Analysis of Irradiation Induced Defects on Carbon Nanostructures and Their Influences on Nanomechnanical and Morphologic...

Permanent Link: http://ufdc.ufl.edu/UFE0022615/00001

Material Information

Title: Analysis of Irradiation Induced Defects on Carbon Nanostructures and Their Influences on Nanomechnanical and Morphological Properties Using Molecular Dynamics Simulation
Physical Description: 1 online resource (132 p.)
Language: english
Creator: Pregler, Sharon
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008


Subjects / Keywords: airebo, carbon, carbonnanotubes, composites, irradiation, nanocomposites, nanotubes, photovoltaic, simulations
Materials Science and Engineering -- Dissertations, Academic -- UF
Genre: Materials Science and Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation


Abstract: Mechanisms such as nanomechanics, changes in chemical structure, and van der Waals interactions are difficult to observe on the atomic scale by experimental methods. It is important to understand the fundamentals of these processes on a small scale to reach conclusions of results that are observed on a larger scale. Computational methods may be readily applied to investigate these mechanisms on models a few nanometers in dimension and the results can give insights to processes that occur during real time experiments. The classical molecular dynamics simulations here utilize the reactive empirical bond-order (REBO) or adaptive intermolecular REBO (AIREBO) potentials, to model short range behavior, coupled with the Lennard Jones potential (and torsion for AIREBO), to model long range interactions of carbon nanostructures and hydrocarbons. The bond order term in the REBO/AIREBO potential allows for the realistic treatment of these materials as it correctly describes carbon (and silicon and germanium) hybridizations, and allows for bond breaking and reformation unlike basic molecular mechanics. This is a key feature for simulating irradiation and pullout mechanics on graphite and carbon nanotube and their composites. The irradiation simulations on graphite, with the same conditions as the experimental irradiation of highly pyrolythic graphite, provide insight to the types of defects that were observed on a larger scale by Scanning Transmission Microscopy (STM) images. Experimental characterization from collaborators mapped out the surface of irradiated graphite while computational theory further described the defects and observed the evolution of the defects during the irradiation procedure. Multi walled carbon nanotubes (MWNT) were irradiated with different particles to compare the effect that incident species have on the nanotubes' surfaces as well as the crosslink distribution of the radial cross sections. Irradiation is a common technique to modify the interfacial areas between the fiber and matrix to improve compatibility in polymer composites. Inducing crosslinks between shells of the MWNT by irradiation drastically decreased the sword in sheath deformation, where inner shells slip out with respect to outer shells, that was computationally demonstrated. A similar procedure was also carried out on carbon nanotube-polystyrene composites. Argon irradiation was simulated for three different types of nanotubes: double-walled, single-walled, and a bundle of four single-walled nanotubes, in a polystyrene matrix. The polymer emission, depth of particle penetration, and nanotube pullouts were observed, it was shown that the presence of carbon nanotubes limited these processes. Atomic Force Microscopy (AFM) and X-Ray Diffraction (XRD) images in conjunction with AIREBO molecular dynamics simulation trajectories of C60 and pentacene films of various ratios gave theoretical and experimental insight on the molecular evolution of donor and acceptor aggregation for optimizing the design of effective organic semiconductors. Atomic-scale simulations are thus shown to be a powerful computational tool to better understand the properties of carbon nanostructures and hydrocarbons. This dissertation illustrates how effective they are for providing insight on chemical modification, nanomechanical deformation, and equilibration mechanisms on the atomic scale.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University 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.
Statement of Responsibility: by Sharon Pregler.
Thesis: Thesis (Ph.D.)--University of Florida, 2008.
Local: Adviser: Sinnott, Susan B.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0022615:00001

Permanent Link: http://ufdc.ufl.edu/UFE0022615/00001

Material Information

Title: Analysis of Irradiation Induced Defects on Carbon Nanostructures and Their Influences on Nanomechnanical and Morphological Properties Using Molecular Dynamics Simulation
Physical Description: 1 online resource (132 p.)
Language: english
Creator: Pregler, Sharon
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008


Subjects / Keywords: airebo, carbon, carbonnanotubes, composites, irradiation, nanocomposites, nanotubes, photovoltaic, simulations
Materials Science and Engineering -- Dissertations, Academic -- UF
Genre: Materials Science and Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation


Abstract: Mechanisms such as nanomechanics, changes in chemical structure, and van der Waals interactions are difficult to observe on the atomic scale by experimental methods. It is important to understand the fundamentals of these processes on a small scale to reach conclusions of results that are observed on a larger scale. Computational methods may be readily applied to investigate these mechanisms on models a few nanometers in dimension and the results can give insights to processes that occur during real time experiments. The classical molecular dynamics simulations here utilize the reactive empirical bond-order (REBO) or adaptive intermolecular REBO (AIREBO) potentials, to model short range behavior, coupled with the Lennard Jones potential (and torsion for AIREBO), to model long range interactions of carbon nanostructures and hydrocarbons. The bond order term in the REBO/AIREBO potential allows for the realistic treatment of these materials as it correctly describes carbon (and silicon and germanium) hybridizations, and allows for bond breaking and reformation unlike basic molecular mechanics. This is a key feature for simulating irradiation and pullout mechanics on graphite and carbon nanotube and their composites. The irradiation simulations on graphite, with the same conditions as the experimental irradiation of highly pyrolythic graphite, provide insight to the types of defects that were observed on a larger scale by Scanning Transmission Microscopy (STM) images. Experimental characterization from collaborators mapped out the surface of irradiated graphite while computational theory further described the defects and observed the evolution of the defects during the irradiation procedure. Multi walled carbon nanotubes (MWNT) were irradiated with different particles to compare the effect that incident species have on the nanotubes' surfaces as well as the crosslink distribution of the radial cross sections. Irradiation is a common technique to modify the interfacial areas between the fiber and matrix to improve compatibility in polymer composites. Inducing crosslinks between shells of the MWNT by irradiation drastically decreased the sword in sheath deformation, where inner shells slip out with respect to outer shells, that was computationally demonstrated. A similar procedure was also carried out on carbon nanotube-polystyrene composites. Argon irradiation was simulated for three different types of nanotubes: double-walled, single-walled, and a bundle of four single-walled nanotubes, in a polystyrene matrix. The polymer emission, depth of particle penetration, and nanotube pullouts were observed, it was shown that the presence of carbon nanotubes limited these processes. Atomic Force Microscopy (AFM) and X-Ray Diffraction (XRD) images in conjunction with AIREBO molecular dynamics simulation trajectories of C60 and pentacene films of various ratios gave theoretical and experimental insight on the molecular evolution of donor and acceptor aggregation for optimizing the design of effective organic semiconductors. Atomic-scale simulations are thus shown to be a powerful computational tool to better understand the properties of carbon nanostructures and hydrocarbons. This dissertation illustrates how effective they are for providing insight on chemical modification, nanomechanical deformation, and equilibration mechanisms on the atomic scale.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University 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.
Statement of Responsibility: by Sharon Pregler.
Thesis: Thesis (Ph.D.)--University of Florida, 2008.
Local: Adviser: Sinnott, Susan B.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0022615:00001

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2008 Sharon Kay Pregler 2


To m y family and friends with love and gratitude 3


ACKNOWL EDGMENTS I would like to express my sincere gratitude to Prof. Susan Sinnott, for her encouragement and support during my graduate career. Her guidance and optimism has helped me accomplish my goals and tackle obstacles in academic res earch. I would also like to thank Prof. Simon Phillpot for guidance and valuable ideas on my research. Their care and enthusiasm for the members of the Computational Focus Group have trul y made my last years at the University of Florida memorable and fulfilling. I would also li ke to acknowledge my supervisory committee, Prof. Jiangeng Xue, Prof. Wolfgang Sigmund, and Prof. Nam-Ho Kim, for their advice and support. I would also like to thank th e members and graduated member s of the computational focus group as well as fellow department colleagues, Abby Queale, Jillian Leifer, and Sean Bishop. Their encouragement and support especially duri ng rough times have greatly impacted my time at UF. Especially, I show my deepes t gratitude and appreciation to my parents, John and Norma Pregler, who have been compassionate and understanding throughout my collegiate studies. 4


TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................4 LIST OF TABLES................................................................................................................. ..........7 LIST OF FIGURES.........................................................................................................................8 ABSTRACT...................................................................................................................................10 CHAPTER 1 INTRODUCTION..................................................................................................................13 General Introduction........................................................................................................... ....13 Carbon Nanostructures.......................................................................................................... .13 Graphene and Graphite....................................................................................................14 Fullerenes........................................................................................................................16 Carbon Nanotubes...........................................................................................................17 Structure and chirality .............................................................................................17 Mechanical properties and sw ord-in-sheath deformation .......................................19 Composites..................................................................................................................... .20 Polymer as the composite matrix .............................................................................21 Carbon nanostructured based composites ...............................................................23 Interfacial Engineering of Nanocomposites....................................................................24 Irradiation Effects in Car bon Systems and Composites.........................................................27 Graphite....................................................................................................................... ....28 Fullerenes and Carbon Onions........................................................................................29 Carbon Nanotubes...........................................................................................................30 Composites..................................................................................................................... .32 Photovoltaic Applications of Fullerenes and Hydrocarbons..................................................34 2 COMPUTATIONAL METHODS..........................................................................................40 Classical Molecular Dynamics...............................................................................................40 Reactive Bond Order Potential...............................................................................................41 Lennard Jones Potential..........................................................................................................46 Adaptive Intermolecular Reac tive Bond Order Potential.......................................................47 Periodic Boundary Conditions................................................................................................49 Predictor Corrector Algorithm................................................................................................50 Langevin Thermostats........................................................................................................... .52 Primary Knock on Atoms.......................................................................................................53 3 ARGON IRRADIATION ON GR APHITE AND EVOLUTION OF DEFECTS.................57 System Setup................................................................................................................... .......57 5


Experim ent......................................................................................................................57 Computation....................................................................................................................58 Irradiation Results............................................................................................................ .......59 Defect Analysis................................................................................................................ .......61 Conclusions.............................................................................................................................65 4 IRRADIATION AND AXIAL PULLOUT EFFECTS ON MWNTS....................................72 System Background................................................................................................................72 Results.....................................................................................................................................74 Irradiation.................................................................................................................... ....74 Pullout..............................................................................................................................76 Conclusions.............................................................................................................................79 5 ARGON BEAM MODIFICATION OF NANOTUBE BASED COMPOSITES..................87 System Background................................................................................................................87 Results.....................................................................................................................................88 Effects on Irradiation.......................................................................................................88 Nanotube Pullout Analysis..............................................................................................92 Conclusions.............................................................................................................................94 6 MOLECULAR DYNAMICS AND MONTE CARLO STRUCTURE EVALUATION WITH ORGANIC SEMICONDUCTORS...........................................................................101 System Background..............................................................................................................101 Ordered Structures.........................................................................................................102 Random Structures........................................................................................................103 Equilibration Using Molecular Dynamics.....................................................................105 Results...................................................................................................................................106 Phase Separation in Pentacene:C60 Mixtures................................................................106 Controlling Film Morphology.......................................................................................109 Conclusions...........................................................................................................................111 7 GENERAL CONCLUSIONS...............................................................................................120 LIST OF REFERENCES.............................................................................................................123 BIOGRAPHICAL SKETCH.......................................................................................................132 6


LIST OF TABLES Table page 3-1 Defect formation energies of defects observed in graphite af ter Ar irradiation.....................66 4-1 The hybridization of the carbon atoms in MWNTs following irradiation.............................81 5-1 Angle effects of the incident beam during C3F5 irradiation...................................................96 6-1 Cohesive energies calculated by AIREBO compared to experiment...................................112 7


LIST OF FI GURES Figure page 1-1 Graphene being transformed into a fullerene, carbon nanotube, and graphite.......................36 1-2 Graphene plane with directiona l vectors mapping the carbon nanotube................................36 1-3 Radial and axial views of armc hair, chiral, and zig zag nanotubes........................................37 1-4 Mechanisms and micrograph images of fracture mechanisms in a nanotube composite.......38 1-5 Aggregation of self in terstitials in gra phite as a result of irradiation.....................................38 1-6 Organic photovoltaic semiconductors....................................................................................39 2-1 Orthogonal peri odic boundary conditions..............................................................................56 2-2 Energetic particle bombardment, descri bing primary knock on behavior in irriadiation.......56 3-1 STM image of graphite surface irradiated by Ar+ at the collision energy of 50 5 eV...........67 3-2 Distribution of the apparent diam eter of the defects measured by STM................................68 3-3 Side view of graph ite during Ar irradiation............................................................................68 3-4 Top view of graphite during Ar irradiation............................................................................69 3-5 Irradiation damage in graphite............................................................................................ ....69 3-6 Percentage of sp3and sp -hybridized carbon atoms in graph ite system after irradiation.......70 3-7 Snapshot of cross-link defects in graphite..............................................................................70 3-8 Snapshots illustrating the formation of a Stone Wales defect................................................71 4-1 Side view snapshots of Ar irradiated MWNTs.......................................................................81 4-2 Side view snapshots of CF3 irradiated MWNTs.....................................................................82 4-3 Crosslink count from the processes of CF3 and Ar impact during irradiation........................82 4-4 Side view snapshots of electron irradiated MWNTs..............................................................83 4-5 Pullout of electron-irradiated, Ar -irradiated MWNT, and pristine MWNT...........................84 4-6 Pullout of the innermost shell at 40 m/s of the FRMWNT and the HRMWNT.....................85 4-7 Pullout of irradiated MWNT compared to FRMWNT and HRMWNT.................................85 8


4-8 Effect of pullout rate on the electron irradiated MWNT ........................................................86 5-1 Nanocomposite structures of bundle, B) DWNT, and C) SWNT before irradiation.............97 5-2 Snapshots of bundle, DWNT, and SWNT composites after Ar irradiation...........................97 5-3 Hybridization analysis of CNT damage under Ar irradiation................................................98 5-4 Average number of trapped Ar atoms....................................................................................98 5-5 Effects of curvature in irradiation damage between DWNT and SWNT bundles.................99 5-6 Average masses of the polymer produc ts after irradiation and equilibration.........................99 5-7 Pullout load curves of CN T-PS composites after irradiation...............................................100 6-1 Plot of interfacial energy between (100) surfaces of FCC C60 and (100) Pentacene...........112 6-2 Pentacene:C60 (1:1) molar ratios of st ructures that were built by the ordered method........113 6-3 Model of pentacene:C60 (6:1) molar ratio mixture...............................................................113 6-4 XRD pattern performed by Ying of pure pentacene and varying weight ratios of C60........114 6-5 AFM images by Ying pentacene, C60, and pentacene:C60 of varios weight ratios...............115 6-6 Pentacene stacking analysis for the pentacene:C60 (6:1) molar ratio...................................116 6-7 Pair distributi on analysis of the C60 interactions in the pentacene:C60 (6:1) mixture...........116 6-8 AFM images of pentacene:C60 weight ratios deposited at 0.6 /s.......................................117 6-9 AFM images of pentacene:C60weight ra tio at 0.6 /s and 6 /s deposition rate...............117 6-10 Random layer built C60:Pentacene (1:1) molar ratio films.................................................117 6-11 Pair distribution plot of FCC ordered (6:1) and random built (1:1) molar ratio................118 6-12 Random layer built films on low deposition......................................................................118 6-13 Pair distribution function plot between pentacene:C60 (1:1) and (1:2) molar ratios..........119 9


Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy ANALYSIS OF IRRADIATION INDUCED DEFECTS ON CARBON NANOSTRUCTURES AND THEIR INFLUENCES ON NANOM ECHNANICAL AND MORPHOLOGICAL PROPERTIES USING MOLECUL AR DYNAMICS SIMULATION By Sharon Pregler August 2008 Chair: Susan B. Sinnott Major: Materials Science and Engineering Mechanisms such as nanomechanics, changes in chemical structure, and van der Waals interactions are difficult to obser ve on the atomic scale by experi mental methods. It is important to understand the fundamentals of these processes on a small scale to reach conclusions of results that are observed on a larger scale. Computationa l methods may be readily applied to investigate these mechanisms on models a few nanometers in dimension and the results can give insights to processes that occur during real time experiments. The classica l molecular dynamics simulations here utilize the reactive empi rical bond-order (REBO) or adaptive intermolecular REBO (AIREBO) potentials, to model short range behavior, coupled w ith the Lennard Jones potential (and torsion for AIREBO), to model long range interactions of carbon nanostructures and hydrocarbons. The bond order term in the REBO/AIREBO potential allows for the rea listic treatment of these materials as it correctly describes carbon (and silicon and germanium) hybridizations, and allows for bond breaking and reformation unlike basic molecular mechanics. This is a key feature for simulating irradiation and pullout mechanics on graphite and carbon nanotube and their composites. 10


The irradiation sim ulations on graphite, with the same conditions as the experimental irradiation of highly pyrolythic graphite, provide insight to th e types of defects that were observed on a larger scale by S canning Transmission Microscopy (STM) images. Experimental characterization from collaborators mapped out the surface of irradiated graphite while computational theory further described the def ects and observed the evolution of the defects during the irradiation procedure. Multi walled carbon nanotubes (MWN T) were irradiated with different particles to compare the effect that incident species have on the nanotubes surfaces as well as the crosslink distribution of the radial cro ss sections. Irradiation is a co mmon technique to modify the interfacial areas between the fiber and matrix to improve co mpatibility in polymer composites. Inducing crosslinks between shells of the MWNT by irradiation drastica lly decreased the sword in sheath deformation, where inner shells slip out with respect to outer shells, that was computationally demonstrated. A similar procedure was also carried out on carbon nanotube polystyrene composites. Argon irradiation was simulated for three differe nt types of nanotubes: double-walled, singlewalled, and a bundle of four single-walled nanotub es, in a polystyrene matrix. The polymer emission, depth of particle pene tration, and nanotube pullouts were observed, it was shown that the presence of carbon nanotubes limited these processes. Atomic Force Microscopy (AFM) and X-Ray Diffraction (XRD) images in conjunction with AIREBO molecular dynamics simulation trajectories of C60 and pentacene films of various ratios gave theoretical and experimental insi ght on the molecular evolution of donor and acceptor aggregation for optimizing the design of effective organic semiconductors. 11


12 Atomic-scale simulations are thus shown to be a powerful computati onal tool to better understand the properties of carbon nanostructures and hydrocarbons. This dissertation illustrates how effective they are for providing insight on chemical modification, nanomechanical deformation, and equilibration m echanisms on the atomic scale.


CHAP TER 1 INTRODUCTION General Introduction By the mid-1980s, the study of carbon nanostructures and technological applications were thought to be well established. The carbon atom has only six electrons, and four valence electrons, and it was possible to accurately perfor m first principles calculations and understand carbon bonding in both molecular and condensed phases.1 On the macroscale, the details of carbon chemistry in soot and the metastable Wurz ite crystal structure phase had been examined and the phase diagram of carbon appeared to be well established.2 Carbon materials were being applied to technologies such as solid and liquid lubricants, batter ies, rubbers, and fillers for polymer matrix composites; thus, carbon was incor porated into applicatio ns of commercial and military interest. The rest of carbon research in the 1980s dealt with diamond-like carbon and deposition, doping, and the growth of single-crystal diamond. Carbon Nanostructures In the mid-1980s Smalley, Kroto, Curl, a nd co-workers opened doors for carbon and revealed that the element may not be as well understood as was thought.3 The group discovered fullerenes and the bulk production of th ese materials by Krtschmer et al.4 ignited a new interest in carbon nanomaterials. When Iijima di scovered carbon nanotubes (CNTs) in 1991,5 research interest in these and related forms of carbon materials explode d, a trend that continues today.6 New technological applications c ontinue to develop that includ e x-ray emitters for medical applications,7 field emitters for display technology, 8 nanowires and junctions for nano and macroelectronics,9 nanofibres for composites, and scanning probe tips.10 One of the popular features of carbon research is the strong interplay between theoretical and experimental work. Theorist s were the first to discover a unique relationship between the 13


band gap and helical structure of CNTs,11 which experimentalists confirmed.12 Another example is the reversible formation of kinks in bent CN Ts that were observed in both experiments and simulations.13 In the field of carbon materi al research, theore tical calculations have thus played an important role in making predictions th at lead the way for experimental work. Graphene and Graphite Graphene is a single sheet of carbon atoms w hose arrangement is p acked into a benzenering structure similar to a honeycomb la ttice. Because of the covalent (sp2-hybridized) bonding of the carbon atoms, graphene is widely used to describe many carbon based materials such as, carbon nanotubes, fullerenes, and gra phite, as illustrated in Figure 1-1.14 Graphene sheets have a density ~1 g/cc in the solid form, and exhibit a diffraction peak at 0.34 nm, which is similar to some single-walled CNT structures.15 Graphene was considered to be the first true two-dimensional crystal.16 However, an infinitely large single crystal of graphene in a 3D environment is subjec t to oscillations and instability over long distances.17 Researchers have observed rippl es in suspended graphene and attributed them to thermal fluctuations.17-19 As an integral part of these three dimensional relatives, graphene was assumed to not exist in the free state and was believed to be unstable.19 Recently, a free-standing graphene was found and e xperiments confirmed their charge carriers to be massless Dirac Fermions.16,20 Fermions are particles with a ha lf-integer spin, such as protons or electrons.20 The electrical transpor t in graphene are goverened by Diracs equations.20 This recent discovery in gra phene has granted graphite a s potlight in research for its potentials in electronic devices. Gr aphene has also been cut in di fferent configurations to form graphene nanoribbons (GNRs)21,22 which have either metallic or semi-conducting properties. They are an attractive choice for ballistic tran sistors due to their hi gh electronic quality. In 14


addition, graphene has high optical transparency that allows for applications in transparent conducting electrodes s uch as organic photovolt aic cells and organic light emitting diodes.23 Another potential applic ation involves using graphene fo r single molecule gas detection.24 In this case the entire volume of graphene can interact with gas molecules, making it efficient for the detection of adsorbed molecule s. Graphene powders are also used in electric batteries, where their large surface-to-volume ratio and high conductivity improve battery efficiency.19,25 Despite the optimism about graphenes electronic properties, graphene-based electr onics are not expected to be fully developed for another decade or two.19 Bulk graphite consists of sheets of graphene arranged in a three-dimensional structure and stacked in a hexagonal closed packed manner. The sheets are bonded to one another through van der Waals interactions. Stacking sheets of graphe ne to form graphite drastically changes the properties of the material. Therefore, graphite has a lower conductivity be tween the basal planes. Although conduction is present across each individual graphene plane, the overall conductance of graphite is lower since graphite is not defect free and contains many grain boundaries. Highly ordered pyrolythic graphite has a low spread of the c -axis, or axis normal to the graphene plane, angle and is generally used as the most crystalline graphite available.26 The thermal conductivity across the graphene plane is comparable to diamond at 1000 W/mK.27 The ballistic thermal conductance of a graphene sheet is at the lower limit of ballistic thermal conductance. 28,29 Graphite is used for many of applications, fr om writing implements (pencils) to advanced aircraft materials; the field of interest for th is dissertation is its us e in fusion reactors.30 The graphite materials in this environment are subj ected to damage from energetic particles, or radiation damage. The irradiation effects in graphite are discusse d in more detail in Chapter 3 and further on in this chapter. 15


The structure of bulk graphite com plicates th e computational study of it by requiring that the computational methodology adequately descri bes both strong covalent bonds and weak van der Waals bonds. It also complicates the experi mental study of graphite, since no true large single crystals of graphite are av ailable. Consequently, most expe rimental studies are carried out with highly pyrolytic graphite. Fullerenes Fullerenes are spherical, closed, cage-like st ructures of carbon that have polygon shaped interatomic arrangements of carbon atoms th at are similar to those of graphite.31 The entire family of fullerenes rang e from thirty carbon atom C30 to structures that contain up to about a thousand atoms.32 The buckyball, or C60, is the most common fullerene. It was discovered by Kroto, Smalley, Curl and coworkers3 and was initially produced in microscopic amounts by laser vaporization techniques. Krtchmer and co-workers4 were able to make gram quantities of fullerenes by producing an arc of carbon between two graphite electrodes. Arc discharge,33-35 laser ablation,36,37 and oxidative combustion of benzene or acetylene38 have all been used to produce mixtures of different sized fullerenes. The buckyball has a unique shape where its f aces of twelve pentagons and twenty hexagons resemble a soccer ball.3 This hollow structure results in its distinctive physical, chemical, and biological characteristics. The electrophilic properties of the buckyball have facilitated its modification through orga nic chemistry and synthesis routes.31 Atoms and molecules can attach to the C60 fullerene without disrupting its spherical hollow shape. Pure C60 has semiconducting properties based on electronic structure observations.31 However C60 can be converted to a conductor or superconductor with electr on donor dopant molecules or atoms, such as alkali metals. 16


Carbon Na notubes Carbon nanotubes may be thought of as graphene ro lled into a cylindrical shape that can be capped at the end with a hemisphere of a fitte d buckyball structure, although in some cases tapered and other non-spherical caps are formed. Since the discovery of CNTs by Iijima in 1991,5 there have been numerous research projects devoted to exploring thei r use in applications that take advantage of their un ique properties. As ballistic conductors, they exhibit unique electrical properties, and ar e efficient heat conductors.28,39 Because of their high length to width ratio, they are considered to be one-dimensional structures.31,40 A single walled tube may be as small as 1 nm in diameter, yet be several millimeters in length. Structure and chirality The face of a nanotube is similar to gr aphene, as it has the same honeycomb carbon structure. However, the curving of the sheet al ters the materials chem ical reactivity and bonding nature. This increased curvature results in -orbital mismatch,41 which makes CNTs with smaller diameters more reactive th an larger-diameter CNTs. Figure 1-2 plots the relevant vectors on graphene that defi ne a carbon nanotube, where the point O is chosen as the origin. The CNT is formed when the head A and tail O of vector Ch meet and points B and B meet, making the CNT axis para llel with vector. The vector Ch is defined as 2 1manaCh (1-1) where a1 and a2 are the unit cell basis vectors with integers (n,m).42 The way that the graphene sheet is wrapped to from a CNT is characterized by the chiral vectors of indices (n,m) These integers signify the number of unit vectors in two directions across the graphene face. If the indices are equal then the nanotube has an armchair arrangement. 17


If n or m =0, the carbon nanotube is term ed as zig-zag. A nanotube is chiral if none of the indices are the same or are zero. Figure 1-3 illustrates the differences in the three types of carbon nanostructures. The diameter of a carbon nanotube is given as 2 23 mnmn a C dcc h t (1-2) where ac-c is the distance between neighboring carbon atoms in the flat sheet, 14.4 nm. The chiral angle, is calculated as 2 22 3 sin mnmn m 2 22 2 cos mnmn mn (1-3) which in turn gives mn m 32 3 tan1 (1-4) The lattice constant L, or vector OB is given as 22 2 2 2223 4 3 1hCsmnmnsaL (1-5) where s depends whether n-m is a multiple of three. The lattice constant is simplified into the following expression with d as the highest common divisor, or tube diameter. d C Lh3 if n m is not a multiple of 3 d d C Lh3 if n m is a multiple of 3 d (1-6) A single rolled graphene sheet as described above is termed a single walled nanotube (SWNT) with a diameter as low as 1 nm. Concentric SWNTs, or multiwalled nanotubes (MWNT), consist of two or more concentric tubes with outer diameters that range from 5 to 350 18


nm MWNTs can be specifically described as (ninnershell,minnershell)@(nmiddleshell,mmiddleshell)@(noutershell,moutershell), where @ implies that the nanotube rests concentrically with the other tubes. Mechanical properties and sword-in-sheath deformation Carbon nanotubes have a high elastic modulus, as do graphene sheets. Experimental results from Treacy et al.43 and Krishnan et al.44 determined the Youngs modulus in the axial direction for isolated nanotubes to be around 1.8 TPa for MWNTs and 1.25 TPa for SWNTs. These values were obtained by measuring intrinsic thermal vibr ations in a transmission electron microscope. Robertson et al.45 explored the elastic properties of CN Ts with empirical potentials and first principle simulator methods. They found that the strain energy per carbon atom relative to an unstrained graphite sheet varies as 1/R2 (where R is the tubule radius). The concentric shells that form the MWNTs make them harder to bend than SWNTs. The buckling force on the MWNT is dependent on the number of inner na notubes or shells.46-49 Simulations of MWNT buckling have shown that th ere is a sudden increase in strain per atom in each shell of an MWNT. Experiments conclude d that MWNT buckling is intrinsic to the nanotube and not mediated by defects and that the buckles appear with a ch aracteristic interval independent of their absolute position on the tube.46-49 Akita estimated th e Youngs moduli for MWNTs of innershells of different diameters ar e to be 0.77 TPa and 0.80 TPa from the Euler's buckling model.50 The outermost shell of a MWNT is shown to absorb applied external stresses. However, the inner shells of th e MWNT contribute to the stiffn ess of the tube in the radial direction and have an effect on buckling and bending modes.51 A direct way to measure the mechanical proper ties of a MWNT was developed by Yu et al. Using two AFM tips to pull the nanotubes ends, Yu found a range of modulus and strength, 19


fro m 11 to 63 GPa.52 Under axial stress, the inner shells slipped out from the outer shells, a failure known as sword in sheath deformation.53 One of the questions that arise concerning innershell sliding of a MWNT is What is the magnitude of the minimum force required to pull the innertube out? With the case of a defectfree MWNT consisting of two shells, also known as a double walled ca rbon nanotube (DWNT), the sliding force depends on two contributions. The first contribution is the retracting or capillary force that is associated with how the tube re sponds when the inner tube is pulled. The second contribution is related to atomic friction, which is more important when sliding a finite tube with respect to a much longer tube.52,54,55 Huhtala et al.56 performed computational studies on pu lling out the inner shell of a DWNT to measure the capillary force needed for pullout During the simulation when the inner tube was far from the end of the outer tube, there were osc illations in the force which indicates that there was only shear contribution to the force since the contact area was the same. A rise in the force developed as the inner tube translated with resp ect to the axial directi on of the outer tube. The rise in the force indicated that the capillary forc e has come into effect due to a decrease in the overlap area. Composites Advanced aerospace, aquatic, and transport applications require materials with unusual combination of properties that may not be achieve d with conventional metal alloys, ceramics, or polymers. Transportation applications, for exampl e, require parts to be lightweight, yet strong and impact resistant and not susceptible to corrosi on. To engineer these characteristics, different materials that posses the features of interest are artificially formed into a composite material. Composites are engineered materials that cons ist of at least two co mponents, usually of different chemical or physical properties. Combining the two materials creat es one material that 20


benefits fro m key features of its constituents. For example, a polymer mixed with carbon fibers may create a composite that has the flexibility from the polymer phase and the strength and stiffness from the carbon phase. Most of the composites simply have only two phases; the matrix phase is the material which encases the other material or the disper sed phase. The properties of the composites are a function of the phases properties and the amoun t. This relation is knows as the rule of mixtures.57 Specifically, these equations predict that the elastic modulus of the composite is defined by an upper bound between the modulus of each phase and their volume fraction: ppmm upper cVEVEE (1-7) Conversely, the lower bound limit is defined as: mppm pm lower cEVEV EE E (1-8) Advances in composite technology have stimulat ed interest in nanocomposites, which are defined as systems that have at least one material with one dimension of the order of 0.1-100 nm and that would produce a material of enha nced properties due to their nano-size.58 In nanomaterials, their construction differs from macroscale proce ssing, since building nanostructures is considered a bottom-up approach, or, building from atoms and molecules.58 Polymer as the composite matrix Polymers are structured as repeating units or monomers that are connected by covalent bonds to form giant chain-like m acromolecules. Generally, polyme rs have a lower strength and modulus than metals and ceramics, are only useful at lower temperatures, and are electrical and thermal insulators. Polymers may be separated into thermoset or thermoplastic types.57,59 21


Therm oset polymers are processed by a curing action where a hardening agent, thermal, irradiation, or pressure increase induces a chemi cal reaction that crosslinks the chains in the resin. Upon heating, thermosetting polymers decompose. Epoxy and polyester are among the common thermosetting polymer matrices. A larg e fraction of polymer composites use epoxy matrices since they have mois ture resistance, low shrinkage on curing, and good adhesion with glass fibers.59 The crosslinking in the matrix that cont ributes to a high modu lus, however, also causes brittleness. In processing a fiber-epoxy co mposite, the fibers are incorporated into a slightly cured epoxy and held at a low temperature until it is ready to be heated processed into a composite with a fully cured and hardened epoxy.59 Thermoplastic polymers are typically bounded by chain entanglement and have the ability to heat and cool while retaini ng their basic chemical structure. Examples include polyethylene and polystyrene. Thermoplastic materials are to ugher than thermosetting polymers and have a failure strain ranging between 30 to 100% where thermosetting polymers fail at strain ranges of roughly 3%.59 Generally, the fracture energy for thermoplastic polymers are an order of magnitude higher than unmodified epoxies and polyesters. The higher fracture energy of the thermoplastic polymers is contributed by the la rger free volume which absorbs crack propagation energy in the material.57,60 The polymer matrix used in this dissertation is polystyrene (PS), a thermoplastic and widely used commercial polymer. Po lystyrene is also computationally inexpensive to model as it only consists of carbon and hydrogen bonds. Polyst yrene-CNT composites have been used in aerospace applications; where th e presence of CNTs on the surface layers of the polystyrene effectively protect the underlying material. The eff ects of CNTs in PS are discussed in detail in Chapter 6. 22


Carbon nanostructured based composites Fullerenes have been incorporated in polymer matrices to form composite films. It has been found that the presence of C60 lowers the thermal degradation of polystyrene which gives the material as a whole improved thermal stability.58,61 In addition, C60 in polyethylene has increased composite hardness comp ared to pristine polyethylene.62,63 The most attractive application of C60 in composites results from the high photoconductivity of the fullerene polymer mixture. Wang measured a fast and co mplete photo-induced discharge in C60/C70 doped polyvinylcarbazole (PVK) at the fullerene polymer interface.64 Furthermore, Sariciftci et al. observed the same behavior in C60 doped poly[2-methoxy,5-(2-ethyl-hexyloxy)-p-phenylene vinylene] (MEH-PPV).65 They showed that photoinduced electrons transfer from the polymer to C60s effectively, since C60 has extraordinary electron acceptability. This induces anions and mobile holes in the polymer Sim ilar charge transfer is found in other composites of fullerenes and conjugated polymers, and the effect has potential use for photovoltaic devices.66-69 Both SWNTs and MWNTs have been used as fibe rs to reinforce polymer materials such as epoxies, polystyrene, nylon 12, and poly ether ether ketone. Tai et al. processed a phenolic-based nanocomposite with MWNT.70 Gojney and coworkers incorpor ated only 0.1 wt% of highly dispersed DWNT in unreinforced epoxy.60 Ogasawara used MWNTs to reinforce phenylethyl terminated polyimide through m echanical mixture and curing.71 All the composite s exhibited an increase in Youngs modulus, strain to failure, and strength relative to the polymers alone. Thostensen and Chou72 dispersed 5 wt% MWNT with a mi cro-scale twin screw extruder to mechanically blend and uniformly disperse the nanotubes in polystyrene. The extrusion induced a continuous ribbon of aligned nanocomposites. 23


Interfacial Engineering of Nanocomposites The effectiveness of a nanocomposite depends to a large extent on th e interaction between the fibers and the matrix, as well as on fiber dispersion and alignment.57,59 The performance of a composite depends critically on its interfacial properties.61 If the interfacial strength of the composite is too strong, the overall composite is not effective. In this case, the interface will have the highest stress to failu re and thus decreasing the comp osites toughness. The composite will fail at weak spots on the br ittle interface, resulting in catastrophic failure. If the interface bonding between the matrix and fibe r is weak, then stress will not effectively transfer to the fibers and composite failure oc curs from matrix fracture. Acquiring a uniform dispersion of the CNTs is an important factor in processing nanocomposites.63 Carbon nanotubes must be separated from their bundled form and dispersed uniformly to maximize their su rface area in the matrix. Exfolia tion of the CNTs from their bundles increases the in terfacial area and thus improves th eir overall effectiveness in a composite. Interfacial sliding between the CNTs occurs if the tubes are grouped in bundles or ropes, which adversely affects their load carrying capability. The alignment of the CNTs in the matrix is important to achieving anisotropic mechanical or electrical properties. They can be processed by applying shear fo rces or an electrical field.58,63,73 The interfacial area to volume ratio is extremely high for CNT composites due to the fibers large aspect ratio. Scha dler and co-workers monitored th e load transfer in a CNT-epoxy nanocomposite in tension and compression by Raman spectrometry.74 They found that the nanocomposites load transfer was effective during compression but was weak in tension, implying poor load transfer acr oss the CNT-polymer interface. Various mechanisms can be responsible for the failure of nanocomposites, including fiber pullout from the polymer matr ix, fiber fracture, fiber/matr ix debonding/crack bridging, and 24


m atrix cracking.75 Figure 1-4 is an illustration of th e types of failure mechanisms at a composites crack tip that is paired with the respective micrograph image. An ideal composite would not have too strong or too weak interfacial strength, and would therefore appropriately transfer load from the matrix to the fiber. Additionally, deformation of a CNT-polymer composite can cause the inner shells of the nanotube to slip out of the outer shells and thus promote failure Therefore, independent of the carbon nanotubes referenced strength, the comp osite strength also depends on the interaction and sliding of the inner tubes, or sword-in-sheath deformation.56 If the bonding between the shells is weak, they will not contribute to th e axial strength of the MW NT regardless of the number of shells present. Instead they will act like ropes of SWNTs where the load is absorbed on the SWNT perimeter.55 However, it would be de sirable for the inner shells of the MWNTs to absorb applied loads as well, especially when MW NTs are used as reinforcements in composites. The combination of these two types of bonding gi ves MWNTs anisotropic mechanical properties because the shells of MWNTs can readily slide and rotate with respect to one another.63 When a nanocomposite without chemical m odification undergoes shearing stress, the pullout forces are normally greater than the weak van der Waals interactions between the nanotube and the matrix. Therefore, the nanotube slid es with respect to the matrix, or pulls out. Frankland et al. modeled CNT pullout in polymer matrices and recorded force variations in displacement and velocities of the nanotube.76,77 On the nanoscale, the behavior of nanotube pullout is closely related to fr iction models. They have shown lin ear trends in the nanotubes velocity to force relationship and estimated an effective viscosity coefficient for interfacial sliding at the interface. The av erage shear stress for the nanotubes sliding is described as r Vz eff pull rz 0 (1-9) 25


where 0 is the initial threshold pullout stress, eff is the effective viscosity for the nanotube sliding in polymer, and r Vz is an estimate of the strain rate, with Vz as the average nanotube velocity for distance r.77 The walls of a carbon nanotube are chemically stab le because of the aromatic nature of the bonding. Therefore the interface between the walls in a MWNT, and between the outershell and most polymer matrices rely on van der Waal in teractions, which may not provide a sufficient load transfer. Unlike conventional carbon fibers, the nanotube length is mu ch shorter than the polymer chains which also lead to weaker interf acial bonding. Due to the lack of load transfer between the matrix and the fiber, pristine carbon nanotubes in a polymer matrix slip out of the polymer during deformation resulting in failure of the composite.78 This type of failure is also seen in MWNTs where innershells slip out from the outershells. Therefore one of the challenges inherent to incorporating inert carbon nanotubes into a composite is engineering the strength of the interaction between the nanotube walls and the surrounding polymer matrix.63 Efforts have been made to chemically modify CNTs to improve the load transfer across the fiber/polymer interface.54,79,80 If the nanotube is chemically functionalized, it may attach to the surrounding pol ymer matrix and would allow for better load transfer during deformation. An optimal level of covalent bonding, as opposed to van der Waals interactions, between the nanotubes and the polymer improved the shear yield strength of the overall composite. Covalent bonds on the nanotube walls weaken their modulus,81 although a slight modification has been shown to effectiv ely reduce pullout forces while maintaining CNT structure, as discussed in Chapter 4. The caps of the CNT are more reactive than th e walls because they are under higher levels of strain as a result of th eir high degree of curvature.82 It has been shown experimentally that an 26


acidic solution rem oves the capped ends of a CNT so that the ne w ends react with functional groups such as carboxylic acids (-COOH groups) or hydroxylic acids (-OH groups). Successful replacements of carbon atoms by functional groups or fluorine have also been performed. These groups have the potential to induce further chemistry in a matrix a nd improve the interfacial load transfer by reducing slippage of the CNT with respect to the matrix. This method of functionalization only improves interfacial interacti on at the tip of the tube. Interfacial properties are more effective with functionalization along the full length of the fiber. As previously mentioned, functionalization methods have been performed on the carbon nanotubes to increase the attr action between the fiber and matrix. It has also decreased delaminating and pullout failure. One of the majo r approaches involves i rradiating the materials with ions or electrons. Their effects on carbon structures and na nocomposites are discussed in the next section. Irradiation Effects in Carbon Systems and Composites Irradiation particle effects in solids have been of interest in res earch since the 1950s. The early studies primarily focused on metals, semiconductors, and insulato rs to determine the materials resistance in a radia tion heavy environment. With th e newly discovered allotropes of carbon, fullerenes and carbon nanotubes, irradi ation on graphitic structures has arisen. A highly energetic particle has several prim ary mechanisms when it impacts its target substrate atom. In ballistic conductors studied und er the computational methods discussed in this dissertation, the mechanisms of interest include, bond breakage or cr osslinking, atom interstitials and displacements, sputtering of atoms and polya tomic products from the surface. Other effects include electronic excitation or ionization of atoms and plasmons, phonon generation, and emissions of photons and/or Auger electrons.83,84 27


Graphite Graphite is an unusual material due to its anisot ropy in the lattice. It can be considered as a two-dimensional metal being electrically condu ctive across the basal plane, or along the graphene sheets. The bulk graph ite relies on van der Waal forces to hold the graphene sheets in its hexagonal lattice. Electronic excitations fr om irradiated particle s are quenched by the conduction electrons therefore negating the effects of this irradi ation mechanism. Knock-on atom displacement is the primary irradiation mechanism in graphite due to its open structure in the normal direction, or c-axis.83,85-88 The irradiation effect in graphite has been studied extensively for its use in fission and fusion reactors. The anisotropic nature in graphi te results in irradiation mechanisms that are distinct from metals or ceramic materials. This is due, in part, to the fact that displacing an atom along the c-axis requires less energy than is required to displace an atom along and within the basal plane because of the open channels between the planes.83 Studies have shown that radi ation in graphite has induced defect agglomerates and a rupture in the basal planes due to atoms ejec ting from the respective graphene sheet. The aggregation and vacancies combine and form di slocation loops between the graphene sheets, illustrated in Figure 1-5. Once the loop is form ed it is stable at high temperatures up to 1000 C.83 One of the unfavorable effects of irradiation on graphite is the dimensional change in the caxis. The agglomerates from Figure 1-5 pus h the graphene sheets apart and swell the c-lattice spacing. The swelling grows when atoms are emitted by knock on displacement and diffuse to the agglomeration site, leading to a formation of new lattice planes. The vacancies in the basal planes also cause shrinkage at that site.83 Consequently, there is a wide range in th e reported data for the atom displacement threshold, Td, simply because of discrepancy in graph ite samples between researchers. Iwata and 28


Nihira found the Td value to be 24 eV along the basal plane and 42 eV along the c-axis.86,89 These findings agree with the result s of Ohr et al., who also found Td of 24 eV90 within the basal plane, and Montet et al., who found Td of 31-33 eV within the basal plane and 60 eV along the c-axis.91 Recent Td reports by Banhart et al. include values between 15-20 eV for the c-axis value.83 Specific defects and their respective activation energies are reviewed in Chapter 3. Fullerenes and Carbon Onions Ionization is the dominant factor with high irradiation of full erenes. The fragmentation of the fullerene leads to smaller fullerenes, for example .92 Irradiation energies that are large enough to break the fulle renes bond energy are 7.4 eV.31 A series of fullerenes under irradiation have been seen to fuse and lead to larger, yet irregular, fullerenes.93,94 When the fullerenes are encased in a SWNT to produce a structure known as a peapod, the system has been shown to transform into a MW NT under electron irradiation.95-98 The displacement energy of a carbon atom from a fullerene is sl ightly lower than for graphite since the knocked out atom has ample space to move away from the cage struct ure and no recombination can occur. Fullerenes have also been known to disintegrate under ir radiation, by Coulomb explosion and knock-on atom displacement.99,100 2 26 60CCFullerenes can also be form ed by irradiation of graphitic nanostructures. Structures of different cage sizes, C32, C60, and C240, can be formed on a graphite surface this way. The formation occurs during an unwinding and curling of a graphene sheet from the graphite surface, until the sheet is closed.93 Carbon onions or a series of concentric full erenes are also formed by irradiation of amorphous carbon; the entropy of the entire system decreases as the ordering increases. Entropy is exported through the irradiation process since a small fraction of energy entering the system is 29


stored in bonding or def ects, thus following nonequilibrium principles.83 The curling of the graphene sheets under irradiation influences the environment until the favorable structure of a sphere is obtained, and stable under irradiation. The irradiation temperature is relatively high enough so that in situ annealing prevents the formation of agglomerates; however, graphene curling also occurs at high temperatures.83,93 The formation is governed partially by geometric structuring as a Stone-Wales transformation which ensures the oni ons spherical shape.101 Irradiating carbon onions has been shown to nucleate diamond structures. Under irradiation the shells of the onion undergo compression toward the core which leads to diamond nucleation. Ion irradiation is more effective th an electron irradiation since it has a cascading effect from incident particles having a much la rger mass transfer than electrons, creating up to 600 displacements by one knocked out atom. The transformation is facilitated by the high pressure in the onion core and the sharp curvature of the inner shells. Once the diamond structure is nucleated, it grows outward and consumes th e shells of the carbon onion with continuing irradiation.83,93 Carbon Nanotubes Irradiating carbon nanostructures chemically modi fies the properties of the tubes whether it is used in composite applications or nanoelectro nics. Recent studies have shown that crosslinks and functionalization can be indu ced through electron or ion irra diation. Carbon nanotubes with several shells can also be used as a protection mask from ion irradiation. The mechanisms for irradiation damage in CNTs are very similar to graphite due to the same carbon hybridizations and open structures. Banhart et al. found the threshold energy to be similar to graphite at dT 15-20 eV for multi-shell tubes.102 30


However, the curvature of the carbon nanotube s is the cause of the differences between graphite and CNT irradiation. Tubes of smaller diameters are under more strain than tubes of larger diameters, thus their bonds are more likely to break under particles of the same incident energy.41 The collision of energetic particles on single-walled carbon nanotubes (SWNTs) results in a carbon atom knocked out leaving one or more vacanci es in the tube walls graphite lattice. If the primary knock-on atom (PKA) has enough energy, it can leave the tube to displace other atoms. If the impact energy is low, and the inci dent particles are chemi cally reactive, they can chemically attach to one or more carbon atom s in the CNT wall, functionalizing the wall and changing the character of th e involved carbon atoms from sp2 to sp3 hybridization, and acting as interstitials. The incident part icles and sputtered carbon atoms that result may also functionalize neighboring nanotubes. Early experiments found that CNTs develop diameter shrinkage and neck-like features under electron irradiation. This phenomenon occurs when irradiation induces vacancies on the walls of the CNTs. These vacancies are unstable and the CNT reconstructs itself to compensate for the atom loss, which results in a reduced diam eter size. However, in most cases the nanotube experienced the most damage in the area beneath and normal to the direction of the beam rather than a uniform damage along the axial direction of the tube.83,84,103 Other defects that occur during irradia tion include non hexagonal faces, amorphous complexes, and the Stone-Wales (SW) defects on the carbon nanotube wall.101 These CNT defects are created only if the en ergy of the incident pa rticle is strong enough to displace atoms in the tube wall. The minimum energy required to produce a Frenkel defect without recombining (threshold energy) on graphite is 20-30 eV.84 Because of their open st ructure, carbon nanotubes 31


respond differently than most other solids; the d isplaced atom from the nanotube structure can travel far from its original position, unlike most other solid materials. These vacancies from irradiation induce coalescence of SWNT with a zipper like motion where the atoms reorganized with adjacent tube s. This method is used in welding carbon nanotubes together under an electron beam.104-107 Generally, MWNTs are more stable than SWNTs during irradiation since the vacancies can easily recombine with an underlying shell in the MWNT. In some ways, irradiating MWNTs is similar to the carbon onion. When an atom is knocked from the outer shell of a MWNT, it can a ffect the atoms of the underling shells and may either form a covalent bond or crosslink the shells, or knock out another atom for a cascading effect. Crosslinks between the she lls of a MWNT is a common defect observed in irradiation, as well as a tool that is used to decrease sword-in-sheath deformation.108 Therefore, the advantages of incorporating covalent bonds between the shel ls without sacrificing too much of the MWNT structure is of concern. Howe ver, researchers have found th at the buckling wavelength of MWNTs does not change appreciably when the tube is axially deformed or bent.49 The effects on irradiating MWNTs and sword in sheath deformation are discusse d in detail in Chapter 4. Composites Irradiation and ion bombardment of polymer ba sed composites have three major effects: electronic excitations and ionization events, dop ing or implantation, and atomic collisions.83,84 Electronic excitations occur at a ll energies of ion irradiation which may result in bond breaking and reformation, luminescence, radiation emi ssion, and electron-hole ge neration. In the doping or implantation processes, the materials compos ition changes with the introduction of new ions. The atomic collision mechanism, or primary knock on of atoms, is a direct momentum transfer of energy from the incident particle to the substrate.83 32


Energetic particles that b ombard a polymer composite induce several effects even when only considering the atomic collision mechanism. Particles that have enough energy may break the bonds in the polymer matrix and emit smaller products and fragments from the surface, creating an etching effect. The presence of car bon nanotubes in the polymer matrix has been found to limit the effects of etchi ng, as the carbon nanotube effectively absorbs the particles energy without deteriorating.79,109 Light ion bombardment can also create cro sslinking between polymer chains, or between polymer chains and the carbon nanotube fibers.79,109 This method of modification has been shown to reduce sliding between the fiber interfaces and improving the interfacial interactions.56 This novel approach to in situ chemical modification of the co mposite avoids deterioration of CNTs by acidic approaches to functionalization. Low energy irradiation has been found to keep CNTs intact.81 Atomic irradiation of CNTs or composites to slightly change the chemical structure are common methods to improve the interfacial load transfer.54,79,108 Inducing crosslinks between the shells of a MWNT or between the outer shell of a CNT and the matrix has been shown to restrict sword-in-sheath deformation. However, excessi ve irradiation creates defects on the nanotubes which have a negative effect on the mechanical properties. It ha s been found that covalent bonds from chemical attachments on a SWNT have decreased the buckli ng force by about 15%.81 This indicates that a functionalized t ube is expected to deform easie r than an unfunctionalized carbon nanotube. Still, the degradation from light irradiati on is generally small, and the overall benefits from an improved fiber-matrix interface are greate r. The effects of irradiating CNT composites are further discussed in Chapter 5. 33


Photovoltaic Applications of Fullerenes and Hydrocarbons The previous sections described carbon nanostr uctures for mechanical applications. This section summarizes organic electronic materials that utilize carbon nanomaterials such as the C60 fullerene and pentacene hydrocarbons. Organic semiconductors have attracted interest in research due to their lightweight, low material cost, processing ease, and flexibility as compared to their inorganic counterparts.110-112 Some of these applications include photovoltaic cells, organic light emitting devices for display and lighting technology, photodetector s, and thing film transistors.113 An efficient organic photovoltaic cell requires good transport of donor and acceptor molecules, or heterogeneous j unction. Figure 1-6 shows a schema tic of the energy level between the donor and acceptor molecules and illustrates the charge transfer process.114 The dissociation of excitons leads to holes in the highest occupied orbital ( HOMO) in the donor material and electrons in the lowest unoccupied molecular orbital (LUMO).115 The LUMO has the highest electron affinity and the HOMO has the smalle r ionization potential. The electrons are transported through the donor molecules to th e anode which create the photocurrent. The external quantum efficiency can be described as: IQE A CC CT EDA EQE (1-10) where A is the absorption efficiency, ED is the exciton diffusion efficiency, 1CT is the charge transfer efficiency at the interface, CC is the charge collection efficiency, IQE is the internal quantum efficiency.115 The efficiency of a heterogeneous junction is dependent on the exciton diffusion, which can be short in films of molecules which ar e bound together with van der Waal forces.111 Blends of conjugated molecules have been used to from bulk mixtures to increase the exciton efficiency, 34


ED The molecules distributed in the bulk stru cture resulted in spatially distributed donoracceptor (DA) molecules, reducing their distance s and effectively improvi ng exciton travel and raising ED However a high density of interfacial area will reduce charge carrier mobility, lowering CC the charge collection efficiency, as conducting holes will be confined in donor materials.110,111 Therefore, it is considered that microstr ucture/nanostructure and degree of phase separation are critical factors in the photovoltaic properties of an organic DA mixture. Large domains of donor and acceptor materials will restri ct the passageway of excitons, thus reducing ED as a high degree of phase separation will percolate charge conduction and raise CC Computational efforts have been performed to better understand the na nostructure of these materials. 35


Figure 1-1. A single sheet of graphene being transformed into a fullerene, carbon nanotube, and graphite.19 Figure 1-2. Graphene plane with directional vectors mapping the carbon nanotube.42,116 36


Figure 1-3. Radial and axial views of A) armchair carbon nano tubes where n=m, B) chiral nanotubes where n m, and C) zig zag nanotube where either n or m = 0. 37


Figure 1-4. The mechanisms and respective micr ograph images of different fracture mechanisms in a nanotube polymer composite.58,117 Figure 1-5. Aggregation of self interstitials in graphite as a result of i rradiation. A dislocation loop has occurred between two graphene sheets.83 38


39 Figure 1-6. Organic photovoltaic semiconductors. A) Schematic of the energy levels between donor and acceptor molecules illustrating th e photovoltaic process. B) Continuous path of charge conduction through a desired degree of phase separation.118


CHAP TER 2 COMPUTATIONAL METHODS Classical Molecular Dynamics Molecular dynamics (MD) simulation is a technique that computes the equilibrium and transport properties of cla ssical many-body systems. Here, classical is termed as nuclear motion of particles that obey the laws of classical mechanics. The structure of MD simulations is similar to real experiments in many respects. Generally, to start an experiment, one starts a nd prepares the material to study, then connects it to a measuring instrument such as a thermometer or manometer, and measures the materials property changes over a given inte rval of time. MD simulations follow the same basic approach. In preparing the sample, a model system of particles is initialized. The MD process then uses N ewtons equations of motion for the particles until their properties no longer change with time, also known as equilibrating the system. After equilibration, an analysis of atom displacements, bond lengths, crystal structure, or other pr operties of interest are calculated. NTherefore, MD sim ulations can be simplified into five general steps. First, parameters are provided as input, which in clude initial temperature, number of particles, density, time step, etc. Second, the system is initialized where starting positions and velocities are assigned to all particles in the system. Third, the forces acting on all the particles in the system are calculated. In our systems we consider many-body interactions and must consider the force on particle i due to its nearest neighbors. There are e fficient techniques we use to calculate the short-range and long range interatomic interactions.119,120 These techniques are discussed in some detail later in this chapter. Fourth, molecular dynamics simulations integrate Newtons equations of motion to calculate the motion of atoms with time and the results are observed from several output files describing properties of interest such as atom placement and bond length. 40


The m otions of the particles are expressed by the second la w of motion where the force vector of atom i is equal to the product of the atoms mass, and acceleration iFimiaiiiamF (2-1) Two more models are needed to relate the position of the particles and time. The first model is based on the conser vation of energy that relate s the forces between atoms i and j to the potential energy: ij ijr PE F (2-2) where is the distance between atoms i and j. The second model uses a numerical analysis algorithm of the acceleration to describe locations with respect to time with the following derivative: ijr dt dr dt d dt dv aij (2-3) where v is the velocity with respect to dt which is on the order of picoseconds. The integration of the Newtonian equations of moti on yield the positions of the particles, and in turn their velocities, accelerations, and higher derivatives of position with respect to time. The integration is handled with a predictor correct or algorithm which is explained in detail later in this chapter. These factors are the basis to de scribe the fundamental properties of a given system. After this central loop completes for the desired length of time, the average output of the measured quantities are analyzed, completing the simulation.119,120 Reactive Bond Order Potential Abell derived a general chemical binding ener gy term which is the starting point for the Reactive Bond Order (REBO) potential. Tersoff developed Abells work to simulate the 41


potential energy and interatom ic forces of the covalent bonds in C and Si systems.121 Brenner modified the Tersoff potential to improve it s performance for carbon and hydrocarbon systems by introducing an analytical bond order form.122 Brenner then further improved the potential in the second generation REBO by refining its analytic al terms and increasing the fitting database used to obtain the potentials parameters, thus creating a better descri ption for conjugation, bond angles, bond lengths, torsion, coordination, and other effects for carbon and hydrocarbon systems.123 Variations of the second-generation REBO potential were then optimized for hydrocarbon and fluorocarbon systems,124 and for C-O and O-H covalent bonding.125 The first generation hydrocarbon expression used Morse-type terms incl uding pairwise and many body terms. This potential can descri be carbon bonding in hydrocarbon molecules and chains, graphite, and diamond. It is, however, to o restrictive to simultaneously fit equilibrium distances, energy, and force constraints for th ese bonds. Furthermore, modeling energetic atom collisions is limited as terms approach finite values. Abell showed that the chemical binding energy is simply a sum over nearest neighbors, as ii j ij A ijij R REBO brVbrV E)(. (2-4) The functions and are pair additive interactions for core-core repuls ive and attractive interactions, respectively, with rij as the distance between atoms i and j. Abell argued that the coordination number N controls the bond order in regular structures and used a Bethe lattice126 to describe the relation as, rVRrVA 2 1Nb (2-5) In equations 2-5 and 2-6, Mor se-type pair interactions de scribe energy versus volume relations that are similar to a general binding energy curve. A universal binding curve, however, 42


is too r estrictive to simultaneously describe energy and equilibrium distances in carbon and Group IV elements. This form also has another disadvantage in wh ich the repulsive and attractive terms approach to a finite value as distances between atoms decrease. This flaw restricts the ability to model bond breaking and reforming. Tersoff built on Abells work and refined the bond order and analytical terms fr om equation 2-5, thus developing the second generation REBO. The analytical form from equati on 2-5 is refined below for the 2nd generation REBO. ijr ij ijcijReA r Q rfrV 1 (2-6) ijr n n ijcijAeBrfrV 3,1 (2-7) where A, B, Q, and are two-body parameters that depend on the types of atoms that are interacting. The function from equation 2-7 and 2-8 rest ricts covalent interactions to only nearest neighbor atom s where defines the distance over where the function varies from one to zero. rfcmin maxij ijDD max max min min min max min0 2 cos1 1ijij ijijij ijij ij ij ijij ijcDr DrD Dr if if if DD Dr rf (2-8) The bond order term bij, is known as the many-body empirical bond-order term and is a key variable in the REBO potential. There are numerous types of ch emical effects that are fitted for this term, including bond angles, torsion angles, coordi nation number, and conjugation 43


effects. This term allows atoms to inhibit these effects according to their environment, whether if its bond breaking, bond formation, or changes in atomic hybridizations. This feature allows a more realistic simulation for a relatively larg e number of carbon atom s while utilizing the computational efficiency of an empirical method. The bond order bij is described below: ij ji ij ijbbbb 2 1 (2-9) Values for and are determined by local coordina tion and bond angles for atom s i and j and are defined as ijbjib 2 1 ),(, cos 1 jik H i C iij ijk ik c ik ijNNPe Grf bijk (2-10) The term ensures that the inte ractions are lim ited to the nearest neighbors. The term rfc jikG cos regulates the dependency on the nearest neighbor according to the bond angle between atoms i and j and atoms i and k, which is determined by the angles in a diamond lattice (109.47 ) and graphite plane (120 ). The term ijk is a fitting parameter that describes three-body transition states around H atoms. The function Pij is a bicubic spline and a correction term to the bond order based on the environment of the atom neighbor i The terms and are the num ber of carbon and hydrogen atoms respectively of atom i. These are defined by C iNH iNcarbon jik ik c ik C irfN),( (2-11) and hydrogen jil il c il H irfN),( (2-12) 44


The neighboring atom is assigned a valu e of 0 to 1 for distances between atoms i and k which guarantees that the overall function, Eb, is continuous during bond breaking and reforming. The term is defined as jbDH ij RC ijijb (2-13) where the radical term and the dihedral term. The value of determines whether the atom s i and j have a radical component or are part of a conjugated system. This term defines a key difference between the first and second generation REBO, since it accounts for the conjugation of carbon atoms and corr ectly describes radical structures such as vacancy formation in diamond and accounts for non-local conjugation eff ects as seen in graphite and benzene. The term is expressed as RC ijRC ijDH ijRC ij conj ij t j t iij RC ijNNNF ,, (2-14) The two spline functions are coupled and yield or is defined as t iNt jNconj ijN2 ),( 2 ),(1 carbon jil jl jl c jl carbon jik ik ik c ik conj ijXFrf XFrf N (2-15) where 3 32 2 0 2 22cos1 1 ik ik ik ik ikx x x x xF (2-16) and ik c ik t kikrfNx (2-17) 45


The term defines the dihedral angle fo r the carbon-carbon bonds as DH ij ), () ,( 2cos1 ,,ji kj il jl c jlik c ikijkl conj ij t j t iij DH ijrfrf NNNT (2-18) where is the torsional angle between atoms i, j, k, and l and the function ijkl conj ij t j t iijNNNT,, is a tricubic spline interpolation. As a result, the binding ener gies and bond length databases were expanded and carbon bonds have the ability to break and rebond or create new bonds while appropriately describing atomic hybridizations.123 This version of the REBO potentia l produces an improved fit for the elastic properties in diamond and gr aphite and is better able to describe defect energies. In addition, hydrocarbon molecules are more accurate ly modeled with a better description for bond length, energies, and force constants. The REBO potential is exclus ively short ranged, which only describes the interaction of two atoms within a less than covalent-bonding cutoff of 2.0 for C-C bonds. Long range potentials such as the Lennard Jones potential have been splined to REBO to account for interactions greater th an 2.0 The REBO potential also lacks a model to describe torsional interactions for hindered rotation about single bo nds which is fixed in the AIREBO potential. maxijrLennard Jones Potential The Lennard Jones potential is smoothly c onnected to the REBO potential by a cubic spline to account for long range, or van der Waal interactions between pa rticles. The research here uses the 12-6 form 6 124ij ij ijLJrr rV (2-19) 46


where ij LJrV is the cohesive energy for the distance r between atoms i and j The LennardJones parameters denoting the depth of the potential well, and finite distance where the interparticle potential is zero, are for particular types of atoms. The 121 r term describes the repulsion interaction of the atoms based on the Pa uli principle, when electron clouds overlap, the energy of the system increases abruptly. The 61 rterm describes the long range attractive interactions derived from dispersion or dipole-dipole interactions. The parameters and between two different types of atoms are calculated with the Lorentz-Berelot rule which is described below 2 )(BB AA AB (2-20) BBAA AB (2-21) The REBO potential is exclus ively short ranged, which only describes the interaction of two atoms within a less than covalent-bondi ng cutoff 2.0 for C-C bonds. The potential has been splined with the 12-6 Lennard Jones potenti al to account for van der Waals interactions however, this results in large barriers for ra dical species and small barriers for saturated compounds. Adaptive Intermolecular Reactive Bond Order Potential A new potential, based on the original RE BO, introduced non-bonded interactions through an adaptive treatment of intermolecular interactions, or AIREBO.127 Chemical characteristics of the system are considered to preser ve the reactive character of the potential, and whether to include the LJ interaction. The decision is made adaptively under three conditions: (i) the di stance between the atom pair of inte rest, (ii) strength of their bonding 47


interaction, and (iii) the networ k of bonds connecting the pair. The com plete expression for the LJ interaction is as follows ij LJ ijijijr ij LJ ijijijbijr LJ ijrVCrtSrVCbtSrtSE 1* (2-22) where the universal switching function is represented by ttttttS23112 (2-23) The switching function is unity for t < 0 and zero for t > 1 and uses a cubic spline to switch smoothly at an intermediate t. The scaling function between the distances of the atom pair that affects the strength of the LJ interaction in ijrrtS as min max minLJ ij LJ ij LJ ijij ijrrr rr rt (2-24) The bonding switch that can aff ect the LJ interaction in *ijbbtS converts the REBO bij to a range to fit with the cubic spline is min max minij ij ij ijbbb bb bt (2-25) The AIREBO potential allows nonbonded interactions to switch smoothly as bonding configurations change. A new term in the AIREBO potential is a torsional model that is dependent on dihedral angles. The generic form for torsio n is a cosine power series in 3 1cos11 2 1k k kk VV (2-26) where the coefficients must depend on changes to the energy barriers, preferably from the local coordination environm ent which is accomplished through a single minimum in kV 48


10 1 2 cos 405 25610 torsV. (2-27) The torsional potential for all dihedral angles with a proportion to contributing bond weights in the system is implemented into the AIREBO model ijkl tors ii jj i kk jil klkljk jk ijij torswVrwrwrw E ,, ,2 1 (2-28) thus updating the entire system energy to tors LJ REBO E E E E (2-29) The introduction of the LJ in teractions predicts the di amonds crystal lattice 0.004 shorter than REBO and experiment and also slightly changes the elastic constants. However this contraction is balanced by an predicted increase in the tensile covalent bonding force parameters which lead to a slightly stiffer force constant and larger elastic consta nts. The properties in graphite display the same trend in diamond, in this case shortened bonds by 0.02 The LJ potential correctly parameterizes the graphite layer distance at rl = 3.354 This parameter is absent in REBO, therefore modeling sheets of graphene require AI REBO. Since REBO has fewer calculations than AIREBO, th e calculation time is significantly (approximately five times) shorter than AIREBO for the same set of atoms. Periodic Boundary Conditions The sample size studied with MD normally models systems sizes on the order of nanometers for efficient calculations. If the propert ies of a small liquid drop or nanocrystal are of interest, then the simulation conditions would be straightforward. The cohesive forces between particles in the system may be strong enough to ho ld the system together during the course of the simulation. However, these conditions are not satisfactory when simulating a bulk material.119,120 49


Im plementing periodic boundary conditions is a technique to repl icate a unit cell to effectively form a bulk lattice. During the simula tion as particles move in their original box, the clone particles in the periodic image move the same way. If a particle leaves its primary boundary, it will reappear on the opposite face of the box, thus the number of particles in the entire system is conserved. It is often thought that th e two-dimension primary box is rolled into a three-dimension doughnut. The number of particles in a cubic cell, N, are surrounded by an infinite array of duplicated cells as shown in Figure 2-1. Each cell has particle i, with its replicated particles at the same relative position in their neighboring cells. All the minimum images of particle i are found within the potential cut-off rc. The contributions to the force are calculated with equation 2-2. The potential cut-off must be less than cell size L to prevent over counting of particles. For a system of Lennard-Jones particles, it is possible to perform simulations w ithout the particles interacting with its duplicates in the primary box of side 6 L. Predictor Corrector Algorithm The predictor-corrector algorithm is a fin ite difference approach to solve ordinary differential equations, such as the Newtonian equations of motions used in MD.119 There are four basic steps for the general scheme of step-wis e MD simulations with a predictor-corrector algorithm. First positions, velocities, and accelerations are predicted at a timett Second, the forces and accelerations are evaluated from the new positions. Next the predicted positions, velocities and accelerations are corrected with new accelerati ons. Lastly, calculations are performed on the variables of interest, such as energy, and the time averages accumulate prior to repeat the steps. 50


Given the particle information at tim e t, position, velocity, and other dynamic data, new dynamic information at a later time tt can be solved by Taylor e xpansion. This dissertation used the third-order Nordsieck-G ear predictor-corrector algorithm.119 tbttattvttrttrp 3 26 1 2 1 tbttattvttvp 22 1 tbttattap tbttbp (2-30) where r and are the atoms position and velocity; v a is the acceleration, and is the third time derivative of the position. The superscript p denotes the terms p redicted version. bThe inte ratomic forces at the predicted positions for time tt are calculated with a potential energy gradient, in this case REBO, AI REBO, LJ, etc. since th e predicted values are not based on physics. Without incorporating the e quations of motion, the predictor equations will not generate accurate trajectories as time progre sses. With the correction step, the new positions at time tt may be calculated with the correct acceleration ttac The estimated size of error in the prediction step is as follows: ttattattap c (2-31) Working backwards from the corrected step, th e new position and derivates can be recalculated to reflect better approximations of the true values: ttacttrttrp c 0 ttacttvttvp c 1 ttacttattap c 2) ( 51


)()()(3ttacttbttbp c (2-32) The new correct accelerations are calculated from c r and compared to the current value of ca to further refine the atoms positions and velocities, etc. The coefficients for the third order are c0 = 1/6, c1 = 5/6, c2 = 1, and c3 = 1/3. The predictor gives an initial guess, but the successive corrector iterations allow the solution to converge into an accu rate answer. Greater accuracy can be achieved by higher orders of deriva tives or using a smaller time step,t ; however this drastically increases the computation time. Langevin Thermostats Thermostats are used in MD simulations to ensure that the system is at a constant temperature.119 They are intended to match experiment al conditions either by fixing particle number, volume or pressure, and temperature. Th ey are also used to study a thermal dependent process, and mitigate excess heat avoiding energy drift from accumulation of numerical errors. The temperature is defined as an average internal kinetic energy Kof all particles N thus allowing to these thermostat atoms to fix the temperature T at a set point Tkmv KB N i i2 3 2 11 2 (2-33) where m is the mass of the particle, v is velocity, and kB is the Boltzmanns constant. The Langevin thermostat is developed from the generalized Brownian motion of theory, instead of the Newtonian equations.128 A frictional force which is pr oportioned to the velocity is added to the conservative force to adjust the kinetic energy of the particles to set the systems temperature to the desired value. Th e Langevin thermostat equation is tftvtftam (2-34) 52


where is the conservative force at a time t The termtf tv is the frictional drag between the particles, decreasing the temperature as is a fixed positive constant for friction. The friction constant is based in terms of the Debye frequency D which is related to the Debye temperature TD. D6 1 (2-35) D = (kBTD)/ (2-36) where is Planks constant. The random force is determined from a Gaussian distribution in order to add kinetic energy to the particle va rying by th e temperature and the simulation time step, The Gaussian distribution is expressed as tf t t TkmB 22 (2-37) The random force is balanced by the frictional force; th erefore, the system s temperature is maintained at the set value. tf Primary Knock on Atoms As indicated earlier in this chapter, th e REBO potential does not include electronic excitations. However, it is assumed that the ball istic electrical and thermal conductive nature in highly conducting carbon material s dissipate this effect, making it negligible. Some materials such as carbon nanotubes and graphene have gene rally high thermal and el ectrical conductivities, thus lessening the importance of ionization a nd electronic excitation mechanisms. Thermostat atoms maintain the systems desired temperat ure and absorb phonons generated which prevent the system from heating. 53


When carbon nanostructures are the target, th e m ost important mechanism involved is primary knock-on atom (PKA).83 Atoms are displaced when a hi ghly energetic electron or ion collide with the nuclei. The geometry of the m echanism is described below in Figure 2-2. The angular dependence of the angle between the direction of motion of the incident particle and the direction of the scattered particle, is defined by T as: 2 maxcosTT (2-38) Tmax is defined as the maximum transferred energy from a head on collision, or when equals 0. The probability of an incident particle skewing fr om the define head on collisions is far greater, so Tmax is defined using momentum conservation laws for the maximum energy transfer of the particle. MEcMm mcEME T 2)( 2222 2 max (2-39) Where M and T is the mass and transferred energy of the target particle, m and E are the mass and initial energy of the incident particle, respec tively. For electron irradiation, the incident mass of the particle is relatively far less than the target mass (mc << M) and initial energy ( E << ) thus reducing equation 2-39 to: 2Mc 2 2 max22 M c cmEE Te (2-40) The minimum energy that is required to displace an atom to form a vacancy interstitial pair is known as the threshold energy, Td. The corresponding threshol d energy of the incident particle Ed, has dependency on the atoms crystal la ttice. In the open st ructure of carbon nanotubes and graphite, the atoms can be displaced more easily if the incident particle hits the atom at an angle normal to the basal plane. 54


W hen an atom is knocked from its initial position with enough energy to exceed the surface binding energy of the specimen, the atom becomes ejected or sputtered. The atoms on the surface are less tightly bound than the atoms unde rneath, so the require d energy for atoms to leave the surface simply needs to overcome the sublimation energy. Ion irradiation produces more sputtering than electron irradiation due the higher energy transfer of ions vs. electrons. 55


56 Figure 2-1. Orthogonal peri odic boundary conditions.129 Figure 2-2. Energetic particle bombarding the incident nucle us, describing primary knock on behavior in irriadiation.83


CHAP TER 3 ARGON IRRADIATION ON GRAPHITE AND EVOLUTION OF DEFECTS Radiation damage in graphite is of particular interest because of its widespread occurrence in nuclear reactors. In the Windscale reactor fire in 1957, defects in graphite led to a spontaneous release of energy.30 This motivated the study of defects in graphite to a ddress safety in reactors that are being decommissioned. There has also been an effort to determine and engineer favorable structures in nanos tructured carbon materials and as sess their effects on defect formation under electron or ion-beam irradiation.86,88,130 The most common processes that occur in graphi te materials as a result of irradiation are bond-breaking, cross-linking, disp lacement of target atoms, electronic excitation, phonon generation, and sputtering of surface atoms. Gr aphitic structures, including carbon nanotubes, are essentially immune to electronic excitation because sp2-hybridized carbon mate rials are ballistic conductors with high thermal and electrical conductivity. However, unlike metals, graphite and carbon nanotubes have more occurrences of atom displacement because of their open structures. This chapter discusses defect formation and growth in graphite under ionic irradiation using a combination of experimental and co mputational methods. This project was in collaboration with the Kondow group at the Cluster Research Labor atory in the Toyota Technological Institute: The East Tokyo Laboratory carried out the reported experimental work.131 In both cases, graphite was i rradiated with Ar atoms with incident energies of 50 eV. The system was replicated by MD simulation an d the nature of the de fects was analyzed. System Setup Experiment Our collaborators setup their apparatus si milar to those disc ussed in reference.131,132 Argon ions, Ar+, were produced by discharging argon ga s (NIPPON SANSO, 99.9995% pure) by a 57


m agnetron. The argon ions selected in a quadrupl e mass-filter were allowed to collide onto a graphite (0001) surface at a collision energy of 50 5 eV. The Ar+ beam of 20 pA was irradiated on the graphite surface in a circular area of 7 mm2 for ~3000 s. The Ar+ beam is deflected by 7 mm off the original beam axis by a parallel-plate deflector placed in front of the surface in order to prevent neutral species in the beam from ad mitting onto the surface. The ion beam deviated by approximately 10 from the surface normal direction. The surface was maintained at a temperature of 300 K under an ambient pressure of 5x10-8 Pa. STM images of the graphite surface were measured with an STM probe made of Pt-Ir alloy at a surface temperature of 300 K and at a pressure less than 1x10-8 Pa. The graphite surface was prepared by cleaving highly oriented pyrolythic graphite (Z Y-A grade, Union Carbide Inc.) in air, and no further cleaning was carried out since this method of cleaving gives an atomically flat surface. An STM image of the graphite (0001) surface prior to Ar+ irradiation (not shown) i ndicated that it was free of defects. Computation The graphite system used in the simulations consists of 5,040 total atoms of four sheets that are 64 nm by 520 nm. A Langevin thermostat is applied to a 50 nm perimeter of atoms in each graphite sheet to maintain the system temperature at 300 K. These thermostat atoms also mimic thermal dissipation properties of the much larger experimental graphite sheets. Ninety atoms of 50 eV/atom were irradiated over a 186,200 nm2 area around the center of the graphite system. After each Ar impact, the structure is allowed to equilibrate before the next deposition event. Although, th e computational flue nce was 5.37 Ar/nm2 which was much higher than the experimental flux of 0.05 Ar/nm2, however, the information gained from the simulations can still be used to interpret the expe rimental findings to determine defect evolution formation and 58


thresholds of da mage. After 90 Ar atoms had bomba rded the graphite, the system was allowed to relax at 300 K for 20 more ps until the total ener gy of the system oscillates around a constant value with time. Irradiation Results Figure 3-1 is an STM image of a graphite surface after Ar+ irradiation performed by our collaborators. The bright spots are an i ndication of defects formed by impinging Ar+ and denote a variation in the electronic structures which is caused by structural change from the pristine structure. Therefore, the bright areas are points of where defect s are present. Our collaborators plotted a distribution of the def ects apparent diamet ers in Figure 3-2. The mean value and the standard deviation of the distri bution are 1.59 nm and 0.42 nm, re spectively. A relatively large standard deviation of the appare nt diameter distribution leads us to conclude that several different types of defects are created on the gr aphite surface although all the defects are observed similarly as small hills. The random dispersion of the br ight spots in Figure 3-1 im plies that the damage is independent of a single ion impact on a larger sc ale. The computational snapshots Figure 3-3 and Figure 3-4 demonstrate the evolution of da mage under continuous Ar irradiation. The simulations predict that defects pr efer to grow on existing defect sites rather than pristine sites. Under continuous irradiation, defect s may be forced to repair back to the pristine structure or develop into a cluster of several defects. For example, a cr oss-link shown in Figure 3-3 after 30 deposited Ar is no longer pres ent as more Ar atoms are depos ited. Instead, the site has transformed into a larger clump which consists of combinations of cross-links, polygons, and other defects. During the early stage of irradi ation, up to 30 deposited Ar pa rticles, a few sites containing defects start to appear. No defects are formed after 10 Ar atoms are deposited but two Frenkel 59


defects appear after 20 The top view in Figure 3-4 suggests th at Ar atom s impact the defective area and break bonds between the two carbon atoms which rehybridize with the graphite layer underneath. As a result, a cross-link is formed shown in Figure 3-3s cross-section view. The defects grow during the middle stage of irradiation, between 40 and 60 deposited Ar atoms have impacted the surface. Various types of defects start to appear: adatom-vacancy pairs, sp3-sp3 cross-links, and another Frenkel defect at the site of the first two. As the interlayer defects increase surface defects grow as well. Carbon atoms transform out of their hexagon arrangement and merge to form larger polygon defects. During this middle stage, defects attempt to find a stable configuration while being bombarded by incoming Ar atoms. This stage suggests processes where defects are grow ing and undamaged areas are struggling to remain pristine. Fewer events occur in the last stage of irra diation when compared to the middle stage. Many interlayer defects find a stable and tougher configuration and are not affected by incoming Ar atoms. However, there is still surface recons truction in response to the existing damage and ongoing irradiation. Carbon atoms swell away from the graphite plane to compensate from the damage. A perfect Stone-Wales 5-77-5 pair appears afte r 60 Ar, but is lost by the end of the irradiation event. A top view of the graphite after irradiation and equilibration is shown in Figure 3-5. The cross-links are shown in purple, and carbon atoms that have curved above their original graphene plane are shown in green The cross-links cause a retracti on toward the defect, thus the surrounding atoms curve up to balance. This finding is consistent with the results of Koike and Pedraza130 and Muto and Tanabe,133 who observe swelling in the di rection perpendicular to the graphite basal plane and contra ctions within the basal plane during electron irradiation. The predicted defects shown in Figure 3-5 are compar able to those in Figure 3-1. Mochiji et al. 60


observed variances in height on grap hite surf aces that underwent high-energy bombardment on the order of 2-15 keV134 which is apparent from the STM a nd computation results. Furthermore, the clusters of defects measured in Figure 3.5 fit with the measurements of the histogram in Figure 3.2 which suggests that damaged areas indi cated in the STM images are clumped, rather than individual, defects. Defect Analysis The hybridizations of the carbon atoms were tracked over the course of the irradiation. Atoms may cross-link and become sp3-hybridized or an atom may partially dislodge itself, punch out, of the graphene plane to become sp-hybridized. Certain types of cross-links have one or two atoms that are sp3-hybridized and some have an interstitial atom connecting the planes that is spor sp2-hybridized. Figure 3-6 indi cates the percentage of sp3and sp-hybridized carbons during the irradiation. The percentage increase of both types of hybridizations indicates that the defects containing these hybridizations are also increased. Figure 3-6 shows the three stages that the gr aphite experienced during irradiation based on the sp3 hybridization results. In the first stage where up to 30 Ar atoms have been deposited, carbon atoms start to dislodge from the graphene plane and contribute to a rise in the sp curve. Here, the atoms try to heal the damaged structure by either forming cross-links or reforming back into its original position. The sp3 slope starts to broaden in th e middle stage, between 40 and 60 deposited Ar, but the sp curve spikes. Carbon atoms that are sp-hybridized are abundant in polygon type surface defects, so an increase in the sp-curve indicates that th ese types of defects are growing. The final stage shows a s light decrease in the sp3 curve and a sharp rise in the sp curve. This trend is a sign that the structure is swelling around the si tes of cross-links to compensate for the retraction. 61


Defect for mation energies were calculated in the AIREBO and compared to DFT results to understand the defect events that occurred in the simulation. Th e defect formation energies ( ) are calculated from the total energies of the supercell with a defect is as follows: fE nEEEbulk df (3-1) Where, is the total energy of the defect containing system and is the total energy of the is are several types o f defects that appeared in the simulations and the defect formation energ he ees s are a defect common in graphite a nd have several different types. The two consi of a is dEbulkE pristine graphite sample, n is the number of carbon at oms that are added and is the chemical potential of carbon. For most defects, no carbons are added, therefore the equation simplified. There ies are listed in Table 1. There are two possible sites for v acancies on the graphite plane. Vacancy A defined as a missing atom that normally sits directly above an atom from the layer beneath, while vacancy B sits directly above the center of a hexagon in the under-layer. The AIREBO potential predicts the Ef of vacancies A and B to be 7.4 eV and 7.8 eV, respectively These values are slightly lower than density functional theory (DFT) calculations,135 however t trends and orders of magnitude are consis tent. During relaxation, carbon atoms around the vacancy site move away from th e defect, which agrees with th e DFT predictions, but disagr with tight-binding results136 which predicted neighboring atoms m ove closer to the vacancy site by 0.03 nm. Adatom dered here are an on top adatom and punc h defect. The on top adatoms consists single carbon atom that sits di rectly above a carbon atom in the basal plane and bonds only to this atom, which strains the surrounding carbon atoms in the graphene plane. Ef for this defect 6.8 eV. The punch defect is a combination of an adatom and vacancy. This type of defect is 62


also very co mmon in irradiated graphite. It o ccurs when an atom receives enough kinetic energ to be displaced from the basal plane, but does not have enough energy to fu lly leave the lattice. Instead, two of the three bonds are broken such that the carbo n atom dangles between two graphite layers. This defect generally does not rema in in this configuration and can revert b its initial location, or bond w ith a carbon atom in the underlyi ng graphene layer, creating a Frenkel defect. There are t y ack to hree different types of cross-links that have occurred dur ing the irradiation: Frenk n r the dominant cross-link defec el defect, sp3-sp3 pair, and bridge or interstitial link. The IV Frenkel defect, illustrated i Figure 3-8A, is a combination of a carbon interstitial and a vacancy is formed when a carbon atom is punched out of the graphene plane and cross-linked with two car bon atoms in the laye below. The other two atoms around the vacancy site, where the carbon atom was punched from, interact through a weakly reconstr ucted bond. It is the most common type of cross-link to form in these simulations, despite having the highest defect formation energy. These outcomes agree with Ewels et al.,137 who found that IV Frenkel pairs can result from irradiation. The defect energy is found to be 11.8 eV in AIREBO which is comparable to Li et al.s value of 10.8 eV from DFT calculations.135 The bond from the interstitial atom to the upper graphite layer is relatively short at 0.133 nm, while the other two bonds are 0.145 nm in DFT and in our simulation. The short bond is a distorted doub le bond which accounts for the stability of Frenkel defect, despite its high formation ener gy. The complex can recombine into perfect graphite structure if the recombina tion barrier of 1.3 eV is overcome.137 The sp3sp3 bond, illustrated in Figure 3-7B, is the second most pre t in our graphite system. It is formed when a carbon atom in one layer impacts the carbon atom in the layer beneath. This defect is also known to occur in large ion irradi ation cases since 63


carbon atoms gain enough kinetic energy over a considerable ar ea on the graphite plane to hybridize with a carbon underneath. However, in order for the top carbon atom to get close enough to the carbon atom below, the graphene pl ane must be strained in that direction, otherwise a vacancy will occur. It is more unsta ble than the interstitia l cross-link based o formation energies, but the orientat ion and incident particle during i rradiation allows this type o cross-link to occur more than th e interstitial type. However as mentioned previously, the Frenkel defect appeared more often in our graphite sy stem after irradiation de spite the higher defect energy formation. A bridged she n the f ar interstiti al defect, shown in Figure 3-7C, is also predicted to form and is seen l ly ation ect to form is the St one-Wales (SW) defect and is also a common defec ng es s often in the simulation than the other two cross-links. Here, the graphite forms crosslinks between the layers through se lf-interstitials. The interstitial sits in between two graphene planes and covalently bonds even ly to four carbon atoms on the top and bottom layers create a four-fold defect with bonds av eraging to be about 0.151 nm l ong. The graphite layers shear around the site to lower th eir energy. In crystalline graphite, the defect may not spontaneous nucleate since it would result in undesired faults and dislocation loops over a large area.88 However, most graphite is natu rally defective so these defect s are known to be attracted to existing shear sites.138 In our case, more interstitial-type de fects are apparent once the irradi dose exceeds 50 Ar atoms. The easiest surface def t in our system, shown in Figure 3.8.139 We found the defect formation energy to be 4.6 eV with AIREBO which is in agreement with ab initio of 4.8 eV. Other values reported for a Stone Wales defect are 5.2 eV and 5.9 eV by Li et al.135 and Jensen et al.140 respectively, usi DFT calculations and 6.02 eV by Zhou and Hi using Hckel calculations.141 The transition state 64


occurs when the rotation angle is 45. The reason fo r the large barrier at this angle is that the carbon atoms need to rearrange th emselves, which involves bond br eaking. However, Li et al. found that the associated en ergy barrier is 4.4 eV above the SW de fect level, or 9.2 eV at the to of the barrier (in DFT calculations).135 Some of the Ef values reported in p Table 1 are close to the ab initio values and some are not. This i Conclusions Layers of graphite were irradi ated e and comput ationally normal to the basal plane ct s because som e defects, for example vacanci es have been included in the fitting for the AIREBO potential. Other defects such as the adatom or Frenkel defect are not included in the potential but are still a close comparison c onsidering that AIREBO does not account for electronic structure or spin polarity. xperim entally The STM image of the graphite shows bright spots which i ndicate areas where Ar+ ions at 50 eV impinged the surfaced and induced defects. The simulations and experiment showed that defects occur over a broad distribution and each s ite contains several co mbinations of defects. The structure shows little damage during the first stage of irradiation, starts to grow during the second stage as well as fighting to retain its pris tine structure, and in the final stage starts to rearrange itself to be stable. Anal ysis shows that severa l types of defects occur, and their defe formation energies are consistent with DFT-calculated values. Comp arison of the defect patterns and sizes formed in the experimental samples are consistent with the defect complexes that are predicted to form in the simulations. Importa ntly, the simulations illustrate how defects accumulate under repeated Ar impacts. 65


Table 3-1. Defect for mation ener gies of various defects observed in graphite after Ar irradiation calculated by AIREBO and DFT. Individual defects fE (eV) from AIREBO fE (eV) from DFT 135 Vacancy A 7.4 7.6 Vacancy B 7.8 8.0 Adatoms 6.8 7.2 Punch 9.5 -Cross-links sp3 Link 7.7 -Interstitial 7.5 7.2 Frenkel 11.8 10.8 Stone-Wales Stone-Wales 4.6 4.8 Stone-Wales Barrier 10.9 9.2 Stone-Wales Transition 5.3 4.4 66


Figure 3-1. STM image of gr aphite surface irradiated by Ar+ at the collision energy of 50 5 eV. 67


Figure 3-2. Distribu tion of the apparent diameter of the defects measured by STM. Figure 3-3. Side view of gra phite during Ar irradiation. Thes e snapshots show how cross-links and punch outs form and evolve with more defects as more Ar atoms are deposited. 68


Figure 3-4. Top view of gra phite during Ar irradiation. These snapshots show how the polygons/Stone-Wales and other surface defects evolve. Figure 3-5. Irradiation damage in graphite. A) Side view snapshot of Ar atoms impacting the graphite surface. The inset shows a top view close-up that illustrates the additional damage that occurs in the graphite as a re sult of the deposition event. No Ar atoms are implanted during the simula tion. B) Top view snapshots of the graphite after the deposition of 90 Ar atoms. Areas shown in green are where atoms have popped out of the basal plane of the graphene sheet. Areas shown in purpl e contain either Frenkel or sp3-sp3 cross-links. The grey atoms in the top view are atoms in the underlying layer. 69


Figure 3-6. Percentage of spand sp-hybridized carbon atoms in graphite system after 90 Ar atoms have been deposited. 3 Figure 3-7. Snapshot of A) a Frenkel defect (an inters titial-vacancy pair), B) a sp3-sp3 cross-link, and C) an interstitial cross-link. 70


71 Figure 3-8. Snapshots illustrati ng the formation of a Stone Wale s defect, where the purple atoms turn 90 The point of highest energy occu rs when the atoms are turned 45 since bonds are being broken to arrange them selves to the Stone Wales defect.


CHAP TER 4 IRRADIATION AND AXIAL PULLOUT EFFECTS ON MWNTS Computational methods, especially molecular dynamics with REBO, have been widely used to study carbon nanotubes. The second generation REBO potential allows for bond breaking and reformation in carbon systems and can accurately model CNTs on the nanometer scale without expensive computation. Because of their small size, certain properties such as irradiation mechanics and shell sliding prove to be difficult to observe in experimental methods.75 The previous chapter investigated defect-formation in graphite during ion-beam irradiation. Since graphite sheets and carbon nanotube walls have similar geometry, the irradiation study was branched to explore ion bombardment and de fect-formation in multi walled carbon nanotubes. The resulting comparison provides information on how curvature influences the results of irradiation. In addition, nanom echanical pullout simulations were performed to analyze the extent of irradiation-induced def ects on the interactions of the nanot ube shells with one another. Here, two different nanotubes were irradiated with three different methods: polyatomic ion (CF3), single ion (Ar), and electron irradiation. After the irradiation process, the innermost shell was pulled axially with respect to the outer shell to examine the effects that different types of irradiation have on pullout forces. System Background Two different types of multi-wa lled nanotubes were used in this study, each with three concentric shells. One was an armchair MWNT that consisted of (5 ,5)@(10,10)@(15,15). The second was a chiral MWNT that consisted of (6 ,4)@(15,4)@(24,4). These different structures were chosen to investigate the effect of chirality between ca rbon nanotubes dur ing irradiation and axial pullout. Both of the tubes were 11 nm in length, but the diameters between the inner, 72


m iddle, and outer shell are the same between the tw o tubes. Only the chirality or arrangement of carbon atoms is different between these systems. The nanotubes were allowed to equilibrate at 300 K before ir radiation. The irradiation area was 4.0 nm long in the axial direction and 1.6 nm long in the radial direction. A region on each end of the nanotube, 2.0 nm wide, was set as Lang evin thermostat atoms to maintain the MWNT at 300 K temperature. A virtual substrate is placed beneat h the nanotube duri ng irradiation to mimic a support plate and to prev ent the nanotube from deflecting. In the case of CF3 ion irradiation, 50 ions were pl aced starting at 1.0 nm above the nanotube and were spaced at 10.7 nm apart so that the MWNT is impacted every 2 ps. The incident energy was 50 eV/ion. This gave enough time for the nanotube to equilibrate after each impact, otherwise the effective result will simulate an irradiation with an extremely high flux. The same procedure was used for the Ar irradiation, 50 incide nt atoms at 50 eV. The electron irradiation had a different approach than the above methods. The method used is known as the primary knock-on method, or PKA. Rather than assigning kinetic energy to an incident particle, a random carbon atom in the na notube received a transfe rred kinetic energy of 10 eV which is the equivalent energy it would receive from a 50 keV electron source. Random PKAs are assigned throughout the MWNT over 3.0 nm axial length, 1.0 nm in the radial length, and 1.0 nm vertical cross-secti on. One PKA is assigned every ten steps for 2 ps followed by 1 ps of system relaxation. The temperature of the ir radiated area rises to a bout 3500 K after the 2 ps collision period and cools to 1600 K after the 1 ps relaxation period that follows, which is higher than the experimental values of 1000 K. Neve rtheless, these computational conditions are acceptable as they allow for reconstruction of the bonds without melting or thermal degradation. 73


After each s et of irradiation events, the MWNT stru cture is cooled to 300 K prior to structural analysis. Results Irradiation The molecular dynamics simulations indicate that the helical stru ctures of MWNTs can influence the outcome after irra diation. Figure 4-1 below shows that the armchair MWNT on the left has considerably fewer defects than the chiral MWNT on the right Figure 4-2 shows that there is slight deformation with the CF3 ion beam irradiation. Both the chiral and armchair have the same atomic concentration so the differences in irradiation outcome are due to the varying carbon arrangements between nanotubes. Particularly in the case of the armchair MWNT, the row of carbon atoms on the outer sh ell are directly above another row of carbon atoms in the underlying sh ells. For the chiral MWNT, the atoms follow a helical arrangement so the underlying shells may not follow the same pattern. The differences in the atom arrangements affect the crosslink concentr ation in the sense that the impact on the outer shell received from an incoming particle may or may not directly transfer the kinetic energy to the atoms in the underlying shell. If the atoms below are shifted or skewed, they may not receive enough kinetic energy from the upper layer to create a bond. The simulations show that different mechanis ms occur when the nanotube is irradiated with Ar as opposed to CF3. Ar is chemically inert so the collisions between the incident ion and the target MWNT are purely elastic. The CF3 ions react with the MW NT surface and dissipate their kinetic energy in various physical and chemical routes, which may not always include crosslinking. Figure 4-3 su mmarizes the processes that occurred during the CF3 irradiation and compares them with the proce sses that occurred from the Ar irradiation. There are many occurrences of dissipation with CF3 and as a result, the incident CF3 particle loses energy and 74


does not always transfer enough energy to a ca rbon atom on the MWNT to induce damage or crosslinks than pure knock on Ar collisions. Mo st of the crosslinks are formed during a pure impact or bounce of the Ar or CF3 ion with the MWNT wall, but other processes that occur during CF3 irradiation can also induce crosslinks. Th ese processes include dissociation of the CF3 particle into various other partic les that either adhere to the MWNT surface or scatter away. Figure 4-4 illustrates the resu lts of an electron beam i rradiation on the MWNTs. The defects and crosslinks are more radially di stributed when compar ed to the Ar and CF3 beam deposition. This reflects that th e electron beam has the ability to affect th e underlying shells and is not surface limited in the way the ions are surf ace limited. The results show that the armchair MWNT experiences more damage than the ch iral MWNT. The extensive damage caused the MWNT to collapse, yet the chiral stru cture maintained its tubular shape. The hybridization of the carbon atoms in the MWNTs following irradiation is shown in Table 4-1. These values consider the areas that were under irradi ation and exclude the thermostat atoms. The analysis shows that the carbon arrangement on the MWNT, armchair or chiral, has little effect on the final distribu tion of carbon hybridization following irradiation. The table also indicates that the damage outcome of the MWNT s following ion-beam irradiation are not greatly different from each other despite the fact that the images shown in Figure 4-1 and Figure 4-4 appear to show signifi cant damage. Since the sp2 hybridization is close to 100% in all cases, the nanotube as a whole has little damage. However the few crosslinks induc ed show significant effects on pullout forces. The snapshots of the irradiated MWNTs indi cate obvious crosslinking and well as clusters of defects that may be difficult to visually organize. The hybridization an alysis indicates what carbon atoms experienced sp3 hybridization, but does not necessa rily give an indication whether 75


the atom is part of a crosslink. Atoms may be partially knocked out of the shells pristine structure and bridge the gap betw een two shells resulting in a sp-hybridized state. The figures show that the electron irradiated samples have mo re crosslinking than the ion irradiated tubes. These differences in damage are indicative of the differences in the in mechanisms on how virtual electrons and physical ions impact the MWNT. For example, an incident ion can hit more than one carbon atom and transf er its energy to two or three atoms upon impact. Consequently, the outer shell of the MWNT will recoil toward the middle sh ell, where two carbon atoms can get close enough to hybridize in a sp3 crosslink. In contrast, the virtual electrons as modeled by PKA affects only one carbon atom at a time, but that carbon atom receives the full energy of an impact and has more chance to form a sp-hybridized crosslink. Pullout A method to explore the effectiv eness of the crosslinks betw een the shells of the MWNT, is axially pulling the innermost shell with respec t to the outermost shell, otherwise known as sword-in-sheath deformation. MD simulations were carried out to pull the innershell completely out of the MWNT that was hydrogen-term inated at the ends at rates of 40 m/s. The MWNT was equilibrated at 300 K and the innershell was pulled 0.05 nm and then relaxed at each step. This process was performed on the ir radiated representative MWNTs as well as a pristine MWNT. A band of 1.0 nm of atoms on the end of th e innershell of the MWNT was assigned as moving atoms while the rest of the atoms on the i nnershell were kept as active. On the outermost shell, a 2.0 nm band of atoms on the opposite end from the moving atoms were assigned to Langevin thermostats. The rest of the atoms incl uding the entire middle shell were kept as active. As the innershell moved out of the MWNT, the fo rce resistance was recorded by the atoms using 76


the 1.0 nm band of moving atoms. The axial load is recorded as a function of displacement until the innershell dislodged from the MWNT. The distances between th e shells of the MWNT are 0.34 nm and are large enough to resist atomic friction on a pristine MWNT. Therefore, th e chiralities of the MWNT have little effect on the pullout forces. When a pristine MWNT is te sted for sword-in-sheath failure by pulling out the innermost shell at a rate of 40 m/s, the simula tions predict that the middle shell also travels in the axial direction of the pullout for 5.0 nm or mo re if the innershell doe s not break free from the middle or outer shells. The variations in the force curves over di splacement during inner-tube sliding for the Arirradiated, electron-irradiated, and non-irradiated MWNTs are plotted in Figure 4-5. The curves show that there is a dramatic increase in th e pullout force on the irradiated MWNTs when compared to the pristine MWNT. There are also differences in the pullout mechanism based on the type of irradiation process. Specifically, the localized defect s from ion irradiation allow the innershell of the MWNT to break its crosslinks. This type of deformation follows a plastic-type behavior. The electron-irr adiated MWNT has a radial distributi on of crosslinks and its innershell breaks during pullout. It require s a higher pullout force and breaks with a much shorter displacement than the ion-irradiated pullout, whic h is comparative to a br ittle type fracture. The differences in the curves for the ion-irradiated and elec tron irradiated pullout suggest that there is a dependence on radial distribution of cross links on the pullout fo rce. To explore the distribution effect, crosslinks were induced in two armchair MWNTs, one with a radial distribution to mimic an electr on irradiated MWNT (full radi al MWNT or FRMWNT) and the other half radially distributed to mimic an ion-irradiated MWNT (half radial MWNT or HRMWNT). Both have a crosslink density of 2. 3/nm which is approximately the same number 77


of crosslinks produced in the electron irradiated MWNT and the same pullout rate of 40 m/s. The results of these simulations are shown in Figure 4-6. In the case of the HRMWNT the innermos t shell does not break, but the crosslinks between the inner shell and the mi ddle shell do break as the inners hell is dragged out. When the innershell of the FRMWNT is pulled, it breaks w ithin itself similar to the electron irradiated MWNT pullout. The FRMWNT needed a higher force for pullout than the HRMWNT. In addition, the FRMWNT shows the same brittle type of fracture as the electron irradiated MWNT since the crosslinks are efficiently holding th e nanotube in place and do not let it plastically deform. The HRMWNT shows the same plastic ty pe of fracture as the ion irradiated MWNT. The crosslinks in these cases are concentrated on one side of the tube and therefore the nanotube is flexible enough to slide with re spect to its outershells. Therefor e, the crosslink distribution of the MWNT has an effect on the breaking m echanism as well as the pullout force. The region of both curves up to 11.0 nm of di splacement in Figure 4-6 indicates that the innershell experienced elastic stre tching as the links between the shells contribute to the linear rise in the force. The drop and oscillations in the HRMWNTs force curve show when bonds between the middle and outer shell have broken. The slight rise in the force curve between 100 ps and 140 ps is indicative of where the links between the middle shell and inner shell contribute to the pullout force, until no more links are left to hold the shell in place. Figure 4-7A and B shows how the ideal FRMWNT and HRMWNT are comparable to the electron irradiated and ion irradi ated MWNT, respectively. In part icular, the electron irradiated MWNT has a similar crosslink formation as the FRMWNT and breaks the same way, as indicated in the sudden drop in the forces in Figur e 4-7A. The trend in the two curves are almost identical yet there is a slight difference in th e time it takes to break the FRMWNTs innermost 78


shell, which is m ost likely due the effect of othe r defects (such as atomic disorder and vacancies) on the behavior of the el ectron irradiated MWNT. Figure 4-7B shows more variati on in the force curve than Fi gure 4-7A, howe ver the trend is the same for the HRMWNT and Ar-irradiated curve. This comparison shows that the MWNT pullout is affected by other defects, such as at omic disorder and vacancies, to a much larger extent than the electron-irradi ated MWNT. Unlike the HRMWNT pullout where the middle shell smoothly separates from the outersh ell first, the innermost shell of the Ar irradiated MWNT rips from the rest of the tube first. In particular, th ere is a slight drop in the force curve of the Arirradiated MWNT at 10 nm where the weakest pa rts of the MWNT break. The rise in the force curve, at displacements of 10.0 nm to 35.0 nm shows where the links between the middle shell and outer shell are resisti ng the inner shell pullout. The effect of pullout rate on the results is examined by considering two pullout rates of 40 and 20 m/s for the electron irradiated MWNT, an d the results are show n in Figure 4-8. The slower pullout rate, or strain ra te, yields a higher modulus than th e faster pullout rate. This is because the lower pullout rate gi ves the nanotube atoms more time to relax. This, in turn, adds resistance to the pullout modulus.57 Nevertheless, the maximum pull out force is about the same for both pullout rates, as ar e the qualitative responses of the nanotubes to pullout. Conclusions The simulations here showed how irradiati on can induce defects a nd crosslinks between shells on MWNTs and how differe nt types of irradiation, CF3, Ar, and electron, effect the sword-in-sheath deformation. Specifically, MW NTs with defects and crosslinks on the upper radial part, as with the ion irradiated MWNTs, shows a plastic type of deformation when the innershell is pulled axially from the outer shell. Conversely, on tubes where the crosslinks are radially distributed, result of the electron irradiated MWNT; the pullout deformation exhibited a 79


brittle type fractu re. The force to pull out the electron irradiated MWNT is significantly higher than the pullout force for the i on irradiated MWNT. In all these cases, the hybridi zation analysis showed that the MWNT maintained its integrity and a relatively small concentration of crosslinks significantly reduce sw ord in sheath deformation. 80


Table 4-1. The hybridization of the carbon atoms in th e armchair and chiral MWNTs following irradiation. Armchair Chiral Ar CF3 Electron Ar CF3 Electron sp3 1.5% 1.7% 1.0% 1.5% 1.6% 1.0% sp2 97.6% 97.7% 92.3% 97.9% 98.2% 90.6% sp 1.2% 0.6% 6.6% 1.1% 0.0% 7.9% Figure 4-1. Side view snapshot s of Ar irradiated A) armchair and B) chiral MWNTs following irradiation by a beam of 50 Ar i ons at 50 eV/ion and equilibration. 81


Figure 4-2. Side view snapshots of CF3 irradiated A) armchair and B) chiral MWNTs following irradiation by a beam of 50 CF3 particles at 50 eV/ion and equilibration. Figure 4-3. Crosslink count from the processes of CF3 and Ar impact during irradiation at 50 eV/ion. Ccnt are carbon atoms pertaini ng to the carbon nanotube. 82


Figure 4-4. Side view snapshots of electron irradiated A) ar mchair and B) chiral MWNTs with a simulated beam of 50 virtual electrons through the PKA approach. The conditions correspond to an electron source of 50 keV. 83


012345 0 20 40 60 80 100 04080120160200 Force (nN)Displacement (nm) E-beam Ar PristineTime (ps) Figure 4-5. Simulated mechanical innershell pullout of electronirradiated MWNT, Ar-irradiated MWNT, and pristine MWNT at 40 m/s. Th e features in the force curves are correlated to snapshots from the respective simulations. 84


Figure 4-6. Simulated mechanical pullout of the innermost she ll at 40 m/s of the FRMWNT and the HRMWNT. Figure 4-7. Simulated mechanical pullout of the innermost she ll at 40 m/s of the A) electron irradiated MWNT compared to the FRMW NT and B) the Ar irradiated MWNT compared to the HRMWNT. 85


86 Figure 4-8. Effect of pullout rate on the electron irradiated MW NT. A slower rate decreases the pullout modulus.


CHAP TER 5 ARGON BEAM MODIFICATION OF NANOTUBE BASED COMPOSITES The previous chapter discussed irradiation and pull out forces in bare MWNTs to simulate an experimental procedure where CNTs were modi fied before they were mixed with a polymer matrix. Here a similar study is performed on pris tine CNTs of different types embedded in a polymer matrix. Different types of carbon nanotubes were used to investigate how the curvature plays a role during irradiation considering neighboring tubes or inner shells, such in a doublewalled CNT. The composite is irradiated and then pulled out with respect to the polymer surrounding, in collaborati on with Byeongwoo Jeong. The study here not only investigates the in terfacial strength betw een the CNT and the polymer matrix post-irritation, bu t also structural changes to the composite as whole. Carbon nanotube composites are used for materials in lo w orbital satellites which are exposed to low energy bombardment from free radicals and ions. The previous chapter ga ve insight to how a MWNT responds to ion bombardment. In pure po lymer systems, irradiation etches the surface away, decreasing the materials longevity.142 The effect that the CNTs have in the polymer and their contribution to etching eff ects after irradiation are observe d, as well as limited sword and sheath deformation. Ar deposition on polystyrenecarbon nanotube composites is ex amined on three different carbon nanotube polystyrene composites. The na notubes where then pulled axially with respect to the polymer surround to analy ze effect of the irradiation-in duced cross-linking and polymer etching on the mechanical pr operties of the composite. System Background Three different composites were examined, a nd each had a different arrangement of the carbon nanotube under two layers of polystyrene, shown in Figure 51. The first structure is a 87


bundle of four (10,10) S WNTs, the second is a (5,5) @ (10,10) DWNT and the last was a (10,10) single walled nanotube (SWNT). Langevin thermostats are applied to each struct ure in a heat bath formation to mimic the thermal dissipation that occurs in macroscale composites. All three composites have the same irradiation area (160 nm2) and percentage of thermostat atoms (60%) even though the bundle composite has 15% more polymer volume than the DWNT-PS and SWNT-PS. The Ar atoms in the beam have an incident energy of 80 eV/atom. The system temperature is maintained at 300 K by the thermostat atoms ev en though local heating at the site of impact may occur at the site of impact. Each structure, singlewalled, double-walled, and bundle composites, has the same temperature during the irradiations. Each structure is allowed to relax at 350 K for 10 ps and then cooled to 300 K before deposition for 20 ps until the potential energy osci llates around a constant value. The spacing of the Ar atoms in the beam is far enough so the stru cture has 1.8 ps to equilibrate between impacts. The entire deposition process takes 200 ps to comp lete and is held at 400 K for 20 ps before being cooled to 300 K for 20 ps. Results Effects on Irradiation Polyatomic irradiation of C3F5 was performed in collaboration with Yanhong Hu on the SWNT-PS structure from Figure 5-1B with vary ing angle and incident energy. The incident beam angles considered are 0 30 and 45 from the normal angle and the energies were 50 eV/ion and 80eV/ion. The results are shown in Table 5-1. The system size and computational resources were too small to effectively simulate the 80 eV beam at 45 Nevertheless, the trend in Table 5-1 indicates that increasing the beam angle decreases the penetration depth of the ion. In addition, there is a higher percentage of ion implantation for both energies at 30 At this angle, 88


the beam s suffer fewer steric interactions with th e PS chains compared to the beams deposited at normal angles and 45 In all cases, the incident energy of the incident particles of 50 eV is not high enough to functionalize the SWNT under two layers of PS chains. In subsequent simulations, the effect of CNT type in a CNT-PS composite during Ar irradiation at normal incidence was considered Figure 5-2 shows snapshots of the final structures after Ar deposition and equilibration The trajectories show that some Ar atoms remain in the surface following deposition, while others bounce off or diffuse out after impact. The figure also illustrates how the nanotubes and the composites as a whole have changed under Ar irradiation. The carbon nanotubes modification is analyzed by the hybridization of the carbon atoms. In particular, the sp and sp3 hybridization of th e carbons are counted after each set of 5 deposited Ar. Each count is averaged over five (four for the DWNT-PS system) trajectories and presented as a percent of the total number of carbon atoms in each nanotube system. Figure 5-3A indicates that the SWNT has more sp-hybridized atoms than the SWNT bundle or the DWNT following irradiation. This is because the carbon atoms on the nanotube wall have more space available to form a punc h-out defect, where a ca rbon atom bonds with the lattice is partially broken but does not break free. The atoms around the defect on the SWNT wall react chemically with atoms from the surro unding PS since there is no inner shell. The opposite trend is seen in Figure 3b, where the DWNT has more occurrences of sp3-hybridization that reflects the fact that the i nner shells of the DWNT are able to form more cross-links. Defects that occur on the outer shell of the DWNT are more readily functionalized with the inner shell than with the neighboring PS, since th e inner shell of the DWNT is under more strain and is there fore more reactive than the PS chains However, the top of the DWNT closest to the surface experiences more damage than the portions further from the surface, and, consequently, 89


has a higher density of cross-links wi th the polym er matrix. Many of the sp3 sites on the SWNT wall are bonded with polymer frag ments or hydrogen atoms rather than linking with the polymer backbone. Under irradiation, the hydrogen at oms on the PS backbone require less energy to dissociate from the backbone than a carbon atom a nd more H atoms are available to react with the CNT. Figure 5-4 indicates the average percentage of Ar atoms trappe d in the composite following irradiation and equilibr ation. The outer shell of th e DWNT and the SWNT are the same diameter so they take up the same volume inside the PS matrix and the volume of polymer in both cases. However, the SWNT composite traps more Ar atoms than does the DWNT composite. The bundle-PS composite has significantly fewer Ar atoms trapped in the matrix than either the SWNT-PS or the DWNT-PS composites. The irradiation area is the same for the three composites, but the bundle-PS composite has less polymer volume than the DWNT-PS or SWNT-PS composites and consequently fewer oppor tunities for the Ar atom s to be trapped in the polymer matrix. Figure 5-2 also indicates that the DWNT-PS composite has fe wer trapped Ar atoms than the SWNT-PS composite. The inner shells in th e DWNT make the overall nanotube stiffer than the SWNT 46,143, which cause incoming Ar atoms to boun ce off the DWNT and still have enough energy to eject from the composite. The SWNT is mo re flexible and absorbs some of the incident energy which prevents the Ar atom from bouncing out. During the collision, some of the Ar atoms incident energy is transferred to the DW NT and, as a result, the number of carbon atoms dislodged from their initial lattice positions is high In the case of the more flexible SWNT, the energy that is transferred from the impacting Ar is more easily dissipa ted by SWNT vibrations 90


and by the surrounding polym er. As the simulations proceed, this difference in mechanical response influences the number of Ar atoms that remain embedded within the composites following impact, with more remaining in the SWNT-PS composite than the DWNT-PS composite. Bare bundles of DWNTs and SWNTs were built and irradiated with Ar at the same incident energy of 80 eV to better understand th e nature of the differing responses of the SWNTPS and DWNT-PS composites under irradiation. Figure 5-5 show s axial views of the bundles after the deposition of 40 Ar atoms. The figure cl early indicates that the structural changes are more significant in the case of the DWNT bundle than the SWNT bundle. Niyogi et al. 41 suggested that the curvat ure of CNTs shift the orbitals so that they are denser on the convex side, which is also consistent with the increa sed bonding predicted here. Therefore, CNTs with smaller radii are more reactive 41 than CNTs with larger radi i since the smaller tubes are under more strain than the larger tubes. There are fewer links between the neighboring DWNTs than the SWNTs, which implies that the inner tubes in the DWNT reacted more readily compared to its outer shells. When a DWNT embedded in a polymer composite is irradiated, its behavior is somewhat different than its bare counterpart. The defectiv e sites that result from Ar bombardment may not necessarily react with the inners hell, but can also r eact with neighboring polymer chains. In the case of the bare SWNT bundle, the nanotubes have many cross-links between their neighbors. In contrast, the SWNT inside the PS matrix does not cross-link with the chains as much as the DWNT. Over the course of the irradi ation, the polymer region above the nanotube is etched away, but the nanotube effectively protects the PS region s below it. On average, the Ar atoms reached a 91


depth of 27 in the Bundle, 27 in the SW NT and 30 in the DWNT. Comparing Ar irradiation simulations on pure PS, the polymer etches away mo re rapidly without any nanotube barriers. On average, the Ar atoms penetrate the pure polymer surface 25% deeper than comparable depositions on the composites. Thus, the simulations predict that the presence of nanotubes embedded within the PS limits th e depth and extent of surface etching. Over time, the polymer over the carbon nanotub e is etched away thus the exposing the nanotube to more direct impacts. Figure 5-6 illustrates the average number of products emitted from the composite after irradia tion and equilibration. Products of lower atomic weight are more common with those with highe r atomic weight. Most of the products consist of C2Hn fragments, such as C2H2, but there are incidents of larger fragments, including some with masses greater than 70 g/mol. Figure 5-6 also indicates that there is no significant differenc e in mass distribution between the DWNT-PS and the SWNT-PS composites. Th e bundle-PS has fewer cross-links than the other two composites. It is interesting to note that the product emission from the bundle-PS composite is greater than the ot her two, even though its polymer mass is lower. The bundle array can be thought of a composite with a low de gree of nanotube dispersion, as opposed to the SWNT-PS composite which is representative of a composite with high dispersion. This analysis implies that composites with low dispersion are more likely to emit polymer fragments upon irradiation than cross-link. Conversely, composites with higher nanotub e dispersion were shown to have less polymer emission since there are hi gher volumes of polymer surrounding each fiber. Nanotube Pullout Analysis The pullout simulations were performed by Byeongwoo Jeong, a Visiting Scientist in the Sinnott group. Figure 5-7 plots the axial pullout forces of the na notube systems before and after irradiation with respect to the surrounding PS. In the case of the unmodified SWNT-PS 92


com posite the onset of slippage between the SWNT and the PS matrix occurs at a pullout load of about 0.1625 nN, as indicated in Figure 5-7A. The interfacial strength is predicted to be about 10.8 MPa, which is higher than the va lue of 2.8 MPa predicted previously.76,77,144 The difference is attributed to variations in the system's size and simulation conditions. For the unmodified DWNT-PS and bundle-PS composites in Figure 5-7A, the onset of slippage between the CNTs and the PS matrix occurs at a pullout load of about 0.095 and 0.100 nN, respectively which are lower rather than the value for the SWNT-PS. However, the pull out load is low and the nanotubes are short (3 nm long) so comparing the pullout loads quantitatively is difficult. In Figure 5-7B, the irradiated SWNT-PS based composites has an onset of initial slippage between the SWNT and the PS matrix at 0.305 nN, and the CNT pulls out from the PS matrix at a pullout load of 0.790 nN. These values are abou t 1.88 and 4.86 times higher, respectively, than the value the unmodified SWNT-PS composite. The hybridization analysis s howed that there are not many cross-links between the PS backbone and the SWNT wall relative to the DWNT-PS system. However, there are many sites wher e the carbon atoms on the SWNT wall bonded with hydrogen. These extensions hinder the pullout m ovement of the SWNT. If there were more cross-links between the PS backbone and the nanot ube the pullout force would be expected to be even higher. In the irradiated DWNT-PS composite, Figure 5-7C, the onset of initial slippage between the DWNT and the PS is 0.560 nN, and then the CNT pulls out of the matrix at a pullout load of about 1.333 nN, 5.89 and 14.03 times higher, respectively, than the value in the unirradiated composite counterpart. The signifi cant increase in pullout force when compared to the SWNTPS composite is because there are more crosslin ks between the shell(s) and polymer in the DWNT-PS. 93


The irradiated bundle-ps system has its two topmost SWNTs in the bundle closest to the surface are bonded to each other and to the PS matr ix, Figure 5-7D. Thus, when the pullout loads are applied to all SWNTs in the bundle, the tw o lower SWNTs are pulled out of polymer matrix in the same way as the unmodified composites. However, the topmost tubes have higher pullout loads. This suggests that bonds between SWNTs in the bundle are as important as those between the SWNTs and the PS to achieve a significant incr ease of pullout forces or interfacial strength between the bundle and matrix. To determine the pullout loads for the topmost SWNTs in the bundle, the pullout loads are applied to only these two SWNTs. In this case, the onset of initial s lippage between top two SWNTs and the PS matrix occurs at a pullout te nsile load of about 0.255 nN, and the CNTs pull out of the PS matrix at a load of about 0.850 nN. These values are about 2.55 and 8.50 times higher, respectively, than the value in the case of un modified bundle-PS composites. Conclusions Three different systems of car bon nanotube-polystyrene compos ites were irradiated with 100 Ar atoms that had incident energies of 80 eV were ex amined: a DWNT-PS composite, a SWNT-PS composite, and a bundle of four SWNT s in PS composite. Th e carbon hybridization analysis shows that there is a significant diffe rence between the three sy stems when considering the bonding of the carbon nanotube(s). The curvature of the carbon na notube plays a role in the defects under irradiation. Nanotubes of smaller curvature are more ready to react, and are more reactive on the outside or convex portion of the t ube. The DWNT has more occurrences of crosslinks between its shells than with the neighborin g PS. A comparative analys is done by irradiating bundles of DWNTs and SWNTs show a similar di stribution of cross-li nks. The DWNTs would rather link the outer shells with the inner shells than form cro ss-links to neighbor ing structures, regardless of whether the neighbors are an other nanotube or the polymer matrix. 94


An analysis of the distribution of the emitte d irradiation products by mass indicates that there is little dependence on th e type of composite considered The occurrences of products for all three systems are similar. Th e majority of the products that were emitted have molecular weights of about 30 g/mol; however there are several occurrences of products with molecular weights up to 100 g/mol. The differences in polymer emission when comparing the bundle-PS results to those of the DWNT-PS and SWNT-P S composites suggest that dispersion among the nanotubes in the matrix does have an effect on product emission and cross-linking. Composites that have less polymer volume around the nanot ube tend to cross-link less and emit more. 95


Table 5-1. Effect of incident angle during C3F5 irradiation on a SWNT-PS composite. The system size and computational resources we re not large enough to effectively model angles higher than 30for 80 eV, however the trends are apparent for 50 eV. Bond means that a chemical bond was predicted to form on the time scales of the MD simulations. The penetration depth is given in terms of nanometers and defines how far below the particle traveled below the substrate surface. 80eV 50eV Penetration Depth % Implants Bonds Penetration Depth % Implants Bonds 0 2.8 38.7 Yes 2.1 42 No 30 1.6 50 Yes 1.5 55 No 45 0 0 No 1.4 45 No 96


Figure 5-1. Nanocomposite st ructures of A) Bundle, B) DWNT, and C) SWNT before irradiation. Figure 5-2. Snapshots of A) Bundle, B) DWNT, and C) SW NT composites after 100 Ar irradiated particles at 80 eV/ion. The Ar partic les are shown in pink. 97


Figure 5-3. Hybridizatio n analysis of CNT, A) sp3 analysis B) sp analysis on the carbon nanotube(s) damage under Ar irradiation. Figure 5-4. Average number of trapped Ar atoms. 98


Figure 5-5. Effects of curvat ure in irradiation damage betw een A) DWNT and B) SWNT. The innershell of the DWNT is stiffer and is more susceptible to breakage. Figure 5-6. Average masses of the polymer products after irradiation and e quilibration. The inset is a blowup view of the produc ts greater than 50 g/mol. 99

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100 Figure 5-7. Pullout load curves of CNTs. A) Unfunctionalized nanocomposites. B) SWNT based composites. C) DWNT based composite s. D) Bundle based composites. The displacement of functionaliz ed Bundle is the value of two SWNTs of upper side

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CHAP TER 6 MOLECULAR DYNAMICS AND MONTE CARLO STRUCTURE EVALUATION WITH ORGANIC SEMICONDUCTORS The previous chapters reviewed the propert ies of carbon nanostruct ures for mechanical applications and composite technologies. Ot her applications of carbon nanostructures, particularly fullerenes and hydrocarbons, include functioning as organic semiconductors, photovoltaic cells, organic light emitting devices for displa y and lighting technology, photo detectors, and thin film transistors. An important condition for the fabrication of organic photovoltaic cells is an active region of phase separated donor and acceptor molecules pe rcolated on the nanoscale to ensure ideal efficient exciton diffusion and charge collection. There have been numerous ways to obtain this ideal structure.145,146 This chapter discusses a joint project with the Xue group at th e University of Florida that combines experimental characterization of pentacene:C60 films with computational simulation. The computational work examines thin films of pentacene and C60 molecules that are mixed together at different molecular ratios to dete rmine how their morphology ultimately affects their performance in experimental devices. System Background Mixtures of pentacene and C60 of different ratios were built with two different methods. In the first approach, named the periodic method, different unit cells of pentacene and C60 were created manually at particular molecular ratios, and replicated in three dimensions. In the second approach, a builder was used to prod uce thin films of pentacene and C60 with random orientation. Both sets of structures were then relaxed in molecular dynamics (MD) simulations. The goal was to investigate the difference th e initial morphology has on the fi nal equilibrated structure. 101

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The cohesiv e energies were calculated for bulk C60 and bulk pentacene using the AIREBO potential and are compared to experimental results in Table 6-1. The calculations show that the energies from AIREBO are relatively cl ose to the values given by experiment.147,148 The AIREBO potential was fitted for hydrocarbon molecular interactions.127 Parameters such as enthalpy, pair correlation func tions, and bond energy were fit w ith experimental values. The relative close values of the cohesi ve energies in Table 6-1 verifies that AIREBO is an adequate tool for studying the short range and l ong range evolution of the pentacene:C60 films. Intermolecular interactions across a pentacene:C60 interface are shown in Figure 6-1. The C60 region packed as a face centered cubic FCC, which is how C60 is in crystalline solid form. Pentacene molecules form a triclinic structure. At a molecular separation of 0.25 nm across the interface of the (100) planes for both crystals, the predicted minimu m interaction energy is -6.31 eV/atom. This value is comparable to the interaction energy for the C60:C60 system of -6.82 eV/atom, while the pentacene-pentacene system interaction energy minimum is -5.50 eV/atom at intermolecular separations of 0.20 nm. Ordered Structures One approach to generating virtual films of pentacene and C60 to be examined in atomicscale simulations was to build a sample unit cel l and repeat it in three dimensions. For this dissertation, this method will be labeled the ord ered structure approach. Three such ordered structures were built in different in itial configurations of pentacene:C60 at a (1:1) molar ratio at various overall molecular densities. In particular the fullerene molecules were arranged into a face-centered closed pack (FCC) or bodycentere d closed pack (BCC) arrangement with the pentacene molecules added in the appropriate mola r ratio to maximize the density of the sample. A simple cubic (SC) structure was al so constructed with a distinct C60 and pentacene interface. Figure 6-2 illustrates the three structures after equilibration for the A) 1.08 g/cm3 density, SC 102

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separated structure, B) 0.78 g/cm3 density, FCC mixed structure and C) the 0.49 g/cm3 density, BCC mixed structure. Figure 62A was built with a distin ct interface be tween the C60 and pentacene molecules, whereas B and C consisted of one pentacene and one C60 in the repeating cell thus creating a distributed arra ngement when the cell was duplicated. Another structure of pentacene:C60 at a 6:1 molar ratio, illustrated in Figure 6-3, was built in attempt to achieve a high density structure. Six pentacene molecules were curved around each C60 molecule, which was labeled the orange-peel pattern. The unit cell was repeated as a SC structure to make a supercel l with a density of 1.0 g/cm3 so the molecules had adequate room to translate in the given periodic boundaries, as was the case for th e structures from Figure 6-2A. Random Structures A different set of films were generated with a film builder program that uses elements from Monte Carlo (MC) simulations to randomize th e rotation and translation of two different molecules. During experimental thermal deposition, the molecules are eject from two separate nodes and are assumed to be completely mixed when they reach the sample substrate. Therefore, a new tool was programmed for computational studies to cons truct films of two different molecules with random orientation. Monte Carlo is ideal for this type of simulation because of its use of randomly generated numbers.119 A general illustration of the MC technique and algorithms is the approximation of A circle is inscribed in a square and random points are plotted throughout the square. If the points are uniformly distribu ted, then the portion of the points those are inside the circle to the portion that are inside the square are approximately, /4, specifically: shot hit 4 (6-1) 103

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The accuracy of depends on the quality of the random number generator. Fo r example, if the points were plotted in a corner of the square, then the points are not uniformly distributed, or if a few points appeared throughout the square then the results would give a poor approximation of The nature of the MC method is used here to construct films that have a truly random orientation. The random number generator constructed films wh ere molecules positions are determined in an arbitrary manne r. The layer would not start with a repeated cell, but would be truly amorphous within the give n periodic boundaries. This appro ach assumes that the initial structures are not ordered, whic h is a better analog to the experimentally deposited films where the molecules are deposited at thermal temperat ures and are not expected to undergo much rearrangement from their initial, random positions on the surface. The random film builder starts with coordinates of two different molecules, and creates a list to match the user defined ratio and number of desired molecules. Each molecule is then randomized about its origin and translated across a given plane. The equations for x, y, and z rotations and translation based on matrices are given as: dxz yx x )sin()cos()sin(0cos()cos(' dyz yx y )sin()sin()cos()cos()sin(' dzzxz )cos()sin(' (6-2) The random film builder program produces an atomic packing factor of 0.56 for bulk, randomized C60 molecules which is consistent with the random packing factor for perfect spheres at 0.59-0.63.149 Before these new random coordinates are accepted, the distances between all the molecules center of masses must be greater than a given value de pending on the types of 104

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m olecules used. If a deposited molecule is not too close to previously deposited molecule then the move is accepted and the new random coordinates are saved. Otherwise, new random translations and rotations are pred icted until it fits on the plane. The random film builder program genera tes single layers of pentacene and C60. Three distinct layers were superimpos ed to create a 5x5x6 nm supercell. The distances between the centers of each layer were placed 1.1 and 1. 3 nm apart depending on how the randomization affects the interface of the layer beneath. The ratios generated were pentacene:C60 (1:1) molar ratio and pentacene:C60 (1:2) molar ratio. Equilibration Using Molecular Dynamics Molecular dynamics simulations were used to relax mixtures of C60 and pentacene, whether the films were built with the random film builder or the pe riodic approach, to allow for the relaxation of the system and molecular mixing or separation to occur. For this system the potential energy curve as a function of molecular position is considered as a flat potential energy surface. However, there are numerous local minima which can be obtained by varying the initial structures of the molecules, which is the motivation for building an ordered and random pentacene:C60 structure. After the films were built, they were allowed to evolve using MD and the AIREBO potential. Two different methods of equilibration were used to mimic experimental deposition rates. Experimental high deposition rates were mimi cked by setting all the atoms in the system to be Langevin thermostat atoms that were heated to 300 K. When the syst em reached the desired temperature, the thermostat was lifted, allowing a ll the molecules to evolve in time according to Newtons equations with no constraints. In contra st, low deposition rates were mimicked by first equilibrating sections of the film (33% of the enti re supercell, one layer at a time) before the next section was deposited. This method was only performed on the random built films. In 105

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experim ental film deposition, lower molecular de position rates give the molecules ample time to equilibrate before the next set of molecules appe ars. On the other hand, during higher deposition rates, the molecules have a shorter time of equilibration as many molecules are being continuously deposited. The morphology of the films w ith differing molecular ratios wa s analyzed. Effects such as molecular segregation, stacking, and mixing were determined and the results compared to the experimental findings. Results Phase Separation in Pentacene:C60 Mixtures The phase separation in the pentacene:C60 films made by experiment was investigated with X-ray diffraction or XRD with varying the mixi ng ratios of the two species. The crystalline planes surfaces of (001) and (001) for pure pentacene was reported at 2 = 5.7 and 6.1 respectively, with the inter-layer spacing d of 1.55 nm and 1.45 nm which agrees with the reported d value of thin film and bulk phase s, shown in Figure 6-4. When C60 is incorporated into the pure pentacene the higher diffraction peaks di minish which indicate there is a loss in the periodicy of the pentacene. The peaks disappear at the pentacene:C60 (1:2) weight ratio. There are weak aggregations that are observed at the (1 :1) weight ratio but no distinct diffraction peaks observed in the pentacene:C60 (1:2) weight ratio suggest th at the structure is amorphous.150 Atomic force microscopy images (AFM) in Fi gure 6-5 were performed on A) pentacene, B) C60, C) pentacene:C60 (3:1) weight ratio D) pentacene:C60 (1:1) weight ratio. Figure 6-5A of the pentacene shows complete coverage for the fi rst layer, and island growth in the second and third layers. The AFM image of C60, Figure 6-5B, shows a smooth surf ace with little features and indicates that the layer is amorphous w ith a root-mean-square surface roughness ( Rrms) at 1.5 nm. The following AFM images of the pentacene:C60 mixtures, C) 3:1 and D) 1:1 weight ratios, have 106

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a higher Rrms than the pure samples and have a differe nt morphology. Between the two ratios, the heavier pentacene mixture has smaller protrusions and more flat domains than the pentacene:C60 (1:1) weight ratio mixture.150 With the intensity changes in pentacene in from XRD results in Figure 6-4, the flat domains are believed to indicate aggregation of pentacene, while the peaks are signs of amorphous pentacene. Molecular dynamics were then used to e quilibrate the structures of pentacene:C60 (1:1) molar ratios whose final configuratio n is shown in Figure 6-2. From the image, it is clear that the C60 molecules have a tendency to aggregate. The pentacene molecules also aggregate, but they do so to a lesser extent then the fullerenes. This is analogous to what is seen in the XRD and the AFM images where a higher concentration of C60 molecules hinders high domains of pentacene aggregation. These simulations show that at low densities the molecu les aggregate in a non uniform manner; however there is a degree of agglomerates between the same molecule types. From the periodic structures, the pentacenes and C60 show aggregation of similar molecules with one another without complete phase separation, as illustrated in Figures 6-2 and 6-3. Figure 6-3 shows snap shots of the pentacene:C60 (6:1) molar ratio system after equilibration at 300 K. The pentacene:C60 (1:1) molar ratio structures showed similar behavior in Figures 6-2B and C. The structure in Figure 62A shows a thicker region of C60 and pentacene when compared to Figure 6-2B and C. The density of the structur e in Figure 6-2A is larger than B and C and the structure started as completely pha se separated rather than mixed as with B and C. However, this shows that the molecules have a preference to mix rather than stay in their respective noncrystalline phases. The pentacene:C60 (6:1) molar ratio structure showed that the pentacene molecules tended to stack commonly in pairs and even up to four molecules whereas the stacking in the (1:1) 107

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molar ratio s tructure had very few pentacene stacki ng. Figure 6-3B is a snapshot of the pentacene structure isolated from the C60 from the (6:1) molar ratio a nd shows the stacking of pentacene molecule. After equilibration the stacked pe ntacene in Figure 6-3B was analyzed by quantitatively counting based on the molecules ag reement in directional vectors and plotted in Figure 6-6. The results indicate th at about 25% of the pentacene molecules stack in pairs while 10% of the molecules form stacks of three or fo ur pentacenes. The stacking of the pentacene is quantified as a combination of pairwise distance calculations with a correlation in a molecular vector. Each pentacene molecule is assigned a longitudinal and tran sverse vector, which are used to match up with neighboring pentacenes to dete rmine a stacked pair. The distances between the pentacenes of interested are within a cutoff of 0.66 nm with a vector angle variation of 10 The aggregation and stacking of the pentacenes were also observed in the XRD and AFM results. The first peak in Figure 6-4 increases its amplitude as the concentration of C60 molecules decrease. There are more pentacene molecules present and more chances for them to form a pair, or stack. The fullerenes were isolated from the pentacenes in Figure 6-3C to show the aggregation of the molecules. A pair distribut ion of the equilibrated pentacene:C60 (6:1) molar ratio structure from Figure 6-3C, showed that the system achie ved an amorphous state and is plotted in Figure 6-7. When compared to the (FCC) mixed C60 crystal, the peaks of the equilibrated C60s show slight bumps in line with the FCC peaks. This s uggests that there is some attraction between the C60 in the mixture, and is not completely amorphous. As molecules transl ate in the supercell, trends such as C60 agglomeration and pentacene stacking are apparent regardless of initial orientation. This phenomena is related to the fl at nature of the surface potential energy and the different configurations are exploring the su rfaces local minima. 108

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Controlling Film Morphology The effects of morphology are described in this section in term s of two processing parameters, the mixing ratio and depositi on rate. Figure 6-8 s hows AFM images of pentacene:C60 at weight ratios A) 1:1, B) 1:2, and C)1:4. As observed in Figure 6-5, the bumps from the AFM images decrease as the density of C60 molecules increase. In the pentacene:C60 (1:1) weight ratio samples, the bumps are clear but they are nearly lost in the (1:4) weight ratio film. It is believed that these bumps are evolved from the flat domains observed in the thin mixed film and related to thin film pentacene phase aggregation. Figure 6-9 shows the pentace:C60 (1:1) weight ratios of different depos ition rates A) 0.6 /s and B) 6 /s. The roughness between the two films is very different which indicates th at deposition rate generates a more uniform structure where pentacene aggregation is suppressed.150 In the MD simulations, pentacene:C60 (1:1) molar ratios and pentacene:C60 (1:2) molar ratios are considered under th e conditions that mimic high a nd low deposition experimental results, that are described earlier in this chapter. Figure 6-10A illustrates the evolution of the (1:1) molar ratio film over 100 ps equilibration time. The aggregation behaviors are similar in this structure as well as distinct aggregation of pentacene and C60 as shown in the previous simulations. Figures 6-10B and 6-10C shows the isolated pentacene and C60 molecules, respectively to clarify the degree of aggregation. At the pentacene:C60 (1:1) molar ratio, the pentacene does not show a strong tendency to stack when compared to films with a higher pentacene concentration. This is comparable to the XRD finding in Figure 6-4, which indicates that an decrease in pentacene concentration diminish es crystallinity or stacking. This trend is also seen in computational results as the pentacene:C60 (6:1) molar ratio systems, where a structure that is pentacene heavy has more stacking than the pentacene:C60 (1:1) molar ratios. The C60 molecules have the same aggrega tion behavior as shown in the pa ir distribution graph in Figure 109

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6-11. The cu rve is higher for the pentacene:C60 (1:1) molar ratio than the pentacene:C60 (6:1) molar ratio, which indicates that a higher concentration of C60 results in more nearest neighbors, or agglomeration. The pentacene:C60 (6:1) molar ratio structure is relatively heavy in pentacenes, which have a tendency to agglomerate and stack. Therefore, these pentacene domains prevent C60 molecules from existing in larger groups. In the low rate deposition simulation, each layer is equilibrated before the next layer is superimposed. In this case, the molecules have ti me to equilibrate on the surface before the next set of molecules is deposited. Within the firs t 10 ps of the MD simulation relaxation of these films, the molecules contracted and showed a tend ency to attract to each other as well as similar molecules aggregating which is comparable to the trends seen in the high deposition random structures and the ordered struct ures. Figure 6-12 shows the traj ectories of the A) pentacene:C60 (1:1) molar ratio and B) pentacene:C60 (1:2) molar ratio structures. The structure with the heavier fullerene concentration, Fi gure 6-12B, showed more C60 aggregation due to the presence of more fullerene molecules than in Figure 6-12A. Howeve r, the pair distribution plot in Figure 6-13 indicates that the radial distribution between the tw o systems is fairly similar. The height of the first nearest-neighbor peak for the pentacene:C60 (1:2) molar ratio structure is slightly higher than the corresponding peak for the pentacene:C60 (1:1) molar ratio. Higher C60 concentrations result in more C60 packing with itself. However, as Figure 6-13 indicates, the height difference is slight, which indicates that the above some critical concentration the extent of C60 packing is relatively invariant. Importantly, the long-range C60 packing is amorphous. Under lower deposition rates, the molecules have more time to relax and organize themselves. Furthermore, the fullerenes have a stronger radial distribution than in the high-deposition case, which indicates that the molecules had time to relax w ithout being affected by steric hindrance. 110

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Conclusions A good understanding of DA mixtures is important to explore in order to achieve efficient organic heterojunction photovol taic device. Experiment a nd computation methods were combined to investigate the morphology of C60 and pentacene films. The cohesive energies of the molecules in AIREBO correspond to the referenced experimental values and provide quantitative information of the mixture morphol ogy. Simulations show a similar trend to XRD and AFM results, where there is st rong aggregation of pentacene. Computation used two different methods to build the mixture for morphology study: cell multiplication and a random layer builder to genera te the thin films. Between these two methods, the equilibration result was nearly indistinguisha ble. Pentacenes have continued to stack as well as C60. However, the stacking nature of the pentacene is lost with a higher concentration of C60. By using MD to equilibrate ordered and random structures of pentacene:C60, similar trends of C60 and pentacene aggregation and stacking were no ticed and compared to experimental values. Pair distribution plots between C60 molecules showed that there is short range order that is dependent on concentration which implies molecule agglomeration, and l ong range order that is independent of concentration a nd implies that the structures are amorphous. Using different initial configurations, whether it was ordered or random, allowed the exploration of different equilibration minima across the potential ener gy surface. Molecular dyna mics allowed us to study the orientation of the films and their behavi or on the molecular scale with varying ratios, initial structure, and simulated deposition rate. 111

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Table 6-1. Cohesive ener gies calculated by AIREBO com pared to experiment. eV / molecule AIREBO Experiment C60 1.70 1.74147 Pentacene 1.38 1.30151 Figure 6-1. Plot of interfacial energy between (100) surfaces of FCC C60 and (100) Pentacene. 112

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Figure 6-2. Pentacene:C60 (1:1) molar ratios of A) 1.08 B) 0.78 and C) 0.49 g/cm3 structures that were built by the ordered met hod and equilibrated at 300K. Figure 6-3. Molecular model of A) pentacene:C60 (6:1) molar ratio mixture after 100 ps equilibration with B) the pentacenes isolat ed to clarify their stacking, and C) C60 isolated Periodic boundaries are applied in three dimensions. 113

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Figure 6-4. XRD pattern performed by Ying of pure pentacene and varyi ng weight ratios of C60. 114

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Figure 6-5. AFM images by Ying of A) pentacene, B) C60, C) pentacene:C60 (3:1) weight ratio D) pentacene:C60 (1:1) weight ratio. 115

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Figure 6-6. Pentacene stacking analysis for the pentacene:C60 (6:1) molar ratio build by the ordered method. Figure 6-7. Pair distri bution analysis of the C60 interactions in the pentacene:C60 (6:1) mixture after 100 ps equilibration. 116

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Figure 6-8. AFM images of pentacene:C60 A) 1:1, B) 1:2, and C)1:4. weight ratios deposited at 0.6 /s. Figure 6-9. AFM images of pentacene:C60 A) 1:1 weight ratio at 0.6 /s deposition rate and B) 1:1 weight ratio de posited at 6 /s. Figure 6-10. Random layer built C60:Pentacene (1:1) molar ratio films A) 25 ps of relaxing at 300 K B) pentacenes isolated, C) C60s isolated. 117

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0 1 2 3 4 5 6 00.511.522.533dist (nm)g(r) .5 Pentacene:C60 (6:1) Pentacene:C60 (1:1) Figure 6-11. Pair distribution plot of FCC ordered (6:1) molar ratio and random built (1:1) molar ratio that were produced by the ordere d method and equilibrated with MD. Figure 6-12. Random layer built films on low deposition A) pentacene:C60 (1:1) molar ratio and B) (1:2) molar ratio. 118

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119 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 00.511.522.53 dist (nm)g(r) Pentacene:C60 (1:1) Pentacene:C60 (1:2) Figure 6-13. Pair distribution function plot between pentacene:C60 (1:1) and (1:2) molar ratios that were produced by the random layer builder and equilibrated with MD.

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CHAP TER 7 GENERAL CONCLUSIONS The fundamentals of irradiation and na nomechanics were investigated in carbon nanostructures, graphite and various forms of carbon nanotubes, and carbon nanotube polymer composites using classical MD simulations wi th the REBO or AIREBO potential. The potentials effectiveness for desc ribing short range and long range interactions was also used for investigating the morphology pentacene and C60 organic semiconductors. The computational findings were compared with experimental re sults and gave insight to the morphology and chemistry on the atomic scale. STM images had shown a broad site of defects over a graphite surface after being bombarded by Ar irradiation. AIREBO simulations of Ar irradiation in graphite showed an evolution of defects in th ree stages. First stage is where there is little damage, then starts to grow at the second stage of irradiation, and in the last stage starts to rearrange it self to be stable. These trajectories would be nearly impossible to monito r during an experimental irradiation procedure. The defect formation energies from AIREBO si mulations were compared to DFT results and were found to be very consistent, therefore AIRE BO is an adequate tool for illustrating how defects accumulate in graphite under repeated impacts. MD has modeled how irradiati on of different particles, CF3, Ar, and an electron, has an effect on a MWNTs chemistry and as a result li miting sword in sheath deformation during axial strain. It has been found that the incident partic le that impacts the MWNT has an effect on the cross link distribution in the radi al direction. The crosslink de nsity across the MWNTs radial face determines how the MW NT will deform under axial load. Particle irradiation that induced crosslinks on the upper portion of the radial face gave a plastic deformation pullout, while 120

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electron irradiation affected the entire radial face of the MW NT which resulted in a b rittle deformation pullout. Since the interest of analyzing sword in shea th deformation in irradiated MWNT concerns with nanocomposite research, similar simulati ons were carried out on carbon nanocomposites embedded in a polystyrene matrix. Composites of this nature are of interest in satellite applications where these materials are in a h eavy irradiation environm ent in the Earths low orbit. Therefore, incorporating carbon nanotube s in polymers have been conducted to improve the surface chemistry of the composite, specificall y resisting polymer etching. Three different structures were studied, DWNT-PS, SWNT-PS, and a bundle of four SWNTs in a PS matrix. Curvature of the nanotubes plays a significant role under irradiation. Tube s of smaller radii are under more stress and have a tendency to break under bombardment and are more reactive on the convex portion of the tube due to a shift in the -orbitals. Emitted products and incident particle depth were analyzed after the composites were irradiated and found that dispersion of the nanotube in the polymer has an effect on product emission and crosslinking. REBO and AIREBO packages were and idea l choice to use when modeling large (few nanometers) systems for carbon and hydrocarbon syst ems. The research topics mentioned above utilized a key feature in usi ng (AI)REBO over standard molecular mechanic in which bonds can be broken and reform while keeping the correct at om hybridization. Other us eful features in the AIREBO package is how effectively it can descri be short and long range interactions in carbon nanostructures and small hydrocarbons. The mo rphology of organic semiconductor films of various pentacene and C60 ratios have been studied with AIREBO and compared to XRD and AFM results to experimental built films. Cohesi ve energies were calculated under the AIREBO 121

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122 potentials and were found to be ve ry consistent with references results. Quantitatively, the computational results have been consistent with the findings from XRD and AFM analysis. REBO and AIREBO have been proven to be an effective tool in modeling systems that are nearly unattainable by experiment. Irradiati on, mechanical pullouts, and small molecule equilibration have shown various applications of research with carbon nanostructures where the features of (AI)REBO bridged with experiment can be a vital tool in carbon research.

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BIOGR APHICAL SKETCH Sharon Pregler was born in Cebu City, Philippines in 1981 to Command Master Chief John J. Pregler and pre-school teacher Norma. M. Preg ler. As part of a military family, she has traveled various parts of the wo rld and lived in many places incl uding Hawaii, Japan, California, and Washington. She has lived in Florida sin ce 1996 and graduated from Orange Park High School in 1999. She received her B.S. in 2003 from the University of Floridas Materials Science and Engineering department and a Ph.D. in Mate rials Science and Engin eering in 2008 in the Department of Materials Engineering at the Univ ersity of Florida with Dr. Susan B. Sinnott.