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Molecular Dynamics Studies of Thin Film Nucleation and Substrate Modification


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MOLECULAR DYNAMICS STUDIES OF THIN FILM NUCLEATION AN D SUBSTRATE MODIFICATION By YANHONG HU A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2003

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Copyright 2003 by Yanhong Hu

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This dissertation is dedicated to my family with love and gratitude.

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iv ACKNOWLEDGMENTS First of all, I would like to thank my s upervisor, Dr. Susan B. Sinnott, for her full support during my four years study in the Unite d States. Her scholarship and enthusiasm always amaze me and stimulate my interest in exploring the wonderful world of computer simulation. Her instructive guidan ce and openness to my ideas have made working in her group a pleasant and learning ex perience. I would also like to thank the members of my supervisory committee for th eir valuable help and kind support when I have bothered them: Dr. Rolf E. Hummel, Dr. Laurie A. Gower, Dr. Elliot P. Douglas, and Dr. Wei Shyy. Special thanks also go to Dr. Boris Ni a nd Thomas Plaisted. Without them, I would not have got started in the lab so smoothly. I also want to extend my gratitude to the present members of the Sinnott research group for many helpful discussions and friendly support. I especially want to thank my husba nd, who has helped me persevere through difficult times. From him, I always can fi nd comfort and encouragement. Finally, my heartfelt appreciation goes out to my pare nts, who always have confidence in me. Without their consistent support, I simp ly could not have come this far.

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v TABLE OF CONTENTS Page ACKNOWLEDGMENTS.................................................................................................iv LIST OF TABLES............................................................................................................vii LIST OF FIGURES.........................................................................................................viii ABSTRACT....................................................................................................................... xi CHAPTER 1 INTRODUCTION........................................................................................................1 1.1 Molecular Dynamics Simulations...........................................................................6 1.2 Cluster Beam Depositi on on Solid Substrate........................................................11 1.2.1 Thin Films from Cl uster Beam Deposition................................................11 1.2.2 Motivation and Objectives.........................................................................17 1.3 Carbon Nanotube/Polymer Composites...............................................................20 1.3.1 Carbon Nanotubes......................................................................................21 1.3.2 Carbon Nanotube/Polymer Composites.....................................................25 1.3.3 Motivation and Objectives.........................................................................30 1.4 Organization of the Dissertation...........................................................................31 2 COMPARISON OF O(N)/NOTB AND REBO POTENTIAL MOLECULAR DYNAMICS SIMULATIONS...................................................................................33 2.1 Order-N Nonorthogonal Tight-Binding (O(N)/NOTB) Method..........................35 2.2 Reactive Empirical Bond-Order (REBO) Potential..............................................37 2.3 Testing Systems....................................................................................................40 2.4 Results and Discussion.........................................................................................42 2.5 Conclusions...........................................................................................................50 3 TEMPERATURE CONTROL METHODS...............................................................53 3.1 Methods of Interest...............................................................................................55 3.1.1 Generalized Langevin Equation (GLEQ) Approach..................................55 3.1.2 Berendsen Method......................................................................................57 3.1.3 Variation of GLEQ Approach and a Combined Thermostat of GLEQ Approach and Berendsen Method....................................................................59 3.2 Testing Systems....................................................................................................61

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vi 3.3 Results and Discussion.........................................................................................62 3.4 Conclusions...........................................................................................................73 4 THIN FILM FORMATION VIA OR GANIC CLUSTER BEAM DEPOSITION....75 4.1 Simulation Details................................................................................................75 4.2 Results...................................................................................................................7 9 4.2.1 van der Waals Clusters of Ethylene............................................................79 4.2.2 Admantane Molecules................................................................................83 4.2.3 C20 Molecules.............................................................................................87 4.3 Discussion.............................................................................................................91 4.4 Conclusions...........................................................................................................99 5 CHEMICAL MODIFICATION OF CARBON NANOTUBE/POLYMER COMPOSITES THROUGH POLYAT OMIC-ION BEAM DEPOSITION............101 5.1 Simulation Details..............................................................................................102 5.2 Results.................................................................................................................107 5.2.1 C3F5 + Ion Beam Deposition on CNT/PS-// Composites...........................109 5.2.2 C3F5 + Ion Beam Deposition on Pristine PS Substrates.............................113 5.2.3 C3F5 + Ion Beam Deposition on CNT/PSComposites..........................115 5.3 Discussion...........................................................................................................116 5.3.1 The Effect of the Incident Energy............................................................118 5.3.2 The Effect of the Composite Structure.....................................................120 5.3.3 Comparison between Pristine Polymer Substrates and Composites........123 5.4 Conclusions.........................................................................................................125 6 CONCLUSIONS AND BEYOND...........................................................................127 6.1 General Conclusions...........................................................................................127 6.2 Future Work........................................................................................................132 LIST OF REFERENCES.................................................................................................134 BIOGRAPHICAL SKETCH...........................................................................................151

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vii LIST OF TABLES Table page 2-1. Details of the hydrogen-terminated diamond (111) surfaces...................................41 2-2. The coordination of the carbon atom s in the film predicted by the O(N)/NOTB-MD and EMD simulations (a veraged over 3 trajectories) (%)...........48 2-3. The coordination of the carbon atom s in the film predicted by the EMD simulations (averaged ove r 10 trajectories) (%).............................................48 2-4. The carbon connectivity of the carbo n atoms in the film predicted by O(N)/NOTB-MD and EMD simulations (a veraged over 3 trajectories) (%)...........50 4-1. Summary of the coordination per centage of the film carbon atoms (%).................91 4-2. Summary of the percentage of carbon connectivity of the film carbon atoms (%).....................................................................................................91 5-1. Summary of the results af ter the ion beam deposition on CNT/PS-// composites at 50 eV/ion.......................................................................110 5-2. Summary of the results af ter the ion beam deposition on CNT/PS-// composites at 80 eV/ion.......................................................................112 5-3. Summary of the results af ter the ion beam deposition on pristine PS substrates at 50 eV/ion and 80 eV/ion.................................................114 5-4. Summary of the results af ter the ion beam deposition on CNT/PScomposites at 50 eV/ion.......................................................................116

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viii LIST OF FIGURES Figure page 1-1. Schematic representation of periodic boundary conditions.......................................3 1-2. Flowchart of the predictor-corrector MD.................................................................10 1-3. Possible phenomena that may occur after the deposition of energetic clusters on a solid substrate...........................................................................................................14 1-4. The principle of the experimental set-up for thin film formation by energetic cluster impact (ECI).............................................................................................................15 1-5. A graphene sheet rolled into a single-walled carbon nanotube (SWNT).................21 1-6. The “rolling up” of a graphene sheet to produce carbon nanotubes of various helical structures..........................................................................................22 1-7. A model of a capped SWNT....................................................................................23 1-8. A SWNT formed in the catalytic carbon arc method...............................................24 1-9. In situ straining of a CNT/ PS compsite in TEM......................................................28 1-10. Cross-linking formed between nanotubes and adjacent shells in the case of MWNT as a result of energe tic ion deposition......................................................................31 2-1. The percentage of incident carbon atoms that adhere to the substrate (averaged over three trajectories) versus the size of the substrate....................................................44 2-2. Potential energy curves calculated with O(N)/NOTB-MD and EMD methods for the three reactions.....................................................................................................45 2-3. The percentage of incident carbon atoms that adhere to the substrate (averaged over ten trajectories) versus the size of the substrate.......................................................47 2-4. Snapshots of the thin film formed on the hydrogen terminated diamond (111) surface containing 3136 atoms.................................................................................47 3-1. The substrate layout. (a) the impact z one; (b) the impact zone embedded in the thermostat zone........................................................................................................62

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ix 3-2. The temporal evolution of the substrate temperature in the reference simulation and the simulations using the four temperatur e control methods at the incident energy of 1 eV/atom.............................................................................................................63 3-3. The temporal evolution of the substrat e temperature in the simulations using the four temperature control me thods at the incident energy of (a) 5 eV/atom, (b) 10 eV/atom.........................................................................................................64 3-4. The temporal evolution of (a) the subs trate temperature and (b) the kinetic energy per active atom in the simulations using th e four temperature c ontrol methods at the incident energy of 20 eV/atom.................................................................................66 3-5. The temporal evolution of (a) the subs trate temperature and (b) the kinetic energy per active atom in the simulations using th e four temperature c ontrol methods at the incident energy of 40 eV/atom.................................................................................68 3-6. Snapshots of the systems using the four temperature control methods at various moments at the incident energy of 40 eV/atom........................................................70 3-7. The displacement fields from t = 0.08 ps to t = 0.24 ps in the cross section of the (111) plane using the four temperatur e control methods at the incident energy of 40 eV/atom...............................................................................................70 3-8. The temporal evolution of (a) the subs trate temperature and (b) the kinetic energy per active atom in the depositions on the small substrate using the four temperature control methods at the incide nt energy of 40 eV/atom............................................72 4-1. The arrangement of the thermostat atoms (gray) and the active atoms (black) within the substrate..............................................................................................................76 4-2. The simulation system prior to the deposition.........................................................79 4-3. Representative snapshots from the simu lations of ethylene cluster beam deposition on the hydrogen terminated diamond (111) surface.................................................80 4-4. Percentage of carbon atoms in the ethylene clusters that adhere to the surface as a function of incident angle.........................................................................................82 4-5. Molecular structure of adamantane..........................................................................83 4-6. Representative snapshots from the simulations of adamantane molecular beam deposition on the hydrogen terminated diamond (111) surface...............................85 4-7. Percentage of adamantane carbon atoms th at adhere to the surface as a function of incident angle...........................................................................................................86 4-8. Representative snapshots from the simulations of C20 molecular beam deposition on the hydrogen terminated diamond (111) surface.................................................89

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x 4-9. Percentage of carbon atoms in C20 clusters that adhere to the surface as a function of incident angle.......................................................................................................90 5-1. The composite structures before ion deposition (only parts of the systems are shown for clarity)...................................................................................................104 5-2. The composite structures after the relaxation while before the ion deposition...................................................................................................105 5-3. A series of snapshots during the ion beam deposition...........................................108 5-4. The CNT/PS-// composites after th e ion beam deposition at 50 eV/ion................109 5-5. The normalized chemical bonding informati on of the trapped ion species after the deposition on CNT/PS-// composites at 50 eV/ion. (a) CNT/PS-//-1; (b) CNT/PS-//-2; (c) CNT/PS-//-3..........................................................................111 5-6. The CNT/PS-// composites after the depostion at 80 eV/ion. (a) CNT/PS-//-1; (b) CNT/PS-//-2; (c) CNT/PS-//-3..........................................................................112 5-7. The normalized chemical bonding informati on of the trapped ion species after the deposition on CNT/PS-// composites at 80 eV/ion. (a) CNT/PS-//-1; (b) CNT/PS-//-2; (c) CNT/PS-//-3..........................................................................113 5-8. The normalized chemical bonding informati on of the trapped ion species after the deposition on pristine PS substrates at (a) 50 eV/ion and (b) 80 eV/ion...............114 5-9. The CNT/PScomposites after the ion b eam deposition at 50 eV/ion................115 5-10. The normalized chemical bonding informati on of the trapped ion species after the deposition on CNT/PScomposites at 50 eV/ion. (a) CNT/PS-1; (b) CNT/PS-2; (c) CNT/PS-3.........................................................................117 5-11. The CNT/PS-//-3 composite structure af ter the deposition at 80 eV/ion generated from the repeated simulation..................................................................................120 5-12. The fraction of functionalized carbon atoms in the carbon nanotube embedded at varying depths........................................................................................................122

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xi 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 MOLECULAR DYNAMICS STUDIES OF THIN FILM NUCLEATION AN D SUBSTRATE MODIFICATION By Yanhong Hu August 2003 Chair: Susan B. Sinnott Major Department: Materials Science and Engineering Deposition of energetic part icles on solid surf aces has found increas ing application in surface science. However, the detaile d surface chemistry and relevant atomic mechanisms are not well understood. Molecula r dynamics (MD) simulations are an ideal method to study these processes atomistically because they usually occur on short time scales (of the order of a few picoseconds). In this dissertatio n, MD simulations are performed to investigate thin film formati on through organic cluster beam deposition and chemical modification of carbon nanotube/pol ymer composites via polyatomic ion beam deposition. The interatomic forces are calculated from the reactive empirical bond-order (REBO) potential for carbon-based systems c oupled with the Lenna rd-Jones potentials. The reliability of this approach is examin ed by comparing its pr edictions for ethylenecluster beam deposition with the results of a more accurate order-N nonorthogonal tight-

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xii binding method. The results show that th e REBO potential captures the general characters of the relevant chemistry. The deposition processes of interest occur at room temperature; hence, appropriate temperature control methods must be empl oyed in the simulations. A comparison study of four temperature control methods during th e simulation of cluster deposition finds that the generalized Langevin equation approach is sufficient for dissipation of excess system energy if the deposition occurs on a large enough substrate at a mode rate incident energy (< 40 eV/cluster-atom). A new temperature co ntrol method has been developed for use at higher incident energies. In the simulations of thin film formation through organic cluster beam deposition, the dependence of the results on the intracluster bonding, in cident angle and deposition direction is examined. Beams of ethylene clusters, adamantane molecules, and C20 molecules are thus deposited on a diamond su rface with varying lateral momenta along two different crystallographic orienta tions at various in cident angles. The simulations of chemical modifi cation of carbon na notube/polystyrene composites via ion beam deposition predict that this process can effectively induce the formation of cross-links between otherwis e unfunctionalized nanot ube and polystyrene chains. Modification efficiency is shown to depend on the incident energy and the composite structure. The responses of the co mposites to ion beam deposition are different from the response of pristine polystyrene. The simulations detail the atomic-scale mechanisms that are responsible for these findings.

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1 CHAPTER 1 INTRODUCTION Molecular simulation is a relatively new technique, which became known to people only in the early 1950s. Since then, it has de veloped rapidly into a valuable tool in scientific research, complementing both anal ytical theory and e xperiment. One major application field of molecular simulations is materials science. Materials science deals with the properties of systems of many atom s or molecules. The interactions between these atoms or molecules determine the overall properties. Therefore, accurate descriptions of these interacti ons are critical to understand th e properties of the material. When they are based on the laws of quantum mechanics, molecular simulations can provide essentially exact estimations of the interatomic interactions by explicitly considering the electrons and nuclei. Of course quantum mechanical calculations of interatomic interactions are very complicat ed and can only be done using computers. Such simulations involve few appr oximations and are usually known as ab initio or first principles simulations. Ab initio simulations can thus be used to predict unknown properties of a material or can be used as a test of an approximate analytical theory by comparing the result of the simulation with the prediction from the theory. Computational demands can be dramatica lly reduced if some approximations are introduced into the description of the in teratomic interactions through the use of appropriate empirical functional forms. However, the results of such classical simulations may contain errors. Depending on how ma ny approximations are introduced, these simulations are termed either semi-empirical or empirical. Between the two, empirical

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2 simulations may contain more errors becau se more approximations are employed. In these cases, the simulation predictions from a microscopic model should be compared with experimental or more exact ab initio results. If the model turns out to be a good one, then the simulation can be used to provide atom ic insights and assist in the interpretation of experimental results. The two most important molecular simula tion methods are the Monte Carlo (MC) method and the method of molecular dynamics (MD). The MC method uses probability laws and random numbers (hence the name “Monte Carlo”) to obtain the ensemble average and standard deviation of a random variable via random sampling.[1] The first MC simulation was carried out by von Neuma nn, Ulam, and Metropolis at the end of World War II to study the diffusion of neutr ons in fissionable mate rial. The MC method is a statistical method, and any problems i nvolving random processes can essentially be simulated via this method. Assuming the appl icability of classical mechanics, MD simulation is a deterministic method in whic h the system evolves according to Newton’s equations of motion.[2] Thus, MD simulations can give full dynamical information and can be used to study time-dependent phe nomena. Both MC and MD methods have advantages and disadvantages. Although MD is the only reliable method to study timedependent properties, conventional MD can only track processes for at most a few nanoseconds. In contrast, MC method is not subject to time limits and can yield thermodynamic properties that may not easily be obtained from MD. Depending on the problem and properties of interest, either MC or MD, or sometimes a combination of MC and MD, is used in an atomistic simulation.

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3 Figure 1-1. Schematic representation of periodic boundary conditions.[2] The purpose of molecular simulations is to model the macroscopic sample and provide information that is not easily detectable from experi ments. Unfortunately, due to the computational limitations of present-day computers, the nu mber of atoms that can be conveniently handled ranges from a few hundred to a few million. This number is still far removed from the real size systems, which contain Avogadro’s number (6.023 1023) of particles. In order to model a macroscopic sy stem in terms of a finite simulation system of N particles, periodic boundary conditions are employed. This idea can be illustrated by Figure 1-1,[2] in which the simulation system of N particles is treated as a basic unit and is replicated throughout space. Therefore, the si mulation unit is essentially embedded in an infinite array of units, all with the same geometrical arrangement of particles. The application of periodic boundary conditi ons has two obvious advantages. Without periodic boundary conditions, the simulation system would simply terminate and be surrounded by surfaces. The surface atoms have fewer neighbors than the atoms inside. For a simulation system containing finite numbe r of atoms that is negligible compared with the real size system, the ratio of its surface at oms to the total number of atoms would be much larger than in reality. In other wo rds, surface effects would appear to be much

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4 more important than what they should be. T hus, the first advantage of the application of periodic boundary conditions is that the surface effects, which would otherwise be proportional to N-1/3, are reduced to be proportional to N-1.[2, 3] Second, as the simulation progresses, for every molecule that leaves the simulation unit, its image will enter through the opposite face. Thus, the volume and the density of the simulation unit can be maintained throughout the simulation. Alt hough the use of periodi c boundary conditions has been proved to be surprisingly effective and successful, it should be noted that such boundary conditions may lead to correlati ons not present in the real system.[2] The point is that the basic simulation unit should be la rge enough so that those correlations will not introduce spurious effects.[4] In molecular simulations, the key is the calculation of the interactions between the particles, which, in principle, should incl ude not only the interactions between the particles contained in the simulation system, but also all the interactions between the particles and their images once the periodic boundary conditions are employed. Even if empirical functions are used to model these in teractions, the computational load is still impractically high. Under circumstances like these, appropriate cutoff distances (cr ) should be used to truncate the interactions between the particles. This means that the effects of the particles beyond a certain cutoff distance are ignored. While this simplification certainly will introduce error in to the calculation, the error can be made arbitrarily small by choosing a large enough cr .[2] The introduction of the cutoff distance is especially meaningful fo r short-range interactions su ch as covalent bonding, where interactions between neighbor ing particles dominate.

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5 Although the use of a cutoff distance sa ves tremendous computational time, a significant amount of CPU time is still sp ent calculating the distance between the particles at every step. In order to reduce the unnecessary labor, for instance, in calculating the distance between tw o particles that are obviously too far apart to interact every time, a “neighbor list” table is constr ucted, which was an idea first introduced by Verlet.[5] The table stores each particle’s neighbo rs and is updated only at predetermined time intervals. The neighbors include all the pa rticles that are within a certain distance r (>cr ) from each particle. The program update s the neighbor list table only when considerable displacements beyond r occur. With the introduc tion of the neighbor list table, the calculation of the interactio n energy between the particles now can be performed by only scanning through the particle s listed in the table instead of scanning through all the particles. Depending on the pr oblem that needs to be solved, some modified “neighbor list” techni ques that update the table more efficiently have been reported.[6, 7] Many processes are carried out experimentally at constant temperatures. In order to model these processes, the te mperature of the simulation system should be controlled. This is achieved by employing thermostat atoms. Thermostat atoms have special constraints such as extra frictional forces pl aced upon them, and evolve differently from the other ordinary atoms as the simulation pr ogresses. The function of these thermostat atoms is to remove extra energy from the si mulation system or to compensate for a loss of energy, depending on which is necessary to maintain the system temperature. There have been several algorithms proposed for te mperature control, such as the velocity

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6 rescaling scheme, the Nos-Hoover method, and the generalized Langevin equation approach. In this dissertation, thin film nucleat ion through organic cluster beam deposition and chemical functionalizati on of carbon nanotube/polymer composites via polyatomic ion beam deposition are investigated using molecular simulations. Since the phenomena of interest are time-dependent and both de position processes are rapid enough that they occur within a few picoseconds (10-12 seconds), molecular dynami cs simulations are used in both cases. 1.1 Molecular Dynamics Simulations In classical mechanics, Newton’s second law states that in order to make a body of mass m undergo an acceleration a a force F is required that is e qual to the product of the mass times the acceleration: a F m (1-1) This equation can also be expresse d in terms of the position vector r of the body as 2 2dt d m r F (1-2) This is the basis of molecular dynamics (MD). Knowing the force F, based on Equation (1-2), we can thus study the trajectory of each particle in space and investigate the time-dependent properties. The problem is how to calculate the force. From the principle of conservation of energy, we know that the kinetic energy ( 22 1 v m ) and the potential energy ( U ) of the body can vary, but their sum ( ) is a constant. U m22 1 v (1-3) In terms of r equation (1-3) can be expressed as

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7 U dt d m2) ( 2 1 r (1-4) Differentiating both sides of Equation (1 -4) with respect to time, we find 0 ] ) ( 2 1 [2 U dt d m dt d r and so 02 2 dt dU dt d dt d m r r This can be rewritten as follows because potential energy is a f unction of the position U ( r ): 02 2 dt d U dt d dt d m r r r Therefore, we get U dt d m 2 2r Referring back to the Newton’s second law (Equa tion (1-2)), the left side of the above equation is the force. Thus, the force can be calculated from the potential energy: U F (1-5) The potential energy, as stated before, can be obtained using either empirical potential energy expressions, semi-emp irical methods, or exact ab initio approaches. In MD simulations, the calculations of the poten tial energy and force are the most timeconsuming parts. Once the force is obtained, Equation (1-2) can be integrated to follow the time evolution of the atoms in response to the applied forces. In practice, numerical integrations instead of algebraic solutions to Equation (1-2) are performed. There are several numerical methods for integrating Newton’s equations,

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8 including the Verlet algorithm, the leap frog algorithm and the predictor-corrector algorithm.[2] In our MD simulations, the predictor-corrector algorithm is used. Based on Taylor’s expansions, if the position ( r ), velocity ( v ), acceleration ( a ) and time derivative of the acceleration ( b ) are known at time t these quantities can be obtained at t+t (t is the time-step), as shown in the following equation: ) ( ) ( ) ( ) ( ) ( ) ( ) ( 2 1 ) ( ) ( ) ( ) ( ) ( 6 1 ) ( ) ( 2 1 ) ( ) ( ) (2 3 2t t t t t t t t t t t t t t t t t t t t t t t tp p p pb b b a a b a v v b a v r r (1-6) If we use the truncated Taylor expansion, where the terms higher than those shown explicitly in Equation (1-6) are ignored, all four quantitie s can thus be “predicted.” However, no force law has been taken into a ccount so far, and the predicted values are not based on physics. This deficiency is re medied at the “correct or” step. Knowing the new position pr at time t+t we are able to evaluate the new potential energy, and thus the force at t+t is obtained. Then, from Equation (1-1), the corrected acceleration ) ( t tc a can be calculated. Comparing this co rrected acceleration with the predicted one, the error at the predicti on step can be evaluated as ) ( ) ( ) ( t t t t t tp c a a a This term is then used to correct all the predicted quantities as follows: ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) (3 2 1 0t t c t t t t t t c t t t t t t c t t t t t t c t t t tp c p c p c p c a b b a a a a v v a r r (1-7)

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9 These values are now better approximations to the true quantities, and are used to predict the quantities in the next iteration. The corrector constants ic are chosen to yield an optimal compromise between the accura cy and the stability of the algorithm.[2] Gear discussed the best choice for these cons tants, which depends on the order of the differential equations and of the Taylor series.[8] These constants are fixed for a given order algorithm. For instance, the one we use is a third-order Nordsieck predictorcorrector algorithm, and the values for ic are 6 10 c 6 51 c 12 c and 3 13 c Figure 1-2 schematically shows the pr edictor-corrector MD procedures used in the simulations described in this dissertation. In MD simulations, short time-steps are requi red to yield reliable results. There are at least two reasons for this. One is due to the quick motion of the atoms (for example, the time-scale of atomic vi brations is typically 10-13 s[9]). In order to capture atomic motions accurately, as MD simu lations desire to do, the time-step must be much smaller than the frequency of the atomic motions. Th e second reason is that, from the integration point of view, a small t is necessary to achieve the predictions calculated in Equation (16) as accurate as possible. Usually, time-steps on the order of a femtosecond (10-15 s) are used. Unfortunately, such short time-steps ma ke the modeling of pr ocesses that occur on time-scales larger than a few nanoseconds out of the reach of conventional MD simulations on present-day computers. MD simulations can generate atomistic in formation such as atomic positions and velocities. Via statistical m echanics, this atomistic information can be related to macroscopic quantities such as pressure, temperat ure, heat capacities, etc. Therefore, MD

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10 Figure 1-2. Flowchart of th e predictor-corrector MD. simulations can be used to study these thermodynamic properties as well as timedependent (kinetic) phenomena. The firs t MD simulation was done by Alder and Wainwright to study the dynamics of an assembly of hard spheres.[10, 11] Their studies provide many important insights concerning the behavior of simple liquids. The first MD simulation of a real material was carried out by Gibson et al. to model radiation damage in crystalline Cu.[12] In 1964, Rahman performed the fi rst MD simulation using a realistic potential for liquid argon.[13] Since then, MD simulations have been widely used in S tar t System Initialization Predictor Potential Energy & Force Calculation Corrector Data Output Time out? En d Yes N o

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11 studying solids, liquids, gases, simple and complex hydrodynamic flows, shock waves, deformation and fracture of materials, chemis try in solutions, conf ormational changes of proteins, etc. MD simulations also find applic ation in experimental procedures such as Xray crystallography, NMR structure determin ation, and inelastic neutron scattering.[14] 1.2 Cluster Beam Deposition on Solid Substrate Clusters typically contain 10 to seve ral thousand atoms. Weakly bound van der Waals clusters (e.g., noble gas clusters), covalently bound clus ters (e.g., fullerenes), as well as ionic and metallic clusters have been observed. As an aggregate of atoms and/or molecules, the cluster is a new state of matte r that lies between isolated atoms/molecules and the condensed phase of bulk matter. Due to their high surface-to-volume ratio, clusters display peculiar propert ies that differ considerably from those of the constituents and the bulk material. The properties depend strongly on the number of atoms in the cluster. By controlling the si ze of the clusters and other ope rating variables, such as the incident energy and substrate temperature, cluster deposition on solid substrates can produce thin films with specifi c structures and properties. 1.2.1 Thin Films from Cl uster Beam Deposition Clusters can be generated in jet and beam experiments in both continuous and pulsed forms.[15] In cluster formation, control of cl uster type (noble ga ses, covalently bound molecules, metals, etc.), cluster size, a nd cluster energy are th e major objectives. In 1956, Becker announced the formation of free jet cluster beams of room temperature gases (Ar and He) produced by e xpansion through cooled nozzles into a vacuum environment.[16] Such gas expansions through sm all nozzles, sometimes with a carrier gas, are effective sour ces of molecular gas clusters. For the clusters formed from

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12 these gas expansion sources, the control of pressure and temp erature of the stagnation gas helps to control the cluster size. Another category of cluster sources, gas aggregation sources, are reported to be particularly suitable for production of meta l clusters of up to thousands of atoms.[17-19] Briefly, metal vapor is first produced by either thermal evaporation[18] or sputter discharge.[19] The vapor is then projected into a co ndensation cell filled with cold rare gas. The supersaturated vapor then nucleates and coalesces to form clusters, the size of which is controlled by adjus ting the carrier gas flow. Laser vaporization source is especially suitable for generating cluster beams of refractory materials.[15] Laser ablation of solids produces plasma via the localized heating induced in the material. By rapid quenching of the plasma, clusters can be produced. This technique was originally used by Smalley (as cited in “Milani and Iannotta[15]”) and led to the discovery of fullerenes C60 and C70 in a molecular beam experiment in which laser vaporized graphite was seed ed and expanded in helium.[20] The size of the clusters generated from the laser vaporization sources is determined by controlling the mean residence time of the plasma-gas mixture.[21, 22] Ionized clusters are usually generated by electron impact after cluster formation. Photon ionization of clusters, for inst ance, by UV lasers, is also reported.[15] The purpose of ionization the clusters is to achieve eas y manipulation and detection of the cluster energy using electromagnetic fields. As far as the effect of ioni zation on the deposition results is concerned, ionized clusters are wide ly assumed to behave in a similar manner to neutral clusters due to the low charge carried in each cluster.[23] The deposition of sizeand energy-selected clusters is the ultimat e goal for the synthesis of nanocrystalline

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13 materials with tailored properties. Although th e deposition of size-se lected clusters in bulk quantities is still in deve lopment, controlled deposition of clusters to study clustersurface and cluster-cluster intera ctions in the sub-monolayer regime have been realized using mass/energy filters.[15] The past three decades have witnessed an exciting development in thin film production through energetic cluster-surface coll isions using methods such as ionized cluster beam deposition (ICBD),[24-32] energetic cluster impact (ECI),[19] and low-energy cluster beam deposition (LECBD).[22, 33, 34] The whole collision process occurs rather rapidly, typically within a few picoseconds.[35] Thin film formation from energetic cluster beam deposition has several advantages over traditional atomic ion beam deposition.[19, 23] These include a high, transient concentrati on of energy and mass that is deposited in a very localized region of the surface, resulti ng in conditions of ex treme temperature and pressure under which novel chemical reactions may happen.[28, 36, 37] In addition, compact, smooth and strongly adhering thin films can easily be made on low temperature substrates. Since the charge/atom ratio of i onized clusters is very low, space-charge problems are negligible. Another intriguing fe ature of energetic cl uster beam deposition is that the surface modification effect is re stricted to a very shallow region of the substrate, avoiding significant property cha nges to the bulk material. Revealed by MD simulations, the reason is the co llective “plunger” effect of a number of cluster atoms interacting with the same substrate atom at the same time.[38] When the deposition occurs at high inci dent energy (in the range of keV per cluster), the clusters will experience dram atic morphological changes upon impact. A variety of outcomes are possibl e, including scattering of clus ter fragments, sputtering of

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14 substrate materials, implantation of cluster at oms, adhesion of the cluster to the surface, and lateral motion of cluster atoms. Thes e phenomena are summarized in Figure 1-3.[26] When the clusters are deposited with an incident energy high enough to stick to the substrate but low enough to maintain their orig inal structure, so-called cluster assembled materials are produced.[34] This technique is known as low energy cluster beam deposition (LECBD). The incident energy is typically less than 0.1 eV/atom in LECBD (in ICBD and ECI, the energy is usually larger than 1 eV/atom).[39] The LECBD technique is fascinating because the generate d thin films keep a “memory” of the freecluster phase and the clusters essentially act as building blocks. Therefore, this technique offers a unique opportunity to prepare thin f ilms from “building bloc ks” that have been well controlled in the gas phase.[34] Figure 1-3. Possible phenomena that may occur after the deposition of energetic clusters on a solid substrate.[26] The group at Kyoto University pioneered thin film creation through the high energetic cluster beam deposition.[24, 27] The technique they deve loped is generally known as ionized cluster beam deposition (ICBD). Si nce its development, ICBD has been widely used to produce thin films from the deposition of a variety of materials, such as metals,[24,

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15 26] nitrides,[31] semiconductors,[24, 32] and organic materials.[25, 28-30] However, theoretical calculations show that standard ICBD conditions do not favor the formation of clusters.[15] Experimentally, it was claimed that small clusters of up to 25 atoms might exist in the clusters produced from a typical ICBD sources but there was no or a very small fraction of large clusters.[26, 40, 41] Figure 1-4. The principle of the experimental set-up for thin film formation by energetic cluster impact (ECI).[19] C1 and C2: magnetron cathods; A1, A2 and A3: apertures (the region between A1 and A2 is the condension zone, which can be cooled by liquid N2); H: heater; R: crystal microbalance; S: substrate holder; TOF: time-of-flight mass spectro meter to measure the cluster size. Energetic cluster impact (ECI) is a te chnique developed by Haberland’s group in Freiburg.[19, 42] Figure 1-4 demonstrates the experimental set-up of thin film deposition by ECI.[19] The size of the clusters formed ranges from 50 to more than 106 atoms per cluster. What is unusual in this technique is that a large percenta ge (30-80%) of these clusters has already been ionized; therefore, no additional electron ionization step is necessary. The cause for this simultaneous ionization is the us e of the magnetron cathodes (C1 and C2 in Figure 14), which not only help to generate vapor by sputtering, but also ionize the clusters by the afterglow fr om the sputter discharg e. Thin films from

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16 the deposition of metal (Mo, Cu, Al and stainless steel) and SiO2 on Si and glass substrates at room temperature us ing ECI have been reported so far.[19, 42] The incident energy of the clusters is shown to be critical in determining the quality of the resultant film. In the past 30 years, a large amount of ef fort has been spent in understanding thin film deposition from cluster-solid collisions Although phenomenologi cal models derived from experimental observations can explain so me of the relationships between deposition conditions (incident energy, cluster size, and s ubstrate temperature) and the resulting film properties and structures, a deep enough unders tanding and, even more importantly, the ability to predict how a change in deposition conditions leads to a change in thin film properties, still remain as a longstanding ch allenge. This challenge has resulted in the exploration of computer simula tion, which has been proved to be a predictive as well as explanatory tool in many cases. Among the va rious simulation techniques that may be used, MD simulation is especially well suited to study the energetic deposition of clusters because this process typically occurs within a few picoseconds. MD simulations allow one to view the atomic motions and alter condi tions of the system that may not be easily varied experimentally. Therefore, simulations can provide valuable information about the atomic mechanisms responsible for the resu lting properties and structures. An added feature of MD simulations is that quantities comparable to experimental results can be obtained, especially after the breakthrough development of atomic scale experimental techniques, such as atomic force micros copy (AFM) and scanning tunneling microscopy (STM).

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17 The first MD simulation of cluster-surf ace collisions was made by Mller with a two-dimensional model using Lennard-Jones potentials.[43] Albeit simple, his simulations disclosed the important role played by the cl uster energy per atom in the quality of the thin film. Following Mller’s lead, resear chers around the world, including those who developed the experimental cluster depositi on techniques, performed a variety of MD simulations, sometimes in combination with experimental work. The nucleation and growth of the thin films,[44-49] evolution of clusters after impact,[35, 44, 46, 50-57] defect formation in the substrates,[46-48, 58-61] and film morphology,[42, 62-64] have been examined and documented. These MD simulations provide atomic scale insights into the effects of cluster energy,[47, 48, 65-73] cluster size,[67, 74] and substrate temperature[67, 75-77] on the resultant film structures and properties. As e xpected, these investigations further people’s understanding of the underlying reaction mechanisms [36, 53, 59, 78, 79] as well as the thin film nucleation[44, 46, 49, 80, 81] and defect formation mechanisms.[59] Together with the experimental studies, these MD simulations he lp to provide a comprehensive picture of cluster-solid interactions. 1.2.2 Motivation and Objectives Among various thin films, organic thin films are technologically important especially in electronic a nd optical device applications. For example, organic electroluminescent (EL) devices can produce a strong light emission with a direct current of relatively low voltage.[82] Additionally, deposition of organic materials can make diamond-like carbon films,[83-86] which have many characteristics of bulk diamond including extreme hardness a nd high thermal conductivity. Conventional solvent-free methods to ma ke organic thin films include physical vapor deposition (PVD) and chem ical vapor deposition (CVD).[82-88] Nevertheless, these

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18 methods are not effective at achieving crystall ine structures in the deposited films, and hence, the desired prope rties are not obtained.[30] Energetic cluster beam deposition, however, appears to be su ccessful in this respect.[30] In fact, polyethylene thin films with a structure close to the si ngle crystalline polyethylene,[25] tetraphenylporphine thin films with preferential crystal orientation,[28] and anthracene thin films with superior photoluminescent and electro luminescent properties[25] have been reported using energetic cluster beam depositions. The rese archers at Charles University found that cluster beam deposition could produce phthalo cyanine thin films w ith structures and properties ranging from those of evaporated films to the plasma polymerized samples.[29] These studies indicate that cluster beam de position is indeed a ve rsatile and promising technique to prepare organic thin films for functional devices. Despite the impressive experimental work in organic thin film formation through energetic cluster-solid collisions, there is li ttle fundamental understanding of the reaction and film nucleation mechanisms that occu r during organic cluste r deposition. These problems can be addressed in MD simula tions. Although a large amount of simulation work has been carried out to st udy cluster-solid collisions as mentioned before, most deal with metallic clusters[35, 42, 46-48, 52, 54, 56, 57, 60, 62, 64, 71-73, 77, 80, 81] or noble gas clusters.[43-45, 50, 51, 53, 61, 66, 78, 79, 89, 90] MD simulations of the deposition of fullerene molecules, i.e., carbon clusters, have also been reported.[36, 63, 65, 66, 70, 75, 91-94] For the last six years, the Sinnott group has used MD simulations to study the deposition of organic clusters on diamond surfaces.[95-105] The clusters that have been considered include organic molecular clusters of ethane,[95] ethylene,[95, 96, 100, 101] acetylene,[95-100] and adamantane.[102] Both single cluster depo sition and cluster beam

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19 deposition have been examined. The simulations show that due to the deposition-induced high system temperature and pressure, nume rous addition reactions may occur among the incident molecules and between the impact cluster and the surface when the incident energy is within 3 eV/molecule of the bi nding energy of a single cluster molecule.[95] This prediction is supported by th e experimental work of Lykt ey et al., who showed that polyethylene could be made from energetic collisions of molecular clusters of ethylene in the gas phase;[106] and Sakashita et al., who reported that solid-state polyacetylene was produced under high pressure.[107] These simulation studies have also addressed the dependence of film nucleation and growth on deposition conditions such as molecular reactivity,[95, 100] cluster size,[99, 101] incident energy,[95, 96, 102] impact frequency,[97] surface reactivity,[98, 100] and surface temperature.[100, 101] The formation of craters on the surface has been considered as well. These craters we re found to be able to activate some surface atoms and promote the adhesion of clusters. These simulation results are in agreement with the reported cluster beam deposition experiments for making organic thin films.[25, 28, 30] Varying the angle of incide nt particles has pronounced effects on the growing film morphology and properties. This ha s been shown in both simulations[64, 108-112] and experiments.[113-118] For instance, in vacuum evaporati on, the oblique incidence of vapor atoms is found to result in th in films with anisotropy in va rious macroscopic properties, such as magnetic properties, electrical re sistance, optical and mechanical properties.[119] In atomic ion beam deposition, the nonperpendicular inciden ce leads to non-local shadowing, which is the s ource of the resulting por ous and columnar growth morphology.[108, 113, 114] The incident angle of atomic i on beams is also found to influence

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20 thin film composition,[110, 115] surface-trapping probability,[117] and kinetic energy distribution of the spu ttering surface fragments.[116] Deposition of energetic cluster beams also shows that the surface smoothing effect[64, 111, 118] and the sputtering effect[118] are strongly affected by incident angle. Although extensive simulations have been done by the Sinnott group in investigating the deposition of organic clusters, the effect of incident angle has not been considered previously. Theref ore, one of the objectives of the study reported in this dissertation is to investigate angle effects on the deposition of orga nic clusters. Since a crystalline substrate is used in the simula tions, film nucleation and growth at oblique deposition angles may have crystallographic orientation dependence, which is another factor examined here. One of our previous studies investigated the deposition of an adamantane cluster beam, while all the rest focused on clusters where the constituent molecules were weakly bonded through van der Waals interactions. In this dissertation, clusters with different types of chemical bonding holding the incident particles together are considered. It is the intent ion of this study to provide a more complete description of thin film nucleation and gr owth from energetic organic cluster beam depositions. 1.3 Carbon Nanotube/Polymer Composites Carbon nanotubes posses unique structural electrical, and thermal properties.[120129] Recent developments in the synthesis of carbon nanotubes have improved both their quality and quantity.[130-133] These advances have paved the way for the expected new material applications of car bon nanotubes. Particular effort has been spent in making nanocomposites using these quasi-one-dimensi onal nanostructures as reinforcement to capitalize on their extraordinary mechanic al properties on a macroscopic scale.

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21 1.3.1 Carbon Nanotubes Carbon nanotubes, also known as t ubular fullerenes, consist of sp2-bonded carbon atoms. They were first re ported in 1991 by Sumio Iijima[134] who was studying the material deposited on the cathode during the arc-evaporation synthesis of fullerenes.[135] Depending on the conditions under which th ey are produced, carbon nanotubes can assemble either as multi-layered co-axial t ubes (multiwalled nanotubes, MWNTs) or as single-layer tubes (single-walle d nanotubes, SWNTs). Each layer of the carbon nanotube can be thought of as a cylinde r rolled from a sheet of gra phite, as shown in Figure 1-5. Depending on the growth process, the lengt hs of carbon nanotubes can vary from approximately 100 nm to several microns and the diameters can range from 1 to 20 nm. The manner in which the graphene sheet is rolled into the cylinder can produce carbon nanotubes of various helical structures. As illu strated in Figure 1-6, the “rolling up” can be performed by adding the integer lattice vectors m and n together and then placing the tail and head of the resulting vector on top of each other.[132] As a result, zigzag nanotubes have vectors (n, 0) or (0, m), wh ile armchair nanotubes have vectors (n, n). These are the two achiral na notubes; all other vectors (n m) correspond to chiral nanotubes. Figure 1-5. A graphene sheet rolled into a single-walle d carbon nanotube (SWNT).

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22 Figure 1-6. The “rolling up” of a graphene sheet to produce carbon nanotubes of various helical structures.[132] The three most common methods to produ ce carbon nanotubes ar e the arc, laser, and chemical vapor deposition techniques. The standard carbon ar c-evaporation method can make carbon nanotubes in large quanti ties by carefully choosing the type and pressure of the gas surrounding the arc, and the cooling of th e electrodes and the chamber.[136, 137] However, in this way, only MWNT s are produced. By introducing metal catalysts such as Co, Fe, or Ni into the carbon arc, significant quantities of SWNTs are formed.[138, 139] In 1996, Smalley’s group found an a lternative way to prepare SWNTs.[130] It involved the laser vaporiza tion of graphite and resulted in a high yield of SWNTs. These tubes tended to form aligned bundles (ropes) and had unusually uniform diameters (~1.4 nm). Chemical vapor deposition (CVD) provides more cont rollable routes to produce nanotubes with defined properties.[132] The general nanotube growth mechanism in a CVD process involves the dissociat ion of hydrocarbon molecules (such as C2H2,

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23 C2H4, xylene, benzene, toluene, etc.)[132] catalyzed by transition metal, and dissolution and saturation of carbon atoms in the metal nanoparticle.[133] The synthesized carbon nanotubes are often found to be capped at the ends. The “caps”, different from the sidewall that is mainly made up of hexagonal rings, contain pentagons and heptagons (Figure 1-7).[140] These non-hexagonal rings help to introduce curvature as well as strain into the tube caps. Figure 1-7. A model of a capped SWNT.[140] The as-produced nanotubes often come w ith a number of impurities whose type and amount vary with synthesis methods and conditions. For example, Figure 1-8 shows a TEM image of a SWNT surrounded by cat alyst particles and amorphous carbon. Carbonaceous impurities, such as amorphous car bon nanoparticles and soot, are the most common impurities.[130, 138, 141] The early gas phase purificat ion method, which burnt the crude nanotubes in the oven and simultaneou sly blew air or oxyge n through the system, only resulted in a very low yield (about 1%) of pure nanotubes.[142] One possible reason for this is the uneven burning of the sample. Therefore, li quid phase purification methods on well-dispersed samples were tried. It wa s discovered that by using oxidants such as H2NO3/ H2SO4 [143] or an acid solution of pot assium permanganate (KMnO4),[144] the amorphous carbon and other impurities could be wa shed away effectively. The yield of pure tubes could be as high as 50%.[144] Nanotubes can survive harsh oxidation environments because, like graphite, nanotube wa lls are relatively inert. However, this is

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24 not the case for the caps due to the strain and high degree of curvature in those regions.[145] As a result, the purified na notubes are opened at the ends.[143, 144] The dangling bonds at the ends are usually stabilized by bondi ng with carboxyl or hydroxide groups. Figure 1-8. A SWNT formed in the catalytic carbon arc method.[141] The reason why carbon nanotubes have attr acted wide attention since their discovery is their unusual electrical, mechani cal, and thermal properties associated with their unique structures. For example, they could be insulating, semi-conducting, or metallic depending on their diameter and chirality. This property was first predicted theoretically [146-149] and then verified experimentally.[150, 151] The sp2 carbon-carbon bond in the basal plane of graphite is the strongest of all chemical bonds,[135] but the weakness of the interplanar for ces make ordinary graphite impossible to be used as a structural material. Because of carbon nanotube’s highly perf ect graphene structure, the mechanical stiffness and strength of carbon na notubes are expected to be very high. It was initially difficult to directly probe the mechanical properties of individual nanotubes due to their nanoscale size. However, break s in nanotubes, either in tension or compression, are rarely observed during specimen cutting.[152] This fact implies that indeed nanotubes have very high strength.

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25 Theoretical calculations of the mechanical properties of SWNTs suggest that the Young’s modulus should be close to the in-p lane elastic modulus of graphite (1.06 TPa).[153] The strength of MWNTs will be lim ited by the ease with which each layer slides with respect to the other. In the last few years, a number of experimental measurements of the Young’s modulus of nanotubes using TEM[128] or AFM[154] techniques have been reported. The averag e results from these experiments suggest values for Young’s modulus of individual nanotube around 1 TPa, in good agreement with the theoretical predictions. It is known that carbon fiber reinforced composites are often stronger than steel, but much lighter. Because of this, they are us ed to replace metals in many applications, from parts for airplanes and space shuttles to sports utilities. Carbon nanotubes have been proposed as the ultimate carbon fibers[135] and are considered excel lent reinforcing fibers for the new generation of high performance nanocomposites. 1.3.2 Carbon Nanotube/Polymer Composites There has been considerable effort devoted to studying nanotube/polymer composites.[152, 155-175] Investigations of na notube/metal composites[176] and nanotube/ceramic composites[177] have also been reported. It is found that the nanotubes do stiffen the composites,[163, 169, 170, 173, 177] change the electronic structure of the polymer,[159] improve the conductivity of the composites,[155, 169, 172, 175] and in some cases retard the onset of thermal degradation[170, 175] and protect the polymer from photodegradation.[158] The successful application of carbon na notubes, especially as structural reinforcement in polymer composites, depends on the ability to transfer load from the matrix to the nanotubes.[164] Effective load transfer require s strong interfaci al interaction

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26 between the matrix and the nanotubes.[154] Without special surface treatment, some work on the carbon nanotube/polymer composite s suggested strong adhesion between the matrix and the nanotubes, while others showed the opposite. Wagner et al. reported the observation of multiple nanotube fragmentation under tensile stresses using a nanotube-containi ng thin polyurethane film cured under a UV lamp.[160] Similar fragmentation te sts are routinely performe d to study the fiber-matrix stress transfer ability in fiber-reinforced composites. T hus, their observation proved a rather good load transfer between the nanotube and the polymer. It wa s suggested that the strong nanotube-polyurethane interface arose from the po ssible chemical bonds formed through a photo-induced “2+2 ” cycloaddition, a mechanism as demonstrated in C60 photopolymerization.[178] The same group also studied nanotube/epoxy composites and nanotube fragmentation was again observed.[166] A recent study of carbon nanotube/carbon fiber hybrid composites sugge sted the presence of carbon nanotubes at the carbon fiber/epoxy interface improved th e interfacial shear strength of the composites, which also supports good adhe sion between the nanotube and the polymer matrix.[179] The microscopic and spectros copic study of carbon nanotube/poly( m phenylenevinyleneco -2,5-dioctyloxyp -phenylenevinylene) (PmPV) composites showed excellent wetting of the nanotubes by the pol ymer, again demonstr ating considerable interactions between the nanotube and the polymer.[157] The study of carbon nanotube/poly(phenylacetylenes) (CNT/PPAs) by Tang et al. was very interesting in that the nanotubes were found to be helically wrapped by the PPA chains.[158] The wrapping process was believed to result from the strong H C hydrogen bonds formed

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27 between the polymer with terminal alkyne groups (H C RC ) and the nanotube that is rich in electrons. However, an earlier study of carbon na notube/epoxy composites indicated weak interfacial bonding between the tubes and the matrix.[152] Schadler and co-workers studied the load transfer in carbon nanot ube/epoxy composites in both tension and compression. By monitoring th e shift of the second-ord er Raman peak at 2700 cm-1 which is sensitive to the applied strain, th ey concluded that the load transfer in compression was effective while in tension it was poor, as demonstrat ed by a significant shift in compression and non-shift in tension.[161] Other work gave mixed results on this topic.[167, 171-173] For example, an investigation of the fracture surface of carbon nanotube/polyhydroxyaminoether composites[171] showed that, in most cases, th e polymer adhered to the nanotube. However, in contrast to Wagner’s studies,[160, 166] no broken carbon nanotubes were observed at the fracture surface, which indicate d that the load transfer from polymer to nanotube was not sufficient to fractu re the nanotubes. In studying carbon nanotube/polystyrene (CNT/PS) composites, Qian et al.[173] found effective load transfer from the matrix to the nanotube by compari ng the measured composite modulus with the calculated value assuming there were strong bonds between the two phases. However, when they were watching crack nucleation and propagation using in situ TEM, the composites failed through nanotube pullout (Fig ure 1-9), a phenomenon that occurs when there is poor adhesion between the reinforcement and the matrix. Based on these experimental results, com puter simulations were carried out to study the nanotube/polymer interface, trying to reveal the underlying mechanisms that are

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28 Figure 1-9. In situ straining of a CNT/PS compsite in TEM.[173] important for reinforcement of the matrix. The molecular mechanics simulations and elasticity calculations of th e interfacial characteristics of a carbon nanotube/polystyrene composite indicated that, in the absence of atomic bonding, the interfacial load transfer ability came from electrostatic and van der Waals interactions, deformation induced by these interactions, and stress arising from mismatch in the coefficient of thermal expansion.[174] A molecular dynamics simulation of carbon nanotube pullout from a polyethylene matrix[180] suggested that the in terfacial friction mode l based on a critical force could be used to describe the entire pr ocess of nanotube pullout. In this study, 0.1 nN was predicted to be this critical fo rce for composites with only van der Waals interactions between the nanotube and the matrix. In composites, a high interfacial shear stress between the fiber and the matrix guarantees good load transfer. Typically, the introduction of mechani cal interlocking and the formation of strong bonds, such as covalent or hydrogen bonds, between the reinforcements and the matrix will increase th e interfacial shear stress. Between the two, the second method is much more effective. It is also applicab le to carbon nanotube containing nanocomposites. In making carbon nanotube/epoxy composites, Gong et al. 500 n m

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29 found the addition of surfactant can increase the elastic modulus of the composites by 30% in contrast to those pr ocessed without the surfactant.[163] There, the surfactant acted as a coupling agent. It in teracted with the carbon nanotubes through the hydrophobic segment, and the hydrophilic segment simu ltaneously interacted with the epoxy via hydrogen bonding. Molecular dyn amics simulations of the carbon nanotube/polyethylene composites with and without chemical bonding between the nanotubes and polymer showed that, in non-bonded systems, no perman ent load transfer was observed; while in bonded systems, the shear strength could be enhanced by one or two orders of magnitude.[181, 182] As a result, in order to take real advant age of the high modulus and high strength of carbon nanotubes, chemical functionalization of carbon nanotube especi ally of the carbon nanotube wall, which will favor strong bond formation between the nanotube and the matrix, is necessary. As mentioned above, th e carbon atoms on the walls of nanotubes are chemically stable due to the aromatic natu re of the bonding. The chemistry available for modification of the nanotube wall without breakin g the tubular structure is thus restricted. Recently developed chemical methods, including fluorination,[183-187] and chemical treatment of carbon nanotube s with dichlorocarbene,[188, 189] can chemically functionalize nanotube walls. These modified carbon nanot ubes have better dispersion in solvent without aggregation, which is essential in composite processing, but do not result in significant increase in the interfacial shear st rength. The oxidation of a nanotube wall by using a 3:1 mixture of concentrated H2SO4 (90%)/HNO3 (70%)[190] and the functionalization of the wall vi a electrochemical reduction by using an aryl diazonium salt[191] have been recently reported. These tech niques can tailor the surface prope rties of

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30 a carbon nanotube to be favorable to form chemical bonds during nanotube composite processing. A combined computational and e xperimental study indi cated that the local reactivity of the nanotube walls could be enhanced by the introduction of local conformational strain, such as “kinks” resulting from be nding and “ridges” resulting from torsional strain.[145] This so-called “kinky chemistry” is quite interesting because of its possibility to selectively functionalize the sidewall. 1.3.3 Motivation and Objectives Since the discovery of carbon nanotubes, TEM has been the most frequently used technique to study their structure. When us ing TEM, people noticed the evolution of carbon nanotubes under the irradi ation of an electron beam.[192] Electron irradiation of carbon nanotubes can result in the formation of various atomic scale defects in the nanotube walls.[192-194] Besides, electron irradiation can cause nanotubes to shrink in diameter[193] or merge with other nanotubes through bond breaking and reformation.[195, 196] In other words, electron irradiation can activate the otherwise inert nanotube wall. Similar findings have been seen in simulati ons and experiments of the ion irradiation[197201] and plasma activation[202] of carbon nanotubes. Specificall y, simulations predict that the deposition of ions, such as CH3 +, C+ and Ar+, at low energies of 10-80 eV/ion[199, 200] or higher,[201] can induce cross-links between nanotubes arranged in bundles,[199, 200] neighboring shells in MWNTs,[200] or the nantube and the underlying substrate.[201] A few examples are shown in Figure 1-10.[200] Experiments of the depos ition of mass-selected CF3 + ion beams deposited at 45 eV find strong ev idence of chemical functionalization of the nanotube wall,[200] which confirms the simulation predictions. In addition, both experiments and simulations of ion depositi on on pure polymers show that the deposition can lead to cross-linking between polymer chains.[203, 204] All these findings suggest a

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31 possible novel approach that carbon nanotube/polymer comp osites could be chemically functionalized to form covalent bond at th e interface without firs t treating the tubes and/or exposing them to strong acidic or the other harsh chemical environments as described before. Figure 1-10. Cross-linking formed between na notubes and adjacent shells in the case of MWNT as a result of energetic ion deposition.[200] In this dissertation, molecular dynamic s simulations are used to explore the modification of a carbon nanotube/polystyrene composite through the deposition of a beam of polyatomic ions of C3F5 +. One objective is to determine if polyatomic ion beam deposition is a suitable appr oach to induce covalent cr oss-links between otherwise unfunctionalized nanotubes and th e polymer matrix. The second objective of this study is to examine the effects of the incident en ergy and the nanotube/polymer geometry. The third objective is to determine how the presence of the nanotube in the polymer affects the outcome of the polyatomic ion beam de position relative to deposition on a pristine polymer substrate. 1.4 Organization of the Dissertation The use of empirical potential energy f unctions to describe the interatomic interactions may not be as quantitatively accurate as ab initio or semi-empirical methods

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32 due to the approximations introduced and pa rameter fitting. But, they have obvious advantages over semi-empirical and ab initio methods, especially when large systems and long timescales are desired. In this disse rtation, the reactive empirical bond order (REBO) potential for carbon-based covalent systems is used to describe the short-range covalent bonding. In order to test the accuracy of the REBO potential, in Chapter 2, the simulation results using the REBO potential and a semi-empirical tight-binding scheme are first compared. Since in experiments, both the cluster beam deposition and polyatomic ion beam deposition usually occur at room temperature, a proper temperature control algorithm should be employed in th e simulations. Chapter 3 thus describes several temperature control methods. Their e fficiency specifically in dealing with the deposition systems is presented. Chapter 4 reports the MD simulation results for thin film nucleation via organic cluster beam depositi ons. Chapter 5 presents the MD simulations of chemical modification of carbon nanotube/polymer composites through polyatomic ion beam deposition. Finally, the overall conclusi ons of this work are given in Chapter 6.

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33 CHAPTER 2 COMPARISON OF O(N)/NOTB AND REBO POTENTIAL MOLECULAR DYNAMICS SIMULATIONS In modeling a many-body system, it is esse ntial to find an appropriate method to calculate the interatomic energies and forces. These interactions can be considered using ab initio calculations, semi-empirical methods, or empirical function expressions. In ab initio calculations, all the electrons are treat ed explicitly and quantum mechanically. Thus, they give the most exact results but are the most computationally demanding. Ab initio calculations are usually limited to m odeling small systems containing several hundred atoms. Semi-empirical methods explicitly consider the contribution of some of the electrons (generally some of or all of the valence electr ons), which is usually denoted as the band structure energy; the contributi ons of the other electrons are taken into account via various mathematical expressions fitted to experime ntal data or first principle ( ab initio ) results. Because of their semi-empirical character, these methods usually give fairly accurate results while the computati onal workload is comparatively small, and relatively large-scale simulations (~ 5,000 atoms) are possible. Empirical potential functions are further simplified mathematical expressions that do not explicitly consider any electron contributions, but model the interatomic forces from the interactions of electrons and nuclei by appropriate parameter fitting reasonably well.[205] Due to their great computational efficiency empirical potential functions have obvious advantages for large systems (more than several thousa nd atoms) and long simulation times, although

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34 the results may be subject to errors that can arise from the assumed functional forms and parameter fitting.[205] The order-N nonorthogonal tight-bindi ng (O(N)/NOTB) method of Wu and Jayanthi[206] is a semi-empirical approach that e xplicitly incorporates the band structure energy. This scheme has been successfully applied to study a wide range of problems associated with nanostructures, including the initial stage of growth of Si/Si(001),[207] carbon nanotubes,[208] and Si nanoclusters.[209] The reactive empirica l bond-order (REBO) potential is a refinement of the Abell-Ters off potential and was parameterized by Brenner et al. initially for hydrocarbons.[210, 211] Due to its flexibility to allow bond breaking and reforming with appropriate changes in atom ic hybridization, the REBO potential gives structural predictions for diamond su rface reconstruction consistent with ab initio studies.[212, 213] It has found extensive uses in modeli ng other structures and processes as well, such as chemical processes in reactive hydrocarbon systems,[95, 214-217] properties of fullerenes and carbon nanotubes,[145, 218-225] and mechanical processes associated with indentation, friction and compression.[225-230] An extended REBO potential for Si-Si, Si-C and Si-H interactions has al so been reported to reproduce ab initio predictions and/or experimental results of the equilibrium st ructures and binding energies for C-Si-H systems reasonably well.[231-234] Despite all these successful applications, as is the case with most empirical potentials, there are cases where the results from the REBO potential lack the quantitative accuracy even while the qualitativ e predictions are correct.[235-237] In this work, simulation results from the O(N)/NOTB method and the REBO potential are compared and contrasted. The process investigated is the collision of hydrocarbon clusters on diamond surfaces. This pr ocess usually occurs on the time scale

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35 of a few picoseconds (ps) if the collision happens at hyperthermal (1-500 eV) or higher energies. Molecular dynamics (MD) simulati ons are thus well suited to study this process. For convenience, the MD simulati on using the REBO potential is denoted as empirical MD (EMD), and the one using the O(N)/NOTB method is O(N)/NOTB-MD. The purpose of this work is to check both the qualitative and quant itative predictions from the REBO potential against the results from the O(N)/NOTB method, and thus to obtain a better knowledge of the reli ability of the REBO potential. 2.1 Order-N Nonorthogonal Tigh t-Binding (O(N)/NOTB) Method In the semi-empirical tight-binding scheme, the total energy of a system can be written as[238]: rep bs totU U U (2-1) wherebsU is the band structure ener gy that considers the electr onic contributions to the atomic forces. repUis a pair wise repulsive term, which considers the effects of the overlap interactions and th e possible charge transfer that are neglected in bsU. repUcan be expressed as a sum of suitable empirical two-body potentials () (ijr ): ij ij repr U ) ( (2-2) where ijr is the distance between the i th and j th atom. ) (ijr is obtained by parameter fitting. In the O(N)/NOTB approach of Jayanthi et al.,[206] the band structure energy is expressed as: j i i j j i occ bsH E U, , ) (2 2 (2-3)

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36 where the multiplier 2 takes account of the electron spin, Eis the electronic eigenenergy of the system, j i,is the density matrix, and i jH,is the Hamiltonian matrix element. Therefore, the electronic contribution to the force acting on the ith atom can be evaluated as: j i i j j i i i j j i i bs el ir S r H r U F, , , ,} { 2 (2-4) where j i ,is the energy dens ity matrix, and i jS,is the overlap matrix element. The total force acting on a given atom i, is thus given by i rep el i ir U F F ,. The application of the tight-binding me thod to study a system containing 103-106 atoms is usually restricted by the N3 scaling of the calculation of the total energy and atomic forces. Using the property that0 ) (,ij j ir and 0 ) (,ij j ir as ijr, the summations in Equations (2-3) and (2-4) can be truncated to include only terms within a sphere of radius cutr if it can be established that 0 ) (, ij j ir and 0 ) (,ij j ir for cut ijr r With the truncation, the calculation of th e total energy and the atomic forces will depend linearly on the si ze of the system. That is, it becomes an order-N (O(N)) scaling procedure. Therefore, this O(N)/NOTB scheme can be efficiently applied to a system that contains more than 1000 atoms. In this O(N)/NOTB approach, the paramete rs characterizing the C-H interactions are fit so that the predicted bond lengths and bond angles for C2H2, CH4, C2H4, and C2H6 are in good agreement with experimental results. The MD simulations using the O(N)/NOTB method were performe d by our collaborators in the University of Louisville.

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37 2.2 Reactive Empirical Bond-Order (REBO) Potential The general analytic bondorder potential energy formalism was originally introduced by Abell,[239] in which he showed that the chemical binding energy bUcan be simply expressed as a su m over nearest neighbors: ii j ij A ij ij R br V b r V U) ()] ( ) ( [ (2-5) The functions ) ( r VRand ) ( r VAare pair-additive terms that describe the interatomic repulsions and attractions, respectively. The term ijb is a bond-order term between atoms i and j. A practical implementation of Abell’s bond-order formalism was first developed by Tersoff for group IV elements.[240, 241] By introducing analytic parameterized forms for the bond order term, the Tersoff potential can accurately treat silicon, germanium and their alloys, but is less reliable for carbon.[213] Carbon is a very unique element in that it has a variety of di fferent types of C-C bonding with very different ener gies and bond lengths, which resu lts in a large variety of polymorphic forms, such as diamond, gr aphite, fullerene, and various amorphous phases.[242] The Tersoff potential does not distin guish the chemical character of the bond;[213] therefore, it cannot describe pr ocesses involving a change of bonding characters, such as surface reconstruction a nd chemical reactions, ve ry well. In 1990, the reactive empirical bond-order (REBO) potential for descri bing solid-state carbon and hydrocarbon molecules was reported by Brenner.[210] In this potential, nonlocal terms, which properly account for the chemical bonding changes based on the change of neighboring atoms, are added to the Tersoff potential. Consequently the REBO potential allows for bond formation and breaking with appropriate changes in atomic hybridization, which is crucia l for realistic treatment of such processes as chemical

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38 reactions. Thanks to the deve lopment of the REBO potential, it is now possible to model simple organic chemical reactions within an empirical scheme. However, in the first generation REBO potential, the terms describing the pair in teractions in Equation (2-5) were found to be too restrictive to simu ltaneously fit equilibrium distances, bond energies, and force constants for carboncarbon bonds. What is more, both terms go to finite values as the distance between atom s decreases, which limit the possibility of modeling processes such as en ergetic atomic collisions. Therefore, the second generation REBO potential, using improved analytic functions for interatomic interactions and an expanded fitting database, was developed.[211] The forces associated with rotation about dihedral angles for carbon-carbon double bonds, as well as angul ar interactions associated with hydrogen centers, have also been included. In this study, the second generation REBO potential[211] is used. The analytic terms describing the pair interactions in Equation (2-5) in the second generation REBO potential are written as: r c RAe r Q r f r V ) 1 )( ( ) ( (2-6) n r n c Ane B r f r V) ( ) ( (2-7) The function for the repulsive interactions (Equation (2-6)) goes to infinity as the interatomic distance (r) approaches zero, and the attr active term (Equation (2-7)) has sufficient flexibility to simultaneously fit the bond properties. The variables Q, A, B and are all parameters that are fit to experimental or ab initio data for both hydrocarbon molecules and solid-state carbon, and are adjust ed using a standard fitting routine. The

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39 function ) (r fclimits the range of the covalent interactions. For carbon, the value of ) (r fcwill be one for nearest neighbors and zero for all other interatomic distances. The bond-order term in the second generation REBO potential is written as the sum of terms: ij ji ij ijb b b b ] [ 2 1 (2-8) Values for the functions ijb and jib depend on the local coordination and bond angles for atoms i and j. The dependence on bond angles is n ecessary to accurate ly model elastic properties and defect energies. The function ijb is further expresse d as a sum of two terms: DH ij RC ij ijb b (2-9) where the value of the first term depends on whether a bond between atoms i and j has radical character and is part of a conjugated system. Th e value of the second term depends on the dihedral angl e for carbon-carbon double bonds. Within a single expression, as introdu ced by Abell (Equation (2-5)), the revised REBO potential accurately reflects the bond energies, bond lengths and force constants for carbon-carbon bonds. It has produced an im proved fit to radical energies, conjugated bonding properties, and diamond surface prope rties. It also gives a reasonable description of diamond, graphitic an d hybrid diamond-graphitic structures.[243] The REBO potential describes short-range covalent intera ctions. In order to take into account long-range van de r Waals molecular interactions, Lennard-Jones (LJ) 6-12 potential can be coupled with the REBO pot ential. Thus, the combined expression to calculate the binding energy between atoms i and j is:

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40 ii j ij vdw ij A ij ij Rr V r V b r V U) ()] ( ) ( ) ( [ (2-10) where vdwV is the contribution from the van der Waals interactions, which, in turn, can be expressed as: ] ) ( ) [( 4 ) (6 12r r r Vvdw (2-11) where and are Lennard-Jones parameters.[244] The LJ potential is turned on only when the REBO potential has gone to zero (at about 2.0 for C-C interactions, 1.8 for C-H interactions, and 1.7 for H-H interactions). 2.3 Testing Systems The energetic cluster-beam investigated in this study contains two molecular ethylene clusters. Each cluster is formed by arranging eight ethylene molecules on a three-dimensional grid in which three-di mensional periodic boundary conditions are applied. Therefore there are 48 atoms per clus ter and 16 of them are carbon atoms. First, the cluster molecules are equili brated at 500 K. When the cluster has fully relaxed, it is quenched to 5 K to minimize the internal clus ter kinetic energy. The clusters are then combined together to form a beam. Before deposition, the whole beam is placed about 4 above the surface. The two clusters ar e deposited along the su rface normal at an incident energy of 25 eV/molecule, which co rresponds to a velocity of 13.1 km/s. The distance between the two clusters in the beam is about 4 . Therefore, the two clusters impact the substrate in a consecutive manner, with the second cluster hitting the surface 30.5 fs after the first. Eight hydrogen-terminated diam ond (111) substrates of va rious sizes are used in this study, as indicated in Ta ble 2-1. The largest substrate contains over ten times as

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41 many atoms as the smallest one. These various substrates are chosen in order to compare the computational capability of the two methods. Prior to cluster deposition, all the substrates are equilibrated at 500 K and then cooled to 300 K, which is the temperature that is maintained throug hout the whole deposition proce ss. Periodic boundaries are applied within the impact plane. Table 2-1. Details of the hydrogenterminated diamond (111) surfaces. # of atoms in the substrate 1260 2352 3136 4480 5824 7168 9216 16128 Impact area (2) 455.8 615.1 1166.2 1166.2 1166.2 1166.2 1509.3 2672.9 Thickness () 13.0 13.0 13.0 19.1 25.3 31.5 31.5 31.5 In order to mimic the heat dissipation of a real substrat e and maintain the system temperature at 300 K during the depo sition, the Berendsen thermostat[245] is used in both the EMD and O(N)/NOTB-MD simulations. A pproximately 3-5 rows of atoms at the edges and the carbon atoms of the lower half pa rt of the whole surface slab are thermostat atoms. Therefore, the thermostat atoms form a bathtub-like shape, helping to control the system temperature. The bottom layer of hydroge n atoms for each surface is held rigid to maintain the substrate structure during the deposition. All the other atoms in the substrate and in the cluster beam evolve w ithout any additional constraints. During the deposition, the majority of the incident energy of the cluster molecules is transformed into excess surface kinetic energy. In the case of the larger substrates, this excess surface kinetic energy is quickly dissip ated by the thermostat atoms and does not bounce back to interfere with the chemical interactions taking place at the surface. However, in the smaller substrates, this dissipation does not take place quickly enough and the excess energy is reflect ed back from the boundary of the substrate (this occurs whether or not the bottom layer is held ri gid). This reflection of energy occurs to somewhat different degrees in the EMD and O(N)/NOTB-MD simulations (see the

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42 discussion below). As the point of this study is the comparison of the predictions of these two methods, this reflection of energy does not detract from our objective as long as the results of the deposition on a same surface are compared. For statistical purposes, several trajectori es are performed for each surface and the results are averaged. In the case of the O( N)/NOTB-MD simulations, three trajectories are run for each of the three smallest su rfaces (1260, 2352 and 3136 atoms/surface). In the case of the EMD simulations, the same th ree trajectories are run on the same three surfaces so that the EMD and O(N)/NOTB-MD results may be compared. In addition, since the EMD method is much faster th an the O(N)/NOTB-MD method and more trajectories lead to better statis tical representation of the results, ten trajectories total were run for each of the eight surfaces considered. The time step is 0.2 fs. The simulations run for at least 1 ps with the clusters impacting on the surface during the first 0.16 ps and the film relaxing thereafter. Each O(N)/NOTB-MD simulation typically re quired 12 nodes of an IBM RS/6000 SP2 supercomputer (with 48 CPUs) and ran for about 4 days, while each EMD simulation typically ran for a few hours (the largest simulations ran about one day) on a Compaq Alpha64 workstation. 2.4 Results and Discussion When the molecular clusters come into contact with the surface, numerous chemical reactions occur among the cluster molecules and between the cluster and the substrate, resulting in hy drocarbon thin film nuclea tion and growth. Both the O(N)/NOTB-MD and EMD methods predict that when the clusters impact the substrate with the short time lag of 30.5 fs, many more of the carbon atoms in the film are from the first incident cluster. Furtherm ore, both methods predict that within a given cluster, more

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43 atoms from the lower half of the cluster (close st to the substrate) remain behind to form the film. The atoms that are identified as being pa rt of the resultant thin film include substrate atoms that are displaced from thei r original positions and pushed up into the film while still maintaining a c onnection to the substrate. In addition, some atoms from the cluster may penetrate deeply into the substrate beyond the range of the film. Although these atoms are included in the calculation of the number of atoms from the cluster that adhere to the surface, they are not considered when the structure of the film is examined. The percentage of carbon atoms in cluste rs adhering to the substrate predicted by O(N)/NOTB-MD and EMD for surfaces w ith 1260, 2352 and 3136 atoms/surface is shown in Figure 2-1 The O(N)/NOTB-MD method predicts a higher percentage of adhesion (approximately 20-30% more) than the EMD does for the same surface. In the EMD simulations, when the distance between two atoms is less than 1.73 , those two atoms are considered to have formed a bond. In the O(N)/NOTB-MD approach, when the number of electrons in the bond region is greater than or equal to 0.04, a bond is considered to be formed.[246] When the distance approach is compared to the electron counting approach for the same set of O( N)/NOTB-MD results, the electron counting approach is found to yield resu lts consistent with those of the distance approach in that there is no bond determined on the basis of the electron counting approach with a bond length greater than 1.73 . Hence, the differe nce in the percentage of adhesion between the two approaches is due to differences inherent to the empi rical and tight-binding methods themselves.

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44 Figure 2-1. The percentage of incident carbon atoms that adhe re to the substrate (averaged over three trajectories) versus the size of the substrate. The total number of atoms in each substrate is used to quan tify the substrate size. The predictions from both O(N)/NOTB-MD and EMD approaches are shown. To better characterize this difference, the potential energy curves of three reactions are considered from static calculations us ing the REBO and O(N) /NOTB-MD potentials with a time step of 0.1 fs. The results are plot ted in Figure 2-2. In the figure, the values of ) 0 ( PE where P E is the calculated potential energy, are plotted for easy comparison. The first case is the movement of two ethyl ene molecules towards each other along a path that is horizontal to the carbon-carbon double bonds, shown in Figure 2-2(a). The second case is the movement of two ethylene molecule s towards each other along a path that is perpendicular to the double bonds, shown in Figure 2-2(b) The final case is the movement of two molecular clusters of et hylene (where each cluster contains eight molecules) towards each other, shown in Figure 2-2(c). If one ignores the fine details, one will be struck by the similarities in the overall shapes of the energy curves obtained by the two approaches. This is particularly true in 44 3434 16 19 13 0 10 20 30 40 50 60 70 80 90 100 126023523136 substrate sizeadhesion (%) O(N)/NOTB-MD EMD

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45 Figure 2-2. Potential energy curves calculated with O(N) /NOTB-MD and EMD methods for the three reactions: (a) the moveme nt of two ethylene molecules towards each other in a direction horizontal to the double bonds; (b) the movement of two ethylene molecules towards each othe r in a direction perpendicular to the double bonds; and (c) the movement of two ethylene clusters towards one another. (a) (b) (c) 0 50 100 150 200 2500.4 0.6 0.75 0.77 0.79 0.81 0.83 0.85 1 1.2 1.4 1.55 1.65 1.75 1.85 1.95DISTANCE (angstrom)ENERGY(eV/atom) O(N)/NOTB-MD EMD 0 50 100 1500.9 1.1 1.3 1.5 1.6 1.7 1.8 1.9 2 0 100 200 300 400 500 6000.4 0.6 0.8 1 1.2 1.4 1.55 1.65 1.75 1.85 1.95 2.2 2.6 3DISTANCE (angstrom)ENERGY(eV/atom) O(N)/NOTB-MD EMD 0 10 20 30 401.5 1.55 1.6 1.65 1.7 1.75 1.8 1.85 1.9 1.95 2 -50 0 50 100 150 200 250 300 350 400 4500. 5 0.9 1 .3 1 .7 2 .1 2. 5 2. 9 3 .3 3 .7 4 .1 4 .5 6. 7 7.1 7 .5 7 .9 8. 3 10. 5 1 5 5DISTANCE (angstrom)ENERGY(eV/atom) O(N)/NOTB-MD EMD 0 50 1000.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 2.5

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46 the third case where the energy curves be tween two molecular cl usters of ethylene obtained by the two methods have remarkably similar shapes. However, there are also crucial differences between the energy curves obtained by the two methods. From Figure 2-2, it can be seen that, in all three cases, there are regions of sepa ration close to the C-C bond length where the energy obtained by the NOTB Hamiltonian is less than that obtained by the REBO potential (see the insert in Figure 2-2( c)). The similarities of the energy curves obtained by the two methods are indications that the REBO potential has indeed captured the general ch aracters of carbon-based chemistry. But the differences show that the NOTB Hamiltonian predicts a more attractive interaction and in general a lower potential barrie r in the region of bond-breaking a nd bond formation than the REBO potential. Therefore, the REBO potential may no t be sufficiently flexible to describe all the relevant processes of bond breaking and bond forming in cluster-beam deposition, thus leading to a lower percentage of adhesion. As shown in Figure 2-1, when the subs trate size changes, both the O(N)/NOTB-MD and EMD simulations predict that th e adhesion percentage is approximately constant. When 10 trajectories of EMD simu lations are averaged for each of the eight substrates, the results also di splay little variation in the adhesion percentage with the changing substrate (see Figure 2-3). The fact ors contributing to the deviation in the adhesion percentage include changes in the precise impact sites on the surfaces, thermal fluctuations, and changes in th e elastic collisions among the cl uster molecules, in addition to the effect of the reflected energy fro m the boundary in the case of the smaller substrates.

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47 Figure 2-3. The percentage of incident carbon atoms that adhe re to the substrate (averaged over ten trajectories) versus the size of the substrate. The total number of atoms in each substrate is used to quan tify the substrate size. The results are predicted by the EMD approach. Figure 2-4. Snapshots of the thin film form ed on the hydrogen terminated diamond (111) surface containing 3136 atoms. The black spheres are carbon atoms in the cluster beam, the gray spheres are substrate carbon atoms, and the white spheres are hydrogen atoms. (a) O(N) /NOTB-MD result; (b) EMD result. Typical snapshots of the nucleated th in films predicted by the O(N)/NOTB-MD and EMD simulations are given in Figures 2-4(a) and (b), respectively. It is clear that the film is denser and spreads more widely in the O(N)/NOTB-MD simulations, while in the EMD simulations the film is more chain-like. These comparisons are made in a more quantitative manner by determining the coordina tion of the carbon atoms in the film and 16 1313 9 16 131313 0 10 20 30 40 50 60 70 80 90 100 126023523136448058247168921616128 substrate sizeadhesion (%) EMD (a) (b)

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48 the manner in which the carbon atoms in th e film are bonded to the other film carbon atoms (hereafter referred to as carbon connectivity). Table 2-2 summarizes the coordination of the carbon atoms in the film predicted from the O(N)/NOTB-MD and EMD simulations for surfaces with 1260, 2352 and 3136 atoms/surface (only the averaged values are re ported). Compared to the EMD results, the film with a higher percentage of sp3-hybridized carbon while less sp2-hybridized carbon and no sp-hybridized carbon is predicted from the O(N)/NOTB-MD method. In the EMD simulations, the hybridizati on of the carbon in the film ranges from sp to sp3. In other words, the O(N)/NOTB-MD simulations predict the forma tion of a highly saturated thinfilm structure while the EMD simulations pr edict the formation of a more unsaturated structure. Table 2-3 summarizes the averaged hybridization of th e carbon atoms in the films formed on all eight surfaces pr edicted from the EMD simulations. Table 2-2. The coordinati on of the carbon atoms in th e film predicted by the O(N)/NOTB-MD and EMD simulations (a veraged over 3 trajectories) (%). # of atoms in the substrate 1260 2352 3136 sp / / / sp2 22 16 13 O(N)/NOTB-MD sp3 78 84 87 sp 8 12 8 sp2 23 65 64 EMD sp3 69 23 28 Table 2-3. The coordination of the carbon atoms in the fi lm predicted by the EMD simulations (averaged over 10 trajectories) (%). # of atoms in the substrate 1260 2352 3136 4480 5824 7168 9216 16128 sp 17 12 7 3 20 20 15 11 sp2 29 58 53 70 53 45 46 44 sp3 54 30 40 27 27 35 39 45 A close examination of Tables 2-2 and 2-3 reveals a role reversal in the percentages of carbon atoms with sp2 and sp3 bonding in the film between the 1260 and 2352

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49 atoms/surfaces for the EMD simulations while no such reversal is seen for the O(N)/NOTB-MD simulations. This observat ion can be understood as follows. For EMD simulations, the 1260-atom surface is just too small to allow for a quick dissipation of any substantial amount of the excess surface kinetic energy. Therefore, the reflected excess energy quickly breaks up the remnant sp2-bonded structures in the incoming clusters. This action, in turn, promotes more chemical reactions at the surface, leading to a larger percentage of sp3-bonded carbon atoms. The 2352atom surface, on the other hand, is large enough to dissipa te some of the excess ener gy such that the reflected energy is not sufficient to break up the remnant stable sp2-bonded structures in the incoming clusters, but still enough to break up some of the newly formed sp3-bonded structures at the surface. This faci litates the formation of additional sp2-bonded structures. As the size of the surface increases further, the effect of the reflected energy decreases more. This trend can be clearly seen from the results shown in Table 2-3, which suggests that the effect of the refl ected energy has almost disappeared for the 7168-atom surface in the case of EMD simulations. For the O(N)/NOTB-MD simulations, because the NOTB Hamiltonian is more flexible, the excess surface kinetic energy diss ipates more quickly than the corresponding situation in the EMD simulations. Hence, ev en for the 1260-atom surface, some of the excess energy has already been dissipated to the extent that the re flected energy is only sufficient to break up the sp3 structures formed as a result of chemical reactions at the surface. Therefore, the differences in th e distribution of the percentages of sp2and sp3bonded structures between the tw o cases can also be attribut ed to the rigidity of the REBO potential vs. the flexibility of the NOTB Hamiltonian.

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50 The carbon connectivity within the nucleated films predicted by the O(N)/NOTB-MD and EMD simulations for surfaces with 1260, 2352 and 3136 atoms/surface is shown in Table 2-4 (only the averages are given). In the table, C1 stands for the percentage of carbon atoms connected to one other carbon atom, C2 stands for the percentage of carbon atoms connected to two other carbon atoms, and so on. Therefore, the summation of C1 and C2 indicates the percentage of carbon atoms bonded in a linear structure, while C3 and C4 indicate the percentage of carbon atom s connected in the branched and networked structure, respectively. For each surface, the carbon connectivity within the film predicted by O(N)/NOTB-MD is different from what is predicted by the EMD simulations. In general, O(N)/NOTB-MD predicts more branched or networke d structures and less linear structure than the EMD simulations. Wh en both the coordination and the carbon connectivity of the f ilm carbon atoms are cons idered, the O(N)/NOTB-MD method is found to predict the formation of a more diamond-like thin film while the EMD simulations predict a more linear unsaturated polymer-like thin film. Table 2-4. The carbon connect ivity of the carbon atoms in the film predicted by O(N)/NOTB-MD and EMD simulations (a veraged over 3 trajectories) (%). # of atoms in the surface 1260 2352 3136 C1 30 29 42 C2 46 37 29 C3 22 34 25 O(N)/NOTBMD C4 2 / 4 C1 49 30 46 C2 37 65 54 EMD C3 14 5 / 2.5 Conclusions The simulation results for ethylene mo lecular cluster depos ition predicted by O(N)/NOTB-MD and EMD using REBO potential ar e compared. The results of these two methods do not agree perfect ly well with each other, es pecially the quantitative

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51 predictions. For instance, the structures of the resultant thin films are significantly different from one another. Nevertheless, th e qualitative predictions are comparable. For example, both methods predict thin-film nucl eation through rapid chem ical reactions and most of the atoms in the nucleated thin film are from those incident clusters closest to the substrate. This comparison study shows that the RE BO potential has in deed captured the general characters of carbon-based chemistry. Ho wever, the differences in the predictions from the two methods indicate that as co mpared to the NOTB Hamiltonian, the REBO potential is more rigid, and hence may not be sufficiently fl exible to describe all the relevant processes of bond breaking and bond forming. A key point is that NOTB Hamiltonian predicts a more attractive interac tion and in general a lower repulsive barrier than the REBO potential. These results a nd conclusions appear in Reference [247].[247] In modeling thin film deposition of amorphous carbons, Jger and Albe observed that the REBO potential predicted a structure with lower sp3 content than the experimental results. But when the cutoff distance (2 for C-C interactions in REBO potential) was slightly increased, a st ructure with realistic density and sp3 content could be produced.[236] The study of H-atom association with diamond surfaces by Hase and coworkers also pointed out that, the major reas on of the quantitative inaccuracy of REBO potential was the potential’s shorter range. But, within the REBO potential cutoff, the predicted results agree very well with the ab initio calculations.[235] Therefore, in the case of energetic collisions, if th e incident energy is high enough to bring the particles into close contact (well within the potential cutoff) prior to any reaction, the predictions from the REBO potential should be reliable.

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52 In this dissertation, the incident energi es used in the following simulations of organic molecular cluster beam deposition and polyatomic ion beam depositions are much higher. The REBO potential’s shorter ra nge is thus not of si gnificant concern. In addition, the systems considered c ontain more than 10,000 atoms. Although O(N)/NOTB-MD is a more accurate method, it is more computationally expensive than the EMD method for a surface of a given size. It is practically impossible for a simulation of a system that consists of more than 10,000 atoms by using the NOTB method within a reasonable period of time. Empirical potenti al is necessary to study the collective phenomena of many atoms or for long times at an atomic scale. Therefore, the second generation REBO potential is used in the fo llowing simulations to consider the shortranged interatomic interactions, and the predictions are believed to be at least qualitatively accurate.

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53 CHAPTER 3 TEMPERATURE CONTROL METHODS Energetic particle deposition is a process that involves a flux of energy into or out of a system. In addition, complex and rapi d chemical reactions may occur between the incident particles and the substrate atoms, which lead to big changes in the system energy. These energy changes are reflected in variations in system temperature. Experimentally, particle deposition is usually carried out at specific temperatures to obtain the desired properties. Furthermore, macroscopic substrates dissipate the excess energy from the deposition process through, fo r example, lattice vibrations through the extended lattice. To model such processes atomistically, molecular dynamics simulations can be performed in a canonical ensemble, where the number of particles, temperature, and volume are held constant. Periodic boundary conditions are often used in these simulations to mimic an infinite or semi-inf inite system with just a few thousand atoms and to keep the volume constant. Sometimes, certain amounts of boundary atoms need to be fixed to keep the structure of the simu lation system from reconstructing. However, these boundary conditions can re sult in the nonphysical refl ection of energy from the boundary, which will then produce spurious eff ects on the simulation results. Therefore, the simulations make use of methods that can allow some atoms to effectively absorb all the extra energy pumped into a system (inc luding any reflected energy) and thus successfully control the system temperature in a physically reasonable manner. Simulations that implement these methods ar e called constant temperature simulations.[2]

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54 Temperature is a thermodynamic qu antity. For a system containing N particles, the temperature can be related to the average kinetic energy ( K) of the system through the principle of equipartition of energy, which states that every degree of freedom has an average energy of 2T kB associated with it.[248] That is, 2 2 12T k N m KB f N i i v (3-1) where fNis the number of degrees of freedom, Bkis the Boltzmann constant, and T is the thermodynamic temperature. Similarly, th e instantaneous kinetic temperature can be defined as B f insk N K T 2 (3-2) The average of the instantaneous kinetic temperature is equal to the thermodynamic temperature. Since the temperature is related to the kinetic energy, in order to control the temperature, the velocities of the particles in the simulation system must be adjusted. One way to do this is to directly rescale the velo city of each particle, as shown in Equation (33): ins old newT T 2v v (3-3) where newv is the rescaled velocity, and oldv is the velocity before the rescaling. Although this method, called the velocity resca ling method, is very simple and adds (or subtracts) energy to (or from) the system effi ciently, it is important to recognize that it actually keeps the kinetic energy constant, wh ich is not equivalent to the condition of

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55 constant temperature. At thermal equilibrium both kinetic energy (i nstantaneous kinetic temperature) and potential energy fluctuate. Therefore, the direct velocity rescaling method is somewhat coarse and far removed from the way energy is actually dissipated.[2] Better and more realistic constant temp erature schemes have been proposed. Among these schemes, the generalized Langevin equation (GLEQ) approach,[249] Berendsen method,[245] and Nos-Hoover thermostat[250-253] are the most widely used. In all these schemes, the velocities of the part icles are adjusted to maintain the system temperature at a constant value. Simulation systems generally consist of an impact zone, where atoms move only in response to normal Newtonian dynamics, that is embedded in a thermostat zone, where the velocities of the atoms are modified using the temperature control schemes. The thermostat zone not only acts as a heat reservoi r but is also used as a cushion to absorb any reflected energy waves. In this study, both the GLEQ approach a nd the Berendsen method are used in the thermostat zone in constant temperatur e MD simulations of cluster deposition on surfaces. A variation of the re gular GLEQ approach and a combined thermostat of the GLEQ and Berendsen methods ar e also tested. The goal of th is work is to determine which thermostat method is the best for use in MD simulations of energetic particle deposition on surfaces to realistically contro l the temperature and reduce the amplitude of reflected waves from the boundaries of the simulation unit cell edges. 3.1 Methods of Interest 3.1.1 Generalized Langevin Equation (GLEQ) Approach The generalized Langevin equation (GLEQ ) approach proposed by Adelman and Doll[249] is developed from generali zed Brownian motion theory. It models solid lattices

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56 at finite temperature using the methods of stochastic theory. In this approach, the molecular system of interest can be thought of as being embedded in a “solvent” that imposes the desired temperature; the molecu les are regarded as solutes. The solvent affects the solute through the addition of two terms to the normal Newtonian equation of motion: one is the frictional force an d the other is the random force. The frictional force takes account of the fr ictional drag from the solvent as the solute moves. Since friction opposes motion, this force is usually take n to be proportional to the velocity of the par ticle but of opposite sign: ) ( ) (t tfrictionv F (3-4) The proportionality constant, is called the friction cons tant. Using the Debye solid model, can be simply expressed as D 6 1 (3-5) where D is the Debye frequency. The Debye freque ncy is related to the experimentally measurable Debye temperature DT by D B DT k (3-6) The random collisions between the solute and the solv ent is controlled by the random force, R(t). This random force is assumed to have no relation to the particle velocity and position, and is often taken to follow a Gaussi an distribution with a zero mean and a variance 2 given by[217] t T k mB 22 (3-7)

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57 where T is the desired temperature, and t is the time step. This random force is balanced with the frictional force to maintain the temperature.[217] Therefore, the equation of moti on for a “solute” particle is ) ( ) ( ) ( ) ( t t t t m R v F a (3-8) which is called the Langevin equation of motion. Following the Langevin equation of motion instead of Newton’s second law, the ve locity of the system particle is thus gradually modified to bring the instantaneous kinetic temperature closer to the desired temperature. The GLEQ appro ach is a proportional contro l algorithm that changes the temperature exponentially as a function of and the initial conditions.[254] This approach often gives a good representation of ener gy relaxation in su rface scattering simulations.[249] It also satisfactorily de scribes heat dissipation at boundaries and has been found to be best suited for thin film deposition processes.[254] In practice, some other expressions for th e frictional force and random force can be selected to better describe the physical condition of the system.[254] However, the expressions mentioned above are the simple st, and hence, the most computationally efficient. In simulations where the thermostat zone is far away form the zone of interest, the results using these expression s have proven to be reliable.[217] In this study, the GLEQ approach using the expressions described a bove for the frictional force and random force is chosen to control the simulation temperature. 3.1.2 Berendsen Method Before the introduction of the Berendsen me thod, it is worthwhile to first mention the Andersen method. The Anderson method of temperature control was proposed in 1980.[255] This method can be thought of as a syst em that is coupled to a thermal bath

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58 held at the desired temperature. The c oupling is simulated by random “collisions” of system particles with thermal bath particles. After each collision, the velocity of the randomly chosen system particle is reset to a new value that is randomly drawn from the Maxwell-Boltzmann distribution corresponding to the desired temperature. In practice, the frequency of random collisi ons is usually chosen such th at the decay rate of energy fluctuations in the simulation is comparable to that in a system of the same size embedded in an infinite thermal bath. This method is simple and consistent with a canonical ensemble, but it intr oduces drastic change to th e system dynamics. It is therefore not appropria te to use the Andersen met hod to study dynamical properties although it is appropriate to study static pr operties such as density or pressure.[2] A more practical approach is the Berendsen method.[245] Just as in the Anderson method, the system is coupled to an imagin ary external thermal bath held at a fixed temperature T However, the exchange of thermal energy between the system and the thermal bath is much gentler. Instead of drastic ally resetting the velocity of the particle to a new value, the velocity of the particle is gradually scaled by multiplying it by a factor given by 2 1) 1 ( 1 ins TT T t (3-9) where t is the time step, and T is the time constant of the coupling. In this way, the velocities of the particles are adjusted such that the instantaneous kinetic temperature insT approaches the desired temperature T The strength of the coupli ng between the system and the thermal bath can be controlled by using an appropriate coupling ti me constant. If a quick temperature control

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59 is desired, a small coupling time constant can be chosen. Consequently, the value of will be big and the change of the velocity wi ll be drastic. On the other hand, if a weak coupling is needed to minimize the disturba nce of the system, a large value can be assigned to the coupling time constant. In the evaluation of their own method,[245] Berendsen et al. concluded that static averag e properties were not significantly affected by the coupling time constant, but the dynamic properties were strongly dependent on the choice of the coupling time constant. Thei r testing showed th at reliable dynamic properties could be derived if the coupling time constant was above 0.1 ps. The Berendsen method is very flexible in that the coupling time constant can easily be varied to suit the needs of a given application. The bigge st advantage of the Berendsen method over the Anderson method is that it gen tly modifies the veloc ities, and therefore, the change of the system dynamics is not so dramatic. However, caution must be taken when using the Berendsen method because it does not rigorously reproduce the canonical ensemble, and thus the distribution genera ted from this method is wrong although the averages are usually correct. The Berendsen method implemented in our simulations is the one used by our collaborators at the University of Louisville. Based on their simulation experience, the ratio of Tt in Equation (3-9) is set to be 0.1 because it gives the best compromise between ideal temperature control and disturbanc e of the physical behavior of the system. 3.1.3 Variation of GLEQ Approach a nd a Combined Thermostat of GLEQ Approach and Berendsen Method In their MD simulations of energetic pa rticle beam deposition, Haberland et al. claimed that the regular G LEQ approach was not good enough to reduce the artificial effects caused by the reflected waves from the boundary of the simulation box.[256] Their

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60 system contained heavy clusters of more than 500 metal atoms per cluster, and the incident energy was typi cally in the keV range.[42, 64, 73, 256-258] They suggested an improved method in which the original thermost at atoms were replaced by fewer, heavier atoms.[256] This allows one to choose a larg e thermostat zone without losing computational efficiency. Therefore, the b ackscattering of the elastic wave could be sufficiently delayed. In addi tion, the atoms at the boundary of the impact zone and the replacing thermostat zone are damped relative to the motion of their neighbors. This is an efficient damping mechanism, especially fo r the high frequency part of the reflected wave.[256] However, the replacing thermostat lattice should have the same elastic properties as the bulk and match th e lattice structure of the impact zone. This is relatively easy to achieve for FCC materials but nontrivial for materials with othe r lattice structures. Although Haberland’s modified GLEQ appro ach is presently restricted to FCC materials, it works well at damping the mo tion and energy of the atoms at the boundary between the impact zone and the thermostat zone. This improvement can be readily included in the conventional GLEQ approach. In this study, a modified GLEQ approach, called the MGLEQ method, that includes extr a damping for those boundary atoms and is applicable to systems of any crys tal structure, is discussed. It is also rigorously tested to assess its effectiveness to both control the system temperature and reduce the amplitude of reflected energy waves. Comparing the GLEQ approach with the Berendsen method, the GLEQ approach makes more physical sense and modifies atomic velocities more gently. Nevertheless, the GLEQ approach involves extra calculations of forces; therefore it is slightly more complicated and time-consuming than the Berendsen method. In this work, a combined

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61 thermostat scheme of the GLEQ approach and the Berendsen met hod (hereafter denoted as BnG) is applied to the thermostat atom s as well. The combination is realized by dividing the original thermostat zone into two smaller zones: the one that directly borders the impact zone has the GLEQ scheme app lied to it while the other has the Berensen scheme applied to it. Testing is done to a ssess whether this combined method combines the advantages of these two methods. 3.2 Testing Systems The deposition of a single C20 molecule on a hydrogen-terminated diamond (111) substrate at room temperature (300 K) is cons idered as a test of these four thermostat schemes. The initial distance between the de positing carbon cluster a nd the substrate is around 4 and the C20 is deposited along the surface norma l. The substrate contains an impact zone of atoms that is 2.4 nm 2.4 nm 1.0 nm. This impact zone is embedded in a thermostat zone of atoms with four walls th at are 1.0 nm thick and a bottom layer that is 1.6 nm deep, as schematically illustrated in Figure 3-1. The dimensions of the whole substrate are therefore 3.4 nm 3.4 nm 2. 6 nm. The number of atoms contained in the impact zone and the thermostat zone is 1,280 and 4,320, respectively. The bottom hydrogen layer is fixed to keep the subs trate from reconstructing or moving. Various incident energies (1 eV/atom, 5 eV/atom, 10 eV/atom, 20 eV/atom and 40 eV/atom) are considered. The REBO potential[211] coupled with long-range LennardJones (LJ) potentials[2] is used to calculate the interatomic forces for the atoms in the cluster and in the impact zone. These atoms ar e denoted as active atom s. The velocities of the atoms in the thermostat zone are modified using the four temper ature control schemes described in Section 3.1 to adjust the ener gy flow within the system. These atoms are therefore called thermostat atoms.

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62 Figure 3-1. The substrate layout. (a) the impact zone; (b) the impact zone embedded in the thermostat zone. 3.3 Results and Discussion Deposition at 1 eV/atom is considered first. This incident energy is well below the binding energy of the carbon atoms in the C20, which is approximately 5.9 eV/atom.[66] Therefore, during deposition, the original fullerene cage structure is not destroyed although deformation is observed. The degree of deformation induced by the collision varies slightly when differen t temperature control methods ar e applied to the thermostat atoms. The cluster only deforms a little in both the GLEQ and MGLEQ approaches, but it deforms more in the Berendsen and BnG method s. In all cases, the cluster does not attach to the substrate; instead, th e deformed cluster bounces back into the vacuum and gradually recovers its original cage structure. A reference simulation, in which the REBO potential coupled with the LJ potential is used to consider the interatomic forces in both the impact and thermostat zones, is performed at the incident energy of 1 eV/ato m. In this case, all the atoms (except the bottom fixed hydrogen atoms) follow normal Newtonian dynamics. Since there is no special temperature control method introduced, a big substrate is requir ed to dissipate the extra energy. In this reference simulation, th e same impact zone is thus embedded in a (b) (a)

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63 much bigger thermostat zone (which contai ns 14,374 thermostat atoms). The dimensions of this reference substrate are 5.2 nm 5.2 nm 3.1 nm. In this reference simulation, although there is no damage to the fullerene molecule upon collision, its original cage structure deforms significantly. The whole defo rmed molecule then leaves the substrate and slowly recovers. The temporal evoluti ons of the substrate temperature in the reference simulation and the simulations usi ng the four temperature control methods are plotted in Figure 3-2. Even if the thermostat zone in the reference substrate is at least Figure 3-2. The temporal evolution of th e substrate temperature in the reference simulation and the simulations using the four temperature control methods at the incident energy of 1 eV/atom. three times as big as the thermostat zone used in the simulations where special temperature control methods are applied, th e energy dissipation obviously is not effective in this reference substrate because the temp erature fluctuates about 392 K. In contrast, after 3 ps, the substrate temperature is less than 320 K when various temperature control methods are employed (314 K in the case of the GLEQ and MGLEQ approaches, 317 K and 318 K when the Berendsen method and the combined thermostat of GLEQ approach and Berendsen method are used, respectively). This finding provides direct evidence as to

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64 why effective temperature control methods ar e necessary in the simulation of energetic deposition at constant temp erature. The four temperat ure control methods perform equally well at this low incident energy in that the four curves essentially overlap, as displayed in Figure 3-2. Figure 3-3. The temporal evolution of the s ubstrate temperature in the simulations using the four temperature control methods at the incident energy of (a) 5 eV/atom, (b) 10 eV/atom. When the same deposition occurs at 5 eV/a tom, the behavior of the system is almost the same in all the four cases where the different temperature control methods are used. This incident energy is high enough to induce reactions between the cluster and the substrate. Therefore, although no apparent dama ge to the fullerene molecule is observed, the severely deformed cluster sticks to the s ubstrate and tends to recover its cage structure during atomic relaxation after the collision. The outcomes of de position at 10 eV/atom are similar to the outcomes predicted to occu r at 5 eV/atom except th at the cage structure of the C20 is destroyed at 10 eV/atom. The damaged cluster also attaches to the top of the substrate. The changes of the substrate temp erature are portrayed in Figures 3-3(a) and 050010001500200025003000 300 350 400 450 500 550 600 Substrate Temperature (K)time (fs) GLEQ Berendsen MGLEQ BnG 5 eV/atom050010001500200025003000 300 350 400 450 500 550 600 Substrate Temperature (K)time (fs) GLEQ Berendsen MGLEQ BnG 10 eV/atom(a) (b)

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65 (b) for depositions at 5 eV/atom and 10 eV/atom, respectively. As shown in these figures, the change of the substrate temperature during the first 1 ps is diffe rent when different temperature control methods are used. It a ppears that the Berends en method reduces the temperature most dramatically at the beginni ng. However, during the subsequent process, the four curves overlap. When the deposition takes place at 20 eV/atom, the cage structure of the C20 molecule is completely destroyed. The fragme nts from the cluster react with the substrate carbon atoms and form a strongly adhered f ilm. The phenomena observed are more or less the same in the systems where different temperature control methods are used, but the difference in the substrate temperature ch ange is more apparent. As shown in Figure 3-4(a), during the first 1 ps, the Berendsen method induces the most dramatic decrease while the reduction in the temp erature is much gentler usi ng the other three methods. At about 1.5 ps, the fluctuation in the temperat ure begins to stabilize at about 340 K in the system using the Berendsen method. However, the stabilization is not achieved in the systems where the other three methods are used until after 2 ps. The GLEQ approach appears to be the best method to control the temperature at this incident energy because the substrate temperature after 3 ps is 327 K in the GLEQ approach but is about 335 K using both the MGLEQ approach and the BnG method. A direct way to demonstrate the energy di ssipation capability of the temperature control scheme is to monitor the change of the system energy. In the deposition system considered here, the largest change in the system energy comes from the kinetic energy change because only those atoms involved in chemical reactions will have a substantial change in their potential en ergy, and the fraction of these atoms in the considered

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66 Figure 3-4. The temporal evolution of (a) th e substrate temperature and (b) the kinetic energy per active atom in the simulations using the four temperature control methods at the incident energy of 20 eV/atom. 050010001500200025003000 0.00 0.05 0.10 0.15 0.20 0.25 10001500200025003000 0.05 0.10 KE (eV/active atom)time (fs) GLEQ Berendsen MGLEQ BnG(a) (b) 050010001500200025003000 300 350 400 450 500 550 600 10001500200025003000 300 350 400 Substrate Temperature (K)time (fs) GLEQ Berendsen MGLEQ BnG

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67 deposition system is very small. Therefore, the change of the kinetic energy can represent the change of the whole system energy. Figure 3-4(b) gives the temporal variations of the kinetic energy per active atom for deposition at an incident energy of 20 eV/atom. This figure better separates the f our curves corresponding to ea ch temperature control method than the temporal evolution of the substrat e temperature. As clearly shown in Figure 34(b), before the relaxation st arts (at about 1 ps), the Be rendsen method dissipates the extra energy most quickly, and the combined thermostat of the G LEQ approach and the Berendsen method dissipates the energy most slowly. The curves generated from the GLEQ and MGLEQ approaches overlap at this early stage. Howeve r, at the relaxation stage, the curve of the GLEQ approach begins to separate from the curve of the MGLEQ approach. Apparently, the MGLEQ approach does not reduce the energy as much as the GLEQ approach under this deposition condi tion. While the average kinetic energy fluctuates about 0.06 eV/atom in the Bere ndsen method after 1.5 ps, this quantity continues to drop in both the GLEQ approach and BnG method. At 3 ps when the simulation stops, the GLEQ approach and th e combined thermostat appear to have performed the best at removing th e excess energy in the system. Although the GLEQ approach is the best among the four methods for energy dissipation and temperature control at 20 eV /atom, it becomes the worst at a higher incident energy of 40 eV/atom. As demonstrat ed in Figure 3-5, bot h the final substrate temperature and the average kinetic energy per active atom are the highest in the system where the GLEQ approach is used. The performance of the Berendsen method is not satisfactory either. The best method in this ca se is the combined thermostat of the GLEQ approach and the Berendsen method, which resu lts in the lowest substrate temperature

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68 Figure 3-5. The temporal evolution of (a) th e substrate temperature and (b) the kinetic energy per active atom in the simulations using the four temperature control methods at the incident energy of 40 eV/atom. 050010001500200025003000 300 400 500 600 700 800 Substrate Temperature (K)time (fs) GLEQ Berendsen MGLEQ BnG050010001500200025003000 0.0 0.1 0.2 0.3 0.4 KE (eV/active atom)time (fs) GLEQ Berendsen MGLEQ BnG(a) (b)

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69 and the average kinetic energy. The modified GLEQ approach also performs better than either the GLEQ approach or the Berendsen method. Snapshots from the simulations at various moments during the deposition at the incident energy of 40 eV/atom demonstrate the different responses of the substrate when different temperature control schemes are used (Figure 3-6). At 3 ps when the simulation stops, the substrate where the GLEQ approach is employed suffers the smallest amount of damage; however, the largest amount of disorder to the substrate structure is observed in the surface where the combined thermostat is used. Between approximately 0.08 ps to 0.24 ps, the compressed substrate moves upward. Such movements are depicted in Figure 3-7 for the four substrates with different temperature control schemes applied. Although the four displacement fields look similar, the details are different, especially the displacements of the atoms in the top right corner (see the circled areas in Figure 3-7). The movement of these atoms shows a pattern of the reflected wave from the edge in the substrate using the GLEQ approach. This reflected wave could cause over-relaxation of the substrate atoms, which somewhat “heals” pa rt of the damage to the structure. Such patterns are also seen in the substrates using the Be rendsen method and the MGLEQ approach, but are not clearly present in the substrate where the combined thermostat is used. Therefore the combined thermostat of the GLEQ approach and the Berendsen method more satisfactorily suppresses the amplit ude of the reflected wave than the other three schemes. In summary, at low incident energies ( 10 eV/atom in this study), the four temperature control methods are all sufficient to control the system temperature and delay the backscattering of the reflected wave. When the incident energy becomes high, the

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70 Figure 3-6. Snapshots of the systems using the four temperature control methods at various moments at the incident energy of 40 eV/atom. Figure 3-7. The displacement fields from t = 0.08 ps to t = 0.24 ps in the cross section of the (111) plane using the four temperat ure control methods at the incident energy of 40 eV/atom. (a) GLEQ ap proach, (b) Berendsen method, (c) modified GLEQ approach, and (d) the combined thermostat of the GLEQ approach and the Berendsen method. GLEQ Berendsen MGLEQ BnG t = 0.08 ps t = 0.24 ps t = 3 ps (a) (b) (c) (d)

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71 different performance of the four methods beco mes apparent. This difference results from their different abilities to absorb energe tic waves propagating through the system at various frequencies. The Berendsen method re duces the energy quickly at the early stage of the process, and quickly brings the system to equilibrium. But the Berendsen method is not as efficient at absorbi ng enough of the reflected wave when the incident energy is high, which results in a relatively high temp erature and energy when the system reaches the equilibrium state. At m oderate incident energies (for example, 20 eV/atom), the GLEQ approach is still capable of dissipating the extra ener gy. Nevertheless, it fails at higher incident energy. This result is c onsistent with Haberl and’s conclusion as mentioned in Section 3.1.3.[256] The modified GLEQ approach that intr oduces extra damping at the boundary atoms between the impact zone and the thermostat zone does indeed improve the capability of the system to control the temperature as we ll as absorb the reflected wave when the incident energy is high. The combined th ermostat of the GLEQ approach and the Berendsen method removes the excess energy in the most gradual manner, and the system is usually the slowest one to reach th e equilibrium. But, this simple combination is superior to either the GLEQ approach or the Berendsen method, especially at a high incident energy if enough time is allowed for the relaxation. This can be explained as follows. The velocity adjustment algorithm in the GLEQ approach is different from that in the Berendsen method. The frequency range of the energetic wave that could be effectively absorbed by the GLEQ approach is therefore different from the Berendsen method. When the cluster collides with the s ubstrate at a high incident energy, the range of the resultant energy wave frequency is wider, which may cover both the effective

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72 ranges of the GLEQ approach and the Berendsen method. Th erefore, when neither the GLEQ approach nor the Berendsen method is able to completely absorb the reflected wave, their combination can do much better. However, if the substrate size is too small relative to the incident energy, none of the temperature control schemes will work well enough to remove the extra energy. In this study, a small substrate with dimensions of 2.8 nm 2.8 nm 1.3 nm is also considered in the deposition at 40 eV/atom. The number of active atoms and thermostat atoms contained in this substrate are about 3 1 of those in the substrate considered above. Both the temporal evolution of the substrat e temperature (Figure 3-8(a)) and the average kinetic energy per active atom (Figure 3-8( b)) are essentially the same in the Figure 3-8. The temporal evolution of (a) th e substrate temperature and (b) the kinetic energy per active atom in the depositions on the small substrate using the four temperature control methods at the incident energy of 40 eV/atom. systems where the four temperature control sc hemes are used. As given in Figure 3-8(a), the substrate temperature finally fluctuates at about 520 K, wh ich is too much higher than the desired temperature. After 1.5 ps, the system appears to re ach equilibrium and 0100020003000400050006000 200 400 600 800 1000 1200 Substrate Temperature (K)time (fs) GLEQ Berendsen MGLEQ BnG0100020003000400050006000 0.0 0.2 0.4 0.6 KE (eV/active atom)time (fs) GLEQ Berendsen MGLEQ BnG(a) (b)

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73 extended relaxation does not help to redu ce the temperature and the energy, which indicates the reflected wave bouncing back and forth within the system. 3.4 Conclusions In deposition experiments, the temperatur e of the substrate experiences a thermal spike when the incident particles collide with the substrate particles. The heat is then conducted away from the site of the collisi on quite quickly through the substrate, causing the temperature to drop exponentially.[254] Appropriate temperat ure control methods, which can effectively dissipate extra energy in a system, are thus necessary to model such processes. The dissipation of extra energy not only helps to control the temperature but also absorbs the artificial reflected wave. In this chapter, four temperature control methods are used to model energetic cluster deposition on a solid substrate, which is a stringent test of temperature control methods. These methods include the GLEQ approach, the Berendsen method, a variation of the GLEQ approach where extra damping is introduced to the boundary atoms between the impact zone and the thermostat zone, and a combined thermostat of the GLEQ approach and the Berendsen method. The performance of the temperature c ontrol methods depends on the incident energy and the substrate size. No matte r which method is chosen, a large enough substrate is first required to realistically model the deposition process. The Berendsen method is very effective at removing excess energy at the early stage; however, the resultant equilibrium properties are not alwa ys the best. The GLEQ approach using the Debye solid model performs well if the incident energy is not too high. At a high incident energy, the modified GLEQ approach is be tter than the regular GLEQ algorithm due to the extra damping. Surprisingly but not une xpectedly, the simple combination of the GLEQ approach and the Berendsen method app ears to be successful at controlling the

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74 system temperature when either the GLEQ a pproach or the Berendsen method fails at a high incident energy. It should be recognized that there is no realistic counterpa rt to the thermostat atoms because they do not obey Newton’s second law. The number of thermostat atoms should be large enough to bring the system temperatur e to the desired value. But in order to get reliable simulation predictions the thermostat zone should be far away from the area where the processes of interest occur. This requires the impact zone, where the atoms follow the normal Newtonian dynamics, to be large enough to be realistic while remaining within the limitations of the available computer system. The following simulations model the deposition of particles at moderate inci dent energies. Each incident particle contains less than 50 atoms whose atomic number is less than 10. In these simulations, the substrate with appropriate size and arrangement of the impact zone and the thermostat zone is first determined de pending on the incident energy and the size of the incident particle. The GLEQ approach is chosen because this approach is good enough to handle the deposition of small particle s at moderate incident energies and it realistically describes th e exponential decrease of the substrate temperature.[254]

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75 CHAPTER 4 THIN FILM FORMATION VIA OR GANIC CLUSTER BEAM DEPOSITION Cluster deposition on solid substrates has received growing attention over the last three decades. Compared to single atom depositi on, cluster deposition is unique in that it produces a high concentration of energy and mass in a very localized region. The interaction between the cluster and the substr ate occurs just near the surface. And the cluster won’t penetrate deeply in to the bulk. As a result, there is relatively little damage to the substrate. This method is theref ore well suited to generate thin films.[19, 24, 25] The properties of the thin film can be controll ed by changing the deposition conditions, such as the incident energy, impact species, cluster size, deposition angle, substrate temperature, etc. In this study, thin film formation through organic molecular cluster beam deposition is examined by using mo lecular dynamics simulations. The second generation reactive empirical bond order (REBO) potential pa rameterized by Brenner et al. for hydrocarbon systems[211] coupled with the long-range Lennard-Jones (LJ) potential is used to calculate the interatomic interactio ns. Incident clusters wi th different types of intracluster bonding are consider ed. The effects of the inci dent angle and the deposition direction are examined. 4.1 Simulation Details The surface investigated in this study is hydrogen-terminated diamond (111) substrate made up of 26 atomic layers th at contains 13700 – 13900 at oms with a planar impact area of 69 40 . This configurati on is chosen because it was found previously that the 26-layer surface is best at removing the artifici al rebounding of the deposition

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76 energy and preventing it from interfering with the reactions occurring at the surface at the highest incident energy considered.[102] Two-dimensional period ic boundary conditions are applied within the impact plane to mimic a semi-infinite system. The bottom hydrogen layer is fixed. The ne xt six carbon layers and 5 to 6 rows of atoms on the slab edges have Langevin frictional forces and ra ndom forces applied. That is, the GLEQ approach is used to dissipate the extra h eat accumulated on the surface upon deposition, and at the same time, to prevent the reflecti on of the impact energy from the edges of the slab. The remaining surface atoms and all the cluster beam atoms are active atoms, which are free to move in response to the applied forces without any constraints. Figure 4-1 shows the arrangement of the thermostat at oms and the active atoms in the substrate. Before the deposition, the surface is equilibr ated at 500 K to achieve a relaxed structure with optimized atomic configurations, and then cooled to the simulation temperature of 300 K. Figure 4-1. The arrangement of the thermostat atoms (gray) and the active atoms (black) within the substrate. The top and bottom spheres in the side view are hydrogen atoms. Side view Top view

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77 Three cluster beams with different types of intracluster bonding are examined in this study. These are a van der Waals cluster beam of ethylene (C2H4) molecules, a beam of adamantane (C10H16) molecules, and a beam of fullerene molecules (C20). In thin film formation through energetic cluster deposition, cluster size is a very important factor. In contrast to the metallic cluster deposition, our previous simulations of thin film formation via organic cluster deposition predicted that smaller clusters of a few tens of atoms produced thin films more efficiently than large clusters of several hundred atoms.[99] This prediction is consistent with the experimental fact that in ICBD technique, which is a successful method to produce organic thin films,[25, 28-30] only small clusters prevail.[26, 40, 41] Therefore, in this study, the van der Waals cluster beam of ethylene contains 8 ethylene molecules per cluster; the beams of adamantane and C20 each contain one molecule per cluster. Although the number of atoms contained in each cluster in these three beams is quite different (48 for et hylene, 26 for adamantane, and 20 for C20), all the individual clusters are roughl y the same size and contain co mparable amounts of carbon (16 C atoms for ethylene, 10 C atoms for adamantane, and 20 C atoms for C20). Each of the three beams contains 20 clusters. All the beams are created through the repetition of a single cluster that has been equilibrated at 500 K and quenched to 5 K to minimize the internal kinetic energy of the cluster. Then 20 of the clus ters are repeated in random translational and angular orientations so that they will not impact the surface with the same orientation or at the sa me point on the surface. Prior to deposition, each beam is placed about 4 above the surface; the distance between two consecutive clusters is also around 4 . This distance is chosen because it is long enough that the individual clusters

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78 do not interact with one anot her in the beam and yet the deposition process is not too slow in these demanding computational studies. This study is designed to compare the form ation of thin films from cluster beams with different types of intr acluster bonding, and to gain a better understanding of the effects of incident angle and impact direction. Therefore, depositions at angles of 0, 15, 45 and 60 from the surface normal for all th e three incident species are considered. When the beam impacts the surface at an angle the total impact momentum (total ), which is related to the total energy (totalE ), can be divided into two none-zero components: the component normal to the surface (normal ), which corresponds to normalE (=2costotalE ); and the component parallel to the surface (lateral ), which corresponds to lateralE (=2sintotalE ). When changes while total and totalE are fixed, both the normal and lateral components vary with angle. Cons equently, two sets of deposition energies are considered one where totalE is constant at 400 eV/clu ster while the ratio of normal to lateral decreases with increasing angle; and another where total and totalE change but normal is constant (corresponding to a constant energy of 400 eV/cluster normal to the surface). Deposition with lateral along the ] 2 1 1 [ and ] 10 1 [ crystallographic orientations are investigated. The deposition system is schema tically shown in Figure 4-2. For statistical purpose, five trajectories are carried out for each set of deposition conditions for each incident species. The averaged results are re ported. All the simulati ons run for about 3 ps with 0.2 fs as the time step. The deposition occurs during the first 1 ps followed by the complete relaxation of the system during the next 2 ps.

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79 Figure 4-2. The simulation syst em prior to the deposition. 4.2 Results 4.2.1 van der Waals Clusters of Ethylene There is only the weak intermolecular van der Waals force keeping the ethylene molecules together within the cluster. During the deposition, the ethyl ene cluster flattens out and the molecules impact each other and dissociate into small segments. Many surface hydrogen atoms and some surface carbon atoms are removed, which facilitates the nucleation of the thin film, as shown in Figure 4-3(a). When the collision occurs at 0 and 15 with totalE of 400 eV/cluster, the surface expe riences a significant amount of elastic deformation upon impact and some pl astic deformation up to 3-4 carbon layers (Figure 4-3(b)). Typically, the thickness of the resu ltant thin films is about 6-7 . As the impact angle increases, a larger fraction of the surface deformation is elastic and the plastic deformation is limited to the top one or two carbon layer(s). At 60, many of the clusters and their fragments “slide” along the surface, and the resultant thin film is only about 3 thick. A typical snapshot is s hown in Figure 4-3(c). The average maximum penetration depth of the beam fragments slightly increa ses as the deposition angle

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80 Figure 4-3. Representative snapshots from the simulations of ethylene cluster beam deposition on the hydrogen terminated diamond (111) surface. The black atoms are incident carbon, the gray atoms are surface carbon, and the white atoms are hydrogen. (a) A representative sh apshot of the configuration at time = 0.05 ps, the early stage of the deposition; (b) the relaxed configuration at time = 3 ps at 0; (c) the relaxed configuration at time = 3 ps with 400 totalE eV/cluster at 60 along ] 10 1 [; (d) the relaxed configuration at time = 3 ps with 400 normalE eV/cluster at 60 along ] 10 1 [. (a) (b) (c) (d)

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81 decreases. But at all the incident angl es, the penetration depth is about 1 . Approximately 1% of the surface atoms are s puttered for all the angles considered. When the deposition occurs with constant normal momentum equivalent to the normal incident energy of 400 eV/cluster, seve re permanent disorder of the surface is predicted to occur, especially at large angl e impacts (compare Figur e 4-3(c) vs. Figure 43(d)). In addition, many more surface car bon atoms are pushed toward the surface region and become part of the film. The film thickness is about 7 at all angles. The average maximum penetration depth of the beam fragme nts increases as the angle increases (from about 0.7 at 15 to about 2.7 at 60). Th e amount of surface sputte ring also increases with the angle, from about 0.7% at 15 to about 4.0% at 60. Figure 4-4 summarizes the percentage of the carbon atoms from the incident ethylene clusters that adhere to the surf ace at various incident angles. When the depositions occur with totalE of 400 eV/cluster, the amount of adhesion decreases monotonically as the incident angle increases, although the resu lt at 15 is about the same as the normal impacts when the standard deviation is considered. This suggests the deposition with high impact momentum normal to the surface would facilitate thin film nucleation. When the cluster beam is directed to the substrate with a constant normal impact momentum (corresponding to normalE = 400 eV/cluster), the a dhesion percentage is about the same for the 0, 15 and 45 depos itions. However, at 60, the amount of the nucleated thin film is still lower than those smaller angle depositions, although the decrease is not so dramatic as when 400 totalE eV/cluster. In fact, if the deposition results at normalE = 400 eV/cluster are compared with the results at 400 totalE eV/cluster, one can see that the amount of adhesion increases significantly in the case of normalE =

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82 400 eV/cluster, especially when the deposition o ccurs at large angles such as 45 and 60. This result again justifies the important role played by the normal impact momentum in the film nucleation and growth. Deposition al ong different crystallogr aphic orientations yields the same trend. The adhesion percenta ge along different dir ections at the same angle is approximately the same. This indicates that the thin-film nucleation and growth has little dependence on the inci dent direction of the beam. Figure 4-4. Percentage of carbon atoms in the ethylene clusters that adhere to the surface as a function of incident angle. (A) Deposition with 400 totalE eV/cluster along ] 2 1 1 [ (B) deposition with 400 normalE eV/cluster along ] 2 1 1 [ (C) deposition with400 totalE eV/cluster along ] 10 1 [; (D) deposition with 400 normalE eV/cluster along ] 10 1 [. The structure of the nucleated thin film is analyzed quantitatively by determining the coordination number and carbon connectivity of the carbon atoms in the film. The former shows the hybridization characteristic s of the carbon atoms in the film, and the latter indicates the relative am ount of linear structure versus branched, and/or networked structure in the film. All the films are f ound to be essentially amorphous. The incident 0 10 20 30 40 50 60 70 0154560 Angle (degree)Adhesion (%) A B C D

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83 angle has little effect on the film structur e. The hybridization of the carbon atoms ranges from sp to sp3 with the majority sp2-hybridized (40-50%). The simulations predict more sp-hybridized carbon atoms and less sp3-hybridized carbon atoms in the film when the total incident energy is higher, in agreement with the previous studies.[95, 97, 98] Most of the carbon atoms are connected to one anot her in linear chains, while about 20% are branched carbons and even fewer (less th an 2%) are networked. Deposition along different crystallographic orient ations does not significantly aff ect the overall structure of the film. 4.2.2 Admantane Molecules Adamantane is a cage hydrocarbon composed of four cyclohexane chairs, as shown in Figure 4-5. This molecule is quite stable because it possesses no angle strain (all the carbon atoms are perfectly tetrahedral and sp3 hybridized) and no torsional strain (all the carbon-carbon bonds are perfectly staggered).[259] Despite the similarity of the bonding in adamantane to the bonding in diamond, the deposition of a beam of adamantane molecules in a previous study was not pred icted to produce diam ond-like thin films; instead, the film contained primarily sp2-hybridized carbon.[102] Figure 4-5. Molecular structure of adamantane. When the beam of adamantane molecules im pacts the surface with a total incident energy of 400 eV/cluster, the adamantane molecules dissociate on contact with the surface and the original cage structure is broke n into chain-like fragments. In addition, the surface deforms and some of the hydrogen atoms from the topmost layer are

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84 displaced, leaving nucleation sites for the fragments to attach to the surface, as shown in Figure 4-6(a). As the incident angle increases, the surface experiences less deformation, and longer chains survive. Nevertheless, no cag e structures remain af ter deposition at any of the angles considered. Representative snaps hots of the resultant thin film are shown in Figure 4-6(b) and (c). The resultant thin f ilms are typically about 4-7 thick. Atoms from the cluster beam can travel approximate ly 1 into the surface, with the deposition processes at 0 and 15 resu lting in slightly deeper penetrations than the deposition processes at 45 and 60. About 1% of the original surface atoms are knocked out of the surface. This sputtering effect is slightly greater at large in cident angles because of the high lateral impact momentum associated with the large angle deposition. As is the case for the ethylene cluster b eam, when the adamantane is deposited with a constant normal momentum that corres ponds to the normal incident energy of 400 eV/cluster, the surface is damaged more severe ly as the incident a ngle increases (Figure 4-6(d)), and large numbers of surface atoms are sputtered out of the surface. The cage structure of the adamantane molecules is de stroyed during depositi on, either from the initial impact with the surface or from gas-pha se collisions with the sputtered fragments leaving the surface. The latter is not seen for depositions with total incident energy of 400 eV/cluster. The molecules consequently break into short chains that contain 2-3 carbon atoms and various numbers of hydrogen. Some of these chains stick to the surface and some scatter away. However, as the depositi on process continues, these short chains can react with one another to form longer chains The resultant thin film is about 7-11 , which is significantly thicker than the film formed when the total incident energy is 400 eV/cluster.

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85 Figure 4-6. Representative snapshots from the simulations of adamantane molecular beam deposition on the hydrogen terminated diamond (111) surface. The same color scheme as in Figure 4-2 applies. (a ) A representative shapshot of the configuration at time = 0.05 ps; (b) the relaxed configur ation at time = 3 ps at 0; (c) the relaxed configurat ion at time = 3 ps with 400 totalE eV/cluster at 60 along ] 10 1 [; (d) the relaxed configuration at time = 3 ps with 400 normalE eV/cluster at 60 along ] 10 1 [. (a) (b) (c) (d)

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86 Figure 4-7. Percentage of adamantane car bon atoms that adhere to the surface as a function of incident angl e. (A) deposition with 400 totalE eV/cluster along ] 2 1 1 [ (B) deposition with 400 normalE eV/cluster along ] 2 1 1 [ (C) deposition with400 totalE eV/cluster along ] 10 1 [; (D) deposition with 400 normalE eV/cluster along ] 10 1 [. The percentage of carbon atoms from the adamantane molecules that remain chemisorbed to the surface at various incident angles is shown in Figure 4-7. As what happens in the deposition of ethylene clusters, the amount of adhesion decreases as the incident angle increases, while 15 impacts are as efficient to produce thin films as the normal impacts. However, as indicated in Fi gure 4-7, the amount of adhesion at 45 when the deposition occurs with 400 totalE eV/cluster is comparable to what happens when the deposition occurs with 400 normalE eV/cluster. This is in contrast to the significant increase in the amount of adhesion predicted for the ethylene cluster beam deposition at 45 when the beam is deposited with 400 normalE eV/cluster (see Figure 4-4). Finally, the deposition of adamantane molecules along di fferent crystallographi c orientations does 0 10 20 30 40 50 60 70 80 90 100 0154560 Angle (degree)Adhesion (% ) A B C D

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87 not result in noticeable differences in the a dhesion percentage, in agreement with the results predicted from the ethylene cluster deposition. As seen in our previous study,[102] the bonding in the film resulted from the adamantane deposition is predominantly sp2-hybridized (40%-60%) and no more than 15% of the carbon atoms remain sp3 hybridized. About 70%-80% of the carbon atoms are connected to one another in a linear fashi on, 30%-20% are branch ed, and less than 3% are networked. Again, the film structure s hows little dependence on either the incident angle or the crystallo graphic orientation. 4.2.3 C20 Molecules C20 with a cage structure is the smallest member in the fullerene family. It has no hexagons but 12 pentagonal faces. Its surface thus has high curvature, which severely bends and strains the bonds be tween the carbon atoms. Beside s the fullerene structure, both experimental and theoretical work has shown that several other structures for C20 exist, such as linear structur e (chain), monocyclic and/or bi cyclic rings, graphitic sheet, and corrannulene structure (bowl).[260-265] However, different theo retical calculations give contradictory results as to the energetic stab ility of these isomers. Quantum Monte Carlo calculations suggest that bowl and ring isomers are more energetically stable than fullerene structure.[260, 261] Quantum molecular dynamics simulations,[262] coupled cluster calculations,[263] and density functional ca lculations with local spin density and gradientcorrected approximations[264] predict the fullerene stru cture is the minimum energy configuration. However, experimental measurem ents show that the fullerene structure of C20 is not favored under the c onditions of experiments. Th e major reason lies in the complicated experimental conditions, for example, high temperatures and charge states.[264, 265] The bonding in C20 fullerene is unique in that it is sp2 hybridized with -

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88 bonding that is so distorte d that it is nearly sp3 hybridized. Several groups have studied the deposition of fu llerene on surfaces[36, 63, 65, 66, 70, 75, 91-94, 112, 266] and find that it can be used as a precursor of thin film growth. In our simulations, the C20 cage flattens and breaks into fragments such as rings and chains when it hits the surface (see Figure 4-8( a)). As is the case in the depositions of both ethylene molecular beam and adaman tane beam, during the deposition of C20 beam, the surface also deforms with the degree of deformation depending on the cluster energy and incident angle. For example, when the deposition occurs with the total incident energy of 400 eV/cluster, at 0 and 15, elastic deformation can reach the 13th surface carbon layer, while plastic deformation remains up to the 5th surface carbon layers, as shown in Figure 4-8(b). When the incident angle is 45 or 60, elastic deformation reaches only the 8th carbon layer while plastic deformation only reaches the 3rd carbon layer, as shown in Figure 48(c). However, when the depos ition occurs at high incident energy, which, in this study, corresponds to the case where the beam is deposited to the surface at a constant normal momentum equiva lent to a normal incident energy of 400 eV/cluster, significant permanent surface deform ation appears at larg e incident angles (compare Figure 4-8(c) with Figure 4-8(d)). During the depositions with the total inci dent energy of 400 eV /cluster, chain-like fragments that contain 56 carbon atoms form, and few surface carbon atoms are knocked loose. The resultant thin film is about 6-10 thick. In addition, the film fragments often have more than one tethering points to the surfac e, giving the film strong adhesion to the diamond. Atoms from the C20 penetrate about 1 into the surface and around 1% of the

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89 Figure 4-8. Representative snapshots from the simulations of C20 molecular beam deposition on the hydrogen terminated diamond (111) surface. The same color scheme as in Figure 4-2 applies. (a ) A representative shapshot of the configuration at time = 0.05 ps; (b) the relaxed configur ation at time = 3 ps at 0; (c) the relaxed configurat ion at time = 3 ps with 400 totalE eV/cluster at 60 along ] 10 1 [; (d) the relaxed configuration at time = 3 ps with 400 normalE eV/cluster at 60 along ] 10 1 [. (a) (b) (c) (d)

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90 surface atoms are sputtered, with the depositi on at large angles producing slightly more sputtering than depos ition at small angles (0.9% at 60 and 0.5% at 0). When the C20 beam is deposited at a constant normal impact momentum that corresponds to the normal in cident energy of 400 eV/clust er, the fullerene cages are broken into smaller fragments and fewer ring st ructures survive. The average penetration depth of atoms from the clusters is also deeper (1 at 15, 1.3 at 45 and 2.3 at 60). Large numbers of surface carbon atoms are s puttered from the surface. Surface sputtering increases significantly as the angle increases, from 0.6% at 15 to 4.8% at 60. The resultant thin film is 8-10 think, and cont ains more surface carbon atoms than when the total incident energy is 400 eV/cluster. Figure 4-9. Percentage of carbon atoms in C20 clusters that adhere to the surface as a function of incident angl e. (A) deposition with 400 totalE eV/cluster along ] 2 1 1 [ (B) deposition with 400 normalE eV/cluster along ] 2 1 1 [ (C) deposition with 400 totalE eV/cluster along ] 10 1 [; (D) deposition with 400 normalE eV/cluster along ] 10 1 [. 0 10 20 30 40 50 60 70 80 90 100 0154560 Angle (degree)Adhesion (%) A B C D

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91 The amount of carbon atoms from the C20 molecular beam adhered to the surface resulting in the thin film formation decreases as the incident angle increases, as shown in Figure 4-9. The results show no significant dependence on crystallographic orientation, and the 15 depositions always generate similar results to the normal angle depositions. Additionally, the amount of adhesi on is relatively insensitive to cluster energy at all the incident angles considered. The coordination number and carbon connect ivity of the film carbon atoms are also examined. The results show that the film contains 40%-50% sp2 hybridized carbon and 30%-50% sp hybridized carbon. Less than 10% are sp3-hybridized. The carbon atoms are mainly connected in a linear manner (50% -70%), a significant number (50%-30%) are branched, and no more than 4% are networke d. These results as well as those for the depositions of ethylene clusters and adamanta ne molecules are summarized in Tables 4-1 and 4-2. Table 4-1. Summary of the coordination percentage of the film carbon atoms (%) Incident species 1 neighbour sp sp2 sp3 Ethylene cluster < 15 20-40 40-50 10-30 Adamantane < 14 30-50 40-60 < 15 C20 < 15 30-50 40-50 < 10 Table 4-2. Summary of the percentage of carbon connectivity of the film carbon atoms (%) Incident species Linear Branched Networked Ethylene cluster 80-90 10-20 < 2 Adamantane 70-80 20-30 < 3 C20 50-70 30-50 < 4 4.3 Discussion During the deposition, about 60%-80% of the clusters’ kinetic energy is transformed into surface kinetic energy, and more than 90% of the excess surface kinetic energy is dissipated through the Langev in thermostat atoms in the surface.[95, 97, 98, 100] The

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92 effectiveness of the application of the Lange vin thermostat is crucial for the realistic dissipation of the excess surface kinetic energy a nd is therefore closely examined in this study. The averaged temperature of the su rface Langevin atoms and the non-thermostat atoms is measured separately after the rela xation. Among the three incident species, C20 deposition results in the highest surface temp erature because it has the most localized energy accumulation, which makes the transf er of incident energy to the surrounding substrate atoms the least efficient. But as e xpected, for all the three species, the average temperature of the surface La ngevin atoms is about 300 K (t he simulation temperature), while the temperature of the non-thermostat atoms is slightly higher than 300 K. Therefore, the current system set-up is effective enough to maintain the system temperature as required for all the three incident cluster beams. Although the three cluster beams used in th is study are quite different from one another, their deposition results share some significant similarities. In all cases, the deposition process destroys the original structur e of the cluster, regardless of the type of bonding holding the cluster togeth er. Both adamantane and C20 disintegrate into chains or rings. This finding for C20 differs from the result s of some other studies,[91, 94] which predict that its cage structure can either surv ive after surface impact or recover during the following relaxation. This is because the incide nt energy used here is at least two times higher than the molecula r binding energy of the C20 (which is about 118 eV/molecule) while the energy considered in those studies is much lower. Despite the rigid nature of the diamond, the substrate experiences various degrees of damage depending on the incident energy and the incident angle. The depth of the damage to the surface varies from 2 to 8 , which indicates that the deposition process

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93 modifies only a shallow region of the surface. When the deposition takes place at a total incident energy of 400 eV/cluster, the damage to the surface decreases with increasing incident angle because of the large compone nt of momentum normal to the surface at small angles. However, when the normal impact momentum is kept constant, which corresponds to an energy of 400 eV/cluster normal to the su rface, the damage to the surface is more severe at large angles, especially in the late ral direction, because of the large lateral component of the impact mome ntum that breaks a large number of surface bonds. Surface sputtering is predicted to occur in all the simulations and the lateral momentum component is a major factor in c ontrolling the sputtering effect. For instance, in the depositions at a constant total impact momentum, which is equivalent to a total incident energy of 400 eV/cluster, more surf ace atoms are sputtered at large incident angles where the lateral impact momentum is large. In cases where the impact momentum normal to the surface are held c onstant, the sputtering of surface atoms at large angles (45 and 60) is about 2-4 tim es the sputtering of surface atoms at small angles (0 and 15) b ecause the lateral component of the impact momentum increases significantly with increasing angle. Deposition of single-atomic ion beam can only result in smooth thin film at oblique angles.[267] While in cluster beam deposition, Ya mamda et al. reported the substrate roughness increased monotonically w ith increasing incident angle.[118, 268] However, the depositions of all the three cluster beams in this study s how little dependence of the smoothing effect on the incident angle. In fact the resultant thin film thickness is about 3-7 from the deposition of ethylene mol ecular clusters, 4-7 from adamantane

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94 clusters, and 6-10 from C20 clusters, when the deposition occurs with a total incident energy of 400 eV/cluster no matter at what angle. It is note d though the incident particles used in this study are clusters containing more than one atom but less than 50 atoms, the size of which is significantly smaller than what is used in Yamada’s study (3000 Ar atoms/cluster). Therefore, it is suggested the dependence of resultant film roughness on the incident angle is essentially controlle d by the size of the en ergetic particles. In the incident energy range used here, th e average penetration depth of atoms from the clusters is no more than 3 . The penetration depth is determined by the initial atomic velocity normal to the surface, normalv and the ability of the burrowing atom to overcome the resistance force exerted by the surface atom s. When the clusters impact the surface with a constant total momentum, the penetrati on depth is a little de eper at small angles than at large angles because of the higher normalv in the former case. When the clusters impact the surface with constant mome ntum normal to the surface, although normalv is the same, the lateral momentum of the incident atoms is much larger at large angles. Therefore, the species impacting at large a ngles have more ability to push surface atoms aside, which facilitates deeper penetration. As a result, the penetration depth of the same incident species increases with increasing in cident angle when the deposition occurs at constant normal momentum. The number of atoms from the molecules th at remain chemisorbe d to the surface is an indication of the efficiency in the gene ration of thin film via energetic particle deposition. These simulations predict that th e amount of adhesion is not only related to the cluster energy (especially the incident en ergy normal to the surface), but also related to the incident angle. At the same incident angle, the greater the incident energy normal

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95 to the surface, the greater the amount of thin-film adhesion. All the three beams considered in this study show a general tr end of decreasing adhe sion with increasing deposition angles. Nevertheless, the thin f ilm generation results for small angles ( 15) are nearly the same as the thin film ge neration results of normal-angle deposition. Despite the differences in the original struct ures of the three clusters, the films that result from their deposition are similar to one another. They consist primarily of sp2hybridized carbon, and most of the carbon atom s in the film are connected to each other in a linear fashion (see Table 4-1 and Ta ble 4-2). This is in agreement with the experimental studies that find the film propert ies are not affected by the specific structure of the incident species.[75] This can be attributed to the hi gh incident energy used here and in those experimental studies. When the cl usters are deposited on solid surface at high enough energy, the strong collision between the cluster and the su rface can lead to a complete destruction of the original cluster structure and only the highly energetic atoms and radicals survive. Therefore, it is the pr operties of these energe tic atoms and radicals, not the properties of the original clusters, that will determine the structure of the resultant thin film. There are also important differences in the results of the depositions of ethylene cluster, adamantane, and C20 beams. These differences arise from the different compositions and intracluster in teractions of these three incident species, as well as the different interactions between the incident cluster and the surface. For example, both the deposition of the ethylene cluster beam and ad amantane beam generate film containing large amounts (60%-70%) of hydrogen, while th e film that results from the deposition of the C20 beam is more like an amorphous car bon film, and only 40%-50% is hydrogen

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96 (that has been incorporated into the fi lm from the surface). This is because C20 is a hydrogen-free molecule, whereas the ethylen e and adamantane contain significant amounts of hydrogen. In addition, although most carbon atoms are sp2 hybridized in all the films generated from these three beams, the amount of sp3-hybridized carbon is the highest (10%-30%) in the film formed fr om ethylene cluster beam deposition and the lowest (<10%) in the film from C20 beam deposition. The carbon connectivity within the films is also slightly different. Specifically the number of branched carbon atoms is the highest (30%-50%) in films produced from C20 and the lowest (10%-20%) in films produced from ethylene. There are also noticeable differences in the chemical reactions that the various species undergo. In the case of ethylene mo lecular clusters, the clusters are easily dissociated because the weak van der Waals bonds are easily broken. It is therefore possible to redistribute the incident kinetic energy to individual molecules through intermolecular collisions. Complex chemi cal reactions can take place among the molecules within the cluster as well as be tween the incident pa rticle and the surface (and/or the sputtering fragme nts). However, in the case of the adamantane and C20 beams, no reactions occur among the incident molecule s because only one molecule exists in each cluster and direct intermolecu lar collisions seldom happen. The biggest difference among the three clus ter beams lies in their efficiency at producing thin films. The number of incident carbon atoms adhering to the surface in the ethylene cluster beam deposition fluctuates between 10% and 55% ove r the entire range of cluster energy and incident angle (Figure 4-4), while th e number of incident carbon atoms adhering to the surface from the adamantane and C20 beam depositions is 20%-

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97 80% and 35%-94%, respectively (see Figure 4-7 and 4-9). Under the same deposition conditions, C20 is the most efficient cluster at ge nerating amorphous thin film, while the ethylene clusters are the least efficient specie s. This can be explained by the differences in the molecular binding energy and the overall reactivity of these sp ecies. The molecular binding energy of ethylene is 23.6 eV/molecu le, adamantane is 112 eV/molecule, and C20 is 118 eV/molecule. Thus, despite the strain in the fullerene, C20 is the most difficult molecule to smash apart. Consequen tly, a relatively big fragment from C20 can survive the deposition process. If an atom in the fr agment is active enough to be bonded to the substrate, the whole fragment will adhere to the substrate, which will result in a very efficient thin film formation. The reactivity of the atom in the cluster is determined by the overall reactivity of each cluster, which is re lated to the saturation of the carbon atoms in the molecules and the external kinetic energy (i.e., the incident energy) per molecule as compared to the molecular binding energy.[95] While ethylene and C20 both contain unsaturated carbon atoms, adamantane does not The lowest incident energy considered in this study is 400 totalE eV/cluster (in the case of the ethylene clusters, it is 50 eV/molecule since there are eight ethylene molecules in each cluster). This energy is about 2.1 times of the ethylene molecular binding energy, while it is at least 3.4-3.5 times the molecular binding energy of adamantane and C20. The highest incident energy considered here is 1600 totalE eV/cluster, corresp onding to the deposition at 60 with a constant incident energy of 400 eV/cluster norm al to the surface. This energy is about 8.5 times of the ethylene molecular binding ener gy, while at least 13.6-14.3 times of the molecular binding energy of adamantane and C20. Therefore, at the same incident energy,

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98 the atom in C20 appears to be the most reactive atom. In other words, C20 is the most efficient species for thin film generation. More differences can be found by studying th e change of the a dhesion percentage with the incident angle and en ergy. When the incident ener gy normal to the surface is 400 eV/cluster, the total incident energy is about 428 eV/cluster at 15, 800 eV/cluster at 45 and 1600 eV/cluster at 60. So the energy cons idered for 15 depositions does not change a lot (400 eV/cluster vs. 428 eV/cluster). Th at is why all three species show similar amounts of adhesion at 15 when the depositio ns occur at the two sets of deposition energies. However, the total incident energy is enhanced dramati cally at 45 and 60 when the energy is kept at 400 eV/cluster norm al to the surface. At these large angles, as expected, ethylene cluster beams produce signif icantly higher adhesi on when the incident energy is higher (see Figure 4-4) because the ethylene atoms are more reactive at high energy. However, adamantane beams do not show such an increase at 45, but do have an improvement in the adhesion at 60 when the deposition occurs at an incident energy of 400 eV/cluster normal to the surface (Figur e 4-7). While at both 45 and 60, C20 beams generate comparable amount of adhesion at the two sets of incident energies considered, as shown in Figure 4-9. One possi ble explanation is that if the external kinetic energy is already high enough to break the molecule(s) in the cluster when it is converted into internal kinetic energy upon depos ition, the increase in extern al kinetic energy won’t help to improve the overall reactivity of the cluster molecule(s) even more. Therefore, the number of reactions and the amount of adhesi on will not increase. In other words, there exists an optimal incident en ergy that will result in the highest overall reactivity of the cluster molecule, which in turn will result in the greatest amount of adhesion. From the

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99 results of this study, this optimal incident energy depends on not only the species but also the incident angle. The simulations of Tang et al. predic ted a strong dependence of the deposition result on the initial orientation of the incident species in the C60-surface collisions.[112] The solid surface they used is a structureles s wall. Thus, this orientation dependence was expected to persist or even intensify when a structured surface was used. While in our study, the depositions of all the three clus ter beams on the diamond (111) surface along different orientations result in thin films th at are not significantly different from one another. However, this result is not consid ered to be contrary to Tang’s conclusion, because the species used here are deposited in a beam of twenty randomly oriented clusters, whereas Tang et al. deposited only one C60 molecule at a time. Therefore, in our simulations, any possible orientat ion effects due to the struct ure of the incident species have been averaged out. 4.4 Conclusions Classical molecular dynamics simulations have been used to examine the thin film formation through the deposition of cluster beams of ethylene, adamantane, and C20 on hydrogen-terminated diamond (111) surface. These results have been reported recently.[269, 270] In summary, during the deposition, the incident species undergo rapid chemical reactions that lead to thin -film formation and surface sputtering. C20 is the most reactive species among the thre e, and therefore, the C20 beam is found to be most efficient at producing thin film. The molecu lar cluster beam of ethylene is the least efficient species. The resultant thin film is essentially amorphous with the majority of carbon atoms sp2-hybridized and connected in a linear manner. Despite the differences in the chemical bonding in the three incident cluste rs, the structure of th e resultant thin film

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100 is predicted to be similar. The effects of in cident angle and the incident energy are also documented. In general, increasing the angle ca uses the amount of thin film nucleation to decrease. However, the incident angle doesn’t affect the film structure. Deposition along various crystallographic orientat ions is not found to have signi ficant effect on the results.

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101 CHAPTER 5 CHEMICAL MODIFICATION OF CARBON NANOTUBE/POLYMER COMPOSITES THROUGH POLYATOMIC-ION BEAM DEPOSITION Carbon nanotubes are promising reinforcements in polymer composites because of their remarkable modulus, extr aordinary strength and high as pect ratio. The performance of a composite depends critically on the inte rfacial properties between the reinforcements and the matrix because these properties determin e the load transfer ability. The formation of a strong chemical bond between the reinforc ing fiber and the matrix is an effective way to ensure successful load transfer from the matrix to the reinforcements. However, previous studies on a number of as-synt hesized carbon nanotube/polymer composites showed that untreated nanotubes are usually bonded to the polyme r matrix only through relatively weak van der Waals interactions, as a result, the interfacial properties are poor.[152, 161, 167, 171-173] To functionalize the nanotube wa ll and thus to form cross-links between the nanotube and the matrix are not easy and are often achieved using severe chemical reactions.[143, 190, 191] However, these harsh chemical treatments can simultaneously result in damage to the nanotube structure,[144, 190, 191] which is undesirable because the nanotube may lose its superior properties. Therefore, a method that can modify the nanotube in situ is desired. Simulations and experiments have found that at incident energy of 10-80 eV/ion, ion deposit ion on carbon nanotube bundles can lead to covalent bond formation between nanotubes or adjacent tube walls.[199, 200] Besides, ion irradiation has the obvious a dvantage over the wet chemical techniques in that it employs no solvents and wastes little reagent,[271] making it an environmentally friendly method.

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102 These previous investigati ons suggest that ion irradi ation of the carbon nanotubecontaining composites would be a possible way to form strong chemical bond between the tubes and matrix without pretreating th e nanotubes. Therefore, molecular dynamics simulations are used in this study to examine the in situ chemical modification of carbon nanotube/polystyrene composites thr ough the deposition of an energetic C3F5 + beam at room temperature (300 K). 5.1 Simulation Details The second generation many-body reactive em pirical bond order (REBO) potential developed from Abell-Tersoff potential a nd parameterized by Brenner et al. for hydrocarbon systems[211] and Sinnott et al. for C-F-H systems[272] is used to describe the intramolecular interactions in the ions, na notubes, polymer chains, and cross-links. The long-range van der Waals interactions are c onsidered by coupling th e short-ranged REBO potential with the Lennard-Jones (LJ) potential.[2] REBO potential does not allow for charging of the atoms. Instead, the potential tr eats the ions as neutral radicals, as is traditionally done in classical MD si mulations with empirical potentials.[4] It is recognized that charge may influence the chem ical reactions that occur on deposition. However, it should also be noted that in experiments, the ions would be rapidly neutralized as they approach the substrate due to the existence of background gas or the use of the electron current to avoid ion beam induced charging of the substrate.[271, 273] This is believed to be especi ally true for hyperthermal (1-500 eV) and higher incident ion energies.[271] This approach has been applied to model the related processes of ion bombardment of polymer surfaces[274, 275] and carbon nanotube bundles[199, 200] with considerable success.

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103 The polymer matrix considered is poly styrene (PS) because it is among the polymers used to make nanotube/pol ymer composites in experiments[172, 173] due to its well-known properties, structural simplicity, and good processability.[172] A (10, 10) SWNT is embedded in the polymer. This nanotube has a diameter of approximately 1.4 nm, the diameter of a typical nanotube s ynthesized in the laser-vaporization of graphite.[130] The (10, 10) SWNTs are also believed to be the predominan t constituents of nanotube ropes produced by the electr ic arc technique using a catalyst.[131] A 3.0 nm long carbon nanotube (CNT) is intro duced into the polymer matrix at the center but is embedded at varying depths. The po lymer chains are parallel to the nanotube axis, as shown in Figure 5-1(a). This type of composite structure is made by replacing an appropriate number of polymer chains w ith the nanotube. The system contains 480 carbon atoms in the nanotube, and 59-60 polysty rene chains. The physical dimensions of the composite substrate are 8.0 nm 5.7 nm 3.0 nm. Periodic boundary conditions are applied only in the direction of the nanotube axis, which is also the direction of polymer chains. Thus, this model mimics an infinitely long CNT embedded in long chains of PS. In order to determine the possible influen ce of the nanotube on the ion beam deposition results, a pristine PS substrate of the same dimensions is used. Another nanotube reinforced composite structure with the polymer chains perpendicular to the nanotube axis (Figure 5-1(b)) is also consid ered. This type of composite structure is made by replacing a number of polymer segments with the nanotube. The physical dimensions are 5.3 nm 5.7 nm 4.6 nm. This system contains a 4.6 nm long nanotube with 840 carbon atoms, and 88 PS chains. Both the nanotube and the polymer chains are infinitely long w ith periodic boundary conditions applied in both

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104 directions of the nanotube ax is and the polymer chains. For simplicity, hereafter, the composite structure with the nanotube parallel to the polym er chains is denoted as CNT/PS-//, and the structure with the nanotube perpendicular to the polymer chains is CNT/PS. Figure 5-1. The composite structures before ion deposition (only parts of the systems are shown for clarity). (a) Carbon nanotube axis parallel to the polymer chains (CNT/PS-//); (b) Carbon nanotube axis perpendicular to the polymer chains (CNT/PS). As displayed in Figure 5-1, the simula tions performed here model the ideal situations where the polystyrene matrix has a cr ystalline structure. It should be noted that amorphous PS other than crystalline PS is most often used experimentally. Therefore, random orientations of the CNT relative to the polymer chains are expected in real experiments. The two orientations considered in this simulation study thus only represent two simple cases out of the numerous situations. It is expected that reasonable predictions would be derived for an amor phous polymer matrix from the results of the deposition on these two CNT-containing co mposite structures. For each composite structure, the carbon nanotube is surrounded by the matrix at varying depths to examine the dependence of the modification eff ects on the location of the nanotube relative to the top of the surface. Three cases are considered. The shallowest (a) (b)

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105 case has only one layer of PS on top of the nanotube, while the deepest one has three layers of polymer covering the nanotube, a nd the one in-between has two layers of polymer on top of the nanotube. Hence, this simulation study considers the composites where the carbon nanotube is essentially embedded close to the surface. Before the deposition, all the substrates are first relaxed at 300 K to obtain the energetically optimized structure. As shown in Figure 5-2, after the relaxation, some carbon atoms on the nanotube capture a hydrogen atom from the PS (Figure 5-2(a)), or even “form” a covalent bond to the PS backbone (Figure 5-2(b)). This behavior has been predicted to occur in other molecular dynamics simulations[181, 182] as well, and is consistent with the predictions of ab initio calculations.[276, 277] This occurs because the nanotube-PS system starts off with some st ored energy that is dissipated during the equilibration steps prior to the ion deposition. However, it is not expe cted that nanotubes in a PS matrix will form covalent bonds to the PS spontaneously in actual composites. Figure 5-2. The composite structures after th e relaxation while before the ion deposition. The gray spheres are carbon atoms. The white spheres are hydrogen atoms. (a) The circled area shows hydrogen atom s captured by the carbon nanotube during the relaxation; (b) The circle d area shows the covalent bond formed between the polymer and the na notube during the relaxation. In order to maintain the system temperature at 300 K and prevent the spurious reflection of pressure waves from the borde rs of the system, the generalized Langevin equation (GLEQ) approach is used to dissipa te the extra energy pumped into the system (a) (b)

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106 after the deposition. That is, about two la yers of the polymer from the bottom and the atoms within 5-12 from the four slab e dges have Langevin frictional force and the associated random force applied. The other su bstrate atoms and the atoms in the ions do not have any constraints and will be treated according to the interactomic potentials described above. Polyatomic ion deposition can transfer a re latively large concentration of atoms and energy to a very localized region of the su rface in a manner that is analogous to the deposition of energetic clusters. Hence, it has higher efficiency to selectively modify the surface region than single-atom ion depositi on. Due to the technological importance of surface fluorination, fluorocarbon ions are widely used to modify various substrates. The C3F5 + ion is among the most prevalent ion sp ecies generated from many fluorocarbon feed gases.[278-280] Therefore, in this simulation study, the ion beam containing 50 C3F5 + ions is considered. The C3F5 + ion has several isomers. A combined experimental and simulation study on the effect of the C3F5 + ion structure during the ion deposition of polymeric thin films suggest ed that most of the C3F5 + ions are at the ground state structure, which is [CF2-CF-CF2]+.[274] Therefore, this ground state structure of C3F5 + is used in our simulations. The ions are deposit ed on the substrate at random positions along the surface normal because the normal impact leads to the most reactive collisions.[281] In order to effectively functi onalize the carbon nanotube, the ion beam is focused on the area where the carbon nanoutube is embedded. Two incident energies of 50 eV/ion and 80 eV/ion are considered. Depending on the in cident energy, there is a 2-3 ps time interval between the impacts of any two consecutive depositi ng ions. In this way, the substrate is allowed to equilibrate between deposition events, and thus well maintain the

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107 system temperature. After the entire ion beam is deposited, the whole system is equilibrated at a higher temp erature of 400 K to accelerate th e relaxation of the substrate and allow the post-depos ition reactions to happen.[274] Then the system is cooled back to 300 K until a steady state is reached. Throughout th e whole simulations, 0.2 fs is used as the time step. 5.2 Results As the ion deposition process progresses, so me incident ions dissociate into smaller fragments (ion fragmentation) upon impact or react with each other. Some ions or ion fragments react with the pol ymer chains, and some react with the embedded carbon nanotube. These are called ion implantation. Other ions or ion fragments get trapped within the polymer matrix but do not form bonds with the PS carbon atoms on the time scales of these simulations. During the relaxa tion, some initially trapped ions or ion fragments will diffuse out of the substrate and scatter away from the surface, especially at a higher temperature. Some polymer atoms are sputtered away by th e incident ion, leav ing an active spot behind either to react with the ion or ion fr agment, or, more importantly, to form crosslinks to the nanotube or between polymer chains. The original crystalline polymer structure becomes amorphous. During the ion deposition, the carbon nanotube experiences elastic deformation due to the ion impacts but then recovers its initial shape during the equilibration, which can be explained by the remarkable flexibility of the carbon nanotube in the direction perpendicular to the tube ax is. Cross-links are predicted to form between the polymer backbone and the nanotube either di rectly or through an ion/ion fragment, depending on th e incident energy and the com posite structure. A typical series of events is illustrated in Figure 5-3.

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108 Figure 5-3. A series of snapshots during the ion beam deposition. (a) At time = 0.4 ps, the depostion of the first ion causes the covalent bond formed between the nanotube and the polymer (see the circ led area); (b) At time = 2.2 ps, the deposition of the second ion has broken the covalent bond formed before (see the circled area); (c) At time = 2.4 ps, the covalent bond has formed again (see the circled area) and the ions are push ed away by the recovery of the carbon nanotube; (d) At time = 26.4 ps, an inci dent ion has hit right on the carbon nanotube and caused significant deform ation of the nanotube; (e) At time = 26.6 ps, the ion is pushed away into th e matrix by the rebounding action of the nanotube. (Black spheres are carbon atoms in the ion, dark gray spheres are fluorine atoms in the ion, light gray s pheres are carbon atoms in the substrate, and white spheres are hydrogen atoms in the PS. The same color scheme is applied throughout this whole chapter.) (a) (b) (c) (d) (e)

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109 5.2.1 C3F5 + Ion Beam Deposition on CNT/PS-// Composites At the incident energy of 50 eV/ion, the simulations predict the carbon nanotube is chemically functionalized after the depositi on when there is only one layer of polymer covering the embedded nanotube, as demonstrat ed in Figure 5-4(a) Covalent bonds are formed between the nanotube and the polymer matrix. In addition, chemical adsorption of some fluorine atoms and ions or ion fragme nts on the nanotube wall occurs. In the other two cases where the nanotube is buried deeper, however, neither the formation of new covalent bond between the polymer and the na notube nor the implan tation of ion or ion fragments on the tube wall is observed, as s hown in Figure 5-4(b) a nd (c). Nevertheless, in all the three cases, the ion beam deposition leads to disorder with in the PS matrix and creating cross-links between PS chains near the surface. Figure 5-4. The CNT/PS-// composites after th e ion beam deposition at 50 eV/ion. (a) The substrate with one layer of polymer on top of the nanotube. (b) The substrate with two layers of polymer on top of the nanotube. (c) The substrate with three layers of polymer on top of the nanotube. (Compare this structure with Figure 5-2(b), where it shows the co rresponding structure of CNT/PS-//-3 before the deposition, no new functi onalization effects are shown after the depostion.) Table 5-1 summarizes the results af ter the deposition of the 50 C3F5 + ions on these CNT/PS-// composites at the incident energy of 50 eV/ion. In the table, the three (a) (b) (c)

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110 composite substrates are denoted as CNT/PS-//-1, CNT/PS-//-2 and CNT/PS-//-3, referring to the composite with one, two and three layer(s) of polymer covering the nanotube, respectively. As shown in the table, th e substrate etching is almost negligible in all the three cases. All the substrate etching comes from the polymer. No atom from the embedded carbon nanotube is lost during the de position. More than half of the incident ions are scattered back into the vacuum after th e deposition. However, among the trapped C3F5 + ions, the amount of the intact ions, i. e., the ion still main tains its ground state structure after the deposition, increases s lightly with the increasing depth of the embedded carbon nanotube. The average penetration depth ( d) of the incident ions is around 2 nm, and is more or less the same for all the three composites. Table 5-1. Summary of the results af ter the ion beam deposition on CNT/PS-// composites at 50 eV/ion. Functionalization of CNT Substrate etching (# of C/ion) Trapped C atoms from ion (%) # of intact C3F5 + Chemical adsorption of ion species Cross-links between PS and CNT d (nm) CNT/PS-//-1 0.3 49.3 7 Yes Yes 1.8 CNT/PS-//-2 0.1 42.0 11 No No 1.9 CNT/PS-//-3 0.2 40.1 12 No No 2.2 Figure 5-5 demonstrates the chemical bondi ng status of those trapped ion and ion fragments. This is of interest because it gives detailed information on the dissociation reaction of the ions and how the ion or i on fragments react with each other or the substrate atoms. This information can be compared with experimental XPS (X-ray photoelectron spectroscopy) spectrum, which is usually used in surface science to determine chemical composition and detect th e change of the chemical environment of the atom. As shown in these figures, the pre dominant ion species af ter the deposition at 50 eV/ion is C3F5, and most of the ion species remain unbonded.

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111 Figure 5-5. The normalized chemical bonding info rmation of the trapped ion species after the deposition on CNT/PS-// composites at 50 eV/ion. (a) CNT/PS-//-1; (b) CNT/PS-//-2; (c) CNT/PS-//-3. Consistent with the results of ion irradiation of car bon nanotube bundles,[199, 200] more significant chemical modification of th e nanotube in the composites occurs at a high incident energy of 80 eV/ion. The na notube in CNT/PS-//-1 is the most easily functionalized. More covalent bonds are fo rmed between the nanotube and PS matrix, and more ion species are chemically adsorbed than at 50 eV/ion, as shown in Figure 56(a). At 80 eV/ion, both crosslink formation and the implan tation of ion species on the nanotube wall are observed in the composite where the nanotube is buried with two C3F5C2F2-3CF2FOthers 0 5 10 15 20 25 30 35 40 45 2.9 2.9 2.8%ion species unbonded bonded to PS bonded to CNT 20.0 20.0 2.8 11.4 8.6 5.7 14.3 8.6 C3F5C2F2-3CF2FOthers 0 5 10 15 20 25 30 35 40 45 50 %ion species unbonded bonded to PS bonded to CNT 37.9 10.4 6.9 3.5 3.4 13.8 24.1 C3F5C2F2-3CF2FOthers 0 10 20 30 40 50 60 3.8 3.8%ion species unbonded bonded to PS 46.3 11.5 3.8 7.8 11.5 11.5(a) (b) (c)

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112 layers of polymer on top of it, as sh own in Figure 5-6(b). Although no new bond is created between the nanotube and the PS, the nanotube in CNT/PS-//-3 has captured a fluorine atom (Figure 5-6(c)), which also demonstrates an improvement in the functionalization efficiency at a high incident energy. Figure 5-6. The CNT/PS-// composites after th e depostion at 80 eV/ion. (a) CNT/PS-//-1; (b) CNT/PS-//-2; (c) CNT/PS-//-3. Table 5-2. Summary of the results af ter the ion beam deposition on CNT/PS-// composites at 80 eV/ion. Functionalization of CNT Substrate etching (# of C/ion) Trapped C atoms from ion (%) # of intact C3F5 + Chemical adsorption of ion species Cross-links between PS and CNT d (nm) CNT/PS-//-1 1.2 37.3 4 Yes Yes 2.5 CNT/PS-//-2 1.2 38.7 1 Yes Yes 2.9 CNT/PS-//-3 1.3 54.7 5 Yes No 3.3 The results after the ion deposition at 80 eV/ion on CNT/PS-// composites are summarized in Table 5-2. As compared with the results at 50 eV/i on (Table 5-1), the substrate etching of the polymer matrix is an order of magnititude higher; the average penetration depth of the ion is larg er; while the number of intact C3F5 + ions is much less; the percentage of the trapped ions is lower for both CNT/PS-//-1 and CNT/PS-//-2 composites at this high incident energy but not for the CNT/PS-//-3 composite. At 80 eV/ion, the predominent trapped ion speci es in all the three composites is CF2 instead of C3F5, and more ion species are bonded to either the polymer chains or the nanotube, as (a) (b) (c)

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113 shown in Figure 5-7. The in crease in the amount of the ion species bonded to the nanotube again demonstrates th e improved efficiency of the chemical functionalization of the carbon nanotube at a high incident energy. Figure 5-7. The normalized chemical bonding info rmation of the trapped ion species after the deposition on CNT/PS-// composites at 80 eV/ion. (a) CNT/PS-//-1; (b) CNT/PS-//-2; (c) CNT/PS-//-3. 5.2.2 C3F5 + Ion Beam Deposition on Pristine PS Substrates Table 5-3 compares the results of the i on deposition on pristine PS substrate at 50 eV/ion and 80 eV/ion. As is the case in the deposition on the CNT/PS-// composites, the C3F5C2F3C2F2CF2CFFOthers 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 8.5 2.9 2.9%ion species unbonded bonded to PS bonded to CNT 11.4 2.9 8.5 5.7 2.9 2.9 11.4 11.4 2.9 10.0 4.3 8.5 2.9(a) (b) (c) C3F5C2F3C2F2CF2CFFOthers 0 2 4 6 8 10 12 14 16 18 20 22 24 26 2.1 6.4 2.1 12.8 2.1 2.1 2.1 17.0%ion species unbonded bonded to PS bonded to CNT 17.0 2.1 12.8 4.3 6.4 10.7 C3F5C2F3C2F2CF2CFFOthers 0 5 10 15 20 25 30 35 2.4 2.4 2.4 4.8 4.8 7.1 7.1 7.1%ion species unbonded bonded to PS bonded to CNT 2.4 7.1 4.8 23.8 14.3 9.5

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114 substrate etching effect is mu ch higher and the ion can go de ep at a high incident energy, however, the number of intact i ons and the amount of trapped incident ions are less. This agrees with the increased reactivity of the incident ions at a high energy. Table 5-3. Summary of the results after th e ion beam deposition on pristine PS substrates at 50 eV/ion and 80 eV/ion. Substrate etching (# of C/ion) Trapped C atoms from ion (%) # of intact C3F5 + d (nm) 50 eV/ion 0 63.3 13 2.1 80 eV/ion 2.0 40.7 3 2.8 In order to compare with the deposition results of the composites, the bonding status of the trapped ion speci es within the pristine PS substrates is also analyzed, as summarized in Figure 5-8. In agreement with what happens in the composites, at 50 eV/ion, the majority of the ion species is C3F5, and most of the ions or ion fragments remain unbonded. In contrast, at a high energy of 80 eV/ion, the major ion species is CF2, and the amount of bonded ion species increases. Figure 5-8. The normalized chemical bonding info rmation of the trapped ion species after the deposition on pristine PS substrates at (a) 50 eV/ion and (b) 80 eV/ion. C3F5C2F2-3CF2FOthers 0 5 10 15 20 25 30 35 40 45 50 17.5 7.5%ion species unbonded bonded to PS 32.5 12.5 7.5 2.5 20.0 C3F5C2F3C2F2CF2CFFOthers 0 5 10 15 20 25 30 35 7.0 2.3 2.3 7.0 7.0 7.0%ion species unbonded bonded to PS 7.0 2.3 25.6 4.7 11.6 16.2(a) (b)

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115 5.2.3 C3F5 + Ion Beam Deposition on CNT/PSComposites Figure 5-9. The CNT/PScomposites after the ion beam deposition at 50 eV/ion. (a) The substrate with one layer of polym er on top of the nanotube (CNT/PS-1). (b) The substrate with two layers of pol ymer on top of the nanotube (CNT/PS2). (c) The substrate with three laye rs of polymer on top of the nanotube (CNT/PS-3). As shown in Figure 5-1, there is more room around the embedded carbon nanotube in the CNT/PScomposite structure than in the CN T/PS-// structure. Therefore, after ion beam deposition on the CNT/PScomposite, the incident ions can gather around the nanotube without being pushed b ack into the matrix once th ey pass through the polymer layers, as indicated in Figure 5-9. It is the easiest for the carbon atoms in the nanotube to react with the incident ions when there is only one layer of polymer covering the nanotube (CNT/PS-1), which is analogous to what is predicted to occur for the CNT/PS-// composites. At the incident energy of 50 eV/ion, although multiple chemisorption of ion species on the carbon na notube is predicted to occur in both CNT/PS-1 and CNT/PS-2 composites, as demonstrated in Figure 5-9(a) and (b), respectively, no covalent bond between the nano tube and the polymer matrix is predicted to form between the nanotube and the polymer matrix. No sign of chemical Only the depositions at 50 eV/ion on CNT/PScomposites have been studied so far. (a) (b) (c)

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116 functionalization of the nanotube is observed when there are three layers of polymer on top of the nanotube (Figure 5-9(c)). Table 5-4. Summary of the results after the ion beam deposition on CNT/PScomposites at 50 eV/ion. Functionalization of CNT Substrate etching (# of C/ion) Trapped C atoms from ion (%) # of intact C3F5 + Chemical adsorption of ion species Cross-links between PS and CNT d (nm) CNT/PS-1 0.2 61.2 16 Yes No 3.1 CNT/PS-2 0.2 74.7 15 Yes No 3.3 CNT/PS-3 0.3 57.3 17 No No 3.2 The results of the ion deposition at 50 eV/ion on the three CNT/PScomposites are summarized in Table 5-4. At this incident energy, the substrate etching effect is not significant and no carbon atom from the carbon nanotube is knocked out of the substrate. More than 50% of the incident ions are ca ught either by the polymer or by the nanotube. Among the trapped ion species, the number of int act incident C3F5 + ion is more than that in CNT/PS-// composites. The average penetrat ion depth of the incident ion is about 3 nm, 1 nm deeper than the de position on the CNT/PS-// compos ites at the same incident energy. The chemical bonding information of th e trapped ion species is demonstrated in Figure 5-10. In behavior that is consistent with what occurs after de position on the CNT/PS-// composites and the pristine PS substrate, the major ion species is C3F5, and only a small amount of the ion species is bonded to the polymer or the nanotube. 5.3 Discussion It has been experimenta lly shown that electron or ion irradiation of carbon nanotube may cause dramatic shrinkage in the nanotube diameter when the incident energy is high enough.[193] Theoretical studies indicate that the reason for this is the removal of the carbon atoms from the nanotube wall through the irradiation.[193] At the two incident energies used in this study, no carbon atom fr om the embedded nanotube is

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117 Figure 5-10. The normalized chemical bonding information of the trapped ion species after the deposition on CNT/PScomposites at 50 eV/ion. (a) CNT/PS-1; (b) CNT/PS-2; (c) CNT/PS-3. found to be knocked out and the substrate etch ing is solely from the polymer, therefore, although the embedded carbon nanotube deforms af ter the deposition, the diameter is still around 1.4 nm. This series of simulations predict that energetic ion beam deposition can indeed lead to the formation of cross-links between the carbon nanotube and the polymer matrix under appropriate deposition conditions. It is found that the chemi cal functionalization C3F5C2F2-3CF2FOthers 0 10 20 30 40 50 60 70 80 3.1 3.1 9.3 6.3 6.3 12.5%ion species unbonded bonded to PS 59.4 C3F5C2F2-3CF2FOthers 0 5 10 15 20 25 30 35 40 45 50 4.9 12.3 7.3 7.3 2.4%ion species unbonded bonded to PS bonded to CNT 39.0 2.4 7.3 12.2 4.9 C3F5C2F2-3CF2FOthers 0 5 10 15 20 25 30 35 40 45 50 55 60 2.2 2.2 4.3 2.2 2.2 2.2 2.2 15.2 6.5%ion species unbonded bonded to PS bonded to CNT 4.3 13.0 37.0 6.5(b) (a) (c)

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118 efficiency of the carbon nanotube depends larg ely on the incident energy of the ions and the composite structure. 5.3.1 The Effect of the Incident Energy During the deposition, part of the external kinetic energy of the incident ion is transformed into its internal kinetic energy, a nd part of it is transfe rred to the substrate. When the internal kinetic energy of the ion is high enough to overcome its binding energy, fragmentation of the ion occurs. At a moderate incident energy of 50 eV/ion, the transformed internal energy af ter the deposition is not hi gh enough to break the strong CC bonding for most incident ions, as a result the majority of th e ion species in the substrate remain as C3F5. In contrast, at 80 eV/ion, more external kinetic energy is transformed into internal kine tic energy of the ion, thus, smaller ion fragments, such as CF2, prevail after the ion depositi on, and the number of intact C3F5 + ions dramatically decreases. This behavior is apparent in th e deposition on the composites (Figures 5-5 and 5-7, and Tables 5-1 and 5-2) as well as on the pristine poly mer substrates (Figure 5-8 and Table 5-3). High incident energy also means more ener gy will be transferred to the substrate and thus activate the substrate atoms. Th erefore, the amount of substrate etching increases substantially when the incident en ergy is high. In the case of carbon nanotube composites, the carbon atoms on the nanotube wa ll may be activated if the energy has not decayed too much. At the high incident en ergy of 80 eV/ion, more cross-links are predicted to form between the nanotube and the polymer matrix (Figure 5-6), and the number of ion species bonded to the carbon nanotube increases (Figure 5-7). These indicate the improved reactivity of both the ion species and the carbon atoms on the tube wall when the deposition occurs at a high ener gy. This, in turn, results in an enhanced

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119 chemical modification efficiency of the car bon nanotube at a high en ergy, especially in the case where there is only one polymer layer on top of the embedded nanotube. For those ions or ion frag ments that do not react with polymer chains or the nanotube, collision may happen between them and the substrate atoms. Therefore, the momentum of these incident particles will change. Some will move upward instead of penetrating deeply into the composite. Once the instantaneous movement of the polymer chains opens a large enough passage, some of these trapped ions or ion fragments will diffuse out of the substrate. Others, which ei ther do not find the right passage or do not have enough energy to escape, rema in trapped in the substrate. For both the composite substrate (for example, CNT/PS-//-1 and CNT/PS-//-2 composites) and the pristine polymer, the pe rcentage of the incident ions remaining within the substrate after the deposition is lo wer at a high incident energy. There are two reasons for this. First, the remaining external kinetic energy of the ion species is high when the initial incident energy is high. Sec ond, at a high incident energy, more ions will dissociate into small ion fragments, which ha s been demonstrated in Figure 5-7 and 58(b). It is therefore easier for these sm all ion fragments to find the lowest energy “escaping” passage. Nevertheless, the deposition on CNT/PS-// -3 composites at 80 eV/ion yields a higher fraction of the trapped ion species th an the deposition at 50 eV/ion. A repeated simulation of the deposition on CNT/PS-//-3 composite at 80 eV/ion gives a similar percentage of the trapped ion species, whic h is about 56.0%. One possible reason is the effective channeling of the incident partic les in the CNT/PS-//-3 composite when the incident energy is 80 eV/ion. In other words, this effective channeling is not only related

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120 to the specific substrate structure but also re lated to the incident energy of the ion beam. In addition, the final composite structure generated from the repeated simulation, as given in Figure 5-11, shows that the incident ion species tend to approach the embedded CNT, which is somehow not clearly shown in Figur e 5-6(c). This tendency may lead to an efficient dissipation of the ion energy because CNT has a comparable thermal conductivity to the diamond. Ther efore, the ion species may qui ckly lose their energy and finally get trapped within the substrate. Figure 5-11. The CNT/PS-//-3 composite st ructure after the deposition at 80 eV/ion generated from the repeated simulation. The incident energy is also found to determ ine the penetration de pth of the incident ion in that both results of the deposition on the pristine polymer substrates (Table 5-3) and the composites (Tables 5-1 and 5-2) show that at the same incident energy, the average penetration depth of the incident ions is about the same. As expected, high incident energy leads to a deep penetration. 5.3.2 The Effect of the Composite Structure The simulations predict that, under the same deposition conditions, 10-30% more incident ions get trapped after the de position on the composites where the carbon nanotube is introduced with its axis perpendi cular to the polymer chains (see Table 5-4) than the composites where the carbon nanotube ax is is parallel to the polymer chains (see

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121 Table 5-1). What is particul ar is that these trapped i on species tend to surround the nanotube in CNT/PScomposites (see Figure 5-9). In a ddition, the ions can go deeper and more incident C3F5 + ions maintain the original ground state structure in the case of the deposition on CNT/PScomposites (compare Tables 54 and 5-1). As indicated in Figure 5-1, the CNT/PScomposite structure is not su ch a compact structure as the CNT/PS-// composite in that the average distance between the nanotube and the surrounding polymer chains in CNT/PSis around 3 longer than that distance in CNT/PS-//. The relatively large empty sp ace between the nanotube and the polymer matrix in CNT/PScomposites provides wide channels for the ions to go deep without collision and resistance. As a result, more inci dent ions can survive and remain within the substrate. In the CNT/PScomposites, the space around the carbon nanotube is 4.3 – 8 , beyond the van der Waals repulsion distance (3 .0 – 3.5 ); therefor e, it is possible for more incident ions to approach th e embedded carbon nanotube in the CNT/PScomposites. Such gathering-around of the ions about the nanotube facilitates the chemical adsorption of the ion species on the nanotube wall and makes it possible to bridge between the polymer chains and the nanotube via these ion species if the ion energy is high enough. However, at 50 eV/ion, the nanotub e is not predicted to cross-link to the polymer in the deposition on CNT/PScomposites because the tube is far removed from the polymer matrix. If amorphous PS instead of crystalline PS is used, based on the deposition results of the two composite structures considered in th is simulation study, it is anticipated that a high fraction of the incident ion species wi ll get trapped between the polymer chains because there is more free volume in amor phous polymer than in crystalline polymer.[282]

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122 On the other hand, the large empty space around the embedded nanotube as shown in Figure 5-1 may be filled with polymer chains if the polymer matrix is amorphous. In other words, the embedded CNT could be clos e to the surrounding polymer; therefore, it might become even more likely to induce the formation of cro ss-links between the nanotube and the amorphous polymer matrix after the ion beam deposition. The depositions on composites with the carbon nanotube embedded at varying depths show a clear dependen ce of the functionalization effi ciency on the location of the nanotube within the matrix relative to the t op of the surface. Figure 5-12 plots the fraction of the functionalized carbon atom s on the carbon nanotube wall as a function of the depth under various deposition conditions. Obviously it is difficult to modify the carbon nanotube when it is buried deep within the matrix because of the rapid energy decay. Figure 5-12. The fraction of functionali zed carbon atoms in the carbon nanotube embedded at varying depths. In this study, once the carbon atom on th e nanotube wall gets functionalized, it typically changes from sp2 hybridization to sp3 hybridization either from the attachment 68101214161820222426 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 CNT/PSat 50 eV/ion CNT/PS-// at 50 eV/ionfunctionalized carbon atoms in CNT (%)depth (angstrom) CNT/PS-// at 80 eV/ion

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123 of ion species or by forming cross-links to the polymer chains. Although there is no damage to the nanotube wall, such as the creation of vacancy, predicted at the energy level used here, the change of the hybridi zation does introduce local deformation since the local bond length changes from 0.14 nm to 0.15 nm[200] and the bond angle approaches the tetrahedral angle.[243] It is of concern that such “defects” on the tube wall may destroy the desirable mechanical propertie s of the carbon nanotube to be used as the reinforcement. A previous computational work by Garg and Sinnott showed that if the fraction of the rehybridized carbon atoms in a (10,10) tube is about 5.2%, the functionalization would decrease th e stiffness of the nanotube by 15%.[223] However, if the introduction of the functi onalized carbon is le ss than 1%, the change in tensile strength of the nanot ube is negligible.[182] Unfortunately, it is still an open question as to the upper limit of rehybridi zed carbon atoms that woul d not induce a significant reduction in the mechanical properties of carbon nanotube. The highest functionalization probability given in Figure 5-12 is about 2.5%, but in most cases, the fraction is less than 1%. Therefore, it is expected that the functionalized carbon nanotube obtained after the ion beam deposition in this study still possess es its remarkable mechanical properties. 5.3.3 Comparison between Pristine Polymer Substrates and Composites A recent experimental study has compared the surface modification of CNT/PAN (polyacrylonitrile) composite films and pure PAN films by proton beam bombardment.[283] This study indicated that the in troduction of CNT would influence both the chemical and structural modifications induced by the proton. Similar results are obtained from our simulations of ion b eam bombardment on CNT/PS composites and pristine PS substrates. Due to the presence of the carbon nanotube, some phenomena that occur in the composites are different from wh at happens in the pristine polymer, although

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124 ion depositions on pristine PS substrates and the composites also display similar behavior, such as the strong dependence of the modification efficiency on the incident energy. As summarized in Tables 5-1, 5-2 and 53, if the deposition results of CNT/PS-// composites and pristine PS substrates are comp ared, the overall trappe d ion percentage is found to be lower in the carbon nanotube com posites than in the pr istine polymer at the same incident energy: 10-20% lower in th e case of the deposition at 50 eV/ion and ~5% lower in the case of the depos ition at 80 eV/ion (except the CNT/PS-//-3 composite). In the CNT/PS-// composites, several polymer chains are replaced by the CNT. Although small ion species can find room between the polymer chains, as what happens in the pristine polymer substrates, their capability to penetrate into the CNT is limited if the incident energy is not high enough. In fact, at both 50 eV/ion and 80 eV/ion, no ion or ion fragment is found inside of the CNT in th is study. Therefore, the replacement of the polymer chains by the nanotube practically excl udes a considerable area for possible ion penetration, which results in a lower percen tage of trapped ions in the composites. However, it is noted that the depositions on CNT/PScomposites at 50 eV/ion actually have comparable trapped ion pe rcentages to the pristine poly mer substrate. As discussed in Section 5.3.2, the reason is the channeling effect due to the available space around the CNT in CNT/PScomposite structure, which essentially compensates for the excluded area enclosed by the CNT. As the simulations indicate, all the subs trate etching comes from the top several layers of polymer. Although th e substrate etching depends mainly on the incident energy, the presence of carbon nanotube is also found to affect this property especially at a

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125 relatively high incident energy. As indicated in Table 5-2 and Table 53, at 80 eV/ion, the amount of the substrate etching in the pristine polymer subs trate is about 1.7 times as much as that in the CNT/PS-// composites. Th e lower substrate etching in the composites can find explanations from the remarkable thermal properties of the carbon nanotube. The high thermal conductivity of the carbon nanot ube facilitates the effective dissipation of the energy; consequently, fewer substrat e atoms in the composites will gain high enough energy to sputter away from the surface. 5.4 Conclusions In composite materials, cross-links between the reinforcements and the matrix will improve the load transfer capability between these two phases. This computational study has demonstrated that when the reinforci ng carbon nanotube is embedded close to the surface, polyatomic ion beam deposition at in cident energies of 50-80 eV/ion can induce the formation of cross-links between the otherwise unfunctionalized carbon nanotube and the polymer matrix without too much damage to the original composite structure. It thus encourages experimental trials using the energetic ion beam deposition or related techniques to effectively harness the outst anding mechanical properties of the carbon nanotube to produce high-performance composite materials. However, due to the rapid energy decay within the substrate, this technique may only be effective at surface modification. The simulations predict the fa vorable conditions for efficient chemical functionalization of the carbon nanotube, su ch as high incident energy and compact composite structure in which the reinforc ing carbon nanotube is close enough to the matrix. It has also shown that the res ponse of a carbon nanotube/PS composite to ion beam deposition is different from the response of a pristine PS substrate. The simulations

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126 reveal the atomic-scale mechanisms that ar e responsible for these differences. Part of these results have been reported in Reference [284].[284] Since this simulation study is highly com putationally intensive, only one trajectory has been carried out for most substrates. It is recognized that the reported quantitative results may lack the statistical reliability, however, the qualitative predictions, which are the major focus of this study, are believed to be correct.

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127 CHAPTER 6 CONCLUSIONS AND BEYOND 6.1 General Conclusions The collision of energetic particles and solid surfaces is one of the most interesting topics in the area of particle-surface inte ractions. Such techniques include plasma deposition, laser ablation, chemical vapor deposition, cluster beam deposition, and ion beam deposition. Depending on the depositi on conditions, a wide range of phenomena can be found, such as implantation, fragme ntation, surface sputte ring, surface cleaning, phase transition, and, more significantly, im pact-induced chemical reactions within the incident species as well as between the incide nt particle and the surface. Such techniques are widely used to generate thin films and have also found promising application in surface modification. Undoubtedly, experimental studies in this field have improved our understanding of how the cha nges in deposition method, st arting material, and impact conditions influence the results. However, th e atomistic mechanisms of the process are not easily obtained from the experimental data and there is much that is not well understood about the process of thin film nuc leation and surface modification. In this respect, molecular dynamics simulations provi de a powerful and complementary tool to the experimental findings. Particle-surface co llisions are especially suitable for study by MD simulations because this process typi cally occurs within a few picoseconds. In this dissertation, thin film formati on through the deposition of organic cluster beams and the impact induced chemical func tionalization of carbon na notube/polystyrene composites via polyatomic ion beam deposition are investigated using MD simulations.

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128 In the simulations, the interatomic forces are calculated from the reactive empirical bond-order (REBO) potential coupled with th e long-range Lennard-J ones potential. The REBO potential allows covalent bond breaking and reforming with associated changes in atomic hybridization. This is crucial for a realistic treatment of organic chemical reactions in an empirical approach. The REBO potential has been s hown to be quite good at characterizing reactive pro cesses involving thousands of atoms, but it is not able to describe processes that depend on the explicit and self-consistent inclusion of electrons. These elements, however, are considered in th e tight-binding approach, which thus gives more accurate quantitative result s than the empirical schemes. In order to obtain a better knowledge of the reliability of the REBO poten tial to describe the energetic particlesurface collisions, the deposition of hydrocarbon clusters on diamond surfaces is first modeled using both the REBO potential a nd the order-N nonorthogonal tight-binding (O(N)/NOTB) method of Jayanthi, Wu, et al The quantitative results of these two methods do not agree perfectly well with each other. The differences in the predictions indicate that as compared to the NOTB Hamiltonian, the REBO potential predicts a higher repulsive barrier, and hence may not be sufficiently flexible to describe all the relevant processes of bo nd-breaking and bond-forming. However, the qualitative predictions are comparable. Therefore, th is comparison study shows that the REBO potential does indeed capture the general characters of carbon-based chemistry. For constant temperature simulations, appr opriate temperature control methods that can effectively dissipate the extra energy must be incorporated in the simulation. One specific role played by these temperature c ontrol methods in mode ling particle-surface collisions is to absorb the wave reflected from the boundary of the simulation system. In

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129 this dissertation, four temper ature control methods are inve stigated in simulations of carbon cluster deposition. These four met hods are the generalized Langevin equation (GLEQ) approach, the Berendsen method, a m odified GLEQ approach where an extra damping mechanism is introduced, and a comb ined thermostat of the GLEQ approach and the Berendsen method. The temperature co ntrol capability and th e effectiveness to reduce the amplitude of the reflected wave of these methods are compared and discussed. Among the four, the Berendsen method is effective at removing the excess energy at the early stage but the resultant equilibrium pr operties are not always optimum. It is found that the realistic performances of these me thods depend on the clus ter incident energy and the substrate size in the simulation. If the substrate is big enough and the incident energy is not too high, the G LEQ approach is sufficient for removal of excess energy. However, the modified GLEQ approach and th e combined thermostat perform better than the regular GLEQ approach and the Berendsen method when the incident energy is high. Collisions between clusters and solid su rfaces can produce high quality thin films with various predetermined properties when the deposition conditions are carefully chosen. Our group has previously used MD simulations to examine the deposition of organic molecular clusters of ethane, ethyl ene, acetylene, and adamantane on diamond surfaces.[95-105] The chemical reactions among the in cident molecules and between the impact cluster and the surface have been stud ied. Film nucleation and growth have been shown to depend on deposition conditions such as molecular reactivity,[95, 96, 100, 102] cluster size,[101] incident energy,[95, 96, 102] impact frequency,[97] surface reactivity,[98, 100] and surface temperature.[100, 101] In this dissertation, MD simulations using the REBO potential are performed to build on the prev ious studies and inve stigate thin film

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130 generation from the deposition of beams of orga nic clusters with different intracluster bondings. The cluster beams considered include a molecular cluster beam of ethylene held together by van der Waal s interactions, a beam of adamantane molecules held together by pure sp3 covalent bonds, and a beam of C20 fullerenes held together by sp2 covalent bonds with distorted p-orbitals. In ad dition, the effects of cluster incident angle and deposition direction are investigated. Ther efore, depositions at various angles and lateral momenta along two different crystallogr aphic orientations are considered. The C20 is found to be the most efficient species at producing an amorphous thin film. Despite the differences in the chemical bonding within the three incident clusters the structures of the resultant thin films are predicted to be similar. Deposition at a large incident angle reduces the efficiency of thin film formation. However, the incident angle does not affect the resultant thin film structure. Furtherm ore, deposition along diffe rent crystallographic orientations is not found to ha ve significant influence on the simulation results due to the randomization of the clusters within the beam in both translational and angular orientations. Since the discovery of carbon nanotubes in the early 1990s, active research has been carried out on this new type of materi als because of their unique mechanical and electrical properties. There has been considerable effort spent to incorporate carbon nanotubes into polymer matrix to make use of their extraordinary modulus and resistance to brittle failure. But when as-synthesized nanotubes are used, the composites fail through nanotube pullout due to poor adhesion be tween the nanotube and polymer matrix.[164, 171, 173] However, nanotubes that are chemically f unctionalized adhere more strongly to the polymer matrix because of efficient load -transfer through covalent bonds between the

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131 polymer and the nanotube.[181, 182] Both experimental and co mputational studies have found that energetic deposition of polyatomic ions can lead to covalent bond formation between nanotubes or adjacent tube walls.[199, 200, 285] Therefore, in the present work, chemical functionalization of carbon nanotube/p olystyrene composite via polyatomic ion beam deposition at incident energies of 50-80 eV/ion is investigated using MD simulations. The simulation results show that this approach is suitable for inducing covalent cross-links between otherwise unf unctionalized nanotube and a polymer matrix to toughen the composite. High incident ener gy and compact composite structures are predicted to be best for effective chem ical functionalization of the nanotube. The simulations also show that the introducti on of carbon nanotubes will influence both the chemical and structural modi fications induced by the ion beam when the deposition results of the composites and pure polystyrene substrates are compared. Most importantly, the simulations reveal the likely atomistic mechanisms responsible for these findings. These MD simulation studies provide valu able information a bout the types of chemical reactions that occur upon deposit ion, detail the atomistic mechanisms responsible for these reactions, and reveal th e dependence of the ch emical reactions and products on a number of factors including de position species, incident angle, impact energy, substrate structure, etc. These studi es provide an enhan ced understanding of the particle-surface interactions and the processing of material s through cluster and/or ion beam deposition. The predictions could lead to improvements in thin film generation and material modification techniques that are us ed to manufacture a nd design a variety of products, from microelectronic devices to medical implants. The simulation results of the

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132 deposition on carbon nanotube/polystyrene com posites could have important implications for the production of lightweight, high-st rength nanocomposites with improved loadbearing capabilities. 6.2 Future Work Throughout this whole dissertation, many of our motivating questions have been answered affirmatively. MD simulations can successfully keep track of the short time scale processes that occur during cluster-su rface reactions. However, some subsequent events (for example, thermally activated at omic migration and surface diffusion), which are very important in determining thin film growth and equilibrium structure, may not be rapid enough to be captured by conventi onal MD simulations. A previous study investigated the subsequent structural relaxa tion of the resultant th in film by performing geometry relaxation through energy minimiza tion for some repres entative thin-film fragments.[101] In this study, it was found that th e structures of the fragments only changed slightly from the relaxed structure pr edicted in the MD simulations. However, to single out the thin-film fragments has introduced significant simplifications that may not represent the situation where those fragments are connected to the remaining structure. Besides, in order to model the entire deposi tion process, most MD simulations (including the simulations reported in this dissertation) use deposition rates that are typically 8-11 orders of magnitude higher than the experimental deposition rates.[286] Consequently, if the employed thermostat is not effective enough at removing extra energy from the system, the collisions of consecutive incident particles may affect each other directly in ways that they would not at a low deposition rate. In order to solve all these problems, a hybrid simulation as presented by Jacobsen et al.[287] for metal systems could be used. In this hybrid simulation, MD simulation

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133 methods are combined with MC (Monte Carlo) simulation methods. In this way, the short time scale collision events can be modeled using MD simulations while, the long time scale events between the collisions, such as surface diffusion and structure relaxation, can be simulated using MC simulation methods This hybrid simulation method is time consuming, but it allows for a more realisti c simulation of the collision at a realistic deposition rate and can predict a more precis ely relaxed structure after the deposition. Another intriguing method is the temp erature-accelerated dynamics (TAD) developed by Srensen and Voter.[288] This method is based on harmonic transition state theory and is a combination of conven tional molecular dynam ics and statistical mechanics. The main idea behind this method is to study the thermally activated behavior of the system by performing an MD simulation at a higher temperature rather than at ordinary temperatures. Therefor e, the rate of the activated processes can be raised and become accessible to the simulation. Of cour se, raising the temperature may also induce transitions that may not occur at the ordina ry temperatures. Such temperature-induced bias is corrected by only allowing those transitio ns that should take place at the ordinary temperature to occur. In this way, the acces sible time scale is extended by orders of magnitude while the correct dyna mics is still maintained. Simulations that can model the depositi on process at an experimental deposition rate and simultaneously address the questi ons such as atomic migration and surface diffusion will give direct insight into the w hole experimental process and provide a more complete picture. Hence, the advanced met hods mentioned above are certainly promising and worth the further exploration and exte nsion to covalently bonded materials.

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PAGE 163

151 BIOGRAPHICAL SKETCH Yanhong Hu was born on November 28, 1972, in Shanghai, P. R. China. Her father is an engineer, and her mother is an account ant. She grew up in Wuxi, a beautiful city near Shanghai. After her graduation from hi gh school in 1991, she enrolled in the East China University of Science and Technology. During her freshman and sophomore years, she became interested in mate rials science and engineering, which led her to choose the College of Materials and major in polymer sc ience and engineering. After she graduated with a bachelor’s degree in 1995, she conti nued her graduate study in the same university and majored in polymer processing. Three year s later, she graduated with her master’s degree and worked in Shanghai Huayi (Group) Company as an engineer. In 1999, she was admitted to the Ph.D program in the Department of Chemical and Materials Engineering at the University of Kentucky and joined Dr. Sinnott’s group. In 2000, she transferred to the University of Florida and was admitted to the Department of Materials Science and Engineering, to continue work on her Ph.D degree.


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MOLECULAR DYNAMICS STUDIES OF
THIN FILM NUCLEATION AND SUBSTRATE MODIFICATION
















By

YANHONG HU


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


2003



























Copyright 2003

by

Yanhong Hu
































This dissertation is dedicated to my family with love and gratitude.















ACKNOWLEDGMENTS

First of all, I would like to thank my supervisor, Dr. Susan B. Sinnott, for her full

support during my four years study in the United States. Her scholarship and enthusiasm

always amaze me and stimulate my interest in exploring the wonderful world of

computer simulation. Her instructive guidance and openness to my ideas have made

working in her group a pleasant and learning experience. I would also like to thank the

members of my supervisory committee for their valuable help and kind support when I

have bothered them: Dr. Rolf E. Hummel, Dr. Laurie A. Gower, Dr. Elliot P. Douglas,

and Dr. Wei Shyy.

Special thanks also go to Dr. Boris Ni and Thomas Plaisted. Without them, I would

not have got started in the lab so smoothly. I also want to extend my gratitude to the

present members of the Sinnott research group for many helpful discussions and friendly

support.

I especially want to thank my husband, who has helped me persevere through

difficult times. From him, I always can find comfort and encouragement. Finally, my

heartfelt appreciation goes out to my parents, who always have confidence in me.

Without their consistent support, I simply could not have come this far.
















TABLE OF CONTENTS
Page

A C K N O W L E D G M E N T S ................................................................................................. iv

LIST OF TABLES ......... .. ... ....... ................ ........ .. .... .. .......... vii

L IST O F FIG U R E S ..................... .. ................................. ... ...... .. .. ........... viii

ABSTRACT .............. .................. .......... .............. xi

CHAPTER

1 IN TR OD U CTION ............................................... .. ......................... ..

1.1 M molecular Dynam ics Simulations.............................................................. 6
1.2 Cluster Beam Deposition on Solid Substrate .............. ..................... .................11
1.2.1 Thin Films from Cluster Beam Deposition ..............................................11
1.2.2 M otivation and O objectives ................................. ..................................... 17
1.3 Carbon Nanotube/Polymer Composites .................................... ............... 20
1.3.1 C arbon N anotubes .......................................................... ............... 21
1.3.2 Carbon Nanotube/Polymer Composites ............................................. 25
1.3.3 M otivation and Objectives ........................................ ...... ............... 30
1.4 O organization of the D issertation................................................ ...... ......... 31

2 COMPARISON OF O(N)/NOTB AND REBO POTENTIAL MOLECULAR
DYNAMICS SIMULATIONS............................ ..... ............33

2.1 Order-N Nonorthogonal Tight-Binding (O(N)/NOTB) Method........................35
2.2 Reactive Empirical Bond-Order (REBO) Potential............... ...............37
2.3 Testing System s .................. ...................................... .. ........ .... 40
2 .4 R results and D iscu ssion ........................................ ...................... .....................42
2 .5 C o n c lu sio n s ..................................................................................................... 5 0

3 TEMPERATURE CONTROL METHODS .................................... ............... 53

3 .1 M ethods of Interest ................... ...... .............. ....................... ................ .. 55
3.1.1 Generalized Langevin Equation (GLEQ) Approach................................55
3.1.2 B erendsen M ethod ....... .. ........................................ ..................... .... 57
3.1.3 Variation of GLEQ Approach and a Combined Thermostat of GLEQ
Approach and Berendsen M ethod......................................... ............... 59
3.2 Testing System s ........................ .......... ........................... .. .. ............ 61


v









3 .3 R results and D iscu ssion .............................................................. .....................62
3 .4 C o n c lu sio n s ..................................................................................................... 7 3

4 THIN FILM FORMATION VIA ORGANIC CLUSTER BEAM DEPOSITION ....75

4 .1 S im u latio n D details ...................................................................... ................. .. 7 5
4.2 Results.................................79.............. ........79
4.2.1 van der Waals Clusters of Ethylene................................. .................79
4.2.2 Admantane Molecules ..........................................................83
4.2.3 C20 M molecules ........... .. ....................... ........ ...... .... .......... .... 87
4 .3 D isc u ssio n ....................................................................................................... 9 1
4 .4 C o n c lu sio n s ..................................................................................................... 9 9

5 CHEMICAL MODIFICATION OF CARBON NANOTUBE/POLYMER
COMPOSITES THROUGH POLYATOMIC-ION BEAM DEPOSITION............101

5.1 Sim ulation D details .......................... .......... ............... ............ 102
5 .2 R e su lts ........................................ ............................ ........................1 0 7
5.2.1 C3F5+ Ion Beam Deposition on CNT/PS-// Composites........................109
5.2.2 C3F5+ Ion Beam Deposition on Pristine PS Substrates............................. 113
5.2.3 C3F5 Ion Beam Deposition on CNT/PS-I Composites .......................115
5.3 D iscu ssion ..................................................... ......................... 116
5.3.1 The Effect of the Incident Energy ........ ............. .................. 118
5.3.2 The Effect of the Composite Structure....................................................120
5.3.3 Comparison between Pristine Polymer Substrates and Composites ........123
5 .4 C o n clu sio n s................................................. ................ 12 5

6 CONCLUSIONS AND BEYOND ................................................................ 127

6.1 G general Conclusions ........................................................................ 127
6 .2 F utu re W ork .................................................................. ................. 132

L IST O F R E FE R E N C E S ....................................................................... .................... 134

BIOGRAPHICAL SKETCH ............................................................. ............... 151















LIST OF TABLES


Table page

2-1. Details of the hydrogen-terminated diamond (111) surfaces..............................41

2-2. The coordination of the carbon atoms in the film predicted by the
O(N)/NOTB-MD and EMD simulations (averaged over 3 trajectories) (%)...........48

2-3. The coordination of the carbon atoms in the film predicted by the
EMD simulations (averaged over 10 trajectories) (%) ............... ...................48

2-4. The carbon connectivity of the carbon atoms in the film predicted by
O(N)/NOTB-MD and EMD simulations (averaged over 3 trajectories) (%)...........50

4-1. Summary of the coordination percentage of the film carbon atoms (%) .................91

4-2. Summary of the percentage of carbon connectivity of the film
carbon atom s (% ) ........ ............. ............................ ............. 91

5-1. Summary of the results after the ion beam deposition on
CNT/PS-// composites at 50 eV/ion................................................... ............... 110

5-2. Summary of the results after the ion beam deposition on
CNT/PS-// composites at 80 eV/ion............................................112

5-3. Summary of the results after the ion beam deposition on
pristine PS substrates at 50 eV/ion and 80 eV/ion. .............................. 114

5-4. Summary of the results after the ion beam deposition on
CNT/PS-I composites at 50 eV/ion............. ......................... ............... 116
















LIST OF FIGURES


Figure pge

1-1. Schematic representation of periodic boundary conditions. ................................3

1-2. Flowchart of the predictor-corrector M D................................... ......... ......... ......10

1-3. Possible phenomena that may occur after the deposition of energetic clusters on a
solid substrate ..................... .... ......... .... ...... ................. 14

1-4. The principle of the experimental set-up for thin film formation by energetic cluster
im pact (E C I). ..........................................................................15

1-5. A graphene sheet rolled into a single-walled carbon nanotube (SWNT) ...............21

1-6. The "rolling up" of a graphene sheet to produce carbon nanotubes of
various helical structures ................................................ .............................. 22

1-7. A m odel of a capped SW N T. ..............................................................................23

1-8. A SWNT formed in the catalytic carbon arc method.............................................24

1-9. In situ straining of a CNT/PS composite in TEM. .............................................. 28

1-10. Cross-linking formed between nanotubes and adjacent shells in the case of MWNT
as a result of energetic ion deposition ....................................................................31

2-1. The percentage of incident carbon atoms that adhere to the substrate (averaged over
three trajectories) versus the size of the substrate. ............................................44

2-2. Potential energy curves calculated with O(N)/NOTB-MD and EMD methods for
th e three reaction s............................................... ................. 4 5

2-3. The percentage of incident carbon atoms that adhere to the substrate (averaged over
ten trajectories) versus the size of the substrate ................................................47

2-4. Snapshots of the thin film formed on the hydrogen terminated diamond (111)
surface containing 3136 atom s. ........................................ ........................... 47

3-1. The substrate layout. (a) the impact zone; (b) the impact zone embedded in the
therm ostat zone. .................................................... ................. 62









3-2. The temporal evolution of the substrate temperature in the reference simulation and
the simulations using the four temperature control methods at the incident energy
of 1 eV /atom .............. ................................. .......... ... ........... 63

3-3. The temporal evolution of the substrate temperature in the simulations using the
four temperature control methods at the incident energy of (a) 5 eV/atom,
(b) 10 eV /atom .......................................................................64

3-4. The temporal evolution of (a) the substrate temperature and (b) the kinetic energy
per active atom in the simulations using the four temperature control methods at the
incident energy of 20 eV/atom ......... ........ .. ............... .. ....... ............... 66

3-5. The temporal evolution of (a) the substrate temperature and (b) the kinetic energy
per active atom in the simulations using the four temperature control methods at the
incident energy of 40 eV/atom ......... ........ .. ............... .. ....... ............... 68

3-6. Snapshots of the systems using the four temperature control methods at various
moments at the incident energy of 40 eV/atom..................................................70

3-7. The displacement fields from t = 0.08 ps to t = 0.24 ps in the cross section of the
(111) plane using the four temperature control methods at the incident
energy of 40 eV /atom ...... ............................. .. ....... ............. ........ .......... .. 70

3-8. The temporal evolution of (a) the substrate temperature and (b) the kinetic energy
per active atom in the depositions on the small substrate using the four temperature
control methods at the incident energy of 40 eV/atom. ............................ .........72

4-1. The arrangement of the thermostat atoms (gray) and the active atoms (black) within
th e su b state ..............................................................................................................7 6

4-2. The simulation system prior to the deposition. .............................. ......... ...... .79

4-3. Representative snapshots from the simulations of ethylene cluster beam deposition
on the hydrogen terminated diamond (111) surface.................. ....... .........80

4-4. Percentage of carbon atoms in the ethylene clusters that adhere to the surface as a
function of incident angle ........................................................................... .... ... 82

4-5. M olecular structure of adamantane. ........................................................................83

4-6. Representative snapshots from the simulations of adamantane molecular beam
deposition on the hydrogen terminated diamond (111) surface.............................85

4-7. Percentage of adamantane carbon atoms that adhere to the surface as a function of
incident angle. ........................................................................86

4-8. Representative snapshots from the simulations of C20 molecular beam deposition
on the hydrogen terminated diamond (111) surface .................. ...... .............89









4-9. Percentage of carbon atoms in C20 clusters that adhere to the surface as a function
of incident angle. ............................... ....................................... ....... 90

5-1. The composite structures before ion deposition (only parts of the systems are
show n for clarity). .............................. ..... .... .. ..... ............... 104

5-2. The composite structures after the relaxation while before
the ion deposition. .............................. ..... ... .. ..... ............... 105

5-3. A series of snapshots during the ion beam deposition. ........................................ 108

5-4. The CNT/PS-// composites after the ion beam deposition at 50 eV/ion................109

5-5. The normalized chemical bonding information of the trapped ion species after the
deposition on CNT/PS-// composites at 50 eV/ion. (a) CNT/PS-//-1;
(b) CN T/P S-//-2; (c) CN T/P S-//-3 ......... ................. ................... .....................111

5-6. The CNT/PS-// composites after the depostion at 80 eV/ion. (a) CNT/PS-//-1;
(b) CNT/PS-//-2; (c) CNT/PS-//-3...........................................................112

5-7. The normalized chemical bonding information of the trapped ion species after the
deposition on CNT/PS-// composites at 80 eV/ion. (a) CNT/PS-//-1;
(b) CN T/P S-//-2; (c) CN T/P S-//-3 ......... ................. ................... .....................113

5-8. The normalized chemical bonding information of the trapped ion species after the
deposition on pristine PS substrates at (a) 50 eV/ion and (b) 80 eV/ion. ............114

5-9. The CNT/PS-I composites after the ion beam deposition at 50 eV/ion................115

5-10. The normalized chemical bonding information of the trapped ion species after the
deposition on CNT/PS-I composites at 50 eV/ion. (a) CNT/PS-I-1;
(b) CN T/PS-I-2; (c) CN T/PS-I-3 ............................... .............. .................. .. 117

5-11. The CNT/PS-//-3 composite structure after the deposition at 80 eV/ion generated
from the repeated sim ulation ................... ...................... ..... ........................ 120

5-12. The fraction of functionalized carbon atoms in the carbon nanotube embedded at
varying depths. ......................................................................122















Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

MOLECULAR DYNAMICS STUDIES OF
THIN FILM NUCLEATION AND SUBSTRATE MODIFICATION

By

Yanhong Hu

August 2003

Chair: Susan B. Sinnott
Major Department: Materials Science and Engineering

Deposition of energetic particles on solid surfaces has found increasing application

in surface science. However, the detailed surface chemistry and relevant atomic

mechanisms are not well understood. Molecular dynamics (MD) simulations are an ideal

method to study these processes atomistically because they usually occur on short time

scales (of the order of a few picoseconds). In this dissertation, MD simulations are

performed to investigate thin film formation through organic cluster beam deposition and

chemical modification of carbon nanotube/polymer composites via polyatomic ion beam

deposition.

The interatomic forces are calculated from the reactive empirical bond-order

(REBO) potential for carbon-based systems coupled with the Lennard-Jones potentials.

The reliability of this approach is examined by comparing its predictions for ethylene-

cluster beam deposition with the results of a more accurate order-N nonorthogonal tight-









binding method. The results show that the REBO potential captures the general

characters of the relevant chemistry.

The deposition processes of interest occur at room temperature; hence, appropriate

temperature control methods must be employed in the simulations. A comparison study

of four temperature control methods during the simulation of cluster deposition finds that

the generalized Langevin equation approach is sufficient for dissipation of excess system

energy if the deposition occurs on a large enough substrate at a moderate incident energy

(< 40 eV/cluster-atom). A new temperature control method has been developed for use at

higher incident energies.

In the simulations of thin film formation through organic cluster beam deposition,

the dependence of the results on the intracluster bonding, incident angle and deposition

direction is examined. Beams of ethylene clusters, adamantane molecules, and C20

molecules are thus deposited on a diamond surface with varying lateral moment along

two different crystallographic orientations at various incident angles.

The simulations of chemical modification of carbon nanotube/polystyrene

composites via ion beam deposition predict that this process can effectively induce the

formation of cross-links between otherwise unfunctionalized nanotube and polystyrene

chains. Modification efficiency is shown to depend on the incident energy and the

composite structure. The responses of the composites to ion beam deposition are different

from the response of pristine polystyrene. The simulations detail the atomic-scale

mechanisms that are responsible for these findings.














CHAPTER 1
INTRODUCTION

Molecular simulation is a relatively new technique, which became known to people

only in the early 1950s. Since then, it has developed rapidly into a valuable tool in

scientific research, complementing both analytical theory and experiment. One major

application field of molecular simulations is materials science. Materials science deals

with the properties of systems of many atoms or molecules. The interactions between

these atoms or molecules determine the overall properties. Therefore, accurate

descriptions of these interactions are critical to understand the properties of the material.

When they are based on the laws of quantum mechanics, molecular simulations can

provide essentially exact estimations of the interatomic interactions by explicitly

considering the electrons and nuclei. Of course quantum mechanical calculations of

interatomic interactions are very complicated and can only be done using computers.

Such simulations involve few approximations and are usually known as ab initio or first

principles simulations. Ab initio simulations can thus be used to predict unknown

properties of a material or can be used as a test of an approximate analytical theory by

comparing the result of the simulation with the prediction from the theory.

Computational demands can be dramatically reduced if some approximations are

introduced into the description of the interatomic interactions through the use of

appropriate empirical functional forms. However, the results of such classical simulations

may contain errors. Depending on how many approximations are introduced, these

simulations are termed either semi-empirical or empirical. Between the two, empirical









simulations may contain more errors because more approximations are employed. In

these cases, the simulation predictions from a microscopic model should be compared

with experimental or more exact ab initio results. If the model turns out to be a good one,

then the simulation can be used to provide atomic insights and assist in the interpretation

of experimental results.

The two most important molecular simulation methods are the Monte Carlo (MC)

method and the method of molecular dynamics (MD). The MC method uses probability

laws and random numbers (hence the name "Monte Carlo") to obtain the ensemble

average and standard deviation of a random variable via random sampling.[P] The first

MC simulation was carried out by von Neumann, Ulam, and Metropolis at the end of

World War II to study the diffusion of neutrons in fissionable material. The MC method

is a statistical method, and any problems involving random processes can essentially be

simulated via this method. Assuming the applicability of classical mechanics, MD

simulation is a deterministic method in which the system evolves according to Newton's

equations of motion.[2] Thus, MD simulations can give full dynamical information and

can be used to study time-dependent phenomena. Both MC and MD methods have

advantages and disadvantages. Although MD is the only reliable method to study time-

dependent properties, conventional MD can only track processes for at most a few

nanoseconds. In contrast, MC method is not subject to time limits and can yield

thermodynamic properties that may not easily be obtained from MD. Depending on the

problem and properties of interest, either MC or MD, or sometimes a combination of MC

and MD, is used in an atomistic simulation.























Figure 1-1.Schematic representation of periodic boundary conditions.[2]

The purpose of molecular simulations is to model the macroscopic sample and

provide information that is not easily detectable from experiments. Unfortunately, due to

the computational limitations of present-day computers, the number of atoms that can be

conveniently handled ranges from a few hundred to a few million. This number is still far

removed from the real size systems, which contain Avogadro's number (6.023 x1023) of

particles. In order to model a macroscopic system in terms of a finite simulation system

of N particles, periodic boundary conditions are employed. This idea can be illustrated by

Figure 1-1,[2] in which the simulation system of N particles is treated as a basic unit and is

replicated throughout space. Therefore, the simulation unit is essentially embedded in an

infinite array of units, all with the same geometrical arrangement of particles. The

application of periodic boundary conditions has two obvious advantages. Without

periodic boundary conditions, the simulation system would simply terminate and be

surrounded by surfaces. The surface atoms have fewer neighbors than the atoms inside.

For a simulation system containing finite number of atoms that is negligible compared

with the real size system, the ratio of its surface atoms to the total number of atoms would

be much larger than in reality. In other words, surface effects would appear to be much


O* .0 0 O Q
0 0 0 .0 0 .0

Q .0 Q -0 Q .0 Q -0


0 0 0 0









more important than what they should be. Thus, the first advantage of the application of

periodic boundary conditions is that the surface effects, which would otherwise be

proportional to N-1/3, are reduced to be proportional to N1.12' 3] Second, as the simulation

progresses, for every molecule that leaves the simulation unit, its image will enter

through the opposite face. Thus, the volume and the density of the simulation unit can be

maintained throughout the simulation. Although the use of periodic boundary conditions

has been proved to be surprisingly effective and successful, it should be noted that such

boundary conditions may lead to correlations not present in the real system.[2] The point

is that the basic simulation unit should be large enough so that those correlations will not

introduce spurious effects.[4]

In molecular simulations, the key is the calculation of the interactions between the

particles, which, in principle, should include not only the interactions between the

particles contained in the simulation system, but also all the interactions between the

particles and their images once the periodic boundary conditions are employed. Even if

empirical functions are used to model these interactions, the computational load is still

impractically high. Under circumstances like these, appropriate cutoff distances (re)

should be used to truncate the interactions between the particles. This means that the

effects of the particles beyond a certain cutoff distance are ignored. While this

simplification certainly will introduce error into the calculation, the error can be made

arbitrarily small by choosing a large enough r, .[2] The introduction of the cutoff distance

is especially meaningful for short-range interactions such as covalent bonding, where

interactions between neighboring particles dominate.









Although the use of a cutoff distance saves tremendous computational time, a

significant amount of CPU time is still spent calculating the distance between the

particles at every step. In order to reduce the unnecessary labor, for instance, in

calculating the distance between two particles that are obviously too far apart to interact

every time, a "neighbor list" table is constructed, which was an idea first introduced by

Verlet. [] The table stores each particle's neighbors and is updated only at predetermined

time intervals. The neighbors include all the particles that are within a certain distance r

(> r ) from each particle. The program updates the neighbor list table only when

considerable displacements beyond r occur. With the introduction of the neighbor list

table, the calculation of the interaction energy between the particles now can be

performed by only scanning through the particles listed in the table instead of scanning

through all the particles. Depending on the problem that needs to be solved, some

modified "neighbor list" techniques that update the table more efficiently have been

reported. [6 7]

Many processes are carried out experimentally at constant temperatures. In order to

model these processes, the temperature of the simulation system should be controlled.

This is achieved by employing thermostat atoms. Thermostat atoms have special

constraints such as extra frictional forces placed upon them, and evolve differently from

the other ordinary atoms as the simulation progresses. The function of these thermostat

atoms is to remove extra energy from the simulation system or to compensate for a loss

of energy, depending on which is necessary to maintain the system temperature. There

have been several algorithms proposed for temperature control, such as the velocity









rescaling scheme, the Nose-Hoover method, and the generalized Langevin equation

approach.

In this dissertation, thin film nucleation through organic cluster beam deposition

and chemical functionalization of carbon nanotube/polymer composites via polyatomic

ion beam deposition are investigated using molecular simulations. Since the phenomena

of interest are time-dependent and both deposition processes are rapid enough that they

occur within a few picoseconds (10-12 seconds), molecular dynamics simulations are used

in both cases.

1.1 Molecular Dynamics Simulations

In classical mechanics, Newton's second law states that in order to make a body of

mass m undergo an acceleration a, a force F is required that is equal to the product of the

mass times the acceleration:

F = ma (1-1)

This equation can also be expressed in terms of the position vector r of the body as

d2r
F=m2 (1-2)
dt2

This is the basis of molecular dynamics (MD). Knowing the force F, based on

Equation (1-2), we can thus study the trajectory of each particle in space and investigate

the time-dependent properties. The problem is how to calculate the force. From the


principle of conservation of energy, we know that the kinetic energy (-mv2 ) and the
2

potential energy (U) of the body can vary, but their sum ( ) is a constant.


-lm2 +U= (1-3)
2


In terms of r, equation (1-3) can be expressed as









1 dr
2m( ) +U=E (1-4)
2 dt

Differentiating both sides of Equation (1-4) with respect to time, we find

d 1 dr
[ m-( ) +)U]= 0
dt 2 dt

and so

dr d2r dU
m + --=0
dt dt2 dt

This can be rewritten as follows because potential energy is a function of the position

U(r):

dr d2r dr
m-- +VU =0
dt dt2 dt

Therefore, we get

d2r
Mn -- =-VU
dt2

Referring back to the Newton's second law (Equation (1-2)), the left side of the above

equation is the force. Thus, the force can be calculated from the potential energy:

F = -VU (1-5)

The potential energy, as stated before, can be obtained using either empirical potential

energy expressions, semi-empirical methods, or exact ab initio approaches. In MD

simulations, the calculations of the potential energy and force are the most time-

consuming parts. Once the force is obtained, Equation (1-2) can be integrated to follow

the time evolution of the atoms in response to the applied forces.

In practice, numerical integration instead of algebraic solutions to Equation (1-2)

are performed. There are several numerical methods for integrating Newton's equations,









including the Verlet algorithm, the leapfrog algorithm and the predictor-corrector

algorithm.[2] In our MD simulations, the predictor-corrector algorithm is used. Based on

Taylor's expansions, if the position (r), velocity (v), acceleration (a) and time derivative

of the acceleration (b) are known at time t, these quantities can be obtained at t+At (At is

the time-step), as shown in the following equation:

1 1
rp(t + At) = r(t) + Atv(t) + (At)a(t) +(At)3 b(t) +***
2 6

vp(t + At) = v(t) + Ata(t) + (At)2 b(t) + .. (1-6)

aP(t + At) = a(t) + Atb(t) + ..
bP(t + At) = b(t)+ -

If we use the truncated Taylor expansion, where the terms higher than those shown

explicitly in Equation (1-6) are ignored, all four quantities can thus be "predicted."

However, no force law has been taken into account so far, and the predicted values are

not based on physics. This deficiency is remedied at the correctorr" step. Knowing the

new position rp at time t+At, we are able to evaluate the new potential energy, and thus

the force at t+At is obtained. Then, from Equation (1-1), the corrected acceleration

a (t + At) can be calculated. Comparing this corrected acceleration with the predicted

one, the error at the prediction step can be evaluated as

Aa(t + At) = ac(t + At) a(t + At)

This term is then used to correct all the predicted quantities as follows:

rc(t + At) = r(t + At) + cAa(t + At)
v (t + At) = vP(t + At) + cAa(t + At) (1-7)
ac(t + At) = a(t + At)+ c2Aa(t + At)
bc(t + At) = b(t +t)+ c3Aa(t + At)









These values are now better approximations to the true quantities, and are used to

predict the quantities in the next iteration. The corrector constants c, are chosen to yield

an optimal compromise between the accuracy and the stability of the algorithm.[2] Gear

discussed the best choice for these constants, which depends on the order of the

differential equations and of the Taylor series.[8] These constants are fixed for a given

order algorithm. For instance, the one we use is a third-order Nordsieck predictor-

1 5 1
corrector algorithm, and the values for c, are co C, -, c2 1, and c3 = Figure
6 6 3

1-2 schematically shows the predictor-corrector MD procedures used in the simulations

described in this dissertation.

In MD simulations, short time-steps are required to yield reliable results. There are

at least two reasons for this. One is due to the quick motion of the atoms (for example,

the time-scale of atomic vibrations is typically 10-13 s[9]). In order to capture atomic

motions accurately, as MD simulations desire to do, the time-step must be much smaller

than the frequency of the atomic motions. The second reason is that, from the integration

point of view, a small At is necessary to achieve the predictions calculated in Equation (1-

6) as accurate as possible. Usually, time-steps on the order of a femtosecond (10-15 s) are

used. Unfortunately, such short time-steps make the modeling of processes that occur on

time-scales larger than a few nanoseconds out of the reach of conventional MD

simulations on present-day computers.

MD simulations can generate atomistic information such as atomic positions and

velocities. Via statistical mechanics, this atomistic information can be related to

macroscopic quantities such as pressure, temperature, heat capacities, etc. Therefore, MD










Start


Figure 1-2.Flowchart of the predictor-corrector MD.

simulations can be used to study these thermodynamic properties as well as time-

dependent (kinetic) phenomena. The first MD simulation was done by Alder and

Wainwright to study the dynamics of an assembly of hard spheres.110' 11] Their studies

provide many important insights concerning the behavior of simple liquids. The first MD

simulation of a real material was carried out by Gibson et al. to model radiation damage

in crystalline Cu.112] In 1964, Rahman performed the first MD simulation using a realistic

potential for liquid argon.[13] Since then, MD simulations have been widely used in









studying solids, liquids, gases, simple and complex hydrodynamic flows, shock waves,

deformation and fracture of materials, chemistry in solutions, conformational changes of

proteins, etc. MD simulations also find application in experimental procedures such as X-

ray crystallography, NMR structure determination, and inelastic neutron scattering.[14]

1.2 Cluster Beam Deposition on Solid Substrate

Clusters typically contain 10 to several thousand atoms. Weakly bound van der

Waals clusters (e.g., noble gas clusters), covalently bound clusters (e.g., fullerenes), as

well as ionic and metallic clusters have been observed. As an aggregate of atoms and/or

molecules, the cluster is a new state of matter that lies between isolated atoms/molecules

and the condensed phase of bulk matter. Due to their high surface-to-volume ratio,

clusters display peculiar properties that differ considerably from those of the constituents

and the bulk material. The properties depend strongly on the number of atoms in the

cluster. By controlling the size of the clusters and other operating variables, such as the

incident energy and substrate temperature, cluster deposition on solid substrates can

produce thin films with specific structures and properties.

1.2.1 Thin Films from Cluster Beam Deposition

Clusters can be generated in jet and beam experiments in both continuous and

pulsed forms.[15] In cluster formation, control of cluster type (noble gases, covalently

bound molecules, metals, etc.), cluster size, and cluster energy are the major objectives.

In 1956, Becker announced the formation of free jet cluster beams of room

temperature gases (Ar and He) produced by expansion through cooled nozzles into a

vacuum environment.[16] Such gas expansions through small nozzles, sometimes with a

carrier gas, are effective sources of molecular gas clusters. For the clusters formed from









these gas expansion sources, the control of pressure and temperature of the stagnation gas

helps to control the cluster size.

Another category of cluster sources, gas aggregation sources, are reported to be

particularly suitable for production of metal clusters of up to thousands of atoms.[17-19]

Briefly, metal vapor is first produced by either thermal evaporation 18] or sputter

discharge.119] The vapor is then projected into a condensation cell filled with cold rare

gas. The supersaturated vapor then nucleates and coalesces to form clusters, the size of

which is controlled by adjusting the carrier gas flow.

Laser vaporization source is especially suitable for generating cluster beams of

refractory materials.[15] Laser ablation of solids produces plasma via the localized heating

induced in the material. By rapid quenching of the plasma, clusters can be produced. This

technique was originally used by Smalley (as cited in "Milani and lannottal15]") and led to

the discovery of fullerenes C60 and C70 in a molecular beam experiment in which laser

vaporized graphite was seeded and expanded in helium.[20] The size of the clusters

generated from the laser vaporization sources is determined by controlling the mean

residence time of the plasma-gas mixture. 21 22]

Ionized clusters are usually generated by electron impact after cluster formation.

Photon ionization of clusters, for instance, by UV lasers, is also reported.[151 The purpose

of ionization the clusters is to achieve easy manipulation and detection of the cluster

energy using electromagnetic fields. As far as the effect of ionization on the deposition

results is concerned, ionized clusters are widely assumed to behave in a similar manner to

neutral clusters due to the low charge carried in each cluster.[23] The deposition of size-

and energy-selected clusters is the ultimate goal for the synthesis of nanocrystalline









materials with tailored properties. Although the deposition of size-selected clusters in

bulk quantities is still in development, controlled deposition of clusters to study cluster-

surface and cluster-cluster interactions in the sub-monolayer regime have been realized

using mass/energy filters.[15]

The past three decades have witnessed an exciting development in thin film

production through energetic cluster-surface collisions using methods such as ionized

cluster beam deposition (ICBD),[24-32] energetic cluster impact (ECI),119] and low-energy

cluster beam deposition (LECBD).122 33, 34] The whole collision process occurs rather

rapidly, typically within a few picoseconds.[35] Thin film formation from energetic cluster

beam deposition has several advantages over traditional atomic ion beam deposition.[19,

23] These include a high, transient concentration of energy and mass that is deposited in a

very localized region of the surface, resulting in conditions of extreme temperature and

pressure under which novel chemical reactions may happen.[28, 36, 37] In addition, compact,

smooth and strongly adhering thin films can easily be made on low temperature

substrates. Since the charge/atom ratio of ionized clusters is very low, space-charge

problems are negligible. Another intriguing feature of energetic cluster beam deposition

is that the surface modification effect is restricted to a very shallow region of the

substrate, avoiding significant property changes to the bulk material. Revealed by MD

simulations, the reason is the collective "plunger" effect of a number of cluster atoms

interacting with the same substrate atom at the same time.[38]

When the deposition occurs at high incident energy (in the range of keV per

cluster), the clusters will experience dramatic morphological changes upon impact. A

variety of outcomes are possible, including scattering of cluster fragments, sputtering of










substrate materials, implantation of cluster atoms, adhesion of the cluster to the surface,

and lateral motion of cluster atoms. These phenomena are summarized in Figure 1-3.[26]

When the clusters are deposited with an incident energy high enough to stick to the

substrate but low enough to maintain their original structure, so-called cluster assembled

materials are produced.[34] This technique is known as low energy cluster beam

deposition (LECBD). The incident energy is typically less than 0.1 eV/atom in LECBD

(in ICBD and ECI, the energy is usually larger than 1 eV/atom).[391 The LECBD

technique is fascinating because the generated thin films keep a "memory" of the free-

cluster phase and the clusters essentially act as building blocks. Therefore, this technique

offers a unique opportunity to prepare thin films from "building blocks" that have been

well controlled in the gas phase.[34]



IONIZED AND
ACCELERATED CLUSTER
DEPOSIT MATERIAL
0 SCATTERING
REEVAPORATION
0
SUBSTRATE -- DEPOSITION
MATERIAL 0 \/11
SPI.ITTERING LATERAL MOTION

IMPLANTATION
SST SUBSTRATE


Figure 1-3.Possible phenomena that may occur after the deposition of energetic clusters
on a solid substrate.[26]

The group at Kyoto University pioneered thin film creation through the high

energetic cluster beam deposition.[24, 27] The technique they developed is generally known

as ionized cluster beam deposition (ICBD). Since its development, ICBD has been widely

used to produce thin films from the deposition of a variety of materials, such as metals,[24'









26] nitrides,[31] semiconductors,[24, 32] and organic materials. [25 28-30] However, theoretical

calculations show that standard ICBD conditions do not favor the formation of

clusters.[151 Experimentally, it was claimed that small clusters of up to 25 atoms might

exist in the clusters produced from a typical ICBD sources, but there was no or a very

small fraction of large clusters. 26, 40, 41]






liquid nitrogen 5




Ar I TOF

c I All IA2




Figure 1-4. The principle of the experimental set-up for thin film formation by energetic
cluster impact (ECI).1191 Cl and C2: magnetron cathods; Al, A2 and A3:
apertures (the region between Al and A2 is the condension zone, which can
be cooled by liquid N2); H: heater; R: crystal microbalance; S: substrate
holder; TOF: time-of-flight mass spectrometer to measure the cluster size.

Energetic cluster impact (ECI) is a technique developed by Haberland's group in

Freiburg.[19' 42] Figure 1-4 demonstrates the experimental set-up of thin film deposition by

ECI.1191 The size of the clusters formed ranges from 50 to more than 106 atoms per

cluster. What is unusual in this technique is that a large percentage (30-80%) of these

clusters has already been ionized; therefore, no additional electron ionization step is

necessary. The cause for this simultaneous ionization is the use of the magnetron

cathodes (C 1 and C2 in Figure 1-4), which not only help to generate vapor by sputtering,

but also ionize the clusters by the afterglow from the sputter discharge. Thin films from









the deposition of metal (Mo, Cu, Al, and stainless steel) and SiO2 on Si and glass

substrates at room temperature using ECI have been reported so far.[19' 42] The incident

energy of the clusters is shown to be critical in determining the quality of the resultant

film.

In the past 30 years, a large amount of effort has been spent in understanding thin

film deposition from cluster-solid collisions. Although phenomenological models derived

from experimental observations can explain some of the relationships between deposition

conditions (incident energy, cluster size, and substrate temperature) and the resulting film

properties and structures, a deep enough understanding and, even more importantly, the

ability to predict how a change in deposition conditions leads to a change in thin film

properties, still remain as a longstanding challenge. This challenge has resulted in the

exploration of computer simulation, which has been proved to be a predictive as well as

explanatory tool in many cases. Among the various simulation techniques that may be

used, MD simulation is especially well suited to study the energetic deposition of clusters

because this process typically occurs within a few picoseconds. MD simulations allow

one to view the atomic motions and alter conditions of the system that may not be easily

varied experimentally. Therefore, simulations can provide valuable information about the

atomic mechanisms responsible for the resulting properties and structures. An added

feature of MD simulations is that quantities comparable to experimental results can be

obtained, especially after the breakthrough development of atomic scale experimental

techniques, such as atomic force microscopy (AFM) and scanning tunneling microscopy

(STM).









The first MD simulation of cluster-surface collisions was made by Muller with a

two-dimensional model using Lennard-Jones potentials.[43] Albeit simple, his simulations

disclosed the important role played by the cluster energy per atom in the quality of the

thin film. Following Muiller's lead, researchers around the world, including those who

developed the experimental cluster deposition techniques, performed a variety of MD

simulations, sometimes in combination with experimental work. The nucleation and

growth of the thin films,[44-49] evolution of clusters after impact, [35, 44, 46, 50-57] defect

formation in the substrates,[46-48' 58-61] and film morphology,[42' 62-64] have been examined

and documented. These MD simulations provide atomic scale insights into the effects of

cluster energy,[47' 48, 65-73] cluster size,[67, 74] and substrate temperature[67' 75-77] on the

resultant film structures and properties. As expected, these investigations further people's

understanding of the underlying reaction mechanisms [36, 53, 59, 78, 79] as well as the thin

film nucleation[44' 46, 49, 80, 81] and defect formation mechanisms.[59] Together with the

experimental studies, these MD simulations help to provide a comprehensive picture of

cluster-solid interactions.

1.2.2 Motivation and Objectives

Among various thin films, organic thin films are technologically important

especially in electronic and optical device applications. For example, organic

electroluminescent (EL) devices can produce a strong light emission with a direct current

of relatively low voltage.[82] Additionally, deposition of organic materials can make

diamond-like carbon films,[83-86] which have many characteristics of bulk diamond

including extreme hardness and high thermal conductivity.

Conventional solvent-free methods to make organic thin films include physical

vapor deposition (PVD) and chemical vapor deposition (CVD).182-88] Nevertheless, these









methods are not effective at achieving crystalline structures in the deposited films, and

hence, the desired properties are not obtained.[30] Energetic cluster beam deposition,

however, appears to be successful in this respect.[30] In fact, polyethylene thin films with

a structure close to the single crystalline polyethylene, 25] tetraphenylporphine thin films

with preferential crystal orientation,[28] and anthracene thin films with superior

photoluminescent and electroluminescent properties[251 have been reported using

energetic cluster beam depositions. The researchers at Charles University found that

cluster beam deposition could produce phthalocyanine thin films with structures and

properties ranging from those of evaporated films to the plasma polymerized samples.[29]

These studies indicate that cluster beam deposition is indeed a versatile and promising

technique to prepare organic thin films for functional devices.

Despite the impressive experimental work in organic thin film formation through

energetic cluster-solid collisions, there is little fundamental understanding of the reaction

and film nucleation mechanisms that occur during organic cluster deposition. These

problems can be addressed in MD simulations. Although a large amount of simulation

work has been carried out to study cluster-solid collisions as mentioned before, most deal

with metallic clusters[35, 42, 46-48, 52, 54, 56, 57, 60, 62, 64, 71-73, 77, 80, 81] or noble gas clusters.[43-45,
50, 51, 53,61, 66,78,79, 89,90] MD simulations of the deposition of fullerene molecules, i.e.,

carbon clusters, have also been reported.[36' 63, 65, 66, 70, 75, 91-94]

For the last six years, the Sinnott group has used MD simulations to study the

deposition of organic clusters on diamond surfaces.[95-105] The clusters that have been

considered include organic molecular clusters of ethane,195] ethylene,195' 96, 100, 101]

acetylene, 95-100] and adamantane.1102] Both single cluster deposition and cluster beam









deposition have been examined. The simulations show that due to the deposition-induced

high system temperature and pressure, numerous addition reactions may occur among the

incident molecules and between the impact cluster and the surface when the incident

energy is within 3 eV/molecule of the binding energy of a single cluster molecule.[95]

This prediction is supported by the experimental work of Lyktey et al., who showed that

polyethylene could be made from energetic collisions of molecular clusters of ethylene in

the gas phase;[106] and Sakashita et al., who reported that solid-state polyacetylene was

produced under high pressure.[1071 These simulation studies have also addressed the

dependence of film nucleation and growth on deposition conditions such as molecular

reactivity, 95, 100] cluster size,199' 101] incident energy, 95, 96, 102] impact frequency,[97] surface

reactivity,198, 100] and surface temperature.1100, 101] The formation of craters on the surface

has been considered as well. These craters were found to be able to activate some surface

atoms and promote the adhesion of clusters. These simulation results are in agreement

with the reported cluster beam deposition experiments for making organic thin films.[25'

28, 30]

Varying the angle of incident particles has pronounced effects on the growing film

morphology and properties. This has been shown in both simulations[64, 108-112] and

experiments.[113-118] For instance, in vacuum evaporation, the oblique incidence of vapor

atoms is found to result in thin films with anisotropy in various macroscopic properties,

such as magnetic properties, electrical resistance, optical and mechanical properties.[119]

In atomic ion beam deposition, the non-perpendicular incidence leads to non-local

shadowing, which is the source of the resulting porous and columnar growth

morphology.1108, 113, 114] The incident angle of atomic ion beams is also found to influence









thin film composition,[110, 115] surface-trapping probability,[1171 and kinetic energy

distribution of the sputtering surface fragments.[116] Deposition of energetic cluster beams

also shows that the surface smoothing effect[64' 111, 118] and the sputtering effect[118] are

strongly affected by incident angle.

Although extensive simulations have been done by the Sinnott group in

investigating the deposition of organic clusters, the effect of incident angle has not been

considered previously. Therefore, one of the objectives of the study reported in this

dissertation is to investigate angle effects on the deposition of organic clusters. Since a

crystalline substrate is used in the simulations, film nucleation and growth at oblique

deposition angles may have crystallographic orientation dependence, which is another

factor examined here. One of our previous studies investigated the deposition of an

adamantane cluster beam, while all the rest focused on clusters where the constituent

molecules were weakly bonded through van der Waals interactions. In this dissertation,

clusters with different types of chemical bonding holding the incident particles together

are considered. It is the intention of this study to provide a more complete description of

thin film nucleation and growth from energetic organic cluster beam depositions.

1.3 Carbon Nanotube/Polymer Composites

Carbon nanotubes posses unique structural, electrical, and thermal properties. 120-
129] Recent developments in the synthesis of carbon nanotubes have improved both their

quality and quantity.[130-133] These advances have paved the way for the expected new

material applications of carbon nanotubes. Particular effort has been spent in making

nanocomposites using these quasi-one-dimensional nanostructures as reinforcement to

capitalize on their extraordinary mechanical properties on a macroscopic scale.









1.3.1 Carbon Nanotubes

Carbon nanotubes, also known as tubular fullerenes, consist of sp2-bonded carbon

atoms. They were first reported in 1991 by Sumio Iijima[134] who was studying the

material deposited on the cathode during the arc-evaporation synthesis of fullerenes.[135]

Depending on the conditions under which they are produced, carbon nanotubes can

assemble either as multi-layered co-axial tubes (multiwalled nanotubes, MWNTs) or as

single-layer tubes (single-walled nanotubes, SWNTs). Each layer of the carbon nanotube

can be thought of as a cylinder rolled from a sheet of graphite, as shown in Figure 1-5.

Depending on the growth process, the lengths of carbon nanotubes can vary from

approximately 100 nm to several microns and the diameters can range from 1 to 20 nm.

The manner in which the graphene sheet is rolled into the cylinder can produce carbon

nanotubes of various helical structures. As illustrated in Figure 1-6, the "rolling up" can

be performed by adding the integer lattice vectors m and n together and then placing the

tail and head of the resulting vector on top of each other.11321 As a result, zigzag

nanotubes have vectors (n, 0) or (0, m), while armchair nanotubes have vectors (n, n).

These are the two achiral nanotubes; all other vectors (n, m) correspond to chiral

nanotubes.





Roll-up, .,
---- -. "-.-. '.'-. .-




graphene sheet SVWT


Figure 1-5.A graphene sheet rolled into a single-walled carbon nanotube (SWNT).










tube
axis




Zigzag Conformation Armchair Conformation


5






1 2 3 4 5
(n,m) lattice vectors


Figure 1-6. The "rolling up" of a graphene sheet to produce carbon nanotubes of various
helical structures.[132]

The three most common methods to produce carbon nanotubes are the arc, laser,

and chemical vapor deposition techniques. The standard carbon arc-evaporation method

can make carbon nanotubes in large quantities by carefully choosing the type and

pressure of the gas surrounding the arc, and the cooling of the electrodes and the

chamber.1136, 137] However, in this way, only MWNTs are produced. By introducing metal

catalysts such as Co, Fe, or Ni into the carbon arc, significant quantities of SWNTs are

formed.[138, 139] In 1996, Smalley's group found an alternative way to prepare SWNTs.1130]

It involved the laser vaporization of graphite and resulted in a high yield of SWNTs.

These tubes tended to form aligned bundles (ropes) and had unusually uniform diameters

(-1.4 nm). Chemical vapor deposition (CVD) provides more controllable routes to

produce nanotubes with defined properties.[132] The general nanotube growth mechanism

in a CVD process involves the dissociation of hydrocarbon molecules (such as C2H2,









C2H4, xylene, benzene, toluene, etc.)[1321 catalyzed by transition metal, and dissolution

and saturation of carbon atoms in the metal nanoparticle.1133]

The synthesized carbon nanotubes are often found to be capped at the ends. The

"caps", different from the sidewall that is mainly made up of hexagonal rings, contain

pentagons and heptagons (Figure 1-7).[140] These non-hexagonal rings help to introduce

curvature as well as strain into the tube caps.









Figure 1-7.A model of a capped SWNT.[140]

The as-produced nanotubes often come with a number of impurities whose type

and amount vary with synthesis methods and conditions. For example, Figure 1-8 shows

a TEM image of a SWNT surrounded by catalyst particles and amorphous carbon.

Carbonaceous impurities, such as amorphous carbon nanoparticles and soot, are the most

common impurities. 130, 138, 141] The early gas phase purification method, which burnt the

crude nanotubes in the oven and simultaneously blew air or oxygen through the system,

only resulted in a very low yield (about 1%) of pure nanotubes.[142] One possible reason

for this is the uneven burning of the sample. Therefore, liquid phase purification methods

on well-dispersed samples were tried. It was discovered that by using oxidants such as

H2NO3/ H2SO4[143] or an acid solution of potassium permanganate (KMnO4),[144] the

amorphous carbon and other impurities could be washed away effectively. The yield of

pure tubes could be as high as 50%.[144] Nanotubes can survive harsh oxidation

environments because, like graphite, nanotube walls are relatively inert. However, this is









not the case for the caps due to the strain and high degree of curvature in those

regions.[145] As a result, the purified nanotubes are opened at the ends.[143' 144] The

dangling bonds at the ends are usually stabilized by bonding with carboxyl or hydroxide

groups.














Figure 1-8.A SWNT formed in the catalytic carbon arc method.[141]

The reason why carbon nanotubes have attracted wide attention since their

discovery is their unusual electrical, mechanical, and thermal properties associated with

their unique structures. For example, they could be insulating, semi-conducting, or

metallic depending on their diameter and chirality. This property was first predicted

theoretically [146-149] and then verified experimentally.1150' 151] The sp2 carbon-carbon

bond in the basal plane of graphite is the strongest of all chemical bonds,[135] but the

weakness of the interplanar forces make ordinary graphite impossible to be used as a

structural material. Because of carbon nanotube's highly perfect graphene structure, the

mechanical stiffness and strength of carbon nanotubes are expected to be very high. It

was initially difficult to directly probe the mechanical properties of individual nanotubes

due to their nanoscale size. However, breaks in nanotubes, either in tension or

compression, are rarely observed during specimen cutting.[152] This fact implies that

indeed nanotubes have very high strength.









Theoretical calculations of the mechanical properties of SWNTs suggest that the

Young's modulus should be close to the in-plane elastic modulus of graphite (1.06

TPa).1153] The strength of MWNTs will be limited by the ease with which each layer

slides with respect to the other. In the last few years, a number of experimental

measurements of the Young's modulus of nanotubes using TEM1128] or AFM[154]

techniques have been reported. The average results from these experiments suggest

values for Young's modulus of individual nanotube around 1 TPa, in good agreement

with the theoretical predictions.

It is known that carbon fiber reinforced composites are often stronger than steel,

but much lighter. Because of this, they are used to replace metals in many applications,

from parts for airplanes and space shuttles to sports utilities. Carbon nanotubes have been

proposed as the ultimate carbon fibers[135] and are considered excellent reinforcing fibers

for the new generation of high performance nanocomposites.

1.3.2 Carbon Nanotube/Polymer Composites

There has been considerable effort devoted to studying nanotube/polymer

composites.1152, 155-175] Investigations of nanotube/metal composites[176] and

nanotube/ceramic composites[1771 have also been reported. It is found that the nanotubes

do stiffen the composites,1163, 169, 170, 173, 177] change the electronic structure of the

polymer,1159] improve the conductivity of the composites,1155' 169, 172, 175] and in some cases

retard the onset of thermal degradation[170' 175] and protect the polymer from

photodegradation.[158]

The successful application of carbon nanotubes, especially as structural

reinforcement in polymer composites, depends on the ability to transfer load from the

matrix to the nanotubes.11641 Effective load transfer requires strong interfacial interaction









between the matrix and the nanotubes.1154] Without special surface treatment, some work

on the carbon nanotube/polymer composites suggested strong adhesion between the

matrix and the nanotubes, while others showed the opposite.

Wagner et al. reported the observation of multiple nanotube fragmentation under

tensile stresses using a nanotube-containing thin polyurethane film cured under a UV

lamp.[160] Similar fragmentation tests are routinely performed to study the fiber-matrix

stress transfer ability in fiber-reinforced composites. Thus, their observation proved a

rather good load transfer between the nanotube and the polymer. It was suggested that the

strong nanotube-polyurethane interface arose from the possible chemical bonds formed

through a photo-induced "2+2" cycloaddition, a mechanism as demonstrated in C60

photopolymerization. 1781 The same group also studied nanotube/epoxy composites and

nanotube fragmentation was again observed.[166] A recent study of carbon

nanotube/carbon fiber hybrid composites suggested the presence of carbon nanotubes at

the carbon fiber/epoxy interface improved the interfacial shear strength of the

composites, which also supports good adhesion between the nanotube and the polymer

matrix.[179] The microscopic and spectroscopic study of carbon nanotube/poly(m-

phenylenevinylene-co-2,5-dioctyloxy-p-phenylenevinylene) (PmPV) composites showed

excellent wetting of the nanotubes by the polymer, again demonstrating considerable

interactions between the nanotube and the polymer.[1571 The study of carbon

nanotube/poly(phenylacetylenes) (CNT/PPAs) by Tang et al. was very interesting in that

the nanotubes were found to be helically wrapped by the PPA chains.[1581 The wrapping

process was believed to result from the strong C H ... z hydrogen bonds formed









between the polymer with terminal alkyne groups (RC C H) and the nanotube that is

rich in '7 electrons.

However, an earlier study of carbon nanotube/epoxy composites indicated weak

interfacial bonding between the tubes and the matrix.[152] Schadler and co-workers

studied the load transfer in carbon nanotube/epoxy composites in both tension and

compression. By monitoring the shift of the second-order Raman peak at 2700 cm-1

which is sensitive to the applied strain, they concluded that the load transfer in

compression was effective while in tension it was poor, as demonstrated by a significant

shift in compression and non-shift in tension.[161]

Other work gave mixed results on this topic. 167, 171-173] For example, an

investigation of the fracture surface of carbon nanotube/polyhydroxyaminoether

composites[1711 showed that, in most cases, the polymer adhered to the nanotube.

However, in contrast to Wagner's studies,[160' 166] no broken carbon nanotubes were

observed at the fracture surface, which indicated that the load transfer from polymer to

nanotube was not sufficient to fracture the nanotubes. In studying carbon

nanotube/polystyrene (CNT/PS) composites, Qian et al.1173] found effective load transfer

from the matrix to the nanotube by comparing the measured composite modulus with the

calculated value assuming there were strong bonds between the two phases. However,

when they were watching crack nucleation and propagation using in situ TEM, the

composites failed through nanotube pullout (Figure 1-9), a phenomenon that occurs when

there is poor adhesion between the reinforcement and the matrix.

Based on these experimental results, computer simulations were carried out to

study the nanotube/polymer interface, trying to reveal the underlying mechanisms that are
























Figure 1-9.In situ straining of a CNT/PS composite in TEM.11731

important for reinforcement of the matrix. The molecular mechanics simulations and

elasticity calculations of the interfacial characteristics of a carbon nanotube/polystyrene

composite indicated that, in the absence of atomic bonding, the interfacial load transfer

ability came from electrostatic and van der Waals interactions, deformation induced by

these interactions, and stress arising from mismatch in the coefficient of thermal

expansion.[1741 A molecular dynamics simulation of carbon nanotube pullout from a

polyethylene matrix[180] suggested that the interfacial friction model based on a critical

force could be used to describe the entire process of nanotube pullout. In this study, 0.1

nN was predicted to be this critical force for composites with only van der Waals

interactions between the nanotube and the matrix.

In composites, a high interfacial shear stress between the fiber and the matrix

guarantees good load transfer. Typically, the introduction of mechanical interlocking and

the formation of strong bonds, such as covalent or hydrogen bonds, between the

reinforcements and the matrix will increase the interfacial shear stress. Between the two,

the second method is much more effective. It is also applicable to carbon nanotube

containing nanocomposites. In making carbon nanotube/epoxy composites, Gong et al.









found the addition of surfactant can increase the elastic modulus of the composites by

30% in contrast to those processed without the surfactant.[163] There, the surfactant acted

as a coupling agent. It interacted with the carbon nanotubes through the hydrophobic

segment, and the hydrophilic segment simultaneously interacted with the epoxy via

hydrogen bonding. Molecular dynamics simulations of the carbon nanotube/polyethylene

composites with and without chemical bonding between the nanotubes and polymer

showed that, in non-bonded systems, no permanent load transfer was observed; while in

bonded systems, the shear strength could be enhanced by one or two orders of

magnitude.[181, 182]

As a result, in order to take real advantage of the high modulus and high strength of

carbon nanotubes, chemical functionalization of carbon nanotube especially of the carbon

nanotube wall, which will favor strong bond formation between the nanotube and the

matrix, is necessary. As mentioned above, the carbon atoms on the walls of nanotubes are

chemically stable due to the aromatic nature of the bonding. The chemistry available for

modification of the nanotube wall without breaking the tubular structure is thus restricted.

Recently developed chemical methods, including fluorination,[183-187] and chemical

treatment of carbon nanotubes with dichlorocarbene, 188, 189] can chemically functionalize

nanotube walls. These modified carbon nanotubes have better dispersion in solvent

without aggregation, which is essential in composite processing, but do not result in

significant increase in the interfacial shear strength. The oxidation of a nanotube wall by

using a 3:1 mixture of concentrated H2SO4 (90%)/HN03 (70%)[190] and the

functionalization of the wall via electrochemical reduction by using an aryl diazonium

salt[1911 have been recently reported. These techniques can tailor the surface properties of









a carbon nanotube to be favorable to form chemical bonds during nanotube composite

processing. A combined computational and experimental study indicated that the local

reactivity of the nanotube walls could be enhanced by the introduction of local

conformational strain, such as "kinks" resulting from bending and "ridges" resulting from

torsional strain.[145] This so-called "kinky chemistry" is quite interesting because of its

possibility to selectively functionalize the sidewall.

1.3.3 Motivation and Objectives

Since the discovery of carbon nanotubes, TEM has been the most frequently used

technique to study their structure. When using TEM, people noticed the evolution of

carbon nanotubes under the irradiation of an electron beam.[1921 Electron irradiation of

carbon nanotubes can result in the formation of various atomic scale defects in the

nanotube walls.[192-194] Besides, electron irradiation can cause nanotubes to shrink in

diameter[193] or merge with other nanotubes through bond breaking and reformation.[195'
196] In other words, electron irradiation can activate the otherwise inert nanotube wall.

Similar findings have been seen in simulations and experiments of the ion irradiation[197-
201] and plasma activation[202] of carbon nanotubes. Specifically, simulations predict that

the deposition of ions, such as CH3 C and Ar+, at low energies of 10-80 eV/ion[199' 200]

or higher,[201] can induce cross-links between nanotubes arranged in bundles,1199' 200]

neighboring shells in MWNTs,1200] or the nantube and the underlying substrate.1201] A few

examples are shown in Figure 1-10.[200] Experiments of the deposition of mass-selected

CF3 ion beams deposited at 45 eV find strong evidence of chemical functionalization of

the nanotube wall,1200] which confirms the simulation predictions. In addition, both

experiments and simulations of ion deposition on pure polymers show that the deposition

can lead to cross-linking between polymer chains.[203, 204] All these findings suggest a









possible novel approach that carbon nanotube/polymer composites could be chemically

functionalized to form covalent bond at the interface without first treating the tubes

and/or exposing them to strong acidic or the other harsh chemical environments as

described before.














Figure 1-10. Cross-linking formed between nanotubes and adjacent shells in the case of
MWNT as a result of energetic ion deposition.[200]

In this dissertation, molecular dynamics simulations are used to explore the

modification of a carbon nanotube/polystyrene composite through the deposition of a

beam of polyatomic ions of C3F5+. One objective is to determine if polyatomic ion beam

deposition is a suitable approach to induce covalent cross-links between otherwise

unfunctionalized nanotubes and the polymer matrix. The second objective of this study is

to examine the effects of the incident energy and the nanotube/polymer geometry. The

third objective is to determine how the presence of the nanotube in the polymer affects

the outcome of the polyatomic ion beam deposition relative to deposition on a pristine

polymer substrate.

1.4 Organization of the Dissertation

The use of empirical potential energy functions to describe the interatomic

interactions may not be as quantitatively accurate as ab initio or semi-empirical methods









due to the approximations introduced and parameter fitting. But, they have obvious

advantages over semi-empirical and ab initio methods, especially when large systems and

long timescales are desired. In this dissertation, the reactive empirical bond order

(REBO) potential for carbon-based covalent systems is used to describe the short-range

covalent bonding. In order to test the accuracy of the REBO potential, in Chapter 2, the

simulation results using the REBO potential and a semi-empirical tight-binding scheme

are first compared. Since in experiments, both the cluster beam deposition and

polyatomic ion beam deposition usually occur at room temperature, a proper temperature

control algorithm should be employed in the simulations. Chapter 3 thus describes

several temperature control methods. Their efficiency specifically in dealing with the

deposition systems is presented. Chapter 4 reports the MD simulation results for thin film

nucleation via organic cluster beam depositions. Chapter 5 presents the MD simulations

of chemical modification of carbon nanotube/polymer composites through polyatomic

ion beam deposition. Finally, the overall conclusions of this work are given in Chapter 6.














CHAPTER 2
COMPARISON OF O(N)/NOTB AND REBO POTENTIAL MOLECULAR
DYNAMICS SIMULATIONS

In modeling a many-body system, it is essential to find an appropriate method to

calculate the interatomic energies and forces. These interactions can be considered using

ab initio calculations, semi-empirical methods, or empirical function expressions. In ab

initio calculations, all the electrons are treated explicitly and quantum mechanically.

Thus, they give the most exact results but are the most computationally demanding. Ab

initio calculations are usually limited to modeling small systems containing several

hundred atoms. Semi-empirical methods explicitly consider the contribution of some of

the electrons (generally some of or all of the valence electrons), which is usually denoted

as the band structure energy; the contributions of the other electrons are taken into

account via various mathematical expressions fitted to experimental data or first principle

(ab initio) results. Because of their semi-empirical character, these methods usually give

fairly accurate results while the computational workload is comparatively small, and

relatively large-scale simulations (- 5,000 atoms) are possible. Empirical potential

functions are further simplified mathematical expressions that do not explicitly consider

any electron contributions, but model the interatomic forces from the interactions of

electrons and nuclei by appropriate parameter fitting reasonably well.1205] Due to their

great computational efficiency, empirical potential functions have obvious advantages for

large systems (more than several thousand atoms) and long simulation times, although









the results may be subject to errors that can arise from the assumed functional forms and

parameter fitting.[205]

The order-N nonorthogonal tight-binding (O(N)/NOTB) method of Wu and

Jayanthi[206] is a semi-empirical approach that explicitly incorporates the band structure

energy. This scheme has been successfully applied to study a wide range of problems

associated with nanostructures, including the initial stage of growth of Si/Si(01),[207]

carbon nanotubes,[208] and Si nanoclusters.[209] The reactive empirical bond-order (REBO)

potential is a refinement of the Abell-Tersoff potential and was parameterized by Brenner

et al. initially for hydrocarbons.[210,211] Due to its flexibility to allow bond breaking and

reforming with appropriate changes in atomic hybridization, the REBO potential gives

structural predictions for diamond surface reconstruction consistent with ab initio

studies.[212, 213] It has found extensive uses in modeling other structures and processes as

well, such as chemical processes in reactive hydrocarbon systems,[95, 214-217] properties of

fullerenes and carbon nanotubes,1145' 218-225] and mechanical processes associated with

indentation, friction and compression.[225-230] An extended REBO potential for Si-Si, Si-C

and Si-H interactions has also been reported to reproduce ab initio predictions and/or

experimental results of the equilibrium structures and binding energies for C-Si-H

systems reasonably well.[231-234] Despite all these successful applications, as is the case

with most empirical potentials, there are cases where the results from the REBO potential

lack the quantitative accuracy even while the qualitative predictions are correct.[235-237]

In this work, simulation results from the O(N)/NOTB method and the REBO

potential are compared and contrasted. The process investigated is the collision of

hydrocarbon clusters on diamond surfaces. This process usually occurs on the time scale









of a few picoseconds (ps) if the collision happens at hyperthermal (1-500 eV) or higher

energies. Molecular dynamics (MD) simulations are thus well suited to study this

process. For convenience, the MD simulation using the REBO potential is denoted as

empirical MD (EMD), and the one using the O(N)/NOTB method is O(N)/NOTB-MD.

The purpose of this work is to check both the qualitative and quantitative predictions

from the REBO potential against the results from the O(N)/NOTB method, and thus to

obtain a better knowledge of the reliability of the REBO potential.

2.1 Order-N Nonorthogonal Tight-Binding (O(N)/NOTB) Method

In the semi-empirical tight-binding scheme, the total energy of a system can be

written as[238]:

Uto =Ub + Urep (2-1)

where Ub, is the band structure energy that considers the electronic contributions to the

atomic forces. Urep is a pair wise repulsive term, which considers the effects of the

overlap interactions and the possible charge transfer that are neglected in Ub~. Urep can be

expressed as a sum of suitable empirical two-body potentials (1(ru )):


Urep (I) (2-2)


where r is the distance between the ith andjth atom. D(r ) is obtained by parameter

fitting.

In the O(N)/NOTB approach of Jayanthi et al.,1206] the band structure energy is

expressed as:

Ubs = 2 E = 2 _. p,'jiHj,8ia (2-3)
2(occ) ia,]P









where the multiplier 2 takes account of the electron spin, E, is the electronic eigenenergy

of the system, Pjp is the density matrix, and Hp,, is the Hamiltonian matrix element.

Therefore, the electronic contribution to the force acting on the ith atom can be evaluated

as:

aUb, aH as
F,e aUb, = _2 P {p,,jP Hj,, ,jp cJs, } (2-4)
i a,]jp O, 01,

where r,,Jp is the energy density matrix, and SJ,, is the overlap matrix element. The


total force acting on a given atom i, is thus given by FI = Fei OU r,


The application of the tight-binding method to study a system containing 103-106

atoms is usually restricted by the N3 scaling of the calculation of the total energy and

atomic forces. Using the property that p p(r ) -> 0 and r,,J p( ) -> 0 as r -> oc, the

summations in Equations (2-3) and (2-4) can be truncated to include only terms within a

sphere of radius r, if it can be established that p ,p(;) = 0 and r,,,jp( ) 0 for

, > r,,,. With the truncation, the calculation of the total energy and the atomic forces will

depend linearly on the size of the system. That is, it becomes an order-N (O(N)) scaling

procedure. Therefore, this O(N)/NOTB scheme can be efficiently applied to a system that

contains more than 1000 atoms.

In this O(N)/NOTB approach, the parameters characterizing the C-H interactions

are fit so that the predicted bond lengths and bond angles for C2H2, CH4, C2H4, and C2H6

are in good agreement with experimental results. The MD simulations using the

O(N)/NOTB method were performed by our collaborators in the University of Louisville.









2.2 Reactive Empirical Bond-Order (REBO) Potential

The general analytic bond-order potential energy formalism was originally

introduced by Abell,1239] in which he showed that the chemical binding energy Ub can be

simply expressed as a sum over nearest neighbors:

Ub =ZZ[V () V -b,VAJ)] (2-5)


The functions VR (r) and VA (r) are pair-additive terms that describe the interatomic

repulsions and attractions, respectively. The term bY is a bond-order term between atoms

i andj. A practical implementation of Abell's bond-order formalism was first developed

by Tersoff for group IV elements.[240, 241] By introducing analytic parameterized forms for

the bond order term, the Tersoff potential can accurately treat silicon, germanium and

their alloys, but is less reliable for carbon.[213]

Carbon is a very unique element in that it has a variety of different types of C-C

bonding with very different energies and bond lengths, which results in a large variety of

polymorphic forms, such as diamond, graphite, fullerene, and various amorphous

phases.[242] The Tersoff potential does not distinguish the chemical character of the

bond;[213] therefore, it cannot describe processes involving a change of bonding

characters, such as surface reconstruction and chemical reactions, very well. In 1990, the

reactive empirical bond-order (REBO) potential for describing solid-state carbon and

hydrocarbon molecules was reported by Brenner.1210] In this potential, nonlocal terms,

which properly account for the chemical bonding changes based on the change of

neighboring atoms, are added to the Tersoff potential. Consequently, the REBO potential

allows for bond formation and breaking with appropriate changes in atomic

hybridization, which is crucial for realistic treatment of such processes as chemical









reactions. Thanks to the development of the REBO potential, it is now possible to model

simple organic chemical reactions within an empirical scheme. However, in the first

generation REBO potential, the terms describing the pair interactions in Equation (2-5)

were found to be too restrictive to simultaneously fit equilibrium distances, bond

energies, and force constants for carbon-carbon bonds. What is more, both terms go to

finite values as the distance between atoms decreases, which limit the possibility of

modeling processes such as energetic atomic collisions. Therefore, the second generation

REBO potential, using improved analytic functions for interatomic interactions and an

expanded fitting database, was developed.[211] The forces associated with rotation about

dihedral angles for carbon-carbon double bonds, as well as angular interactions

associated with hydrogen centers, have also been included. In this study, the second

generation REBO potential[211] is used.

The analytic terms describing the pair interactions in Equation (2-5) in the second

generation REBO potential are written as:


VR(r) fc(r)(1+ )Ae (2-6)


VA(r) =f (r)Z Be -' (2-7)
n

The function for the repulsive interactions (Equation (2-6)) goes to infinity as the

interatomic distance (r) approaches zero, and the attractive term (Equation (2-7)) has

sufficient flexibility to simultaneously fit the bond properties. The variables Q, A, a, B

and / are all parameters that are fit to experimental or ab initio data for both hydrocarbon

molecules and solid-state carbon, and are adjusted using a standard fitting routine. The









function fC (r) limits the range of the covalent interactions. For carbon, the value of

f (r) will be one for nearest neighbors and zero for all other interatomic distances.

The bond-order term in the second generation REBO potential is written as the sum

of terms:


b, =[b-" + b "] + b" (2-8)


Values for the functions b'" and b depend on the local coordination and bond angles

for atoms i andj. The dependence on bond angles is necessary to accurately model elastic

properties and defect energies. The function b, is further expressed as a sum of two

terms:

b r + bD (2-9)

where the value of the first term depends on whether a bond between atoms i andj has

radical character and is part of a conjugated system. The value of the second term

depends on the dihedral angle for carbon-carbon double bonds.

Within a single expression, as introduced by Abell (Equation (2-5)), the revised

REBO potential accurately reflects the bond energies, bond lengths and force constants

for carbon-carbon bonds. It has produced an improved fit to radical energies, conjugated

7T bonding properties, and diamond surface properties. It also gives a reasonable

description of diamond, graphitic and hybrid diamond-graphitic structures.[243]

The REBO potential describes short-range covalent interactions. In order to take

into account long-range van der Waals molecular interactions, Lennard-Jones (LJ) 6-12

potential can be coupled with the REBO potential. Thus, the combined expression to

calculate the binding energy between atoms i andj is:









U ZZ[VR()- bA( J, )+ VVd(,)] (2-10)


where Vdw is the contribution from the van der Waals interactions, which, in turn, can be

expressed as:


Vd (r) = 4E[(C12- (C)6] (2-11)
r r

where E and a are Lennard-Jones parameters.[244] The LJ potential is turned on only

when the REBO potential has gone to zero (at about 2.0 A for C-C interactions, 1.8 A for

C-H interactions, and 1.7 A for H-H interactions).

2.3 Testing Systems

The energetic cluster-beam investigated in this study contains two molecular

ethylene clusters. Each cluster is formed by arranging eight ethylene molecules on a

three-dimensional grid in which three-dimensional periodic boundary conditions are

applied. Therefore there are 48 atoms per cluster and 16 of them are carbon atoms. First,

the cluster molecules are equilibrated at 500 K. When the cluster has fully relaxed, it is

quenched to 5 K to minimize the internal cluster kinetic energy. The clusters are then

combined together to form a beam. Before deposition, the whole beam is placed about 4

A above the surface. The two clusters are deposited along the surface normal at an

incident energy of 25 eV/molecule, which corresponds to a velocity of 13.1 km/s. The

distance between the two clusters in the beam is about 4 A. Therefore, the two clusters

impact the substrate in a consecutive manner, with the second cluster hitting the surface

30.5 fs after the first.

Eight hydrogen-terminated diamond (111) substrates of various sizes are used in

this study, as indicated in Table 2-1. The largest substrate contains over ten times as









many atoms as the smallest one. These various substrates are chosen in order to compare

the computational capability of the two methods. Prior to cluster deposition, all the

substrates are equilibrated at 500 K and then cooled to 300 K, which is the temperature

that is maintained throughout the whole deposition process. Periodic boundaries are

applied within the impact plane.

Table 2-1. Details of the hydrogen-terminated diamond (111) surfaces.
# of atoms in the 1260 2352 3136 4480 5824 7168 9216 16128
substrate
Impact area (A2) 455.8 615.1 1166.2 1166.2 1166.2 1166.2 1509.3 2672.9
Thickness (A) 13.0 13.0 13.0 19.1 25.3 31.5 31.5 31.5

In order to mimic the heat dissipation of a real substrate and maintain the system

temperature at 300 K during the deposition, the Berendsen thermostatl2451 is used in both

the EMD and O(N)/NOTB-MD simulations. Approximately 3-5 rows of atoms at the

edges and the carbon atoms of the lower half part of the whole surface slab are thermostat

atoms. Therefore, the thermostat atoms form a bathtub-like shape, helping to control the

system temperature. The bottom layer of hydrogen atoms for each surface is held rigid to

maintain the substrate structure during the deposition. All the other atoms in the substrate

and in the cluster beam evolve without any additional constraints.

During the deposition, the majority of the incident energy of the cluster molecules

is transformed into excess surface kinetic energy. In the case of the larger substrates, this

excess surface kinetic energy is quickly dissipated by the thermostat atoms and does not

bounce back to interfere with the chemical interactions taking place at the surface.

However, in the smaller substrates, this dissipation does not take place quickly enough

and the excess energy is reflected back from the boundary of the substrate (this occurs

whether or not the bottom layer is held rigid). This reflection of energy occurs to

somewhat different degrees in the EMD and O(N)/NOTB-MD simulations (see the









discussion below). As the point of this study is the comparison of the predictions of these

two methods, this reflection of energy does not detract from our objective as long as the

results of the deposition on a same surface are compared.

For statistical purposes, several trajectories are performed for each surface and the

results are averaged. In the case of the O(N)/NOTB-MD simulations, three trajectories

are run for each of the three smallest surfaces (1260, 2352 and 3136 atoms/surface). In

the case of the EMD simulations, the same three trajectories are run on the same three

surfaces so that the EMD and O(N)/NOTB-MD results may be compared. In addition,

since the EMD method is much faster than the O(N)/NOTB-MD method and more

trajectories lead to better statistical representation of the results, ten trajectories total were

run for each of the eight surfaces considered.

The time step is 0.2 fs. The simulations run for at least 1 ps with the clusters

impacting on the surface during the first 0.16 ps and the film relaxing thereafter. Each

O(N)/NOTB-MD simulation typically required 12 nodes of an IBM RS/6000 SP2

supercomputer (with 48 CPUs) and ran for about 4 days, while each EMD simulation

typically ran for a few hours (the largest simulations ran about one day) on a Compaq

Alpha64 workstation.

2.4 Results and Discussion

When the molecular clusters come into contact with the surface, numerous

chemical reactions occur among the cluster molecules and between the cluster and the

substrate, resulting in hydrocarbon thin film nucleation and growth. Both the

O(N)/NOTB-MD and EMD methods predict that when the clusters impact the substrate

with the short time lag of 30.5 fs, many more of the carbon atoms in the film are from the

first incident cluster. Furthermore, both methods predict that within a given cluster, more









atoms from the lower half of the cluster (closest to the substrate) remain behind to form

the film.

The atoms that are identified as being part of the resultant thin film include

substrate atoms that are displaced from their original positions and pushed up into the

film while still maintaining a connection to the substrate. In addition, some atoms from

the cluster may penetrate deeply into the substrate beyond the range of the film. Although

these atoms are included in the calculation of the number of atoms from the cluster that

adhere to the surface, they are not considered when the structure of the film is examined.

The percentage of carbon atoms in clusters adhering to the substrate predicted by

O(N)/NOTB-MD and EMD for surfaces with 1260, 2352 and 3136 atoms/surface is

shown in Figure 2-1 The O(N)/NOTB-MD method predicts a higher percentage of

adhesion (approximately 20-30% more) than the EMD does for the same surface. In the

EMD simulations, when the distance between two atoms is less than 1.73 A, those two

atoms are considered to have formed a bond. In the O(N)/NOTB-MD approach, when the

number of electrons in the bond region is greater than or equal to 0.04, a bond is

considered to be formed.[246] When the distance approach is compared to the electron

counting approach for the same set of O(N)/NOTB-MD results, the electron counting

approach is found to yield results consistent with those of the distance approach in that

there is no bond determined on the basis of the electron counting approach with a bond

length greater than 1.73 A. Hence, the difference in the percentage of adhesion between

the two approaches is due to differences inherent to the empirical and tight-binding

methods themselves.











100
90 -- O(N)/NOTB-MD
80o --iEMD
70
i60-
o 50
6 40
40 x34
30 -
20-
10- 13
0
1260 2352 3136
substrate size


Figure 2-1. The percentage of incident carbon atoms that adhere to the substrate (averaged
over three trajectories) versus the size of the substrate. The total number of
atoms in each substrate is used to quantify the substrate size. The predictions
from both O(N)/NOTB-MD and EMD approaches are shown.

To better characterize this difference, the potential energy curves of three reactions

are considered from static calculations using the REBO and O(N)/NOTB-MD potentials

with a time step of 0.1 fs. The results are plotted in Figure 2-2. In the figure, the values of

(0 PE), where PE is the calculated potential energy, are plotted for easy comparison.

The first case is the movement of two ethylene molecules towards each other along a path

that is horizontal to the carbon-carbon double bonds, shown in Figure 2-2(a). The second

case is the movement of two ethylene molecules towards each other along a path that is

perpendicular to the double bonds, shown in Figure 2-2(b). The final case is the

movement of two molecular clusters of ethylene (where each cluster contains eight

molecules) towards each other, shown in Figure 2-2(c).

If one ignores the fine details, one will be struck by the similarities in the overall

shapes of the energy curves obtained by the two approaches. This is particularly true in













250

200
E
. 150
>-
100
z
UJ
50

0


150
100
50
0 pp^p==


oDISTANCE (angstrom)
DISTANCE (angstrom)


600

500
E
S400

S300

200

S100

0


40
30
20

0 . '* ---- "-




-- O(N)/NOTB-MD
-in- EMDO


0 0 0


DISTANCE (angstrom)


450 100
400- so
350 -
E 300 o
250
200
150
1 -*--O(N)/NOTB-MD
z 100
S100 -m-EMD
50


-50

0- 0A N N V3 V 'V '` b 'b' by b1

DISTANCE (angstrom)


(c)


Figure 2-2.Potential energy curves calculated with O(N)/NOTB-MD and EMD methods

for the three reactions: (a) the movement of two ethylene molecules towards

each other in a direction horizontal to the double bonds; (b) the movement of

two ethylene molecules towards each other in a direction perpendicular to the

double bonds; and (c) the movement of two ethylene clusters towards one
another.









the third case where the energy curves between two molecular clusters of ethylene

obtained by the two methods have remarkably similar shapes. However, there are also

crucial differences between the energy curves obtained by the two methods. From Figure

2-2, it can be seen that, in all three cases, there are regions of separation close to the C-C

bond length where the energy obtained by the NOTB Hamiltonian is less than that

obtained by the REBO potential (see the insert in Figure 2-2(c)). The similarities of the

energy curves obtained by the two methods are indications that the REBO potential has

indeed captured the general characters of carbon-based chemistry. But the differences

show that the NOTB Hamiltonian predicts a more attractive interaction and in general a

lower potential barrier in the region of bond-breaking and bond formation than the REBO

potential. Therefore, the REBO potential may not be sufficiently flexible to describe all

the relevant processes of bond breaking and bond forming in cluster-beam deposition,

thus leading to a lower percentage of adhesion.

As shown in Figure 2-1, when the substrate size changes, both the O(N)/NOTB-

MD and EMD simulations predict that the adhesion percentage is approximately

constant. When 10 trajectories of EMD simulations are averaged for each of the eight

substrates, the results also display little variation in the adhesion percentage with the

changing substrate (see Figure 2-3). The factors contributing to the deviation in the

adhesion percentage include changes in the precise impact sites on the surfaces, thermal

fluctuations, and changes in the elastic collisions among the cluster molecules, in addition

to the effect of the reflected energy from the boundary in the case of the smaller

substrates.












-- EMD


T-13


1260 2352 3136 4480 5824 7168 9216 16128
substrate size

Figure 2-3. The percentage of incident carbon atoms that adhere to the substrate (averaged
over ten trajectories) versus the size of the substrate. The total number of
atoms in each substrate is used to quantify the substrate size. The results are
predicted by the EMD approach.


(a)


(b)


Figure 2-4. Snapshots of the thin film formed on the hydrogen terminated diamond (111)
surface containing 3136 atoms. The black spheres are carbon atoms in the
cluster beam, the gray spheres are substrate carbon atoms, and the white
spheres are hydrogen atoms. (a) O(N)/NOTB-MD result; (b) EMD result.

Typical snapshots of the nucleated thin films predicted by the O(N)/NOTB-MD

and EMD simulations are given in Figures 2-4(a) and (b), respectively. It is clear that the

film is denser and spreads more widely in the O(N)/NOTB-MD simulations, while in the

EMD simulations the film is more chain-like. These comparisons are made in a more

quantitative manner by determining the coordination of the carbon atoms in the film and









the manner in which the carbon atoms in the film are bonded to the other film carbon

atoms (hereafter referred to as carbon connectivity).

Table 2-2 summarizes the coordination of the carbon atoms in the film predicted

from the O(N)/NOTB-MD and EMD simulations for surfaces with 1260, 2352 and 3136

atoms/surface (only the averaged values are reported). Compared to the EMD results, the

film with a higher percentage of sp3-hybridized carbon while less sp2-hybridized carbon

and no sp-hybridized carbon is predicted from the O(N)/NOTB-MD method. In the EMD

simulations, the hybridization of the carbon in the film ranges from sp to sp3. In other

words, the O(N)/NOTB-MD simulations predict the formation of a highly saturated thin-

film structure while the EMD simulations predict the formation of a more unsaturated

structure. Table 2-3 summarizes the averaged hybridization of the carbon atoms in the

films formed on all eight surfaces predicted from the EMD simulations.

Table 2-2. The coordination of the carbon atoms in the film predicted by the
O(N)/NOTB-MD and EMD simulations (averaged over 3 trajectories) (%).
# of atoms in the substrate 1260 2352 3136
sp / / /
O(N)/NOTB-MD sp2 22 16 13
sp3 78 84 87
sp 8 12 8
EMD sp2 23 65 64
sp3 69 23 28

Table 2-3. The coordination of the carbon atoms in the film predicted by the EMD
simulations (averaged over 10 trajectories) (%).
# of atoms in 1260 2352 3136 4480 5824 7168 9216 16128
the substrate
sp 17 12 7 3 20 20 15 11
sp2 29 58 53 70 53 45 46 44
sp3 54 30 40 27 27 35 39 45

A close examination of Tables 2-2 and 2-3 reveals a role reversal in the percentages

of carbon atoms with sp2 and sp3 bonding in the film between the 1260 and 2352









atoms/surfaces for the EMD simulations while no such reversal is seen for the

O(N)/NOTB-MD simulations. This observation can be understood as follows. For EMD

simulations, the 1260-atom surface is just too small to allow for a quick dissipation of

any substantial amount of the excess surface kinetic energy. Therefore, the reflected

excess energy quickly breaks up the remnant sp2-bonded structures in the incoming

clusters. This action, in turn, promotes more chemical reactions at the surface, leading to

a larger percentage of sp3-bonded carbon atoms. The 2352-atom surface, on the other

hand, is large enough to dissipate some of the excess energy such that the reflected

energy is not sufficient to break up the remnant stable sp2-bonded structures in the

incoming clusters, but still enough to break up some of the newly formed sp3-bonded

structures at the surface. This facilitates the formation of additional sp2-bonded

structures. As the size of the surface increases further, the effect of the reflected energy

decreases more. This trend can be clearly seen from the results shown in Table 2-3,

which suggests that the effect of the reflected energy has almost disappeared for the

7168-atom surface in the case of EMD simulations.

For the O(N)/NOTB-MD simulations, because the NOTB Hamiltonian is more

flexible, the excess surface kinetic energy dissipates more quickly than the corresponding

situation in the EMD simulations. Hence, even for the 1260-atom surface, some of the

excess energy has already been dissipated to the extent that the reflected energy is only

sufficient to break up the sp3 structures formed as a result of chemical reactions at the

surface. Therefore, the differences in the distribution of the percentages of sp2- and sp3-

bonded structures between the two cases can also be attributed to the rigidity of the

REBO potential vs. the flexibility of the NOTB Hamiltonian.









The carbon connectivity within the nucleated films predicted by the O(N)/NOTB-

MD and EMD simulations for surfaces with 1260, 2352 and 3136 atoms/surface is shown

in Table 2-4 (only the averages are given). In the table, Cl stands for the percentage of

carbon atoms connected to one other carbon atom, C2 stands for the percentage of carbon

atoms connected to two other carbon atoms, and so on. Therefore, the summation of C

and C2 indicates the percentage of carbon atoms bonded in a linear structure, while C3

and C4 indicate the percentage of carbon atoms connected in the branched and networked

structure, respectively. For each surface, the carbon connectivity within the film predicted

by O(N)/NOTB-MD is different from what is predicted by the EMD simulations. In

general, O(N)/NOTB-MD predicts more branched or networked structures and less linear

structure than the EMD simulations. When both the coordination and the carbon

connectivity of the film carbon atoms are considered, the O(N)/NOTB-MD method is

found to predict the formation of a more diamond-like thin film while the EMD

simulations predict a more linear unsaturated polymer-like thin film.

Table 2-4. The carbon connectivity of the carbon atoms in the film predicted by
O(N)/NOTB-MD and EMD simulations (averaged over 3 trajectories) (%).
# of atoms in the surface 1260 2352 3136
Cl 30 29 42
O(N)/NOTB- C2 46 37 29
MD C3 22 34 25
C4 2 / 4
Cl 49 30 46
EMD C2 37 65 54
C3 14 5 /

2.5 Conclusions

The simulation results for ethylene molecular cluster deposition predicted by

O(N)/NOTB-MD and EMD using REBO potential are compared. The results of these

two methods do not agree perfectly well with each other, especially the quantitative









predictions. For instance, the structures of the resultant thin films are significantly

different from one another. Nevertheless, the qualitative predictions are comparable. For

example, both methods predict thin-film nucleation through rapid chemical reactions and

most of the atoms in the nucleated thin film are from those incident clusters closest to the

substrate.

This comparison study shows that the REBO potential has indeed captured the

general characters of carbon-based chemistry. However, the differences in the predictions

from the two methods indicate that as compared to the NOTB Hamiltonian, the REBO

potential is more rigid, and hence may not be sufficiently flexible to describe all the

relevant processes of bond breaking and bond forming. A key point is that NOTB

Hamiltonian predicts a more attractive interaction and in general a lower repulsive barrier

than the REBO potential. These results and conclusions appear in Reference [247].[247]

In modeling thin film deposition of amorphous carbons, Jager and Albe observed

that the REBO potential predicted a structure with lower sp3 content than the

experimental results. But when the cutoff distance (2 A for C-C interactions in REBO

potential) was slightly increased, a structure with realistic density and sp3 content could

be produced.[236] The study of H-atom association with diamond surfaces by Hase and co-

workers also pointed out that, the major reason of the quantitative inaccuracy of REBO

potential was the potential's shorter range. But, within the REBO potential cutoff, the

predicted results agree very well with the ab initio calculations.[235] Therefore, in the case

of energetic collisions, if the incident energy is high enough to bring the particles into

close contact (well within the potential cutoff) prior to any reaction, the predictions from

the REBO potential should be reliable.









In this dissertation, the incident energies used in the following simulations of

organic molecular cluster beam deposition and polyatomic ion beam depositions are

much higher. The REBO potential's shorter range is thus not of significant concern. In

addition, the systems considered contain more than 10,000 atoms. Although

O(N)/NOTB-MD is a more accurate method, it is more computationally expensive than

the EMD method for a surface of a given size. It is practically impossible for a simulation

of a system that consists of more than 10,000 atoms by using the NOTB method within a

reasonable period of time. Empirical potential is necessary to study the collective

phenomena of many atoms or for long times at an atomic scale. Therefore, the second

generation REBO potential is used in the following simulations to consider the short-

ranged interatomic interactions, and the predictions are believed to be at least

qualitatively accurate.














CHAPTER 3
TEMPERATURE CONTROL METHODS

Energetic particle deposition is a process that involves a flux of energy into or out

of a system. In addition, complex and rapid chemical reactions may occur between the

incident particles and the substrate atoms, which lead to big changes in the system

energy. These energy changes are reflected in variations in system temperature.

Experimentally, particle deposition is usually carried out at specific temperatures to

obtain the desired properties. Furthermore, macroscopic substrates dissipate the excess

energy from the deposition process through, for example, lattice vibrations through the

extended lattice.

To model such processes atomistically, molecular dynamics simulations can be

performed in a canonical ensemble, where the number of particles, temperature, and

volume are held constant. Periodic boundary conditions are often used in these

simulations to mimic an infinite or semi-infinite system with just a few thousand atoms

and to keep the volume constant. Sometimes, certain amounts of boundary atoms need to

be fixed to keep the structure of the simulation system from reconstructing. However,

these boundary conditions can result in the nonphysical reflection of energy from the

boundary, which will then produce spurious effects on the simulation results. Therefore,

the simulations make use of methods that can allow some atoms to effectively absorb all

the extra energy pumped into a system (including any reflected energy) and thus

successfully control the system temperature in a physically reasonable manner.

Simulations that implement these methods are called constant temperature simulations.[2]









Temperature is a thermodynamic quantity. For a system containing N particles, the

temperature can be related to the average kinetic energy ((K)) of the system through the

principle of equipartition of energy, which states that every degree of freedom has an


average energy of kBT associated with it.12481 That is,


(K) = mv 2 N=fkB (3-1)
\ 2 / 2 (


where Nf is the number of degrees of freedom, k is the Boltzmann constant, and Tis

the thermodynamic temperature. Similarly, the instantaneous kinetic temperature can be

defined as

2K
7 = -2 (3-2)
NfkB

The average of the instantaneous kinetic temperature is equal to the thermodynamic

temperature.

Since the temperature is related to the kinetic energy, in order to control the

temperature, the velocities of the particles in the simulation system must be adjusted. One

way to do this is to directly rescale the velocity of each particle, as shown in Equation (3-

3):

2
v new T (3-3)
\Vold ) ns

where vnew is the rescaled velocity, and void is the velocity before the rescaling.

Although this method, called the velocity rescaling method, is very simple and adds (or

subtracts) energy to (or from) the system efficiently, it is important to recognize that it

actually keeps the kinetic energy constant, which is not equivalent to the condition of









constant temperature. At thermal equilibrium, both kinetic energy (instantaneous kinetic

temperature) and potential energy fluctuate. Therefore, the direct velocity rescaling

method is somewhat coarse and far removed from the way energy is actually dissipated.[2]

Better and more realistic constant temperature schemes have been proposed.

Among these schemes, the generalized Langevin equation (GLEQ) approach,[249]

Berendsen method,[245] and Nose-Hoover thermostat[250-2531 are the most widely used. In

all these schemes, the velocities of the particles are adjusted to maintain the system

temperature at a constant value.

Simulation systems generally consist of an impact zone, where atoms move only in

response to normal Newtonian dynamics, that is embedded in a thermostat zone, where

the velocities of the atoms are modified using the temperature control schemes. The

thermostat zone not only acts as a heat reservoir but is also used as a cushion to absorb

any reflected energy waves.

In this study, both the GLEQ approach and the Berendsen method are used in the

thermostat zone in constant temperature MD simulations of cluster deposition on

surfaces. A variation of the regular GLEQ approach and a combined thermostat of the

GLEQ and Berendsen methods are also tested. The goal of this work is to determine

which thermostat method is the best for use in MD simulations of energetic particle

deposition on surfaces to realistically control the temperature and reduce the amplitude of

reflected waves from the boundaries of the simulation unit cell edges.

3.1 Methods of Interest

3.1.1 Generalized Langevin Equation (GLEQ) Approach

The generalized Langevin equation (GLEQ) approach proposed by Adelman and

Doll249] is developed from generalized Brownian motion theory. It models solid lattices









at finite temperature using the methods of stochastic theory. In this approach, the

molecular system of interest can be thought of as being embedded in a "solvent" that

imposes the desired temperature; the molecules are regarded as solutes. The solvent

affects the solute through the addition of two terms to the normal Newtonian equation of

motion: one is the frictional force and the other is the random force.

The frictional force takes account of the frictional drag from the solvent as the

solute moves. Since friction opposes motion, this force is usually taken to be proportional

to the velocity of the particle but of opposite sign:

Ffnch-on(t) = -8v(t) (3-4)

The proportionality constant, /f, is called the friction constant. Using the Debye solid

model, / can be simply expressed as

1
P = mOD (3-5)
6

where ) D is the Debye frequency. The Debye frequency is related to the experimentally

measurable Debye temperature TD by

kT,
D = kD (3-6)
h

The random collisions between the solute and the solvent is controlled by the

random force, R(t). This random force is assumed to have no relation to the particle

velocity and position, and is often taken to follow a Gaussian distribution with a zero

mean and a variance c2 given by[217]

2mpk, T
S2m BT (3-7)
At









where Tis the desired temperature, and At is the time step. This random force is balanced

with the frictional force to maintain the temperature.[217]

Therefore, the equation of motion for a solutee" particle is

ma(t) = F(t) 8v(t) + R(t) (3-8)

which is called the Langevin equation of motion. Following the Langevin equation of

motion instead of Newton's second law, the velocity of the system particle is thus

gradually modified to bring the instantaneous kinetic temperature closer to the desired

temperature. The GLEQ approach is a proportional control algorithm that changes the

temperature exponentially as a function of / and the initial conditions.[254] This approach

often gives a good representation of energy relaxation in surface scattering

simulations.[249] It also satisfactorily describes heat dissipation at boundaries and has been

found to be best suited for thin film deposition processes.[254]

In practice, some other expressions for the frictional force and random force can be

selected to better describe the physical condition of the system.[254] However, the

expressions mentioned above are the simplest, and hence, the most computationally

efficient. In simulations where the thermostat zone is far away form the zone of interest,

the results using these expressions have proven to be reliable.[217] In this study, the GLEQ

approach using the expressions described above for the frictional force and random force

is chosen to control the simulation temperature.

3.1.2 Berendsen Method

Before the introduction of the Berendsen method, it is worthwhile to first mention

the Andersen method. The Anderson method of temperature control was proposed in

1980.[255] This method can be thought of as a system that is coupled to a thermal bath









held at the desired temperature. The coupling is simulated by random "collisions" of

system particles with thermal bath particles. After each collision, the velocity of the

randomly chosen system particle is reset to a new value that is randomly drawn from the

Maxwell-Boltzmann distribution corresponding to the desired temperature. In practice,

the frequency of random collisions is usually chosen such that the decay rate of energy

fluctuations in the simulation is comparable to that in a system of the same size

embedded in an infinite thermal bath. This method is simple and consistent with a

canonical ensemble, but it introduces drastic change to the system dynamics. It is

therefore not appropriate to use the Andersen method to study dynamical properties

although it is appropriate to study static properties such as density or pressure.[2]

A more practical approach is the Berendsen method.[245] Just as in the Anderson

method, the system is coupled to an imaginary external thermal bath held at a fixed

temperature T. However, the exchange of thermal energy between the system and the

thermal bath is much gentler. Instead of drastically resetting the velocity of the particle to

a new value, the velocity of the particle is gradually scaled by multiplying it by a factor X

given by


A= (T -- 1) 2 (3-9)
7 LT Tns

where At is the time step, and r, is the time constant of the coupling. In this way, the

velocities of the particles are adjusted such that the instantaneous kinetic temperature 7T

approaches the desired temperature T.

The strength of the coupling between the system and the thermal bath can be

controlled by using an appropriate coupling time constant. If a quick temperature control









is desired, a small coupling time constant can be chosen. Consequently, the value of k

will be big and the change of the velocity will be drastic. On the other hand, if a weak

coupling is needed to minimize the disturbance of the system, a large value can be

assigned to the coupling time constant. In the evaluation of their own method,[245]

Berendsen et al. concluded that static average properties were not significantly affected

by the coupling time constant, but the dynamic properties were strongly dependent on the

choice of the coupling time constant. Their testing showed that reliable dynamic

properties could be derived if the coupling time constant was above 0.1 ps.

The Berendsen method is very flexible in that the coupling time constant can easily

be varied to suit the needs of a given application. The biggest advantage of the Berendsen

method over the Anderson method is that it gently modifies the velocities, and therefore,

the change of the system dynamics is not so dramatic. However, caution must be taken

when using the Berendsen method because it does not rigorously reproduce the canonical

ensemble, and thus the distribution generated from this method is wrong although the

averages are usually correct.

The Berendsen method implemented in our simulations is the one used by our

collaborators at the University of Louisville. Based on their simulation experience, the

ratio of A/ in Equation (3-9) is set to be 0.1 because it gives the best compromise


between ideal temperature control and disturbance of the physical behavior of the system.

3.1.3 Variation of GLEQ Approach and a Combined Thermostat of GLEQ
Approach and Berendsen Method

In their MD simulations of energetic particle beam deposition, Haberland et al.

claimed that the regular GLEQ approach was not good enough to reduce the artificial

effects caused by the reflected waves from the boundary of the simulation box.[2561 Their









system contained heavy clusters of more than 500 metal atoms per cluster, and the

incident energy was typically in the keV range.142' 64, 73, 256-258] They suggested an

improved method in which the original thermostat atoms were replaced by fewer, heavier

atoms.[256] This allows one to choose a large thermostat zone without losing

computational efficiency. Therefore, the backscattering of the elastic wave could be

sufficiently delayed. In addition, the atoms at the boundary of the impact zone and the

replacing thermostat zone are damped relative to the motion of their neighbors. This is an

efficient damping mechanism, especially for the high frequency part of the reflected

wave.1256] However, the replacing thermostat lattice should have the same elastic

properties as the bulk and match the lattice structure of the impact zone. This is relatively

easy to achieve for FCC materials but nontrivial for materials with other lattice structures.

Although Haberland's modified GLEQ approach is presently restricted to FCC

materials, it works well at damping the motion and energy of the atoms at the boundary

between the impact zone and the thermostat zone. This improvement can be readily

included in the conventional GLEQ approach. In this study, a modified GLEQ approach,

called the MGLEQ method, that includes extra damping for those boundary atoms and is

applicable to systems of any crystal structure, is discussed. It is also rigorously tested to

assess its effectiveness to both control the system temperature and reduce the amplitude

of reflected energy waves.

Comparing the GLEQ approach with the Berendsen method, the GLEQ approach

makes more physical sense and modifies atomic velocities more gently. Nevertheless, the

GLEQ approach involves extra calculations of forces; therefore it is slightly more

complicated and time-consuming than the Berendsen method. In this work, a combined









thermostat scheme of the GLEQ approach and the Berendsen method (hereafter denoted

as BnG) is applied to the thermostat atoms as well. The combination is realized by

dividing the original thermostat zone into two smaller zones: the one that directly borders

the impact zone has the GLEQ scheme applied to it while the other has the Berensen

scheme applied to it. Testing is done to assess whether this combined method combines

the advantages of these two methods.

3.2 Testing Systems

The deposition of a single C20 molecule on a hydrogen-terminated diamond (111)

substrate at room temperature (300 K) is considered as a test of these four thermostat

schemes. The initial distance between the depositing carbon cluster and the substrate is

around 4 A and the C20 is deposited along the surface normal. The substrate contains an

impact zone of atoms that is 2.4 nm x 2.4 nm x 1.0 nm. This impact zone is embedded in

a thermostat zone of atoms with four walls that are 1.0 nm thick and a bottom layer that is

1.6 nm deep, as schematically illustrated in Figure 3-1. The dimensions of the whole

substrate are therefore 3.4 nm x 3.4 nm x 2.6 nm. The number of atoms contained in the

impact zone and the thermostat zone is 1,280 and 4,320, respectively. The bottom

hydrogen layer is fixed to keep the substrate from reconstructing or moving.

Various incident energies (1 eV/atom, 5 eV/atom, 10 eV/atom, 20 eV/atom and 40

eV/atom) are considered. The REBO potential[211] coupled with long-range Lennard-

Jones (LJ) potentials2]1 is used to calculate the interatomic forces for the atoms in the

cluster and in the impact zone. These atoms are denoted as active atoms. The velocities of

the atoms in the thermostat zone are modified using the four temperature control schemes

described in Section 3.1 to adjust the energy flow within the system. These atoms are

therefore called thermostat atoms.










/ --- /

-I I I


I II1
I I-------



(a)

(b)

Figure 3-1.The substrate layout. (a) the impact zone; (b) the impact zone embedded in the
thermostat zone.

3.3 Results and Discussion

Deposition at 1 eV/atom is considered first. This incident energy is well below the

binding energy of the carbon atoms in the C20, which is approximately 5.9 eV/atom.[66]

Therefore, during deposition, the original fullerene cage structure is not destroyed

although deformation is observed. The degree of deformation induced by the collision

varies slightly when different temperature control methods are applied to the thermostat

atoms. The cluster only deforms a little in both the GLEQ and MGLEQ approaches, but it

deforms more in the Berendsen and BnG methods. In all cases, the cluster does not attach

to the substrate; instead, the deformed cluster bounces back into the vacuum and

gradually recovers its original cage structure.

A reference simulation, in which the REBO potential coupled with the LJ potential

is used to consider the interatomic forces in both the impact and thermostat zones, is

performed at the incident energy of 1 eV/atom. In this case, all the atoms (except the

bottom fixed hydrogen atoms) follow normal Newtonian dynamics. Since there is no

special temperature control method introduced, a big substrate is required to dissipate the

extra energy. In this reference simulation, the same impact zone is thus embedded in a







63



much bigger thermostat zone (which contains 14,374 thermostat atoms). The dimensions


of this reference substrate are 5.2 nm x 5.2 nm x 3.1 nm. In this reference simulation,


although there is no damage to the fullerene molecule upon collision, its original cage


structure deforms significantly. The whole deformed molecule then leaves the substrate


and slowly recovers. The temporal evolutions of the substrate temperature in the


reference simulation and the simulations using the four temperature control methods are


plotted in Figure 3-2. Even if the thermostat zone in the reference substrate is at least


600 -- Reference
580 GLEQ
560 1 eViatom Berendsen
54o- MGLEQ
520 BIG
500
480-
a 460
E
W 440
I-
420
400
380
o 360
340
320
300
280
0 50 1000 1500 2000 2500 3000
time (fs)

Figure 3-2.The temporal evolution of the substrate temperature in the reference
simulation and the simulations using the four temperature control methods at
the incident energy of 1 eV/atom.

three times as big as the thermostat zone used in the simulations where special


temperature control methods are applied, the energy dissipation obviously is not effective


in this reference substrate because the temperature fluctuates about 392 K. In contrast,


after 3 ps, the substrate temperature is less than 320 K when various temperature control


methods are employed (314 K in the case of the GLEQ and MGLEQ approaches, 317 K


and 318 K when the Berendsen method and the combined thermostat of GLEQ approach


and Berendsen method are used, respectively). This finding provides direct evidence as to







64


why effective temperature control methods are necessary in the simulation of energetic

deposition at constant temperature. The four temperature control methods perform

equally well at this low incident energy in that the four curves essentially overlap, as

displayed in Figure 3-2.



600- GLEQ600 GLEQ
Berendsen 10 eV/atom Berendsen
550- 5eV/atom MGLEQ 550- MGLEQ
BnG BnG
500- oo-

E 450 E 450-
I-- .
400 400

) 350- 350

300- 300

0 500 1000 1500 2000 2500 3000 0 500 1000 1500 2000 2500 3000
time (fs) time (fs)
(a) (b)

Figure 3-3.The temporal evolution of the substrate temperature in the simulations using
the four temperature control methods at the incident energy of (a) 5 eV/atom,
(b) 10 eV/atom.

When the same deposition occurs at 5 eV/atom, the behavior of the system is

almost the same in all the four cases where the different temperature control methods are

used. This incident energy is high enough to induce reactions between the cluster and the

substrate. Therefore, although no apparent damage to the fullerene molecule is observed,

the severely deformed cluster sticks to the substrate and tends to recover its cage structure

during atomic relaxation after the collision. The outcomes of deposition at 10 eV/atom

are similar to the outcomes predicted to occur at 5 eV/atom except that the cage structure

of the C20 is destroyed at 10 eV/atom. The damaged cluster also attaches to the top of the

substrate. The changes of the substrate temperature are portrayed in Figures 3-3(a) and









(b) for depositions at 5 eV/atom and 10 eV/atom, respectively. As shown in these figures,

the change of the substrate temperature during the first 1 ps is different when different

temperature control methods are used. It appears that the Berendsen method reduces the

temperature most dramatically at the beginning. However, during the subsequent process,

the four curves overlap.

When the deposition takes place at 20 eV/atom, the cage structure of the C20

molecule is completely destroyed. The fragments from the cluster react with the substrate

carbon atoms and form a strongly adhered film. The phenomena observed are more or

less the same in the systems where different temperature control methods are used, but

the difference in the substrate temperature change is more apparent. As shown in Figure

3-4(a), during the first 1 ps, the Berendsen method induces the most dramatic decrease

while the reduction in the temperature is much gentler using the other three methods. At

about 1.5 ps, the fluctuation in the temperature begins to stabilize at about 340 K in the

system using the Berendsen method. However, the stabilization is not achieved in the

systems where the other three methods are used until after 2 ps. The GLEQ approach

appears to be the best method to control the temperature at this incident energy because

the substrate temperature after 3 ps is 327 K in the GLEQ approach but is about 335 K

using both the MGLEQ approach and the BnG method.

A direct way to demonstrate the energy dissipation capability of the temperature

control scheme is to monitor the change of the system energy. In the deposition system

considered here, the largest change in the system energy comes from the kinetic energy

change because only those atoms involved in chemical reactions will have a substantial

change in their potential energy, and the fraction of these atoms in the considered








































0.25-



0.20-


0.15-



0.10-



0.05-



n nf


3000


0 500 1000 1500 2000 2500 3000
time (fs)
(a)


o --GLEQ
Berendsen
MGLEQ
-- BnG








105-00 1500 2000 2500 3000
1000 1500 2000 2500 3000


0 500 1000 1500 2000 2500 3000
time (fs)

(b)


Figure 3-4. The temporal evolution of (a) the substrate temperature and (b) the kinetic
energy per active atom in the simulations using the four temperature control
methods at the incident energy of 20 eV/atom.









deposition system is very small. Therefore, the change of the kinetic energy can represent

the change of the whole system energy. Figure 3-4(b) gives the temporal variations of the

kinetic energy per active atom for deposition at an incident energy of 20 eV/atom. This

figure better separates the four curves corresponding to each temperature control method

than the temporal evolution of the substrate temperature. As clearly shown in Figure 3-

4(b), before the relaxation starts (at about 1 ps), the Berendsen method dissipates the

extra energy most quickly, and the combined thermostat of the GLEQ approach and the

Berendsen method dissipates the energy most slowly. The curves generated from the

GLEQ and MGLEQ approaches overlap at this early stage. However, at the relaxation

stage, the curve of the GLEQ approach begins to separate from the curve of the MGLEQ

approach. Apparently, the MGLEQ approach does not reduce the energy as much as the

GLEQ approach under this deposition condition. While the average kinetic energy

fluctuates about 0.06 eV/atom in the Berendsen method after 1.5 ps, this quantity

continues to drop in both the GLEQ approach and BnG method. At 3 ps when the

simulation stops, the GLEQ approach and the combined thermostat appear to have

performed the best at removing the excess energy in the system.

Although the GLEQ approach is the best among the four methods for energy

dissipation and temperature control at 20 eV/atom, it becomes the worst at a higher

incident energy of 40 eV/atom. As demonstrated in Figure 3-5, both the final substrate

temperature and the average kinetic energy per active atom are the highest in the system

where the GLEQ approach is used. The performance of the Berendsen method is not

satisfactory either. The best method in this case is the combined thermostat of the GLEQ

approach and the Berendsen method, which results in the lowest substrate temperature













GLEQ
Berendsen
MGLEQ
-BnG


800-



700-



600-



500-



400-



300-


0 500 1000 1500
time (fs)


2000 2500 3000


-- GLEQ
- Berendsen
MGLEQ
-- BnG


0 500 1000 1500

time (fs)


Figure 3-5.The temporal evolution of (a) the substrate temperature and (b) the kinetic
energy per active atom in the simulations using the four temperature control
methods at the incident energy of 40 eV/atom.


I I I I


2000 2500 3000









and the average kinetic energy. The modified GLEQ approach also performs better than

either the GLEQ approach or the Berendsen method.

Snapshots from the simulations at various moments during the deposition at the

incident energy of 40 eV/atom demonstrate the different responses of the substrate when

different temperature control schemes are used (Figure 3-6). At 3 ps when the simulation

stops, the substrate where the GLEQ approach is employed suffers the smallest amount of

damage; however, the largest amount of disorder to the substrate structure is observed in

the surface where the combined thermostat is used. Between approximately 0.08 ps to

0.24 ps, the compressed substrate moves upward. Such movements are depicted in Figure

3-7 for the four substrates with different temperature control schemes applied. Although

the four displacement fields look similar, the details are different, especially the

displacements of the atoms in the top right corner (see the circled areas in Figure 3-7).

The movement of these atoms shows a pattern of the reflected wave from the edge in the

substrate using the GLEQ approach. This reflected wave could cause over-relaxation of

the substrate atoms, which somewhat "heals" part of the damage to the structure. Such

patterns are also seen in the substrates using the Berendsen method and the MGLEQ

approach, but are not clearly present in the substrate where the combined thermostat is

used. Therefore the combined thermostat of the GLEQ approach and the Berendsen

method more satisfactorily suppresses the amplitude of the reflected wave than the other

three schemes.

In summary, at low incident energies (< 10 eV/atom in this study), the four

temperature control methods are all sufficient to control the system temperature and delay

the backscattering of the reflected wave. When the incident energy becomes high, the











Berendsen


BnG


t= 0.08 ps






t = 0.24 ps







t= 3 ps


Figure 3-6. Snapshots of the systems using the four temperature control methods at
various moments at the incident energy of 40 eV/atom.


-~ 9 / 6,'\} v ^ .
P ; **1 -
'^ ~ ~ ~ .. 'i I1 '7........ ....

\" -a / jp ,'

i t *dr? \. '^
- .' ij Jj i *- '-- N
t J "/ l !
)I




SL ^ -^ 1/ y
N 7T. T ,\




(a)
it / ..
r /-
(c)


-' di '/ -/ '^ '-.* -.
A^ ', V. -
'. -
II *L
I *^ I- -

-7 / Y


(c)


..:.. ..... ..
"/ N /
p' 7 ,P"" '


' .
\\ f ^ i -^ \-*.^ .


*-~ "" ';'i ti t-/
---' *-






,/^ "/ 'i ^. ''
(b)


S4' 4% Z/ A \ v 'r
p r t fl 't\ w, i

# I
-I ^ ~t I 'tk /

7 A / T\ -
I, r r /^ ^/ /
'e, 1 s-- <- \
,, -V t.. ^ 1 !

(d)


Figure 3-7.The displacement fields from t = 0.08 ps to t = 0.24 ps in the cross section of
the (111) plane using the four temperature control methods at the incident
energy of 40 eV/atom. (a) GLEQ approach, (b) Berendsen method, (c)
modified GLEQ approach, and (d) the combined thermostat of the GLEQ
approach and the Berendsen method.









different performance of the four methods becomes apparent. This difference results from

their different abilities to absorb energetic waves propagating through the system at

various frequencies. The Berendsen method reduces the energy quickly at the early stage

of the process, and quickly brings the system to equilibrium. But the Berendsen method is

not as efficient at absorbing enough of the reflected wave when the incident energy is

high, which results in a relatively high temperature and energy when the system reaches

the equilibrium state. At moderate incident energies (for example, 20 eV/atom), the

GLEQ approach is still capable of dissipating the extra energy. Nevertheless, it fails at

higher incident energy. This result is consistent with Haberland's conclusion as

mentioned in Section 3.1.3.1256]

The modified GLEQ approach that introduces extra damping at the boundary atoms

between the impact zone and the thermostat zone does indeed improve the capability of

the system to control the temperature as well as absorb the reflected wave when the

incident energy is high. The combined thermostat of the GLEQ approach and the

Berendsen method removes the excess energy in the most gradual manner, and the

system is usually the slowest one to reach the equilibrium. But, this simple combination

is superior to either the GLEQ approach or the Berendsen method, especially at a high

incident energy if enough time is allowed for the relaxation. This can be explained as

follows. The velocity adjustment algorithm in the GLEQ approach is different from that

in the Berendsen method. The frequency range of the energetic wave that could be

effectively absorbed by the GLEQ approach is therefore different from the Berendsen

method. When the cluster collides with the substrate at a high incident energy, the range

of the resultant energy wave frequency is wider, which may cover both the effective











ranges of the GLEQ approach and the Berendsen method. Therefore, when neither the

GLEQ approach nor the Berendsen method is able to completely absorb the reflected

wave, their combination can do much better.

However, if the substrate size is too small relative to the incident energy, none of

the temperature control schemes will work well enough to remove the extra energy. In

this study, a small substrate with dimensions of 2.8 nm x 2.8 nm x 1.3 nm is also

considered in the deposition at 40 eV/atom. The number of active atoms and thermostat


atoms contained in this substrate are about 3 of those in the substrate considered above.


Both the temporal evolution of the substrate temperature (Figure 3-8(a)) and the average

kinetic energy per active atom (Figure 3-8(b)) are essentially the same in the


1200-
GLEQ GLEQ
Berendsen 0.6 Berendsen
S1000- MGLEQ MGLEQ
-E BnG BnG
800-
S 8 -00 0.4-

600 -
0.2
400 -

200 ,, 0.0
0 1000 2000 3000 4000 5000 6000 0 1000 2000 3000 4000 5000 6000
time (fs) time (fs)

(a) (b)

Figure 3-8. The temporal evolution of (a) the substrate temperature and (b) the kinetic
energy per active atom in the depositions on the small substrate using the four
temperature control methods at the incident energy of 40 eV/atom.

systems where the four temperature control schemes are used. As given in Figure 3-8(a),

the substrate temperature finally fluctuates at about 520 K, which is too much higher than

the desired temperature. After 1.5 ps, the system appears to reach equilibrium and









extended relaxation does not help to reduce the temperature and the energy, which

indicates the reflected wave bouncing back and forth within the system.

3.4 Conclusions

In deposition experiments, the temperature of the substrate experiences a thermal

spike when the incident particles collide with the substrate particles. The heat is then

conducted away from the site of the collision quite quickly through the substrate, causing

the temperature to drop exponentially.[254] Appropriate temperature control methods,

which can effectively dissipate extra energy in a system, are thus necessary to model such

processes. The dissipation of extra energy not only helps to control the temperature but

also absorbs the artificial reflected wave. In this chapter, four temperature control

methods are used to model energetic cluster deposition on a solid substrate, which is a

stringent test of temperature control methods. These methods include the GLEQ

approach, the Berendsen method, a variation of the GLEQ approach where extra damping

is introduced to the boundary atoms between the impact zone and the thermostat zone,

and a combined thermostat of the GLEQ approach and the Berendsen method.

The performance of the temperature control methods depends on the incident

energy and the substrate size. No matter which method is chosen, a large enough

substrate is first required to realistically model the deposition process. The Berendsen

method is very effective at removing excess energy at the early stage; however, the

resultant equilibrium properties are not always the best. The GLEQ approach using the

Debye solid model performs well if the incident energy is not too high. At a high incident

energy, the modified GLEQ approach is better than the regular GLEQ algorithm due to

the extra damping. Surprisingly but not unexpectedly, the simple combination of the

GLEQ approach and the Berendsen method appears to be successful at controlling the









system temperature when either the GLEQ approach or the Berendsen method fails at a

high incident energy.

It should be recognized that there is no realistic counterpart to the thermostat atoms

because they do not obey Newton's second law. The number of thermostat atoms should

be large enough to bring the system temperature to the desired value. But in order to get

reliable simulation predictions, the thermostat zone should be far away from the area

where the processes of interest occur. This requires the impact zone, where the atoms

follow the normal Newtonian dynamics, to be large enough to be realistic while

remaining within the limitations of the available computer system. The following

simulations model the deposition of particles at moderate incident energies. Each incident

particle contains less than 50 atoms whose atomic number is less than 10. In these

simulations, the substrate with appropriate size and arrangement of the impact zone and

the thermostat zone is first determined depending on the incident energy and the size of

the incident particle. The GLEQ approach is chosen because this approach is good

enough to handle the deposition of small particles at moderate incident energies and it

realistically describes the exponential decrease of the substrate temperature.[254]














CHAPTER 4
THIN FILM FORMATION VIA ORGANIC CLUSTER BEAM DEPOSITION

Cluster deposition on solid substrates has received growing attention over the last

three decades. Compared to single atom deposition, cluster deposition is unique in that it

produces a high concentration of energy and mass in a very localized region. The

interaction between the cluster and the substrate occurs just near the surface. And the

cluster won't penetrate deeply into the bulk. As a result, there is relatively little damage

to the substrate. This method is therefore well suited to generate thin films.[19'24, 25] The

properties of the thin film can be controlled by changing the deposition conditions, such

as the incident energy, impact species, cluster size, deposition angle, substrate

temperature, etc. In this study, thin film formation through organic molecular cluster

beam deposition is examined by using molecular dynamics simulations. The second

generation reactive empirical bond order (REBO) potential parameterized by Brenner et

al. for hydrocarbon systems[211] coupled with the long-range Lennard-Jones (LJ) potential

is used to calculate the interatomic interactions. Incident clusters with different types of

intracluster bonding are considered. The effects of the incident angle and the deposition

direction are examined.

4.1 Simulation Details

The surface investigated in this study is hydrogen-terminated diamond (111)

substrate made up of 26 atomic layers that contains 13700 13900 atoms with a planar

impact area of 69 A x 40 A. This configuration is chosen because it was found previously

that the 26-layer surface is best at removing the artificial rebounding of the deposition






energy and preventing it from interfering with the reactions occurring at the surface at the
highest incident energy considered.[102] Two-dimensional periodic boundary conditions
are applied within the impact plane to mimic a semi-infinite system. The bottom
hydrogen layer is fixed. The next six carbon layers and 5 to 6 rows of atoms on the slab
edges have Langevin frictional forces and random forces applied. That is, the GLEQ
approach is used to dissipate the extra heat accumulated on the surface upon deposition,
and at the same time, to prevent the reflection of the impact energy from the edges of the
slab. The remaining surface atoms and all the cluster beam atoms are active atoms, which
are free to move in response to the applied forces without any constraints. Figure 4-1
shows the arrangement of the thermostat atoms and the active atoms in the substrate.
Before the deposition, the surface is equilibrated at 500 K to achieve a relaxed structure
with optimized atomic configurations, and then cooled to the simulation temperature of
300 K.


Side view


Top view
Figure 4-1. The arrangement of the thermostat atoms (gray) and the active atoms (black)
within the substrate. The top and bottom spheres in the side view are hydrogen
atoms.


RI









Three cluster beams with different types of intracluster bonding are examined in

this study. These are a van der Waals cluster beam of ethylene (C2H4) molecules, a beam

of adamantane (C10H16) molecules, and a beam of fullerene molecules (C20). In thin film

formation through energetic cluster deposition, cluster size is a very important factor. In

contrast to the metallic cluster deposition, our previous simulations of thin film formation

via organic cluster deposition predicted that smaller clusters of a few tens of atoms

produced thin films more efficiently than large clusters of several hundred atoms.[99] This

prediction is consistent with the experimental fact that in ICBD technique, which is a

successful method to produce organic thin films, 25' 28-30] only small clusters prevail.126' 40,

41] Therefore, in this study, the van der Waals cluster beam of ethylene contains 8

ethylene molecules per cluster; the beams of adamantane and C20 each contain one

molecule per cluster. Although the number of atoms contained in each cluster in these

three beams is quite different (48 for ethylene, 26 for adamantane, and 20 for C20), all the

individual clusters are roughly the same size and contain comparable amounts of carbon

(16 C atoms for ethylene, 10 C atoms for adamantane, and 20 C atoms for C20). Each of

the three beams contains 20 clusters. All the beams are created through the repetition of a

single cluster that has been equilibrated at 500 K and quenched to 5 K to minimize the

internal kinetic energy of the cluster. Then 20 of the clusters are repeated in random

translational and angular orientations so that they will not impact the surface with the

same orientation or at the same point on the surface. Prior to deposition, each beam is

placed about 4 A above the surface; the distance between two consecutive clusters is also

around 4 A. This distance is chosen because it is long enough that the individual clusters









do not interact with one another in the beam and yet the deposition process is not too

slow in these demanding computational studies.

This study is designed to compare the formation of thin films from cluster beams

with different types of intracluster bonding, and to gain a better understanding of the

effects of incident angle and impact direction. Therefore, depositions at angles of 0, 15,

45 and 600 from the surface normal for all the three incident species are considered.

When the beam impacts the surface at an angle 0, the total impact momentum (p ota),

which is related to the total energy (Etoa, ), can be divided into two none-zero

components: the component normal to the surface ( pnormai), which corresponds to E,,norm

(= Etota cos2 0 ); and the component parallel to the surface ( paterai), which corresponds to

Elateral (= Etota sin2 0). When 0 changes while po,.a and Eto.1 are fixed, both the normal

and lateral components vary with angle. Consequently, two sets of deposition energies

are considered one where Eoal is constant at 400 eV/cluster while the ratio of Porma,

to Plateral decreases with increasing angle; and another where po.l and E,.o1 change but

P norma is constant (corresponding to a constant energy of 400 eV/cluster normal to the

surface).


Deposition with platral along the [112] and [110] crystallographic orientations are

investigated. The deposition system is schematically shown in Figure 4-2. For statistical

purpose, five trajectories are carried out for each set of deposition conditions for each

incident species. The averaged results are reported. All the simulations run for about 3 ps

with 0.2 fs as the time step. The deposition occurs during the first 1 ps followed by the

complete relaxation of the system during the next 2 ps.










.. .t"
I II
-- [112] [110]














Figure 4-2.The simulation system prior to the deposition.

4.2 Results

4.2.1 van der Waals Clusters of Ethylene

There is only the weak intermolecular van der Waals force keeping the ethylene

molecules together within the cluster. During the deposition, the ethylene cluster flattens

out and the molecules impact each other and dissociate into small segments. Many

surface hydrogen atoms and some surface carbon atoms are removed, which facilitates

the nucleation of the thin film, as shown in Figure 4-3(a). When the collision occurs at 00

and 150 with Etotl of 400 eV/cluster, the surface experiences a significant amount of

elastic deformation upon impact and some plastic deformation up to 3-4 carbon layers

(Figure 4-3(b)). Typically, the thickness of the resultant thin films is about 6-7 A. As the

impact angle increases, a larger fraction of the surface deformation is elastic and the

plastic deformation is limited to the top one or two carbon layer(s). At 600, many of the

clusters and their fragments "slide" along the surface, and the resultant thin film is only

about 3 A thick. A typical snapshot is shown in Figure 4-3(c). The average maximum

penetration depth of the beam fragments slightly increases as the deposition angle












































(c) (d)


Figure 4-3.Representative snapshots from the simulations of ethylene cluster beam
deposition on the hydrogen terminated diamond (111) surface. The black
atoms are incident carbon, the gray atoms are surface carbon, and the white
atoms are hydrogen. (a) A representative shapshot of the configuration at time
= 0.05 ps, the early stage of the deposition; (b) the relaxed configuration at
time = 3 ps at 0; (c) the relaxed configuration at time = 3 ps with
E ta = 400 eV/cluster at 600 along [110]; (d) the relaxed configuration at time


3 ps with Enorm = 400eV/cluster at 600 along [110].


3NI


0









decreases. But at all the incident angles, the penetration depth is about 1 A.

Approximately 1% of the surface atoms are sputtered for all the angles considered.

When the deposition occurs with constant normal momentum equivalent to the

normal incident energy of 400 eV/cluster, severe permanent disorder of the surface is

predicted to occur, especially at large angle impacts (compare Figure 4-3(c) vs. Figure 4-

3(d)). In addition, many more surface carbon atoms are pushed toward the surface region

and become part of the film. The film thickness is about 7 A at all angles. The average

maximum penetration depth of the beam fragments increases as the angle increases (from

about 0.7 A at 150 to about 2.7 A at 600). The amount of surface sputtering also increases

with the angle, from about 0.7% at 150 to about 4.0% at 600.

Figure 4-4 summarizes the percentage of the carbon atoms from the incident

ethylene clusters that adhere to the surface at various incident angles. When the

depositions occur with Eltota of 400 eV/cluster, the amount of adhesion decreases

monotonically as the incident angle increases, although the result at 150 is about the same

as the normal impacts when the standard deviation is considered. This suggests the

deposition with high impact momentum normal to the surface would facilitate thin film

nucleation. When the cluster beam is directed to the substrate with a constant normal

impact momentum (corresponding to Enorm, = 400 eV/cluster), the adhesion percentage is

about the same for the 0, 15 and 45 depositions. However, at 600, the amount of the

nucleated thin film is still lower than those smaller angle depositions, although the

decrease is not so dramatic as when Etoa = 400 eV/cluster. In fact, if the deposition

results at Eno .m = 400 eV/cluster are compared with the results at Eora = 400 eV/cluster,

one can see that the amount of adhesion increases significantly in the case of E norma










400 eV/cluster, especially when the deposition occurs at large angles such as 45 and 60.

This result again justifies the important role played by the normal impact momentum in

the film nucleation and growth. Deposition along different crystallographic orientations

yields the same trend. The adhesion percentage along different directions at the same

angle is approximately the same. This indicates that the thin-film nucleation and growth

has little dependence on the incident direction of the beam.



70 -O-A
--0--B
60
50 -
40
3 30
20 -
10 -
0
0 15 45 60
Angle (degree)


Figure 4-4.Percentage of carbon atoms in the ethylene clusters that adhere to the surface
as a function of incident angle. (A) Deposition with E,,a = 400 eV/cluster

along [112], (B) deposition with Enora = 400 eV/cluster along [112], (C)

deposition with Etoa = 400 eV/cluster along [110]; (D) deposition with

E norma = 400 eV/cluster along [110].

The structure of the nucleated thin film is analyzed quantitatively by determining

the coordination number and carbon connectivity of the carbon atoms in the film. The

former shows the hybridization characteristics of the carbon atoms in the film, and the

latter indicates the relative amount of linear structure versus branched, and/or networked

structure in the film. All the films are found to be essentially amorphous. The incident









angle has little effect on the film structure. The hybridization of the carbon atoms ranges

from sp to sp3 with the majority sp2-hybridized (40-50%). The simulations predict more

sp-hybridized carbon atoms and less sp3-hybridized carbon atoms in the film when the

total incident energy is higher, in agreement with the previous studies.[95, 97, 98] Most of

the carbon atoms are connected to one another in linear chains, while about 20% are

branched carbons and even fewer (less than 2%) are networked. Deposition along

different crystallographic orientations does not significantly affect the overall structure of

the film.

4.2.2 Admantane Molecules

Adamantane is a cage hydrocarbon composed of four cyclohexane chairs, as shown

in Figure 4-5. This molecule is quite stable because it possesses no angle strain (all the

carbon atoms are perfectly tetrahedral and sp3 hybridized) and no torsional strain (all the

carbon-carbon bonds are perfectly staggered).[259] Despite the similarity of the bonding in

adamantane to the bonding in diamond, the deposition of a beam of adamantane

molecules in a previous study was not predicted to produce diamond-like thin films;

instead, the film contained primarily sp2-hybridized carbon.[102]







Figure 4-5.Molecular structure of adamantane.

When the beam of adamantane molecules impacts the surface with a total incident

energy of 400 eV/cluster, the adamantane molecules dissociate on contact with the

surface and the original cage structure is broken into chain-like fragments. In addition,

the surface deforms and some of the hydrogen atoms from the topmost layer are









displaced, leaving nucleation sites for the fragments to attach to the surface, as shown in

Figure 4-6(a). As the incident angle increases, the surface experiences less deformation,

and longer chains survive. Nevertheless, no cage structures remain after deposition at any

of the angles considered. Representative snapshots of the resultant thin film are shown in

Figure 4-6(b) and (c). The resultant thin films are typically about 4-7 A thick. Atoms

from the cluster beam can travel approximately 1 A into the surface, with the deposition

processes at 0 and 15 resulting in slightly deeper penetrations than the deposition

processes at 450 and 600. About 1% of the original surface atoms are knocked out of the

surface. This sputtering effect is slightly greater at large incident angles because of the

high lateral impact momentum associated with the large angle deposition.

As is the case for the ethylene cluster beam, when the adamantane is deposited with

a constant normal momentum that corresponds to the normal incident energy of 400

eV/cluster, the surface is damaged more severely as the incident angle increases (Figure

4-6(d)), and large numbers of surface atoms are sputtered out of the surface. The cage

structure of the adamantane molecules is destroyed during deposition, either from the

initial impact with the surface or from gas-phase collisions with the sputtered fragments

leaving the surface. The latter is not seen for depositions with total incident energy of 400

eV/cluster. The molecules consequently break into short chains that contain 2-3 carbon

atoms and various numbers of hydrogen. Some of these chains stick to the surface and

some scatter away. However, as the deposition process continues, these short chains can

react with one another to form longer chains. The resultant thin film is about 7-11 A,

which is significantly thicker than the film formed when the total incident energy is 400

eV/cluster.
















80







(a)


ft


0


oo 8


Figure 4-6.Representative snapshots from the simulations of adamantane molecular beam
deposition on the hydrogen terminated diamond (111) surface. The same color
scheme as in Figure 4-2 applies. (a) A representative shapshot of the
configuration at time = 0.05 ps; (b) the relaxed configuration at time = 3 ps at
0; (c) the relaxed configuration at time = 3 ps with E,,a = 400 eV/cluster at


600 along [110]; (d) the relaxed configuration at time = 3 ps with


Enormal = 400 eV/cluster at 600 along [110].












100 --- A
90 -0- B
80 -D- C
70 A D
60
0 -50
4 40
30 -
20 -
10
0
0 15 45 60
Angle (degree)


Figure 4-7.Percentage of adamantane carbon atoms that adhere to the surface as a
function of incident angle. (A) deposition with E,,, = 400 eV/cluster along

[112], (B) deposition with Enora = 400 eV/cluster along [112], (C)

deposition with E,,a = 400 eV/cluster along [110]; (D) deposition with

Enorma = 400 eV/cluster along [110].

The percentage of carbon atoms from the adamantane molecules that remain

chemisorbed to the surface at various incident angles is shown in Figure 4-7. As what

happens in the deposition of ethylene clusters, the amount of adhesion decreases as the

incident angle increases, while 150 impacts are as efficient to produce thin films as the

normal impacts. However, as indicated in Figure 4-7, the amount of adhesion at 450 when

the deposition occurs with E,o, = 400 eV/cluster is comparable to what happens when


the deposition occurs with Enorma = 400 eV/cluster. This is in contrast to the significant


increase in the amount of adhesion predicted for the ethylene cluster beam deposition at

450 when the beam is deposited with Enorma = 400 eV/cluster (see Figure 4-4). Finally,


the deposition of adamantane molecules along different crystallographic orientations does









not result in noticeable differences in the adhesion percentage, in agreement with the

results predicted from the ethylene cluster deposition.

As seen in our previous study,[102] the bonding in the film resulted from the

adamantane deposition is predominantly sp2-hybridized (40%-60%) and no more than

15% of the carbon atoms remain sp3 hybridized. About 70%-80% of the carbon atoms are

connected to one another in a linear fashion, 30%-20% are branched, and less than 3%

are networked. Again, the film structure shows little dependence on either the incident

angle or the crystallographic orientation.

4.2.3 C20 Molecules

C20 with a cage structure is the smallest member in the fullerene family. It has no

hexagons but 12 pentagonal faces. Its surface thus has high curvature, which severely

bends and strains the bonds between the carbon atoms. Besides the fullerene structure,

both experimental and theoretical work has shown that several other structures for C20

exist, such as linear structure (chain), monocyclic and/or bicyclic rings, graphitic sheet,

and corrannulene structure (bowl).[260-265] However, different theoretical calculations give

contradictory results as to the energetic stability of these isomers. Quantum Monte Carlo

calculations suggest that bowl and ring isomers are more energetically stable than

fullerene structure.[260' 261] Quantum molecular dynamics simulations,[262] coupled cluster

calculations,[263] and density functional calculations with local spin density and gradient-

corrected approximations[264] predict the fullerene structure is the minimum energy

configuration. However, experimental measurements show that the fullerene structure of

C20 is not favored under the conditions of experiments. The major reason lies in the

complicated experimental conditions, for example, high temperatures and charge

states.1264, 265] The bonding in C20 fullerene is unique in that it is sp2 hybridized with 7n-









bonding that is so distorted that it is nearly sp3 hybridized. Several groups have studied

the deposition of fullerene on surfaces[36, 63, 65, 66, 70, 75, 91-94, 112, 266] and find that it can be

used as a precursor of thin film growth.

In our simulations, the C20 cage flattens and breaks into fragments such as rings and

chains when it hits the surface (see Figure 4-8(a)). As is the case in the depositions of

both ethylene molecular beam and adamantane beam, during the deposition of C20 beam,

the surface also deforms with the degree of deformation depending on the cluster energy

and incident angle. For example, when the deposition occurs with the total incident

energy of 400 eV/cluster, at 0 and 15, elastic deformation can reach the 13th surface

carbon layer, while plastic deformation remains up to the 5th surface carbon layers, as

shown in Figure 4-8(b). When the incident angle is 450 or 600, elastic deformation

reaches only the 8th carbon layer while plastic deformation only reaches the 3rd carbon

layer, as shown in Figure 4-8(c). However, when the deposition occurs at high incident

energy, which, in this study, corresponds to the case where the beam is deposited to the

surface at a constant normal momentum equivalent to a normal incident energy of 400

eV/cluster, significant permanent surface deformation appears at large incident angles

(compare Figure 4-8(c) with Figure 4-8(d)).

During the depositions with the total incident energy of 400 eV/cluster, chain-like

fragments that contain 5-6 carbon atoms form, and few surface carbon atoms are knocked

loose. The resultant thin film is about 6-10 A thick. In addition, the film fragments often

have more than one tethering points to the surface, giving the film strong adhesion to the

diamond. Atoms from the C20 penetrate about 1 A into the surface and around 1% of the