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THE NANOTUBULAR HELIX

Permanent Link: http://ncf.sobek.ufl.edu/NCFE004776/00001

Material Information

Title: THE NANOTUBULAR HELIX CARBON'S REVOLUTION
Physical Description: Book
Language: English
Creator: Hamilton, Ian
Publisher: New College of Florida
Place of Publication: Sarasota, Fla.
Creation Date: 2013
Publication Date: 2013

Subjects

Subjects / Keywords: Tubes
Helix
Carbon
Materials
Nanotube
Genre: bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The tube is a ubiquitous motif which manifests throughout physical systems across the energy scales. Current progress in materials science is bringing tubes at smaller scales than ever into focus: nanotubes. Exhibiting remarkable physiochemical properties, these tubes are at the forefront of scientific thought. Their structure-function correlation is deeply understood, and tunable synthesis techniques can create specified tubular geometries. Obscenely strong and conductive, the possibilities they offer seem to defy limitation. One consideration of their tendency to assume helical morphology is that they can be grown into molecular springs. This thesis considers carbonaceous form's structure-function correlation, synthesis techniques, and growth models for nanotubes. Culmination ensues in suggesting novel elastic behavior that helical carbon nanotubes embedded will lend composite polymer matrices. The tube's role in ocean waves provides context for appreciating such amazing dynamics.
Statement of Responsibility: by Ian Hamilton
Thesis: Thesis (B.A.) -- New College of Florida, 2013
Electronic Access: RESTRICTED TO NCF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE
Bibliography: Includes bibliographical references.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The New College of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Local: Faculty Sponsor: Sendova, Mariana

Record Information

Source Institution: New College of Florida
Holding Location: New College of Florida
Rights Management: Applicable rights reserved.
Classification: local - S.T. 2013 H2
System ID: NCFE004776:00001

Permanent Link: http://ncf.sobek.ufl.edu/NCFE004776/00001

Material Information

Title: THE NANOTUBULAR HELIX CARBON'S REVOLUTION
Physical Description: Book
Language: English
Creator: Hamilton, Ian
Publisher: New College of Florida
Place of Publication: Sarasota, Fla.
Creation Date: 2013
Publication Date: 2013

Subjects

Subjects / Keywords: Tubes
Helix
Carbon
Materials
Nanotube
Genre: bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The tube is a ubiquitous motif which manifests throughout physical systems across the energy scales. Current progress in materials science is bringing tubes at smaller scales than ever into focus: nanotubes. Exhibiting remarkable physiochemical properties, these tubes are at the forefront of scientific thought. Their structure-function correlation is deeply understood, and tunable synthesis techniques can create specified tubular geometries. Obscenely strong and conductive, the possibilities they offer seem to defy limitation. One consideration of their tendency to assume helical morphology is that they can be grown into molecular springs. This thesis considers carbonaceous form's structure-function correlation, synthesis techniques, and growth models for nanotubes. Culmination ensues in suggesting novel elastic behavior that helical carbon nanotubes embedded will lend composite polymer matrices. The tube's role in ocean waves provides context for appreciating such amazing dynamics.
Statement of Responsibility: by Ian Hamilton
Thesis: Thesis (B.A.) -- New College of Florida, 2013
Electronic Access: RESTRICTED TO NCF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE
Bibliography: Includes bibliographical references.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The New College of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Local: Faculty Sponsor: Sendova, Mariana

Record Information

Source Institution: New College of Florida
Holding Location: New College of Florida
Rights Management: Applicable rights reserved.
Classification: local - S.T. 2013 H2
System ID: NCFE004776:00001


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THE NANOTUBULAR HELIX: BY IAN HAMILTON A Thesis Submitted to the Division of Natural Sciences New College of Florida in partial fulfillment of the requirements for the degree Bachelor of Arts in Natural Sciences Under the sponsorship of Dr. Mariana Sendova Sarasota, Florida May, 2013

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1 THE NANOTUBULAR HELIX Ian Hamilton New College of Florida, 2013 ABSTRACT The t ube is a ubiquitous motif which manifests throughout physical systems across the energy scales. Current progress in materials science is bringing tubes at smaller scales than ever into focus: nanotubes. Exhibiting remarkable physiochemical properties, these tubes are at the forefront of scientific thought. Their structure function correlation is deeply understood, and tunable synthesis techniques can create specified tubular geometries. Obscenely strong and conductive, the possibili ti es they offer seem to defy limitation. One consider ation of their tendency to assume helical morphology is that they can be grown into molecular springs. This thesis considers the structure function correlation, synthesis techniques and growth models of nanotubes coming to suggest novel elastic behavior when embedded in composite polymer matrices.

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2 Table of Contents ................................ ................................ 5 Introduction ................................ ................................ ................................ ......................... 5 Chapter 1: Carbon Nanotubes: Structure and Properties ................................ ................... 9 1.1 The Graphene Lattice ................................ ................................ ................................ 9 1. 1.1 Crystallography ................................ ................................ ................................ 12 1.1.2 Rolling the Graphene Lattice ................................ ................................ ............ 14 1.2 Waves Through The Lattice ................................ ................................ ............... 15 1.2.1 Spectroscopic Observations ................................ ................................ .............. 16 1.3 Lattice Defects ................................ ................................ ................................ .... 18 ................................ ................................ ............... 19 1.4 Tube Classification ................................ ................................ ............................. 21 1.4.1 Curvature and Strain Energy ................................ ................................ ............. 25 1.5 ................................ ................................ ....... 26 1.6 Helical Tubes ................................ ................................ ................................ ...... 29 Chapter 2: Carbon Nanotube Synthesis ................................ ................................ ............ 32 2.1 Historical overview: Pyrolysis, Laser Ablation, & Arc Evaporation ................. 32 2.1.1 Chirality Control ................................ ................................ ............................... 34 2.2 Catlytic Chemical Vapor Deposition ................................ ................................ 34 2.2.1 Growth Support ................................ ................................ ................................ 36

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3 2.2.2 Supergrowth CVD Using Water ................................ ................................ ....... 38 2.2.3 Tube Distribution ................................ ................................ .............................. 38 2.2.4 Catalytic CVD parameters ................................ ................................ ................ 40 Chapter 3: Growth Models ................................ ................................ ................................ 43 3.1 Thermodynamics of Helix Growth ................................ ................................ ......... 44 3.2 Catalytic Particle Interaction ................................ ................................ ................... 47 3.3 Pentagonal and Heptagonal Ring Pairing ................................ ............................... 48 3.4 Pentagon/Heptagon Pair Reconsiderations ................................ ............................ 50 3.5 The Double Helix: Interfacial Adhesion ................................ ................................ 51 Chapter 4: Some Applications ................................ ................................ .......................... 53 4.1 Carbon Dioxide as Precursor ................................ ................................ .................. 53 4.4 Nanotube Functualization ................................ ................................ ....................... 54 4.5 Composite Materials ................................ ................................ .......................... 56 4.6 Surfing Waves Contextualizes Tubes ................................ ................................ 59 Conclusion ................................ ................................ ................................ ........................ 61 Table of Figures Figure 1: Eight allotropes of carbon: a) Diamond, b) Graphite, c) Lonsdaleite, d) C60 Buckminsterfullerene, e) C540, f) C70, g) amorphous carbon, and h) single walled carbon nanotube ................................ ................................ ................................ .................. 8 Figure 2: Ethylene exhibits sp2 hybridization [5] ................................ ............................... 10 Figure 3: basic ring bond structure of graphene sheets [6] d ................................ ............ 11 Figure 4: Specifying directions in a hexagonal system [21] ................................ ............. 13 Figure 5: 4x4 Cell of the Diamond Lattice [10] ................................ ................................ 14 Figure 6: Graphite: Gr aphene Layers [42] ................................ ................................ ........ 14 Figure 7: Graphitic Structures [9] ................................ ................................ ...................... 15 Figure 8: SALG under uniaxial stretch in the zigzag direction; energy per atom vs. nominal strain [12]. ................................ ................................ ................................ ......... 17 Figure 9: The Stone Wales Defect [13] ................................ ................................ ............. 18 Figure 10: a) (5, 0) Zigzag tubes: pristine upper tube, and tubes with the Stone Wales defect in inclined (center) and circumferential (lower) orientation. b ) Same schema, for a (10, 0) zigzag tube. [13] ................................ ................................ ................................ ............... 19 Figure 11: (10, 10) Armchair SWNT ................................ ................................ ................ 26 Figure 12: Coiled nanotubes with variable pitch and diameter, (b) nanotubes twisted together, (c) compressed tubes showing nodes, (d) looped tubes ................................ ..... 29

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4 Figure 13: Coordinate system for a helical nanoube [23] ................................ ................... 30 Figure 14: Electronic bands of a (15,15) HCNT; sp 3 atomic orbital model [23] ................ 31 ................................ .............. 33 Figure 16: An Appara tus for Arc Discharge Synthesis ................................ .................... 33 Figure 17: Catalytic CVD Reactor labeling A the electric furnace, B tubular reactor, C humidity absorber, D bubbler for liquid precursors, E command panel; To the right, an internal view of CNT synthesis [4] ................................ ................................ ................... 35 Fi gure 18: (a) Relative concentrations of CNT type phase diagram. (b) Plot of mean diameter's dependence on Fe film thickness [21]. ................................ ............................. 37 Figure 19: Densely packed array of coiled tubes imaged with SEM [33] ........................ 38 Figure 20: Possible tube morphologies from C plane sap phire miscut, annealing, CVD; graphoepitaxy [21] ................................ ................................ ................................ ............. 39 Figure 21: Catalytic growth mechanisms, root and tip carbon extrusion [22] ..................... 40 Figure 22: Random CCVD Initial Conditions ................................ ................................ ... 42 Figure 23: Vapor Density Effects [24] ................................ ................................ ................ 43 Figure 24: Helical Nanotubes [science art.com] ................................ ................................ 43 Figure 25: The enthalpy and entropy of indium oxidation [40] ................................ ........ 46 Figure 26: (a) pentagon nucleation, (b) quasi icosahedron shell growth, (c) a catalyst particle is engulfed by spiralling growth, a straight CNT grows, (e) The CNT forms a node, (f) Formation of a coiled tube [33] ................................ ................................ .......... 49 Figure 27: Metal Catalyzed Cap Growth [24] ................................ ................................ .... 50 Figure 28: SEM images of CNTs with (a) coiled, (b) spring like, (c) helical, and (d) double helical morphologies [40] ................................ ................................ ..................... 52 Figure 29: Functionalization with the carboxyl groups, subsequently undergoing esterification or amidization [22] ................................ ................................ ...................... 55 .... 55 Figure 31: A Panamanian tube endangers the structural integrity of an unreinforced epoxy matrix ................................ ................................ ................................ ................................ 56 Figure 32: Stress strain curves ................................ ................................ ........................... 57 Figure 33: Thermal stresses in a MWNT polystyrene matrix cause cracks to nucleate and propagate [22] ................................ ................................ ................................ ................... 58 Figure 34: Straight CNTs integrated into crosslinked polymer structure [34] .................... 59 Figure 35: A wave breaks, setting up a surfer for a bottom turn ................................ ...... 62 Figure 36: The author illustrates a bottom turn ................................ ................................ 62 Figure 37: A shwack, throwing about two bu ckets above the lip in El Salvador ............. 63 Figure 38: Tube riding would be a novel application for nanotube reinforced composite materi als. ................................ ................................ ................................ ........................... 65

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5 Figure 1 : Unreinforced polymer matrices demonstrate the need for novel composite materials Introduction Prior to observation, the energy available to any quantum mechanical system exists in an imaginary superposition of all possible configurations [1] Upon collapse of the wave function, the system orients its observables: the eigenvalues are real. The degree to which a particle spins specifies its statistics. Fermions experience a degeneracy pressure which pushes them apart. This constitutes the p eriodic table, shaping microscopic and macroscopic energy flows. How is the inquiring scientist to optimally consider these fundamental principles of organization? Let us look back to Kekul that imaginative Austrian whose d ream s were chemical epiphanies. Indeed, his serpent smelled so sweet it actually devoured itself by the tail [1]

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6 H is characterization of benzene was a notable event in the chain of discoveries which continues shaping the eve r growing reference fra me with which science models this universe today Various models have been constructed for the observable universe each applicable in its own context of inquiry. Certain physical laws are commonly recognized across the spectrum. For example, energy (momentarily ignoring the particulate side of its duality) travels in waves. Different sorts of waves exist, of course, and propagate through the beach, it only takes a bit of observation to see that when waves encounter a suitable boundary such as shallow water, they form tubes. Early chemists labeled a certain class of cyclic molecules aromatic, in that they were unusually stable and smelle d rather sweet. Since the advent of quantum mechanics, theory and experimental techniques allow nose. Nanoscience takes advantage of resonance on various scales to characterize and model the behavior of molecules and crystals [2] [3] [4] Typical observation of microscopic system takes advantage of the interaction between light and matter. An illumined sample may a bsorb light of a known frequency, if its energy levels are spaced suitably. Furthermore, selection rules determine the utility of various spectroscopic instruments, a subject of extensive analysis [5] [6] A brief discussion of Raman and IR spectroscopy is included, but the scope of this work is necessarily limited. A cursory, qualitative illustration of electronic excitations is useful, however. The collective oscillations in a periodic, elasti c medium called phonons will prove useful when we turn to specifying the desirable properties a material may exhibit.

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7 Kekul shook the foundation of natural science [1] H is carbon aceous ever bitten tail has since been actively engaged in weaving physics and chemistry. This thesis begins by examining several allotropes of carbon and posits models for the rise of specific novel form : carbon nanotubes S ynthesis techniques are then introduced, as they exploit the predictive power of kinetics and thermodynamics [2] Recent progress in materials science allows for the construction of desired forms through the o ptim ization of synthetic parameters. Among the most salient advances is the emergence of helical tubes a molecular form that promises bountiful application. E ver improving quantitative models enable the synthesis of desired structures. Quantum mechanical considerations enable t he creation of complex structures depend ent up falling in to a stable configuration Indeed, kinetics and thermodynamics both shape the novel carbonaceous form; transition state accessibility is determined by the concentrations of in volved molecules, as well as the temperature of the system. Spatial proximity allows overlap of the individual at omic wave functions [7] Thi s shared electron density between atoms pulls them together, form ing strong chemical bonds, a process governed by the laws of thermodynamics

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8 Figure 2 : Eight allotropes of carbon: a) Diamond, b) Graphite, c) Lonsdaleite, d ) C60 Buckminsterfullerene, e) C540, f) C70, g) a morphous carbon, and h) single walled carbon nanotube [11] The allowed configurations manifest as different allotropes of carbon, eight of which are shown above [11] H exagonal carbon rings a re a n ideal repeating unit; aside from forming larger molecules, they fuse into extensive networks called lattice structures A flat plane comprised of carbonaceous hexagons just one atom thick is known as graphene [2] Graphite, a familiar (pencil lead) allotrope of carbon, is composed of multiple graphene sheets stacked atop one another. The hexagonal ring lattice has strong in plane bonds, which correlat e with the stable cha racter of its constituent rings Due to the aromatic nature of cyclic molecule s with 4n+2 electrons planar molecules can be exceptionally stable. The attractive potential be tween the sheets is weak, as it is due primarily to Van Der Walls forces apart with Scotch t ape [2] In fact, t his isolation technique landed two Russians the 2010 Nobel Prize in physics. The need for m aterials with a desired property, i.e. the very high elastic moduli specific to helical nano tubes [2] has steered recent scientific inquir y and technological

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9 development New synthesis methods allow for an ever improving degree of specificity in synthetic carbon nanotube material s geometry, size, structural distribution, and purity depend on synthetic methods In turn, these characteristics A sketch of the history, structure and properties of carbon nanotubes comprises Chapte r 1. Chapter 2 further considers nanotube synthesis. Chemical vapor deposition techniques have been honed to such a degree that planned synthetic design optimizes arbitrarily desired tube morphology. The temperature and gaseous environment in a quartz reaction tube, coupled with various catalysis parameters, selectively shapes tubular morphology. The literature is rife with proposed nanotubular growth mechanisms several of which will be discussed in Chapter 3. A thermodynamic model serves as a basis for appreciating the evolution of helical nanotubes. Parameterization of the growth variables enables ever more specifically shaped nanotubes to be synthesized, while the relevant kinetics shed light on the dynamics of catalysis [1 ] [3] Chapter 4 considers some novel applications, considering chemical effects, elasticity an d effects on polymer matrices. C hapter 1 : Carbon Nanotubes: Structure and Properties 1.1 The Graphene Lattice Carbon is a nonmetallic element, but in certain three dimensional configurations, all carbon lattices may exhibit remarkable electrical conductivity. An understanding of the energetic tendencies of all carbon lattices invites the introduction of the stabl e lattices that it

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10 forms. Carbon's ground state electron configuration is (1s) 2 (2s) 2 (2 p) 2 To bond, 2s raised blending with 2p orbital s, resulting in hybridizations. Figure 3 : Ethylene exhibits sp2 hybridization [5] A tetravalent atom, carbon will ideally form four bonds with its neighbors [4] For graphite, a 2s electron orbital mixes with two 2p orbitals, yielding sp 2 hybridization. This corresponds to three orbitals in a plane at 120 O to the plane in a pz orbital [3] The overlap of the lo west energy electron orbitals alone yields a bond between the atoms. When the atomic wavefunctions z orbitals also contribute to the overlap, a multiple bond is formed. This is a stronger bond which hold s the atoms together with higher bond energy In the case of the graphene lattice, sp 2 intraplanar bonds hold each sheet together strongly. The overlapping p o rbitals of adjacent layers, however, are very weak in comparison Bond s, in their spatial rigidity allow molecules to assume diverse, yet resilient coexisting structures Bond formation depends on appropriate conditions being met : a higher temperature correlates with more frequent intermolecular collisions,

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11 necessary for bonds to result T he rate limiting transition state is the highest energy configuration that serves as a bottleneck for molecular interaction [7] Figure 4 : basic ring bond structure of graphene sheets [6] With numerous electron flow paths available, diverse configurations with lower free energy may be stable. T molecular architect ure may assemble complex shapes is not a trivial matter. In many cases, the overall change in Gibbs free energy gives a good sense of equilibrium in fact serving to define it The competitive balance between enthalpy an d entropy depen d on numerous variables [15] The balance between these energetic limitations dictates which allotropes will be formed in synthesis. Carbons with sp 3 bonds are disordered and will transform into graphite at high temperatures. C onsider the oxidation of gaseous acetylene: C 2 H 2 It is a stable compound, but will readily react with oxygen and a spark in an intensely exothermic reaction. It is a useful gas in its own right, enabling its use in oxy acetylene welding. Acetylene gas is commonly used as a precursor carbon source gas in the catalytic chemic al vapor deposition (CCVD) technique of nanotube synthesis [6]

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12 1.1.1 Crystallography A d escription & classification of crystal structures is most commonly performed through referencing the unit cell. size and shape, together with positions in it, allows for consideration of its three dimensional structure. Considering the relative atomic arrangement with coordination numbers, interatomic distances and bonding types may allow for a cohesive visualization with numerous me thods [7] A useful approach for considering the close packing of spheres will provide insight supplemental to unit cell specifications All crystal structures are systematized in 14 Bravais lattices [7] More specifically, hexagonal close packed structure s result in two case s (face centered cubic and hexagonal close packed) which maximize average density. I n these cases, crystal structures possess a minimal surface energy, with the fewest bonds broken in the event of cleavage. The natural minimization of free energy forms the largest facets admissible. [8] 1.1.2 Miller Bravais Indices The four Miller Bravais indices (h k i l) are encountered when describing node density in crystals. They denote planes which are orthogonal to the reciprocal lattice vector. while crystallographic planes link the nodes. Prop erties dependent on node density include birefringence, adsorption, reactivity, surface tension, and dislocations [7] [3]

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13 Figure 5 : Specifying directions in a hexagonal system [21] Carbon does not limit its assumed form to lone chains and rings; carbonaceous fragments themselves can join covalently into more complex structures [9] As carbon forms bonds with three different hybridizations, the specific hybridization dictates the angles of neighboring atoms [6] [9] Until 1985 when the Buckyball was discovered, the only all carbon crystalline allotropes known to the scientific community were diamond and graphite. Diamond c sees each atom joined to four others in tetrahedrons. A good conductor of heat, it has a high refractive in dex near 2.4 It follows a face centered cubic Bravais lattice and a t room temperatures has a relatively wide bandgap of 5.5 eV.

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14 Figure 6 : 4x4 Cell of the Diamond L attice [10] Diamond s cubic lattice exhibits euhedral crystalline form ; that is, its edges are sharp, and readily recognizable. This contrasts with amorphous growth which predominates when no free space for crystal face form ation is available, and is termed anhedral growth This competitive growth environment allows for a facet s formation with a low Miller index. This corresponds with a low surface energy, and leads to a high rate of facet formation [7] 1.1.2 Rolling t he G raphene L attice Imperfect graphite has an interplanar spacing of approxim ately 0.344nm [11] A graphene sheet, when rolled in to a tube and capped Figure 7 : Graphite: Graphene Layers [42]

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15 with half a 60 carbon atom Buckminsterfullerene on each end illustrates the prototypical nanotube. C60 better known as the Buckyball, is a truncated icosahedron made of 20 hexagons and 12 pentagons. Figure 8 : Graphitic s tructures [9] 1.2 Waves Through The Lattice unstable in three dimensions. Bloch waves may be used in a tight binding approximation [23] :

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16 Considering immediate neighbors, a dispersion relation for graphene arises [23] : Thermal fluctuations in the third dimension had been predicted by Landau, then later by Mermin to destroy long range order. However, the ir decades old theory was put to the test; observation s with TEM and nanobeam electron diffraction showed otherwise. The prediction of thermodynamic instability was based on the standard harmonic approximation, which omitted the anharmonic interactions with stretching and long wavelength bending phonons [12] The conduction and valence bands form conical valleys that touch the six corners of the Brillouin zone. The Dirac points, or K points, have the Fermi level pass through them. Their dispersion here is given by |E| = v F | k| ; with k = k K, v F 106 m / s 1.2.1 Spectroscopic Observation s Atomic vibrations in solids range through 10 13 Hz. A bsorption of light with a frequency corresponding to the energy difference between states may induce a transition between quantized vibrational modes IR and Raman spectra measure intensity of absorption against frequency, measured in wavenumbers. With IR spectros copy, information on absorbed radiation is obtained by varying frequency of the incident light [3] In Raman spectroscopy, a laser generates monochromatic light of frequency v 0 which illuminates the sample. Resulting scattere d light of the same energy is called Rayleigh scatter, while the less intense Raman scatter consists of photons of a different wavelength than the incident light. The spectra consist of peaks corresponding to

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17 vibrational transitions ( v 0 v 1 ). The techn iques obey different selection rules. IR active modes must vary their dipole moments during the vibrational cycle. So in absorbing light, the electronic oscillation which comprises the phonon will deviate from equilibrium by establishing a time dependen t dipole moment. This leads to centrosymmetric vibrational modes to be IR inactive, whereas Raman active modes see a change in polarizability in involved nuclear motions [7] Single atomic layer graphene (SALG) simulated phonons varies with the model used; molecular mechanics programs show them bending in ways fundamentally different than does a large membrane. Large membranes are predicted to buckle by the continuum membrane theory, with the membrane size scaling with th e buckle amplitude. Monte Carlo simulations carried out in 2007 showed ripples for ming in SALG with a wavelength of approximately 8 nm with amplitude nearly equal to the carb on carbon interatomic spacing, 0.142 nm. This behavior extends even to very lar ge lattice sheets. Figure 9 : SALG under uniaxial stretch in the zigzag direction; energy per atom vs. nominal strain [12]

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18 Equilibrium atomic structural snapshots are shown in F igure 9 above. T he lattice is commonly illustrated with the constituent hexagons arranged in horizontal rows, with their pointed tips protruding above and below. The zigzag direction is aligned with the chiral vector pointing straight u p; the armchair direction has a chiral angle of 30 its mechanical and electronic properties [12] Lu et al investigated the mechanics through a combination of atomis tic and continuum approaches. They applied in plane and bending deformations to a theoretical framework; graphene exhibits a nonlinear and anisotropic response to finite strain uniaxial stretch. Stretch and shear do not significantly occur for zigzag or armchair directions, but do arise in chiral dir ections. The zigzag point at which bond breaki ng would occur is the limit for perfect graphene [12] 1.3 Lattice Defects Figure 10 : The Stone Wales d efect [13] Numerous crystallographic defects occur in CNTs which drastically alter their mechanical properties. The Stone Wales defect (seen in the above Figure ) was first

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19 two carbon atoms with respect to their bond midpoint. Figure 11 : a) (5, 0) Z igzag tube s: pristine upper tube ; tubes with the Stone Wales defect in inclined (center) and circumferential (lower) orientation. b) Same schema for a (10, 0) zigzag tu be. [13] The presence of t he Stone Wales defect a e ductile transitions, fulleren e coalescence, and nanoscale plasticity. The rearrangement transforms four hexagons into two penta g ons and two heptagons. The process has an activation barrier of several electron volts and creates sites with increased reactivity to nucleophilic attack. Such reactivity characterizes electron deficiency, and correlates with increased strain energy and re duced resonance stabilization throughout the fullerene [3] Fundamental in determining material properties is the consideration of dislocations. Central to such analysis is the Frank energy criterion: only the dislocations with the shortest possible Burgers vectors are stable. Thus will a large dislocation dissociate into multip le

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20 perfect dislocations, with a net reduction of the formation energy The dislocation formation energy formula says that vector length [24] : Nanotubes are very ductile with rising temperature, remaining intact even after 280% elongation and 80% mass loss Edge dislocations are experimentally observed as kinks, major contributions to the high degree of plasticity [24] Nanotubes do not obey the Frank energy criterion, however, and large dislocations are energetically favored. The dislocation w i heptagonal. The pair (5|7) may act as a junction that c ) : b Upon approaching one another, multiple pairs may join, at which point their net dislocation is the summation : The dynamics of the dislocations is a fascinating area of research, serving to quantify Figure 12 :a) A perfect edge dislocation (left) of a graphene lattice equals the lattice constant while larger dislocations by a factor of 2 (center) and (right) are also shown ( Lattice c onstant ) [24]

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21 deformation from stresses on the lattice. The reader is referred to the literature for more information [24] 1.4 Tube Classification Di fferent synthesis environments, with controllable parameterized growth conditions, allo w the creation of a myria d of structure Characterization of a nanotube may distinguish between several variables. Fifty years ago, the catalysis literature searched for ways to end [14] Now, these tubes are a ppreciated and sought out; leading a revolution in materials science. A particular tube as will be elucidated shortly, determines the orbital overlap, controlling its electrical conduct i vi ty. Specifying electrical conductivity allows tube use in nanoscale circuitry. Scientists are increasingly able to modulate the flow of charge carriers along single tubes or through bundle s of them. The f rontier of electronics is now progressing through a state of constant redefinition There are currently teams of physicists, chemists and engineers all over the world, working together to further develop nanotechnology [14] [11] [15] [16] In 2008, nanowires were developed by Stanford University and Toshiba which operated at 1 GHz on silicon chips [17] This marked the point at which nanotubes matched industry for circuitry speed Alternative chip designs to that of silicon (immediately under carbon on the periodic table) are underway. Ralph Erickson at t he University of Pennsylvania conducted a study on the close packing of spheres in cylindrical arrays [ 11] H e labeled symmetrical patterns of points viz. the centers of the spheres, section, there are a minimum number of

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22 generative helices necessary to specify an array of points on i t s surface. Jugacy ( denoted k ) is the number of generative helices necessary for such specification. Parastichy numbers m, n, and (m+n) specify screw displacements; k tells the frequency of rotational symmetry. A ny jugate. Figure 13 : Tubularly arranged spheres, labelled with jugacy and parastichy n umbers [5] His model indexed the tubular arrays in the form k(m, n) or k(m, n, m+n) B iologically pertinent results include the modeling of actin microfilaments (1, 2) microtubules (6, 7, 13) the tobacco mosaic virus capsid (1, 16, 17) and the flagella of Salmonella 2(2, 3, 5) [18] The specification was first carried out studying phyllotaxis but

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23 Indeed, c ubic and hexagonal close packing describe ionic, metallic, covalent and molecular crystal structures. Efficiency in packing equal sized spheres is guided to lead to maximally dense structures. In two dimensions, a sphere A is in contact with six others. Repetition across an infinite plane forms close packed layers [8] Six is the maximum coordination number for identical spheres in two dimensions, in contact with one another. Three close packed directions relative to translations of the unit cell onto equivalent points Close packed structures arise from stacking close packed layers on top of each other in the most efficient ways. Generative helices do not need to be made of adjacent points. Patterns may consist of two, three or k generative helices, respectivel y referenced as bijugate, trijugate or k jugate. Two sets of parastichies (helices made of adjacent points) are labeled x and y parastichies. Structural classification correlates with molecular stability, physiochemical properties and allowed electronic transitions with symmetry Protein monomers regular ly packed into a tube structure a re a common motif in biology. Cytoskeletal microtubules and bacteria l flagella are biological structures which may be cl assified by jugacy and angles of inclination [11] Most CNT s are believed to be structured such that their hexagons are arranged around the tube axis in helices, not exhibiting the high symmetry configurations of zig zags and armchairs [11] There are two distinct carbons in the graphen e lattice. A tube with chiral vector C = na 1 + ma 2 between two equivalent points on a graphene lattice is specif ied by the integer pair (n, m). C's magnitude is where a c c is the carbon bond length in graphene, 1.41

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24 Figure 14 : Graphene's unit c ell (A,B are distinct carbon atoms) [30] The unit cell basis vectors for a sheet of graphene may be derived from a quantum mechanical consideration of a periodic potential, i n terms of Bloch functions. Zig zag tubes have m=0 and the archetypal tube is represented by (9 0 ). The armchair tubes have n= m ; a common case is the (10, 10 ) tube Chiralit y ensues in every case that is not zigzag. Lower symmetry in chiral tubes will yield larger unit cells than for zig zag or armchair tube s [11] In considering a nanotube as a one dimensional crystalline structure, a cylindrical translational unit cell may be defined along the tube axis. The archetypal NT is capped with half a C60 on each end the width of the cell of an armchair tube. Any clo the dictation that a hexagonal lattice m ust be closed with exactly twelve pentagons when folded into a polygon Thus a cap comprising exactly half of a Buckyball must contain six pentagons. Strain induced by adjacent pentagons necessitates the presence of heptagons for stability to develop. Projection mapping allows possible caps, for nanotubes larger than the archetypal ones, to be calculated [15] [9]

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25 A map may be traced over the standard honeycomb lattice and may be folded to form a fullerene. Pentagons are formed by removing a triangular lattice positive wedge disinclination. Nanotubes may be visual ized as a rolled graphene sheet by superimposing the chiral vect or's ends The folded lattice allows the head and tail of the vector to coincide, spanning the straight cylindrical single walled nano tube [11] The symmetry of a honeycomb's lattice allows cylinders produced thus to be equivalent. An irreducible wedge refers to one twelfth of the lattice, inside which unique chiral indices (n, m ) [11] [16] CNT's form various shapes : straight, planar spiral, curved, helical; as carbon rings form heptagon, pentagon and hexagon rings. Formation of out of plane shapes occurs because of sp, sp 2 and sp 3 bonding hybridizations that correspond to pentagons and heptagons in the folded lattice [9] Variable p character in the hybrid orbital hexagonal rings. This induces overlap of otherwise disparate orbitals. 1.4.1 Curvature and Strain Energy It is interesting to relate the strain energy which is relieved by coiling to the electronic transition state's dependence on catalyst geometry The strain energy of a thin tube is inversely proportional to the diameter. Consequent ly, the strain energy of a bond decreases as the inverse square of the diameter [11] Naval Rese arch Laboratory, John Mintmire calculated the strain energy for tubes of diameter less than 1.8 nm with empirical potentials, confirming the invers e square relation. If the tube has a

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26 diameter greater than 1.6 rather well [11] 1.5 Metallic single walled and multi walled tubes exhibit ballistic conduction [1] This allows high current to propagate down the length of a tube without scattering, and no d tensile Figure 15 : (10, 10) Armchair SWNT [31]

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27 Single walled armchair NTs are quasi one dimensional conductors with two open conduction channels. Their energy sub bands are laterally confined and cross the Fermi level. Recall the graphene lattice: T he K point is where the valence and conduction bands touch in the Brillouin zone; hence very little energy is required to excite electrons there, which behave as though they are nearly massless. Early work theorizing them to be metallic was verified experiment ally, illustrating nanowires' ability to support coherent electron transport. The initial experiments showed an effective path length of 140 nm [18] The K point sits at When dotted with the chiral vector if it yields an integer multiple of 2 the K point is in an allowed state, and a folded tube will be metallic. Otherwise it will exhibit a bandgap characteristic of a semiconductor [31] The electrons, seen as massless, are described with a Dirac Hamiltonian: H graphene = v | | [31] Figure 16 : Allowed K values for g raphene [31]

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28 The tight binding model is used to elucidate band structure, usually retaining only like, nearest neighbor interactions in the Hamiltonian matrix. These elements between the p orbitals are limited to one per carbon atom, and are oriented normal to the tube's surface. Den sity functional theoretical calculations support a model for perfect armchair nanotubes [27] The valence bands may be described near the Fermi level with all the matrix's diagonal elements set at the Fermi level, and all non zero o ff diagonal elements set at V 0 = 2.7 eV. There are as many bands as carbon atoms per ring; they are presented as a function of the quasi momentum k. k labels an eigenstate of the helical screw operator, which is used to generate the armchair t ube. Gen eration comprises taking a ring and duplicating it. The new ring is rotated and translationally displaced, to specify As an armchair tube's length increases, however, the electrons in the conduction band experience an increasing degree of localization. This is due to disorder that results from tube environment interactions. In 1998, White and Todorov published a letter in Nature that included calculations which demonstrated that armchair tubes' electronic dynamics are fundamentally different than ordinary metallic wires. The effective disorder encountered by these electrons is averaged over the tube's circumference. This enables the charge carriers' mean free paths to increase with the nanotube's diameter within syn thetic range Thus do select experimentally produced CNTs demonstrate ballistic transport, with localization lengths of over ten microns [18] Localization length is the average distance an electron may be conducted before being scattered by impurities in the lattice; a shorter length correlates with the mean free path function no longer appre ciably resembles a plane wave in the lattice oscillations.

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29 1.6 Helical Tubes T he t echnological development of nanosprings has finally become possible on a large scale [14] elasticity, and stabilizing effects on polymer matrices that will prove revolutionary in coming years. Figure 17 : Coiled nanotubes with variable pitch and diameter (b) nanotubes twisted together, (c) compressed tubes showing nod es, (d) looped tubes [14] The structure function correlation of carbonaceous materials necessitates understanding the mechanisms underlying their growth [9] [7] [11] [31] [6] [22] It is also valuable to be clear about the properties which we hope to optimize by growing HCNTs. For example, the loo ps in the tubes in Figure 16 (d) can be produced in CVD by reducing the ambient pressure. Symmetry arguments paired with density functional numerical methods reveal seven relaxation parameters [23] HCNTs were first reported in 1994,

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30 allowing nineteen years of experiments on their growth and properties to have been carried out [32] Figure 18 : Coordinate system for a helical nanot ube [23] A carbon microcoil with a diameter of 0.5 m, and a coil pitch of 5.0 m was probed with a silicon cantilever to determine its elastic response [7] It was shown to be able to extend to three a nd a half times its length while being able to return to its original shape upon being released. However, when extended to five and a half times its length, becoming nearly linear, it experienced plastic deformation. The tube did not return to its helica l form [17] are (a, r, z) T radius and angle of inclination ( R and ) only require the position of the tube relative to the helix Though it does not specify the twisting of the rings along the tube the m odel

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31 confirms that HCNTs are exceedingly likely to be conductive [23] They have a higher concentration of allowed states at and close to the Fermi level relative to straight tube s. Figure 19 : Electronic bands of a (15,15) HCNT; sp 3 atomic orbital model [23] Note that helices have comparably low symmetry, with respect to straight tubes. noncrossing rule to take effect in helical tubes [23] The secondary gaps in the enlarged Fermi level illustrate this in the figure above. Their springy spatial structure holds great potential in mechanical, chemical, and electrical regimes of applicability. Molecular springs may be used for energy transduction, drug delivery, and circuitry on the nanoscale [23 ] dependence on synthetic techniques enables examination of the relevant kinetics. Reactions under kinetic control are highly sensitive to catalytic parameters.

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32 Chapter 2 : Carbon Nanotube S ynthesis 2.1 His tor ical overview: Pyrolysis, Laser Abla tion, & Arc Evaporation In the 1960's, Harry Kroto at the University of Sussex sought insight on the chemical processes occurring on the surfaces of stars. In August of 1985 he met Richard Smalley, who was actively engaged in vaporizing semiconductors, constructed with silicon and gallium arsenide, with lasers. Together they conducted several experiments vaporizing graphite and examining the resultant material. Mass spectrom etric analyses showed C60 to be the dominant species in the distribution of gas phase carbon clusters [11] Experimental attempts to minimize the time necessary for the clusters to anneal showed higher yields by introducing Hel ium, an inert gas into the atmosphere. At Rice University, Smalley initially carried out experiments with laser vaporization in 1995. The technique was developed to study effects of carrier gas on producing C60, in which a laser vaporizes graphite in an oven at 1200C. Their catalyst was molecules of molybdenum ( with a diameter of a few nanometers) on alumina support. Carbon monoxide gas was passed t hrough a tube furnace at 1200C, and r aising the temperature raised the single walled nanotubes (SWNTs) yield [11] The apparatus shown below would vaporize one kilogram of graphite anode per hour of use. The cathodic deposits were produced after an hour long run, from an anode of variable diameter. The front, smallest deposit corresponds to a diameter of 8 mm, the central to a diameter of 25 mm, and the top, largest had been in contact with a 65 mm

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33 diameter anode [22] Figure 20 : a) Arc di scharge reactor; (b) C d eposit [38] The deposit's macroscopic structure depends on the electrode's cooling efficiency. Poor cooling leads to a layered deposit. The CNT's are randomly oriented and found in small pockets. Multiw alled tubes are found i n the cathodic soot after arc evaporation. Lengths range from tens of nanometers to several micrometers. Efficient cooling on the other hand produces a cylindrical, homogeneous deposit. Figure 21 : An apparatus for arc d isc harge s ynthesis [38] A hard outer shell made of fused material surrounds a fibrous cor e of nanotubes & nanoparticles. The nanotubes may be extracted by cutting the outer shell. Poor samples

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34 have a powdery texture, whereas those of better quality give gray metallic flakes when smeared. Scanning Electron Microscopy shows that the cores have aligned microfibrils. To prepare SEM, samples are dispersed in a solvent (typically IPA), ultrasonicated and deposited on carbon film support grids (whic h may have NTs as contaminants) [11] 2.1.1 Chirality Control Synthetic strategies for producing chirality controlled SWNTs have finally been validated! Using specifically singly chiral tubes of exceptional purity, selectively chiral tubes can now be seeded. Furthermore, the se catalysts [19] An overview of several synthesis techniques accompan ies a sketch of the historical development of nanotube synthesis. 2.2 Cat lytic Chemical Vapor D eposition Chemical vapor deposition is a technique well known for the production of synthetic diamond in a low pressure environment of 1 27 kPa. Feeding a carbon precursor gas into a tubular quartz chamber allows the growth of carbon materials on a substrate. Microwaves, arc discharge and hot filaments each may serve as a source of sufficient energy to create carbonaceous plasma that can crystalize into desired st ructures. CVD is well known for the growth of synthetic diamond and is now tunable for specified tubules [7]

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35 Figure 22 : C atalytic CVD Reactor labeling A) the electric furnace, B) tubular reactor, C) humidity absorber, D) bu bbler for liquid precursors, E) command panel; To the right, an internal view of CNT synthesis [40] Chemical Vapor Deposition is industrially used in the production of solid material s with a high degree of purity and is useful in producing semiconducting thin films The substrate is known as the wafer and reacts with volatile precursors that decompose on its surface. Several formats of CVD are used and may be characterized by pres sure, vapor type s, plasma utilization, catalyst presence combustion, meta l organic CVD, rapid thermal, at omic layer epitaxy, among st numerous other speci alizations [7] The technique was first used by Leonid Chernozatonskii in 1992 at the Russian Academy of Sciences with an external field of E=0 in a high vacuum of 10 6 Torr. He used

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36 an electron beam to vaporize graphite and aligned fibers formed on the quartz reaction tube [20] High Resolutio n Electron Microscopy allowed observation of imperfect multi walled NT's in the film produced. Catalytic synthesis was first carried out with molybdenum particles supported on alumina. These particles ranged a few nanometers in diameter, ideal for nucleat passed through a tube furnace. Catalytic tubes normally have small metal particles attached to one end [5] It is upon the surface of this cata lyst that the tubes nucleate and grow In 1993, Maohui Ge and Klaus Sattler at the University of Hawaii conducted experiments by heating carbon foil, producing carbon vapor. The vapor condensed upon exposure to freshly cleaved highly oriented pyrolitic graphite (HOPG), in a high vacuum of 10 8 Torr [11] Kinetics allows the production of multiwalled and single walled tube s and both were observed 2.2.1 Growth Support Alumina and Gold support s can be used to conduct observations on the nanoscale with scanning tunneling electron microscopy (STM) [16] STM is a pow erful technique in chirality; it enabled the first r esolution of multiwalled T he effects of orbitals on scanning tunneling electrons were then observed. As t wo cylindrical sheets cannot realize perfect lattice Figure 23 : A Moire Super Pattern [78]

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37 coherence, a M oir super pattern can b e seen, form result s from the impossibility of two concentri c hexagonal lattices lin ing up evenly. Tube forests may be grown on an iron film, and their type and diameter depend on the thickness of the film as demonstrated in Figure 23 below [21] Figure 23 : (a) Relative concentrations of CNT type phase diagram. (b) Plot of mean diameter's dependence on Fe film thickness [21] A letter to the Japanese Journal of Appl ied Physics in 2000 reported growth of nanocoils with a yield over 95% [27] The carbon precursor was acetylene and it grew on an iron coated indium tin oxide catalyst. Notable characteristics of the synthesized helical tub es include their propensity to grow in pairs, due to entropic effects, each with its own diameter and pitch. nanometers. I n 2008 Joselevich et al analyzed tube organization in terms of various parameters. The CVD process was examined focusing on resultant tube patterns. Horizontal and vertically aligned growth boosts different potentials for exploitation [21] Spinning tub es

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38 from solution, dry fo rests and directly from the gas phase have all been successfully reported [15] Vertical growth is common, seen with efficient catalysis. Moreover external fields a horizontal surface, or gas flow can direct the CVD vector of growth. 2.2.2 Supergrowth CVD Using Water Catalysts have limited ability in nucleating tubes, as they become dea ctivated by amorphous carbon forming on their nucleation sites [21] Further, the catalysts act as impurities in the grown tubes, which must be subsequently purified. Water vapor added to the growth ambient is a new approach which increases catalytic lifetime and activity This supergrowth, as it is known, allows n anotube forests to be grown exceptionally quickly 2.2.3 Tube Distribution Figure 24 : Densely packed array of coiled tubes imaged with SEM [33] SWNTs have formed looped structures when crossbar architectures were attempted with electric field directed growth. When coupled with surface direction, crossbar architectures were achieved [21] Several approaches exist for growing SWNTs in a desired orientation. Lithographic alumina p atterns create a local E field via static charging. Alternatively, electrodes enable field direction to produce transistors. SWNTs exhibit a

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39 may be directed by atomic steps, rows or nanofacets in their growth by epitaxy on well defined crystal surfaces. all factors allowing nu cleating CNTs with 100% yield is developing nanotube electronics [21] Figure 25 : Possible tube morphologies from C plane sapphire miscut, annealing, CVD; graphoepitaxy [21] Figured miscut sapphire planes above : (a) shows the equilibrium shape of Al 2 O 3 Its facets are arranged in the order of increasing surface energy: C ,R,S,P,A The miscut in (b) yields a vicinal Al 2 O 3 There are 0.2 nm steps, which are thermodynamically unstable for the growing tube to take. It is possible that the steps get grouped together in [38] High Miller index direction steps taken in growth tend to make SWNTs grow kinked, whereas lower energy directions have very straight tubes

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40 be behind, where it is observed on the substrate surface. 2.2.4 Cat alytic CVD parameters Experimental conditions provide a synthetic basis for considering nanotube growth. Models which relate synthetic environment to observed structure may be paramete rized in distinct contexts. The combination of flow directed and field directed growth promises to generate ever more complex CNT morphologies [21] Sought out tubular geometry is exemplified by the structure of co mputing These are based on crossbar architectures, which have been produced with CVD. By pairing field direction with perpendicular graphoepitaxy the crossbar shape may be created in a single step Figure 26 : Catalytic growth m echanisms root and tip carbon extrusion [22]

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41 Catalyst geometry a Trapezoid shaped Cu catalyst particles are conducive to the formation of nanotubes embodying the Fibo nacci spiral ; whereas a planar p entagon shape may give rise to a double helix. T he planar hexagon shaped catalyst leads to helical fiber formation [6] Figure 27 : Fiber catalyst morpholgy relationships [20] Metallic catalyst use nece ssitates interaction between catalytic particle and carbonaceous precursor gas. Adsorption of the precursor gas onto the catalyst surface allows the gas to dissociate. Individual carbon atoms diffuse across the surface and are extruded into a growing nanotube. Unequal extrusion velocities can introduce a twist into a growing tube. Dueling theories claim pairs of five and seven carbon rings as instigating the curvature, while other theories criticize the model, showing helices develop with deformed hexagonal rings [23] Rotation of the substrate helps shape [46] By determinin g if the catalyst particle is in an ideal position to coil the tube as it grows. In 2000, In Whang source gasses were H 2 N 2 and thiophene makes it a useful precursor.

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42 Figure 28 : Random CCVD initial c onditions [24] M ixture of 500 carbon Vide supra refers to flow directed growth, an external force which is compatible with epitaxy in efficiently organizing SWNT aligned arrays [21] Catalyst islands of microns in length have been utilized in catalytic CVD yield ing patterned growth on SiO 2 /Si wafers [21] This scale is much larger than the single catalyst particle Fe clusters (which are on the order of two nm). Catalytic CVD syntheses with acetylene as precursor have shown that if vapor density is too high in the reaction tube, supersaturation of the catalyst will c ause the catalyst to burn out. Proposed explanations include carbene formation fusing to its surface. A simulated effect of higher than optimal vapor composition is shown below. Models for nanotube growth resulting from catalyst/precursor/substrate foll ow.

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43 Figure 29 : Vapor density e ffects [24] Chapter 3 : Growth Models Figure 30 : Heli cal n anotubes ( pentagons + heptagons ) [46]

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44 This chapter present s a thermodynamic model for helical tube formation as a centerpiece for further con ceptualization of its growth Numerous models have been proposed taking in to account various factors for nanotubes manifestation of helical morphology [9] [14] [25] [11] [26] [23] [16] [22] Thermodynamic considerations of entropic effects correlate with novel, extraordinary, physiochemical properties emerging? As a helical carbon nanotube nucleates and grows, the nature of molecular architecture allows some perspective in examining the interactions of metallic catalyst particles with hot carbon gas Transition states reflect their stability in shaping tubular morphology. Classification in terms of symmetry; provides a valu 3.1 Thermodynamics of Helix Growth The following model decomposes nanocoil and nan oheli cal growth into three modes; a mode of linear growth, one of bending, an d a twist ing mode [25] The X and Y directions correlate with in plane growth, while the nanostructure vertical growth occurs along the Z axis. The supply of growth catalyst dictates the degree of growth A, and is the divergence of the directorial growth vector: The bending (above) is assumed a priori t o increase linearly with tube length, while t he overall twist (below) relates to differential in p lane deposition rates, likely in orthogonal directions:

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45 The coiling is a combination of bending and twisting, and results from nonwet ting catalyst particles in the cat CVD reaction tube [25] The bend and twist modes serve as contributions to the net elastic free energy (F elastic ), parameterized by elastic constants K 1 K 2 and K 3 : metals indium, copper and tin have a large wetting angle, over 150. This correlates with repulsive interaction, promoting nonlinear growth. Conversely, nickel, iron and cobalt have small wetting angles, and thus attractive interactions. Figure 31 : Wettability effects of catalyst: a) In (non wetting) causes nonlinear growth; b) K (wetting) provides a template for coils to form A chemical poten tial term contributes to nanotube will avoid specific catalyst particles [25] This term promotes nonlinear growth as it relates growth to interactio ns with the ambient environment. This term promotes nonlinear growth, with s interactions with the ambient.

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46 Self consistent solution of these equations yields the components of the directoral vector n (n x n y n z ), parameterized by t, which is proportional to Bandaru et al showing higher concentrations making tighter coils of the helices grown. The more indium present to interact the more bends were induced in the growing tubes. Bending, paired with twisti ng, comprises the coils, which were observed to increase in frequency [16] The interfacial adhesion present between metallic catalyst particles and the carbonaceous surface enables the particles to be considered as external s tresses. The thermodynamics rationalize the balance with ambient entropy rising as the helical tube assumes lower symmetry. Figure 32 : The enthalpy and entropy of indium oxidation contributes to determining reaction rate [40]

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47 Enthalpy and e ntropy considerations are related to the rate of synthetic progress by the Arrhenius equation : where k is the reaction rate, K B constant, R the ideal gas constant, is P free energy is Minimization of Gibbs free energy drives a system into equilibrium, which is balanced by enthalpy and entropy concerns : The entropic contribution scales up with temperature. Careful combinations of variables allow s for the creation of fibers with quantified ly optimized spinnibility. This supersedes our focus, and [12] Surf ace energetic dominance generally yields to coiled growth, while straight tubes tend to grow when elastic effects become more important [25] Carbon n anofibers (CNFs) differ from CNTs in that they are not hollow. Rather than a rolled grapheme lattice, their core is made of stacked sheets. They tend to twist to a greater minimizes the amount of space for a given volume of nanostructures grown. The ambient compensates for the SWCNT 3.2 Catalytic Particle Interaction Uniform Coil F ormation models have been considered in which the nanotube grows while retaining hexagons, but pentagon/hexagon pairs have been shown necessary for coil growth. Ramachandran & Sathymurthy proposed a simple model in 1994 in which adjacent layers of carbon atoms introduce twisting via rotational distortion [27]

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48 Verissimo et al grew multi walled tube s, amongst other carbonaceous nanostructures, with catalytic thermal CVD at atmospheric pressure in a horizontal tubular quartz furnace in 2009 [20] [22] Their growth mechani sm analysis constructed a new model. A specific instability occurring on the catalyst particle surface supersaturated with carbon underlies nanotube nucleation. Axially symmetric instability, leading to nanotube nucleation, arises upon meeting critical conditions in temperature, supersatur ation and catalyst volume. In the case of lower temperatures, flat graphitic layers are formed rather than tubes, exemplifying another carbon segregation mechanism from supersaturated catalysts 3.3 Pentagonal and H eptagonal Ring P airing Gao, Wang, & Fan conducted an analysis of zigzag and helical tube s Their p ropo sed growth mechanism emphasizes kinetics' role in shaping the helices [9] Their data support kinetics contro lling growth. Specifically, the c reation rates of pentagon al and heptagon al carbo geometry. A pair of penta g ons will cause a conic defect to arise, while a pair of heptagons creates a saddle point [17] Standard models for HCNTs put the paired pentagons on the outer face of the helix, with convex character. Similarly, the heptagon pairs are positioned on the inner coil surface, with negative curvature.

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49 Figure 33 : (a) pentago n nucleation, (b) quasi icosahedron shell growth, (c) a catalyst particle is engulfed by spiralling growth, a straight CNT grows, (e) The CNT forms a node, (f) Formation of a coiled tube [33] A carbon cluster grows into a nanotube following nucleation from a pentagonal carbon ring through spiral shell growth. Pentagonal heptagonal (P H) pairing is necessary for both zigzag and helical morphology to arise. A twist in the P H orientation allows for deviation from an otherwise planar spiral formation. Helices form with a twisting of the P H pairs' orientations along the nanotube's growth direction. The distance between adjacent P H pairs and the angle of their twist determine the helix's coiling d iameter and periodicity [9] Dense accumulation of P H pairs, when coupled with a small interpair distance, leads to the formation of a node and the morphological manifestation of zigzag growth. Pentagons and heptagons arise due to geometric dependence of carbon extrusion from the catalyst between catalytic activities, viz. the carbon atoms' diffusion rates, on each side of the catalyzing particle. This growth mechanism offers insight to crystallographic catalytic activity. Moreover, p aired pentagon and heptagon rings' orientation determines stretched and relaxed helices' geometries [9]

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50 3.4 Pentagon/ H eptagon Pair R econsideration s Periodicity suggest s crystalline stability principles should apply to nanotube structure [28] [29] Ding et al claim that viewing the nanotube as having a screw dislocation along the axis leads to its growth rate being proportional to the Burgers dislocation vector and to the chiral angle of the tube. Their ab initio energy calculations agree with diverse experime ntal measurements and support their mechanism. Figure 34 : Metal Catalyzed Cap Growth [24] The interacting particle model (IPM) developed in 2005, attributes nanotube growth initiation to the physical interaction between catalyst particles. Coalescence of multiple catalyst particles partially blocks the particle surface, disrupting rates carbon deposition over the particle surface. Generation of a n et diffusive flux toward the interparticle contact point results from the resu lting concentration gradient [28] Such catalytic aggregates can support continuous nanotube growth between the particles. The model also extends to multiple particles, accounting for complex morphologies. The IPM is consistent with many structures experimentally observed in

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51 flame produced material. Height et al e valuated t he validity of the model through the analysis of diffusion dynamics and force s of particle binding and separation. The IPM identifies the requirements and optimal conditions for supporting nanotube growth in premixed flame. Formation of nanotube s between particles indicates that multiple pathways exist with varying rates dependent on process conditions; no single mechanism can completely describe nanotube synthesis [28] Nonetheless, outlined mechanisms successfully allow knowledge of kinetics and thermodynamic driving principles to design successful syntheses. 3.5 The Double Helix : Interfacial Adhesion Exploration is currently underway to determine how and why quasi one dimensional nanomaterials tend to aggregate. Observed double & multi stranded helical conformations invite the construction of new models Using continuum mechanics analysis, I n April of 2012 J i et al demonstrated that interfacial adhesion effects are signi cant in the formation mechanism of some double helices They are nontrivial especially at micro and nanometer scales, as well as for soft materials. The formation of a double helical structure by two nanowires decreases their surface energy, while the elasti c strain energy increases. This energetic competition will dictate how more specific geometries may be manifes t ed. The adhere nce between micro/nanowires /tubes will help determine their macroscopic distributions. Their model agrees well with relevant experiments [ 29]

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52 Figure 35 : SEM images of CNTs with (a) coiled, (b) spring like, (c) helical, and (d) double helical morphologies [40] An interpretation of the kinetics a nd subsequent predictions was given in terms of dislocation theory [29] Vapor liquid solid model and atomistic simulations have also made contribution s to understanding nanot ube growth, associating an axial screw dislocation with zig zag growth. Bathgate et al compared the produ ction of straight and helical nanotube s in vertical Swirled Fluid CVD. They found that the helical tubes were lifted out of the reactor in the inert gas currents whilst the straight tubes remained in the reactor [14] Who knew ? It seems that helical tubes can fly. The drag forces of the swirled vapor are strong enough to lift the HCNTs because of their greater cross sectional area. The revolutionary integration of CNTs in materials science is marked by their extraordinary physiochemical properties [7] Neither r ational prediction nor production

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53 constitute d the method of discovery for bihelical nanotubes [1] Rather, their kinked structure, resultant from helicity change, was fortuitously noticed in a normal sample. This structure may see widespread use as a diode [8] Chapter 4 : Some Application s A comprehensive list of possible applications would be much longer than this thesis; a few notable uses are developed in this chapter Indeed, the construction of a space elevator may be possible with the use of nanotubular fibers [44] CNTs are extremely efficient sens ors [1] and coiled tubes are extremely efficient microscopic inductors, certainly hold ing unprecedented properties. They also have the capacity to be grown from carbon dioxide. Another astounding possible use for nanotubes t hus arises, in the context of greenhouse gas sequestering: if CO 2 could be effectively channeled from the atmosphere onto metallic catalysts and spun into fibers, perhaps humanity has a chance to lessen the severity of climate change. 4.1 Carbon Dioxide as Precursor Optimizing SWNT production entailed considering the specific standard chemical exergy, as was carried out by Gutowski et al in 2010. Exergy measures the capacity to do useful work in a system per unit mass to reversibly transform a reference identified chemical components into the finished product [33] CO 2 in the air would begin the process of creating a single walled tube in the high pressure carbon monoxide (HiPco ) manufacturing process. The carbon dioxide first must be concentrated, purified, and

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54 reduced to its chemical const ituents: graphite and oxygen. For reference, t he standard chemical exergy of graphite is to 410.26 kJ/mol, or 34.16 kJ/g. The subsequent task is the separation of a graphene layer from the graphite and the act of bending it into a single walled tube [34] kJ/g). The reversible separation of a layer from a bulk mater ial requires twice the new ion [33] Interatomic interactions yie ld a high bending stiffness, due to the bond angle effect. When lattice atoms are twisted against one another, or pulle d slightly out o f their equilibrium positions, orbital overlap decreases. Compensation comes in the form of strain energy. This form of trapped heat is a result of external forces on the system. This detraction from the aromatic character urge to minimize the free energy. 4.4 Nanotube Functualization Nanotubes are susceptible to attack by nitric acid, especially where there is strain from lattice defects [22] The addition of the nitro grou p allows substitution reactions to further modify the functional groups attached.

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55 Figure 36 : Functionalization with the carboxyl groups, subsequently undergoing esterification or amidization [22] The addition of functional groups to the surfac e resemble s dislocations, as they add resistance, and strength. However, the potential of nanotubes in organic chemistry is only now being discovered. Figure 37 : Potential functualization reactions on a nanotube surface [27]

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56 An exhaustive review of the chemistry which can be done on the surface of the tubes (not to mention inside them) is beyond the scope of this work. It is worth noting, however, that the amidization and esterification techniques shown above may prove valuab le in securing the ends to polymer matrices. 4.5 Composite Materials Figure 38 : A Panamanian tube endangers the structural integrity of an unreinforced epoxy matrix Materials engineers have parameterized useful properties with various moduli. Extensive experiments and calculations have geometry with its response to external stimuli [41] range from 1.5 to 5.0 TPa [38] Compared to steel, straight tubes can bear enormous stress before they are inclined to strain.

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57 Figure 39 : Stress s train curves [45] T ensile stress strain curves of CNT composites and relative matrices. (a) and (b) Samples with soft matrices (9 wt% hardener 48 h curing time for (a) and 72 h for (b)), CNTs show a significant reinforcement role ; the fracture strain of the composites shows no evident de crease. (c) and (d) For t he stiffer matrices (with 12 wt% and 13 wt% for (c) and (d), respectively, and 48 h curing time), CNTs slight ly reinforce the matrix [45] The elas t ic modulus actually refers to several different moduli, depending on the location of the stress before the point at which plastic deformation takes place. What does the ratio between stress and strain imply?

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58 Figure 40 : Thermal stresses in a MWNT polystyrene matrix cause cracks to nucleate and propagate [22] The introduction of nanotubes into polymer composites provides a particularly fascinating potentia l for technological development [34] T he construction of a high performance surfboard strong enough not to break even upon experi encing intense stress is highly s ought The above figure shows cracks tending to spread through areas of low MWNT concentration, or along the weak interfaces between tube and polymer [22] As the crack spreads, the tube serves to bridge it while the gap is not too large. Lack of substantial crosslinking fails to keep the tube f rom pulling out of the matrix [57] Functionalization is therefore a valuable part of composite preparation; well known functional group reactivity allow s the tubes to form covalent bonds, effectively a nchoring them in the polymer. Further consideration of composites invites the question: Could helical morphology be beneficial in strengthening a polymer matrix? Surely, an ideal use f or helical nanotubes finds affirmative response by Lau et al [45]

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59 The tubular geometry as well as attached functional groups determine the m olecular interactions between a nanotube and the polymerized matrix in which it may be embedded [35] The desired effect is to a dd resistance against s t ress cracking. This is the process responsible for the irreversible deformation in the matrix which we hope to guard against. 4.6 Surfing Wave s Contextualizes Tubes A falling lip from a large wave may impart so much stress to a surfboard polymer matrix that the structure i s snapped clean ly in half. Even slight stress fractures may allow water to traverse an epoxy resinous layer and soak into the traditional porous f oam core subjecting it to rot and decay [47] This stress cracking can be reduced by incorporating nanotubes into the surfboard. However, one i ssue to consider i s the tubes tendency to slide out of the matrix [48] Even then, successful bridging support may allow water to diffuse inwards if the polymer matrix is not sufficiently cross linked. Figure 41 : Straight CNTs integrated into crosslinked polymer structure [34] In order to design the ideal surfboard, the necessary incorporation of a few properties is obvious. Durability and strength are important, as is minimizing the weight of the board so as to best flow with the sought after waves. Durability entails strong bonds holding the

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60 material together, able to keep water out and to degrade as slowly as po ssible in exposure to salt and sunlight. Aerogels are very light, and are the newest allotrope of carbon. Their density makes them ideal candidates to replace traditional foams. The conventional aerogels are very brittle however, with low tensile stren gth and elastic modulus [36] This results in readily fragmenting in response to stress, not an ideal behavior in a surfboard The 3D network branches of aerogels are interlinked nanocrystallites, which applied forces break easily. More recent incarnations of aerogel research accommodate an elastic bending response through incorporating nanotubes. Super elastic behavior was demonstrated in MnO2 nanowire aerogels, promising potential for bring ing springiness to high performa nce surfboards. Among the springiest materials to be considered for shaping into a board is a highly elastic form of graphene, modeled in the structure of natural cork [37] The honeycomb structure has close packed layers whi ch make it strong enough to avoid the brittle, weak fate of early attempts at 3D graphene structures. Regardless, the incorporation of helical carbon nanotubes into polymeric composites increases the mechanical strength of the matrix as they are less apt to slide out due to the winding of the helix. The twist allows them to be relatively well anchored even without functionalization and covalent attachment [37] This is tremendous news for surfers, and likely holds application outside of extreme sports equipment improvement.

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61 Conclusion The r ealization of nanotubular possibilities is sure to manifest itself broadly across a number of industrial and scientific applications The first three chapters of this thesis have attempted to provide context for novel applications and a foundation for dream ing up new ones T he relation b etween synthesis parameter s and material properties was approached with numerous models The substrate upon which arrays of nanotubes are synthetically prepared must fulfill its duty in providing support with precise form. I conclude with illustrating a novel possibility for helical carbon nanotube appl ication s : the construction of a surfboard with elastic properties due to the enhancement of its matrix The ideal flexural response would depend on distribution The materials science literature contains many models of beams to optimize elasti c behavior Extension of these to a useful, novel system would examine HCNT composite s subjected to the periodic stressing which is characterized with riding a wave. Here I identify the need for a neural net algorithm to be applied to a n idealized wave/ surfer system. A surfboard into which HCNT composite material has been incorporated would be subjected to this downwards force into translational motion, as it is the interface between the surfer and the wave. The desired flex would subsequently specify synthetic and purification techniques. How to optimize the nanotubular distribution?

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62 Figure 42 : A wave breaks, setting up a surfer for a bottom turn The surfer standing over the board should be considered be initially considered a harmonic oscillator, expanding and contracting over the board. Moreover, the surfer and board move together along the wave: up and down the surface, as it brea ks; and sideways, along the open face. When the wave is first caught, the surfer accelerates downwards with gravity in the same direction as the wave energy propagates Upon reaching the bottom of the wave, he commits to turn sideways by digging one rai l of the surfboard into the water. Figure 43 : The author illustrates a bottom turn

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63 His momentum, initially in the same direction as the wave propagation, may be redirected by the board water interface A well executed bottom turn can effectively launch the surfer back up the wave, towards the breaking lip enabling the execution of a shwack The shwack is a characterized by a net excess of upwards momentum contacting the falling lip of a breaking wave. The goal is to displace as much water as possible from the top of the wave, which is traditionally quantified in buckets. In optimal conditions, severa l buckets of water may be displaced at once. How is such generatio n of speed possible? When he is finished compressing he extends, coupling the harmonic oscillation with his overall sinusoidal path up the wave. H is rail is pushing against the water an Figure 44 : A shwack throwing about two buckets above the lip in El Salvador Expansion comes in kicking against th e bottom of the wave. If timed correctly, the resonance between coupled oscillations can propel the surfer back up the wave perfectly set up for a huge schwack. The subtleties of coupling the various oscillations are exceptionally difficult to master ; g ood surfing is hard In e xpanding to his full height, his d irection changes push the board, imparting a large amount of stress to the composite matrix. This thesis hopes to provide d enough context to establish the possibility of creating

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64 a neural net whi ch could distribute HCNTs into a standard s urfboard shape. Ideally, they restoring force contributes to his momentum. This upward motion might not just improve surfing but it might also enable entirely novel aerial maneuvers. Though surfing is an extreme example, its illustration makes a gesture toward other areas of materials science to which HCNTs are/can make contributions. Future line s of scientific inquiry will surely create novel HCNTs and apply them in interesting ways. The highly anticipated space elevator may not be long off now that the linking of thermodynamics and nanotubes is being understood. Catalytic CVD may hold the key to optimizing future scientific endeavors. I seek to illustrate its utility in showing how elastic energy may be utilized, coupled in the bottom turn of a surfer, to generate net upwards momentum. The drop in to bottom turn to shwack process is convenient ly periodic: it conclude s with the surfer at the top of the wave, having just displaced the equivalent volume of several buckets of wa t er into the air with the momentum garnered in the bottom turn. Now ready to drop back down the wave, the surfer hopes on ly to pull under the lip continuing down the wave in a frothing tube.

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65 Figure 45 : Tube riding would be a novel application for nanotube reinforced composite materials

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