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Manuscript # B10-0882R

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Submission Date 2011-07-21 12:13:09 Days to Render Final Decision: 31

Current Stage Manuscript Ready for Publication

TitleStochastic Reconstruction at Two Scales and Experimental Validation to Determine

the Effective Electrical Resistivity of a PEMFC Catalyst Layer

Manuscript Type Regular Paper

Abstract # 882

Issue Polymer Electrolyte Fuel Cells 11

Corresponding Author Romeli Barbosa (Universidad Nacional Autonma de Mxico)

Co-AuthorsBeatriz Escobar , Ulises Cano , Rolando Pedicini , Rubn Ornelas , Enza

Passalacqua

Short Abstract

In this paper we report on the application of statistical information obtained from 2D

micrographs of catalyst layers (CL) of proton exchange membrane fuel cell

(PEMFC), to derive stochastic replicas of their 3D pore networks at two scales. Themain focus is on assessing the scaling strategy to determine effective transport

coefficients and the analysis of the experimental results. The continuity equation for

charge transport is solved directly on the 3D reconstructed CL to determine effective

electrical conductivities at "internal-scale" and to simulate the electrical global

performance at "macro-scale". The electrical performance is experimentally

determined. The applied image processing method makes use of two immediate

scales to improve the image resolution. Pore size distribution of the reconstructed

scales is used to avoid the superposition of equal pore sizes. The relative porosities

were determined by the statistical analysis of SEM micrographs and verified by

mercury intrusion porosimetry.

Issue Editor Hubert Gasteiger

Transfer of CopyrightWe agree to the ECS Transfer of Copyright Agreement and hereby transfer the

copyright for this manuscript to The Electrochemical Society.

Decision Publish as is / 2011-08-01

Stage Start Date

Manuscript Ready for Publication 2011-08-01 10:10:42

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R. Barbosa, et al. The Electrochemical Society Proceedings Series (2011) 41: 2061-2072

1

Stochastic reconstruction at two scales and experimental validation to determine the

effective electrical resistivity of a PEMFC catalyst layer

R. Barbosaa, B. Escobarb, U. Canoc, R. Pedicinid, R. Ornelase and E. Passalacquad

aCentro de Investigacin en Energa (CIE-UNAM), Temixco, Morelos 62580, Mxico.

b Instituto Tecnolgico de Cancn, Cancn, Q. Roo 77515, Mxico.c Instituto de Investigaciones Elctricas, Cuernavaca, Morelos 62490, Mxico.

dInstitute for advanced energy technologies "Nicola Giordano" (CNR-ITAE), Messina

98126, Italy.e Tozzi Renewable Energy SpA, Mezzano, RA 48010, Italy.

In this paper we report on the application of statistical information(two-point and linear-path correlation function), obtained from 2D

micrographs of catalyst layers (CL) of proton exchange membrane

fuel cell (PEMFC), to derive stochastic replicas of their 3D porenetworks at two scales. The main focus is on assessing the scaling

strategy to determine effective transport coefficients and theanalysis of the experimental results. The continuity equation forcharge transport is solved directly on the 3D reconstructed CL, to

determine effective electrical conductivities at internal-scale andto simulate the electrical global performance at macro-scale. The

electrical performance is experimentally determined. The appliedimage processing method makes use of two immediate scales to

improve the image resolution. Pore size distribution of the

reconstructed scales is used to avoid the superposition of equalpore sizes. The relative porosities were determined by the

statistical analysis of SEM micrographs and verified by the total

experimental porosity obtained by mercury intrusion porosimetry.

Introduction

It is well recognized that the catalyst layer (CL) has a great influence on the performanceof a proton exchange membrane fuel cell (PEMFC). This is because this component is

central to the operation of a fuel cell, as it not only provides reactive sites for electricity

generation, but also its structure defines the efficiency of many of the processes involvedduring the operation of a PEMFC, in particular transport phenomena. On the other hand,

the CLs structure strongly depends on several factors particularly ink composition and

the deposition technique used for MEA manufacturing. Once a certain structure isattained properties such as electrical and ionic conduction, gas and liquid transport and

catalytic properties are defined for a given operating condition. This in turn, defines the

overall efficiency of the PEMFC (1-3).

The structure and composition of a PEMFC CL define this component as a random

heterogeneous material. This heterogeneity arises from the fact that it is constituted by

different phases, a phase being an identifiable domain with its own particular propertiesthat differentiate it from the rest of the other phases in the CL (i.e. voids, gases, liquids or


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representative structures). Proportionality coefficients for mass, energy and charge

transport in a heterogeneous material are significantly affected by the properties of the

phases from which this is composed, by the volume fraction composition, and by thestructure of such phases. For this reason, an effective transport coefficient (ETC) is

defined for a heterogeneous material as a proportionality coefficient, which characterizes

the domain of the material. For a randomly formed heterogeneous material with Mphases, a general ETC, Ke is:

Ke = f (K1, K2,,KM; 1, 2,,M; ) [1]

where subscript of variables indicates a respective phase, K is the proportionality

constant for that phase, is the phase volume fraction and is a microstructuralinformation of the domain (4). In literature there are different mathematical relationships

to determine ETCs (5-7). However, a more powerful technique to determine effective

properties of random heterogeneous materials, is the so called stochastic reconstruction

(8-10). Unfortunately, the large number of control volumes required to detail the mainelements that form the CL, in a computing domain that covers the whole electrode, makes

it an expensive computation-wise method. Barbosa et al. (11) recently proposed a scaling

method to determine effective transport coefficients in a CL PEMFC.

In this work, the scaling method was applied for two scales. Scales are defined based

on different observable structures at different resolutions of scanning electron microscopy

(SEM) and their statistical information. The annealing stochastic reconstruction, thedirect simulation of the charge continuity equation and experimental resistivity of three

manufactured CLs with different microstructures is presented.

Theory and calculation

Most of the PEMFC CL can be defined as a randomly-distributed heterogeneousmaterial. In these stochastic CLs, internal substructures can be defined at different

scale levels. One way to explain these apparent structural changes at different scale levels

is by picturing you infinitely faraway and getting closer and closer into the CL structure.In a hypothetical example, when the vision scale is ~50000 nm, one will observe a

homogenous dispersion of mesoporous structure; for a scale of ~5000 nm and focusing

areas where mesoporous are absent, the structure is defined by agglomerates andmicropores; finally at a vision scale of ~500 nm and focusing at an agglomerate the

observer will distinguish a structure formed by a random distribution of Pt/C particles,

ionomer and probably nanometric pores. Although the scales are defined by an empirical

observation, the relative porosities of each scale are related mathematically to the total

porosity by equation 2,

T=1-(1-i ) [2]

where Trepresents the total porosity of the complete CL and i the relative porosity of

each i scale. On the other hand, the total porosity (T), the thickness () and the CL

composition (design parameters) are related by the following equation:


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= [1/Pt + 1/PtC + N(1+Pt)/Pt/(1-N)/N] Pt / (1-T) [3]

where Pt, C, N are platinum, carbon and nafion densities respectively; pt is the

platinum load, N the ionomer load and pt the platinum to carbon weight ratio. The

design parameters (pt, Nand pt), are controlled before CL manufacturing but can be

assumed the same in the CL microstructures fabricated by physical techniques, in whichchemical reactions do not occur. Other important structural information that can be

assumed as the same before and after the CL manufacturing is the individual platinum

and carbon particle sizes and the fact that platinum is supported on carbon.

Structural reconstruction algorithm

The simulated annealing method (4) was applied for the microstructural

reconstruction. This method generates a system that has the same statistical correlationfunctions as a specified reference system. It involves finding a state of minimum

energy by interchanging the phases of the pixels in the digitized system. The energy

(E) is defined in terms of the squared difference of the reference (f(r)) and simulated

(f(r)) correlation functions.

E = f [f(r)-f(r)]2

[4]

Where f is an arbitrary weight that assigns the relative importance of eachindividual correlation function. The first moment of the algorithm generates a stochastic

microstructure with the same volume fraction of the reference system as the initialstructure. After this initialization, the states of two random pixels of different phases are

interchanged. The energy change (E=E'-E) between the two successive states is

computed. This phase interchange is accepted with probability P(E).

P(E)=1, if (E 0); P(E)=exp(-E/T), if (E>0) [5]

where T is a fictitious temperature. Thismethod causes fs(r) to converge gradually tofs(r). The algorithm ends when the energy E is less than a tolerance value. The concept of

finding the lowest error state (lowest energy) by simulated annealing is based on a well

known physical fact: If a system is heated to a high temperature T and then slowly cooled

down to absolute zero, the system equilibrates to its ground state.

Two correlation functions were used: (i) the two-point correlation function (S2F)

which is obtained by randomly tossing a line segment of r length with a specificorientation and counting the number of times that the beginning (x) and the end (x+r) of

the line fall in phase j. (ii) The lineal-path function (LPF) which is defined as the

probability of finding a line segment with end points at x and x+r entirely in phase j. TheS2F was applied at the two phases and the LPF only at the most relevant phase. In this

way, the total energy was defined by equation 6,

E = 0.33[S2s-S2s]2+0.33[S2v-S2v]

2+0.33[LPFs-LPFs ]

2[6]

where S2s and S2v is the simulated S2F of the solid phase and the empty phase

respectively; S2s and S2v is the reference S2F of the solid phase and the empty phase


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respectively; LPFs and LPFs is respectively the simulated and the reference LPF of thesolid phase; and 0.33 is the assigned function weight.

Theoretical effective electric resistivity

The effective resistivity (eff) of a heterogeneous material, composed by a conductivephase and one or more insulating phases, of an element formed by subdomains of smaller

scales is:

eff= m Leff_i/Aeff_i Am_i/Lm_i [7]

where eff is the effective resistivity of the global domain formed by various smaller

scale subdomains i, mis the materials resistivity, Leff_i is the effective length and Aeff_i is

the effective area of the phase under study in every subdomain and Lm_i is the length andAm_i is the area of the scale of every subdomain.

To normalize and generalize results, in this work calculated resistivities are used to

estimate conduction efficiency (k). As conductivity is the inverse of resistivity, the

CLs effective conductivity is the inverse of the effective resistivity value keff=eff-1. k iscalculated by comparing the effective conductivity with a reference or nominalconductivity, as described by equation 8. By substituting equation 7 in equation 8, we can

obtain a relation that provides the conduction efficiency of the global domain which is

formed by several subdomains (equation 9),

k= keff/ km [8]

k=Aeff_i/Leff_i Lm_i/Am_i [9]

Experimental procedure

Three electrodes, with different pore promoter load, were manufactured in this study.

Its microstructure at two different scales and the electric resistivity were characterized. In

this section we describe the experimental methodology used.

Electrode manufacture

The decal process was used to prepare all CLs used in this study. The ink mixture,made of the catalyst carbon (50 wt % Pt/C), 5% Nafion solution, and water solution of

ammonium carbonate, was mixed using ultrasound for 30min. Then it was spray-

deposited on an inert decal substrate (PTFE). The decal was heated in an oven at 70C for~5 min. The process of spray and heating was repeated until the desired catalyst loading

was reached, which in this study was equivalent to ~0.5 mg Pt/cm2 (nominal). When the

desired loading is reached a drying step at 70C and 125C for 30 min each was carried

out. Three loads of pore former (ammonium carbonate) were studied: 40, 20 and 0 %wt.

To characterize the CL without the proton exchange membrane (PEM), the single CL

(without membrane) was hot-pressed at 100 kg/cm2

and 125C for 5 minutes betweentwo graphite plates. This technique emulates the microstructural condition of a


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membrane-electrode assembly (MEA) but without separating the CL of the decal

substrate (PTFE). A 40 x 100 mm sample of electrode was used for the mercury intrusion

porosimetry measurements, a 10 x 10 mm sample was cut for scanning electronmicroscopy (SEM) examination and a 25 x 25 mm sample was also cut for electronic

resistivity characterization.

Experimental electronic resistivity

The electronic resistivity was measured exclusively for the CL by a four-point probe

method using the combined system of a current supplier and a voltmeter. Four in-line,equally spaced probes are placed in contact with the CL surface. A current (I) is passed

through the outside two points of the probe and measuring the voltage (E) across the

inside two points. Electrostatic analysis of the electric potential and field distributions in

this configuration yields:

= E/I [10]

where is a constant dependent on the configuration and spacing of the contacts and is

the thickness of the film. This method is a long established technique to measure theaverage resistivity () of a thin layer (12, 13). In this work, the device was specified tohave in-line fixed four probes made of platinum wire (diameter of 0.52 mm), equal probe

spacing was 2.2 mm and downward force was approximately of 12.25 kPa per probe.

Two currents were imposed (1 and 3 mA).

CL microstructural characterization

Relative porosities (i) were determined by the statistical analysis of SEMmicrographs and verified by the total experimental porosity obtained by mercury

intrusion porosimetry. CL thickness () was also determined by SEM.

CLs were studied by SEM at different resolutions. Nevertheless, for the simulation

study, two micrometric scales were empirically selected: (i) superficial scale at 500 X

resolution, where we can obtain samples of ~120 m and (ii) micropores scale at 5000X resolution, where we can obtain samples of ~12 m. It is important to point out that the

nanometric scale (inside an agglomerate scale) was not experimentally studied.

CL internal microstructure is characterized at 5000 X resolution. In this scale we can

define stochastic micropores but is not possible to define CL primary components (Pt, Cand ionomer). On the other hand, because the DECAL technique generates very thin

CLs (10-20 m), the 500 X resolution characterizes a macro-superficial and isotropic

structure.

Image processing method

Empty phase was selected by the pixel intensity in two stages: (i) the superficialfraction at double resolution of the studied scale was empirically determined by the

intensity, (ii) the intensity at the studied resolution was automatically selected by the

superficial fraction of the first stage. In this work, intensity at 1000X resolution fixes thesuperficial fraction of 500X resolution and 10000X resolution fixes the superficial


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fraction of 5000X resolution. This permits the study of a predetermined area with more

resolution. Figure 1 shows schematically this micrograph initial process (P1).

Figure 1. Initial process (P1) of the micrographs. The Internal box is twice resolutionthan dotted box. The Internal box fixes the superficial fraction of dotted box.

After intensity selection process o micrograph initial process (P1) the pore size

distribution at the two studied scales are adjusted for avoid the superposition of the samepore size by pore elimination. Figure 2 shows a representative example of the total image

process: from (a) to (b) the P1 process is applied; from (b) to (c) the pore size distribution

is analyzed and the proper size pores are deleted; from (c) to (d) the correlation functions(S2F and LPF) are obtained.

Figure 2. Total image process. a)b) pixel intensity selection; b)c) proper pore

deleted; c)(d) statistical characterization.


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Results and discussion

Three CLs with different pore former load (PFL) were manufactured and

characterized: (i) PCL40 with PFL 40.0 %wt, (ii) PCL20 with PFL 20.0 %wt and (iii)

PCL00 with PFL 0.0%wt. The electronic resistivity and SEM analysis of each CL were

characterized at three different locations on each CL specimen. In Table 1 theexperimental results are presented: Pt load (pt), total porosity (T), CL thickness (),electronic conductivity (keff) and electric conduction efficiency (k). k was estimated by

considering the electric conductivity of Vulcan carbon (~400 S/m) (14).

Table I. Experimental results.

Electrode

name

PFL

(%)

pt

(mg/cm2)

T

(%)

(m)

keff

(S/m)

k

PCL40 40.0 0.47 13.42 9.59 0.27 40 0.10PCL20 20.0 0.57 19.93 14.83 0.36 58 0.14

PCL00 00.0 0.47 14.59 9.64 0.52 140 0.35

In this work, the electrical performance of the nanometric structure was fixed to

adjust the experimental data with the simulated results. Table 2 briefs the dimension of

the computing domain (Nx, Ny and Nz) and the finite control volumes (dx, dy and dz)

used for the reconstruction and simulation procedure.

Table II. Dimensions of the domain and control volume for the studied samplesSample Nx; Ny; Nz (m) dx; dy; dz (m)

500 X 161; 161; 10 0.5; 0.5; 0.5

5000 X 10; 10; 10 0.1; 0.1; 0.1

Original and processed images of some studied CLs are showing in Figure 3. Figures

3(a) and 3(b) correspond to PCL40, 3(c) and 3(d) correspond to PCL20 and 3(e) and 3(f)

correspond to PCL00. The left side of figure is for 500 X resolution and the right is for5000 X resolution. 5000 X resolution characterizes a micropores scale. Statistical

information of these samples was used for a 3D isotropic reconstruction. However, the

microstructure at 500 X resolution has elements with a longer dimension than CLthickness. These samples were reconstructed in two stages: i) representative elements

with a dimension greater than 1/3 of the CL thickness were considered as anisotropic

gaps, therefore they were first reconstructed by 2D isotropic way and then extruded to the

CL thickness. ii) Representative elements with a dimension less than 1/3 of the CLthickness were reconstructed by a 3D isotropic way.


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Figure 3. Original and processed images of some studied CLs.

Figure 4 shows the two-point correlation (S2F) and lineal-path (LPF) functions for

the CLs studied. These mean values are plotted versus a non-dimensional distance r/N,

where r is the distance between two points and N the domain lattice. Each curve

corresponds to a different pore promoter load (PCL) and is calculated for the pseudo-solid phase. Figures 4(a) and 4(b) correspond to 500 X resolution with elementsdimension less than 1/3 of the CL thickness. Figures 4(c) and 4(d) correspond to 500 X

resolution with elements dimension greater than 1/3 of the CL thickness. Figures 4(e) and4(f) correspond to 5000 X resolution. The left side of figure is for S2F and the right is for

LPF.


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Figure 4. Two-point correlation (S2) and lineal-path (LP) function for the CLs.

These statistical correlation functions were used as the reference systems in the

annealing microstructural reconstruction. Each sample was reconstructed and simulated

five times with different random series. Figure 5 shows representative images ofreconstructed samples. Figures 5(a) and 5(d) correspond to PCL40, 5(b) and 5(e)

correspond to PCL20 and 5(c) and 5(f) correspond to PCL00. The white color represents

the pseudo-solid phase and black color the empty phase. In 5000X resolution (top side offigure), the reconstructed structures look alike in the three planes for each samples. In

500X resolution (bottom side of figure) there are two representative structures: i)

elements with dimension greater than 1/3 of the CL thickness (anisotropic gabs) and ii)

elements with dimension less than 1/3 of the CL thickness (isotropic structure).


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Figure 5. Images of some reconstructed samples. Figures 6(a) and 6(d) correspond to

PCL40, 6(b) and 6(e) correspond to PCL20 and 6(c) and 6(f) correspond to PCL00. The

white color represents the pseudo-solid phase and black color the empty phase.

The electric conduction efficiency (k) obtained by direct simulation of the charge

continuity equation in 500X (k,500) and 5000X (k,5000) resolution, can be generalized

by its product in a single micrometric efficiency parameter (micro= k,500k,5000). In this

way, the electric conduction efficiency of the nanometric structure can be estimated by

equation 11.

nano=keff/ km/ micro [11]

where keff is the effective electric conductivity of the material, in this work it isexperimentally obtained by the four-point probe; km is the electric conductivity of the

pseudo-solid phase, in this work is the Vulcan carbon conductivity (km400 S/m). Table3 resumes the electric conduction efficiencies in the studied scales (k,500 and k,5000), the

generalized micrometric efficiency (micro) and the estimated nanometric efficiency

(nano).

Table III. Electric conduction efficiency.Sample k,500 k,5000 micro nano

PCL40 0.90 0.93 0.84 0.12

PCL20 0.97 0.92 0.89 0.16

PCL00 0.88 0.87 0.77 0.45

In micrometric scale, PCL20 shows higher micro value than the other two

manufactured CLs. However experimental results (see table I) shows that PCL00 has thehighest global conduction efficiency (k). This suggests that the nanometric scale has a


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significant influence in the electric global performance. In this work, the conduction

efficiency increases while the pore promoter load diminishes. On the other hand, the

sample without pore promoter (PCL00) is particularly different than the other CLs.

Conclusions

In this article, theoretical and experimental techniques were applied for the study of

electric charge transport of PEMFC CLs. Experimental study includes: electrode

manufacture, effective electrical conduction and microstructural physic characterization.

Theoretical study includes: processing and statistical characterization of micrographs,stochastic reconstruction of CLs structure and charge continuity direct simulation. The

simulated annealing method and three correlation functions were applied for the

reconstruction. SEM micrographs were processed to obtain the reference statistical

functions at two micrometric scales. These micrometric-structures were generalized to

obtain conduction efficiency at local micrometric scale (micro). The nanometric scale

performance (nano) was estimated from the experimental total effective electric

conductivity, a reference electric conductivity of the pseudo-solid phase and micro. It is

interesting to observe that nano is more significant than micro. However, more work,

including the nanometric structural study and local experimental resistivity (atrepresentative scale) are required in order to draw a clear perspective directed toward thephenomenology. Finally, the techniques presented in this work can be applied to study

already existent CL microstructures as well as to propose new and more efficient CLs.

Acknowledgments

B. Escobar recognizes the support to REDFE CONACYT and CONACYT

FORDECYT under grant No. 116157.

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3. J. Ledesma-Garca, R. Barbosa, T.W. Chapman, L.G. Arriaga, L. A. Godnez, Int. J.Hydrogen Energy, 34, 2008 (2009).

4. S. Torquato, Random Heterogeneous Materials: Microstructure and MacroscopicProperties, p. 12, Springer-Verlag, New York (2002).

5. P.K. Das, X. Li, Z.-S. Liu,Appl. Energy, 87, 2785 (2010).6. Maxwell-Garnett, Philos. Trans. R. Soc. London Ser. A, 203, 385 (1904).7. D. Bruggeman,Ann. Phys., 24, 636 (1935).8. Quiblier, J.A.,J. Colloid Interf. Sci., 98, 84 (1984).9. S. H. Kim and H. Pitsch,J. Electrochem. Soc., 156, B673 (2009).10.G. Wang, P. P. Mukherjee and C.-Y. Wang, Electrochim. Acta, 51, 3151 (2006).11.R. Barbosa, J. Andaverde, B. Escobar and U. Cano,J. Power Sources, 196, 1248 (2011).12.A. E. Yarimbiyik, H. A. Schafft, R. A. Allen, M. D. Vaudin, M. E. Zaghloul,

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0 R. Barbosa ECS Boston 2011