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KINETICS OF CARBON NANOTUBE GROWTH WITH APPLICATIONS IN
HYDROGEN STORAGE
A DISSERTATION
SUBMITTED TO THE DEPARTMENT OF MATERIALS SCIENCE AND
ENGINEERING
AND THE COMMITTEE ON GRADUATE STUDIES
OF STANFORD UNIVERSITY
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
Ranadeep Bhowmick
June 2010
This dissertation is online at: http://purl.stanford.edu/zz418br0139
© 2010 by Ranadeep Bhowmick. All Rights Reserved.
Re-distributed by Stanford University under license with the author.
ii
I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.
Bruce Clemens, Primary Adviser
I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.
Brett Cruden, Co-Adviser
I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.
Mark Brongersma
Approved for the Stanford University Committee on Graduate Studies.
Patricia J. Gumport, Vice Provost Graduate Education
This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file inUniversity Archives.
iii
Abstract
Carbon nanotubes (CNTs) have unique transport and elastic properties due to their high aspect
ratios. Hence there is considerable interest in using these tubes as field emitter cathodes, composite
materials with enhanced electrical and mechanical properties, electronic components and recently
for hydrogen storage applications taking advantage of the high specific surface areas. In this thesis
three different aspects of carbon nanotubes were studied: (1) Controlled growth of single walled
nanotubes (SWNTs), (2) Electric field directed Chemical Vapor Deposition (CVD) of multi walled
(MWNTs) and (3) Spillover Mechanism of hydrogen storage in Pt-SWNT composites.
The kinetics of carbon nanotube growth was studied in the context of the CVD process. A
generic model for growth of 1-d nano structures via the Vapor-Liquid-Solid (VLS) mechanism is ap-
plied to the nanotube growth. This model considers the energetics of individual mass transfer steps
through each phase and at the phase interfaces. The flux is then written in terms of the change in
chemical potential. Laser interferometry was applied in a cold-wall thermal CVD reactor to measure
the growth of the MWNT films in-situ. Temperature dependent studies in the steady-state regime
were used to obtain activation energies which are consistent with the interfacial transport step.
Consideration of the catalyst activation/de-activation process in the non-steady regimes requires
the rate limiting step to be in the vapor-liquid transition. Application of an electric field during
the MWNT growth was found to enhance both the growth rate and alignment of the MWNTs.
Temperature dependent studies in the presence and absence of the electric field show that there are
actually two activated processes involved, with rate-limiting step being independent of applied field
at high temperature. At higher temperatures, the rate-limiting step is the carbon dissolution into
the catalyst particle, while at lower temperatures it is the carbon dissociation at the catalyst-vapor
interface that limits the growth. Application of an electric field enhances the decomposition of the
C precursor in the vapor phase, thus circumventing this low temperature activation barrier. The
enhanced alignment of the MWNTs with the electric field is explained by tensile stretching over-
coming the defect-induced kinking of the MWNTs. Calculations show that this benefit is obtained
at a minimum field level, with no benefit arising from further increase in field strength.
The catalyst particle size is one of the key parameters that determine the morphology of the 1D
iv
carbon nanostructures in both processes studied. The thermodynamics of the nano-particle forma-
tion and carbon dissolution are studied and applied to these processes. While the diameter serves
to template the CNT diameter, the Gibbs Thompson effect predicts a size dependent suppression of
melting point which determines the nature of CNT formed. In the CVD process, higher pressures
were found to form larger particle sizes which led to nanofiber growth. At these diameters, the melt-
ing point suppression puts the Fe-C particle in a dual solid-liquid phase. Carbon flux accumulates
in the dual phase during growth until the dual phase becomes energetically unfavorable. At this
point, the particle reverts to a single solid phase regime by discarding excess carbon, resulting in
a discontinuous graphitic structure characteristic of Carbon nanofibers. For smaller particles, the
phase is entirely liquid and leads to steady state carbon flux and CNT growth. Controlling the iron
bearing precursor concentration of the solution fed into the floating catalyst reactor was found to
control particle size, and hence SWNT diameter, within this regime. For similar catalyst particle
size distributions, increasing the temperature increased the range of SWNT diameters and chiralities
obtained. The thermodynamic energy barrier for SWNT formation at the different diameters was
calculated and shown to be consistent with the observed variation.
Finally, the mechanism of hydrogen uptake in transition metal-doped SWNT was studied. Molec-
ular hydrogen, dissociated by metal catalyst nanoparticles, diffuses to the nanotube surface forming
stronger bonds. In-situ 4-probe conductivity tests were performed on mats of Pt doped SWNT dur-
ing hydrogen uptake. On hydrogen charging the resistivity of the Pt doped SWNT mat increased.
This is due to the formation of C-H bonds, which breaks the symmetry of the CNT electronic struc-
ture resulting in formation of localized defects, thereby increasing the resistivity. Initial studies of
the temporal dependence of hydrogen uptake suggest a diffusion-limited process. XPS was employed
to measure the extent of sp3 C-H bonding.
v
Acknowledgments
The 3,160th and final ”Calvin and Hobbes” strip ran on Sunday, 31st December, 1995. It depicted
Calvin and Hobbes outside in freshly-fallen snow, reveling in the wonder and excitement of the
winter scene. ”It’s a magical world, Hobbes, ol’ buddy... Let’s go exploring!” wrote Bill Watterson.
I arrived at Stanford almost six years back bearing a similar sentiment. The journey since has
continued to be exciting; not only because of the knowledge I gained but more importantly because
of all the extraordinary people with whom i came to share the ride.
My thesis work depended a lot on valuable contributions from many people. I would first like
to thank my thesis advisors, Prof. Bruce Clemens and Dr. Brett Cruden. I am deeply indebted
for their guidance, knowledge and experience. They gave me enough freedom to take the project
in whichever direction I wanted, while guiding me back to the right path when I strayed from the
problem in hand. Prof. Clemens has a natural affinity for identifying the fundamentals of a problem
and coming up with simple mathematical models to describe it. Talking with him always gave me
new insights and he also encouraged me to think outside the box. Dr. Cruden’s door was always open
(at least to the time he moved to a separate building) and I could approach him with the smallest
of problems. His help and constant support, particularly during the initial years, was invaluable. I
am indebted to him for a lot of the experimental and theoretical work that went into this thesis.
Thanks Bruce and Brett.
I would also like to thank Professors Tom Jaramillo, Paul McIntyre and Marc Brongersma for
their time and for serving on my thesis committee. I know Profs have very busy schedules but I
would like to thank them for taking time off to help me in making my thesis so much more cohesive.
A special mention should be made to Stephanie Sorensen, Fi Verplanke and Christina Konjevich
for helping me on all the administrative issues, particularly in making me turn in the right forms at
the right time, an area I am prone to procrastination.
I received much help for the different characterization techniques used for this work. I would
like to thank Ann Marshall, Bob Jones and Chuck Hitzman for training and help with the TEM ,
SEM, and AES respectively. I would like to thank Prof. Anders Nilsson and his group at SLAC,
particularly Srivats, Daniel and Hiro for their help with the XPS studies. I would like to thank Dr.
Cattien Nguyen for letting me use his instruments and the ”dirty” clean room at NASA, Ames. I
vi
would like to thank Dr. Alan Cassell and Lance Delzeit for their advice at the beginning of my stint
at NASA Ames. A special thanks to John Roth for his Igor codes to interpret the Interferometry
scan data.
I spent little time at my home office, 210 McCullough. But, will always cherish the stimulating
discussions I had with the Clemen’s gang specially Cara, Steve, and Randy. I would like to thank
Yong, Gloria, and Aditi for their help during the qualifiers. Thanks to Vardaan, Melody, and Chia
for their help with all things lab related. Also mention has to be made of the study group Randy,
Angie, Tania, Joav, Owen,Yen Chen, Kemal, Jason, and Nathan who made it possible to stay afloat
through the 20 odd course requirements for MatSci.
Over and onto NASA; I would like to express my gratitude to all of Brett’s crew mostly from the
past: Sarah, DJ, Alex, Quoc, Dmitry, Terry, and Hiro. A special thanks to Jay, for all his help in
the lab and for being a good sounding board for all my ideas. Even if one tenth of our ideas worked
we would have been ”rich and famous” by now. Thanks to Cattien’s group: Setha, Jeremy, Bryan,
Jovi, Darrell for sharing instruments, and for lunches and coffee breaks in the afternoon. These guys
made life at NASA fun.
I had some memorable times during my stay at Stanford thanks to the ”Bong group” Abhirup,
Pijush, Avishekda, Somdattadi, Samantak, Avisek and many others. They made the transition from
India to USA easy and were my cultural and culinary link to India.
Thanks to my aunt and cousin for always being there. Thanks to my parents and my sister
for their ever-embracing support of my desired studies. Last, but certainly not the least, thanks
to Denise for bearing with me during a busy final year. I wish I knew you earlier. Thank you
everybody.
vii
Contents
Abstract iv
Acknowledgments vi
1 Introduction 1
1.1 The number ’4’ and the number ’6’ . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Hybridization and relevant C isomers . . . . . . . . . . . . . . . . . . . . . . 2
1.2 sp2 derived C configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.1 3D Graphite and 2D Graphene . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.2 0D Fullerene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.3 1D Carbon Nanotubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Electronic Structure of SWNTs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3.1 Electronic structure of graphene . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3.2 Energy Dispersion for SWNT . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3.3 Band gaps, Kataura Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.4 Synthesis of Carbon Nanotubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.4.1 Physical methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.4.2 Chemical methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.5 Overview of Hydrogen Storage Technologies . . . . . . . . . . . . . . . . . . . . . . . 16
1.5.1 Hydrogen storage in SWNTs involving a chemical bond . . . . . . . . . . . . 18
1.6 Dissertation Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2 Experimental Methods 21
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2 Reactor Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2.1 CVD reactor for MWNT growth . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2.2 Vertical flow reactor for SWNT growth . . . . . . . . . . . . . . . . . . . . . 23
2.3 Deposition Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.3.1 Sputter Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
viii
2.3.2 Quartz Crystal Microbalance (QCM) . . . . . . . . . . . . . . . . . . . . . . . 25
2.4 In-situ diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.4.1 Laser Interferometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.4.2 Residual Gas Analyzer (RGA) . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.4.3 4 Probe Resistivity studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.5 Ex-situ Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.5.1 Raman spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.5.2 UV-Vis-NIR absorption spectroscopy . . . . . . . . . . . . . . . . . . . . . . . 41
2.5.3 X-ray Photoelectron spectroscopy (XPS) . . . . . . . . . . . . . . . . . . . . . 43
2.5.4 Auger Electron Spectroscopy (AES) . . . . . . . . . . . . . . . . . . . . . . . 44
2.5.5 Electron Microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.5.6 Thermogravimetric Analyzer (TGA) . . . . . . . . . . . . . . . . . . . . . . . 46
3 Kinetics of MWNT Growth 47
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.2 Catalyst for growth of MWNT films . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.2.1 Importance of the Al buffer layer . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.3 MWNT growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.4 Kinetic Model for MWNT growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.4.1 Mass Transport processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.4.2 Steady State growth rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.4.3 Thermodynamic Driving force for MWNT growth . . . . . . . . . . . . . . . 57
3.4.4 Rate Limiting Steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.4.5 Catalyst Activation and Poisoning . . . . . . . . . . . . . . . . . . . . . . . . 60
3.5 Results and Validation of the Kinetic Model . . . . . . . . . . . . . . . . . . . . . . . 61
3.5.1 Temperature dependent MWNT growth at P=265 Torr . . . . . . . . . . . . 62
3.5.2 Pressure dependent growth runs at T = 750oC . . . . . . . . . . . . . . . . . 67
3.5.3 Temperature dependent MWNT growth at P=760 Torr . . . . . . . . . . . . 71
3.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4 Growth Transition from CNT to CNF 75
4.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.3 Experimental details and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.3.1 Growth of MWNT/CNFs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.3.2 Characterization of catalyst particle size . . . . . . . . . . . . . . . . . . . . . 80
4.3.3 TEM characterization of growths as a function of particle size . . . . . . . . . 87
4.4 Brief literature review on CNFs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
ix
4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4.5.1 Thermodynamic Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5 Electric field assisted MWNT growth 98
5.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
5.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.3 Experimental Technique: Catalyst preparation by Block Co-polymer Micelle Templates100
5.3.1 Characterization of the catalyst particles . . . . . . . . . . . . . . . . . . . . 101
5.3.2 Control of catalyst size and separation using micelle templates . . . . . . . . 103
5.4 Experimental technique: MWNT growth . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5.5.1 Characterization of the MWNT forests from sputter deposited Fe films . . . . 106
5.5.2 Characterization of the MWNT grown from catalysts obtained from micelle
templates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.6 Discussion: Tube Alignment and applied field . . . . . . . . . . . . . . . . . . . . . . 112
5.6.1 Alignment for isolated MWNT . . . . . . . . . . . . . . . . . . . . . . . . . . 113
5.6.2 Alignment of nanotubes in a dense MWNT array . . . . . . . . . . . . . . . . 116
5.7 Discussion: Growth kinetics and electric field . . . . . . . . . . . . . . . . . . . . . . 119
5.7.1 Further investigations of growth: time resolved reflectivity studies . . . . . . 120
5.7.2 RGA Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
5.7.3 Analysis of the kinetic data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
5.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
6 Diameter control of SWNTs 130
6.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
6.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
6.3 Experimental Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
6.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
6.4.1 Dependence on the reaction time . . . . . . . . . . . . . . . . . . . . . . . . . 133
6.4.2 Effects of Ferrocene concentration . . . . . . . . . . . . . . . . . . . . . . . . 139
6.5 Temperature Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
6.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
7 H2 Storage in Pt-SWNT composites 153
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
7.2 Prior studies on hydrogen storage in Pt-SWNT composites . . . . . . . . . . . . . . 154
7.3 Sample Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
x
7.4 Conductivity Tests on Pt-SWNT composite samples during hydrogen charging . . . 157
7.4.1 In-situ 4 probe conductivity tests . . . . . . . . . . . . . . . . . . . . . . . . . 159
7.5 XPS characterization of SWNT films . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
7.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
8 Conclusions and Future Work 169
8.1 MWNT growth model and in-situ tracking of tube height . . . . . . . . . . . . . . . 169
8.2 Catalyst size and nanotube morphology . . . . . . . . . . . . . . . . . . . . . . . . . 170
8.3 Electric-field assisted MWNT growth . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
8.4 Chirality, Diameter control of SWNT . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
8.5 Hydrogen Storage in Pt-doped SWNT . . . . . . . . . . . . . . . . . . . . . . . . . . 171
A Tip Amplitude of MWNT 173
B Algorithm for analyzing interferometer scans 177
B.1 Savitzky-Golay filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
B.2 Fourier Transform Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
C Quantifying alignment of Carbon Nanotubes 189
C.1 Orientation Analysis of nanotubes in MWNT forests . . . . . . . . . . . . . . . . . . 189
C.2 Orientation Analysis of isolated MWNTs . . . . . . . . . . . . . . . . . . . . . . . . 190
xi
List of Tables
1.1 Candidate materials for Hydrogen Storage . . . . . . . . . . . . . . . . . . . . 17
3.1 Activation energy values of rate limiting steps obtained from the literature 74
5.1 Cycle periods and steady state growth rates as a function of temperature
and bias magnitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
7.1 Hydrogen uptake with catalyst particle density. . . . . . . . . . . . . . . . . . 156
xii
List of Figures
1.1 The elements of Group 14 (IV A) of the periodic table. . . . . . . . . . . . . . . . . . 1
1.2 spn hybridization of the C atoms, and the corresponding orientation of the C-C bonds.
Also shown are the graphite and diamond crystalline structures. . . . . . . . . . . . 3
1.3 (a) Unit Cell of Graphite (b) Graphene unit cell (c) Brillouin zone of graphene is
represented by the shaded hexagon. The high symmetry points Γ, K,M are shown in
the schematic. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 Honeycomb lattice of a nanotube. Shown in the figure is the chiral vector, Ch,
that determines the orientation of the nanotube lattice. Also shown are the achiral
nanotubes, armchair and zig-zag. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.5 Brillouin Zone of (4,2) chirality SWNT is represented by the line segment WW’, which
is parallel to K‖ . K‖ and K⊥ are reciprocal lattice vectors corresponding to T and
Ch respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.6 Energy dispersion relation for graphene over the Brillouin zone. (b) is a contour
plot for the electronic band structure of graphene. Fig. (c) is a schematic of real and
reciprocal space for a chiral SWNT. Such diagrams help to illustrate the metallic/semi-
conducting nature of the SWNT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.7 1D Energy dispersion relation for (9,0) SWNT. Fig. (a) is part of the unit cell and
Brillouin zone of a zigzag SWNT. X points for the zigzag nanotubes correspond to k =
±π/√
(3)ao. The corresponding 1D DOS for (9,0) SWNT per unit cell of a graphene
are also shown. The dotted line is the DOS corresponding to graphene . . . . . . . 10
1.8 (a) Scematic of DOS for semiconducting and metallic SWNT with the S11, S22,M11
transitions shown . Fig. (b) Kataura plot for graphing the optical transitions between
van Hove singularities as a function of SWNT diameter. . . . . . . . . . . . . . . . 12
1.9 Dissociation of molecular H2 over catalytic metal doped SWNT . . . . . . . . . . . 18
1.10 Atomic Hydrogen pump: Schematic of the sequential steps of an atomic hydrogen
pump: dissociation of molecular hydrogen, spillover, and surface diffusion on a nan-
otube surface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
xiii
2.1 Schematic of the reactor used to grow MWNT with an applied DC bias . . . . . . . 22
2.2 Schematic of the top and bottom electrode/flange assembly . . . . . . . . . . . . . . 23
2.3 Uniformity of MWNT growth across the bottom electrode . . . . . . . . . . . . . . . 24
2.4 Vertical reactor setup for SWCNT growth. . . . . . . . . . . . . . . . . . . . . . . . 25
2.5 The principle of interferometry. (a) Schematic of light reflection by a single, non-
absorbing layer bounded on either side by semi-infinite non-absorbing layers. The
incident laser beam reflects off the film surface and the substrate-film interface. The
reflected beams interfere as described in the text. (b) Fresnel coefficients for the two
interfaces considered. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.6 Schematic of the interferometer set-up, used as an in-situ diagnostic to determine the
height of the MWNT films. Fig. (a) plots the fringe thickness corresponding to the
maxima and the minima in the interferogram as a function of the incident angle. It
also plots the magnitude of beam attenuation corresponding to the fringe thickness.
(b) The reflected laser beam is made to focus on a photovoltaic cell by a concave
mirror. The intensity of the beam is tracked by measuring the photovoltaic current
using a pico-ammeter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.7 Interferometer scans recorded in-situ during MWNT growth. The first three reflec-
tivity plots correspond to same growth conditions but different growth times. The
fourth reflectivity plot is from a higher pressure growth. The rectangles on the plots
show when the growth stopped. Also shown are SEM images of MWNT forests cor-
responding to three of the growth runs. . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.8 Algorithm for analyzing the interferometer scans. In Fig.(a) an attenuating back-
ground signal is obtained from the plot, by using the Savitzky-Golay smoothing func-
tion. (b) The background is subtracted from the normalized raw signal to obtain the
interfering signal. The amplitude of this signal decays with height of the MWNT.
The solid lines are Beer-Lamber law . MWNT heights and the growth rates obtained
from the interferometer scans are plotted in Fig. (c). . . . . . . . . . . . . . . . . . 32
2.9 (a) Schematic of a RGA . (b) Sample mass spectrum obtained for MWNT growth; T
= 750oC,gas pressure= 400 Torr, H2 : C2H4 flow rates = 150:250 sccm; imposed field
= .45V/µm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.10 Schematic of the 4 probe setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.11 Raman spectrum obtained from a HiPCO sample, with 785 nm laser . . . . . . . . . 37
xiv
2.12 Comparison of the line-shape of the G-band for a metallic, semiconducting SWNT
and that of a MWNT. The Raman spectrum of the SWNTs were obtained from the
same sample, but with different laser energies (514 nm for the metallic and 785 for
the semiconducting). This shows the importance of using different wavelengths to
fully characterize a given sample. The MWNT spectrum was obtained with a 514 nm
laser. Also shown in the plots are the D-bands . . . . . . . . . . . . . . . . . . . . . 39
2.13 Assigning (n,m) to SWNTs from RBM signals. (b) Kataura plot, charting the exper-
imental optical transition as a function of SWNT diameter. (a) RBM signal obtained
from HiPCO nanotubes with 785 nm laser excitation. From a comparison of the res-
onant energy and the diameter of the tube (obtained from the RBM frequency) the
chirality of the SWNT can be determined. As an example, two of the RBMs observed
in the sample spectrum are assigned chiralities (9,4) and (10,5). These SWNTs belong
respectively to the chiral family, ”2n+m” , 22 and 25 respectively. . . . . . . . . . . 40
2.14 Absorption spectrum obtained for HiPCO SWNTs. Marked in the plot are absorption
lines corresponding to S11, S22 and M11 transitions . . . . . . . . . . . . . . . . . . 42
2.15 (a) Emission of a photoelectron.(b) A sample XPS spectrum . . . . . . . . . . . . . 43
2.16 (a) Schematic of the Auger process. (b) Auger spectrum of micelle patterned iron
catalyst particles on a Si substrate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.1 Characterization of the catalyst particles obtained by annealing sputtered Fe films
on a buffer layer of Al. (a) Cartoon of the process. (b) SEM image of the catalyst
particles after the annealing step. (c) Catalyst particle size distribution (d) Line scan
of the substrate using an Auger probe. . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.2 Comparison of MWNT growths with and without the Al buffer layer . . . . . . . . . 51
3.3 Auger depth profile of as-sputtered films with and without the Al buffer layer. The
nominal thickness of Fe directly deposited on the Si substrate was 13nm, while 5nm
of Fe was deposited on 10 nm Al, sputter deposited on Si . . . . . . . . . . . . . . . 52
3.4 Time resolved reflectivity plots off the catalyst substrate during the pre-MWNT
growth regime. Also plotted are the corresponding chamber temperatures. . . . . . . 53
3.5 (a) Schematic of the four mass transfer processes. Figure (b) is a schematic of the
chemical potential drop that results in the carbon flux from the vapor phase across the
vapor-liquid interface, through the liquid catalyst and finally across the liquid-solid
interface to form the MWNT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
xv
3.6 The rate limiting steps for the MWNT synthesis process. The driving force for the
MWNT growth approximately equals the chemical potential drop across the rate-
limiting step. Fig.(a) is a schematic of the chemical potential drop for interface-limited
growth, with the two limiting cases vapor-liquid interface and liquid-solid interface
shown. Fig.(b) is a schematic of the diffusion limited MWNT growth processes,
limited liquid and vapor phase diffusivities respectively. The dotted line is a schematic
of the chemical potential change for a growth condition where the rate limiting step
is a combination of the diffusive and interface transport processes. . . . . . . . . . . 59
3.7 Keeping count; (a) available attachment sites on the catalyst surface, (b)the number
of catalyst particles initiating MWNT growth in the time interval dt. The mean time
for catalyst activation is τn, while the mean time for catalyst poisoning is τp. No and
Ng are respectively the total number of particles and number of catalyst particles that
have resulted in MWNT growth at time ’t’ . . . . . . . . . . . . . . . . . . . . . . . 60
3.8 SEM images of the MWNT forests obtained after the completion of growth runs in
each of the above cases. These heights, marked by rectangles are plotted in Fig.3.9(c).
A tilted sample holder was used for the SEM imaging, with the angle of the tilt
being 45o. Thus to obtain the actual height of the CNTs corrections were made to
compensate for the tilt angle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.9 Normalized interferometer scans for temperature dependent growth of MWNTs at
pressures of 265 Torr, Fig (a). The heights obtained from the interference fringes are
plotted in Fig (b), while Figure (c) plots the growth rates of the MWNTs. The solid
dark lines in (c) mark the linear regime for MWNT growth, corresponding to the
steady state growth conditions, described in the kinetic model. The corresponding
growth rates from Fig (c) are used in the article for analysis/validation of the growth
model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.10 Fig. (a) is an Arrhenius plot of the temperature dependent thermal CVD growth of
MWNT in the temperature range 700-800oC. The activation barrier obtained from the
linear fit is ∼190 kJ/mol. Fig. (b) is a plot of the experimental interferometer heights
and the corresponding theoretical fits of the growth model. The fitting parameters
being the experimental growth rates, and the mean lifetime for catalyst activation
and poisoning. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.11 Time evolution of pressure and reflectivity during the interrupted growth experiment. 66
xvi
3.12 Pressure dependent growth of MWNT at T=750oC. Fig. (a) plots normalized in-
tensity as obtained from the photovoltaic currents. Increasing pressure increases the
growth rate of the MWNT as is evident from (a) and plotted in (b). Fig. (b) also
shows that higher the pressure shorter is the time to reach steady state values. The
catalyst poisoning mean lifetime is also shorter at higher pressures. (c) SEM images
of the MWNT revealing their final heights at pressures of 151, 405 and 760 Torr
respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.13 Fig. (a) plots the experimental growth rates ’o’ and the predicted growth rates (solid
line) for the pressure dependent growths. The growth rates were predicted by ex-
trapolating the average experimental growth rate at P=265 Torr after accounting
for the changes in pressure and gas composition. Increasing pressures decrease the
driving force for MWNT growth, but results in enhanced kinetics accounting for the
increased growth rates. Fig. (b) plots the experimental and theoretical fits for the
MWNT heights. With increase in pressure the height of the MWNT films first increase
and then decrease. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.14 Temperature dependent growth of MWNT at P=760 Torr. Fig. (a) plots normalized
intensity as obtained from the interferometer plots. Fig. (b) plots the experimental
and predicted growth rates. The growth rates were predicted again starting from
the T=750oC / P=265 Torr growth velocity, while accounting for temperature and
pressure changes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.1 Effect of pressure on the morphology of nanotubes. (a-b)Catalyst particles prepared
by annealing sputter deposited thin Fe films. (c) Particles prepared from block co-
polymer micelle templates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.2 1D Carbon nanostructures. (a-b) carbon nanotubes. Schematic downloaded from
www.ibmc.u−strasbg.fr/ict/images/SWNT−MWNT.jpg (c) Examples of CNF mor-
phologies. Schematic from www.pyrografproducts.com/Merchant5/graphics/sfnt −orangecones.gif . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.3 SEM images showing the dependence of the thickness of the sputtered Fe layer and
growth pressures on the nature of carbon morphologies obtained . . . . . . . . . . . 78
4.4 Heights of CNTs/CNFs plotted as a function of growth pressure . . . . . . . . . . . 79
4.5 Raman spectrum obtained using 514 nm excitation laser for nanostructures grown
from a 8nm sputtered Fe film as a function of pressure . . . . . . . . . . . . . . . . . 80
4.6 Evolution of particle sizes vs. catalyst thickness and annealing pressures . . . . . . . 81
4.7 Plot of particle sizes obtained from Fig.4.6 for the 2nm and 5nm sputtered Fe film
thickness. The particles were assumed to be circular for simplicity. The X-axis is the
calculated diameter corresponding to the particulate area. . . . . . . . . . . . . . . . 82
xvii
4.8 Auger depth profile for an annealed 2nm Fe/10nm Al/ Si substrate. (a) Depth profile
for an as deposited sample(5nm sputtered Fe). (b) cartoon of the annealing process
and SEM image of the catalyst particles formed after annealing. (c ,d) Profiles ob-
tained by sputtering on the substrate and a particle respectively. The same elemental
color codes and markers are used for all the depth profiles discussed in this chapter . 84
4.9 Auger depth profile for annealed 13nm Fe/10nm Al/ Si substrate as function of anneal-
ing pressure(a) Depth profile obtained from sputtering on the substrate. (b) Depth
profile from a particle. (c) Schematic of particle evolution with annealing pressure . 86
4.10 TEM characterization of 1D carbon structures as a function of particle size. (a)
CNTs formed from small catalyst particles, (b) Defective, kinky fibers formed from
large particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.11 TEM characterization of 1D carbon structures obtained from intermediate particle sizes 88
4.12 (a) In-situ TEM studies of nanofiber growth (1). (b) Atomic scale observation of the
formation of SWNTs (2). (c) Distribution of fiber diameter with temperature from
data reported by various groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.13 Plot of size dependent melting point of Fe. The dotted line marks the growth tem-
perature used for this study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.14 (a) Relevant portion of the binary Fe-C phase diagram. (b) Schematic of the evolution
of the stacked-cup morphology of the CNFs . . . . . . . . . . . . . . . . . . . . . . . 93
4.15 Energetics of the CNF formation process. The black dashed line marks the volume
fraction that triggers the contraction of the catalyst leaving behind a graphitic ledge 95
5.1 Patterned carbon nanotube structures for enhanced field emission. Also plotted are
field emission currents from the two different cathode structure. Introducing an extra
edge in the donut structure leads to current enhancement . . . . . . . . . . . . . . . 99
5.2 Schematic of the different steps to synthesize Fe nanoparticles via a block copolymer
micellar route . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.3 Size and density distribution of the Fe catalyst particles obtained from (a) block
copolymer templates and (b) from sputter depositing 2.5 nm thin Fe film. The Y-axis
for both the plots are percentage values . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.4 Fe mapping of the particles obtained from the micelle template.(a) SEM image and
(b)corresponding Fe map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.5 EM studies of MWNT yield from micellar nanoparticles. (c,d) Bright and dark field
TEM images of particles subsequent to MWNT growth . . . . . . . . . . . . . . . . 104
5.6 Controlling spatial density by controlling the size of the PS polymer . . . . . . . . . 105
5.7 Controlling particle size by controlling the metal loading ratio . . . . . . . . . . . . . 106
5.8 SEM images of MWNT films grown at 400 Torr as a function of bias . . . . . . . . . 106
5.9 SEM images of MWNT films grown at 760 Torr as a function of bias . . . . . . . . . 107
xviii
5.10 Height of the CNTs as a function of imposed electric field . . . . . . . . . . . . . . . 108
5.11 Characterization of the alignment of the e-field aligned MWNT forests. Fig. (a-c)
describes the methodology for quantifying the alignment of the forests. Fig. (a) is
the original SEM image of the forests ;(b) the edges has been blurred to remove the
edges from showing up when doing the 2D FFT of the images;(c) contour plot of the
FFT of (b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5.12 (a) High magnification SEM side-view images of MWNT films grown at different
biases. Fig.(b) plots the alignment and the height of the forests vs. the applied
biasing voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.13 SEM images of MWNT grown from micelle templates. MWNTs (a-d) are grown
under the influence of increasing electric fields. The magnitude of the bias is printed
on the respective images. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5.14 Alignment of MWNT for different biasing conditions. Figs (a-c) describe the align-
ment algorithm. Fig (b) defines the edges from the original SEM image (a). Straight
segments are fitted to the edges so obtained, and the angles made by these segments
are measured with respect to the horizontal plane. Fig (d) is a bar chart that com-
pares the fraction of lengths oriented with in an angular range for different applied
electric fields. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.15 Schematic of a MWNT oriented at an angle θ to an applied electric field (a). Fig (b)
is a schematic of two different vibrating growth models; case (I) where the CNTs are
not touching and case (II) where the tip of the CNTs might interact. . . . . . . . . . 113
5.16 Plots the lower order vibrating amplitudes of the tube tip as a function of the applied
field and the tube height. The , ∆ correspond to the first and second order ampli-
tudes. The area between the dashed line corresponds to the distribution of half the
inter tube separation, D; amplitudes greater than these values will result in case (ii)
growth mode. (1V/µm = 106V/m) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
5.17 (a) Schematic of a forest of MWNT, simulated as a bundle of springs. Parameters of
the spring, coil radius = D, pitch = λ. Fig (b) plots the alignment of MWNT in the
forests, measured by the angle 〈ϕ〉(see text for details), as a function of the applied
field. The markers are angles obtained from the FFT of SEM images of the MWNT
forests, while the dotted lines are theoretical fits, simulating the forests as springs
with constant Ks. Fig. (c) is a plot of MWNT heights while the dashed lines are
simulated plots of MWNT height if they were only being stretched by electrostatic
forces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
xix
5.18 (a) Time resolved reflectivity plots for the temperature dependent growth runs. The
solid lines are interferometer scans for zero bias growth, while the dashed lines are
the corresponding scans for a negative bias of 0.3V/µm. In between the two sets
is the interferogram for a bias of 0.22V/µm and growth temperature of 750oC. The
plots are offset for clarity, with scans obtained from the same bias magnitude grouped
together. Fig. (b) plots the experimental heights obtained from the interferometer
scans and their theoretical fits. Fig. (c) is a plot of the relative change in density of the
MWNT film with change in bias and temperature. The reference density corresponds
to MWNT films grown at T=700oC with zero bias . . . . . . . . . . . . . . . . . . . 121
5.19 Characterization of the reactor gases: (a)RGA results; Bar chart showing the change
in mole fraction of the relevant gaseous compounds between the start and the end
of the MWNT growth runs. The change in species density are normalized by the
residual fractions in the RGA before the admission of the reacting gases into the mass
analyzer at the onset of growth. Fig. (b) plots the change in reactor pressure for the
different growth runs, while keeping the in and outflow of gases constant. . . . . . . 125
5.20 Arrhenius plots of normalized steady state growth rates plotted as a function of the
inverse of temperature. Three sets of data are presented; MWNT growth under no
bias at lower (265 Torr.) and higher pressures(760 Torr.) in the absence of an electric
field and temperature dependent growth runs for an applied electric field of 0.3 V/µm.
The activation energy calculated from the plots are printed on the figure . . . . . . . 126
5.21 Plot of energy of the carbon precursor and CHx (dissociation products of ethylene)
as a function of distance form the catalyst interface. The orange, red dotted lines
corresponds to the energetics for a zero bias growth. The blue line represents the
energetics of the vapor-catalyst mass transfer step for an electric field assisted growth 128
6.1 Tem images of SWCNT bundles grown at (a) 1000oC and (b) 1050oC with 0.25-wt%
ferrocene and 1000 sccm of H2 flow, S/Fe =0.2. . . . . . . . . . . . . . . . . . . . . 132
6.2 Raman of the SWNT samples collected from different parts of the furnace (a)RBM
modes (b)D and G bands (c) Normalized IRBM/IG (d) IG/ID ratio as a function of
the furnace position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
6.3 Kataura plot for the S22, M11 and S33 transitions. Also plotted in the Fig. is the
position of the 785 and 635 laser lines, and a 50 nm shift to account for the bundling
of SWNTs. The 2n+m family of the SWCNT are shown for the MOD1 and MOD2
S22 transitions (joined by black solid line) and for the M11 transitions (joined by green
dashed line). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
6.4 UV-Vis-NIR of the samples collected from different parts of the furnace (b) S22 tran-
sitions after subtracting the background (c) Comparison of the absorbance % from
the spectra corresponding to the peaks obtained from Fig. (b) . . . . . . . . . . . . 136
xx
6.5 TGA of the samples from different parts of the furnace . . . . . . . . . . . . . . . . . 138
6.6 Raman of the SWCNT samples as a function of ferrocene concentration. (a) RBM
modes with 785 nm laser, 635 nm laser (inset). (b) D and G bands from 785 nm laser.
(c) Normalized IRBM/IG (d) IG/ID ratio and the extent of G split as a function of
temperature. The labels for Fig. (a) and (b) are the same. The label for Fig. (d) is
also true for Fig. (a). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
6.7 TEM images of the samples. Fig. (a) and (b) are TEM images from 1.0 wt% sample
while (c) is the image from SWCNTs formed with 0.25 wt% ferrocene. . . . . . . . . 141
6.8 SWCNT diameter and (b) Fe catalyst particle size distribution for sample prepared
with 0.25 and 1.0 wt% ferrocene respectively, obtained from the TEM images. . . . . 142
6.9 UV-Vis-NIR of the samples collected as a function of ferrocene concentration. (b)
S22 transitions after subtracting the background (c) Comparison of the absorbance %
from the spectra corresponding to the peaks obtained from Fig (b) . . . . . . . . . . 143
6.10 TGA of the samples prepared with different amount of ferrocene in the precursor
solution. For the fit data x is the wt% of ferrocene in the sample. . . . . . . . . . . 144
6.11 Raman of the SWNT samples synthesized at different temperatures. (a) RBM modes
with 785 nm laser and (b) 635 nm laser. (c) D and G bands from 785 nm laser. (d)
Normalized IRBM/IG as a function of temperature (e) Shows the variation of IG/ID
and the extent of G split with temperature. The color legend for Fig. (a) and (c) is
the same. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
6.12 UV-Vis-NIR of the samples collected as a function of SWNT growth temperature.
(inset, a)M11 and S33 transitions.(b) S22 transitions after subtracting the background.
The color legend for all the Figures is the same. . . . . . . . . . . . . . . . . . . . . 147
6.13 (a) SWCNT diameter and (b) Fe catalyst particle size distribution for SWCNTs,
obtained from TEM analysis, grown at 900oC and 1100oC. . . . . . . . . . . . . . . 148
6.14 Theoretical plot to show the temperature dependence for the critical radius for SWC-
NTs. The solid circles show the mean for the diameter distribution from TEM analysis
at 900 and 1000oC. The arrows mark the most abundant range for the SWNT from
absorption spectroscopy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
6.15 Abundance maps for SWCNT grown at 900oC (a) and 1100oC (b). For comparison
the abundance map for HIPCO characterized using a similar procedure is shown. A
darker color implies a larger abundance of SWCNT, from absorbance studies. The
red dotted line shows the positions of the SWCNT diameter distributions obtained
from TEM study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
xxi
7.1 TEM morphologies of deposited Pt nanoparticles on SWNTs as a function of the
nominal thickness of the deposited films: (a) 0.2nm, (b) 0.5nm, (c) 1.0nm and (d)
3.0nm. (e) Room temperature isotherms for Sp-Pt SWCNT hybrids with different
nominal thickness of the sputtered catalyst. (f) Pt catalyst number density for Sp
Pt hybrids with 0.2 and 0.5 nm thick films. (Inset) Schematic of SWCNT bundle
decorated with Pt nanoparticles, for the density calculation. . . . . . . . . . . . . . 155
7.2 SEM images of SWNT films used for the conductivity and spectroscopy studies. (a,b)
Dense and sparse distribution of as grown SWNT films. (c) Spin cast HiPCO SWNT
films (d) Monolayer coverage of SWNT films prepared by LB technique (e) AFM
scan of the LB films. (f) Representative Raman spectrum obtained from the HiPCO
SWNT samples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
7.3 Change in current passing through a Pt-doped SWNT film (nominal thickness =
0.5 nm) on repeated exposure to hydrogen. Also plotted is the change in hydrogen
pressure inside the chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
7.4 Resistance change as function of hydrogen charging for as-deposited and Pt sputtered
SWNT samples. Also shown is the change in resistance of the Pt-SWNT hybrid film
on exposure to air. For comparison, changes to a 0.6 nm thick sputtered Pt film on
quartz on exposure to hydrogen is also plotted. . . . . . . . . . . . . . . . . . . . . 160
7.5 Resistivity changes with hydrogen exposure for CNTs with different Pt loadings . . . 161
7.6 Hydrogen uptake efficiency for SWNT films with varying thickness. The Pt loading
was kept identical for all samples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
7.7 Hydrogen uptake measured at different temperatures. The Pt loading and the film
thicknesses are the same for all the runs. . . . . . . . . . . . . . . . . . . . . . . . . . 164
7.8 XPS overview of the samples before and after hydrogenation. 0.6nm Pt+ LB SWNT
film composite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
7.9 (a)XPS before and after hydrogenation of As-grown films. Fitted XPS peaks of as-
grown samples, before (b); and after Hydrogen exposure(c) . . . . . . . . . . . . . . 166
7.10 (a)XPS before and after hydrogenation of 0.6 nm Pt-LB film hybrids. Fitted XPS
peaks of as-grown samples, before (b); and after hydrogen charging(c) . . . . . . . . 167
A.1 Allowed frequencies for the lower order modes as a function of height and strength of
applied electric field during growth. . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
xxii
Chapter 1
Introduction
1.1 The number ’4’ and the number ’6’
The elements with four valence electrons, group 14 of the periodic table, are special. Its the only
group containing solid elements at ambient conditions, which exhibit three distinct property domains
: ranging from non-metallic to metalloid to weakly metallic, Fig.1.1. Si, [Ne]3s23p2, the second most
abundant element in the earth’s crust is the backbone of the semiconductor industry with a band
gap of 1.12 eV at 300K. The next element in the group Ge,[Ar]3d104s24p2, is also a semiconductor
material with a band gap of 0.74 eV at 300K, used mostly in fiber-optic systems and infra-red
optics. Sn, with electronic configuration [Kr]4d105s25p2, is the first metal of the group. It is also
the element which has the largest number of stable isotopes, 10. The next element in the group is
the heavy metal, Pb,[Xe]4f145d106s26p2. This along with Bi, are the heaviest elements known that
have a stable nuclei. Even so, in a group having such unique elements as those mentioned above, C
is the enigma.
Gro
up
14
(IV
A)
[He]2s22p2
[Ne]3s23p2
[Ar]3d104s24p2
[Kr]4d105s25p2
[Xe]4f145d106s26p2
C
Si
Ge
Sn
Pb
14
6
32
50
82
Figure 1.1: The elements of Group 14 (IV A) of the periodic table.
1
CHAPTER 1. INTRODUCTION 2
The reason being the atomic number of C, 6. The atomic number 6 leads to an electronic
configuration of 1s22s22p2. The inner 1s2 orbital contains two strongly bound core electrons. The
four valence electrons in the 2nd orbital are relatively weakly bound and the energy difference between
the upper 2p energy levels and the lower 2s energy levels is small compared to C-C chemical bond
energies. Hence the electronic wavefunction for these four electrons can mix, changing the occupation
of the 2s and 2p atomic orbitals, to enhance the binding strength of C with the neighboring atoms.
This ability of C to exhibit spn hybridization sets it apart from the rest of the group 14 elements. C
exhibits all three possible hybridizations, sp, sp2 and sp3; while the other group 14 elements, e.g. Si,
Ge, exhibit primarily sp3 hybridization. (It is interesting to note that as a consequence , all elements
of this group assume a diamond cubic crystalline shape in their 3d state, stable or not. Diamond is
an insulator but depending on how tightly packed to the inner core the outer level electrons are, the
diamond cubic forms of the other elements in the group first transition to form semiconductors, Si
and Ge, and further down the group they are metallic.) The lack of sp and sp2 bond formation in
Si and Ge is possibly due to the prolate structure of the outermost p-orbitals. For C, the absence of
nearby oriented inner orbitals facilitates hybridization, and hence the importance of the number ’6’.
1.1.1 Hybridization and relevant C isomers
The spn hybridization of the C atoms is responsible for the dimensionality of the C - based solids. C
is the only element that has isomers across all dimensions, fullerenes (0-D) to diamond(3-D)(3). In
the following subsections the C solid phase structures vis-a-vis their spn hybridization are described.
In spn hybridization, (n+1) σ bonds are formed per carbon atom. These σ bonds form the skeleton
of the local structure for the n-dimensional morphology. In Fig.1.2 the sigma bonds are shown by
the lighter colored lobes, while the darker lobes represent the relatively weaker π bonds.
sp hybrids
In this, the 2s orbital mixes with only one of the three p-orbitals resulting in the formation of two
sp hybrid orbitals, and two unchanged p orbitals. The subsequent bond formation involves sp-sp
overlap between adjacent C atoms forming σ bonds and two additional π bonds formed by p-p
overlap. The two σ bonds can make only a one-dimensional chain structure, [−C ≡ C−]n. The 3D
structure formed by gathering these chains, carbyne, is formed at high temperatures and pressures.
sp3 hybrids
The 2s orbital mix with three 2p orbitals to form four sp3 orbitals. The four resulting σ bonds
define a regular tetrahedron that results in the formation of a 3-D diamond structure (Fig.1.2). As a
result diamond is an isotropic, cubic, high band-gap (5.3 eV) insulator. The strong σ bonds make it
CHAPTER 1. INTRODUCTION 3
s orbital
p orbital
2 sp orbital
3 sp2 orbital
4 sp3 orbital
Linear
Planar
Tetrahedral
graphite
diamond
Figure 1.2: spn hybridization of the C atoms, and the corresponding orientation of the C-C bonds.Also shown are the graphite and diamond crystalline structures.
one of the most thermally conductive and highest melting point solids known. Along with graphite,
diamond is the main allotropic form of C.
sp2 hybrids
In sp2 hybridization the 2s orbital mixes with two of the three available 2p orbitals, forming three
sp2 orbitals with one p-orbital remaining unchanged. All σ bonds formed with adjacent C atoms are
in the same plane, while the π orbital for each C atom exists perpendicular to this plane, resulting in
the formation of a planar 2-D structure. Graphite is formed by ABAB stacking of these 2D planes.
Under ambient conditions, and in bulk form the graphite phase with strong in-plane trigonal bonding
is the stable phase. It is interesting to note that sp2 hybridization which forms a planar structure
also forms a planar local structure in the closed polyhedra ( 0-D ) of the fullerene family and in the
cylindrical morphology (1-D) of carbon nanotubes (CNTs).
Amorphous C, the other ubiquitous form of C, refers to a highly disorganized network of C atoms
that have no long range ordering. The C atoms have predominantly sp2 bonding, with about ∼ 10%
sp3 bonds and almost no sp bonding(3). Hence they exhibit some short range order, though the
nature of this order varies significantly from one growth condition to another. For characterizing
the short range order of amorphous C two parameters are the most important. First is the ratio
CHAPTER 1. INTRODUCTION 4
of sp3/sp2 bonding, and second the hydrogen content (H impurities are present to passivate the
dangling bonds present in the disordered structure).
1.2 sp2 derived C configurations
1.2.1 3D Graphite and 2D Graphene
As mentioned before, graphite is a 3D layered hexagonal lattice of C atoms (Fig.1.3). A single layer
of graphite forms the 2D material graphene. The in-plane nearest neighbor distance aC−C of 1.421A
in graphite results in an in-plane lattice constant, ao = |~a1| = |~a2| = 2.46A. The z-axis lattice
constant of 6.70A results in an interplanar distance of 3.35A. Hence the interaction between two
adjacent layers is small compared to the intra-layer interactions. Thus the electronic structure of
2D graphene acts as a good first approximation for 3D graphite.
In Fig.1.3, the unit cell and the corresponding Brillouin zone of graphene is shown; ~a1,~a2 are
unit vectors in real space, and ~b1,~b2 are the reciprocal lattice vectors.
~a1 = (
√3
2ao,
ao2
), ~a2 = (
√3
2ao,−
ao2
)
~b1 = (2π√3ao
,2π
ao), ~b1 = (
2π√3ao
,−2π
ao)
The reciprocal space lattice constant has the magnitude |~b1| = |~b1| = 4π/√
3ao. The first Brillouin
zone is obtained by constructing the Wigner-Seitz unit cell of the graphene reciprocal lattice. It is
shown in the figure by a shaded hexagon. Three high symmetry points of the Brillouin zone; center,
corner and center of the edge are defined by Γ, K and M respectively. The significance of these
points will be discussed in a later section dealing with the electronic structure of graphene.
1.2.2 0D Fullerene
The 60 C atoms in C60 are located at the vertices of a truncated icosahedron(3). This molecule
is often thought of as a ”rolled up” graphene sheet. This is because, (1) the aC−C distance in
C60 is almost identical to that of graphene (2) each C atom is trigonally bonded to three other C
atoms in a sp2 derived bonding configuration and (3) most of the faces on the truncated icosahedron
are hexagons ( 20 hexagons and 12 pentagons). It is energetically unfavorable for two pentagons
to be adjacent to each other, as this will lead to higher local curvature and larger strain. Hence
in general the pentagons are surrounded by hexagons. This tendency of the pentagons not to be
adjacent to one another is called the ”isolated pentagon rule”. The smallest molecule to satisfy
the rule is C60, where each pentagon is surrounded by 5 hexagons, and each hexagon by 3 other
hexagons and 3 pentagons. Because of the closed shell characteristic of C60 and other fullerenes,
the nominal sp2 bonding between C atoms occur on a curved surface, in contrast to the trigonal
CHAPTER 1. INTRODUCTION 5
M
graphite graphene
Unit Cell
Brillouin Zone
(a) (b)
(c)
a1
a2
b1
b2
x
y
kx
kyK
Figure 1.3: (a) Unit Cell of Graphite (b) Graphene unit cell (c) Brillouin zone of graphene isrepresented by the shaded hexagon. The high symmetry points Γ, K,M are shown in the schematic.
bonds of graphene that are truly planar. This curvature of the bonds leads to some admixture of
sp3 bonding, characteristic of tetrahedrally bonded diamond. The extent of the sp3 bonding and
hence the strain in the fullerenes decrease with increasing size of the molecule.
1.2.3 1D Carbon Nanotubes
Carbon nanotubes are essentially members of the extended fullerene family. Structurally they can
be described as concentric tubes formed by rolling graphene sheets into cylinders. Depending on the
number of conformal tubes, the carbon nanotubes are classified as single-walled carbon nanotube
(SWNT), double-walled carbon nanotube (DWNT),CNTs having more than two concentric cylinders
are generally termed multi-walled carbon nanotube (MWNT). Neglecting the hemispherical ends,
the nanotubes are generally considered to be 1D owing to the large aspect ratio of the cylinders
(∼ 104− 106). It has to be mentioned here that other forms of 1D carbon isomers exist, but instead
of having a tubular structure they typically have a stacked cone or bamboo like structure (i.e. the
interior of the 1D morphology is not hollow). These are known as carbon nanofibers; Chapter 4 will
deal with these nanostructures in more details. Also, formation mechanism of carbon nanofibers in
preference to nanotubes will be discussed.
CHAPTER 1. INTRODUCTION 6
a1
a2
Tube axis
armchair (n,n)
zigzag (n,0)
chiral (n,m)
Ch= na1+ ma2
0
T
Figure 1.4: Honeycomb lattice of a nanotube. Shown in the figure is the chiral vector, Ch, thatdetermines the orientation of the nanotube lattice. Also shown are the achiral nanotubes, armchairand zig-zag.
The orientation of the hexagonal ring in the lattice relative to the nanotube axis has impor-
tant bearing on the carbon nanotube structure and its transport properties, Fig.1.4. The primary
morphological classification of SWNT is achiral (symmorphic, mirror image identical to the original
morphology) and chiral (non-symmorphic). The two possible cases for achiral tubes are armchair
and zigzag, as shown in the figure. These SWNTs are named after the shape of the edge of the
cross-sectional ring of the carbon nanotubes. The chiral nanotubes have a spiral symmetry whose
mirror image cannot be superimposed on the original. In MWNT the interaction between the tubes
are relatively weak. Hence the lattice structure of the different layers are generally incommensurate
with each other, resulting in the turbostratic structure.
Unit Cell of SWNT
The unit cell for SWNT is given by the rectangle generated by the chiral vector, Ch and the
translational vector, T , as shown by the shaded rectangle on the unrolled honeycomb lattice of the
carbon nanotube in Fig.1.4. The chiral vector which is perpendicular to the nanotube axis defines
the morphology and the properties of the SWNT. It can be expressed by real space vectors of the
hexagonal lattice as:
Ch = n~a1 +m~a2; (n,m are integers, 0 ≤ |m| ≤ n)
CHAPTER 1. INTRODUCTION 7
The diameter of the SWNT is given by the relation, dt = L/π, where ’L’ is the circumferential length
of the tube.
L = |Ch| =√
Ch ·Ch = ao√n2 +m2 + nm (1.1)
It has to be noted here, that in a reciprocal manner the diameter of the SWNT will control the chiral
vector and hence the property of the CNTs. Advantage of this is taken while synthesizing SWNT
with controlled parameters in chapter 6. The chiral angle, θ,(0 ≤ θ ≤ 30o) is defined between the
vectors Ch and ~a1
θ = cos−1 =Ch · a1
|Ch||a1|=
2n + m
2√
n2 + m2 + nm
In particular the armchair and zigzag SWNT have θ equal to 30o and 00 respectively.
The translation vector T is parallel to the nanotube axis and is normal to Ch in the unrolled
honeycomb lattice, Fig.1.4. It can be expressed in terms of the basis vectors ~a1 and ~a2 as T =
t1 ~a1 + t2 ~a2. Thus the nanotube unit cell is formed by a cylinder of diameter, |Ch|/π, and height
T . Next knowing the area of the nanotube unit cell, the number of hexagons N per unit cell can be
obtained.
N =|Ch × T || ~a1 × ~a2|
(1.2)
Each hexagon, has 2 C atoms. Therefore there are 2N C atoms (or 2pz orbitals) in each cell of the
carbon nanotube.
Brillouin Zone of SWNT
Formulations for the reciprocal lattice vectors K‖ along the nanotube axis and K⊥ in the circum-
ferential direction are obtained from the relation
Ch.K⊥ = 2π, Ch.K‖ = 0
T .K⊥ = 0, T .K‖ = 2π
Solving which we get the relations;
K‖ =1
N(−t2~b1 + t1~b2), K⊥ =
1
N(m~b1 − n~b2)
In the direction of the tube axis, K‖ corresponds to the translational period |T |, its length being
|K‖| = 2/|T |. As the nanotubes are considered to be infinitely long, the wave vector along K‖
is continuous. The first Brillouin zone in this direction is the interval (−1/|T |, 1/|T |], as shown
by WW’ in Fig.1.5. Since SWNTs are 1D materials, only K‖ is a reciprocal lattice vector. K⊥
gives discrete k values in the direction of the chiral vector. The wave vector K⊥ is quantized and
has dimensions of K⊥ = 2/dt. It is easily noticed that N K⊥ = (−t2~b1 + t1~b2) corresponds to a
reciprocal lattice vector of 2D graphene sheet, and hence any two vectors differing by NK⊥ should
CHAPTER 1. INTRODUCTION 8
Ch = 4a1+2a2
a1
a2
M
KW
W’K K
ll l l
b2
b1
Brillouin Zone of (4,2) SWNT
Figure 1.5: Brillouin Zone of (4,2) chirality SWNT is represented by the line segment WW’, which isparallel to K‖ . K‖ and K⊥ are reciprocal lattice vectors corresponding to T and Ch respectively.
be equivalent. It can also be shown that t1 and t2 do not have a common divisor and hence the
N wave vectors µK⊥ ( µ = 1, . . . , N − 1) are discrete. The first Brillouin zone of SWNT therefore
consists of N lines parallel to the nanotube axis separated by |K⊥| = 2/dt and k ∈ (−π/|T |, π/|T |]as shown in Fig.1.5.
1.3 Electronic Structure of SWNTs
The electronic structure of SWNTs are derivative of that of graphene. As mentioned in the last
sub-section the Brillouin zone of SWNT consists of wave vectors parallel to the nanotube axis.
The energy bands will then consist of 1D energy dispersion relationships which are in essence cross
sections of the dispersion for graphene.
1.3.1 Electronic structure of graphene
The three σ bonds of graphene are planar, while the unchanged 2p orbital that is perpendicular
to the plane forms the π covalent bond. These π electrons are the valence electrons and hence are
most relevant for calculating the electronic structure, transport and other solid state properties for
graphene based materials. In general a tight binding calculation for the π electrons is sufficient to
describe the electronic band structure.
CHAPTER 1. INTRODUCTION 9
Fig.1.6(a) is a schematic of the energy dispersion for graphene through out its Brillouin zone.
The upper half of the curves describe the anti-bonding π∗ energy bands, while the lower half is
the bonding π energy bands. The upper antibonding and the lower bonding bands are degenerate
at K, the high symmetry corner point for the graphene Brillouin zone. The Fermi energy passes
through the K points. Since there are two π electrons per unit cell of graphene, they occupy the
lower bonding band. Hence graphene is a semi metal. The existence of a zero band gap at the K
points gives rise to the quantum effects in the electronic structure of CNTs. As shown in Fig.1.6(a)
the energy difference between the bonding and the antibonding bands is maximum at Γ, the center
of the Brillouin zone.
MM
(a) (b)
Ch a1
a2
M
KW
W’
K
Kll
l l
b1
VO
real space
reciprocal space
b2
(c)
Figure 1.6: Energy dispersion relation for graphene over the Brillouin zone. (b) is a contour plot forthe electronic band structure of graphene. Fig. (c) is a schematic of real and reciprocal space for achiral SWNT. Such diagrams help to illustrate the metallic/semi-conducting nature of the SWNT
CHAPTER 1. INTRODUCTION 10
1.3.2 Energy Dispersion for SWNT
For a SWNT, which has 2N C atoms per unit cell, the 1D dispersion relations are given by the
expression(4):
Eq(k) = Eq(kK‖
|K‖|+ qK⊥), (q = 0, 1, . . . , N − 1; and− π
|T |< k <
π
|T |) (1.3)
The N pairs of energy dispersion curves given by eqn. (1.3) correspond to cross sections of the
energy dispersion curves of graphene where cuts were made by the lines[k
K‖|K‖|
+ qK⊥
]. Fig.1.7
shows the 1D dispersion energy plots for a high symmetry zigzag SWNT. If for a (n,m) SWNT one
of the cutting lines passes through the corner point, K, of the graphene Brillouin zone, where the
bonding π and antibonding π∗ bands are degenerate, then the 1D energy bands have a zero energy
gap and the (n,m) SWNT is metallic at room temperature. But if the cutting line does not pass
through a K point, the corresponding SWNT will be semiconducting. The (n,m) SWNT is metallic
Figure 1.7: 1D Energy dispersion relation for (9,0) SWNT. Fig. (a) is part of the unit cell andBrillouin zone of a zigzag SWNT. X points for the zigzag nanotubes correspond to k = ±π/
√(3)ao.
The corresponding 1D DOS for (9,0) SWNT per unit cell of a graphene are also shown. The dottedline is the DOS corresponding to graphene
if | ~V K| is an integral multiple of |K⊥|, Fig. 1.6(c).
V K = ΓKcosθ =|b1|2
cos(π
6)cosθ
CHAPTER 1. INTRODUCTION 11
On substituting the expressions for the cosine of the chiral angle, cosθ, and the diameter dt of the
(n,m) SWNT we get the relation:
V K =2n+m
3
2
dt∵ |K⊥| = 2/dt
V K =2n+m
3|K⊥| (1.4)
Hence the condition for metallic nanotubes is that (2n+m) or equivalently (n-m) is a multiple of 3.
By this token for a completely random distribution of SWNT one third of the CNTs are metallic,
the rest semi-conducting.
Density of States for SWNT
Fig.1.7 plots the 1D density of states for a zigzag SWNT. The DOS of nanotubes have a high
energy dependance, but the DOS near the Fermi energy level is of most importance. The DOS for a
metallic SWNT is non zero at E=0, while it is zero for semiconducting SWNTs. The most prominent
feature for the DOS is the presence of singularities (van Hove peaks) corresponding to extrema in
the Eq(k) relations, characteristic of 1D nanomaterials. Van Hove singularities result in remarkable
optical properties of SWNTs. Optical transitions occur between (v1 − c1, v2 − c2) etc states of
the semiconducting and metallic SWNTs as shown in Fig. 1.8, and are labeled as S11, S22,M11 . . .
transitions. The energies between the singularities depend on the nanotube structure, and hence are
used for fingerprinting SWNTs in spectroscopic studies.
1.3.3 Band gaps, Kataura Plots
The simple tight binding model predicts that the energy band gap for the semiconducting nanotubes
varies inversely with the diameter of the tube, and are independent of the chiral angle of the SWNTs.
Eg,11 =2γoaC−C
dtEg,22 =
4γoaC−Cdt
(1.5)
where γo is the interaction energy between the neighboring C atoms. Deviations from the linear rela-
tion predicted by eqn. 1.5 are expected because of the trigonal equi-energy contours in the graphene
Brillouin zone (Fig.1.6) rather than circular contours around K assumed for simpler calculations.
It is also observed that chirality also plays a significant role in determining the transition energies
since it determines the angle of the cutting lines with respect to the trigonally distorted contours
(5; 6).These effects are more pronounced for smaller diameter SWNTs. Such effects shift transition
frequencies, corresponding to the energy gap, from linear relations in directions related to the values
of (n-m) mod 3, and the direction of shift reverses between the first and second van Hove branches.
Calculations taking into consideration all these have been performed but are complex in nature.
CHAPTER 1. INTRODUCTION 12
Hence to provide a ready reference for these optical transitions an experimental graph named the
”Kataura plot” is generally used that relates the band gap energies (generally in units of frequency,
as it is used mostly for spectrographic analysis) with that of diameter. Fig.1.8 is a Kataura plot
derived from the experimental work and theoretical chirality assignment done by the Strano at al.
(7). Kataura plots will be revisited while discussing Raman spectroscopy for SWNT in the next
chapter.
v1
v1v2
c1
c1c2
Figure 1.8: (a) Scematic of DOS for semiconducting and metallic SWNT with the S11, S22,M11
transitions shown . Fig. (b) Kataura plot for graphing the optical transitions between van Hovesingularities as a function of SWNT diameter.
A brief note about the electronic property of MWNT. In general the MWNT have a much larger
diameter(∼ 5 − 50nm) compared to the SWNT, where the diameters are typically less than 2nm.
As predicted by eqn. 1.5, in general the bandgap varies inversely with the diameter. Hence for all
practical purposes MWNT are metallic in nature.
1.4 Synthesis of Carbon Nanotubes
In this section the different methods for carbon nanotube growth are briefly explained. Extensive
research effort over the last two decades have led to discovery of a wide variety of techniques,
catalyst combinations, growth conditions etc for synthesis of CNTs. The synthesis techniques can
be divided into two broad categories: physical methods, which rely on the high energies to release
the C atoms from their precursors, such as arc discharge, laser vaporization and flame synthesis.
CHAPTER 1. INTRODUCTION 13
Chemical methods, which catalytically decompose the carbon precursors to release the C atoms, is
the other category and has become the method of choice for most researchers.
1.4.1 Physical methods
Arc Discharge
In arc discharge method, C atoms are evaporated by plasma of an inert gas (He, Ar) at low pressures
ignited by passing high currents between two carbon rods placed end to end. Arc discharge has
been developed into an excellent technique for producing both high quality MWNTs and SWNTs.
MWNTs can be obtained by controlling the growth conditions such as the pressure of the inert gas in
the discharge chamber and the arcing current (8). For the growth of SWNT a metal catalyst is needed
in the arc discharge system. Bethune et al. (9) used a carbon anode containing a small percentage
of Co catalyst to generate decent amounts of SWNTs in the soot material. The disadvantage of this
technique is that it produces a mixture of components and hence requires purification of CNTs from
soot and other impurities.
Laser ablation
Synthesis of CNTs by laser vaporization was first demonstrated by Guo et al. (10). In this method a
pulsed or a continuous laser is used to vaporize a graphite target in a reactor filled with an inert gas
and maintained at high temperatures. The vapor so formed forms a very hot plume that expands
and hence cools rapidly. As the vaporized species cool, small C atoms and other molecules condense
to form clusters. From these initial clusters tubular molecules grow into CNTs. The condensates
obtained by laser ablation are contaminated with CNTs and other forms of carbon nanoparticles.
MWNTs are generally formed if pure graphite electrodes are used. Synthesis of SWNT have been
reported on introduction of small amounts of Co,Ni, Fe etc to the graphite electrodes.
Flame Synthesis
This method is based on the synthesis of SWNTs in a controlled flame environment, that produces
the temperature to form C atoms from inexpensive hydrocarbon precursors (11). Small aerosol
metal catalyst islands are also formed in the process, and the CNTs grow from these islands to form
predominantly SWNTs by a mechanism similar to the arc discharge and laser ablation methods.
1.4.2 Chemical methods
Chemical methods can be further classified into the substrate based chemical vapor deposition (CVD)
method and the floating catalyst, aerosol method.
CHAPTER 1. INTRODUCTION 14
Chemical Vapor Deposition
CVD of CNTs is essentially a 2 step process, catalyst preparation generally by heating carbide
forming transition metal thin films. This is followed by heating the reactor to the high growth
temperature at which point a carbon precursor generally a hydrocarbon is flowed into the reaction
chamber. The hydrocarbon dissociates by pyrolysis and in most cases the catalyst particles aid
the dissociative process. Subsequently it is generally accepted that the C atoms so formed undergo
dissolution and saturation in the catalyst nanoparticle. The precipitation of the C atoms from
the saturated particle leads to the formation of carbon nanotubes. The process described above is
called the thermal CVD process (12). Over time different methods for CNT synthesis with CVD
have been developed. One of the most common variations is the plasma enhanced CVD (PECVD)
method where a glow discharge is generated in the reactor chamber(13; 14). The plasma aids in
dissociating the precursor molecules. By carefully selecting the growth conditions the synthesized
product formed can range from SWNT, for a far field plasma , to MWNT and carbon nanofibers. In
another variation of the CVD process, a continuous wave CO2 laser was used to pyrolyse sensitized
gas mixtures of metalo-orgacene and a hydrocarbons(15).
In Chapter 3, the kinetics of carbon nanotube growth is studied in the context of the CVD process.
A generic model for growth of 1-d nanostructures via the Vapor-Liquid-Solid (VLS) mechanism is
applied to the nanotube growth. Laser interferometry is applied in a cold-wall thermal CVD reactor
to measure the growth of the MWNT films in-situ. The combination of experimental studies and
theoretical modeling is done to better understand the rate limiting step of the MWNT growth
process and to provide a road map for similar studies for different growth conditions.
Controlled Nanotube growth
The popularity of the CVD method over the physical methods is attributed to aligned and
ordered nanotube structures that can be grown on surfaces with control impossible to achieve by
arc discharge or laser ablation techniques.
One field of CNT synthesis that has gained much prominence in recent years is directed growth of
CNTs. This is due to the increased research for using of CNTs as transistors, interconnects, sensors,
field emission cathodes etc. For example long arrays of well aligned CNTs was achieved by orienting
the substrates with respect to the gas flow directions (16). Various groups have also demonstrated
directional growth of high- density single-walled carbon nanotubes on a- and r-plane sapphire sub-
strates over large areas (17; 18). It is believed that strong nanotube/substrate interaction plays an
important role in attaining the observed nanotube orientation.
External electric field has been applied during growth to orient CNTs. Advantage is take of the
anisotropy of the CNTs, the polarizability in the axial direction of the tubes being greater than in
the radial direction (19).The most popular technique to date being plasma enhanced chemical vapor
deposition (PECVD) (20; 21; 22; 13). In PECVD, a high bias voltage is applied for generating a
CHAPTER 1. INTRODUCTION 15
glow discharge. In this case the potential does not vary linearly between the electrodes, but rather
is constant except in the sheath region near the cathode where it decreases approximately linearly
(23). The height of the CNTs is smaller than the characteristic Debye length of the plasma, and
hence the CNTs are oriented by the high plasma sheath electric fields. However, complimentary
studies show that along with the electric fields generated in the sheath region other mechanisms like
crowding effect of the high density films, non-uniform stresses across the catalyst particle surface etc
(22) helped in aligning the CNTs. High rates of flame synthesis of aligned MWNTs using a DC field
in flames have also been reported (24).Hongjie Dais group successfully demonstrated electric field
directed growth of single-walled carbon nanotube (SWNT) by thermal chemical vapor deposition
process (CVD) (25; 26). They were able to horizontally align SWNTs suspended over trenches
and also directly on substrates by suitable choice of electrode materials, directed electric fields of
optimal strengths, and suitable surface treatments. Further studies have been made to characterize
and model horizontally directed SWNT growth with a local field (27; 28). Interactions primarily
with the substrate were considered and two growth modes, surface and free growing, were proposed.
Avigal et al. were the first to study aligned growth of MWNT under a DC electric field applied
perpendicular to the substrate (29). They observed that aligned growth of MWNT was possible
only under a positive sample bias. A negative bias resulted in random growth while in the absence
of an applied electric field there was no growth.
In Chapter 5, we report the results of applying an electric field for producing vertically aligned
MWNT films and individual MWNTs. The electric field applied here is perpendicular to the sub-
strate. We address there the two most important issues believed to control the alignment of the
CNTs, spatial density of the MWNT and the magnitude of the applied bias. Also studied was the
effect of the applied field on the growth kinetics of the MWNT films.
Floating Catalyst / Vapor Phase Growth method
In the floating catalyst method, catalyst particles are suspended in a flow of a carbon containing gas,
both being continuously fed into the reactor. This presents a viable way for continuous production
of SWCNTs and avoids catalyst-poisoning issues. Sen et al. (30) were the first to use pyrolysis of
metallocenes such as ferrocene, cobaltocene and nickelocene to produce the transition metal catalyst
particles. An Ar-H2 atmosphere was used for the pyrolysis of metallocene/benzene mixtures to give
high yields of carbon nanotubes and metal-filled onion-like structures. Cheng et al. (31) improved
upon the floating catalyst method, used previously for the production of carbon nanofibers, to pro-
duce SWNTs, with a diameter distribution of 1.69 ± 0.34 nm. Ferrocene was used as the catalyst and
carbon was provided by the decomposition of benzene at temperatures of 1100− 1200oC. Hydrogen
was used as the carrier gas; while a sulfur-containing additive, thiophene, was used to enhance the
growth of the SWNTS. Ci et al. (32) synthesized SWNTs without an amorphous carbon coating by
thermally decomposing acetylene in the temperature range of 750 − 1200oC using Fe(CO)5 as the
CHAPTER 1. INTRODUCTION 16
Fe catalyst precursor. In all these above cases, Fe-precursors were pyrolized in a separate furnace
before being introduced to the reactor where the SWNTs were synthesized. Nasibulin et al. (33)
developed a true aerosol method for the growth of SWNT, where the two steps of formation of the
SWNT and their sampling were done directly from the gaseous phase rather than collecting SWNTs
from the cooler parts of the furnace as in the previous studies. Catalyst particles were formed by
a hot wire generator and introduced directly into the reactor. Disproportionation of CO provided
the car- bon atoms while the reaction took place in a H2/N2 ambient. The SWNT produced were
collected using an electrostatic precipitator. Smalley and co-workers developed the so-called HiPCO
procedure, which has become the benchmark for bulk SWNT production. In this method (34), the
Fe catalyst for the SWNT growth was obtained by thermal decomposition of Fe(CO)5 in a heated
flow of carbon monoxide at high temperatures and pressures.
Alcohol precursors have more recently been introduced instead of traditional hydrocarbon sources.
These resulted in a better yield of the SWNT presumably because of the role of the decomposed
OH radicals. The reaction of OH radical with solid carbon reduces the formation of soot and hence
restricts the generation of amorphous carbon in the SWNT product (35). Zhu et al. (36), were
the first to report the direct synthesis of long strands of ordered single-walled carbon nanotubes
with a floating catalyst method in a vertical furnace. n-Hexane with ferrocene and thiophene was
introduced into the reactor after heating the reactor to the pyrolysis temperature. SWNTs formed
in abundance during this continuous process, and SWNT production of ∼ 0.5g/h were reported. Li
et al. (37) developed a technique to spin continuous fibers and ribbons of carbon nanotubes, spun
directly from the synthesis zone of a vertical flow reactor. They used ethanol and ferrocene as the
carbon and catalyst precursor, respectively, H2 as the carrier gas and thiophene as a yield promoter.
In Chapter 6 synthesis of SWNTs using a variation of Li’s method will be described. A detailed
investigation of the reaction parameter space of the vertical furnace for SWCNT production was
performed as a function of temperature, carrier gas flow rate and the precursor solution flow rate.
1.5 Overview of Hydrogen Storage Technologies
Concern over dwindling oil reserves and the environmental impact of greenhouse gas emissions have
motivated intense research and development of alternative fuels in the past few decades. Among
possible candidates, hydrogen is a promising fuel resource since it is the lightest and most abundant
element in the universe. It is nontoxic and highly volatile. The delivered energy per mass of hydrogen
is very high compared to other conventional fuel materials. When hydrogen is combusted with air,
carbon dioxide is not produced by the reaction.
But, there are many challenges to be overcome to establish a viable hydrogen economy. These
include production cost, safety, efficient storage, public acceptance, and competition with other tech-
nologies. Among these challenges, efficient hydrogen storage seems to be the key technical problem.
CHAPTER 1. INTRODUCTION 17
Table 1.1: Candidate materials for Hydrogen Storage
Examples Nature Desorption Kinetics Pros Consof H bond Temp
Metal MgH2 Chemical Too Slow High Irrev.Hydrides Mg2NiH4 high capacityChemical NaAlH4 Chemical High Medium Very high Regene-.Hydrides Mg(BH4)2 capacity rationCarbon CNT Physical Too Fast Rev Lowbased AC∗ Low Capacity
Carbon CNT Chemical Low Slow Less Lowbased AC∗ Energy Capacity
(doped)Metal MOF ! Physical Too Fast Large Low
organic low surface capacityhybrids area
An ideal technique for hydrogen storage should meet three important criteria; high storage den-
sity on both gravimetric and volumetric base, safety, and ease of use (fast uptake/release kinetics
and reasonable thermodynamics). This is most easily realized in solid state storage methods. Cur-
rently promising candidate storage materials are considered to be metal hydrides, chemical hydrides,
carbon-based materials, and organic/inorganic hybrid materials. General features of these materials
and their hydrogen storage properties are summarized in Table (1.1)(AC∗:activated Carbon; MOF !
: Metal-Organic framework).
Metal hydrides (MHx) typically accommodate hydrogen atoms in octahedral or tetrahedral in-
terstitial sites in the host metal lattice structure. Due to the incorporation of hydrogen in lattice,
the metal structure experiences a volume expansion during the hydrogen absorption process. The
hydride formed is stable and requires an appreciable amount of energy to release the hydrogen from
these materials (38). Chemical hydrides are chemical compounds formed between Li, Mg, B, Al, N
and hydrogen; usually as metal-borohydrides or amides. Theoretically, very high gravimetric density
can be achieved since light elements are used. But, the irreversibility of hydrogen regeneration from
these materials needs to be improved for their viable use.Hydrogen storage techniques in carbon
based materials and metal-organic hybrids basically depend on the physical adsorption of hydrogen
at cryogenic temperatures. Large surface areas can capture the hydrogen at the low temperatures.
Due to the weak interaction of hydrogen with those materials, it is challenging to achieve high stor-
age densities under ambient conditions. A more detailed discussion of hydrogen storage in carbon
nanotubes that involves chemical bonding is described in the following section.
CHAPTER 1. INTRODUCTION 18
Pote
ntia
l Ene
rgy
“2H+M”
“H2+ M”
Edissc
without Pt (activated dissc.)
with Pt (spontaneous diisc.)
distance from SWNT surface
activation
barrier Ea
bulkinterfacegas
Figure 1.9: Dissociation of molecular H2 over catalytic metal doped SWNT
1.5.1 Hydrogen storage in SWNTs involving a chemical bond
A more viable option for ambient condition hydrogen storage in SWNTs is via the formation of
hydrogen chemical bonds with SWNT. This route showed initial promise, with initial investigations
showing a hydrogen uptake capacity of 5-10 wt% (39). However, in contrast, recent papers tend
to report storage capacities in pure carbon-based materials at ambient temperature of far less than
1wt% (40). Today it is widely agreed that the combination of pure carbon nanotubes and molecular
hydrogen is capable of storing only a very small amount of hydrogen under ambient conditions.
Fig(1.9), a schematic of the Lennard-Jones potential for molecular H2 and two H atoms as a function
of distance from the SWNT interface, explains the limited bond forming capability of pristine SWNT.
The flat minima in the H2 + M curve corresponds to the physisorbed H2. The deep minima in the
2H+M curve corresponds to chemisorbed H. When the two plots intersect above the zero energy
line (corresponding to the potential energy of H2 far form the surface), the chemisorption requires
an activation energy. This is the scenario for the pristine SWNT.
But pristine SWNT has been known to form bonds with an atomic hydrogen source, which can
significantly increase the amount of stored hydrogen (41; 42; 43). With this in mind an alternate
technique for hydrogen storage in CNTs was developed. The hydrogen molecule can be spontaneously
dissociated at the surface of catalyst metals such as Pd, Pt, Ni, Ru, and Rh. A schematic of the
dissociation path is drawn in Fig(1.9) where the Lennard-Jones potential plots for molecular and
atomic hydrogen intersect below the zero energy line. The dissociated hydrogen atoms can then
spill onto the underlying carbon nanotube structure by spillover mechanism. The hydrogen atoms
CHAPTER 1. INTRODUCTION 19
H2
H
Pt
dissociation spillover diffusion
sample chamber
Figure 1.10: Atomic Hydrogen pump: Schematic of the sequential steps of an atomic hydrogenpump: dissociation of molecular hydrogen, spillover, and surface diffusion on a nanotube surface.
can then find favorable sites on the nanotube surface through surface diffusion ultimately forming
bonds. This is graphically represented in Fig(1.10). Thus, stable C-H bond can be created even
though a conventional molecular hydrogen storage is used.
”Spillover” mechanism has been exploited by several groups for enhanced hydrogen uptake in
SWNTs and other carbon based materials such as MWNTs, Carbon nanofibers, activated carbon
etc (40; 44; 45; 46; 47). Despite this there is a healthy amount of speculation about the validity
of the spillover mechanism. Also further investigations need to be done to improve the low uptake
capacity and slow kinetics. This was the motivation for in-situ 4-probe conductivity tests during
hydrogen uptake reported in Chapter 7.
1.6 Dissertation Overview
Chapter 2 describes in some detail the experimental set-ups (reactors for CNT growth), and char-
acterization techniques used in the remainder of the thesis. Chapter 3 discusses the growth kinetics
of thermal CVD grown MWNTs. Chapter 4 describes the evolution of catalyst particle size as a
function of sputtered film thickness and annealing pressures. Size determines the phase of particles
during nanotube growth, which is shown to have implications in determining the nanotube morphol-
ogy. Chapter 5 studies the effects of an imposed electric field in altering the orientation and growth
kinetics of MWNTs. Chapter 6 reports a detailed parametric analysis of chirality families and diam-
eter distributions in SWNT production by the floating catalyst method. Chapter 7 presents the work
CHAPTER 1. INTRODUCTION 20
on Pt-doped SWNTs. Change in resistivity of the composite mats and spectroscopic determination
of the nature and extent of C-H bonds on hydrogen charging are reported.
Chapter 2
Experimental Methods
2.1 Introduction
In this chapter reactors used for CNT growth, catalyst deposition tools, in-situ characterization tools
for monitoring growth and finally different techniques used to characterize CNT and CNT composites
are introduced. A short write-up is written about each technique followed by the rationale in using
it. Wherever appropriate, details of sample preparation, experimental procedure and analysis steps
are described.
2.2 Reactor Configurations
2.2.1 CVD reactor for MWNT growth
Fig.2.1 is a schematic of the cold-wall CVD reactor used for this study. A linear translation stage
controls the distance between the two stainless steel electrodes. The grounded lower electrode serves
as a hot plate for CNT growth, embedded with a Joule heater and thermocouple, controlled by a
temperature controller (Fuji). The top electrode is maintained at a positive or negative DC bias with
respect to the grounded substrate. Pressure inside the chamber is monitored with a transducer and is
controlled by a manual valve. The precursor gases are flown into the reactor chamber from the sides.
The relative flow rates for the C precursor, ethylene, and the carrier gas, hydrogen, were controlled
by mass flow controllers (MKS Type 247). A Residual Gas Analyzer is connected downstream of
the reactor to determine the reacting gas composition. The other important accessory for the CVD
reactor is the interferometer setup used to monitor the MWNT heights in-situ.
Fig.2.2(a) shows the top electrode/reactor assembly. There are two conflat flange (NW80) ports
in the top flange. One is for the linear motion feedthrough (MDC) that controls the separation
between the top and bottom electrodes. Total linear travel is 2 inches with a least count of 0.001
21
CHAPTER 2. EXPERIMENTAL METHODS 22
motion controller
electrical feed through
to RGA
to vacuum
pump
substrate
heating stage
thermocoupletemperature
controller
MFC
+ / -
H2
C2H
4
Figure 2.1: Schematic of the reactor used to grow MWNT with an applied DC bias
inch. The other port is for an electrical feedthrough. This is used to maintain the top electrode at
a positive or negative bias with respect to the bottom electrode assembly which is grounded. The
power supply used for the electric field assisted growth studies is a Matsusada AU15R2 (voltage range
= 15kV, current = 2mA). The top electrode is electrically isolated from the rest of the chamber.
Schematic of the bottom electrode assembly is shown in Fig.2.2(b). The bottom electrode doubles
up as the hot plate for the thermal CVD reactor. The resistive heating element is NiCr (80:20) which
seats flush on grooves cut into a ceramic (Zirconia phosphate) block. A thermocouple located close
to the center of the bottom electrode is used to measure the substrate temperature. This feedback is
used to set the desired growth temperature and control temperature ramp rates. Electrical insulation
is maintained through teflon spacers.
The hot plate is approximately 2.4 inches in diameter. Jay Longson studied the uniformity
of the MWNT growth across the hot plate area. For this MWNT growths were done on 1cm2
substrates placed along the diameter of the bottom electrode, both parallel and normal to the gas
flow direction. The MWNT heights were measured using the SEM, and the normalized heights
plotted in Fig.2.3. It is observed from the plots that MWNT growth rates are faster towards the
center of the plate than towards the edges. This can be attributed to non-uniform heating of the
CHAPTER 2. EXPERIMENTAL METHODS 23
bottom electrode
thermocouple
heatingelement
reactorchamber
teflon
teflon
ceramic stagefor the heating element
top electrode
mot
ion
trans
lato
r
Cu
clam
pC
u cl
amp
ceramic rod
iso flange NW80
toelectrical feed through
(a) (b)
Figure 2.2: Schematic of the top and bottom electrode/flange assembly
substrates due to greater heat loss at the edges of the hot plate. The MWNT growth rates further
dip down towards the electrode edge closest to the entry port for the cold precursor gases into the
chamber. Comparatively uniform growth were obtained in an approximate 20mm2 area near the
center of the hot plate. All the growth results reported in this work is from MWNT growths from
substrates placed within this area.
2.2.2 Vertical flow reactor for SWNT growth
Fig. 2.4 is a schematic showing the details of the vertical flow reactor used for bulk SWNT growth.
The reactor is a 3-inch diameter 5 feet long quartz tube. It is placed in a three-zone vertical tube
furnace (Lindgerg Blue). The temperature of each of these zones can be independently controlled.
The temperature of the vertical flow reactor was maintained between 900 and 1100oC. The furnace
output runs through ∼4 feet unheated tubing to an exhaust hood, and hence the entire SWNT
production takes place at near atmospheric pressure. The exhaust runs through a bubbler filled
with water, this strips the exhaust gas off any residual carbon content. Precursor solution is made
of ethanol, the chosen carbon source, in which ferrocene is dissolved. Hydrogen is used as the carrier
gas. The precursor solution was pumped into the carrier gas using a peristaltic pump (VWR, flow
rates 0.03-2 ml/min). The precursor solution was vaporized at temperatures of 150 to 200 oC in
the delivery tube; the gaseous products were carried directly to the bottom of the furnace through
a nozzle. The temperature of the vertical flow reactor was maintained between 900 and 1100oC.
Ar was used for ramping up the reactor temperature to the desired value, and also for cooling
CHAPTER 2. EXPERIMENTAL METHODS 24
Figure 2.3: Uniformity of MWNT growth across the bottom electrode
the reactor after the growth run. The flow rates were controlled by mass flow controllers (MKS
247). The gaseous mixture is expected to be pyrolized in the first zone/bottom of the furnace with
nucleation and growth of the SWNTs in the other zones. The grown nanotubes were transported
out of the reaction zone by the flowing gases and were collected on the cooler parts of the furnace in
the form of very light, diaphanous membrane. These thin films could be easily peeled off from the
reactor walls using tweezers.
2.3 Deposition Tools
2.3.1 Sputter Deposition
Sputtering is one of the most widely-used fabrication methods for metal thin film deposition. Two
different sputtering systems were used for this work. Catalyst thin films for MWNT growth were
sputter deposited using a IBS/e system from South Bay Technologies. Substrates for MWNT growth
were prepared by sputter depositing requisite thicknesses of Fe films on top of a 10 nm Al buffer layer
on C-type Si. Most of the Pt-SWNT composites used for hydrogen storage studies were prepared
by sputter depositing Pt using the ”Kobe” chamber in the Geballe Advanced Materials lab.
For deposition of Pt on nanotube sample, the SWNTs is first dispersed in isopropyl alcohol by
ultrasound-sonication. The SWNT-alcohol solution is then spin coated on a glass substrate. The
alcohol residue is removed by outgassing at ∼ 250oC in an evacuated chamber prior to subsequent
metal deposition. The sample is loaded into the load-lock, and then is translated into the main
chamber. The load-lock is pumped out by a turbo molecular pump that is backed by a mechanical
rotary pump. The deposition chamber is pumped out by a cryogenic pump which traps molecules
CHAPTER 2. EXPERIMENTAL METHODS 25
Ar / airH
2 carrier gas
to exhaust
bubbler
vert
ical fu
rnace
precursor
solutionMFC
MFC
top flange
peristaltic
pump
bottom
flange
heating
tape
quartz
tube
inlet
tube
(1)
(2)
(3)
Figure 2.4: Vertical reactor setup for SWCNT growth.
in a sorption matrix at cryogenic temperature which is cooled by the vaporization of compressed
He gas. The metal target is negatively biased at several hundred volts against nearby surrounding
chamber which is grounded. Once the working gas is ionized, they are accelerated toward the target
with high kinetic energy. The metal atoms can then be sputtered off through momentum transfer
and deposited onto a substrate. In our sputtering system, Ar is used at pressure range between 1.5
to 5 mTorr. The deposition rate is monitored by a quartz crystal microbalance. (The deposition
rate at the substrate position is calibrated by measuring the actual thickness of the deposited film.
By comparing the thickness measured by the rate monitor and the actual film thickness, a geometric
factor(referred as to tooling factor) can be calculated.The deposited sample thickness is measured
by a low-angle symmetric Xray diffraction technique.) The thickness of the sputter deposited film
on SWNT mats is referred to as the nominal thickness (thickness of the deposited film assuming it
to be on an ideally flat surface).
2.3.2 Quartz Crystal Microbalance (QCM)
QCM is a technique often used to detect small changes in mass. This technique operates by measuring
the resonant frequency of a single quartz crystal. The resonance of the crystal varies as the mass on
CHAPTER 2. EXPERIMENTAL METHODS 26
the crystal varies. Thus, it can be used to detect very small quantities of mass change, and hence
deposition on an atomic scale. The change in resonant frequency is related to film thickness by the
following equation:
Tf =NqρqπρfZf
tan−1
[Z tan
(π(fo − f)
fo
)](2.1)
where Tf is the film thickness, ρq and ρf are the quartz crystal and film densities, f is the measured
frequency,fo is the frequency of the crystal with the film on it, and Z is a material property known
as the Z-factor. The Z-factor is given by the relation:
Z =
√ρqUqρfUf
(2.2)
where U is the shear modulus of the films. The QCM is used inside the sputterer to measure the
thickness of the thin film deposited. For MWNT catalysts a 2.5 nm Fe thin film is deposited on a
10 nm buffer layer of Al, which in turn was deposited on (110) Si wafer. For hydrogen storage in
SWNT films, Pt is sputter deposited on a thin mat of SWNT prior deposited on a suitable substrate.
For this Pt of nominal thickness in the range of 0.1nm to 1.5 nm was used. All these thicknesses
are measured using a QCM. For the Pt doped SWNT samples, tooling factors of the samples were
performed prior to the actual deposition in order to determine the sputter rates.
2.4 In-situ diagnostics
2.4.1 Laser Interferometry
Laser interferometry is a technique used to monitor changes in thickness for a thin film, and is based
on the interference of light reflected off a thin film.
The reflectance from an interface is defined as the ratio of reflected to incident energies. For
reflection from a transparent medium,
R =E2or
E2oi
= r2 =(ni cos θo − no cos θ1)2
(ni cos θo + no cos θ1)2
where r denotes the reflection amplitude coefficient or the fresnel coefficient, no and ni being the
refractive index of the ambient and the transparent medium respectively. The incident beam and the
refracted beam makes an angle θo and θ1 respectively with the surface normal. The corresponding
expression for an absorbing medium is obtained by replacing n with n+ ik, where k the imaginary
part of the refractive index is related to the absorption coefficient of the medium.
Reflection of light by a single film
To derive the expression for reflection from a single film, we consider the simplest case of a
single non-absorbing layer bounded on either side by semi-infinite non-absorbing layers, Fig. 2.5.
CHAPTER 2. EXPERIMENTAL METHODS 27
substrate (2)
film (1)
air (0)
01
2d
incident reflected
o
1 1
r1 , t1’
t1 , r1’
r2 , t2’
t2 , r2’
r1 t1r2t1’
t1r2r1’t1
t1r2 t1r22r1’
t1r22r1’t1’
t1r22r1’2
t1r23r1’2
t1r23r1’2t1’
(a) (b)
Figure 2.5: The principle of interferometry. (a) Schematic of light reflection by a single, non-absorbing layer bounded on either side by semi-infinite non-absorbing layers. The incident laserbeam reflects off the film surface and the substrate-film interface. The reflected beams interfere asdescribed in the text. (b) Fresnel coefficients for the two interfaces considered.
The notation for the amplitude coefficients are such that, the fraction of the amplitude of a wave
reflected when entering a film is r and while leaving r′. The subscript denotes the medium in which it
is reflected. A similar notation is used for the amplitude-transmission coefficients, t (Fig. 2.5(b). The
incident beam will generate a large number of multiply internally reflected rays. Each of the reflected
rays bears a fixed phase relation to all other rays. The phase difference arise from the optical path
length and from phase shifts occurring at various reflections. But the waves are mutually coherent
and if brought to focus at a point will interfere.
Apart from the first all the waves undergo an odd number of reflections within the film. As
shown in Fig. 2.5(a) the amplitudes of the reflected waves are respectively r1, t1r2t′1, t1r2
2r′1t′1 ,
t1r23r′1
2t′1 . . . Hence the total reflected amplitude at the focal point will be:
reff = r1 + t1r2t′1 exp(−2iδo) + t1r2
2r′1t′1 exp(−4iδo) + . . . (2.3)
where δo is the phase difference between adjacent reflected waves due to the optical path length
difference corresponding to a film thickness of d.
δo =2π
λn1d cos θ1 (2.4)
For a non-absorbing medium it can be shown from the conservation of energy that t1t′1 = 1 − r2
1.
CHAPTER 2. EXPERIMENTAL METHODS 28
Because of a 180o phase shift r = −r′, so that on summation eqn.(2.3) becomes:
reff =r1 + r2 exp(−2iδo)
1 + r1r2 exp(−2iδo)(2.5)
The corresponding reflectance is given by R = reff · r∗eff :
R =r21 + 2r1r2 cos(2δo) + r2
2
1 + 2r1r2 cos(2δo) + r21r
22
(2.6)
The above relation describes the oscillatory nature of the reflected intensity of the interfering beams
with a change in the thin film thickness, having a maximum of Rmax =( r1+r21+r1r2
)2
and a minimum of
Rmin =( r1−r21−r1r2 )2. The phase change resulting in this peak to trough transition is 2δo = π and from
eqn(2.4) the corresponding change in film thickness is given by:
∆dC =λ
4n1 cos(θ1)(2.7)
cos(θ1) =
√1−
[sin(θo)
n1
]2
(2.8)
where λ is the wavelength of the incident laser beam. This thickness, ∆dC , will be referred to as the
fringe thickness. Thus eqns. (5) and (2.8) can be used to estimate the thickness of a film from the
interferometer signal. By counting the number of peaks and troughs in the interferometer signal the
MWNT height and hence the growth rates can be estimated after calibrating the fringe thickness
corresponding to a given growth condition.
Interferometer set-up
Fig. 2.6 is a schematic of the interferometer setup. Side viewports allow the entry and exit of a laser
beam (630 - 680 nm), emitted from a DC power supply stabilized diode, into the chamber. The
separation between the two electrodes constrains the incident angle of the beam. The maximum
separation in between the electrodes is limited because: (i) strength of the applied electric field
decreases for an applied potential with increasing distance between plates and (ii) the top electrode
reflects heat thus helping in pyrolysis of the precursor gases. Hence, larger the separation between
plates higher is the heat loss and smaller the growth rates. For all the interferometer scans used
in the present study the distance between the electrodes were maintained at 10 mm. Given this
separation between the electrodes and their relative position with respect to the view ports a di-
rect reflection from the MWNT surface could be obtained only for almost grazing incidence. But,
beam incident at large angles to the normal (Fig.2.6(b)) limits the MWNT height resolution. The
MWNT forest height corresponding to adjacent peak and valleys in the interference pattern is given
by the eqn.2.8.The relation predicts that with increasing angle the fringe height increases, hence
CHAPTER 2. EXPERIMENTAL METHODS 29
500
400
300
200
cyc
le th
ickn
ess
(nm
)
806040200
angle (degrees)
0.8
0.7
0.6
0.5
I/Io
500400300200
cycle thickness (nm)
(a)
630 nm 680 nm
Laser Diode stabilized by DCpower supply
view
port
concavemirror
PVcell
pico-ammeter
Si substrate
catalystlayer
o
1
Figure 2.6: Schematic of the interferometer set-up, used as an in-situ diagnostic to determine theheight of the MWNT films. Fig. (a) plots the fringe thickness corresponding to the maxima andthe minima in the interferogram as a function of the incident angle. It also plots the magnitude ofbeam attenuation corresponding to the fringe thickness. (b) The reflected laser beam is made tofocus on a photovoltaic cell by a concave mirror. The intensity of the beam is tracked by measuringthe photovoltaic current using a pico-ammeter.
CHAPTER 2. EXPERIMENTAL METHODS 30
decreasing the resolution, Fig.2.6(a). Also for higher angles of incidence the beam that reflects off
the MWNT-substrate interface travels a larger distance through the MWNT forest, for the same
height of MWNT. This will result in attenuation of this beam, Fig.2.6(a), resulting in lesser number
of interference fringes, thereby restricting the maximum height that can be monitored by this tech-
nique. To overcome this difficulty the beam was made to reflect multiple times off the Si substrate
and the polished top stainless steel electrode. The beam reflects off the MWNT forest only once, as
shown in the schematic. This way the beam incident angle was reduced, increasing the measured
height resolution. The exit beam is made to reflect off a concave mirror onto a photo-voltaic cell
placed at the focal point of the mirror. The intensity of the beam reflected from the MWNT surface
is monitored by tracking the photo-induced current from the cell using a pico-ammeter (Keithley
487), in 100 µsec time intervals.
Plots in Fig. 2.7 are examples of the interferometry scans recorded during MWNT Growth. The
plots have two distinct features, attenuation of the reflected intensity accompanied by an oscillatory
character. The oscillations called the Fabry Perot fringes occur due to the interference of two beams,
as has been described in the previous section. The first beam is reflected off the top of the MWNT
film, while the second beam is reflected from the MWNT-substrate interface. The amplitude of the
fringes decay rapidly as the second beam is being absorbed during its path through the MWNT
films. The overall decay of the total reflected signal is a function of the extinction coefficient of the
MWNT films grown.
Figure 2.7: Interferometer scans recorded in-situ during MWNT growth. The first three reflectivityplots correspond to same growth conditions but different growth times. The fourth reflectivity plotis from a higher pressure growth. The rectangles on the plots show when the growth stopped. Alsoshown are SEM images of MWNT forests corresponding to three of the growth runs.
CHAPTER 2. EXPERIMENTAL METHODS 31
Reproducibility of growth and diagnostic technique
To estimate the reproducibility of growth and the reliability of the interferometer technique in mea-
suring film heights, MWNT growths were done for different time durations. The growth of the
MWNT films were halted and the chamber rapidly evacuated after the appearance of different num-
ber of fringes in successive experiments. The corresponding heights of the MWNT were determined
from SEM images. The first three scans in Fig. 2.7 were all done under the same conditions,
T=250oC, P = 265 Torr for the same mass flow rates of hydrogen and ethylene. The same ap-
proximate temporal position of the interference fringes attests to the reproducibility of the method.
The SEM heights for the growths terminated after 1 and 3 cycles are 440 and 2.6 µm respec-
tively, setting the cycle thickness to be approximately 425 nm. The fourth scan shown in Fig.2.7
was performed for same temperature and flow rates but at higher pressure of P = 400 Torr. The
growth was stopped after the appearance of 5 approximate fringes, the corresponding SEM height
measured at 4.0 µm, setting the approximate fringe thickness to 400 nm. The difference in fringe
thickness could be attributed to a change in the refractive index value for the MWNT film, possible
due to differences in the densities of the MWNT films grown at different conditions . Indeed the
cycle thickness has been found to vary by as much as ±50nm from the 425 nm value for the 750oC
growth. Therefore an universal fringe thickness cannot be attributed for all the growth runs.
Calibration and Analysis method of the Interferometer scans
Fig. 2.8 details the algorithm for analyzing the interferograms. The obtained raw interferometer scan
data is normalized by the photovoltaic current at the onset of growth. Due to decay in intensity
of the interfering beams, determining the exact position of the peaks and valleys of the scan is a
problem. To get around this problem, a procedure was developed to fit the scan with a background,
Fig. 2.8(a). This was done using a Savitzky-Golay filter. The filter does a kth order local polynomial
regression on a series of at-least ’k+1’ values to determine the smoothed value at each point. This
is widely used in analytical chemistry studies (48). The analysis range is determined by the range
where the peaks and valleys due to the interference were observed. The number of points used
for the Savitzky Golay smoothing depended upon the frequency of the interfering signal. The net
interfering signal is obtained after subtracting the fitted background from the original scan data,
and is plotted in Fig (b). The position of the peaks and valleys are obtained and knowing the
average fringe thickness for the growth, the corresponding heights and hence the growth rates of
the MWNTs were determined. This is plotted in Fig.2.8(c). As mentioned in the last section an
universal fringe thickness cannot be used for all conditions; hence the fringe thickness has to be
calibrated for each of the growth conditions studied. This is done by setting up growth parameters
such that the interference fringes were visible to the end of the growth run. In such a case the
fringe thickness was estimated by dividing the final SEM heights of the CNTs with the number of
observed cycles (i.e. assuming same approximate cycle heights for the entire run). The final height
CHAPTER 2. EXPERIMENTAL METHODS 32
1.0
0.8
0.6
0.4
0.2 N
orm
aliz
ed In
tens
ity
700600500400300200100 time(secs)
-60x10-3
-40
-20
0
20
40
60
net
Sig
nal
700600500400300200100
25
20
15
10 Gro
wth
rate
(nm
/sec
)
12x103
8
4
0
Height of M
WN
T (nm)
Growth started Growth stopped
Height of MWNT from SEM
normalized raw intensity fitted background net Signal Height of MWNT growth rates
Figure 2.8: Algorithm for analyzing the interferometer scans. In Fig.(a) an attenuating backgroundsignal is obtained from the plot, by using the Savitzky-Golay smoothing function. (b) The back-ground is subtracted from the normalized raw signal to obtain the interfering signal. The amplitudeof this signal decays with height of the MWNT. The solid lines are Beer-Lamber law . MWNTheights and the growth rates obtained from the interferometer scans are plotted in Fig. (c).
of the MWNT film, determined from SEM analysis, is also plotted in Fig.2.8. The Igor macro which
performs this entire analysis starting from the raw scan data can be found in Appendix B.
The interferometer scans can also be used to quantify the density of the MWNT films that can
be used as a metric for nanotube yield. As seen in Fig.(b) the amplitude of the net interfering signal
decays with time, due to absorption of the part of the incident beam passing through the growing
MWNT film. This beam is in the same phase at points that correspond to the peaks and valleys of
the net interfering signal. Knowing the height corresponding to these points in the interferometer
scans, the decaying intensity data can be fitted by the Lambert-Beer law: IIo = exp(−αl), where α is
the absorption coefficient and l the distance travelled by the beam through the MWNT film. This
fit is shown by solid lines in Fig.2.8(b). The absorption coefficient so obtained is dependent among
CHAPTER 2. EXPERIMENTAL METHODS 33
other factors the density of the MWNT forest. The method for extracting the density information
from the absorption coefficient will be discussed in Chapter 5.
A caveat about using the interferometer technique for determining growth rates and carbon nan-
otube heights. This technique works well for heights below 10 µm. Beyond this height range for
most cases the interference fringes cannot be detected, and hence height/growth information lost.
Thus the time resolved reflectivity method could not be used to study the decay in growth rates due
to catalyst poisoning for most growth conditions. Hence the primary focus of this study is in the
steady state growth regime, or the linear part of the sigmoidal shape of the MWNT growth plot.
Complimented by other microscopic characterization tools, e.g. time lapse photography, the inter-
ference method can be a very important tool in determining the complete kinetics of nanomaterial
growth(49).
2.4.2 Residual Gas Analyzer (RGA)
Figure 2.9: (a) Schematic of a RGA . (b) Sample mass spectrum obtained for MWNT growth; T =750oC,gas pressure= 400 Torr, H2 : C2H4 flow rates = 150:250 sccm; imposed field = .45V/µm
Residual Gas Analyzer (MKS Spectra products, microvision plus) was attached downstream of
the system to obtain mass spectra of the effluent gas. This was done to investigate the composition
CHAPTER 2. EXPERIMENTAL METHODS 34
of the reacting gas for different growth conditions, particularly as a function of the bias magnitude
of the applied electric field. Fig.2.9(a) is a schematic of the essential parts of the RGA. Electrons
emitted from hot filaments are used to ionize atoms and molecules. Ions with a specific mass-to-
charge ratio are then filtered by applying a combination of DC and RF voltages to each of the
quadra-pole. The mass filtered ions are then collected by the Faraday cup. A sample mass spectra
collected is shown in Fig2.9(b). For neutral species measurements, the acquired mass spectra must
be de-convoluted, as the resulting intensities, i, from the RGA are products of the original species’
cracking patterns (50). For a system of n species and m spectra, the following matrix must be solved
to estimate the neutral species density,D.
[im,1] = [am,n][Dn,1] (2.9)
where ai,n represents the cracking patterns for the nth species. The cracking patters are obtained
from the NIST chemistry web-book (51) and from in-house databases obtained from prior RGA
studies of nanotube and nanofiber growth conditions (50; 52). Results obtained in this way can be
compared relatively for a single species at varying conditions.
2.4.3 4 Probe Resistivity studies
v
to vacuum pump
view port
-+
CNT films
on quartz
- I + I
H2 inlet
xyz motion
control
ah
AB
(a) (b)
Figure 2.10: Schematic of the 4 probe setup
The presence of H induces a substantial component of sp3 bonding in SWNTs and as a result
the π and π∗ components to the electronic structure vanish. Hence the resistivity of the films should
change as a function of hydrogen charging time. Therefore in-situ 4-probe resistivity tests were
performed on mats of doped SWNT during hydrogen uptake. The four point probe is a versatile
technique to investigate electrical properties of materials, mostly resistivity of semiconducting thin
films. A 4 probe test is needed because it eliminates the contact resistance between the probes
and the material, and hence any change in resistance of the sample is solely due to the change in
CHAPTER 2. EXPERIMENTAL METHODS 35
resistivity of the material. Typically 4-probe resistivity measurement involves setting four, equally-
spaced point contacts down on the surface of a ”large” conductor, as shown in the Fig.2.10(b). Let a
be the probe spacing and h be the sample thickness. We assume that the sample is infinite (i.e., its
horizontal dimensions are much larger than the probe spacing). A current I is passed through the
sample via the outer two probes, and the voltage drop is measured between the inner two probes.
The high impedance of the voltmeter minimizes the current flow through the portion of the circuit
consisting of the voltmeter. Since, there is no potential drop across the contact resistance associated
with the inner probes, only the resistance associated with the material between the inner probes is
measured. For an infinitely thin specimen( h << a) like in our case of thin SWNT mats, the sample
resistivity in terms of I and ∆V , measured between the inner probes, is given by the relation:
ρ =π
ln 2h
(∆V
I
)For the two-dimensional case, the quantity ρ/h (which has units of Ohms) is called the two- dimen-
sional resistivity, sheet resistance, or resistance-per-square. In many thin film applications, one does
not know the film thickness or resistivity, only the sheet resistance.
Fig.2.10(a) is a schematic of the 4-probe set-up used for this study. The chamber can be evacuated
using a turbo pump backed by a roughing pump. All the four probes have xyz motion controls, and
an optical microscope connected to a CCD camera is used to ensure electrical contact with the
material. The only disadvantage is that the view port is not rated for positive pressures and hence
hydrogen pressure above an atmosphere cannot be used. To increase the signal to noise ratio the
4 probes are connected to an Agilent 4156B Semiconductor Parameter Analyzer via biaxial and
triaxial cables. Ports on the side can be used for gas flow into the chamber and also for electrical
feed throughs. An embedded heating element is used for temperature dependent hydrogen charging
experiments.
2.5 Ex-situ Diagnostics
Spectroscopic studies
Spectroscopy is the study of interaction of electro-magnetic waves with matter. The matter can
be atoms, molecules, atomic or molecular ions, or solids. The interaction of radiation with matter
can cause redirection of the radiation and/or transitions between the energy levels of the atoms or
molecules. There are basically 3 branches of spectroscopy:
Absorption: A transition from a lower level to a higher level with transfer of energy from the
radiation field to an absorber, atom, molecule, or solid.
Emission: A transition from a higher level to a lower level with transfer of energy from the
emitter to the radiation field. If no radiation is emitted, the transition from higher to lower energy
CHAPTER 2. EXPERIMENTAL METHODS 36
levels is called non radiative decay.
Scattering: Redirection of light due to its interaction with matter. Scattering might or might
not occur with a transfer of energy, i.e., the scattered radiation might or might not have a slightly
different wavelength compared to the light incident on the sample.
In this work four different spectroscopic techniques were used: Raman spectroscopy , UV-Vis-
NIR spectroscopy, X-Ray Absorption spectroscopy and Auger Electron Spectroscopy. Raman and
absorption spectroscopy characterizations complimented each other as these techniques were used
to study respectively the vibration and electronic transitions of SWNT, giving information about
SWNT diameter and chirality. Surface compositional analysis were done using X-ray and Auger
electron spectroscopy. The former was used to study the extent of sp3 bond formation in nanotubes,
while the later was chosen because of its high spatial resolution to obtain compositional maps of
catalyst nanoparticles.
2.5.1 Raman spectroscopy
Raman spectroscopy is used to study vibrational, rotational, and other low-frequency modes in a
system. It relies on inelastic scattering, or Raman scattering, of monochromatic light, usually from
a laser in the visible, near infrared, or near ultraviolet range. The laser light interacts with phonons
or other excitations in the system, resulting in the energy of the laser photons being shifted up
(Anti-Stokes) or down (Stokes). The shift in energy gives information about the phonon modes in
the system. Typically, a sample is illuminated with a laser beam. Light from the illuminated spot
is collected with a lens and sent through a monochromator. Wavelengths close to the laser line,
due to elastic Rayleigh scattering, are filtered out while the rest of the collected light is dispersed
onto a detector. A Renishaw NIR 780TF spectrometer with three lasers, Ar ion (514nm), HeNe(633
nm) and NIR (785nm) was used for this study, and only the Stokes signal was recorded. Raman
spectrum was obtained in the reflection mode, most often from CNTs dispersed onto a Si wafer.
RayleighScattering
StokesRamanScattering
Anti- StokesRamanScattering
virtualenergy states
vibrationalenergy states
CHAPTER 2. EXPERIMENTAL METHODS 37
Raman spectroscopy has proved to be a very powerful tool for characterizing nanotubes, SWNTs
in particular(53). The unique optical and spectroscopic properties observed in SWNTs are largely
due to the presence of van Hove singularities (vHSs) in the nanotube electronic and phonon DOS.
Whenever the energy of incident photons matches a vHS in the DOS of the valence and conduction
bands (subject to selection rules for optical transitions), one expects to find resonant enhancement.
There are two resonant conditions for optical transitions: (1) incidence resonance (resonance with
the incident light) EL = ∆E and (2) scattered resonance (resonance with the scattered photon)EL =
∆E + ~ω, where EL is the incident energy of the laser light, ∆E energy separation between two
electronic states and ω the frequency of the scattered phonon. The resonantly enhanced Raman
scattering intensity allows one to obtain detailed information about the vibrational properties of
nanotubes, even at the isolated individual SWNT level. Fig.2.11 is a representative Raman spectrum
of a SWNT. The most important features, namely the G-band, the D-band and the radial breathing
modes are tagged in the plot. Following subsections describes in some detail how these features can be
used to extensively characterize SWNT samples, revealing information about diameter distribution,
optical transition energies, chirality, metallic or semiconducting nature of the SWNTs, quality/purity
of the SWNTs etc.
1.0
0.8
0.6
0.4
0.2
0.0
Nor
mal
ized
inte
nsity
300250200150
wavenumber (cm-1)
1.0
0.8
0.6
0.4
0.2
0.0160014001200
RBMs
D-band
G-Band
Figure 2.11: Raman spectrum obtained from a HiPCO sample, with 785 nm laser
The G-band
The G band arises due to a first-order (implying that the lattice relaxes by emitting one phonon)
1-phonon emission Raman scattering event. The G-band involves an optical phonon mode between
the two dissimilar carbon atoms A and B in the graphite unit cell. In contrast to the graphite
Raman G band, which exhibits one single Lorentzian peak at 1582 cm−1 related to the tangential
mode vibrations of the C atoms, the SWNT G-band is composed of several peaks due to the phonon
wave vector confinement along the SWNT circumferential direction and due to symmetry-breaking
CHAPTER 2. EXPERIMENTAL METHODS 38
effects associated with SWNT curvature. The G-band frequency and lineshape can be used for (1)
diameter characterization, (2) to distinguish between metallic and semiconducting SWNTs, through
strong differences in their Raman lineshapes (53).
Fig2.12 indicates that the G-band feature for SWNTs consists of two main components, one
at 1590 cm−1 (G+) and the other peaked at about 1570cm−1 (G-). The G+ feature is associated
with carbon atom vibrations along the nanotube axis (Longitudinal Optical phonon mode) and its
frequency ωG+ is sensitive to charge transfer from dopant additions to SWNTs (up-shifts in ωG+ for
acceptors, and downshifts for donors ). The G- feature, in contrast, is associated with vibrations of
carbon atoms along the circumferential direction of the SWNT (Transverse Optical phonon), and
its line-shape is highly sensitive to whether the SWNT is metallic (BreitWignerFano line-shape) or
semiconducting (Lorentzian line-shape), as shown in Fig2.12. The BWF signal appears only when
the electronic density of states at the Fermi energy has a finite value. Thus we observe a BWF
line-shape only in metallic SWNTs, but not in semiconducting SWNTs or in graphite.
The frequency ωG+ is essentially independent of dt or chiral angle θ, while ωG− is dependent on
dt and whether the SWNT is metallic or semiconducting, but not on chiral angle θ:
ωG− = 1591− C/d2t (2.10)
where C for semiconducting and metallic SWNTs have values of 47.7 cm−1nm2 and 79.5cm−1nm2
respectively. Such diameter-dependent measurements can be used to corroborate (n, m) assignments
carried out on the basis of the RBM feature (as will be shown in Chapter 6). From the diameter
dependence for the G band modes shown in eqn.(2.10), it is clear that the G band for large diameter
carbon nanotubes is similar to the one peak G-band observed in graphite. This is actually the case
for the G band for large diameter MWNTs, where a single peak at 1582 cm−1 is observed,Fig2.12 ,
just like in graphite.
The D-band
Defect induced D mode in graphite/CNTs is assigned to a double-resonance Raman effect in sp2
carbon (54). Double resonance is similar to resonant Raman,but here in addition to the incoming or
outgoing resonances the elementary excitation makes a real transition. Double resonances are much
stronger than single resonances. The intensity of the D band is known to be inversely related to
crystallite size, and disappears for perfect crystals. Although, the contribution of defects in the tube
walls to the D band is still not completely understood, the intensity ratio of the D-band vis-a-vis the
intensity of the G-band has been found to be a good metric in determining the quality/purity of the
SWNT. From Fig2.12 it can be seen that the D-band is much more intense for MWNT than SWNT
implying that MWNT structure is more defective. The D-band appears at 1350 cm−1, though its
position has a strong dependence on the excitation energy (note the difference in position of the D
CHAPTER 2. EXPERIMENTAL METHODS 39
1.0
0.8
0.6
0.4
0.2
0.0
Nor
mal
ized
Inte
nsity
160014001200
wavenumber (cm-1)
160014001200 160014001200
metallic SWNT semiconducting SWNT
MWNT
! !
!
!
G+G+
G-
G-
D D
D
G
Figure 2.12: Comparison of the line-shape of the G-band for a metallic, semiconducting SWNT andthat of a MWNT. The Raman spectrum of the SWNTs were obtained from the same sample, butwith different laser energies (514 nm for the metallic and 785 for the semiconducting). This showsthe importance of using different wavelengths to fully characterize a given sample. The MWNTspectrum was obtained with a 514 nm laser. Also shown in the plots are the D-bands
band for the SWNTs excited with different laser wavelengths in Fig2.12).
Radial Breathing Modes (RBMs) in SWNTs
For SWNTs along with the G-band, the lower frequency radial breathing mode (RBM) are usually
the strongest features in SWNT Raman spectra. Both are first-order Raman modes. The RBM
is a unique phonon mode, appearing only in carbon nanotubes and its observation in the Raman
spectrum provides direct evidence that a sample contains SWNTs. The RBM is a bond-stretching
out-of-plane phonon mode for which all the carbon atoms move coherently in the radial direction,
as if the tube were breathing. They occur with frequencies ωRBM between about 100-300 cm−1.
These RBM frequencies are used for characterizing the nanotube diameter distribution in the
sample by the use of the relation ωRBM = A/dt +B, where the parameters A and B are experimen-
tally determined (53). The dependence A/dt comes form the fact that the mass of all the C atoms
along the circumferential direction is proportional to the diameter. The parameter B accounts for
tube-tube and tube-substrate interactions. For typical SWNT bundles on native Si-oxide surface in
the diameter range 1 < dt < 2nm, A = 234cm−1nm and B = 10cm−1 has been found. For isolated
SWNTs on an oxidized Si substrate, A = 248 −1nm and B = 0. However, for dt < 1 nm, the simple
ωRBM = A/dt + B relation is not expected to hold exactly, due to nanotube lattice distortions
leading to a chirality dependence of ωRBM . For large diameter SWNTs (dt > 2 nm), the intensity
of the RBM feature is weak and is hardly observable.Therefore, from the ωRBM measurement of
a RBM, it is possible to obtain the corresponding dt value. The RBM spectra for SWNT bundles
CHAPTER 2. EXPERIMENTAL METHODS 40
contain an RBM contribution from different SWNTs in resonance with the excitation laser line. For
a diameter characterization of the sample, analysis of the resonance condition should also be per-
formed. A single Raman measurement gives an idea of the SWNTs that are in resonance with that
laser line, but does not give a complete characterization of the diameter distribution of the sample.
However, by taking Raman spectra using many laser lines, a good characterization of the diameter
distribution in the sample can be obtained. Since semiconducting and metallic SWNTs of similar
diameters do not occur at similar Eii values, ωRBM measurements using several laser energies can
be used to characterize the ratio of metallic to semiconducting SWNTs in a given sample.
Figure 2.13: Assigning (n,m) to SWNTs from RBM signals. (b) Kataura plot, charting the experi-mental optical transition as a function of SWNT diameter. (a) RBM signal obtained from HiPCOnanotubes with 785 nm laser excitation. From a comparison of the resonant energy and the diameterof the tube (obtained from the RBM frequency) the chirality of the SWNT can be determined. Asan example, two of the RBMs observed in the sample spectrum are assigned chiralities (9,4) and(10,5). These SWNTs belong respectively to the chiral family, ”2n+m” , 22 and 25 respectively.
Next, knowing the dt values obtained from the measurements of ωRBM , and Eii ∼ EL from the
resonance condition, the RBM features can be used for making (n,m) assignments for SWNTs by
utilizing the Kataura plot, described in Chapter 1. As mentioned before, Kataura plots are experi-
mental graphs of optical transition energies vs nanotube diameter and hence act as a map to identify
CHAPTER 2. EXPERIMENTAL METHODS 41
the chiralities of the SWNT in a given sample. Simplest theoretical tight-binding treatments predict
that the optical transition energies of semi-conducting and metallic nanotubes depend linearly on
the diameter according to the relations(5; 55):
S11 =2aC−Cγo
dt
S22 =4aC−Cγo
dt
M11 =6aC−Cγo
dt
Such simplistic theoretical calculations neglect interactions between distant neighbors, the diam-
eter and chirality dependence of the curvature effects on transition energies, the interaction between
the SWNTs and the surfactant/solution used to disperse/ debundle the SWNTs etc. The net result
being a considerable discrepancies between the theoretical predicted value and the experimental ob-
servations. Hence rigorous studies have been made to come up with empirical relations that account
for these deviations and provide a reasonable fit between experimentally determined transition en-
ergies and the RBM frequencies(generally expressed as wavenumbers)(56; 7; 57; 6). Fig2.13(b) is a
Kataura plot that charts the empirical transition energies obtained from the work of Jorio et al(6).
as a function of wavenumber (ωRBM = A/dt + B; A and B for our data set had the best fit for A
= 230.78 cm−1nm and B = 7.14 cm−1).
One other factor that has to be considered when determining the chirality is the effect of bundling
of SWNTs. For bundled SWNTs, the spectral features are red shifted by 50-70 nm with the mag-
nitude of the shift depending on the extent of bundling and inter-nanotube contact area(58). Also,
due to the broadening of the electronic transitions the individual RBM spectrum is less resolved.
One important note is that the bundling effect has almost no effect on the frequency of the phonon
modes. Therefore the dotted blue line, blue shifted from the original position of the NIR laser by
50 nm, with no change to the wavenumber axis, will be a more appropriate representation of the
effective laser energy for bundled SWNT. Similarly the red dotted line accounts for the shift for the
HeNe laser,Fig2.13(b).
Hence knowing the frequency of the phonon modes (and therefore the diameter of the SWNTs)
and the incident laser energies; (n,m) assignments can be made to the SWNTs present in a sample
after accounting for the red shift due to bundling,Fig2.13 .
2.5.2 UV-Vis-NIR absorption spectroscopy
Absorption spectroscopy refers to spectroscopic techniques that measure the absorption of radiation,
as a function wavelength, due to its interaction with a sample. A material’s absorption spectrum
is the fraction of incident radiation absorbed by the material over a range of frequencies. The
transmitted energy can be used to calculate the absorption.The most common arrangement is to
CHAPTER 2. EXPERIMENTAL METHODS 42
direct a generated beam of radiation at a sample and detect the intensity of the radiation that
passes through it. Radiation is more likely to be absorbed at frequencies that match the energy
difference between two quantum mechanical states of the molecules, and hence are like fingerprints
for the molecule in consideration. Therefore absorption spectroscopy is employed as an analytical
chemistry tool to determine the presence of a particular substance in a sample. The absorption
frequencies also depend on the interactions between molecules in the sample, the crystal structure
and hence symmetry(in solids) and on several environmental factors (e.g., temperature, pressure,
electromagnetic field). Absorption spectroscopy can also be used to measure the concentration of
an analyte by measuring the absorbance at some wavelength and applying the Beer-Lambert Law.
Absorption spectroscopy is performed across the electromagnetic spectrum. The UV-Vis-NIR
spectral range for the Lambda 950 (Perkin Elmer) used is 190 to 3300 nm.The light source is a
deuterium discharge lamp for UV measurements and a tungsten-halogen lamp for visible and NIR
measurements. The instruments automatically swap lamps when scanning between the UV and
visible regions. The wavelengths of these continuous light sources are dispersed by a holographic
grating. UV-Vis-NIR spectrometers utilize a combination of a Photo multiplier tube and a Peltier-
cooled PbS IR detector. The light beam is redirected automatically to the appropriate detector
when scanning between the visible and NIR regions.
For absorption analysis, dimethyl- formamide (DMF) was chosen as the solvent of interest since
it does not have absorption peaks in the same region as the SWNTs. Samples were prepared by
dissolving 0.1 mg of the sample in 10 ml of DMF and sonication for 15 min.
Figure 2.14: Absorption spectrum obtained for HiPCO SWNTs. Marked in the plot are absorptionlines corresponding to S11, S22 and M11 transitions
CHAPTER 2. EXPERIMENTAL METHODS 43
2.5.3 X-ray Photoelectron spectroscopy (XPS)
XPS (or ESCA, Electron spectroscopy for chemical analysis) is very useful for determining the
elemental composition on the surface (depths of 1-10 nm) of all non-volatile materials. It is a
quantitative spectroscopic technique that measures the elemental composition, empirical formula,
chemical state and electronic state of the elements that exist within a material. When the energy is
transferred from an X-ray photon to a core-level electron of an atom, the electron can be emitted.
The kinetic energy and the number of ejected photoelectrons is measured. Knowing the wavelength
of the incident X-rays and the kinetic energy of the emitted photoelectron the binding energy can
be retrieved from the equation:
Ebinding = Ephoton − (EK.E. + φ)
φ being the workfunction that needs to be calibrated with a known standard. XPS measurement is
surface sensitive since only the atoms near the surface lose their electrons without energy loss. But,
it can be used to provide elemental composition as a function of depth by analyzing a sample while
removing surface layers by ion etching. It is sensitive to all elements except H . The experiments
were carried out at the elliptical undulator Beam line 13-2 in SSRL, in the UHV end station. The
detector used was Scienta R3000 which has a kinetic energy resolution of 200meV. XPS was used
to quantify the extent of hydrogen uptake in the Pt-SWNT composite samples. This was done by
looking for spectral changes of the C1s peak before and after hydrogenation. The photon energy
used to probe the C1s peak was 400eV, while the overview scan was done at 700eV photon energy.
Nanotube samples are usually prepared on silicon substrates to avoid electron charging problems.
Fig.2.15 shows a XPS spectrum obtained before and after sputter deposition of Pt on a SWNT film.
The Pt 4f peak is used for calibration of the workfunction.
Figure 2.15: (a) Emission of a photoelectron.(b) A sample XPS spectrum
CHAPTER 2. EXPERIMENTAL METHODS 44
2.5.4 Auger Electron Spectroscopy (AES)
Auger electron spectroscopy (AES) has emerged as one of the most widely used analytical techniques
for obtaining the chemical composition of solid surfaces. It uses a primary electron beam (energies
in the range of 2 keV to 50 keV) to probe the surface of a solid material. Secondary electrons that
are emitted as a result of the Auger process are analyzed and their kinetic energy is determined.
The identity and quantity of the elements are determined from the kinetic energy and intensity of
the Auger peaks. The basic advantages of this technique are its high sensitivity for chemical analysis
in the 5- to 50-A region near the surface, a rapid data acquisition speed, its ability to detect all
elements above helium, and its capability of high-spatial resolution. The high-spatial resolution is
achieved because the specimen is excited by an electron beam that can be focused into a fine probe.
The spectroscope used for the study is a PHI 700 Scanning Auger Nanoprobe that provides down to
6nm secondary electron image resolution and 8nm Auger resolution with high elemental sensitivity.
Figure 2.16: (a) Schematic of the Auger process. (b) Auger spectrum of micelle patterned ironcatalyst particles on a Si substrate
The Auger process can be understood by considering the ionization process of an isolated atom
CHAPTER 2. EXPERIMENTAL METHODS 45
under electron bombardment. The incident electron with sufficient primary energy, Ep, ionizes the
core level, such as a K level. The vacancy thus produced is immediately filled by another electron
from L1. This process is shown in Fig.2.16. The energy (EK − EL1) released from this transition
can be transferred to another electron, as in the L2 level. This electron is ejected from the atom as
an Auger electron. The Auger electron will have energy given by
E = EK − EL1− EL2
and the excitation process is denoted as a KL1L2 Auger transition. The essential parts of an AES
therefore are an electron gun, electron energy analyzer and an electron detector. A typical Auger
electron spectrometer collects the data in the N(E) versus E integral mode. The data are then
mathematically differentiated using computer software to yield E dN(E)dE versus E Auger spectra.
For this work AES was used to characterize the iron catalyst nano particles, prepared form sputter
deposited thin films and also from block co-polymer templates. Depth profiling of the sputtered
catalyst thin films before and after annealing at different conditions were used to investigate the
amount of mixing between layers which has important consequences in the evolution of the catalyst
particle sizes.
2.5.5 Electron Microscopy
Scanning electron microscopy (SEM) was extensively used to characterize the nanotubes.The instru-
ment is an FEI XL30 Sirion SEM with FEG source and EDX detector. In conjunction with Raman
spectroscopy it was used as an initial diagnostic tool to characterize the quality and morphology
of the CNTs grown. It was used to determine the final heights of the MWNT films grown, which
complimented the interferometry scans to give growth rates. Image analysis of cross-sectional SEM
images of MWNT films and individual CNTs were used to quantify the alignment of the CNTs with
and without an applied electric field. SEM was also used to characterize the size distribution and
particle separation of the catalyst particles used for MWNT growths. Finally SEM was also used to
characterize the different types of Pt-doped SWNT films used for hydrogen uptake studies.
Transmission electron microscopy (TEM) was used for visual characterization of various carbon
nanotubes, carbon nanofibers and CNT-metal composites. Philips CM 20 TEM and FEI Tecnai
G2 F20 X-TWIN were used, both of which operated at a 200 kV accelerating voltage. Typically
the nanotube samples were dispersed in ultrasound-sonicated isopropyl alcohol solution, and then
coated on lacey- carbon supported Cu TEM grids for observation. High resolution (HRTEM) images
are typically taken at a magnification between 100 and 300k for nanotubes and composite samples.
A bright field imaging mode is operated by taking the transmitted beam through the objective
aperture and is useful for these samples since high contrast between carbon nanotubes and metals
CHAPTER 2. EXPERIMENTAL METHODS 46
is observed at relatively low magnification. For diffraction experiments, conventional and micro-
diffraction techniques are utilized. Conventional diffraction mode illuminates the parallel electron
beam (defocused C2 lens for small beam divergence) on a sample while micro-diffraction uses a
highly focused incident beam (focused C2 lens with large C2 aperture). By focusing the electron
beam on a sample, diffraction information from a small area of interest (typically beam diameter is
10-12 nm) can be retrieved.
2.5.6 Thermogravimetric Analyzer (TGA)
TGA, as the name implies, is a characterization technique that determines the change in weight
in relation to change in temperature. The analyzer consists of a high precision balance with an
alumina pan loaded with the sample. The pan is placed in a small electrically heated oven with
a thermocouple to measure the temperature. In some cases, there is a sheath of inert gas, Ar in
general, to prevent undesired reactions like oxidation of the sample. Analysis is carried out by
ramping the temperature, while recording the corresponding change in weight. The instrument used
is a Pyris1 TGA (Perkin Elmer).
The impurity content in a carbon nanotube sample can be measured using a TGA. Impurity
content is generally of two types: catalyst metal nanoparticles and amorphous carbon/soot that is
formed along with the nanotubes. The nanotube samples were loaded in ambient air. Since the
measurements are performed in a gas ambient, buoyancy effects become critical. To counter this,
sample weights taken for the measurements is 2-5 mg that is sufficient to obtain an accuracy of
around 0.5%. The typical operating temperatures range from 50 - 1000oC, with a ramp rate of
10oC/min for all the experiments. By subtracting the residual mass from the initial mass the metal
content of the samples can be calculated. The catalyst used for SWNT/MWNT growth for all the
studies were Fe nanoparticles. Fe oxidizes in the temperature range 200-400oC, hence the residue
after the TGA scan is Fe2O3. This has to be kept in mind while doing the relevant calculations.
Chapter 3
Kinetics of Multi-walled Carbon
Nanotube growth
3.1 Introduction
In this chapter we report the kinetics of carbon nanotube growth studied in the context of the
CVD process. A generic model for growth of 1-D nanostructures via the Vapor-Liquid-Solid (VLS)
mechanism is developed. Growth rates of MWNTs are determined using a time-resolved reflectivity
technique and are interpreted vis a vis the proposed model.
Growth of 1D nanomaterials via the CVD route has been well established. Initially it was in the
form of whiskers and platelets both inorganic (59; 60) and organic (carbon filaments) (61; 62; 63).
This field received further interest with the advent of carbon nanotubes and inorganic nanowires.
The VLS process, first proposed by Wagner et.al (59), is conventionally assumed to be the most
important growth mode for nanowires. In this model material from the vapor is incorporated
into a growing 1D structure via a liquid catalyst. Seminal work has been done to establish the
fundamental aspects of this mechanism (60) and to understand variations to this basic mechanism
(64). The carbon nanotube/nanofiber community in general also proscribe to the VLS mechanism
(63). Changes to this model have been suggested for growth conditions where the catalyst is in a
solid state at lower growth temperatures and/or larger catalyst particle dimensions (62). While there
has been general agreement about the approximate growth mechanism, the rate limiting step that
controls the growth rate of the CNT has been found to vary widely. Surface diffusion (65) and bulk
diffusion (61; 62; 66; 67) of carbon, the chemistry at the vapor-catalyst interface (68; 69; 70), the
diffusion of carbon on the nanotube surface(71), thermal decomposition of the gaseous precursors
(72), or a combination of two or more of these processes (71; 73) have been identified as the rate
limiting step. This is mostly because of the very wide range of parameter space studied: growth
47
CHAPTER 3. KINETICS OF MWNT GROWTH 48
conditions, catalyst combinations, choice of carbon precursors etc. Various mechanisms have been
proposed, mostly related to possible reaction steps at the catalyst interface, in an attempt to describe
the different morphologies of the CNTs and also to establish the occurrence of one rate limiting step
over another. This has led to the absence of a generic model to quantify the nanotube growth as one
particular mechanism for a given condition does not necessarily extrapolate to some other growth
condition. The basic idea behind the development of the model was the realization that the carbon
flux from the vapor to the CNT is driven by the favorable energetics of the entire process, a drop in
chemical potential of carbon. Hence instead of delving into the specifics of each mass transfer step,
the steady state carbon flux is described in terms of the chemical potential change for each step.
Equally interesting are the various methods that have been used to experimentally study the
kinetics of the CNT growth process. The absence of a robust characterization technique has also
contributed to the lack of understanding of growth mechanism. SEM observation of CNT heights
at different growth intervals (66), growth mark method (68) by interrupting the growth at different
time intervals are some of the post-situ techniques. These suffer from the disadvantage of inter-
rupted growth, reproducibility of the exact same growth conditions and finally, the number of data
points and hence the height resolution achievable. In-situ diagnostics employed include controlled
environment electron microscopy (67; 1) and field-emission microscopy (74; 75) during CNT growth.
These techniques are limited by the very low pressures involved. In situ time-lapse photography (49)
has been used, but suffers from height resolution problems particularly during the initial stages of
growth. Puretzky et al. (76) developed time resolved reflectivity (interferometry) as a tool to mon-
itor the MWNT height. This is a simple but at the same time very powerful technique, particularly
at smaller length scales, to monitor MWNT growth and has been adopted as the diagnostic of choice
for this study. The details of the thermal CVD reactor for MWNT growth and the interferometer
set-up have been described in detail in Chapter 2.
The layout of this chapter is such that details of preparation and characterization of the catalysts
used for growing MWNT films is described first. Next the kinetic model for MWNT growth is
described and in the final section experimental results are analyzed/compared in context of the
growth model.
3.2 Catalyst for growth of MWNT films
Catalysts for the growth of dense MWNT films were prepared by sputter depositing Fe film of the
required thickness on top of a 10 nm Al buffer layer on C-type Si. For all the growths in this
chapter the thickness of the sputtered Fe film is 2.5 nm. Next the deposited films were annealed
in an hydrogen atmosphere for 10 minutes. On annealing the Fe thin film balls up and results in
the formation of catalyst nanoparticles. Hydrogen ambient reduces the Fe-oxides formed during
transfer of the substrates from the sputterer to the growth reactor. The temperature is maintained
CHAPTER 3. KINETICS OF MWNT GROWTH 49
approximately at 550oC for the duration of the anneal. The hydrogen annealing pressure along with
the thickness of the sputtered Fe film are important in controlling the catalyst particle size. These
dependencies will be discussed in detail in Chapter 4.
Fig.3.1(b) is a representative SEM image of the catalyst particles obtained from annealing the
sputtered thin films. Particle density and size distribution analyses were done using Image J(77)
. Fig 3.1(c) is a histogram of particle sizes. The mean diameter of particles formed from the
continuous Fe film is 6.5 nm.The particle density was obtained by measuring the distance between
centers of two adjacent particles; the mean separation was estimated to be 25.2 nm. The chemical
composition of the catalyst particles obtained from annealing the sputtered films was studied using
Auger spectroscopy. Survey scans show the presence of oxygen, carbon, iron and aluminum. Carbon
is mostly from contamination of the substrate and the spectrometer chamber.
Fe
Al
Si
Fe-Al
Fe
6055504540
wt%
0.50.40.30.20.10.0 distance(µm)
6055504540
wt%
6055504540
wt%
6055504540
wt%
linescan 1
linescan 2
linescan 3
linescan 4
Al Fe
14
12
10
8
6
4
2
0
per
cent
age
20181614121086420
particle size (nm)
(a)
(b)
(c)
(d)
1 2
34
200 nm
Figure 3.1: Characterization of the catalyst particles obtained by annealing sputtered Fe films ona buffer layer of Al. (a) Cartoon of the process. (b) SEM image of the catalyst particles after theannealing step. (c) Catalyst particle size distribution (d) Line scan of the substrate using an Augerprobe.
Oxygen is possibly from oxides formed by iron and aluminum. The relative abundances of the Fe
(654eV) versus Fe (705eV) in the survey scans indicates formation of Fe-oxide (formed possibly post
CHAPTER 3. KINETICS OF MWNT GROWTH 50
annealing during sample transfer). Iron oxides do not catalyze carbon nanotube growth, hence care
was taken not to expose the catalyst particles after the annealing step. Compositional analysis of the
particles as opposed to the substrate reveal a larger oxygen content in the substrate implying most
of the oxygen comes from the Al. Fig 3.1(d) are line-scans obtained using the Auger probe. They
expectedly reveal an abundance of iron in the catalyst particle and that of Al in the substrate. The
presence of a significant amount of Al in the particles are probably due to significant background
noise arising from resolution limits of the Auger probe.
3.2.1 Importance of the Al buffer layer
The importance of the Al layer for MWNT growths can be observed in Fig.3.2. Figs (a,b) are
SEM images of sparse MWNT growth obtained from catalyst layers without Al (5 nm of Fe on
Si). Growth temperatures were 750oC and 800oC respectively. On introduction of the buffer Al
layer (2.5 nm Fe on 10 nm Al on Si) there was a dramatic increase in MWNT yield. Except from
the catalyst layers, the growth conditions were the same. It has been reported that a buffer layer
between the catalyst and substrate considerably affects the CNT growth. The buffer layer may act
as a diffusion barrier between Si and catalyst metal to prevent forming metal silicide deteriorating
catalytic activity (78; 79). Al or Al oxide is generally used as a buffer layer for the growth of SWNTs.
Delzeit at al.(80) and Zhang et al.(81) reported that Al film enhanced the formation of CNTs. Al
oxide was reported to be more efficient sub-layer for CNT growth than Al. It was proposed that Al
oxide formed during the heating prior to the CNT growth acted as a diffusion barrier preventing the
mixing of the catalyst with Si.
Auger depth profiles of as-sputtered substrates with and without the Al buffer layer is shown
in Fig.3.3. The sputter deposited Fe layers for the two cases have different thicknesses, and hence
the differences in time to etch away the Fe layer. The elemental atom fraction obtained from the
depth profile matches the composition of the different metal layers deposited. There is very little
intermixing between the layers, which is expected because the substrates were not annealed. The
interesting part is the variation of the atomic percentages of oxygen in the as-deposited layers. For
Fe sputtered directly on Si, oxygen can be seen at the Fe/Si interface due to the presence of a native
oxide layer on Si (which was not removed prior to deposition). Some amount of oxygen was present
on the Fe surface as this layer was exposed to air during transfer of the substrates. The absence
of oxygen in the bulk Fe evidences that the oxygen uptake was not during the sputter deposition
process. Interestingly this surface oxide is absent for the Fe/Al/Si substrate. The oxide layer might
have been etched away during the steps prior to Auger depth profiling. The oxygen concentration
varies with the Al composition, implying the presence of an Al-oxide. The reported at% of O is more
than that of Al only at the Al/Si interface, which as mentioned before, has to do with the native
Si-oxide. The Al-oxide formed during the sputter deposition process owing to the large affinity of Al
for oxygen. This Al-oxide layer sandwiched between the Fe and Si is responsible for the increased
CHAPTER 3. KINETICS OF MWNT GROWTH 51
(a)
(b)
(c)
(d)
500 nm
500 nm
500 nm
2 m T = 750oC
T = 750oC
T = 750oC
T = 800oC
Figure 3.2: Comparison of MWNT growths with and without the Al buffer layer
MWNT yield.
In-stiu reflectivity monitoring of substrate during the pre-MWNT growth step
The goal of the pretreatment procedure is to convert a catalyst film to nanoparticles for carbon
nanotube growth. Fig.3.4 shows the time evolution of the substrate temperature (hollow circles) and
the reflected light intensity (solid lines) during pretreatment step. For this study, the temperature
was ramped in a hydrogen ambient (P=100 Torr, flow rate =100 sccm), the annealing temperature
was 550oC and a hold time 10 minutes. Subsequent to the annealing step, the temperature was
ramped to 750oC, the set MWNT growth temperature. The reflectivity of two surfaces are shown
here, 10 nm Al/Si and 2.5nm Fe/ 10 nm Al/Si. The reflectivity of a bare Si film does not change
much in the temperature range studied, so all changes in the reflectivity plot should be due to the
deposited films. For Al/Si the reflectivity of the substrate remains approximately the same to 640oC,
subsequent to which there is a drastic reduction in reflectivity. This is due to the melting of the
residual Al in the film (Al, melting point = 660oC). In contrast, for the Fe/Al/Si the reflectivity
of the film starts dropping at 200oC, with a sharp drop in reflectivity around 550oC. This sharp
drop is probably due to surface roughening, coincident with the formation of catalyst particles. On
increasing the temperature, after the annealing step, the reflectivity starts increasing. It reaches a
plateau on holding the substrate temperature at the set MWNT growth temperature,corresponding
to ∼ 95% of the initial intensity. The interferometer scans for the MWNT growth were obtained
CHAPTER 3. KINETICS OF MWNT GROWTH 52
Fe
Si
Fe
Al
Si
100
80
60
40
20
0
at%
86420 sputter time (secs)
86420 sputter time (secs)
13nm Fe/ Si
5nm Fe/10nm Al/Si
C O Al Si Fe
Figure 3.3: Auger depth profile of as-sputtered films with and without the Al buffer layer. Thenominal thickness of Fe directly deposited on the Si substrate was 13nm, while 5nm of Fe wasdeposited on 10 nm Al, sputter deposited on Si
only after the reflectivity attained a steady value.
3.3 MWNT growth
Subsequent to the annealing step, the temperature is ramped up to the desired growth temperature.
After letting the temperature stabilize, the precursor gases, a mixture of ethylene and hydrogen,
were flown into the reactor at predetermined rates, and the interferograms recorded. Typical MWNT
growth durations were 10 minutes. The parameter space for MWNT growth is broad, an example of
catalyst composition was cited above. In the next chapter we report the dependencies of particle size
(determined by catalyst film thicknesses and annealing pressures) in determining the morphology
of the 1-D carbon nano structures. In this chapter we report the effects of temperature, pressure
and precursor chemical composition on MWNT growth rates and how well they can be predicted by
using the model developed. The MWNTs grown were characterized by SEM, TEM and Raman spec-
troscopy. Details of growth conditions will be described when discussing the results of a particular
set of experiments.
CHAPTER 3. KINETICS OF MWNT GROWTH 53
Figure 3.4: Time resolved reflectivity plots off the catalyst substrate during the pre-MWNT growthregime. Also plotted are the corresponding chamber temperatures.
3.4 Kinetic Model for MWNT growth
A simple kinetic model has been developed to quantify the synthesis of 1D nanomaterials (82).
The model developed here relies on that work. For this work we assume that the Fe catalyst
nanoparticle is in a liquid state under the MWNT growth conditions. This is a valid assumption
given the catalyst particle size and the corresponding suppression of the Fe-C eutectic temperature,
from Gibbs-Thompson effect. In general, these calculations are done taking into consideration only
the vapor-catalyst interfacial energy. The presence of a second interface between the catalyst and
the substrate is expected to further suppress the melting point, since the interfacial energy of a liquid
catalyst-solid substrate is lower. For the given size of catalyst particles, the vapor liquid solid (VLS)
process, discussed here, is the dominant mechanism for most 1-D materials. Carbon is obtained by
the thermal decomposition of ethylene. The Fe particles get saturated with carbon by reaction with
the vapor phase, and on supersaturation the extra carbon precipitates in the form of CNTs.
3.4.1 Mass Transport processes
Akin to (60) we consider four mass transport processes,Fig.3.5(a). First, the vapor phase transport
of molecules to the catalyst surface. Next is the vapor-liquid catalyst interaction, decomposition
reaction of gaseous molecules at the catalyst surface followed by transport of the carbon atoms
across the vapor-liquid interface. The next process is the liquid phase transport of C atoms across
the liquid catalyst nanoparticle. The final step is the incorporation of the C atoms into the growing
CHAPTER 3. KINETICS OF MWNT GROWTH 54
MWNT across the catalyst-tube interface. Such mass transfer steps have been considered for almost
all models describing 1D nanomaterial growth process. The novelty of this model over previous
models is instead of looking into the mechanism of each transfer process we consider the energetics
involved. Each step requires a thermodynamic diving force, in the form of a gradient in chemical
potential along a phase or a drop in the chemical potential across an interface (Fig.3.5 b). The mass
flux in each of the transfer processes is described in terms of these chemical potential changes. A
steady state is assumed, i.e. there is no accumulation of C atoms in any of the steps. This implies
the flux in each step is the same and the overall flux is determined by the slowest mass transfer step,
the ”rate limiting step”.
Figure 3.5: (a) Schematic of the four mass transfer processes. Figure (b) is a schematic of thechemical potential drop that results in the carbon flux from the vapor phase across the vapor-liquidinterface, through the liquid catalyst and finally across the liquid-solid interface to form the MWNT.
Diffusive Transport
Vapor Phase Transport
The first step is the vapor phase diffusion of the C containing precursor molecules to the catalyst
surface. The steady state condition in spherical co-ordinates is given by the relation:
∂2CVc
∂r2+
2
r
∂CVc
∂r= 0
CHAPTER 3. KINETICS OF MWNT GROWTH 55
where, CVc (r) is the concentration of the C-containing gas in the vapor phase. The boundary
conditions for the above equation are CVc (rp) = CV Lc ;CVc (∞) = CV∞c , where CV∞c and CVL
c are the
concentrations of the gas in the bulk and at the vapor-catalyst interface respectively. On solving,
the variation in C concentration as a function of distance from the catalyst particle (radius = rp) is
obtained:
CVc (r) = CV∞
c − [CV∞c − CVL
c ]rp
r(3.1)
The diffusive flux in the vapor phase is given by the relation
|JV| = Dv∂CV
c
∂r‖r=rp (3.2)
On substituting (3.1) above, and converting the concentration of the gas at the bulk and the interface
to their corresponding chemical potentials, µV∞c and µVL
c the vapor phase flux can be calculated.
JV =DvCV∞
c
RT[µV∞
c − µVLc
rNT] (3.3)
The catalyst particle size controls the outer diameter of the MWNT (83), and for simplicity it is
assumed, here, that the radius of the MWNT, rNT , is same as that of the catalyst particle, rp.
Liquid phase Diffusion
Diffusive flux of C through the liquid catalyst particle was similarly obtained. For simplicity,
the catalyst particle was assigned a cylindrical shape. Because of this simplification 1D diffusion of
carbon species through the catalyst can be assumed. For a steady state 1D transport,
JL = DLCLV
c − CLSc
rNT(3.4)
where CLVc and CLS
c are respectively the C concentrations at the liquid catalyst-vapor and catalyst-
MWNT interfaces. The relation, µ = µo+RT ln(γx) is used to relate the liquid state flux in eqn.( 3.4)
to a chemical potential change.
JL =DLCL
c
RT[µLS
c − µLVc
rNT] (3.5)
Interfacial Transport
Transport across the Vapor-Liquid Catalyst interface
The composition at the vapor-liquid interface is different from the equilibrium composition. The
corresponding drop in chemical potential is the driving force for transport of carbon across the
interface. The net flux across the interface, hence will depend on the magnitude of deviation of the
interface composition from the equilibrium. This simplistic model is valid only for small magnitude
of driving forces. The flux across the interface will also depend upon the net interface attachment
CHAPTER 3. KINETICS OF MWNT GROWTH 56
rate,RN,L, and the number of available sites on the liquid catalyst surface,σL.
JVL = RN,LσL(t) =kVL
RT[µVL
c − µLVc ] (3.6)
The first order reaction actually includes three processes, the attachment of the molecule to the
liquid surface, molecular dissociation and or reaction at the catalyst interface and finally the carbon
incorporation into the liquid surface. The reaction constant, kVL, is given by the relation:
kVL = σL(t)ν exp(−4G∗,VL
kBT) (3.7)
Here 4G∗,V Land ν are respectively the effective activation energy for all the vapor-liquid transfer
processes and the frequency of successful collisions of the gas molecules with the catalyst surface.
The number of available sites on the liquid catalyst particle has a temporal dependence as will be
shown in a later section dealing with catalyst activation and poisoning.
Transport across Liquid-Solid interface
Similar to the transport across the vapor-liquid interface, the driving force across the liquid
catalyst-solid CNT interface is driven by the drop in chemical potential of carbon from the liquid
catalyst to the solid nanotube.
JLS = RN,SσS =kLS
RT[µLS
c − µSc ]
kLS = σSν∗ exp(−4G∗,LS
kBT)
The stable carbon phase, under the growth conditions is graphite. But the carbon is precipitating
out in the form of nanotubes. Hence it is necessary to find the chemical potential of carbon in the
MWNTs. This can be done by adding to the chemical potential of graphite the energy required to
bend the planes into CNTs (63). The total elastic energy stored per unit length in a MWNT, of
inner radius rin and outer radius rNT , formed by bending of graphite planes is given by:
Ebend =πEa2
o
12ln(
rNT
rin) (3.8)
where E is the Young’s modulus of MWNT and ao the inter-planar spacing in graphite. Also
from Gibbs Thompson effect, for a given MWNT-vapor interfacial energy, γSV, the curvature of the
MWNTs results in a chemical potential increment by
4µ =γsv
CSc (rNT − rin)
(3.9)
where CSc is the concentration of C in the MWNT. Accounting for (3.8) and (3.9) the flux across
CHAPTER 3. KINETICS OF MWNT GROWTH 57
the liquid-solid interface is given by the relationship:
JLS =kLS
RT[µLS
c − [µSc,graphite +
1
CSc
(Ea2
o
12(r2NT − r2
in)ln(
rNT
rin) +
γsv
rNT − rin)]] (3.10)
3.4.2 Steady State growth rate
As mentioned before a steady state condition is assumed. Hence solving for the four flux equations
and eliminating the intermediate chemical potentials,the carbon flux from the vapor to the nanotube
is determined to be:
JVS =[µV∞
c − [µSc,graph + 1
CSc(
Ea2o
12(r2NT−r2in)ln( rNT
rin) + γsv
rNT−rin)]]
RT[ 1kVL
+ 1kLS
+ rNT
DvCV∞c
+ rNT
DLCLc
](3.11)
The corresponding steady state growth rate for the MWNT can be obtained by dividing the carbon
flux with the concentration of carbon in the MWNT.
vss =JVS
CSc
(3.12)
3.4.3 Thermodynamic Driving force for MWNT growth
The driving force for growth of the MWNT, is given by the relation ∆µ = µV∞c − (µS
c,graph +1
CSc(
Ea2o
12(r2NT−r2in)ln( rNT
rin))), as obtained from eqn.(3.11). Therefore to estimate the driving force for
growth of the nanotube the chemical potential for C in the precursor gas (ethylene was used for this
study) has to be determined. A way of doing so is to assume that gaseous C atom is in equilibrium
with ethylene vapor and then estimate the corresponding chemical potential of C. This can be
calculated from the following set of chemical reactions:
(1) C2H4(g)↔ 2C(s) + 2H2(g); ∆G1 = ∆Go1 + RT ln[
(aSC)2(pH2
)2
pC2H4
]
(2) 2C(s)↔ 2C(g); ∆G2 = ∆Go2 + RT ln[
p2C
(aSC)2
]
(3) C2H4(g)↔ 2C(g) + 2H2(g); ∆G3 = ∆Go3 + RT ln[
(pC)2(pH2)2
pC2H4
] (3.13)
The chemical potential of C in the vapor phase, in equilibrium with ethylene, is given by the relation:
µV∞C = µoV
C + RT ln(pC), where µoVC is the chemical potential of pure C vapor at 1 atmosphere, and
pC is the effective partial pressure of C corresponding to the chemical potential µV∞c . To calculate
this pressure we assume that the reaction (3) is in chemical equilibrium. Hence ∆G3 = 0, and we
CHAPTER 3. KINETICS OF MWNT GROWTH 58
get from eqn.(3.13),the partial pressure of C in the vapor phase:
p2C = [
pC2H4
(pH2)2
] exp
(−∆Go
3
RT
)It is also known that ∆Go
3 = ∆Go1 + ∆Go
2 = ∆Go1 + 2(µoV
c − µoSC ) and the stable solid C phase is
graphite, and hence
µV∞c − µo,S
c,graph = −1
2∆Go
1 +RT
2ln[
pC2H4
(pH2)2]
Replacing the partial pressures of ethylene and hydrogen by their molar fractions and the absolute
pressure,P, the total thermodynamic driving force for the MWNT formation , ∆µ = µV∞c −µS
c,MWNT,
equals
∆µ = −1
2∆Go
1 +RT
2ln[
xC2H4
(xH2)2]− lnP − 1
CSc
[Ea2
o
12(r2NT − r2
in)ln(
rNT
rin)
](3.14)
This driving force drives all the kinetic processes, vapor phase diffusion, vapor-liquid transport,
liquid phase diffusion and the final transport across the liquid-solid interface to form the MWNTs.
Eqn.(3.14) also reveals the parameters that can be used to control this driving force. The main
contenders are temperature, absolute pressure, the composition of the gas phase which in turn is
determined by the flow rates and also the radius of the catalyst particle since studies have shown a
relation between radius of MWNTs and catalyst particle sizes. Formation of MWNT also creates a
vapor-MWNT interface. Hence the energy to form this interface, eqn.(3.9), has to be subtracted from
the total thermodynamic driving force to get the net driving force for the reaction. A thermodynamic
length scale thus can be defined which formulates the balance between driving force and interfacial
energy cost.
rTh =γsv
CSc ∆µ(1− rin
rNT)
(3.15)
The magnitude of this length scale vis-a -vis the radius of the tube determines whether conditions
are favorable for MWNT growth. If the two length scales are the same, the net C flux from vapor
to MWNT is zero. If the radius of the tube is greater than rTh then the nanotube grows, while if
its smaller then the interface cost for growing the CNTs is too high and the MWNTs will not form.
3.4.4 Rate Limiting Steps
The steady state assumption of the kinetic MWNT growth model implies constant flux across the
four mass transfer steps. Hence the flux of the MWNT growth process will be controlled by the
slowest step or the rate limiting step. This rate limiting process can be either one or both of the
transport steps across the two interfaces, vapor-liquid and liquid-solid. On the other hand, diffusive
transport of the C atoms or the C bearing molecules across the vapor or/and liquid phases could
also control the growth rate of the MWNT. A kinetic length scale, rKin, can be defined as a balance
between the diffusive and interfacial kinetic processes;rKin = <DCc><k> . The effective diffusion term
CHAPTER 3. KINETICS OF MWNT GROWTH 59
vapor - liquid interface limited
liquid - solid interface limited
vapor
CNT/solid
liquid
(a)
µcVµcVL
µcLVµcLS
µcS
µcV
µcV
µcLV
µcLV
µcVL
µcVL
µcLS
µcS
µcSµcLS
limited vapor phase diffusion
limited liquid phase diffusion
vapor
CNT/solid
liquid
(b)µcV µcVL
µcLV µcLS µcS
µcV
µcV
µcVL
µcVL
µcLV
µcLV
µcS
µcS
µcLS
µcLS
Figure 3.6: The rate limiting steps for the MWNT synthesis process. The driving force for theMWNT growth approximately equals the chemical potential drop across the rate-limiting step.Fig.(a) is a schematic of the chemical potential drop for interface-limited growth, with the twolimiting cases vapor-liquid interface and liquid-solid interface shown. Fig.(b) is a schematic of thediffusion limited MWNT growth processes, limited liquid and vapor phase diffusivities respectively.The dotted line is a schematic of the chemical potential change for a growth condition where therate limiting step is a combination of the diffusive and interface transport processes.
,< DCc >, and the effective interface reaction term,< k >, being defined as
< DCc >= [1
DvCV∞c
+1
DvCLc
]−1
< k >= [1
kVL+
1
kLS]−1
The overall flux for the MWNT growth process, eqn.(3.11), then can be re-formulated in terms of
the rKin and rTh as
JVS = (∆µ
RT) < kCc > (
1− rTh
rNT
1 + rNT
rKin
) = (∆µ
RT) < DCc > (
1− rTh
rNT
rNT + rKin) (3.16)
If the growth process is interface limited, rKin >> rNT; opposite is the case for diffusion limited
growth. Schematic of the chemical potential distribution for all the four possible cases are shown
in Fig. 3.6. For diffusion limited growth (Fig. 3.6(b)) the driving force is used up to drive diffusion
across the relevant phase. For interface limited transport Fig. (a) the driving force for the growth
is used up mostly to account for the chemical potential drop across the corresponding interface. A
case in point is the transfer of C across the vapor-liquid interface. In this case the driving force is
used up to drive transport across the vapor-liquid interface. Hence the chemical potential of the
vapor-liquid interface will approximately be equal to the potential in the vapor phase, while the
CHAPTER 3. KINETICS OF MWNT GROWTH 60
potential of C at the liquid-vapor interface approximates that of the MWNT (lower left Fig. 3.6(a)).
3.4.5 Catalyst Activation and Poisoning
Figure 3.7: Keeping count; (a) available attachment sites on the catalyst surface, (b)the numberof catalyst particles initiating MWNT growth in the time interval dt. The mean time for catalystactivation is τn, while the mean time for catalyst poisoning is τp. No and Ng are respectively thetotal number of particles and number of catalyst particles that have resulted in MWNT growth attime ’t’
As mentioned while describing the interferometer set-up that the main focus of this article is in
modeling the steady state condition because of lack of experimental data on catalyst activation and
poisoning. But, for the sake of completeness in terms of a kinetic model formulating MWNT growth,
we include here the evolution of the average height of the MWNT films. The fitting parameters
for formulating the average length of the MWNT film are the steady state velocity, vss, that is
experimentally determinable, and the mean lifetimes of catalyst activation and poisoning. We assume
a mean lifetime for catalyst poisoning to be τp, where τp = τp,o exp(Ep/RT), Ep being the activation
energy for the poisoning process.
dσa = −σadt
τp(3.17)
∴ σa = σoexp[−t/τp] (3.18)
where σa is the number of available binding site on the catalyst particle at time ’t’, that initially
CHAPTER 3. KINETICS OF MWNT GROWTH 61
had σo binding sites. If all the catalyst particles were growing at the same time then, the average
catalyst activity will be the same as that of (3.18). But all catalyst particles are not activated at the
same time. Assuming mean lifetime for catalyst activation to be τn (again,τn = τn,o exp[En/RT], En
being the energy barrier for the catalyst activation process) the following relation is obtained.
dNg = [No −Ng]dt
τn(3.19)
where Ng is the number of catalyst particles growing CNTs at time t and No the total number
of catalyst particles. Solving for the above differential equation, knowing the boundary conditions
Ng(0) = 0,Ng(t) = Ng; results in
Ng(t) = No(1− exp[−t/τn])
The average number of binding sites available per catalyst then is given byNgσa
Nowhich equals
σL,avg(t) = σoexp[−t/τp](1− exp[−t/τn]) (3.20)
This value when substituted in eqn.(3.7) controls the flux of C atoms across the vapor-catalyst
interface, and hence is important in determining the growth rate of the MWNT. At intermediate
growth times τn < t < τp the MWNT growth rate is the steady state growth rate, while during
the incubation period it is influenced by the catalyst activation mechanism and at longer timescales
the rates are determined by the catalyst poisoning processes. As a first approximation the average
length increment of the MWNT forest in the time interval ’dt’ will be given by the relation
dLMWNT =vssσa,avg(t)dt
σo.
∴ LMWNT(t) =
∫ t
0
vssσa,avgdt
σo
= vssτp[1− exp[−t/τp] +τn
τn + τpexp[−t(
1
τn+
1
τp)]− 1] (3.21)
3.5 Results and Validation of the Kinetic Model
In this section interferometer scans obtained are presented and the data evaluated in terms of the
growth model developed in the previous section. Three sets of data will be discussed. The first
set is a temperature dependent growth of MWNT at intermediate pressures. For this set of data,
growth rates are determined, the corresponding activation energy and hence the rate limiting step
identified. The second set of data is from pressure dependent growth runs, and the final set of data
is again temperature dependent growth runs performed at atmospheric pressures. Results obtained
CHAPTER 3. KINETICS OF MWNT GROWTH 62
Figure 3.8: SEM images of the MWNT forests obtained after the completion of growth runs in eachof the above cases. These heights, marked by rectangles are plotted in Fig.3.9(c). A tilted sampleholder was used for the SEM imaging, with the angle of the tilt being 45o. Thus to obtain the actualheight of the CNTs corrections were made to compensate for the tilt angle.
from the first two data sets are then used along with the kinetic model to predict the results for the
third dataset, in an attempt to test the accuracy of the developed model.
3.5.1 Temperature dependent MWNT growth at P=265 Torr
For this set of experiments, the absolute pressure of the reactor chamber was maintained at 265
Torr. The growth temperature was increased in increments of 25oC from 700oC to 800oC. The mass
flow rates of hydrogen and ethylene were maintained at 110 sccm and 155 sccm respectively, during
the entire growth duration. Typical growth times are 600 seconds except for the 700oC sample, for
which the growth duration was 900 seconds. This was done to compensate for the low growth rates
observed at this temperature and obtain enough number of interfering fringes in the time resolved
reflectivity scans. The final heights of the MWNTs formed were measured using SEM and are shown
in Fig.3.8. Increasing growth temperatures result in the formation of straighter, taller and denser
MWNTs.
The corresponding interferograms are shown in Fig.3.9(a). At lower temperatures the curves
show pronounced oscillations in intensity. With increasing temperatures the oscillation frequency
of the reflectivity plots increase significantly, alluding to faster growth rates. At the same time the
amplitude of the oscillations decrease and the fringes become less discernible. The intensity of the
background signal also increases with temperature.
The background intensity is attributed to the laser beam reflected off the top of the CNT film,
while the oscillations are a result of the interference of this beam and the beam reflected off the
CHAPTER 3. KINETICS OF MWNT GROWTH 63
1.0
0.8
0.6
0.4
0.2
Nor
mal
ized
Inte
nsity
700600500400300200100 Time(secs)
Growth started
Growth stopped
(a) 700oC 725oC 750oC 775oC 800oC
30x103
25
20
15
10
5
0
Hei
ght o
f MW
NT
(nm
)
10008006004002000 Growth time(secs)
growth stopped
growth stoppedT=700 oC
(b) 700oC 725oC 750oC 775oC 800oC
70
60
50
40
30
20
10
0
Gro
wth
rate
s (n
m/s
ec)
6004002000 Growth time(secs)
(c)
700oC 725oC 750oC 775oC 800oC
Figure 3.9: Normalized interferometer scans for temperature dependent growth of MWNTs at pres-sures of 265 Torr, Fig (a). The heights obtained from the interference fringes are plotted in Fig(b), while Figure (c) plots the growth rates of the MWNTs. The solid dark lines in (c) mark thelinear regime for MWNT growth, corresponding to the steady state growth conditions, described inthe kinetic model. The corresponding growth rates from Fig (c) are used in the article for analy-sis/validation of the growth model.
CHAPTER 3. KINETICS OF MWNT GROWTH 64
interface between the MWNT and the substrate. Reflectance of a beam incident normal to the
surface is given by the relation:
R =(1− n)2 + k2
(1 + n)2 + k2= 1− 4n
(1 + n)2 + k2
where n,k are the real and imaginary parts of the refractive index of the reflecting surface. Increase
in density of the MWNT films, increases the n and k thereby increasing the reflectivity of the top
surface and hence the background intensity. At the same time density of the CNTs attenuates
the intensity of the beam reflected off the MWNT-substrate interface in accordance with the Beer-
Lambert law. These twin effects of increasing density of the MWNT films explain the decrease in
prominence of the interference fringes.
Fig. 3.9 (b) plots the MWNT heights obtained from the interference plots as a function of growth
time. As mentioned above, SEM images of the final heights were recorded from the same region of
the MWNT film that was probed by the laser beam for the interferometer curves. These heights
marked by rectangles are plotted in the figure also. Knowing the heights, the next step was to plot
the experimental growth rates, Fig. 3.9 (c). For the 700oC case, the maximum growth rate achieved
was 5.2 nm/sec obtained after approximately 350 seconds of growth. Increasing the temperature
to 725oC increases the growth rate to a maximum of 14 nm/sec achieved after a growth time of
approximate 280 seconds. Increasing temperatures further increased the growth rates, with growth
rates of 60nm/sec reported at 800oC, i.e. more than an order of magnitude increase from that
reported for 700oC. The observed growth rates in this study are relatively lower compared to those
reported in the literature. The reason for this is attributed to the cold-wall CVD reactor used
in contrast to those used in other studies. The other interesting feature observed was that with
increasing temperatures, the time required to reach steady state rates decreased. The linear, steady
state regime of the MWNT growth described by the model are marked by solid straight lines in
the in-situ MWNT height vs. growth time plot. The corresponding steady state growth rates from
Fig.(b) are used to determine the activation barrier for the rate limiting step.
The kinetic model developed in the last section describes four different mass transfer steps, each
characterized by either a diffusivity term or a rate constant. Both of these terms are generally as-
sociated with an Arrhenius type equation, described by a pre-factor, and an exponential term that
contains the activation energy for that process. Given the relatively small temperature range of the
current study, the activation barrier is approximately constant. Hence the motivation for the temper-
ature dependent experiments was to determine the activation barrier related to the MWNT growth
process and therefore identify the rate limiting step. The steady state growth rates determined
from the reflectivity plots are used for this purpose. The MWNT radius used for the calculations
has an outer radius of 5.8 nm. This is the same as the mean catalyst particle size, obtained under
the given growth conditions (84). The inner diameter of the MWNT was determined by solving
CHAPTER 3. KINETICS OF MWNT GROWTH 65
5.5
5.0
4.5
4.0
3.5
3.0
ln(vRT/∆µ)
1.02x10-31.000.980.960.94
1/T (K-1)
y = -23261x + 23.538linear fit
(a)
35x103
30
25
20
15
10
5
0
MW
NT
heig
ht (n
m)
10008006004002000 time(secs)
growth stoppedT = 700 oC
growth stopped(b) Experimental 700oC Experimental 725oC Experimental 750oC Experimental 775oC Experimental 800oC
fit 700oC fit 725oC fit 750oC fit 775oC fit 800oC
Figure 3.10: Fig. (a) is an Arrhenius plot of the temperature dependent thermal CVD growth ofMWNT in the temperature range 700-800oC. The activation barrier obtained from the linear fit is∼190 kJ/mol. Fig. (b) is a plot of the experimental interferometer heights and the correspondingtheoretical fits of the growth model. The fitting parameters being the experimental growth rates,and the mean lifetime for catalyst activation and poisoning.
for maxima condition of the change in chemical potential driving the formation of MWNT for a
given outer radius (63), which for an outer radius of 5.8 nm was 3.93 nm. The interfacial energy
γsv assumed is 0.077J/m2 (85) , and the Young’s modulus 1 TPa (86). The molar concentration
of C in the CNTs was obtained by the relation CMWNTc = Cgraphitec (1 − rin
2
rNT2 ), with Cgraphitec
assumed to be 1.8 × 105mole/m3 (87). The absolute pressure,P, for this set of experiments was
265 Torr and the molar fraction of the hydrogen and ethylene at the steady state growth condition
was approximated to be equal to their molar volume flow rate fractions. The remaining term to be
evaluated is the standard free energy of decomposition of ethylene at the growth temperature. This
can be obtained from the standard free energy of formation of ethylene from graphite and hydrogen
at the growth temperature. The thermochemistry data needed for this calculation, e.g. the standard
heats of formation of ethylene, and the constant pressure heat capacities, was obtained from the
CHAPTER 3. KINETICS OF MWNT GROWTH 66
NIST chemistry webbook (51). The experimental steady state growth rates were then normalized
by the calculated ′∆µ/RT′ from the model. Fig.3.10(a) is a logarithmic plot of these normalized
growth rates as a function of ’1/T’. The Arrhenius plot so obtained is approximately linear, giving
an activation barrier for the MWNT growth process of 192 kJ/mol under these conditions.
Table 1. contains a list of activation energy barriers reported in literature for the CNT growth
process. Diffusion limited processes have activation barriers typically in the range of 35 - 140 kJ/mol
and hence cannot be the rate limiting step. C diffusivity in liquid Fe is of the order of 10−5cm2/sec
, which leads to a growth rates in the order of mm/sec for T = 750oC , hence this cannot be the
rate limiting step. For catalyst in the solid state typical C diffusivities are 10−8cm2/sec giving
approximate growth rates of 100 µ/min , which is still much higher than the observed growth rates
here. Hence the MWNT growth process in this case has to be interface limited. The specifics of
which interface is limiting the growth is not uniquely identified, since the first order reaction rate
assumed for the C jump across the interfaces comprises of more than one reaction step. References in
Table 1 assign Ea values in the proximity range of 190 kJ/mol to the vapor-liquid interface processes.
Fig. 3.10(b) is a plot of the experimental heights determined from the interferometer studies
and the corresponding theoretical fits as predicted by (eqn.3.21) The fitting parameters being the
average experimental steady state growth rate and the mean life time for catalyst activation and
poisoning. The activation barriers obtained from an Arrhenius plot of the fitting parameters used
for the temperature dependent growth runs, τn and τp , were respectively 180 kJ/mol and 205
kJ/mol. The mean life time for the activation and poisoning for the T=750oC run used for fitting
the data is 2100 seconds and 115 seconds. The activation barriers obtained are remarkably close
to that reported in (76). They identify C dissolution(Ea = 210 kJ/mol) as the catalyst activation
step. The activation barriers for the poisoning of the catalyst particles by gas-phase decomposition
products(Ea = 260 kJ/mol) is also fairly close to that obtained from the catalyst poisoning mean
lifetime parameter values.
1.0
0.8
0.6
0.4
0.2
Inte
nsity
500400300200100Time(secs)
0.35
0.30
0.25
0.20
Intensity
1600140012001000Time(secs)
300
200
100
0 Pre
ssur
e(To
rr)
start growth
stop growth stop growth
restart growth
Figure 3.11: Time evolution of pressure and reflectivity during the interrupted growth experiment.
CHAPTER 3. KINETICS OF MWNT GROWTH 67
There is a finite time lag between the the onset of ethylene flow and the growth conditions
reaching a steady state in terms of pressure etc. set for a particular growth. This time lag and
not a catalyst activation could explain the incubation regime of CNT growth before the steady
state growth rates are achieved. To evaluate the validity of this hypothesis, an interrupted MWNT
growth experiment was performed, Fig.3.11. MWNT growth was stopped by evacuating the chamber
and cooling down the substrate. After waiting for 5 minutes the reactor temperature was ramped
back up to the 750oC, same as before interruption. On introduction of ethylene, growth resumed
instantaneously. This is in contrast to a time lag at the onset of growth (as observed in longer
time interval for the first interference fringe to appear). This proves that initial incubation period is
related to the mean life time of some activation process and is not due to growth conditions reaching
a steady state. Since the catalyst was already activated, on resumption of ethylene flow the MWNT
films started growing instantaneously.
(On a side note, while talking about numbers it has to be mentioned that the contribution of the
interfacial energy term to the net thermodynamic driving force is small. The ’rTh’ value calculated
for the given condition is only 0.04 nm, implying that under these conditions the MWNT will always
grow).
3.5.2 Pressure dependent growth runs at T = 750oC
Prior experiments have suggested the dependence of MWNT growth morphology and growth rates
on the absolute pressure. In separate studies, a transition from MWNT to carbon nanofibers has
been observed with increasing pressure (this is discussed in details in Chapter 4). This transition was
a function of the pressure and also of the catalyst particle size. The thermodynamic driving force for
the nanotubes described also suggests a pressure dependence. This set of experiments were therefore
designed to explore the pressure dependence of MWNT growth from catalyst particles obtained by
annealing 2.5nm Fe/10nm Al/ Si sample. For this set of experiments the growth temperature was
held at 750oC. The growth pressures used were 151 Torr, 265 Torr, 315 Torr, 405 Torr and 760 Torr.
The total gas flow during the experiment was maintained at 250 sccm, with the H2/(C2H4 + H2)
flow varied from 0.3, 0.4, 0.4, 0.5 and 0.6 respectively.
Fig.3.12(a) plots the normalized intensity curves recorded for the pressure dependent runs. The
frequency of oscillations increase with an increase in pressure. Unlike the temperature dependent
growths, the amplitude of oscillations and the background reflectivity are almost the same, implying
similar densities of the growing MWNT films. The signal attenuates much faster at higher pressures
and reaches the constant value faster. For the top four plots, interference fringes could be detected
untill the end of the 10 minute growth scan. In contrast for the P = 760 Torr run, the temporal
frequency first increases, reaches a constant value, then decreases and finally disappear. This implies
termination of growth for the high pressure condition. The growth rates obtained from the interfer-
ograms are plotted in Fig. (b). For the P=760 Torr case, the critical height was approximated by
CHAPTER 3. KINETICS OF MWNT GROWTH 68
Figure 3.12: Pressure dependent growth of MWNT at T=750oC. Fig. (a) plots normalized intensityas obtained from the photovoltaic currents. Increasing pressure increases the growth rate of theMWNT as is evident from (a) and plotted in (b). Fig. (b) also shows that higher the pressureshorter is the time to reach steady state values. The catalyst poisoning mean lifetime is also shorterat higher pressures. (c) SEM images of the MWNT revealing their final heights at pressures of 151,405 and 760 Torr respectively.
dividing the final SEM height of the CNTs by the number of fringes observed in the scan before the
fringes disappeared from the reflectivity plot. The average steady state growth rates increase from
an average of 20 nm/sec at P = 151 Torr to 35 nm/sec at P = 760 Torr. The growth rates reach
their steady state value faster with increasing pressure, 300 seconds for the P = 151 Torr growth as
opposed to 100 seconds for growth at atmospheric pressures. This implies a decrease in the mean
lifetime for catalyst activation. The P = 760 Torr growth also shows a decay in growth rates after
reaching a steady state. This possibly implies a decrease in mean lifetime of the catalyst poisoning
as a function of pressure. The final heights of the MWNT films grown were obtained from their
SEM images(e.g. Fig.3.12(c) ) and plotted along with the experimental heights from the reflectivity
curves in Fig.3.12(b). The SEM images show that the MWNT film height increases initially with
CHAPTER 3. KINETICS OF MWNT GROWTH 69
absolute pressure and then decreases, consistent with increased growth rate and poisoning at high
pressures.
The net driving force for the MWNT reaction actually decreases with increasing pressure,
eqn.(3.14), Fig.3.13(a). But the experimental results show an opposite trend, the steady state
growth rates increasing with pressure. To reconcile these two contrasting results, we note that the
pre-exponential factor for the rate constant for the vapor-liquid interface has an attempted frequency
term, ν. The collision frequency of gas molecules is given by the relation ν =< vavg > / < λmfp >,
where < vavg >= 8kBTπm
1/2is the average velocity of the gas molecules and < λmfp >= kBT√
2πd2P is
the mean free path for the gas molecules for an absolute pressure ,P. Taking into account that the
number of successful attempts should be proportional to the number of ethylene molecules colliding
with the catalyst, the attempt frequency should be of the form, ν = νoxC2H4P . Hence the steady
state growth rates for the conditions studied, that takes into account temperature, pressure and
compositional changes in the gas will be of the form :
vss ≈ (∆µ
RT)< k∗V L >
CScxC2H4
P (3.22)
Hence knowing the steady state growth rate for one condition, the growth rate for the other
conditions can be predicted. Taking the growth rate for P=265 Torr, T= 750oC case to be the
fitting parameter, the steady state growth rates for the remaining MWNT growth runs in the
pressure dependent set was predicted. This was done after accounting for the pressure induced
changes to the MWNT inner and outer radius. This theoretical fit is plotted as a solid line in
Fig.3.13(a). For comparison the experimental growth rates from the time resolved reflectivity plots
are also included. The remarkable proximity of the two plots attest to the validity of the growth
model. Hence with an increase of pressure the steady state growth rate increase but at a decreasing
rate.
Finally equation (3.21) was used to obtain theoretical fits for the height of the CNTs as deter-
mined from the interferograms and SEM imaging . The fitting parameters, similar to the temperature
dependent growth, being the experimental growth rates, and the catalyst activation and poisoning
mean lifetimes, τn and τp. τn values used for the fit ranged from a high of 270 seconds for the P =
151 Torr case, decreased to 50 sec for P = 405 Torr run, and bottomed out at 11 seconds for the P
= 760 Torr study. Similarly the mean lifetimes for the catalyst poisoning used for the fit decreased
from a high of 4500 seconds for the P = 151 Torr, to a low of 430 seconds for the P =760 Torr case.
From the temperature dependent growth studies we know both the catalyst activation and poison-
ing steps are related to the vapor-catalyst interface. Hence the corresponding rate constants for
activation and poisoning will have a similar dependence on pressure as that of the rate constant for
the mass transfer across the interface. Further studies are required to establish the functional form
of dependence of pressure on these mean lifetimes. Therefore to summarize, increasing pressures
increase the maximum attainable growth rates, but at the same time terminates growth faster, due
CHAPTER 3. KINETICS OF MWNT GROWTH 70
35
30
25
20
gro
wth
rate
s(nm
/sec
)
1.00.80.60.40.2 Pressure(atm)
68x103
64
60
56 ∆ µ
(J/m
ole)
0.40
0.35
0.30
0.25
0.20
0.15
xP (atm)
(a)
20x103
15
10
5
0
Hei
ght o
f tub
e (n
m)
10008006004002000 growth time (secs)
growth stopped
(b) Experimental 151 Torr Experimental 265 Torr Experimental 315 Torr Experimental 405 Torr Experimental 760 Torr
fit 151 Torr fit 265 Torr fit 315 Torr fit 405 Torr fit 760 Torr
Figure 3.13: Fig. (a) plots the experimental growth rates ’o’ and the predicted growth rates (solidline) for the pressure dependent growths. The growth rates were predicted by extrapolating theaverage experimental growth rate at P=265 Torr after accounting for the changes in pressure andgas composition. Increasing pressures decrease the driving force for MWNT growth, but results inenhanced kinetics accounting for the increased growth rates. Fig. (b) plots the experimental andtheoretical fits for the MWNT heights. With increase in pressure the height of the MWNT filmsfirst increase and then decrease.
CHAPTER 3. KINETICS OF MWNT GROWTH 71
to the simultaneous faster kinetics of catalyst poisoning. Hence with increasing pressures MWNT
heights first increase and then decrease beyond a threshold pressure.
While discussing the temperature dependent growth runs, mass transfer at the interface was
identified as the rate limiting step. But which of the two interfaces (vapor-catalyst or the catalyst-
CNT) that limits growth was not identified. From analysis of the catalyst deactivation it was
established that soot formation on the catalyst particles is the poisoning process. From the pressure
dependent studies, increase in collision frequency of the C precursor gas with the catalyst was found
to be responsible for the enhanced kinetics. Both of these processes are related to the vapor-liquid
interface and hence we can attribute the vapor-catalyst interface to be the rate limiting step for the
growth conditions studied.
3.5.3 Temperature dependent MWNT growth at P=760 Torr
The final set of experiments described here were performed at atmospheric pressures, the temperature
being varied from 700oC to 775oC in increments of 25oC, while the mass flow rates were kept constant
at 150 sccm for hydrogen and 100 sccm for ethylene. The corresponding time resolved reflectivity
plots are shown in Fig.3.14(a). Similar to the temperature dependent study at lower pressures, we
see that the temporal frequency of the fringes increase with temperature, but at the same time they
become less prominent. The scans are similar to the pressure dependent plots, in the sense that the
growth rates are higher, but also at the same time the height of the MWNT gets saturated much
faster, leading to the disappearance of fringes towards the end of the growth run.
Next the growth rates were predicted using eqn.(3.22) with the experimental steady state growth
rate for P = 265 Torr and T = 750oC condition as the fitting parameter. The pressure dependance
was mainly accounted for by the xC2H4P term in the expression, while the temperature dependence
was accounted for by the Arrhenius dependence of the interface transport constant, k, (activation
barrier = 192kJ/mole).The predicted growth rate also takes into account the changes in total driving
force, chemical composition of the gas, the absolute pressures, and the MWNT inner and outer radii.
It also discounts for the temperature change of the growth conditions, via the the activation energy
term, Ea, in the exponential part of the interferogram. This is plotted as the dark solid line in
Fig.3.14(b). The growth rates obtained experimentally are also plotted in the same figure. The
close proximity between the plots further reinforces the validity of the kinetic model developed, and
the identification of mass transport across the vapor-liquid interface as the rate limiting step.
It is to be noted that the activation energy of this growth set is similar to that for the temperature
dependent growth runs performed at 265 Torr, implying that both the growth conditions have the
same rate limiting step. If the rate limiting steps for these two sets of growths were different the
predicted and experimental steady state growth rates will not have matched.
CHAPTER 3. KINETICS OF MWNT GROWTH 72
1.0
0.8
0.6
0.4
0.2
0.0
Nor
mal
ized
Inte
nsity
600500400300200100 Time(secs)
(a) 700oC 725oC 750oC 775oC
140
120
100
80
60
40
20 Gro
wth
Rat
es (n
m/s
ec)
110010501000950 Temperature (K)
(b)
predicted growth rates experimental growth rates
Figure 3.14: Temperature dependent growth of MWNT at P=760 Torr. Fig. (a) plots normalizedintensity as obtained from the interferometer plots. Fig. (b) plots the experimental and predictedgrowth rates. The growth rates were predicted again starting from the T=750oC / P=265 Torrgrowth velocity, while accounting for temperature and pressure changes.
CHAPTER 3. KINETICS OF MWNT GROWTH 73
3.6 Conclusions
To conclude this chapter, a summary of the important points made are given below. An analysis
method was established based on the time resolved reflectivity plots and the SEM images of the
final heights of the MWNT films, to extract growth rate and hence height of the CNTs as a function
of time. The average density of the MWNT films can also be obtained. A kinetic model was
developed to quantify the steady state regime of 1D nanomaterial growth. Four mass transfer steps,
namely: the vapor phase diffusion of carbon containing molecules, their transport across the vapor
-liquid catalyst interface, diffusive flux through the liquid phase and the final transport across the
liquid catalyst-MWNT interface were identified. In contrast to earlier studies the model does not
delve into the specifics/mechanisms of each of the mass transfer steps. The novelty of this growth
model is that it considers the energetics of each transfer step instead, and equates the flux for each
step to a change in chemical potential along a phase or to a drop in chemical potential across an
interface. The average height of the MWNT film was formulated in terms of the experimental steady
state growth rate, and mean life times for catalyst activation and poisoning. The accuracy of this
model was then tested against growth data obtained. Temperature dependent studies established
the rate limiting step to be the vapor-liquid interface for the given growth conditions. Increasing the
absolute pressure decreased the thermodynamic driving force but increased the reaction rate kinetics
for MWNT growth, resulting in increased steady state growth rates. Simultaneously increase in
pressure enhanced the rate of catalyst poisoning thereby saturating the MWNT growth faster. This
leads to formation of shorter CNTs beyond a threshold pressure. Finally the kinetic model was used
to make a fairly accurate prediction for steady state growth rates for temperature dependent growth
of MWNT films at higher pressures. This attests to the validity of the growth model. This study
also helps establish the power of the interferometer as a tool to study the kinetics of nanomaterial
growth processes.
CHAPTER 3. KINETICS OF MWNT GROWTH 74
Tab
le3.
1:A
cti
vati
on
en
erg
yvalu
es
of
rate
lim
itin
gst
ep
sob
tain
ed
from
the
lite
ratu
re
Ea(k
J/m
ole)
Rate
lim
itin
gst
ep
T(K
)C
ata
lyst
Pre
cu
rsor
Morp
holo
gy
Refs
.
145
bu
lk/s
urf
ace
diff
usi
on
800-1
100
Ni
C2H
2fi
lam
ent
(61)
35su
rfac
ed
iffu
sion
425-8
05
Fe
C2H
2M
WN
T(6
5)
130
bu
lkd
iffu
sion
800-1
100
γF
eC
2H
2C
NF
(66)
43.9
-63
surf
ace
diff
usi
on
925
αF
eC
2H
2fi
lam
ent
(62)
94b
ulk
diff
usi
on
Fe 3
CC
2H
2C
NF
/C
NT
(68)
160
surf
ace
reac
tion
/dec
omp
osi
tion
of
C2H
4800-1
100
Fe
C2H
2C
NF
/C
NT
(68)
surf
ace
diff
usi
onof
Cov
erC
NT
+b
ulk
diff
usi
on
1050-1
100
CN
T(7
1)
67b
ulk
diff
usi
on
625-8
75
αF
eC
2H
2C
NF
(67)
142
bu
lkd
iffu
sion
625-8
75
γF
eC
2H
2C
NF
(67)
bu
lkd
iffu
sion
810-1
175
Fe/
Mo
C2H
2M
WN
T/S
WN
T(7
6)
79d
iffu
sion
atca
rbid
e/m
etal
inte
rface
900-1
000
Fe
C2H
2M
WN
T(8
8)
224
bu
lkd
iffu
sion
and
carb
on
solu
bil
ity
900
Fe
C2H
2(8
9)
180
Cd
isso
luti
on+
diff
usi
on
MW
NT
(73)
100
adso
rpti
onof
Cat
the
cata
lyst
surf
ace
900-1
100
Fe/
Al 2
O3
C2H
6M
WN
T(6
9)
145
HC
adso
rpti
on+
chem
ical
react
ion
900-1
100
Fe-
Co/A
l 2O
3C
2H
4M
WN
T(7
0)
100-
160
gas
ph
ase
dec
om
posi
tion
Co/M
o/M
gO
CH
4M
WN
T(7
2)
Chapter 4
Growth Transition from Carbon
Nanotubes to Carbon Nanofibers
4.1 Motivation
Chapter 3 dealt with MWNT growth from 2.5nm sputtered Fe film catalysts. All the growth runs
were done below or at atmospheric pressure. The next Chapter deals with the influence of an
applied field on MWNT growth kinetics. As explained in Chapter 5, it was necessary to grow CNTs
at pressures much higher than the ambient to apply large electric fields. Increasing pressure, though,
changed the structure of the MWNTs grown. The magnitude of the change varied changed with
the growth conditions. Fig.4.1 are SEM images attesting to the above statement. Fig(a) shows
the change in morphology for MWNTs grown from a 2.5 nm sputtered Fe film. At low pressures
the nanotubes formed are vertically aligned. Increasing the pressure resulted in the formation of
coiled CNTs, the extent of coiling being dependent on the growth pressure. The effect of increasing
the particle size was more drastic. Fig.4.1(b) shows the formation of carbon nanofibers, instead of
MWNTs, for growths from a 5nm sputtered Fe film at pressures of 1660 Torr. Similar observations
were made form MWNTs grown from catalysts prepared by block co-polymer micelle templates. The
formation of Fe catalysts from the micellar templates will be discussed in detail in the next chapter.
The pressure ranges that triggered the transition in the micellar particles was higher compared to
the 5nm sputtered Fe catalysts. The motivation then is to understand the cause behind the CNT to
CNF transition. This is important because CNFs have a different set of properties to that of CNTs
and hence are avoided for many applications.
75
CHAPTER 4. GROWTH TRANSITION FROM CNT TO CNF 76
Figure 4.1: Effect of pressure on the morphology of nanotubes. (a-b)Catalyst particles preparedby annealing sputter deposited thin Fe films. (c) Particles prepared from block co-polymer micelletemplates
4.2 Introduction
There is some confusion regarding terminology for carbon nanotubes and carbon nanofibers. For
the purposes of this study CNTs are those structures that have a hollow core and straight side walls,
i.e. the basal graphite planes are parallel to the tube axis. Fig.4.2 (a-b) shows schematics and TEM
images for CNTs with single and multi walls. Apart form these, all carbon 1D structures that have
any graphitic ledges inside the core of the tubes will be referred to as CNFs. Fig.4.2 (c) are examples
of different CNF morphologies reported. They range from stacked cup to stacked cone structure,
and includes intermediate morphologies where the graphitic ledges are not so well defined.
The chapter is structured such that we discuss a systematic variation of MWNT growth condi-
tions, followed by rigorous SEM, Raman and TEM characterization of the structures obtained. This
is followed by investigations into the evolution of particle sizes as a function of the thickness of the
deposited Fe films and annealing pressure. In the last section we develop a thermodynamic model
to explain the formation of fibers as opposed to CNTs.
CHAPTER 4. GROWTH TRANSITION FROM CNT TO CNF 77
Figure 4.2: 1D Carbon nanostructures. (a-b) carbon nanotubes. Schematic downloaded fromwww.ibmc.u − strasbg.fr/ict/images/SWNT − MWNT.jpg (c) Examples of CNF morphologies.Schematic from www.pyrografproducts.com/Merchant5/graphics/sfnt− orangecones.gif
4.3 Experimental details and Results
4.3.1 Growth of MWNT/CNFs
From the initial observations, two parameter that were found to be of importance for the formation
of CNTs or CNFs were pressure and size of the catalyst particles. Hence we varied these two
parameters in a systematic manner to study their relative influences on the growth morphologies.
Four different catalyst substrates were prepared. The nominal thickness of the deposited Fe
layers were 2nm, 5nm, 8nm and 13nm respectively. All of these were deposited on a buffer Al layer
(10 nm thick), which was sputter deposited on Si. The substrates were cut into 1cm2 pieces and
transferred into the reactor chamber. All four substrates were grown from simultaneously to negate
any variations between different sets of growth. The reactor was evacuated and then the temperature
ramped up to 550oC under a hydrogen ambient (flow rate: 100 sccm and reactor pressure: 120 Torr).
The substrate was held at this temperature for 5 minutes. Following this the reactor temperature
was ramped up to the growth temperature of 750oC. The desired base pressure at the on-set of the
growth was achieved by manipulating the hydrogen flow rates and the valve positions. When the
temperature of the hot plate reached a steady value ethylene was flown into the chamber. The flow
rates of ethylene and hydrogen was maintained at 350 and 100 sccm respectively. The four different
growth pressures used for this study was 200, 760, 1120 and 1680 Torr. The growth duration for all
the runs was 10 minutes.
Fig.4.3 is a collage of SEM images of the MWNTs/CNFs obtained from the growth runs men-
tioned above. SEM images from growths on substrates with the same catalyst thickness are arranged
CHAPTER 4. GROWTH TRANSITION FROM CNT TO CNF 78
Figure 4.3: SEM images showing the dependence of the thickness of the sputtered Fe layer andgrowth pressures on the nature of carbon morphologies obtained
in a column, showing the dependence of growth pressure. Along the rows, the growth pressures are
the same, so the SEM images illustrate the influence of catalyst thickness on growth morphologies.
The final thickness of the films grown have a strong dependence on the growth conditions. This is
plotted in Fig.4.4. With an increase in pressure the height of the films decreased irrespective of the
nominal thickness of the deposited Fe layer. This decrease in thickness of the film has been explained
in the previous chapter. Increasing the pressure results in a higher growth rate, but at the same time
the rates of the competing process of catalyst poisoning also increases. This restricts the final height
of the films grown. The height of the films grown also have a strong dependence on the nominal Fe
thickness. As will be shown in a later section that the catalyst size is proportional to the catalyst
thickness. The diameter of the 1D structures in its turn is proportional to the particle size. The con-
centration of C in the CNTs can be obtained by the relation CMWNTc = Cgraphitec (1− rin
2
rNT2 ), showing
that the density of the MWNT is proportional to its diameter. Hence a simplistic explanation is
that with increasing particle size, for the same amount of C flux the height of the MWNT/CNFs
formed decreases (vss = Jvs/Cc).
More interesting, though, is the change in morphology of the CNTs. For the 2nm Fe catalyst
films MWNTs are obtained irrespective of the growth pressures. There is a significant change in
height of the film accompanied by formation of coiled CNTs, but the structures obtained are tubular.
This is evidenced by similar intensity ratios of the D-band and the G-band in the Raman spectrum,
CHAPTER 4. GROWTH TRANSITION FROM CNT TO CNF 79
30x103
25
20
15
10
5 Hei
ght
of C
NTs/
CNFs
(nm
)
1412108642
Thickness of Sputtered Fe (nm)
300 Torr 760 Torr 1220 Torr 1680 Torr
Figure 4.4: Heights of CNTs/CNFs plotted as a function of growth pressure
irrespective of the growth pressures. For thicker catalysts with an increase in pressure there is
a definite transition in morphology from CNTs to fibers. For example for the 8 nm thick films,
this transition takes place for growth pressures of 1120 Torr. Fig.4.5 plots the Raman spectrum
corresponding to the D and G-band positions for growths from the 8 nm sputtered film. The
intensity of the D band is inversely related to size of crystallites, and disappears for perfect tubular
structures. The intensity ratio of the D-band and the G- band has been found to be a good metric
in determining the quality of CNTs. Typically for MWNTs the intensity of the D-band is less than
that of the G-band, this is seen for plots for the 200 and 760 Torr growth. For higher pressures the
intensity of the D-band is greater than that of the G-band implying a presence of larger fraction
of defective structures in the sample studied. This agrees well with the SEM observations, where
we see an increasing fraction of CNFs in the sample for growths at absolute pressures of 1120 and
1680 Torr. The number fraction of fibers in the sample is even higher for growths from the 13nm
sputtered Fe film. For this thickness, the tube to fiber transition occurs at an even lower pressure
of 760 Torr. In spite of the transition from CNTs to CNFs, it has has to be noted that there is a
considerable faction of CNTs in the sample for the thicker films annealed at higher pressures.
The SEM images also show a transition from a root-growth (catalyst is rooted to the substrate)
to a tip-growth mode with increasing Fe film thickness and hence size of the catalyst particles. This
has been observed by other groups (90). The transition in growth mode was explained by interaction
between small carbon patches (poly-aromatic carbon or reticulated carbon chains) and the catalyst.
A strong interaction favors the formation of a graphene cap on the catalyst and leads to CNT growth
via the base-growth mode. On the contrary, a weak interaction induces a diffusion of the graphitic
section to the catalyst/substrate interface which drives the tip-growth mechanism.
CHAPTER 4. GROWTH TRANSITION FROM CNT TO CNF 80
1.0
0.8
0.6
0.4
0.2
0.0
norm
aliz
ed in
tens
ity
200018001600140012001000800600wavenumber(cm-1)
1620 Torr 1120 Torr 760 Torr 200 Torr
Figure 4.5: Raman spectrum obtained using 514 nm excitation laser for nanostructures grown froma 8nm sputtered Fe film as a function of pressure
4.3.2 Characterization of catalyst particle size
The last section studied the effect of pressure on growth. A major contributing factor if not the
most important one to the changes observed was the catalyst film thickness. This is because the
catalyst thickness influences the size of the catalyst particle. Therefore there is need to determine
the size of the catalyst particles used for the growth runs.
Like in the case for growth studies four identical substrates, with 2,5,8,13 nm of Fe sputtered on
a 10nm Al buffer layer sputter deposited on Si was used. These substrates went through the same
processing steps including the 5 minute annealing step. Following which the reactor temperature
and pressure was ramped to the same base values as used for the growth runs. On reaching a steady
750oC, the substrates were annealed at the same absolute pressure of 200, 760, 1120 and 1680 Torr
for 10 minutes (similar to the growth runs) using only hydrogen. This was done to investigate the
effect of the absolute pressure on the evolution of the catalyst particle sizes.
Fig.4.6 are representative images of the catalyst particles formed subsequent to the process
described above. The first thing to notice is the large difference in range of the catalyst particles
produced. On closer examination two general trends appear albeit one or two exceptions. First,
as expected the size of the catalyst particles increases with the thickness of the sputter deposited
Fe film, particularly for the higher annealing pressures. Secondly increasing the annealing pressure
resulted in formation of larger particle sizes. One exception being the 2nm sputtered Fe film. For the
CHAPTER 4. GROWTH TRANSITION FROM CNT TO CNF 81
Figure 4.6: Evolution of particle sizes vs. catalyst thickness and annealing pressures
2nm sputtered film, the mean particle size actually decreased on increasing the annealing pressure.
This can be seen from Fig.4.7 which plots the size distribution of the particles (percentage spatial
coverage of particles), obtained by Image J analysis of the SEM images of the particles from Fig.4.6.
The mean radius (approximating the particles to be circular in shape) of the particles for the 200
Torr anneal is 6.35 nm while for the 1680 Torr growth case the mean is 4.32 nm. This is probably due
to enhanced mixing between the Fe/Al layers at higher annealing pressures. For the 5nm sputtered
film, increasing annealing pressure resulted in an increase in the range of catalyst particle sizes, the
increase in range mostly due to the formation of larger particle sizes. The mean calculated particle
radius increased from a mean of 6.25 nm to 8.1 nm, on increasing the annealing pressure form 200 to
1680 Torr. Similar increase in particle sizes were observed for the thicker 8nm and 13 nm sputtered
films. Though, for the 13 nm sputtered films the largest particle size was obtained for annealing
pressure of 1120 Torr.
It has to be noted that the evolution of particle size on exposure to a combined flow of hydrogen
and ethylene might be different from that obtained when annealed under a hydrogen ambient. But
the above particle size trends should serve as a good indicator for actual values.
CHAPTER 4. GROWTH TRANSITION FROM CNT TO CNF 82
1086420
302520151050 particle size (nm)
15
10
5
0
% a
rea
cove
red
12
8
4
0
12
8
4
0
(a) 2nm Fe/ 10nm Al/ Si
16
12
8
4
03020100
particle size (nm)
8
6
4
2
0
6
4
2
0
% a
rea
cove
red
6
4
2
0
1620 Torr 1120 Torr 760 Torr 200 Torr
(b) 5nm Fe/ 10nm Al/ Si
Figure 4.7: Plot of particle sizes obtained from Fig.4.6 for the 2nm and 5nm sputtered Fe filmthickness. The particles were assumed to be circular for simplicity. The X-axis is the calculateddiameter corresponding to the particulate area.
CHAPTER 4. GROWTH TRANSITION FROM CNT TO CNF 83
Co-relation of the particle size and the MWNT/CNF growth runs
Nasibulin et al.(83) established a close relation between the catalyst particle size and the diameter
of the SWNTs grown. A rigorous statistical analysis of the particle sizes and diameter of the SWNT
obtained from the particles, established an approximate tube to particle radius ratio. Though,
strictly true for SWNTs, intuitively a similar co-relation between the diameter of the 1D carbon
structure and catalyst particle size should exist. A comparison of the SEM images of particle size
distributions, Fig.4.6, with that of SEM images for CNTs/CNFs, Fig.4.3, shows a close correspon-
dence between the two. Smaller particle sizes, obtained from the thin Fe catalyst films and even from
the thicker catalyst films at low annealing pressures, resulted in the formation of CNTs. For larger
particle sizes (8nm and 13nm sputtered films, annealing pressures 1120 and 1680 Torr) nanofibers
form. Intermediate particles result in a mixture of tube and fibrous growth. A significant amount
of small particles were obtained from annealing 8nm and 13nm sputtered films at high annealing
pressures. Correspondingly for these thick sputtered films and high growth pressures there is a con-
siderable fraction of MWNTs in the sample. These observations imply, catalyst particle size rather
than growth pressures is the contributing factor controlling the morphology of the 1D carbon nanos-
tructures. Pressure facilitates the process by influencing the size of the catalyst particles formed
during annealing and subsequent processing of the catalyst films.
Auger depth profiles of the annealed substrates
Annealing pressure influences the particle sizes formed. Auger depth profiling of the annealed sub-
strates were performed to investigate possible causes for this size dependence. Precise depth milling
through sputtering has made profiling an invaluable technique for chemical analysis of nanostruc-
tured materials and thin films. Depth profiles are shown as atomic concentration vs. sputtering
time. But, despite the advantages of high spatial resolution and precise chemical sensitivity at-
tributed to AES, quantification of AES data is difficult due to several limiting factors e.g. charging
of non-conducting samples. Still, the atomic concentration data is a good indication of the change
in chemical composition with depth. Typically the bombarding energies used for this study is 2kV
with a beam current of 1µA. This corresponds to a sputtering rate of 20nm/min for a Si standard.
Fig.4.8(c-d) are depth profiles of 2nm Fe/10 nm Al/ Si after annealing at 1120 Torr. As mentioned
before annealing results in the sputtered Fe thin film to ball up resulting in the formation of particles.
The high spatial resolution of the Auger probe allows the compositional analysis as a function of
depth from the particles so formed (d). Depth profile was also obtained from the substrate free of
particles (c). To compare depth profile obtained from an as-sputtered 5nm Fe film (discussed in the
last chapter) is also shown. In contrast to the as-sputtered film, the annealed film shows extensive
intermixing between the layers. The concentration plots show intermixing between Fe/Al layers
for profiles obtained both from the substrate and the particle. For the particle depth profile, Fe
signal intensity is more than the Al only at the interface implying as expected the particles formed
CHAPTER 4. GROWTH TRANSITION FROM CNT TO CNF 84
100
80
60
40
20
0
at%
86420 sputter time (secs)
5nm Fe/10nm Al/Si
C O Al Si Fe
(a) as sputtered
Fe
Al
Si
Fe-Al
Fe
80
60
40
20
0
at%
6543210 sputter time (secs)
2nm Fe/10 nm Al /Si
(c) substrate
80
60
40
20
0
at%
6543210 sputter time (secs)
C O Al Si Fe
(d) particle
Figure 4.8: Auger depth profile for an annealed 2nm Fe/10nm Al/ Si substrate. (a) Depth profile foran as deposited sample(5nm sputtered Fe). (b) cartoon of the annealing process and SEM image ofthe catalyst particles formed after annealing. (c ,d) Profiles obtained by sputtering on the substrateand a particle respectively. The same elemental color codes and markers are used for all the depthprofiles discussed in this chapter
CHAPTER 4. GROWTH TRANSITION FROM CNT TO CNF 85
are indeed Fe/Fe-oxide particles. The depth profiles described above is fairly representative of the
2nm Fe sputtered film irrespective of the annealing pressure. The only difference being enhanced
Fe/Al mixing between layers for signals obtained from the particles at higher annealing pressure. As
mentioned, while discussing the evolution of particle sizes for the 2nm sputtered film, this enhanced
mixing may account for the decrease in particle size with increase in annealing pressures.
Fig.4.9 are depth profiles obtained from post-annealed 13nm Fe/10nmAl/Si sputtered substrates.
The annealing pressures are tagged on to the corresponding depth profiles. The foremost observable
fact is the extensive intermixing between the layers. Extensive intermixing between Fe and Al have
been reported by other groups (91). This mixing also illustrates the need for the buffer layer to
be thicker compared to the catalyst layer. If the buffer layer is not thick enough Fe woul diffuse
through to the underlying Si, similar to this case. This is because Fe has an affinity for Si and
forms different complexes with it (92). For annealing at 200 Torr the depth profiles obtained from
the particle and substrate is the same, implying relatively limited mixing. The Fe concentration for
this case shows a double hump, Fe enrichment at the surface (which is expected) and also at the Si
interface. This looks like an impossible situation since it would imply Fe diffusing towards the Si
interface against a Fe concentration gradient. But it has been reported that Fe can precipitate at
the Si/Si-oxide interface (92) and is also known to form FeSix complexes with Si (e.g. FeSi, FeSi2)
at the Fe-Si interface (93). Thus the diffusion of Fe towards the Si interface is driven by a decrease
in chemical potential of Fe from elemental state to FeSix, and the increase in atomic concentration
reported is an artifact of the Fe-Si compound formed at the interface.
The extent of intermixing increases with annealing pressure. Another important trend observed
is with increasing annealing pressure, the Fe content for the substrate decreases while the iron
content for the particle is increasing. This implies there are two types of Fe diffusion taking place:
(i) Fe diffusing towards the Si layer as mentioned above and (ii) Lateral diffusion of Fe away from
the substrate towards already formed particles. The second effect is known as Ostwald ripening,
where the decrease in chemical potential (due to its inverse dependence on particle size) drives the
coarsening / agglomeration of smaller particles into a larger particle. This explains the formation
of larger particles with increasing annealing pressures (as was observed in Fig.4.6).
To conclude the increased intermixing between the different layers and enhanced Ostwald ripening
with increase in annealing pressure is responsible for the evolution of the observed particle size
distribution. The effect of pressure in facilitating intermixing or ripening is not clearly understood.
One possible explanation could be increasing chamber pressure increases the thermal contact between
the substrate and the hot plate, thereby increasing the effective temperature of the substrate which
drives the above mentioned processes.
CHAPTER 4. GROWTH TRANSITION FROM CNT TO CNF 86
10080604020
0
at%
121086420 sputter time (secs)
10080604020
0100
80604020
0100
80604020
0
200 Torr
760 Torr
1120 Torr
1620 Torr
C O Al Si Fe
(a) substrate
100
80
60
40
20
0
121086420 sputter time(secs)
100
80
60
40
20
0 at%
100
80
60
40
20
0
100
80
60
40
20
0
200 Torr
760 Torr
1120 Torr
1620 Torr
(b) particle
Fe
Al
Si
FeSixFe-Al
Fe
Figure 4.9: Auger depth profile for annealed 13nm Fe/10nm Al/ Si substrate as function of annealingpressure(a) Depth profile obtained from sputtering on the substrate. (b) Depth profile from aparticle. (c) Schematic of particle evolution with annealing pressure
CHAPTER 4. GROWTH TRANSITION FROM CNT TO CNF 87
Figure 4.10: TEM characterization of 1D carbon structures as a function of particle size. (a) CNTsformed from small catalyst particles, (b) Defective, kinky fibers formed from large particles
4.3.3 TEM characterization of growths as a function of particle size
Small catalyst particle sizes resulted in the formation of smaller diameter MWNTs, Fig.4.10. The
MWNTs have only 2-3 side walls. There is some bending observed in the CNTs, but they have
straight side walls. On the other extreme the large catalyst particles (8nm sputtered Fe film, annealed
at 1680 Torr) results in formation of very defective, kinky, seemingly amorphous fibers of large
diameters. A closer look, though, reveals extensive graphitization of the thick side walls and the
presence of a very narrow hollow core. The graphitization pattern of the side walls followed the
shape of the catalyst particle.
Fig.4.11 are TEM images obtained from intermediate particle sizes formed from annealing a
8nm sputtered film at 1120 Torr. For the relatively smaller particles the 1D structures formed are
defective in that there are more kinks and bends compared to the CNTs reported in the previous
figure. Also graphitic ledges (marked by arrows) start to form across the tubes. These ledges are
not prominent as they are made of only a few graphitic planes. With increasing particle size the
stacked cup arrangement becomes prominent, as the number of graphitic planes bridging the hollow
core increases. The other notable feature is the very regular arrangement of the stacked cups in the
CNFs formed, indicative of a recurring origin.
CHAPTER 4. GROWTH TRANSITION FROM CNT TO CNF 88
Figure 4.11: TEM characterization of 1D carbon structures obtained from intermediate particle sizes
4.4 Brief literature review on CNFs
The methods for producing the carbon nanofibers have been developed and are in use since the early
1980s, due to the great effort carried out especially by Endo and co-workers (94) and Tibbetts et
al. (63). Most of carbon nanofibers are produced by catalytic CVD from a carbon feedstock (light
or aromatic hydrocarbons, CO) using an elemental transition metal (Fe, Ni, Co and Cu) as catalyst
(95; 96; 97; 98; 99; 100; 101; 102; 103; 104; 105; 106; 107). Plasma enhanced CVD (PECVD) is
another popular method of growing vertically aligned CNFs (13; 108; 109; 110; 111; 112). Fig.4.12
plots the diameter of CNFs obtained from the references mentioned above.
Two important observations can be made form the plot. For lower growth temperatures the
diameter of the nanofibers formed is small. Increasing temperature results in an increase in range of
fiber diameters. But, the diameter of the smallest fiber reported for a given temperature increases
almost linearly with increasing growth temperature (this is marked by the dashed red line in the
plot).
More recently,following the pathbreaking work by Helveg et al. (1), HRTEM has been employed
CHAPTER 4. GROWTH TRANSITION FROM CNT TO CNF 89
140
120
100
80
60
40
20
0
Nano
fiber
dia
met
er (
nm)
12001000800600400Temperature(oC)
(c)
Fe catalyst Ni catalyst PECVD
Figure 4.12: (a) In-situ TEM studies of nanofiber growth (1). (b) Atomic scale observation of theformation of SWNTs (2). (c) Distribution of fiber diameter with temperature from data reportedby various groups
to observe in-situ CNT/CNF growth in an atomic scale. This has resulted in fresh insight into the
mechanisms of 1D nanomaterial growth. Yoshida et al. (2) observed the nucleation and growth
process of carbon nanotubes (CNTs) from iron carbide (Fe3C) nanoparticles in CVD with C2H2
Fig.4.12(b). The size of the catalyst particle was 2nm and the growth temperature 600oC. After
the initial nucleation and incubation period the nanotube grows at a slow but constant growth
rate. The important thing to notice is that the catalyst particle does not change shape during
growth. Helveg et al. observed the formation of nanofibers Fig.4.12(a). Contrary to CNT growth,
the initial equilibrium shape of the catalyst particle transformed into a highly elongated shape. The
elongation of the Ni nanocrystal continues until it achieves an aspect ratio of up to, 4, before it
abruptly contracts to a spherical shape within less than, 0.5 sec, leaving behind a graphitic ledge.
The elongation/contraction scenario continues in a periodic manner as the nanofiber grows. Similar
observations were made by other researchers(113; 114).
CHAPTER 4. GROWTH TRANSITION FROM CNT TO CNF 90
4.5 Discussion
To summarize, particle size was found to be the most important contributing factor in determining
the morphology of the 1D nanostructure. For the growth conditions studied, particle sizes rp < 5
nm resulted in formation of MWNTs, and large particle sizes rp > 20 nm resulted in formation
of defective, kinky structures. Intermediate sizes resulted in the formation of carbon nanofibers,
with a very regular stacked-cup morphology. High pressures facilitated formation of nanofibers by
influencing the size of the catalyst particles formed. The other important factor that controls CNF
formation is the growth temperature. The smallest diameter CNF, reported at a particular growth
temperature, increased with increasing temperature. Also lowering the temperature resulted in a
decrease in diameter range of the fibers formed. HRTEM in-situ imaging of fiber growth reported
by other groups further revealed three important features: (i) the catalyst particle alter shape
(for CNT growth the catalyst particle retained their shape through out the growth process) (ii)
expansion/contraction of the particle is periodic resulting in the regular stacked morphology of the
CNFs and (iii) the time for contraction to the original size is almost an order of magnitude smaller
than the time taken for the particle to elongate.
Though oscillatory nature of the particle is considered to be integral to the formation of CNFs, to
date there is a lack of understanding of the origin/driving force for this oscillatory nature. We believe
the regular and abrupt nature of the contractions is due to a phase transition of the particle. The
most studied catalysts for CNT/CNF growth are the transition metals Fe, Co, Ni. It is important to
note that all three of them are carbide formers, have limited C solid solubility and forms an eutectic
at small weight percentages of C.
To reconcile the above observations we propose that the catalyst particles have to be in the
binary (liquid/solid) phase region to form CNFs, and the small particles resulting in CNT growth
is in the single liquid phase.
4.5.1 Thermodynamic Modeling
In this section we will describe the model in some detail and provide theoretical calculations in
support of the proposed model. First we will discuss the case for nanotube growth, followed by
carbon nanofiber growth.
Small single liquid phase catalyst particle
For the small particle sizes we have proposed that the particle is in a single liquid phase under
the MWNT growth conditions reported. CNT forms from these particles via a VLS mechanism
described in the last chapter. Four mass transfer steps: the vapor phase diffusion of carbon containing
molecules, their transport across the vapor -liquid catalyst interface, diffusive flux through the liquid
phase and the final transport across the liquid catalyst- MWNT interface were identified. CNT
CHAPTER 4. GROWTH TRANSITION FROM CNT TO CNF 91
growth was described as a steady state process, with no C accumulation inside the particle, the
slowest of the 4 mass transfer steps described being the rate limiting step.
1800
1600
1400
1200
1000
800
600
400
200
0
Mel
ting
Poin
t (K
)
0.1 1 10 100 1000Radius of Fe nanoparticle (nm)
Growth temperature (750 oC)
Figure 4.13: Plot of size dependent melting point of Fe. The dotted line marks the growth temper-ature used for this study.
The first question to be answered is the discrepancy in the growth temperature, 750oC and the
melting point (1536oC) or the eutectic temperature of 1175oC. This can be explained due to the
curvature dependance of chemical potential, Gibbs-Thompson effect.
For a solid particle of radius, rs, and a liquid particle of radius,rl the accompanying increment
in chemical potential is given by the relation:
µs = µs,∞ +2γsΩsrs
µl = µl,∞ +2γlΩsrl
where γ , Ω and µ∞ are interfacial energy, molar volume and the bulk chemical potential respectively.
At the melting point the chemical potential of the solid and liquid particles are equal. Hence from
the above two equations and the Turnbull approximation, ∆µ∞ =∆Hf∆TTMP
, we get the following
relation for size-dependent suppression of melting point:
T = TMP −2TMP
rs∆Hf
[γlΩl
(ρlρs
)1/3
− γsΩs
](4.1)
where ∆Hf = 13.80kJ/mole is the latent heat of fusion at TMP . The above equation also accounts
for mass conservation while transforming from the solid to the liquid state. The plot was obtained
by assigning the following parametric values: density of solid austenite is 7875 kg/m3, liquid iron
CHAPTER 4. GROWTH TRANSITION FROM CNT TO CNF 92
6980 kg/m3, molar volume of austenite = 7.117 cm3, the interfacial energies for austenite and liquid
iron being 2.55 and 1.92 J/m2 respectively. These values were obtained from the work of Sayama et
al.(115) on the eutectic growth of unidirectionally solidified iron-carbon alloy.
The size dependence of the suppression in melting point is plotted in Fig4.13. In effect with a
decrease in size of the particles (rp < 10nm) the entire phase diagram shifts downwards in tempera-
ture. From the plot we can see that a particle of approximate diameter 2nm will be in a liquid phase
at the growth conditions. This particle size is an underestimate because of the following reasons.
First, we considered pure Fe for the calculations, while in reality it is a Fe-C alloy which has a lower
liquidus temperature than the melting point of pure iron. Next the catalyst particle sizes are in
contact with a substrate, and in general the interfacial energy between two solid interfaces are larger
than between a solid-liquid interface. This will further bring down the liquidus temperature of the
catalyst particle. Thus in reality the largest particle size that will be in a liquid phase at the growth
temperatures is higher than that predicted by the above plot. These liquid phase catalyst particles
will form CNTs.
Intermediate catalyst particle sizes
For particles in this size range, the depression in liquidus temperature is not enough for it to be in
the liquid phase. But the downward shift in the phase diagram is enough for these particles to be
in the temperature range corresponding to a binary solid austenite-liquid Fe phase at the growth
temperatures, Fig.4.14. As observed from the in-situ TEM images CNF formation is a non-steady
state process.
Initially the catalyst is in the solid austenite phase. With the onset of growth, C starts accu-
mulating inside the particle. The C concentration goes up and eventually crosses the solidus line,
at that point the particle enters a two phase regime. Further increase in C concentration inside the
particle leads to an increase in volume fraction of the liquid phase. This results in an elongated
tail, encapsulated by the side walls, as seen in the TEM images. Fig.4.14(b) is a schematic of the
process. But, the formation of the liquid phase is accompanied by formation of different interfaces,
namely the solid-liquid interface inside the particle, the liquid-tube interface. With increase in the
carbon concentration inside the particle, the volume fraction of the liquid phase increases and along
with it the energy cost to pay for these extra interfaces (as shown in the ∆Gmix vs x schematic).
At some point this interfacial energy cost cannot be sustained. The particle wants to decrease its
energy content; the way to do so is to revert back to the original austenite solid solution phase. This
can be achieved only by casting away the excess carbon. The extruded C takes on the shape of the
contracting liquid phase giving the graphitic ledges, so formed, the stacked-cop morphology of the
CNFs. C diffusing through a liquid phase accounts for the much faster time scales for contraction of
the particle than for its elongation, which is accompanied by solid state diffusion. The entire process
described above keeps on repeating to form the regular ordered structure.
CHAPTER 4. GROWTH TRANSITION FROM CNT TO CNF 93
G
x
+L (vol. energy)
+L
liquid
LL
1150oCTe
mpe
ratu
re
graphene
+L +graphene
Figure 4.14: (a) Relevant portion of the binary Fe-C phase diagram. (b) Schematic of the evolutionof the stacked-cup morphology of the CNFs
Next we develop a thermodynamic model to predict the crossover point which initiates the phase
reversal. We consider a initial solid austenite particle of radius r. When the C wt% in the catalyst
particle crosses over the solidus line, a liquid phase starts forming as shown in the schematic on the
left of Fig.4.15, with the propagating solid-liquid circular interface at a distance z from the side of
the particle. If we assume same density for the solid and liquid phase; then the volume fraction of
the liquid phase formed, f , can be expressed as:
f =z2
4r2(3− z
r) (4.2)
But in reality, the density of the liquid iron phase is smaller, resulting in the formation of an
CHAPTER 4. GROWTH TRANSITION FROM CNT TO CNF 94
elongated tail as mentioned above. For simplicity we assume a cylindrical shape for the elongated
tail, the cylinder being encapsulated in a graphitic tubular structure, of outer diameter ro and inner
diameter ri. The length of the cylinder, l, being
l = fρsVs
πρlr2i
= kf (4.3)
Initially the particle was in the austenitic phase with volumetric free energy, Gs. On crossing
the liquidus line, the volumetric free energy of the binary phase particle can be expressed as:
GFeC = (1− f)Gs + fGl
= Gs + f [Gl −Gs]
where Gl is the volumetric free energy of the liquid phase. The change in volumetric free energy
accompanying the formation of the liquid phase is then given by:
∆G1 = f [Gl −Gs] (4.4)
Next we add the interfacial energy terms: the solid liquid interface that replaces the solid-vapor
interface and the new liquid-tube interface.
∆G2 = πr2i (γs,l + γl,v − γs,v) + 2πrikfγl,gr (4.5)
The first term of the above equation is negative, because the solid-vapor interfacial energy is larger
compared to the solid-liquid and liquid-vapor interfacial energy.
There is a simultaneous increase in the height of the graphitic tubular structure, and the accom-
panying decrease in chemical potential of C going from the vapor to the tubular structure provides
the driving force for the entire process.
∆G3 = −πr2okf(µVC − µNTC ) + 2πrokfγv,gr (4.6)
The total change in energy in going from the single phase austenitic particle to the binary phase
catalyst particle with the liquid phase encapsulated in a growing tubular shell is given by ∆Gtotal.
∆Gtotal = ∆G1 + ∆G2 + ∆G3 (4.7)
These energy changes are plotted in Fig.4.15. The plots correspond to a particle radius of 5 nm.
Given the particle size, the Gibbs Thompson relation is used to calculate the downshift of the phase
diagram and from there the weight fractions of C corresponding to the liquidus and the solidus lines.
Knowing these weight fractions, we substituted them into analytical expressions for volumetric free
CHAPTER 4. GROWTH TRANSITION FROM CNT TO CNF 95
-800x10-18
-600
-400
-200
0
200G
(J)
0.50.40.30.20.10.0 f
GIGIIGIIIGtotal
-vapor
-liquid
liquid-vapor
CNT-vapor
CNT-liquid
liquid
radius “r”
z
Figure 4.15: Energetics of the CNF formation process. The black dashed line marks the volumefraction that triggers the contraction of the catalyst leaving behind a graphitic ledge
energies from the work on thermodynamic analysis of Fe-C phase diagrams by Agren(116) to obtain
Gs and Gl. The outer radius of the tubular structure formed is assumed to be the same as the
particle size, which gives an inner radius of 3.5 nm from the work of Tibbetts (63). The formulation
for the change in chemical potential of C going from the vapor phase to the tubular structure was
dealt with in the previous chapter and is used here to estimate the driving force. The interfacial
energy values were again obtained from the work of Sayama et al.(115).
∆G2, that sums the interfacial energy contributions of the growing liquid phase, is the only
term that switches polarity as a function of the volume fraction of liquid phase formed. This is
because initially on formation of a binary phase, the solid-liquid interface replaces the higher energy
solid-vapor interface. But with increasing f the liquid-tube interfacial energy dominates and the
initial energy advantage is lost. Hence, ∆Gtotal, which corresponds to the energy change for the
elongated particle, eventually becomes energetically unfavorable compared to ∆G3, which in turn
CHAPTER 4. GROWTH TRANSITION FROM CNT TO CNF 96
is the energy change due to the formation of tubular section only. This will trigger the contraction
of the particle back to its original single phase state leaving behind the graphitic planes bridging
across the energetically stable tubular section.
Other factors that influence fiber formation
As was observed from literature review temperature plays an important part in controlling the
fiber diameter. For low growth temperatures only small particles can transform into a binary phase.
This puts an upper limit to the diameter range. On increasing the growth temperatures the diameter
range of particles forming CNTs will increase, but the smaller particles will be in a liquid state and
will form CNTs rather than fibers. This would set a lower limit for particle sizes forming fibers.
The principal effect of pressure is to facilitate the evolution of catalyst particle sizes. Increasing
pressure further aids fiber formation due to the dependence of chemical potential on pressure: δµδp |T =
Ω. The molar volume of liquid being larger than solid, higher pressures would result in an elevation
of melting point and hence responsible for the pressure dependent transition to fiber formation. But
since both solid and liquid are condensed phases the shift in melting point due to increasing pressures
would be minor. A more significant contribution is due to the pressure dependence of C flux across
the vapor-liquid interface as discussed in the last chapter. Carbon concentration inside the particle
will increase with increasing pressure, driving CNF formation due to formation of a mixed phase.
The ubiquitous use of PECVD for CNF growth has a similar origin. The plasma results in
decomposition of C precursor in the vapor phase itself, increasing the flux of C into the catalyst
particle which enhances C accumulation and hence fiber formation.
Large catalyst particles
For large catalyst particle sizes (rp > 15nm) the melting point suppression is negligible. Hence
the particles will be in a solid state at the growth conditions. Reshaping/restructuring of the
facets/planes of solid particles have been reported in contact with graphene (113; 2). This occurs to
minimize the interfacial energy of the graphene-solid interface. Subsequently, the side walls of the
tube replicate the facets of the solid catalyst particle. For example, catalysts exhibiting fcc facets
results in the formation of stacked-cone CNF morphology (117).
4.6 Conclusion
To summarize this chapter, it was established that catalyst particle size is one of the key parameters
that determine the morphology of the 1D carbon nanostructures. The inverse dependence of chemical
potential on size determines the nature of the particle under growth conditions. Smaller particle
exhibit a single liquid phase, conducive to the growth of CNTs. However, larger particles, are in a
dual solid-liquid phase during growth. The relative fraction of liquid phase increases with increasing
accumulation of carbon flux. Beyond a threshold carbon concentration, the dual phase becomes
CHAPTER 4. GROWTH TRANSITION FROM CNT TO CNF 97
energetically unfavorable, causing the particle to revert to a single solid phase regime by discarding
excess carbon. The resulting carbon layers replicate the morphology of the catalyst particle, leading
to the observed CNF structure. In the CVD process, higher pressures were found to form larger
particle sizes. AES depth profiles attributed this behavior to particle coarsening.
Chapter 5
Electric field directed Vertically
Aligned growth of Multiwalled
Carbon Nanotubes
5.1 Motivation
Carbon nanotube based field emission cathodes are sought for various applications such as microwave
amplifiers, x-ray tubes, Tetrahertz sources etc. Continuous or patterned CNT films are generally the
cathodes of choice. Continuous CNT film arrays have field enhancement β values typically between
1000 and 3000 . Patterning CNT films further improve the field emission characteristics and stable
current densities as high as 10 mA/cm2 for applied fields for 5-6 V/µm have been achieved (118).
The increased emission current is attributed to the electric field enhancement along the edge of the
patterned structures (known as the edge effect) due to a reduced field screening. Increasing the
edges of the pillars, by introducing new patterned film geometries, leads to a greater total current
from the cathode due to an increased number of emission sites(119), Fig.5.1.
Hence, the ideal field emission cathode would be an array of individual CNTs of optimal density
(to minimize the field screening effect). Similar cathode structures made of vertically aligned carbon
nanofiber arrays have been achieved. But the emission characteristics of CNFs are less than optimal
due to the their inherently disordered stacked structure and relatively larger diameters. Conse-
quently, CNF arrays tend to have β values lower than 1000 and experience structural degradation
at high emission currents. In contrast, both SWNTs and MWNTs have a smaller tip radius and a
ordered tubular structure yielding a higher field enhancement factor and greater mechanical stability
than CNFs(118). But, nanotubes tend not to grow vertically from a sparse catalyst distribution.
They grow vertically in dense films propped by the large van der Waals interaction between CNTs.
98
CHAPTER 5. ELECTRIC FIELD ASSISTED MWNT GROWTH 99
-+
applied V
pillarsdonuts
I FE(A
mp
s)
Figure 5.1: Patterned carbon nanotube structures for enhanced field emission. Also plotted are fieldemission currents from the two different cathode structure. Introducing an extra edge in the donutstructure leads to current enhancement
One possible way to align individual CNTs would be application of a suitably directed electric field
during their growth.
5.2 Introduction
Electric field directed alignment of carbon nanotubes has been an active area of research since the
first study of carbon nanotube alignment and manipulation by electrostatic fields by Fishbine (120).
The basic mechanism takes advantage of the anisotropy of the CNTs, the polarizability along the
axial direction of the CNTs being greater than in the radial direction (19). The initial investigations
were restricted to orientation of CNTs dispersed in solutions by AC and DC electrophoresis (121;
122; 123; 124) . However these methods were not very successful due to the low solubility and
impurity of the CNTs and because of considerable viscous drag force involved.
Later investigations looked into aligning CNTs by incorporating an electric field during growth.
The most popular technique to date being plasma enhanced chemical vapor deposition (PECVD)
(20; 21; 22; 13; 24). In PECVD, a high bias voltage is applied for generating a glow discharge. In
this case the potential does not vary linearly between the electrodes, but rather is constant except
in the sheath region near the cathode where it decreases approximately linearly (23). The height
of the CNTs is smaller than the characteristic Debye length of the plasma, and hence the CNTs
are oriented by the high plasma sheath electric fields. However, complimentary studies show that
CHAPTER 5. ELECTRIC FIELD ASSISTED MWNT GROWTH 100
along with the electric fields generated in the sheath region other mechanisms like crowding effect
of the high density films, non-uniform stresses across the catalyst particle surface etc (22) helped in
aligning the CNTs. PECVD though, suffers from the disadvantage that it most often forms carbon
nanofibers rather than nanotubes, and nanotubes that do form are less oriented than the nanofibers.
Formation of CNTs or fibers is influenced by the growth conditions(13). High rates of flame synthesis
of aligned MWNTs using a DC field in flames have also been reported (24), though this technique
results in the formation of other carbon nanoforms depending upon the flame temperature and
concentration of chemical species.
Zhang et al. successfully demonstrated electric field directed growth of single-walled carbon
nanotube (SWNT) by thermal chemical vapor deposition process (CVD)(25; 26). They were able to
horizontally align SWNTs suspended over trenches and also directly on substrates by suitable choice
of electrode materials, directed electric fields of optimal strengths, and suitable surface treatments.
Further studies have been made to characterize and model horizontally directed SWNT growth with
a local field (27; 28). Interactions primarily with the substrate were considered and two growth
modes, surface and free growing, were proposed. Avigal et al. were the first to study aligned growth
of MWNT under a DC electric field applied perpendicular to the substrate (29). They observed that
aligned growth of MWNT was possible only under a positive sample bias. A negative bias resulted
in random growth while in the absence of an applied electric field there was no growth.
In this chapter, we use electric field directed growth for producing vertically aligned MWNT by
CVD. The electric field applied here is perpendicular to the substrate. The first part of the chapter
deals with the dependence of bias on the change in alignment of MWNTs. We address here the two
most important issues believed to control the alignment of the CNTs, spatial density of the MWNT
and the magnitude of the applied bias. To quantify the alignment of dense CNTs we develop a
novel technique, based on a two dimensional Fast Fourier Transform image analysis of Scanning
Electron Microscope images of nanotubes. A different technique based on the ability to detect
straight edges was developed to study the alignment of sparse MWNT grown from self-assembled
catalyst nanoparticles.
In the second part of the chapter we investigate the growth kinetics of field directed vertically
aligned MWNT. Interferograms recorded to monitor growth rates with and without bias were used
to determine activation barriers and corresponding rate limiting steps.
5.3 Experimental Technique: Catalyst preparation by Block
Co-polymer Micelle Templates
Two types of substrates are used to study the e-field effects on MWNT growth. Substrates for dense
MWNT growth were prepared by sputter depositing 2.5 nm of Fe on top of a 10 nm Al buffer layer
on C-type Si, as has been mentioned in the last two chapters. This technique has limited particle
CHAPTER 5. ELECTRIC FIELD ASSISTED MWNT GROWTH 101
Figure 5.2: Schematic of the different steps to synthesize Fe nanoparticles via a block copolymermicellar route
size control and results in formation of dense particle distributions. Hence to obtain a sparse but
uniform spatial distribution of catalyst nano particles we used a block co-polymer micelle template.
Block copolymers have been used extensively as self- assembled templates for the preparation of
periodic nanoparticle arrays. The choice of diblock copolymer determines the size of the nanoparti-
cles and more importantly determines the particle- particle spacing and therefore the spatial density
of catalyst particles. This approach has been applied successfully to form Au nanoparticle(125; 126).
Bennett et al.(127) and Liu et al.(128) used iron-loaded amphiphilic block copolymer polystyrene-
poly(acrylic acid) (PS-PAA) as templates to produce CNTs by thermal CVD.
The method of preparing the catalyst particles used is similar to that developed by Liu et al.(128).
For our experiments, PS-PAA di-block copolymer, with molecular weights of PS 42000= g/mol and
PAA =4300 g/mol, was dissolved in toluene with a concentration of 12 mg/mL and stirred for 4
hours. To convert all of the polymer material to the spherical micelle phase, the solution was heated
to 150oC for 20 minutes and then cooled to room temperature. FeCl3 was then added to the solution
with a 3:1 PAA monomer/ Fe mole ratio, as this reflects the charge ratio of the acrylic acid monomer
to the iron cation. The color of the micelle solution changed to dark yellow when the iron salts were
added. After adding the Fe salt the solution was stirred for 6 hours. Subsequent to this the solution
was diluted to 3.6 mg/ml. This was then spin-coated at 1500 rpm for 1 minute onto 10nm of
Al sputter deposited on Si(100). One drop was enough to form a monolayer coverage for a 1cm2
substrate. The micelle films were then heated in air to 400oC for 2 hours to remove the polymer,
leaving iron oxide particles on the Si substrate. Fig.5.2 is a schematic of the process described
above. For the right concentration and spin speeds a monolayer thick polymer can be deposited
which following calcination will result in the formation of self assembled uniform quasi-hexagonal
array of dots.
5.3.1 Characterization of the catalyst particles
The catalyst particle size and distribution controls the diameter and the density of the CNTs grown.
Fig.5.3 compares the catalyst particles obtained from the two different methods mentioned above.
CHAPTER 5. ELECTRIC FIELD ASSISTED MWNT GROWTH 102
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Figure 5.3: Size and density distribution of the Fe catalyst particles obtained from (a) block copoly-mer templates and (b) from sputter depositing 2.5 nm thin Fe film. The Y-axis for both the plotsare percentage values
Fig.5.3(a) shows the SEM image of the Fe particles formed by the micelle approach after thermally
removing the polymer. The particles so formed have a tighter size spread, and are arranged in a
quasi-hexagonal pattern. Fig. 5.3(b) is a representative image of the particles formed from the
continuous 2.5 nm Fe layer after annealing at 550oC. Fig.5.3(c) is a histogram of particle sizes.
The Fe particles obtained from the micelles have a narrow size distribution of 6.9± 0.8nm. Though
the mean diameter of particles formed from the continuous Fe film is similar, 6.5 nm, the spread
in the distribution is large. Fig.5.3(d) is a histogram of the particle density, obtained by measuring
the distance between centers of two adjacent particles. The sputter deposited films had a denser
particle distribution, with the mean separation between particles 25.2 nm. The particles formed
from the copolymer templates had a mean separation of 51.7 nm. Auger spectroscopy confirms
that the particles obtained by the micellar route is Fe-oxide. Fig.5.4 is an elemental map of a sparse
dispersion of micellar particles, attesting to the above fact. Also seen in the image is a large particle,
formed probably due to agglomeration of smaller particles.
For the catalyst particles obtained from the micelle templates the CNT yield is low, only about
20% of the catalysts grew CNTs, Fig. 5.5(a). Such behavior has been reported elsewhere (128).
CHAPTER 5. ELECTRIC FIELD ASSISTED MWNT GROWTH 103
Figure 5.4: Fe mapping of the particles obtained from the micelle template.(a) SEM image and(b)corresponding Fe map
One possible reason for the low yield could be micro-loading, where the chemical species present at
the surface are altered by catalytic surface reactions when the catalyst density is high. TEM of the
micellar particles was performed post MWNT growth. The motive was to look for distinguishing
features in particles that grew CNTs as opposed to those which did not catalyze MWNT growth.
For this, particles were deposited on an e-beam transparent Si-nitride TEM grid (50 nm thick).
TEM micrographs supported the observation that the MWNT yield of the particles were very low
Fig. 5.5(b). Due to the relatively thicker nitride membrane lattice images or proper CBED patterns
could not be obtained from the individual particles. Hence a crude dark field imaging method was
used to determine the crystallinity of the particles. To obtain a dark field image the metal strip
between the selected area diffraction apertures was used to block the transmitted image. Hence only
crystalline particles (diffracting in the right direction) can be observed as bright spots on the dark
field TEM images. Comparing the bright and dark field images from Fig. 5.5(d) we can see that
not all particles formed from the micelle template are crystalline. From Fig.(c) we observe that not
all crystalline particles resulted in formation of MWNTs. Only crystalline particles of intermediate
sizes resulted in MWNT growth. Thus, nanotube density obtained from the self-assembled particles
is sparse, and hence are relatively free of the steric crowding of neighboring CNTs. Therefore, we
were able to study the effect of electric field on arrays of isolated MWNT.
5.3.2 Control of catalyst size and separation using micelle templates
One of the advantages of the micellar route over the sputtered film method is the relatively stricter
and easier control of particle size and density. There are many simple strategies to control spatial
distribution. Increasing the concentration of the copolymer loaded in the toluene solution or by
decreasing the rpm during spin casting multilayers of polymer can be deposited which will increase
the density of the particles deposited.
A more controlled method of changing the spatial distribution is by choosing a block co-polymer
CHAPTER 5. ELECTRIC FIELD ASSISTED MWNT GROWTH 104
Figure 5.5: EM studies of MWNT yield from micellar nanoparticles. (c,d) Bright and dark fieldTEM images of particles subsequent to MWNT growth
with a different molecular weight PS polymer, Fig.5.6. This method is limited by the volume fraction
of PS:PAA, since only for a certain volume fraction spherical micelles form. Beyond this fraction
other forms of block copolymer templates form e.g lamellar, hexagonal arrangement of cylinders,
bi-continuous gyroids etc. Other methods of controlling density is adding PS polymer or blank
PS-PAA polymers to solution containing PS-PAA and Fe salt.
Increasing the size of PAA on the other hand can be used to increase the size of the catalyst
particle. This method is again limited by the relative volume fractions of PS and PAA. Another
method of controlling particle size is by changing the metal loading ratio. In Fig.5.7(a) FeCl3 was
added to the copolymer micellar solution at a loading ratio ∼ 0.3, leaving an excess carboxylic acid
groups. The Fe-oxide clusters, so formed, have a mean diameter of 3.61 nm. In Fig. (c) FeCl3
loading ratio is increased to ∼ 3. There is a significant excess of Fe compared to the carboxylic
groups, resulting in the formation of larger particles, mean diameter = 6.12 nm; almost doubling the
particle size by controlling the loading ratio. This method is limited by the saturation in the loading
capacity of the micelles, increasing the loading ratio beyond this limit will result in precipitation of
the excess Fe bearing salt from the micelle solution.
CHAPTER 5. ELECTRIC FIELD ASSISTED MWNT GROWTH 105
Figure 5.6: Controlling spatial density by controlling the size of the PS polymer
5.4 Experimental technique: MWNT growth
A brief recapitulation of the steps for growing MWNTs. The gap between the two electrodes is
maintained at 4 mm. Before growth the reactor was evacuated to a few mTorr pressure. The
substrate is annealed at 550oC for 5 minutes under hydrogen ambient. Following this step the
temperature is ramped to the growth temperature of 750oC. For CNTs grown from Fe nanoparticles
prepared by the micellar route, the annealing step is not performed. Ethylene and hydrogen flow
are maintained at 350 and 100 sccm respectively. Variations on the above operating conditions are
performed as described below. The most significant operating parameters for this study are the
chamber pressures and the magnitude of the biasing electric field. These two parameters are inter-
dependent. The breakdown voltage of the gas, between the parallel plates, determines the valid
ranges of these two parameters. The Paschen curve, which describes this behavior, shows that the
voltage necessary to arc across a fixed gap decreases with pressure to a minimum value, beyond which
it starts increasing with pressure. Similarly for decreasing gaps at fixed pressure (23). Maintaining
low gaseous pressure and small gap could be used to achieve high fields. Geometrical considerations
limit the minimum gap between the plates. Hence to achieve high fields it is either necessary to
drastically lower the pressure of the precursor gases or to operate at high-pressure regimes. Since
the precursor flux would be substantially diminished at low-pressure conditions, it is necessary to
operate at high pressure to apply high electric field. However, a pressure induced transition from
MWNT to carbon nanofibers limits maximum pressure in the reactor as discussed in the previous
chapter. The critical pressure that induces the change in morphology increases with a decreasing
catalyst particle size. At intermediate pressure regimes coiled MWNTs form, opposed to the straight
CNTs at lower pressures. Care has been taken to avoid the nanofiber formation pressure domain
for all the growth runs.
5.5 Results
The main motivation of this work was to study the effect of electric field on alignment of sparse
MWNT growth not hindered by steric effects suffered by dense MWNT forests. The initial field
CHAPTER 5. ELECTRIC FIELD ASSISTED MWNT GROWTH 106
0
5
10
15
20
25
1.5-
2
2-2.
5
2.5-
3
3.0-
3.5
3.5-
4.0
4.0-
4.5
4.5-
5.0
5.0-
5.5
5.5-
6.0
6.0-
6.5
6.5-
7.0
7.0-
7.5
7.5-
8.0
8.0-
8.5
perc
enta
ge
particle radius (nm)
PAA:FeCl3=1:3
PAA:FeCl3=3:1
Figure 5.7: Controlling particle size by controlling the metal loading ratio
assisted dense MWNT growths were dummy runs performed to get an idea of the parameter space.
But, interesting trends started to appear on application of bias even for the dense films, which called
for further investigation. In this section we report the height and alignment dependence of dense
MWNT films on the applied field followed by the alignment dependence for MWNTs grown form
block co-polymer micelle templates.
5.5.1 Characterization of the MWNT forests from sputter deposited Fe
films
Figure 5.8: SEM images of MWNT films grown at 400 Torr as a function of bias
CHAPTER 5. ELECTRIC FIELD ASSISTED MWNT GROWTH 107
SEM images of CNTs grown at a temperature of 750oC and a total pressure of 400 Torr are
shown in Fig.(5.8). The magnitude of the applied electric fields are zero, 0.75 and 1.0V/µm. In the
negative bias condition described here, the bottom electrode is grounded while the top is maintained
at negative potential with respect to the bottom. The SEM characterization of the CNTs reveal that
MWNTs grown with an applied bias resulted in cleaner, taller, straighter tubes Fig.(5.8). MWNT
were also grown under reverse bias (the top electrode is held at a positive potential in reference to
the grounded bottom electrode). Unlike (29)(where growth was reported only for the negative bias
condition) good growth was obtained for all these runs, with the MWNT morphology and height
showing similar trends.
However, for the 400 Torr growth, arcing was observed for higher applied fields. This has to
be avoided since various studies on plasma enhanced CVD growth of CNTs reveal that in the glow
discharge regime and higher current densities carbon nanofibers form in preference to CNTs (13; 22).
Hence following the Paschen curve, the reactor chamber pressure was maintained at 760 Torr to
access a larger range of biasing magnitude for manipulating the MWNT growth while remaining
within the dark discharge regime.
5 m
5 m
5 m
2 m
2 m
4 m
E = 0V/ m
E = +2V/ m
E = +6V/ m
E = -4V/ m
E = -6V/ m
E = -10V/ m
Figure 5.9: SEM images of MWNT films grown at 760 Torr as a function of bias
CHAPTER 5. ELECTRIC FIELD ASSISTED MWNT GROWTH 108
Fig. 5.9 shows SEM images of MWNT grown at a higher pressure of 760 Torr. The flow rates of
hydrogen and ethylene into the chamber were maintained at 350 sccm and 100 sccm respectively. To
systematically study the effect of increasing fields on the height and morphology of the CNTs, six
samples were grown with increasing biases from 0 to 1.0V/µm in increments of 0.2V/µm. Another set
of MWNTs were grown for the same conditions but with a reverse bias. However, arcing commenced
at lower fields (∼+0.8V/µm) relative to the negative bias case (∼ -1.4V/µm). Arcing for the reversed
bias conditions at lower fields than that of negative bias can be explained due to field emission and
thermionic emission from the growing carbon nanotubes (129). Electron emission from the MWNTs
can induce collision cascade ionization resulting in arcing between the plates. In the negative bias
growth, emitted electrons will be drawn back to the electrodes, reducing their interaction with the
gas. Fig.5.10 shows the increasing height of the CNTs with increasing bias. The height of the CNTs
increases with bias up to almost three times at 1.0V/µm compared to growth in the absence of a
field. Thus, with an applied electric field there is a definite enhancement in the growth rates.
14
12
10
8
6
4 Hei
ght
of t
he M
WNT
film
(µm
)
-1.0 -0.5 0.0 0.5
E-field magnitude (V/µm)
Figure 5.10: Height of the CNTs as a function of imposed electric field
Orientation analysis of nanotubes in MWNT forests
The extent of alignment of the CNTs is characterized by two-dimensional Fast Fourier Transform
(FFT) analysis of high magnification SEM images of the MWNT forests under different biasing
conditions. FFT has been used by Acharya et al. (130) to qualitatively describe the alignment of
electro-spun nanofibers. We have further developed the technique to include an orientation factor to
quantify the degree of alignment. The analysis procedure is shown schematically in Figs 5.11(a-c).
All image analysis was done using Matlab R2008a. To prevent edge effects in the FFT data, the edges
were blurred using a Gaussian low-pass filter as shown in Fig5.11(b). The FFT was then performed
on the edge-blurred images. Fig. 5.11(c) is a contour plot of the logarithm of magnitude of the
intensities, after the zero-frequency component of the Fourier transformed image has been shifted to
CHAPTER 5. ELECTRIC FIELD ASSISTED MWNT GROWTH 109
Figure 5.11: Characterization of the alignment of the e-field aligned MWNT forests. Fig. (a-c)describes the methodology for quantifying the alignment of the forests. Fig. (a) is the original SEMimage of the forests ;(b) the edges has been blurred to remove the edges from showing up whendoing the 2D FFT of the images;(c) contour plot of the FFT of (b).
the center of the spectrum. The intensities of this transformed image are used to quantify alignment.
For this we introduce the Hermans orientation factor, f . This quantity has been frequently used to
quantify orientation. For example, polymer scientists have used the Hermans orientation factor to
quantify in-plane orientations in semi-crystalline polymers (131). It is defined as:
f =3〈cos2 ϕ〉 − 1
2(5.1)
where
〈cos2 ϕ〉 =
∫I(ϕ) cos2 ϕ sinϕdϕ∫
I(ϕ) sinϕdϕ(5.2)
where I(ϕ) for this case is the absolute intensity of the FFT image at the azimuthal angle ϕ, defined
with respect to the ky = 0 line, as shown in Fig. 5.11(c). For perfectly straight nanotubes oriented
vertically with respect to the substrate, the FFT contour will be a straight line along ky = 0, hence
f = 1. For complete random orientation of the CNTs, the contour plot will be circular (instead of
elliptical as shown in Fig. 5.11(c)) and the correspondingly f= 0.
High magnification (50,000X) SEM images of the MWNT forests were taken for all the biasing
conditions as shown in Fig 5.12(a). It is important to recollect that pressure of the reactor has
important consequences on the morphology of the MWNT grown. As mentioned in the previous
chapter increasing pressure leads to the formation of coiled nanotubes, which can be evidenced from
comparing the SEM images Fig.5.12(a) with that of CNTs grown at lower pressures, Fig.5.8. At
least three images were taken for each sample to quantify the alignment of the base, middle and
the top regions of the forests. All SEM images were of the same magnification and size to avoid
introducing artifacts. Fig.5.12(b) plots the orientation factor vs. the magnitude of the applied bias.
Orientations factor for the base, middle and top of the forests for each biasing condition are reported.
The Herman orientation factor increased from an average of 0.16 for no bias to approximately 0.27
for the 1.0V/µm condition, showing a definite increase in alignment of the CNTs. For the same
sample, an increased alignment can be seen towards the top and middle of the forest as compared to
CHAPTER 5. ELECTRIC FIELD ASSISTED MWNT GROWTH 110
0.36
0.34
0.32
0.30
0.28
0.26
0.24
0.22
0.20
0.18
0.16
0.14
0.12
alig
nmen
t (H
erm
an p
aram
eter
)
-1.2 -0.8 -0.4 0.0 0.4 0.8 E-field magnitude(V/µm)
bottom alignment factor middle alignment factor top alignment factor
Figure 5.12: (a) High magnification SEM side-view images of MWNT films grown at different biases.Fig.(b) plots the alignment and the height of the forests vs. the applied biasing voltage
the portion of the MWNT forests near the substrate. This is true for almost all biasing conditions.
5.5.2 Characterization of the MWNT grown from catalysts obtained from
micelle templates
Next the effect of electric field on the growth of low density MWNTs was studied. Particles deposited
as a monolayer film show regular ordering but have a sparse coverage. These low-density particles
result in sparse non-uniform growth. Hence due to the absence of a crowding effect and with
no localized field to direct the growth of the CNTs, the MWNTs grown are randomly oriented,
Fig5.13(a). Figs 5.13(b-d) are representative images for MWNT growth under an increasing applied
bias, of the order of 1V/µm. All these growths were done under operating pressures of 1000 Torr.
This enabled us to achieve high electric fields of 1.2V/µm. Even with increasing bias, the SEM
images show the presence of nanotubes randomly oriented near the surface. This is particularly true
for regions where the density of MWNTs is high. In regions where the density of CNTs is sparse,
the MWNTs align along the direction of the applied bias, Fig. (b-d). Higher bias resulted in the
formation of taller and straighter CNTs. The number of CNTs aligning in the direction of the fields
also increased with increasing field.
CHAPTER 5. ELECTRIC FIELD ASSISTED MWNT GROWTH 111
Figure 5.13: SEM images of MWNT grown from micelle templates. MWNTs (a-d) are grown underthe influence of increasing electric fields. The magnitude of the bias is printed on the respectiveimages.
Orientation analysis of isolated MWNTs
The FFT based image analysis technique cannot quantify alignment of the isolated CNTs. For this,
an edge tracking method was developed based on the approach of Kovesi et al. (132). The basic
algorithm is described in Figs 5.14(a-c). The first step is to detect the edges of the CNTs. This is
done by looking for local maxima in the gradient of intensities of the SEM images of the isolated
nanotubes. The co-ordinates of the maxima positions are listed and linked together to obtain the
nanotube edges (Fig.5.14(b)). Straight segments are then fitted to each edge after defining minimum
length specifications (Fig.5.14(c)). Next, the angles made by the straight edges with respect to the
substrate are obtained. At least 25 CNTs were analyzed for each of the growth runs. Fig.5.14(d)
shows the alignment data in the form of a bar chart that plots fraction of tube lengths within a
certain angular range. The bar chart confirms the observations made from the SEM images. The
fraction of tube segments aligned along the direction of the field increases with bias, with fraction
of tube segments making an angle of 80− 90o to the substrate going up from 6% for no bias to more
than 20% for an applied bias of 1.2V/µm. The probability of a tube segment inclined more towards
the normal away from the base is near 30% for growth without a field. For growths under an applied
bias the probability of CNTs being inclined towards the direction of the applied field increases to
more than 60%. This probability appears independent of electric field magnitude above 0.65V/µm.
CHAPTER 5. ELECTRIC FIELD ASSISTED MWNT GROWTH 112
(a)
(b)
(c)
20
15
10
5
00-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90
angle (degrees)
20
15
10
5
0
20
15
10
5
0
per
cent
age
20
15
10
5
0
e-field = -1.20V/um e-field = -0.90V/um e-field = -0.65V/um no bias
Figure 5.14: Alignment of MWNT for different biasing conditions. Figs (a-c) describe the alignmentalgorithm. Fig (b) defines the edges from the original SEM image (a). Straight segments are fittedto the edges so obtained, and the angles made by these segments are measured with respect to thehorizontal plane. Fig (d) is a bar chart that compares the fraction of lengths oriented with in anangular range for different applied electric fields.
5.6 Discussion: Tube Alignment and applied field
Electrostatic alignment of CNT takes advantage of the unique 1D morphology of the CNTs. The
polarization coefficient along the axial direction of the tube is significantly larger than the radial
direction(19). The difference in polarizability, results in a net dipole moment that aligns the tube
in the direction of the field. However the nature and magnitude of the force may vary depending
on the nature of the CNTs (MWNT, metallic or semi-conducting SWNT), the spatial density and
the length of the CNTs. The discussion section is divided into two parts. First we consider the field
effects on the sparsely dispersed MWNT growing on isolated catalyst islands and then the dense
MWNT forests.
CHAPTER 5. ELECTRIC FIELD ASSISTED MWNT GROWTH 113
5.6.1 Alignment for isolated MWNT
Fig. 5.15(a) is a schematic of a MWNT oriented at an angle θ with respect to the field. The
dipole moment of a tube is ~p = αijLEj , where αij is the polarization tensor. For MWNTs the
axial polarizability tends to be a sum of the polarizabilities of all its constituent tubes, while the
transverse probability tends to that of the outermost tube of the MWNT (133). Hence, for all
subsequent calculations the effect of the transverse component will be neglected (i.e. αij ≈ α‖,
where α‖ is the polarizability along the tubular axis). Since, the dipole moment of the MWNT is
large, MWNTs are easier to align in the direction of the electric field. The magnitude of the torque
aligning the MWNT along the direction of the electric field is given by:
|τ | = 1
2α‖LE2 sin 2θ (5.3)
and the associated energy by:
|U| = 1
2α‖LE2 cos2 θ (5.4)
U is minimized for θ = 0, hence the torque tends to align the tube along the direction of the field.
D
L
x
y
u~L(1-‐u/2D)
(a) (b)
Figure 5.15: Schematic of a MWNT oriented at an angle θ to an applied electric field (a). Fig (b)is a schematic of two different vibrating growth models; case (I) where the CNTs are not touchingand case (II) where the tip of the CNTs might interact.
Similar to the approach of Lieber et al. (27) and Hongo et al. (28), two growth modes for the
vertical growth of MWNT are proposed, Fig 5.15(b), free growing and growing while in contact with
neighboring CNTs. For the vertical growth mode we neglect the interaction between the CNTs and
the surface. The nanotube grows vertically from the catalyst, with the tip of the CNTs vibrating
CHAPTER 5. ELECTRIC FIELD ASSISTED MWNT GROWTH 114
thermally with amplitude, u. In case of u <D/2 (Case I), where D is the separation between CNTs,
two neighboring tubes would never interact. This is true for short tube heights or for CNTs grown
from low-density catalyst particles. In case of u >D/2 (Case II), the CNTs have a finite chance of
touching the neighbors. This case corresponds to longer CNTs and for tubes grown from closely
spaced catalyst particles. When the two CNTs come in contact with each other, the probability of
short-range interaction forces (e.g. van der Waals, dipole-dipole interaction etc.) become significant
in controlling the orientation of the nanotubes.
To estimate the amplitude, the MWNTs are simulated as cantilever beams fixed at one end. In
the limit of small amplitude the motion of a vibrating rod under the influence of an electric field is
given by the equation (28):
ρAδ2y(x, t)
δ2t+ YI
δ4y(x, t)
δx4−α‖E
2
2
δ2y(x, t)
δx2= 0 (5.5)
The above differential equation balances the kinetic energy of the vibrating CNTs, and the elastic
energy due to bending and electrostatic forces due to the applied field on the polarizable CNTs. For
no bias growth the third term is zero. The vibration amplitude is controlled by the strain energy
to bend the tube. This amplitude for a tube of outer and inner radius, rNT and rin respectively is
given by (86)
u2E=0 =
0.424L3kBT
Y(r4NT − r4
in). (5.6)
Fig. 5.16 plots u as function of height of the tube (outer radius 5 nm, inner radius = 3.3 nm,
and Youngs modulus, Y = 1.0 TPa). Its also known from Fig.5.3, D/2 ∼ 25 nm. From the plot
we see that the vibration amplitude becomes greater than this value when the height of the tube is
3µm. For taller CNTs the growth crosses over to Case II mode, where the van der Waals interaction
becomes significant. The van der Waals interaction energy between two CNTs of radius R touching
is given by the relation (134)
EvdW ≈A√
R
24a3/2g
L(1− u
2D) (5.7)
where A is the Hamaker constant (for MWNT A ∼ 1eV), and ag is the gap between two graphene
sheets. The magnitude of this interaction energy is orders of magnitude higher even for short contact
lengths than the thermal energy at the growth temperature (∼0.086 eV). Hence, for taller CNTs
van der Waals causes stiction and prevents freestanding tube growth. The SEM image of growth
under no bias attests the above observation.
For biased growth, the solution of eqn. (5.5) is cumbersome. An analytical solution is not
possible. A numerical solution to the partial differential equation (5.5) was performed to obtain the
values for the allowed frequencies (please see the Appendix). The total elastic energy contained in
CHAPTER 5. ELECTRIC FIELD ASSISTED MWNT GROWTH 115
10-5
10-4
10-3
10-2
10-1
100
101
102
Am
plitu
de o
f the
tube
tip
(nm
)
108642 Height of the MWNT (!m)
E= 0V/m E= 10V/m E= 100V/m E= 1000V/m E= 10
4 V/m
E= 105 V/m
E= 106 V/m
Figure 5.16: Plots the lower order vibrating amplitudes of the tube tip as a function of the appliedfield and the tube height. The , ∆ correspond to the first and second order amplitudes. Thearea between the dashed line corresponds to the distribution of half the inter tube separation, D;amplitudes greater than these values will result in case (ii) growth mode. (1V/µm = 106V/m)
the vibration mode n is given by the relation :
Eelasticn = |YI
2
∫ L
0
(δ2yn
δx2)2dx|sin(ωt)=1 =
1
2celasticn u2
n (5.8)
where ω is the frequency of vibration, and cn, un are respectively the effective spring constant and
deflection of the nth vibrational mode.
Also the average energy of the nth mode is 〈En〉 = kT , half of which comes from the elastic
energy degree of freedom. Thus comparing equation (5.8) with kT we can obtain the amplitude for
each vibrational mode (28).
δn = (kBT
celasticn
)12 (5.9)
CHAPTER 5. ELECTRIC FIELD ASSISTED MWNT GROWTH 116
Knowing the allowed frequencies, the amplitude of each vibrational mode can be calculated. The
amplitudes for the lower order modes so obtained are plotted as a function of nanotube height
and applied field strength in Fig. 5.16. For no bias and low applied fields the amplitude of the
fundamental mode is greater than the higher order modes. But for large bias these amplitudes
are similar. The most important effect, though, is a decrease in the vibration amplitude of the
CNTs by a few orders of magnitude on application of an electric field. This is a consequence of the
large polarization tensor of the MWNT along the axial direction, of the order of 106A2 (135). The
amplitude of the tip is larger than D/2 only at very low applied fields of the order of ∼ 102V/m.
For the e-fields used in our study ∼ 106V/m and for tube heights typically obtained ( < 10µm) the
vibration amplitude is never greater than D/2. Hence the model suggests that the main impact of
the applied field is to keep growth in Case I regime. This is achieved at relatively small applied
fields. The above observations support the experimental results. Application of an electric field
enhances alignment, the presence of vertical CNTs, Fig 5.13(b-d), attests to that. But subsequent
increase in applied field from 0.65V/µm → 1.2V/µm does not result in any significant increase in
alignment.
We have neglected the contribution of the van der Waals interaction between the CNTs and the
substrate. This is a non-trivial interaction particularly during the initial stages of growth, when the
effect of the imposed electric field is limited as α‖ is length dependent. This attractive force with
the substrate will bend the CNTs, resulting in tube growths parallel to the substrate. In regions of
dense MWNT growth, this will increase inter tube interactions that would dictate alignment and
result in randomly oriented growth; as is seen from the SEM images. CNTs growing in a sparse
region free of these interactions in the early growth stages therefore should be perfectly oriented due
to the presence of the electric field. It has to be noted that even for these sparse CNTs, we dont
get straight tubes growing perpendicularly to the substrates. This is because defects in the tube
structure, introduced due to high-pressure growth conditions, result in the formation of kinks that
cannot be straightened by the imposed field.
For Case II growth with an imposed field, the dipole-dipole repulsive interaction between CNTs
would have to be considered. The maximum repulsive force between two dipoles separated by a
distance r is given by Edipole = p1p22πεεor3
(134). Due to the high value of the axial polarization and
the large applied fields, the dipole-dipole interaction would be the dominant short-range force. This
short range repulsive forces would further limit interaction between CNTs.
5.6.2 Alignment of nanotubes in a dense MWNT array
Calculations from the last section show that for field strengths used in this study the vibration
amplitudes of the MWNT tips are in the sub-Angstrom level. The spatial density of the catalyst
particles is not high enough to result in Case II growth even for the continuous Fe thin film substrates.
Thus the short-range forces are not significant and hence there should be limited or no interaction
CHAPTER 5. ELECTRIC FIELD ASSISTED MWNT GROWTH 117
between the CNTs. But the high magnification SEM images (Fig. 5.12(d-f)), even in the presence of
large electric field, show a coiled morphology. This is due to the presence of pressure-induced defects
to the MWNT structure that result in the formation of kinks. Thus, the MWNTs in the dense
forest can be simulated as a bunch of closely packed helical springs, as shown in Fig. 5.17(a). In
the absence of an electric field the main force acting on these CNTs is van der Waals that results in
the dense MWNT being aligned parallel to the growth direction. With the application of an electric
field, there is separation of charges along the length of the CNTs, resulting in significant repulsion
between tubes, which keeps them aligned. SEM images show straighter MWNTs with increasing
strength of applied fields, a fact also reflected by the FFT image analysis of the CNTs. The forces,
mentioned above, explain the general alignment of the MWNTs along the growth direction in the
presence and absence of an electric field but cannot explain formation of straighter CNTs with
increase in applied bias. Thus it calls for further investigation.
There is unbalanced stretching force acting on the CNTs in the direction of the applied field
(Fig 5.17(a)) that has not been considered. This tensile force may result in stretching of the spring
(the pitch changes, but the arc length of one coil remains the same) and hence may account for the
increased alignment by forming straighter CNTs. Thus its worthwhile to find the magnitude of the
forces involved. Parameters of the nano-coiled spring being considered are the coil radius, R, pitch
λ, and D, the spring diameter. It is also implicit in the model, that these parameters in the absence
of an applied field have average values characteristic of the growth conditions, e.g. temperature and
pressure. The spring constant K of the nanocoil is defined as the total applied force divided by the
total elongation. In terms of shear modulus of the material, G, and the geometry of the nanocoil,
K can be expressed as (136):
K =GR4
8D3NK =
Ks
N(5.10)
where Ks is the spring constant of a single turn of the MWNT coil and N, the total number of turns.
The value of Ks has been reported to vary between 10N/m to 1N/m (136; 137). The force needed
to stretch the coil by a distance x is then given by the equation:
Fspring = −Kx = −Ks∆λ (5.11)
where ∆λ is the elongation for a single coil, Fig.5.17(b). Next the magnitude of the electrostatic
force needs to be calculated. The charge on the nanocoil can be calculated by approximating it as
a cylindrical Gaussian surface. Hence
∵ εo
∮εE · dS = q ∴ qcoil ≈ πεεoDLE
The electrostatic force acting on the cylinder, in presence of an electric field of strength E, is given
CHAPTER 5. ELECTRIC FIELD ASSISTED MWNT GROWTH 118
by the relation:
Fe = −πεεoDLE2 (5.12)
Equating (5.11) and (5.12) the elongation per coil of the MWNT can be obtained.
∆λ(E) =πεεoDLE2
Ks(5.13)
D
~(D- D)
L
Fe(a)
0.40
0.35
0.30
0.25
0.20
0.15
alig
nmen
t (H
erm
an p
aram
eter
)
-1.2 -0.8 -0.4 0.0 0.4 0.8 E-field magnitude(V/µm)
(b) bottom alignment factor middle alignment factor top alignment factorcalculated parameter bottom Ks = 2.1 N/mcalculated parameter bottom Ks = 2.3 N/mcalculated parameter bottom Ks = 1.8 N/m
Figure 5.17: (a) Schematic of a forest of MWNT, simulated as a bundle of springs. Parameters of thespring, coil radius = D, pitch = λ. Fig (b) plots the alignment of MWNT in the forests, measuredby the angle 〈ϕ〉(see text for details), as a function of the applied field. The markers are anglesobtained from the FFT of SEM images of the MWNT forests, while the dotted lines are theoreticalfits, simulating the forests as springs with constant Ks. Fig. (c) is a plot of MWNT heights while thedashed lines are simulated plots of MWNT height if they were only being stretched by electrostaticforces.
Next step will be to check if this elongation per coil of the helical spring, can account for the
observed increase in alignment as a function of applied bias. To quantify the alignment of the CNTs
we used the Hermans orientation parameter. This parameter is basically the weighted average of the
square of cosine of the angle made with respect to the Kx axis of the transformed image; weighted
by the integrated intensity of the FFT-ed SEM image along that angle. The tangent of the average
of the angle so obtained is hence the ratio of the magnitudes of the resultant Ky and Kx vectors.
Ky and Kx are the axes of the transformed image along the x and y direction of the original SEM
images. Now a 2D image of the bundle of helical springs can be represented by a series of sinusoidal
curves, very similar to that shown in Fig 5.17(a). This in effect can be described by a cosine function
along the y direction, with amplitude 0.5D and wavelength λ, and a series of delta functions along
the x direction. Fourier transform of a cosine function results in an impulse function while a series
CHAPTER 5. ELECTRIC FIELD ASSISTED MWNT GROWTH 119
of delta functions transforms to a summation of exponential functions.
F〈D〉2
cos(2π
〈λ〉y) =
〈D〉4
(δ(Ky − 〈λ〉) + δ(Ky + 〈λ〉)) (5.14)
F∑
n
δ(x− n〈D〉) = (∑
n
exp(−i2πKxna)) (5.15)
where < D > and < λ > are respectively the average spring diameter and pitch for a particular
applied field. Hence, the expression for the average angle for the FFT image is given by the relation:
〈ϕ(E)〉 = tan−1[
C1〈λ(E)〉
C2〈D(E)〉
] (5.16)
= tan−1[C1
C2× 〈D(0)〉+ ∆D(E)
〈λ(0) + ∆λ(E)] (5.17)
For simplicity we assume that ∆D(E) ∼ −∆λ(E) , then the above equation takes the following form
〈ϕ(E)〉 = tan−1[tanϕ(0)1− ∆λ(E)
〈D(0)〉
1 + ∆λ(E)〈λ(0)〉
(5.18)
Substituting (5.13) in (5.18) we can calculate the dependence of ϕ(E) on the magnitude of the
applied field. Knowing ϕ(E) the Hermans orientation parameter f can be calculated from eqn.(1).
This is plotted in Fig. 5.17(b). The markers are angular data obtained from the FFT of the MWNT
images. The three dotted lines are theoretical fits for the Herman alignment parameter for the
bottom, middle and top portions of the MWNT. The spring constant is the fitting parameter, while
assigning ε = 1000 (138),< D > = 30 nm and L = 5.2µm as obtained from SEM images of the
MWNT forest grown in the absence of a local field. The theoretical fit predicts well the trends
observed from that of the experimental values. The relevant spring constants range from 1.8N/m
to 2.3 N/m, and these values fall within the range of spring constant values (1-10N/m) reported in
the literature. Therefore the increased degree of alignment can be attributed to the stretching of
the MWNT forests by the unbalanced out of plane electrostatic force acting on the CNTs.
It has to be noted that, stretching of the MWNT forests due to electrostatic forces does not
account for the increased height of the CNTs. It accounts only for an approximate height increase
of about 20% or about a tenth of the total height increase between E=0 to E=1V/µm condition.
5.7 Discussion: Growth kinetics and electric field
As discussed in the foregoing sections an applied electric field enhances the MWNT film heights
compared to that of a zero bias condition. This height enhancement could not be accounted for
by the formation of straighter CNTs obtained on application of a bias. Therefore we investigated
CHAPTER 5. ELECTRIC FIELD ASSISTED MWNT GROWTH 120
further the effect of electric field on MWNT film heights.
5.7.1 Further investigations of growth: time resolved reflectivity studies
Interferograms were recorded to track the height of the CNTs during growth in real time. In order to
accommodate the interferometer setup the minimum gap between the two electrodes was increased
to 10 mm. The view ports were not rated for positive pressures and hence the operating pressure
was restricted to 760 Torr. As a consequence, the magnitude of the maximum applied field without
electrically breaking down the precursor and carrier gases was limited to 0.3V/µm, about a third
of the maximum field used in 5.1. The flow rates of hydrogen and ethylene into the chamber were
maintained at 150 sccm and 100 sccm respectively. Lower flow rates were used here to reduce the
growth rate and improve the resolution of the interference fringes. Typical growth times are 10-15
minutes.
Fig.5.18(a) plots the interferometric signal recorded for nine different growth conditions. This
signal is indicative of the reflected intensity off the substrate. Attenuation of the reflected intensity
by absorption and scattering is accompanied by formation of fringes due to interference between the
beams reflected off the top of the MWNT surface and the catalyst substrate. At lower temperatures
the curves show pronounced oscillations in intensity. With increasing temperatures the oscillation
frequency increase significantly indicating faster growth rates. Fig.5.18(b)shows the experimental
heights as obtained from the interferometer scans and SEM imaging with the corresponding theoret-
ical fits, developed in Chapter 3. A closer look at the interferograms also reveal that the oscillation
time period decreases with increasing magnitude of the bias (See Table 5.1). These numbers also
show that the difference in cycle period between MWNT growth with and without a field decreases
with increasing growth temperature. At T = 775oC the cycle periods are approximately the same. In
other words, growth rates increased with an applied electric field, but the relative change decreased
with an increase in growth temperature.
Table 5.1: Cycle periods and steady state growth rates as a function of temperature andbias magnitude
Temp. electric field 1st period 2nd period growth rate(oC) (V/µm) (secs) (secs) (nm/sec)
700 0 153 162.2 7.80.3 120.7 115 11.8
725 0 67 65.8 18.80.3 59.8 60.1 22.4
750 0 33.5 31.5 34.50.22 32.8 28.2 35.80.3 29.1 26.8 39.4
775 0 21.28 17.7 610.3 21.7 18.0 60.7
CHAPTER 5. ELECTRIC FIELD ASSISTED MWNT GROWTH 121
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
Nor
mal
ized
Ref
lect
ivity
4003603202802402001601208040
Time (secs)
Gro
wth
sta
rted
(a) no bias (T=700
oC) no bias (T=725
oC) no bias (T=750
oC) no bias (T=775
oC) E = 0.3V/!m (T=700
oC) E = 0.3V/!m (T=725
oC) E = 0.3V/!m (T=750
oC) E = 0.3V/!m (T=775
oC) E = 0.22V/!m (T=750
oC)
28x103
26
24
22
20
18
16
14
12
10
8
6
4
2
0
MW
NT h
eigh
t (n
m)
10008006004002000 Time(secs)
SEM heights
SEM heights
(b) 775oC; E= 0V/µm 750oC; E= 0V/µm 725oC; E= 0V/µm 700oC; E= 0V/µm
775oC; E= 0.3 V/µm 750oC; E= 0.3 V/µm 725oC; E= 0.3 V/µm 700oC; E= 0.3 V/µm
1.4
1.3
1.2
1.1
1.0
ratio
MW
NT v
olum
e fr
actio
n
780760740720700
Temperature (oC)
(c)
E= 0V/µm E= 0.3V/µm
Figure 5.18: (a) Time resolved reflectivity plots for the temperature dependent growth runs. Thesolid lines are interferometer scans for zero bias growth, while the dashed lines are the correspondingscans for a negative bias of 0.3V/µm. In between the two sets is the interferogram for a bias of0.22V/µm and growth temperature of 750oC. The plots are offset for clarity, with scans obtainedfrom the same bias magnitude grouped together. Fig. (b) plots the experimental heights obtainedfrom the interferometer scans and their theoretical fits. Fig. (c) is a plot of the relative change indensity of the MWNT film with change in bias and temperature. The reference density correspondsto MWNT films grown at T=700oC with zero bias
CHAPTER 5. ELECTRIC FIELD ASSISTED MWNT GROWTH 122
The interferometer signals have two other distinguishing features. First, it can be seen that the
intensity of the background signal (non-oscillatory) increases with temperature. The background
intensity is attributed to the intensity of the laser beam reflected off the top of the CNT film in the
absence of interference effects. Reflectance of a beam incident normal to the surface is given by the
relation (139):
R = 1− 4n
(1 + n)2 + k2
where n, k are the real and imaginary parts of the refractive index of the reflecting surface. For an
effective medium material such as the MWNT forest, n and k, will increase with film density. This
indicates that the MWNT density is increased at higher temperature.
Secondly, the amplitude of the oscillations decrease, making the interference fringes less promi-
nent with an increase in temperature. A smaller decrease in oscillation amplitude is seen on applying
an electric field. Similar to the change in MWNT growth rates the relative change in amplitudes
with bias decrease with increasing temperature. This trend can be understood considering the origin
of the amplitude. The oscillations are a result of the interference of the beams reflected off the top
of the MWNT forest and the beam reflected off the nanotube-substrate interface. The intensity of
the second beam going through the MWNT forest will be attenuated following Beer Lambert law.
I
Io= exp(−αl) (5.19)
α = −1
I
dI
dx=
4πk
λo(5.20)
where α is the absorption coefficient, λo the wavelength of the incident beam and l the distance
travelled by the beam in the absorbing MWNT film. The absorption coefficient increases with
increasing density of the film, decreasing the beam intensity and hence the oscillation amplitude. At
the same time oscillation amplitude will reduce as l increases. These effects are separated by first
subtracting the attenuating background from the raw interferometer data (See Chapter 3 for details).
The MWNT film height, is determined from the interference signal facilitating the determination of
the absorption coefficient from eqns.(19 & 5.20).
The absorption coefficient can be alternatively defined as
α =4πσeff
εeff1/2c
(5.21)
where σeff is the effective conductivity, εeff the dielectric constant and c the speed of light in
vacuum (139). The effective dielectric constant and conductivity of the MWNT films can estimated
using formulae for a two component system, air and MWNT. Different formulations are available to
evaluate these properties, the simplest being the one due to Looyenga. This formulation has been
used by researchers to evaluate the density of nanotubes, optical properties of porous silicon etc.
CHAPTER 5. ELECTRIC FIELD ASSISTED MWNT GROWTH 123
(76; 140). The Looyenga formulation
ε1/3eff = ε
1/31 + f(ε
1/32 − ε1/31 )
σ1/3eff = σ
1/31 + f(σ
1/32 − σ1/3
1 )
where f is the volume fraction of the second phase, works well for systems away from the percolation
threshold (141). Applying the Looyenga formula to eqn.(5.21) and from the fact that the dielectric
coefficient and conductivity of the MWNT are orders of magnitude more than that of air, the effective
absorption coefficient of the MWNT films can be related to the volume fraction f and hence the
density of the films by the relation:
α ≈ 4πf3/2σMWNT
cε1/2MWNT
(5.22)
It is assumed that the intrinsic properties of the MWNTs do not change much with conditions.
Hence from eqn.(5.22) the absorption coefficients are proportional to f3/2, which is proportional to
the 3/2 power of spatial density. This is plotted in Fig.5.18(c). It is observed that the density of
the films increase with increasing temperature, as discussed based on the background intensity of
the scans. The density also increases with an imposed field for lower growth temperatures, while for
MWNT grown at 750oC and 775oC the densities are independent of the field.
5.7.2 RGA Analysis
As discussed in the previous sections increasing magnitude of the applied bias increases the height
and alignment of the MWNT films. The interferometer data supports this and also reveals that
the enhancement is temperature dependent. The height and density of the MWNTs increases on
application of an electric field, implying that the carbon yield in the MWNT forests is more. This
requires an increase in the carbon flux through the catalysts. Carbon flux can increase due to a
variety of reasons. For example, the increase in flux could be due to an increase in vapor phase
diffusive flux due to an increase in the chemical potential of the gases on application of an external
field. Alternatively, gas phase decomposition due to the applied field might add to the decomposition
reactions on the catalyst surface, increasing the net transport across the vapor phase-catalyst inter-
face. Either way this enhanced flux must be a consequence of imposing an external field. To verify
this, the reactor gas composition was monitored using the RGA. For neutral species measurements,
the acquired mass spectra must be de-convoluted, as the resulting intensities, i, from the RGA are
products of the original species’ cracking patterns (50). For a system of n species and m spectra,
the following matrix must be solved to estimate the neutral species density,D.
[im,1] = [am,n][Dn,1] (5.23)
CHAPTER 5. ELECTRIC FIELD ASSISTED MWNT GROWTH 124
where ai,n represents the cracking patterns for the nth species. The cracking patters are obtained
from the NIST chemistry web-book (51) and from in-house databases obtained from prior RGA
studies of nanotube and nanofiber growth conditions (50; 52). Results obtained in this way can
be compared relatively for a single species at varying conditions. Fig.5.19(a) shows the difference
between the density of species recorded after steady state condition was achieved and just before the
onset of growth. Five different conditions are shown,: without catalyst, growth in the absence of an
electric field, and growth with applied biases of 0.3V/µm, 0.4V/µm and 0.5V/µm. The pressure was
maintained at 400 Torr and temperature at 750oC. For the last case arcing was observed towards
the end of the growth run.
The chemical species tracked in Fig5.19(a) demonstrate the effect of field on the decomposition
of carbon precursor. The volume fraction of ethylene decreases by a small amount in the presence of
a catalyst and more significantly on application of a bias, suggesting that ethylene is decomposed on
the application of a field. Hydrogen does not show an appreciable change with the change of bias.
Concentration of the byproducts of ethylene decomposition show small but consistent increase on
application of an electric field, except for two of the higher molecular weight species. The amount
of carbon monoxide in chamber also increases particularly at a field strength of 0.5V/µm. This may
indicate an increase in carbon radicals which recombine with the residual oxygen in the RGA. The
net conclusion of the RGA data is therefore that the electric field assists in decomposition of the
carbon precursor.
The pressure change in the chamber maintained at constant pumping speeds during the growth
was monitored . For a constant inflow of gas, maintained by mass flow controllers, and an ap-
proximately constant pumping speed as determined by the valve conductance the change in reactor
pressure depends upon the number of moles of the gaseous species generated in the reactor. The
pressure change as a function of growth time is plotted in Fig.5.19(b) for the same MWNT growth
runs for which RGA analysis was performed. It is observed that with application of an electric field
there is a small but observable pressure increase. Similar small pressure increments were observed
for all growths on imposing an electric field. This suggests that electric field assisted breakdown of
the gaseous mixture results in the conversion of ethylene to its byproducts.
5.7.3 Analysis of the kinetic data
The current flowing between the two electrodes was measured to be non-zero but less than 1µA
implying that the field assisted MWNT growth conditions fall within the Townsend discharge regime.
The current density flowing in between the plates is given by the following expression (23):
I(z) = I(0) exp
(∫ z
0
αn(x′)dx′)
(5.24)
CHAPTER 5. ELECTRIC FIELD ASSISTED MWNT GROWTH 125
0.125
0.25
0.5
1
2
4
8
16
32
64
128
Cha
nge
in In
tens
ity
H2 C CH4 H2O C2 C2H2 C2H4 CO N2 O2 CO2
(a) no catalyst with catalyst 0.3V/µm 0.4V/µm 0.5V/µm (arcing)
120
100
80
60
40
20
0
cha
nge
in P
ress
ure
(Tor
r)
4003002001000 time(secs)
(b)
no catalyst with catalyst 0.3V/µm 0.4V/µm 0.5V/µm
Figure 5.19: Characterization of the reactor gases: (a)RGA results; Bar chart showing the changein mole fraction of the relevant gaseous compounds between the start and the end of the MWNTgrowth runs. The change in species density are normalized by the residual fractions in the RGAbefore the admission of the reacting gases into the mass analyzer at the onset of growth. Fig. (b)plots the change in reactor pressure for the different growth runs, while keeping the in and outflowof gases constant.
where I(0) is the current generated at the cathode, z is the separation in between the electrodes
and αn ,the first Townsend coefficient , is the inverse of an ”ionization” mean free path. Assuming
the discharge coefficient to be constant and for an electrode spacing d, the current density can be
written as I(d) = I(0) exp(αnd). The Townsend coefficient is a function of pressure and accelerating
field between the electrodes. Plugging in the typical form for αn the current density between the
parallel plates due to an applied field E can be expressed as:
I(d) = I(0) exp
(Apd exp
(−BpE
))(5.25)
where A,B are experimentally determined constants specific for a given gas and p is the cham-
ber pressure. Assuming that the density of dissociated products obtained from the field assisted
CHAPTER 5. ELECTRIC FIELD ASSISTED MWNT GROWTH 126
decomposition of ethylene, is determined from the current and hence charged species density, the
additional carbon flux may be written as :
Jef = KI(d) (5.26)
where K is a proportionality constant.
This hypothesis explains the field assisted height increase due to enhanced carbon flux through
the catalyst particle. But it fails to explain the observed height and growth rate dependencies on
temperature, and also the weakening impact of field at higher field magnitudes, Fig(5.10). These
trends may be explained by considering the overall kinetics of growth. Fig.(5.20) shows an Arrhenius
plot of steady state growth rates of MWNT with and without applied field, obtained from the analysis
of the interferometer data reported above. For reference, growth rates from another temperature
dependent study at growth pressures of 265 Torr is also shown(Chapter 3, Sec 5.1).
6.0
5.5
5.0
4.5
4.0
3.5
3.0
ln(v
RT/∆
µ)
1.04x10-31.021.000.980.960.94 1/T (K-1)
194 kJ/mole
189 kJ/mole
327 kJ/mole
198 kJ/mole
316 kJ/mole
P=265 Torr, no bias P=760 Torr, no bias P=760 Torr,E = 0.3V/µm
Figure 5.20: Arrhenius plots of normalized steady state growth rates plotted as a function of theinverse of temperature. Three sets of data are presented; MWNT growth under no bias at lower(265 Torr.) and higher pressures(760 Torr.) in the absence of an electric field and temperaturedependent growth runs for an applied electric field of 0.3 V/µm. The activation energy calculatedfrom the plots are printed on the figure
While a single activation energy could be extracted for the cases without field, the deviation
from such a fit at low temperature, and the similarity of the field enhanced case at high tempera-
ture, prompt us to consider a two activation energy model. The high temperature growth rates are
CHAPTER 5. ELECTRIC FIELD ASSISTED MWNT GROWTH 127
well fit by a straight line, giving an activation barrier of 198 kJ/mole, while the lower temperature
growths have an activation energy of ∼316 kJ/mole. Similar behavior was seen for the low pressure
growth runs, with an activation energy of 189 kJ/mole at high temperature and 327 kJ/mole for low
temperature. For the lower activation barrier, the rate limiting step was identified to be interface
transport limited. The activation energy obtained at lower temperatures is also too high to be asso-
ciated with a diffusive process (refer to Chapter 3. Table 1). The activation barrier of ∼320kJ/mole
is closer to the bond energies of the three types of bonds present in ethylene( C-H : 410 kJ/mole,
the π and σ bonds of C=C are respectively 264 kJ/mole and 347 kJ/mole ). This suggests that the
rate limiting step for the lower growth temperatures is the dissociation of the precursor molecule.
For the electric field assisted MWNT growth at 0.3V/µm, the normalized growth rates show a single
activation energy of 194 kJ/mole. This implies that for the field assisted case, the rate limiting step
for the MWNT growth is the same as the high temperature mechanism without an electric field.
To summarize, two rate limiting steps were identified for MWNT growth without an electric field.
The activation energies ∼194 kJ/mole and ∼335 kJ/mole are too high to be related to a diffusive
transport of C in the vapor phase or through the iron catalyst particle. Hence, both the rate limiting
steps must be related to interfacial transport. In the kinetic model developed, a first order reaction
was used to describe transport across the vapor-catalyst interface. This first order reaction basically
involves there processes, attachment of the C bearing molecules to the catalyst surface, molecular
dissociation/reaction at the catalyst surface and finally the carbon incorporation into the liquid
catalyst surface. Attachment/physisorption generally has a negative activation barrier. The high
temperature activation barrier, 194 kJ/mole is similar to the activation energy for the dissolution
of C into iron (210 kJ/mole, (76)). The activation energy of the low temperature rate limiting step
corresponds to the bond energies in ethylene, leading to the hypothesis that precursor dissociation
at the interface is the rate limiting step. A schematic of the processes described above is represented
in Fig.5.21. The C flux for the mass transfer step at the vapor-catalyst interface can then be written
as:
J−1VL =
k−11
∆µ1exp (E1/RT) +
k−12
∆µ2exp (E2/RT) (5.27)
where E1 and E2 are the activation barriers for precursor decomposition and C dissolution into the
catalyst particle respectively, and ∆µ1 and ∆µ2 the corresponding changes in chemical potential of
C.
Precursor decomposition on catalyst surface has the higher activation barrier, E1 ≈ 320kJ/mole,
implying it will be the rate limiting step at lower temperature, as is observed in Fig.5.20. With an
increase in growth temperature the process with the lower energy barrier (C incorporation into the
Fe catalyst particle) becomes the rate limiting step. On application of an electric field, we find that
precursor decomposition is no longer the rate limiting step at lower temperatures. From the RGA
analysis we have established dissociation of ethylene in the vapor phase itself on application of an
electric field. Thus the only activation barrier that the C atoms have to overcome in going from the
CHAPTER 5. ELECTRIC FIELD ASSISTED MWNT GROWTH 128
dissociated C species in the vapor phase to the catalyst particle is that due to C dissolution in Fe,
same as that for the no-field case at higher temperature, Fig.5.21. Thus the enhanced steady state
growth rates at low temperatures on application of an electric field can be explained by a change in
the rate limiting step.Po
tent
ial E
nerg
y
“CHx+catalyst”
“C2H4+catalyst”
vapor vapor-catalyst interface surface/bulk diffusion
Edissol=E2Ediff
Edissc=E1
without fieldwith field
Figure 5.21: Plot of energy of the carbon precursor and CHx (dissociation products of ethylene) asa function of distance form the catalyst interface. The orange, red dotted lines corresponds to theenergetics for a zero bias growth. The blue line represents the energetics of the vapor-catalyst masstransfer step for an electric field assisted growth
The change in rate limiting mechanism at the vapor-catalyst interface also explains the non-
uniform dependence of MWNT heights with the magnitude of applied field, Fig.5.10. The total
flux of the C atoms depends mostly on the chemical potential change of the rate limiting step. For
smaller fields, dissociation of C is the rate limiting step. Hence, increasing the applied electric field
increases the C flux due to the dissociation of the C bearing precursor molecules ,(eqn.5.26), resulting
initially in enhanced height of the MWNTs. But this flux, eventually , becomes larger than the flux
of C atoms dissolving into the catalyst. This makes carbon dissolution the rate limiting step, which
is not influenced by the presence of an electric field. Therefore further increase of applied field has
little or no effect in increasing the growth rates and hence the final MWNT heights.
5.8 Conclusion
To summarize, vertically aligned MWNT growth due to the imposition of an applied DC field was
demonstrated. A FFT based image analysis technique was used to quantify degree of alignment in
CHAPTER 5. ELECTRIC FIELD ASSISTED MWNT GROWTH 129
the MWNT bundles. An analytical model simulating the CNTs as helical springs was developed to
find the elongation of the CNTs due to tensile stretching by the electrostatic forces. This electrostatic
stretching resulted in straighter CNTs and hence increased alignment. Isolated MWNTs were also
grown from catalyst particles with low spatial coverage under a localized static field. An algorithm
based on the ability to detect edges of the CNTs in SEM images was used to measure the alignment
of the isolated CNTs. Increased alignment for isolated MWNT growth was obtained by orienting the
CNTs vertically along the direction of the imposed field. Three important factors were identified that
control the alignment of the CNTs. The catalyst particle spatial density that controls the probability
of tube-tube interaction, the growth conditions that controls the morphology of the CNTs. Finally,
growth under an applied bias that restricts the growth to Case I regime, taking advantage of its
high axial polarizabilities.
Growth kinetics of field assisted CVD grown MWNT were studied. Application of an electric
field enhances the growth rates. But, the growth enhancement decreased with increasing growth
temperature. Similarly, at the same growth temperature increasing the applied field increased the
height of the CNTs, but for larger fields the height starts leveling off towards a constant value. These
observations were explained in terms of a change in rate limiting step. For an unbiased growth, at
higher temperatures the rate limiting step is the carbon dissolution into the catalyst particle, while
at lower temperatures it is the carbon dissociation at the catalyst-vapor interface which limits the
growth. Application of an electric field enhances the decomposition of the C precursor in the vapor
phase itself, increasing the total carbon flux through the catalyst particles. These increases the
growth rates initially but only to the limit of the growth rates due to the dissolution of carbon into
the iron catalyst particles. These results have potential implications in bringing down the nanotube
growth temperature, on application of an electric field, to levels amenable for CMOS fabrication
procedures.
Chapter 6
Chirality and Diameter Control of
Single-walled Carbon Nanotubes
6.1 Motivation
Carbon nanotubes, particularly SWNTs, have unique transport and elastic properties [1]. Hence
there is considerable interest in using these SWNTs as sensors, composite materials with enhanced
electrical and mechanical properties, electronic components and recently for energy storage and fuel
cell applications. The properties vary as a function of diameter and chirality of the SWNTs. The
bottleneck for the assimilation of the SWNT into devices/materials is the limited control over the
nature of the tube produced and the small laboratory scale production rates. The motivation for this
work was to look for ways to increase production rates. For this, the floating catalyst CVD method
was chosen (please refer to Chapter 1, for other commonly used techniques for SWNT growth) as it
has the largest scope of scalability, since it can be developed as a continuous process as opposed to
batch type processes (e.g. substrate based thermal CVD processes). Simultaneously investigations
for diameter and chirality control were made and is the focus of this chapter.
6.2 Introduction
In the floating catalyst method, catalyst particles are suspended in a flow of a carbon containing
gas, both being continuously fed into the reactor. There has been numerous studies on the produc-
tion of SWNTs by floating catalyst methods; the parameters varied being catalysts (different sizes
and chemical composition), different carbon precursors, different growth temperature and pressure
ranges, introduction of a growth promoter etc (30; 142; 143; 144; 33; 145; 35; 36). One of the more
130
CHAPTER 6. DIAMETER CONTROL OF SWNTS 131
successful techniques was developed by Li. et al (37).They developed a technique to spin continu-
ous fibers and ribbons of carbon nanotubes spun directly from the synthesis zone of a vertical flow
reactor. They used ethanol and ferrocene as the carbon and catalyst precursor respectively, H2 as
the carrier gas and thiophene as a yield promoter. SWNT production rates as high as ∼ 0.5 g/hour
were reported.
In this work, we have used a variation of Lis method for producing SWCNTs. This chapter is
divided such that in the experimental section we talk about the general protocol followed for growing
SWNTs. In the next section we develop a semi-quantitative way of estimating the abundance of the
SWNT diameters based on a combination of transmission electron microscopy, Raman and UV-Vis-
NIR spectroscopy data. Estimating the abundance of SWNT produced (146) has recently gained
a lot of significance with the need for diameter and property selective SWNT growth. We use
the methodology so developed to investigate the reaction space of the vertical furnace for SWNT
production as a function of temperature, carrier gas flow rate and the precursor solution flow rate.
Furthermore we report the sample morphology, catalyst impurities and the nanotube purity as a
function of each of these reaction conditions.
6.3 Experimental Procedure
Ethanol was the chosen carbon source, in which ferrocene and the growth promoter, thiophene, were
dissolved. Various chemical compositions were tried before obtaining the ideal compositions for the
growth of the SWCNTs. For this study, the ferrocene weight percent was varied between 0.25 to
1.0 weight percent (wt%). The thiophene concentration was varied with the amount of ferrocene
in the sample, an atomic S/Fe ratio of 0.2 was experimentally found to be optimum. This solution
was fed into the reactor using a peristaltic pump with flow rates of 0.01 ml/min to 5 ml/min. The
optimum flow rate was found to be approximately 0.1 ml/min. The precursor solution was vaporized
at temperatures of 150 to 200 oC in the delivery tube; the gaseous products were carried directly to
the bottom of the furnace using a controlled H2 flow. The details of the reactor has been mentioned
in Chapter 2. The temperature of the vertical flow reactor was maintained between 900 and 1100oC.
For studying the effect of a particular parameter, all other variables were kept fixed while varying
just the one parameter. Details of these will be mentioned while discussing the effects of individual
parameters on the growth process.
The gaseous mixture is expected to be pyrolized in the first zone/bottom of the furnace with
nucleation and growth of the SWCNTs in the other zones. A typical reaction time was 2 hours,
though it was found that the product mass increased linearly with the reaction time (i.e. constant
production rate). The furnace output runs through ∼4 feet unheated tubing to an exhaust hood, and
hence the entire SWNT production takes place at near atmospheric pressure. The grown nanotubes
were transported out of the reaction zone by the flowing gases and were collected on the cooler parts
CHAPTER 6. DIAMETER CONTROL OF SWNTS 132
of the furnace in the form of very light, diaphanous membrane. These thin films could be easily
peeled off from the reactor walls using tweezers. For characterization of the nature of the CNT
produced, products were collected from the nozzle, the cold portion of the quartz tube protruding
out from the top and bottom ends of the furnace, and the top flange just before the CNT product
entered the exhaust stream. The sample was characterized using transmission electron microscopy
(TEM), thermo-gravimetric analysis (TGA), and Raman and UV-Vis-NIR Absorption spectroscopy.
Raman and TGA were done on the as-prepared sample.
6.4 Results and Discussion
Figure 6.1: Tem images of SWCNT bundles grown at (a) 1000oC and (b) 1050oC with 0.25-wt%ferrocene and 1000 sccm of H2 flow, S/Fe =0.2.
Fig.6.1 is a typical TEM image of the as-synthesized product. The product consists mostly
of bundles of SWCNTs (Fig.6.1(b)). Since the SWNT is lightweight they align along the gas flow
direction and form bundles by adhering to other SWNTs by the Van der Waals forces. This formation
of well-aligned SWNT bundles is characteristic of the floating catalyst method (142) From Fig.6.1
it is observed that particles or particle clusters cling to the surface of the SWNT bundles. These
are mostly either encapsulated Fe catalyst particles or amorphous carbon impurities. It is apparent
that most of the large Fe catalyst particles did not contribute to the growth of the nanotubes, but
rather adhered to the independently formed SWNT bundles during the process.
The purity of the SWNT and also the diameter distribution was found to be very much dependent
on the reaction conditions. The nature of the product was particularly sensitive to the injection rate
of the liquid precursor solution into the carrier gas stream. Higher and very low flow rates resulted
in the formation of soot. There was only a very small window around 0.1 ml/min, which resulted
in the growth of SWCNTs. Similarly, the carrier gas flow rate was found to influence the diameter
of the SWNT produced. Lower flow rates resulted in the growth of larger diameter SWNTs. More
CHAPTER 6. DIAMETER CONTROL OF SWNTS 133
significant influences on the SWNT diameter distribution were observed with varying ferrocene
concentration in the precursor solution and reaction temperature. The detailed influence of these
parameters in determining the carbon nanotube population will be reported in the following sections.
6.4.1 Dependence on the reaction time
(a) (b)
(c)
(d)
150 200 250 300 350 1250 1300 1350 1400 1450 1500 1550 1600 1650 1700
top flangetop of quartz tube
bottom of quartz tubemiddle of quartz tube
nozzle
wavenumber (cm-1) wavenumber (cm-1)
nozzle bottom of tube rope top of tube top flange
nozzle bottom of tube rope top of tube top flange
Inte
nsit
y
Abu
ndan
ce R
atio
I G/I
D
Figure 6.2: Raman of the SWNT samples collected from different parts of the furnace (a)RBMmodes (b)D and G bands (c) Normalized IRBM/IG (d) IG/ID ratio as a function of the furnaceposition
Before discussing the effects of temperature and catalyst metal concentration, the influence of
the reaction time is reported. Also, the semi-quantitative way of estimating SWNT abundance used
throughout this study is described. The as prepared product was collected from different parts of the
quartz tube, with larger distances from the inlet nozzle implying longer reaction times. The reaction
conditions for these set of samples were T = 1000 oC, 1 wt% ferrocene in ethanol, a 1: 5 molar ratio of
thiophene to ferrocene, a precursor solution flow rate of 0.067 ml/min and a H2 gas flow rate of 1000
CHAPTER 6. DIAMETER CONTROL OF SWNTS 134
sccm. Under these conditions, ropes of SWCTs formed that stretched across the entire 6 ft length of
the quartz tube from the nozzle to the top flange. Fig.6.2 shows the Raman spectroscopy data of the
product collected under near IR (NIR) laser (λ =785 nm) excitation. Fig.6.2(a) is a staggered plot
of the radial breathing modes (RBM) of the SWNT samples collected. The RBM Raman features
correspond to the coherent vibration of the carbon atoms in the radial direction, and is a signature
of the CNT product in terms of the nanotube diameter (dt) through its frequency ωRBM and the
electronic structure through its resonant response to the incident laser energy (Resonance Raman
spectroscopy). The diameter distribution of the sample can be found from the position of the RBM
by using the relation ωRBM = A/dt + B, where A and B are empirical fit parameters. A and B
for this set of data had the best fit for A = 230.78 cm−1nm and B = 7.14 cm−1. RBM peaks were
observed at 154, 206, 234 and 266 cm−1, corresponding to nanotube diameters of 1.57, 1.16, 1.02
and 0.89 nm. Fig.6.2(b) is the plot of the corresponding D and G bands. The G-band involves an
optical phonon mode between the two dissimilar C atoms in the graphite unit cell, while the D band
originates from the disorder-induced mode in SWCNT. Therefore the ratio of the G and D band
intensities has long been used as a first estimate of the quality of the SWNT sample. Fig. 6.2(d)
plots the ratio of G and D band. The highest G to D band ratio was obtained for the SWNT sample
collected from the middle of tube, and hence is of the highest quality.
The intensity of the RBMs depend on the chirality of the specific SWCNT, since it determines
the band gap transitions, Sii and Mii, that determine the resonance condition with the incident
laser energy. The band gap energy influences the electron-phonon interaction and the electric-
dipole interaction matrices, which go into the calculation of the Raman intensities (147). The RBM
intensities also depend on the density of SWCNTs in the sample probed and the abundance of
SWNT chiralities. To make an estimate of the abundance of SWCNTs of particular chirality the
two other competing effects have to be corrected for. Normalizing the intensity of the RBM modes
with that of the G band intensities can approximately account for dependence of the sample density.
The best way to correct for the different excitation cross-sections of each chirality present is to find
the theoretical intensity and divide the experimental RBM intensities by it (146). An alternative
way would be to assume a standard and then normalize the IRBM/IG for each RBM peak from a
given sample with the corresponding peak from the standard. These intensity ratios will then give
an estimate of the population abundance of SWNT chiralities in the SWNT sample with respect
to that of the standard. Fig.6.2(c) plots the normalized IRBM/IG ratios that have been described
above, with the samples collected from the nozzle acting as the standard. From Fig.6.2(c) its evident
that population of the larger diameter SWNT(154 cm−1) increases with vertical distance along the
furnace. For example the SWNT product collected from the top flange has twice the number of 1.57
nm SWNTs compared to the nozzle. On the other hand, the abundance of the smaller diameter
SWNT(corresponding to 206-266 cm−1) decreases with height of the furnace.
However, it would be imprudent to come to a conclusion about the population distribution from
CHAPTER 6. DIAMETER CONTROL OF SWNTS 135
Figure 6.3: Kataura plot for the S22, M11 and S33 transitions. Also plotted in the Fig. is theposition of the 785 and 635 laser lines, and a 50 nm shift to account for the bundling of SWNTs.The 2n+m family of the SWCNT are shown for the MOD1 and MOD2 S22 transitions (joined byblack solid line) and for the M11 transitions (joined by green dashed line).
only a single energy excitation resonant Raman study, since it does not probe the entire population
of SWNT chiralities that might be present in a given sample. Fig. 6.3 is a Kataura plot, plotting
the band gap energies as a function of the diameter of the SWNT(and hence the wavenumber).
The values for the interband energies for the S11, S22 and M11 type transitions were obtained from
the model proposed by Strano, et al., (7), while the S33 transition energies were obtained from the
extended tight binding calculations (53). Also shown in the Kataura plot are the 2n+m families of
the SWNT for the MOD1 (n-m mod 3 = 1) and MOD2 (n-m mod 3 =2) S22 transitions (joined
by black solid line) and for the M11 transitions (joined by green dashed line). The solid blue line
gives the energy of the NIR laser. SWNTs having band transitions in this vicinity should give rise
to a RBM peak, due to the resonance Raman effect. However, the 154 and 266 cm−1 RBM peaks
are not in this range. To account for these two peaks we have to include into the Kataura plot the
effects of bundling. For bundled SWNTs, the spectral features are red shifted by 50 to 70 nm with
the magnitude of the shift depending on the extent of bundling and inter-nanotube contact area
(148; 149). Further evidence of the decrease in the transition energies of SWCNTs upon bundling
has been established by Rayleigh Scattering Spectroscopy studies (150). Also due to the broadening
of the electronic transitions the individual RBM spectrum looks less well resolved. One important
note is that the bundling effect has almost no effect on the frequency of the phonon modes (58).
Therefore the dotted blue line, blue shifted from the original position of the NIR laser by 50 nm, with
CHAPTER 6. DIAMETER CONTROL OF SWNTS 136
no change to the wavenumber axis, would be a more appropriate representation of the laser energy
level for bundled SWNT. TEM study of our samples show SWNT bundles of various dimensions
and the actual magnitude of the red shift has not been established, hence instead of establishing a
particular chirality with a given radial peak, we assign the peak to a 2n+m family. This shift now
shows how the 266 cm−1 RBM mode may be excited through the 2n+m = 22 family, MOD2 S22
transitions, and S33 transitions may contribute at or below 150 cm−1. The 150-160 cm−1 region,
however, falls between the M11 and S33 transition energies, with neither being in resonance with
this shifted line. For reasons that will be explained in the next section, we believe that the M11
excitation does not experience the same magnitude of red shift, if any, and thus can be considered
responsible for this peak.
(a) (b)
(c)
wavelength (nm) wavelength (nm)
Abs
orba
nce
%
Abs
orba
nce
Abs
orba
nce
2n+m family
Figure 6.4: UV-Vis-NIR of the samples collected from different parts of the furnace (b) S22 tran-sitions after subtracting the background (c) Comparison of the absorbance % from the spectracorresponding to the peaks obtained from Fig. (b)
Next, to have a better picture of the diameter distribution of the SWNTs, we characterized the
samples using UV-Vis-NIR spectroscopy (Fig. 6.4). This technique has been utilized to estimate
the purity of the nanotubes (151) by comparing the ratio of the area under the S22 peaks with
CHAPTER 6. DIAMETER CONTROL OF SWNTS 137
background intensity, which arises from π-plasmon absorption and particulate scattering from the
SWNT and other carbonaceous impurities. From Fig.6.4(a) it can be seen that the purity of the
SWNT obtained was higher for sample collected from the rope and the top portion of the furnace as
supported by the G to D band ratios from Raman spectroscopy. Further, by noting the positions of
the transition peaks one can also estimate the SWNTs present since the band gap of each SWNT is
unique and has an inverse relation with the diameter. The simplest theoretical treatment predicts
the optical transition wavelengths of semiconducting nanotubes depends linearly on the diameter
according to the relations λ11 = hcdt/2accγo and λ22 = hcdt/4accγo; where acc is the C-C bond
distance and γo the interaction energy between neighboring C atoms [1]. For this paper, the Strano
empirical model was used to estimate the band gaps as in Kataura plot. Similar to the intensity of
the RBM modes, the intensity of the optical transitions is related to the abundance of the SWCNTs
(151; 152). To analyze the peaks, the optical response from the background is subtracted by fitting
to a Lorentzian tail (as expected for a plasmon feature).
For analysis of the UV spectrum we chose a range corresponding to the S22 type transitions. The
M11 features were not used because they were not well resolved, and the S11 transition region was
neglected due to overlap of the solvent (DMF) peaks. Fig. 6.4(b) shows the UV spectrum from the
S22 region after background subtraction. In bundled SWNT systems, intertube interactions broaden
and suppress the van Hove transitions to the extent that the individual features of spectral chiralities
are not resolvable. So instead of trying to identify individual chiralities, the spectral features were
correlated with the 2n+m family corresponding to the S22 transitions. Doing so is straightforward
for the MOD2 S22 transitions, which are very close together in energy, though more questionable
for MOD1 transitions that span a larger, but finite, range. Nevertheless, the approach is useful for a
semi-quantitative interpretation. As shown in Fig. 6.4(b), a multi-peak Lorentzian fit was performed
with the observed peaks assigned to individual 2n + m families as marked in Fig. 6.3 using solid
black lines. The expected location for 2n + m = 28 falls between the major peaks near 810 and
890 nm, thus the dotted vertical lines in the figure are used to assign contributions to the MOD1
2n+m = 29 and 32 families. The areas under the fitted Lorentzian curves were calculated and then
divided by the total area from all the Lorentzian fits for a particular sample to get the absorbance
percentage from each 2n+m family. This was then presented in the form of a bar chart, Fig.6.4(c),
to get a comparison of the SWNT 2n + m families present in each sample. Fig.6.4(c) agrees with
what was observed by comparing the normalized RBM intensities in Fig.6.2(c). Absorbance peaks
were observed from 2n+m families of higher magnitude for samples collected from the top regions
of the furnace. These peaks were almost entirely absent for the sample collected from the bottom
part of the furnace (e.g. the spectral feature corresponding to 2n+m = 37, which also corresponds
to the diameter range for the RBM peak at 154 cm−1). We also note the relatively lower percentage
of the lower 2n+m families from the samples collected from the top part of the furnace. This again
shows that samples collected from the top regions of the furnace have a higher range of diameters,
CHAPTER 6. DIAMETER CONTROL OF SWNTS 138
with a larger fraction of larger diameter SWNTs.
(a)
(b)
Wei
ght %
Wei
ght %
nozzle rope top flange
Figure 6.5: TGA of the samples from different parts of the furnace
Finally, TGA analysis of the samples collected from various parts of the furnace was used to
estimate the SWNT and impurity fractions (Fig.6.5). The initial weight loss on ramping up the
temperature is attributed to amorphous carbon and the residual weight at the end of the temperature
ramp is due to Fe-oxide. The remaining weight loss in between 400 to 900oC is attributed to SWNTs.
While the boundary between SWNT and amorphous carbon may not be distinguished with absolute
certainty via TGA measurement, this metric is used to provide approximations of the SWNT purity
in the sample. On this basis, the fraction of SWNT increases with height as seen from Fig.6.5(b).
The residual Fe-oxide percentage in the samples is relatively high, and will be further discussed in
the following sections.
To summarize, the percentage of larger SWNT diameter in the samples collected increases with
height of the furnace. The higher position in the furnace corresponds to a larger distance from the
nozzle where the precursors enter the reaction zone, and hence a longer residence time. Longer
residence times result in a greater opportunity for the smaller Fe catalyst particles to collide and
agglomerate to bigger particles, as observed in TEM studies. The larger catalyst particles result in
the formation of SWNTs with larger diameter. This explains the increasing diameters of SWNT
samples with position in furnace. The higher purity observed may be attributed to an annealing
effect due to greater exposure to elevated temperature. Also, impurities and amorphous carbon may
CHAPTER 6. DIAMETER CONTROL OF SWNTS 139
form early in the process and thus be preferentially collected near the inlet rather than the outlet.
The rope formed in the middle of the furnace experiences longest exposure to high temperature
conditions and therefore displays the highest purity of all the samples.
6.4.2 Effects of Ferrocene concentration
Catalyst particles are known to influence the nature of the SWNT product (83). The iron catalyst
precursor (ferrocene) concentration in the solution was systematically varied to study the influence
of the metal concentration on this particular process of SWNT growth. Ferrocene concentrations of
0.25wt%, 0.5wt% and 1.0 wt% were used in the precursor solution. Also, for each set of ferrocene
wt% studied, two sets of samples were collected from the top and bottom of the quartz tube. The
other growth parameters held constant for this study were: growth temperature of 1000oC, H2 gas
flow rate of 1000 sccm, solution flow rate of 0.66 ml/min and S/Fe atomic ratio of 0.2.
Fig.6.6(a) plots the RBM intensities under 785 nm laser excitation for all three weight percentages
of ferrocene tried. The two dominant RBM Modes from the 785 laser for all these samples are at 154
and 206 cm−1 wavenumbers. The intensity of the Raman modes for the 206 cm−1 wavenumber did
not vary much with the ferrocene wt%, but there was a noticeably large increase in the intensity of
the 154 cm−1 wavenumber as a function of the ferrocene wt%. In fact, for the sample collected from
the top of the quartz tube prepared from 1wt% of ferrocene, the intensity of the 154 cm−1 RBM mode
was greater than that of the corresponding G band. To extract semi-quantitative information about
the SWNT abundance in the sample from the Raman data, the data was normalized as described
above. The normalized IRBM/IG data are plotted in Fig. 6.6(c), with the sample collected from
the bottom of the tube for 0.25wt% ferrocene concentration being the reference. There is a 10-fold
increase in the abundance of the 1.57 nm (corresponding to a wavenumber of 154 cm−1) nanotubes
for samples with higher ferrocene concentrations, implying that higher metal concentrations spawn
larger quantities of larger diameter SWNTs. This trend is also observed using 633 nm excitation.
The inset of Fig. (a) shows the RBM modes with 633 nm laser excitation. The 633 nm laser probes a
different band gap energy region than the 785 nm laser as shown on the Kataura plot (Fig. 6.3). The
red line and the dotted red line in Fig. 6.3 shows the position of the 633 laser and the approximate
effective position of the laser after the red shift due to bundling effects have been accounted for. The
0.25 wt% and the 0.5 wt% sample exhibits RBM peaks at 190 and 210 cm−1. The 1.0-wt% sample
gives rise to an additional RBM peak at 150 cm-1also weakly present for 0.5wt% sample. This again
implies that a larger metal concentration also results in the formation of larger diameter SWNTs.
The normalized D and G bands for these sets of samples are shown in Fig. 6.6(c). Fig. 6.6(d)
compares the ratio of the G band and D band intensities and shows no particular trend. However,
the shape of the G band changes significantly with ferrocene weight percentage. The more intense
G+ feature ( at 1585 cm−1) is associated with the C atom vibrations along the direction of the
tube axis, while the overlapping lower wavenumber G- band is associated with the vibrations of the
CHAPTER 6. DIAMETER CONTROL OF SWNTS 140
(a) (b)
(c)
(d)
120 140 160 180 200 220 240 260 280 1250 1300 1350 1400 1450 1500 1550 1600 1650 1700
wavenumber (cm-1) wavenumber (cm-1)
bottom(0.25) top(0.25) bottom(0.5) top(0.5) bottom(1.0) top (1.0)
Inte
nsit
y
Abu
ndan
ce R
atio
I G/I
D
bottom(0.25) top(0.25) bottom(0.5) top(0.5) bottom(1.0) top (1.0)
Figure 6.6: Raman of the SWCNT samples as a function of ferrocene concentration. (a) RBM modeswith 785 nm laser, 635 nm laser (inset). (b) D and G bands from 785 nm laser. (c) NormalizedIRBM/IG (d) IG/ID ratio and the extent of G split as a function of temperature. The labels for Fig.(a) and (b) are the same. The label for Fig. (d) is also true for Fig. (a).
C atoms along the circumferential direction of the SWCNT. The G- line shape is highly sensitive to
whether the SWNTis metallic (Breit-Wigner-Fano (BWF) line shape) or semiconducting (Lorentzian
line shape)(53). The samples from 0.5% and 1.0wt% ferrocene have the BWF line-shape while the
0.25wt% sample has the Lorentzian line shape. This implies that the resonant chiralities at 785
nm are primarily metallic for the SWNT prepared from 1.0 wt% ferrocene. Comparison with the
RBM trends suggests this arises from the CNTs contributing the 154 cm−1 feature. Referring back
to Fig. 6.3, we observe that the CNTs contributing to the 154 cm−1 RBM are resonant between
800-900 nm excitation. That this is higher than the effective excitation wavelengths suggest that
bundling effects are different for these SWNTs than the other SWNTs previously described. The
data suggests that red shifting might be completely absent in metallic SWNTs, though tunable laser
Raman spectroscopy will be required to demonstrate this unambiguously. The 150cm-1 RBM for
CHAPTER 6. DIAMETER CONTROL OF SWNTS 141
the 1.0wt% sample with the 633 laser, on the other hand, may be attributed to the S33 transitions
shown in Fig. 6.3, which is corroborated by the Lorentzian shape of the corresponding G band (not
shown here).
Figure 6.7: TEM images of the samples. Fig. (a) and (b) are TEM images from 1.0 wt% samplewhile (c) is the image from SWCNTs formed with 0.25 wt% ferrocene.
TEM on the 0.25wt% and 1.0wt% sample was performed to investigate the validity of the diam-
eter trends from the Raman studies and also to elucidate reasons behind these trends. Fig.6.7(a-b)
are TEM images of SWNT samples that were grown with 1.0 wt% ferrocene, while Fig.(c) is the
TEM image of SWNT sample collected from the 0.25 wt% sample. Fig. 6.8 (a) is a histogram of the
diameter distribution of the SWNT samples obtained from the TEM analysis. The 0.25wt% sample,
on average, has lower diameters compared with the 1.0-wt% sample. The population density for the
former has a maximum at 1.3 nm with a mean value of 1.36 nm (std. deviation = 0.2 nm), while the
percentage distribution for the 1.0 wt% sample peaks at 1.7 nm (mean = 1.86 nm, std. deviation
=0.19 nm). This compares well with the Raman data.
Other groups have reported similar results. Kim, et al., (153)grew CNTs by filling the pores
of well-ordered porous anodic oxide with a metal ion solution. They reported that increasing con-
centration of the metal ion resulted in the formation of larger diameter multiwall CNTs. SWNTs
were grown by Jeong, et al., (154) using methane as the C precursor and ferritin as a source for the
catalysts. They reported that decreasing the Fe concentration resulted in a smaller diameter range
of the SWNTs and also a smaller mean diameter. Singh, et al., (155) did a similar study for the in-
jection CVD growth of aligned CNTs, and observed that decreasing the Fe concentration resulted in
smaller tube diameters, a decrease in CNT purity and width of the diameter distribution. They also
reported that concentration of the encapsulated particles increased with an increase in the ferrocene
concentration. Nasibulin, et al., (83) reported that increasing the metal concentration resulted in
CHAPTER 6. DIAMETER CONTROL OF SWNTS 142
the formation of larger bundles of SWNT, a fact that was substantiated from TEM studies.
(a)
(b)
Abu
ndan
ce %
Abu
ndan
ce %
Figure 6.8: SWCNT diameter and (b) Fe catalyst particle size distribution for sample prepared with0.25 and 1.0 wt% ferrocene respectively, obtained from the TEM images.
The reason for all the above observations was that higher catalyst concentration resulted in the
formation of larger catalyst particles. To check this we did an analysis of the catalyst particle size
for the lower and higher concentration of the ferrocene concentration in the samples (Fig.6.8(b)).
The average particle size for the 1.0 wt% sample (8.65 nm) was found to be larger than that for
the 0.25wt% sample (mean = 3.40 nm). Considering that the CNT diameter bears a certain ratio
with that of the particle size, (reported ratios vary from 2 to 3, (156)) it is not expected that these
large particles are contributing to the growth of the SWNT bundles. This can be verified from the
TEM images of the samples. Both small and large particles are seen in Fig.6.7(a) for the 1.0-wt%
sample. It is apparent that the largest particle is not terminating the growth of any SWNTs and is
in fact coated with an amorphous carbon shell. Therefore, it is not acting as a catalyst for nanotube
growth. On the other hand, a bundle of SWNTs can be observed to terminate at the smaller particle,
implying it is serving as a catalyst.
Fig.6.7(b) is another example of a larger particle forming a carbon onion rather than SWNT
bundles, while a TEM image from the 0.25 wt% sample, Fig. 6.7(c), shows the growth of SWNT from
a smaller catalyst particle. This suggests that there is an optimum concentration of Fe that aids in the
growth of the SWNT by forming catalyst particles. Beyond this level, the Fe particles agglomerate
CHAPTER 6. DIAMETER CONTROL OF SWNTS 143
to form larger particles that do not aid in the growth of SWCNT. This result in the formation of
carbon impurities, thus decreasing the quality of the products formed. This interpretation is also
consistent with the residence time dependencies discussed previously.
(a) (b)
(c)wavelength (nm) wavelength (nm)
Abs
orba
nce
%
Abs
orba
nce
Abs
orba
nce
2n+m family
400 600 800 1000 1200 1400 600 700 800 900 1000
Figure 6.9: UV-Vis-NIR of the samples collected as a function of ferrocene concentration. (b) S22
transitions after subtracting the background (c) Comparison of the absorbance % from the spectracorresponding to the peaks obtained from Fig (b)
UV-Vis-NIR spectroscopy data may provide a larger picture than that given by Raman and
TEM alone. Fig.6.9 plots the absorbance as a function of the weight percentage of the samples.
We concentrate only in the 650-1050 nm region that corresponds to the S22 transition region. Fig.
6.9(b) plots the background subtracted absorbance data, along with the fitted Lorentzian peaks.
Each of the peaks is identified to the 2n+m family; solid lines mark the MOD2 2n + m families.
The two most intense peaks of the absorption spectrum, observed around 815 nm for all samples
and near 885 nm for the higher wt% samples cannot be accounted for using the MOD2 families.
Since Raman spectroscopy suggests that a large fraction of the SWNT near 785 nm are metallic in
nature, the peaks can be identified with the M11 type 2n+m = 33 and 36/39 families respectively.
The 645 nm peak for the 0.25 wt% sample was identified with 2n + m = 23 family of MOD1 S22
transitions. The absorbance percentages for each of the three samples are plotted in Fig.6.9(c). We
see that the abundance of the higher order families are greater for the samples grown with 1 wt%
ferrocene than for the 0.25 wt% sample, consistent with the Raman and TEM data. Thus we can
CHAPTER 6. DIAMETER CONTROL OF SWNTS 144
say that increasing the ferrocene percentage increase the diameter range of the SWNT produced
and also results in preferable growth of the higher diameter SWNTs.
(a)
(b)
Wei
ght %
Wei
ght
frac
tion
Figure 6.10: TGA of the samples prepared with different amount of ferrocene in the precursorsolution. For the fit data x is the wt% of ferrocene in the sample.
Finally, TGA analysis of the samples as a function of the ferrocene concentration was done
(Fig.6.10). The percentage of the SWNT decreases linearly with increasing ferrocene concentra-
tion in the sample. 30% by weight of the product collected is the metal oxide for 0.25% ferrocene
in precursor solution, (comparable with values reported by other groups for oxide content in the
sample (151)) while the 1.0-wt% sample has a residual weight of 65%. The trend of residual iron
content is consistent with first order reaction kinetics for iron formation and constant carbon pro-
duction, i.e. if rFe = knFerrocene and rC+CNT = C, then, wFe = wFerrocene
wFerrocene+C/kM where wFe is the
weight percentage of iron in the product, wFerrocene is the percentage of ferrocene in solution, and
M is a constant conversion factor to convert mass percent to number density. Using C/kM as
the fitting parameter, we find that the above expression reflects the experimental data well for a
value of C/kM = 0.5 (Fig.6.10(b)). Another interesting point is that ratio of the two carbon mass
fractions, Mamorphous/MCNT , decreases with greater ferrocene percentage. This implies that the
CHAPTER 6. DIAMETER CONTROL OF SWNTS 145
two competing processes for formation of amorphous carbon and SWNT are impacted in favor of
SWNT formation when more ferrocene is present. But it is noteworthy that a sizable portion of
the catalyst particles do not contribute to the growth process, as observed in TEM for the 1.0 wt%
ferrocence, due to formation of larger particles from a high concentration of catalyst particles in
solution. Therefore, there is a large metal impurity product, even though the SWCNTs may be of
higher quality, as shown by Raman and TGA. This tradeoff thus points to an optimum value for
catalyst concentrations for SWNT growth.
6.5 Temperature Effects
The effect of the temperature on the growth of the SWNTs was also studied, for this has been
reported to be perhaps the most important factor determining the nature of the CNTs formed
(157; 158; 159; 35; 160). SWNT were grown at temperatures of 900, 1000, 1050 and 1100oC. The
other growth parameters for these set of samples were fixed at 0.25 wt% ferrocene with atomic S/Fe
= 0.2, 1000 sccm of H2 gas flow and a precursor solution flow rate of 0.067 ml/min.
RBMs were observed at 150 cm−1 wavenumber and also in the 200-250 cm−1 wavenumber range
(Fig. 6.11a). As discussed previously, it is probable that the M11 transitions gave rise to the 150
cm−1 RBM mode because the distinct BWF line-shape for the G- band in the 900oC sample (Fig.
6.11(c)). The most important observation from this plot is that, as the SWNT growth temperature
is increased, the intensity of the RBM modes corresponding to the 200-250 cm−1 become more
prominent, implying a definite increase in the range of the SWNT diameters produced with a greater
abundance of the smaller diameter semi-conducting SWCNT. The RBM modes due to the 633 nm
laser (Fig. 6.11b) show an increase in RBM intensity at 190 cm−1, probably due to the (15,0) metallic
M11 transition, based on the position of the RBM mode and the shape of the G band (not shown).
Note that this RBM mode resonance is predicted to be near 720 nm, yet is not observed under 785
nm excitation; again suggesting that the metallic SWCNTs are not red shifted by bundling, and
may even blue shift. Fig. 6.11(d) compares the intensity of the RBMs normalized by the G band
intensity, with the SWNT sample grown at 900oC being the reference. The corresponding histogram
shows that the abundance of the higher diameter SWNTs does not vary much with an increase in
the growth temperature. Contrary to that, the abundance of the smaller diameter semiconducting
SWNTs, corresponding to those exhibiting RBM at 206 and 234 cm−1 wavenumber, increased by 3
and 5 fold respectively when the growth temperature was increased from 900oC to 1100oC.
Fig.6.11 (c) plots the Raman spectrum in the D and G band region. The 900oC sample shows a
distinct metallic BWF line-shape, while the 1100oC sample shows a distinct splitting of the G band
to the two symmetric G+ and G- bands, a signature of semiconducting SWNTs. This supports the
observations made in discussion of the RBM. The G bands of the samples grown at intermediate
temperatures feature a combination of these two types of line-shapes. Furthermore, the quality of
CHAPTER 6. DIAMETER CONTROL OF SWNTS 146
wavenumber (cm-1)
Inte
nsit
y
wavenumber (cm-1)
wavenumber (cm-1)
150 200 250
1300 1400 1500 1600 1700
120 140 160 180 200 220 240 260 280 300
900oC 1000oC 1050oC 1100oC(bot) 1100oC(top)
900oC 1000oC 1050oC 1100oC(bot) 1100oC(top)
IG/ID
G split
I R B
M /I G
Figure 6.11: Raman of the SWNT samples synthesized at different temperatures. (a) RBM modeswith 785 nm laser and (b) 635 nm laser. (c) D and G bands from 785 nm laser. (d) NormalizedIRBM/IG as a function of temperature (e) Shows the variation of IG/ID and the extent of G splitwith temperature. The color legend for Fig. (a) and (c) is the same.
the SWNT produced increases as a function of the growth temperature, evidenced by the increase
in the intensity ratio of the G to D band for the higher temperature samples (Fig. 6.11(d)). This is
to be expected because it is well known that processing at higher temperature anneals away defects
resulting in the formation of more crystalline graphitic nanotube walls (151). Fig.6.11(e) also plots
the G split, defined as the difference between the G+ and G- band wavenumbers, as a function
of the growth temperature. The position of the G- band varies as the inverse of diameter of he
tube, while the extent of G split varies as the inverse of the square of the diameter of the SWNTs
(161) Specifically the relation for the position of the G- band is ωG− = 1591 − C/d2t , the values of
the constant C being different for semi-conducting and metallic SWNT(Cs= 47.7 cm−1nm2; Cm=
79.5 cm−1nm2). This relation can be used to estimate the average diameter of the SWNTs. The
magnitude of the G split for the 900 and 1100oC samples is nearly identical at 29 cm−1, and these
CHAPTER 6. DIAMETER CONTROL OF SWNTS 147
samples are predominantly metallic and semiconducting, respectively. Thus, we have the average
diameter for the 900 and 1100 oC samples to be 1.65 nm and 1.28 nm, respectively. Such an estimate
cannot be made for the sample grown at intermediate temperatures as they show a mixture of the
semi-conducting and the metallic character.
(a) (b)
wavelength (nm)
Abs
orba
nce
Abs
orba
nce
Abs
orba
nce
wavelength (nm)
wavelength (nm)
400 600 800 1000 1200 1400 650 700 750 800 850 900 950 1000
Figure 6.12: UV-Vis-NIR of the samples collected as a function of SWNT growth temperature.(inset, a) M11 and S33 transitions.(b) S22 transitions after subtracting the background. The colorlegend for all the Figures is the same.
Next, absorption spectroscopy was used to estimate the overall diameter distribution of the
samples. As can be seen from Fig. 6.12(a) the absorption peaks for the 1100 oC are present over a
wider range and are also better defined than for the SWNT samples grown at lower temperatures. A
wider range of spread of the absorption peaks implies a wider range of diameter distribution for the
1100oC case. Both smaller and larger diameter SWNTs as compared to the 900oC sample show up
for the higher temperature sample. The larger area under the peaks implies a larger ratio of SWNT
absorption to impurity scattering, meaning a higher purity of SWNT(83), consistent with the Raman
data. To look into more detail at the 2n + m families that gives rise to the absorption peaks, we
plotted the absorption data corresponding to the S22 transition (650-1100 nm) in Fig.6.12(b). As
in previous sections, the first attempt was to correlate the spectra with 2n + m MOD2 families,
because of their distinct inter-band transition wavelengths, marked in bold lines. From Raman
spectroscopy data for the 785 nm laser we had concluded that the higher temperature samples
were predominantly semiconducting in nature near 785 nm and hence the remaining peaks were
identified with the MOD1 S22 families rather than the M11 families. These peaks were assigned
to be MOD2 S22 2n + m = 26,29,32,35 families, the dotted lines identifying the mean value of the
interband transition wavelengths for their respective families. Raman data for the 900oC grown
CHAPTER 6. DIAMETER CONTROL OF SWNTS 148
sample suggested more metallic SWNTs near 633 and 785 nm. Hence the absorption spectra for the
900oC sample could be identified with the 2n + m = 30 and 39 M11 families. It should be noted
that the absorption spectrum for the 1100oC sample exhibits a much wider distribution of transition
wavelengths. Also with increasing temperature, the intensity of the peaks and the resolution of the
interband transition features increases. This point to higher quality SWNTs, which can be attributed
to higher temperatures facilitating the kinetics of the SWNT growth process and simultaneously
annealing defects resulting in tubes with high crystalline quality.
(a)
(b)
Abu
ndan
ce %
Diameter of tubes (nm)
Diameter of nanocatalyst particles (nm)
Figure 6.13: (a) SWCNT diameter and (b) Fe catalyst particle size distribution for SWCNTs,obtained from TEM analysis, grown at 900oC and 1100oC.
Extensive TEM studies of the SWNT grown at 900oC and 1100oC were conducted to verify the
relationships noted. The SWNT diameter distribution is plotted in Fig. 6.13(a). At 900oC, SWNT
with diameters in the range of 1.6-1.8 nm are most abundant, with a mean of 2.03 nm (std. deviation
= 0.27 nm). For the 1100oC sample, the TEM data shows a bi-modal distribution for the SWNTs,
with peak values at 1.3 and 1.9 nm. The mean of the diameter distributions was 1.625 nm, with a
standard deviation of 0.19 nm. The TEM data thus supports the spectroscopic observations. Next,
the size distribution of the catalyst particles was investigated (Fig. 6.13(b)). The overall catalyst
particle size distribution for growth temperatures of 900oC and 1100oC were similar, though the
high temperature case appears to have bimodal characteristics. Therefore, from the known values
of catalyst particle size to tube diameter ratio, the catalyst particle size optimum for the growth of
SWNTs of diameter ranges reported here will be 3.0-4.0 nm. There are a larger fraction of catalysts
for the 1100oC sample in this range. This might partially account for the increased yield of SWNTat
CHAPTER 6. DIAMETER CONTROL OF SWNTS 149
this temperature.
Temperature effects on the type of SWNT produced have been investigated in some detail.
Bandow, et al., (159) did so for pulsed laser vaporization process and found temperatures of 750oC
resulted in formation of 0.81 nm SWNTs, while 1050 oC resulted in average diameter of 1.51 nm.
Kataura et al.,(157), while using the laser furnace technique, noticed that the purity of the SWNT
increased with temperature up to 1300 oC, beyond which it dropped rapidly. Perhaps most studies
for the temperature effects on SWNT growth have been done for CVD processes. Kumar, et al.,
(160) found that the diameter of the SWNTs, irrespective of them being SWNT or MWNT, increase
with temperature. Above 850oC, SWNT were found to coexist with the MWNT. They also noticed
the formation of metal encapsulated C fibers and other carbon impurities at temperatures greater
than 1000 oC. Singh, et al. (155), in addition to above, noticed that the range of tube diameters
increased with increasing temperature. Nasibulin, et al., (83) studied the diameter dependence
between SWNTs and the catalyst particles in a laminar flow aerosol reactor. They reported an
increase in catalyst diameter with temperature, which resulted in the formation of larger diameter
SWNTs. Similar results were observed for the floating catalyst method of growing SWCNTs and
while using alcohol precursors (35; 156). Our results, as indicated by the Raman and absorption
studies, support the above-mentioned trends with one notable exception. Though we also notice
an increase in the range of production diameters with increasing temperatures, there is a relative
increase in both larger and smaller diameter SWNTs. This is in contrast to observation of other
groups that the average diameter increases with temperature. In all these prior works, this trend
was attributed to the formation of larger catalyst particles at high temperature.
However, the variations in the catalyst sizes by themselves may not fully account for the growth
of smaller diameter SWNTs at higher temperatures. While the kinetics of Fe agglomeration will
control the particle size distribution, thermodynamics suggests an increased preference for smaller
diameter SWNTs at high temperature. Curvature plays an important role in determining the ther-
modynamically favorable product. For smaller diameter SWNTs, the larger curvature leads to
a greater bending energy required to form the SWNTs relative to graphene sheet. Therefore, a
larger energy barrier exists to form smaller SWNTs, thus requiring higher temperatures to nucleate
SWNTs out of smaller diameter particles. To get an approximate idea about the dependence of the
critical SWNT radius on the growth temperature, we have adapted the simple model proposed by
Kuznetsov. (162). The change in Gibbs free energy for the formation of a nucleus is given by the
summation of the energy required to precipitate out carbon from iron-carbon solution, the energy
required to create new surfaces and the strain energy that arises from bending the graphene layer
during bonding with the metal surface (curvature dependent). Our formalism is same as that of
Kuznetsov, except, instead of comparing the volume of the nucleus with the molar volume of the
graphene to calculate the number of moles of carbon, we have compared surface area with respect
to the molar area for graphene. This approach is more appropriate because the SWNT is essentially
CHAPTER 6. DIAMETER CONTROL OF SWNTS 150
a curved 2D surface instead of a solid volume. Hence, for a 2D nucleus with perimeter l and height
h we have:
∆G =γl2 + lh
Am∆Gnucleus + γl2(σnucleus−gas + σnucleus−surface − σsurface−gas)+
lε+ Estr
where γl2 is the surface area (γ being a geometric factor),ε is the specific edge free energy. Next, the
change in free energy for formation of the nucleus is equated with the saturation coefficient of the
solution (∆Gnucleus = −RT ln(x/xo)) and expressing the strain energy, Estr, as Estr = Qcl4.4h , with
Qc = 4.5 eV, as in (162). Since the critical size of the nucleus corresponds to a maximum of ∆G,
the change in free energy is differentiated with respect to l and equated to zero. After simplification
and noting that l = 2πr, the corresponding expression for the critical radius takes the form:
rcrit =−(ε+Qc/4.5h− hRT ln(x/xo)/Am)
−RT ln(x/xo)/Am + (σnucleus−gas + σnucleus−surface − σsurface−gas)(6.1)
Figure 6.14: Theoretical plot to show the temperature dependence for the critical radius for SWC-NTs. The solid circles show the mean for the diameter distribution from TEM analysis at 900 and1000oC. The arrows mark the most abundant range for the SWNT from absorption spectroscopy.
Fig.6.14, which plots the temperature dependence of critical radius, shows that, at higher tem-
peratures it is thermodynamically possible to obtain smaller diameter SWCNTs. For comparison,
the plot also charts the SWNT radii distribution from the current study as a function of temperature.
The actual presence of these smaller diameter SWNTs at higher temperatures, though, depends on
CHAPTER 6. DIAMETER CONTROL OF SWNTS 151
the presence of the right size of catalyst particles, which in turn is controlled by the kinetics of the
agglomeration of the Fe particles. The other groups that have reported an increase in diameter of
the SWNTs with temperature have also reported an increase in the diameter of the catalyst parti-
cles. In contrast, TEM studies for the current study show a similar distribution of particle sizes at
both temperatures, with an overlap in the diameters of the particle suitable for growth of SWNTs
in the range observed, thereby permitting thermodynamic factors to alter the size distribution in
the low diameter range. Further work is required to understand the kinetics of the catalyst particle
formation in this reactor.
(a)
(b) (c)
2n+m =26
(n)
(m)
2n+m =26
2n+m =29
2n+m =30
2n+m =34
Figure 6.15: Abundance maps for SWCNT grown at 900oC (a) and 1100oC (b). For comparison theabundance map for HIPCO characterized using a similar procedure is shown. A darker color impliesa larger abundance of SWCNT, from absorbance studies. The red dotted line shows the positionsof the SWCNT diameter distributions obtained from TEM study.
Fig.6.15 maps the abundance of the SWCNTs grown at 900 and 1100oC, by combining the
TEM and UV-Vis-NIR spectroscopy results together. For comparison, the HIPCO 2n + m family
abundances are also shown as characterized by the same approach in our lab. Thus, we see that
increasing the temperature from 900 to 1100oC significantly increases the range of SWNTs produced.
The diameter distribution for the samples grown by this process is different from that for the HIPCO
sample. The average diameter of the HIPCO SWNTs are in the range of 0.9-1.25 nm, while the
SWNTs grown by this process are in the range of 1.3-1.8 nm. SWNTs in this diameter range are
CHAPTER 6. DIAMETER CONTROL OF SWNTS 152
sought for various applications. Simply varying the temperature also results in some control over
the nanotube size.
6.6 Conclusion
To summarize the work in this chapter, we developed a method of analysis via combined two wave-
lengths Raman and Absorption spectroscopy with TEM validation for diameter and chirality family
populations. Next we used the method developed to report the influence of three important growth
parameters namely reaction time, temperature and metal catalyst concentration on the nature of
product obtained by using a floating catalyst method to grow SWNT from ethanol and ferrocene
using a vertical flow reactor. Larger residence time forms larger catalyst particles resulting in for-
mation of larger diameter SWNTs. Increased residence time also increases the purity of the SWNTs
due to annealing for longer time in the hot zone of the furnace. Greater ferrocene percentage, in
the precursor solution, led to the formation of larger particles and hence larger SWNTs. While
analyzing the corresponding Raman spectrum, we came across experimental evidence that suggest
that the shift due to bundling of SWNTs could be different for metallic SWNTs when compared
to the smaller diameter semiconducting SWNTs. Also the percentage of iron content in the sample
scales with ferrocene percentage in the solution, suggesting constant carbon production rate. Also
increased ferrocene gives less amorphous carbon, suggesting that there are two competing pathways
for pyrolized iron and carbon: carbon and metal to form amorphous carbon and carbon diffusing out
of a supersaturated iron-carbon solution to form carbon nanotubes. We also observed that increasing
the metal concentration and the growth temperature increase the purity of the SWNT produced.
We report that higher temperature leads to the formation of smaller diameter SWNTs, in contrast
to other literature reports. Thermodynamics of SWNT formation suggest that it is feasible to form
smaller diameter SWNTs at higher temperatures if catalyst particle sizes of adequate dimensions
are present. Larger ferrocene concentration and higher temperatures increase the range of SWNT
produced. A larger concentration of metal catalyst increases the diameter of the SWNTs. While,
higher temperature increases the range by forming both smaller and larger diameter SWNTs, but
with a bias for the smaller tubes. These contrasting trends along with optimum levels of carrier gas
and precursor solution flow rate can be used to control the diameter of the SWNTs produced.
Chapter 7
Hydrogen Storage in Pt-Single
walled Carbon Nanotube
Composites
7.1 Introduction
In this chapter we investigate the ”spillover mechanism” of hydrogen storage in SWNT-Pt compos-
ites. The spillover mechanism proposes that hydrogen molecule can be spontaneously dissociated on
the surface of Pt. The dissociated hydrogen atoms can then spill onto the underlying carbon nan-
otube structure. The hydrogen atoms can then find favorable sites on the nanotube surface through
surface diffusion ultimately forming bonds. Pt was the catalyst of choice since Pt does not store
hydrogen or form a bulk platinum hydride phase under ambient conditions(163; 164). Thus the hy-
drogen uptake enhancement of SWNTs can be simply calculated by calibrating the mass fraction of
Pt in a composite sample. ”Spillover” mechanism has been exploited by several groups for enhanced
hydrogen uptake in SWNTs and other carbon based materials such as MWNTs, Carbon nanofibers,
activated carbon etc(40; 44; 45; 46; 47). Despite this, there is a healthy amount of speculation about
the validity of the spillover mechanism. Also further investigations need to be done to improve the
low uptake capacity and slow kinetics. These were the motivation for the current study.
In the first part of this chapter we discuss briefly our previous work on Pt-SWNT composites
and insights obtained from that work. This is followed by a description of the samples used for this
study and the conductivity and XPS studies done on the SWNT-Pt composite samples before and
after hydrogenation.
153
CHAPTER 7. H2 STORAGE IN PT-SWNT COMPOSITES 154
7.2 Prior studies on hydrogen storage in Pt-SWNT compos-
ites
One of the important factors for increased hydrogen uptake is the optimal distribution of Pt particles
on the SWNT matter. Hence the effect of Pt nominal thickness on hydrogen uptake was investigated.
Nominal thickness is the deposited thickness of a film on an ideally smooth substrate. Figure 7.1(a-
d) shows the TEM morphological evolution of deposited Pt catalyst nanoparticles in the SP-Pt
hybrids with nominal film thickness varying from 0.2 to 3.0 nm. The Pt film does not wet the
nanotube surface, resulting in small nanoparticles from thin Pt layers. It is observed that the size
of the deposited Pt nanoparticles becomes larger from 0.2 to 0.5 nm thickness, while the number
density on the bundle does not increase substantially. For hybrids with 1.0 nm or thicker nominal
thickness, the particles tend to agglomerate with each other resulting in large island formation on
nanotube bundles during deposition. Significant decrease in the particle number density due to
impingement is observed for SWNT-Pt hybrids with 1.0 and 3.0 nm nominal thickness as shown in
figure 7.1 (c) and (d), respectively. Hydrogen uptake was estimated by measuring small pressure
changes arising from hydrogen uptake, using a modified Sievert’s apparatus (44), and equating it
to the change in the samples hydrogen content using the gas law equation. The isotherms were
measured for the samples at room temperature with a pressure increment of 4 Bar. The uptake
capacity of the hybrids increases with Pt thickness to 0.5 nm and then decreases for samples with
greater thickness.
The number density of nanoparticles was measured for SWNT-Pt hybrids with 0.2 and 0.5 nm of
Pt nominal thickness. It is reasonable to compare the particle density between these two composites
because the Pt particles tend to form agglomerated islands for thicker films. For simplicity, a
cylindrical geometry of SWCNT bundle is assumed as shown in the inset of figure 7.1(f). The
assumption is valid because the particle density was measured from relatively straight portion of
nanotube bundles, and the deposited catalyst particles are presumably outside of bundles. The
number of Pt particles was counted from several HR TEM images in terms of the calculated surface
area of corresponding carbon nanotube bundle. The numerical density of the particles for the 0.2
and 0.5 nm sputter deposited films were 0.023 and 0.031 particle#/nm2 respectively, Table 7.1. The
Table also shows that the relative ratio of measured uptake capacities at 30 Bar is similar to the
particle density ratio. Therefore it can be concluded that the hydrogen uptake of the total sample
or the uptake enhancement by the nanoparticles is proportional to the number of catalyst particles
in a unit area.
Knowing the total hydrogen uptake for the composite samples, particle density and average size
of the Pt particle (the Pt particle shape on the SWNT surface is assumed to be hemispherical),
an estimate of the H diffusion length on SWNT surface that accounts for the amount of hydrogen
uptake can be made. For this estimate, we further assume that all the C atoms in the affected
CHAPTER 7. H2 STORAGE IN PT-SWNT COMPOSITES 155
10 nm 10 nm
10 nm 10 nm
(a)
(c)
(b)
(d)
Figure 7.1: TEM morphologies of deposited Pt nanoparticles on SWNTs as a function of the nom-inal thickness of the deposited films: (a) 0.2nm, (b) 0.5nm, (c) 1.0nm and (d) 3.0nm. (e) Roomtemperature isotherms for Sp-Pt SWCNT hybrids with different nominal thickness of the sputteredcatalyst. (f) Pt catalyst number density for Sp Pt hybrids with 0.2 and 0.5 nm thick films. (Inset)Schematic of SWCNT bundle decorated with Pt nanoparticles, for the density calculation.
region forms a C-H bond giving the absorbed hydrogen density on the basal plane of graphene to be
76.32/nm2. The radius of the H diffusion circle thus estimated from the assumed and experimental
values are 1.0 and 1.32 nm for the 0.2 and 0.5 nm sputter deposited films respectively. This implies
that the hydrogen diffusion length in either case is less than 0.5nm. The other source for hydrogen
uptake for the Pt-SWNT hybrid could be surface hydride formation on Pt. It would be interesting
to make an estimate of the amount of surface H coverage on Pt required to account for the reported
uptake values in Table 7.1. For this calculation we assume a Pt (111) surface and 1:1 H:Pt ratio
(H density of 15.05/nm2). To account for 0.37 and 0.52 wt% hydrogen uptake by the 0.2nm and
0.5nm Pt-SWNT composite the surface hydride forming on the Pt has to be respectively 5.5 and
3.0 layers thick. Theoretical calculations show that the maximum surface coverage for H on Pt is
CHAPTER 7. H2 STORAGE IN PT-SWNT COMPOSITES 156
Table 7.1: Hydrogen uptake with catalyst particle density.
Pt thickness 2A 5A Ratio
Numerical Density 0.023 0.031 1.35(particle #/ nm2)
Avg. particle φ (nm) 1.14± 0.28 2.05± 0.36Htotal at 30 bar (wt%) 0.37 0.52 1.38HCNT at 30 bar (wt%) 0.41 0.57 1.39
Avg. radius of CHx (nm) 1.00 1.32Avg. #ML (if PtHx) 5.46 3.04
two monolayers (one surface and one sub-surface layer)(163).
Two important observations can be made from the above study on the dependance of hydrogen
uptake as a function of nominal thickness of the sputter deposited Pt. One, surface hydrogenation
of Pt cannot solely account for all the hydrogen uptake, hence providing circumstantial evidence for
the spillover mechanism. Secondly, the diffusion length scales for the spill over process are in the
sub-nm range, implying slow kinetics. Thus, there is need to investigate optimal hydrogen charging
conditions to hasten the process and optimal Pt coverage of SWNT surface so that a larger surface
area can be made available for hydrogen uptake.
7.3 Sample Preparation
A rigorous investigation of the sample space dependance on hydrogen uptake was performed. For
these, SWNTs from different sources were used to prepare films of different thicknesses and different
catalyst concentration. The SWNTs used were from two different sources : (i) as grown SWNT and
(ii) commercially procured HiPCO SWNTs.
The as grown CVD mat samples used in both the XPS measurements and the conductivity
measurements were grown in an atmospheric CVD system utilizing isopropanol as the carbon source.
The growth temperature was varied from 700oC to 800oC in order to change the density of SWNTs
in the mat and the overall mat thickness. The gas flow rates were also used to influence the density
and thickness of the mats produced. All of the samples were grown on ∼ 2A thick film of cobalt
metal deposited on silicon oxide wafers with 50 nm of oxide, Fig.7.2(a,b). The advantage of using
these samples was that these samples did not undergo any treatment procedure: i.e. were not mixed
with any alcohol or surfactant to obtain a well dispersed film.
The HiPCO SWNTs were used to prepare samples by two different methods. For the ticker
samples, the SWNTs were dispersed in isopropanol (1mg/10ml), sonicated for 15 minutes, and
then spin cast on a quartz slide, Fig.7.2(c). Before Pt deposition the samples were annealed in
an evacuated chamber at 250oC for one hour to get rid of the alcohol. To maintain uniformity
of the samples the same deposition steps were rigorously followed each time. These samples were
CHAPTER 7. H2 STORAGE IN PT-SWNT COMPOSITES 157
extensively used for the conductivity studies. The advantage of these samples was preparatory ease.
But, this technique resulted in the formation of thick films made of bundled SWNTs and hence had
the worst Pt to SWNT coverage of all the films studied.
The optimal SWNT mat for hydrogen storage will be a compact but uniform distribution of a
monolayer of unbundled SWNTs. This will have the highest Pt to SWNT coverage and also have
the lowest weight. To de-bundle the SWNTs a density gradient centrifugation (DGC) rate (zonal)
separation for sodium-cholate suspended SWNTs through an iodixanol step-gradient at 300,000
g was performed. This method separates nanotubes by mass, with fractions rich in single CNTs
floating on top of the column and bundles settling at the lower parts of the centrifuge column. Long,
individual SWNTs are obtained and characterized by spectroscopic methods. Xiaolin et al. (165)
used these individual SWNTs to prepare monolayer assemblies of SWNT films by the Langmuir-
Blodgett (LB) method. This LB method involved dispersing of SWNT functionalized by PmPV in
an organic solvent 1,2-dichloroethane (DCE). Pressure cycling during LB film compression facilitates
high-degree alignment and packing of SWNTs. Fig.7.2(d,e) are SEM and AFM images of the SWNT
films prepared by this technique. Once the LB films formed they were calcined to get rid of the
organic solvents/surfactants etc. One disadvantage of this technique is that the SWNT undergoes a
number of processing steps and is contaminated with other organic compounds (residual following
the calcination step). Hence extreme care has to be taken in interpreting spectroscopic data.
Fig.7.2(f) is a representative Raman spectrum obtained from the HiPCO SWNT. Comparing the
spectra obtained using three different excitation lasers with the Kataura plot, the diameter range
of SWNT samples was found to be within the limit 0.8-1.6 nm. The as grown SWNTs also had
a similar diameter range. The 514 nm Raman spectrum shows a distinct BWF line-shape. This
implies that the SWNT samples used have a high fraction of metallic nanotubes. The presence of
these metallic nanotubes are important for the 4-probe conductivity tests.
7.4 Conductivity Tests on Pt-SWNT composite samples dur-
ing hydrogen charging
Anton et al.(43) performed X-ray Absorption spectroscopy (XAS) on SWNT samples to show the
presence of two prominent spectral features corresponding to π∗ and σ∗ resonances as expected
of π conjugated C materials. After exposing the SWNT to an atomic hydrogen source, the π∗
resonance spectra was seen to loose intensity. Subsequent theoretical calculations showed that C
atoms to which a H atom is attached have a structural geometry and a chemical bonding that have a
substantial component from sp3 hybrids. As a result the π and π∗ components to the electronic DOS
vanish, resulting in a complete disappearance of the corresponding features in a XA spectrum(166).
Further evidence of decrease in conductance due to C-H bond formation was obtained from electrical
transport measurements of individual SWNT field effect transistors. Zhang et al.(42) consistently
CHAPTER 7. H2 STORAGE IN PT-SWNT COMPOSITES 158
1.2
1.0
0.8
0.6
0.4
0.2
0.0
Nor
mal
ized
Inte
nsity
1800160014001200
wavenumber(cm-1)
0.4
0.3
0.2
0.1
0.0280240200160
wavenumber(cm-1)
514 nm 632 nm 785 nm
Figure 7.2: SEM images of SWNT films used for the conductivity and spectroscopy studies. (a,b)Dense and sparse distribution of as grown SWNT films. (c) Spin cast HiPCO SWNT films (d)Monolayer coverage of SWNT films prepared by LB technique (e) AFM scan of the LB films. (f)Representative Raman spectrum obtained from the HiPCO SWNT samples.
CHAPTER 7. H2 STORAGE IN PT-SWNT COMPOSITES 159
observed a drastic decrease in conductance for SWNT devices after room temperature H-plasma
treatment. The conductance decrease upon hydrogenation can be attributed to the sp2 → sp3
structure change of an SWNT, leading to localization of π-electrons. Hence, conductivity tests were
performed to study the change in conductivity of the Pt doped SWNT film on being exposed to a
molecular hydrogen source.
80
60
40
20
0
pres
sure
(psi
)
50004000300020001000time(secs)
1.00
0.98
0.96
0.94
0.92
curr
ent (
norm
aliz
ed)
norm
aliz
ed c
urre
nt
Figure 7.3: Change in current passing through a Pt-doped SWNT film (nominal thickness = 0.5nm) on repeated exposure to hydrogen. Also plotted is the change in hydrogen pressure inside thechamber
Fig. 7.3 plots the change in current across a Pt doped SWNT film (a steady voltage was main-
tained across the two probes) on exposure to hydrogen. Initially a constant current flowed through
the SWNT film, but on exposure to 80 psi of hydrogen the current decreased. On evacuating the
chamber the current was approximately constant, while on re-exposing the film to hydrogen the
conductance of the film decreased further, though the drop in conductivity was relatively small.
Similar response was observed for one more hydrogen exposure. Thus it was established that the
exposure to hydrogen resulted in a definite decrease in conductance of the SWNT film. But from
a two probe experiment it is hard to determine whether the change is due to a change in contact
resistance or due to change in the intrinsic property of the film. Hence for subsequent conductivity
tests a 4-probe set-up was used, since it eliminates the contact resistance between the probes and the
material, and hence any change in resistance of the sample is solely due to the change in resistivity
of the material.
7.4.1 In-situ 4 probe conductivity tests
The details of the 4-probe setup has been described in Chapter 2. A constant current is passed
through the sample via the outer two probes, and the potential difference between the inner two
CHAPTER 7. H2 STORAGE IN PT-SWNT COMPOSITES 160
1.0
0.8
0.6
0.4
0.2
0.030x1032520151050
time (secs)
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
∆R/Ro
150010005000
0.20
0.15
0.10
0.05
0.00
∆R/R
o
302520151050
x103
-50
-40
-30
-20
-10
0
10x10
-3 150010005000
H2, 7
00 T
orr
expo
sed
to a
ir
pum
ping
expo
sed
to a
ir
no p
umpi
ng
H2 c
harg
ing
0.6 Pt (charging) 0.6 Pt (cycling)
HiPCO (charging) HiPCO + 0.6 nm Pt (charging) HiPCO + 0.6 nm Pt (cycling)
Figure 7.4: Resistance change as function of hydrogen charging for as-deposited and Pt sputteredSWNT samples. Also shown is the change in resistance of the Pt-SWNT hybrid film on exposure toair. For comparison, changes to a 0.6 nm thick sputtered Pt film on quartz on exposure to hydrogenis also plotted.
probes was constantly monitored as a function of time. The pressure inside the 4-probe chamber is
limited to atmospheric pressure, hence all the conductivity studies reported here were performed at
a pressure of 700 Torr. Before exposing the films to air the chamber was evacuated using a turbo
pump. SWNT films for the tests were prepared as mentioned in a previous section. Metal pads were
sputter deposited on the films to facilitate good electrical contact with the 4 probes. The resistance
of the as-deposited film was measured. Subsequent to which a desired amount of Pt was sputter
deposited on the film with the contact pads. These sputter deposited Pt-SWNT films were then
used for the in-situ conductivity tests.
Fig.7.4 plots the change in resistance (normalised by the resistance of the Pt-SWNT hybrid film
at the onset of exposure to hydrogen) as a function of hydrogen charging time before and after
sputtering Pt on the thin SWNT films. The films were exposed to 700 Torr of hydrogen pressure,
after evacuating the chamber down mTorr. The change in resistance of the Pt-SWNT composite
film is approximately 4 times the resistance change for the un-doped film. The increase in resistance
CHAPTER 7. H2 STORAGE IN PT-SWNT COMPOSITES 161
is directly related to the change in intrinsic property of the SWNT film and can be attributed to the
formation of C-H bonds on exposure to hydrogen. The higher change in resistivity of the doped films
then is due to enhanced C-H bond formation a direct consequence of spillover of H atoms obtained
by dissociative chemisorption of hydrogen molecules on the Pt nano catalyst particle surface.
Of, special note is the plot of the resistance change of a bare 0.6 nm Pt thin film exposed to
hydrogen. Similar to the SWNT-Pt composite films, the resistance of the Pt film increases probably
due to the change in Fermi level of Pt on exposure to hydrogen. But, the time scale for the change
in resistance of the Pt film is much smaller than the SWNT-Pt composites. In fact, the bare Pt film
undergoes a drastic resistance change and reaches a plateau level within a short interval of the onset
of hydrogen flow. On the other hand the resistivity of the Pt-SWNT hybrid did not reach a steady
state even after 8 hours of hydrogen charging. This implies that for most of the hydrogen uptake
process for SWNT-Pt hybrid the surface hydrogenation reaction of Pt has reached steady state.
Thus the molecular hydrogen in the gas phase is in equilibrium with the chemisorbed hydrogen on
the Pt sites and chemisorption is certainly not the rate determining step.
H2(gas) + 2ch ↔ [2H]ch (7.1)
where ch denotes an empty chemisorbtion site on the Pt surface.
0.20
0.15
0.10
0.05
0.00
∆R/
R
30x103252015105
Time(secs)
0.2nm Pt 0.4nm Pt 0.6nm Pt1.0nm Pt1.5nm Pt
Figure 7.5: Resistivity changes with hydrogen exposure for CNTs with different Pt loadings
CHAPTER 7. H2 STORAGE IN PT-SWNT COMPOSITES 162
Fig.7.4 also plots the resistance change in the 0.6nm P film and the Pt-SWNT hybrid sample
when air is leaked into the 4 probe chamber. On exposure to air the resistance of the Pt film
increases further, probably due to the higher affinity for oxygen of the hydrogenated Pt surface
(167). The resistance of the Pt film shows further changes on subsequent evacuation, hydrogen
charging and re-entry of air into the chamber. On the other hand, the resistance of the Pt-SWNT
film remains relatively unchanged while undergoing the same processes. Actually on exposure to air
there is a small decrease in resistivity of the film, in contrast to the bare Pt film. These studies thus
establish that the change in resistivity of the Pt-SWNT film is not due to changes in resistivity of
the Pt catalyst particles but is due to intrinsic change in SWNT film itself, and hence consolidate
the evidence for spillover mechanism of hydrogen storage.
Function of nominal thickness of Pt on SWNT mats
Next we studied the increase in resistance of the films as a function of the nominal thickness of
the sputter deposited Pt films. This is shown in Fig.7.5. The sputtered Pt film does not wet the
SWNT surface, but as mentioned before, it balls up forming particles. The size and distribution of
the particles formed depend on the thickness of the sputtered Pt. This study was done to find the
optimal catalyst particle size.
With increase in nominal thickness of the catalyst particles the normalized resistance initially
increases to an optimal level, beyond which it decreases. The optimal thickness of the deposited
Pt film is 0.6 nm. This supports the hydrogen uptake measurements with the Sieverts apparatus,
mentioned in Section 2 of this chapter, where it was observed that the hydrogen uptake by a Pt-
SWNT composite film varies linearly with the density of the Pt particles. With an increase in the
nominal thickness of the Pt film, the density as well as the size of the catalyst particles increase. But,
beyond a certain thickness of sputtered film, the Pt particles start agglomerating, thus decreasing
the number density of the particles and hence decreasing the extent of H spillover onto the SWNT
surface.
Function of SWNT film thickness
For the next experimental set, the nominal thickness of the sputtered Pt film was kept constant
(0.6 nm, the optimal nominal thickness determined from the previous set of experiments), but the
thickness of the SWNT film was varied. For this study five different SWNT films were used: HiPCO
SWNT dispersed in iso-propanol and spin cast on glass, dense and sparse distributions of horizontal
SWNT mats grown from Co catalysts on glass, and finally two monolayer thick SWNT films of
varying densities assembled by the Langmuir Blodgett (LB) method. The resistance of the films
so prepared are inversely proportional to the thicknesses, Fig.7.6(b). It is to be noted that the
resistances of the films before and after Pt deposition remains almost the same implying that the
sputtered Pt even for the LB films are not continuous but are in the form of catalyst particles
CHAPTER 7. H2 STORAGE IN PT-SWNT COMPOSITES 163
2.4
2.2
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
Norm
aliz
ed in
crea
se in
resis
tivity
30x1032520151050time(secs)
LB film (sparse) LB film (dense) as grown SWNT (sparse) HiPCO spun on glass as grown SWNT (dense)
100
101
102
103
104
105
106
107
Res
istan
ce (Ω)
as grown SWNT
dense
sparse
LB films
sparsedense
as deposited SWNT SWNT + 0.6nm Pt
Figure 7.6: Hydrogen uptake efficiency for SWNT films with varying thickness. The Pt loading waskept identical for all samples.
CHAPTER 7. H2 STORAGE IN PT-SWNT COMPOSITES 164
0.4
0.3
0.2
0.1
0.0
∆R/
R
30x1032520151050 time (secs)
-5oC 25oC 45oC 69oC 94oC 127oC
0.8
0.6
0.4
0.2
0.0
∆R/R
(no
rmal
ized
)
500040003000200010000 time (secs)
-5oC 25oC 45oC 69oC 127oC
Figure 7.7: Hydrogen uptake measured at different temperatures. The Pt loading and the filmthicknesses are the same for all the runs.
dispersed on the nanotube surface.
Hydrogen uptake by the Pt-SWNT composites has a strong dependence on the thickness of the
SWNT mats; the sparse SWNT LB films show an increment of more than an order of magnitude
in normalized change in resistance values compared to the HiPCO SWNT films spun cast on glass.
This dependence is attributed to the numerical density of Pt particles per area of the SWNT film
exposed to hydrogenation, which is the least for the thick HiPCO films and highest for the LB films.
Thus for maximum hydrogen storage it is necessary to obtain a uniform dispersion of monolayer
thick unbundled SWNTs, doped with optimal size and density of Pt catalyst particles. This will
ensure a high specific hydrogen uptake per weight of Pt-SWNT composite.
Function of hydrogen charging temperature
The time for all the hydrogenation experiments mentioned so far is approximately 8 hours. It was
observed that even after 8 hours the resistance plots do not reach a plateau region, implying very
slow kinetics. If the hydrogen uptake is via the spill over mechanism, then the kinetics will be limited
by the diffusion of C over the SWNT surface. In that case, the temperature of the charging process
would influence the kinetics and possibly result in an uptake increment with temperature. Fig. 7.7
plots the temperature dependence of resistance change for a film on exposure to 700 Torr of hydrogen.
An embedded heater was used to set the temperature for the hydrogen charging experiments. The
maximum substrate temperature attained by the heater is 127oC.
It is observed that the rate of change in resistance increased on ramping up the hydrogenation
CHAPTER 7. H2 STORAGE IN PT-SWNT COMPOSITES 165
temperature from −5oC to 127oC (Fig.7.7(b), shows that with increasing temperature the resistivity
changes reaches a plateau region faster). This again provides indirect evidence for the spillover
process. But, interestingly the net change in resistance of the films decreased on ramping up the
temperature. The net change in resistance and hence the amount of hydrogen uptake is largest for
−5oC and kept on decreasing monotonically on increasing the hydrogenation temperature. This
behavior can be attributed to the exothermic nature of the hydrogen dissociation reaction on Pt.
Increasing the temperature will decrease the Pt- surface hydride formation (163) and hence the
amount of H spilling over onto the SWNT surface.
7.5 XPS characterization of SWNT films
Ex-situ XPS measurements were performed on SWNT- Pt composites before and after hydrogena-
tion. The experiment was performed based upon the observation that the hydrogen release from
the composite sample took a long time even under ∼mTorr level vacuum. Hence XPS can be used
to establish the presence/absence of C-H bond subsequent to hydrogen charging. LB films and as
grown SWNT mats were chosen for the XPS studies, as they showed the most promise from the
thickness dependence studies mentioned in the last section. After depositing 0.6nm Pt of nominal
thickness on the SWNT films, the samples were baked overnight in an evacuated chamber at 250oC.
XPS spectra was collected. Next following another anneal, the hybrid samples were exposed to a
hydrogen pressure of 120 psi for 6 hours. Subsequent to which, XPS spectra of the hydrogenated
samples were collected. A glove bag containing forming gas was used during the sample transfer,
hence the hydrogenated samples were not exposed to air before the measurements were performed.
100
80
60
40
20
0
Cou
nts
[a.u
.]
700600500400300200100Kinetic Energy [eV]
O2
C Auger N2
Pt 4d
C 1s
O Auger
Pt 4f LB films + 6A Pt hydrogenated LB films + 6A Pt
Figure 7.8: XPS overview of the samples before and after hydrogenation. 0.6nm Pt+ LB SWNTfilm composite
CHAPTER 7. H2 STORAGE IN PT-SWNT COMPOSITES 166
Fig.7.8 plots XPS overview spectrum from 0.6 nm Pt doped LB film before and after hydrogena-
tion obtained using 700 eV incident photon energy. The spectral features include C 1s and C Auger
from the SWNT, Pt 4f and 4d peaks from the catalyst particles decorating the LB films, and O and
N spectral features most probably from the organic residues generated during the calcination step.
The Pt 4f peak is used to calibrate the XP spectrum.
The XPS of the samples before and after hydrogen exposure was measured, Fig.(7.9,7.10). For
comparison, the signal intensities were normalized through linear background subtraction of the
lower binding energy side.The strongest component at 284.8 eV binding energy is the C 1s peak and
is assigned to sp2 hybridized C atoms in the nanotubes. After exposure to hydrogen at a pressure
of 120 psi, the spectra of the hydrogenated samples showed a different peak profile particularly
in the higher binding energy side of the primary carbon C1s peak. From Fig.7.9,7.10(a) we can
observe a significant shoulder at 285.6 eV binding energy . This new contribution is assigned to the
re-hybridization of C atoms to sp3 due to the breaking of π-bonds and C-H bond formation and can
be seen as a direct evidence for the proposed spillover effect.
1.0
0.8
0.6
0.4
0.2
0.0
Nor
mal
ized
Inte
nsity
294292290288286284282280
Binding energy(eV)
As grown SWNT+6A Pt As grown SWNT+6A Pt (hydrogenated)
Figure 7.9: (a)XPS before and after hydrogenation of As-grown films. Fitted XPS peaks of as-grownsamples, before (b); and after Hydrogen exposure(c)
Furthermore, an additional new peak at 288 eV can be detected for both hydrogenated samples.
We conjecture that this peak arises from a metal-to-semiconductor transition of the nanotubes that
is induced by the hydrogenation. The accompanying decrease of the electric conductivity can cause a
reduction of the core hole screening, resulting in a ∼4 eV higher final state energy (41). Alternatively,
the creation of a band gap can give rise to a shake-up line.
By de convoluting the XP spectra as shown in Fig.7.9,7.10(b,c), we can estimate the amount of
carbon atoms that has undergone a change from sp2 to sp3 hybridization, which corresponds to the
CHAPTER 7. H2 STORAGE IN PT-SWNT COMPOSITES 167
1.0
0.8
0.6
0.4
0.2
0.0
Nor
mal
ized
Inte
nsity
294292290288286284282280
Binding energy (eV)
LB film + 6A Pt LB film + 6A Pt (hydrogenated)
Figure 7.10: (a)XPS before and after hydrogenation of 0.6 nm Pt-LB film hybrids. Fitted XPSpeaks of as-grown samples, before (b); and after hydrogen charging(c)
amount of stored hydrogen. The asymmetric C1s principal peak was fitted with a Voigt line shape
with a tail. The same relative amplitudes for the Voigt line-shape and the accompanying tail were
maintained for fits before and after exposure. The shoulder that appears on hydrogenation were
fitted with Lorentzian line shapes at 285.6 and 288 eV. The relative weights of the sp2(sp3) peaks
are 0.84 (0.17) for the LB film and 0.87 (0.13) for the as-grown film. The third peak at 288 eV
has a relative weight of 0.05 in both samples. Since the fraction of hydrogenated carbon atoms is
proportional to the relative peak intensity, we obtain atomic hydrogen percentages of 16% for the LB
film and 12% for the as-grown film. If all carbon atoms were hydrogenated, the hydrogenation will
be 7.7 weight percent. Therefore in this experiment the weight percentage hydrogen uptake is 1.2%
for LB films and 1 % for the as-grown films. This is consistent with the conductivity experiments
where we also observed a higher percentage of hydrogen uptake for the LB films. Similar trends
were observed from the 4A Pt samples for the LB and as-grown SWNT films. This leads us to the
conclusion that the exposure of Pt-modified SWNTs to molecular hydrogen results in the formation
of stable C-H bonds.
7.6 Conclusion
In this chapter, hydrogen uptake of the Pt catalyst doped SWNT composites were investigated.
Qualitatively the results are analogous to previous reports of hydrogen uptake by doped SWNT
samples. 4-probe conductivity was used to study in-situ hydrogen uptake properties. Hydrogen
CHAPTER 7. H2 STORAGE IN PT-SWNT COMPOSITES 168
uptake capacity of sputtered Pt composite showed significant increases by a factor of four over un-
doped SWNT films. Very different timescales and nature of the resistivity change of the doped
SWNT films and thin Pt films during the conductivity tests established that hydrogen uptake in the
composites is solely due to formation of C-H bonds. The 4-probe conductivity plots were used to
identify optimal nominal thicknesses of the sputtered Pt and SWNT film thicknesses for enhanced
hydrogen uptake. Finally temperature dependent charging experiments showed that kinetics of
the hydrogen uptake process is fastened at higher temperature, providing evidence of the diffusion
limited nature of the process. Most importantly, the above sets of experiments show that 4-probe
studies can be used as a simple, sensitive probe to optimize the hydrogen uptake conditions for
doped SWNT films. XPS experiments evidenced the possible switch from sp2 orbital structure
of the carbon nanotube to the sp3-type structure upon the formation of C-H bonds. Our results
demonstrate that the hydrogenation mechanism is a spillover process where hydrogen molecules first
dissociatively adsorb on the Pt surface, and the chemisorbed H atoms subsequently diffuse onto the
nanotube surface where they form C-H bonds.
Chapter 8
Conclusions and Future Work
8.1 MWNT growth model and in-situ tracking of tube height
A generic model for growth of 1-d nano structures via VLS mechanism is applied to the nanotube
growth. The model formulated steady state flux in terms of change/drop in chemical potential for
the basic four mass transfer steps identified. The flux is then written in terms of the total change
in chemical potential in going from the vapor state to the nanotube and in terms of the diffusive
and/or interface reaction rates. The growth rates of the MWNT was then measured using time
resolved reflectivity data obtained from the interferometer set up as a function of temperature and
pressure. The idea is to identify the rate limiting step by interpreting the experimental conditions
and results in terms of the model. Once the rate limiting step is identified growth rates, final heights
etc can be and was predicted as a function of growth time, temperature, pressure, gas flow rates
etc. provided the limiting step remains unchanged. Further experiments can also be designed to
further the understanding of the rate limiting step. For example, study of MWNT growth under the
influence of an electric field was used to identify two different limiting reaction mechanisms within
the purview of the vapor-catalyst interfacial transport limited growth. Thus, we have developed a
protocol/template which can be used to understand and predict growth of 1D materials.
The model was tested for different growth conditions using ethylene as a hydrogen source. To
further validate the model more studies need to be performed using different C precursors, in par-
ticular higher molecular weight carbon precursor sources. This is because the decomposition of
these hydrocarbons and incorporation of the C or the C- bearing species into the growing SWNTs
could be very different from the simpler molecules used for this study. Further the interferometry
technique could be complimented by other techniques (e.g the time-lapse photography) so that the
maximum limit of film heights studied can be increased. This will also help to investigate in detail
the important catalyst deactivation/growth termination step. A good case study, could be the incor-
poration of controlled amount of water into the growth process which is supposed to delay catalyst
169
CHAPTER 8. CONCLUSIONS AND FUTURE WORK 170
deactivation by etching away the carbon soot formed on catalyst particles.
8.2 Catalyst size and nanotube morphology
The catalyst particle size is one of the key parameters that determine the morphology of the 1D car-
bon nanostructures. The diameter controls the diameter of the nanotube formed. Gibbs Thompson
effect predicts a size dependent suppression of melting point, determining the phase of the particle
at the time of growth which in turn was shown to affect the 1D structure formed. In the CVD
process, higher annealing pressures were found to form larger particle sizes which led to nanofiber
growth. At these diameters, the melting point suppression puts the Fe-C particle in a dual solid-
liquid phase. Carbon flux accumulates in the dual phase during growth until the dual phase becomes
energetically unfavorable because of the growing contribution of the surface energy. At this point,
the particle reverts to a single solid phase regime by discarding excess carbon, resulting in a discon-
tinuous graphitic structure characteristic of Carbon nanofibers. Ex-situ TEM studies was used to
determine the morphology of growth. Though convincing, the experimental evidence for the model
proposed is circumstantial. In-situ TEM characterization of MWNT during growth from a range of
diameters will resolve the ambiguity. So environmental TEM in situ studies should be performed to
study the particle diameter dependence of the 1D morphology.
8.3 Electric-field assisted MWNT growth
Application of an electric field during MWNT growth enhanced the growth rate and alignment of
the MWNTs. It was observed that increasing the magnitude of the field enhanced the growth rate
but the growth rates leveled off to a constant value on increasing the field. On the other hand,
for the same magnitude of bias, the height enhancement on application of an electric field was
largest for the lower growth temperatures. Further analysis of temperature dependent studies in
the presence and absence of the electric field reveal that there are actually two activated processes
involved, with rate-limiting step being independent of applied field at high temperature. At higher
temperatures, the rate-limiting step is the carbon dissolution into the catalyst particle, while at lower
temperatures it is the carbon dissociation at the catalyst-vapor interface that limits the growth.
Application of an electric field enhances the decomposition of the C precursor in the vapor phase,
thus circumventing this low temperature activation barrier. The main advantage of an imposed field,
that took advantage of the high polarizability of the CNTs along the axial direction, was to restrict
the tube-tube interaction. Calculations show that this benefit is obtained at a minimum field level,
with no benefit arising from further increase in field strength. The enhanced alignment of the CNTs
in the dense MWNT films with the electric field is explained by tensile stretching overcoming the
defect-induced kinking of the MWNTs.
CHAPTER 8. CONCLUSIONS AND FUTURE WORK 171
Two other factors found to be important for enhanced alignment were, spatial density and the
growth induced kink formation that resulted in the formation of defective MWNTs. Future studies
are needed to identify growth conditions that will decrease the defect concentration in the CNTs
and also identify catalyst preparation techniques to further reduce their spatial density. Subsequent
application of an electric field for those conditions should result in formation of an array of vertically
aligned nanotubes.
8.4 Chirality, Diameter control of SWNT
The bottleneck for the assimilation of the SWCNT into devices/materials is the limited control over
the nature of the tube produced and the small laboratory scale production rates. In this work we
reported the influence of three important growth parameters namely reaction time, temperature and
metal catalyst concentration on the nature of product obtained by using a floating catalyst method
to grow SWCNT. Larger residence time forms larger catalyst particles resulting in formation of
larger diameter CNTs. Greater ferrocene percentage, in the precursor solution, led to the formation
of larger particles and hence larger CNTs. Thus particle size has a direct relation to the diameter of
the SWNT formed. Temperature increase increased the diameter range of the SWNTs synthesized
but with a bias for the smaller diameter tubes. These conditions were tried independent of each
other, but, in future studies, a combination of two or more of these trends can be used to narrow
down further the chirality/diameter range. In the process, we developed a method of analysis via
combined two wavelengths Raman and Absorption spectroscopy with TEM validation for diameter
and chirality family populations.
One further knob in controlling the chirality of the SWNTs could be the use of different types of C
precursors, which is being studied by Cara Beasely from Prof. B. M. Clemen’s and Prof. P.Wong’s
group. Another future avenue could be to use the growth model developed for 1D nanomaterial
growth to identify growth conditions for which the catalyst-CNT interface is the rate limiting case.
Under these rate limiting conditions, any changes to the catalyst, carbon precursor and growth
parameters should reflect in the nature of the SWNT formed. It is worth putting an effort to come
up with a method to control the diameter and chirality of the SWNTs during the growth process
itself, rather than isolating nanotubes via post growth techniques. This is because most of the post
SWNT separation techniques involve functionalization of the SWNTs or use of a surfactant which
could change the physical properties of the SWNT.
8.5 Hydrogen Storage in Pt-doped SWNT
The mechanism of hydrogen uptake in transition metal-doped SWNT was studied. In-situ 4-probe
conductivity tests were performed on mats of Pt doped SWNT during hydrogen uptake. On hydrogen
CHAPTER 8. CONCLUSIONS AND FUTURE WORK 172
charging the resistivity of the Pt doped SWNT mat increased. This is due to the formation of C-H
bonds, which consumes the π and π∗ electrons from the affected SWNT regions, thereby increasing
the resistivity. Initial studies of the temporal dependence of hydrogen uptake suggest a diffusion-
limited process. XPS was employed to measure the extent of sp3 C-H bonding.
Future studies should completely avoid the use of molecular hydrogen in the energy storage /
transport /release cycle, thus making it more practical. The electrochemical hydrogen reduction at
pure carbon nanotube surfaces involves electron tunneling between the nanotube surface and the
outer Helmholtz plane, and thus a significant over-potential. Hydrogen atoms will thus be generated
at a greater distance from the nanotube, and will likely recombine to form molecular hydrogen
before they could reach the nanotube surface. Therefore electrochemical hydrogen reduction at
pure nanotube electrodes will merely lead to the production of hydrogen gas. If SWNTs were to be
replaced with Pt-SWNT composites then the molecular hydrogen formed above can be dissociatively
chemisorbed to the Pt surface, from where it will spillover to the SWNT surface, same as the
process described for a gaseous H2 source. The amount of stored hydrogen could be determined
either by 4-probe conductivity or XPS measurements. Prof Nilsson’s group at SLAC is studying
this electrochemical route for hydrogen storage.
Appendix A
Derivation of tip amplitude of a
vibrating carbon nanotube under
the influence of an electrical field
The carbon nanotube is simulated as a cantilever beam, fixed at one end. For small deflections,
the amplitude of a vibrating cantilever beam under the influence of an electric field is given by the
equation:
ρAδ2y
δt2+ YI
δ4y
δx4− αE2
2
δ2y
δx2= 0 (A.1)
where ρ is the density of the material, I is the second moment of inertia of the cross-sectional area
A, Y the Youngs modulus , α the polarizability coefficient, and E the electric field acting on the rod.
Solving A.1 is cumbersome, so previous efforts to describe the amplitude of the nanotube under a
localized applied field involved simplifying assumptions. Hongo et al.(28) assumed that the second
term in A.1 which describes the potential energy due to the bending of the nanotube can be ignored
and its influence approximated by an effective polarizability term. The effective polarizability term
approaches the actual polarizability values only in the limit of dipole-field interaction being more
dominant than the bending. Hence it was necessary to estimate the effective polarizability values
from the experimental dataset. Here we present a more rigorous solution for the partial differential
equation described in A.1. Assuming that the nanotube vibrations are in equilibrium with the
ambient temperature the solution is of the form: y = f(x) sin(ωt); f(x) = exp(λx).
Substituting in A.1 we get the relation
−ρAω2 + YIλ4 − αE2
2λ2 = 0 (A.2)
173
APPENDIX A. TIP AMPLITUDE OF MWNT 174
Solving for the quadratic, in ’λ’ we get,
λ2 =
αE2
2 ±√
α2E4
4 + 4ρAω2YI
2YI(A.3)
.
Hence the solution of the partial differential equation, A.1, should be of the form
f = sin(ωt)[A sinh(mx) + B cosh(mx) + C sin(nx) + D cos(nx)] (A.4)
where the roots of A.3 are, ± m, ± in, are given by the relation:
m2 =αE2
4YI+
√α2E4
16Y2I2+ρAω2
YI(A.5)
n2 =
√α2E4
16Y 2I2+ρAω2
Y I− αE2
4Y I(A.6)
The boundary conditions for a cantilever beam of length,L, clamped at one end is given by the
relations:
f|x=0 =δf
δx|x=0 =
δ2f
δx2|x=L =
δ3f
δx3|x=L = 0 (A.7)
This leads to the following solution for the nth harmonic
yn =un
2sin(ωt)sinh(mnL)− mn
nnsin(nnx)− m2
n sinh(mnL) + mnnn sin(nnL)
m2n cosh(mnL) + n2
n cos(nnL)[cosh(mnx)− cos(nnx)]
(A.8)
with un being the amplitude of the nth harmonic at the tip x=L. The constraints on the possible
values of mn and nn are given by the two equations below.
m4n + n4
n + 2m2nn2
n cosh(mnL) cos(nnL) + (mnn3n −m3
nnn) sinh(mnL) sin(nnL) = 0 (A.9)
m2n − n2
n =αE2
2YI(A.10)
This can be simplified realizing:
m4n + n4
n = 4A2 + 2B2
m2nn
2n = B2
(mnn3n −m3
nnn) = B(n2n −m2
n) = −2AB
APPENDIX A. TIP AMPLITUDE OF MWNT 175
where
A =αE2
4YIB = ω
√ρA
YI(A.11)
Substituting A.11 in A.9 and A.10 , we solved for the frequency, ω. An analytical solution for
A.9 and A.10 is not possible and hence the above equations were numerically solved to obtain the
allowed eigenvalues, ωn, for a given height and applied field. The allowed values of frequencies are
plotted as a function of field strengths and lengths in Fig.A.1. The energy in the mode n is therefore
quantized in units of ~ωn. In the limit of large bias, cosh(mL) = sinh(mL) = exp(mL/2), m >> n,
cos(nL) = (1− nL) and sin(nL) = nL. This results in n2 = 2m exp(−mL)/L, or
ω = [YI
ρA]1/2[
αE2
2YI]3/4√
2
Lexp[−1
2
√αE2
2YIL] (A.12)
103
104
105
106
107
108
109
1010
1011
1012
Freq
uenc
y(H
z)
108642
Height of tubes
wo(0) w1(0) w2(0) wo(10V/m) w1(10V/m) w2(10V/m) wo(100V/m) w1(100V/m) w2(100V/m) wo(10e3V/m) w1(10e3V/m)_ w2(10e3V/m) wo(10e4V/m) w1(10e4V/m) wo(10e5V/m) w1(10e5V/m) wo(10e6V/m) w1(10e6V/m)
Figure A.1: Allowed frequencies for the lower order modes as a function of height and strength ofapplied electric field during growth.
This solution differs from that of Hongo et al. and other papers mentioned therein, because
the approximation of neglecting the 4th derivative in results in a solution that does not satisfy two
of the four boundary conditions. Retaining the 4th order term to properly satisfy the boundary
condition changes the solution significantly. The plot reveals some interesting trends. The allowed
frequencies decrease as a function of height of the CNTs. The allowed frequencies of the higher order
APPENDIX A. TIP AMPLITUDE OF MWNT 176
modes increase with increasing bias magnitudes. In contrast the fundamental mode frequencies
decrease with an increase in magnitude of the applied field, as expected from A.12. For applied
fields > 1000V/m , the ω values approach zero, which will lead to a trivial solution (as can be seen
from A.9 and A.10). Hence for larger fields the next higher mode is considered the fundamental
mode. The total elastic energy contained in the vibration mode n can be obtained at the instant of
maximum deflection when the cantilever is momentarily stationary, sin(ωt) = 1.
Eelasticn = |YI
2
∫ L
0
(δ2yn
δx2)2dx|sin(ωt)=1 =
1
2celasticn u2
n (A.13)
The elastic energy in the absence of an applied bias simplifies to Eelasticn =
YILu2nn4
8 , the same as
obtained in (86). In the limit of large bias the relation is Eelasticn = YI
16 m3n . The average energy of
the nth mode is < En >= kT , half of which comes form the elastic energy degree of freedom. Thus
comparing A.13 with kT, the amplitude of each vibrational mode can be determined.
δn = (kBT
celasticn
)1/2 (A.14)
This is unlike (86) where the authors were looking for the root mean square amplitude, since here
we are concerned about the maximum amplitude for a given length and biasing magnitude, which
in turn determines the growth mode for the nanotubes. The vibration amplitude for the lower order
modes are plotted in Fig. 5.16 as a function of the length of the multi-walled carbon nanotubes and
the strength of the electric field.
Appendix B
Algorithm for analyzing
interferometer scans
There were two methods that were developed for analyzing the interferometer scans. The first one
fitted the attenuating background signal using a Savitzky-Golay (SG) filter. The second removed
the background by taking a Fourier Transform of the signal and removing the contributions from
the low frequency components. An inverse transform was performed to obtain the interfering signal.
B.1 Savitzky-Golay filter
Following is the algorithm written for Igor Pro 6 and above. It is to be noted that the algorithm
does not work on a lower platform since the number of averaging points required for the SG filter
are much more than 25 (the maximum number of points handled by the older platforms).
# pragma rtGlobals=1 // Use modern global access method.
Variable/G gStartPt, gEndPt, gNpeak // global variables to hold parameters from previous
execution of ’Smooth F indPeaks’
Variable/G gBkgndSmoothWidth, gNumBkgSmooths
Variable/G gFirstTime=1 // flag to indicate if function has been called previously
****************************************************
Menu ”Macros”
”Analyze CNT Data”,Smooth F indPeaks()
177
APPENDIX B. ALGORITHM FOR ANALYZING INTERFEROMETER SCANS 178
End
****************************************************
Function Smooth F indPeaks()
WAVE Timex, Signal
NVAR gStartPt, gEndPt, gNpeaks
NVAR gBkgndSmoothWidth, gNumBkgSmooths
NVAR gFirstTime
Variable Tstart, Tend, StartPt, EndPt, Npts, Npeaks=10
Variable index
————————————————————————————-
Variable peakToValleyDistance=425
// physical distance (in nm) corresponding to peak-to-valley separation in the interferogram
————————————————————————————–
Variable ptsPerCyc, oneEighthCyc
Variable hiFreqSmoothWidth, bkgndSmoothWidth
Variable numBkgSmooths
Variable numHiFreqSmooths=6
// Kill graphs or tables left from previous execution of this Function
DoWindow/K Signal Graph
DoWindow/K Rate Table
DoWindow/K Rate Graph
// Make graph of raw signal vs time
Display /W=(9,49,493,374) Signal vs Timex as ”Graph of Signal vs Time”
DoWindow/C Signal Graph
ModifyGraph lSize=0.5
ModifyGraph grid=1
ModifyGraph tick=2
ModifyGraph mirror=1
ModifyGraph fSize=12
ModifyGraph standoff=0
Label left ”Signal x”
Label bottom ”Time, s”
SetAxis/A/N=1
ShowInfo
If (gFirstTime == 0) // check to see if the function has already been executed – if so, replace the
cursors and reset Npeaks
Cursor/P A,Signal,gStartPt
APPENDIX B. ALGORITHM FOR ANALYZING INTERFEROMETER SCANS 179
Cursor/P B,Signal,gEndPt
Npeaks = gNpeaks
// Pause to let the user place or adjust cursors on the graph of signal vs time.
// Cursors should span the region with oscillations, such
// that only the ”real” oscillations” are included.
// The following ’If’ statement is used only to call the special function ’PlaceCursors’, which
// places a small window beneath the graph, and suspends all operations other than changes
// to the main graph, until the user clicks ’Continue’.
If (PlaceCursors(”Signal Graph”,”Set the Cursors ”,”Adjust cursors ’A’ and ’B’”,” to span the
region of interest.”,”When finished,
click on CONTINUE.”) != 0)
return -1;
Endif
Else If (PlaceCursors(”Signal Graph”,”Set the Cursors ”,”Place cursors ’A’ and ’B’ on the Raw
Signal trace,”,” spanning the region of
interest.”,”When finished, click on CONTINUE.”) != 0)
return -1;
Endif
Endif
// Prompt user for the input parameters:
Prompt Npeaks,”Approximate number of Peaks (cycles) between the cursors?”
DoPrompt ”Inputs”,Npeaks //,loCutoff,hiCutoff,windowChoice
gNpeaks = Npeaks // save in global variable for next execution of function
// Figure the times (Timex) corresponding to the cursor locations.
StartPt=pcsr(A)
EndPt=pcsr(B)
gStartPt = StartPt // save the StartPt in a global variable so it can be resurrected for subsequent
calls to this function
gEndPt = EndPt // same for EndPt
Tstart=Timex[StartPt]
Tend=Timex[EndPt]
// Figure the number of pts between the cursors.
Npts=1+EndPt - StartPt
ptsPerCyc=trunc(Npts/Npeaks)
oneEighthCyc = trunc(ptsPerCyc/8)
Print ”Pts per cycle = ”,ptsPerCyc
If (gFirstTime==1)
APPENDIX B. ALGORITHM FOR ANALYZING INTERFEROMETER SCANS 180
bkgndSmoothWidth = trunc(Npts/3)
numBkgSmooths = 3
gFirstTime = 0
Else
bkgndSmoothWidth = gBkgndSmoothWidth
numBkgSmooths = gNumBkgSmooths
Endif
Prompt bkgndSmoothWidth,”Width (in points) of Background smooth?”
Prompt numBkgSmooths,”Number of Background smoothing passes?”
DoPrompt ”Background Smoothing:”,bkgndSmoothWidth,numBkgSmooths
gBkgndSmoothWidth = bkgndSmoothWidth
gNumBkgSmooths = numBkgSmooths
Duplicate/O signal,background,netSignal
// First, extend the signal to the right, past the location of the right-hand cursor, to
// avoid end-region problems with the Savitsky-Golay smoothing.
background[EndPt + 1,]=background[EndPt]
// Determine the ”background” by over-smoothing the ”signal” to eliminate oscillations
////bkgndSmoothWidth = trunc(2*ptsPerCyc) // set the width for the S-V smoothing; make sure
it’s ODD
If (mod(bkgndSmoothWidth,2)==0) // if it’s EVEN
bkgndSmoothWidth += 1 // make it ODD
Endif
// Now, do the smoothing
For (index=1;index¡=numBkgSmooths;index+=1)
smooth/S=2 bkgndSmoothWidth,background
EndFor
netSignal = signal - background // subtract the ”background” from the original signal
Duplicate/O netSignal,smoothedNetSignal // make a wave to hold the result of hi-freq filtering
// Filter out the high-frequency noise by S-V smoothing
hiFreqSmoothWidth = trunc(ptsPerCyc/2) // set the width for the S-V smoothing; make sure it’s
ODD
If (mod(hiFreqSmoothWidth,2)==0) // if it’s EVEN
hiFreqSmoothWidth += 1 // make it ODD
Endif
// Now, do the smoothing
For (index=1;index¡=numHiFreqSmooths;index+=1)
smooth/S=2 hiFreqSmoothWidth,smoothedNetSignal
APPENDIX B. ALGORITHM FOR ANALYZING INTERFEROMETER SCANS 181
EndFor
// Add the background and the final smoothed net signal to the Signal Graph
DoWindow/F Signal Graph
AppendToGraph background vs Timex
ModifyGraph lsize(background)=1,rgb(background)=(3,52428,1) // green
AppendToGraph smoothedNetSignal vs Timex
ModifyGraph lSize=0.5
ModifyGraph rgb(smoothedNetSignal)=(1,4,52428) // blue
HideInfo
******************************
// Find Peaks and Valleys
******************************
Make/O/n=0 PVpointNum
Variable numPVsFound
Variable noPeaks,noValleys
Variable firstValleyLoc=0,firstPeakLoc=0,lastPVloc
FindPeak/Q/B=(oneEighthCyc)/R=[startPt,endPt] smoothedNetSignal // find first Peak
If (V flag == 0) // i.e., found a peak first
firstPeakLoc = V peakLoc
Else
DoAlert 0,”Didn’t find any peaks !!!”
Endif
FindPeak/Q/N/B=(oneEighthCyc)/R=[startPt,endPt] smoothedNetSignal // find first Valley
If (V flag == 0) // i.e., found a peak first
firstValleyLoc =V peakLoc Else
DoAlert 0,”Didn’t find any valleys !!!”
Endif
If (noPeaks ‖ noValleys)
DoAlert 0, ”No peaks or valleys were found – must abort!!”
Abort
Endif
numPVsfound = 1
If (firstPeakLoc < firstValleyLoc)
insertpoints (numpnts(PVpointNum)),1,PVpointNum // NOTE: this statement increases
numpnts(PVpointNum) by 1.
PVpointNum[numpnts(PVpointNum)-1] = firstPeakLoc
APPENDIX B. ALGORITHM FOR ANALYZING INTERFEROMETER SCANS 182
lastPVLoc = firstPeakLoc
Tag /F=0/L=1/Y=10/X=0/A=MB smoothedNetSignal, firstPeakLoc,” ”
Else
lastPVLoc = firstValleyLoc
Endif
DO
// Look for next VALLEY
FindPeak/Q/N/B=(oneEighthCyc)/R=[lastPVloc,endPt] smoothedNetSignal // look for next
VALLEY
If (numtype(V TrailingEdgeLoc)==0)
insertpoints (numpnts(PVpointNum)),1,PVpointNum
PVpointNum[numpnts(PVpointNum)-1] = V peakLoc
lastPVloc = V peakLoc
numPVsFound +=1
Tag /F=0/L=1/Y=10/X=0/A=MB smoothedNetSignal, V peakloc,” ”
Else
Break // break out of loop when there are no more extrema
Endif
// Look for next PEAK
FindPeak/Q/B=(oneEighthCyc)/R=[lastPVloc,endPt] smoothedNetSignal // look for next PEAK
If (numtype(V TrailingEdgeLoc)==0)
insertpoints (numpnts(PVpointNum)),1,PVpointNum
PVpointNum[numpnts(PVpointNum)-1] = V peakLoc
lastPVloc = V peakLoc
numPVsFound +=1
Tag /F=0/L=1/Y=10/X=0/A=MB smoothedNetSignal, V peakloc,” ”
Else
Break // break out of loop when there are no more Peaks or Valleys
Endif
WHILE(1)
Make/O/n=(numpnts(PVpointNum)),PVtimes
PVtimes = Timex[PVpointNum]
Make/O/n=(numpnts(PVtimes)-1) PVavgTimes,PVrates
PVavgTimes = (PVtimes[p]+PVtimes[p+1])/2 // mid-way between peak and valley times
PVrates = peakToValleyDistance/(PVtimes[p+1]-PVtimes[p])
// Make graph of rates vs time
Display /W=(497,49,981,375) PVrates vs PVavgTimes
APPENDIX B. ALGORITHM FOR ANALYZING INTERFEROMETER SCANS 183
DoWindow/C Rate Graph
ModifyGraph mode=4
ModifyGraph marker=8
ModifyGraph lSize=2
ModifyGraph msize=4
ModifyGraph grid=1
ModifyGraph tick=2
ModifyGraph mirror=1
ModifyGraph fSize=12
ModifyGraph standoff=0
Label left ”Growth Rate, nm/s”
Label bottom ”Elapsed Time, s”
SetAxis/A/N=1/E=1 left
SetAxis/A/N=1/E=1 bottom
// Make a Table with the Peak and Valley locations, avg times, and rates
Edit/W=(999,49,1342,437) PVpointNum,PVavgTimes,PVrates
DoWindow/C Rate Table
END // end of Function ’Smooth F indPeaks’
*****************************************************
Function PlaceCursors(grfName, ctrlName,str1, str2, str3)
String grfName, ctrlName, str1, str2, str3
DoWindow/F $grfName // Bring graph to front
if (V F lag == 0) // Verify that graph exists
Abort ”No such graph.”
return -1
endif
NewPanel/K=2 /W=(139,341,550,432) as ctrlName
DoWindow/C tmp PauseforCursor // Set to an unlikely name
AutoPositionWindow/E/M=1/R=$grfName // Put panel near the graph
DrawText 21,20,str1
DrawText 21,35,str2
DrawText 21,50,str3
Button button0,pos=80,58,size=92,20,title=”Continue”
Button button0,proc=UserCursorAdjust ContButtonProc
PauseForUser tmp PauseforCursor,$grfName
return 0
APPENDIX B. ALGORITHM FOR ANALYZING INTERFEROMETER SCANS 184
End
************************************************ Function
UserCursorAdjust ContButtonProc(ctrlName) : ButtonControl
String ctrlName
DoWindow/Ktmp PauseforCursor // Kill self
End
************************************************
APPENDIX B. ALGORITHM FOR ANALYZING INTERFEROMETER SCANS 185
B.2 Fourier Transform Method
The next code uses a Hanning function to do a FFT of the interfering signal, and then subtracts
off the low frequency components to eliminate the attenuating background. The rest of the code is
same as that of the SG filter algorithm. Here only the first part of the code pertaining to the FFT
approach is given.
# pragma rtGlobals=1 // Use modern global access method.
Variable/G gStartPt,gEndPt Menu ”Macros”
”Analyze CNT Data”,FFT FindPeaks()
****************************************************
Function FFT FindPeaks()
WAVE Timex,Signal
NVAR gStartPt,gEndPt
Variable peakToValleyDistance=425 // physical distance corresponding to the peak-to-valley
separation in the interferogram
Variable hiCutoff,loCutoff
// Kill any graphs or tables left over from previous execution
// of this Function
DoWindow/K Raw Graph
DoWindow/K Rate Table
DoWindow/K Rate Graph
// Make graph of raw signal vs time
Display /W=(9,49,493,374) Signal vs Timex as ”Graph of Raw Signal vs Time”
DoWindow/C Raw Graph
ModifyGraph lSize=0.5
ModifyGraph grid=1
ModifyGraph tick=2
ModifyGraph mirror=1
ModifyGraph fSize=12
ModifyGraph standoff=0
Label left ”Raw Signal, x”
Label bottom ”Time, s”
SetAxis/A/N=1/E=1
ShowInfo
If (gStartPt>0) // check to see if the function has already been executed – if so, replace the cursors
Cursor/P A, Signal, gStartPt
APPENDIX B. ALGORITHM FOR ANALYZING INTERFEROMETER SCANS 186
Cursor/P B, Signal, gEndPt // Pause to let the user place or adjust cursors on the graph of signal
vs time.
// Cursors should span (include) the region with oscillations, such
// that only the ”real” oscillations” are included.
// The following ’If’ statement is used only to call the special function ’PlaceCursors’, which
// places a small window beneath the graph, and suspends all operations other than changes
// to the main graph, until the user clicks ’Continue’.
If (PlaceCursors(”Raw Graph”,”Set the Cursors ”,”Adjust cursors ’A’ and ’B’”,” to span the
region of interest.”,”When finished, click on CONTINUE.”) != 0)
return -1;
Endif
Else
If (PlaceCursors(”Raw Graph”,”Set the Cursors ”,”Place cursors ’A’ and ’B’ on the Raw Signal
trace,”,” spanning the region of interest.”,”When finished, click on CONTINUE.”) != 0)
return -1;
Endif Endif
Variable Tstart,Tend,StartPt,EndPt,Npts,Npow,Npeaks,Save DC
String windowChoice
// Set default values for the input parameters:
Npeaks = 6
loCutoff = (Npeaks/2)
hiCutoff = (2*Npeaks)
// Prompt user for the input parameters:
Prompt Npeaks,”Approximate number of Peaks (cycles)?”
Prompt loCutoff,”Low-freq Cutoff in Cycles:”
Prompt hiCutoff,”High-freq Cutoff in Cycles:”
Prompt windowChoice,”Type of FFT window function:”,popup,”Hanning;Hamming;Cosine;None”
DoPrompt ”Inputs”,Npeaks,loCutoff,hiCutoff,windowChoice
Print ”Npeaks = ”,Npeaks,”, loCutoff = ”,loCutoff,”, hiCutoff = ”,hiCutoff,”, Window Type =
”,windowChoice
// Figure the times (Timex) corresponding to the cursor locations.
StartPt=pcsr(A)
EndPt=pcsr(B)
gStartPt = StartPt // save the StartPt in a global variable so it can be resurrected for subsequent
calls to this function
gEndPt = EndPt // same for EndPt
Tstart=Timex[StartPt]
APPENDIX B. ALGORITHM FOR ANALYZING INTERFEROMETER SCANS 187
Tend=Timex[EndPt]
// Figure the number of pts between the cursors.
Npts=1+EndPt - StartPt
// Make sure the number of points is EVEN (FFT requires EVEN)
If (mod(Npts,2))
EndPt += 1 // add a point at the end, if necessary
Npts += 1
EndIf
Make/O/n=(Npts) filteredSignal,filteredTime // prepare waves to hold the FFT’d output
// Figure the average value (DC level) between the cursors.
// Save for later so it can be added back after the FFT.
WaveStats /Q/R=[StartPt,EndPt] Signal
Save DC = V avg
// Take the FFT.
// Use a ”Window Filter Function” to minimize the effects
// of the data values at the start and end not being equal, as nominally
// required for a good Fourier transform. The user gets to select
// the specific window funtion that will be used to pre-multiply
// the ”signal” data.
StrSwitch (windowChoice)
Case ”None”:
FFT/OUT=1/RP=[StartPt,EndPt]/DEST=Signal FFTSignal
Break
Case ”Hanning”:
FFT/OUT=1/WINF=Hanning/RP=[StartPt,EndPt]/DEST=Signal FFTSignal
Break
Case ”Hamming”:
FFT/OUT=1/WINF=Hamming/RP=[StartPt,EndPt]/DEST=Signal FFTSignal
Break
Case ”Cosine”:
FFT/OUT=1/WINF=Cos1/RP=[StartPt,EndPt]/DEST=Signal FFTSignal
Break
EndSwitch
// Set the DC component to zero.
Signal FFT [0]=0
// NOTE: The nth point in the FFT corresponds to that many cycles
// in the original wave; i.e., filter above point 10 if you
APPENDIX B. ALGORITHM FOR ANALYZING INTERFEROMETER SCANS 188
// want to keep 10 peaks.
// FILTER to leave only freq’s below ’hiCutoff’ (cycles)
Signal FFT [hiCutoff,]=0
// FILTER to leave only freq’s above ’loCutoff’ (cycles)
Signal FFT [0,loCutoff]=0
// Now take the Inverse FFT.
IFFT/DEST=Signal FFT IFFTSignal FFT
filteredSignal=Signal FFT IFFT
filteredTime = Timex[p+startPt]
// Shift it up and add back the DC component.
filteredSignal += Save DC
// Display the result in the raw data graph.
DoWindow/F raw Graph
AppendToGraph filteredSignal vs filteredTime
ModifyGraph lSize=0.5
ModifyGraph rgb(filteredSignal)=(1,4,52428)
HideInfo
Appendix C
Quantifying alignment of Carbon
Nanotubes
C.1 Orientation Analysis of nanotubes in MWNT forests
To quantify alignment of the CNTs a Fast Fourier Transform (FFT) based image analysis technique
was developed. High magnification SEM images were taken of the cross section of the vertical
nanotube forests. All SEM images were of the same magnification and size to avoid introducing
artifacts.. To prevent edge effects in the FFT data, the edges were blurred using a Gaussian low-pass
filter. The FFT was then performed on the edge-blurred images. The intensities of this transformed
image are used to quantify alignment using the Hermans orientation factor, f . The Matlab R2008a
image analysis code is given below.
% call the images
im=imread(’hipco.TIF’);
% select part of the image for the FFT s=size(im);
im=imcrop(im,[100,100,s(2)-200,s(1)-200]);
figure,imshow(im);
% blurr the edges using a Gaussian filter
PSF = fspecial(’gaussian’,60,10);
edgeblurred = edgetaper(im, PSF);
figure,imshow(edgeblurred,[]);
% do a FFT on the edge blurred image, and shift the zero-frequency component of the FFT image
to the center of the spectrum
F = fftshift(fft2(edgeblurred));
F1 = log(abs(F));
189
APPENDIX C. QUANTIFYING ALIGNMENT OF CARBON NANOTUBES 190
figure, imshow(F1,[0,10]);colormap(jet);colorbar
% determine the absolute intensity corresponding to a point on the transformed image and also
calculate the angle made by a straight line joining the point to the center of the FFT.
i = 1;
for x = 225:446
for y = 1:161
angle(i)= atan(abs((y-162)/(x-224)));
I(i) = abs(F(y,x));
i = i+1;
end
end
Inum =0;
Iden =0;
% determine the Herman’s parameter f from the intensity and the azimuthal angle so obtained
for i = 1:length(I)
Inum = Inum + I(i) ∗ (cos(angle(i))2) ∗ sin(angle(i));
Iden = Iden + I(i)*sin(angle(i));
end
avgcos2phi = Inum/Iden;
f = 0.5 ∗ (3 ∗ avgcos2phi− 1);
C.2 Orientation Analysis of isolated MWNTs
To quantify alignment of isolated MWNTs an edge tracking method was developed based on the
approach of Kovesi et al. (132). Please go to his website to download the relevant part of the code
corresponding to different embedded functions used below. The first step is to detect the edges of
the CNTs. This is done by looking for local maxima in the gradient of intensities of the SEM images
of the isolated nanotubes. The co-ordinates of the maxima positions are listed and linked together
to obtain the nanotube edges. Straight segments are then fitted to each edge after defining minimum
length specifications. Next, the angles made by the straight edges with respect to the substrate are
obtained.
% call the image and select section of the image on which orientation analysis has to be performed
im=imread(’deep.jpg’);
im=rgb2gray(im);
imshow(im); axis on;
s=size(im);
im=imcrop(im,[25,25,s(2)-50,s(1)-50]);
APPENDIX C. QUANTIFYING ALIGNMENT OF CARBON NANOTUBES 191
% detect edges of the MWNTs
edgeim=edge(im,’canny’,[0.01 0.3],1);
imshow(edgeim);
% link the edge points detected from the images into lists; connect the points to draw just the
edges of the MWNTs
[edgelist, labelededgeim] = edgelink(edgeim,10);
drawedgelist(edgelist, size(im), 1, ’rand’, 2); axis on;
figure;
imshow(im);
hold on;
% form edge line segments from the edge list; draw the straight line segments and superimpose
them on the image showing the MWNT edges.
tol=2;
seglist = lineseg(edgelist, tol);
drawedgelist(seglist, size(im), 2, ’rand’,3); axis on;
hold on;
for r=1:length(seglist)
plot(seglist(r)(:,2),seglist(r)(:,1),’sr’)
end
% determine and plot the angles made by the straight line segments with the substrate
k=0;
for i=1:length(seglist)
for j=1:length(seglist(i))-1
k=k+1;
angle(k) = atan((seglist(i)(j, 1)− seglist(i)(j + 1, 1))/(seglist(i)(j, 2)− seglist(i)(j + 1, 2)));
if angle(k) < 0
angle(k) = angle(k) + π;
end
dist(k) = sqrt((seglist(i)(j, 1)− seglist(i)(j + 1, 1))2 + (seglist(i)(j, 2)− seglist(i)(j + 1, 2))2);
end
k=k+1;
angle(k) = atan((seglist(i)(length(seglist(i)), 1)− seglist(i)(1, 1))/(seglist(i)(length(seglist(i)), 2)−seglist(i)(1, 2)));
if angle(k) < 0
angle(k) = angle(k) + π;
end
APPENDIX C. QUANTIFYING ALIGNMENT OF CARBON NANOTUBES 192
dist(k) = sqrt((seglist(i)(length(seglist(i)), 1)− seglist(i)(1, 1))2 + (seglist(i)(length(seglist(i)), 2)−seglist(i)(1, 2))2);
end
figure;
s=0;
for p=1:length(angle)
for q=1:round(dist(p))
s=s+1;
a(s)=angle(p);
end
end
hist(a,90);
[N,X]=hist(a,90);
filledPixles=sum(N);
xlim([0 pi])
set(gca,’XTick’,0:pi/4:pi)
set(gca,’XTickLabel’,’0’,’pi/4’,’pi/2’,’3pi/4’,’pi’)
h = findobj(gca,’Type’,’patch’);
set(h,’FaceColor’,[.6 .6 .6],’EdgeColor’,’w’)
plotsizey=ylim;
textsetpoint1=plotsizey(2)*2/3;
textsetpoint2=plotsizey(2)*1.8/3;
title(’Distribution of Angles’)
xlabel(’Angles (radians)’)
ylabel(’Number of pixles contributing to specified angle’)
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