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Electronic Theses, Treatises and Dissertations The Graduate School

2007 A Study of Nanostructure and Properties of Mixed Nanotube Buckypaper Materials: Fabrication, Process Modeling Characterization, and Property Modeling Cherng-Shii Yeh

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THE FLORIDA STATE UNIVERSITY

COLLEGE OF ENGINEERING

A STUDY OF NANOSTRUCTURE AND PROPERTIES OF MIXED NANOTUBE BUCKYPAPER MATERIALS: FABRICATION, PROCESS MODELING CHARACTERIZATION, AND PROPERTY MODELING

By CHERNG-SHII YEH

A Dissertation submitted to the Department of Industrial and Manufacturing Engineering in partial fulfillment of the requirements for the degree of Doctor of Philosophy

Degree Awarded: Fall Semester, 2007 The members of the Committee approve the dissertation of Cherng-Shii Yeh defended on November 14.

______Zhiyong Liang Professor Directing Dissertation ______Jim P. Zheng Outside Committee Member ______Ben Wang Committee Member ______Chuck Zhang Committee Member ______David Jack Committee Member

Approved: ______Chuck Zhang, Chair, Department of Industrial & Manufacturing Engineering ______Ching-Jen Chen, Dean, FAMU-FSU College of Engineering

The Office of Graduate Studies has verified and approved the above named committee members.

ii TABLE OF CONTENTS LIST OF FIGURES...... vi LIST OF TABLES...... ix ABSTRACT ...... x CHAPTER 1 INTRODUCTION...... 1 1.1 MOTIVATION ...... 1 1.2 TECHNICAL CHALLENGES...... 2 1.3 RESEARCH OBJECTIVES ...... 3 1.4 STRUCTURE OF THE DISSERTATION ...... 4 CHAPTER 2 LITERATURE REVIEW...... 5 2.1 STRUCTURE OF NANOTUBES...... 5 2.2 PROPERTIES OF NANOTUBES...... 9 2.1.1 Single-walled Nanotubes (SWNTs) ...... 9 2.1.2 Multi-walled Nanotubes (MWNTs) ...... 10 2.1.3 Carbon Nanofiber (CNF)...... 11 2.3 DISPERSING NANOTUBES...... 12 2.3.1 Mechanical Methods...... 12 2.3.2 Chemical Methods...... 14 2.4 CARBON NANOTUBE BUCKYPAPER ...... 16 2.5 CHARACTERIZATION OF NANOSTRUCTURE...... 21 2.5.1 Rope Size Distribution ...... 21 2.5.2 Length Distribution...... 24 2.6 SURFACE AREA OF BUCKYPAPER ...... 25 2.7 ELECTRICAL CONDUCTIVITY OF BUCKYPAPERS ...... 27 2.8 SUMMARY ...... 29 CHAPTER 3 OPTIMIZATION OF A SWNT BUCKYPAPER FABRICATION PROCESS...... 30 3.1 INTRODUCTION...... 30 3.2 METHODOLOGY...... 32 3.2.1 Characterization of Nanostructure and SWNT Rope Size Distribution ...... 32 3.2.2 Statistical Analysis of the Manufacturing Process of SWNT Buckypaper...... 34 3.3 OPTIMIZATION OF THE MANUFACTURING PROCESS OF SWNT BUCKYPAPER ...... 38 3.4 EXPERIMENTAL VALIDATIONS ...... 41 3.5 OPTIMUM DESIGN OF SONICATION USING FLOCELL...... 42 3.6 SUMMARY ...... 44 CHAPTER 4 MANUFACTURING PROCESS AND EXPERIMENTAL DESIGN OF MIXED BUCKYPAPERS ...... 46 4.1 INTRODUCTION...... 46 4.2 EXPERIMENTS...... 47 4.3 EXPERIMENTAL DESIGN OF MIXED BUCKYPAPER MANUFACTURING PROCESS...... 49 4.4.1 Factor Selections...... 51 4.4.2 Responses of Interest...... 52 4.5 EXPERIMENTAL DESIGN AND STATISTICAL ANALYSIS OF MBPS ...... 53 4.5.1 Uniformity...... 53 4.5.2 Purity ...... 55 4.5.3 BET Surface Area...... 56 4.5.4 Electrical Conductivity ...... 56 4.5.5 Nanostructure and Properties of MBP...... 57 4.6 SUMMARY ...... 59

iii CHAPTER 5 STATISTICAL CHARACTERIZATION OF NANOSTRUCTURE OF MIXED BUCKYPAPERS ...... 60 5.1 INTRODUCTION...... 60 5.2 METHODOLOGY...... 60 5.2.1 Rope Size Measurement ...... 61 5.2.2 Length Measurement...... 62 5.2.3 Pore Size Measurement...... 64 5.2.4 Expectation-Maximization Algorithm ...... 66 5.2.5 Goodness of Fit...... 70 5.3 ROPE SIZE DISTRIBUTION OF MIXED BUCKYPAPERS ...... 71 5.3.1 Mixed Rope Size Distributions of Mixed Buckypapers...... 71 5.3.2 Rope Size Distribution of SWNTs...... 75 5.3.3 Diameter Distribution of MWNTs...... 78 5.3.4 Diameter Distribution of CNFs...... 80 5.4 LENGTH DISTRIBUTION OF MIXED BUCKYPAPER ...... 81 5.4.1 Length Distribution of SWNT...... 81 5.4.2 Length Distribution of MWNTs...... 82 5.4.3 Length Distribution of CNFs...... 84 5.5 PORE SIZE DISTRIBUTION OF MIXED BUCKYPAPER ...... 87 5.5.1 Pore Size Distribution of SMBP...... 87 5.5.2 Pore Size Distribution of SFBP...... 88 5.6 SUMMARY ...... 89 CHAPTER 6 BET SURFACE AREA OF BUCKYPAPERS ...... 92 6.1 INTRODUCTION...... 92 6.2 METHODOLOGY...... 94 6.3 SPECIFIC SURFACE AREA OF NANOMATERIALS ...... 94 6.3.1 Specific Surface Area of a Single SWNT...... 95 6.3.2 Specific Surface Area of a SWNT Bundle...... 96 6.3.3 Specific Surface Area of a Multi-walled Nanotube (MWNT)...... 99 6.3.4 Specific Surface Area of a Carbon Nanofiber (CNF) ...... 102 6.4 SPECIFIC SURFACE AREA OF BUCKYPAPERS...... 103 6.4.1 Specific Surface Area of SWNT Buckypaper...... 103 6.4.2 Specific Surface Area of Mixed Buckypaper ...... 104 6.5 NANOSTRUCTURE AND BET SURFACE AREA ...... 108 6.5.1 BET Surface Area of SMBP ...... 109 6.5.2 BET Surface Area of SFBP ...... 110 6.7 SUMMARY ...... 111 CHAPTER 7 ELECTRICAL RESISTIVITY OF BUCKYPAPERS ...... 112 7.1 INTRODUCTION...... 112 7.2 EXPERIMENT...... 112 7.3 METHODOLOGY...... 113 7.3.1 Intrinsic Resistance of SWNTs ...... 114 7.3.2 Intercontact Resistance of SWNT...... 116 7.3.2.1 Intercontact Resistance and Contact Angle ...... 118 7.3.2.2 Intercontact Resistance and Contact Area...... 120 7.3.2.3 Intercontact Resistance and Type of Contact...... 121 7.3.2.4 Intercontact Resistance with Diameter and Length Effects ...... 123 7.4 ELECTRONIC CIRCUIT MODEL OF BUCKYPAPER ...... 126 7.4.1 Assumption...... 126 7.4 2 Electric Circuit Model Parameters...... 128 7.4.3 Model Development ...... 129 7.5 Case Studies...... 135 7.5.1 Diameter Effect ...... 136

iv 7.5.2 Length Effect ...... 137 7.5.3 Random and Aligned Buckypaper...... 139 7.6 SUMMARY ...... 147 CHAPTER 8 CONCLUSIONS AND FUTURE WORKS ...... 149 8.1 CONCLUSIONS ...... 149 8.2 FUTURE WORKS ...... 151 8.2.1 New Manufacturing Process Development ...... 151 8.2.2 Improve Electric Circuit Model ...... 151 REFERENCES ...... 158 BIOGRAPHICAL SKETCH...... 174

v LIST OF FIGURES

FIGURE 1. 1 STRUCTURE OF CARBON NANOPARTICLES ...... 1 FIGURE 2.1 SCHEMATIC DIAGRAM OF (A) A GRAPHENE SHEET AND (B) A NANOTUBE ROLLED UP FROM (A).....5 FIGURE 2.2 SCHEMATIC DIAGRAM OF A MWNT COMPOSE OF CONCENTRIC SWNTS ...... 5 FIGURE 2.3 CLASSIFICATION OF CARBON NANOTUBES: (A) ARMCHAIR, (B) ZIGZAG, AND (C) CHIRAL NANOTUBES...... 7 FIGURE 2.4 SCHEMATIC DIAGRAM OF A CHIRAL VECTOR ROLLING UP TO FORM A SWNT WITH DIFFERENT LATTICE VECTORS ...... 8 FIGURE 2.5 TEMPERATURE DEPENDENT ELECTRICAL RESISTANCE OF SINGLE MWNT...... 10 FIGURE 2.6 ELECTRICAL RESISTANCE VS. TEMPERATURE OF NANOFIBER MAT...... 11 FIGURE 2.7 KINEMATIC VISCOSITY VS. PERCENT WEIGHT OF SWNT ...... 14 FIGURE 2.8 CHEMICAL METHODS FOR DISPERSING NANOTUBES. (A) COVALENT SIDEWALL FUNCTIONALIZATION; (B) DEFECT GROUP FUNCTIONALIZATION; (C) NANCOVALENT EXOHEDRAL FUNCTIONALIZATION WITH SURFACTANT; (D) NONCOVALENT EXOHEDRAL FUNCTIONALIZATION WITH POLYMERS...... 15 FIGURE 2.9 SWNT BUCKYPAPER. (A) SEM IMAGE OF THE SURFACE OF BUCKYPAPER; (B) CROSS-SECTIONAL VIEW OF SWNT ROPE...... 17 FIGURE 2.10 DWNT BUCKYPAPER. (A) SEM AND LOW RESOLUTION TEM IMAGE OF DWNT BUCKYPAPER; (B) CROSS-SECTION HRTEM IMAGE TO SHOW TWO CONCENTRIC SHELLS OF DWNT...... 18 FIGURE 2.11 DWNT MEMBRANE. (A) SEM IMAGE OF A DWCNT MEMBRANE. SCALE BAR: 2 NM; (B) HIGH- RESOLUTION TEM IMAGE, SHOWING THE COAXIAL STRUCTURE OF THE DWCNTS. SCALE BAR: 5 NM...... 19 FIGURE 2.12 THE POROUS STRUCTURE FORMED BY CNFS WITHIN THE PAPER ...... 19 FIGURE 2.13 BUCKYPAPER MADE BY A MIXTURE OF MWNT+SWNT 1:1 ...... 20 FIGURE 2.14 ACTUATION CURVES OF BUCKYPAPER AT TWO DIFFERENT APPLIED VOLTAGES: (A) 0.3 V AND (B) 0.7 V...... 21 FIGURE 2.15 GAUSSIAN FIT OF SWNT DIAMETER DISTRIBUTION...... 22 FIGURE 2.16 SHIFT OF DIAMETER DISTRIBUTION IN DIFFERENT APPARATUSES...... 23 FIGURE 2.17 LENGTH DISTRIBUTION OF SWNTS ...... 24 FIGURE 2.18 (A) LENGTH EFFECT FACTOR VS. VOLUME FRACTION; (B) VOLUME FRACTION VS. ELASTIC MODULUS ...... 25 FIGURE 2.19 ISOTHERMS OF COMPOSITION VS. PRESSURE AT 80 K FOR SAMPLES OF AS-PREPARED SWNT MATERIAL, THE SWNT MATERIAL AFTER SONICATION IN DIMETHYL FORMAMIDE, AND A HIGH SURFACE AREA SARAN CARBON...... 26 FIGURE 2.20 RELATIVE RESISTIVITY OF BUCKYPAPER IN DIFFERENT DIRECTIONS AND DIFFERENT PROCESSES ...... 28 FIGURE 2.21 TEMPERATURE-DEPENDENT ELECTRICAL RESISTANCE OF THE BUCKYPAPER SAMPLE...... 29 FIGURE 3.1 MANUFACTURING PROCESS OF SWNT BUCKYPAPER ...... 31 FIGURE 3.2 SWNT BUCKYPAPER AND ITS NANOSTRUCTURE. (A) 90MM CIRCULAR BUCKYPAPER SAMPLE; (B) NANOSTRUCTURE OF A BUCKYPAPER...... 32 FIGURE 3.3 BUCKYPAPER CHARACTERIZATION USING SIMAGIS IMAGE PROCESSING SOFTWARE. (A) ORIGINAL SEM IMAGE; (B) IMAGE PROCESSING IMAGE WITH LOCAL MAGNIFIED...... 33 FIGURE 3.4 RESPONSE SURFACE OF ROPE SIZE OF SWNT BUCKYPAPER...... 38 FIGURE 3.5 DISPERSION OF NANOTUBES AT DIFFERENT SONICATION TIME...... 40 FIGURE 3.6 (A) SWNT DIAMETER VS. SONICATION TIME; (B) SWNT LENGTH VS. SONICATION TIME...... 41 FIGURE 3.7 SEM IMAGE OF NANOSTRUCTURE OF VALIDATED EXPERIMENT ...... 42 FIGURE 3.8 OPTIMIZED BUCKYPAPER (A) ROPE SIZE DISTRIBUTION; (B) ROPE SIZE STATISTICS...... 42 FIGURE 3.9 APPARATUS OF FLOCELL SONICATION...... 43 FIGURE 3.10 NANOSTRUCTURE AND ROPE SIZE DISTRIBUTION OF SWNT BUCKYPAPER: (A) SAME BATCH (SWNT-13); (B) DIFFERENT BATCH (SWNT-89); (C) DIFFERENT BATCH WITH FLOCELL SONICATION...... 45 FIGURE 4.1 COST SAVING VS MIXED RATIO OF SMBP. (0:PURE SWNT BUCKYPAPER)...... 47 FIGURE 4.2 MANUFACTURING PROCESS OF MIXED BUCKYPAPER ...... 48 FIGURE 4.3 NANOSTRUCTURE AND ROPE SIZE DISTRIBUTION OF (A) SBP (B) SMBP (1:3) AND (C) SFBP (1:3)...... 50 FIGURE 5.1SEM IMAGE PROCESSING USING SIMAGIS...... 62

vi FIGURE 5.2AFM IMAGE PROCESSING USING SIMAGIS (SCALE BAR: 10ΜM)...... 63 FIGURE 5.3 SEM IMAGE PROCESSING OF MWNT SUSPENSION ...... 63 FIGURE 5.4 PORE SIZE DISTRIBUTION CALCULATED BY BJH METHOD OF GAS SORPTION OF MBP SAMPLE....66 FIGURE 5.5 FLOW CHART OF EM ALGORITHM...... 69 FIGURE 5.7 ROPE SIZE DISTRIBUTION OF A SMBP SAMPLE WITH A MIXTURE RATIO OF 1:2...... 73 FIGURE 5.8 ROPE SIZE DISTRIBUTION OF A SFBP SAMPLE WITH A MIXTURE RATIO OF 1:2...... 73 FIGURE 5.9 SEPARATION OF ROPE SIZE DISTRIBUTIONS OF SWNTS AND MWNTS...... 74 FIGURE 5.10 SEPARATION OF ROPE SIZE DISTRIBUTIONS OF SWNTS AND CNFS ...... 74 FIGURE 5.11 WEIBULL FIT OF SWNT ROPE SIZE DISTRIBUTION IN THE SMBP WITH MIXTURE RATIO OF 1:2.76 FIGURE 5.12 WEIBULL FIT OF SWNT ROPE SIZE DISTRIBUTION IN SFBP WITH MIXTURE RATIO OF OF 1:2 ....77 FIGURE 5. 13 WEIBULL FIT OF MWNT ROPE SIZE DISTRIBUTION...... 79 FIGURE 5.14 WEIBULL FIT OF CNF ROPE SIZE DISTRIBUTION...... 81 FIGURE 5.15 WEIBULL FIT OF SWNT LENGTH DISTRIBUTION ...... 82 FIGURE 5.16 WEIBULL FIT OF MWNT LENGTH DISTRIBUTION...... 83 FIGURE 5.17 WEIBULL FIT OF CNF LENGTH DISTRIBUTION...... 84 FIGURE 5.18 (A) WEIBULL LENGTH DISTRIBUTION OF SWNTS, MWNTS, AND CNFS, (B) LOCAL MAGNIFICATION OF (A)...... 86 FIGURE 5.19 PORE SIZE DISTRIBUTION OF SMBP WITH MIXTURE RATIO OF 1:7 ...... 88 FIGURE 5.20 PORE SIZE DISTRIBUTION OF SFBP SAMPLE WITH MIXTURE RATIO 1:7...... 89 FIGURE 6.1SCHEMATIC REPRESENTATION OF THE ARRANGEMENT OF CARBON ATOMS WITHIN GRAPHIC SHEET ...... 95 FIGURE 6.2 SCHEMATIC REPRESENTATION OF THE ARRANGEMENT OF CARBON NANOTUBES OF A SWNT BUNDLE ...... 96 FIGURE 6.3 SCHEMATIC REPRESENTATION OF A TWO-LAYER BUNDLE ...... 97 FIGURE 6. 4 SCHEMATIC REPRESENTATION OF A MULTI-WALLED CARBON NANOTUBE MADE UP OF CONCENTRIC GRAPHIC SHELLS ...... 100 FIGURE 6.5 TEM IMAGES OF (A) A MWNT AND (B) A CNF...... 102 FIGURE 6.6 SPECIFIC SURFACE AREA OF SBP VS. SWNT BUNDLE DIAMETER. THE DOT REPRESENTS THE MEASURED SURFACE AREA OF THE SBP, AND THE INSET IS THE ROPE SIZE DISTRIBUTION OF THE SBP SAMPLE...... 104 FIGURE 6.7 PREDICTION OF BET SURFACE AREAS OF MBP OVER DIAMETERS OF SWNT BUNDLES, MWNTS AND CNFS, WITH A MIXTURE RATIO OF 1:3. (A) SMBP WITH RATIO OF 1:3(B) SFBP WITH RATIO OF 1:3. ..106 FIGURE 6.8 MIXED RATIOS VS. COST SAVING AND SURFACE AREAS OF SMBP. THE DASH LINE IS COST SAVING PERCENTAGE AND THE SOLID LINE IS THE ESTIMATED SURFACE AREA...... 108 FIGURE 6.9 MODEL ESTIMATION AND EXPERIMENTAL RESULT OF BET SURFACE AREA OF SMBP WITH DIFFERENT MIXED RATIOS ...... 110 FIGURE 6.10 MODEL ESTIMATION AND EXPERIMENTAL RESULT OF BET SURFACE AREA OF SFBP WITH DIFFERENT MIXED RATIOS ...... 111 FIGURE 7.1 FOUR-PROBE APPARATUS OF MEASURING RESISTIVITY OF BUCKYPAPER [171]...... 113 FIGURE 7.2 LINEAR RELATIONSHIP OF INTRINSIC RESISTANCE AND LENGTH [182]...... 116 FIGURE 7.3 CONFIGURATION OF THE DROP OF CONDUCTANCE AND CORRESPONDING INTERCONTACT POINTS [185] ...... 117 FIGURE 7.4 CONFIGURATION OF DIFFERENT TYPES OF STACKING [188] ...... 118 FIGURE 7.5 CONFIGURATION OF NANOTUBE JUNCTION [187]...... 119 FIGURE 7.6 CONTACT RESISTANCE OF (A) A (18,0) AND (10,10) JUNCTION AS A FUNCTION OF ROTATION ANGLE Θ , (B) A (10,10) AND (10,10) JUNCTION AS A FUNCTION OF ROTATION ANGLE Θ [187] ...... 120 FIGURE 7.7 RELAXED CROSS JUNCTION WITH APPLIED FORCES [191]...... 121 FIGURE 7.8 I-V CURVE OF DIFFERENT CONTACT AREA [191]...... 121 FIGURE 7.9 AFM IMAGE OF A FOUR-TERMINAL DEVICE [192] ...... 123 FIGURE 7.10 (A) I-V CURVE OF MM AND MS JUNCTIONS; (B) THE MM, (C) THE SS AND (D) THE MS JUNCTIONS [192]...... 123 FIGURE 7.11 CONFIGURATION OF CONDUCTIVITY RELATIVE TO (A) LENGTH EFFECT AND (B) DIAMETER EFFECT...... 124 FIGURE 7.12 CONDUCTIVITY VS. AVERAGE BUNDLE LENGTH [195] ...... 125 FIGURE 7.13 GENERATE NANOTUBES IN SPECIFIC AREA ...... 130 FIGURE 7.14 CREATING PERIODICY IN THE AREA ...... 130

vii FIGURE 7.15 RENUMBER PERIODIC NANOTUBES...... 131 FIGURE 7.16 FIND AND NUMBER INTERCONTACT NODES...... 131 FIGURE 7.17 FIND PATHWAYS OF CURRENT FLOW...... 132 FIGURE 7.18 CONFIGURATION OF RESISTANCE OF SPECIFIC AREA AND SAMPLE ...... 134 FIGURE 7.19 RESISTANCE VS. SAMPLE SIZE...... 135 FIGURE 7.20 DIAGRAM OF THE DIAMETER OF A SWNT BUNDLE...... 136 FIGURE 7.21 CONDUCTIVITY VS. DIAMETER OF SWNT BUNDLE...... 137 FIGURE 7.22 CONDUCTIVITY VS. LENGTH OF SWNT ...... 139 FIGURE 7.23 SEM IMAGES OF (A) ALIGNED AND (B) RANDOM BUCKYPAPER...... 140 FIGURE 7.24 NORMALIZED INTENSITY OF NANOTUBE ORIENTATION ...... 141 FIGURE 7.25 CONDUCTIVITY AT PARALLEL AND PERPENDICULAR DIRECTION WITH CORRESPONDING MAGNETIC FILED ...... 142 FIGURE 7.26 DENSITY FUNCTION OF ORIENTATION ANGLE...... 143 FIGURE 7.27 NORMALIZED DENSITY FUNCTION OF ORIENTATION ANGLE...... 143 FIGURE 7.28 COMPARISON OF THE EXPERIMENTAL RESULT AND MODEL ESTIMATION ON CONDUCTIVITY ALONG THE PARALLEL DIRECTION...... 145 FIGURE 7.29 NORMALIZED TRENDS OF THE EXPERIMENTAL RESULT AND MODEL ESTIMATION ON CONDUCTIVITY ALONG THE PARALLEL DIRECTION ...... 146 FIGURE 7.30 COMPARISON OF THE EXPERIMENTAL RESULT AND MODEL ESTIMATION ON CONDUCTIVITY ALONG BOTH PARALLEL AND PERPENDICULAR DIRECTIONS ...... 146 FIGURE 7.31 NORMALIZED TRENDS OF THE EXPERIMENTAL RESULT AND MODEL ESTIMATION ON CONDUCTIVITY ALONG BOTH PARALLEL AND PERPENDICULAR DIRECTIONS ...... 147 FIGURE 8.1 SCHEMATIC CHIRALITY OF A SWNT...... 152 FIGURE 8.2 STM IMAGE OF AN INDIVIDUAL SWNT...... 153 FIGURE 8.3 SCHEMATIC INTERPRETATION OF A BUNDLE ...... 154 FIGURE 8.4 SCHEMATIC INTERPRETATION OF INTERCONTACT BETWEEN BUNDLES ...... 154 FIGURE 8.5 INTERCONTACT OF TWO BENDING NANOTUBES...... 155 FIGURE 8.6 CONFIGURATION OF A TWO-PROBE APPARATUS...... 156

viii LIST OF TABLES

TABLE 2.1 TENSILE TEST PERFORMED ON THE COMPOSITES WITH AND WITHOUT CNF PAPER ...... 20 TABLE 2.2 RESISTIVITY OF BUCKYPAPER WITH DIFFERENT THICKNESSES, DIRECTIONS AND PROCESSES ...... 27 TABLE 3.1 FACTOR LEVEL AND RESPONSES OF THE DESIGN OF EXPERIMENT ...... 34 TABLE 3.2 ANOVA OF AVERAGE ROPE SIZE...... 35 TABLE 3.3 ANOVA OF STANDARD DEVIATION OF ROPE SIZE ...... 35 TABLE 3.4 STATISTICS OF SWNT BUCKYPAPER OVER DIFFERENT BATCHES AND PROCESSES ...... 44 TABLE 4.1 DESIGN OF SCREEN EXPERIMENTS...... 53 TABLE 4.2 ANOVA OF SWNT ROPE SIZE IN THE MBPS ...... 54 TABLE 4.3 ANOVA OF PURITY ...... 55 TABLE 4.4 ANOVA OF BET SURFACE AREA ...... 56 TABLE 4.5 ANOVA OF ELECTRICAL CONDUCTIVITY ...... 57 TABLE 4.6 REGRESSION ANALYSIS OF SURFACE AREA VS. UNIFORMITY AND PURITY ...... 58 TABLE 4.7 REGRESSION ANALYSIS OF ELECTRICAL CONDUCTIVITY VS. UNIFORMITY AND PURITY ...... 58 TABLE 5.1 CHI SQUARE TEST OF ROPE SIZE DISTRIBUTION OF SWNT IN SMBP WITH MIXTURE RATIO OF 1:2 ...... 75 TABLE 5.2 CHI SQUARE TEST OF ROPE SIZE DISTRIBUTION OF SWNT IN SFBP WITH MIXTURE RATIO OF 1:2 77 TABLE 5.3 AVERAGE ROPE SIZE OF SWNT IN SMBP...... 78 TABLE 5.4 AVERAGE ROPE SIZE OF SWNT IN SFBP...... 78 TABLE 5.5 CHI SQUARE TEST OF ROPE SIZE DISTRIBUTION OF MWNT ...... 79 TABLE 5.6 CHI SQUARE TEST OF ROPE SIZE DISTRIBUTION OF CNF...... 80 TABLE 5.7 CHI SQUARE TEST OF LENGTH DISTRIBUTION OF SWNTS...... 82 TABLE 5.8 CHI SQUARE TEST OF LENGTH DISTRIBUTION OF MWNTS ...... 83 TABLE 5.9 CHI SQUARE TEST OF LENGTH DISTRIBUTION OF CNFS ...... 84 TABLE 5.10 LENGTH DISTRIBUTIONS OF SWNTS, MWNTS AND CNFS...... 85 TABLE 5.11 CHI SQUARE TEST OF PORE DISTRIBUTION OF SMBP WITH MIXTURE RATIO OF 1:7...... 88 TABLE 5.12 CHI SQUARE TEST OF PORE DISTRIBUTION OF SFBP WITH MIXTURE RATIO OF 1:7 ...... 89 TABLE 6.1 NUMBER OF LAYERS, EFFECTIVE COEFFICIENTS OF SWNT BUNDLES AND SURFACE AREAS OF SBPS ...... 99 TABLE 7.1 CONTACT RESISTANCE WITH DIFFERENT REGISTRIES AND CONTACT AREA ...... 121 TABLE 7.2 ASSIGN RESISTANCES TO NODES ...... 132 TABLE 7.3 DIAMETER OF SWNT BUNDLE AND CORRESPONDING SAMPLE SIZE...... 136 TABLE 7.4 LENGTH OF SWNT BUNDLE AND CORRESPONDING SAMPLE SIZE...... 138 TABLE 7.5 ALIGNED FIELD, SAMPLE SIZE AND VOLUME FRACTION ...... 141 TABLE 7.6 EXPERIMENTAL RESULT AND MODEL PREDICTION OF CONDUCTIVITY OF ALIGNED AND RANDOM BUCKYPAPER (S/CM) ...... 145

ix ABSTRACT

Single-walled carbon nanotube buckypaper (SBP) is a thin film of preformed nanotube networks that possesses many excellent properties. SBP is considered to be very promising in the development of high-performance composite materials; however, the high cost of single-walled nanotubes (SWNTs) limits industrial applications of SBP materials. Mixed buckypaper (MBP) is a more affordable alternative that combines SWNTs with low-cost multi-walled nanotubes (MWNTs) or carbon nanofibers (CNFs) to retain most of the excellent properties of SBP while significantly reducing the cost.

This study proposes a manufacturing process of MBPs. The process parameters were studied through experimental design and statistical analysis. The parameters included mixing material type, mixing ratio, sonication effect, surfactant amount, and cleaning effect. The effects of the parameters on nanostructure uniformity, purity, Brunauer- Emmett-Teller (BET) surface area and electrical conductivity of the resultant MBPs were revealed. Results of the study show that all those parameters and their interactions are influential to the dispersion and uniformity of nanostructure and purity, but only mixing material type and ratio are influential to the BET surface area and electrical conductivity.

To systematically reveal the process-nanostructure-property relationship of SBP and MBP materials, the nanostructures of the buckypapers were characterized as rope size, length and pore size distributions of the nanomaterials in resultant buckypapers. These distributions featured bimodal phenomenon due to different material mixtures; therefore, the distributions were further separated into two individual ones and fitted into Weibull distributions.

Two nanostructure-property models of buckypaper materials were developed. The specific surface area model was built upon the characterization and analysis of buckypaper nanostructures. The model showed that rope size distribution and mixed ratio of nanomaterials are governing factors for the resultant specific surface area of buckypaper. The electrical conductivity model captured multiscale electrical transport

x phenomenon of nanotube networks in buckypapers. The model considered chirality, contact area, contact type, diameter, length and orientation distributions of nanotubes in buckypapers.

The proposed models not only can predict property trends correctly, but can also reveal the critical process-nanostructure-property relationships of buckypaper materials. The results are important for the further tailoring and optimization of the manufacturing process and properties of nanotube buckypapers.

Key Words: Carbon nanotubes, buckypaper, statistical analysis, uniformity, surface area, electrical conductivity

xi CHAPTER 1 INTRODUCTION

1.1 Motivation

The discovery of carbon nanotubes brought on a whole new world of nanotechnology; as a result, various forms of carbons materials were developed, which are shown in

Figure 1.1. In 1985, Smalley et al. [1] discovered a geometrical form of carbon, C60, called Bucky Fullerene, which is a convex cage of atoms with only hexagonal and pentagonal faces. In 1991, Iijima [2] observed rolled-up carbon graphite to make a tube, and discovered multi-walled nanobube (MWNT). Bethune and colleagues [3] discovered single-walled nanotube (SWNT) in 1993. Another common type of nanoparticle is carbon nanofiber (CNF), which is a cylindrical nanostructure with graphene layers arranged as stacked cup or spiral sheet of graphene planes, with the edges of the planes along the tube’s surface. CNF has been adopted more frequently into many applications because of its scale-up capability [4].

C60 SWNT MWNT CNF

Figure 1.1 Structure of Carbon Nanoparticles

Subsequent investigations have shown that carbon nanotubes (CNTs) integrate amazing rigid and tough properties, such as exceptionally high elastic properties, large elastic strain, and fracture strain sustaining capability, which seem impossible in the current materials [5-11]. CNTs are the strongest fibers known. The Young’s modulus of a SWNT is around 1TPa, which is 5 times greater than steel (200 GPa) while the density is only 1.2~1.4 g/cm3 [12]. This means that materials made of nanotubes are lighter and

1 stronger. Guo et al. [13] have measured the strength of a nanotube rope (around 15 nanotubes) as high as 63 GPa. Nanotubes also have a very high aspect ratio. The lengths of nanotubes are usually around 1μm, while the diameter for SWNT is only 0.6~1 nm (50 nm for MWNT). Recently, much longer nanotubes have been produced, reaching as long as 10~20 centimeters [14]. Apart from their well-known extremely high mechanical properties, SWNTs offer either metallic or semiconductor characteristics based on the chiral structure of fullerene [15]. They possess superior thermal and electrical properties: thermal stability up to 2800oC in a vacuum and 750oC in air, thermal conductivity about twice as high as diamond, and an electric current transfer capacity 1000 times greater than copper wire [16]. The high surface area of SWNTs is another attraction to researchers. SWNTs have a high specific surface area among carbon materials, and a single tube can reach as high as 1,300m2/g [17]. Therefore, SWNTs are regarded as the most promising reinforcement material for the next generation of high-performance structural and multifunctional composites, and evoke great interest in polymer-based composites research.

1.2 Technical Challenges

Among different types of the carbon family, SWNTs have been considered to be a very promising reinforcement material for developing high-performance nanocomposites [18]. However, due to nanometric dimensions and strong inter-tube van der Waals attractions, SWNTs have the tendency to align parallel to each other and pack into crystalline ropes [19]. Those aggregations were found to act as an obstacle to most applications, diminishing the mechanical and electrical properties of resulting composite materials. Good dispersion and uniform distribution of SWNTs are essential in achieving better mechanical properties in nanocomposites [20-21]. One effective method to achieve uniform dispersion is to preform nanotubes into nanotube buckypaper (NBP) [22]. The nanotubes were preformed into buckypapers of free-standing, well-dispersed nanotube networks to control nanotube dispersion and loading, as well as the microstructures in the resulting composites [23]. A high-quality NBP is characterized by the formation of even

2 nanotube networks with small and uniform rope size distribution. Because the NBP manufacturing process involves multiple steps and the resulting NBPs have delicate three-dimensional nanostructures, large quality variations were observed and the processes also required to be standardized and optimized [18].

Buckypapers are made up of robust networks of SWNTs, which compensates for the variations from individual nanotubes and offers interesting properties [24]. Research on dispersing SWNT bundles have been reported extensively. Initially most of the research work was performed on SWNT buckypaper (SBP) because SWNTs have superior thermal, mechanical, and electrical properties compared to other nanomaterials [25-27]. However, the expensive and delicate nanoscale of SWNTs impeded the development and commercial applications of buckypaper. An alternative was proposed, based on the success of SBP, by mixing SWNT with relatively cheaper MWNTs or CNFs, a so-called mixed buckypaper (MBP). Because MWNTs and CNFs are more affordable and also have attractive properties, MBPs seem to open another door for developing nanotube buckypapers (NBPs). Recipes of low-cost NBPs have been reported [28-29], including pure MWNT mats, pure CNF films, and mixing SWNTs with MWNTs or CNFs. These research endeavors emphasize the superior mechanical properties and lower cost, but lack reliable and reproducible quality control, detail nanostructure information and cost analysis, which are required for developing structure-property models.

1.3 Research Objectives

Buckypaper is an important material platform for developing high-performance composite materials. The ultimate goal of this research is to improve the SBP manufacturing process and introduces MBPs into applications as a flexible alternative of SBPs. Realizing the full potential of MBPs requires an intimate knowledge of these nanomaterials, including the manufacturing process, nanostructure-property relationship, models, and cost analysis. Through this investigation, the process-nanostructure-property relationships of MBPs and SBPs are understood further. Material properties including the

3 uniformity of nanostructure, purity, specific surface area and electrical conductivity were studied. Eventually, we were able to tailor the properties of MBPs through processing parameter design to achieve desired nanostructures, properties and cost efficiency.

1.4 Structure of the Dissertation

The arrangement of this dissertation is discussed in the following sequence. Chapters 1 and 2 summarize the current technologies on dispersing nanotubes and different properties of interest. In Chapter 3, optimization and evaluation of manufacturing process of SBPs are discussed. A new manufacturing process of SBP that shortens the idle time of suspension is proposed and compared with previous processing parameters. At the same time, in Chapter 4, a novel approach of producing mixed buckypaper is discussed with a broad range of mixing ratios and materials. Electronic microscopes were used to observe the nanostructure of these MBPs, and image processing software was used to characterize the nanostructures. In addition, experiments were designed in advance so that an objective analysis could be carried out with a limited number of experiments. Several process parameters of interest were selected in the design, and a statistical analysis was performed on several properties of MBPs. Effects of statistical influential factors and interactions on properties are also discussed, respectively.

Chapters 5-7 characterizes nanostructure of buckypaper and reveal the relationships of these nano-features to the resultant properties of interest, including BET surface area and electrical conductivity. The specific surface area and electric circuit models of buckypaper were proposed and compared to experimental results. The predicted results are compared to the experimental data. These models reveal the process-nanostructure- property relationships of nanotube buckypaper materials.

4 CHAPTER 2 LITERATURE REVIEW

2.1 Structure of Nanotubes

The structure of nanotubes can be thought of as a graphene sheet that has been rolled up to form a cylinder with axial symmetry along the long axis of the tube. Diameter of nanotubes can range from 0.3 nm to around 10 nm. By comparison, the length of the 5 6 cylinder can reach into a millimeter-scale, and thus having an aspect ratios of 10 ~10 Many research scientists use SWNTs to approximate one-dimensional systems in dimensionally-constricted experiments [29]. Figure 2.1 shows the schematic diagram of a graphene sheet rolled up to form a nanotube.

Figure 2.1 Schematic diagram of (a) a graphene sheet and (b) a nanotube rolled up from (a)

The other general class of nanotubes is the multi-walled variety (MWNT). For a MWNT the graphene layers are coaxially arranged around the central axis of the tube, with a constant separation between the layers of 0.339 nm [30-32]. Figure 2.2 demonstrates how a schematic diagram of concentric SWNTs becomes incorporated into a MWNT.

Figure 2.2 Schematic diagram of a MWNT compose of concentric SWNTs

5 In a SWNT, the helicity of a hexagonal structure is observed using electron diffraction techniques to register the signature spots that originate from the top and bottom of the tube. For a MWNT, constant inter-layer separation of continuous tubes is an additional constraint requiring each cylinder to have its own helicity. Though different spots appear for differing helicities, MWNTs generally show a smaller number of sets of observed spots than the number of layers. This suggests that a number of layers in a MWNT have the same helicity [11].

To understand the helical properties of nanotubes further, we can look at the periodic arrangement in structure along the tube axis. A single tube can primarily be classified as achiral (symmorphic) or chiral (non-symmorphic) [33-34]. An achiral CNF is defined by a CNT whose mirror image has an identical structure to the original one. Only two kinds of achiral nanotubes have been found to exist—“armchair” and ‘zigzag’ tubes. The names refer to the arrangement of hexagons around the circumference of the tube, as illustrated in Figure 2.3 (a) and (b), respectively. Chiral CNT exhibit a spiral symmetry whose mirror image cannot be superposed on to the original, as illustrated in Figure 2.3 (c). It is the inherent chirality of the nanotubes which leads to such a range of geometries; and thus, a wide-range of properties of the individual tubes and the composites they make up.

6

Figure 2.3 Classification of carbon nanotubes: (a) armchair, (b) zigzag, and (c) chiral nanotubes

→ The chiral vector, C h , known as the roll-up vector, was defined in terms of two

→ → primitive lattice vectors ( a1 ,a2 ) and a pair of integer indices (n, m).

→ → → C h = an 1 + m a2 (2.1) Figure 2.4 illustrates the definition of a chiral vector.

7

Figure 2.4 Schematic diagram of a chiral vector rolling up to form a SWNT with different lattice vectors

Generally, SWNTs remain straight and relatively defect-free for most of the tube length, until the ends are reached, where cones and polyhedral cap structures occur due to the presence of pentagonal defects [29]. Nanotubes with diameters less than 2nm tend to be more structurally perfect than tubes with a diameter of more than 2nm. Thus, MWNTs, which always have larger diameters, are relatively more densely populated with defects along the tube axis, as has been experimentally observed [35-37].

As it stands, knowledge of Ch and diameter are enough to derive many, if not all, the properties of individual SWNTs, and to some degree, MWNTs. The helicity information contained in Ch can be used as an indexing scheme for different nanotubes, and it is this unique feature, indigenous to carbon nanotube structures, which in part makes them so special.

It is also interesting to study the transport properties of carbon nanofibers because the structure is different to both SWNT and MWNT. Vapor-grown carbon fibers (VGCFs) are produced by depositing a layer of pyrocarbon from the vapor phase on a catalytically grown C filament. This morphology determines many properties of the fiber, since the filament is more graphitic than the pyrocarbon. VGCFs produced by a continuous process

8 are compared with those grown on a substrate [38]. CNFs have excellent graphitic crystallinity with graphite layers stacked neatly parallel to fiber axis. It has a duplex structure, a hollow and high-crystallinity graphite filament called primary carbon fiber surrounded by a pyrocarbon layer with low graphite crystallinity [39]. CNFs have several tens to hundreds of nanometer in diameter and it has been suggested that subtle differences are expected between their physical properties relative to the corresponding properties in MWNTs [40].

2.2 Properties of Nanotubes

2.1.1 Single-walled Nanotubes (SWNTs)

Due to their special structure, carbon nanotube show exceptional properties. One of the important properties of carbon nanotubes is that they can exhibit characteristics of a metal or a semiconductor. It is determined by chirality that carbon nanotube acts as metal or semiconductor. If (n+m)/3 = integer, nanotube acts as a metal; otherwise nanotube acts as a semiconductor [29]. SWNTs also show some other outstanding properties, such as electromechanic properties, and thermal properties. In this section, the initial theoretical and computation work in this area is reviewed.

SWNTs are the strongest fibers that are currently known [41]. The Young’s modulus of SWNTs is around 1.4 TPa, which is 5 times greater than steel, while density is only 1.2~1.4 g/cm3. The tensile modulus of SWNTs is measured around 65 GPa [42]. The aspect ratio of SWNTs is very high, length of SWNTs is usually 100~1000nm, while the average diameter is 0.8~1.2nm. It is well-known that SWNTs have excellent mechanical properties; thermal conductivity is about twice that of diamond and its current carrying capacity is 1000 times greater than copper wire [43]. Therefore, SWNTs are regarded as the most promising reinforcement material for the next generation of high-performance and multifunctional composites.

9 2.1.2 Multi-walled Nanotubes (MWNTs)

MWNTs, different from SWNTs, consisting of a series of coaxial graphitic cylinders, have a wide-range of size distributions. Their diameters ranges from 2~100nm, while the length is up to 10μm. Ebbesen et al. [44] measured the Young's modulus of multiwall nanotubes, which is close to 1TPa. Tensile strength is around 20 GPa, with a specific surface area around 300-400 g/cm3. When compared to SWNTs, MWNTs do not present such a remarkable electrical conductivity as SWNTs do. However, Saito et al. [45] reported metallic as well as semiconducting temperature dependence of MWNTs. Salvetat and Forr´o [46-47] reported electric transport measurements for MWNTs. The electrical current of contacted MWNTs has been demonstrated to flow through the outermost carbon tube at low temperatures. From a large number of MWNTs, each with four low-ohmic contacts, the average contact resistance is 3.8 kΩ with a standard deviation of 5 kΩ at room temperature. For all measured MWNTs, it was found that the resistance was around 10 kΩ at low temperatures and similar temperature dependence. The resistance increased by a factor of around 2 to 3 if the temperature was lowered from room temperature to a few Kelvin. Figure 2.5 demonstrates the temperature dependence of MWNTs.

Figure 2.5 Temperature dependent electrical resistance of single MWNT

10 2.1.3 Carbon Nanofiber (CNF)

CNFs are much smaller than conventional continuous carbon fibers (5~10μm) but significantly larger than carbon nanotubes (1~10nm). The average diameter of CNFs is around 70~200nm with a length of about 50~100μm. Mechanical properties are lower than carbon nanotube family. Tensile strength is up to 7 GPa, with a modulus around 600 GPa. However, the cost of CNFs is more economical than SWNTs and MWNTs, and the production rate is much faster. Hammel et al. [48] has considered CNFs as relatively thick nanotubes in the composite area. Without compromising on composite properties compared to SWNT and MWNT composites, CNFs have a relatively short to realistic time to market and low cost scenarios. The electrical conductivity of CNFs is still under investigation. Mendoza [49] explained the electrical conductivity of a CNF mat within the Luttinger liquid model. A very good fit to the experimental data is found if one assumes that the body of the nanofiber behaves as a Luttinger liquid system, but it is necessary to add a linear temperature contribution to the electrical resistance to take into account the interconnections between the CNFs in the mat. The electrical resistance ranging from 0.4 kΩ to 0.32 kΩ from temperatures 100 to 400K, as demonstrated in Figure 2.6.

Figure 2.6 Electrical resistance vs. temperature of nanofiber mat

11 2.3 Dispersing Nanotubes

Nanotubes can be synthesized using many different methods, and three major methods are electric-arc discharge, laser vaporization, and chemical vapor deposition [29]. Detailed procedures and parameters will not be discussed in this section; however, the synthesized nanotubes are physically entangled and require a dispersion procedure to detangle nanotube aggregation for further use.

There are two different approaches for nanotube dispersion: mechanical methods and chemical methods. The mechanical techniques involve physically separating the tubes from each other, but this can also fragment the tubes and decrease their aspect ratio. Chemical methods often use surfactant or chemical functionalization on the tube surface, which in turn can affect surface energies as well as wetting or adhesion characteristics, leading to the prevention of re-aggregation. Both mechanical and chemical methods can alter the aspect ratio distribution of the nanotubes, resulting in changes of their dispersions. To utilize the superior properties of nanotubes, uniform dispersion techniques need to be developed.

2.3.1 Mechanical Methods

To physically separate tubes that are bundled together by van der Waals forces, requires an external mechanical force. Three main mechanical processes have been partially successful in dispersing tubes in various media, including ultrasonication, milling, and shear mixing.

Ultrasonication can disperse nanotubes in a solvent, and two main instruments are used: ultrasonic bath and ultrasonic horn. The ultrasonication bath has a higher frequency (40-50 kHz) than horns (25kHz), and the ultrasonic process has three particular mechanisms: bubble nucleation and subsequent implosion (cavitation), localized heating, and the formation of free radicals [50].

12 SWNT lengths decrease only after the bundle size has gotten smaller during sonication [51]. Ultrasonication creates expansion and peeling or fractionation of MWNT graphene layers. The destruction of MWNTs seems to initiate on the external layers and travel towards the center. It has been reported that the nanotube layers seem quite independent, so MWNTs would not only get shorter, but actually get thinner with sonication time [52].

The mixing method uses a rotating cylinder filled with grinding media, such as iron balls, to wear down the aggregated tubes. Ball-milling can be used to break up nanotube aggregates and reduce nanotube length and diameter distributions [53]. There is also substantial evidence that the ball-milling technique is among the most destructive toward nanotubes and produces a large amount of amorphous carbon [54-55]. Another gentler route to break up large nanotube aggregates is to use a traditional mortar and pestle before more aggressive physical or chemical treatments are employed. There are few reports on the subject of grinding CNTs to decrease their size, and it is more destructive than any other methods. The grinding process cuts and bends the SWNTs, both lengths and bundle diameters were noticeably reduced [52]. MWNTs were also reported to be hand-ground with mortar and pestle [50]. The MWNTs were mixed with a small amount of toluene, creating a thick paste. The paste was ground for approximately an hour. The length and diameter were measured before and after grinding. The MWNT aggregates existed before and after the grinding process, but the average diameter decreased by a factor of 5. The process changed the aspect ratio of the aggregates, but might have also produced significant defects in the MWNTs.

Shear mixing is another option with which nanotube aggregates can be mechanically forced apart in a viscous monomer or polymer solvent. The technique allows us to directly disperse nanotubes into a host matrix without chemical modification, and nanotubes are prevented from re-aggregation by viscous forces. The viscosity of the dispersion increases significantly along with the increase the SWNT loading; and therefore, the concentration of SWNTs in viscous resin matrix is usually lower. Figure 2.7 illustrates the kinematic viscosity of SWNT dispersed in a synthetic oil, four

13 centistokes poly(a-olefin) with the aid of a nonionic dispersant at 40oC and 100oC. A significant increase of viscosity was observed when the concentration of SWNTs increased to 0.1%. The increase in temperature also helped keep the SWNTs dispersed at a lower viscosity system [52].

Figure 2.7 Kinematic viscosity vs. percent weight of SWNT

2.3.2 Chemical Methods

The sp2 hybridized structure of nanotubes makes them insoluble in common organic solvents. Therefore, choosing a proper functionalization may provide another practical route to disperse these nanomaterials. There have thus been many interests in mastering chemical functionalization of the nanotube surface to make tubes more soluble and/or separable in a given solvent. A chemical route toward dispersion would be scalable by default. It would also ensure homogeneous dispersion throughout the solvent and thus a host matrix, allowing a good deal of technical flexibility in polymer-nanotube composite manufacturing. Two general classes of chemical dispersion methods are considered, covalent and non-covalent. Figure 2.8 demonstrates the different types of

14 functionalization to improve functionalities of SWNTs through specific modifications [56].

Figure 2.8 Chemical methods for dispersing nanotubes. (a) covalent sidewall functionalization; (b) defect group functionalization; (c) nancovalent exohedral functionalization with surfactant; (d) noncovalent exohedral functionalization with polymers.

Covalent methods refer to functionalization treatments involving covalent bonds on the nanotube surface, which disrupts the nanotube delocalized electrons and bonds, and hence incorporates other species across the exterior of the tube shell. The mechanisms may preferentially occur at defect sites, or where tube curvature is highest, i.e., tube-ends. Examples of covalent functionalization are illustrated in Figure 2.8 (a) and (b). Acid treatment is commonly used for the thermal oxidation or decomposition of nanotubes [57-58]. Oxidation may separate SWNTs into individual tubes [59-60]. Furthermore, oxidation also cuts the nanotubes in sites with high-structure damage or defect density, which leads to the production of shorter nanotubes [61-63]. Also, smaller tubes are usually more reactive than tubes with a larger diameter, due to the greater strain on the bonds in the small tubes [64-65].

15 Non-covalent functionalization generally involves the use of surfactant to bind ionically to the nanotube surface and prevent the tubes from aggregating, as illustrated in Figures 2.8 (c) and (d). This can be a much less destructive route toward dispersion than covalent bonding. The role of a surfactant is to produce an efficient coating and induce electrostatic or static repulsions that could counterbalance van der Waals attractions [66]. [66] The electrostatic repulsion provided by adsorbed surfactants stabilizes the nanotubes against the strong van der Waals interaction between the tubes, hence preventing agglomeration. Surfactants have been used to disperse carbon nanotubes in several cases [67-70]. Some examples of commonly used surfactants are sodium dodecyl sulfate (SDS), both for SWNTs [71-73] and MWNTs [74-75], and Triton X-100 [73-74,76] for SWNTs. Single-walled carbon nanotubes have also been dispersed using lithium dodecyl sulfate (LDS) as surfactant [77-78]. In contrast, poly(vinyl alcohol) (PVA) is not efficient for stabilizing the tubes [72]. It has also been reported that neither negatively charged SDS, positively charged cetyltrimethyl ammonium chloride (CTAC) and dodecyl-trimethyl ammonium bromide (DTAB), nonionic pen-taoxoethylenedodecyl ether (C12E5), polysaccharide (Dextrin), nor long chain synthetic polymer poly(ethyl-ene oxide) (PEO) could act as efficient dispersing agents for SWNTs in aqueous solutions [79]. However, Gum Arabic (GA) is reported to be an excellent stabilizer for SWNTs in water. Both SDS [80-82] and Triton X-100 [83-86] have previously been used as surfactants for carbon black. A problem with surfactant-induced dispersions is finding a feasible way to remove the surfactant from the final product [87]. It is believed residual impurities will obstruct properties of materials and therefore need to be cleaned well.

2.4 Carbon Nanotube Buckypaper

SWNTs are considered very promising reinforcement materials for developing high- performance nanocomposites [88]. However, due to their nanometric dimensions and strong inter-tube van der Waals attractions, SWNTs have a tendency to pack into crystalline ropes [89]. These aggregations act as an obstacle to most applications, diminishing the mechanical and electrical properties of resulting composite materials.

16 Uniform dispersion of SWNTs is essential in achieving high mechanical properties in nanocomposites [90-91]. One effective method to achieve uniform dispersion is to preform nanotubes into a thin film, which is called buckypapers [92]. The nanotubes are uniformly preformed into buckypapers, which consist of free-standing, well-dispersed nanotube networks to control nanotube dispersion, loading and nanostructures for use in composites [93]. Liu [94] converted nearly endless and highly tangled single-walled nanoropes into shorter, dispersed pipes in buckypaper, as shown in Figure 2.9. The stable SWNT suspension could be made by cutting nanotubes with the assistance of an anionic surfactant such as sodium dodecyl sulfate (SDS) and nonionic surfactant Triton X-100. By vacuum filtrating suspension through PTFE membrane, a uniform network of nanotube buckypaper can be obtained [95]. After SWNT buckypaper was introduced, several applications were developed using SWNT buckypaper, including field-emission, actuators, and EMI shielding [96-100].

(a) (b) Figure 2.9 SWNT Buckypaper. (a) SEM image of the surface of buckypaper; (b) cross-sectional view of SWNT rope.

Muramatsu [111] developed buckypaper materials fabricated by filtering a stable suspension of double-walled carbon nanotubes (DWNTs), as shown in Figure 2.10. The DWNT solution was sonicated without the use of any surfactant. By filtering the suspension, a black DWNT buckypaper can be obtained. The DWNT buckypaper is thin, flexible and tough enough mechanically to be folded. The expected high mechanical and

17 electrical properties when combined with their high surface area and high structural integrity make the DWNT buckypaper a promising material for numerous applications.

(a) (b) Figure 2.10 DWNT BuckyPaper. (a) SEM and low resolution TEM image of DWNT buckypaper; (b) cross-section HRTEM image to show two concentric shells of DWNT.

Wei et al. [112] reported different novel techniques to produce an ultra-thin DWNT membrane only a few tenths of a nanometer in thickness, as shown in Figure 2.11. By post-purifying thick DWNT buckypaper with acid solution and neutralization with distilled water, and the resulting thin film can be collected from the water surface. The thickness of the DWNT film was effectively reduced by the H2O2 and HCl purification processes as the amorphous carbon and metal catalyst particles were successfully removed. The resulting membranes were so thin that they appeared to be fully transparent. The DWNT membrane showed a tensile strength from 680 to 850 MPa and an average strength of about 750 MPa. The Young’s modulus of the DWNT membrane ranges from 10.8 to 12.2 GPa with a high tensile strain of 7.6 to 11%.

18

(a) (b) Figure 2.11 DWNT membrane. (a) SEM image of a DWCNT membrane. Scale bar: 2 nm; (b) High- resolution TEM image, showing the coaxial structure of the DWCNTs. Scale bar: 5 nm.

Gou [113] reported the nanocomposite integration of CNF paper into traditional glass fiber-reinforced composites. Figure 2.12 shows the pore structure of CNF buckypaper. The CNF paper was employed as an inter-layer and surface layer of composite laminates to enhance the damping properties. Experiments conducted using the nanofiber composite indicated up to 200-700% increase of the damping ratio at higher frequencies. Table 2.1 compares the tensile test of composites with and without reinforcing CNF paper.

Figure 2.12 The porous structure formed by CNFs within the paper

19 Table 2.1 Tensile test performed on the composites with and without CNF paper

Vohrer et al. [114] introduced low-voltage artificial muscles using buckypaper consisting of a mix of SWNTs and MWNTs. SWNTs and MWNTs were mixed with a ratio of 1:1, and were mixed in 1% SDS solution by sonication and filtered, as shown in Figure 2.13. The dried buckypaper sample was 75-80 μ m in thickness and 3.75 cm in diameter. The actuation response was compared with that of mixed buckypaper at 0.3 v and 0.7 v . The mixed buckypaper showed a fast actuation. These results indicate a clear voltage dependency of the actuation amplitude within a certain region.

Figure 2.13 Buckypaper made by a mixture of MWNT+SWNT 1:1

20

Figure 2.14 Actuation curves of buckypaper at two different applied voltages: (a) 0.3 V and (b) 0.7 V.

2.5 Characterization of Nanostructure

In each step of an advanced nanotechnology system, characterization of the nanomaterials and nanostructures is a critical phase. In fact, it is crucial to perform a quantitative evaluation on the characteristics of the nanostructure and develop our fundamental understanding of process-nanostructure-property relationships. The following section summarizes efforts on the characterization of nanostructures of nanotubes and buckypapers.

2.5.1 Rope Size Distribution

The excellent properties of nanotubes are usually referring to an individual SWNT in most cases. Nanotubes tend to form into large bundles due to strong inter-tube van der Waals forces which reduce the properties of nanotubes. It is believed that breaking nanotube bundles through different kinds of dispersion methods can improve the properties of nanotube significantly. For example, the elastic modulus of a nanotube bundle less than 10nm can reach as high as 290 GPa, which is comparable to the conventional IM7 carbon fiber [115]. Researchers have been relating rope size of nanotubes to their excellent properties.

A good example was carried out by Dresselhaus et al. [116] when they characterized the synthesized SWNTs by the catalytic decomposition of hydrocarbon. The SWNTs were observed via high-resolution transmission electron microscope (HRTTM), and the

21 diameters of the SWNTs were measured and fitted into a Gaussian distribution, as shown in Figure 2.15. The average diameter of the SWNTs was 1.69nm with standard deviation of 0.34nm, indicating larger SWNTs than those synthesized by other techniques and are promising for gas storage application.

Figure 2.15 Gaussian fit of SWNT diameter distribution

Dr. Smalley’s group [117] also characterized purification process of SWNTs using Scanning Electron Microscopy (SEM), Transmission Electron Microscopy (TEM), X-ray Diffraction (XRD), Raman scattering, and Thermal Gravimetric Analysis (TGA). In Figure 2.16, the diameter distribution of SWNTs made in the 2” system at 1200oC was compared with that made in the 4” system at 1100oC. The materials made under the distinct conditions encountered in these systems caused a change in the diameter distributions such that the peak in the 4” apparatus material was at around 1.2 nm rather than the 1.4 nm obtained in the 2” apparatus.

22 (a) Counts

(b) Counts

Figure 2.16 Shift of diameter distribution in different apparatuses

Raman scattering is another powerful tool to probe diameter of nanotubes. It has been experimentally demonstrated that Raman scattering is dominated by a resonant process which has been associated with optical transitions between the 1D state in the electronic band structure. In the low-frequency range (100 to 300cm−1), the measurement of the A1g radial breathing mode (RBM) is a convenient way of probing the SWNT diameter distribution [118]. However, no clear quantitative agreement has been found

23 between the distribution of diameters estimated by Raman and other techniques, such as diffraction or electron microscopy [119].

2.5.2 Length Distribution

Another important character in understanding carbon nanotube synthesis and industrial application is the accurate measurement and characterization of nanotube length. Wang et al. [120] characterized the dispersion of nanotubes using Atomic Force Microscopy (AFM) and SIMAGIS software which was used to quantify the large population of nanotubes. The length distribution of nanotubes was fitted into a Weibull distribution and further used to estimate nanotube reinforced composite stiffness, as illustrated in Figures 2.17Figure 2.17 and 2.18.

Figure 2.17 Length distribution of SWNTs

24

Figure 2.18 (a) Length effect factor vs. volume fraction; (b) volume fraction vs. elastic modulus

The results showed AFM and SIMAGIS can be used to quantify the length of SWNTs. The Weibull distribution is reasonable for describing the SWNT length distribution. The statistical distribution of the SWNT length helps to reveal the micromechanical characteristics of SWNTs and accurately predict the performance of the final product, especially in the SWNT-reinforced polymer composite. The theoretical prediction shows that the length effect factor for modulus tends to decrease with the rise of the rope diameter and increase with enhanced SWNT loading, which leads to change in the final material properties.

2.6 Surface Area of Buckypaper

Nanotubes have large aspect ratios, large surface areas, and are attractive materials for new types of nanofluidic devices, absorbents, and catalysis supports in many applications.

The Brunauer-Emmett-Teller (BET) method is widely used to calculate the specific surface areas of nanotubes by the physical adsorption of gas molecules [121-124]. The BET theory is based on estimating the monolayer capacity from multilayer adsorption data at relative pressures generally ranging from 0.05 to around 0.3 [125]. The pressure is increased then decreased incrementally, and the gas adsorption and desorption is

25 measured proportional to the change of equivalent pressure. From the gas sorption isotherm, the surface area can be calculated.

SWNTs have large aspect ratios and the BET surface area of a single SWNT can reach as high as 1300 m2/g [125]. However, Figure 2.19 shows the BET surface area decreased as SWNTs formed into large bundles, to 285 m2/g. MWNTs had BET surface area as high as 1000 m2/g with acid treatment [126]. It was found that CNFs were remarkably oxidation-resistant, and the BET surface area had slightly changed after 10- 90 min of oxidation, which increased from 20–25 m2/g to 41–73 m2/g [127]. However, it was found that the impurities that aggregated on the bundle surface of SWNTs reduced the active surface, and the capacitance of buckypaper [128].

Figure 2.19 Isotherms of composition vs. pressure at 80 K for samples of as-prepared SWNT material, the SWNT material after sonication in dimethyl formamide, and a high surface area saran carbon.

26 The buckypaper also has a high BET surface area and flexible networks, which can be utilized for applications of energy generation, biochemistry, gas storage and other nanotechnologies.

2.7 Electrical Conductivity of Buckypapers

Electrical conductivity of nanomaterials is another important research topic. SWNTs possess such superior electrical conductivity that their electric current-carrying capacity is 1000 times greater than copper wire [129-133]. The average contact resistance of MWNTs is 3.8 kΩ and is temperature dependent [4]. The electrical resistance of CNFs varied from 0.4 kΩ to 0.32 kΩ from temperatures 100 to 400K [49]. Hone et al. [134] reported the electrical conductivity of aligned buckypaper. Figure 2.20 demonstrates that the electrical resistivity exhibited moderate anisotropy with respect to the alignment axial, and had temperature dependencies in the two orientations. In all cases, resistivity was higher in the perpendicular direction than in the parallel direction, reflecting the structural anisotropy, see Table 2.2. Especially in the parallel direction, the resistivity is close to that of individual SWNTs, which was typically displayed by four-probe method resistivity 100~ 200μOhm-cm.

Table 2.2 Resistivity of buckypaper with different thicknesses, directions and processes

27

Figure 2.20 Relative resistivity of buckypaper in different directions and different processes

Kulesza et al. [135] measured the active energy of buckypaper from 300 to 800 K. As Figure 2.21 shows, two distinct regimes of the electrical conductivity are observed: 12 meV at moderate temperatures and 745 meV at high-temperatures. Inset is the resistance vs. probe distance plot used to estimate the contribution of the contact resistance to the overall resistance. At moderate temperatures of 300 to 500 K, the activation energy is 90 MeV, and while at high temperatures of 500 to 800 K, the activation energy increased up to 370 MeV. The latter activation energy is consistent with that obtained by using the parallel resistance model (EA = 399 meV, the asymptotic resistance R ∞ = 0.93Ω , and the linear resistance coefficient α = 53 Ω / K).

28

Figure 2.21 Temperature-dependent electrical resistance of the buckypaper sample

2.8 Summary

Due to its perfect molecular structure, nanoscale dimension and large aspect ratio, the excellent properties of nanomaterials have inspired a great deal of researches in different areas. One of the major challenges in nanotube research is to overcome inter- tube van der Waals forces. Therefore, several dispersion methods have been introduced, including mechanical and chemical dispersion. Buckypaper is an effective method to utilize dispersed networks of nanotubes. Different recipes for buckypapers have been reported and proved useful in many applications. Characteristics including rope diameter, length and pore distribution can be well-captured by analytical tools and further used to develop process-nanostructure-property relationship models of nanotube buckypaper. BET surface area and electrical properties are two important properties of buckypaper in many applications including fuel cells, highly conductive composites…, etc.

However, there is still a lack of systematic efforts to investigate manufacturing processes and nanostructures of buckypaper materials. More importantly, the process- nanostructure-property relationship of buckypaper needs to be studied further.

29 Chapter 3 Optimization of a SWNT Buckypaper Fabrication Process

3.1 Introduction

The molecular perfection of SWNTs generates great interest because of their unique electrical [136] and mechanical properties [137], along with their outstanding chemical stability [138]. SWNTs are considered to be a very promising reinforcement material for developing high-performance nanocomposites [139]. However, due to their nanometric dimensions and strong inter-tube van der Waals attractions, SWNTs have a tendency to pack into crystalline ropes [140]. These aggregations act as an obstacle to most applications, diminishing the mechanical and electrical properties of resulting composite materials. Uniform dispersion of SWNTs is essential in achieving high mechanical properties in nanocomposites [141-142]. Nanotube buckypaper is an effective method to achieve uniform dispersion and control of the nanostructure. A high-quality buckypaper is characterized by the formation of even nanotube networks with small and uniform rope size distribution. Yet, the buckypaper manufacturing process involves multiple steps with a wide-range of processing parameters, and the resulting buckypapers have delicate nanostructures, which lead to large variations in the quality of buckypaper [143]. From previous studies [144], several influential factors of buckypaper fabrication were discussed, including vacuum pressure, concentration, sonication level and time, and surfactant types. Suspension concentration refers to the content of the nanotubes suspended in water. The more nanotubes involved, the harder the SWNT bundles are to be broken. Sonication power and duration are two important factors. Ultrasound can break large bundles of nanotubes into small bundles and individual nanotubes, but excessive sonication can result in fragmenting nanotubes, which reduces their aspect ratios and diminishes their mechanical properties. Vacuum pressure controls suspension flow through the membrane during filtration. The applied vacuum pressure determines filtration time; the shorter the filtration time, the better the suspension stability, dispersion and production rate. Three types of selected surfactants were used to disperse nanotubes: sodium dodecylbenzene sulfonate (NaDDBS), Polyoxyethylene t -octylphenol (Triton X-

30 100) and Sodium Dodecyl Sulfate (SDS). Two quantitative responses were used to determine the quality of the buckypapers: average rope size and standard deviation of rope size of the preformed nanotube networks. The average rope size evaluated the dispersion effect of the process, while the standard deviation of rope size measured the rope size uniformity. These performances were considered the most significant indication of high-quality buckypapers. The manufacturing process of SWNT buckypaper is summarized in Figure 3.1, with factors of interest indicated in bold and italic fonts.

Ground into powder manually in 3 inches mortar Sonicating for 10 min SWNT Powder with power 30~50 BuckyPearl TM for 10 min with 10~20 ml deionized water watts

Add deionized water Intensive Sonication for Add Surfactant (E) according to different Time (C) and 0.4% by volume and Concentration (B) Power (D) add water to 100 ml

Sonicating for 20 min Filtration with Use water 250 ml to with power 30~50 watts Vacuum Pressure(A) wash out surfactant

Dry NBP in air for 12 Dry in vacuum Use acetone 50ml Storage hr, and then peel off oven for 15 min from membrane to wash out water

Figure 3.1 Manufacturing process of SWNT buckypaper

31 A statistical analysis was performed on these factors towards average rope size and standard deviation of rope size. Results showed that not only were those factors influential, but factor interactions were highly influential to the nanotube rope size in buckypapers [145]. Triton X-100 was found to be the most effective surfactant to disperse nanotubes, and higher sonication level and time were also helpful to the dispersion. With a sufficient concentration of SWNTs in suspension, uniform dispersion was achieved and high-quality buckypaper can be made by filtrating suspension through moderate vacuum pressure. This chapter will discuss the response surface methodology utilized to optimize buckypaper quality, where average rope size of SWNT was used as a quality index.

3.2 Methodology

3.2.1 Characterization of Nanostructure and SWNT Rope Size Distribution

SWNT rope size is considered an important indication of dispersion in buckypaper Small average rope size and standard deviation indicate uniform SWNT networks throughout the buckypaper sample.

90 mm

(a) (b) Figure 3.2 SWNT buckypaper and its nanostructure. (a) 90mm circular buckypaper sample; (b) Nanostructure of a buckypaper.

32 Scanning Electron Microscopy (SEM) JSM-7401F from JEOL was used to observe the nanostructure of the produced buckypapers and characterized dispersion effects and final quality of buckypaper. Figure 3.2 shows a 90mm circular buckypaper sample produced and SEM image of its nanostructure.

An SIMAGIS system from Smart Image Technologies carried the measurement of nanotube rope size and its distribution. The system automates measuring the sizes of nanotubes on the SEM images. Nanotube diameters can be determined using the SIMAGIS’ Carbon Nanorope Analysis Module, which yields an accurate measure of rope size distribution [146]. The software reveals the ropes on a SEM image with the contour mask and skeleton of the rope images. The mask, including the contour and skeletal lines of the ropes, was superimposed over the initial image. The contour line defines the boundary of each rope, and the skeletal line finds the center of each rope and then calculates the rope diameter. Figure 3.3 demonstrates the image processing of SIMAGIS. Analytical results included statistics of minimum, maximum, average, and median value of the rope size statistical distribution, which provided objective information of rope size distribution in buckypapers.

(a) (b) Figure 3.3 Buckypaper characterization using SIMAGIS image processing software. (a) Original SEM image; (b) Image processing image with local magnified.

33 3.2.2 Statistical Analysis of the Manufacturing Process of SWNT Buckypaper

The experimental design including five factors and two responses was employed to study the process. The resulting design was a 24-1 × 31 mixed-level fractional factorial design, representing 4 two-level factors and 1 three-level factor. The superscript minus one denotes a half fraction was used instead of the full factorial experimental design. Additionally, center points with 2 replicates at each surfactant level were added to evaluate model adequacy and repeatability of the process. Hence, the design included 30 experimental runs, listed in Table 3.1.

Table 3.1 Factor level and responses of the design of experiment Factors Low Center High Responses Vacuum Pressure Avg: Average A 9 19 29 (Hg/inch) Rope Size (nm) Std dev: Concentration B 10 40 70 Standard (mg/l) Deviation of Sonication Power C 6 8 10 Rope Size (nm) (level) Sonication Time D 20 60 100 (min)

E Surfactant Type S3 S2 S1

A statistical analysis was carried out using the commercial software package Design Expert 6.0 developed by State-Ease, Inc. Table 3.2 and Table 3.3 show the analyses of variance (ANOVA) of rope size average and standard deviation.

34 Table 3.2 ANOVA of average rope size Response: Average Rope Size Sum of Mean Source DF F Value Prob > F Squares Square Model 1070.17 14.00 76.44 22.86 < 0.0001 significant A 7.93 1.00 7.93 2.37 0.1476 B 24.99 1.00 24.99 7.48 0.0170 C 29.12 1.00 29.12 8.71 0.0112 D 15.47 1.00 15.47 4.63 0.0509 E 39.93 2.00 19.97 5.97 0.0145 AB 270.34 1.00 270.34 80.85 < 0.0001 AC 271.77 1.00 271.77 81.28 < 0.0001 BD 293.89 1.00 293.89 87.90 < 0.0001 BE 326.16 2.00 163.08 48.77 < 0.0001 CD 369.54 1.00 369.54 110.52 < 0.0001 CE 340.72 2.00 170.36 50.95 < 0.0001 Residual 43.47 13.00 3.34 Lack-of-Fit 35.10 11.00 3.19 0.76 0.6915 not significant

Std. Dev. 1.82 R-Squared 0.96 (nm) Mean (nm) 13.79 Adj R-Squared 0.92

Table 3.3 ANOVA of standard deviation of rope size Response: Standard Deviation of Rope Size Sum of Mean Source DF F Value Prob > F Squares Square Model 180.70 14.00 12.91 15.21 < 0.0001 significant A 0.41 1.00 0.41 0.48 0.4993 B 5.93 1.00 5.93 6.99 0.0202 C 5.89 1.00 5.89 6.94 0.0206 D 1.21 1.00 1.21 1.43 0.2531 E 5.44 2.00 2.72 3.21 0.0738 AB 34.99 1.00 34.99 41.24 < 0.0001 AC 44.55 1.00 44.55 52.52 < 0.0001 BD 43.70 1.00 43.70 51.52 < 0.0001 BE 67.54 2.00 33.77 39.80 < 0.0001 CD 64.09 1.00 64.09 75.54 < 0.0001 CE 60.68 2.00 30.34 35.76 < 0.0001

35 Table 3.3 (Con’d) Residual 11.03 13.00 0.85 Lack-of-Fit 9.91 11.00 0.90 1.61 0.4443 not significant

Std. Dev. 0.92 R-Squared 0.94 (nm) Mean (nm) 6.04 Adj R-Squared 0.88

Both statistical analyses indicated that all factors of interest were statistically influential to the average rope size of buckypaper samples, but the interactions of these factors were more influential than the individual factors. In other words, the interactions among the vacuum, suspension concentration, and sonication effect and surfactant type are more dominant to the dispersion and quality of buckypaper than factors themselves.

Among ten two-factor interactions, only five interactions were highly significant, including AB (vacuum pressure×concentration), AC (vacuum pressure×sonication level), BD (concentration × sonication time), BE (concentration × surfactant), CD (sonication level× sonication time) and CE (sonication level× surfactant). If shorter filtration time was desired, then vacuum pressure can be set at a higher level along with high suspension concentration to ensure the dispersion quality. Sonication level had a slightly different effect at high vacuum pressures. Suspension concentration was a variable, but longer sonication time can disperse nanotubes in a diluted suspension better than in a highly concentrated suspension. However, short sonication time did not significantly change the dispersion effect over different suspension concentrations. Sonication level and time were two factors that controlled the sonication effect. Higher power and longer sonication can achieve the highest sonication effect; yet, short sonication time did not change the dispersion effect as sonication level. On the other hand, three types of surfactant had varied dispersion effects on different suspension concentration and sonication effect. Overall, surfactants Triton X-100 had more stable dispersion effects over different concentrations, but surfactants NaDDBS and SDS underwent a dramatic change of effects over different concentrations. The responses of rope size standard deviations show similar trends.

36 Based upon the above observations, Triton X-100 was selected because of its uniform dispersion effect and repeatable results. Therefore, two regression models based on average rope size and standard deviation of rope size were obtained. Two linear regressions only include statistical influential factors and factor interactions.

Average rope size = 12.172 (3.1) - 1.041×Vacuum Pressure + 0.030×Suspension Concentration - 0.180×Sonication Level + 0.325×Sonication Time - 0.013×Vacuum Pressure×Suspension Concentration + 0.201×Vacuum Pressure×Sonication Level + 0.003×Suspension Concentration×Sonication Time - 0.059×Sonication Level×Sonication Time

Standard deviation of rope size = 5.943 (3.2) + 0.437×Vacuum Pressure + 0.002×Suspension Concentration - 0.090×Sonication Level + 0.137×Sonication Time - 0.005×Vacuum Pressure×Suspension Concentration + 0.082×Vacuum Pressure×Sonication Level + 0.001×Suspension Concentration×Sonication Time - 0.024×Sonication Level×Sonication Time

Regression models 3.1 and 3.2 provided quantitative analyses of the buckypaper manufacturing process, and desired rope size can be predicted and achieved by controlling those processing factors and their interactions. Smaller average rope sizes and standard deviations represented uniform and efficient dispersion effects, an indication of high-quality buckypapers. Figure 3.4 shows the response surface based on the regression model (3.1). Process parameters clearly have a significant impact on buckypaper quality.

37 X = C: Sonication Level Y= D: Sonication Time

Actual Factors A: Vacuum Pressure= 16 B: Suspension Concentration= 40 Average Rope Size (nm) E: Surfactant = Triton X-100

D: Sonication Time (min)

C: Sonication Level

Figure 3.4 Response surface of rope size of SWNT buckypaper

3.3 Optimization of the Manufacturing Process of SWNT Buckypaper

Based on the regression models, a steepest ascent method of response surface methodology [147] was used to optimize the processing parameters to achieve better buckypaper quality, consisting of small average rope sizes and small standard deviation rope sizes. The method of steepest ascent is constituted by a sequential experimentation attempted to improve response used to search for a region that optimized the response. Optimization of steepest ascent of the buckypaper process was carried out by Design Expert 6.0 and suggested the following process settings based on the regression models:

Vacuum pressure: 16 Hg/inch Suspension concentration: 40 mg/L Sonication level: 10 Sonication time: 100 min Surfactant: Triton X-100

The model predicted an average rope size of 6.54 nm and standard deviation of 2.6 nm for the buckypaper with the optimized parameters. The suggested level settings were close to the current experimental levels of five factors, and the improved properties can

38 be achieved by slightly modifying processing parameters. By reducing vacuum pressure to 16 Hg/inch, keeping concentration at 40 mg/l, increasing sonication levels and selecting surfactant Triton X-100, the dispersion effect and buckypaper quality can be significantly improved.

Comparing optimized parameters to current ones, sonication time was increased from 15 min to 100min and filtration pressure was reduced from 26 inch-Hg to 16 inch- Hg. In a filtration process, buckypaper was formed like a cake next to membrane. In the beginning, a skin layer begins to be formed next to the filter membrane, which is about 10 to 20% of the entire cake thickness but exhibits about 90% of the overall filtration resistance. Therefore, by reducing filtration pressure, the moderate pressure gives the momentum of filtration flow, and build up a compact cake that still allows successive SWNT to filtrate through the membrane.

Longer sonication times help in breaking nanotube aggregations into smaller bundles. However, intensive sonication also breaks nanotubes into segments. Figure 3.5 shows an AFM image of SWNT suspension at different sonication times. Large bundles were observed at 10 to 20 minutes of sonication time. At 100 minutes, SWNT bundles obviously shortened. After 200 minutes, the length of the SWNTs significantly decreased. Figure 3.6 compares SWNT diameter and length over sonication time. It is observed that SWNT bundle size and length decreased effectively during 10 to 100 minutes of sonication; after 100 minutes, the bundle size of the SWNTs didn’t change much, but length kept decreasing to less than 500 nm. This demonstrated that sufficient sonication is crucial, which can keep nanotubes dispersed without too much segmenting the length of nanotubes.

39 (a) (b)

(c) (d)

Figure 3.5 Dispersion of nanotubes at different sonication time. (a) 5min; (b) 10min; (c) 100 min; (d) 200 min. (Scale bar: 10μm).

From the optimization of the SBP manufacturing process, uniform SWNT networks of buckypaper can be obtained by keeping most of the current operating parameters and slightly increasing the sonication time and decreasing filtration pressure. The optimum SWNT rope size predicted by response surface is 6.54nm, and the result was validated with experiments discussed in section 3.4.

40 (a)

Diameter (nm) Diameter (nm) Sonication Time (min) (b)

Length (nm)

Sonication Time (min) Figure 3.6 (a) SWNT diameter vs. sonication time; (b) SWNT length vs. sonication time.

3.4 Experimental Validations

Validation experiments were conducted according to the optimized condition proposed in previous discussion. The filtration vacuum pressure was reduced to 16 inch- Hg, and sonication time was increased to 100min. The resultant buckypaper sample was characterized and analyzed by the same procedure. Figure 3.7 shows the nanostructure of buckypaper from SEM and exhibited uniform SWNT networks. Figure 3.8 shows the analytical results of rope size and statistics from SIMAGIS. The average rope size was 5.67 nm and the standard deviation was 2.57 nm. Estimation error of the average rope size was 13.3% and 1.2% for the standard deviation of rope size, which falls within 90%

41 of the prediction interval. Therefore, the regression model is capable of predicting the quality of buckypaper.

Figure 3.7 SEM image of nanostructure of validated experiment

Number of measurements 75113 Minimum value, nm 1.59 Maximum value, nm 16.67 Average value, nm 5.67 Median value, nm 5.40 Std. dev., nm 2.57

(a) (b) Figure 3.8 Optimized buckypaper (a) rope size distribution; (b) rope size statistics.

3.5 Optimum Design of Sonication Using FLOCELL

To avoid variations from different nanotube batches, previous studies only focused on one batch of raw material (SWNT-13, HPMI). Applying optimum processing parameters on different batches of SWNTs (SWNT-89, HPMI) were attempted. The

42 average rope size of resultant SBP increased 48% (8.38nm), which means unknown variation between the batches still significantly impacts the final quality of the resultant buckypaper.

Therefore, FLOCELL sonication was introduced to further improve dispersion [148]. In liquid, the rapid vibration of the sonication tip causes cavitation, the formation and violent collapse of microscopic bubbles. The collapse of thousands of cavitation bubbles releases tremendous energy in the cavitation field. Objects and surfaces within the cavitational field are sonicated. The FLOCELL has a high-intensity cavitational field, and because it is a compact system (1.5” X 1.5” X 14”) and contains one of the smallest horn sizes (1/2”), a higher chance of a direct cavitational effect will result under applied pressure. By producing suspension when it is needed, the chance of the solution forming agglomerates becomes reduced significantly. Figure 3.9 shows the apparatus of FLOCELL sonication.

Figure 3.9 Apparatus of FLOCELL sonication

Therefore, the same manufacturing process was applied to SWNT-89 suspension, but FLOCELL was added after 100min of tip sonication, and filtration immediately took

43 place after FLOCELL sonication. The average rope size of the resultant SBP decreased to 7.7nm. This implied that FLOCELL sonication is capable of dispersing nanotubes more effectively. Table 3.4 compares SWNT rope distribution over different manufacturing processes and Figure 3.10 demonstrates the nanostructure of three SWNT buckypapers from different batches with the same optimum processing parameters and process with FLOCELL added.

Table 3.4 Statistics of SWNT buckypaper over different batches and processes

SWNT-13 SWNT-89 SWNT-89

(same batch) (different batch) FLOCELL Number of measurements 75113 72001 74632 Minimum value (nm) 1.59 2.34 2.3 Maximum value (nm) 16.67 33.33 25.2 Average value (nm) 5.67 8.38 7.7 Median value (nm) 5.4 7.94 6.9 Standard deviation (nm) 2.57 3.88 3.8

3.6 Summary

This chapter goes over the manufacturing process of SWNT buckypaper, characterizing the nanostructure and analyzing processing parameters to optimize quality of buckypaper materials. Average and standard deviation rope size of SWNTs were considered two indices of buckypaper quality. The regression models of manufacturing process were proposed based on statistical study. These two regression models exhibited similar trends of the effects of statistically influential factors and factor interactions. Average rope size was used to optimize process parameters to achieve high-quality buckypapers. The predicted results were compared to experimental validations and in agreement. FLOCELL filtration was introduced to the manufacturing process which can achieve better dispersion and keep suspension fresh from re-aggregation throughout filtration process. The SWNT network in buckypaper was observed by using the optimized parameters and FLOCELL apparatus.

44 (a)

(b)

(c)

Figure 3.10 Nanostructure and rope size distribution of SWNT buckypaper: (a) same batch (SWNT- 13); (b) different batch (SWNT-89); (c) different batch with FLOCELL sonication.

45 Chapter 4 Manufacturing Process and Experimental Design of Mixed Buckypapers

4.1 Introduction

Inspired by the success of SWNT buckypapers (SBP) in many applications, different recipes of producing nanotube buckypapers were proposed to improve the properties of buckypapers. Mixed buckypaper (MBP) is one of the alternatives in maintaining superior properties while keeping costs down.

MWNTs and CNFs are also nanoscale materials and possess exceptional mechanical, electrical, and thermal properties, and the cost of these materials is significantly lower when compared to SWNTs. They demonstrate excellent potential for mass-production in broad applications. However, they are usually difficult to form into flexible buckypapers by themselves without the addition of chemical bonders or agents. The additional chemical bonders or agents are undesirable due to the difficulty of eliminating the residual chemicals from MWNT and CNF films. The residual chemical bonding agents may also detrimentally affect the material properties of the resulting film. It therefore would be desirable to provide a new method for fabricating MWNT and CNF material films that does not require the use of chemical bonding agents. In this research, we propose a cost-efficient method of mixing SWNTs with MWNTs or CNFs to produce buckypapers without the addition of chemical bonders or agents [149]. Figure 4.1 shows the cost-saving capability of MBP against different mixed ratios. In the calculation, the cost of SWNT is $500/gram, MWNT is $7/gram and CNF is $0.21/gram. It can be seen that more than 80% cost reduction can be achieved by a MBP with a SWNT-MWNT ratio of 1:5.

46 Cost Saving(%)

Mixed Ratio

Figure 4.1 Cost saving vs mixed ratio of SMBP. (0:pure SWNT buckypaper).

MBPs have drawn a great deal of attention because of their cost-saving advantages; however, the manufacturing process of MBPs needs an in-depth understanding. Based on the success of SBPs, many researchers investigated different factors towards quality improvement. In this research, we are not only interested in the factors affecting the quality of dispersion, but also the properties of MBPs comparing to SBPs. To investigate these important aspects of MBPs systematically, we used statistical approaches to model the manufacturing process and the relationship between nanostructures and properties. These statistical analyses were used as screening analyses, and directed us towards a correct understanding of how the nanostructure affects the properties of resulting MBPs, as well as search for reasonable models to explain the unique phenomena of MBPs and the physics behind them. Later on, more details on nanostructure and its effect on surface area and electrical conductivity of buckypaper will be discussed in Chapters 6 and 7.

4.2 Experiments

The goal of this research is to investigate the process and nanostructure-property relationships of buckypapers. High noise and variation were expected since the delicate nanoscale materials and structures, as well as complicated manufacturing steps, were involved. We standardized the procedure to eliminate some variance in the system [144].

47 The standardized procedure of producing SBP and MBP were summarized into several steps and are shown in Figure 4.2. The factors of interest are in bold fonts.

1. Weigh SWNT and mixed material according to different mixed ratio. 2. Grind mixed material well in mortar. 3. Add surfactant to grind material and de-ionized water. 4. Dilute suspension by adding water to 250ml, 500ml, and 1000ml sequentially. 5. Sonicate suspension. 6. Filtrate through nylon filter membrane. 7. Wash out surfactant from sample. 8. Dry sample. 9. Peel off buckypaper sample from the membrane.

Material Slight sonication for Weigh mtls Ground into SWNT powdering effect for 3 according to ratio powder in mortar MWNT/CNF for 5 min min

Dilute suspension by Intensive Add Surfactant adding water Sonication

Dry MBP in air for 12 Filtration thr membrane Wash out hr, and then peel off with vacuum pressure surfactant Storage from membrane

Figure 4.2 Manufacturing process of mixed buckypaper

Figure 4.3 shows the SEM images of SBP, SMBP with ratio of 1:3 and SFBP with ratio of 1:3, respectively. SWNTs typically have small diameters (~ 1-2 nm) and large aspect ratios, but usually form into various sizes of bundles in buckypapers (~5-15 nm in

48 diameter). The average diameter of SWNT ropes is 10nm in the SBP. MWNTs have relatively larger diameter (inner diameter ~3-10 nm, outer diameter ~10-30nm, length ~1~10μm) and wide distribution, and the diameter overlapped with that of the SWNT bundles (10~20nm) in the SMBP. It is not easy to distinguish SWNTs from MWNTs in the image. However, the MWNTs can be characterized by their contorted structure compared to SWNTs. The estimated average diameter of SWNT bundles in SMBP is 10nm, and estimated average diameter of MWNT is 25nm.

Comparatively, SWNTs are more distinguishable in the SFBP because of their distinctive rope sizes. The SEM image exhibits that large CNFs were wrapped by SWNT ropes. The pore spaces have various sizes that vary much more than that of the SMBP. The estimated average diameter of the SWNT bundles is 10nm, and the estimated average diameter of the CNFs is 90 nm.

4.3 Experimental Design of Mixed Buckypaper Manufacturing Process

Many researchers have investigated the buckypaper manufacturing process. Gou [150] investigated the effects of suspension concentration, sonication and surfactant. Suspension concentration refers to the content of nanotubes suspended in water; the more nanotubes involved, the harder the bundles were to be broken. Sonication power and duration are two important factors. The ultrasound can break large nanotube bundles into small bundles or even individual nanotubes. Thess et al. [151] stated that strong power and long sonication time can efficiently disperse nanotubes, but excess sonication could result in damaging or breaking the nanotubes into pieces and reducing their mechanical property. Vacuum pressure drives suspension flow through the membrane during filtration of NBP fabrication [152]. The applied vacuum pressure determines the filtration time – the shorter the filtration time, the better the suspension stability, dispersion and production rate. Wang et al.[153] investigated the surfactant effect in the manufacturing of NBPs and provided an intensive simulation of the surfactant molecules interactions [147,154]. Our previous study also included some of these factors and found that all of these factors were highly influential towards the quality of the SBPs.

49 (a)

20

15

10

5

0

(b)

25

20

15

10

5

0

(c)

Figure 4.3 Nanostructure and rope size distribution of (a) SBP (b) SMBP (1:3) and (c) SFBP (1:3).

50 Therefore, to investigate the MBP manufacturing process further, a selection of factors and response of interests will be discussed in detail in the following sections.

4.4.1 Factor Selections

The high cost of SWNTs challenges the commercialization of SBP in real-world applications. Comparatively, MWNTs and CNFs also offer exceptional mechanical, electrical, and thermal properties, but their cost is substantially less than that of SWNTs. Therefore, MWNT and CNFs were chosen as two mixing materials in MBP.

The mixed ratio, defined as weight ratio of SWNTs to MWNTs or SWNTs to CNFs, varies within range from 1:1 to 1:10. Theoretically, more SWNTs should result in better properties but high cost. However, the relationship between ratios and properties need to be further studied. It is noticed that, the portion of SWNTs in MBPs is under a technical constraint. MBPs with SWNTs less than 10% may have networks too weak to be peeled off from the filtration membrane. Therefore, we selected ratios between 1:1 and 1:10 as our experimental operating region.

It is known that ultrasonication is an effective method to disperse nanotubes mechanically, but it can also fragment the tubes, decrease their aspect ratio and reduce the mechanical properties of nanotubes. With two different materials mixed in fluids, sonication effects need to be carefully studied. From previous research [144], we know that the sonication effect is determined by both sonication power and time. Therefore, these two factors need to be studied.

Triton X-100 has proven to be a very effective surfactant of dispersing nanotubes and therefore, was selected as a surfactant to disperse mixed materials. However, different amounts of surfactant may result in different dispersion effects. A sufficient amount of surfactant disperses nanotubes effectively, but is hard to clean with isopropanol afterwards. Therefore, different amounts of surfactant and isopropanol to clean buckypaper also need to be discussed.

51 4.4.2 Responses of Interest

There are four important properties of MBPs which need to be studied. The following paragraphs summarize these four properties.

The uniformity of the nanostructure of buckypaper represents the dispersion effect of suspension. Through the sonication, nanotube bundles can be dispersed into individual tubes. The uniformity of the nanostructure is characterized by uniform networks of small ropes, which is also an indication of high-quality buckypaper. The uniformity can be characterized by the average of the rope size distribution.

Purity is defined as the cleaning degree of buckypapers, because the residuals of surfactants can become trapped in the buckypaper and lead to the key properties being compromised. The surfactant needs to be rinsed out in order to utilize the inherently superior properties of buckypaper. Therefore, the elemental composition and Thermogravimetic Analysis (TGA) will provide a quantitative result of the purity of the buckypaper.

Surface area stands for the specific surface area of buckypapers to interact with other molecules. By measuring and modeling the specific surface area of SBP, SMBP, and SFBP, we will be able to quantify the gas adsorption and pore distribution of buckypaper, as well as their relationship with its nanostructures.

The electrical conductivity of buckypaper is critical for applications such as electrical devices, like actuators and sensors. By characterizing the nanostructure of MBPs, we will explore the nanostructure-electrical conductivity relationship of buckypaper.

52 4.5 Experimental Design and Statistical Analysis of MBPs

Based on the selected factors and responses, we performed the experiments sequentially. A screen experiment was designed and is listed in Table 4.1. There is one qualitative factor, mixed materials, and four quantitative factors, mixed ratio, sonication effect, amount of surfactant and amount of cleaning solvent. The qualitative factor contains two levels, and each of the quantitative factors contains three levels. The resulting screen design is a 25-1 full-factorial design with 2 extra replicates at each center point, resulting in a total of 20 experiments.

Table 4.1 Design of screen experiments

Factors Low Medium High Response A Mixed materials CNF - MWNT B Mixed ratio 1:7 1:2 1:1 Uniformity (nm) Purity (% wt) Sonication effect C 40 420 800 Electrical Conductivity (time×level) (10-3Ω -cm) Surfactant amount 2 D ×1 ×5 ×9 BET Surface Area(m /g) (multiple) E Clean amount (ml) 100 300 500

4.5.1 Uniformity

The uniformity of nano-networks in buckypaper can be represented by the rope size distribution of nanomaterials. Rope size was calculated using SIMAGIS image processing software, and classified to the rope size distributions of SWNTs, MWNTs and CNFs, respectively. Methods of separating the distribution of two mixing materials in MBPs will be discussed in chapter 5. Factors towards small, even and uniform networks of MBPs were discussed. Table 4.2 demonstrates the statistical analysis of SWNT rope size. Similar to the SBP case, the factor interactions are more statistically significant than the factors themselves. The cleaning amount of isopropanol is the only influential factor (factor E). A sufficient amount of isopropanol dissolved surfactant molecules wrapping around the SWNTs, and consequently, the sample can be cleaned better and the rope size of SWNTs measured from SIMAGIS will also decrease. Sonication effect is defined as

53 the product of time and level, and all of the influential factor interactions involved sonication. This implies that sufficient sonication is essential toward small and uniform SWNT ropes in MBP.

Table 4.2 ANOVA of SWNT rope size in the MBPs

Sum of Mean Source DF F-Value Prob > F Significance Squares Square Model 88.52 8 11.06 3.51 0.0334 significant A 0.96 1 0.96 0.30 0.5915 B 0.71 1 0.71 0.22 0.6447 C 0.62 1 0.62 0.19 0.6658 D 5.60 1 5.60 1.78 0.2114 E 16.81 1 16.81 5.34 0.0434 significant AC 18.97 1 18.97 6.02 0.0340 significant BC 16.51 1 16.51 5.24 0.0450 significant CD 28.31 1 28.31 8.99 0.0134 significant Curvature 19.24 1 19.24 6.11 0.0329 Residual 31.47 10 3.14 Lack of 28.84 8 3.60 2.73 0.2949 Fit Pure Err 2.63 2 1.31 Cor Total 139.24 19

As for the rope size of MWNTs and CNFs, the mixed ratio is influential in both cases. As more SWNT was mixed in the MBP, MWNTs and CNFs became harder to disperse and resulted in larger rope sizes and tangled networks. The rope size distributions of MWNTs and CNFs are more complicated than that of SWNTs. High variances were found and curvature was significant. More information may be needed before further conclusions can be drawn from the statistical analysis.

54 4.5.2 Purity

The purity of MBPs is defined as the weight percentage of residual surfactant in a sample. A higher percentage of residual surfactant weight indicates low-purity of the MBP sample. It is believed that surfactant trapped in buckypaper will decrease the performance of the buckypaper; therefore, factors toward high-purity MBP are discussed in this section.

The statistical analysis of purity is shown in Table 4.3. Influential factors toward purity of MBP were not as highly significant as other responses. This implied that isopropanol can clean MBP samples effectively, and the residual surfactant molecules trapped in the sample after cleaning has a very limited influence to the weight of the MBP sample.

Table 4.3 ANOVA of Purity

Sum of Mean Source DF F-Value Prob > F Significance Squares Square Model 33.23 8 4.15 4.01 0.0220 significant A 4.59 1 4.60 4.43 0.0615 significant B 9.81 1 9.81 9.46 0.0117 significant C 1.74 1 1.74 1.68 0.2239 D 1.98 1 1.98 1.91 0.1971 E 0.21 1 0.21 0.21 0.6593 AD 5.27 1 5.27 5.08 0.0478 significant CD 4.97 1 4.97 4.79 0.0534 significant DE 4.66 1 4.66 4.50 0.0600 significant Curvature 0.74 1 0.74 0.72 0.4170 Residual 10.37 10 1.04 Lack of Fit 9.33 8 1.17 2.24 0.3445 Pure Err 1.04 2 0.52 Cor Total 44.35 19

55 4.5.3 BET Surface Area

BET surface area is defined as the amount of N2 molecules adsorbed on the surface of nanotubes. A large surface area indicates the high-capacity of gas storage and high active surface area, and can be utilized as active materials in fuel cells, pharmaceutics, and batteries, etc.

The statistical analysis of BET surface area is shown in Table 4.4. Mixing material types and ratios outperformed other factors and became only two significant factors. The relationship of nanostructure and BET surface area and modeling will be discussed in detail in Chapter 6.

Table 4.4 ANOVA of BET surface area Sum of Mean Source DF F-Value Prob > F Significance Squares Square Model 152980.50 3 50993.50 22.83 < 0.0001 significant A 21039.91 1 21039.91 9.42 0.0090 significant B 126486.70 1 126486.70 56.63 < 0.0001 significant AB 5453.86 1 5453.86 2.44 0.1421 Curvature 80.10 1 80.10 0.04 0.8527 Residual 29036.38 13 2233.57 Cor Total 182097.00 17

4.5.4 Electrical Conductivity

Four-probe methods were used to measure the electrical conductivities of the buckypaper materials. This method offers a standard accurate procedure to find the electrical resistivity of the samples. The high conductivity of MBPs can be utilized in many applications, including conductive composite materials, devices and sensors. The statistical analysis is shown in Table 4.5. Mixing material types and ratios outperformed other factors and became only two significant factors and interactions. This indicated further studies on nanostructure are important toward discovering more about the electrical conductivity of MBPs. The relationship of nanostructure and electrical

56 conductivity and the proposed electrical circuit model of MBP will be discussed in detail in Chapter 7.

Table 4.5 ANOVA of Electrical Conductivity Sum of Mean Source DF F-Value Prob > F Significance Squares Square Model 790.37 3 263.46 8.47 0.0016 significant A 313.07 1 313.07 10.07 0.0063 significant B 266.21 1 266.21 8.56 0.0104 significant AB 211.09 1 211.09 6.79 0.0199 significant Curvature 27.92 1 27.92 0.90 0.3584 Residual 466.51 15 31.10 Lack of Fit 459.04 13 35.31 9.46 0.0996 Pure Error 7.47 2 3.73 Cor Total 1284.79 19

4.5.5 Nanostructure and Properties of MBP

From previous discussions, it can be seen that the chosen factors are more influential to uniformity and purity than surface area and electrical conductivity. In the case of surface area and electrical conductivity, mixed material types and ratios are the only two influential factors. This implies that these chosen factors may have more of a direct influence on the nanostructure, including uniformity and purity, than on the properties of MBPs, like surface area and electrical conductivity. Based on those observations, we will discuss the relationship between the nanostructure and properties of MBPs in the following text.

Regression analysis was used to analyze the relationship between the nanostructure and resulting properties of MBPs. Table 4.6 and Table 4.7 show the statistical analysis of regressing properties on nanostructure. The regression coefficients were tested first for their significance in the regression. Uniformity has significant statistics and implies a strong relationship between nanostructure and surface area. On the other hand, purity showed insignificant relationships to surface area. The second step is to use an analysis of variance approach to test the significance of the regression. The results showed the

57 regression on surface area to uniformity is statistically significant. Similar results were observed from the regression analysis of electrical conductivity that the uniformity of nanostructure has a strong relationship to the resulting electrical conductivity of MBPs.

Based on the regression analysis, nanostructure has a direct influence on the properties of MBPs. Therefore, more characterization of the nanostructure is beneficial in developing the models of surface area and electrical conductivity, which will be studied in later chapters.

Table 4.6 Regression Analysis of surface area vs. uniformity and purity Regression on surface area: BET Surface Area = 211 - 1.73 average size + 17.3 Purity Predictor Coefficient SE Coef T P Constant 211.21 69.07 3.06 0.008 Uniformity -17340 0.6865 2.53 0.023 Purity 17.34 14.15 1.23 0.239

Source DF SS MS F P Regression 2 56829 28415 3.4 0.04 Residual Error 17 125268 8351 Total 19 182097

Table 4.7 Regression analysis of electrical conductivity vs. uniformity and purity Regression on electrical conductivity: Electrical Resistivity= - 4.49 + 0.149 Uniformity + 1.02 Purity Predictor Coefficient SE Coef T P Constant -4.489 4.906 -0.91 0.373 Uniformity 0.14892 0.04731 3.15 0.006 Purity 1.018 1.008 1.01 0.327

Source DF SS MS F P Regression 2 588.67 279.33 6.54 0.005 Residual Error 17 726.13 42.71 Total 19 1284.79

58 4.6 Summary

This chapter introduced mixed buckypapers, which can reduce the cost of SWNT buckypaper while maintaining properties of buckypaper at attractive levels. The manufacturing process of MBP was proposed to disperse both materials in solvent effectively, then filtrated through membrane and formed into a uniform network of mixed materials. The experimental design was conducted to investigate the manufacturing process of MBPs. From the statistical analysis of the screen experiments, the nanostructure of MBPs is highly related to sonication. This is consistent with the SBP manufacturing process. Both analyses of BET surface area and electrical conductivity share similar results that only mixing material types and their ratios as well as their interactions are influential.

59 CHAPTER 5 STATISTICAL CHARACTERIZATION OF NANOSTRUCTURE OF MIXED BUCKYPAPERS

5.1 Introduction

Mixed buckypapers share the same nano-features with SWNT buckypapers. Both materials possess a delicate and porous nanostructure; however, due to the nanometric scale and variation among different batches of raw materials, large variances in nanostructure and property are expected in buckypapers. Therefore, a standardized and systematic procedure of analysis is crucial to explore the impact of different nanostructures on the final properties of MBPs.

From the statistical analysis of the MBP manufacturing process, we know that the nanostructure is crucial to the resulting properties of MBPs. This chapter discusses how we systematically characterized the nanostructures and distinguished the distribution of SWNTs from mixed materials using analytical tools. These indices of nanostructure will be used to construct models of surface area and electrical conductivity.

5.2 Methodology

Three indices were used to characterize the nanostructure of MBPs, rope size distribution, length distribution and pore size distribution. The rope size was used to evaluate the dispersion effect of the process, length distribution calculated the aspect ratio of nanomaterials in MBPs, and the pore size evaluated the uniformity and structure of networks. Three indices provided objective information to quantify the nanostructure of MBPs.

Mixed distributions coexisted in the MBP due to different nanomaterials mixed together and their similar geometries, which is statistically known as bimodal distribution.

60 This requires further processes to separate two distributions to reveal detailed structure information on the different materials. The Expectation-Maximization algorithm was a useful tool to distinguish a bimodal situation [157]. To characterize the nanostructure in MBP, two distributions from the two mixed nanomaterials will be fitted into statistical distributions after separation. The goodness of fit method was used to test the significance of the chosen distribution. The resultant distribution will be further used to construct models of MBP properties.

5.2.1 Rope Size Measurement

The small average and standard deviation of the rope size distribution in the nanostructure represents a uniform nanostructure and effective dispersion in buckypaper materials. The nanostructure was observed by scanning electron microscopy (SEM), and the Carbon Nanorope Thickness Analysis of SIMAGIS from Smart Imaging Technologies was used to analyze these images and characterize nanostructure with statistics including minimum, maximum, average, median, and standard deviation of the rope size distribution.

SIMAGIS processes the image by revealing the ropes on the SEM image with the contour mask and skeleton of the rope images. The mask, including the contour and skeletal lines of the ropes, is superimposed over the initial image. The contour line finds the boundary of each rope, and the skeletal line finds the center of each rope and then calculates its diameter. The distribution was generated from thousands of measurements at different representative areas; and therefore, provides objective information to quantify rope size distribution of the MBPs. Figure 5.1 demonstrates the SEM image processing using SIMAGIS.

61

Figure 5.1SEM image processing using SIMAGIS

5.2.2 Length Measurement

Although sufficient sonication breaks nanotube bundles effectively, it also breaks nanotubes into segments. Length distribution is important to check for sufficient sonication without sacrificing the aspect ratio of the nanomaterials in buckypaper. Nanotubes and nanofibers form into tangled networks in MBPs and are very challenging to characterize their length distribution in buckypaper form. Comparatively, diluted suspension contains fewer nanoparticles, and is more suitable for observing the length of materials.

Length distribution was observed by both atomic force microscopy (AFM) and SEM. Carbon Nanotube Diameter Analysis from SIMAGIS was used to calculate distributions. This special module of SIMAGIS automatically identifies and classifies nanotubes and other nanoparticles, and then analyzes nanotube lengths based on recognizing the intersections, contacts and curvature of the tubes. The distribution was generated from thousands of measurements using different representative areas; and therefore, provides objective information to quantify length distribution of nanomaterials in the MBPs. Figure 5.2 demonstrates the AFM image processing using SIMAGIS.

Figure 5.3 show the nanostructure of MWNT suspension. When compared to SWNTs, MWNTs exhibited contorted clusters in the suspension. These wavy MWNTs

62 resulted in high curvature, and reduced the projected length in MWNTs. This increased the difficulty to form a flexible network made up solely of MWNTs. The short and curved clusters may become caught in the pores of the filter membrane and left lots of MWNTs stuck in the membrane during buckypaper factorization. CNFs in the suspension exhibited large variations in length.

Figure 5.2AFM image processing using SIMAGIS (scale bar: 10μm)

Figure 5.3 SEM image processing of MWNT suspension

63 5.2.3 Pore Size Measurement

Pore size represents the space among networks in MBPs. Small average and standard deviation of pore size means high volume fraction and uniform networks of materials in MBPs. In previous chapters, we defined pore size as a two-dimensional pore area; however, information in the third dimension was missing [144]. With Tristar 3000 from Micromeritics Inc., we were able to measure the pore size as pore volume in three dimensions by gas adsorption porosimetry. Gas adsorption measures pore size by recording isotherms from low pressures to saturation pressures. The pressure range is determined by the size range of the pores to be measured. Pore size can be classified into micropore, mesopore and macropore. Micropores are small with a pore size within 2nm, and isotherms of microporous materials are measured over a pressure range of approximately 0.00001 mmHg to 0.1 mmHg. Mesopores are intermediate with a pore size ranging from 2 to 50nm, and isotherms of mesoporous materials are typically measured over a pressure range of 1 mmHg to approximately 760 mmHg. Macropores are large with a pore size above 50nm, and isotherm of macroporous material are measured continuously till saturated. Once details of the isotherm curve are accurately expressed as a series of pressure vs. quantity adsorbed data pairs, a number of different theories or models can be applied to determine the pore size distribution. In our analysis, the Barret- Joyner-Halenda (BJH) method was used to calculate pore size distribution [121].

The Barret-Joyner-Halenda scheme was proposed for the calculation of mesopore distribution from nitrogen adsorption data summarized in the following formula:

k n vads (xk ) = ∑∑ΔV (rii ≤ rc (xk )) + Δ tS (riii > rc (xk )) (5.1) i=+11=ki

3 vads(xk) is the volume of adsorbate (cm /g) at relative pressure xk , which was calculated from the value of adsorption. v is pore volume (cm3/g), S is surface area (m2/g), and t is the thickness of adsorbed layer (nm).

This formula shows that the adsorbed amount at the k-th point of adsorption isotherm may be divided into two distinct parts: first is a volume in condensate in all

64 pores smaller than some characteristic size depending on current relative pressure, rc(xk). The second part is a volume of adsorbed film on all larger pores, calculated by a sum of the terms: Σ (pore surface) (thickness of film in pore).

For adsorption and desorption isotherm branches the calculation scheme is the same. It always starts from the point where all pores are filled-up, i.e. the last point of adsorption branch, xads,K where the adsorbed amount becomes the same as on the desorption branch xdes,L, and the pore system is oversaturated. Then it goes along decreasing pressure, i.e. iterate isotherm point counter downwards (xads,i , i = K, K- 1, K-

2 ... ) whereas for desorption upwards (xdes,i, i = L, L+1, L+2 ...).

In the 1st step, the change of the adsorbate amount corresponds to processes in a single, averaged pore size. This pore size is calculated with appropriate form using the Kelvin equation

1 1 RT ⎛ pc ⎞ + = − ln⎜ ⎟ (5.2) r ,xK r , yK σVm ⎝ ps ⎠

Eq(5.2) defining the adsorbed film thickness for two limiting radiuses (corresponding to maximum, xi, and minimum, xi+1, pressure).

Figure 5.4 illustrates the isotherm of gas desorption of a MBP sample and corresponding pore size distribution. It was observed that most of the pores in MBP are mesopores to macropores. Micropores were rare in the sample. This demonstrates that MBPs contained high porosity, and also applicable to resin impregnation through MBP and produce high-performance MBP composite materials.

65

/g) 3 m (c

e m u l Vo

e r o P

Figure 5.4 Pore size distribution calculated by BJH method of gas sorption of MBP sample

5.2.4 Expectation-Maximization Algorithm

The expectation-maximization (EM) algorithm is used in statistics for finding the maximum likelihood estimates of parameters in probabilistic models, where the model depends on unobserved latent variables [157]. MBP exhibited such characteristics that two distributions of mixed materials coexist in a system that required further distinction.

EM alternates between performing an expectation (E) step, which computes an expectation of the likelihood by including the latent variables as if they were observed, and a maximization (M) step, which computes the maximum likelihood estimates of the parameters by maximizing the expected likelihood found on the E step. The parameters found on the M step are then used to begin another E step, and the process is repeated. The flowchart of the EM algorithm is summarized in Figure 5.5.

In EM algorithm, we maximized the likelihood for parameter θ given an observation x and a likelihood function f x θ )|( . We set the data vector x to be made up of two components x=[x0 xm], where x0 denotes the observed part of x and xm stands for the missing part. Assuming that given the partial data x, like calculating rope size

66 distribution from SEM images of partial area, we can solve the maximizer for the maximum likelihood estimate ofθ ,

^ θ = arg max f (x0 θ )| (5.3) θ

To estimate the value of θ , the EM algorithm involved 4 steps,

1. Choose the initial value forθ0 and set m=0. 2. Expectation step, compute

Q(θ |θm , x0 ) = E[log( f (x0 , xm |θ |)) θm , x0 ] (5.4) 3. Maximization step

θm+1 = arg maxθ Q(θ |θm , x0 ) (5.5) 4. Check convergence. In not converged, set m=m+1 and go back to step 1.

For example, a Gaussian bimodal distribution is a special case of the EM algorithm.

Consider Yi is observed data, x0=Y, which is a mixture of two Gaussian random variables,

i)( 2 and Y=Y(i) with probability α j , where Y ~ N(μ j ,σ j ) and ∑α j = 1. The goal is to j use independent observations of Y to estimate the maximum likelihood of unknown

2 2 parameters θ = (μ1 , μ 2 ,σ 1 ,σ ,2 α1 ,α 2 ) . In addition to Yi, we also have a label li that

⎧l i = ,1 if Yi ~ f1 ⎨ ⎩l i = ,2 if Yi ~ f 2 in other words, li tells us what density Yi came from. From a larger observation (Y, l ) where l=(l1, l2, …, ln), and then we derive the log-likelihood function:

n log( f lY |,( θ )) = ∑log( f (Y ,lii |θ )) (5.6) i=1

n = ∑log( f (Yi li θ ),| lP i |( θ )) i=1 = log(α f (Y l ,| μ ,σ 2 )) + log(α f (Y l ,| μ ,σ 2 )) ∑ li 1 i i 1 1 ∑ li 2 i i 2 2 li i =1: li i =2:

67 Here, we have used the fact that (lP i θ )| = α i . Now, the data breaks into two groups: one from f1 and the other from f2, and one can use this to separate data sets and to estimate parameters for those respective densities.

In the E step, we compute the expectation of the log-likelihood function with respect to the probability lP Y,|( θ ) , where l is an n-vector of labels. The resulting expectation is given by eq (5.7)

Q θ |( θ m Y), = E[log( f Yl |),(( θ Y,|)) θ m ] (5.7)

= ∑log( f Yl |),(( θ )) lP Y,|( θ m ) l

n = ∑∑( log( f ((l ,Yii |) θ )) lP i |( Yi ,θ m )) l i=1

n 2 = ∑∑( log( f ((l ,Yii |) θ )) lP i |( Yi ,θ m ) il==1 i 1

n 2 2 = ∑∑( log(α , f (Yijmj | μ j ,σ j )P j |( Yi ,θ m )) ij==1 1

68 Set m=0 Initialize θ0

Expectation-step: Compute

Q θ |( θm , x0 ) = E[log( xf 0 ,( xm |θ |)) θm , x0 ]

Maximization-step: Set n = n +1 θm+1 = arg maxθ Q(θ |θm , x0 )

Check

No convergence Q(θm+1 |θm ) − Q(θm |θm−1) ≤ ξ

θ : maximum-likelihood ML estimate Yes ξ : termination threshold

θML = θm+1

Figure 5.5 Flow chart of EM algorithm

In the M step, we maximize the expected log-likelihood Q θ |( θ m ) , and we can obtain the following updates,

n (Y −μ )2 P j Y ,|( θ ) 2 ∑i=1 i mj +1, i m σ = n (5.8) mj +1, P j Y ,|( θ ) ∑i=1 i m

2 α ,mj N Yi ,( μ ,mj ,σ ,mj ) P j Yi ,|( θm ) = 2 (5.9) α N Y ,( μ ,σ 2 ) ∑ j=1 ,mj i ,mj ,mj

69 1 n α mj +1, = ∑ P j Yi ,|( θm ) (5.10) n i=1

n Y P j |( Y ,θ ) ∑i=1 i i m μ mj +1, = n (5.11) P j |( Y ,θ ) ∑i=1 i m

We keep updating the log-likelihood until the difference between iteration is below the termination criteria and find an optimum estimation to separate two distributions.

The Gaussian distribution is a special case in the EM algorithm that results in explicit formulas of the log-likelihood estimation. According to the central limit theorem, if the sum of the variables has a finite variance, then it will be approximately Gaussian distributed. Therefore, all of our data are analyzed using the assumption of Gaussian distributions to separate two distributions of mixed materials. After separation, goodness of fit will be used to find approximate distributions .

5.2.5 Goodness of Fit

After separating data using the EM algorithm, distributions of two mixed materials are fitted into specified distribution and goodness of fit was used to test the significance of these chosen distributions.

Goodness of fit tests demonstrate how well a statistical model fits a set of observations. Measurements of goodness of fit typically summarize the discrepancy between observed values and the values expected under the model in question. Such measurements can be used in statistical hypothesis testing, i.e. to test for normality of residuals, to test whether two samples are drawn from identical distributions, or whether outcome frequencies follow a specified distribution.

The test of hypothesis assumed,

70

H0: the data are governed by the assumed distribution

H1: the data are not from the assumed distribution

The chi-square statistic calculates the sum of the differences between observed and expected values estimated from a chosen distribution, each squared and divided by the expectation. m (O − E )2 χ 2 = ∑ i i ~ χ 2 (m − )1 (5.12) i=1 Ei where Oi is the observed data and Ei is the expected value from the chosen distribution.

The result can be compared to the chi-square distribution and determine the goodness of fit, i.e. the significance of the chosen distribution.

5.3 Rope Size Distribution of Mixed Buckypapers

As addressed in section 5.2.1, rope size distribution evaluates the network quality of materials in MBPs. Small average and standardization represents uniform nanostructure and effective dispersion of the sample. The rope size distribution was captured by scanning electron microscopy (SEM), and the rope size distribution was carried by Carbon Nanorope Thickness Analysis of SIMAGIS from Smart Imaging Technologies. A mixed distribution was observed from analysis, and the EM algorithm separated two distributions of SWNT and MWNT or CNF. Goodness of fit was then used to test the significance of the assumed distribution. The following section discusses the analytical process in detail.

5.3.1 Mixed Rope Size Distributions of Mixed Buckypapers

The rope distribution of the MBPs was a wide-spread distribution because it contained two different distributions, SWNT and MWNT in SMBP and SWNT and CNF

71 in SFBP. Figure 5.6 demonstrates the rope size distribution of a SMBP sample. High density of rope size was observed between 10 and 15nm. This is a typical phenomenon of SMBP samples because the rope size distributions of both SWNT and MWNT exhibited diameters between 10 and 15nm. It makes the differentiation between SWNTs and MWNTs challenging. On the other hand, Figure 5.7 demonstrates the rope size distribution of a SFBP sample. Two distinguishing distributions can be observed from the rope size distribution of the MBP. Because of the distinctive rope sizes of SWNT and CNF, the rope size distribution of SFBP is unique and easy to separate one distribution from the other.

The EM algorithm was used to separate the rope size distribution of SWNTs from MWNTs and SWNTs from CNFs. Figure 5.8 demonstrates two separated rope size distributions of the SMBP. The rope size distribution of SWNTs was plotted in dash bars and the rope size distribution of MWNTs was plotted in dot bars. The result shows the EM algorithm separate two distributions effectively. The average diameter of SWNTs was 9.42nm with a standard deviation of 4.42nm. The average rope size of MWNTs was 15.63nm with a standard deviation of 6.09nm. Although it is hard to evaluate the accuracy of EM separation, we can utilize the unique distribution of SFBP to double check the accuracy of the EM algorithm. Figure 5.9 demonstrates two separated rope size distributions of the SFBP. Two rope size distributions were correctly separated by the EM algorithm, and proved the accuracy and effectiveness of the method. The average rope size of SWNTs was 11.23nm with a standard deviation of 5.45nm. The average rope size of CNF was 159nm with a standard deviation of 60.85nm.

72 0.25

0.20

0.15 Density 0.10

0.05

0.00 5 10 15 20 25 30 35 40 45 Rope Size (nm)

Figure 5.6 Rope size distribution of a SMBP sample with a mixture ratio of 1:2

0.025

0.020

0.015 Density 0.010

0.005

0.000 0 60 120 180 240 300 360 420 Rope Size (nm)

Figure 5.7 Rope size distribution of a SFBP sample with a mixture ratio of 1:2

73 0.35

0.3

0.25

0.2 y ti s n e D 0.15

0.1

0.05

0 5 10 15 20 25 30 35 40 Rope Size (nm)

Figure 5.8 Separation of rope size distributions of SWNTs and MWNTs

0.08

0.07

0.06

0.05 y ti s 0.04 n e D 0.03

0.02

0.01

0 0 50 100 150 200 250 300 350 400 450 Rope Size (nm)

Figure 5.9 Separation of rope size distributions of SWNTs and CNFs

74

5.3.2 Rope Size Distribution of SWNTs

After separation by the EM algorithm, the distributions of SWNTs in both SMBP and SFBP can be fit into a chosen statistical distribution. Normal and Weibull distributions are two popular statistical distributions used in many applications, and were chosen to fit the rope size distribution [146]. Table 5.1 shows the goodness of fit of the SWNT distribution in SMBP, using both normal and Weibull distributions. The results show that both distributions were statistically suitable to fit the rope size distribution of SWNTs; however, the square error, which is defined as the difference between model estimation and real data, of the Weibull distribution is smaller than that of the normal distribution. This implies that both distributions are a good fit of SWNT rope size distribution, but the Weibull distribution can better fit the SWNT distribution with smaller prediction error. Therefore, the Weibull distribution was chosen to fit the rope size distribution, and the scale parameter was 8.225nm and shape parameter was 1.6nm. The average rope size of SWNT was 9.42nm and standard deviation was 4.42nm. Figure 5.10 shows the fitted curve of the Weibull distribution.

Table 5.1 Chi square test of rope size distribution of SWNT in SMBP with mixture ratio of 1:2 Normal Weibull Square error 0.0088 0.0085 Chi Square Test (p-value) < 0.005 < 0.005

75 0.18 2+weibull (8.225, 1.63) 0.16

0.14

0.12

0.10

Density 0.08

0.06

0.04

0.02

0.00 0 3 6 9 12 15 18 21 Rope Size (nm)

Figure 5.10 Weibull fit of SWNT rope size distribution in the SMBP with mixture ratio of 1:2

Table 5.2 shows the goodness of fit of SWNT distribution in SFBP using both normal and Weibull distributions. The results show that both distributions were statistically suitable to fit the rope size distribution of SWNT; however, the square error, which is defined as the difference between model estimation and real data, of the Weibull distribution was smaller than that of a normal distribution. This implied that both distributions are good fit of SWNT rope size distribution, but Weibull distribution can better fit the SWNT distribution with smaller prediction error. Therefore, the Weibull distribution was chosen to fit the rope size distribution, and the scale parameter was 10.29nm and shape parameter was 1.69nm. The average rope size of SWNT was 11.23nm and standard deviation was 5.45nm. Figure 5.11 shows the fitted curve of the Weibull distribution.

76 Table 5.2 Chi square test of rope size distribution of SWNT in SFBP with mixture ratio of 1:2 Normal Weibull Square error 0.0164 0.0160 Chi Square Test (p-value) < 0.005 < 0.005

0.20 2+weibull (10.29, 1.69)

0.15

0.10 Density

0.05

0.00 0.0 5.6 11.2 16.8 22.4 28.0 33.6 Rope Size (nm)

Figure 5.11 Weibull fit of SWNT rope size distribution in SFBP with mixture ratio of of 1:2

The rope size distribution of SWNTs in the SMBP was compared to that in the SFBP. Table 5.3 and Table 5.4 calculate the average rope size of SWNTs in SMBP and SFBP sampled from the experiments. Similar average rope size and standard deviation were observed, this implied the proposed manufacturing process is objective and repeatable, and data collected representative of whole sample.

77 Table 5.3 Average rope size of SWNT in SMBP Sample standard number Rope Size (nm) 1 14.66 3 8.41 5 9.46 7 13.64 9 14.92 11 13.05 13 8.4 15 9.25 17 11.23 19 10.65 Average (nm) 12.56 Standard deviation (nm) 3.74

Table 5.4 Average rope size of SWNT in SFBP Sample standard number Rope Size (nm) 2 11.72 4 11.36 6 17.63 8 14.48 10 12.71 12 18.94 14 8.81 16 13.37 18 7.2 20 9.42 Average (nm) 11.37 Standard deviation (nm) 2.53

5.3.3 Diameter Distribution of MWNTs

The diameter distribution of MWNTs was fitted into statistical distributions after separation by the EM algorithm. Normal and Weibull distributions were chosen to fit the rope size distribution. Table 5.5 shows the goodness of fit of MWNT distribution using both normal and Weibull distributions. The results show that both distributions were

78 statistically suitable to fit the rope size distribution of MWNT. However, the square error, which is defined as the difference between model estimation and real data, of Weibull distribution was smaller than that of normal distribution. This implied that both distributions are good fit of MWNT rope size distribution, but the Weibull distribution can better fit the MWNT distribution with smaller prediction error. Therefore, the Weibull distribution was chosen to fit the rope size distribution, and the scale parameter was 14.13nm and shape parameter was 1.53nm. The average rope size of MWNT was 15.63nm and standard deviation was 6.09nm. Figure 5.12 shows the fitted curve of Weibull distribution.

Table 5.5 Chi square test of rope size distribution of MWNT Normal Weibull Square Error 0.0898 0.0383 Chi Square Test (p-value) < 0.005 < 0.005

0.18 10+weibull (14.13, 1.52)

0.16

0.14

0.12

0.10 Density 0.08

0.06

0.04

0.02

0.00 0 5 10 15 20 25 30 35 40 45 50 Rope Size (nm) Figure 5. 12 Weibull fit of MWNT rope size distribution

79 5.3.4 Diameter Distribution of CNFs

The diameter distribution of CNFs was fit into statistical distributions after separation by the EM algorithm. Normal and Weibull distributions were chosen to fit the rope size distribution. Table 5.6 shows the goodness of fit of the CNFs’ distribution using both normal and Weibull distributions. The results show that both distributions were statistically suitable to fit the rope size distribution of CNF; however, the square error, which is defined as the difference between model estimation and real data, of Weibull distribution was smaller than that of the normal distribution. This implies that both distributions are good fit of CNF rope size distribution, but the Weibull distribution can better fit the CNF distribution with smaller prediction error. Therefore, the Weibull distribution was chosen to fit the rope size distribution, and the scale parameter was 149.8nm and shape parameter was 2.329nm. The average rope size of CNF was 159nm and standard deviation was 60.85nm. Figure 5.13 shows the fitted curve of the Weibull distribution.

Table 5.6 Chi square test of rope size distribution of CNF Normal Weibull Square Error 0.0601 0.0552 Chi Square Test (p-value) < 0.005 < 0.005

80 0.025 27+weibull (149.8, 2.329)

0.020

0.015 Density 0.010

0.005

0.000 0 60 120 180 240 300 360 420 Rope Size (nm)

Figure 5.13 Weibull fit of CNF rope size distribution

5.4 Length Distribution of Mixed Buckypaper

Length distribution is important in checking the sonication effect without sacrificing too much in aspect ratio of the nanomaterials in MBPs. Nanotubes and nanofibers form into tangled networks in MBPs and are challenging when characterizing their length distribution in buckypaper form. Comparatively, diluted suspension contains less materials, and is more suitable for observing the length of materials. Therefore, the length distribution is measured using the suspensions of SWNTs, MWNTs and CNFs.

5.4.1 Length Distribution of SWNT

The length distribution of SWNTs in solution was fitted into both normal and Weibull distributions. The goodness of fit can be seen in Table 5.7. It shows that the normal distribution was not a statistically significant distribution to fit the length distribution, and the Weibull distribution was suitable to fit the length distribution of

81 SWNTs. Therefore, the Weibull distribution was chosen to fit the rope size distribution, and the scale parameter was 1.89μm and shape parameter was 1.93μm. The average length of SWNT was 2.1μm and the standard deviation was 0.92um. Figure 5.14 shows the fitted curve of the Weibull distribution.

Table 5.7 Chi square test of length distribution of SWNTs Normal Weibull Square Error 0.0146 0.0071 Chi Square Test (p-value) 0.0141 < 0.005

0.9 weibull (1.89, 1.93)

0.8

0.7

0.6

0.5

Density 0.4

0.3

0.2

0.1

0.0 0.0 0.7 1.4 2.1 2.8 3.5 4.2 4.9 Length (um)

Figure 5.14 Weibull fit of SWNT length distribution

5.4.2 Length Distribution of MWNTs

From the image of MWNT suspension, it was observed that MWNTs exhibited contorted and tangled configurations compared to SWNT suspension.

82 The length distribution of MWNTs in solution was fitted into both normal and Weibull distributions. The goodness of fit is shown in Table 5.8 and the results show that both distributions were statistically suitable to fit the length distribution of MWNTs. However, the square error, which is defined as the difference between the model estimation and real data, of the Weibull distribution was smaller than that of normal distribution. This implied that both distributions were good fit of MWNT length distribution but the Weibull distribution can better fit the MWNT length distribution with smaller prediction error. Therefore, the Weibull distribution was chosen to fit the length distribution, and the scale parameter was 1.16μm and shape parameter was 1.51μm. The average length of MWNTs was 1.04μm and standard deviation was 0.75μm. Figure 5.15 shows the fitted curve of the Weibull distribution.

Table 5.8 Chi square test of length distribution of MWNTs Normal Weibull Square Error 0.0146 0.00197 Chi Square Test (p-value) < 0.005 < 0.005

0.9 Weibull (1.16, 1.51) 0.8

0.7

0.6

0.5

Density 0.4

0.3

0.2

0.1

0.0 0.0 0.5 1.0 2.0 3.0 4.0 5.0 Length (um)

Figure 5.15 Weibull fit of MWNT length distribution

83 5.4.3 Length Distribution of CNFs

The length distribution of CNFs in suspension was fit into both normal and Weibull distributions. The goodness of fit shown in Table 5.9 proves that the normal distribution was not a statistical significant distribution to fit the length distribution, and the Weibull distribution was suitable to fit the length distribution of CNF. Therefore, the Weibull distribution was chosen to fit the rope size distribution, and scale parameter was 5.11μm and the shape parameter was 0.65μm. The average length of CNFs was 7.8μm and standard deviation was 17.85μm. Figure 5.16 shows the fitted curve of the Weibull distribution.

Table 5.9 Chi square test of length distribution of CNFs Normal Weibull Square Error 0.44 0.0118 Chi Square Test (p-value) < 0.005 < 0.005

0.35

weibull (5.11, 0.65) 0.30

0.25

0.20

Density 0.15

0.10

0.05

0.00 0 20 40 60 80 100 120 140 Length (um)

Figure 5.16 Weibull fit of CNF length distribution

84 When comparing the length distributions of SWNTs, MWNTs and CNFs, MWNTs had the shortest length distribution, with the average length around 1um and standard deviation of 0.75μm. SWNTs had a median length distribution with an average length of 3.72μm and standard deviation of 1.86μm. The length distribution of CNFs exhibited large variation, and the length distribution was wide-spread from several microns to hundreds of microns. The average length was 7.8μm but the standard deviation was 2.5 times higher than the average length. The large variation may come from the raw material PR-19 that contained a wide-range length of CNFs varied from 30μm to 100μm. The results are summarized in Table 5.10 and Figure 5.17.

It needs to be mentioned that after the diluted suspension was filtrated through the membrane, the compact networks may lead these nanomaterials self-assembled to longer tubes in MBPs. Especially because strong van der Waal forces among SWNTs would allow a higher chance to self-assemble to longer SWNTs. Therefore, the measurement of length in diluted suspension has the tendency of underestimating the length of nanomaterials in MBPs. .

Table 5.10 Length distributions of SWNTs, MWNTs and CNFs

SWNT MWNT CNF Average length (μm) 3.72 1.04 7.8 Standard deviation length (μm) 1.86 0.75 17.85

85 0.7 Variable (a) L_MWNT L_SWNT 0.6 L_CNF

Shape Scale N 0.5 1.506 1.164 270 1.931 1.893 139 0.6497 5.113 342 0.4

Density 0.3

0.2

0.1

0.0 0 30 60 90 120 150 Length (um)

0.7 (b) Shape Scale N 1.506 1.164 270 0.6 MWNT 1.931 1.893 139 0.6497 5.113 342

0.5

0.4 SWNT

Density 0.3

0.2 CNF

0.1

0.0 0 1 2 3 4 5 6 7 8 9 10 15 20 Length (um) Figure 5.17 (a) Weibull length distribution of SWNTs, MWNTs, and CNFs, (b) local magnification of (a).

86 5.5 Pore Size Distribution of Mixed Buckypaper

Pore size is defined as the space among nanomaterials in MBPs. Small average and standard deviation of pore size means high volume fraction and uniform networks of materials in MBPs. The gas adsorption provided an accurate estimation of the three dimensional structure of the pore volume in buckypapers.

Figure 5.19 illustrates the pore size distribution of a SFBP sample with mixed ratio of 1:7. The statistics showed that the pore size distribution of MBPs belong to mesopore, which ranges from 2nm to 50nm. All of the MBP samples exhibited high intensity of pore size around 2 to 5nm, which corresponds to pore volume of 30 to 500 nm3.

5.5.1 Pore Size Distribution of SMBP

The pore distribution of SMBP was fit into both normal and Weibull distributions. The goodness of fit is shown in Table 5.11 and the results show that both distributions were statistically suitable to fit the pore size distribution of SMBP. However, the square error of the Weibull distribution was smaller than that of the normal distribution. This implied that both distributions were good fit of SMBP pore size distribution, but the Weibull distribution can better fit it with smaller prediction error. Therefore, the Weibull distribution was chosen to fit the length distribution. The scale parameter was 4.2um and shape parameter was 1.6um. The average pore size was 3.05nm and standard deviation was 2.03nm. The large standard deviation was a typical phenomenon observed from buckypaper materials because buckypaper is a high porous structure and composed of all micropores, mesopores and macropores. Therefore, the pore size distribution is expected to have a wide spread range and high intensity at the mesopore level. Figure 5.18 shows the fitted curve of the Weibull distribution.

87 Table 5.11 Chi square test of pore distribution of SMBP with mixture ratio of 1:7 Normal Weibull Square Error 0.8241 0.3313 Chi Square Test (p-value) < 0.005 < 0.005

0.35 weibull (4.2,1.6) 0.30

0.25

0.20

Density 0.15

0.10

0.05

0.00 0 20 40 60 80 100 120 Pore Size (nm)

Figure 5.18 Pore size distribution of SMBP with mixture ratio of 1:7

5.5.2 Pore Size Distribution of SFBP

The pore distribution of SFBP was fit into both normal and Weibull distributions. The goodness of fit is shown in Table 5.12 and the results show that both distributions were statistically suitable to fit the pore size distribution of SFBP. However, the square error of the Weibull distribution was smaller than that of the normal distribution. This implied that both distributions were a good fit of SFBP pore size distribution, but the Weibull distribution can better fit it with smaller prediction error. Therefore, the Weibull distribution was chosen to fit the length distribution. The scale parameter was 3.6nm and shape parameter was 2.06nm. The average pore size was 3.28nm and standard deviation

88 was 1.6nm. The characteristics of SFBP pore size distribution is very similar to SMBP with large variation and included all three types of pores. Also, high intensity at mesopore was also observed. Figure 5.19 shows the fitted curve of the Weibull distribution.

Table 5.12 Chi square test of pore distribution of SFBP with mixture ratio of 1:7 Normal Weibull Square Error 0.8968 0.0739 Chi Square Test (p-value) < 0.005 < 0.005

0.30

weibull (3.6,2.06) 0.25

0.20

0.15 Density

0.10

0.05

0.00 0 20 40 60 80 100 120 140 Pore Size (nm)

Figure 5.19 Pore size distribution of SFBP sample with mixture ratio 1:7

5.6 Summary

This chapter systematically characterized nanostructures of the MBPs by quantifying indices from statistical distributions, including rope size, length, aspect ratio and pore size. The mixed distributions of two materials were separated by the EM

89 algorithm and then fit into Weibull distribution tested by goodness of fit. The results show that the EM algorithm was capable of separating distributions of two materials accurately and goodness of fit found the Weibull distribution was the best distribution in the test to fit the distributions of nanostructure indices in buckypaper.

In the rope size distribution, SWNT was evenly dispersed in both SMBP and SFBP. The average rope size of SWNT in SMBP was close to that of SFBP. The average rope size of SWNT was 10nm and standard deviation 5.45nm, and fitted into Weibull distribution of scale parameter 10.29nm and shape parameter of 1.69nm. The rope size distribution of MWNT overlaps with that of SWNT, after separation of the EM algorithm, the average rope size of MWNT was 15.62nm and standard deviation was 6.09nm, and fitted into Weibull distribution of scale parameter 14.13nm and scale parameter 1.53nm. The large rope size distribution of CNF was distinctive from SWNT in SFBP. The average rope size of CNF was 159nm and standard deviation was 60.85nm, and fitted into the Weibull distribution of scale parameter 149.8nm and shape parameter 2.33nm.

In the length distribution, nanomaterials were characterized and measured in their suspension. SWNT had intermediate length among three materials. The length of SWNT exhibited long and well-dispersed feature in suspension, which is capable of forming flexible networks through self-assembly in MBP. The average length was 3.72μm with standard deviation 1.86μm, and fitted into the Weibull distribution with scale parameter 3.75μm and shape parameter 1.91μm. The length distribution of MWNT had the shortest length among the three materials. The length of MWNT exhibit contorted cluster in suspension, and projection length was close to the mesh size of the filter membrane. This increased the chance of wavy MWNTs stuck into membrane and hard to form a flexible network solely by MWNTs. The average length was 1.04μm with standard deviation 0.75μm, and fitted into the Weibull distribution with scale parameter 1.16μm and shape parameter 1.51μm. The length distribution of CNF had the longest and also most wide- spread distribution among the three materials. The average length was 7.8μm and standard deviation was 17.85μm, and fitted into the Weibull distribution with scale parameter 5.11μm and shape parameter 0.65μm.

90

Finally, the pore size distributions were revealed using sorption isotherms. Large variation was observed from both SMBP and SFBP samples, because buckypaper is a high porous structure and composed of all micropores, mesopores and macropores. Therefore, the pore size distribution is expected to have wide-spread of range and high intensity at the mesopore level. Overall, the pore size distribution of SMBP is very similar to that of SFBP, with average pore size 3nm and pore volume 15nm3.

The detailed information of nanostructures of buckypaper is essential for us to understand dispersion quality and develop process-nanostructure-property relationship model in the following chapters.

91 Chapter 6 BET Surface Area of Buckypapers

6.1 Introduction

BET surface area is an important property for many types of advanced materials such as nanomaterials, pharmaceutical materials, powder metallurgy materials, battery active materials, fibers, pigments, thermal spray powders, minerals, and additives. BET stands for Brunauer, Emmett, and Teller, the three scientists who optimized the theory for measuring surface area.

Owing to its nanometric diameter, nanotubes have a very large surface area, and it is determined by the measurement of gas adsorption and calculation using the Brunauer- Emmett-Teller (BET) isotherm [158]. The concept of the BET theory is based on multilayer molecular adsorption, with hypotheses: (a) gas molecules physically adsorb on a solid in layers infinitely; (b) there is no interaction between each adsorption layer; and (c) the Langmuir theory can be applied to each layer. The resulting BET equation is expressed by

(6.1)

P and Po are the equilibrium and saturation pressure of adsorbates at the temperature of adsorption, v is the adsorbed gas quantity (moles per gram of adsorbent) at the relative pressure p / p0 , and vm is the monolayer adsorbed gas quantity (moles of molecules needed to make a monolayer coverage on the surface of one gram of adsorbent) [124]. c is the BET constant, which is expressed by

(6.2)

E1 is the heat of adsorption for the first layer, and EL is that for the second and higher layers and is equal to the heat of liquefaction.

92 1 Eq (6.1) is an adsorption isotherm and can be plotted as a straight line with on P v[ 0 − ]1 P P the y-axis and on the x-axis according to experimental results. The plot is called a P0 BET plot. The linear relationship of this equation is maintained only in the range of P 05.0 < < 35.0 . The value of the slope and the y-intercept of the line are used to P0 calculate the monolayer adsorbed gas quantity vm and the BET constant c .

The BET method is widely used to calculate surface areas of nanotubes by the physical adsorption of gas molecules. A total surface area Stotal and a specific surface area S are evaluated by the following equations,

(6.3)

(6.4)

N: Avogadro's number, s: adsorption cross section, M: molecular weight of adsorbate, a: weight of sample solid

In this chapter, we propose the model of the specific surface area of buckypaper materials based on the characterization of nanostructure discussed in Chapter 5. We focused on the mixed buckypaper system, and provide several experimental results to validate modeling estimations. The nanostructure-surface area relationships of different MBPs will be discussed.

93 6.2 Methodology

The TriStar 3000 Analyzer uses physical adsorption and capillary condensation principles to obtain information about the surface area and porosity of a solid material. The analytical technique is addressed as the following: a sample is contained in an evacuated sample tube and is cooled to cryogenic temperature, and then is exposed to analysis gas at a series of precisely controlled pressures. With each incremental pressure increase, the number of gas molecules adsorbed on the surface increases. The equilibrated pressure (P) is compared to the saturation pressure (Po) and their relative pressure ratio (P/Po) is recorded along with the quantity of gas adsorbed by the sample at each equilibrated pressure.

As adsorption proceeds, the thickness of the adsorbed film increases. Any micropores in the surface are filled first, then the free surface becomes completely covered, and finally the larger pores are filled by capillary condensation. The process may continue to the point of bulk condensation of the analysis gas. Then, the desorption process may begin in which pressure is reduced systematically, resulting in the liberation of the adsorbed molecules. As with the adsorption process, the changing quantity of gas on the solid surface at each decreasing equilibrium pressure is quantified. These two sets of data describe the adsorption and desorption isotherms. Analysis of the shape of the isotherms yields information about the surface and internal pore characteristics of the material.

6.3 Specific Surface Area of Nanomaterials

In order to develop a specific surface area model of nanotubes and nanofibers in SBPs and MBPs, we need to first review and discuss the surface area models developed from previous work on SWNT bundles and MWNTs by Peigney et al. [159]. Although Peigney’s model only focused on isolated SWNT bundles and MWNTs, it gave us a clear overview of the geometric surface area of SWNT bundles and MWNTs, and a solid basis

94 of describing the nanostructure in SBPs and MBPs. Based on Peigney’s single nanotube and bundle models, we further modified the surface area models by taking both nanostructures and mixed ratios into account and expanded the analysis to surface area of both pure SWNT and mixed buckypapers. The predicted results were compared to those of experimental measurements to verify the developed models.

The model of surface area was based on the following assumptions: 1. All nanostructures were close, and only the external surface of each material was taken into account, which was the outermost surface area exposed to gas adsorption.

2. Length ( d −CC ) of the C-C bonds in the curved grapheme sheets was the same as in

the planar sheet, as shown in Figure 6.1, and d −CC is 0.1421 nm. 3. MWNTs and CNFs were composed of concentric walls and the inter-wall distance

( d −SS ) was 0.34 nm. 4. Aspect ratios of these nanomaterials were sufficiently high (>1000) to neglect the area of the cap surfaces in comparison to the area of the cylindrical surfaces. 5. Contact of SWNT bundle to bundle in buckypaper was neglected since during BET tests, gas molecules could get between bundles because of pressure and van der Waals interaction.

dc-c=0.1421nm

Figure 6.1Schematic representation of the arrangement of carbon atoms within graphic sheet

6.3.1 Specific Surface Area of a Single SWNT

The surface area ( S h ) of one hexagon in graphic structure is

95 3 S = 3d 2 = .5 246×10−20 m 2 (6.5) h −CC 2

S h corresponds to two carbon atoms, which can be calculated based on atomic weight of

23 −1 carbon ( M C = 01.12 g / mol ), and the Avogadro number ( N = .6 023×10 mol ):

−23 wh = 2( M C / N) = .3 988×10 g (6.6) Combining (6.5) and (6.6) gives the specific surface area of one side of a graphic sheet

(ς GS ):

Sh 2 ς GS = = ,1 315m / g (6.7) wh

The surface area of a single SWNT is that of one side of a graphic sheet, regardless of its diameter if we ignored the curvature. Therefore, the specific surface area of a single nanotube was 1,315 m2/g.

6.3.2 Specific Surface Area of a SWNT Bundle

SWNTs usually form into bundles in buckypapers due to van der Waals interactions. Following Peigney’s models, we assumed that each bundle was composed of N identical

SWNTs with a diameter of de, which were perfectly arranged in a hexagon network at an inter-tube distance ( d NT −NT ) of 0.34 nm, as shown in Figure 6.2. It was assumed that the only the outer surface area of the individual nanotubes is contributed to the surface area and the inner surface between nanotubes in a bundle was not accessible to gas adsorption.

Figure 6.2 Schematic representation of the arrangement of carbon nanotubes of a SWNT bundle

96

When N identical nanotubes gather together to form a perfect bundle, the surface area of a bundle is calculated as the outmost surface area of the bundle. As a result, an efficient coefficient (ε ) was applied to calculate the specific surface area of the bundle, which is defined as N ε = eq (6.8) n N where n is the number of layers, and Neq is defined as the number of individual SWNTs with a total accessible surface area equal to that of a bundle made up of N SWNTs. Figure 6.3 shows how individual SWNTs formed into a perfect bundle with successive layers of SWNTs.

Figure 6.3 Schematic representation of a two-layer bundle

From the characterization of nanostructure in Chapter 5, the average diameter of single SWNT was about 2 nm, and the average diameter of the SWNT bundles in the buckypaper was 10 nm. We assumed the surface area of the bundles was made up of around 19 individual SWNTs and formed a two-layer bundle, as shown in Figure 6.3. In a two-layer structure, the surface area can be calculated as the accessible surface area made up of these 19 SWNTs, which is equivalent to the surface area of 7 SWNTs. The efficient coefficient of a two-layer SWNT bundle (ε 2 ) can be calculated as

97 7 ε = = .0 368 2 19

Therefore, the surface area of a two-layer SWNT bundle can be calculated by applying the effective coefficient of the two-layer structure to the surface area of single SWNT. 2 ς (SWNT bundle) = ς (SWNT )×ε 2 = 483.93 (m /g)

If the average diameter of SWNT bundles in the buckypaper was around 14 nm. We assumed the surface area of each bundle was made of approximately 37 individual SWNTs and formed a three-layer structure. In a three-layer structure, we can calculate the surface area as the accessible surface area made up of 37 SWNTs, which is equivalent to the surface area of 10 SWNTs. The efficient coefficient of a three-layer SWNT bundle

(ε 3 ) can be calculated as 10 ε = = .0 176 3 37

Therefore, the surface area of a three-layer SWNT bundle can be calculated by applying the effective coefficient of the three-layer structure to the surface area of a single SWNT. 2 ς (SWNT bundle) = ς (SWNT)×ε3 = 355.4 (m /g)

As a result, an estimation of the surface area contributed from SWNT bundles in buckypapers can be achieved by applying an effective coefficient based on SWNT bundle size. The diameter of the SWNT bundle is critical for calculating the surface area of buckypapers. We calculated the surface area of SWNT bundles of different sizes. Table

6.1 summarizes the effects of bundle diameters of SWNT and effective coefficients (ε n ) on surface areas of SBPs.

98

Table 6.1 Number of layers, effective coefficients of SWNT bundles and surface areas of SBPs

SWNT and ς (SWNT,bundles) n ε bundle n (m2/g) Diameter (nm) 0 0 2 1315 1 7/4 = 57.0 6 749.55 2 19/7 = 36.0 10 473.40 3 10 / 37 = 27.0 14 355.40 4 13/ 61 = 21.0 18 231.44 5 16 / 91 = 17.0 22 244.59 6 19 /127 = 15.0 26 197.25 7 22 /169 = 13.0 30 170.95 8 25/ 217 = 12.0 34 151.23

6.3.3 Specific Surface Area of a Multi-walled Nanotube (MWNT)

MWNTs have concentric walls of graphic sheet with an external diameter d e , a length L and n walls. Its external surface is:

S MWNT = π Ld e (6.9) The surface of all the graphic sheets is:

SGS ,MWNT = π .. dL e + π.L.(de − 2d −ss ) + π.L.(de − 4d −ss ) + ... + π.L.(de − (n − )1 d −ss ) ⎡ n−1 ⎤ = πL⎢nd e − 2d −ss ∑i⎥ (6.10) ⎣ i=1 ⎦ where ds-s is 0.34 nm. The structure of a MWNT is demonstrated in Figure 6. 4. The different terms successively represent the surface of the external wall (wall 1) of the first internal wall (wall 2) and so on, up to the innermost wall (wall n).

99 wall 1 wall 2

wall n

de

ds-s=0.34nm

n walls

Figure 6. 4 Schematic representation of a multi-walled carbon nanotube made up of concentric graphic shells

The weight of individual single graphic sheet in MWNT is

1 −4 2 wGS = = .7 602×10 g / m ς GS ,SWNT

The weight of this MWNT ( wMWNT ) is the total weight of all the graphic sheets, which is written as

n−1 −4 wMWNT = wGS × SGS ,MWNT = .7 602×10 ×πL[nde − 2d −ss ∑i] (6.11) i=1 The specific surface area of the MWNT, ς (MWNT ) , is defined as the surface area per unit weight, as a result, S S ⋅ d 1315⋅ d ς (MWNT) = MWNT = GS e = e (6.12) n−1 n−1 wWWNT ⎡ ⎤ ⎡ ⎤ nde − 2d −ss ⎢∑i⎥ nde − 68.0 ⎢∑i⎥ ⎣ i=1 ⎦ ⎣ i=1 ⎦

2 where n ≥ 2, d e is in nm and ς (MWNT ) is in m / g unit.

100 Eq(6.12) shows that ς (MWNT ) depends on MWNTs’ diameter and number of walls. The number of walls appear to be the predominant parameter influencing theς (MWNT ) , because each additional wall does not increase the surface area of the MWNT but causes a much larger increase in its weight.

To calculate number of walls of a MWNT, TEM images were taken, which are shown in Figure 6.5 (a). We measured the inner diameter of a MWNT to be 10 nm, and the distance between each layer was 0.34 nm. The number of walls (n) can be calculated as d OD − d ID n = MWNT MWNT (6.13) MWNT 68.0

OD ID where d MWNT and d MWNT are inner and outer diameters of MWNT. Therefore, from Eq (6.13), the specific surface area of MWNTs can be calculated as a

OD function of d MWNT , assuming the inner diameter of MWNTs is constant, 10 nm.

1315⋅ d OD 1778 4. ⋅ d OD SA(MWNT) = MWNT = MWNT (6.14) n−1 OD 2 OD ⎡ ⎤ (d MWNT ) −100 ndMWNT − 68.0 ⎢∑i⎥ ⎣ i=1 ⎦

Based on the assumption that the inter-wall distance d −SS =0.34 nm, the average diameter of MWNTs was 20 nm, and the inner diameter was about 10 nm, and the number of walls of MWNTs was 15. Therefore, the specific surface area of the MWNTs used in our research can be obtained by Eq (6.14), ς (MWNT) =119.23 (m2/g)

101 (a) (b)

Figure 6.5 TEM images of (a) a MWNT and (b) a CNF.

6.3.4 Specific Surface Area of a Carbon Nanofiber (CNF)

The structure of CNFs is comprised of multiple walls of less graphitic sheets, but these walls usually are not perfectly parallel to the fiber axis. In order to approximate the irregular surface area of CNFs, we assumed the concentric graphitic sheets of CNFs is approximately parallel to the tube axis, and used the same model of MWNT with more sidewalls to calculate CNFs’ surface area. Therefore, the number of walls also dominates the specific surface area of CNFs. To calculate number of walls of CNFs in our study, TEM images were taken, which are shown in Figure 6.5 (b). Assuming the inter-wall distance was d −SS =0.34 nm, the average diameter of CNFs was 87 nm and inner diameter was 40 nm, the number of walls (n) can be calculated as d OD − d ID n = CNF CNF (6.15) CNF 68.0

OD ID where, dCNF and dCNF are inner and outer diameters of the CNF respectively.

Therefore, from Eq (6.15), the specific surface area of CNFs can be calculated as a

OD function of dCNF , assuming the inner diameter of CNF is a constant, 40 nm.

102 1315⋅ d OD 1778 4. ⋅ d OD SA(CNF) = CNF = CNF (6.16) n−1 OD 2 OD ⎡ ⎤ (dCNF ) − 40 ndCNF − 68.0 ⎢∑i⎥ ⎣ i=1 ⎦

Therefore, we can assume the diameter of CNFs was 87 nm with 70 walls of graphic sheets. The specific surface area of the CNF can be obtained by Eq (6.16) ς (CNF) =26.07 (m2/g)

6.4 Specific Surface Area of Buckypapers

We then expanded the scale from a single nanotube to nanotube network, and used the characterization of nanostructure to estimate the surface area of buckypapers.

6.4.1 Specific Surface Area of SWNT Buckypaper

SWNT is the basic element in buckypaper because of its large aspect ratio and self- assembling effect. Figure 6.6 shows a concave function of surface area vs. SWNT bundle size. The specific surface area decreased as bundle diameter increased. The dot in the figure shows the actual BET surface area of the SBP sample as measured by the Tristar 3000, and the corresponding bundle diameter was 10 nm, which is consistent with the characterization of the nanostructure (the inset) in our experiments. By achieving better dispersion, the diameter of SWNT bundles can be reduced below 5 nm, as discussed in Chapter 3, and the resulting specific surface area is expected to improve 40 to 50%.

103 522.24 m2/g SBP

Figure 6.6 Specific Surface area of SBP vs. SWNT bundle diameter. The dot represents the measured surface area of the SBP, and the inset is the rope size distribution of the SBP sample.

6.4.2 Specific Surface Area of Mixed Buckypaper

The mixed buckypaper is a hybrid network of SWNT bundles, MWNTs or CNFs. As a result, the specific surface area of MBPs is a combination ofς (SWNT ) ,)ς (MWNT , andς (CNF ) . Eq (6.7) demonstrates the specific surface area calculation based on its components (A and B). When two materials were mixed in a system, the specific surface area takes both materials according to rule of mixture.

S A S B S S + S ⋅ wA + ⋅ wB ς A)( ⋅ w + ς B)( ⋅ w ς (A + B) = = A B = wA wB = A B (6.17) w wA + wB wA + wB wA + wB

104 where SA and SB are the surface area of two components individually, and wA and wB are weights of two components, respectively. The specific surface area follows the rule of mixture.

Consequently, specific the surface area of MBPs can be calculated as

OD ⎡ 28.46 ⋅ d MWNT ⎤ ς (SMBP) = r[]ς (SWNT ) + 1( − r)⎢ OD ⎥ (6.18) ⎣ d MWNT −10 ⎦

OD ⎡ 87.11 ⋅ dCNF ⎤ ς (SFBP) = r[]ς (SWNT ) + 1( − r)⎢ OD ⎥ (6.19) ⎣ dCNF − 38 ⎦ where r is the weight ratio of SWNT content in a mixed buckypaper.

The diameter of SWNT bundles and number of walls of MWNTs and CNFs are the key factors in determining the surface area of the resulting buckypapers. These effects of nanostructure on specific surface area of MBPs are plotted in Figure 6.7, as examples of 1:3 SMBP and 1:3 SFBP.

Taking SMBP and SFBP buckypapers with a mixture ratio of 1: 3 as the examples, Figure 6.7 (a) and (b) demonstrate the change of surface area over the diameter of SWNT bundles, diameter of MWNTs, and the diameter of CNFs. The surface area of SMBP can be as high as 895.41 m2/g when the diameter of SWNT bundles is below 6 nm and diameter of MWNTs is below 15 nm. The specific surface area decreases as a separated concave functions as the diameter of SWNT bundles increased, and was down to 75.14 m2/g when the diameter of the SWNT bundles was up to 22 nm and the diameter of MWNTs was over 40 nm.

105 (a)

1-layer SWNT bundle

2-layer SWNT bundle

3-layer SWNT bundle

4-layer SWNT bundle

5-layer SWNT bundle

(b)

1-layer SWNT 5-layer SWNT

2-layer SWNT 6-layer SWNT 7-layer SWNT 3-layer SWNT 8-layer SWNT 4-layer SWNT

Figure 6.7 Prediction of BET surface areas of MBP over diameters of SWNT bundles, MWNTs and CNFs, with a mixture ratio of 1:3. (a) SMBP with ratio of 1:3(b) SFBP with ratio of 1:3.

106 The surface area of SFBP with a weight ratio of 1:3 reached as high as 864.35m2/g when the diameter of the SWNT bundles was below 6 nm and the diameter of CNFs was below 60 nm. The surface area decreased as a separate concave functions as the diameter of SWNT bundles and the diameter of CNFs increased, and was down to 43.3m2/g when the diameter of SWNT bundles was up to 34 nm and the diameter of CNFs was up to 200 nm. MBPs with different mixed ratios were also studied. Similar trends were found in both SMBP and SFBP that the surface area of MBPs are primarily determined by the diameter of SWNT bundles and number of walls in MWNTs or CNFs.

MBP is proposed as an alternative because of its excellent properties similar to SBP and also because it is cost-efficient. Mixing ratios have large effects on cost reduction. We explained the relationship of cost reduction in percentage and the surface area by using SMBP as an example, illustrated in Figure 6.8. For instance, we assumed the diameter of SWNT bundles in SMBP was 6 nm, MWNT has 7 walls and diameter 15 nm. It is also assumed the cost of SWNT is dominating by factoring in the cost of buckypaper. The axis of cost saving starting from pure SBP (mixed ratio=0), the cost reduction is zero. By replacing 50% (1:1), 75% (1:5), 83% (1:5), 87.5% (1:7) and 90% (1:9) of weight by MWNTs to the buckypaper, the cost of MBP is reduced gradually from 50% to 87%. Effects of the mixing ratios on surface area (solid line) and cost saving (dash line) estimates of the SMBP are demonstrated in Figure 6.8. It can be seen that the surface area gradually decreases as the weight ratios of SWNT decrease, but the reduction of SWNTs also provokes the cost saving sharply. As a result, a ratio of 1:1 is probably the most economical way to produce SMBP, and the resulting surface area remained 500 m2/g but saved 50% of the cost when compared to SBP.

107 Cost Reduction (%) Cost Reduction

Figure 6.8 Mixed ratios vs. cost saving and surface areas of SMBP. The dash line is cost saving percentage and the solid line is the estimated surface area.

The models displayed above allowed us to tailor the surface area of MBPs based on their nanostructure. The cost reduction also can be calculated based on the mixing ratios. This information allows us to optimize the performance/cost ratio of buckypaper products.

6.5 Nanostructure and BET Surface Area

Based on the proposed model of specific surface area, we can estimate the surface area of buckypaper based on the characterization of rope size distribution of nanomaterials. In Chapter 5, the rope size distribution was fitted into a continuous Weibull distribution. However, according to the assumption of the specific surface area model, the diameter of SWNTs was defined as discrete clusters. For example a 6nm bundle is composed of 7 nanotubes, and the next size is a 10nm bundle composed of 19 nanotubes, and so on. To further explore the surface area of an SWNT network, both

108 average rope size and the discrete distribution of rope sizes were used to estimate the surface area of buckypaper. The continuous Weibull distribution was divided into several segments to fit the discrete bundle size. The result showed that the estimation of using distribution resulted in a higher surface area than estimated using average rope size. This suspects a disproportionate effect on different rope size, and the surface area of SWNT buckypaper is primarily driven by small-size and high-surface-area nanotube ropes. The Specific surface area of MBP predicted from specific surface area model was compared and validated with experimental results of BET surface area using a Tristar 3000. The results showed that the experimental measurement agreed well with model prediction and fell within the prediction range between the estimations based on average rope size and discrete distribution. More details on estimation of surface area using average rope size and discrete distribution are given in the following text.

6.5.1 BET Surface Area of SMBP

BET surface area of SMBP is estimated using both average rope size and discrete distribution. Figure 6.9 plots the estimated surface area using both average rope size and discrete distribution. The trend of surface area was estimated using average rope size agreed with using discrete distribution, but was lower by 30 to 50%. The significance demonstrates the difference in assumptions of proportionate and disproportionate effects on different rope sizes.

The change of surface area along with mixed ratio is relatively flat, which implies that the surface area of SMBP is less sensitive to the mixed ratio. Because the surface area of few-layered MWNT is comparable to that of SWNT. The specific surface area of a SMBP can be determined by the rope size distribution of SWNTs and MWNTs, the rope size distribution plays an important role in SMBPs.

109

Model(Average)

/g) Model(Distribuiton) 2 Experiment

Specific Surface Area (m Surface Specific :SMP :SMP :SMP :SMP Mixed Ratio

Figure 6.9 Model estimation and experimental result of BET surface area of SMBP with different mixed ratios

6.5.2 BET Surface Area of SFBP

BET surface area of SFBPs is estimated by using both average rope size and discrete distribution. Figure 6.10 plots the estimated surface area using both average rope size and discrete distribution. The trend of surface area estimated using average rope size agreed with using discrete distribution, and closer than that of SMBP, around 10 to 30%. The change of surface along with mixed ratio is highly related. Because of the distinctive sizes of SWNTs and CNFs, the rope size of CNFs is almost one order of magnitude higher than that of SWNTs. Therefore, the BET surface area of a SFBP is expected to be dominated by the BET surface area of SWNTs, and its volume a fraction.

110 600

Molvrg /g)

2 500 Molistriuiton 400 xprimnt

300

200

100 Specific Surface Area (m Surface Specific 0 1:1SFBP 1:2SFBP 1:3SFBP 1:7SFBP Mixed Ratio

Figure 6.10 Model estimation and experimental result of BET surface area of SFBP with different mixed ratios

6.7 Summary

This chapter discussed the BET surface area of mixed buckypapers, and proposed models of specific surface area based on the nanostructure of MBPs. Both average rope size and discrete distribution of rope size were used to estimate the BET surface area of MBPs with different mixed ratios. The estimation of specific surface area model agreed well with experimental measurements of the BET surface area. The results showed that the BET surface area is highly dependent on the nanostructure and mixed ratio of MBPs. The BET surface area of SMBP is more dependent on the rope size distribution than mixed ratio because of the comparative surface area of SWNTs and MWNTs. On the other hand, the BET surface area of SFBP exhibits high dependency on the mixed ratio and rope size of SWNT because of the distinct rope sizes of SWNTs and CNFs. The rope size and volume fraction of SWNTs dominates the surface area of SFBP.

111 CHAPTER 7 ELECTRICAL RESISTIVITY OF BUCKYPAPERS

7.1 Introduction

SWNT networks have been found to perform a variety of electronic functions and can be utilized as a conductor or a semiconductor. Researchers can make such SWNT networks mimic the conductivity of a metal such as copper or as a semiconductor such as silicon [160]. These innovations have paved the way for applications with carbon nanotubes to assume multifunctional roles in electronic devices. SWNTs have been proposed as an ideal system for the realization of molecular electronics [161]. The applications of SWNTs include devices such as field-effect transistors [162-163], single- electron-tunneling transistors [164-165], and rectifiers [166-170]. However, the use of joining individual SWNTs to form a network for device application and, ultimately, complex circuits remains unclear. We will discuss multicale electrical transport phenomenon and construct an electric circuit model of SWNT networks in buckypapers.

7.2 Experiment

Before developing a working model for the resistivity of buckypaper, experiments were performed to provide a physical reference to compare with the proposed model. The four-probe method was used to measure the conductivity of buckypaper, based on the IEEE Standard Test Methods for Measurement of Electrical Properties of Carbon Nanotubes (IEEE std 1650-2005) [171-173]. The method is a force-current and measure- voltage (FCMV) method, which employs the four-wire (Kelvin) connection scheme. The resistance of the sample is determined by passing a known direct current I and measuring the resulting voltage drop ∆V. The resistance is found by simply applying Ohm’s law to obtain R= ∆V /I. The scheme of the apparatus is shown in Figure 7.1. The test current (I) supplied by a current source is forced through the resistor (R) through one set of test cables, meanwhile the voltage (V) across the unknown resistance (R) is measured through

112 a second set of leads connected to the voltmeter. Although some small current may flow through the voltmeter leads, it is usually negligible and contact resistance between resistor and apparatus can generally be ignored for all practical purposes. The voltage measured by the measurement unit is essentially the same as the voltage across the unknown resistance (R).

Figure 7.1 Four-probe apparatus of measuring resistivity of buckypaper [171]

7.3 Methodology

In a macroscopic conductor, the resistivity and the conductivity are physical properties which do not generally depend on either the length of the wire or the applied voltage to the sample but only on the material [29]. However, when the size of the wire becomes small compared with the characteristic lengths for the motion of electrons, then resistivity and conductivity will both depend on the length through quantum effects. At the quantum scale, the electrons act like waves that show interference effects, depending on the boundary conductions, the impurities and defects that are present in the nanotube [29].

113 7.3.1 Intrinsic Resistance of SWNTs

We considered two lengths for the nanotube characteristic intrinsic resistance. First is the momentum relaxation length, also called the mean free path ( Lm ). Lm is the average length that an electron travels before it starts scattering. Second is the phase- relaxation length ( Lφ ), which over an electron retains its coherence as a wave. These characteristic lengths define the transport regimes: ballistic and diffusive.

At room temperatures, a SWNT is a quantum wire in which the electrons in the SWNT move without scattering, and such SWNT was defined as ballistic [174]. Ballistic transport consists of single electron conduction with no phase or momentum relaxation. The length of a ballistic SWNT is smaller than both the momentum relaxation length and phase-relaxation length ( L << Lm , Lφ ). In the diffusive regime where elastic scattering occurred, the conductance of a diffusive SWNT satisfies Ohm’s law, and both momentum and phase relaxation occur ( Lm ,)Lφ << L .

Nieuwoudt et al. [175-178] discussed electrical resistance of SWNT bundles for very-large-scale integration (VLSI) applications. They assumed each SWNT had an effective resistance from both the intrinsic ballistic resistance (Ri) and a contact resistance

(Rc) between SWNTs and on-chip metal components. Nieuwoudt et al. defined a distributed resistance (R0) which captures the ohmic resistance of the SWNT. To model the ohmic and contact resistances for SWNT bundle interconnectivity, a diameter- dependent model was utilized. For nanotubes operating in the low bias regime

(Vb ≤ 1.0 V ), the total resistance is

R = Ri + Rc if lb ≤ Lm (7.1)

R = R0+Ri + Rc if lb > Lm (7.2) where lb is the bundle length and Lm is the mean free path.

The intrinsic resistance (R ) of a ballistic SWNT is R = h ≈ 5.6 kΩ , h is i i 4e 2 Planck’s constant, and e is the charge of a single electron [179]. The ohmic resistance of

114 h lb a SWNT is R0 = ( 2 )( ) . Recent experimental evidence and theoretical 4e Lm formulations have demonstrated that Lm is proportional to the diameter of a single nanotube, dt [179-180]. The resistance of an individual SWNT versus diameter is

hα bTl governed by R0 = ( 2 ) where vF is the Fermi velocity in graphene, T is the 4 ve dtF temperature in Kelvin, and α is the scattering rate [179]. Therefore, the diameter- dependent equivalent ohmic resistivity of a SWNT is h ρ SWNT = 2 (7.3) 4e Cλ dt where Cλ is the proportionality constant of Lm to dt, which was defined as L C = m (7.4) λ d t0 based on the experimental data obtained in Park et al. [179], where d was measured as t0

1.8nm and Lm as 1600nm.

The resistance of the SWNT bundle is defined by the parallel combination of individual SWNT resistance, Rbundle = Rt / nb , where Rt is the total resistance of an individual SWNT and nb is the number of nanotubes in a bundle.

Li et al. [182] measured resistance against different lengths from the literature [183-185], as plotted in Figure 7.2. The results demonstrated a linear relationship with a resistance per unit length of 6 kΩ / um . The resistance is close to the ballistic limit in nanotubes less than 10μm, and the increase of resistance within this range is considered to be negligible when compared to the contact resistances in a SWNT network [182].

115 [182] [183] [184] [185]

Figure 7.2 Linear relationship of intrinsic resistance and length [182]

7.3.2 Intercontact Resistance of SWNT

In addition to the intrinsic resistance of SWNTs, intercontact resistance between nanotubes must be addressed as well. Li et al. [182] suggested for very short CNTs in the ballistic limit, contact resistance dominates the resistance of a SWNT network. Conversely, for long CNTs, the contact resistance is negligible. A parting length is around 10μm, and intrinsic resistance of SWNT is below 100 kΩ . The average length of the SWNT bundle, measured in Chapter 5, is within this range, and therefore, we considered the intrinsic resistance of SWNTs in buckypaper as negligible and focused on several other sources of resistance.

116 Stadermann et al. [186] measured the local conductance of carbon nanotube networks and demonstrated that the conductance does not decrease linearly with the distance from the electrode. These discontinuities in conductance are shown Figure 7.3 and demonstrate the significance of intercontact resistance. The conductance through the network stays at the same order of magnitude throughout the network, but then decreases dramatically at intercontact points in the network.

Figure 7.3 Configuration of the drop of conductance and corresponding intercontact points [185]

117 7.3.2.1 Intercontact Resistance and Contact Angle

Buldum et al. [187] described the contact resistance between nanotubes as a simple two-terminal nanotube junction. The junctions of individual nanotubes are considered as quantum conductors and the ohmic behavior of these junctions is related to their positions, orientations and chiralities. Nanotube junctions can be formed into many geometrical forms as depicted in Figure 7.4. In the equilibrium position, a nanotube junction can be in atomic scale registry and the contact region structure is like the AB stacking of graphite. Two types of registry are considered in-registry and out-of-registry. Figure 7.4 illustrates the different types of stacking. In-registry refers to two parallel graphite sheets coaxial in both the x and y direction, like AA stacking in the diagram, or in the x or y direction, like AB stacking in the diagram. Comparatively, out-of-registry is referred to two parallel graphite sheets deviated from one another, like ABC stacking in the figure [188].

Figure 7.4 Configuration of different types of stacking [188]

It was found that the conductance values are high and comparable to ideal tubes when the tubes are in-registry. Therefore, simple end-end contact geometry is an ideal way of connecting multiple tubes. Small displacements of tubes from the in-registry configuration lead to a dramatic reduction for the intertube conductance. The low contact resistance for in-registry configurations can be understood by considering the strong coupling of electronic states between the tubes that are in-registry. Although the magnitudes of individual hopping integrals between the atoms of different nanotubes are similar for in-registry and out-of-registry junctions, phase coherence is achieved in the registry junction, which enhances the coupling of the electronic states between the nanotubes [187].

118 A mixed junction of an armchair (10,10) and a zigzag (18,0) tube junction was studied [187]. A four-terminal junction may be formed by placing one nanotube perpendicular to another, as shown in Figure 7.5. Conductance was measured by passing current through two terminals and the voltage was measured using the other two. Results from [187] showed that the conductance between nanotubes depends strongly on the atomic structure in the contact region. The conductance is high when two nanotubes are in-registry. Thus, an armchair nanotube crossing a zigzag nanotube forms an in registry junction and the conductance is high. In contrast, two perpendicular armchair nanotubes form an out-of-registry junction, and the resulting conductance between the nanotubes is considerably decreased.

Figure 7.5 Configuration of nanotube junction [187]

In general, electrical conducting properties can be achieved by rotating the junctions. Figure 7.6 presents the contact resistance with respect to rotation angle Θ on tubes of different chiralities, with the lowest resistance found when the junction is in the registry configuration. In the case of the (18,0)-(10,10) junction, the nanotubes are in- registry at Θ =30 o, 90 o and 150o. In the (10,10)-(10,10) junction, the nanotubes are in- registry at Θ =0 o, 60 o, 120 o, 180 o. Even when the nanotubes are in registry, the contact resistance can be different at different Θ due to difference in registry levels. The lowest resistance is achieved when the contact structure is in-registry, like AA stacking of graphite sheets.

119 (a) (b)

Figure 7.6 Contact resistance of (a) a (18,0) and (10,10) junction as a function of rotation angle Θ , (b) a (10,10) and (10,10) junction as a function of rotation angle Θ [187] .

7.3.2.2 Intercontact Resistance and Contact Area

The intercontact resistance can be considered as a function of the contact area between the intercontact nanotubes. Buldum et al. [187] discussed three structural configurations: rigid contact, relaxed contact, and force contact. These effects were investigated by performing molecular dynamic simulations. An example of a junction with a 3nN applied force is shown in Figure 7.7. Ohmic characteristics of rigid, relaxed and force cross junctions are presented in Figure 7.8. Results from [191] demonstrated that nanotubes in-registry experience a resistance drops for both relaxed and applied force contacts. In contrast, when the nanotubes are out-of-registry, the change in resistance between a relaxed state and applied force state is small. Table 7.1 summarizes the contact resistance of in-registry and out-of-registry situations with respect to the three different contact areas.

The obtained literature work had only discussed the two extreme cases at in- registry and out-of-registry, but states in betweens the two are possible, like AB stacking depicted in Figure 7.4. Therefore, the resistance of intercontact is assumed to be a random uniform distribution with resistance between in-registry and out-of-registry considered as two extreme values of the distribution.

120

Figure 7.7 Relaxed cross junction with applied forces [191]

Figure 7.8 I-V curve of different contact area [191]

Table 7.1 Contact resistance with different registries and contact area In-registry Out-of-registry Rigid 2.05 MOhm 3.36MOhm Relaxation 682kOhm 3.21MOhm Force 121kOhm 1.66MOhm

7.3.2.3 Intercontact Resistance and Type of Contact

Nanotubes may be metallic or semiconducting, depending on their chirality, and the intercontact resistance is strongly dependent on the type of respective [189-191].

121 Fuhrer et al. [192] studied the effects of intercontact types using both two-terminal and four-terminal devices, where a four-terminal configuration is exhibited in Figure 7.9.

The type of intercontact between two nanotubes can be metal-metal (MM), metal- semiconducting (MS) or semiconducting-semiconducting contacts (SS). From a two- terminal apparatus, the conductance of SS junction is measured as high as 0.06e2/h [192]. This value is an upper bond for the true SS junction conductance and indicates that SS junctions, like MM junctions, make relatively good tunnel contacts. The I-V curve of different types of junctions is shown in Figure 7.10.

The MS junction is fundamentally different from both MM and MS junctions. The mismatch of energy gap of semiconducting SWNT and Fermi level of metallic SWNT is expected to form a Schottky barrier. Because the charge transferred at the junction between a semiconducting SWNT and metallic SWNT creates an energy barrier between two states [191]. Hence, the Fermi level EF of the metallic SWNT should align within a band gap of the semiconducting at the junction, depleting the doping of the semiconducting SWNT at the junction. Far from the junction, however, EF is in the valance band of the semiconducting SWNT [193].

Thus, in addition to the tunnel barrier between the two SWNTs, there also exists a Schottky barrier approximately equal to half the band gap of the semiconducting SWNT. The depletion region in the semiconducting SWNT associated with the Schottky barrier represents an additional tunneling barrier Ebarrier [192]. The V intercept of the linear region of Figure 7.10 (c) gives a measure of the barrier height, Ebarrier =190~290 meV.

This agrees reasonably well with the expected barrier height Ebarrier = Eg /2 ≈ 250 to 350 meV, where Eg ≈ 500 to 700 meV for 1 to 1.5nm semiconducting SWNTs.

122

Figure 7.9 AFM image of a four-terminal device [192]

(b) (a)

(c)

(d)

Figure 7.10 (a) I-V curve of MM and MS junctions; (b) the MM, (c) the SS and (d) the MS junctions [192].

7.3.2.4 Intercontact Resistance with Diameter and Length Effects

Besides the contact area and type of nanotubes at the intercontact, the geometry of the nanotube bundles that comprise the network is also expected to have a substantial

123 impact on the conductivity of the SWNT network. Hecht et al. [194] measured the conductivity of the SWNT network as a function of the average diameter and length of SWNT bundles within the network, respectively. It was assumed that in a SWNT network, the junction resistance dominates the total network resistance. The conductivity of the network will be higher for networks comprised of longer nanotubes, because there will be fewer nanotube-nanotube junctions across the sample. Figure 7.11 shows that longer tubes lead to fewer junctions across the surface and lead to higher conductivity. On the other hand, large bundles lead to lower conductivity as σ ~d −β (7.5) where σ is the conductivity and d is the average diameter of a SWNT network, and β =2 is an upper limit to the exponent [194]. This implies that sufficient sonication can result in more uniform and smaller SWNT bundles in the dispersion, and lead to increasing conductivity of SWNT networks.

(a) (b) Figure 7.11 Configuration of conductivity relative to (a) length effect and (b) diameter effect.

Hecht et al. [194] demonstrated that, under the same diameter range, the resistivity is exponentially proportional to length with exponent, σ ~Lα (7.6) where L is the average length of a SWNT network, and α is a exponent between 0 and 2.48 [195]. Figure 7.12 presents experimental results from Hecht et al. [194] for conductivity against the corresponding average bundle length, and yields a best fit

124 relationship of σ ~ L 46.1 . However, the result only applies to samples where the bundle diameter does not vary concurrently with the average bundle length, because the diameter of bundle should also have an effect on the sample conductivity. On the other hand, since SWNT networks with equal length can not be created, the exponent β cannot be determined.

Figure 7.12 Conductivity vs. average bundle length [195]

Hecht et al. [194] mentioned that when the average length within the network approaches 20-30 μm , the resistance along the nanotube itself becomes comparable to the resistance of the junction. Therefore, further increases in the nanotube length will have a limited impact on the conductivity of the networks. Nevertheless, the conductivity of SWNT networks can be improved by doping, purification of tubes or enhancement the number of metallic SWNTs in the network.

125 7.4 Electronic Circuit Model of Buckypaper

There have been reports on the conductivity of SWNT networks, with values ranging from 400 to 6600 S/cm [196-197]. The discrepancy in these values arises due to many factors that can affect the conductivity of SWNT networks, including the doping level of the semiconducting SWNTs, sample purity, and the metallic to semiconducting volume fraction. In this section, the electric circuit model of buckypaper is presented to estimate the electrical conductivity of a SWNT network.

7.4.1 Assumption

A SWNT buckypaper is comprised of two distinct sources of resistance, the intrinsic resistance along the SWNT itself, and the intercontact resistance due to the nanotube to nanotube junction. However, from the characterization of length distribution discussed in Chapter 5, the average length of SWNT is 1.89μm. According to Li [182] and Hecht [194], the intrinsic resistance of SWNT with length less than 10μm is negligible and the resistance of SWNT networks is dominated by the contact resistance. In fact, the calculated intrinsic resistance of SWNTs of 2μm in length is nearly two orders of magnitude lower than the intercontact resistance. Therefore, we assumed the resistance of SWNT buckypaper is dominated by intercontact resistance and neglected the intrinsic resistance.

As for the intercontact area between SWNT, the rigid assumption of SWNT is far from reality and the force assumption requires a significant pressure to be applied on the intercontacts, which is not the case for the investigated buckypaper. Therefore, the intercontacts within the buckypaper are assumed relaxed, and the intercontact of two bundles take place at individual nanotubes within each SWNT bundle and these nanotubes are slightly deformed during intercontact. The intercontact resistance is assumed to follow a uniform distribution between 600 and 3210 kOhm.

Ric ~ U[600kΩ,3210kΩ]

126 The volume fraction of metallic nanotubes is not available from the raw materials vender. However, the metallic properties are determined by the chiral vector (m,n). If (n+m)/3 = integer, the nanotube acts as a metal, otherwise it acts as a semiconductor [30]. Therefore, the metallic portion of SWNT network for typical buckypapers is assumed to have a probability of 1/3 with the remaining 2/3 being semiconducting [26]. In a network of SWNTs, a junction of nanotubes can be composed of MM, MS, or SS, as discussed previously in 7.3.2.3. The probability of metallic nanotubes intercontact with semiconducting nanotubes is twice higher than metallic nanotubes, and the probability of semiconducting nanotubes intercontact with semiconducting nanotubes is twice more than metallic nanotubes. Therefore, the probability of MM contact is 1/9, MS contact is 4/9 and SS contact is 4/9. The estimated resistance of MM intercontact is 200~300kOhm, SS intercontact is 300~400kOhm and MS contact is 1 order of magnitude higher than the other contact, 2~4MOhm.

The chirality and angle of two intercontact tubes determined the registry situation of the intercontact. However, chirality information is hard to obtain from the manufacturer and the registry cannot be modeled without the given chirality. Therefore, to represent unknown chirality of our nanotubes, we considered all of the entire range of estimates given in the literature to cover most situations [185-194]. The nanotubes are assumed to be in the relaxed state; therefore, the nanotubes are slightly deformed during intercontact, and the intercontact of two bundles take place at individual nanotubes.

Therefore, the MM intercontacts of both registry situations are assumed to be random uniform distribution, ranging from 200kOhm to 3.2MOhm. The MS intercontacts of both registry situations are assumed to be random distribution, ranging from 2MOhm to 32MOhm, and SS intercontacts of both registry situations are assumed to be random uniform distribution, ranging from 300k to 3.2kOhm.

127 7.4 2 Electric Circuit Model Parameters

Several parameters of resistance of SWNT network were discussed in the literatures [185-194], and many of them are based on solely experimental data or simulation results. We selected the relevant parameters to generate the function of resistance, and discuss the impact of these parameters in the following text.

Seven parameters were outlined from the previous discussion, intercontact angle (θ ), chirality (C), contact area (A), registry (R), volume fraction of metallic nanotube (V), diameter of SWNT bundle (d), and length of the SWNT bundle (L). Therefore, the intercontact resistance of SWNT buckypaper can be expressed as

Ric = f θ C A R V d L),,,,,,( (7.7)

The intercontact angle,θ , is assumed to be random uniform distribution between 0 and 2π for an isotropic buckypaper, and for an aligned buckypaper, it is assumed to belong to a cosine distribution, f θ )( = k cos 2n θ (7.8) n =0, if f(θ ) is a random distribution n =1,2,…, if f(θ ) is aligned distributions

The diameter of the bundle is considered as a function of the number of individual nanotubes in a bundle, as discussed in Chapter 6. Therefore, the diameter of a nanotube is classified into 8 categories, representing bundles of 0 to 7 layers of SWNTs in a bundle, ranging from 2 to 30nm. From the characterization of nanostructure discussed in Chapter 5, the proposed range of diameters covers the experimentally measured nanotube diameter distribution after dispersion. The length of nanotubes has been increased as technology improves [182]. Therefore, we investigate the length range from the shortest to the longest in the intercontact resistance dominant regime, 0.5 to 10μm.

Each of the previously discussed parameters is observed from experimental data, or our best estimate of the unknown parameters. Unknown parameters of chirality, contact

128 area and contact type were assumed reasonable random uniform distributions of possible ranges. Therefore, the resistance of an intercontact resistance dominant SWNT network is a function of intercontact angle, diameter and length.

Ric = f θ d L),,( (7.9) and case studies based on three parameters will be discussed.

7.4.3 Model Development

The algorithm for the proposed electric circuit model of buckypaper is given by the following steps:

1. Generate parameters (Ni, Xi,θi , di, Li): Ni is the number of nanotubes generated in

the sample; Xi is the coordinate of each nanotube in the sample;θi is the angle of

each nanotubes sampled from Eq(7.8); di is the diameter of nanotube sampled from

the Weibull distribution and Li is the nanotube length which is also sampled from the Weibull distribution.

2. Generate nanotubes in the representative area: the number of nanotubes generated in the representative area is the same as the volume fraction of nanotubes in the buckypaper (about 60% by volume). Figure 7.13 illustrates 10 nanotubes generated in a 6μm by 6μm area.

129

Figure 7.13 Generate nanotubes in specific area

3. Create periodicy of sample. Nanotubes that exit one side are cut at the point of exit, and mapped periodically to the opposite side, as illustrated in Figure 7.14.

Figure 7.14 Creating periodicy in the area

4. Renumber the nanotubes. The periodic nanotubes are given the same number so that current flow exiting either the top or bottom enters from the opposite side. Those nanotubes entered from left boundary or exited from right boundary are renumbered the same number, respectively, so that current has uniform flow front from left to right or vise-versa, as illustrated in Figure 7.15.

130 − I

Figure 7.15 Renumber periodic nanotubes

5. Find the intercontact node ni. Overlapping nanotubes are found and the intercontact

node ni is numbered. Only connected pathways are left in the sample, and non- connected tubes are removed. Figure 7.16 illustrates intercontacted nodes are tabulated and numbered.

Figure 7.16 Find and number intercontact nodes

6. Assign resistance to each node ni. The resistance at each node is randomly selected such that each sample is a random variable from section 7.4.1. Table 7.2 represents random resistances assigned to the nodes for our simple example.

131 Table 7.2 Assign resistances to nodes Node (i) SWNT_a SWNT_b Resistance (kOm)

1 1 2 26714.7 2 1 3 391.3497 3 1 8 25633.37 4 2 3 294.69 5 4 5 350.96 6 4 8 330.26 7 5 6 224882.43 8 5 7 24069.66 9 6 8 229.95 10 6 7 277110.04

7. Generate master matrix. Figure 7.17 illustrates pathways of current flow were found from tube 3 to tube 6. Eq (7.10) demonstrates an 8 by 8 electric circuit matrix from the configuration using a simplified finite element technique.

Figure 7.17 Find pathways of current flow

132

⎡ 1 1 1 1 1 1 ⎤ − − − 0 0 0 0 ⎢ R R R R R R ⎥ ⎢ 1 2 3 1 2 3 ⎥ 1 1 1 1 ⎢ − − 0 0 0 0 0 ⎥ ⎢ R R R R ⎥ (7.10) 1 1 4 4 ⎡v ⎤ ⎡ 0 ⎤ ⎢ 1 1 1 1 ⎥ 1 ⎢ − − 0 0 0 0 0 ⎥⎢ ⎥ ⎢ ⎥ v2 0 ⎢ R2 R4 R2 R4 ⎥⎢ ⎥ ⎢ ⎥ ⎢ 1 1 1 1 ⎥⎢v3 ⎥ ⎢ I ⎥ 0 0 0 − − 0 0 ⎢ ⎥ ⎢ ⎥ ⎢ R R R R ⎥ v 0 ⎢ 5 6 5 6 ⎥⎢ 4 ⎥ = ⎢ ⎥ 1 1 1 1 1 1 ⎢v ⎥ ⎢ 0 ⎥ ⎢ 0 0 0 − − − 0 ⎥ 5 ⎢ ⎥⎢ ⎥ ⎢ ⎥ R5 R5 R7 R8 R7 R8 v − I ⎢ ⎥⎢ 6 ⎥ ⎢ ⎥ 1 1 1 1 1 1 ⎢ ⎥ ⎢ ⎥ ⎢ 0 0 0 0 − − − ⎥ v7 0 ⎢ R R R R R R ⎥⎢ ⎥ ⎢ ⎥ 7 7 9 10 10 9 v 0 ⎢ 1 1 1 1 ⎥⎣⎢ 8 ⎦⎥ ⎣⎢ ⎦⎥ ⎢ 0 0 0 0 − − 0 ⎥ ⎢ R8 R10 R8 R10 ⎥ ⎢ 1 1 1 1 1 1 ⎥ ⎢ 0 0 0 0 − − − ⎥ ⎣ R3 R6 R9 R3 R6 R9 ⎦

The master matrix is formed according to Kirchhoff’s current rule [198]. The charge flows from the left hand side is equal to the charge that flows out of the right hand side. Therefore, at any node in an electrical circuit where charge density is not changing in time, the sum of currents flowing into the node is equal to the sum of currents flowing away from the node.

8. Compute effective resistance Reff, of the specific area. Eq (7.11) calculates effective resistance of the representative element. I R = (7.11) eff v where v is the potential drop from the left hand side nodes to the right hand side nodes.

9. Compute resistivity ρ , and conductivityσ of the whole sample. The buckypaper in

Figure 7.18 shows a representative area of a sample. The effective resistivity ρeff can be calculated from the effective resistance of the representative area with area a’ and width w’, which is shown in Figure 7.18. The resistivity is dimensionless, and therefore, the effective resistivity of the representative area is the same as the resistivity of the 1st layer ( ρ ). L1

133 a' ρ = R = ρ (7.12) eff eff w' L1

The resistance of the first layer is calculated with the following w w R = ρ = ρ (7.13) L1 L1 a eff a

The resistance of sample is assumed to be a parallel circuit of layers L1 to LN, and can be calculated as. R ρ × w R = L1 = eff (7.14) sample N N × a

The resistivity of the representative sample ρ sample can be calculated from the resistance of sample Rsample, as Eq (7.12). a× N ρ × w× a× N ρ = R ⋅ = eff = ρ (7.15) sample sample w N × a× w eff The above equation demonstrates how the resistivity of a sample is equivalent to the effective resistivity of the specific area. Therefore, the conductivity of the sampleσ sample can be calculated as the inverse of ρ sample . 1 σ sample = (7.16) ρeff

w’ Reff a’

L1 w …. L a N

Figure 7.18 Configuration of resistance of specific area and sample

134 7.5 Case Studies

In this section, several case studies for the resistivity of the buckypaper will be discussed using the proposed electric circuit model.

First, a representative sample size must be decided. Modeling all nanotubes in the buckypaper is beyond the computational capability of a modern computer. Therefore, a representative unit sufficiently large enough to represent the system is more efficient and less time-consuming. This representative unit is able to give an accurate estimation of the conductivity of the buckypaper. Figure 7.19 demonstrates the change of decreasing resistance respect to increasing boundary widths under the same volume fraction of nanotubes. Assuming the width of the specific square area (w) is a multiple of nanotube length L, where w=1L, 2L, 5L, 7L and 10L. The change in resistance with increasing w is considered negligible at w=5L and the change in resistivity is less than 10% afterward. This implies that a specific area with length w=5L is representative of the resistivity of the buckypaper. Therefore, a representative area of w=5L will be used throughout all the case studies.

100% y = 1.01 x-1.46 80% R2 = 0.99 60%

40% Resistance (kOhm) 20%

0%

01234567891Sample Length (w) 0

Figure 7.19 Resistance vs. sample size

135 7.5.1 Diameter Effect

In Chapter 6, the diameter of the bundle is considered a function of the number of individual nanotubes in a bundle. From the characterization of nanostructure, the range of rope sizes of SWNT bundles is from 2 to 30nm. A 2nm SWNT implies that there is a single nanotube in the bundle, while a 30nm SWNT bundle means there are 7-layers of nanotubes forming the bundle, as reiterated in Figure 7.20.

2nm 6nm 10nm

Figure 7.20 Diagram of the diameter of a SWNT bundle

We investigated 8 different diameters of bundles. The volume fraction of nanotubes in a buckypaper is 60%, with a length of 2μm, the sample area is a 10μm by 10μm square. For the above geometric constraints, the number of bundles generated for a given bundle diameter is listed in Table 7.3.

Table 7.3 Diameter of SWNT bundle and corresponding sample size Diameter 2 6 10 14 18 22 26 30 N 23961 3423 1261 648 393 263 189 142

The results showed that the conductivity increases as the nanotube diameter decreases, as shown in Figure 7.21. Small bundles of nanotubes create more pathways than large bundles under the same volume fraction, allowing more routes for current to traverse the sample, and result in higher conductivity. Increasing the nanotube size, though increasing the geometrical contact area, in fact reduce the relative weight of conducting channel wave function around the contact [187]. When the diameter of nanotubes reduces to 2nm, the conductivity of a SWNT network (1.5×105 S/cm) of 60%

136 volume fraction is only 1 order of magnitude lower than individual nanotube (1× 106 ~3×106S/cm).

A regression function is proposed to fit the data in Figure 7.21 assumes the conductivity follows a power law relationship with the diameter of SWNT bundle. Conductivity = 108 × d − 32.4 (7.17) The R2 is 0.97, implying the selection of the power relationship of diameter and conductivity is statistically acceptable and captures the relationship between conductivity and SWNT bundle diameter satisfactorily. A reduction in bundle diameter of SWNT is expected to improve the conductivity significantly. From the statistical analysis of SWNT rope size in Chapter 3, sonication is critical to the diameter of SWNT bundle, and sufficient sonication can break SWNTs into smaller size bundles and result in higher conductivity of the buckypaper.

8.0E+06

6.0E+06

4.0E+06

Conductivity (S/cm) 2.0E+06

0.0E+00 0 5 10 15 20 25 30 35 Diameter of SWNT bundle (nm) Figure 7.21 Conductivity vs. diameter of SWNT bundle

7.5.2 Length Effect

The length of a SWNT bundle is subject to sonication effects and different SWNT synthesis methods. It was addressed in Chapter 4 that strong sonication can break

137 nanotubes into smaller bundles, while also cutting nanotubes into segments. Therefore, sufficient sonication is crucial to de-bundle nanotubes while retaining the length of SWNT bundle of sufficient size to form a flexible network of buckypaper. Therefore, the length effect of SWNTs discussed in this section includes from 0.5μm to 10μm.

Several different lengths of SWNT are investigated, for a SWNT bundle diameter of 10nm, volume fraction of 60%, and representative area dimension of 5 times the SWNT length. The length effect is summarized in Table 7.4.

Table 7.4 Length of SWNT bundle and corresponding sample size Length 0.5 1 2 5 10 w 2.5 5 10 25 50 N 315 631 1261 3153 6306

The results showed that the conductivity increased with increasing nanotube length, as shown in Figure 7.22. In long nanotubes, current can cross the buckypaper through fewer intercontact nodes than short nanotubes. When the nanotube length reaches 10μm, the conductivity of the SWNT network (5×105 S/cm) becomes comparable to individual nanotubes (1×106 ~3×106S/cm).

A regression function is proposed assuming the conductivity satisfies a power law relationship with the length of a SWNT. Conductivity = 3180× L 16.2 (7.18) The R2 is 0.98, which means the power relationship of length and conductivity is statistically acceptable and captures the relationship of conductivity and SWNT length satisfactorily. The proposed regression model agreed well with [194] where conductivity was shown to follow a power-law dependence on the length of the nanotubes given as σ ∝ Lα , where 0 < α < 48.2 (7.19) where the α is 0 when intercontact resistance is negligible and 2.48 when intercontact resistance dominates the network resistance. With α =2.16 in an intercontact resistance

138 dominant case, the estimation of proposed electric circuit model agrees well with literature that conductivity increases with increasing nanotube length.

6.0E+05

5.0E+05

4.0E+05

3.0E+05

2.0E+05

Conductivity (S/cm) 1.0E+05

0.0E+00 024681012 Length of SWNT bundle ( m) μ

Figure 7.22 Conductivity vs. length of SWNT

However, the conductivity will not go to infinity. When the length of a nanotube kept increasing, the intrinsic resistance of SWNT will increase as well and become comparable to intercontact resistance. Therefore, the electrons transport in buckypaper become more complicated when the length of nanotubes reaches 10μm. When the current enters the network of SWNT, not only does intercontact contribute to the voltage drop, but also the intrinsic resistance. As a result, the voltage throughout a nanotube will decrease gradually along with both intercontacts and length of SWNT bundles. We will further discuss the length effect in long nanotubes over 10μm in Chapter 8.

7.5.3 Random and Aligned Buckypaper

The alignment state of nanotubes has a strong effect on the conductivity of buckypaper. Figure 7.23 shows two SEM images of aligned and random buckypapers, respectively. The aligned nanotubes are fabricated in a magnetic field, and the conductivities of both parallel and perpendicular to the aligned direction were measured.

139 Random buckypaper has isotropic nanotubes that the orientation of the nanotubes is assumed to be an isotropic distribution in a plane. The thickness of random buckypapers is thicker than the aligned buckypapers because of better packing of nanotubes along the aligned direction. The volume fraction of nanotubes in a random buckypaper is 60%, with the diameter (di) and length (Li) following the Weibull distributions, as discussed in Chapter 5. The volume fraction of aligned buckypaper is assumed to be 5 to 20% higher than random buckypaper.

di~Weibull (13.52,2.84), Li~Weibull (2.03,1.91) (7.20)

The orientation of nanotubes in the aligned buckypaper is assumed to belong to the distribution defined by the aligned angle (θ ) given as

θ = k cos 2n θ )( , where n = 2,1 .. (7.21)

Table 7.5 listed all different cases studied in this section, including random, aligned, perpendicular and parallel directions, where n is the aligned degree from Eq (7.21) and N is the number of nanotube generated.

Figure 7.23 SEM images of (a) aligned and (b) random buckypaper.

140 Table 7.5 Aligned field, sample size and volume fraction Megnetic Field (T) 0 5 5 8.5 8.5 17.3 17.3 n 0 1 1 2 2 5 5 N 648 705 705 760 760 862 862 Direction ⊥ // ⊥ // ⊥ // ⊥ Volume fraction (%) 60 65 65 70 70 80 80

The Raman spectrum was used to quantify the orientation intensity of nanotubes in the buckypaper. Figure 7.24 and Figure 7.25 shows the normalized intensity of nanotube orientation and conductivity in the parallel and perpendicular directions for the buckypaper. It can be seen that the random nanotube buckypaper has constant orientation through 0 to 2π . Aligned buckypaper has a higher intensity along 0o, 180 o and 360 o, and intensity along aligned direction increases with increasing magnetic field. The conductivity in the parallel direction increases as the magnetic field increases. The anisotropy of the conductivity increases with increasing magnetic field as well.

Figure 7.24 Normalized intensity of nanotube orientation

141

Figure 7.25 Conductivity at parallel and perpendicular direction with corresponding magnetic filed

To model the orientation degree (θ ) of buckypaper, the density of θ was plotted in Figure 7.26 according to Eq(7.4). The normalized density function of θ is also plotted, and exhibited in Figure 7.27. Comparing Figure 2.27 to Figure 7.24, n=0 refers to the random buckypapers, n=1 refers to the aligned buckypaper at 5T, n=2 refers to aligned buckypaper at 8.5T, and n=5 refers to the aligned buckypaper at 17.3T.

142 0.7

0.6 n=5

0.5

0.4 n=2 Density Density 0.3 n=1

n=0 0.2

0.1

0 0 60 120 180 240 300 360 θ (o) Figure 7.26 Density function of orientation angle

1 n=0 random 0.9

0.8 n=1 5T 0.7 n=2 8.5T 0.6 ormalized Density N

0.5 n=5 0.4 17.3T

0 60 120 180 240 300 360 θ (o)

Figure 7.27 Normalized density function of orientation angle

143 The results of conductivity are summarized in Table 7.6. The conductivity of aligned buckypapers is 1.5 to 3 times higher than random buckypapers. In directional conductivity, parallel conductivity is higher than perpendicular conductivity. The conductivity along the parallel direction increased as magnetic field increased, but conductivity along the perpendicular direction decreased as the magnetic field increases. This phenomenon is attributed to the nanotube alignment increases in the parallel direction with less contact resistance as the magnetic field increases, and more nanotubes direct the current flows along the parallel direction across the sample. On the other hand, the intensity of nanotube orientation decrease in the perpendicular direction as the magnetic field increases, and current flow is tunneling through longer pathways and encounters more intercontacts in order to cross the sample. Therefore, the alignment of nanotubes has a strong influence on the conductivity of the buckypaper, and the magnetic field determines the orientation intensity of nanotubes. This also leads to the increasing the difference in resistance anisotropy as magnetic field increases.

When comparing the experimental result to the model’s estimation, the conductivity of electric circuit model is around 6 to 7 times higher than experimental measurements, and the result is plotted in Figure 7.28 and Figure 7.31. The discrepancy can be explained from two aspects: from the experiment and from the model. First, the electric circuit assumes high purity in buckypaper, free from impurities like amorous carbon or defects. However, the purity of raw buckypearls is around 95% and sonication might create defects on nanotube side walls. It is well-known that the impurities and defects will decrease the conductivity of nanotubes [194], but the exact degradation is unclear. Second, the model assumes intercontact takes place between two individual nanotubes within each bundle. However, the assumption of contact of two single nanotubes might be biased owing to the flexibility of each bundle. Third, the model assumed the chirality and metallic portion of nanotubes. However, the real distribution of chirality distribution is unclear, and the metallic portion is determined based on chirality distribution. These reasons are expected to have a strong influence on the electrical conductivity, and obtaining this information relies on technological advancements. The results of conductivity is normalized and compared to the experimental normalized ones.

144 Figure 7.29 and Figure 7.31 showed that the conductivity trends computed from the electric circuit model agreed well with experimental data. This implies that the proposed model is capable of reflecting changes in conductivity along with different magnetic fields and with different directions. Suggestions for improvement will be addressed in Chapter 8.

Table 7.6 Experimental result and model prediction of conductivity of aligned and random buckypaper (S/cm) Experiment (//) Experiment ( ⊥ ) Model (//) Model ( ⊥ ) 0 150 150 1010 1010 5 250 83 1528 603 8.5 300 75 2026 447 17.3 400 40 3157 155

xprimnt Mol

Conductivity (S/cm)

Magnetic Field (T)

Figure 7.28 Comparison of the experimental result and model estimation on conductivity along the parallel direction

145

xprimnt Mol

ormalized Conductivity

N

Magnetic Field (T)

Figure 7.29 Normalized trends of the experimental result and model estimation on conductivity along the parallel direction

xprimnt xprimnt + Mol Mol + Conductivity (S/cm)

Magnetic Field (T)

Figure 7.30 Comparison of the experimental result and model estimation on conductivity along both parallel and perpendicular directions

xprimnt xprimnt + Mol Mol + ormalized Conductivity

N

Magnetic Field (T)

146 Figure 7.31 Normalized trends of the experimental result and model estimation on conductivity along both parallel and perpendicular directions

7.6 Summary

This chapter proposed an electric circuit model for buckypapers conductivity. The resistance of the buckypaper is assumed to be dominated by intercontact resistance. The parameters contributing to intercontact resistance were discussed, including chirality, registry, contact area, metallic portion of nanotubes, diameter, length and orientation angle of nanotubes in buckypaper. Assumptions are made for chirality, registry, contact area and metallic portion of nanotubes due to lack of experimental results. Three case studies were conducted to investigate the effects of diameter, length and orientation angle.

The results demonstrate that the conductivity increases with decreasing nanotube diameter. Small bundles of nanotube create more pathways than large bundles, allowing more routes for current to cross the sample, and result in a higher conductivity. A regression function is proposed assuming the conductivity decreases as power law of the increasing diameter of SWNT bundle. From previous discussion in Chapter 4, achieving small bundle of SWNTs relied on sufficient sonication. The sonication effect directly influences on the rope size distribution in buckypaper and therefore contributes to the resultant conductivity of buckypaper.

As for the length effect on the conductivity of buckypapers, the conductivity increased with increasing nanotube length. In longer nanotubes, current may pass across the buckypaper through fewer intercontact nodes than in shorter nanotubes, resulting in higher conductivity. A regression function is proposed assuming the conductivity increases as a power law of the increasing length of the SWNT. The proposed regression model also agreed well with previous investigations in the literature where demonstrated a power law dependence on the length of the nanotubes to the conductivity of a SWNT network.

147 The conductivity of a buckypaper is dependent on the nanotube alignment. The conductivity of aligned buckypapers is higher than that of random buckypapers, and is higher in the parallel rather than in the perpendicular direction. It also exhibited increasing anisotropy in conductivity with increasing magnetic field. A higher magnetic field increases the intensity of nanotube orientation along the parallel direction, and decreases the alignment along the perpendicular direction. Therefore, there are more nanotubes to direct the current flow along the parallel direction across the sample than along the perpendicular direction. The trends of conductivity predicted from the electric circuit model agreed well with experimental results, and proved that the model developed can properly predict the effects of diameter, length and alignment of nanotubes in buckypaper.

148 Chapter 8 CONCLUSIONS AND FUTURE WORKS

8.1 Conclusions

In this research, the manufacturing process of SWNT buckypaper was investigated and several significant effects were optimized and validated experimentally. The new proposed manufacturing process of SBP is expected to reduce average rope size to around 6~7nm in the resultant SBP and minimize variation among different batches of raw materials. The manufacturing process of MBPs were also proposed and analyzed statistically. Nanostructure was found to be highly dependant on the interactions of manufacturing parameters, and crucial to the final specific surface area and electrical properties of MBPs. The nanostructures of MBP were characterized and quantified statistically and property models of MBP were constructed based on the characterization results. The model of specific surface area of MBP was built based on rule of mixture, and highly dependant on the rope size distribution and mixed ratio of two materials. The model of electrical conductivity of buckypaper involved multiscale electrical transport nanofeatures of nanotube networks. The model prediction was in good agreement to experimental trends.

Mixing SWNTs with low-cost MWNTs or CNFs to produce mixed buckypaper is an effective way for retaining excellent properties of SBPs while significantly reducing cost. Manufacturing parameters were discussed through the design of experiment approach, including mixed material type, mixed ratio, sonication effect, surfactant usage and cleaning process. Statistical analysis was performed on uniformity, purity, BET surface area and electrical conductivity of the resultant MBPs. The results of the analysis demonstrate that the manufacturing parameters have a direct impact on uniformity, and sonication effect is crucial to the rope size distribution of buckypaper. On the other hand, only mixed material type and ratio were statistically influential to the BET surface area and electrical conductivity of MBPs, which implied that these manufacturing parameters were not directly affecting these properties of MBPs. The nanostructures of the MBPs

149 were further investigated and found that uniformity of nanostructure were highly influential to the BET surface and electrical conductivity of MBPs. Therefore, the bimodal system of MBPs was characterized into rope size distribution, length distribution and pore size distribution. These indices of nanostructure was further separated statistically and fitted into Weibull distributions.

The model of the surface area was proposed based on the nanostructure of buckypaper, and compared to the experimental measurement of BET surface area of MBPs. The surface area of MBPs was proven to follow the rule of mixture of two mixed materials’ specific surface areas. The results showed that the bundle size of SWNTs, number of MWNTs and CNF walls and mixed ratios were critical to the surface area of MBPs. The estimation based on rope size distribution agreed well with experimental results. By using the specific surface area model, we can design and tailor the surface area and cost of MBPs for different applications.

The model of electrical conductivity was proposed based on the electrical transport phenomenon and the nanostructure of buckypaper as well. In the current buckypapers composed of relatively short tubes, the contribution of intrinsic resistance of nanotube was negligible. The resistance of buckypaper is considered dominated by intercontact resistance between nanotubes for the networks with SWNTs less than 10μm. The chirality, metallic/semiconducting ratio, contact area, type of contact, diameter, length and alignment of nanotubes determine the conductivity of the SWNT network. The proposed electric circuit model of buckypaper included the above parameters. Three case studies were discussed to reveal the effects of nanotube diameter, length, and alignment effects. The power law relationship of conductivity with diameter and length of SWNT bundles are presented. The model also demonstrated the anisotropic behavior of aligned buckypapers. The predicted trends of conductivity in the electric circuit model agreed well with experimental results, but the values were 5 times deviated from the experimental ones. Further studies on bundle contacts and the chirality distribution of nanotubes are expected to improve the accuracy of the electric circuit model.

150 The research systematically characterized nanostructures of buckypaper materials. The process-nanostructure-property relationships of special surface area and electrical conductivity were revealed. The results are valuable viable to improve the quality of buckypaper and to tailor the nanostructures of buckypapers for different applications.

8.2 Future works

8.2.1 New Manufacturing Process Development

MBP has proved to be an economical alternative to SBP and different manufacturing processes are proposed to achieve lower SWNT content or even pure MWNT or CNF buckypapers. Several manufacturing processes are proposed for future works. First is filter treatments, using binder to entwine the network structure while van der Waals forces of MWNTs and CNFs are not as strong as SWNTs. Second is to apply a surface veil of carbon fiber as substrate, to block large pores and hold the network structure of buckypaper. Third is to use a very thin layer of SWNTs at the bottom and top of the buckypaper, and sandwich MWNTs or CNFs as fillers in between. This way, the finished surface is smooth and easy to peel off from membrane.

8.2.2 Improve Electric Circuit Model

8.2.2.1 Chirality Distribution The electronic properties of SWNTs were predicted to be strongly dependent on the atomic structure; and therefore, extensive studies of chirality will provide useful insight of the SWNT network and improve the electric circuit model. Scanning Tunneling Microscopy (STM) can be used to observe the atomic structure of nanotubes and characterize the relationship between the hexagonal carbon lattice and the chirality [199] , as illustrated in Figure 8.1. The electrical conductivity of an individual nanotube depends strongly on the tube diameter and wrapping angle, which is the helicity of the tube lattice. With only slight differences in these parameters causing a shift from a metallic to a semiconducting state, Figure 8.2 demonstrates the chirality of an SWNT. T is the tube

151 axis, the sheet will wrap along the vector C such that the origin (0,0) coincides with point C(11,7). The H vector specifies the direction of the nearest-neighbor hexagon rows indicated by the block dots. The angle between T and H is the chiral angleφ .

The chiral vector, C was defined in terms of two primitive lattice vectors ( a1 ,a2 )

and a pair of integer indices, (n, m), so thatC = an 1 + m a2 . The indices (n ,m) determine the structure of the nanotube. A nanotube is armchair if n=m, and is zigzag if m=0. Otherwise, the nanotube is chiral, where 0o < φ < 30o .

The electric property of an SWNT is determined by chiral indices. Armchair (n=m) is metallic, and for all other tubes (zigzag and chiral), there exist two possibilities. If n- m=3l, where l is an integer, the nanotube is metallic. Otherwise, if n-m ≠ 3l, the nanotube is semiconducting.

Assuming that the diameter of a single SWNT is a uniform distribution from 1.2 to 2nm, d~U[1,2], and chiral angle φ is a uniform distribution from 0o to 30 o,

φ ~ U o 30,0[ o ] . We can generate chirality as a function of d andφ .

C = f d φ),( (8.1) Metallic = f (C | m n), (8.2)

Figure 8.1 Schematic chirality of a SWNT

152

Figure 8.2 STM image of an individual SWNT

8.2.2.2 Intercontacts between Bundles According the Chapter 6, a bundle is defined as layers of nanotube surrounded by a center tube. Figure 8.3(a) demonstrates a 1-layer bundle of SWNTs. Assuming the minimum van der Waal distance between two intercontact bundles is 0.34nm. Therefore, an intercontact contact angle α can be calculated, which is defined as the intercontact area of two bundles, as demonstrated in Figure 8.3(b). r − h α = cos−1( ) (8.3) r

153 (a) (b) α r

h = 0.34 nm 0.34nm

Figure 8.3 Schematic interpretation of a bundle

Figure 8.4 Schematic interpretation of intercontact between bundles

The relaxation assumption says that the nanotube becomes slightly deformed during intercontact. Therefore, we can rotate the tube with angleα , and calculate how many tubes are involved during the intercontact. Figure 8.4 illustrates examples of a 1-1 and 2- 2 intercontact. Comparing the 1-1 intercontact and the 2-2 intercontact, Eq(8.4) calculates intercontact as parallel circuits and the resistance of a 2-2 intercontact is half of a 1-1 resistance.

1 1 1 R R21 = + , Ric = (8.4) Ric R1 R2 R1 + R2

1 2 2 R R21 = + , Ric = (8.5) Ric R1 R2 (2 R1 + R2 )

154 The result is reasonable, because when 2 tubes are intercontact with other 2 tubes, the contact area is twice as large than the 1-1 intercontact, and resistance is expected to be reduced by half.

8.2.2.3 Intercontact of Bending Nanotubes It is well-known that SWNT has a high and wavy length structure, and the intercontact angle Θ is a random distribution from 0 o to 180o. When Θ is close to 0 o to 180o, two bending nanotubes could have a long and thin intercontact area instead of point contact with minimum distance of 0.34nm, illustrated in Figure 8.5. The contact in this situation is expected to be larger, and resistance to be lower. The contact area can be related to the curvature of bending nanotubes by assuming curvature as

Pr ojectionLength curvature = (8.6) ActualLength

The curvature of nanotube ranges from 0 to 1, and the curvature close to 0 means highly bended nanotubes and 1 means a completely straight nanotube. When Θ is close to 0 o and 180o, and curvature is close to 1, the intercontact area of two nanotubes becomes a long and thin area with many intercontact points. In this situation, the contact area will be 1 a parallel circuit of N tubes, and resistance is expected to reduce to . N

0.34 nm

Projection Length

Figure 8.5 Intercontact of two bending nanotubes

155 8.2.2.4 Electrical Conductivity of Long Nanotube Network As discussed previously, the intrinsic resistance of nanotubes becomes comparable to intercontact resistance when the length of nanotubes is beyond 10um. In this situation, the resistance of SWNT networks becomes more complicated. When the current enters the network of SWNTs, not only does intercontact contribute to the voltage drop, but also the intrinsic resistance. Therefore, the voltage throughout a nanotube will decrease gradually along with both intercontacts and length.

The Kirchhoff’s voltage rule comes in handy in this case. The voltage rule based on conservation of voltage, that the sum of voltages around a closed conducting loop must be zero. The idea is close to the two-probe method, where voltage was applied to the circuit and the change of current flow was measured. In this circuit, a constant voltage source (V) is placed in series with the unknown resistance (R) and an ammeter (Im). Since the voltage drop across the ammeter is negligible, essentially all the voltage appears across R. The resulting current is measured by the ammeter and the resistance is calculated using Ohm’s Law: 1 J = σE = E ( 8.7) ρ where J is the current density (J=I/A), σ is the electrical conductivity, E is the electric field (E=V/L) and ρ is the electrical resistivity. An apparatus of two-probe configuration is shown in Figure 8.6.

Figure 8.6 Configuration of a two-probe apparatus

156 In fact, the resistance of a long SWNT network is expected to have resistance over 100k Ω and two-probe method is specific for materials of large resistance.

8.2.2.5 3D Electric Circuit Model of Buckypaper Apparently, buckypaper is a 3-dimensional network of SWNTs, although thickness is only 0.02% of the sample diameter. The most significant difference between a 2D and 3D network is the conductivity through-thickness. Current works only assumed that the thickness of buckypaper is a parallel circuit of many thin layers. However, in a 3D network, we can create the current flow in the through-thickness direction by including pathways of current flow in the z direction. Of course, the model symmetry will still hold in a 3D network, and we will cut tubes exits above or below the representative cube, and mapped over to the opposite side. Renumber the new network to assure the current flow exit on above or below is always directed back from the opposite side. However, a 3D cube involves generating more nanotubes in the space. When current 2D assumptions already reached the limit of matlab virtual memory, the FORTRAN program with higher computation ability will be handy in a 3D cube sample.

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BIOGRAPHICAL SKETCH

Cherng-Shii Yeh obtained her Bachelor’s degree in Industrial Engineering at Tung-Hai University, in July 2002. Subsequently she pursued on to the graduate studies at Florida State University. She was conferred a Master degree in Industrial and Manufacturing in Aug, 2004.

From 2004 to 2007, Cherng-Shii worked as research assistant at Florida Advanced Center for Composite Technologies (FA2CT) and High Performance Material Institute (HPMI). Her major responsibility is to support research of buckypaper characterization and manufacturing. During these periods, she participated in the several national funded projects, investigation and development of buckypaper performances and nanocomposites with carbon nanotubes, EMI shielding and lightning strike protection tests using SWNT buckypapers, impregnating buckypapers with polycarbonate thermoplastic and preparation of thermoplastic molding compounds for twin screw extrusion, investigation and optimization of high performance nanocomposites produced with nanotube buckypaper materials, commercial-scaled nanotube buckypaper fabrication and property investigation, and affordable buckypaper production

In July 2002, she continued her studying at Florida State University in the advanced manufacturing technology. Since then she has been working on the nanoscale materials and related fabrications.

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