The Pennsylvania State University. The Graduate School. Department of Physics. A Thesis in. Physics. Hugo E. Romero Hugo E.

Transcription

1 The Pennsylvania State University The Graduate School Department of Physics EFFECTS OF GAS INTERACTIONS ON THE TRANSPORT PROPERTIES OF SINGLE-WALLED CARBON NANOTUBES A Thesis in Physics by Hugo E. Romero 24 Hugo E. Romero Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy May 24

2 The thesis of Hugo E. Romero has been reviewed and approved* by the following: Peter C. Eklund Professor of Physics and Professor of Materials Science and Engineering Thesis Adviser Chair of Committee Gerald D. Mahan Distinguished Professor of Physics Vincent H. Crespi Downsbrough Professor of Physics and Professor of Materials Science and Engineering James H. Adair Professor of Materials Science and Engineering Jayanth R. Banavar Professor of Physics Head of the Department of Physics * Signatures are on file in the Graduate School

3 ABSTRACT The work presented in this thesis discusses a series of in situ transport properties measurements (thermoelectric power S and electrical resistance R) on networks of randomly oriented single-walled carbon nanotube (SWNT) bundles (e.g., thin films, mats, and buckypapers), in contact with various gases and chemical vapors. Results are presented on the effects of gases that chemisorb and undergo weak charge transfer reactions with the carbon nanotubes (e.g., O 2 and NH 3 ), gases and chemical vapors that physisorb on the tube wall (e.g., H 2, alcohols, water and cyclic hydrocarbons), and gases and small molecules that undergo collisions with the carbon nanotube walls (e.g., inert gases, N 2, CH 4 ). The strong, systematic effects on the transport properties of SWNTs due to exposure to six-membered ring and polar molecules (alcohol and water) are found to increase with the quantity E a /A, where E a is the adsorption energy and A is the molecular projection area. The magnitudes of the remarkable effects of collisions of inert gases (He, Ne, Ar, Kr, and Xe) and small molecules (N 2 and CH 4 ) on the transport properties of SWNTs are found to be proportional to ~ M 1/3, where M is the mass of the colliding species. This is approximately the same mass dependence exhibited by the maximum deformation of the tube wall and the energy exchanged between the tube wall and the colliding atoms as a result of this collision. A model is proposed to explain the unusual behavior of the thermoelectric power in SWNTs, wherein the metallic tubes provide the dominant contribution to this physical quantity and the observed peak at ~ 1 K is attributed to the phonon drag effect. In addition, the details of our transport model for the behavior of the carbon nanotubes in the presence of gases and chemical vapors are presented, incorporating the effects of a new scattering channel for the iii

4 charge carriers, associated with the adsorbed (or colliding) atoms and molecules. The model is found to explain qualitatively the various transport phenomena observed. iv

5 TABLE OF CONTENTS LIST OF TABLES... VIII LIST OF FIGURES... IX CHAPTER 1. INTRODUCTION Structure of Carbon Nanotubes Electronic Structure of Nanotubes Motivations for this Work CHAPTER 2. EXPERIMENTAL TECHNIQUES Sample Preparation The Arc-Discharge Method Thermoelectric Power Measurements The Analog Subtraction Circuit The Thermopower Probe Experimental Setup The Thermopower Program Calibration of the Thermocouples Four-Probe Resistance Measurements Gas/Chemical Adsorption Measurements CHAPTER 3. THERMOELECTRIC POWER OF SINGLE-WALLED CARBON NANOTUBES Seebeck Effect: Theory Thermoelectric Power of Carbon Nanotubes: Background v

6 Parallel Heterogeneous Model of Metallic and Semiconducting Pathways Variable-Range Hopping Electron-Phonon Enhancement Fluctuation-Assisted Tunneling Kondo Effect Thermoelectric Power of Oxidized SWNT Networks Thermoelectric Power of SWNT Films Role of Contact Barriers on the Transport Properties of SWNTs Effect of Oxygen Doping on the Thermoelectric Power of SWNTs Compensating Doping and Defect Chemistry Model Calculations of the Thermoelectric Power of SWNTs Thermopower from Enhanced D(E F ) due to Impurities CHAPTER 4. PHONON DRAG THERMOELECTRIC POWER OF SINGLE-WALLED CARBON NANOTUBES Introduction Phonon Drag Model Phonon Lifetimes Baylin Formalism Applied to Metallic Carbon Nanotubes CHAPTER 5. CARBON NANOTUBES: A THERMOELECTRIC NANO-NOSE Introduction Effects of Gas Adsorption on the Electrical Transport Properties of SWNTs Thermoelectric Power from Multiple Scattering Processes vi

7 CHAPTER 6. EFFECTS OF MOLECULAR PHYSISORPTION ON THE TRANSPORT PROPERTIES OF CARBON NANOTUBES Introduction Effects of Adsorption of Six-Membered Ring Molecules Effects of Adsorption of Polar Molecules CHAPTER 7. EFFECTS OF GAS COLLISIONS ON THE TRANSPORT PROPERTIES OF CARBON NANOTUBES Introduction Collision-Induced Electrical Transport of Carbon Nanotubes Molecular Dynamics Simulations CHAPTER 8. CONCLUSIONS AND FUTURE WORK APPENDIX A: DERIVATION OF THE MOTT RELATION APPENDIX B: DERIVATION OF THE PHONON DRAG THERMOPOWER BIBLIOGRAPHY vii

8 List of Tables Table 4 1. Best fit parameter values achieved with Eq. (4.12) Table 6 1. Comparison of the T = 4 ºC thermoelectric power and resistive responses of a SWNT thin film to adsorbed C 6 H 2n molecules. The vapor pressure at 24 ºC and the adsorption energy E a of the corresponding molecule (measured on graphitic surfaces) are also listed. S and R refer to the degassed film before exposure to C 6 H 2n molecules Table 6 2. Comparison of the T = 4 ºC thermoelectric power and resistive responses of a SWNT thin film to adsorbed water and C n H 2n+1 OH; n = 1-4. The vapor pressure p at 24 ºC, the molecular area A, the static dipole moment µ, and the adsorption energy E a of the corresponding molecule (measured on graphitc surfaces) are also listed. S and R refer to the degassed film before exposure to water and alcohols. An increase in vapor pressure did not change the values of S max or R max ; see text Table 6 3. Adsorption time constants for thermoelectric ( τ S ) and resistive ( τ R ) response of a SWNT thin film to adsorbed water and alcohol molecules viii

9 List of Figures Figure 1.1. Stable forms of carbon clusters: (a) a piece of graphene sheet, (b) the fullerene C 6, and (c) a model for a carbon nanotube (Adapted from Dresselhaus 11 )... 2 Figure 1.2. (a) The unrolled honeycomb lattice of a nanotube. When the lattice sites O and A, and sites B and B are connected, an (n,m) = (4,2) nanotube can be constructed. 5 (b) STM image of a SWNT exposed at the surface of a rope. A portion of a 2D graphene sheet is overlaid to highlight the atomic structure Figure 1.3. (a) Computer-generated images of (1,1) armchair, (1,) zigzag, and chiral type SWNTs. The numbers in parenthesis are the chiral indices. (b) A 2D graphene sheet showing the schematic of the indexing used for SWNTs. The large dots denote metallic tubes while the small dots are for semiconducting tubes Figure 1.4. X-ray diffraction patterns at low angle of a SWNT sample obtained by (a) the arc-discharge technique by Journet et al. 43 and (b) the laser ablation technique by Thess et al. 42 The graphite peak, due to remaining graphitic particles, has been removed for clarity; its position is shown by an asterisk. The inset shows a single SWNT rope made up of ~1 SWNTs as it bends through the image plane of the microscope, showing uniform diameter and triangular packing of the tubes within the rope ix

10 Figure 1.5. Graphene π band structure in the first Brillouin zone, constructed using Eq. (1.4). The conduction and valence bands touch at the six Fermi points K indicated at E = Figure 1.6. Examples of the allowed 1D subbands for (a) a (5,5) armchair, (b) a (5,) zigzag, and (c) a (7,1) chiral carbon nanotube. The hexagon defines the first Brillouin zone of graphene and the dots in the corners are the graphene K points... 1 Figure 1.7. One-dimensional energy dispersion relations for (a) armchair (1,1) tubes, (b) zigzag (1,) tubes, and (c) chiral (6,4) tubes, computed using the zonefolded tight-binding dispersion relations described in the text Figure 1.8. Electronic 1D density of states per unit cell for a series of metallic tubes, showing discrete peaks at the positions of the 1D band maxima or minima (Adapted from Dresselhaus 55 ) Figure 2.1. Room-temperature Raman spectrum for unpurified arc-derived SWNTs excited at nm Figure 2.2. Right: SEM image of a SWNT film showing entangled ropes synthesized by the arc-discharge method. Left: High-resolution TEM image of an end view of the SWNT bundles, showing the 2D hexagonal lattice arrangement of the tubes Figure 2.3. TEM images of SWNT bundles before (right) and after (left) purification. Dark spots are catalyst clusters Figure 2.4. Block diagram of the analog subtraction circuit to measure the thermoelectric power x

11 Figure 2.5. Schematic diagram of the thermopower and resistance measurements probe suitable for the temperature range 4-5 K Figure 2.6. Schematic diagram of the sample holder for the thermoelectric power and four-probe resistance measurements Figure 2.7. Block diagram of the system for thermoelectric power and four-probe resistance measurements instrumentation Figure 2.8. The program Thermopower Auto.vi, showing the time evolution of the thermoelectric power of a SWNT film during vacuum-degassing at 5 K. 28 Figure 2.9. The program Thermopower Manual.vi, showing the temperature dependence of the thermoelectric power of constantan... 3 Figure 2.1. Schematic diagram of the connections to A 2 amplifier to measure the sample temperature (top) and the equivalent circuit (bottom) Figure The output voltage of amplifier A 2 as a function of the sample temperature (left) and the temperature dependence of the relative thermoelectric power of a chromel-au:fe thermocouple pair (right) Figure Temperature dependence of the thermoelectric power of chromel and gold:iron alloy with respect to copper. The solid lines represent polynomial fits to the data Figure The program DC 4-Probe Resistance.vi showing the resistance as a function of temperature for a SWNT mat Figure Schematic diagram of the gas handling system for gas/chemical adsorption experiments xi

12 Figure 3.1. (a) Basic thermoelectric open circuit that displays the Seebeck effect. (b) The Seebeck effect: A temperature gradient along a conductor gives rise to a potential difference Figure 3.2. Temperature dependence of the thermoelectric power for an air-saturated SWNT mat. The solid line is a guide to the eye. The dashed lines (a) and (b) represent the ways in which metallic behavior could be incorporated in the thermoelectric behavior of SWNTs Figure 3.3. Illustration of the combination of thermoelectric powers for conductors in parallel (also applicable to the two-band model) Figure 3.4. Fits to measured thermoelectric power of a SWNT mat using a parallel heterogeneous model of semiconducting and metallic tubes. The solid line represents a fit to the data using Eq.(3.13). Fitting parameters extracted from our fit are also shown in the figure Figure 3.5. Fits to measured thermoelectric power of a SWNT mat using a parallel heterogeneous model of disordered semiconducting and metallic tubes. The solid line represents a fit to the data using Eq. (3.16). Fitting parameters extracted from the fit are also shown in the figure Figure 3.6. The temperature dependence of the thermoelectric power for an as-prepared SWNT mat in its air-saturated and degassed states. The solid lines are guides to the eye Figure 3.7. Sketch of crystalline SWNT ropes, where fibrillar carbon nanotubes are separated by disordered regions (Adapted from Kaiser et al. 17 ) xii

13 Figure 3.8. Uniaxial pressure dependence of (a) the normalized room temperature resistance R/R and (b) the thermopower S for two different as-prepared SWNT mats. The inset shows the experimental geometry where the applied force F is perpendicular to the sample Figure 3.9. Thermopower response to vacuum and O 2 (1 atm) at T = 5 K. (A C): Vacuum-degassing of a sample initially O 2 -doped under ambient conditions for several days. (C D): Exposure of the degassed sample to 1 atm of O 2 established at C Figure 3.1. Temperature dependence of the thermopower S for a SWNT thin film after successively longer periods of O 2 degassing at T = 5 K in vacuum. The labels A, B, and C refer to a vacuum-degassing interval indicated in Figure 3.9. Curve D is for the same sample exposed to 1 atm O 2 at T = 5 K for about 4 h after being fully degassed to point C Figure Calculated thermoelectric power of a (1,1) carbon nanotube as a function of the Fermi level position Figure 4.1. Sketch of the thermoelectric power of a simple quasi-free electron pure metal as a function of temperature. A: Electron diffusion component of thermoelectric power approximately proportional to T. B: Phonon drag component with magnitude increasing as T 3 at very low temperatures (T << T D ), and decaying as 1/T at high temperatures (T > T D ) (Adapted from MacDonald 69 ) Figure 4.2. Temperature dependence of the thermoelectric power for a purified SWNT thin film after successively longer periods of O 2 degassing at 5 K in xiii

14 vacuum. Curve 1 corresponds to the same sample exposed to 1 atm O 2 at 5 K for about 4 h, after being fully degassed (curve 4). The solid lines in the figure represent the fits to the data using Eq. (4.12) Figure 4.3. Temperature dependence of the thermoelectric power for SWNT mats prepared using different catalysts. The samples were not purified and contained ~ 5 at% residual catalyst. The data were measured by Grigorian et al. 76 The solid lines represent the best fits to the data using Eq. (4.12) Figure 4.4. Fits to the measured thermoelectric power data (curve 1 in Figure 4.2) using a model involving diffusion and phonon drag contributions to the thermoelectric power. The solid curve represents a fit to the data using Eq. (4.12). The dashed lines represent the contributions from S d [Eq. (3.3)] and S g [Eq. (4.1)] Figure 5.1. Schematic structure of a SWNT bundle showing the sites available for gas adsorption. The dashed line indicates the nuclear skeleton of the nanotubes. Binding energies E B and specific surface area contributions σ for hydrogen adsorption on these sites are indicated Figure 5.2. The time dependence of the thermoelectric power response of a SWNT mat to 1 atm overpressure of He gas (filled circles), and to the subsequent application of a vacuum over the sample (open circles). The dashed lines are exponential fits of the data (see text) Figure 5.3. In situ thermoelectric power versus time after exposure of a vacuum-degassed SWNT mat to 1 atm overpressure of H 2 at T = 5 K (solid symbols). The response of the H 2 -loaded SWNT sample to a vacuum is also represented xiv

15 (open symbols). The dashed lines are fits to the data using exponential functions (see text) Figure 5.4. In situ thermoelectric power as a function of time after exposure of degassed SWNT mats to a 1 atm overpressure of H 2 at T = 5 K (solid symbols). The open symbols are the response of the H 2 loaded SWNT system to a vacuum. Data are shown for three samples: not purified (bottom), HCl reflux for 4 h (middle), HCl reflux for 24 h (top). The dashed lines are guides to the eye. The catalyst residue in at% is indicated Figure 5.5. Nordheim-Gorter plots showing the effect of gas adsorption on the electrical transport properties of a SWNT mat. The amount of gas stored in the bundles increases to the right, tracking the increase in ρ. For the H 2 data, the open circles are from the time dependent response to 1 atm of H 2 at T = 5 K and the closed circles are from a pressure study at the same temperature. The inset shows the Nordheim-Gorter plots for O 2 (electron acceptor) and NH 3 (electron donor). Note that the data in the inset, as opposed to that in the main plot, is non-linear. The non-linearity is consistent with charge transfer and Fermi energy shifts Figure 6.1. In situ (a) thermoelectric power and (b) resistance responses at 4 ºC as a function of time during successive exposure of a degassed SWNT thin film to vapors of six-membered ring molecules C 6 H 2n ; n = 3-6. The dashed lines are guides to the eye. The vapor pressure was ~ 12 kpa Figure 6.2. Maximum change of the thermoelectric power of a SWNT film as a function of the adsorption energy of the adsorbed molecule. The dashed line is a guide xv

16 to the eye Figure 6.3. S vs. R/R plots during exposure to C 6 H 2n (n = 3-6). The dashed curve is a fit to the data using a quadratic function... 1 Figure 6.4. Temperature dependence of the thermoelectric power of the degassed SWNT after saturation coverage of the various C 6 H 2n molecules. The dashed lines are guides to the eye Figure 6.5. Time dependence of the (a) thermoelectric power and (b) normalized fourprobe resistance responses to vapors of water and alcohol molecules (C n H 2n+1 OH; n = 1-4) at 4 ºC. The dashed lines are fit to S(t) and R(t) data using an exponential function. The inset shows a simple schematic of the measurement apparatus. The liquid temperature T 2 establishes the vapor pressure in the sample chamber which is at a temperature T 1 > T 2. The system is evacuated through V 2. After degassing, V 2 is closed and V 1 is opened. The responses of S and R are then measured simultaneously Figure 6.6. S vs. R/R plots during exposure of degassed SWNT bundles to water and C n H 2n+1 OH (n = 1-4). The solid lines are linear fits to the data until saturation is established Figure 6.7. Maximum thermoelectric power change S max of a SWNT thin film successively exposed to vapors of water and alcohol molecules (C n H 2n+1 OH; n = 1-4) as a function of the quantity β E a A, where E a and A are, respectively, the molecular adsorption energy and the projection area. The solid and dashed lines are guides to the eye xvi

17 Figure 7.1. Time dependence of the thermoelectric power response of (a) PLV buckypaper and (b) arc-derived thin film exposed to 1 atm of inert gas (closed symbols), and to subsequent application of vacuum over the sample (open symbols) at T = 5 K. The different values of S in (a) and (b) reflect differences in defect densities in the PLV and the arc-derived material (see Chapter 5) Figure 7.2. S vs. R/R plots showing the effect of inert gases on the transport properties of a SWNT buckypaper prepared from PLV material. The closed symbols are from the time evolution of S and R to 1 atm of gas at T = 5 K and the open symbols are from a pressure study at the same temperature, where the maximum response of S and R to a given pressure was measured. The inset shows the pressure dependence of the maximum change of thermopower for the same sample Figure 7.3. Computed power spectra of the radial motion of a C-atom nearest the point of contact in a (1,) carbon nanotube at K. The figure shows the phonons induced during (a) the first 5 ps of the collision (and includes the gas-tube impact) and (b) the second 5 ps after the collision. The inset to (a) shows the side view of a collision between a Xe atom (θ i = º, E i = 13 kcal/mol) and a nanotube. The inset to (b) shows the schematic representation of the tube wall deformation in response to an atom collision Figure 7.4. Maximum thermoelectric power change S max of two SWNT samples exposed to gases indicated (ARC: open circles and PLV: closed circles; data from Figure 7.1), calculated total energy gained by a (1,) nanotube upon xvii

18 collision with a gas atom (θ i = º, E i = 3.97 kcal/mol, squares), and maximum radial displacement D max of the tube C-atom immediately after impact with a gas atom (θ i = 45º, E i = 1.99 kcal/mol, triangles) as a function of the mass of the colliding inert gas. The lines are power law fits to the data of the forms.35 S max = 3. 8M, E =.91M.39, and.35 D max =. 4M Figure 7.5. Dipole polarizability α as a function of the mass of the inert atom or small molecule xviii

19 DEDICATION To my beloved parents, Guillermo and Sergia, who taught me the values I treasure, who gave me the freedom of choice. For their dedication and commitment to furnish their children with the best possible future. Without their sacrifice none of this would be possible. To my brothers and sisters, Zulay, Alba, Guillermo, John, Ana, Zulma, and Celeste, my best friends. I have been blessed with the good fortune and privilege of having such wonderful people in my life. To my wife, Francelys, for her love and support, for her tolerance and patience, for the joy and happiness she has brought to my life. Gracias. Los amos a todos. xix

20 Chapter 1. Introduction Carbon nanotubes have aroused worldwide excitement since their discovery by Sumio Iijima in In retrospect, it is quite likely that such fascinating materials were produced as early as the 197s during research on carbon fibers by Morinobu Endo. 2 The discovery of carbon nanotubes was stimulated, in part, by the discovery in 1985 of fullerene C 6 by groups led by Harold Kroto at Sussex University and Richard Smalley at Rice University. C 6 is a nearly spherical molecule made of 6 identical carbon atoms bonded in hexagonal and pentagonal rings [Figure 1.1(b)]. The pentagonal rings are necessary to close the structure. Exactly 12 pentagonal rings are needed, as can be proven using Euler s polyhedron theorem. 3 Carbon nanotubes, on the other hand [Figure 1.1(c)], do not require any pentagonal ring in the curved cylindrical surface. The ends of the nanotube can be closed by a hemispherical fullerene molecule. By Euler s theorem, each end cap has exactly 6 pentagonal rings. It is clear that a nanotube can be considered to be a graphene sheet [Figure 1.1(a)] rolled into a seamless cylinder. However, it is not clear that this can be done in so many ways to produce a variety of chiral tubular structures. Carbon nanotubes may be one of the key materials for nanoscale technology. It is hoped that nanotube electronics may lead to progress in miniaturization of computing and power devices. Small-diameter carbon nanotubes are attractive materials for nanoelectronics because they provide a remarkable one-dimensional (1D) system, i.e., their electronic and phonon states are described by a wave vector along the tube axis. They do not have a Fermi surface but exhibit only two Fermi wave vectors ± k F. Because of the nearly 1D electronic structure, electronic transport in carbon nanotubes can occur ballistically (i.e., without scattering) at low temperatures -1-

21 and over long nanotube lengths, enabling them to carry high currents with essentially no heat dissipation. 4-7 Phonons also propagate easily along nanotubes; the measured room temperature thermal conductivity of an individual nanotube (> 3 W/m K) is greater than that of natural diamond and the basal plane of graphite (both 2 W/m K). 8 Whether one considers phonon or electron scattering, the interesting point is the limited number of final states into which these excitations can scatter. This is the benefit from a crystalline 1D material. Small-diameter nanotubes are also quite stiff in tension and exceptionally strong with Young s modulus of 1.28 TPa and high tensile strength of 28.5 GPa, exceeding those of steel and SiC. 9,1 Figure 1.1. Stable forms of carbon clusters: (a) a piece of graphene sheet, (b) the fullerene C 6, and (c) a model for a carbon nanotube (Adapted from Dresselhaus 11 ). Among the potential applications 12,13 proposed for carbon nanotubes are conductive and high-strength composites, 14,15 energy storage and energy conversion devices, 16,17 chemical 18 and -2-

22 gas 19 sensors, electron field emission displays 2-22 and radiation sources, hydrogen storage media, nanoprobes for AFM and STM tips, electronic interconnects 35,36 and semiconductor devices (e.g., field effect transistors, 37,38 logic gates, 39 etc.) Iijima actually observed multi-walled carbon nanotubes (MWNTs) in his electron microscope images. They showed tubular filaments consisting of multiple concentric shells. Approximately two years after the discovery of MWNTs, single-walled nanotubes (SWNTs) consisting of only one shell of carbon atoms were discovered independently by groups led by Iijima at the NEC Fundamental Research Laboratory 4 and Bethune at IBM s Almaden Research Center in California. 41 Later work by Richard Smalley and his co-workers at Rice University enabled the bulk production (i.e., 1s of mg) of ~ 1 nm diameter SWNTs. 42 The bulk production, increased by the arc-discharge approach, 43 has led to a vast array of experiments on these materials to explore their unique and remarkable physical properties, which span a wide range from structural to electronic. Here, we will concentrate on the electrical transport properties of bundles of SWNTs. The literature contains some good reviews on this subject Structure of Carbon Nanotubes Carbon nanotubes can be described as cylindrical molecules. They have been produced in the laboratory with diameters as small as ~.4 nm 47,48 and lengths up to several millimeters. 49 They consist only of carbon atoms and can essentially be thought as a single atomic layer of graphite (graphene) that has been wrapped into a seamless hollow cylinder; the ends of which can be open or capped with half a fullerene molecule. 3,5 A graphene sheet, depicted in Figure 1.2(a), is an sp 2 bonded network of carbon atoms arranged in a hexagonal lattice with two atoms -3-

23 per unit cell. The experimental verification of the honeycomb structure of a carbon nanotube became possible via the scanning tunneling microscope (STM) images. A typical atomically resolved image of the tube s hexagonal lattice is shown in Figure 1.2(b). y (a) (b) B B x θ A O C h a 1 a 2 Figure 1.2. (a) The unrolled honeycomb lattice of a nanotube. When the lattice sites O and A, and sites B and B are connected, an (n,m) = (4,2) nanotube can be constructed. 5 (b) STM image of a SWNT exposed at the surface of a rope. A portion of a 2D graphene sheet is overlaid to highlight the atomic structure. 51 The nanotube is uniquely characterized by the so-called chiral vector C h, defined by C na 1 + ma ( n,m), (1.1) h = 2 where a 1 and a 2 are the unit vectors in the two-dimensional (2D) hexagonal lattice, while n and m are integers. As shown in Figure 1.2(a), the vector C h connects two crystallographically equivalent sites O and A on a 2D graphene sheet, where a carbon atom is located at each vertex of the hexagonal structure. The chiral angle θ is defined as the angle between the vectors C h and a

24 (a) d = Å d = 7.94 Å d = 6.83 Å (1,1) (1,) (6,4) (b) (,) (1,) (2,) (3,) (4,) (5,) (6,) (7,) (8,) (9,) (1,) (11,) zigzag (1,1) (2,1) (3,1) (4,1) (5,1) (6,1) (7,1) (8,1) (9,1) (1,1) (2,2) (3,2) (4,2) (5,2) (6,2) (7,2) (8,2) (9,2) (1,2) a 1 (3,3) (4,3) (5,3) (6,3) (7,3) (8,3) (9,3) (4,4) (5,4) (6,4) (7,4) (8,4) (9,4) a 2 (5,5) (6,5) (7,5) (8,5) (6,6) (7,6) (8,6) armchair Figure 1.3. (a) Computer-generated images of (1,1) armchair, (1,) zigzag, and chiral type SWNTs. The numbers in parenthesis are the chiral indices. (b) A 2D graphene sheet showing the schematic of the indexing used for SWNTs. The large dots denote metallic tubes while the small dots are for semiconducting tubes. 5 When the graphene sheet is rolled up to form the cylindrical part of the nanotube, the ends OA of the chiral vector meet each other and the cylinder joint is made by joining the line AB to the parallel line OB in Figure 1.2(a). The chiral vector thus forms the circumference of the nanotube s circular cross-section. In terms of the integers (n,m), the nanotube diameter d is given -5-

25 by the relation d 3 2 h 2 = C = ac-c m + mn + n, (1.2) π π where a C-C is the nearest-neighbor carbon-carbon distance (1.421 Å in graphite). SWNT diameters are typically found in the range ~.4 nm < d < 3 nm. For example [Eq. (1.2)], the diameter of a (1,1) armchair nanotube, shown in Figure 1.3(a), is ~ Å. In MWNTs, the outer tube can be as large as 3-5 nm. Every pair of integers (n,m) leads to different nanotube structures [Figure 1.3(a)]: armchair (n,n), zigzag (n,) and chiral (n,m) nanotubes. Many of the possible vectors specified by the pairs of integers (n,m) are shown in Figure 1.3(b), which define different ways of rolling the graphene sheet to form the carbon nanotube with a specific chirality. Because of the point group symmetry of the honeycomb lattice, several different integers (n,m) will give rise to equivalent nanotubes. To define each nanotube once, and only once, it is only necessary to consider the nanotubes arising in the 3º wedge of the 2D Bravais lattice shown in Figure 1.3(b). The physical properties of nanotubes are determined by their diameter and chiral angle, both of which depend on n and m. Typically, SWNT samples have a distribution of diameters and chiral angles. One interesting characteristic of the growth of the carbon nanotubes is the tendency for large numbers of nanotubes to grow nearly parallel to each other, forming crystalline-like bundles or ropes of nanotubes of about 1-5 nm in diameter. These bundles contain from tens to hundreds of carbon nanotubes of nearly uniform diameter, self-organized in a close-packed triangular lattice with a typical lattice constant a = 17 Å through van der Waals inter-tube bonding. Thus, a raw macroscopic SWNT sample consists of a collection of bundles of different size, with their axes isotropically distributed over all possible orientations. -6-

26 Figure 1.4. X-ray diffraction patterns at low angle of a SWNT sample obtained by (a) the arc-discharge technique by Journet et al. 43 and (b) the laser ablation technique by Thess et al. 42 The graphite peak, due to remaining graphitic particles, has been removed for clarity; its position is shown by an asterisk. The inset shows a single SWNT rope made up of ~1 SWNTs as it bends through the image plane of the microscope, showing uniform diameter and triangular packing of the tubes within the rope. 42 Figure 1.4 shows the X-ray diffraction patterns for SWNT samples obtained by the arcdischarge 43 and the laser ablation techniques. 42 In an electron microscope, the nanotube material produced by either of these methods looks like a mat of ropes or bundles of SWNTs. The ropes are between 1 and 2 nm across and up to 1 µm long. 42 The strong discrete peak near Q =.44 Å -1, as well as the four weaker peaks up to Q = 1.8 Å -1 in Figure 1.4, indicates the existence of a 2D triangular lattice of SWNTs organized in bundles. 42 The X-ray diffraction also shows that the diameters of SWNTs in the bundles have a narrow distribution with a strong peak. -7-

27 1.2. Electronic Structure of Nanotubes The remarkable variety of electrical properties of SWNTs stems from the unusual electronic structure of graphene the 2D material from which they are made. Calculations for the electronic structure of SWNTs show that carbon nanotubes can be either metallic or semiconducting, depending on the choice of (n,m). It can be shown that metallic conduction in a (n,m) carbon nanotube is achieved when n m = 3q, (1.3) where q is an integer. Equation (1.3) shows that all armchair carbon nanotubes are metallic but only one third of the possible zigzag and chiral nanotubes are metallic. Therefore, from Figure 1.3(b), about 1/3 of nanotubes are metallic and 2/3 are semiconducting. In the simplest possible model, the band structure of nanotubes can be derived directly from the 2D band structure of graphene, whose π bands are constructed from the overlapping p z orbitals of adjacent carbon atoms. The simplest analytical form of the 2D dispersion relation for the π bands of a single graphene sheet can be expressed in the nearest-neighbor tight-binding approximation: 52 3k k a 2 k a 2 (, ) 1 4cos xa y y E = ±γ + cos + 4cos, g D k x k y (1.4) where a = Å is the lattice constant for a 2D graphene sheet and γ is the nearestneighbor carbon-carbon overlap integral. Currently, the value γ ~ 2.9 ev is used to fit optical data. 53 We have used the tight-binding scheme [Eq. (1.4)] to compute the π bands of graphene in the first Brillouin zone and the results are shown in Figure 1.5. The π * antibonding band and the π bonding band, respectively, form the conduction and the valence bands of graphene. Since

28 there are two atoms per unit cell in a graphene sheet, the valence band is completely filled. Only the π electrons contribute to the graphene electrical conduction. Note that the conduction and the valence bands touch at the six corners (K points) of the hexagonal Brillouin zone, where the Fermi energy E F =. Figure 1.5. Graphene π band structure in the first Brillouin zone, constructed using Eq. (1.4). The conduction and valence bands touch at the six Fermi points K indicated at E =. Using Eq. (1.4), 1D dispersion relations for carbon nanotube (n,m) can be calculated based on a simple zone folding consideration, i.e., by imposing a periodic boundary condition around the waist of a SWNT. The allowed wave vectors k in the direction parallel to the chiral vector, resulting from radial confinement, follow from C k = 2πq, (1.5) h where q is an integer. The 1D energy dispersion curves of a nanotube correspond to the crosssection of the 2D energy dispersion surface shown in Figure 1.5, where the cuts are made on -9-

29 parallel lines corresponding to the particular set of allowed states. 3 In Figure 1.6 several cutting lines, representing the allowed subbands of a nanotube, are shown. On the basis of this simple scheme, if one of the allowed wave vectors passes through a Fermi point of the graphene sheet, the SWNT should be metallic with a nonzero density of states at the Fermi level [Figure 1.6(a)]. When the K point of the 2D Brillouin zone [Figure 1.6(b)] is located between two cutting lines, the K point is always located in a position one-third of the distance between two adjacent lines and thus a semiconducting nanotube with a finite energy gap appears. It is important to note that the states near the Fermi energy in both metallic and semiconducting tubes result from states near the K point, and hence their transport and other properties are related to the properties of the states on the allowed lines. (a) (b) (c) K K K K (5,5) (5,) (7,1) Figure 1.6. Examples of the allowed 1D subbands for (a) a (5,5) armchair, (b) a (5,) zigzag, and (c) a (7,1) chiral carbon nanotube. The hexagon defines the first Brillouin zone of graphene and the dots in the corners are the graphene K points. The resulting 1D energy dispersion relations of a (n,m) nanotube are given by, qπ ka E( n, n ) = ±γ 1 ± 4cos cos n 2 for armchair nanotubes : 2 ka + 4cos 2 ( π < ka < π), ( q = 1,..., n) 1/ 2 (1.6) -1-

30 E n (,) = ±γ qπ 1 ± 4cos cos n for zigzag nanotubes : π < ka 3 3ka qπ mka ka E( n, m ) = ±γ 1 ± 4cos cos n 2n 2 for chiral nanotubes :( π < ka < π). 2 < q 2 π + 4cos 2 π, 3 ( q = 1,..., n) + 4cos 2 ka 2 1/ 2 1/ 2 (1.7) (1.8) We have constructed the band structures for metallic nanotubes (n,m) = (1,1) and for semiconducting nanotubes (1,) and (6,4) as shown in Figure 1.7. Note that only two of the 1D 3 (a) 3 (b) 3 (c) E(k)/γ π a k π 3a k π 3a k subbands cross the Fermi energy in metallic nanotubes. Figure 1.7. One-dimensional energy dispersion relations for (a) armchair (1,1) tubes, (b) zigzag (1,) tubes, and (c) chiral (6,4) tubes, computed using the zone-folded tightbinding dispersion relations described in the text. The results for the 1D electronic density of states (DOS) show sharp peaks associated with the van Hove singularities about each subband edge (Figure 1.8). At a band edge, -11-

31 ( E' ) k k ( is the gradient with respect to k) and singularities arise in the DOS at E (the energy of the particular band maxima or minima). Resonances in Raman scattering experiments have provided evidence for such sharp peaks in the DOS of nanotubes. 54 The electronic DOS also shows that the metallic nanotubes have a small, but non-vanishing 1D density of states at the Fermi level. In contrast, the DOS for the semiconducting nanotubes is zero throughout the bandgap. (8,8) Density of States (9,9) (1,1) (11,11) Energy/γ Figure 1.8. Electronic 1D density of states per unit cell for a series of metallic tubes, showing discrete peaks at the positions of the 1D band maxima or minima (Adapted from Dresselhaus 55 ). -12-

32 1.3. Motivations for this Work Research and knowledge about carbon nanotubes have been developing at a very fast pace. Although a number of basic features in the electron transport through nanotubes were discovered, many challenges and questions remain before most of the proposed applications can be realized. For example, how molecules interact with carbon nanotubes and affect their physical properties is of fundamental interest. This knowledge may have important implications for their production and growth as well as their applications. The nanometer-scale spaces inside and among the SWNTs in a bundle should provide large gas-adsorption capacities, 56 which are especially exciting when we consider, for example, methane and hydrogen adsorption. Adsorption and storage of hydrogen on nanotubes have been studied extensively due to the potential application in the next generation of energy sources, e.g., fuel cells However, experimental reports of high storage capacities are so controversial that it is impossible to assess the potential applications. 13 Numerous claims of high hydrogen storage levels have been shown to be incorrect; other reports of room temperature capacities above 6.5 wt% (a U.S Department of Energy benchmark) await confirmation. 57 Adsorption phenomena are also of interest from a fundamental point of view because gases adsorbed on SWNTs provide an excellent model system to study the effect on conduction electrons. There is also the possibility for the development of high-sensitivity gas/chemical sensors based on carbon nanotubes. 18,19 In addition, the control of the electronic properties of nanotube devices using vapor phase chemical doping was shown to be crucial to the design and tuning of these devices. 58 Indeed, the modulation doping of a semiconducting SWNT along its length can lead to intramolecular wire electronic devices. 59 Another motivation for doping experiments has -13-

33 been the search for superconductivity in carbon nanotubes. Production and growth of carbon nanotubes often take place in inert gas environments at elevated temperatures. 58 It is also expected that the collision dynamics between the gas and the outside of the nanotube affect the growth. However, the detailed collision dynamics between the gas molecules and the nanotube, the diffusion of the adsorbed atom along the nanotube, and its incorporation in the nanotube are not well understood, nor are the effects of these impacts on the nanotube conductance. The latter is studied in this Ph.D. thesis. From a broader perspective, SWNTs provide a unique opportunity to study the interaction of molecules with a conducting surface. This stems from the unique structure of the nanotube. The electron and phonon states of this unique all-surface solid state system are, by comparison to many other solids, relatively simple, thereby allowing fundamental calculations addressing the experimental observations presented here to be carried out. In this Ph.D. research, we have sought a greater understanding of gas-swnt interactions. A series of electrical transport measurements (thermoelectric power and electrical resistance) will be discussed in the remainder of this thesis. Chapter 2 discusses the experimental methods used to study transport in SWNTs. Chapters 3 and 4 review previous treatments for the thermoelectric power of SWNTs, before presenting a new model of the thermoelectric power in these materials. In Chapter 3, only the diffusion thermopower is considered, while Chapter 4 is devoted to a formulation of the phonon drag effect problem in metallic SWNTs. Chapter 5 gives some details on the effects of adsorption of small gas molecules on the thermopower and the electrical resistance of SWNTs. Chapter 6 deals with the effects of gaseous chemicals adsorption on the transport properties of SWNTs. Chapter 7 discusses the effects of inert gas collisions on the thermoelectric power and the electrical resistance of SWNTs. -14-

34 Chapter 2. Experimental Techniques 2.1. Sample Preparation The single-walled carbon nanotubes studied in our experiments were in the form of thin films, thin pellets or mats of tangled ropes. In most cases, the SWNT material was obtained from CarboLex, Inc. and produced by the arc-discharge method using a Ni-Y catalyst. The approximate volumetric yield was estimated on the basis of Raman scattering to be ~ 5-7 vol% carbon as SWNT. The SWNT material was removed from the growth chamber and handled in ambient conditions. Figure 2.1 shows a typical Raman spectrum (514.5 nm excitation) of arc-derived SWNT bundles at room temperature. The SWNT material was always found to exhibit the characteristic Raman spectrum published previously, 54 including the radial breathing mode band at 186 cm -1 and the stronger tangential mode band at 1593 cm -1. The high-frequency bands can be decomposed into two main peaks around 1593 and 1567 cm -1 with shoulders at 155 and 1526 cm -1. These features have previously been assigned to a splitting of the E 2g mode of graphite. 6 The peaks in the frequency range 3-12 cm -1 can be mostly identified as overtones and combinations of lower-frequency modes. The low-frequency domain shows at least two components at 141 and 186 cm -1. According to earlier calculations, 54 these modes are expected to be of A 1g symmetry, and are identified with the radial breathing modes. For an isolated nanotube of any chirality (n,m), the radial breathing mode ω RBM has been -15-

35 shown theoretically to exhibit a simple inverse diameter relationship, i.e., ω 224 d for ωrbm RBM in cm -1 and d in nm, where the proportionality factor is somewhat sensitive to the details of the calculation. 61 This simple relationship for ω RBM must be corrected for weak inter-tube interactions within a bundle to obtain the measured mode frequency ω RBM. Theoretical calculations have predicted that these interactions are responsible for a 6-21 cm -1 frequency upshift, depending on the details of the calculation The expression linking the radial breathing ω RBM to the nanotube diameter d has been reported to be well approximated by the expression ω = ω + ω = ω + ω (2.1) RBM RBM RBM RBM ( 1,1) d ( 1,1) d, where ω is the radial breathing mode frequency for an isolated SWNT, ω is a frequency RBM upshift which is a constant for nanotube diameters near to that of a (1,1) armchair nanotube d (1,1) ω (1,1), and is the radial breathing mode frequency of an isolated (1,1) nanotube. The calculated values of these parameters reported by various research groups vary from one another, ω RBM ( 1,1) d(1,1) but some typical values are (, ω ) = (14 cm -1, 224 cm -1 nm), 62 (6.5 cm -1, 232 cm - 1 nm), 65 and (6 cm -1, 214 cm -1 nm). 64 RBM Using Eq. (2.1), we found that the average diameter of the tubes from the arc-derived material was therefore close to that of a (1,1) tube. The tube diameter distribution in this material was mainly confined to the range 1.2 < d < 1.6 nm, based on the Raman spectra of the radial breathing modes collected at six different excitation wavelengths. Typical high-resolution transmission electron microscopy images (see Figure 2.2) showed that the nanotubes were present in the form of bundles. The bundle diameter for arcderived material was in the range 1-15 nm, i.e., the bundles contained ~ 1-2 tubes. -16-

36 1593 Raman intensity (a.u) Frequency (cm -1 ) 16 2 Figure 2.1. Room-temperature Raman spectrum for unpurified arc-derived SWNTs excited at nm. Some of our samples were prepared from as-grown SWNT material, i.e., without any post-synthesis chemical or thermal treatment. Others were prepared from purified SWNT material. Purification of our SWNT material was done first by a selective oxidation step at 425 ºC in dry air for ~ 2 min to remove amorphous carbon and weaken the carbon shell covering the metal catalyst. This treatment was followed by an acid reflux for 24 h in 4. M HCl to remove the metal residue. The material was then vacuum-annealed at 1-7 Torr and ~ 1-12 ºC for 24 h. The final metal content after this purification process, as determined by ash analysis (combustion in dry air) in an IGA thermogravimetric analyzer (Hiden Analytical, Inc.), yielded a value of.2 at% metal. Figure 2.3 shows TEM images of SWNT bundles before and after the purification process. -17-

37 Figure 2.2. Right: SEM image of a SWNT film showing entangled ropes synthesized by the arc-discharge method. Left: High-resolution TEM image of an end view of the SWNT bundles, showing the 2D hexagonal lattice arrangement of the tubes. Figure 2.3. TEM images of SWNT bundles before (right) and after (left) purification. Dark spots are catalyst clusters. The SWNT films were prepared by placing drops of an alcohol solution containing SWNTs onto thin (.25 mm), ground and polished clear quartz substrates (Chemglass Scientific, Inc.) The alcohol solution was mildly sonicated (medium power) before the sample preparation using a microtip horn connected to a Misonix Sonicator Ultrasonic Cell Disruptor/Processor XL22. The substrates were cleaned first in a boiling bath of isopropanol, followed by a -18-

38 refluxing vapor of the same alcohol. Nanotube paper or buckypaper was produced using the conventional method, 66 i.e., by filtering SWNTs dispersed in a liquid and peeling the resulting sheet from the filter after washing and drying. Finally, the sheet was vacuum-annealed at ~ 12 ºC for 12 h to remove volatile impurities and repair tube wall damage incurred during the purification The Arc-Discharge Method Carbon nanotubes can be synthesized through various process routes. The carbon arcdischarge method, used initially for producing C 6 fullerenes, is perhaps the most common and easiest way to produce carbon nanotubes. The method became popular for the production of carbon nanotubes after a group of researchers at the University of Montpellier in France demonstrated that this technique can produce high yields of SWNTs. 43 The arc-discharge method synthesizes nanotubes through the arc-vaporization of carbon from the ends of two electrodes separated by approximately 1 mm. A direct current of 5 to 1 A driven by approximately 2 V creates a high temperature discharge between the two electrodes. The discharge vaporizes one of the carbon electrodes and forms a small rod shaped deposit on the other electrode. Both the anode and the cathode are made of graphite rods (purity ~ 99.99%), and only the anode is loaded with 2-4 at% metal for synthesizing SWNTs. Production of nanotubes takes place inside a stainless steel chamber filled with helium gas at low pressure (~ 5 Torr). The electrodes may be positioned manually, or automatically, based on the measured voltage between them. The electrodes and the chamber are cooled by a flow of low pressure water. The gas pressure is controlled via a He flow system, assisted by a mechanical vacuum -19-

39 pump. An electronic flow/pressure controller is used to regulate added gas. Large-scale production of carbon nanotubes depends on many factors including the uniformity and stability of the plasma arc, the stability of the temperature distribution, gas pressure, etc. One interesting and useful characteristic of the growth of the carbon nanotubes by the arc-discharge method is the tendency for large numbers of nanotubes to grow parallel to each other, forming bundles or ropes of nanotubes, which consist of 1-1 tubes. This is thought to be a curious multifilament outcome of vapor-liquid-solid (VLS) growth where a metal nanoparticle is thought to act like a solvent for carbon, and the nanotube is viewed as growing from the surface of a carbon saturated particle. The precipitation of carbon from the saturated metal particle leads to the formation of tubular carbon solids in a sp 2 structure. Tubule formation is favored over other forms of carbons because a nanotube contains no dangling bonds and therefore is in a low energy form. To maximize van der Waals contact and lower their free energy, individual SWNTs align themselves with each other to form ropes growing over large metal particles (> 1 nm diameter) Thermoelectric Power Measurements In essence, the experiment to measure the thermoelectric power consists of generating a thermal gradient along a conductor and measuring the resultant open-circuit voltage. In this study, the thermoelectric power was measured using a heat-pulse method developed by Eklund and coworkers 67,68 and which employs a simple analog subtraction circuit. -2-

40 The Analog Subtraction Circuit The analog subtraction circuit, shown in Figure 2.4, allows simultaneous measurements of the temperature difference and the Seebeck voltage, using two thermocouples electrically connected to the sample. Figure 2.4 also identifies the primary thermoelectric voltages V i (i = 1,2,3) used to determine the absolute thermoelectric power S U of the sample. The absolute thermoelectric power S is conveniently defined as the potential difference developed per unit temperature difference, i.e., 69 dv S =. (2.2) dt Thus, given the Seebeck coefficient S(T) for a homogeneous material, the voltage difference between two points where the temperatures are T 1 and T 2, is given as V = T2 T1 SdT. (2.3) Figure 2.4. Block diagram of the analog subtraction circuit to measure the thermoelectric power. The voltages in Figure 2.4 can therefore be written as -21-

41 V 1 = = T T T S AdT + SU dt + T + T T T + T T + T ( S S ) dt = ( S S ) T, U A T U S A A dt (2.4) V 2 = = T T T T S A dt + T S dt ( S S ) dt = V ( T ), B A T B BA (2.5) V 3 = = T T T S BdT + SU dt + T + T T T + T T + T ( S S ) dt = ( S S ) T, U B T U S B B dt (2.6) where T is the small temperature difference between the two thermocouple junctions attached to the sample and T is the reference junction temperature (~ 3 K). The thermocouples in Figure 2.4 are thermally but not electrically anchored to the temperature reservoir at T. In these experiments, the voltages V i are generated by applying a small heat pulse to one of the two ends of the sample, which establishes a time-dependent temperature difference. The amplifiers A i (i =1,2,3,4) respond as indicated in Figure 2.4. For small temperature differences, a straight line should be obtained when plotting the output of A 1 (or A 3 ) versus the output of A 4. The slope is related to the sample thermopower measured relative to the conducting leads. Taking into account the actual gains (g, G) of the amplifiers, we find or U ( slope)( S S ) S, S = g + (2.7) U B ( slope)( S S ) S. B A A A S = g + (2.8) -22- B

42 The sample temperature T is determined from an independent measurement of V AB (T). For this, the output of A 2 is polled just before the heat pulse is started, and just after it is terminated to determine the average temperature of the sample during the measurement. The temperature dependence of the relative thermopower of the thermocouple pair V AB (T) is previously measured by attaching the thermocouple pair to the surface of a silicon-diode thermometer, which determines the temperature while measuring the output of A The Thermopower Probe A schematic of the thermopower probe is shown in Figure 2.5. The probe consists of a header with a hermetic multipin connector for electrical input/output, a vacuum valve, a vent valve and a sample stage. The sample holder is fastened, using Teflon screws, to a stainless steel stage at the end of a.635 cm outer diameter, thin-walled stainless steel tube attached to the header (the supporting tube). The supporting tube is also a gas vent line with an opening at the lowest part of the probe. The overall probe length is 16 cm, which allows its insertion into an ordinary liquid-helium-storage container or a tube furnace. An O-ring seals the vacuum jacket to the header. -23-

43 Figure 2.5. Schematic diagram of the thermopower and resistance measurements probe suitable for the temperature range 4-5 K. -24-

44 The sample holder, shown in Figure 2.6, consists of a rectangular piece made of Macor, which is a white machineable ceramic. This material can be used continuously up to 1 ºC, is vacuum compatible (no outgassing) and provides good electrical and thermal insulation. Eight equally spaced screws are used to provide the electrical connections. Twisted copper leads connect the sample heater to the multipin electrical connector on the header. Similarly, twisted thermocouple leads (.3 diameter, Omega Engineering, Inc.) carry the thermoelectric response to the multipin connector and from there, via copper leads, to the analog subtraction amplifiers. Two additional copper leads (.3 diameter, Omega Engineering, Inc.) are used to measure the voltage during four-probe resistance measurements, as explained later in this section. A platinum resistor (type H214, Omega Engineering, Inc.) is thermally clamped at one end of the sample holder and serves as the heat source. Figure 2.6. Schematic diagram of the sample holder for the thermoelectric power and four-probe resistance measurements. Three types of differential thermocouples could be used in our experiments: chromel- -25-

45 alumel (type K), copper-constantan (type T) and chromel-gold (7 at% Fe). The thermocouple wires (.3 diameter, Omega Engineering, Inc.) are bonded together using a spark-bonding technique. This is done with a device consisting of two tweezers connected, through copper wires, to opposite polarities of a power supply set to 12 volts. The thermocouple wires are picked up together at their bare ends with one of the tweezers, and momentarily touched with the other tweezers. If properly held, the wires spark-bond at the junction and the sections of the wires being held by the tweezers burn off. The sample is mounted onto the copper heater clamp (Figure 2.6) by cementing one of the sample ends with silver paint. Thermocouples and voltage leads for four-probe resistance measurements also make contact with the sample via silver paint, which provides reasonably low contact resistances especially after thermal annealing at 1 ºC. We have tried to use silverloaded epoxy resin, which can withstand higher temperatures and exhibits better adhesion than silver paint, but have found that it is susceptible to cracking upon cooling. Both silver paint and silver-loaded epoxy exhibit excellent electrical and thermal conductivity as well as environmental resistance Experimental Setup A schematic of the experimental setup is shown in Figure 2.7, including the computerinterfaced system. The output from the analog subtraction circuit is sent to independent preamplifiers before being collected by the computer. An IEEE interface card and an analogto-digital converter (A/D) card DAS8 (Keithley MetraByte) are used for the data acquisition with LabVIEW (National Instruments Corp.) programs. The heat-pulse generator with variable pulse -26-

46 width and height is built using a micro controller (PIC 16C56, Microchip Technology, Inc.), which can be triggered by an external TTL signal. The pulse height and duration are adjustable in the ranges of -1 V and 1-2 s, respectively. DC Pre-amplifiers Power DAS8 A/D Board Pulse Generator 1 Voltage A Output Analog Subtraction Circuit B C Out put Output 1 Power ON OFF 2 2 PULSE GENERATOR ANALOG SUBTRACTION CIRCUIT TTL triggering signal Heater IEEE Interface Board SourceMeter 4-Wire Sense Figure 2.7. Block diagram of the system for thermoelectric power and four-probe resistance measurements instrumentation. When the sample is at the desired stable temperature, the computer sends a TTL pulse via one of the digital output lines of the A/D card to trigger the pulse generator. As a result, a voltage pulse with the appropriate width and height is applied to the heater, which causes a temperature gradient to develop and relax with time along the sample. Depending on the thermal mass of the sample and heater block, a temperature gradient of about.5 K is typically developed and relaxed over an interval of 5-2 s. After additional amplification, the thermopower data are collected via the A/D card as T increases and relaxes. -27-

47 The Thermopower Program Figure 2.8. The program Thermopower Auto.vi, showing the time evolution of the thermoelectric power of a SWNT film during vacuum-degassing at 5 K. To measure the thermoelectric power, we created two LabVIEW (National Instruments Corporation) programs entitled Thermopower Auto and Thermopower Manual. The principles of operation of both programs are the same except for the fact that the former allows us to collect data continuously, at regular intervals of time without further intervention by the operator. Figure 2.8 shows a sample set of thermoelectric power data as it was being taken with Thermopower Auto. The program collects thermopower data at every interval of time specified by the parameter Data Recording. Before each data collection, the program may be -28-

48 instructed on the gain of the pre-amplifiers (Output Gain), the type of thermocouple pair used (Thermocouple Selection), and the file where data is going to be saved (Filename). The variable Front Panel Connections specifies whether the output of amplifier A 1 or A 3 in Figure 2.4 is used to measure the thermopower. A selected number of the outputs of the amplifiers A 4 and A 1 (or A 3 ) are continuously collected at a sampling rate specified by the parameter Scan time. When these two voltages are plotted against each other, a straight line should be generated, which retraces itself as the temperature difference relaxes to zero (provided the thermocouples are in good thermal contact with the sample and are properly heat stationed), as shown in the lower left chart in Figure 2.8. At the end of the data collection, the same data are plotted in the lower right graph, together with a linear-least-square fitting curve. As we have discussed [Eq. (2.7)], the slope of this line is used to deduce the sample thermoelectric power. The upper graph in Figure 2.8 shows the thermoelectric power of a SWNT film as a function of time, as the sample was vacuum-degassed at 5 K. The same graph in Figure 2.9 shows the thermoelectric power as a function of the temperature of a small piece of constantan, measured according to the aforementioned method using the program Thermopower Manual. The data are in good agreement with the tabulated values. -29-

49 Figure 2.9. The program Thermopower Manual.vi, showing the temperature dependence of the thermoelectric power of constantan Calibration of the Thermocouples The sample temperature, as well as the quantities S S, S, and S in Eqs. (2.7) and B A A B (2.8), is known from calibration experiments which is checked frequently. The sample temperature is known by simply measuring the temperature dependence of the thermocouple voltage VAB(T). This is done by attaching the thermocouple pair to the surface of a silicon-diode thermometer and measuring the output voltage of amplifier A 2 as a function of the temperature determined by the silicon-diode thermometer. These data are then fitted with a polynomial function. -3-

50 The reference junction temperature T is needed for the calculation of the sample temperature T. Rather than using the cumbersome ice bath (T = ºC), T is measured by thermally anchoring a type-k thermocouple to two pins on the hermetic connector of the thermopower probe. A schematic of the connections is shown in Figure 2.1. Figure 2.1. Schematic diagram of the connections to A 2 amplifier to measure the sample temperature (top) and the equivalent circuit (bottom). The junctions J 2 and J 3 and the thermocouple (or thermistor) are all assumed to be at the same temperature T. We can easily show, using Eq. (2.2), that the output voltage V 2 is proportional to the temperature difference (T T ). Usage of an ice bath at the reference junction allows one to determine the temperature directly from a V 2 versus T calibration curve. If T needs to be known to higher accuracy, perhaps a secondary thermometer such as a silicon diode -31-

51 should be used. Although slow temperature drifts in room temperature T could cause some error in absolute temperature, they are too slow to affect measurements of the thermopower, because each data point is collected during a short period of time (~ 2 s) g T V 2 (V) (S KP S Au:Fe ) (µv/k) T (K) T (K) Figure The output voltage of amplifier A 2 as a function of the sample temperature (left) and the temperature dependence of the relative thermoelectric power of a chromel- Au:Fe thermocouple pair (right). According to Eq. (2.5), the temperature-dependent relative thermopower of the thermocouple pair is given by the relation S dvba S A. (2.9) dt B = Therefore, by simply evaluating the derivative of the V 2 versus T calibration curve, we can determine the temperature dependence of S S B A. Figure 2.11 shows the temperature dependence of the output voltage V 2 of the thermocouple amplifier A 2 and the temperature derivative of that calibration curve for a chromel-au:fe thermocouple pair ( S ). KP S Au:Fe The absolute thermopower of an unknown sample is obtained from either Eq. (2.7) or (2.8) by using calibration data for S A (T) or S B (T) with respect to copper. These quantities are determined by simply using a piece of high-purity copper as the sample. Figure 2.12 shows the -32-

52 relative thermopower data of chromel ( SKP S Cu ) and Au:Fe ( Cu S Au:Fe ) S with respect to copper, measured according to the aforementioned method. Finally, tabulated values for the thermopower of copper are used to obtain absolute thermoelectric power values S KP S Cu S (µv/k) 1 5 S Cu S Au:Fe T (K) Figure Temperature dependence of the thermoelectric power of chromel and gold:iron alloy with respect to copper. The solid lines represent polynomial fits to the data Four-Probe Resistance Measurements To measure the resistance of our samples the four-probe method was employed. This is a very versatile means, used widely in physics, for the investigation of electrical phenomena. Resistance measurements in the normal range (> 1 kω) are generally made using the two-probe -33-

53 method. Here, a test current is forced through two test leads and the resistance being measured. Then, the voltmeter measures the voltage across the resistance through the same set of test leads and computes the resistance accordingly. The main problem with the two-probe method, particularly for samples of low resistance, is that one inadvertently also measures the contact resistance of the wires to the sample. Since the test current causes a small, but significant, voltage drop across the contact resistances, the voltage measured by the meter will not be exactly the same as the voltage directly across the test resistance and considerable error can result. For example, one ohm of cable and contact resistance in a conventional two-probe circuit adds a.1% error to the 1-kΩ measurement. When one is measuring a very small resistance, especially under variable temperature conditions, the contact resistance can dominate and completely obscure changes in the resistance of the sample itself. This is the situation that exists for SWNT networks. The effect of cabling and contact resistances, as well as other series resistance errors, can be eliminated with the use of a four-probe method, often called a Kelvin measurement. A schematic of a four-probe connection, as well as the experimental arrangement, is shown in Figure 2.7. In this method, four wires attached to the sample are used for resistance measurements. A constant current is made to flow along the length of the sample through one set of test leads (probes labeled 1 and 4 in the figure), while the voltage across the sample is measured through a second set of leads called sense leads (probes labeled 2 and 3 in the figure). In our case, one arm of each thermocouple is used as the current lead. Although some small current may flow through the sense leads, it is usually negligible (typically pa or less) and can generally be ignored for all practical purposes. Since the voltage drop across the sense leads is negligible, the voltage measured by the meter is essentially the -34-

54 same as the voltage across the sample. Consequently, the resistance value can be determined much more accurately than with the two-probe method. Figure The program DC 4-Probe Resistance.vi showing the resistance as a function of temperature for a SWNT mat. A SourceMeter 24 (Keithley Instruments, Inc.) was used to provide a constant current to the experiment and measure the voltage. This instrument combines a precise, low-noise, highly stable DC power supply with a low-noise, highly repeatable, high-impedance multimeter. To cancel thermal emf, the current reversal algorithm is employed. That is, two measurements with currents of opposite polarity are programmed. Then, the two measurements are combined to eliminate unwanted offsets. Data acquisition is carried out remotely via an IEEE connection with a computer as shown in Figure 2.7. For this purpose, we created a LabVIEW program entitled DC 4-Probe -35-

55 Resistance, shown in Figure The program collects sample and thermocouple voltages either continuously at a specified rate (Scan rate) or at the user command from the front panel. After colleting a specified number of data points (No. Samples), the program plots the calculated sample s resistance versus temperature or time (Type of Measurement). The variables under Control Settings specify the methods used to measure resistance with the Keithley SourceMeter 24. The program allows four-probe and two-probe resistance measurements. The offset-compensation method cancels out unwanted offset in the voltage and current readings by measuring resistance at the specific source level, and then subtracts a resistance measurement made with the source set to zero. Temperature changes across components within the instrument can cause the reference and zero values for the A/D converter of the SourceMeter to drift due to thermoelectric effects. Auto zero acts to negate the effects of drift in order to maintain measurement accuracy over time. Without auto zero enabled, measurements can drift and become erroneous. Note that auto zero and offset-compensation measurements are additional corrections to the one obtained by using the current reversal algorithm, but the use of all these correction procedures simultaneously will decrease the measurement speed. Control display command is used to enable and disable the front panel display circuitry of the SourceMeter. When disabled, the instrument operates at a higher speed. The variables under Power Source Parameters allow the configuration of the current source. The operator can set the current level (I-Source), the limit voltage (V-compliance), auto/manual range for voltage measurements (V-AutoRange), the range for manual current (Irange) and voltage (V-range) measurements. Before each data collection, the program may also be instructed on the type of thermocouple pair used to measure the temperature (Thermocouple Selection) and the file where -36-

56 data is going to be saved (Filename) Gas/Chemical Adsorption Measurements Figure Schematic diagram of the gas handling system for gas/chemical adsorption experiments. For gas adsorption measurements, a gas handling system is attached to the vent valve of the thermopower probe. The basic components are shown in Figure This system consists of an oxygen/moisture trap (OT-4-SS, R&D Separations, Inc.), capable of reducing the oxygen and moisture content of a gas stream to less than 2 ppb; a general purpose differential capacitance manometer (Baratron 221, MKS Instruments, Inc.), a vacuum valve and a vent valve. Before admitting the gas into the thermopower probe, the gas handling system is properly evacuated and leak checked through the vacuum valve. An ultra-high purity grade gas cylinder is connected to the vent valve of the gas handling system for gas adsorption experiments. If needed, a side arm attached to a glass bulb containing a spectral grade liquid chemical (Sigma-Aldrich, Co.) is -37-

57 connected to the vent valve of the gas handling system for chemical adsorption studies. -38-

58 Chapter 3. Thermoelectric Power of Single-Walled Carbon Nanotubes 3.1. Seebeck Effect: Theory The Seebeck effect, depicted schematically in Figure 3.1, is the open-circuit (zero current) voltage response to a temperature gradient in a material. This phenomenon was discovered in 1821 by the German physicist Thomas Johann Seebeck who observed that a voltage (electromotive force, emf) was developed in a loop containing two dissimilar metals, labeled A and B in Figure 3.1(a), provided that the two junctions c and d were maintained at different temperatures. 69,7 The voltage across the loop was found to depend on the type of metals used and the temperature of the junctions. Physically, the phenomenon arises in a single material [Figure 3.1(b)] because the electrons at the hot end of such a conductor can find states of lower energy at the cold end, towards which they diffuse. This diffusion current is accompanied by the accumulation of extra electrons at the cold end, setting up an electric field or a potential difference between the two ends of the material. The electric field builds up until a state of dynamic equilibrium is established between electrons rushing down the temperature gradient and those moving against the gradient due to the electrostatic field. This thermoelectric effect is sometimes referred to as the diffusion thermoelectric power. -39-

59 Figure 3.1. (a) Basic thermoelectric open circuit that displays the Seebeck effect. (b) The Seebeck effect: A temperature gradient along a conductor gives rise to a potential difference. The Seebeck coefficient, thermoelectric power or simply thermopower S is the ratio of the open-circuit voltage developed V to the temperature difference T: S = lim V T T. (3.1) Almost all the theoretical treatments of thermoelectric power in macroscopic systems are based on the Boltzmann transport equation, from which the following expression for the thermopower can be derived: 71 S = 1 et f dkτ( k) v( k) v( k) [ ε( k) EF ] ε f dkτ( k) v( k) v( k) ε ε=ε( k) ε=ε( k), (3.2) where τ is the electron relaxation time, v is the electron group velocity, e is the electronic charge, -4-

60 f is the equilibrium distribution function of the electrons, ε is the energy of the electron relative to the chemical potential E F, and the integral is taken over all momentum states k. Note that the thermoelectric power is related to the energy carried by the electrons per unit charge, which is a function of the relative contribution of the electron to the total conduction. The sign of the thermopower is determined by whether the dominant conduction takes place in states above, or below, the chemical potential E F. For a degenerate metallic conductor, a calculation based on Eq. (3.2) (see Appendix A) leads to the following expression for the diffusion thermopower: S 2 2 π k BT d ln σ = e de ( E) 3 E= EF AT, (3.3) where σ(e) is the conductivity that would be found in a metal for electrons of energy E, given by the well known relation 2 2 ( E) = e υ( E) N( E) τ( E). σ (3.4) Here N(E) is the density of states, and υ(e) and τ(e) are, respectively, the free carrier velocity and relaxation time at energy E. For an electron-like band, the thermopower is negative, while for a hole-like band the thermopower is positive. The energy dependence of the relaxation time is often written as τ( E) = βe m, (3.5) where β is a constant and m a number that depends on the type of scattering that is dominant. Consequently, it is easily shown that in the free-electron approximation Eq. (3.3) reduces to S 2 2 π k BT 3 = + m, e E 2 3 F (3.6) which indicates that S is expected to vary linearly with temperature. Elementary calculations

61 predict that m = 3/2 in the temperature range where the relaxation time is limited primarily by electron-phonon scattering, and m = 1/2 at very low temperatures where τ(e) is limited by impurity scattering. Hence, a change in the slope expected in the free-electron approximation, i.e. ds dt as the temperature is reduced would be S 2 2 π kbt = very low T (residual resistance region) (3.7) e E F S 2 2 π kbt = high T (phonon scattering region) (3.8) 3e E F The thermopower of semiconductors with relatively few conduction electrons (nondegenerate semiconductors) shows temperature dependence different from that found in metals. In the case of semiconductors, one has to replace the Fermi-Dirac statistics in Eq. (3.2) by the Boltzmann statistics, in which case one obtains k B Ec EF S = + Ac for E > Ec, (3.9) e k BT k B EF Ev S = + Av for E < Ev, (3.1) e k BT where A c and A v are temperature-independent constants. In general, the thermoelectric power for a non-degenerate semiconductor is of the form S = k B e λ T + β, (3.11) where λ is the gap temperature measured from the midgap to the band edge and β is a constant. β = 3 when both the density of states and the mobility increase linearly with E. β = 1 for constant density of states and mobility. 72 Using the energy dependence of the relaxation time in Eq. (3.5), β = 5 2 m

62 Thus, in contrast to the linear temperature dependence observed in metals, a semiconductor should exhibit a thermoelectric power which is proportional to the reciprocal of temperature. In addition, the thermoelectric power of a semiconductor is usually large at room temperature (in the mv/k range). Metals, on the other hand, usually display a small thermoelectric power (in the order of a few µv/k). 69 In recent years, there has been increasing interest in the thermoelectric phenomena in carbon nanotubes. Thermoelectricity has been shown to be a valuable and effective probe of electronic structures, and a suitable tool for understanding the scattering dynamics of electrons and phonons and the electron-phonon interactions in solids Thermoelectric Power of Carbon Nanotubes: Background Figure 3.2 shows a typical temperature dependence of the thermoelectric power for an as-prepared SWNT mat. The thermoelectric power data is in reasonably good agreement with the earliest results, which yielded surprising results: at high temperatures the thermoelectric power has a large positive value (i.e., S ~ 4-6 µv/k at 3 K, depending on the sample history) that decreases monotonically with decreasing temperature, while at low temperatures the thermoelectric power is quasi-linear in temperature and rapidly approaches zero as T. There is also a strong non-linearity in the range ~ 8-1 K, either in the form of a superimposed knee (change of slope) or a more pronounced bump or peak. The temperature dependence of the thermoelectric power of SWNT bundles is unusual; it does not correspond to that of a simple metal or semiconductor. However, a metallic behavior could be incorporated at low temperatures (below ~ 1 K), or by considering an extension of -43-

63 the linear section at very low temperature (below 5 K) as shown, respectively, by the curves (a) and (b) in Figure 3.2. This behavior is in sharp contrast with the thermoelectric power observed for the basal plane of graphite which exhibits a small value for the thermoelectric power (S = 4 µv/k at 3 K) and nearly linear temperature dependence. 77 Graphite has a pair of weakly overlapping electron and hole π bands with near mirror symmetry about the Fermi level. Approximately equal numbers of electrons and holes in these symmetric π bands are consistent with the small (negative) linear thermoelectric power observed below room temperature. 4 3 (a) S (µv/k) 2 (b) T (K) Figure 3.2. Temperature dependence of the thermoelectric power for an air-saturated SWNT mat. The solid line is a guide to the eye. The dashed lines (a) and (b) represent the ways in which metallic behavior could be incorporated in the thermoelectric behavior of SWNTs. -44-

64 Based on the fact that the sign of the thermoelectric power is always positive in the measuring temperature range, it was implied that the majority charge carriers in the carbon nanotubes should be p-type, and the hole carriers are dominant. The large magnitude of the thermoelectric power is surprising because metallic tubes are predicted to have electron-hole symmetry and hence, a thermoelectric power close to zero. The obtained temperature dependence of the thermoelectric power is also unusual, and cannot be simply explained by a single-band model for a metal [Eq. (3.3)] or a non-degenerate semiconductor [Eq. (3.11)], over the studied temperature range. Numerous models, however, have been proposed to explain this complicated behavior, including parallel metallic and semiconducting pathways, 74,78 variablerange hopping, 78 electron-phonon enhancement, 78 fluctuation-induced tunneling, 79 and Kondo effect. 76 More complicated heterogeneous models have also been considered. 8 We discuss next the merits and difficulties of some of these approaches Parallel Heterogeneous Model of Metallic and Semiconducting Pathways The observed temperature dependence of the thermoelectric power for SWNT mats suggests a parallel heterogeneous model of metallic and semiconducting nanotubes within the ropes. 74,78 In principle, since a nanotube bundle consists of various nanotubes, the total thermoelectric power should result from the combination of the contributions from all nanotubes with different (n,m). For two types of parallel conductors (metallic and semiconducting), we can write the total thermopower S as a weighted average Gm Gs S = Sm + Ss, (3.12) G G where S m and S s are the thermopower of the metallic and semiconducting tubes, respectively, G m -45-

65 and G s are the corresponding electrical conductances, and G is the total conductance of the rope. To derive Eq. (3.12) let us consider the situation shown in Figure 3.3. From Eq. (3.1), the open-circuit potential difference produced across conductor a alone would be given by V a = S T a, and similarly V = S T for conductor b acting alone. It then follows from b b simple circuit theory that the resultant open-circuit voltage produced by the two conductors in parallel is given by an expression similar to Eq. (3.12). This circuit theorem is sometimes known as the ladder theorem. Figure 3.3. Illustration of the combination of thermoelectric powers for conductors in parallel (also applicable to the two-band model). The conductance from the metallic tubes is expected to be proportional to the reciprocal of temperature, i.e., G m 1 T, at least at high temperatures. Assuming an activated form for the semiconducting conductance, exp ( λ T ) G s, and that the total conductance is dominated by the metallic tubes, then from Eqs. (3.3) and (3.11), the total thermopower is 74 λ S = AT + ( Bλ + CT )exp, (3.13) T where A, B, and C are constants. The solid line in Figure 3.4 represents our fit of Eq. (3.13) to our data set shown in Figure 3.2. Even though this model provides a reasonably good fit to the -46-

66 thermoelectric power data, the fitting parameters are less than satisfactory in several respects. 74 The fitted thermoelectric power for a mat of SWNTs is seen to be dominated by the first term in Eq. (3.13), where the positive value of the temperature coefficient A implies a thermoelectric power contributed by the holes of metallic nanotubes, with a room temperature magnitude of S ~ 8 µv/k. In general, the model predicts an unphysically large magnitude of the diffusion thermoelectric power for the metallic tubes (S m ~ 8-2 µv/k at 3 K) S (µv/k) 2 1 A =.249 µv/k 2 B = µv/k 2 C =.486 µv/k 2 λ = 521 K T (K) Figure 3.4. Fits to measured thermoelectric power of a SWNT mat using a parallel heterogeneous model of semiconducting and metallic tubes. The solid line represents a fit to the data using Eq.(3.13). Fitting parameters extracted from our fit are also shown in the figure. The negative term would presumably be contributed by the electrons of the conduction band for the semiconducting nanotubes. Therefore, within this model, the measured magnitude -47-

67 of the temperature-dependent thermoelectric power is due to a near cancellation of very large metallic and semiconducting thermopowers of opposite sign; a situation regarded as unlikely. The value of semiconducting tube energy gap, obtained from the parameter λ, is ~.9 ev. Previous studies have found values of 1-2 mev, which are significantly smaller than values expected for the energy gap. In general, the energy gap of a semiconducting nanotube is expected to vary from.5 ev to a few ev in the diameter range 1 nm < d < 2 nm, depending upon the geometry. 51,81 The mean tube diameter measured for the sample whose data appear in Figure 3.4 is ~ 1.4 nm. This model consequently predicts very small semiconducting gaps and conductances that are considerably larger than typical observations. 82,83 Moreover, the model with metallic and semiconducting conduction in parallel cannot by itself account for the resistivity behavior, because the semiconductor contribution to conductivity is frozen out at lower temperatures where it is observed experimentally Variable-Range Hopping An alternative parallel tube model was proposed where metallic conduction is in parallel with disordered semiconductor conduction via 3D variable-range hopping. 78 For conduction by variable-range hopping, the expected thermopower (which is positive for hole conduction) is given by 84 S ( E) 2 k B d ln N 2 = ( T ) 1 T, e de (3.14) 2 E= EF where N(E) is the density of states at the Fermi level and T is the parameter appearing in the Mott variable-range hopping law of conduction: -48-

68 G is usually considered to be weakly dependent on temperature. Using Eq. (3.12) one now obtains 1 4 T G = G exp, (3.15) T T 2 S = AT + BT exp. (3.16) T 4 3 S (µv/k) 2 1 A = µv/k 2 B = µv/k 3/2 T = 636 K T (K) Figure 3.5. Fits to measured thermoelectric power of a SWNT mat using a parallel heterogeneous model of disordered semiconducting and metallic tubes. The solid line represents a fit to the data using Eq. (3.16). Fitting parameters extracted from the fit are also shown in the figure. As shown in Figure 3.5, this expression does not provide a reasonable fit to the observed thermoelectric power (Figure 3.2), as the predicted change in slope is smoother than that -49-

69 predicted. The model also gives an even larger metallic contribution when fitted to the data. On the other hand, the simple combination of metallic and hopping conduction regions suggested by the resistivity behavior of SWNTs fails to provide reasonable fitting to both the resistivity and the thermopower using the same set of parameters; mainly T Electron-Phonon Enhancement The quasi-linear temperature dependence of the thermoelectric power in a metal can be understood by the electron-phonon enhancement effect. 78,85 The enhancement of the linear temperature dependence of metallic thermoelectric power can be expressed as S [ 1+ λ ( T )] AT, = (3.17) S where λ S (T) denotes the temperature dependent enhancement from the coupling of the electrons and phonons and A is the coefficient of diffusive thermoelectric power. The fits to the thermoelectric power data using Eq. (3.17) give the reduction of slope above ~ 1 K. However, the values of the effective enhancement λ S () are as large as those expected for good superconductors. 78 Since nanotubes have not been observed to superconduct at temperatures as low as 1.5 K, a very large value for λ seems inappropriate Fluctuation-Assisted Tunneling A SWNT network can be assumed to contain many metallic regions separated by small insulating barriers (for example, due to poor connectivity between individual nanotubes). The contact resistance of these barriers can dominate the overall resistance of the system. Such -5-

70 systems can be described phenomenologically by Sheng s theory of fluctuation-induced tunneling. 86 According to this theory, the electrical conductivity is given by the relation T1 exp σ = σ. T + T (3.18) The thermoelectric power can also be calculated from this theory. 79 The contribution to the thermoelectric power would be weighted by the fraction of the temperature difference appearing across the barriers compared to that appearing across the metallic portions. This model can describe the thermoelectric power data of SWNTs reasonably well and a knee, such as that occurring in the thermopower data at ~ 1 K, is predicted by this theory. However, additional contributions to the thermoelectric power must be considered in order to achieve the positive curvature seen in the data for T 1 K Kondo Effect An anomalously large peak superimposed on the metallic thermopower has been observed in the range 8-1 K in some transition-metal doped SWNT mats, and has been tentatively attributed to a Kondo anomaly associated with the residual (magnetic) catalyst residing as particles on the bundles or rope surface, or trapped as atoms or small clusters within the bundles. 76 In other materials, the interaction between the magnetic moments of the impurity atoms and the spin of the conduction electrons has been shown to lead to a new spin-dependent scattering mechanism and a narrow hybridization peak or Kondo resonance in the electronic density of states positioned near the Fermi level. 87 The Kondo mechanism was also suggested because the particular catalyst caused a -51-

71 concomitant change in the strength of the upturn in the electrical resistivity with decreasing temperature below ~ 1 K. Further support for this argument is that the chemical treatment of the SWNT samples with iodine, significantly reduces the Kondo contribution. 76 The drawback in the Kondo proposition to explain the thermoelectric power of SWNTs is that the thermoelectric power peak should occur at T = T E k, where E is the width of the Kondo resonance K B near the Fermi level. One might expect a stronger variation in T K with various magnetic impurities (e.g., Fe, Ni, Co), unless the effect is associated with Y, which is a common element in all of the catalysts considered in that study Thermoelectric Power of Oxidized SWNT Networks Recent experimental studies 88,89 have reported that the measured SWNT electronic properties (including the thermoelectric power and the electrical resistance) are extremely sensitive to the presence of molecular oxygen in the nanotube. Specifically, it has been found that, at room temperature, the resistance changes by 1-15% when SWNT mats are cycled between vacuum and air exposure. In addition, after exposure for ~ 2-3 h under ambient conditions to room air, SWNTs were found to acquire thermopower values unusually large compared to those of ordinary metals and graphite. Most strikingly, it was reported that some small-gap semiconducting nanotubes exhibit metallic behavior when they are exposed to oxygen. 9 Our in situ measurements while heating these O 2 -doped samples in a ~ 1-7 Torr vacuum at ~ 5 K (i.e., to remove the adsorbed O 2 ) showed that the large positive thermopower identified with O 2 doping first decreases with time and then changes sign, with the fully degassed -52-

72 sample finally exhibiting a large negative thermopower after 1-15 h. These results were interpreted as due to the formation of a charge transfer complex +δ δ C p O 2. For the semiconducting tubes, the position of the Fermi level must shift toward the valence band. This will be discussed in detail in the following section Air-saturated S (µv/k) K in vacuum T (K) Figure 3.6. The temperature dependence of the thermoelectric power for an as-prepared SWNT mat in its air-saturated and degassed states. The solid lines are guides to the eye. Figure 3.6 shows our S(T) data for the same SWNT sample for two cases: air-saturated and degassed states. For the air-saturated sample, the thermoelectric power is always positive and approaches smoothly S = as T, from a large value S ~ 4 µv/k at 3 K. For the sample degassed at 5 K for 24 h in a 1-7 Torr vacuum, the thermoelectric power is negative over the entire temperature range 4 K < T < 3 K, with a room temperature magnitude -53-

73 comparable to that measured under air-saturated condition. As can be seen, the functional forms of S(T) for air-saturated and degassed samples appear to be almost mirror images of each other, reflected about the horizontal temperature axis. The results in Figure 3.6 demonstrate that the previously published large positive thermoelectric power data should not be considered as an intrinsic SWNT behavior, but rather the result of various degrees of oxygen doping. The interactions of O 2 with carbon nanotubes have been investigated in several recent theoretical studies According to the results, there are three different pathways for oxygen adsorption on SWNTs: (a) Molecular oxygen (in its spin-triplet ground state) physisorbs on the outer surface of a perfect tube wall with relatively small binding energies up to.25 ev, accompanied by a small charge transfer of.1 electron from the carbon nanotube to the O 2 molecule. There may be no barrier for O 2 physisorption onto perfect carbon nanotubes. 11 On the basis of the calculated density of states, it was also suggested that the adsorbed O 2 molecules can dope the semiconducting nanotubes with hole carriers and that conducting states are present near the band gap. 92 (b) Molecular oxygen (in its spin-singlet excited state) exothermically chemisorbs to the tube wall through an intermediate cycloaddition step to give two spatially well-separated epoxide groups or two single C O bonds, with significant charge transfer from the nanotubes to the O 2 molecules. 94,97,99,13 The adsorption is high (~.34 ev) and the activation barrier can be as low as ~.6 ev, which is accessible at room temperature. 97 O 2 molecules can be excited into a more reactive spin-singlet state by UV-light, 1 sunlight, photosynthesizers (e.g., fullerene impurities), 97 or by topological defects. 11 In addition, adsorption at defect and impurity sites may help overcome the kinetic activation barrier. 1,11 (c) Molecular oxygen diffuses to the edge of open tubes where it dissociatively chemisorbs with -54-

74 an adsorption energy of up to 8.4 ev to form strong C O bonds, even without any activation barrier Thermoelectric Power of SWNT Films Here we present the results of a systematic study on a purified thin film of tangled SWNT ropes, which show that the thermoelectric power is determined by coordinated effects in both the semiconducting and the metallic tubes. However, the thermoelectric power will be shown to be dominated by the metallic tubes in the ropes. The sign and magnitude of the thermoelectric δ power will be shown to be determined by the relative concentrations of (acceptor state; δ = fractional charge) and an unidentified donor state in the semiconducting tubes, possibly due to wall defects. In fact, we show that a fully compensated sample can exhibit a thermopower S ~ over a wide temperature range (4 < T < 5 K). In the compensated case, we will argue that the Fermi level for a rope containing semiconducting and metallic tubes is very near the intrinsic position. Furthermore, in this case, the mirror symmetry of the metallic band structure makes offsetting contributions from electrons and holes. In contrast to this view, Avouris and coworkers have demonstrated a similar behavior using SWNT field effect transistors (CNT- FET), i.e., the p-type electronic character can be turned into a fully n-type one by simply annealing in vacuum. Based on the observation that oxygen treatment has no effect on the threshold voltage for turning on a CNT-FET, they argued that barriers at the metalsemiconducting contact control the carrier injection even though bulk doping may take place. O 2 According to Avouris and co-workers, the dependence of these barriers on oxygen determines the electrical character of the CNT-FET. It may be that the nanotubes in the CNT- -55-

75 FET studied were defect-free and contained only weakly interacting (physisorbed) oxygen. In contrast, our samples contained sufficient defect density that could bind strongly with O 2 involving charge transfer. Despite the numerous theoretical and experimental investigations, the microscopic mechanism responsible for the observed changes in the electronic-transport properties of SWNTs is still discussed controversially. The sensitivity of carbon nanotubes to O 2 exposure is an important issue, as it raises questions about the stability of devices made of carbon nanotubes upon air exposure. On the other hand, the observed effect of oxygen exposure on the properties of carbon nanotubes raises the possibility that unintentional oxygen contamination during preparation of nanotubes samples might have led to incorrect analysis of the experimental data Role of Contact Barriers on the Transport Properties of SWNTs It has been argued 79,8 that the measured thermoelectric power of a SWNT network may be affected by rope-rope contacts and other barriers (e.g., defects, tube-tube contacts, etc.) in the SWNT mat or film and their random orientations relative to the thermal gradient. This is a reasonable concern, particularly if we note that a SWNT network consists of ropes, themselves containing metallic and semiconducting tubes that may be loosely touching each other through semiconducting tubes and/or amorphous carbon on the rope surface, not eliminated by the purification process (Figure 3.7). -56-

76 Figure 3.7. Sketch of crystalline SWNT ropes, where fibrillar carbon nanotubes are separated by disordered regions (Adapted from Kaiser et al. 17 ) In this picture, the thermoelectric power could be the result of a pathway of semiconducting tubes broken by series-connected inter-tube barriers, where the thermopower due to the insulating barriers could be described by either an activated hopping-like conduction model 8 or a fluctuation-induced tunneling model. 79 We investigated the possible influence of rope-rope contacts on the four-probe resistance [Figure 3.8(a)] and the thermoelectric power [Figure 3.8(b)] on film or mat samples by observing the change in these quantities under the action of uniaxial stress. The experimental geometry is shown schematically in the inset to Figure 3.8(b). The measurements were made in air at T ~ 3 K as a function of the loading force F applied normal to the substrate supporting the SWNT mat. Thermocouples [TC(1), TC(2)] and voltage leads [V(1), V(2)] made contact with the SWNT mat via silver epoxy outside the region of applied stress. The pressure was calculated directly form the cross-sectional surface area of the insulating rod and the weights placed on top of it. -57-

77 1. (a) 7 (b).95 6 F R/R.9.85 S (µv/k) 5 4 TC(1) V(1) V(2) TC(2) Pressure (MPa) Pressure (MPa) Figure 3.8. Uniaxial pressure dependence of (a) the normalized room temperature resistance R/R and (b) the thermopower S for two different as-prepared SWNT mats. The inset shows the experimental geometry where the applied force F is perpendicular to the sample. 18 As can be seen in Figure 3.8, the applied force (stress) impacts the four-probe resistance but not the thermopower. It should be noted that the data are for two O 2 -doped samples under ambient conditions. If the contact regions among the ropes dominated the thermopower, when these regions become better heat conductors under the applied stress, the thermopower might be expected to decrease. However, as shown in Figure 3.8(b), the pressure has little effect on the thermopower. The insensitivity of S to the improved rope-rope contact resistance, observed via the decreasing R in Figure 3.8(a), is taken as direct evidence that the contact barrier between ropes is not significantly involved in the thermoelectric power of the SWNT sample. This is consistent with the measurement of the thermoelectric power under open-circuit (zero current) conditions Effect of Oxygen Doping on the Thermoelectric Power of SWNTs Figure 3.9 shows the time evolution of the thermoelectric power at T = 5 K for a -58-

78 typical purified SWNT thin film sample under vacuum. The SWNT sample was previously exposed to air under ambient conditions for several days, then mounted in the measurement apparatus, evacuated to ~ 1-7 Torr and heated from 3 to 5 K. At point A, the sample is still nearly air-saturated which was accomplished under ambient conditions. 3 T = 5 K (D) 2 O 2 adsorption S (µv/k) 1 (A) O 2 desorption (B) -1 (C) Time (h) Figure 3.9. Thermopower response to vacuum and O 2 (1 atm) at T = 5 K. (A C): Vacuum-degassing of a sample initially O 2 -doped under ambient conditions for several days. (C D): Exposure of the degassed sample to 1 atm of O 2 established at C. 18 As the sample was degassed at T = 5 K in a vacuum of 1-7 Torr, the thermopower was observed to decrease slowly from an initial value S = 8 µv/k, change sign at B (fully compensated state), and then gradually approach a constant value of S = 1 µv/k near C (fully degassed state). The observed thermoelectric behavior at T = 5 K in vacuum is in agreement with previously reported results on similar samples. 88,89 However, very recently, -59-

79 Goldoni et al. 19 have used high resolution core-level photoemission spectroscopy to study the interaction between O 2 and SWNTs at low temperature (15 K). A strong interaction with O 2 was found for samples contaminated with traces of Na (mainly chemical residues of the purification, dispersion, and filtration processes) due to charge transfer from the tube to the Na O complex, whereas weak interaction with O 2 was observed when dosing the Na-free sample. Thus, Goldoni et al. 19 suggested that O 2 molecules have no effect on the transport properties of SWNTs if impurities (i.e., catalyst particles, contaminants and defects coming from the chemical treatments) are carefully removed from the nanotube samples. Note that, in our purification procedure, we do not use surfactants or NaOH, which might leave residual Na in the SWNTs. Besides, as mentioned in Ref. 19, the high-t annealing at ultrahigh-vacuum completely removes any Na contamination and strongly reduces the number of defects introduced by the purification treatments, restoring the nanotube structure and the bundle network. Our samples were annealed at ~ 12 ºC in a 1-7 Torr vacuum for 24 h. We also note that the experiments in Ref. 19 have been carried out by exposing nanotubes to O 2 at 15 K. At this low temperature, we expect O 2 to interact weakly with SWNTs through a physisorption process only. Due to the negligible charge transfer between physisorbed oxygen and SWNTs, such O 2 species are not expected to facilitate the doping responsible for the observed change in the transport properties of SWNTs. 11 As suggested by Ulbricht et al., 11 based on thermal desorption experiments and molecular mechanics calculations, it seems likely that the observed effect of O 2 on the transport properties of SWNTs is predominantly due to charge transfer by minority oxygen species, weakly bound either at defect sites on the SWNT bundles or at tube-metal contacts in electronic devices Exposure of the fully degassed film to 1 atm overpressure of pure oxygen at T = 5 K -6-

80 irreversibly changes the thermopower to large, positive value S = 25 µv/k, as indicated by the point labeled D (high-t O 2 -doped state) in Figure 3.9. This indicates that O 2 exposure at T = 5 K results in a more strongly bound oxygen acceptor, possibly a C O bond at a wall defect. When vacuum was applied at D, we were unable to change the thermoelectric power. Note that the sample was fully degassed for ~ 8 h. Such a long equilibration time taken to attain the negative value of the thermoelectric power representative of the degassed state of purified SWNT films exposed to ambient air suggests that some of the O 2 must reside in the interstitial channels and/or within the central pore of the opened SWNTs. Fujiwara et al. 111 have used adsorption isotherms and X-ray diffraction at 77 K to investigate the gas adsorption properties of bundled carbon nanotubes and have concluded that O 2 molecules are adsorbed preferentially inside the bundles, and then mostly in the interstitial channels. Single-file diffusion would be necessary to empty the interstitial channels. Figure 3.1 displays the temperature dependence of the thermoelectric power for the same sample at the points A to D indicated in Figure 3.9. The series of curves S(T), also labeled A, B, and C in Figure 3.1, are observed after successively longer periods of vacuum-degassing that removes successively larger amounts of O 2 from the ropes. We note that it is possible to tune reliably to any intermediate metallic thermopower between the air-saturated state and the fully degassed state, including an almost zero thermopower state (curve B). For example, the thermopower for an initially air-saturated sample (under ambient conditions) and the same sample O 2 -doped by exposure at T = 5 K to 1 atm O 2, are both positive and almost linear over the entire temperature range. A positive knee is observed around ~ 1 K, and changes sign tracking the sign of the linear background on which it is superimposed. -61-

81 25 2 (D) High-T O 2 -doped (irreversible) S (µv/k) (A) Ambient O 2 -doped (reversible) (B) Compensated T (K) 3 (C) K in vacuum 4 5 Figure 3.1. Temperature dependence of the thermopower S for a SWNT thin film after successively longer periods of O 2 degassing at T = 5 K in vacuum. The labels A, B, and C refer to a vacuum-degassing interval indicated in Figure 3.9. Curve D is for the same sample exposed to 1 atm O 2 at T = 5 K for about 4 h after being fully degassed to point C. 18 The thermoelectric power of the degassed sample, on the other hand, is negative over the entire temperature range and also shows a linear metallic variation with temperature, with a superimposed negative hump around ~ 8 K. A low-t hump is often identified with phonon drag, 7 which enhances the diffusion thermopower. Our assignment of phonon drag is consistent with the sign change of the hump. Phonon drag thermoelectric power in SWNTs will be discussed in the following chapter. -62-

82 Compensating Doping and Defect Chemistry We assume that each rope consists of a mixture of metallic and semiconducting tubes, in the approximate ratio 1:2. There are probably defect states in the tubes, among which some are donors and some are acceptors. Prior calculations have shown that defects in metallic nanotubes introduce resonances in the density of states at the Fermi energy. 112,113 They are discussed in a later section. Donors in a semiconducting tube introduce an additional electron into the system, while acceptors contribute an additional hole. In both cases, we show that the additional electron or hole is transferred to the metallic tubes and controls the chemical potential of the rope. 18 We assign the acceptor states to chemisorbed oxygen. Calculations by Jhi el al. 92 predicted a charge transfer of about.1 electrons to the O 2 molecules in contact with the semiconducting tube wall. The origin of the donor state is less clear. It may be associated with wall defects. Consider the case of doped semiconducting carbon nanotubes with donor states, in close contact with the metallic nanotubes in a rope. The total negative charges (electrons) must equal the total positive charges (holes and ionized donors). Hence, the following charge neutrality condition governs the position of the Fermi level in a rope: + 2n se + nme = 2ND + 2nsh, (3.19) where n me is the electron density of the metallic tubes, n se and n sh are respectively the electron and hole density from the semiconducting tubes, and + N D is the density of ionized donors. Next, we use the definition of n se for a non-degenerate semiconductor, n se dk = ( E( k ) EF ) kbt 2 e 2π (3.2) ( Eg 2 EF ) kbt = n e, -63-

83 where E g is the semiconducting gap, E(k) is the tight-binding energy dispersion, and n is the effective density of states in the conduction band of the semiconducting tube. Similarly, the hole density can be calculated to give, n sh ( EF + Eg 2) kbt = n e. (3.21) The concentration of ionized donors is given to a good approximation by N + D ND = ( ), (3.22) EF ED k BT 1+ 2e where N D is the density of donors, E D is the donor binding energy with respect to the conduction band minimum, and the Fermi-Dirac distribution function is modified by the presence of the factor 2 before the exponential term in the denominator because of the spin degeneracy of the donor states, which can be occupied by either a spin-up or a spin-down electron. We can rewrite the above equation to obtain + γ ND = ND, (3.23) 2x + γ where ( E g 2 EF ) k T x = e B and ( Eg 2 ED ) kbt γ = e. Next we consider the metallic carbon nanotube. We assume that it is charge neutral if the chemical potential is at the energy zero where the bands cross. If this point is defined as E F =, then the excess charge density on the metallic tube is x nme = g mef = k BTg m ln, (3.24) α where g m is the total density of states for the four metallic bands and E 2k T g B α = e. Using Eqs. (3.2)-(3.24), we can finally rewrite Eq. (3.19) in the form = 2 α x γ x + sln r, (3.25) x α 2x + γ -64-

84 with s = k Tg 2n and r = N n. B m D At r = (i.e., no donors), the solution is x = α. In this case, the chemical potential is at midgap, and there are equal numbers of electrons and holes in the semiconductor. There is no charge transfer to the metallic tubes. In the limit of low doping, r is small. Assuming that α << γ, the last two terms in Eq. (3.25) are the largest and must cancel to give r x αe s =. In this case, there is complete charge transfer. All the donors ionize and transfer their electrons to the metallic tube. The chemical potential rises in the metallic tube, but by a small amount. In equilibrium, the chemical potential must be the same for all tubes. If the donor density becomes large, then the chemical potential approaches the donor density in the semiconductor and the charge transfer decreases for additional donors. A similar analysis applies for acceptor states. Because of the charge transfer, there is negligible electrical conductivity in the semiconducting nanotubes Model Calculations of the Thermoelectric Power of SWNTs Since S ~ T, the thermoelectric power of the SWNT film (Figure 3.1) is consistent with a diffusion thermopower dominated by metallic tubes in a rope. The metallic character of the thermopower can be understood from the following argument. The thermopower for a SWNT rope can be written as the sum of the conductanceweighted contributions from all nanotubes in a rope because they are connected in parallel (c.f. p. 45), N 1 S = G S j j, (3.26) G =1 j -65-

85 where N G = j =1 G j, (3.27) and the index j runs over all N tubes in a rope, G j and S j are the conductance and the thermopower, respectively, of the jth tube and G is the total conductance of the entire SWNT rope. If the semiconducting nanotubes are not degenerately doped, then G j (metal) >> G j (semiconductor) and we find that S S (metal) and G ~ G j (metal) N 3, where L ~ j indicates the average number of metallic nanotubes in a rope. If some semiconducting nanotubes were degenerately doped, they would mimic, to some extent, the temperature dependence of the conductivity and the thermopower of the metallic nanotubes. Specifically, the thermopower for the degenerately doped semiconducting nanotubes would exhibit a S ~ T E behavior. However, E F is small and hence, the thermopower for these F tubes would be high. The relative contribution of the degenerately doped semiconducting nanotubes would be controlled by their conductance, and we anticipate that this conductance is significantly lower than those for intrinsic metallic nanotubes. There is no clear evidence that some of the nanotubes in our samples are degenerately doped semiconducting nanotubes. However, if they exist they may enhance a smaller metallic thermopower. We note that the thermopower has been shown (Figure 3.8) to depend only weakly on the rope-rope contacts, but the film resistance is affected. The value of G one might compute from Eq. (3.27) does not represent the mat/film conductance, i.e., the rope-rope contact resistance is in series and must be added into the calculation. We next show that the magnitude of the experimental thermoelectric power cannot be -66-

86 explained by a simple two-band model for a metallic tube with electron-hole symmetry, except for the fully compensated sample. To do this, we take the simplifying assumption that our samples are mainly composed of metallic (1,1) tubes, whose band structure near E F is characterized by two pairs of 1D tight-binding bands crossing at zero energy (cf. Eq. (1.6), n = q = 1) E E e h ka = γ 1 2cos 2 ka = γ 1 2cos 2,, (3.28) where e, h refer to the electron and the hole bands. In the frequently used two-band model for the thermoelectric power, one obtains 69 S σe σ h = se + sh, (3.29) σ σ where σ i and s i are, respectively, the conductivity and the thermopower of the i = e, h (electron, hole) band, and σ = σe + σ h is the total conductivity. Now, using Eqs. (3.3)-(3.5), we obtain 2 2 π k BT S = 3e γ K ± = ± ( K + K ) +, m ( 1 ε )( 1± ε ) 2 m 1 + m 4 ( 1m ε ) ( 1± ε ) 2 4 ( 1m ε ) 2 m 2 4 ( 1 ε ) ( 1+ ε ) + 4 ( 1+ ε ) ( 1 ε ) m (3.3) Here, ε = E γ is the reduced energy. In Figure 3.11, we plot the result for S at T = 3 K for m = 3/2 as a function of E F. We allowed the Fermi energy to move up and down in rigid π bands in response to the balance between donor and acceptor states. We note that on moving E F by as much as ± 1 ev relative to the mirror symmetry plane in the band structure, we obtain a thermoelectric power value S ~ 1 m. -67-

87 µv/k, which is a factor of 4 less than the experimental data for the O 2 -doped material or the fully degassed material. On the other hand, the thermoelectric power of a fully compensated sample (S ~ ) is consistent with this calculation (curve B, Figure 3.1), in agreement with early theoretical calculations. 74 In our model, transport in states above and below the Fermi level cancel to give no net contribution to the diffusion thermopower when the Fermi level lies at the band crossing. This is due to the exact electron-hole symmetry assumed in the system. 2 E F (ev) S (µv/k) E F /γ Figure Calculated thermoelectric power of a (1,1) carbon nanotube as a function of the Fermi level position. Therefore, though the thermoelectric power of a compensated sample can be understood on the basis of our model and using mirror symmetry bands [Eq. (3.28)], the same calculation is unable to explain the large positive or negative values of S in the doped material. -68-

88 Thermopower from Enhanced D(E F ) due to Impurities Previous calculations of the thermoelectric power in a doped metallic tube provide an explanation for the large values of the thermoelectric power These calculations have reported that the density of states of metallic SWNTs containing nitrogen impurity donor states exhibit a broad resonance in the density of states near the chemical potential. These broad resonances have been identified as the donor bound states derived from the next highest-lying electron band. Electron states in the metallic bands that cross near E F overlap in energy with these bound states and create a broad resonance state. The conduction electrons in the metallic bands can spend part of their time in a virtual bound state of the donor. The broad resonances in the density of states D(E) overlap with the chemical potential and provide a larger nonzero value for S, consistent with an enhanced D(E). An additional contribution to the thermoelectric power may be provided by the carrier lifetime τ(e). This quantity has not yet been calculated. According to Lammert et al., 113 boron is an acceptor impurity and its broad D(E) resonances are from holes bound to the next lowest-lying hole-like band in the metallic tubes. Here the resonance is below the chemical potential and the thermoelectric power will have the opposite sign when compared to the case where donor impurities are dominant. We suspect that these metallic DOS resonances located near E F can occur for many different impurities. An additional contribution to the thermoelectric power from phonon drag will be discussed next. -69-

89 Chapter 4. Phonon Drag Thermoelectric Power of Single-Walled Carbon Nanotubes 4.1. Introduction Until now, it has been assumed implicitly that the flow of charge carriers and phonons in response to a temperature gradient could be treated separately. However, many cases have been studied where the interdependence of the flows must be taken into account, particularly at low temperatures. The resultant phenomenon is known as the phonon drag effect. 69,71 In the phonon drag effect, the flux of phonons proceeding from the hot end to the cold end of the conductor sweeps or drags additional electrons along than what could occur under normal diffusion. More specifically, phonons can impart momentum and energy to the electrons via the phonon-electron interaction. In such scattering events, phonons are absorbed (or emitted) and the electrons gain (or lose) the appropriate energy and momentum. This effect, often extending up to room temperature and beyond, may bring about an increase in the thermoelectric power, which usually takes the form of a hump in the temperature dependence of the thermopower. The phonon drag effect on the thermoelectric power of metals was first proposed by Gurevich. 115,116 The interpretation of these effects in semiconductors was given by Herring. 117 For metals, a simple derivation of the phonon drag component of the thermoelectric power S g leads to 69-7-

90 1 C g S g = α, (4.1) 3 Ne where C g is the lattice specific heat per unit volume, N is the density of conduction electrons, and the transfer factor α represents a measure of the relative probability of a phonon colliding with the conduction electrons as compared to colliding with something else (e.g., phonons, impurity centers, physical defects, etc.) The probability of phonons to collide with each other increases as the temperature increases (due to increasing anharmonic coupling), so that phonon-phonon collisions rapidly become more frequent compared to the vital phonon-electron collisions which are responsible for the phonon drag effect. Roughly speaking, the number of phonon-phonon collisions increases with T. In turn, α in Eq. (4.1) should diminish as 1/T. At sufficiently low temperatures (comparable to the Debye temperature T D ) in reasonably pure metals, phonon collisions with conduction electrons become dominant, so that α approaches unity and the phonon drag contribution increases significantly. But, on the other hand, the lattice heat capacity for bulk metals at low temperatures begins to fall off very rapidly as T 3 and thus S g decays to zero as T. A maximum in the phonon drag contribution would be expected when both the probability of phonon collisions with other phonons and that with conduction electrons are comparable. The qualitative variation in S g as a function of temperature is shown in Figure

91 Figure 4.1. Sketch of the thermoelectric power of a simple quasi-free electron pure metal as a function of temperature. A: Electron diffusion component of thermoelectric power approximately proportional to T. B: Phonon drag component with magnitude increasing as T 3 at very low temperatures (T << T D ), and decaying as 1/T at high temperatures (T > T D ) (Adapted from MacDonald 69 ). The shape of the temperature dependence of the thermoelectric power for a SWNT network (Figure 3.1) suggests that phonon drag may be responsible for the peak observed at ~ 1 K. However, the lattice specific heat of SWNTs is nearly linear in temperature 118 and does not show the strong temperature dependence required to explain the experimental data. Moreover, in the case of a metallic SWNT, if we consider only intraband scattering, the contributions from states filling the electron and the hole bands should cancel to give no net phonon drag thermopower. It is therefore clear that Eq. (4.1) for the phonon drag contribution probably cannot be successful for metallic carbon nanotubes for at least two reasons: (1) the derivation of Eq. (4.1) relies on a free, electronic band structure where transitions lie only within the parabolic bands, and (2) the dominant decay mechanism for phonons is assumed to be phonon-electron scattering. Applying Eq. (4.1) to metallic nanotubes with electron and hole bands yields a negligible contribution to the thermopower due to phonon drag because of the electron-hole mirror band -72-

92 symmetry Phonon Drag Model A more general formulation of the phonon drag is obtained by considering the phonon driven interband transitions near the Fermi level and by assuming that mechanisms other than electron-phonon scattering limit phonon lifetimes. To do this, Scarola and Mahan 119 have used a variational solution to the coupled electron-phonon Boltzmann equations developed by Baylin The phonon drag thermoelectric power, S g, can be obtained from the resulting transport coefficients. The most general form is (see derivation in Appendix 2), 122 S 2 e = Ωσd q N T ( q) kj; k' j' α ( q; kj, k' j' )[ v τ v τ V. kj kj k' j' k' j' ] (4.2) q Here σ is the electrical conductivity, d is the dimensionality of the system, Ω is the volume, N is the Bose distribution function, and τ and are, respectively, the electron relaxation time and kj v k j the group velocity at wave vector k in the band j. Similarly Vq is the phonon group velocity at wave vector q. The factor of 2 results from a sum over the spin degrees of freedom. For convenience, it has been assumed that only one phonon branch contributes to S g. In Eq. (4.2), details of the phonon-electron interaction are included in the factor α, which as mentioned before, is the relative probability that a phonon of wave vector q will scatter an electron from the state kj to the state k j. Symbolically, α = τ τ 1 pe 1 pe + τ 1 p, (4.3) where τ pe is the phonon relaxation time due to the phonon-electron interaction and τ p is the -73-

93 phonon relaxation time due to all other interactions (e.g., phonon-phonon, phonon-boundary, and phonon-impurity scattering). Using first order perturbation, one finds 121 α ( q; kj, k' j' ) = T hω τ q p ( q) I N kj, k ' j T + kj, k' j I kj, k' j, (4.4) I ( q) M = f E 2k Thω [ ε( kj) ]( 1 f [ ε( k' j' )]) N ( q) δ[ ε( k' j' ) ε( kj) ( q) ] δ( k' k, kj, k' j' q B q ) (4.5) where M ( q) is the electron-phonon coupling matrix element, f is the Fermi-Dirac distribution ε ( ) ( ) q function, and kj and E q = hω are the electron and the phonon energies, respectively. In the deformation ion model, ( ) = D( h ) 2 M q ω q where D is a constant related to the deformation energy, and other tube parameters including the radius and lattice spacing. This constant has been evaluated for (1,1) carbon nanotubes. 123 Assuming that the phonon relaxation time is dominated by mechanisms other than phonon-electron scattering, then τ p is relatively small. If phonon-electron scattering dominates phonon decay, one can show that at low temperatures, S g is nearly independent of temperature. Under this assumption, T hω τ q p ( q) N T >> k j, k ' j' I kj, k' j'. (4.6) The above approximation has been made in phonon drag studies of GaAs quantum wires. 124, Phonon Lifetimes The phonon-drag thermoelectric power depends, as we have seen, on the magnitudes of -74-

94 the various relaxation times associated with phonons, which also determine the lattice thermal conductivity. In this section, we will briefly examine the phonon interactions. Three different mechanisms contribute to the scattering of a phonon: 1. Phonon scattering by electrons. * 2. Phonon-phonon anharmonic scattering. 3. Phonon scattering by mass defects such as impurities and/or isotopes. Phonon-phonon scattering is usually the most important phonon scattering at higher temperatures. It arises from the fact that the normal modes of the lattice are weakly coupled to one another by the anharmonic part of the lattice potential. Thus, the anharmonic terms can cause transitions between acoustic phonon modes. Under certain conditions, the relaxation time due to phonon-phonon scattering satisfies 7 τ pp T 1, T > T D (4.7) and Tu τ pp exp, T < TD. (4.8) T Here T u is the temperature of the onset behavior of Umklapp processes and T D is the Debye temperature. At low temperatures, the Umklapp processes freeze out and the phonon relaxation time is dominated by the impurity scattering. The transition between the Umklapp region and the impurity scattering region manifests as a peak in the temperature dependence of the thermal conductivity. For carbon nanotubes, this peak is observed at T ~ 32 K. 8 Thus, impurity * We must be careful not to confuse the phonon-electron relaxation time, τ p, with the electron-phonon relaxation time which we will continue to describe by the generic symbol τ. -75-

95 scattering becomes the dominant scattering mechanism at low temperatures, i.e., T < 3 K for carbon nanotubes. In one dimension, Mahan 126 have found that the lifetime due to impurity scattering is ( ), 1 2 where the constant r depends on the density of defects. τ = r h ω q (4.9) 4.3. Baylin Formalism Applied to Metallic Carbon Nanotubes The above formalism was applied to (1,1) carbon nanotubes where the dispersion of electron and phonon modes is linear near E F, with group velocities υ and c, respectively. Only the two pairs of nearly linear electronic bands crossing at the zero energy point are considered. In the linear electronic band approximation, Eq. (4.2) vanishes when only intraband scattering between the electronic bands is allowed. Therefore, only the interband scattering is considered. For k T << µ << k T υ c, one has 119 B B D 2 S g = B T sgn ( µ ) ε µ B ( e 1) k T ε µ 1 +, 2k BT (4.1) where B e τcl D 2 π σh υr 2 is independent of temperature and may be taken as a fitting parameter. Here ε µ (4.11) = 2 c µ υ, τ is the electron relaxation time, T D is the Debye temperature, µ = E F is the chemical potential, and γ ( υ + c) ( υ c). The above expressions were obtained taking into account the fact that the -76-

96 scattering is strongest for phonons which have q = hc. The thermoelectric power data for a SWNT sample can be fitted with an equation of the form ε µ ( T ), S = S d + S g (4.12) where S d is given by Eq. (3.3). To determine the parameters A, B, and µ in Eqs. (3.3) and (4.1), we used c = m/s (longitudinal acoustic mode), 53 υ = m/s (1) High-T O 2 -doped (irreversible) S (µv/k) 1 5 (2) Ambient O 2 -doped (reversible) (3) Compensated -5-1 (4) K in vacuum T (K) Figure 4.2. Temperature dependence of the thermoelectric power for a purified SWNT thin film after successively longer periods of O 2 degassing at 5 K in vacuum. Curve 1 corresponds to the same sample exposed to 1 atm O 2 at 5 K for about 4 h, after being fully degassed (curve 4). The solid lines in the figure represent the fits to the data using Eq. (4.12). In Figure 4.2, we show the experimental temperature dependence (below 3 K) for the -77-

97 same sample dealt with in Figure 3.1. The solid lines in Figure 4.2 are fits to the data using Eq. (4.12). The best fits to the data are achieved for values of the parameters (A, B, and µ) given in Table 4 1. Unfortunately, the magnitude of the parameter B is difficult to estimate from first principles. The sign of the parameter A (temperature coefficient of the diffusive thermopower) indicates a positive diffusion thermoelectric power for curves 1 and 2, and a negative thermoelectric power for curve 4. The diffusion thermoelectric power for the sample represented by curve 3 is negligibly small, in agreement with previous observations that this curve corresponds to a sample almost fully compensated by the balance between an unidentified -δ positively charged donor state, tentatively assigned to wall defects, and charged species (δ = fractional charge), which can be removed by vacuum-degassing. 18 Note from Table 4 1 that both the diffusion and the phonon drag contributions to the thermoelectric power are of the same sign for a particular curve as indicated by the parameters A and B sgn( µ). The third column in Table 4 1 represents the Fermi energy, measured with respect to the band crossing point for the armchair nanotube. These values for µ are computed from the phonon drag term [Eq. (4.1)]. In principle, µ could also be calculated from the parameter A in Eq. (3.3). However, µ should be located near impurity states, and this complicates the problem considerably because impurity state resonances are possible. 112,114 The temperature dependence of S g induces a smooth change of slope or a small knee on the temperature dependence of the thermoelectric power at low T. S g, with a temperatureindependent scattering mechanism for phonons, cannot introduce a more pronounced hump or a broad peak superimposed on the linear S d. The thermoelectric power data in Figure 4.3, reported by Grigorian et al., 76 show this kind of behavior. These data were obtained from mats of as-prepared SWNT ropes using the specific catalyst indicated in the figure. Best fit curves O 2-78-

98 derived from our model [Eq. (4.12)] are given by the solid lines, except for the sample grown using Fe-Y catalyst. Table 4 1. Best fit parameter values achieved with Eq. (4.12) Curve A (µv/k 2 ) B (µv) µ (ev) (1) (2) (3) ~ 1-4 (4) Y and Ni-Y catalysts were previously assigned to the Kondo effect involving residual magnetic catalyst (e.g., Fe, Ni, Co) residing as small magnetic particles on the bundles or rope surfaces, or trapped as atoms or small clusters within the bundles. 76 The Kondo mechanism was also suggested because the particular catalyst caused a simultaneous change in the magnitude of the upturn in the electrical resistivity with decreasing temperature below ~ 1 K. 76 The drawback of the Kondo proposition of Grigorian et al. is that the thermoelectric power peak should occur at T = T K ~ E/k B, where E is the width of the Kondo resonance near E F. One might expect a stronger variation in T K with various magnetic impurities (Ni, Co, Fe), unless the effect is associated with Y, which is a common element in all three samples in Figure 4.3. That a relatively small knee was observed in the thermoelectric power of iodine-treated material (bottom trace, Figure 4.3) was tentatively explained by Grigorian et al. as to be due to the fact that iodine either complexed with the residual metal catalyst or vapor-transported the metal away as, e.g., FeI. As our fits to the data of the unpurified SWNT material of Grigorian et al. 76 indicate, The broad peaks and the small knees in Figure 4.3 for the samples grown from Fe-Y, Co- -79-

99 a phonon drag contribution superimposed on a linear metallic diffusion thermoelectric power background fits the data very well, except for the more pronounced peaks in samples grown with Co-Y and Fe-Y catalysts. 8 Fe-Y S (µv/k) 6 4 Co-Y 2 Ni-Y Iodine-treated (Fe-,Co-,Ni-Y) T (K) Figure 4.3. Temperature dependence of the thermoelectric power for SWNT mats prepared using different catalysts. The samples were not purified and contained ~ 5 at% residual catalyst. The data were measured by Grigorian et al. 76 The solid lines represent the best fits to the data using Eq. (4.12). The solid line in Figure 4.4 represents the fit of Eq. (4.12) to typical thermoelectric power data (curve 1 in Figure 4.2) of a purified SWNT material. The dashed lines in this figure represent the fits of Eqs. (3.3) and (4.1) to the data. Note that the diffusion contribution to the thermoelectric power fits well to the observed linear metallic thermoelectric power below 5 K. -8-

100 In this temperature range, the phonon drag contribution is nearly zero and increases smoothly with T before decreasing slowly above ~ 15 K. The contribution from phonon drag flattens out for large temperatures. The lack of suppression of the phonon drag at high temperatures clearly results in only a smooth change of slope or small knee, but not a pronounced peak characteristic of SWNT samples grown with Co-Y and Fe-Y catalysts. It is likely that these impurities impose a different scattering mechanism (for either electrons or phonons) in nanotubes which can significantly alter the temperature dependence of the phonon drag thermopower S (µv/k) S d S g T (K) Figure 4.4. Fits to the measured thermoelectric power data (curve 1 in Figure 4.2) using a model involving diffusion and phonon drag contributions to the thermoelectric power. The solid curve represents a fit to the data using Eq. (4.12). The dashed lines represent the contributions from S d [Eq. (3.3)] and S g [Eq. (4.1)]. -81-

101 Chapter 5. Carbon Nanotubes: A Thermoelectric Nano-Nose 5.1. Introduction Chemical doping effects on the electrical properties of SWNTs have been investigated by several groups. SWNT doping experiments with electron withdrawing (Br 2, I 2 ) and donating species (K, Cs) were first carried out on bundled SWNT mats by Lee et al. 127 and Grigorian et al. 128 Individual bundles of SWNTs have also been studied after doping in situ with potassium. 129,13 The early studies have demonstrated the amphoteric character of carbon nanotubes. In particular, Rao et al. 131 first demonstrated the amphoteric character of SWNTs by observing the sign of frequency change in the tangential Raman modes. In general, chemical doping can change the electronic behavior of SWNTs from p-type to n-type or vice versa, accompanied by orders of magnitude changes in the resistance of the material. The largest changes are expected for semiconducting nanotubes. The doping species can also absorb and charge transfer with the nanotube surfaces and/or intercalate into the interstitial sites of bundles of SWNTs. We will show that carbon nanotubes are also sensitive to gas molecule physisorption, exhibiting significant changes in their electrical transport properties. In previous chapters, we already studied how molecular oxygen adsorption (which probably is weakly chemisorbed due to charge transfer) affects the thermoelectric power and electrical resistance of carbon nanotubes. Amphoteric means that it can be doped to produce additional electrons and holes. -82-

102 Elegant work by Kong et al. 18 have found that individual semiconducting SWNT transistors (CHEM-FET) can be used in miniature chemical sensors to detect small concentrations (2-2 ppm) of gas molecules (NO 2 and NH 3 ) with high sensitivity at room temperature. Exposure to 2 ppm of NO 2 can increase the electrical conductance by up to three orders of magnitude in a few seconds. On the other hand, exposure to 2% NH 3 caused the conductance to decrease by up to two orders of magnitude. Thus, CHEM-FET sensors made from SWNTs have high sensitivity and fast response time at room temperature, which are important advantages for sensing applications. NO 2 and NH 3 are known to be an electron acceptor and an electron donor, respectively. Therefore, Kong et al. have proposed that the charge transfer between the tube wall and the adsorbed molecules was driving the observed changes in the electrical conductance of semiconducting nanotubes. Interestingly, changes in the electrical resistance and the thermoelectric power of SWNTs were observed in cases where gas adsorption (i.e., N 2, He, H 2 ) should not induce any charge transfer. 89,132 In such cases, the changes in the electrical properties upon gas adsorption were tentatively assigned to changes in the electron and the hole free carrier lifetime (or equivalently, to the carrier mobility). We have assigned these changes in the carrier lifetime to increased carrier scattering from dynamic defect states associated with either physisorbed gas molecules or collisions of the gas molecules with the tube walls. 89 Despite all these considerations, no microscopic or atomistic explanation of the transport changes induced by molecular adsorption on SWNTs has been given yet. It is reasonable to expect the effects of molecules on the transport properties of SWNTs to be an outcome of a delicate interplay among various factors including the charge transfer, possible pinning of the Fermi energy, the creation of impurity band and its location relative to E F. -83-

103 However, the contribution from each one of these factors to the transport properties of SWNTs has not been established yet. It is apparent that a quantitative understanding of their contributions to the transport properties of SWNTs is essential and timely in its own right, as well as for understanding the true intrinsic properties of SWNTs. surface channel groove pore E B =.119 ev σ = 45 m 2 /g E B =.62 ev σ = 783 m 2 /g E B =.89 ev σ = 22 m 2 /g E B =.49 ev σ = 483 m 2 /g Figure 5.1. Schematic structure of a SWNT bundle showing the sites available for gas adsorption. The dashed line indicates the nuclear skeleton of the nanotubes. Binding energies E B and specific surface area contributions σ for hydrogen adsorption on these sites are indicated. 133 The bundle structure of SWNTs produces at least four distinct sites in which gas molecules can adsorb, as shown in Figure 5.1: on the external bundle surface, in a groove formed at the contact between adjacent tubes on the outside of the bundle, within an interior pore of an individual tube and inside an interstitial channel formed at the contact of three tubes in the bundle interior. For a particular gas molecule, some sites can be excluded on size considerations -84-

104 alone (assuming the bundle or tube does not swell to accommodate the adsorbed molecule). For molecular hydrogen, calculations ignoring swelling have ordered the binding energy E B in these various sites as E B (channels) > E B (grooves) > E B (pores) > E B (surface). 56,134 Access of molecules to the internal tube pores is either through open SWNT ends or defects (holes) in the tube walls. It is commonly believed that these gateways must be produced by post-synthesis chemical treatment. Small molecules have access to the interstitial channels between nanotubes, and their adsorption there could conceivably lead to a swelling of the bundle diameter Effects of Gas Adsorption on the Electrical Transport Properties of SWNTs Figure 5.2 shows the thermoelectric power response over time of a degassed asprepared SWNT mat to 1 atm overpressure of He gas at T = 5 K (filled symbols). The initial thermopower (or S ) is due, in part, to defects in the structure, as discussed above. S is therefore expected to be sample dependent. The thermopower is seen to rise exponentially with time, saturating at 12 µv/k above the initial thermopower S. Removing the He overpressure above the SWNT mat induces an exponential decay of S with time (open symbols). The dashed lines in the figure represent exponential fits to S(t). The four-probe resistance R (not shown) was found to exhibit a similar exponential rise and fall. A concomitant increase of 1% in R was also observed. Note that the response times to these treatments are long (several hours). We interpret these long time constants as due to the slow diffusion of the gas into and out of the internal pores and the channels of SWNT ropes. Simulations by Tuzun et al. 135 of the dynamic flow of helium -85-

105 and argon atoms through nanotubes have predicted that the flow slows down rapidly when both the nanotube and the fluid are kept at high temperatures. When the tube moves (due to thermal vibrations), it perturbs the motion of the nearest fluid atoms. This causes the fluid motion to randomize faster, leading to hard collisions with the tube. Thus, fluid-nanotube collisions tend to slow down the fluid flow. In general, fluid-fluid interactions are stronger for heavier atoms, leading to the excitation of larger amplitude vibrations in the tube. This, in turn, randomizes the fluid motion faster. -25 He (1atm) T = 5 K -3 S (µv/k) -35 τ ads =.28 h τ des = 1.9 h Time (h) Figure 5.2. The time dependence of the thermoelectric power response of a SWNT mat to 1 atm overpressure of He gas (filled circles), and to the subsequent application of a vacuum over the sample (open circles). The dashed lines are exponential fits of the data (see text). 136 The dashed lines in Figure 5.2 are the fits to the S(t) data using exponential functions of -86-

106 the form, t τ S = S + S ( 1 e ), (5.1) max and t τ S = S + S e, (5.2) for adsorption and desorption, respectively. Here, S is the initial or degassed thermopower, S max is the maximum response to gas exposure (t ), and τ is the time constant for the response. The dashed curves are seen to fit the data for adsorption and desorption rather well. It should be noted that the desorption time is ~ 3 times larger than the adsorption time constant, in agreement with the results of Tuzun et al. 135 A collective effort is needed for the atoms to find their way out of the internal pore and channels. We therefore have indirect evidence for singlefile diffusion during the bundle desorption process. Figure 5.3 shows the time response of the thermopower of a vacuum-degassed SWNT mat to a sudden 1 atm overpressure of H 2 gas at T = 5 K (solid symbols). The response of the H 2 -loaded mat to a vacuum (open symbols) is also shown. With increasing exposure time to H 2, the thermopower is driven to more negative values, eventually saturating after ~ 6 h. Note that max τads 3τ des in contrast to He exposure (Figure 5.2). The negative thermoelectric response of SWNTs to H2 is truly special. Exposure of carbon nanotubes to inert gases will be discussed later in this thesis. We found that the initial thermopower of the degassed sample and its maximum change upon H 2 exposure depends somewhat on the post-synthesis processing (Figure 5.4). 132 We believe that this difference is most likely due to different concentrations of wall defects, perhaps introduced during post-synthesis (acid) purification. It is interesting to note from Figure 5.4 that the equilibration time for S(t) in 1 atm H 2 is reduced with increasing reflux time in HCl. This -87-

107 would be consistent with the introduction of physical holes in the tube wall with exposure to HCl, possibly at defect sites associated with carbidic (Ni-C) bonds to residual growth catalyst. It may also have something to do with spillover involving residual catalyst in the sample. 137 Spillover describes the catalytic process of the dissociation of molecular into atomic hydrogen. It could be that atomic hydrogen is changing the moieties attached to the tube wall H 2 (1atm) T = 5 K S (µv/k) τ ads =.81 h τ des =.28 h Time (h) Figure 5.3. In situ thermoelectric power versus time after exposure of a vacuum-degassed SWNT mat to 1 atm overpressure of H 2 at T = 5 K (solid symbols). The response of the H 2 -loaded SWNT sample to a vacuum is also represented (open symbols). The dashed lines are fits to the data using exponential functions (see text). These two observations document a rather remarkable sensitivity of the electrical transport parameters to adsorbed gases, even an inert gas such as He. Both the thermoelectric power and the electrical resistance were completely reversible in all these experiments. -88-

108 -1 (.2 at%) -2 S max = 4 µv/k S (µv/k) -3-4 (2 at%) S max = 6 µv/k -5 (5 at%) S max = 7 µv/k Time (h) Figure 5.4. In situ thermoelectric power as a function of time after exposure of degassed SWNT mats to a 1 atm overpressure of H 2 at T = 5 K (solid symbols). The open symbols are the response of the H 2 loaded SWNT system to a vacuum. Data are shown for three samples: not purified (bottom), HCl reflux for 4 h (middle), HCl reflux for 24 h (top). The dashed lines are guides to the eye. The catalyst residue in at% is indicated Thermoelectric Power from Multiple Scattering Processes As mentioned before, the electrical transport response of a bundle of SWNTs to a variety of gases can be understood in terms of the change in the thermoelectric power of the metallic tubes due to either a charge-transfer-induced change in the Fermi energy (i.e., molecule donates an electron to the conduction band) or the creation of an additional scattering channel for conduction electrons in the metallic nanotube wall. This scattering channel might be identified -89-

109 with impurity sites associated with the adsorbed gas molecules or be attributed to gas collisions. We briefly develop the equations necessary to understand this point of view. We have shown earlier that the metallic behavior of the SWNT mat thermopower is a consequence of the percolating pathways through the metallic tube components in the mats. According to the Mott relation (derived in Appendix A), the thermoelectric power associated with the diffusion of free carriers in a metal can be written compactly as a logarithmic energy derivative of the electrical resistivity ρ, S ( E) d ln ρ = CT, (5.3) de E= E F where 2 2 C = π k 3 B e. For our purposes, it is convenient to explicitly separate the contributions to the resistivity from (a) scattering intrinsic to the degassed tube, ρ (identified with phonons and permanent tube wall defects), and (b) additional carrier scattering processes associated with perturbations in the local tube wall potential due to adsorbed gas molecules or collisions of gas molecules with the tube wall, ρ I. We assume that these scattering contributions follow Mattheissen s rule, which is equivalent to the additive nature of independent scattering rates, i.e. ρ = ρ + ρ. (5.4) I If these contributions are incorporated into Eq. (5.3), it follows that S ρs + ρ I S I ρ I = = S + ( S I S ), (5.5) ρ + ρ ρ I where S 2 2 π k BT 1 dρ =, (5.6) 3e ρ de E= EF -9-

110 and S I 2 2 π k BT 1 dρ I =. (5.7) 3e ρ I de E= EF The variables S and S I are, respectively, the thermopower of the degassed tube and the additional impurity contribution from adsorbed gas molecules. It is usually understood that ρ >> ρ I, i.e., the intrinsic resistivity is much greater than the additional resistivity due to impurities. This is certainly the case here, as verified by experiment. Equation (5.5) has the same form as the well-known Nordheim-Gorter (N-G) expression, developed to explain the thermoelectric power of binary alloys. 7 In this case ρ and ρ I refer, respectively, to resistivity contributions from the host and a dopant. The significance of Eq. (5.5) for our work is that, for fixed T, the thermopower is linear in ρ I, if ( S I S ) is constant and not affected by the contact with the gas and if ρ I << ρ. This should occur if the gas contact leaves the SWNT band structure intact and E F unchanged, i.e., charge transfer between the adsorbed gas and the host lattice does not occur. This situation is consistent with physisorption, NOT a chemisorption process. If the particular molecules under study are physisorbed, i.e., van der Waals bonded to the tube walls, they will induce only a small perturbation on the SWNT band structure and an almost linear N-G plot should be obtained. If, on the other hand, the N-G plot for a particular adsorbed gas on SWNTs were strongly curved, this nonlinearity would indicate that the molecules are chemisorbed onto the tube walls. Chemisorption, of course, has a much more pronounced effect on the host band structure and/or the value of E F, and thus ( S I S ) must then depend on gas coverage or storage and the linearity of a N-G plot is lost. N-G plots, therefore, should be very valuable in identifying the nature of the gas adsorption process in SWNTs. Below we further -91-

111 develop Eq. (5.5) and the validity of these remarks will be more apparent. 1 2 O S (µv/k) NH 3 6 8x1-3 S (µv/k) -3 N 2 ρ I / ρ o He T = 5 K H x1-3 ρ I / ρ o Figure 5.5. Nordheim-Gorter plots showing the effect of gas adsorption on the electrical transport properties of a SWNT mat. The amount of gas stored in the bundles increases to the right, tracking the increase in ρ. For the H 2 data, the open circles are from the time dependent response to 1 atm of H 2 at T = 5 K and the closed circles are from a pressure study at the same temperature. The inset shows the Nordheim-Gorter plots for O 2 (electron acceptor) and NH 3 (electron donor). Note that the data in the inset, as opposed to that in the main plot, is non-linear. The non-linearity is consistent with charge transfer and Fermi energy shifts. -92-

112 In Figure 5.5, we display the N-G plots (S vs. ρ I ) for isothermal adsorption of He, N 2, and H 2 in SWNTs at 5 K. As can be seen in the figure, the data are linear for these three gases, consistent with molecular physisorption and Eq. (5.5). In the inset to Figure 5.5, we display N-G plots for NH 3 and O 2 ; these are strongly curved, indicating, as discussed above, that these molecules must chemisorb on the tube walls. These results confirm the point of view, previously discussed, that the large changes in the thermoelectric power of SWNT exposed to O 2 can be identified with chemisorption. Returning to the discussion of the linear N-G plots in Figure 5.5 (for He, N 2, and H 2 ), some interesting points remain. First, the N-G slope for He and N 2 are positive, while that for H 2 is negative. According to Eq. (5.5), the sign of the slope is determined by ( S I S ). This conclusion is best seen by writing down the form of the thermopower explicitly. We use the Mott relation [Eq. (5.3)] and the well known expression σ ( E) = [ ρ( E) ] = e v( E) D( E) τ( E). (5.8) Then, the Nordheim-Gorter equation [Eq. (5.5)] becomes S 2 2 π k BT ρ I 1 dτ I 1 dτ = S +. (5.9) 3e ρ τ I de τ de E= EF We can further understand the equation above by allowing τ j ( E) = f g ( E) 1, where f and g are functions and f is not a function of E. For impurity scattering we might expect that 1 τ ~ Nαg( E), where N is the number of molecules adsorbed per unit length of tube and α g( E) I is the scattering cross-section. With this factorization in mind we notice that j j 1 τ I dτ I de 1 = g dg de E= EF E= E F. (5.1) Therefore, the first term between square brackets in Eq. (5.9) is independent of the constant -93-

113 prefactor α of the scattering cross-section and the molecular coverage N, hence independent of ρ I, as long as E F is constant (no charge transfer). We can now anticipate either a positive or a negative slope to the data S vs. ρ I collected at fixed temperature, depending on the sign and magnitude of the derivatives in Eq. (5.9). Fundamentally different energy dependence for the electron scattering rates associated with He and H 2 adsorption sites must exist. In Figure 5.5 we also note a significant difference in slope (but not sign) for He and N 2 sites. Indeed, it is the sensitivity of the N-G plots at fixed temperature to different molecules that can be the basis for the utility of a SWNT thermoelectric nano-nose. -94-

114 Chapter 6. Effects of Molecular Physisorption on the Transport Properties of Carbon Nanotubes 6.1. Introduction Molecular adsorbates that engage in charge transfer with the nanotube wall might be expected to have a significant impact on the transport of charge and heat down the nanotube wall. Although weaker than common dopants for carbon materials, the chemical doping effects of small organic molecules are far from negligible. Recent work 138 has showed that adsorption of several small amine-containing organic molecules on nanotubes can cause significant changes in the electrical conductance of the nanotube samples. Modulated chemical gating of individual semiconducting SWNTs by these molecules has also been demonstrated. 138 In this chapter we discuss the results of a systematic study of the changes in the thermoelectric power and electrical resistance of vacuum-degassed films of nanotube bundles induced by adsorption of six-membered ring molecules (C 6 H 2n ; n = 3-6), alcohols (C n H 2n+1 OH; n = 1-4) and water molecules. For six-membered ring molecules, as n increases from 3 (benzene) to 6 (cyclohexane), π electrons are removed from the molecule. For n = 6, cyclohexane, only σ bonds remain. Thus the C 6 H 2n /SWNT is an interesting model system to study the coupling between a molecule and a carbon nanotube, as regulated by the π-electron character of the adsorbed molecule. For polar molecules, we show that the measured perturbation on the electronic properties of the nanotubes is sensitive to these molecules. Interestingly, exposure to -95-

115 water, which is also strongly polar in nature, produces virtually no change in the thermoelectric power, though the electrical resistance shows a change of ~ 4%, typical for the alcohols. We also present the results here for exposure of SWNTs to water vapor Effects of Adsorption of Six-Membered Ring Molecules The experiments began with an in situ vacuum-degassing of the SWNT film in the measurement apparatus at 5 K. After the thermopower remained constant and negative for ~ 8 h, the sample was cooled to 4 ºC and the vapors of the particular six-membered ring compounds (C 6 H 2n ; n = 3-6) were admitted. A sample temperature of 4 ºC was chosen to avoid condensation of liquid on the nanotube bundles. The molecular vapor pressure of the C 6 H 2n is essentially independent of n and equal to that of the vapor in equilibrium with the liquid (vapor pressure 12 kpa at 24 ºC). Figure 6.1(a) shows the in situ thermopower response with time to the vapors of benzene (C 6 H 6 ), 1,3-cyclohexadiene (C 6 H 8 ), cyclohexene (C 6 H 1 ), and cyclohexane (C 6 H 12 ). The sample temperature was maintained at 4 ºC. After each curve in Figure 6.1 was collected, the sample was heated again under vacuum at 5 K for a few hours in order to fully recover the original degassed values S and R. For benzene, with increasing exposure time, the thermopower increases with time from its initial degassed value at 4 ºC (S = 6.4 µv/k), eventually saturating after ~ 6 h at a positive value S max = +1.3 µv/k. Subsequent exposure to 1,3- cyclohexadiene leads to a similar time dependence of the thermopower and a saturation at S max ~ 3.6 µv/k. Cyclohexene was found to induce a smaller change in the thermopower, saturating at S max ~ 4.6 µv/k. Cyclohexane, which has no π electrons, was found to produce no -96-

116 detectable change in the thermopower. 2 (a) C 6 H 2n n = 3 S (µv/k) -2-4 n = 4-6 n = 5 n = Time (h) (b) C 6 H 2n n = 3 R (Ω) n = 4 n = n = Time (h) 4 5 Figure 6.1. In situ (a) thermoelectric power and (b) resistance responses at 4 ºC as a function of time during successive exposure of a degassed SWNT thin film to vapors of six-membered ring molecules C 6 H 2n ; n = 3-6. The dashed lines are guides to the eye. The vapor pressure was ~ 12 kpa. -97-

117 Figure 6.1(b) shows the concurrent time evolution of the four-probe resistance for exposure to each molecular vapor at 4 ºC. Exposure to benzene produces the largest change in resistance with an increase of R/R ~ 13% at saturation. 1,3-cyclohexadiene and cyclohexene induce increases in resistance saturating at R/R ~ 1% and 7%, respectively. Exposure to cyclohexane induces essentially no change in the four-probe resistance, consistent with the thermopower results. It is clear that both the thermoelectric power and the electrical resistance follow similar trends with varying n in C 6 H 2n. The results are tabulated in Table 6 1. Table 6 1. Comparison of the T = 4 ºC thermoelectric power and resistive responses of a SWNT thin film to adsorbed C 6 H 2n molecules. The vapor pressure at 24 ºC and the adsorption energy E a of the corresponding molecule (measured on graphitic surfaces) are also listed. S and R refer to the degassed film before exposure to C 6 H 2n molecules. Molecule n S max C 6 H 2n (µv/k) a S max (µv/k) ( R/R ) max (%) b p (kpa) 139 E a (kj/mol) 14,141 Benzene ±.6 1,3-Cyclohexadiene ±.8 Cyclohexene ±.8 Cyclohexane ±.7 a S max = S max S. b R max = R max R. All of these C 6 H 2n molecules are almost of the same size and have approximately the same molecular weight. We therefore suggest that the observed differences in the thermopower and the resistive responses should be attributed to the number of π electrons in the molecule. Adsorption of benzene (n = 3) induces the largest increase in the thermopower and the resistance. As the number of π electrons per molecule is reduced (increasing n), the impact of the molecular adsorption on the transport properties coefficients of the SWNT disappears. The data are -98-

118 therefore consistent with the idea of a new scattering channel created by the molecular adsorbate, and the size of the effect is apparently driven by the coupling of π electrons in the molecule to π electrons in the metallic nanotube wall. We have discussed the connection of S and R in metallic tubes in section 5.3 above. 8 7 C 6 H 6 S max (µv/k) C 6 H 1 C 6 H 8 1 C 6 H E a (kj/mol) Figure 6.2. Maximum change of the thermoelectric power of a SWNT film as a function of the adsorption energy of the adsorbed molecule. The dashed line is a guide to the eye. It is interesting to compare the values of the thermoelectric power and the resistance at saturated coverage to the heat of adsorption E a of C 6 H 2n on graphitic carbons (Table 6 1). 14,141 The tabulated data show that the maximum responses S max and ( R/R ) max at 4 ºC correlate with the adsorption energy of the C 6 H 2n molecules to a sp 2 carbon surface (see also Figure 6.2). Zhao et al. 142 have used first principles calculations to study the interaction between carbon -99-

119 nanotubes and organic molecules including benzene and cyclohexane. They have found that benzene and cyclohexane are very weak charge donors (.1-.4e) to carbon nanotubes, similar to most inorganic gas molecules. However, adsorption of benzene molecules on the carbon nanotube surface brings, as a consequence, a hybridization between molecular levels and nanotube valence bands. In contrast, the electron density in the top valence band of a carbon nanotube is localized on the nanotube and has no density on an adsorbed cyclohexane molecule. This result clearly shows that the difference between the electronic configurations of benzene and cyclohexane molecules plays a role in the perturbation of the transport properties. 2 T = 4 ºC S (µv/k) -2-4 C 6 H 6 C 6 H 8 C 6 H R/R Figure 6.3. S vs. R/R plots during exposure to C 6 H 2n (n = 3-6). The dashed curve is a fit to the data using a quadratic function. In Figure 6.3, we plot the evolution of the thermopower as a function of the fractional -1-

120 change in the four-probe resistance R/R at 4 ºC and at fixed molecular vapor pressure p ~ 12 kpa. As the coverage of the molecules on the SWNTs increases with increasing exposure time to the respective molecular vapor, both the thermoelectric power and the relative change of the resistance R/R increase, as shown in Figure 6.1. Data for the adsorption of three molecules C 6 H 2n (n = 3-5) are shown. Cyclohexane C 6 H 12 did not produce a detectable thermoelectric response (i.e., a change in S and R). Although the maximum variations in the thermoelectric power and the resistance observed in the same SWNT film sample after long term exposures to various molecules are very different, a universal behavior (i.e., independent of n) is observed for the dependence of the thermoelectric power on the change in resistance R/R (Figure 6.3). We appeal to the following expression we derived earlier, S 2 2 π kbt ρ I 1 dτi 1 dτ = S +. 3 e (6.1) ρ τi de τ de E = EF First, we associate ρ I ρ in the above equation with the experimental quantity R R, assuming that the C 6 H 2n adsorption does not change the contact resistance between bundles in the SWNT film. Therefore, if the lifetime factor in brackets is independent of the molecular coverage and the constant prefactor of the scattering cross-section, Eq. (6.1) predicts a universal relationship between S and R R. For small values of R R = ρi ρ, Eq. (6.1) predicts a linear relationship between S and R. At low coverage, i.e., for R R <. 6 we do observe an approximately linear behavior. R However, at higher values of R R, S increases faster than a linear variation. In fact, we can fit 2 the data reasonably well with the quadratic relation S a + b( R R ) + c( R = ) over most of R the data range. This quadratic function is plotted as the dashed line in Figure 6.3. The nonlinear -11-

121 behavior is tentatively assigned to multiple scattering processes associated with larger molecular coverage. Further work is necessary to understand the observed non-linearity in the S vs. R/R plots of Figure 6.3. S (µv/k) C 6 H 2n n = 3 n = 4 n = 5 S (T) T (K) Figure 6.4. Temperature dependence of the thermoelectric power of the degassed SWNT after saturation coverage of the various C 6 H 2n molecules. The dashed lines are guides to the eye. In Figure 6.4, we display the temperature dependence of the thermoelectric power after saturation coverage at 4 ºC. Before cooling the sample to collect the data, the valve to the hydrocarbon bulb was closed. As the temperature of the sample was reduced, residual vapor in the thermopower probe should first condense at the bottom of the sample compartment. Some of the molecules may condense on the saturated surface of the bundles forming a second monolayer -12-

122 over the initial primary layer. However, the effect of this second monolayer or overlayer on the transport properties should be small. As shown in Figure 6.4, the thermoelectric power S (T) for the degassed film is nearly constant down to 1 K and approaches zero quasi-linearly at lower temperatures. The temperature dependence of the thermoelectric power for the SWNT film after exposure to C 6 H 2n, can also be understood from Eq. (6.1). We assume that metallic tubes exhibit an intrinsic resistivity, i.e. ρ const, low T T, high T (6.2) and the impurity resistivity ρ I is independent of temperature. Then, we have S ( T ) S T, low T const, high T (6.3) Thus, the thermoelectric power should vanish at low temperatures and should be a constant at high temperatures, as observed in Figure Effects of Adsorption of Polar Molecules As in the case of six-membered ring molecules, the experiments started with an in situ vacuum-degassing (for ~ 15 h) of a purified SWNT thin film in the measurement apparatus at 5 K, before water or the various C n H 2n+1 OH molecular vapors were introduced. A glass bulb containing the water or alcohol was connected via a valve to the measurement apparatus [see inset to Figure 6.5(b)]. All the alcohols were spectra grade (Sigma-Aldrich, Co) and had been previously vacuum-degassed. The water was de-ionized and had a resistivity of ~ 18 MΩ-cm. -13-

123 The vapor pressure p above the SWNT sample for each liquid was that known to be in equilibrium with the liquid in the bulb at 24 ºC (Table 6 2). After the thermoelectric and resistive responses to a particular molecular vapor were recorded, the sample was then degassed in situ at 5 K again until the thermoelectric power and four-probe resistance of the sample returned to the original degassed values (S, R ). Then the same film was exposed to the next molecular vapor and so on. Data are presented here from one such SWNT thin film; other samples, prepared in the same way, showed similar behavior. Figure 6.5 shows the in situ thermoelectric power and the normalized four-probe resistance responses with time t to the vapors of methanol (CH 3 OH), ethanol (C 2 H 5 OH), isopropanol (C 3 H 7 OH), butanol (C 4 H 9 OH), and H 2 O. Dashed lines in Figure 6.5 are fits to the data using a simple exponential function S t τs = S + S ( 1 e ), (6.4) max where S is the initial or degassed thermopower, S max is the maximum response to physisorption (t ), and τ S is the time constant for the response. The same function is used for the resistive response, but R, R max, and τ R replace their counterparts in Eq. (6.4). After each set of curves in Figure 6.5 was collected for a specific adsorbate, the sample was then heated again in situ under vacuum ( 1-7 Torr) at 5 K to remove the molecules. After a few hours at 5 K, the sample was found to fully recover the original degassed values S and R. In Figure 6.5(a), it is seen that, for methanol, ethanol, isopropanol, and butanol, the thermoelectric power also rises exponentially with time from the degassed value S ~ 2.7 µv/k to a higher plateau after ~ 1 h. For methanol and ethanol, S is even driven positive, saturating at S max ~ 1.1 and.1 µv/k, respectively. Exposure to larger alcohol molecules, i.e., isopropanol and butanol, is found to lead to smaller changes in S and a saturation at S max ~.5 and

124 µv/k, respectively. 2 1 (a) C n H 2n+1 OH n = 1 S (µv/k) -1-2 n = 2 n = 3 n = 4-3 H 2 O S Time (h) (b) C n H 2n+1 OH n = n = 4 R/R 1.4 H 2 O 1.2 T 1 V 1 1. V 2 T 2.98 vacuum Time (h).8 1. Figure 6.5. Time dependence of the (a) thermoelectric power and (b) normalized fourprobe resistance responses to vapors of water and alcohol molecules (C n H 2n+1 OH; n = 1-4) at 4 ºC. The dashed lines are fit to S(t) and R(t) data using an exponential function. The inset shows a simple schematic of the measurement apparatus. The liquid temperature T 2 establishes the vapor pressure in the sample chamber which is at a temperature T 1 > T 2. The system is evacuated through V 2. After degassing, V 2 is closed and V 1 is opened. The responses of S and R are then measured simultaneously. -15-

125 Interestingly, exposure to water vapor (another small, but very polar molecule) induces virtually no change in the thermoelectric power. Bradley et al. 88 have also found very weak or no response of the thermoelectric power of mats of bundled SWNTs to water vapor. This lack of sensitivity of the thermoelectric power to water is very interesting and will be discussed later. Table 6 2 shows some relevant parameters of the molecules including the molecular projection area and the dipole moment. Table 6 2. Comparison of the T = 4 ºC thermoelectric power and resistive responses of a SWNT thin film to adsorbed water and C n H 2n+1 OH; n = 1-4. The vapor pressure p at 24 ºC, the molecular area A, the static dipole moment µ, and the adsorption energy E a of the corresponding molecule (measured on graphitc surfaces) are also listed. S and R refer to the degassed film before exposure to water and alcohols. An increase in vapor pressure did not change the values of S max or R max ; see text. Molecule S max (µv/k) a ( R/R ) max (%) b p (kpa) 139 A E a µ (Å 2 ) 143,144 (ev) (Debye) 139 Methanol Ethanol propanol Butanol Water ~ a S max = S max S. b R max = R max R. In a separate study, we have investigated the effect of an increase in molecular vapor pressure on S max and R max for each alcohol. After the values S max and R max were observed from exposure to vapor pressure in equilibrium with the liquid at 24 ºC, and before any vacuumdegassing, the bulb containing the alcohol [inset to Figure 6.5(b)] was heated from 24 ºC to a higher temperature (~ 6 ºC) to increase the vapor pressure. After ~ 3 min of exposure to the higher vapor pressure, no further changes in S and R were observed. This suggests that the values -16-

126 of S max and R max observed in earlier experiments correspond to the response of a maximum molecular coverage attainable for our bundled SWNT sample at 4 ºC. In effect, our experiments suggest that the surface saturates at 4 ºC. Also, we should mention that we have no direct evidence as to what extent the nanotubes are open or closed at their ends, although step (1) in the nanotube purification process is expected to open the tubes. Furthermore, all the molecules investigated in this work satisfy the inequality D K > d I, where D K is the kinetic diameter of the molecule and d I is the diameter of a typical interstitial channel (d I ~.21 nm for (1,1) tube bundles). This suggests that the molecule cannot easily enter the channel, unless the bundles swell to accommodate these molecules. However, they are all small enough to enter an internal pore of a (1,1) or larger tube, if the tube end is open, or if a large hole is present in the tube wall. Figure 6.5(b) shows the time-evolution of the normalized four-probe resistance. The data for each molecule type were taken concurrently with the thermoelectric power data in Figure 6.5(a). The trends for R max vs. n for the alcohols (C n H 2n+1 OH; n = 1-4) match those observed for S max [Figure 6.5(a)], i.e., exposure to methanol shows the largest change in R, with an increase of ~ 8.2 %. Ethanol, isopropanol, butanol and water induce an increase in R, with R/R saturating at 7.5 %, 6.8 %, 5.4 %, and 4.4 %, respectively. As can be seen from the fits in Figure 6.5, both R(t) and S(t) exhibit a simple exponential behavior, as described by Eq. (6.4). The time constants obtained from the fits to R(t) are all in excellent agreement with those obtained from the fits to S(t) (Table 6 3). According to simple molecular kinetic theory, the diffusion time should be proportional to the square root of the molecular mass, i.e., τ ~ M. However, the time constants obtained in our study do not exhibit any systematic dependence. This result indicates that the rate limiting step may not be ordinary diffusion, but perhaps the success rate to -17-

127 enter the tube pore through an open end. In a computational study of molecular diffusion through carbon nanotubes, Mao and Sinnott 146 have shown that the intermolecular and moleculenanotube interactions strongly affect the molecular diffusion ranging from normal mode (individual molecules can pass each other within the pore) to single-file diffusion (individual molecules cannot pass each other in the pore due to their large size relative to the pore diameter). Table 6 3. Adsorption time constants for thermoelectric ( τ S ) and resistive ( of a SWNT thin film to adsorbed water and alcohol molecules. τ R ) response Molecule τ R (min) τ S (min) τr + τ τ = S (min) 2 M M alcohol H O 2 Methanol ± Ethanol ± propanol ± Butanol ± Water The increase in R max is identified with an additional impurity scattering of conduction electrons in metallic tubes within the bundles due to physisorbed molecules. This will be discussed in detail later. Interestingly, when exposed to water vapor, the resistance of the SWNT films increased by ~ 4.4%, even though the thermoelectric power was constant and equal to its initial degassed value. Although we see no change in the thermoelectric power ( S max = ) for H 2 O, in agreement with Bradley et al., 88 we do see a strong response and saturation in R for the same exposure to H 2 O. This result is in contrast to the results of Zahab et al., 147 who have reported an initial increase of resistance of the SWNTs when exposed to water vapor, with an -18-

128 eventual crossover to a decrease of resistance for increasing exposure, reaching a resistance value lower than the starting value. We have not observed this crossover in three separate studies of H 2 O/SWNT systems. Furthermore, Zahab et al. 147 have interpreted their results on the basis that the outgassed SWNTs are p-type semiconductors and water molecules act as compensating donors. It is difficult to speculate about the different behavior on R(t) observed in our samples with respect to Zahab et al. s samples. We do note, however, that they have initially degassed their sample at 22 ºC in a vacuum of mbar for only 5 h. According to our experiments, this may not be sufficient time to remove all the weakly chemisorbed oxygen. We also do not know if they have annealed their samples at 1 ºC as we have done. In our work, we have monitored S and R vs. t during vacuum-degassing and have waited for an exponential approach to a lower plateau in S(t) and R(t) before exposing the sample to a particular vapor for study. Previous studies on the thermoelectric power behavior of SWNT films have been found to be consistent with a diffusion thermoelectric power dominated by metallic tubes in a rope. 18 Recently, a broad peak in S(T), observed below 1 K and superimposed on a linear T background, has been attributed to an additional contribution from phonon drag. 18,148 The reader is referred to section 3.3 for further details. As our measurements in this study were made at T = 4 ºC, we ignore a phonon drag contribution which is a low-temperature effect. We have discussed the connection of S and R in metallic tubes in section 6.2 above. -19-

129 S (µv/k) C n H 2n+1 OH H 2 O n = 4 n = 1 n = 3 n = x1-2 R/R Figure 6.6. S vs. R/R plots during exposure of degassed SWNT bundles to water and C n H 2n+1 OH (n = 1-4). The solid lines are linear fits to the data until saturation is established. Figure 6.6 shows the evolution of the thermoelectric power versus the fractional change in the four-probe resistance ( R/R ) at fixed temperature (4 ºC). As the coverage of the molecules on the SWNTs increases with increasing exposure time to the respective molecular vapor, both S and R R increase. It is very important to note that the data for all the alcohols show linear behavior for S vs. R/R, consistent with Eq. (6.1) (i.e., S ~ ρ I for ρ I << ρ ). 136 It should be noted that the Fermi level E F is kept constant in the derivation of Eq. (6.1). Therefore, this result [Eq. (6.1)] is appropriate for physisorption and NOT for a chemisorption process involving significant charge transfer. Thus, the linearity of S vs. R/R implies that little or no -11-

130 charge transfer is taking place between the adsorbed molecules and the SWNTs, i.e., H 2 O and the alcohols that are physisorbed onto high-t annealed films do not chemically dope the SNWTs. In our previous study on the effects of physisorption of six-membered ring molecules (C 6 H 2n ; n = 3-6) on SWNTs, we have found a slightly non-linear behavior of S vs. R/R data (Figure 6.3). This non-linear character in the C 6 H 2n /SWNT system is not well understood and we have tentatively identified it with a multiple electron scattering process. 149 From Figure 6.5, it seems that the physisorbed behavior of water on the surface of carbon nanotubes is markedly different from that of the alcohols. Adsorption of strongly polar molecules, such as water vapor, is thought to occur by hydrogen bonding on graphitic surfaces and on carbon nanotubes, 145 but it appears that the predominant interaction for all alcohols is the relative contribution (i.e., van der Waals) contribution from the alkyl chains, which increases with alkyl chain length. 15 In fact, H 2 O has a behavior different from all the molecules we have studied, i.e., a zero response of the thermoelectric power and yet a normal resistive response. At this time, all we can conclude is that Eq. (6.1) may hold the answer for our observations (i.e., S max ~ ), although we do not have a microscopic model for the scattering mechanism required to apply Eq. (6.1). From a similar study on the effects of physisorption of C 6 H 2n family of molecules on S and R for bundled SWNTs, we were able to correlate the strengths of the thermoelectric power and resistive responses to the molecular adsorption energy on graphitic surfaces. 149 In the former case, 149 all the C 6 H 2n molecules have adsorption energy E a that is related to the number of π electrons on the molecule and is therefore a measure of the coupling of the molecule to the nanotube surface. E a was then presumed to be a measure of the perturbative interaction of the gas molecules on the nanotube wall potential, responsible for the enhanced electron scattering rate

131 In the present study, all the molecules share a dipolar character, but have different projection area A (see Table 6 2). Furthermore, we have found that the surface appears saturated. We presume that the scattering rate w, and thus ρ I in Eq. (6.1), is related to the product of the molecular coverage ξ and the adsorption energy, i.e., w ~ E a ξ, (6.5) where ξ is the areal density of physisorbed molecules on the nanotube surfaces. We furthermore expect that ξ ~ 1 Aj, where A j is the projection area of the particular molecule j. Thus, from Eqs. (6.1) and (6.5) we expect that ~ βρ βe A (β is the slope of the S vs. R/R straight Smax I ~ a lines in Figure 6.6), i.e., the maximum change in S is proportional to the adsorption energy and inversely proportional to the projection area of the molecule. Yang et al. 151 have recently studied the adsorption of butanol and methanol on HiPCO (High-Pressure Carbon Monoxide Synthesis) SWNTs at 3 ºC, and have found that the number of adsorbed moles of molecules of butanol per unit weight is smaller than that of methanol. This result has been identified with the difference in molecular volumes. 151 The explanation should be equivalent to one involving molecular projection areas. Thus, in an attempt to explain the systematics of S max against the molecular properties, we have plotted S max versus the quantity β A in Figure 6.7. Interestingly, all the data fall on E a a quasi-linear curve, motivating the concept that the extra electron scattering in the nanotube wall due to physisorption is proportional to the product of the adsorption energy and the molecular coverage. The curvature of this quasi-linear curve at high β A could be an E a indication of the saturation of the thermoelectric and resistive responses. On the other hand, methanol might be too small to be expected to follow the linear trend established for butanol, -112-

132 isopropanol, and ethanol in Figure 6.7 (dashed line). 4 C n H 2n+1 OH n = 1 3 S max (µv/k) 2 n = 4 n = 3 n = 2 1 H 2 O..4.8 βe a /A (ev/å 2 µv/k) Figure 6.7. Maximum thermoelectric power change S max of a SWNT thin film successively exposed to vapors of water and alcohol molecules (C n H 2n+1 OH; n = 1-4) as a function of the quantity β E a A, where E a and A are, respectively, the molecular adsorption energy and the projection area. The solid and dashed lines are guides to the eye. In conclusion, we have utilized in situ measurements of the thermoelectric power and electrical resistance to investigate the adsorption of various polar molecules (alcohol and water) in bundled SWNTs. We observe a strong effect on both the thermoelectric power and electrical resistance for methanol, ethanol, isopropanol, and butanol. Surprisingly, water vapor does not have any effect on the thermoelectric power, i.e., S max ~, but has a significant impact on the resistance, i.e., ( R/R ) max ~ 4.4%. The fact that S max ~ may be due to a fortuitous cancellation -113-

133 of scattering terms in Eq. (6.1). We have also observed that S exhibits a linear relationship with R/R, consistent with creation of a new impurity scattering channel via physisorption, and that the slopes of the S vs. R/R data are specific to the particular molecules. In an effort to correlate what we have observed with molecular properties, we have found that, for water and the C 1 C 4 alcohols, the maximum change in the thermoelectric power is proportional to the product of the molecular adsorption energy (measured on graphitic surfaces) and the molecular coverage ~ 1 A, where A is the molecular projection area on the host surface

134 Chapter 7. Effects of Gas Collisions on the Transport Properties of Carbon Nanotubes 7.1. Introduction Recently, much attention has been focussed on the problem of gas adsorption within bundles of carbon nanotubes, as evidenced by the wealth of theoretical and computer calculations studies on the physisorption of rare gases and methane 16 in SWNTs. Phase transitions, capillary condensation, adsorption capacities, and effects of dimensionality have been investigated over a range of tube radii and temperatures. Classical and path integral molecular simulations have also been used to study physisorption and fluid dynamics of helium, 135,161,162 neon, 163,164 argon, 135, xenon, 163,164,167 krypton, 166 methane, 163,164,168 and nitrogen 165,169 in SWNTs and SWNT bundles for a range of pressures, temperatures, tube radii, and bundle structures. Adsorption capacities and molecular density distribution in different adsorption sites have been reported in these studies. Experimental studies have dealt with adsorption of helium, neon, 171,174,175 argon, 171,176 xenon, 171,174,175, kypton, 171,18 methane, 174,175, and nitrogen. 111,185 Adsorption and storage of hydrogen on carbon nanotubes have also been studied extensively. 133,186,187 There are only a few reports in the literature on collisions of atoms or molecules with carbon nanotubes. 188,189 The importance of these studies stems from the fact that production and growth of carbon nanotubes often take place in gas environments at elevated temperatures. 19 For -115-

135 instance, inert atmospheres (helium and argon in most cases) have been used for preparation of nanotubes by the arc-discharge method. 191,192 Methane, hydrogen and nitrogen atmospheres have also been used to grow carbon nanotubes In all cases, the quality, yield, and growth rate of nanotubes depend sensitively on the gas environment and the pressures. In this chapter, the results of a systematic study of the effects of collisions of inert gas atoms, CH 4, and N 2 on the electrical transport properties of SWNTs are presented. We have observed unusually strong and systematic changes in the electrical transport properties in metallic SWNTs that are undergoing collisions with inert gas atoms. At a fixed gas temperature (~ 5 K) and pressure (1 atm), the changes in the resistance and the thermoelectric power are observed to scale as ~ M 1/3, where M is the mass of the colliding gas atom (He, Ar, Ne, Kr, Xe). The results of molecular dynamics simulations carried out in collaboration with Göteborg University and Chalmers University of Technology are also presented here. They show that the radial energy transfer between the colliding atom and the nanotube also exhibits ~ M 1/3 dependence. A significant transient population of low-frequency optical phonons is observed to stem from a single collision of an atom with the nanotube wall. These long-lived vibrations may provide a new scattering mechanism needed to explain the collision-induced changes in the electrical transport Collision-Induced Electrical Transport of Carbon Nanotubes Thermoelectric power and four-probe resistance measurements were carried out on samples in the form of thin films of bundled nanotubes (CarboLex, Inc.; arc-discharge method (ARC)) and purified buckypaper (Rice University; pulsed laser vaporization (PLV)). 66 The -116-

136 arc-material was also purified, 44 and thin films were prepared by deposition of a sonicated ethanol solution containing purified SWNT bundles onto a warm (~ 5 ºC) quartz substrate. The films and buckypaper samples (Rice University) were vacuum annealed at ~ 1 C for 12 h before attaching thermocouples (chromel-au/7 at% Fe) and electrical (copper) leads with silver epoxy to four corners of the sample for the TEP and resistance measurements. The 2 mm 2 mm specimens that contained ropes of 1 s to 1 s SWNTs of nm in diameter and several microns long were placed in a turbo-pumped vacuum chamber (~ 1-7 Torr) where transport measurements were made in situ in the presence of various gases. The gases (e.g., Ar, N 2, etc.) were first passed through a purification cartridge (OT-4-SS, R&D Separations, Inc.) to remove residual O 2 and H 2 O. Details of the electrical measurements are available in Chapter 2. Before collecting data, the samples were first vacuum-degassed in situ at 5 K to remove adsorbed oxygen and water. During the vacuum-degassing process, the thermoelectric power S was observed to decrease slowly over several days from a positive initial value, change sign, and then asymptotically approach a negative value representative of the degassed state S. This behavior is in agreement with previous results on similar mats or film samples. 89,9,18 For the interpretation of the degassing effects on S and R see Chapter

137 -25 (a) Xe T = 5 K -3 Kr Ar S (µv/k) Ne He S PLV SWNTs Time (h) (b) Xe S (µv/k) Ar N 2 CH 4 He -12 S Arc SWNTs Time (h) Figure 7.1. Time dependence of the thermoelectric power response of (a) PLV buckypaper and (b) arc-derived thin film exposed to 1 atm of inert gas (closed symbols), and to subsequent application of vacuum over the sample (open symbols) at T = 5 K. The different values of S in (a) and (b) reflect differences in defect densities in the PLV and the arc-derived material (see Chapter 5)

138 In Figure 7.1 we show the reversible thermoelectric response of a vacuum-degassed PLV buckypaper (a) and an arc-derived thin film (b) to sequential exposure of a sudden pressure (p = 1 atm) of various gases at T = 5 K. The samples were degassed in vacuum at 5 K between successive exposures to the various gases. The data from exposure to the series of gases have been superimposed in Figure 7.1. The thermoelectric power of the degassed state is indicated as S. The difference between the S values (S ~ 11 µv/k: ARC; S ~ 45 µv/k: PLV) for the two samples depends on the different concentrations of tube wall defects and the functionalization introduced during growth or post-synthesis (acid) purification. 18,132 The reversible response on exposure to the various inert gases and the molecular gases N 2 and CH 4 is also shown in Figure 7.1(b) for the arc-derived film sample. Under vacuum, S can be seen to return slowly to the degassed value S. The long time constants for S > and S < of the system, which also depend on the mass of the gas atoms/molecules, are identified with the slow diffusion of gas into, and out of, the pore structure of the SWNT bundles (i.e., into and out of interstitial channels between tubes and also the internal pores of the tubes). We emphasize that the same sample was sequentially exposed to a series of gases, so that the relative response of a single sample to each gas could be observed. As can be seen in Figure 7.1, the effect of exposure to each gas (1 atm, 5 K) on S is fully reversible. That is, the system can be returned to the degassed value S. Furthermore, it is clear that the maximum change in thermopower S max increases with the mass M of the colliding gas species

139 S (µv/k) S max (µv/k) Xe Ar He p (atm) Xe Kr Ne Ar -4 He R/R Figure 7.2. S vs. R/R plots showing the effect of inert gases on the transport properties of a SWNT buckypaper prepared from PLV material. The closed symbols are from the time evolution of S and R to 1 atm of gas at T = 5 K and the open symbols are from a pressure study at the same temperature, where the maximum response of S and R to a given pressure was measured. The inset shows the pressure dependence of the maximum change of thermopower for the same sample. Figure 7.2 shows the thermopower vs. the fractional change in the four-probe resistance -12-

140 R/R for the PLV buckypaper sample at 5 K. R = R R represents the extra resistance due to the colliding atoms and R is the initial sample resistance in the degassed state. In the experiments, both S and R were measured simultaneously as they evolve with time. R (not shown) was found to exhibit the same time behavior as S, and therefore a linear relationship between them was observed, i.e., S ~ R/R. The data plotted as S vs. R/R in Figure 7.2 show that the slope is related to the mass M of the particular gas. The data represented by open circles were taken with a gas pressure p = 1 atm in the chamber and the closed circles refer to data taken at various pressures in the range < p < 2 atm (p is a measure of the collision frequency of the atoms with the nanotube walls). Since both sets of data (open and closed symbols) fall on the same line for a particular gas, it is clear that the slope of the lines S vs. R/R in Figure 7.2 depends on the mass of the gas atom/molecule and not on the chamber pressure. As discussed previously, the thermoelectric power of bundles of SWNTs should be dominated by the metallic tubes. 18 Furthermore, we have shown on the basis of Boltzmann transport theory that the linear relationship between S and R/R is consistent with the creation of a new scattering channel for the conduction electrons in the metallic tubes, provided that the nanotube Fermi energy E F remains constant. 136 In the data presented here, the scattering channel is identified with gas collisions with the tube walls. The variation in slope with mass M observed in Figure 7.2 suggests that the impulse delivered to the tube wall per collision may be an important variable. The inset to Figure 7.2 shows S max vs. p for selected inert gases (He, Ar, Xe), where S max is the maximum change of the thermopower measured relative to the degassed state (S ). We see that S max saturates with pressure at relatively low pressure (~ 1 atm) and that the saturation value depends on the gas species (e.g., He, Ar, Xe). A related saturation of the electrical resistance (not shown) was also observed. Resistivity saturation phenomena are well -121-

141 known in solid state physics, and several reviews 197,198 have been published on this topic. The basic idea usually invoked is that resistivity saturation is associated with a minimum mean free path for the conduction electrons. This saturation can be associated with many scattering mechanisms and it has been concluded that resistivity saturation usually occurs when the electron mean free path approaches the interatomic spacing in the material. 197,198 In the inset to Figure 7.2, the saturation with pressure may be due to a limiting mean free path resulting from increased collisions of the gas atoms with the nanotube wall and might represent the pressure at which neighboring transient deformations in the same tube begin to overlap Molecular Dynamics Simulations Because of the extreme flexibility of the nanotube wall, it is interesting to consider what wall deformations might be generated by the collisions of gas atoms or molecules with the tube wall. We have used molecular dynamics simulations to study this question. 189 Here we have considered the effect of approaching Xe, Ar, Ne, and He atoms on a finite length (1,) carbon nanotube at K. The (1,) nanotube is semiconducting and has a diameter of 7.83 Å. It is sufficiently small to facilitate the simulation of a large number of scattering events required for statistical analysis. Calculations were made at K so that complications from the thermal phonon background can be eliminated. Phonons generated in the dent created by a gas collision will propagate slowly away from the collision site and are absorbed in the thermal reservoirs at the tube ends. This was done by scaling the velocity of the carbon atoms at the tube ends to zero at each trajectory time step. In this way, the energy flowing along the tube axis direction was adsorbed, but not energy that flows along the tube radial or circumferential -122-

142 directions. The phonons are primarily low frequency (q = ) optical modes that have almost zero group velocity. For the dent to diffuse, it may be necessary for these phonons to decay to two oppositely directed acoustic phonons. Further details of the molecular dynamics methods are described elsewhere. 189 To study the transient character of the tube deformations (or phonons) induced by a collision, the displacements of the carbon atoms in a short (4 atoms) nanotube were followed over time. Figure 7.3 shows the power spectrum of the radial C-atom motion generated by collisions of Xe, Ne, and He during (a) the first 5 ps of the collision which includes the gas-nanotube impact and (b) during the second 5 ps. The C-atom monitored was the one closest to the impact site, but the features of the power spectra are insensitive to the C-atom chosen. The colliding atoms were incident at θ i = 45º to the tube surface normal and with an initial energy of E i = 13 kcal/mol (θ i = º is an exactly radial trajectory). The power spectra, shown in Figure 7.3, are weighted so that the area under the spectrum equals the average total energy of the carbon nanotube. The average vibrational energies of the carbon nanotube during the first 5 ps of the collision (see Figure 7.3(a)) are 4.2, 3.7, and 2.7 kcal/mol for Xe, Ne, and He, respectively. During the next 5 ps interval (see Figure 7.3), we find that the nanotube still retains 2., 2.2, and 1.8 kcal/mol for Xe, Ne, and He, respectively

143 (a) Intensity Xe Ne He (b) Intensity Xe Ne He Frequency (cm -1 ) 4 5 Figure 7.3. Computed power spectra of the radial motion of a C-atom nearest the point of contact in a (1,) carbon nanotube at K. The figure shows the phonons induced during (a) the first 5 ps of the collision (and includes the gas-tube impact) and (b) the second 5 ps after the collision. The inset to (a) shows the side view of a collision between a Xe atom (θ i = º, E i = 13 kcal/mol) and a nanotube. The inset to (b) shows the schematic representation of the tube wall deformation in response to an atom collision