and ohmic losses
within the electrolyte (and more specifically inside the diffusion layer) become more
important and must be taken into account. For the ramp-up waveform, however, the
deposition current density continues to rise as long as the current is on. This would
greatly diminish the concentration of the platinum ion in the diffusion layer, leading to a
higher concentration overvoltage and, consequently, creating an electroplating system
where diffusion of the electroactive species into the diffusion layer becomes the rate-
determining factor.
281
Figure 9-13 Comparison of experimental and model microhardness data for various
pulse waveforms: a) Ramp-down, b) Triangular, c) Ramp-up and d) Rectangular,
deposited at different peak current densities (4% duty cycle; 50 mM Pt concentration)
282
For the rectangular waveform, the deposition current density rises very quickly, similar to
that of the ramp-down waveform; however, it maintains its highest value (i.e., peak
current density) throughout the pulse on-time. Similar to the ramp-up waveform, the
platinum concentration in the diffusion layer begins to decline and never recovers until
the onset of pulse off-time. Similar to the ramp-up waveform, the diffusion of the
electroactive species from the bulk solution into the diffusion layer becomes the
dominant factor, influencing the plating process and inevitably the microhardness of the
resulting layer.
Figure 9-14 shows the microhardness of platinum layers predicted by the modified
mathematical model as well as the corresponding experimental values deposited by
various waveforms at different peak deposition current densities. Similar to nickel
electrodeposition, ramp-down waveform generates the highest hardness followed closely
by triangular waveform and then by ramp-up and rectangular waveforms. These trends
can be explained by considering the influence of each waveform on a number of
parameters during electrodeposition such as the variation of platinum concentration in the
cathode diffusion layer, changes in concentration overvoltage, critical nucleus size, and
platinum nucleation rate. These are discussed in the following sections.
Figure 9-14 Influence of different waveforms on platinum microhardness deposited at
various peak deposition current densities
283
9.3.3.3 Platinum Concentration Variation in the Cathode Diffusion Layer
The calculated variation of platinum ion concentration in the diffusion layer adjacent to
the cathode with a pulse on-time of 5.0 ms for the four different waveforms is shown in
Figure 9-15. As in the case of nickel electrodeposition, the concentration profiles are
markedly different and are characteristic of each waveform. The highest initial decrease
in platinum concentration during pulse on-time is observed for the rectangular and ramp-
down waveforms. This is attributed to the sharp increase in the applied current density at
the beginning of the pulse on-time, resulting in a higher deposition rate and a marked
decline in platinum concentration near the surface of the cathode for both waveforms.
The platinum ion concentration in the cathode diffusion layer will, however, recover and
start to increase as the pulse progresses for the ramp-down waveform, while, in case of
the rectangular waveform the concentration continues to decrease with the progression of
pulse on-time due to the application of a continuous high current density.
Figure 9-15 Platinum concentration in the cathode diffusion layer for various
waveforms with a peak deposition current density of 400 mA cm-2
, on-time and off-
time of 5.0 ms each (50% duty cycle) and 100 Hz (showing the first full cycle)
284
For the triangular and ramp-up waveforms, on the other hand, the initial decline in the
concentration of platinum ion in the diffusion layer is subtler than for the previous two
waveforms. This is due to the gradual increase in the applied current density during the
pulse on-time, compared with the sharp increase in current density for the ramp-down
and rectangular waveforms. Furthermore, the diminution of platinum ion concentration
for the triangular waveform is initially more pronounced than for the ramp-up waveform,
since the peak current density of the former is reached in half the time as the latter.
Additionally, for the triangular waveform, the platinum concentration in the diffusion
layer begins to increase as the applied current density approaches its maximum and then
starts to level off. At this point, the rate of platinum electrodeposition begins to fall and
the diffusion rate from the bulk solution into the diffusion layer becomes greater, leading
to an increase in the metal ion concentration within the diffusion layer. The platinum ion
concentration in the diffusion layer for the ramp-up waveform, however, continues to
decrease as the electrodeposition proceeds because of the continuous rise in the applied
cathodic current density until the completion of the pulse on-time and the onset of the
pulse off-time.
Figure 9-15 shows the concentration of the platinum ion in the cathode diffusion layer for
a complete pulse cycle for each waveform with a duty cycle of 50%. As can be seen, the
platinum concentration begins to recover before the conclusion of the pulse on-time in
the case of the ramp-down and triangular waveforms, while a recovery does not take
place until the onset of pulse off-time for the ramp-up and rectangular waveforms. For
the ramp-down and triangular waveforms, the applied current density rapidly increases,
reaching its maximum, and begins to decline before the pulse on-time is concluded. After
reaching the peak current density the rate of electrodeposition begins to fall, while the
platinum diffusion rate into the cathode diffusion layer starts to rise. This is clearly
demonstrated in Figure 9-15, where the platinum concentration in the diffusion layer
reaches its minimum half way through the pulse on-time in case of the ramp-down
waveform and around the 3.5-ms mark for the triangular waveform. On the other hand,
for both the rectangular and ramp-up waveforms, the platinum ion concentration close to
the cathode continues to decrease as electrodeposition advances until the end of pulse on-
time. Since, the minimum concentration is reached at the conclusion of the pulse on-time,
285
the ion replenishment in the cathode diffusion layer does not occur until the
commencement of the pulse off-time, resulting in a lower platinum concentration at the
end of the pulse off-time and an increase in the possibility of crystal growth due to
insufficient platinum ions in the diffusion layer when the current begins to flow again.
This is especially critical when high duty cycles are employed (e.g., 50% or greater) as is
the case with most pulse electrodeposition studies [502, 642].
9.3.3.4 Concentration Overvoltage and Pulse Current Waveforms
The concentration overvoltage has been linked directly to the size of the critical radius
and nucleation rate via equations (6-40) and (6-47), respectively. It can be seen that as the
concentration overvoltage increases, the nucleation rate also increases, while the size of
the critical radius diminishes. Accordingly, higher concentration overvoltages are
desirable in electroplating. Figure 9-16 shows the model predictions for the concentration
overvoltage of platinum electrodeposition using the four waveforms for a full pulse cycle.
As can be seen, the ramp-down waveform generates the highest overvoltage initially,
followed by the rectangular waveform. The explanations for these observations are
similar to those for the nickel electrodeposition and the reader is referred to section 9.2.3
for a more complete discussion.
Figure 9-16 Concentration overvoltage for various waveforms with a peak deposition
current density of 400 mA cm-2
, on-time & off-time of 5 ms (50% duty cycle) and 100
Hz (showing the first fuel cycle)
286
When the rectangular waveform is applied, the concentration overvoltage initially
increases in the same manner as the ramp-down waveform; but, continues to rise for the
duration of pulse on-time because of the high and continuous peak current density. One
key observation is the marked difference between the magnitudes of the concentration
overvoltages of these two waveforms where that of the rectangular waveform is
significantly lower than that of the ramp-down waveform. This is anticipated since the
peak current density of the former is half that of the latter (and other waveforms as well)
in order to generate the same average current density.
According to Figure 9-16, the concentration overvoltages of the triangular and ramp-up
waveforms exhibit a more gradual rise than those of the ramp-down and rectangular
waveforms. The explanation provided in section 9.2.3 for nickel electrodeposition also is
valid in the case of platinum.
9.3.3.5 Nucleation Rate and Pulse Current Waveforms
Figure 9-17 shows the nucleation rate associated with the four waveforms. Initially, the
ramp-down and rectangular waveforms exhibit the highest nuclei formation per unit time,
with the former beginning to decline as electrodeposition progresses, while the latter
maintains a constant rise during pulse on-time. The explanation given in the previous
section for nickel electrodeposition also is true here and the reader is referred to the
discussion provided in section 9.3.2. From Figure 9-17, it is clear that the ramp-down and
rectangular waveforms generate the smallest and the largest number of nuclei during the
first pulse cycle, respectively. The number of nuclei formed during the first pulse cycle is
obtained by determining the area under each curve. The number of nuclei generated by
each waveform for different pulse cycles (i.e., 1st, 10
th, 30
th, 50
th, and the cumulative of
the first 100 cycles) with a peak current density of 400 mA cm-2
, pulse on-time of 5.0 ms,
and a duty cycle of 50% predicted by our model is shown in Table 9-7.
287
Figure 9-17 Nucleation rate for various waveforms with a peak deposition current
density of 400 mA cm-2
, on-time of 5 ms and 100 Hz (showing the first half-cycle)
Table 9-7 Nucleation rate for all waveforms for the first pulse cycle with a pulse on-time
of 5.0 ms and a peak deposition current density of 400 mA cm-2
Waveform
Number of Nuclei
1st C 1
st Cycle 10
th Cycle 30
th Cycle 50
th Cycle Cumulative for 100 Cycles
Rectangular
3.96 х1011
1.76х1014
0.00 0.00 1.44 х1017
Triangular 3.34 х1011
6.13 х1013
3.61 х1015
1.08 х1017
1.11 х1018
Ramp-up 3.31 х1011
7.07 х1013
4.79 х1015
0.00 1.18 х1018
Ramp-down 2.51 х1011
5.18 х1013
2.83 х1015
1.50 х1017
1.30 х1018
Contrary to experimental findings where electrodeposited layers produced with a ramp-
down waveform exhibit the best results both in terms of microhardness and fuel cell
performance, the model data, at least for the first pulse cycle, predict that the most
number of nuclei will be generated by employing a rectangular waveform, while a ramp-
down waveform generates the least number of nuclei. This is anticipated since at the
onset of pulse on-time, the concentration of the electroactive species in the cathode
diffusion layer is virtually identical to its bulk concentration, and the continuous high
288
peak current density of a rectangular pulse current ensures high concentration
overvoltages, leading to higher nucleation rates. However, as electrodeposition advances,
the concentration of platinum ion in the cathode diffusion layer begins to decrease faster
than for other waveforms, causing a sharp decline in nucleation rate, as can be seen from
Table 9-7. This is more pronounced at high duty cycles, where the off-time is not long
enough to ensure the replenishment of fresh platinum ions in the cathode diffusion layer.
9.3.3.6 Duty Cycle and Pulse Current Waveforms
The influence of low duty cycles (i.e., 2% – 10%) on platinum ion concentration in the
cathode diffusion layer both in millisecond and microsecond ranges is shown in Figures
9-18 and 9-19, respectively. The total pulse on-time, bulk platinum ion concentration, and
peak cathodic current density were kept constant at 200 ms, 0.05 M, and 400 mA cm-2
,
respectively, for all waveforms in both millisecond and microsecond ranges. Pulse duty
cycles for all waveforms were varied by keeping the pulse on-time constant (0.002 s and
0.0002 s for millisecond and microsecond pulses, respectively) and varying the pulse off-
time. For low duty cycles in the millisecond range, as can be seen from Figure 9-18, the
concentration of platinum ion in the cathode diffusion layer drops sharply as duty cycle
increases from 2% to 10% for a rectangular waveform and approaches zero when duty
cycle is greater than 8%. Even at a duty cycle of 5%, the platinum ion concentration is
one-fifth of its initial value. The decline in platinum ion concentration in the diffusion
layer for other pulse waveforms is more gradual under the same conditions; nevertheless,
they all tend to decrease as duty cycle increases.
The above predictions based on the model developed in this study are in good agreement
with the experimental results presented in section 8.5.4.2.2.2, where the best and worst
fuel cell performances were found to be for MEAs prepared by ramp-down and
rectangular pulse current waveforms, respectively. Additionally, the best fuel cell
performance was observed with MEAs fabricated with the lowest duty cycle of 2%, as
discussed in section 8.5.4.2.2.2. Furthermore, as the duty cycle decreases, the applied
peak cathodic current density can be increased, leading to higher nucleation rates and
smaller deposited particle size. It is evident that the assumption that a 50% duty cycle in
289
Figure 9-18 Platinum ion concentration in the cathode diffusion layer as a function of
duty cycle in the Millisecond Range for all four waveforms with a peak deposition
current density of 400 mA cm-2
, on-time of 0.002 s and 100 pulse cycles
Figure 9-19 Platinum ion concentration in the cathode diffusion layer as a function of
duty cycle in the Microsecond Range for all four waveforms with a peak deposition
current density of 400 mA cm-2
, on-time of 0.0002 s and 1000 pulse cycles
Millisecond
Range
Microsecond
Range
Rectangular
Rectangular
290
pulse current electrodeposition is adequate for replenishment of electroactive species in
the cathode diffusion layer is not valid, at least for the rectangular waveform in the
millisecond range.
Figure 9-19 shows the platinum ion concentration in the cathode diffusion layer when
both pulse on-time and off-time are in the microsecond range for all four waveforms. It
can be seen that the decline in platinum ion concentration is more gradual for all
waveforms than with the pulses in the millisecond range (Figure 9-18). This is to be
expected, since, in the microsecond pulses, the on-time is relatively short, resulting in a
faster platinum ion recovery during the off-time. Even in the case of the rectangular
waveform, the platinum ion concentration in the cathode diffusion layer stays close to the
bulk concentration even at higher duty cycles. The presence of a high concentration of
platinum ions close to the surface of the substrate during pulse on-time ensures a high
nucleation rate and avoids crystal growth and the formation of dendrites by increasing the
corresponding limiting current density. Predicted values of platinum ion concentration in
the cathode diffusion layer for both milli- and micro-second pulses are given in Tables 9-
8 and 9-9, respectively. It is evident that longer pulses (e.g., in the millisecond range)
result in a sharper decline of the electroactive species in the close vicinity of the cathode
during pulse on-time. Although the ion concentration in the above layer may recover
during the pulse off-time, the possibility of full recovery decreases significantly as the
duty cycle increases and/or the pulse on-time becomes relatively long (i.e.; going from
micro to milli or even second pulses) regardless of the pulse off-time.
Table 9-8 Platinum ion concentration in the cathode diffusion layer as a function of duty
cycle in the Millisecond Range for all four waveforms with a peak deposition current
density of 400 mA cm-2
# of pulse on-time off-time Duty Cycle Pt Concentration (mmol L-1
)
cycles (s) (s) (%) Rectangular Ramp up Triangular Ramp down
50.00 50.00 50.00 50.00
100 0.002 0.0980 2 25.52 37.24 37.85 37.86
100 0.002 0.0480 4 16.15 32.51 33.16 33.21
100 0.002 0.0314 6 8.38 28.58 29.28 29.38
100 0.002 0.0230 8 1.90 25.28 26.04 26.21
100 0.002 0.0180 10 0.00 20.84 21.68 21.85
291
Table 9-9 Platinum ion concentration in the cathode diffusion layer as a function of duty
cycle in the Microsecond Range for all four waveforms with a peak deposition current
density of 400 mA cm-2
# of pulse on-time off-time duty cycle Pt Concentration (mmol L-1
)
cycles (s) (s) (%) Rectangular Ramp up Triangular Ramp down
50.0000 50.0000 50.0000 50.0000
1000 0.0002 0.00980 2 42.2538 46.1169 46.1270 46.1369
1000 0.0002 0.00480 4 39.0518 44.3892 44.7562 44.9055
1000 0.0002 0.00314 6 36.8392 43.2266 43.4473 43.4808
1000 0.0002 0.00230 8 34.7900 42.1818 42.4232 42.4763
1000 0.0002 0.00180 10 32.8258 41.1742 41.4419 41.5198
The influence of high duty cycle (i.e., 10% – 100%) on the platinum ion concentration in
the cathode diffusion layer in both the millisecond and microsecond ranges is shown in
Figures 9-20 and 9-21, respectively. As with low duty cycles, the platinum ion
concentration decreases as the duty cycle increases from 10% to 100% (100% being
direct current with no interruption). As with low duty cycles discussed previously, the
application of a rectangular waveform results in the sharpest decline of the diffusion layer
platinum ion concentration during electrodeposition. This is anticipated since the high
and continuous application of peak current density during pulse on-time leads to the
consumption of almost all the available platinum ions in the cathode diffusion layer. At
duty cycles greater than 90%, the platinum ion concentration in the diffusion layer
reaches zero before the end of the pulse on-time, leading to the possible formation of
dendrites and the promotion of crystal growth. Similar trends can be observed for the
other waveforms; however, for these waveforms the extent of the concentration drop is
more gradual than for the rectangular waveform, and never reaches zero, with the ramp-
down waveform exhibiting the highest platinum concentration at the end of the pulse
cycle for all duty cycles. As expected, the variation in platinum ion concentration when
high duty cycles are employed is greater than that observed with low duty cycles. The
main reason for such marked changes is the longer pulse on-time with respect to pulse
off-time in the former compared with the latter.
292
Figure 9-20 Platinum ion concentration in the cathode diffusion layer as a function of
duty cycle in the Millisecond Range for all four waveforms with a peak deposition
current density of 50 mA cm-2
, on-time of 0.02 s and 50 pulse cycles
Figure 9-21 Platinum ion concentration in the cathode diffusion layer as a function of
duty cycle in the Microsecond Range for all four waveforms with a peak deposition
current density of 50 mA cm-2
, on-time of 0.0002 s and 5000 pulse cycles
293
However, unlike low duty cycles, the model predictions for the variations in platinum
concentration in the cathode diffusion layer for both milli- and micro-second pulses are
somehow similar. This is primarily attributed to the lower peak cathodic current density
(i.e., 50 mA cm-2
compared with 400 mA cm-2
for low duty cycles) when duty cycles
greater than 10% are used. Comparing milli- and micro-second pulses (Figures 9-20 and
9-21) for duty cycles ranging from 10%-100%, it is apparent that the decline in platinum
ion concentration in the cathode diffusion layer at the end of each pulse period is very
similar, leading to the conclusion that, regardless of the type of waveform, the duration of
the pulses in the milli- and micro-second ranges has a minimal influence on the
concentration of the electroactive species in the cathode diffusion layer during
electrodeposition.
9.3.3.7 Influence of Waveform on Critical Nucleus Size
In catalyst deposition, one of the main objectives is to produce catalyst particles with the
smallest size possible in order to increase their surface area and, ultimately, enhance their
catalytic activity. Figure 9-22 shows the critical nucleus size of platinum as a function of
time for a single 5-ms pulse on-time for the four waveforms examined in this study. High
nucleation rates yield small nucleus sizes and, as can be seen from Figure 9-22, for the
ramp-down waveform at the beginning of the pulse on-time when the applied current
density is at its highest value, the critical nucleus size is at a minimum, but increases as
the current density decreases, resulting in the greatest critical nucleus size amongst all the
waveforms at the end of the pulse on-time. A similar trend was observed for the
rectangular waveform at the start of the pulse on-time; however, unlike the ramp-down
waveform, the critical nucleus size continued to decrease as the pulse on-time progressed,
on account of the high and continuous peak current density.
As expected, the critical nucleus size of the platinum particles predicted by the model for
the triangular and ramp-up waveforms was greater than that predicted for the rectangular
and ramp-down waveforms at the beginning of the pulse on-time, primarily owing to the
gradual rise in the cathodic current density of the first two waveforms. The ramp-up
waveform exhibited the largest critical nucleus size initially, but the smallest towards the
294
end of the on-time. In the case of the ramp-up waveform, the cathodic current density
rises very slowly initially and does not reach its maximum until the end of the pulse on-
time, leading to low nucleation rates for much of the pulse on-time and, subsequently,
higher critical nucleus size. However, after the 4-ms mark of the pulse on-time, the ramp-
up waveform produces the smallest platinum particles, owing to its high cathodic peak
current density. As can be seen from Figure 9-22, the ramp-down and ramp-up
waveforms generate the smallest and largest critical nucleus sizes, respectively, for a 5-
ms pulse on-time with a peak cathodic current density of 400 mA cm-2
and 50% duty
cycle.
Figure 9-22 Critical nucleus size of platinum as a function of time for various
waveforms with a peak deposition current density of 400 mA cm-2
, on-time of 5 ms and
100 Hz (showing the first half-cycle)
295
9.3.3.8 Influence of Cathodic Peak Deposition Current Density on Nucleation Rate
of Platinum for Various Waveforms
Figures 9-23 and 9-24 present the influence of the cathodic peak current density on the
nucleation of platinum at both low and high peak current densities, respectively. It is
evident that changes in the shape of the applied peak current density, while maintaining
the other parameters constant, results in significant variations in the platinum nucleation
rate. More importantly, the impact of the cathodic peak current density is correctly
predicted, which is in good agreement with the experimental results discussed in section
8.5.3.2.1. For a low duty cycle of 2%, a peak deposition current density of 400 mA cm-2
is predicted to yield the highest number of nuclei per unit time for all waveforms, with
the ramp-down waveform generating the largest number of nuclei per unit time (100 ms
in this case). For a high duty cycle of 20%, a peak deposition current density of 40 mA
cm-2
is predicted to produce the highest number of nuclei per unit time for all waveforms
with the ramp-down waveform yielding the largest number of nuclei per unit time (10 s
in this case).
Figure 9-23 Nucleation rate for various waveforms with an on-time of 1.0 ms, off-time
of 49 ms, 2% duty cycle, and 100 pulse cycles at different peak deposition current
densities
296
Figure 9-24 Nucleation rate for various waveforms with an on-time of 100 ms, off-time
of 400 ms, 20% duty cycle, and 100 pulse cycles at different peak current densities
According to Figure 9-23, for a low duty cycle of 2% with a 1.0 ms pulse on-time and
49.0 ms pulse off-time, the highest nucleation rate is achieved by employing a peak
deposition current density of 400 mA cm-2
regardless of the shape of the pulse current
waveform. This is supported by our experimental findings, where MEAs fabricated at
low duty cycles of 2% and 4% and a peak deposition current density of 400 mA cm-2
delivered the best fuel cell performance. It also was observed that MEAs prepared with a
peak deposition current density of 780 mA cm-2
and a low duty cycle of 2% perform
equally well (section 8.5.3.2.1). The model predictions as well as the experimental
observations can be explained by considering the electrodeposition mechanism, in which
there is a competition between nucleation and crystal growth. At low peak deposition
current densities, the rate of charge transfer needed for the reduction of platinum adatoms
is very slow compared with the diffusion rate of platinum ions from the bulk solution into
the diffusion layer. Consequently, platinum adatoms have sufficient time to reach the
existing crystals and crystal growth becomes the dominant process, resulting in a low
nucleation rate. As the peak deposition current density increases, however, the rate of
charge transfer also increases, and most platinum adatoms become single nuclei or part of
a small nucleus. This, of course, requires an adequate diffusion rate to ensure the
presence of fresh platinum ions in the diffusion layer during pulse on-time; however, as
297
the peak deposition current density further increases (beyond 400 mA cm-2
), the diffusion
rate becomes the rate-determining step and, once again, crystal growth becomes the
dominant process, lowering the nucleation rate as shown in Figure 9-23.
For a duty cycle of 20%, Figure 9-24 shows that a peak deposition current density of 40
mA cm-2
generates the highest number of platinum nuclei, regardless of the shape of the
waveform. Our experimental results indicated that MEAs prepared with a peak deposition
current density of 50 mA cm-2
and a duty cycle of 20% delivered the best result when
tested in a single fuel cell (Figure 8-34) followed by MEAs fabricated with a peak
deposition current density of 40 mA cm-2
. The model prediction is slightly different from
the experimental one, nevertheless they are reasonably close.
High peak deposition current densities lead to higher concentration overvoltages, which,
in turn, enhance nucleation according to equation (6-47). However, as the concentration
overvoltage increases, the concentration of the electroactive species in the diffusion layer
decreases, increasing the possibility of dendrite formation. Therefore, the peak deposition
current density for an electroplating system must be carefully selected.
Figure 9-25 shows the model predictions for the concentration overvoltage of a platinum
electroplating system for four different waveforms at high peak deposition current
densities (i.e., 50 – 600 mA cm-2
). As can be seen, at low peak current densities, the
resulting overvoltages are virtually identical for all the waveforms; however, as the peak
current density increases beyond 200 mA cm-2
, the concentration overvoltage generated
by the rectangular waveform begins to rise faster than for the other waveforms. This is
primarily attributed to the high and continuous application of the peak deposition current
density during the pulse on-time, and may lead to the incorrect conclusion that the
rectangular waveform yields the highest nucleation rate. It is imperative to consider the
concentration of the electroactive species in the cathode diffusion layer during pulse on-
time. Figure 9-26 predicts the concentrations as a function of peak current density. It can
be seen that for the rectangular waveform, the concentration of platinum ion in the
diffusion layer drops at a faster rate as the peak deposition current density increases from
50 to 600 mA cm-2
compared with the other waveforms. This, of course, influences the
298
Figure 9-25 Concentration overvoltage (overpotential) as a function of peak deposition
current density for all waveforms with a pulse on-time of 1.0 ms, pulse off-time of 49 ms,
duty cycle of 2%, and 100 pulse cycles
Figure 9-26 Platinum concentration as a function of peak deposition current density for
all waveforms with a pulse on-time of 1.0 ms, pulse off-time of 49.0 ms, duty cycle of
2%, and 100 pulse cycles
Figure 9-27 Platinum concentration as a function of peak deposition current density for
all waveforms with a pulse on-time of 1.0 ms, pulse off-time of 4.0 ms, duty cycle of
20%, and 100 pulse cycles
299
nucleation rate and, ultimately, the surface area of the deposited platinum particles. A
similar trend also is predicted for low peak deposition current densities; i.e., 10 – 80 mA
cm-2
(Figure 9-27), concurring indirectly with the experimental results that MEAs
prepared using a rectangular waveform deliver poorer fuel cell performance than MEAs
prepared using the other three waveforms.
Figure 9-28 shows a series of graphs illustrating the influence of peak deposition current
density (50 – 600 mA cm-2
) on nucleation rate for the four waveforms as predicted by the
model. It can be seen that at high peak deposition current densities (≥ 400 mA cm-2
), the
ramp-down waveform yields the highest nucleation rates, again indirectly confirming the
experimental findings in which MEAs fabricated with a ramp-down waveform employing
high peak deposition current densities of 400 mA cm-2
delivered the best fuel cell
performance.
At low current densities, the rate of platinum ion diffusion from the bulk solution into the
diffusion layer and, consequently into the substrate macropores is higher than the rate of
charge transfer; as a result, metal ions have sufficient time to find stable places on
existing crystals and the crystal grows, leading to lower catalyst surface area. As the
pulse deposition current density increases, there is no longer adequate time for adatoms to
diffuse across the surface to be incorporated into a growing crystal. Instead, as each new
adatom is deposited, it becomes a single nucleus or part of a very small number of nuclei.
The result is an increase in the number, but a decrease in the size of the Pt crystallites,
resulting in a catalyst layer with superior catalytic properties. This trend can be seen for
all waveforms for peak current densities from 50 to 400 mA cm-2
. As the peak deposition
current density increases beyond 400 mA cm-2
, surface diffusion becomes the rate-
determining step, the system approaches its ―limiting current density‖, and no further
increase in nucleation rate is observed. At low current densities (50-100 mA cm-2
), the
rectangular waveform generates the highest number of nuclei per unit time, due to its
continuous high cathodic current density. Furthermore, the peak current density is not
high enough to diminish the platinum concentration in the diffusion layer during pulse
on-time, and the crystal growth is minimal. As the peak current density increases and
reaches 400 mA cm-2
and beyond, however, ramp-down waveform exhibits the highest
300
ip = 50 mA cm-2
Figure 9-28 Nucleation as a function of
peak deposition current density for all
waveforms with a duty cycle of 2%,
pulse on-time of 2 ms, pulse off-time of
98 ms and 1000 pulse cycles: (a) 50 mA
cm-2
(b) 100 mA cm-2
, (c) 200 mA cm-2
,
(d) 300 mA cm-2
, (e) 400 mA cm-2
, (f)
500 mA cm-2
, and (g) 600 mA cm-2
(a) (b)
(c) (d)
(e) (f)
(g)
301
nucleation rate amongst all the waveforms, followed by the triangular waveform. It is
interesting to note that the highest nucleation rate for ramp-up and triangular waveforms
takes place at a peak deposition current density of 400 mA cm-2
, while for the ramp-down
waveform, it almost stays the same from 400 - 600 mA cm-2
. Another important
observation is the fact that the onset of the highest nucleation rate for any of the peak
deposition current densities happens faster for the rectangular waveform relative to the
other three waveforms. This is again due to different inherent characteristics of the
rectangular waveform compared with others.
Furthermore, Figures 9-29 and 9-30 show the model predictions for the influence of peak
deposition current density on microhardness and grain diameter and the relationship
between the microhardness and the grain diameter of an electrodeposited platinum layer,
respectively. As expected, the microhardness of the Pt layer increases as the peak
deposition current density increases, while its average grain diameter decreases (Fig. 9-
29). According to Fig. 9-30, as microhardness increases, average grain diameter
decreases, leading to smaller nanoparticles.
Figure 29 Influence of peak deposition current density on microhardness and grain
diameter of a Pt electrodeposited layer (ramp-down waveform; 2% duty cycle;
microsecond pulses)
302
Figure 30 Influence of average grain diameter on microhardness of an electrodeposited Pt
layer (ramp-down waveform; 2% duty cycle; microsecond pulses)
9.3.3.9 Comparison of Commercial and In-House MEAs
Two MEAs with different platinum loadings, one containing 0.05 and another 0.35 mg Pt
cm-2
per electrode (anode and cathode), were prepared using the technique developed in
this research. Based on our experimental and theoretical findings and the optimization
process utilized to select the best electrodeposition parameters, both in-house MEAs were
fabricated using a ramp-down waveform with a duty cycle of 4%, peak deposition current
density of 400 mA cm-2
and pulses generated and delivered in the microsecond range.
The above MEAs were tested in a single 5-cm2 fuel cell and their performance was
compared with a commercial MEA (from E-TEK) with 0.50 mg Pt cm-2
per electrode. All
fabrication and operating parameters were kept constant with the exception of the catalyst
loading method and the amount of catalyst per electrode, as can be seen from Table 9-10.
Figure 9-31 shows the polarization curves of the above MEAs using pure hydrogen and
air as fuel and oxidant, respectively. The in-house MEA with 0.35 mg Pt cm-2
outperformed the commercial MEA with 0.50 mg Pt cm-2
. The maximum power output
from the in-house MEA (0.35 mg Pt cm-2
) was 379 mW cm-2
, compared with a maximum
power output from the commercial MEA (0.50 mg Pt cm-2
) of only 318 mW cm-2
. This
represents a 19% improvement with 30% less platinum catalyst. Furthermore, when the
Pt loading of the in-house MEA was lowered by a factor of 7 from 0.35 mg Pt cm-2
to
0.05 mg Pt/cm2, its power output still was almost identical (312 mW cm
-2) with that from
303
the commercial MEA containing 0.50 mg Pt cm-2
(318 mW cm-2
). These results clearly
confirm the superiority of pulse current (PC) electrodeposition over the conventional
methods currently employed for fabricating high performance MEAs.
Table 9-10 Performance comparison of conventional and PC electrodeposited MEAs
Commercial MEA In-House MEA In-House MEA
0.50 mg Pt/cm2 0.35 mg Pt/cm
2 0.05 mg Pt/cm
2
Substrate Carbon Cloth (E-TEK) Carbon Cloth (E-TEK) Carbon Cloth (E-TEK)
Solid Polymer Electrolyte Nafion® 112 Nafion® 112 Nafion® 112
Microporous Layer Loading (mg cm
-2)
Not Known 1.5 1.5
Carbon Powder Vulcan XC-72 Vulcan XC-72 Vulcan XC-72
Catalyst Type Platinum Platinum Platinum
PTFE Loading (wt%) 20 20 20
Catalyst Loading Method Conventional
(Rolling) PC Electrodeposition
(Ramp-down Waveform) PC Electrodeposition
(Ramp-down Waveform)
Fuel/Oxidant H2/Air (both dry) H2/Air (both dry) H2/Air (both dry)
Fuel Cell Operating Pressure (bar)
1.00 1.00 1.00
Fuel Cell Operating Temperature (°C)
40 40 40
Maximum Power (mW) 318 379 312
Figure 9-31 Influence of catalyst deposition method and loading on fuel cell
performance (ramp-down waveform, H2/Air, 20 wt% PTFE, cell temperature = 40 °C,
Hydrogen and air are used as fuel and oxidant entering the cell at 100% RH with
stoichiometries of 1.2 and 2.5, respectively)
304
Membrane-electrode assemblies with low platinum loadings have been reported to
perform equally well compared with conventional MEAs with higher catalyst loadings.
Su et al. employed a novel catalyst-sprayed membrane technique to lower the platinum
loadings of the anodes and the cathodes of MEAs to 0.04 and 0.12 mg cm-2
, respectively,
without lowering MEA performance [656]. Platinum loadings of 0.10-0.20 mg cm-2
also
have been reported to deliver high performance by a number of researchers [657-658].
However, MEAs with ultra-low platinum loadings (i.e.; less than 0.1 mg cm-2
) have been
known to significantly lower its performance. Leimin et al. [659] claimed only a 5%
decrease in cell performance, when the platinum loading was decreased from 0.30 to 0.15
mg cm-2
, but a 35% decrease in cell performance when the catalyst loading was further
lowered to 0.06 mg cm-2
. Martin et al. [660] utilized scanning electron microscopy and
single-cell fuel cells to examine MEAs prepared by a novel electrospray method, where
platinum loadings as low as 0.0125 mg cm-2
were employed. MEAs with ultra-low
platinum loadings (less than 0.10 mg cm-2
) exhibited inferior performance compared with
MEAs containing 0.10 mg cm-2
. More recently, Gasteiger and Markovic [661] and
Secanell et al. [662] presented novel non-precious metal catalysts for oxygen reduction
and an MEA optimization method based on a two-dimensional isothermal, isobaric and
single phase MEA model, respectively.
305
10.0 CONCLUSIONS
The main conclusions drawn from the research are as follows:
1. Membrane-electrode assemblies (MEAs) prepared by pulse current (PC)
electrodeposition using a ramp-down waveform show performance comparable with
commercial MEAs, but with only one-tenth of the platinum of the latter. When the
platinum loading of in-house MEAs is increased to almost two-thirds that of
commercial E-TEK electrodes, the in-house MEAs exhibit better performance than
the commercial electrodes. MEAs fabricated using a triangular waveform performed
equally well, while those prepared using rectangular and ramp-up waveforms
performed slightly less well.
2. The thickness of the pulse electrodeposited Pt electrocatalyst layer is about 5-7 m,
which is about ten times thinner than that of commercial electrodes. In all likelihood,
this reduction in catalyst layer thickness has a significant impact on MEAs
performance and may arguably be the most important factor in improving fuel cell
performance.
3. MEAs prepared with pulse electrodeposition exhibit better fuel cell performance than
those fabricated by direct current electrodeposition. This is primarily attributed to the
deposition of smaller platinum crystallites and thinner catalyst layers using PC
electrodeposition.
4. For the plating cell employed, the optimal plating conditions were found to be: (i) a
peak deposition current density of 400 mA cm-2
, (ii) a duty cycle of 4%, (iii) pulses
generated and delivered in the microsecond range, (iv) a platinum bath concentration
of 0.05 M aqueous Pt2(NH3)4Cl2, (v) a plating solution flow rate of about 450 mL
min-1
, and (vi) a ramp-down waveform.
5. Based on the combination of parameters used in this study, a deposition current
density of 15 mA cm-2
produced the electrode with the best performance in DC
electrodeposition, while in PC electrodeposition a pulse current density of 50 mA
cm-2
and 400 mA cm-2
in high (10%-90%) and low (2%-10%) duty cycles,
respectively, give the best results.
306
6. MEAs fabricated using a 4% duty cycle (at a pulse deposition current density of 400
mA cm-2
) exhibited the best fuel cell performance, while at high duty cycles (10%-
90%), MEAs prepared with a duty cycle of 20% (at a pulse current density of 50 mA
cm-2
) delivered the best performance. However, MEAs fabricated using lower duty
cycles (less than 10%) generally outperformed those fabricated using higher duty
cycles. Other combination of parameters would have to be verified and optimized.
7. In a series of lifetime tests MEAs prepared by pulse electrodeposition performed
better than commercial MEAs. In static lifetime tests (constant load), the average cell
voltages over a 3000-h period at a constant current density of 619 mA cm-2
for the in-
house and the commercial MEAs were 564 mV and 505 mV, respectively. More
importantly, the decrease in cell voltage for the in-house MEA was only 2.1%, while
the commercial MEA experienced a drop of 2.8% by the end of the experiment.
Furthermore, there was significantly less variation in the output cell voltage of the in-
house MEA compared with the commercial MEA during the 3000-h operation.
8. In dynamic (varying load) lifetime experiments, an adult tricycle powered by a fuel
cell stack containing 42 in-house MEAs outperformed a similar fuel stack containing
commercial MEAs. Both stacks were used to charge a battery bank comprising three
12-V lead acid batteries sixty-three times over a 60 day period. The initial
performance of the stack containing the in-house MEAs was slightly superior to that
of the commercial MEAs, where, for the first 30 charges, the average stack power
outputs were, respectively, 218 W and 214 W. The variation in stack output also was
lower for the in-house MEAs for the first 30 charges. Furthermore, the average final
OCV of the fuel cell stack employing in-house MEAs was 1.022 V, while that of the
commercial stack was 1.012 V; this is an increase of 10 mV (about 1%). This small
improvement may result from a more effective catalyst layer based on the deposition
method described in this thesis.
9. A mathematical model, based on the works of Molina et al. [642] and Milchev [643,
652-654], for the electrodeposition based on joint diffusion, ohmic and charge
transfer control in the absence of any supporting electrolyte correctly predicted the
influence of peak deposition current density, duty cycle, and type of waveform on the
microhardness of the deposited layer. A strong correlation between microhardness
307
and particle size of the deposited layer was established. According to this model, the
highest nucleation rate of both platinum and nickel is obtained by employing the
ramp-down waveform, followed by the triangular waveform and then ramp-up, and,
finally, the rectangular waveform.
10. According to the model, as the peak deposition current density increases, the
microhardness rises, owing to a decrease in metal grain size, thereby improving the
catalytic activity of the catalyst layer in the fuel cell. The model predictions were
consistent with the experimental results.
11. At high peak deposition current densities (≥ 400 mA cm-2
), the ramp-down waveform
yielded the highest nucleation rates, indirectly confirming the experimental findings
in which MEAs fabricated with a ramp-down waveform employing a high peak
deposition current density of 400 mA cm-2
delivered the best fuel cell performance.
12. A hydrophobic polymer (PTFE) loading of 20 wt% on both cathode and anode on
carbon substrates gives the best results.
13. Under low fuel cell load conditions (< 200 mA cm-2
), MEAs prepared with different
carbon/graphite powders show similar performance. However, at current densities
greater than 300 mA cm-2
, the cell voltage increases with increasing macropore (> 1
µm) volume. Shawinigan Acetylene Black (SAB) had the highest macropore volume
of all the carbon/graphite materials investigated in this study and delivered the best
performance when tested in a single fuel cell, while Mogul L had the smallest volume
of macropores, and, consequently exhibited the poorest fuel cell performance under
identical test conditions. The improvement in gas diffusion layers prepared with SAB
is attributed to reduced mass transport limitations, most likely as a result of better
water management, especially at high current densities.
14. A diffusion layer loading (PTFE + carbon powder) of 1.5 mg cm-2
delivers the best
performance. Electrodes with less than 1.0 mg PTFE-C/cm2 exhibit poor cell
performance, while excessive loadings—greater than 2.0 mg PTFE-C/cm2—in most
cases, can pose other limitations, thereby lowering fuel cell performance. A slight
improvement in performance is observed when the carbon loading is increased from
308
1.0 to 3.0 mg cm-2
for MEAs prepared with Asbury 850 and Mogul L. This marginal
improvement is attributed to a better coverage of the electrode surface.
15. Carbon paper (TGP090, Toray Inc.) and carbon cloth (Elat, E-TEK Inc.) exhibit very
similar performance when the PC electrodeposition technique is employed. At low
current densities (less than 300 mA cm-2
) all MEAs performed equally well; however,
the performance at current densities higher than 300 mA cm-2
of the thickest and the
thinest GDLs from Toray Industries Inc.—TGP-H-120 (370 µm) and TGP-H-030
(110 µm)—starts to lag behind the others. These differences in fuel cell performance
become very apparent when the current density reaches 1500 mA cm-2
using pure
oxygen as the oxidant. This variation in performance is attributed to the differences in
the electronic conduction and the water management (related to the amount of
macropores) capability of each substrate.
16. Reducing the platinum loading at the anode from 0.35 to 0.15 mg cm-2
using the PC
electrodeposition technique has a negligible impact on the performance of a PEM fuel
cell.
17. Thirty-second impregnation time (floating method) for Nafion® loading produces
carbon substrates with a sufficient amount of Nafion®. Higher Nafion
® loadings can
be obtained using the brushing method.
309
11.0 RECOMMENDATIONS AND FUTURE WORK
1. Examine the impact of fuel cell temperature on MEAs preparation using the PC
electrodeposition technique.
2. Study the influence of external humidification of reactant gases on MEAs fabricated
using the PC electrodeposition technique.
3. Further characterize both diffusion and catalyst layers utilizing various techniques
such as cyclic voltammetry (CV), Inductively coupled plasma atomic emission
spectroscopy (ICP-AES) and electrochemical impedance spectroscopy (EIS).
4. Further develop the mathematical model based on nucleation theory.
310
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334
APPENDIX A
Table A-1 Physical data for Platinum Group Metals [655]
Property/Metal Ru Rh Pd Os Ir Pt
Atomic Number 44 45 46 76 77 78
Atomic Weight (g mol-1
) 101.07 102.9 106.4 190.2 192.2 195.09
Group, Period, Block 8, 5, d 9, 5, d 10, 5, d 8, 6, d 9, 6, d 10, 6, d
Ionic Radii (Å) / ox. State 0.82 (+3) 0.81 (+3) 0.78 (+2) 0.78 (+2) 0.82 (+3) 0.74 (+2)
Density at 20 °C (g cm-3
) 12.45 12.41 12.02 22.61 21.65 21.45
Liquid Density at m.p. (g cm-3
) 10.65 10.7 10.38 20 19 19.77
Crystal Structure hcp fcc fcc hcp fcc fcc
Melting Point (K) 2607 2237 1828.05 3306 2739 2041.4
Boiling Point (K) 4423 3968 3236 5285 4701 4098
Heat of Fusion (kJ mol-1
) 38.59 26.59 16.74 57.85 41.12 22.17
Heat of Vaporization (kJ mol-1
) 591.6 494 362 738 563 469
Specific Heat Capacity (J mol-1
K-1
) 24.06 24.98 25.98 24.7 25.1 25.86
Oxidation States 1,2,3,4,6,8 1, 2, 3, 4 2, 4 -1, -2, 1-8 2, 3, 4, 6 1,2,3,4,5,6
Electronegativity (Pauline Scale) 2.3 2.28 2.2 2.2 2.28
Ionization Energies (kJ mol-1
)
1st: 710.2 719.7 804.4 840 880 870
2nd: 1620 1740 1870 1600 1600 1791
3rd: 2747 2997 3177
Electrical Resistivity at 273 K (nΩ m) 71 43.3 105.4 (293K)81.2 47.1 105 (293 K)
Thermal Conductivity at 300 K (w m-1
K-1
) 117 150 71.8 87.6 147 71.6
emf (vs. SHE) (M/M2+
) +0.680 +0.758 +0.951 +0.850 +1.156 +1.188
Speed of Sound (thin rod) (m s-1
) 5970 4700 3070 4940 4825 2800
Young's Modulus (Gpa) 447 380 121 528 168
Shear Modulus (Gpa) 173 150 44 222 210 61
Bulk Modulus (Gpa) 220 275 180 320 230
Poisson Ratio 0.3 0.26 0.39 0.25 0.26 0.38
Hardness (kg mm-2
)
(i) Metal (annealed) 200-350 120-140 37-40 300-500 200-240 37-42
(ii) Electrodeposited 900-1000 800-900 200-400 n/a 900 200-400
Mohs Hardness 6.5 6 4.75 7 6.5 4.0-4.5
CAS Registry Number 7440-18-8 7440-16-6 7440-05-3 7440-04-2 7439-88-5 7440-06-4
335
APPENDIX B
The Electrical Double Layer
Introduction
Electrical double layer phenomena arise when two different phases come in contact. The
resulting interphase has a different composition than both bulk phases and its structure is
of great importance in electrochemistry. This is important in electrodeposition, where a
substrate (usually a metal) and an electrolyte solution (containing the metallic ions) come
in contact. A good understanding of the structure of this substrate-electrolyte interphase
is important since the electrodeposition process takes place in this very thin region, where
the electric field is in the neighbourhood of 106 to 10
7 V cm
-1 [333]. In an electrical
double layer between two different phases, one phase carries a positive charge and the
other a negative charge at the phase boundary, analogous to a simple parallel plate
capacitor (Figure B-1).
Figure B-1 A parallel-plate capacitor
The structural properties of the interphase play a vital role in the nature of the
electrodeposited layer. Water contains dissolved ions of interest that are hydrated to a
varying degree, while water molecules have the ability to form clusters. Such clusters
either can be structured, where they contain hydrogen-bonded water molecules, or
unstructured, where single and independent water molecules exist. According to this
- - -
- - -
+
+
+
+
+
+
336
model, the lifetime of such clusters is about 10-10
s [333, 334]. On the other hand, metals
contain a fixed lattice of positive ions surrounded by a number of negatively-charged
electrons. A distinction is made between the bulk structure of a metal and that of its
surface. The latter is often referred to as the top layer of atoms, but in electrochemistry
the metal surface is considered to contain the top two to three atomic layers. A thorough
discussion of the electrical double layer is provided by Paunovic and Schlesinger [333].
Electrical Double Layer Models
It is clear that the formation of any interface between an electrolyte and a metal will
inevitably impact the reactions taking place at the metal surface, and such reactions will
be markedly different from those occurring in the bulk solution. In electrodeposition, the
electrode will often be under potentiostatic or galvanostatic control via an external power
supply or current rectifier, hence not only adding to the complexity of the system, but
also imparting additional constraints on the metal by dictating the amount of charge that
can be held at the electrode. All these factors strongly influence the rates and the types of
interactions that can take place between ions and molecules in the electrolyte and the
electrode surface. With this interface being the locus of the electrodeposition, where all
desired reactions take place, it becomes important not only to gain an understanding of all
the factors influencing such reactions, but also be able to control them to achieve
desirable outcomes. The first step in attaining the above goals is to successfully explain
the behaviour of such interfaces under different conditions. Many models have been put
forward to explain the behaviour of the metal-electrolyte interface, including the
Helmholtz, Gouy-Chapman, Stern, Grahame, and Bockris, Devanathan & Muller models.
For reference purposes only, simple schematics of the above models are shown in Figures
B-2 to B-5.
337
Figure B-2 Helmholtz compact double-layer model
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
XH
Metal Solution
Hydrated
Anions
Distance from the
Metal Surface
Helmholtz
Fixed Plane
(volts)
Distance into Solution
Adsorbed
Water Dipoles
+
338
Figure B-3 Gouy-Chapman model of electrical double layer
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Metal Solution
+
+
+
Distance into Solution
1
+
+
+
+
+
+
+
+
+
-
-
-
-
-
-
-
-
-
339
Figure B-4 Stern model of electrical double layer [333]
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Metal Solution
+
Distance into Solution
+
+
Helmholtz Plane
Fixed Ions
Mobile Ions
Diffuse Layer
Compact
layer
CH CGC
340
Figure B-5 Grahame triple-layer model
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
XH,i
Metal Solution
Helmholtz Planes
(inner & outer)
+
- -
+
+
+
XH,O
Distance to Solution
Diffuse Layer
-
Partially-Hydrated Ion
Fully-Hydrated Ion
341
APPENDIX C
Table C-1 Pump calibration, Tygon L/S 16 Tubing, 25 °C
SPEED
Flow rate
(mL min-1
)
(%) Run 1 Run 2 Run 3 Run 4 Average
5 13 13 13 13 13
10 41 39 39 39 40
20 92 94 93 93 93
30 168 170 169 169 169
40 235 235 236 237 236
50 304 301 300 307 303
60 375 377 375 378 376
70 454 454 452 456 454
80 515 514 517 517 516
90 572 574 574 576 574
92 (Maximum) 581 582 582 585 583
Table C-2 Pump calibration, Tygon L/S 16 Tubing, 50 °C
Speed
Flow
rate ( (mL
min-1
)
(%) Run 1 Run 2 Run 3 Run 4 Average
5 13 14 14 13 14
10 42 40 39 39 40
20 94 95 94 93 94
30 170 170 171 169 170
40 237 236 236 237 237
50 304 303 302 306 304
60 378 377 379 378 378
70 454 457 456 456 456
80 516 517 516 517 517
90 578 577 575 576 577
92 (Maximum) 583 584 584 585 584
342
Table C-3 Pump calibration, Tygon L/S 25 Tubing, 25 °C
Speed
Flow rate
(mL min-1
)
(%) Run 1 Run 2 Run 3 Run 4 Average
5 27 27 28 27 27
10 84 85 85 85 85
20 193 194 193 192 193
30 350 348 350 351 350
40 490 490 492 490 491
50 633 632 632 630 632
60 781 782 781 784 782
70 945 944 947 944 945
80 1073 1076 1078 1075 1076
90 1190 1193 1191 1190 1191
92
(Maximum) 1210 1208 1212 1209 1210
Table C-4 Pump calibration, Tygon L/S 25 Tubing, 50 °C
Speed
Flow rate
(mL min-1
)
(%) Run 1 Run 2 Run 3 Run 4 Average
5 28 27 29 28 28
10 86 86 87 85 86
20 195 196 194 194 195
30 352 351 350 350 351
40 493 494 492 490 492
50 632 635 634 631 633
60 78 783 780 783 783
70 949 946 946 948 947
80 1075 1078 1079 1078 1078
90 1192 1193 1194 1194 1193
92
(Maximum) 1212 1211 1215 1216 1214
344
APPENDIX D
Derivation of Equations
Obtaining an Analytical Solution for the Ramp-Down Waveform
The mass transfer in most electrochemical systems, including electrodeposition processes
employing different waveforms, is customarily described by Fick’s second law of
diffusion—equation (9-15). Taking the Laplace transform of this equation yields:
02
2
ccsdx
cdD (1)
According to the initial condition—equation (9-16)—the concentration at the start of the
first pulse (t = 0) is equal to the bulk concentration; the Laplace transform of (9-16)
results in:
s
cxc 0),0( (2)
Similarly, the Laplace transform of the boundary condition (9-17) gives:
s
csc 0),( (3)
Applying the Laplace transform to the mathematical expression representing the ramp-
down waveform, expression (9-25), yields:
22)(
s
e
s
e
s
ea
a
iti
kswswsp
(4)
Substituting the transformed Heaviside function—(4)—into boundary condition (9-18)
results in:
22
0s
e
s
e
s
ea
aDFz
i
x
c kswswsp
x
(5)
The ordinary differential equation (ODE) that was derived from Fick’s second law of
diffusion can readily be solved using expressions (2) and (3) to give
345
s
ceAc
xD
s
0
(6)
The constant A in the above expression can be evaluated by taking its derivative and
putting it into equation (5):
s
c
s
Da
DFz
i
s
c
edx
cdA
p
D
s
001
(7)
Simplifying the above equation:
)8(
1
2/52/52/3
22
s
e
s
e
s
ea
aDFz
i
s
e
s
e
s
ea
saDFz
iA
kswswsp
kswswsp
Putting equation (8) into (6):
s
ce
s
e
s
e
s
ea
aDFz
ixsc
xD
skswsws
p 0
2/52/52/3),(
(9)
The surface concentration can be expressed as follow:
s
ce
s
e
s
e
s
ea
aDFz
isc
D
skswsws
p 0)0(
2/52/52/3)0,(
(10)
2/52/52/3
0)0,(s
e
s
e
s
ea
aDFz
i
s
csc
kswswsp
(11)
The solution to the original diffusion equation is obtained by applying the inverse
Laplace transform to equation (11):
)12()(
)2/5()(
)2/5()(
2/3)0,(
2/32/32/1
0
tS
kttSw
wttS
awt
aDFz
ictc kw
p
346
The concentration overvoltage for a diffusion-controlled process is represented by:
0
)0,(ln
c
tc
Fz
TR (9-42)
Substituting equation (12) into (9-42) yields the overvoltage equation for a ramp-down
waveform:
0
2/32/32/1
0 )()2/5(
)()2/5(
)(2/3
lnc
tSkt
tSwwt
tSawt
aDFz
ic
zF
RTkw
p
)(
)2/5()(
)2/5()(
2/31ln
2/32/32/1
0
tSkt
tSwwt
tSawt
aDFcz
i
Fz
TRkw
p
347
Derivation of Eqn (9-66)
Faraday’s Law for Hemispherical Cluster
If n = number of moles, then, from Faraday’s law the total current I is given by
I zFdn
dt
eqmol
Ceq
mols C
s . . . (a)
The volume V of a hemisphere of radius R is
V 12
43 R
3 23 R
3
No. moles in the hemisphere: n V
vM
23R3
vM
2R3
3vM
. . . (b)
Rate of deposition mol
s
: dn
dt =
dn
dRdR
dt
= d
dR
2R3
3vM
dR
dt
= 2R2
vM
dR
dt . . . (c)
Putting (c) into (a): I zFdn
dt zF
2R 2
vM
dR
dt
Therefore I 2zF
vM
R
2 dR
dt (9-66)
348
Derivation of Eqns (9-67) and (9-68)
I1(t) 2R2io exp
zF
R T
exp
(1 )zF
R T
. . . (9-65)
where SR is the cluster surface area and io is the exchange current density. In order not to
confuse the gas constant with the cluster radius, R is used for the gas constant and R for
the radius of the hemispherical cluster.
I1(t) 2zF
vM
R2 dR
dt . . . (9-66)
from which dR
dt
vMI1(t)
2zFR2 . . . (a)
Substituting (9-65) into (a):
dR
dt =
vM
2zFR2 2R
2io exp
zF
R T
exp
(1)zF
R T
= vMio
zFexp
zF
R T
exp
(1)zF
R T
. . . (b)
dR vMio
zFexp
zF
R T
exp
(1)zF
R T
dt
Integrating, noting that at t = 0, R = 0, gives
R(t) vMio
zFexp
zF
R T
exp
(1)zF
R T
t . . . (9-67)
Substituting (9-67) into (9-65):
I1(t) =
2vMio
zFexp
zF
R T
exp
(1 )zF
R T
t
2
io expzF
R T
exp
(1 )zF
R T
i.e., I1(t) = 2vMio
3
(zF)2 exp
zF
R T
exp
(1)zF
R T
3
t2
. . . (9-68)
349
Derivation of Eqns (9-69) and (9-70)
co = bulk concentration
c = concentration at r
cS = concentration at surface of cluster
At r = , c = co
At r = r, c = c
At r = R, c = cS
If the total cation flux is diffusion flux, then J Ddc
dr
i
zF
I
AzF (I = total current)
Therefore, I
AzF D
dc
dr
dc
dr
I
AzFD . . . (a)
Area of hemispherical surface is A = 12 4r
2 = 2πr2 . . . (b)
Putting (b) into (a): dc
dr
I
2r2zFD
Cross-multiplying: dc I
2zFD
dr
r2
dcc1
c 2
I
2zFD
dr
r2
r1
r2
Integrating: c2 – c1 = I
2zFD
1
r2
1
r1
k
1
r2
1
r1
. . . (c)
When c2 c, r2 r
c1 co, r1
c co k1
r
1
k
1
r
. . . (d)
When c2 co, r2
c1 cS, r1 R
co cS k1
1
R
k
1
R
. . . (e)
Dividing (d) by (e): c co
co cS
1 r
1 R
R
r
Cross-multiplying: c co R
rco cS
dr
r
R
350
c = co R
rco cS co
R
rco
co
co cS . . . (f)
= co 1R
r
co
co
cS
co
i.e., c co 1R
r1
cS
co
. . . (9-69)
From (f), c co R
rco cS
Differentiating: dc
dr
dco
drR co cS
d(1 r)
dr 0 R co cS
1
r2
Therefore, dc
dr
R co cS r
2
When r = R, dc
dr
rR
R co cS
R2
i.e., dc
dr
rR
co cS
R . . . (9-70)
351
Derivation of Eqn (9-71)
We start with I1(t) 2zF
vM
R2 dR
dt . . . (9-66)
from which dR
dt
vMI1(t)
2zFR2 . . . (a)
Also, I1(t) 2R2io
cS
co
expzF
R T
exp
(1 )zF
R T
. . . (9-61d)
Substituting (9-61d) into (a):
dR
dt =
vM
2zFR2 2R
2io
cS
co
expzF
R T
exp
(1 )zF
R T
= iovM
zF
cS
co
expzF
R T
exp
(1 )zF
R T
. . . (b)
Also, I1(t) 2RzFDco 1cS
co
. . . (9-61b)
from which 1cS
co
I1(t)
2RzFDco
or cS
co
1I1(t)
2RzFDco
. . . (c)
Substituting (c) into (b):
dR
dt =
iovM
zF1
I1(t)
2zFRDco
exp
zF
R T
exp
(1 )zF
R T
= iovM
zFexp
zF
R T
I1(t)
2zFRDco
expzF
R T
exp
(1 )zF
R T
. . . (d)
Substituting (9-57) into (d):
dR
dt =
iovM
zFexp
zF
R T
2zF
vM
R2 dR
dt
2zFRDco
expzF
R T
exp
(1 )zF
R T
= iovM
zFexp
zF
R T
R
vMDco
expzF
R T
dR
dt exp
(1 )zF
R T
352
= iovM
zF exp
zF
R T
Rio
zFDco
expzF
R T
dR
dt
iovM
zF exp
(1 )zF
R T
dR
dt1
Rio
zFDco
expzF
R T
iovM
zF exp
zF
R T
iovM
zFexp
(1 )zF
R T
dR
dt =
iovM
zF exp
zF
R T
iovM
zFexp
(1 )zF
R T
1Rio
zFDco
expzF
R T
=
iovM
zFexp
zF
R T
exp
(1 )zF
R T
1Rio
zFDco
expzF
R T
. . . (e)
Multiplying both top and bottom of (e) by zFDco:
dR
dt =
zFDcoiovM
zFexp
zF
R T
exp
(1 )zF
R T
zFDco Rio expzF
R T
Finally, dR
dt
DcovMio expzF
R T
exp
(1 )zF
R T
zFDco Rio expzF
R T
. . . (9-71)
353
Derivation of Eqn (9-72)
Start with: dR
dt
DcovMio expzF
R T
exp
(1 )zF
R T
zFDco Rio expzF
R T
dR zFDco Rio expzF
R T
Dco vMio exp
zF
R T
exp
(1 )zF
R T
dt
zFDco dR io expzF
R T
RdR DcovMio expzF
R T
exp
(1 )zF
R T
dt
zFDco dR0
R
io expzF
R T
RdR0
R
DcovMio expzF
R T
exp
(1)zF
R T
dt0
t
zFDco R io expzF
R T
R2
2 DcovMio exp
zF
R T
exp
(1 )zF
R T
t
io expzF
R T
R2
2 zFDco R DcovMio exp
zF
R T
exp
(1)zF
R T
t 0
This is a quadratic equation. Rearranging:
R2
zFDco
io
2 exp
zF
R T
R
DcovMio expzF
R T
exp
(1 )zF
R T
t
io
2 exp
zF
R T
0
R2
2zFDco
io expzF
R T
R
2DcovMio expzF
R T
exp
(1 )zF
R T
t
io expzF
R T
0
R2
2zFDco
io expzF
R T
R 2DcovM 1 expzF
R T
t 0
354
Solving the quadratic, taking the positive root since the radius R of the cluster must be >0:
R =
2zFDco
io expzF
R T
2zFDco
2
io
2 exp
2zF
R T
4 1 2DcovM 1 exp(1 )zF
R T
expzF
R T
t
2 1
=
2zFDco
io expzF
R T
2zFDco
2
io
2 exp
2zF
R T
4 1 2DcovM 1 expzF
R T
t
2 1
= zFDco
io expzF
R T
1
2
2zFDco 2
io
2 exp2zF
R T
4 1 2DcovM 1 expzF
R T
t
= zFDco
io expzF
R T
1
4
2zFDco 2
io
2 exp2zF
R T
2D covM 1 expzF
R T
t
= zFDco
io expzF
R T
zFDco
2
io
2 exp2zF
R T
2DcovM 1 expzF
R T
t
= zFDco
io expzF
R T
zFDco
2
io
2 exp2zF
R T
zFDco
2
zFDco 2 2Dco vM 1 exp
zF
R T
t
= zFDco
io expzF
R T
zFDco
1
io
2 exp2zF
R T
1
zFDco 2 2DcovM 1 exp
zF
R T
t
= zFDco
io expzF
R T
zFDco
exp2zF
R T
io
2
2
zF 2
Dco
vM 1 expzF
R T
t
355
= zFDco
io expzF
R T
zFDco
exp2zF
R T
io
2
io
2
io
2
2
zF 2
Dco
vM 1 expzF
R T
t
= zFDco
io expzF
R T
zFDco
io
exp2zF
R T
2io
2
zF 2
Dco
vM 1 expzF
R T
t
=
zFDco
io expzF
R T
zFDco
io
exp2zF
R T
exp2zF
R T
exp2zF
R T
2io
2
zF 2
Dco
vM 1 expzF
R T
t
=
zFDco
io expzF
R T
zFDco
io
exp2zF
R T
11
exp2zF
R T
2io
2
zF 2
Dco
vM 1 expzF
R T
t
=
zFDco
io expzF
R T
zFDco
io
expzF
R T
11
exp2zF
R T
2io
2
zF 2
Dco
vM 1 expzF
R T
t
=
zFDco
io expzF
R T
zFDco
io
expzF
R T
1 exp2zF
R T
2io
2
zF 2
Dco
vM 1 expzF
R T
t
=
zFDco
io expzF
R T
zFDco
io expzF
R T
1 2vMio
2
zF 2
Dco
exp2zF
R T
exp
2zF
R T
exp
zF
R T
t
356
=
zFDco
io expzF
R T
zFDco
io expzF
R T
1 2vMio
2
zF 2
Dco
exp2zF
R T
exp
(2 1)zF
R T
t
. . . (a)
Define the following:
P = expzF
R T
. . . (b)
m = zFDco
ioP . . . (c)
Q = exp2zF
R T
exp
(2 1)zF
R T
. . . (d)
n = vMio
2Q
zF 2
Dco
. . . (e)
Substituting (b), (c), (d), and (e) into (a) transforms (a) to
R(t) = zFDco
io P
zFDco
io P1 2
vMio
2
zF 2
Dco
Q t
= m m 1 2n t
= m 1 2n t 1
Therefore, R(t) = m 1 2nt 1 / 2
1 . . . (9-72)
357
Derivation of Eqn (9-77)
Show that I p1 nt
1 2nt 1 / 2 1
We showed earlier that I 2zF
vM
R
2 dR
dt . . . (9-66)
and also that R m 1 2nt 1 / 2
1 . . . (9-72)
We have defined: p 4 zFDco
2Q
io P3 . . . (a)
n = vMio
2Q
zF 2
Dco
. . . (b)
Q = exp2zF
R T
exp
(2 1)zF
R T
. . . (c)
P = expzF
R T
. . . (d)
m = zFDco
ioP . . . (e)
Noting that p, n, Q, P, and m are not functions of t, we can differentiate (9-72) to give
dR
dt =
d
dtm 1 2nt
1 / 21 m
d
dt1 2nt
1/ 2
= m 12 1 2nt
1/ 22n
= mn
1 2nt 1/ 2 . . . (f)
Dividing (a) by (b): p
n=
4 zFDco 2
Q
io P3
vMio
2Q
zF 2Dco
= 4 zFDco
2
io P3
zF 2D co
vMio
2
= 4zF
vM
zFDco
io P
3
358
= 4zF
vM
m3
Rearranging: 2zF
vM
p
2m3n
. . . (g)
Substituting (g), (9-72), and (f) into (9-66):
I = p
2m3n m 1 2nt
1 / 21
2
mn
1 2nt 1/ 2
= p1
2mn1 2nt
1/ 21
2
mn
1 2nt 1 / 2
= p1
2 1 2nt 1/ 2 1 2nt 1/ 2
1 2
= p1 2nt 2 1 2nt 1/ 2
1
2 1 2nt 1 / 2
= p12 1 2nt 1
2 2 1 2nt 1 / 2 1
2
1 2nt 1/ 2
= p
12 nt 1 2nt 1/ 2
12
1 2nt 1 / 2
= p1 nt
1 2nt 1 / 2 1 2nt 1/ 2
1 2nt 1/ 2
= p1 nt
1 2nt 1 / 2 1
. . . (9-77)
359
Derivation of Eqn (9-78)
Pure Diffusion Control
From Eqn (9-72), R(t) m 1 2nt 1/ 2
1 . . . (9-72)
When io is very large or t is very long, nt >> 50, and 12nt 1/21 2nt
1/2
Therefore, under these conditions, R(t) m 2nt 1/ 2
. . . (a)
Putting in values for m and n:
R(t) ≈zFDc
io expzF
R T
2vMio
2
zF 2
Dc
exp
2zF
R T
exp
(2 1)zF
R T
t
1/ 2
=
zFDc
io
2vMio
2
zF 2
Dc
1 / 2
expzF
R T
exp
2zF
R T
exp
(21)zF
R T
1/ 2
t1/ 2
=
zFDc
io
2vMio
2
zF 2
Dc
1 / 2
exp2zF
R T
1 / 2
exp2zF
R T
exp
(21)zF
R T
1 / 2
t1/ 2
=
2vMDc 1 / 2
exp2zF
R T
exp
2zF
R T
exp
2zF
R T
exp
(2 1)zF
R T
1/ 2
t1/ 2
= 2vMDc 1 / 2
exp 0 expzF
R T
1 / 2
t1/ 2
= 2DcvM 1 / 2
1 expzF
R T
1/ 2
t1 / 2
. . . (9-78)
where R is the radius of the cluster and R is the gas constant.
360
Derivation of Eqn (9-79)
Pure Diffusion Control
From Eqn (9-77) I1(t) p1 nt
1 2nt 1/ 2 1
. . . (9-77)
where p 4 zFDc
2Q
ioP3 . . . (a)
When io is very large or t is very long, nt >> 50,
and 1+nt ≈ nt and 1+2nt ≈ 2nt
and (9-77) reduces to I1(t) pnt
2nt 1/ 2
p
nt 1/ 2
2
. . . (b)
Putting the expressions for p and n into (b):
I1(t) = 4 zFDc
2Q
2 ioP3
vMio
2Qt
(zF)2Dc
1/ 2
= 4 zFDc
2
2 io
vM
1 / 2io
zF(Dc)1/ 2
Q3 / 2
P3 t
1 / 2
= zF 2DcvM
1/ 3 3 / 2 Q3 / 2
(P2)
3/ 2 t1/ 2
. . . (c)
Q
P2
3 / 2
=
exp2zF
R T
exp
(2 1)zF
R T
expzF
R T
2
3 / 2
=
exp2zF
R T
exp
(2 1)zF
R T
exp2zF
R T
3 / 2
= 1 exp(zF
R T
3 / 2
. . . (d)
Putting (d) into (c):
362
Derivation of Eqn (9-83)
The ohmic resistance of an electrolyte is given by
1
A
where is the length of the conduction path and A is the cross-sectional area
perpendicular to the flow of current.
Therefore d 1
d
A . . . (a)
Referring to the figure below:
The area of a hemisphere of radius r is A = 12 4r
2 = 2πr2 . . . (b)
and the differential path length is d = dr . . . (c)
Putting (b) and (c) into (a): d1
dr
2r2
Integrating: dr=R
r=L
1
2
dr
r2
R
L
R-L = 1
2
1
r
R
L
= 1
2
1
L
1
R
= 1
2
1
R
1
L
= 1
2
R
R
1
R
1
L
= 1
2R
R
R
1
L
i.e., R -L 1
2R1
1
L
. . . (9-83)
Location ofreference electrode
dr
r
L
R
363
Derivation of Eqns (9-87) and (9-88)
From Eqn (9-86a), I = 2elR . . . (9-86a)
and from Eqn (9-66), I 2zF
vM
R
2 dR
dt . . . (9-66)
Equating the two expressions for I:
2 e lR2zF
vM
R2 dR
dt
dR
dt
2 e lRvM
2zFR2
e lvM
zFR . . . (a)
RdR e lvM
zFt
Integrating, with R = 0 at t = 0, R2
2 elvM
zF t . . . (b)
R 2 e lvM
zF
1 / 2
t1/ 2
. . . (9-87)
Substituting (9-87) and (a) into (9-66):
I = 2zF
vM
2e lvMt
zF
e lvM
zF (2e lvMt) (zF) 1/ 2
= 2zF
vM
2e lvM
zF
t
(zF)1/ 2 e lvM
zF(2e lvM)1 / 2
t1 / 2
= 23/ 2 e l
3/ 2 vM
zF
1/ 2
t1/ 2
. . . (9-88)
364
Derivation of Eqn (9-91)
Eqn (9-66): I 2zF
vM
R
2 dR
dt . . . (9-66)
from which dR
dt
vMI
2zFR2 . . . (a)
Eqn (9-90):
I 2R2io exp
zF
R T
I
2R
exp
(1)zF
R T
I
2R
. . . (9-90)
Substituting (9-90) into (a):
dR
dt =
vM
2zFR2 2R
2io exp
zF
R T
I
2R
exp
(1)zF
R T
I
2R
= vMio
zFexp
zF
R T
I
2R
exp
(1)zF
R T
I
2R
. . . (b)
Using the expression for I given by Eqn (9-66),
I
2R
2zFR2 vM dR dt
2R
zFR
vM
dR
dt . . . (c)
Therefore,
zF
R T
I
2R
zF
R T
zFR
vM
dR
dt
zF
R T zF
2R
R TvM
dR
dt . . . (d)
and, similarly,
(1 )zF
R T
I
2R
= (1 )zF
R T
zFR
vM
dR
dt
= (1 )zF
R T
(1 ) zF 2R
R TvM
dR
dt . . . (e)
Therefore expzF
R T
I
2R
= exp
zF
R T zF
2R
R TvM
dR
dt
= expzF
R T
exp
zF 2R
R TvM
dR
dt
. . . (f)
365
Similarly,
exp(1 )zF
R T
I
2R
= exp
(1 )zF
R T
(1 ) zF 2R
R TvM
dR
dt
= exp(1)zF
R T
exp
(1) zF 2R
R TvM
dR
dt
. . . (g)
Substituting (f) and (g) into (b) gives
dR
dt
vMio
zFexp
zF
R T
exp
zF 2R
R TvM
dR
dt
vMio
zFexp
(1 )zF
R T
exp
(1) zF 2R
R TvM
dR
dt
By using the definitions
TR
Fz
Fz
iv oM exp1P ,
MvTR
Fz
2
2P
TR
Fz
Fz
iv oM )1(exp3P ,
MvTR
Fz
2)1(
4P
we can make Eqn (g) more compact, giving
dR
dt P1 exp P2R
dR
dt
P3 exp P4R
dR
dt
. . . (9-91)
366
Derivation of Eqn (9-93): io,S io cS co 1
[Appears on page 267 following Eqn (1) in J. Electrochim. Acta, 312 (1991) 267-275]
For the metal deposition reaction Mzze
M
the forward (cathodic) reaction partial current density is
if zFk f[Mz
]expzFa ct
R T
zFkf co exp
zFa ct
R T
. . . (a)
and the backward (anodic) reaction partial current density is
ib zFkb[M]exp(1 )zFact
R T
zFkb (1)exp
(1 )zFact
R T
. . . (b)
where kf and kb are the electrochemical rate constants and co is the bulk concentration of
the metal ion. Note that since the activity of the metallic phase is unity, there is no
concentration term for the backward (anodic) contribution to the current density. Again,
cathodic overvoltages and currents are taken as positive.
At electrochemical equilibrium, = 0 and if = ib so that
zFkfco zFkb io . . . (c)
putting (c) into Eqns (a) and (b) gives the net current density as
i = if – ib
i = zFk fco expzFact
R T
– zFk b exp(1 )zFa ct
R T
= io expzFact
R T
exp
(1 )zFact
R T
. . . (d)
Eqn (d) is the standard Butler-Volmer equation, which assumes that the concentration cS
of the metal ion at the electrode surface is the same as the concentration co in the bulk
solution. If cS is less than co, Eqn (a) for the forward reaction must be modified to
i f zFk f
cS
co
exp
zFa ct
R T
. . . (e)
and the net current density then becomes
i = zFk f
cS
co
exp
zF a ct
R T
– zFkb exp(1 )zF act
R T
. . . (f)
367
Owing to the presence of the concentration gradient between the bulk solution and the
metal surface, part of the total applied cathode overpotential ∆E will consist of a
concentration overpotential C as well as an activation overpotential act. It is the
activation overpotential act that must be used in Eqn (f). Exchange current densities
usually are expressed in terms of bulk concentrations; therefore it is useful to find an
expression that can relate the surface exchange current density io,S to the bulk solution
exchange current density io.
We let this relationship be io,S io f . . . (g)
such that i = io,S expzF act
R T
exp
(1)zF act
R T
. . . (h)
The parameter f is determined as follows:
The total applied overpotential is = ∆E = act C . . . (i)
from which act = EC
= E RT
zFln
co
cS
= E RT
zFln
cS
co
. . . (j)
Substituting (g) and (j) into (h):
i = io f expzF
R TE
RT
zFln
cS
co
exp
(1)zF
R TE
RT
zFln
cS
co
= io f expzFE
R T
exp
zF
R T
RT
zFln
cS
co
– exp(1 )zFE
R T
exp
(1 )zF
R T
RT
zFln
cS
co
= io f expzFE
R T
exp ln
cS
co
– exp(1 )zFE
R T
exp (1 )ln
cS
co
368
= io f expzFE
R T
exp ln
cS
co
exp(1 )zFE
R T
exp ln
cS
co
(1)
= io f expzFE
R T
cS
co
exp(1 )zFE
R T
cS
co
(1 )
. . . (k)
For reasons discussed above, for a metal deposition reaction, as indicated in Eqn (h),
there should be no pre-exponential term associated with the anodic partial current density
in Eqn (k). The unwanted term cS co ()
following the second exponential term in
Eqn (k) is removed by setting
f cS
co
1
. . . (l)
and, consequently, from Eqn (g), io,S iocS
co
1
. . . (m)
Substituting (l) into (k):
i = io
cS
co
1
expzFE
R T
cS
co
exp(1 )zFE
R T
cS
co
(1 )
= io
cS
co
expzFE
R T
exp(1 )zFE
R T
. . . (n)
Eqn (n) must hold for all values of cS , including the limiting case when cS co ; i.e.,
when there is no concentration overpotential and C 0. Under this limiting condition,
from Eqn (i),
∆E = act . . . (o)
and Eqn (n) becomes
i = io expzFact
R T
exp(1 )zFact
R T
. . . (p)
Eqn [n] is the form of the Butler-Volmer equation that is used for the electrodeposition of
369
a metal when the concentration of the metal ion at the electrode surface is less than the
concentration of the metal ion in the bulk solution. In the limiting case when cS co ,
Eqn (n) reduces to Eqn (p), which is just the standard Butler-Volmer equation given as
Eqn (d).
370
Derivation of Eqn ( 1 ) in Milchev Transport Paper Part I
[Milchev, A., Electrochim. Acta, 312 (1991) 267-275]
[Numerically-numbered equations are the numbers used by Milchev in his paper.]
Putting SR 2R2 into Eqn (1): gives
I 2R2io,S exp
zFact
R T
exp
(1 )zFact
R T
. . . (a)
Eqn (8): act E R T
zF1 a ln
co
cS
E
R T
zF1 a ln
cS
co
. . . (8)
Putting (8) into (a):
I =
2R2io,S exp
zF
R TE
R T(1 a)
zFln
cS
co
exp
(1)zF
R TE
R T(1 a)
zFln
cS
co
= 2R2io,S exp
zFE
R T
exp
zF
R T
R T(1 a)
zFln
cS
co
– exp(1)zFE
R T
exp
(1)zF
R T
R T(1 a)
zFln
cS
co
= 2R2io,S exp
zFE
R T
exp (1 a)ln
cS
co
–
exp(1 )zFE
R T
exp (1 )(1 a)ln
cS
co
= 2R2io,S exp
zFE
R T
exp ln
cS
co
(1a)
– exp(1 )zFE
R T
exp ln
cS
co
(1)(1a)
= 2R2io,S exp
zFE
R T
cS
co
(1a)
exp(1 )zFE
R T
cS
co
(1) (1a)
371
= 2R2
io,S
cS
co
(1a)
expzFE
R T
io,S
cS
co
(1) (1a)
exp(1 )zFE
R T
. . . (b)
The relationship between io, S, the exchange current density related to the concentration cS
of the metal ions at the cluster surface and io, the exchange current density related to the
bulk concentration of the metal ions can be shown to be [see separate derivation]
io,S iocS
co
1
. . . (c)
Therefore
io,S cS
co
(1a)
iocS
co
1
cS
co
(1a)
io
cS
co
1a
io
cS
co
1a
. . . (d)
Similarly,
io,S cS
co
(1) (1a)
= io
cS
co
1
cS
co
(1 )(1a)
io
cS
co
(1)(1aa)
= io
cS
co
11aa
io
cS
co
aa
iocS
co
(1)a
= o
cS
co
(1)a
. . . (e)
Substituting (d) and (e) into (b):
I = 2R2
io
cS
co
1a
expzFE
R T
io
cS
co
(1)a
exp(1 )zFE
R T
Therefore,
I = 2R2io
cS
co
1a
expzFE
R T
cS
co
(1)a
exp(1 )zFE
R T
. . . ( 1 )
372
Derivation of Eqn (9-139)
Given dR
dt A1F1 A2F2
. . . (9-131)
where F1 1 A3RdR
dt
A4
. . . (9-132)
F2 1 A3RdR
dt
A5
. . . (9-133)
and, defining f zFE R T ,
A1 vMio
zF exp
zFE
R T
vMio
zF exp f . . . (9-134)
A2 A1 expzFE
R T
vMio
zF exp f exp f
vMio
zFexp (1 ) f
. . . (9-135)
A3 zF
2
vMt 1 a R T . . . (9-136)
A4 1a . . . (9-137)
A5 1 a . . . (9-138)
Using the binomial expansions for x2 < 1 that 1 x n
1 nx and 1 x n 1 nx
Eqn (9-132) becomes F1 1A3RdR
dt
A4
1 A4A3RdR
dt . . . (a)
373
and (9-133) becomes F2 1A3RdR
dt
A5
1A5A3RdR
dt . . . (b)
Putting (a) and (b) into (9-131):
dR
dt= A1 1 A 4A3R
dR
dt
A2 1A5A3R
dR
dt
= A1 A2 A3 A1A4 A2A5 RdR
dt
Rearranging: dR
dt1 A3 A1A4 A2A5 R A1 A2
from which dR A3 A1A4 A2A5 RdR A1 A2 dt . . . (c)
Integrating (c) with the boundary condition that R = 0 at t = 0,
R A3 A1A4 A2A5
2R
2 A1 A2 t . . . (d)
Eqn (d) rearranges into the quadratic equation
A3 A1A4 A2A5
2R
2R A2 A1 t 0
i.e., R2
2
A3 A1A4 A2A5
R
2 A2 A1 tA3 A1A4 A2A5
0 . . . (e)
Solving the quadratic:
374
R =
2
A3 A1A 4 A 2A 5
2
A3 A1A 4 A2A5
2
4 1 2 A 2 A1 t
A3 A1A4 A2A5
2
= 1
A3 A1A4 A 2A5
2
2 A1 A2 t
A3 A1A4 A2A5
–
1
A3 A1A 4 A 2A 5
= 1
A3 A1A4 A2A5 2
2 A1 A2 A3 A1A4 A2A5 t
A3 A1A4 A2A5 2
1
A3 A1A4 A2A5
= 1
A3 A1A4 A2A5 1 2 A1 A2 A3 A1A4 A2A5 t
1
A3 A1A4 A2A5
= 1
A3 A1A4 A2A5 1 2 A1 A2 A3 A1A4 A2A5 t 1 . . . (f)
Substituting Eqns (9-1344), (9-135), (9-136), (9-137) and (9-138) into (f) gives
R = 1
zF 2
vMt 1 a R T
vMio
zF exp f 1 a
vMio
zF exp (1 ) f (1 )a
1 2vMio
zF exp f
vMio
zF exp (1) f
zF 2
vMt 1 a R T
vMio
zF exp f 1a
vMio
zFexp (1) f
vMio
zF exp (1) f t
1
= R Tt 1 a
zF io 1a exp f 1 a exp (1) f
375
1 2vMio
zF
exp f exp (1) f
zF 2
vMt 1 a R T
vMio
zF
exp f 1a exp (1) f exp (1) f t
1/ 2
1
= R Tt 1 a
zF io 1a exp f 1 a exp (1) f
1 2vMio
zF
2
zF 21
vMt 1 a R T
exp f exp (1) f exp f 1a exp (1) f exp (1) f t
1/2
1
= R Tt 1 a
zF io 1a exp f 1 a exp (1) f
12vMio
2
t 1 a R T
exp f exp (1 ) f exp f 1 a exp (1 ) f exp (1 ) f t
1 / 2
1
= R Tt 1 a
zF io 1a exp f 1 a exp (1) f
12vMio
2exp f exp (1 ) f exp f 1 a exp (1 ) f exp (1 ) f t
t 1 a R T
1 / 2
1
. . . (g)
Defining A expf exp(1) f . . . (h)
376
and B 1a expf 1 aexp(1) f . . . (i)
and substituting these into (g) gives
R R Tt 1 a
zFio B1
2vMio
2 AB t
R Tt 1 a
1/ 2
1
. . . Eqn (9-139)
377
Derivation of Eqn (9-150) in Effect of Supporting Electrolyte
Eqn (9-66): I 2zF
vM
R2 dR
dt . . . (1)
Eqn (9-147): R R Tt
iozFP1
2vMio2(1 a)Qt
R Tt+
1/2
1
. . . (2)
Re-write (1) as I C1R2 dR
dt . . . (3)
where C1 2zF
vM
. . . (4)
Re-write (2) as R C2 1 2C3t 1 /21 . . . (5)
where C2 R Tt
iozFP . . . (6)
C3 vMio
2(1 a)Q
R Tt+ . . . (7)
Differentiating (5): dR
dt C2
12 1 2C3t 1/2
2C3 C2C3
1 2C3t 1/ 2 . . . (8)
Substituting (5) and (8) into (3):
I = C1 C2 1 2C3t 1/ 21
1 / 2
2C2C3
1 2C3t 1/ 2
= C1C23C3
1 2C3t 2 1 2C3t 1/ 2
1
1 2C3t 1/ 2
= C1C23C3
2 2C3t 2 1 2C3t 1/ 2
1 2C3t 1/ 2
= C1C23C3
2 1C3t 2 1 2C3t 1/ 2
1 2C3t 1/ 2
= 2C1C23C3
1C3t 1 2C3t 1/ 2
1 2C3t 1/ 2
378
= 2C1C23C3
1C3t 1 2C3t
1/2 1 2C3t
1/2
1 2C3t 1/2
= 2C1C23C3
1C3t 1 2C3t
1/2 1
. . . (9)
Finally, putting (4), (6), and (7) into (9):
I = 22zF
vM
R Tt
iozFP
3v
Mio2(1 a)Q
R Tt+
1v
Mio2 (1 a)Q t
R Tt+
12v
Mio2(1 a)Q t
R Tt+
1 /2 1
= 4 R Tt
2(1 a)Q
io zF 2P3
1 vMio2(1 a)Q t R Tt
1 2vMio2(1 a)Q t R Tt
1 / 2 1
. . . Eqn (9-150)
379
Derivation of Eqn (9-163)
We start with Eqn (9-162): 1 A 3 A 1 A 4 A 2 A 3 R dR
dt A 1 A 2 0 . . . (9-162)
where A 1 vMio 1
zFexp f . . . (a)
in which f =zFE
R T
A 2 vMio
zFexp f exp (1 ) f . . . (b)
A 3 = vMDco 1 1 1
. . . (c)
A 4 = 1a . . . (d)
A 5 a 1 . . . (e)
which, upon integration yields the quadratic equation
i.e., R2
2
A 3 A 1 A 4 A 2 A 5
R
2 A 2 A 1 tA 3 A 1 A 4 A 2 A 5
0
the solution of which is
R = 1
A 3 A 1 A 4 A 2 A 5 1 2 A 1 A 2 A 3 A 1 A 4 A 2 A 5 t 1 . . . (f)
[For clarity, below we shall drop the ―primes‖ from the A terms.]
We evaluate the two main terms in (f) in two parts, starting with the term
1
A3 A1A 4 A 2A 5 . . . (g)
Substituting (a), (b), (c), (d), and (e) into (g):
1
A3 A1A 4 A 2A 5
=
1
vMDco 1 a 1 1 vMio 1
zF exp f 1 a
vMio
zFexp f exp (1 ) f a 1
380
= vMDco 1 a 1
vMio
zF1 exp f 1 a exp f exp (1 ) f a 1
= DcozF 1 a 1
io 1a 1 exp f a 1 exp f a 1 exp (1) f
= DcozF 1 a 1
1a 1 a 1 io exp f a 1 io exp (1) f . . . (h)
Expand the term in front of the first exponential:
1a 1 a 1 = 1aa aa
= 1a 1a . . . (i)
Substituting (i) into (h):
= DcozF 1 a 1
1 a 1a io exp f a 1 io exp (1) f
= DcozF 1 a 1
1 a 1a io exp f a 1 io exp f exp f
= DcozF 1 a 1
io exp f 1 a 1a a 1 exp f
= DcozF 1
io exp f 1 a 1 a a 1 exp f
1 a
= DcozF 1
io exp f 1a
1 a
a 1
1 a exp f
. . . (j)
Defining B 1a
1 a
a 1
1 a exp f . . . (k)
Eqn (j) becomes 1
A3 A1A4 A2A5
DcozF
io exp f 1
B . . . (l)
Next evaluate the square root term in (f) by substituting (a), (b), and (m) into this term:
381
12 A1 A2 A3 A1A4 A2A5 t
= 1 2 A1 A2 DcozF
io exp f 1
B
1
t
= 1 2 A1 A2 io exp f DcozF
B
1
t
= 1 2vMio 1
zF exp f
vMio
zFexp f exp (1 ) f
io exp f
DcozF B
1
t
= 12vMio
2
Dco zF 2 1 exp f exp f exp (1) f exp f
B
1
t
= 12vMio
2
Dco zF 2 1 exp 2f exp (1) f exp f
B
1
t
= 12vMio
2
Dco zF 2 exp 2f exp (1 2) f
B
1
t . . . (m)
If we define A exp 2f exp (12) f
then (m) becomes
12 A1 A2 A3 A1A4 A2A5 t = 12vMio
2A
Dco zF 2
B
1
t . . . (n)
Finally, substituting (l) and (n) into (f) gives
R = 1
A3 A1A4 A2A5 1 2 A1 A2 A3 A1A4 A2A5 t 1
= DcozF
io exp f 1
B1
2io2vM A
Dco zF 2
B
1t
1/2
1
. . . Eqn (163)
382
APPENDIX E
Vickers Microhardness Test
The description for the Vickers microhardness test presented below is taken from ASTM
E384-05a: Standard Test Method for Microindentation Hardness of Materials.7
The Vickers hardness test involves indenting the test material with a square-based
pyramidal-shaped diamond indenter with face angles of 136° subject to a force (i.e.; load)
of 1 to 1000 gf ( 9.8 х 10-3
to 9.8 N), as shown in Figure E1. The full load is usually
applied for a period of 10 to 15 seconds and the indentation diagonals are measured with
a light microscope after load removal. It is important to assume that the indentation does
not undergo elastic recovery after force removal. For optimum accuracy of measurement,
the test samples must be free of oil, grease and foriegn objects and the test must be
performed on a flat specimen. Accordingly, all the speciemen were rinsed with acetone
and deionized water and further cleaned in an ultrasonic bath filled with deionized water
for atleast 20 minutes prior to testing. The following procedure was employed to test all
the speciemen:
Examine the indenter and replace if it is worn, dulled, chipped or cracked. Clean
the indeter, if necessary,
Turn on the illumination system and power and select the appropriate indenter,
Place the test sample inside the stage clamps and make sure that the specimen
surface is perpendicular to the indenter axis,
Turn on the microscope and select a low power objective so that the specimen
surface can clearly be observed,
Adjust the light intensity and apertures for optimum resolution and contrast,
Select the appropriate area for the microhardness determination, and change the
microscope setting to the highest magnification available,
7 Manual Book of ASTM Standards (2006), Section Three: Metals Test Methods and Analytical
Procedures, Vol. 03.01, Metals-Mechanical Testing; Elevated and Low-Temperature Tests: Metallography,
pp. 444-476.
383
Figure E1 Vickers indenter
Select the desired force (micro force ranges: 10 g – 1.0 kg) and activate the tester
so that the indenter is automatically lowered, making contact with the specimen
for the selected time period,
Remove the load and change to measuring mode, selecting the appropriate
objective lens, light intensity, and apertures to attain optimum resolution and
contrast,
136 ° between
opposite faces
Force
d1
d2
384
Inspect the indentation to ensure its occurrence at the desired spot, if one half of
either diagonal is more than 5% longer than the other half of that diagonal, or if
the four corners of the indentation are not in sharp focus, the test must be
repeated. Consult manufacturer’s manual for proper alignment procedure,
Determine the lengths of both diagonals of the Vickers indentation to within 0.1
µm and then average the two diagonal length measurements,
Compute the Vickers hardness number using the following equations, noting that
test loads are in grams-force and indentation diagonals are in micrometers,
HV = 1.000 х 103 х P/As = 2.000 х 10
3 х P sin(α/2)/d
2
OR
HV = 1854.4 х P/d2
where: P = force, gf,
As = surface area of the indentation, µm2,
d = mean diagonal length of the indentation, µm, and,
α = face angle of the indenter, 136° 0'
The Vickers hardness reported with units of kgf mm-2
is determined as follows:
HV = 1.8544 х P1/d12
where: P1 = force, kgf,
d1 = length of long diagonal, mm.