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Computational Modeling of Collision-Induced Chemical Reactions: Gas Phase and Solid-State Reactions Induced by Ionic or ...

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1 COMPUTATIONAL MODELING OF COLLISI ON-INDUCED CHEMICAL REACTIONS: GAS PHASE AND SOLID-STATE REACTION S INDUCED BY IONIC OR CLUSTER IMPACTS By WEN-DUNG HSU 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 2007

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2 2007 Wen-Dung Hsu

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3 To my parents and to the Computational Fo cus Materials Science Group (CMSFG) at the University of Florida

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4 ACKNOWLEDGMENTS First of all, I would like to acknowledge Prof Susan B. Sinnott with my sincere gratitude. Her faith and encouragement helped me handle the difficult times in research. I have learnt the beauty of simulation under her guidance. Her ki ndness and scientific expertise have made my graduate career smooth and enabled me to fulfill my research goal. She was a constant source of inspiration for me. This study would not have be en successful without her support and guidance. Secondly, I would like to extend my special ack nowledgement to Prof. Simon R. Phillpot. His knowledge in the field of simulation is incompar able. His helpful advice and encouragement has helped me a lot to expand my exposure to th e filed of simulation. Th irdly, I would like to acknowledge Dr. Sanja Tepavcevic and Prof. L uke Hanley from Department of Chemistry, University of Illinois at Chicago. Their support s in experiments make this study more sound and meaningful. I would also like to thank Prof. Hai-Ping Cheng, Prof. Paul H. Holloway, and Prof. Juan C. Nino for their support throughout the research work. Besides, I would like to express my appr eciation to all of the members in the computational focus group, especially SeongJ un Heo, Rakesh Kumar Behera, Taku Watanabe and Donghwa Lee who have encouraged and supported me during my hard times and have brought me a lot of fun throughout my graduate study.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................4 LIST OF TABLES................................................................................................................. ..........8 LIST OF FIGURES................................................................................................................ .........9 ABSTRACT....................................................................................................................... ............11 CHAPTER 1 INTRODUCTION..................................................................................................................13 General Introduction........................................................................................................... ....13 Surface Polymerization of Polythiophene Thin Film.............................................................13 Growth of Polythiophene Thin Films..............................................................................13 Surface Polymerization by I on-Assisted Deposition.......................................................14 Adsorption of Methanol Molecule on Copper Clusters..........................................................15 Catalytic Process of Methanol Oxidation........................................................................15 Collision Reaction of Copper Cluster and Methanol Molecule......................................16 Chemical Modifications of Polymer Surface.........................................................................18 Modifications of Polymer Surface by Plasma Treatment................................................18 Polyatomic Ion Beam Depositions..................................................................................19 Computational Modeling of Collision Induced Reactions.....................................................20 2 SIMULATION METHODS...................................................................................................24 Molecular Dynamics Simulations...........................................................................................24 Density Functional Theory Molecula r Dynamics (DFT-MD) Simulation..........................25 First Principle Calculations.............................................................................................25 Thomas-Fermi theory...............................................................................................27 Density functional theory.........................................................................................28 Hohenberg-Kohn theorems......................................................................................28 Kohn-Sham formulation...........................................................................................29 Exchange-correlation functional..............................................................................32 Plane-wave implementation of DFT........................................................................32 The K-point sampling...............................................................................................34 Pseudopotentials.......................................................................................................34 DFT-MD Simulation in CASTEP...................................................................................36 Molecular Dynamics Simulation Using Reactive Empirical Bond Order (REBO) Potential...................................................................................................................... ........37 Reactive Empirical Bond Order Potential.......................................................................37 Lennard-Jones Potential..................................................................................................41 Periodic Boundary Conditions........................................................................................41 Predictor-Corrector Algorithm........................................................................................42

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6 Temperature Control Method..........................................................................................43 Acceleration and Parallelization of REBO-MD Code............................................................44 Link-Cell Technique........................................................................................................45 Spatial Decomposition Method.......................................................................................46 Massive Parallelization Method......................................................................................47 Dynamic Memory Allocation..........................................................................................48 Results of Parallel Implementation.................................................................................48 3 MECHANISTIC STUDY OF SURFACE POLYMERIZATION OF TERTHIOPHENE OLIGOMERS BY ION-ASSISTED DEPOSITION..............................................................55 Introduction................................................................................................................... ..........55 Computational Details.......................................................................................................... ..55 Experimental Methods........................................................................................................... .57 Simulation Results............................................................................................................. .....58 Neutral Systems...............................................................................................................58 Charged Systems.............................................................................................................61 Hybridization Analysis....................................................................................................63 Experimental Results........................................................................................................... ...65 Discussion..................................................................................................................... ..........68 Mechanisms Supported by Experimental Data and Simulations....................................68 Differences between Simulations and Experiments........................................................72 Conclusions.................................................................................................................... .........74 4 STUDY OF METHANOL MOLECULE ADS ORPTION ON COPPER CLUSTER...........84 Introduction................................................................................................................... ..........84 Computational Details.......................................................................................................... ..84 Results and Discussion......................................................................................................... ..85 Structure of Neutral Copper Clusters..............................................................................85 Collision of Methanol Molecules with Copper Clusters.................................................91 Conclusions.................................................................................................................... .........96 5 CHEMICAL MODIFICATIONS OF PO LYMER SURFACES BY ION BEAM DEPOSITIONS.................................................................................................................... .107 Comparison of Chemical Modifications of Polystyrene Surface by Hydrocarbon and Fluorocarbon Ion Beams...................................................................................................107 Introduction...................................................................................................................107 Computational Details...................................................................................................108 Results and Discussion..................................................................................................109 Conclusions...................................................................................................................117 Chemical Modification of the Poly(vinylid ene fluoride-trifluoroethylene) Copolymer Surface through Fluorocarbon Ion Beam Deposition.......................................................118 Introduction...................................................................................................................118 Computational Details...................................................................................................119 Results........................................................................................................................ ...121

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7 Discussion..................................................................................................................... .127 Conclusions...................................................................................................................129 6 GENERAL CONCLUSIONS...............................................................................................144 LIST OF REFERENCES.............................................................................................................147 BIOGRAPHICAL SKETCH.......................................................................................................209H155

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8 LIST OF TABLES Table page 3-1 Deposition results predic ted by the simulations................................................................75 3-2 Chemical state of the surface carbon atoms.......................................................................75 3-3 Relative intensities of the M+1 and M+2 peaks from the mass spectra............................75 4-1 Comparison of ground-state struct ure of neutral copper clusters......................................97 4-2 Average bond length and mean coordination number of Cun clusters...............................97 4-3 Atomic populations for Cu2-Cu9........................................................................................98 5-1 ercentage of intact PS chains as a function of depth........................................................130 5-2 Percentage of intact phenyl rings as a function of depth.................................................130 5-3 Number of backbone an d phenyl ring carbon atoms.......................................................130 5-4 Percentage of intact P(VDF-trFE) chains as a function of depth.....................................130

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9 LIST OF FIGURES Figure page 1-1 Time and length scale of differe nt types of simulation methods.......................................23 2-1 Concept of pseudopotential................................................................................................50 2-2 Periodic boundary conditions............................................................................................50 2-3 Computational time for r unning one MD step in different size of the systems.................51 2-4 Spatial decomposition method...........................................................................................51 2-5 Force relationships in REBO potential..............................................................................52 2-6 Massive parallelization method.........................................................................................52 2-7 Speedup and time for running thoudsand steps in 1-D parallelization..............................53 2-8 Time for running thoudsand steps and length of neighbor list in 2-D parallelization.......53 2-9 Time for running thousand MD st eps in five chosen cases...............................................54 3-1 Equilibrium simulation model before deposition..............................................................76 3-2 Snapshots of the neutra l thiophene depositions.................................................................77 3-3 Molecular weight distribution of chem ical products of neutral depositions......................78 3-4 Snapshots of the charged thiophene depositions...............................................................79 3-5 Molecular weight distribution of chemi cal products of the charged depositions..............80 3-6 S/Si elemental ratio from XPS...........................................................................................81 3-7 Mass spectra (MS) of the SPIAD films.............................................................................82 3-8 Mass spectra of HT+ and DT+ SPIAD films........................................................................83 4-1 Ground state structures of the neutral copper clusters.......................................................99 4-2 Average Cu-Cu bond lengths in the clusters....................................................................100 4-3Binding energies in the copper clusters..................................................................................100 4-4 Binding energies per Cu-Cu bond....................................................................................101 4-5 Bond order of the copper clusters....................................................................................101

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10 4-6 Relative stability of the copper clusters...........................................................................102 4-7 Snapshots of methanol molecule co llisions on low-coordination number sites..............103 4-8 Snapshots of methanol molecule collisions on high-coordination sites..........................103 4-9 Potential energy evolution of adsorp tion of methanol on the Cu clusters.......................104 4-10 Cu-O bond length in the copper clusters..........................................................................105 4-11 C-O bond length and O-H bond length in the copper clusters.........................................105 4-12 Bonding angles in CunCH3OH.........................................................................................106 4-13 Binding energy in th e copper clusters..............................................................................106 5-1 Snapshot of the pristine PS surface..................................................................................131 5-2 Snapshots of the PS surface after deposition...................................................................132 5-3 Depth profiles of carbon hydrogen, and fluorine atoms.................................................133 5-4 Densities of various chemical products...........................................................................134 5-5 Penetration depths of th e various chemical products.......................................................135 5-6 Distribution of molecular weights...................................................................................136 5-7 Density of cross-linked points.........................................................................................137 5-8 Snapshots of the pristine P(VDF-trFE) substrate.............................................................138 5-9 Snapshots of P(VDF-trFE) surface after depositions.......................................................139 5-10 Depth profiles of carbon and fluorine atoms...................................................................140 5-11 Densities of the various chemical products.....................................................................140 5-12 Distribution of molecular weights...................................................................................141 5-13 Density of fluorine and carbon atom uptake....................................................................141 5-14 Deposition yield of fl uorine and carbon atoms................................................................142 5-15 Degree of etch of the P(VDF-trFE) surface.....................................................................142 5-16 Density of chemical products formed fr om incident ions that leave the surface.............143 5-17 Density of chemical products formed from chain fragments that leave the surface........143

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11 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 COMPUTATIONAL MODELING OF COLLISI ON-INDUCED CHEMICAL REACTIONS: GAS PHASE AND SOLID-STATE REACTION S INDUCED BY IONIC OR CLUSTER IMPACTS By Wen-Dung Hsu May 2007 Chair: Susan B. Sinnott Major: Materials Science and Engineering Collision-induced chemical reactions are f undamental for many science and engineering applications. The mechanisms responsible for th e reactions, however, are difficult to detect or measure directly using experimental methods. Thus atomistic simulations are important and complementary approaches to experimental t echniques that provide in sights into the way systems reach their final states. In these studies, molecular dynami cs (MD) simulations are used to investigate (i) the surface polymerization mechanism associated with the growth of polythiophene thin films, (ii) the adsorption of methanol molecules on coppe r clusters of various sizes and (iii) the chemical modification of polymer substrate surfaces through polyatomic ion beam deposition. Mass-selected beams of thi ophene ions are deposited on -terthiophene oligomers in experiments, and density functional theory-m olecular dynamics (DFT-MD) simulations are carried out to determine the dominant mechanis ms responsible for the surface polymerization by ion-assisted deposition (SPIAD) process. The experimental resu lts show that polymerization occurs preferentially under a narrow set of ion energy and io n/neutral ratio conditions. The DFT-MD simulations illustrate the manner in wh ich ion energies aff ect polymerization and

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12 reveal how secondary chemical reactions can su bstantially modify both the thin film and the substrate. In the study of methanol-copper cl uster interactio n, the preferential struct ures of small copper clusters Cun ( n = 2-9) and the adsorption of meth anol molecules on these clusters are examined with DFT-MD simulations. The results indicate th at low coordination numb er sites on the copper clusters are the most favorable for methanol adsorption and have the greatest localization of electronic charge. The simulations thus predict th at charge transfer between the neutral copper clusters and the incident methanol molecules is a key process by which ad sorption is stabilized. In the studies of chemical modification of polymer surface thr ough polyatomic ion beam deposition, two main topics ar e carried out: the effect of continuous hydrocarbon (HC) and fluorocarbon (FC) ion beam deposition on a pol ystyrene (PS) surface and the effects of continuous FC ion beam deposition on a poly( vinylidene fluoride-trifluoroethylene) [P(VDF-trFE)] surface. In the firs t topic, the simulations predict that HC ions dissociate more readily than FC ions during deposition. Conseque ntly, HC ions are predicted to chemically modify the polystyrene to a greater extent than FC ions. In the second topic, the differences in the chemical interactions of C3F5 + ions and CF3 + ions with the P(VDF -trFE) surfaces, a ferroelectric polymer, are explored. The CF3 + ions are predicted to be more effective at fluorinating the polymer surface and at the same time, the C3F5 + ions are predicted to be more effective at growing fluorocarbon thin films. The simulations also reveal how the deposition process might ultimately modify the electrom echanical properties of this polymer surface. In short, the atomic level, computational si mulations used in the studies reported here reveal important details of the relevant reacti on mechanisms and provide predictions to help guide future experimental work.

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13 CHAPTER 1 INTRODUCTION General Introduction Collision induced reactions are widely used in materials engineering. For example collision-induced reactions play an important role in some thin film growth processes. In these processes, there is a substrate on which deposi tion will occur, and a target that contains functional materials that will ultimately be de posited on the substrate. A hyper-thermal energy such as using plasma, laser beam, or ion beam, am ong others then acts on the target. Due to the absorption of the energy, the target materials tran slate to the substrate su rface. Thus, to tailor specific thin film properties it is important to control the details of how the target material approaches the substrate and ultimately reacts. Therefore, it is nece ssary to study collision induced reactions in various situations, in cluding in the gas phase and solid phase. In this dissertation, the study of collision i nduced reactions are focused on three main topics: (i) Mechanism studies of surface pol ymerization of polythiophene thin films by ion-assisted deposition, (ii) Study of methanol molecular ad sorption on copper clusters of various sizes and (iii) Chemical modifications of polymer surfaces by polyatomic ion beam deposition. Surface Polymerization of Polythiophene Thin Film Growth of Polythiophene Thin Films Conductive polymers, such as polythiophene, ha ve generated consider able interest in recent years due to their electri cal properties, low cost, light weight, and high processability. These properties have led to a wide range of applications in electro nic and optical devices including light emitting diodes, field effect transistors, photovoltaics, sensor films, recording materials and rechargeable batteries.1,2 Properties of conducting polymer thin films such as

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14 charge injection, mobility and recombination e fficiency, which are essential to the device performance, depend on the molecular packing, the extent of grain boundaries and roughness of the interface with the electrodes. Thus optimizat ion of such devices requires the development of processing methods that can control film chemistry and morphology on the nanoscale.3,4 Typically conductive polymer thin films ar e grown by direct thermal deposition or solution-based growth methods. Direct therma l deposition requires e ither lower molecular weight oligomers or polymers that can degrade to produce gaseous species. However, while the oligomers or gaseous species deposit on the substr ate surface, the small molecules sublime back to the chamber due to low molecular weight. So lution-based growth met hods such as printing, casting or spin coating rely on self-assembly of molecules, but the methods suffer from inadequate or uncontrolled ordering when the fi lm thickness exceeds a few monolayers. It is also difficult to control the film thic kness by solution-based growth met hod. All these issues make the growth of high quality, robust, polymer thin film challenging. Surface Polymerization by Ion-Assisted Deposition Surface polymerization by ion-assisted deposition (SPIAD),5-9 which deposit hyper-thermal polyatomic ions and thermal neutra ls in vacuum simultaneously, can avoid the issues mentioned above in the growth of c onducting polymer thin films on substrates. SPIAD can be performed by using both mass-selected a nd non-mass-selected ions. Since the kinds of deposited ions are controlled in the mass-select ed ion method, it can be used for mechanistic studies. On the other hand, the non-mass-selected ion method consists of a broad beam ion source that is suitable for prot otype manufacturing processes. The advantage of SPIAD includes the fact that ion energy, ion stru cture, ion kinetic energy, neutral structure, the ion/neutral ratio, and substrate temperature can all be systematically varied to crea te libraries of candidate films.10 These film libraries can then be used for optimizing morphology, film thickness, electronic

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15 structure, and target prop erties in various purposes.7,8,11 SPIAD, thus, allows fine tuning of film optical band gaps and other optoelectroni c properties by modifying the chemical and morphological structure of the film. For exam ple, polythiophene and polyphenyl SPIAD films display narrower band gaps and reduced barrie rs to hole injection compared with their evaporated film counterparts.6,9 SPIAD displays other advantages for the deposition of conducting polymer films, including the absenc e of entrained solvent molecules and the utilization of sustainable (g reen) production strategies. Previous experimental work on SPIAD investigated mechanisms of the ion-induced surface polymerization reactions and found that po lymerization occurs for specific ion/neutral ratios and ion energies.7,8 Surface polymerization was also shown to form a distribution of species and not just a single oligomer.6,8 Contrasting experiments with atomic vs. polyatomic ions showed that the latter behave both as catalyst and reagent by energetically inducing polymerization and forming adducts with the neutral reagent, respectively.5 Thus utilization of SPIAD for combinatorial materials preparation relies on a compre hensive understa nding of how these various mechanisms contribute to the ov erall film formation event; however, such a mechanistic understanding remains elusive. Adsorption of Methanol Molecule on Copper Clusters Catalytic Process of Methanol Oxidation Methanol is predicted to be an important co mponent for the next generation of renewable green fuels and recently there has been intere st in the use of methanol in fuel-cells.12 It is produced using transition me tal catalysts. Therefore, there is considerable interest in better understanding the reactivity of surface in termediates during methanol synthesis13-25 to improve the efficiency of surface reactions and the he terogeneous catalysis process as a whole.

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16 Current experimental studies propose th at methanol oxidation to formate (HCO2) through an intermediate, dioxymethylene (H2CO2), is a preferred reaction route on the copper surface.23 At 470 490 K, formate decomposes to hydrogen and carbon dioxide (CO2).26 Based on this experimental data, Gomes and co-workers21 propose a reaction path of methanol with oxygen preadsorbed on the Cu(111) surface. The methanol molecule is first physisorbed on the metal surface. Then it reacts with an oxygen atom to form methoxy (CH3O) and water. The methoxy molecule next gives up one hydroge n atom and forms formaldehyde (H2CO) and hydrogen gas. The formaldehyde molecule reacts with an oxygen atom and forms dioxymethylene, which decomposes to formate plus hydrogen gas. Finally, the formate decomposes to hydrogen gas and carbon dioxide. The whole reaction contains many sub-steps in which hydrogen gas is the main product. Thus methanol has been applied as fuel in the fuel cells. A possible mechanism for the oxidation of methanol is summarized as follows: ) ( 2 2 ) ( 2 ) ( 2 ) ( 2 2 ) ( ) ( 2 ) ( 2 ) ( ) ( 2 ) ( 3 3 ) ( 3 ) ( 32 2 2 2 2 2 2 2 2) ( 2 ) ( 2 ) ( 2 ) (g H g ads ads H ads g ads O H ads g ads O ads gH CO H HCO CO H O H CO H O O H O CH OH CH OH CHg g g ads Mavrikakis and co-workers24 propose other reaction routes for methanol decomposition on bare Cu(111). In their proposal, methanol is also physisorbed on the metal surface, which is follow by the formation of methoxy, formaldehyde formyl (HCO), carbon monoxide and atomic hydrogen in order. Collision Reaction of Copper Cluster and Methanol Molecule Atomic clusters effectively connect the atom ic scale to the macroscopic scale of bulk crystals and provide an excellent platform from which one can study the heterogeneous catalysis process on various surface structures. Experimentally, there has been tremendous progress in

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17 recent years in the production and study of clusters.27-31 There have also been numerous computational studies32-37 that have provided insight into the structure, stability and reactivity of clusters that is complementar y to the experimental data. The interaction of methanol molecules with metal clusters changes with the size (number of the constituent atoms) of the cluster, and ha s been shown to be quite different from their interaction with metal surfaces. For instance, experiments find that methanol molecules undergo chemisorption primarily with clus ters that consist of six atoms, demethanation occurs mainly with clusters that consist of four atoms, and carbide formation occurs with clusters that consist of seven-eight atoms for nickel cluster ions.38 In contrast, in the case of copper cluster ions chemisorption occurs at clusters that consist of four atoms with a gradual increase above this size, demethanation at clusters that consist of six atoms, and HOH formation on clusters that consist of four-five atoms.39 Note that not only the reaction cross section but also the reaction itself changes dramatically with the size of the cluste r. In contrast, physisor ption dominates on metal surfaces.21,40 The dissociation energy of a ba re copper cluster is found to oscillate as the size of the cluster increases.32,33 This oscillation behavi or is also found in many other metal clusters.41,42 In general, clusters with the sizes of magic num bers have high dissociation energies and are considered to be stable. In a typical metal cluster, such as an alkali meta l cluster (in a liquid-like state), this oscillatory behavior can be explai ned by the jellium model.43,44 In this model, the delocalized valence electrons of the metal clus ter interact with a uniform background built by the positive core ions to form a spheroidal potential well. This leads to discrete electronic levels (shells) with angular momentum L and degeneracy 2L+1.45 According to the energy levels of these shells, the clusters with completely filled shells are more stable a nd harder to dissociate

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18 than those with partially fille d shells. Although the jellium mode l provides good insight into the characteristics of metal clusters its application is limited to qu alitative discussion. For instance, in a theoretical study of the re action of a methanol molecule on a copper cluster, both the properties of the cluster and the metha nol molecules need to be considered. Experiments on the collision of a meth anol molecule with a metal cluster yield the reaction products, from which one may infer possible reacti on paths. However, it is possible to directly determine only the mass of the products and not thei r structures from these experiments. In this regard, theoretical calculations are helpful in understanding the details of the reactions. Typically, the electronic structures of various rigid isomer s are calculated to determine local minima on the potential energy surface. These theo retical results may then be compared with the experimental data to determine wh ich cluster isomers actually emerge in the real reactions.46 An adduct, i.e., an adsorbed methanol molecule on a metal cluster, can be studied by similar methods. Of course, the behavior of the adduct is diverse and there are many questions that need to be solved such as, how does th e molecule adsorb (adsorption si te and geometry), what is the nature of the bonding between the molecule and the metal cluster, do the properties of the adsorbed molecule change as the cluster grows, and so forth. Chemical Modifications of Polymer Surface Modifications of Polymer Sur face by Plasma Treatment Plasma is typically an ionized gas. Ionized m eans at least one electr on has been dissociated from atom, molecule or cluster. Thus an oscillati ng electric field is usually used to generate the plasma. Particles in an oscillating electric field are easier to ionize. Afte r ionization, they can be accelerated by an electric field and generate more collision with other particles. This collision cascade process is the key process to ignite the plasma. In some cases magnetic fields are also used to increase the collision frequency and t hus enhance the probability to ignite the plasma.

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19 Since there are many energetic ions with high translational energy in the plasma, plasma treatment is usually used in gr owing functional thin films or m odifying substrate surface. For the growth of functional thin films, usually there is a target containing the functional material and the target is put in the plasma environment. Part s of the target material then dissociate from the target by colliding with the ionized particle s in the plasma. These dissociated materials eventually become part of the plasma and deposit on the surface of the substrate. For the surface modification, the gas which is expected to have special reaction with the substrate surface, such as fluorination reaction etc., is us ed to ionize to form the plasma. Then the substrate is exposed to the plasma to modify the substrate surface. Plasma treatment has been widely used to m odify the properties of polymer surfaces. For example, FC plasma deposition has been used to grow fluorinated polymer thin films on various substrates with high thermal and chemical resist ance, high dielectric c onstant, and low friction coefficients.47-50 Hydrocarbon plasma deposition has also been used to produce thin films with high hardness.51,52 Polyatomic Ion Beam Depositions Despite its use in diverse applications, pl asma processing suffers from control and reproducibility problems during practical im plementation. This is due to the complex environment in the plasma. There are many kinds of possible species that are formed in the plasma and they are very hard to identify individually. It is already known that the effects of plasma are highly localized to the topmost layers of the substrate su rface. Therefore, if the major species is identified in the plasma, experiment ally the polyatomic ion beam with the major species can be used to mimic the plas ma treatment on the substrate surface. Improving the fundamental understanding of th e physical and chemical interaction of plasma particles with surfaces is critical to the development of strategies to solve these problems.

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20 Experimental studies of mass-selected polyatomi c ion beam deposition of a single type of ion, which can isolate the effects of the various particles that make up the plasma, have been carried out to provide insight into the physical and chemical interactions of the ions with the target surface. Molecular dynamics (MD) si mulations have been carried out53,54 to establish an atomic level understanding of the mechanisms by wh ich surface modification occurs in these experiments. Computational Modeling of Collision Induced Reactions Since collision induced reactions involv e many complicated processes, such as determining reaction paths and reaction mechanis ms, it is difficult to understand all the details associated with a reaction by experimental t echniques. Computational modeling can provide many of the details about atomic interaction and/ or electronic-structure information that are complementary to experimental data, and are thus become useful tool to tailor the details of collision-induced chemical reactions. Computational modeling in materials science can be classified into four broad categories according to the time scales and size scales. Figure 1-1 shows the details of the different simulation methods at various length and time s cales. The continuum methods, such as finite element methods or finite differential methods wh ich solve differential equa tions like Ficks law, Fouriers law numerically are excellent for the simulation of length scal es that are over a micrometer and time scales longer than 10-3 second. However, atomic-scale details cannot be obtained from these methods. The mesoscale methods, such as phase-field and kinetic Monte Carlo (KMC) methods, are suitable for length scales that range from around 20 nm to a micrometer and time scales that are about 10-9 to 10-3 seconds. The phase-field model is a general name for a class of diffuse interface models used to examine a wide variety of materials phenomenon. It is usually used to

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21 simulate the evolution of interf aces in materials. In phase field models, microstructure-like compositional or structural domains and interface s as a whole are described by a set of field variables. The total free energy of the system can be obtained by the function of field variables, which reflect the feature of the system. There are two type of field variables, conserved and nonconserved. Conserved variables have to sa tisfy the local conservation condition. The evolution of field variables can be obtained by solving Cahn-Hilliard equation55 and Allen-Cahn equation56 for conserved field variables and noncons erved field variables, respectively, in a numerical manner. The KMC method uses the Monte Carlo approach, which randomly changes the configuration of the system, judges if the change s are acceptable or not by comparing the total energies of the initial and fina l structures at the temperature of interest, and using a special algorithm, predicts the evolution of the system with time. The two main ingredients in a KMC simulation are the identification of all of the possi ble events and the determ ination of the rates at which these events can occur. Th e occurrence of events is the same as in Monte Carlo methods and depends on the energy of the system. It is usually used to simula te deposition process over long time scales. The disadvantage of these meso-scal e approaches is the lo ss of atomic detail as the system evolves. Thus, these methods cannot be used to determine reaction mechanisms. Atomistic methods, such as the molecula r dynamics (MD) and Monte Carlo (MC) approaches, are used at smaller length and time s cales. Typically the length scale is between 1 nm and 20 nm, and the time scale range is 10-15 to 10-9 seconds. This approach can simulate the system explicitly at the atomic scale. The MD method integrates Newt ons equations of motion to predict the evolution of systems in which time-step is inhe rently limited to small scales to satisfy the accurate requirement. However, with the small time step it can capture the details of

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22 atomic vibrations and movements that occur in the systems. Thus the evolution of the systems can be investigated in atomic detail and th e reaction mechanisms, which are the key point throughout these studies, also can be explored. The MC method, which does not include time as a variable in the algorithm, can overcome the tim e-scale limitation that is inherent to the MD method. It is therefore useful in obtaining th e final equilibrium state of the systems. Electronic-structure methods, such as quant um mechanical, Hatree-Fock and density functional theory (DFT), which in concept solve the many-body Schr dinger equation with some approximations, are also widely used in the fiel d of materials researc h. They not only provide atomic-level information but also provide details of the behavior of the electrons in the system. They are used to provide information about the systems electronic struct ure, including band gap, density of states, and optical properties, among othe rs. This is the biggest advantage over all the methods mentioned before. Because of their accur acy and ability to model a variety of materials from first principles, these methods can also act as a database provider for the development of empirical, atomistic methods. The drawbacks of these kinds of methods are larger simulation time and smaller system size. To date these methods can only simulate systems consisting of hundreds of atoms, which are too small to study ma ny interesting issues in materials science, such as large scale surface modification. It is also noted that there are overlap areas for different levels of simulation methods. These overlapped regions provide an avenue to te st the validity of the parameters for the more approximate methods in each case. Consistent pr edictions at the overlapped regions give more confidence for the simulation methods. This feat ure allows multi-scale modeling of materials ranging from electronic to continuum level.

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23 Figure 1-1. The approximate range of time and length scale over which simulation methods of different types can operate. 10-1910-1610-1310-1010-710-410-110-1010-810-610-410-2100 Length (m)time (second) E H FF with MD / MC Mesoscale methods Phase field / KMC Quantum based calculations Continuum methods finite differential / finite element Empirical force fields

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24 CHAPTER 2 SIMULATION METHODS Since the goals of this work ar e to investigate col lision induced chemical reactions in the gas and solid phases, the methods used in the research should be ab le to accurately and predictably model the processes that occur during the reactions. This means that the methods should be able to appropriately de scribe the changes in the system in response to changes in the environment. Molecular Dynamics Simulations Molecular dynamics (MD) simulations are an at omic level approach. In this approach, the evolution of atoms with time are done by numerica lly integrating Newtons equations of motion in response to the applied forces.57 Thus, MD simulations are one of the ideal methods to study collision induced reactions at the atomistic leve l. The results of MD simulations provide the positions, velocities and accelerations of all the particles in the system as a function of time. The accuracy of the MD simulation relies on the way in which the forces are evaluated in Newtons equations of motion. Typically, this is accomplished using empirical inter-atomic potentials that contain paramete rs obtained from quantum based methods or experimental data. In some cases, the forces are calculated using first principles, electroni c structure approaches. First principles start from the Schrdinger equa tion and use some approximations and theorems to reduce the complexity of the equation to make it practically solvable. From the approximate equations the energies and forces can be obtaine d. These methods are thus expected to describe the bonding between the atoms with high accuracy and require only the atomic numbers of the constituents as input. However, they still require signi ficant computational e ffort and are limited to system sizes of hundreds of atoms.

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25 On the other hand, the empirical methods that use special-designed empirical mathematical equations with fitted parameters to describe the interactions between the atoms are considerably more efficient than first principles methods to use in MD simulations. For example, systems consisting of billions of atoms can be examined with empirical potentials if the simulations make use of special computational techni que such as parallel computing. Density Functional Theory Molecu lar Dynamics (DFT-MD) Simulation The DFT-MD simulation used in these studies is the classical MD me thod that treats the movement of the ions by Newtons equations of motion and obtains the inte r-atomic forces from first principles calculations. This appr oximation is based on the Born-Oppenheimer approximation58 that states that, in most cases, the m ovement of nuclear and electronic can be decoupled since the nuclei are of the order of 103 times heavier than th e electrons and so are considered to be stationary w ith respect to the electrons. Th e procedure of DFT-MD is as follows: the ground state of the electron orbitals is first calculated. Then the forces on each nucleus are calculated from the el ectron-nuclei and nuclei-nuclei in teractions in the system. The forces on each nucleus are used to calculate th e position in the next time steps through MD algorithm. After that the ground state of the el ectron orbitals in the new position then is calculated. The procedure iterates for many steps until the system reaches its equilibration. Then the analysis of the evolution and final structure will be perf ormed to extract the required information. First Principle Calculations Since the systems of interest contain many atom s, it is inevitable to encounter the solving of the many-body Schrdinger equation. However, the quantum many-body problem cannot be solved directly. The time-independent many-body Schr dinger equation is as follows,

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26 ) ,... ( ) ,... (2 1 2 1 n nr r r E r r r H (2.1) where H is the Hamiltonian, ) ,... (2 1 nr r r is the many-body wave-function and E is total energy of the system. The system consists of elec trons and nuclei and they interact with each other via Coulombic interactions. Therefore, the Hamiltonian for the system can be written as, N i N i j j i N i M i j j i j M i M i j j i j i N i r e M i R Zr r e R r e Z R R Z Z m M Hi i i2 0 0 1 2 2 1 2 24 1 4 1 2 2 (2.2) where M and Nare the number of nuclei and electrons in the system. iZM, iZand iRare the mass, charge and position of th e nuclei respectively for atom i. em, eand irare the mass, charge and the position of the el ectrons, respectively. The first two terms in Equation (2.2) are the kinetic energy of nuclei and electrons. The rest are Coulombic potential energy terms coming from the nuclei-nuclei repulsion, nuclei-electron attraction, and the elect ron-electron repulsion respectively. Due to the complexity of the Hamiltonian shown in Equation (2.2), the exact wave-function needed to solve Equation (2.1) is unknown. Thus, the goal of the quantum many-body problem is to solve the many-body Schr dinger equation with some approximations that can reduce the complexity of the problem but still maintain the physics of the system. The first approximation is the Born-Oppenheimer approximation58 that decouples the electrons and nuclei in the Hamiltonian show n in Equation (2.2). Thus the electron-only Hamiltonian can be written as, N i N i j j i N i M i j j i j N i r er r e R r e Z m Hi2 0 1 2 24 1 2 (2.3)

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27 However, it is still difficult to solve Equa tion (2.3) since the el ectron wave-function has 3N variables for a system with N electrons. This is still a large number of degrees of freedom and there is no way to obtain the exact solution. Thomas-Fermi theory The first breakthrough to solve the many-body Hamiltonian was proposed by Thomas and Fermi59. In their model the electron density is the main variable instead of the electron wave-function. This will decrease number of degrees of freedom in the Equation (2.3). In their model, the exact electronic ki netic energy is assumed equal to the kinetic energy of a non-interacting electron system in a homogeneous electron gas. The nuclus-electron interaction is assumed the same as the static Coulomb poten tial and the electron-electron interaction can be obtained from the classical Coulomb interaction. Thus all terms in Equation (2.3) are simplified to what is called Thomas-Fermi energy functiona l. By applying the constraint that the total number of electrons is conserved and usi ng the method of Lagrange multipliers, the Thomas-Fermi energy functional yields the T homas-Fermi equations which can be solved directly to obtain the groundstate electron density. The Thomas -Fermi equation is as follow: 0 ) ( ) ( ) ( 3 5' ' 3 2 dr r r r n r r n AEXT k (2.4) where kA is a constant ) ( r n is the electron density and is the Lagrange multiplier. In Equation (2.4) the first term comes from the kine tic energy of the non-inte racting electrons, the second term is from the nuclei-el ectron interaction and the third term is the electron-electron interaction. Though Thomas-Fermi theory was the first breakthrough, it did not give correct predictions in most cases. The most serious problem is it cannot predict bonding between

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28 atoms60, so molecules and solids are not stable using this theory. The reason for this is first it assumes that the exact kinetic en ergy is the same as the kine tic energy in the non-interacting electron system, which leads to a proportional re lationship between electr on density and kinetic energy. The other reason is that it over simplifies electron-electron interactions to only classical Coulomb interactions, and did not consider addi tional quantum mechanical behavior, such as exchange interactions, in whic h the wave-functions of the syst em should be anti-symmetric, between electrons. Dirac61 later developed an approximation for the exchange interaction based on the homogeneous electron gas. The results, however did not improve the Thomas-Fermi theory. Therefore it is concluded that the electron kinetic energy contribut es a large portion to the total system energy. Density functional theory As discussed before, Thomas-Fermi theory was the first breakthrough for solving the many-body problem based on electron density. T hough the result was not satisfactory, the concept of using the electron dens ity instead of wave-functions as main variables motivated the generation of density-function theo ry. In 1964, Hohenberg and Kohn62 had shown that this concept was indeed workable. They proposed two remarkably powerful theorems in which the electron density is the main variable. This l eads to the formally exact groundstate method density functional theory (DFT). Hohenberg-Kohn theorems The Hohenberg-Kohn theorems are suitable for any system consisting of electrons that move in response to the external potential. Here, the external potential mainly arises from the nuclei. The first Hohenberg-Kohn theorems state as: The external potential, ) ( rEXT and hence

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29 the total energy, is a unique f unctional of the electron density ) ( r n .62 in other words, the ground-state density determines the external pot ential uniquely. Thus, both the external potential and its electron density completely define the Hamiltonian. The energy functional of the system, therefore, can be written as, ) ( ) ( ) ( ) ( r n F dr r r n r n EEXT (2.5)where ) ( r n F is a universal function which contain all other interactions in the system.The second Hohenberg-Kohn theorem states that: The ground-state energy can be obtained variationally: the dens ity that minimizes the total en ergy is the exact ground-state density.62 Since the intention of this section is only to introduce density functional theory, the details of the mathematical equations used to prove the theorems are not provided here. Kohn-Sham formulation Although the Hohenberg-Kohn theorems are ex tremely powerful, they do not provide a way of computing the ground state density of a system in a practical manner. Kohn and Sham63 thus proposed a simpler approach to perf orm DFT calculations. The method is based on calculating the full interacting system of the real potential by a fictitious non-interacting system in which the electrons move in an effective Kohn-Shan single-particle potential, ) ( rKS The ground state energy of a many-electron system can be obtained by minimizing the energy functional in Equation (2.5) with the constraint of the total number of electrons. This lead to the Euler equation as follows, ) ( ) ( ) ( r r n r n FEXT (2.6)

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30 where is the Lagrange multiplier. The idea of Ko hn and Sham was to set up a system where the kinetic energy could be de termined exactly and any inconsistencies are included in a correctional term. This is achieved by invoki ng a non-interacting sy stem of electrons. The universal functional, ) ( r n F, thus is partitioned into three terms, ) ( ) ( ) ( ) ( r n E r n E r n T r n FXC H S (2.7) ) ( r n TS is the kinetic energy of a non-interac ting electron with electron density of ) ( r n ) ( r n EH is the classical electrostatic energy of the electrons and is given by, ' ') ( ) ( 2 1 ) ( drdr r r r n r n r n EH (2.8) These two terms are known exactly. ) ( r n EXC is the exchange-correlation energy, a correctional term, which contains the differen ce between the exact and non-interacting kinetic energies and also the non-classical contri bution to the electron-electron interactions. In the Kohn-Shams method the Euler equation in Equation (2.6) becomes, ) ( ) ( ) ( r r n r n TKS S (2.9) where, the Kohn-Sham potential, ) ( rKS is given by, ) ( ) ( ) ( ) ( r r r rXC H EXT KS (2.10) in which ' ') ( ) ( ) ( ) ( dr r r r n r n r n E rH H and the exchange-correlation potential, ) ( ) ( ) ( r n r n E rXC XC The main point to understand the KohnSham theory is that Equation (2.9) is only a rearrangement of Equation (2.6). So th e density obtained by so lving the non-interacting

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31 Kohn-Sham system is the same as the exact gr oundstate density. Thus the Schrdinger equation for this system can be decomposed into N one-electron equations shown as, ) ( ) ( ) ( 2 12r r ri i i KS (2.11) where, i are the Lagrange multipliers for one of the orthonormal N single-particle states. Equation (2.11) is the K ohn-Sham equation and the ) ( ri are the Kohn-Sham orbitals. This decomposability of the Schrdinger equation ma kes the Kohn-Sham theory useful from a practical point of view, even as it increases the complexity of the system. For example, when the number of electrons increases, the problem b ecomes no more difficult, only the number of single-particle equations to be solved increases. Since ) ( rKS contains the exchange-correlation potential term that depends on the electron density, ) ( r n, as shown in Equation (2.10), the Kohn-Sham equations must be solved in a self -consistent manner. Thus, the procedure by which the equations are solved starts from the initial guess of ) ( r n, which leads to the evaluation of the exchange-correlation potential term in Equati on (2.10). The evaluated value is then used to obtain the new ) ( r n. This procedure is repeated until the self-consistent condition is achieved. The issue now is how to determine the exchange-corre lation functional, ) ( r n EXC. An implicit definition of ) ( r n EXC can be obtained through Equation (2.7) and is shown as, ) ( ) ( ) ( ) ( ) ( r n E r n E r n T r n T r n EH ee S XC (2.12) where ) ( r n T and ) ( r n Eee are the exact kinetic and electr on-electron inter action energies, respectively. The inten tion of Kohn-Sham theory is to make the unknown contribution to the total energy, contained in the exchange-correlatio n energy term, as small as possible. However, in many systems the binding energy has about th e same value as the exchange-correlation

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32 energy, ) ( r n EXC. Thus it is important to choose a good exchange-correlation approximation for the system of interest. Exchange-correlation functional The first exchange-correlation functi onal, proposed by Hohenberg and Kohn,62 starts from the evaluation of the homogeneous electron gas sy stem, are therefore valid for systems with slowly varying electron density. These functionals only include th e density but not the gradient of the density at a given point and are called local density approximation (LDA) functionals. Since in real systems the electrons are far fr om being a homogeneous gas, more elaborate functionals that include the grad ient of the electron density, know n as the generalized gradient approximation (GGA),64 have been proposed. The improvement is achieved by taking the gradient term from the Tayor series expansion of ) ( r n Exc. Currently there are numerous sophisticated exchange-correlation functionals av ailable. However, the LDA and GGA are still the most popular exchange-correlation f unctionals in the DFT calculations. Plane-wave implementation of DFT If one wants to apply the DFT to a solid-state system, the number of electrons is often prohibitively large; if they are each treated explicitly, the DFT method is effectively impractical. Fortunately, most solid state systems can be treat ed as periodic. Accord ing to Bloch's theorem,65 the wave function can be described by the product of a lattice periodic component ) ( r Uj and a plane-wave-like component r iKe for a periodic system. Thus, r iK j K je r U r ) ( ) (, (2.13) in which the plane-wave wave-vector K is unique only up to the first Brillouin zone in reciprocal space. For a given wave-vector and pote ntial, there are a number of solutions that are indexed by j in Equation (2.13). Since ) ( r Ujis also a periodic f unction with the same

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33 periodicity as the system, it can be expressed as a summation of discrete plane-wave basis sets with wave-vectors G that are reciprocal latti ce vectors of the crystal, G r iG G j je c r U,) ( (2.14) In Equation (2.14), G jc, is the plane-wave coefficient and G is defined by m G 2 in which mis an integral and is the lattice vector. Thus the wave-function can be written as, G r G K i G K i K je c r) ( ,) ( (2.15) The advantages of using plane-wave lik e wave-function is that their form is mathematically simple, they can offer a complete basis set that is independent of the type of crystal, and they treat all areas of space equally. Consequently, the method is quite suitable for solid-state systems with high accuracy and relativel y low computational cost. This is in contrast to orbital-type wave-functi ons that are dependent on th e positions of the nuclei. Another advantage of using plane-wave type functions is that when they are used, the Kohn-Sham equations become relatively simple. Fo r example, substituting Equation (2.15) into Equation (2.11), gives the Kohn-Sham equation in the following form, G K j i G G K j XC H EXT G Gc K c G G G G G G G K , ' 2) ( ) ( ) ( ) ( 2 1' ' (2.16) In this form it is found that the reciprocal spa ce representation of the kinetic energy is diagonal and the various potentials can be described in term s of their Fourier components. It is thus easier to solve mathematically. For an exact calculation, the dimension of th e plane-wave basis se t should be infinite. Fortunately the plane-waves of the lower order te rms contribute the most to the kinetic energy, so a practical solution is obtaine d by truncating the basi s set to a finite number of plane-waves. This is defined by the kinetic energy cutoff,

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34 cutE G K 22 1 (2.17) Thus the accuracy of the calculation can be im proved systematically by increasing the cutoff energy, cutE which means including higher order terms (more terms) in the plane-wave basis set. The K-point sampling According to the Blochs theorem, the wave function for a periodic system can be described by the product of a lattice periodic part ) (r Ujand a plane-wave like part r iKe. This allows the calculation to be pe rformed in reciprocal space. Th e calculation of the expectation value that requires solving the integral over all of real space can thus be replaced by solving the integral in reciprocal-space over only the first Brillouin zone. However, the calculation still needs to integrate over an infinite number of K points in reciprocal space. Fortunately, electron wave-functions do not change appr eciably over small distances in reciprocal space. Thus the integrations can be replaced by summations over a finite numb er of K points. This gives, j j j BZK F w dK K F) ( 1 ) ( (2.18) where, ) (K F is the Fourier transform of any integral function, such as the electron density or total energy, is the cell volume, and jw is the weighting factor. The number of K points that is needed to achie ve the desired accuracy can be determined by testing the total energy conve rgence with increasing number of K points. This procedure is termed K-point sampling. Pseudopotentials The main drawback of plane-waves is that they require a large number of plane-wave-function to describe la rge curvature, such as electron density near the core region

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35 atoms. Consequently, the kinetic energy cutoff, cutE, is very high, which leads to the unaffordable computational costs. This pr oblem is overcome with the pseudopotential approximation.66 The pseudo-wave-functions replace the rapidly oscillating wave-functions of electrons in the core region by a smoother wave -function that leads to a weaker pseudopotential compared to the strong electron-nuclei interac tion potentials. In most cases only the valance electrons are involved in the interactions. Thus, the idea of the pseudopotential is to replace the strongly oscillating wave-function that is associated with all-electron wave-functions with smoother wave-functions in the core regi on. In this way the pseudopoten tial not only reduces the amount of time needed for each calculation, but also ma intains the accuracy of the calculation. The pseudo-wave-functions and the allelectron wave-functions are iden tical outside a chosen cutoff radius, but do not have the nodal structure that appears in the all-electron wave-function inside the cutoff radius (Figure 2-167). To generate pseudopotentials, the all-electron wave-functions need to be determined first. Thus, initially, all-electron atomic calculations are performed self-consistently. Then the pseudopotential is built subject to the following four conventional conditions: (i) the valence pseudo-wave-function must be the same as a ll-electron wave-function outside a given cutoff radius, (ii) the charge enclosed within th e cutoff radius must be equal for the two wave-functions, (iii) pseudo-wave-function must not contain any nodes insi de the cutoff radius and must be continuous at cutoff, including the first and second derivatives, (iv) the valence all-electron and pseudop otential eigenvalues must be equal. There are two types of pesudopotentials th at are currently most popular that are implemented in the CASTEP68 software. One is the class of norm-conserving pseudopotentials69

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36 and the other is the class of ultrasoft-pseodopotentials.70 Norm-conserving pseudopotentials are harder in the core region comp ared to the ultrasoft-pseodopoten tials. Here the term harder means that in the core region the pseudopotential is very close to the all-electron potential. In other words, norm-conserving pseu dopotentials have larger curvat ure in the core region than ultrasoft-pseudopotentials. Ther efore, higher kinetic energy cutoffs are needed and the calculations are computationally more extens ive. Ultrasoft-pseudopot entials attain much smoother (softer) pseudo-wave-functions, so cons iderably fewer plane-waves are needed for calculations of the same accuracy. DFT-MD Simulation in CASTEP The DFT-MD used in the simulations discusse d in Chapters 3 and 4 treats the movement of the nuclei by Newtons equations of motion and obtains the in ter-atomic forces from first principle calculations. Therefore, in every MD step the self-consistent fi eld (SCF) procedure needs to be performed in order to obtain the gr ound-state electronic stru cture and the forces on each nucleus. This process, however, takes an ex tremely long time to finish the required MD steps needed to equilibrate the system. Therefor e, an alternative approach, termed wave-function and density extrapolation, is used to accelerate the DFT-MD calculation steps, and this approach is implemented in the CASTEP68 software. The idea is based on the fact that the nuclei actually only move a short distance in each MD step. Therefore, the wave-functions at time dt t will not be too different from the wave-functions at time t. Thus, the initial guess for the wave-function associate with the next MD st ep can be achieved by using the multi-linear extrapolation approach proposed by Arias et al.71 By using this method, improved initial guesses for wave-functions at each MD st ep can be obtained. This pro cedure decreases the number of iterations in the SCF procedure, whic h accelerates the DFT-MD calculation.

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37 Molecular Dynamics Simulation Using Reac tive Empirical Bond Order (REBO) Potential In this section, classical MD simulation ar e discussed, where the MD procedure is the same as discussed in the last section, but the inter-atomic fo rce calculations are based on an empirical, reactive empirical bond -order (REBO) potential. The REBO potential was designed to predict bond breaking and bond reforming accordi ng to changes in the environmental. The method is used in the studies that will be discussed in chapter 5. Reactive Empirical Bond Order Potential The bond-order potential was first proposed by Tersoff72 for modeling silicon systems and Brenner73 further modified it for the more complicat ed carbon-based systems. Jang and Sinnott54 later extended the parameterizatio n of the second-generation REBO74 for hydrocarbons to fluorocarbons. It is capable of predicting ne w bond breaking and bond formation, both of which are crucial to accurately model the processes that occur in polyatomic ion beam deposition. Since this class of bond-order potentials were developed, they have b een successfully used to obtain insight into various processes that involve chemical reactions at surfaces, such as molecule-surface collisions,75-80 cluster-beam surface deposition,81,82 growth of diamond-like carbon films by hydrocarbon ion beams,83,84 etching of silicon surfaces by fluorocarbon (FC) ion beams,53,85,86 and the chemical vapor deposition of diamond.87 However, because of the empirical and classical nature of the REBO potential, electronic effects, such as electronic excitations or true charging of the atoms, are not included. Therefore, ions with positive charges are treated as reactive ra dicals. Charged ions might be expect ed to react more readily than the simulated radicals. However, it is also true th at many incident ions are quickly neutralized as they approach the surface. Thes e potentials are thus expected to provide qualitatively correct results and important insights in the study of collision induced reactions in solid phases.

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38 The expression of the REBO74 potential used to calculate the binding energy (bE) between atoms i and j is: ii j ij A ij ij R br V b r V E (2.19) where, ij Rr V and ij Ar V are repulsive and attractive pairwise potentials, respectively, between atom i and j which only depend on the distance ijr between the two atoms. They are given as, ijr ij ij c ij Re A r Q r f r V 1 ) ( ) ( (2.20) 3 1) ( ) (n r n ij c ij Aij ne B r f r V (2.21) where A, B, Q, and are two-body parameters determined by the type of interaction. The function ) (ij cr fis a cutoff function that limits the range of the covalent interactions to insure that the interactions include neares t neighbors only and is written as, max max min min max min min0 2 cos 1 1 ) (ij ij ij ij ij ij ij ij ij ij ij ij cD r if D r D if D D D r D r if r f (2.22) in which min max ij ijD D defines the distance over which the function varies from one to zero. In Equation (2.19) the ijb is a many-body empirical bond-order term, which is characteristic of a Tersoff-type potential. A variety of chemical e ffects that affect the covalent bond strength are all accounted for in this term such as the coordina tion numbers, bond angles,

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39 torsion angles and conjugation effects. This bond-order term can weigh the bond strength according to the local environment, which allo ws the REBO potential to model covalent bond breaking and reforming with associated changes in atomic hybridization. This term is thus important for the realistic treatment of chemical reactions that involve changes to the bonding to carbon atoms. The empirical bond-order te rm is written as a sum of terms: ij ji ij ijb b b b 2 1 (2.23) where ijb and jib identical forms but swap the i and j indices. These two terms depend on the local coordination and bond angles for atoms i and j The term ijb is given as, 2 1 ( ) () ( )) (cos( ) ( 1 H i C i ij j i k R r R r ijk ik c ijN N P e G r f be ik ik e ij ij ijk (2.24) where, )) (cos(ijkG is a polynomial function and controls th e influence of the nearest neighbors to the bond order according to the bond angle among atoms i, j and k, and ijk is a fitting parameter used to describe three-body tran sition states around Hatoms. The function ijP is a correction term that accounts for th e different chemistry around atom i. C iN and H iN are the number of neighboring Cand H-atoms of atom i and are given in the following form, carbon j i k ik c C ir f N) () ( (2.25) Thus the neighboring atom can be counted according to the distance between atom i and k and the value is ranged from 0 to 1. This ensures that the changing of bond order is continuous, and bE is continuous during bond breaki ng or reforming. The function ijP is not defined analytically, but the values are determ ined by cubic spline interpolation with some

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40 predetermined values that are obtained by fittin g to the properties (bond energies, bond lengths) of known solid-state structures or molecules. The term ijb is further written as a sum of two terms: DH ij RC ij ijb (2.26) where, RC ij is the radical term and DH ij is the dihedral term. The value of the RC ij term depends on whether a bond between atoms i and j has radical character or is a part of a conjugated system. This term is given as ) , (conj ij t j t i ij RC ijN N N Y (2.27) where, ijY is determined by tricubic spline interpolation and t iN and t jN are the total number of neighboring atoms around atom i and j respectively. conj ijN can be further written as, 2 ) ( 2 ) () ( ) ( ) ( ) ( 1 carbon j i l jl jl c carbon j i k ik ik c conj ijx F r f x F r f N (2.28) where ) (ik c t k ikr f N x (2.29) and 3 0 3 2 2 ) 2 ( 2 cos 1 2 1 ) (ik ik ik ik ikx if x if x x if x F (2.30) The DH ij term depends on the dihedral angl e for carbon-carbon bonds which considers the torsion effect in the molecule and is given as, ) () ( 2) ( ) ( ) ( cos 1 ) , (j i kj i l jl c ik c ijkl conj ij t j t i ij DH ijr f r f N N N T (2.31)

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41 where ijkl is the torsion angle between atom i j k and l The function ijT is determined by tricubic spline interpolation. The DH ij term has values only when the bond between atom i and j is a double bond and is zero when atoms i and j are not carbon. Thus, the second generation REBO potential determines atomic bonding configurations strictly from the local bondi ng neighbors and non-local conjugation, which influences the effective interatomic interactions and the rehybridization of atomic orbitals. Therefore, the second generation REBO potentia l predicts covalent bond break ing and reforming within a classical formalism. Lennard-Jones Potential The dispersion effect from long-range interac tions is modeled using a Lennard-Jones (L-J) potential88 that is coupled to the short-range REBO potential with a cubic spline function. The L-J potential used here is the so-calle d 12-6 L-J potential that is given as, 6 124 ) (ij ij ij LJr r r V (2.32) where and are the L-J parameters for particular types of atoms and ijr is the interatomic distance. For the interaction betw een different types of atoms, and are determined by B A AB 2 1 (2.33) B A AB (2.34) Periodic Boundary Conditions Periodic boundary conditions (PBCs) are used in the simulations to avoid unphysical edge effect, since the simulation models are substantially smaller than the actual systems. By applying PBCs, the models can be effectively extended to in finite sizes. The concept of PBCs is shown in

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42 Figure 2-2.57 The system containing N particles is treated as the primitive cell, and the primitive cell continuously repeats along each of the periodic boundaries. A given particle A in figure 2-2 will interact with all other particles in this infinite periodic system, that is, all other particles in the same periodic cell and all the nearest particle images in all other cells. In practical systems, the interaction distance is limited to a specific range that depends on the potential setup. Therefore, particle A only interacts with other particles within the cutoff radius. Predictor-Corrector Algorithm The evolution of the system is accomplished by Nordsieck predictor-corrector algorithm, which is one of the higher order algorithms used to carry out MD simulations. The idea of the predictor-corrector is that the position, veloci ty, acceleration, and highe r order derivatives of position with respect to time of each particle at time t t are predicted by a Taylor expansion based on the previous time step, then the predicte d values are corrected by the interatomic forces calculated from the interatomic potentials. The REBO-MD simulations used in the study are performed with the forth order predictor-corrector algorithm. The form of the predictor is, ) ( ) ( ) ( ) ( ) ( ) ( 2 1 ) ( ) ( ) ( ) ( 6 1 ) ( 2 1 ) ( ) ( ) (2 3 2t b t t b t t b t a t t a t t b t t a t v t t v t t b t t a t t v t r t t rp p p p (2.35) where pr, pv, pa and pb are the predicted position, ve locity, acceleration and third derivative of position with respect to time, respectively, of each atom at t t Then the interatomic forces are calculated based on the predicted position of each atom and the corrected accelerations, ) (t t ac are obtained. The difference between ) (t t ap and ) (t t ac

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43 ) (t t a is the adjustment parameter that is used to correct the predicted values.. Hence, the position and other derivatives can be co rrected by the following equations, ) ( 3 1 ) ( ) ( ) ( ) ( ) ( ) ( 6 5 ) ( ) ( ) ( 6 1 ) ( ) ( t t a t t b t t b t t a t t a t t a t t a t t v t t v t t a t t r t t rp c p c p c p c (2.36) These corrected values are used to predict the positions and first n derivatives at the next step of the simulation, and then the same procedure is repeated. The error for an nth order algorithm is on the order of nt Higher order derivatives can be used to obtain better accuracy, but this same level of accuracy can also be achieved using smaller time steps. Temperature Control Method In the simplest MD simulation, which calcu lates the system evolution only by Newtons equations of motion, the entire system is subjec ted to the conservation of the total number of atoms, volume and energy (NVE). Therefore, in this MD simulation, the system properties are measured in the microcanonical (NVE) ensemble. However, in real cases the properties of the system is measured in the ca nonical (NVT/NPT) ensembles. In order to bring the simulations into better agreement with actual conditions, it is necessary to perform the simulations in the canonical ensemble. The way to achieve this requirement is thr ough the control of the system temperature. There are many methods to control system temperature.89-92 In these studies, the Langevin thermostat is used to control the system te mperature. The Langevin thermostat follows the Langevin equation of motion instead of Newtons equations of moti on. In particular, a friction force that is proportional to the ve locity is added to the conservati on force that adjusts the kinetic

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44 energy of the particle so that the temperat ure matches the set temperature. The Langevin equation of motion93 is expressed as, ') (f r f v a m (2.37) where, mis the mass of the particle, a is the acceleration, ) ( r f is the conservation force obtained from interatomic potential, is the velocity of the particle, is a friction constant and 'f is the random force. The friction force decreases the temper ature of the system, since is set as a positive value. The random for ce is randomly determined from a Gaussian distribution to add kinetic ener gy to the particle. The random fo rce is a function of the set temperature and time step. Thus, the system temper ature is maintained by balancing the friction force and random force. The advantage of the La ngevin thermostat is that it is simple to implement and able to mimic real situations accurately. Acceleration and Parallelization of REBO-MD Code The MD simulations calculate the information of the system (position, velocity, force on each atom) at the next time by using the integration of Newtons equations of motion. In order to maintain the accuracy of the simulation, a small time step (on the order of a femto-second) is required. Using small time steps in the calculations means that the system will evolve very slowly because 105-106 time steps are needed to reach the eq uilibrium state or the state that could be compared to experimental data. Acquiring fo rces between the atoms makes the software loop over all the neighbor atoms of each atom. This incr eases the computational effort needed to find the neighbor atoms of each atom. Due to these inherent limitations, in some cases it takes an unreasonably long computational time to finish one simulation trajector y. It is therefore

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45 necessary to develop certain techniques to ove rcome these limitations and make MD simulation practical. Since the algorithm that allows MD simulati ons to calculate the system evolution cannot be changed to a significant degree, the small time step cannot be modified. The efficiency of the force calculation of each atom in every time step, however, can be improved. Traditional methods that are used to find the neighbor atom s of each atom require looping over all the atoms in the system. This met hod turns out to scale as 2N in the calculation, where N is the number of atoms in the system. Figure 2-3 shows the comput ational time can be perf ectly fitted by a second order polynomial function (red line). Link-Cell Technique A new approach combines the neighbor list technique, which is a pre-stored array containing neighbors of each atom, and th e link-cell technique to solve the ) (2N O problem within the REBO MD software. The link-cell techni que is described as follows: First the system is divided into several cells to which the system atoms are sorted. The size of the cell is a little larger than the potential cut-o ff, beyond which the interactions are neglected. Thus every atoms neighboring atoms should be within the same cell as itself and th e 26 neighbor cells (9 cells in the upper level, 9 cells in the lo wer level and 8 cells in the same level). During the determination of neighbor atoms, the software loops over only the atoms in the same cell and the 26 neighbor cells. Therefore, the calculation is scaled down to an ) (N O calculation, which means that the calculation time increases linearly with system size. The result of the implementation of combination of link-cell and neighbor list is show n in figure 2-3 and can be perfectly fitted by a linear line (shown in blue).

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46 Though the implementation of th e link-cell technique can impr ove the efficiency of the MD software, there are additional limitations that must be overcome. For example, in a common machine the memory is large enough to store position, energy, etc. of approximately 100,000 atoms. A 100,000 atom system is around 10 nm3 and is too small to many systems of interest. An additional limitation is the long calculation time for each MD step when the system size is large. To handle larger system sizes a parallel computing scheme is required. Spatial Decomposition Method The idea behind parallel computing is to divide the system into several blocks such that each block is computed by a processor independen tly. The information of the whole system is then obtained through communication among the pro cessors in a parallel computer cluster. Ideally, the cost of the calculation will be scaled down to the order of M1 where, M is number of processors used in the calculation. For example, it will take half the time to finish the simulation when twice as many pro cessors are used for the same system size. This method also provides the flexibility of using computer memory effectively by storing pa rt of the information of the system in each node. This allows for th e simulation of larger systems that are more complex and can be more readily compared to experimental data. As part of this dissertation, the scalar form of the REBO-MD software was parallelized using the spatial decomposition method, which can theoretically run effi ciently over thousands of processors. The idea behind th e spatial decomposition method is to divide the system into different cells spatially correspond ing to the number of nodes that is used in the calculation. Figure 2-4 shows the schematic re presentation of the spatial deco mposition in one dimension and two dimensions that is implemente d in the parallel REBO-MD code.

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47 The main issue in the parallelization is to deal with the inter-atomic forces near the node boundaries. For example, as discussed above, the REBO potential is a many body potential. Therefore, the forces acting on atom i come from not only the nearest neighbors, j and k, but also the second neighbors, mand l,and third neighbors, n shown in figure 2-5. If those atoms are to stay on different nod es, then the information on the neighbor atoms is not complete on each node. Consequently, some forces will be missed during the calculation. To overcome this problem, every node is assigned a buffer laye r that includes neighboring atoms to that node, so that during the calculation all the forces can be evaluated. Then the collected forces in the buffer layer are passed to the neighboring node s and summed for the corresponding atoms. In this way all the forces on each atom can be obt ained and the total force for each atom can be calculated correctly. Massive Parallelization Method MD simulations allow each atom to move in response to the for ces acting on them, so during the evolution of the system, atom s may move across the node boundary to the neighboring nodes. In this situati on, it is necessary to pass th e atoms information, including position, velocity, acceleration, n derivative, and index number, to the neighboring nodes. Also, as discussed above for spatial decomposition, it is necessary to pass the forces of the buffer layer atoms to the neighbor nodes in each MD step. Therefore, passing information is unavoidable in parallel MD simulations. The data transfer rate, however, is limited by the hardware of the computer cluster. Conseque ntly, preventing unnecessary communication among the nodes is key to boosting the e fficiency of MD simulations. The passing method implemented in the para llelized REBO-MD software allows each node to only communicate with its neighboring nodes, instead of global communication where

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48 each node communicates with the master node se quentially. The local co mmunication thus will not increase the extent of communication when the number of nodes increases. Figure 2-6 shows a schematic of how the massi ve parallelization method works. In every passing step, all the even nodes pass inform ation to odd nodes and then odd nodes pass information to even nodes. The process repeats in two directions for one-dimensional spatial decomposition and eight directions for two-dime nsional spatial decomposition in the current implementation. Dynamic Memory Allocation Since the parallelized software will be used for various system sizes, to enhance the convenience of usage dynamic memory allocation is us ed to allocate the si ze of the arrays that are used to store and pass information about the atoms. The advantages of dynamic memory allocation are not only convenience in use but also the array size is adjusted automatically according to the system size (number of atoms in the system). Therefore the array size will not be too large for the computer to locate the variable address in the memory slots and maintains the efficiency of the simulation. Results of Parallel Implementation Figure 2-7 shows an efficiency test of one-d imensional parallelization implementation. The test was performed by relaxing a 10,000 atom car bon nanotube. The parallel implementation in this case is efficient up to 16 processors. The real time for calculating 100 0 MD steps is reduced from 400 seconds to 54 seconds, and the total sp eedup is 7.4 times faster than serial code. Figure 2-8 shows the efficiency test of tw o-dimensional paralleliz ation implementation. The test was performed by relaxing the alpha-phase of isotactic po lypropylene of various system sizes. The real time for ca lculating the 1000 MD steps wa s measured. The algorithm of parallelization was also tested by measuring the length of the L-J ne ighbor list. In fi gure 2-8, the

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49 length of the L-J neighbor list is shown by open symbols. The curv es illustrate how the length decreases linearly as both axes ar e plotted on a logarithm scale and the curves slope is close to -1. This result proves that the parallelization algorithm is correct. The real time of the calculation (solid symbols shown in figure 28) ideally should follow this curv e closely. In our results, the time for 1000 MD steps follows the curve but it shows little deviati on when the number of processors is large. Thus, in general, the two-dimensional, parallel implementation is able to model systems consisting of millions of atoms. Implementation is more clear if the number of atoms per node versus calculation time for 1000 MD steps is plotted. In figur e 2-9, different combinations of system size and number of processors used was chosen so that the number of atoms per node is constant. For example, a system of 15552 atoms with one processor, 62208 atoms with four processors, 248832 atoms with 16 processors, 559872 atoms with 36 pro cessors, and 995328 atoms with 64 processors were chosen such that all have 15552 atoms per node. The calculation time should be the same in these five cases. Figure 2-9, however, shows that the calculation time increases as the system size increases. The problem may come from the global communication that occurs to calculate the properties of the entire system during the simulation and the large arrays used in the larger systems. To solve this problem it will be necessary to check the time spent on passing information and decrease the number of large arrays used for larger systems.

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50 Figure 2-1. Schematic illustration of the concep t of pseudopotential. The solid lines represent the all-electron wavefunnction, and the associate all-electron potential, r Z/. The dashed lines represent the pseudo wavefunnction, pseudo and the associate pseodopoetntial, pseudoV. Figure 2-2. Schematic repres entation of periodic boundary A

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51 3000400050006000700080009000 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 Computational time (second/step)Number of atoms Figure 2-3. The computational time for running one MD step in different size of the systems. The open symbol represents the code cont ains only neighbor list technique and the solid symbol shows that the code which combine the link-cell t echnique and neighbor list technique. The red line is fitted by th e second order polynomia l function. The blue line is fitted by a linear function. Figure 2-4. Schematic representation of sp atial decomposition method. a) one-dimensional decomposition and b) two-dimensional decomposition a) b)

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52 Figure 2-5. Schematic representation of the for ce relationships in REBO potential. The circles mean the cutoff radius for the fi rst neighbors for the center atom. Figure 2-6. Schematic representation of the massive parallelization method in a) two-dimensional spatial decompositi on and b) one-dimensional spatial decomposition. a) b)

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53 0246810121416182022 50 100 150 200 250 300 350 400 450 0 1 2 3 4 5 6 7 8 time for running 1000 MD step (second)Number of processors Speedup Figure 2-7. Time for running 1000 MD steps and sp eedup vs. number of processors in one-dimensional parallelization. 110100101102103 105106107 Time for 1000 MD steps (s)Number of Processors 15552 62208 248832 559872 995328 1555170Number of atoms in L-J neighbor list 15552 62208 248832 559872 995328 1555170 Figure 2-8. The time for running 1000 MD steps (solid symbol) a nd the length of Lennard-Jones neighbor list ( open symbol) by using various numbers of processors in different sizes of the systems.

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54 481216202428323640444852566064 600 800 1000 1200 1400 1600 1800 2000 Time for 1000 MD steps (s)Number of Processors Figure 2-9. The time for running 1000 MD steps in five chosen cases.

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55 CHAPTER 3 MECHANISTIC STUDY OF SURFACE POLYMERIZATION OF TERTHIOPHENE OLIGOMERS BY ION-ASSISTED DEPOSITION Introduction This chapter focuses on surface polymerizati on mechanisms in ion-assisted deposition processes. The study is carried out using both experimental and computational methods. The experiments described here utili ze a mass-selected beam of thiophene ions to remove fragment ions, radicals, and protons (all present in non-ma ss-selected ion sources) that can contribute to the film growth process and ther eby complicate mechanistic studies of the polymerization event. They were carried out by Dr. Sanja Tepavcevic and Prof. Luke Hanley at Department of Chemistry, University of Illinois at Chica go. Mass-selected SPIAD experiments are readily modeled by computer simulations that allow de tailed elucidation of mechanistic aspects. Therefore, DFT-MD simulations are also applied to examine energetic thiophene molecular deposition on 3T thiophene oligomers. These simu lations provide key insights into the complex, cross-link forming chemical reactions that oc cur during SPIAD. Comparison of experiments and computer simulations is a powerful strategy in understanding ion-induced surface processes.94-97 Computational Details The DFT-MD simulations described here are performed using the CASTEP software67,98 with the generalized gradient approximation (GGA-PW91). The core electrons are represented by ultrasoft pseudopotentials and the valence electr ons are described with plane waves that have a kinetic energy cutoff of 240 eV, and the k-point me shes used in the calculation is 1. The convergence of total energy was tested with resp ective to kinetic energy cutoffs up to 310 eV and k-point meshes up to 1. The results show that the difference in total energy between the conditions used in the study and the more comput ationally intensive cond itions is within 0.08

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56 eV/atom. This indicates that the conditions us ed in the DFT-MD simulations represent a good balance between computational efficiency and accuracy. The simulation system consists of a supercell that is 13.3 15.4 25 and contains three layers of hydrogen-terminated Si (111) covered on one side by a 3T thin film that consists of four 3T oligomers, two of which are arranged parallel to one another and 3.2 from the Si surface, while the other two oligomers are arranged parallel to each other but perpendicular to the first two. The total number of atoms in the film and s ubstrate is 220 atoms and the setup is shown in Figure 3-1a). The dist ance between the oligomers in the film is about 3.2 The system is allowed to equilibrate for 200 fs prior to thiophene molecule deposition and the simulations evolve for about 240 fs/collision event. The NVT ensemble is used in all the simulations to maintain the system temperature at 300 K and the simulation timestep is 1 fs. This system configuration mimics the experimental system in which the oligomers are physisorbed on the silicon surface in random arrangements while at the same time maximizing the contact area in the relatively small supercell necessitated by th e high computational cost associated with the DFT-MD simulations. Importantly, the simulations should be able to model localized chemical reactions that occur when ions or neutral molecu les collide with the oligomers at locations close to the substrate surface. The thiophene incident energi es considered in the simula tions are 100, 200, 250, and 500 eV/molecule. In the case of the three lowest de position energies, the effect of charge on the deposition process is investigated. In particular, both systems that have a +1 charge and that are neutral are considered. The DFT approach smears the charge throughout the system rather than localizing it on the incident molecules. However, as the simulations represent only a localized portion of the actual experimental system over s hort (nanosecond) time scal es, the comparison of

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57 neutral and charged systems is still indicative of wh at occurs in parts of the experimental system, especially as the incident mol ecules approach the surface and ar e increasingly likely to share charge with it. The simulations consider the de position of a single thiophene particle at each incident energy, except for the 250 eV/molecule deposition case, where two thiophene particles are deposited to investigate the effect s associated with higher fluences. In all the simulations, the molecules or ions are deposited at the points where the 3T oligomers cross each other (see Figure 3-1b)) to maximize opportunities fo r crosslink formation. This choice ensures that the most energe tic phenomena in the SPIAD process will be investigated in the simulations and shed light on the most complex aspects of polymerization. Since there are four crossed sites in the model and each of them is slightly different in 3T oligomer orientation (the thiophene rings tilt to slightly different de grees and in different directions), in some cases the th iophene molecule or ion is depo sited on site #1 in Figure 3-1b), while in other cases it is deposited on site #2 in Figure 3-1b). Specifically site #1 is chosen in the 100 eV deposition case and in the first de position event at 250 eV for the neutral system, while site #2 is chosen in th e 200 eV deposition case, the first deposition event at 250 eV in the case of charged-system, the sec ond deposition event at 250 eV for the neutral system, and at 500 eV. The chemical reactions that occur on deposition are then documented and analyzed. Experimental Methods SPIAD is performing by combining deposition of thiophene ions with simultaneous dosing of 3T vapor under vacuum. The vacuum apparatus us ed to perform SPIAD a nd x-ray photoelectron spectra (XPS) analysis is only briefly described here.8,99 The apparatus consists of a differentially pumped ion source, a preparation chamber and analysis chamber. Thiophene (99+%, Aldrich Chemical Co.) was used as the ion precursor. Fo r the isotopic experiment we used deuterated thiophene (D4, 97%, Chambridge Isotope Laboratori es Inc). Mass-selected beams of C4H4S+

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58 (thiophene) ions are produced by electron impact. Terthiophene crys tals (2,2:5,2-Terthiophene, 99%, Aldrich Chemical Co.) are used as recei ved. Terthiophene dosing is accomplished with a resistively heated homemade source mounted on the preparation chamber whose beam is incident on the surface during ion bombardment. Di fferent ion/neutral ratios are utilized for ion energies in the range of 50 200 eV by ch anging the fluence of neutrals (1 6 1017neutrals/cm2) or ions (2 4 1015 ions/cm2). Silicon wafers are used as substrates for deposition, after etching with 5% HF to produce the hydrogen terminated surface H-Si (100) with a minimum of oxide. The HF-etched Si surfaces prior to deposition di splay an elemental content of 10% C, 4% O and 86% Si, as recorded by monochr omatic XPS. All XPS of the cl ean substrates and SPIAD films are recorded at 44 eV pass energy and normal take-off angle without air exposure following deposition, as previously described.8,99 SPIAD films are also depos ited onto a photopatterned silicon wafer on which a nanostructured oxide la yer has been formed (Mass Consortium Corp.) for desorption ionization with 337 nm nitrogen la ser radiation followed by mass spectral analysis in a reflection time-of-flight instrument (Voyager-DE PRO 6275, Applied Biosystems).6 Simulation Results Neutral Systems Figure 3-2 shows snapshots from the five de position events considered in the DFT-MD simulations of the neutral systems, where th e incident energy ranges from 100 to 500 eV. The molecular weight distribution of the chemical pr oducts that are generated after these deposition events are shown in Figure 3-3. As expected, the higher the deposition energy, the greater the damage to both the incident molecule and the 3T oligomer thin film. In the 100 eV deposition event, shown in Figure 3-2a), th e incident thiophene molecule breaks into two small fragments (C2H2 and C2H2S) during impact, which chemically modi fies only the impacted 3T oligomer.

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59 The resulting chemical produc ts (illustrated in Figure 33a)) are formed through bonding between these fragments and collision induced de composition of the impacted 3T oligomer to form a product such as C4H3S2.100 There are also two C2H2 fragments that form, one from the incident thiophene and the other from the impacted 3T oligomer. In the 200 eV deposition event, illustrated in Figure 3-2b), however, the incident molecule breaks into five small fragments (2CH, CH2, C, S) during impact, breaks apart a thiophene ring within the first layer of the 3T oligomer thin film and modifies the oligomer chains in the films second layer. Polymerization occurs between two 3T oligomers in the bottom layer through interactions with the collision fragment C3H3, which is generated from an incident thiophene fragment (CH) and an impact ed 3T oligomer fragment (C2H2). The 3T oligomer which adjacent to the impacted 3T oligomer also undergoes chemical modification, where one H atom is replaced by CS, where the C atom is from the in cident molecule and the S atom is knocked loose from the impacted thiophene ring. Other chemical products, such as [T][TC] and C2H2, are formed as a result of bonding between fragments from incident molecules and fragments from the collision induced decomposition of the 3T oligomer (see Figure 3-3b)). The first 250 eV event is somewhat simila r to the 200 eV deposition event in that the simulation predicts that the impacting thiophene molecule breaks into six small fragments of three CH, C, S and H on impact, and breaks the im pacted thiophene ring of the 3T oligomer (see Figure 3-2c)). The incident ener gy is high enough that the frag ments generated by the impact scatter and modify the oligomers beside and bene ath the oligomer at which the initial collision occurs. Consequently, polymerization is predic ted to occur through bonding between the oligomers beside and beneath the impact site through a (CH)S(CH) fragment, in which the CH are from the incident molecule and the S is fr om the impacted thiophene ring. The polymerized

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60 chemical product, [2T][TS][3T]C4H4S2, is also found to form bonds with the Si substrate. Other chemical products, [3T]C3H3 and [T]C5H3S, are formed by adding 3T oligomer fragments and incident molecule fragments. Overall, there ar e two intact 3T oligomers that remain unchanged following deposition. The majority of the chemi cal products produced are trapped between the top and bottom 3T oligomer layers. The molecu lar weight distribution of these products is summarized in Figure 3-3c). A second 250 eV deposition event is performed on the system modified by this first event that targets a different location on the surface, as shown in Figure 3-2d). This chemically modifies the targeted oligomer, which polymerized during the course of first deposition event, and the oligomer beneath it. T hus over the course of these two deposition events, every 3T oligomer on the surface is chemically modified and fragmentized. Some of the chemical products, such as [2T][TS][T]2C12H8S6 and C13H11S, evolve from the products formed in the first collision event, while others, such as C2H and H, are formed from the bonding of small incident molecule fragments and 3T oligom er fragments. Because of the la rge extent of modifications of the 3T oligomers in the film following th ese two deposition events, simple surface polymerization between two 3T oligomers is no longer present. Instead, large fragments bond to one another to create a new chemi cal product, such as [2T][TS][T]2C12H8S6, with a larger overall molecular weight. Again, most of the energe tic fragments that are produced are ultimately trapped between the top and bottom oligomer la yers. A detailed summary of the chemical products that are formed after the second de position event is given in Figure 3-3d). In the 500 eV deposition event, illustrated in Figure 3-2e), the incident thiophene molecule breaks into individual atoms or CH fragments wh en it collides with the surface. The impacted thiophene ring is also broken into individual atoms of 3C, 3H and S. These products and incident

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61 molecule fragments then collide with the bot tom layer of oligomers and break them apart because of their high kinetic energy. Additionally some of the fragments form chemical bonds with the Si substrate by the end of the simulation. In other words, a small collision cascade is predicted to occur and most of the energetic fr agments that are produced are trapped between the Si surface and the bottom layer of the 3T oligomer thin film or form covalent bonds to the Si substrate. The chemical products are much sma ller than the products produced at the lower incident energies, as shown in Figure 3-3e), a nd there are only two 3T oligomers that remain intact after the deposition process is complete. Table 3-1 provides a statistical analysis of the chemical products predicted from the simulations. As expected, the to tal number of chemical products varies substantially with deposition energy. In addition, the percentage of chemical products that are covalently bonded to the underlying Si substrate increases as the depositi on energy increases. The percentage of intact 3T oligomer thiophene rings also decreases as the deposition ener gy increases until 250 eV, after which this percentage remains essentially uncha nged. Furthermore, increasing the number of deposited thiophene molecules furt her decreases the percentage of intact 3T oligomer thiophene rings. Lastly, surface polymerizati on between 3T oligomers is pred icted to occur at incident energies of 200 and 250 eV. Charged Systems Table 3-1 also lists the results of statistical analysis of the chemical products that are produced in the charged systems. It indicates that the differences in the collision outcomes between the neutral events and positively charge d events are small in most cases. However, a careful comparison of the forces and velocity va riations of the atoms in the system (data not shown) indicate that the atoms in the +1 charged system experien ce slightly larger forces and velocity variations than the atoms in the neut ral system. The results further indicate that the

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62 system with the +1 charge makes the potential we ll between the atoms sligh tly deeper than in the case of the neutral system. In the case of the 100 eV deposition event, th e results and mechanisms for the neutral and charged systems are very similar. The deposited thiophene ion breaks into C3H3 and CHS fragments during the initial collis ion. The incident energy is onl y sufficient enough to modify the impacted 3T oligomer. Thus, ther e are two intact 3T oligomers that remain following deposition, and one 3T oligomer that is beneath the impacted 3T oligomer and has been slightly modified through the adsorption of a S atom from the impa cted thiophene ring. Ot her chemical products include a large fragment from the collision i nduced decomposition of a 3T oligomer, such as [2T]C2H, and a ring shape molecule (C6H6S) formed from bonding of the incident thiophene fragments (C4H4S) and a fragment of an impacted 3T oligomer (C2H2). A snapshot of the system following deposition is shown in Figure 3-4a) and the chemical products are summarized in Figure 3-5a). In the case of 200 eV deposition, illustrated in Figure 3-4b), the incident ion breaks into four fragments, 3CH and CHS, during impact. The 3T oligomer that had a H atom be replaced by a CS fragment in the neutral case now rema ins intact. Other chemical products, [3T]C3H2S, [3T]C3H4, are formed from bonding between the incident molecule fragments and 3T oligomers. Chemical products, such as [T][TC] and CS, are formed from bonding of 3T oligomer fragments and thiophene ion fragments (see Figure 3-5b)). There are two major differences between the neutral and charged cases. The first is that there is a chemical product, [3T]C3H2S, that forms a bond with the Si substrate in th e charged case. In the neutra l case, the same fragment, C2H, from the impacted thiophene ring that forms the [3T]C3H2S bond to the Si substrate is instead bonded to a H-terminated atom from the Si substrate to produce HCCH. The second is that there is no

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63 surface polymerization observed in the charged case but there is in the neutral case. Additionally, in the case of the charged system, the fragment that contributes to surf ace polymerization in the neutral system instead bonds to a hydrogen atom that is knocked out of the incident thiophene molecule. This prevents the fragment from form ing a bond to another 3T oligomer to polymerize the film. These differences i llustrate how scattered hydrogen atoms can restrain surface polymerization even when the deposition ener gy is high enough to trigger the process. In the case of the 250 eV deposition event (Fig ure 3-4c)), the incident thiophene ion breaks into six small fragments (three CH, C, S and H) on impact and breaks a thiophene ring on the targeted 3T oligomer. Although the ta rget site is different from the target site in the neutral case (the impacted thiophene ring tilt s around 30 towards to Si subs trate in this case, while the impacted thiophene ring tilts only about 10 towards to Si substrat e in the neutral case), the same polymerization mechanism is predicted to occu r in both cases. In particular, polymerization occurs through bonding of the oligomers next to and beneath the impacted oligomer by CS(CH) fragments, where C and CH are from the incident molecule or ion, and S is from impacted thiophene ring. This result indicates that the DF T-MD simulations are able to capture the key mechanisms that contribute to the comp licated surface polymerization phenomenon in ionassisted deposition. Othe r chemical products ([T]C5H3S and C3H3) are formed by adding 3T oligomer fragments and incident ion fragments, and the results ar e shown in Figure 3-5c). It is also predicted that some of th e products are covalently bonded to the underlying Si substrate and, overall, there are two intact 3T oligomers that remain un modified following deposition. Hybridization Analysis Examination of the change in the number of sp2-hybridized carbon atoms is another way to characterize the extent of system chemical m odification as a result of deposition. Prior to deposition all the carbon atoms in the 3T oligomers and incident thiophene molecule are

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64 sp2-hybridized. When the incident thiophene imp acts the 3T oligomer, th e hybridization of the carbon atoms change if they are involved in ch emical reactions. Transition state carbon atoms, with temporarily more than four neighbors, are also monitored. Similar transition state hydrogen and sulfur atoms are also observe d in the simulations. The percen tages of transition state carbon atoms that are generated immediately following th e thiophene molecule collision range from 4% in the cases of 100 eV/molecule collisions to 17 % in the case of the 500 eV/molecule collision. Following the initial collision, th e transition state atoms move aw ay from the impact side and modify the 3T oligomers, simultaneously transfor ming to more stable hybridization states. Most of the transition-state atoms finish reacting within 30 fs of each collision. In addition, a small number (< 4%) of new transition state atoms is ge nerated during the equilibr ation process as part of additional atomic rearrangements. Importantly, all the transition state atoms have completely reacted by the end of the equilibr ation process that follows deposit ion and are ultimately part of the chemical products discussed above. Table 3-2 provides details of the hybridization states and transition states of carbon atoms in the simulations. The number of transition st ate atoms is summed from each MD step. The hybridization states are obtained from the final equilibration. It is found that the sum of the transition state atoms increases as the deposition energy increase but decreases at the highest 500 eV incident energy. This is because in the 500 eV deposition event the incident energy is high enough for the fragments to scatter over a large fract ion of the supercell and to penetrate into the Si substarte. Thus the incident energy dissipates more efficien tly, which restrains the transition state atoms from regenerating duri ng equilibration. In the case of the 200 and 250 eV deposition events, the fragments are generally trapped be tween the upper layer 3T oligomers and bottom layer 3T oligomers. Thus, although the transition state atoms are fewer than in the 500 eV

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65 deposition event immediately following impact, more transition state atoms on the whole are formed at 200 and 250 eV. The number of transition state carbon atoms is s lightly smaller in the neutral case than in the charge d case for 100 and 200 eV, while th e opposite is true for 250 eV. In general, after deposition the amount of sp2-hybridization decreases as the deposition energy increases, which indicate s the greater degree of modifica tion of the 3T oligomers at higher energies. Comparing the neutral and charge d system results, Table 3-2 indicates that the charged systems have less sp-hybridization than the neutral systems. In other words, carbon atoms in charged systems generally have more neighboring atoms than neutral systems after equilibration is complete. The result is consistent with the finding that the potential well between the atoms in the charged-system is slightly deep er than in the neutral system. Thus, carbon atoms more readily attract a nd bond to neighboring atoms in charged systems, which results to higher degrees of hybridization. Experimental Results In conjunction with these simulations, experi mental SPIAD is performed by combining the deposition of thiophene ions with the simultane ous dosing of 3T vapor. The vacuum apparatus and conditions used to perform SPIAD and XPS anal ysis are similar to t hose used in previous studies.8,99 The incident ion energy and the ion/neutra l ratio are correlated parameters for efficient ion-induced surface polymerization. Ther efore, experiments are performed in which the ion energy is varied from 25 to 200 eV and the i on/neutral ratio is varied from 1/50 1/900. The extent of polymerization is determined from XP S by measuring the S/Si ratio, which increases as an organic film is formed on the Si substrate from the thiophenic species. By varying the ion/neutral ratio at a constant ion energy of 200 eV, it is determined that polymerization occurs in a well-defined region of ion energy and ion/neut ral ratio space. Figure 3-6 compares the S/Si ratio from XPS for direct ion deposition at various fluences (empty bars,

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66 no 3T dosing) with SPIAD at similar ion fluences (~1015 ions/cm2) at various ion/neutral ratios (solid bars). Figure 3-6a) shows that polymerization occurs at 200 eV for ion/neutral ratios of 1/150, 1/450 and 1/900 but not for 1/50. For 200 eV deposition, an ion/neut ral ratio of 1/150 is optimal, as it shows the largest (~10 ) increase in S/Si ratio compar ed to direct ion deposition at similar ion fluence. By contrast, the 1/50 ratio shows a decrease in S/Si ratio compared to direct ion deposition (Figure 3-6a)).8,99 Varying both the ion energy and th e ion/neutral ratio indicates th at lower ion/neutral ratios are optimal for polymerization at lower ion ener gies. Figure 3-6 illustra tes that the optimal ion/neutral ratios are 1/100 for ion energies of 100 eV, 1/75 for 50 eV, and 1/50 for 25 eV. This is likely due to the reduc ed desorption and sputtering of 3T oligomers at lower ion energies, which requires less 3T deposition101. All SPIAD films are stable in vacuum for over four hours, a period during which pure 3T films are observed to completely sublime. The C/S ratio is around four for all SPIAD and direct ion deposited films, which is consis tent with thi ophene containing species. The mass spectra (MS) of the SPIAD films ar e shown in Figure 3-7, and are obtained by laser desorption from films directly deposited on to nanoporous silicon oxid e substrates. Previous work used isotopic distributions to assign the observed mass spectra.6 The ion/neutral ratio used for MS experiments of each ion energy shown is the optimal value determined by XPS, as discussed above. Many smaller polym erization products, such as [3T]2 +, are observed by MS for all ion energies from 25 to 200 eV. However, the 50 eV SPIAD film displays the highest molecular weight species, with peaks as large as [3T]4 + (see the inset in Figure 3-7c)). Formation of the polymerization products [3T]x + (x=2-4) are indirectly indu ced by hyperthermal ion impact. Additionally, a unique series of adduct species displaying loss or pickup of a single sulfur atom

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67 are observed. Sulfur atom loss species include [3T]x-S+ (x=1-4) while sulfur atom pickup species include [3T]S+. By contrast, deposition of only 3T neutra ls on the DIOS substrate leads to the appearance of only 3T+10. Previous results show that most of the ions observed from SPIAD films display a mixture of protonated and radi cal cations, indicating the presence of free hydrogen in the films.5 The mass spectra across 25-200 eV display ma ny similar peaks, but there are other differences besides those noted above for 50 eV films. 100 and 200 eV SPIAD film mass spectra are very similar and di splay peaks up to [3T]2 +, [3T]T+, and other adduct-3T species. Higher mass peaks are occasionally observed in these spectra, including [3T]2CH2 +, [3T]2TC3H3 + and [3T]2T2CHS+ (data not shown). The 25 eV SPIAD fi lm shows the formation of a strong [3T]2CH+ signal and only weak [3T]2 + signal, in addition to the 3T signal. To further investigate the mechanism of polymerization, SPIAD is performed with deuterated thiophene ions combin ed with the evaporated 3T ne utrals and compared with SPIAD by hydrogenated thiophene ions at otherwise sim ilar conditions. Figure 3-8 shows mass spectra of the SPIAD films at 50 eV with hydrogenated (a) and c)) and deuterated (b) and d)) thiophene ions in the mass ranges of 3T and 5T peaks. De uterated thiophene ion deposition does not shift the 5T peak at m/z 411 towards higher masses, indicating that only thiophene fragments are introduced into the film. Table 3-3 shows relative intensities of the M+1 peaks from the mass spectra prepared from 50 eV hydrogenated and deuterated thiophene ions, normalized to the parent ion peak intensity of 3T and 5T. Large di fferences can be seen in the intensity of the (M+1) peaks of D[5T]+ vs H[5T]+ and similar intensity increases are observed for some higher peaks such as 7T (data not shown). D[5T]+ and H[5T]+ show similar values for (M+2) peaks. The largest deuterated thiophene i on that could have in corporated into th e film would be C4D1-2S+,

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68 but this could lead to formation of (M+1) a nd (M+2) peaks for 5T only if an additional, non-deuterated thiophene monomer is made availa ble by fragmentation of 3T. However, a more likely interpretation of the deuterated ion resu lts is that only small deuterated thiophene fragments incorporated into the films. Discussion Mechanisms Supported by Experimental Data and Simulations Several processes occur during deposition that are both detect ed in the experiments and predicted by the simulations shed light on the most important bond dissociation and polymerization mechanisms that occur duri ng SPIAD. For example, both simulations and experiments indicate that incide nt thiophene ions break apart on collision with th e 3T film. In particular, C3H3 + is seen experimentally at 200 eV and has previously been observed to result from the dissociative scattering of thiophene ions from surfaces, in a process referred to as surface induced dissociation.97 Both experiments and simulations indicate that incident thio phene ions undergo dissociation during deposition. Comparing SPIAD deposition of deuterated vs. hydrogenated thiophene ions, the mass spectra do not show any sh ift (Figure 3-8) expected if there had been incorporation of an intact, deut erated thiophene unit. This is in agreement with the simulation results that predict that intact thiophene ions do not survive the collis ions with the surface. Adducts such as [3T]T+ at 25 eV and [3T]2T+ at 50 eV that are seen experimentally might be the result of dissociation of 3T ne utrals upon ion impact. Previous results with non-mass selected ion deposition show that most of the ions obser ved from SPIAD films display a mixture of protonated and radical cations, indicating the presence of free hydrogen in the films5. Comparing Ar+ and T+ SPIAD films prepared with non-mass selected Ar+ and T+ ions and 3T neutrals it was

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69 shown that most of the extra hydrogen originates from inci dent thiophene ions since Ar+ SPIAD films did not show a high intensity M+1 peak. Both the experiments and simulations indicate that incident thiophe ne ions chemically modify the structure of the oligomer film by c ovalently bonding to 3T oligomers. This covalent bonding occurs primarily via incident thiophene fragments and small 3T fragments to form adducts such as [3T]C3H4 +, [3T]C2H2 +, [3T]2TS+, and [3T]2CH+ observed in the experiments and [3T]CS, [3T]CxHy (x=3, y=3,4), [3T]2CxHySz (x=4, y=5,2, z=1,2) in the simulations. The combination of experiments and simulations provide important information regarding the surface polymerization of 3T oligomers. Thiophene ion fragments are thought to act as polymerization initiators. In the simulations, C atoms that come from the incident molecules or broken 3T rings have high kinetic energy and r eadily abstract hydrogen atoms from other 3T molecules or directly add on to other 3T molecules. Once this process occurs on two adjacent 3T molecules, it is highly likely that these molecules will bond to each other. Hyperthermal protons also can trigger the formation of polymerization initiators in a process that is similar to the behavior of hyperthermal organic cations, where the kinematic nature of proton collisio ns with simple organic molecules co ndensed on the substrate is exploited to preferentially break C-H bonds.102 The simulations also show that hydrogen atoms may, however, act as restraining agents to prevent surface polymerizati on. Since polymerization relies on the bonding of chemical produ cts through carbon atoms, sca ttered low energy hydrogen atom may react with terminating carbon atoms and decr ease the probability of cross-link formation between fragments. Importantly, the S atom transfer observed experimentally is also predicted to occur in the simulations.

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70 The experiments and simulations further indicate that fragmentation of the 3T oligomers is an important mechanism in SPI AD. Products such as [2T]C4H3S2 in the 100 eV neutral system deposition event, [2T]C2H, in the 100 eV charged system deposition event, [T][TC] in the 200 eV neutral and charged system deposition events, [T]C5H3S in the first deposition event of the 250 eV neutral and charged systems, [T]C5H2S2 in the 500 eV deposition event, and [2T][TS][T]2C12H8S6 in the 250 eV second deposition even t involve dissociation of a 3T oligomer through direct impact are predicted to occur in the simulations. Similar products, such as [T]2C3H3 +, [3T]TC3H3 +, are also observed experimentally by MS at 25 and 50 eV. Analogous products seen at 100 and 200 eV correspond to [3T]2T2CxHy +. In addition, products such as 3T-S+ and T2C3H3 + are observed experimentally at 50 eV and the formation of similar (albeit not identical) species is pred icted by the simulations. That simila r classes of products form in the simulations and are observed in the experiments highlights the usefulness of this combined computational and experimental approach to stud ying SPIAD, despite the i nherent differences in the systems under consideration. The simulations also predict that the amount of small fragments (molecular weight < 50 g/mole) increases in the 250 eV second deposit ion event and in the 500 eV deposition event. Examples of these products are S, Hx, where x<2, and CxHy, where x <2 and y<2. Some of these products form bonds with the Si substrate and some of them embed into the thiophene thin film. These predictions are supported by experimental data that indicat es a drop in polymerization efficiency for higher ion/neutral ra tios. It should be pointed out that the experiments require high neutral fluxes since 3T does not permanently st ick to surfaces under vacuum due to very low binding energy (see below).

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71 The simulations performed here predict that the incident thiophene molecules damage the structure of the 3T oligomers locally and the incident molecules also break apart on collision with the surface. They further i ndicate that the C atoms which come from the incident molecules or broken 3T oligomers have high kinetic energy. Thus they are energetic and readily abstract hydrogen atoms from other 3T molecules or adduct on other 3T molecules directly. This is a polymerization initiation process. Once this process occurs on two adjacent 3T oligomers, it is highly likely that these molecule s will bond to each other. The simu lations therefore predict that in an ideal case where one incident thiophene mo lecule is in contact w ith two 3T molecules on its two sides, the most efficient energy for su rface polymerization should be slightly higher than the C-H bond energy in the thiophene ring. In the experiments it is difficult to ensure this ideal case. Thus, the incident molecules should gene rally have enough energy to produce energetic atoms and/or polyatomic fragments that will subsequently react with 3T molecules and initiate the polymerization process. This energy should co rrespond to the energy requi red to dissociate a thiophene ring plus the energy that will be di ssipated through the film and surface through the collision process. Similarly, balance is required for the ion/neutral ratio to generate the proper polymerization between 3T oligomers. Too ma ny hyperthermal ions (t wo vs. one) cause a decrease in polymerization effici ency, more fragmentation, deso rption and sputtering. Increasing the energy/molecule results in more damage to a nd sputtering of the 3T oligomers, but it also produces more polymerization initiators. Thus, th e amount of energy in the system should be a balance between damaging or sputtering 3T thiophene oligomers and forming new polymerization initiators.

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72 Differences between Simulations and Experiments There are several fundamental differences be tween the experiments and simulations that must be taken into account, despite the large ar ea of agreement between the two. The efficiency of energy transfer during depositi on is different in the simulation and experimental systems. This can be attributed to several factors. There is a difference in effective surface coverage between the experimental and computati onal systems: the experimental systems consist of thicker 3T films than are considered in the simulations. Th e 3T multilayer present experimental is expected to recoil more than a 3T b ilayer upon thiophene ion impact as suggested by previous experiments studying the scattering of thi ophene ions off of disparate surfaces.103 Different surface coverage configurations influence the diss ipation of incident energy since the softer organic layer recoils more upon hyperthermal ion im pact than a stiff semiconductor substrate. Another significant difference can be attribut ed to the deposition sites chosen for the simulation are direct impact sites that need higher incident energies to damage the 3T oligomers. By contrast, the experimental imp act sites vary from direct to gr azing (i.e., integrated over all possible impact parameters). Thus, the incident ions might experimentally just graze the 3T oligomers and generate only minor damage, whic h could generate fragments with terminated carbon atoms or transition state atoms to initiate the surface polymerization process. The incident energy to fulfill this surface polymerization process is much less than the direct impact. Related to the above differences is that of collis ion number. The experimental data result from of multiple ion-surface col lision events combined continua l redosing of the surface with 3T. The simulations involve either one or two collisions per simulation. The system size is also confin ed in the simulation compared with the experiment. Thus the incident energy can only be dissipated within the supercell. This makes that the higher incident energy simulations show greater modificati on of 3T oligomers th an the corresponding

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73 experiments. Consequently, direct comparison of incident energies between the simulations and experiment might not be strictly correct. Howeve r, the trends predicted in the simulations and observed in the experiments are comparable to one another. The substrates are also not identical in the computational and experimental systems. The simulations use clean, flat, hydr ogen-terminated silicon substrat es while the XPS experiments use flat silicon surfaces and the mass spectra us e nanostructured silicon oxide covered substrate. However, these substrate differences are less re levant here for several reasons. The phenomena of greatest interest occur between 3T oligomer s and incident ions and are therefore largely independent of the nature of the substrate. The ch emical reactions predicted in the simulations to occur between the surface and the 3T oligomers or the incident i ons cannot be directly observed experimentally by the methods util ized here, as discussed above. Yet another significant difference between the experimental and computational systems is their timescales. Specifically, the simulations c onsider phenomena and relaxation events that occur on the order of several picoseconds, while the experiments consider phenomena that occur over hours. Thus, the reactive specie s formed in simulation (i.e., C or H atoms) may take longer than simulation timescale to form the polymer ization products observed experimentally. In addition, the experiments allow rearra ngement and reorganization over time. Lastly, the experimental conditi ons are sufficient to stimulat e electronic excitation process that could influence the chemical reactions that occur. In contrast, the DFT-MD simulations do not allow electronic exc itations to occur. Despite all of these differences, the simulations are able to provide important insight into the chemical reactions that occu r during deposition. The most si gnificant of which these appear to occur on the same time scale as the simulations.

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74 Conclusions The combination of the two strategies vastly improves the mechanis tic understanding of the use of SPIAD for the growth of conducting pol ymer thin films, de spite the significant differences between the experiments and simula tion. Variation of the experimental reaction conditions indicates that polymerization occurs preferentially under a na rrow set of ion energy and ion/neutral ratio conditions. Th e first principles MD simulations reported here illustrate the manner in which ion energies aff ect polymerization and other chemi cal reactions that modify the substrate. Specifically, ideal incident energies sh ould be balanced between values that are too high and lead to damage or sputtering of the -terthiophene on the substrate, and values that are too low to produce the necessary polymerization initiato rs. Importantly, this study indicates that polymerization and fragmentation of ions and/or neutral species are critical steps in the SPIAD process. In addition, the simulations predict that free protons and ot her radicals are formed during SPIAD that could potenti ally survive for long enough timescales to contribute in a significant manner to the propertie s of the conducting polymer. Th is insight can be used to optimize the SPIAD process for polythiophene and other conduc ting polymer systems. More generally, studies such as this indicate that it sh ould be possible to use computational studies to guide experiments towards the production of opt imized films for part icular applications.

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75 Table 3-1. Statistical analysis of deposition re sults predicted by the simulations. Intact means that the C and S atoms in the thiophene ring maintain the same hybridization as initial. Incident energy 100 eV 200 eV 250 eV 500 eV Deposition event 1(neutral) (site #1) 1(charged) (site #1) 1(neutral) (site #2) 1(charged) (site #2) 1(neutral) (site #1) 1(charged) (site #2) 2(neutral) (site #2) 1(neutral) (site #2)Total # of products 654534414 % Products bonded to Si substrate 0002533335057 % Intact 3T rings 7567504250581750 # Surface polymerization reactions 00101110 Table 3-2. Chemical state of the surface carbon atoms following each deposition event. Incident energy 100 eV 200 eV 250 eV 500 eV Deposition event 1(neutral) (site #1) 1(charged) (site #1) 1(neutral) (site #2) 1(charged) (site #2) 1(neutral) (site #1) 1(charged) (site #2) 2(neutral) (site #2) 1(neutral) (site #2)Sum of transition state atoms 345211712717416418299 sp hybridization 7.69%3.85%7.69%1.92%5.77%3.85%12.50%19.23% sp2 hybridization 90.38%94.23%82.69%88.46%90.38%84.62%69.64%75.00% sp3 hybridization 1.92%1.92%9.62%7.69%3.85%11.54%16.07%5.77% Terminal C atom 0.00%0.00%0.00%1.92%0.00%0.00%1.77%0.00% Table 3-3. Relative intensities of the M+1 and M+2 peaks from the mass spectra prepared from 50 eV hydrogenated (HT+) and deuterated (DT+) thiophene ions, normalized to 3T and 5T peak intensity (M). m/z of M Ion structure M+1 M+2 Exp Calculated Exp Calculated 248 [3T]+ only (no SPIAD) 20% 16% 18% 16% H[3T]+ from SPIAD 21% 17% D[3T]+ from SPIAD 59% 30% 411 H[5T]+ from SPIAD 38% 28% 29% 28% D[5T]+ from SPIAD 71% 33%

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76 Figure 3-1. a) The equilibrium simulation model before deposition. Two layers of 3T oligomers sit on the hydrogen-terminated Si (111) substrate surface. b) The top view of equilibrium simulation model. Two thiophe ne molecules marked in black represent the two deposition sites in the simulations. a) b)

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77 Figure 3-2. Snapshots from the DFT-MD simulati ons of the neutral system which simulate the deposition of a thiophene molecule on a te rthiophene oligomer thin film and Si substrate. a) The final snap shot of deposition in the 100 eV deposition event (time = 240 fs). b) The final snapshot of depos ition in the 200 eV deposition event (time = 240) fs. c) The final snapshot of the firs t deposition in the 250 eV deposition event (time = 240) fs. d) The final snapshot of the second deposition in the 250 eV deposition event (time = 480) fs. E) The fi nal snapshot of deposition in the 500 eV deposition event (time = 240) fs. C atom in 3T oligomer S atom in 3T oligomer H atom in 3T oligomer C atom in incident thiophene S atom in incident thiophene H atom in incident thiophene H-terminate atom on Si substrate Si atom a) b) c) d) e)

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78 0100200300400500600700800 0 2 4 0100200300400500600700800 0 2 4 0100200300400500600700800 0 2 4 0100200300400500600700800 0 2 4 0100200300400500600700800 0 2 4 Number of Chemical ProductsMolecular Weight (g/mol) 100 eV [2T]C4H3S2C2H2C2H2200 eV[3T]CS[T][TC] [3T]2C4H5S [T]C5H3S 1st event in 250 eV [3T]C3H3[2T][TS][3T]C4H4S2 (Si) 2nd event in 250 eV H C2H [T]C5H3S C13H11S(Si)[2T][TS][T]2C12H8S6 (Si) [T]C5H2S2 500 eV [3T] [3T] C6H5S(Si)C5HS Figure 3-3. The molecular weight distribution of chemical products that are generated after the neutral deposition events. Chemical products that form bonds with the Si substrate are marked with a (Si) super script. [TC] and [T S] indicates that there is a C and S atom, respectively, being includ ed in a thiophene ring. a) b) c) d) e)

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79 Figure 3-4. Snapshots from the DFT-MD simulati ons of the +1 charged system which simulate the deposition of a thiophene molecule on a thiophene thin film and Si substrate. a) The final snapshot of deposition in the 100 eV deposition event (time = 240 fs). b) The final snapshot of deposition in the 200 eV deposition event (time = 240) fs. c) The final snapshot of the deposition in the 250 eV deposition event (time =240) fs.. C atom in 3T oligomer S atom in 3T oligomer H atom in 3T oligomer C atom in incident thiophene S atom in incident thiophene H atom in incident thiophene H-terminate atom on Si substrate Si atom a) b) c)

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80 0100200300400500600700800 0 1 2 3 0100200300400500600700800 0 1 2 3 0100200300400500600700800 0 1 2 3 Number of Chemical ProductsMolecular Weight (g/mol) 100 eV [3T] [3T]S [2T]C2H C6H6S 200 eV [3T] [3T]C3H4[3T]C3H2S(Si)[T][TC] CS 250 eV [3T] [3T]2C4H2S2 (Si)[T]C5H3S C3H3H Figure 3-5. The molecular weight distribution of chemical products that are generated after the positively charged deposition events. Chemical products that form bonds with the Si substrate are marked with a (Si) super script [TC] and [TS] indicates that there is a C and S atom, respectively, being included in a thiophene ring. a) b) c)

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81 Figure 3-6. S/Si elemental rati o from XPS for direct ion deposi tion at various fluences (empty bars) compared with S/Si ratios for SPIAD at similar ion fluences (~1015 ions/cm2) for various ion/neutral ratios (solid bars). Data recorded at the four ion energies shown.

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82 Figure 3-7. Mass spectra (MS) of the SPIAD fi lms at four ion energies and the optimal ion/neutral ratios (from Fi gure 3-6), obtained by lase r desorption of conducting polymer films that have been deposited directly onto nanoporous silicon oxide substrates.

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83 Figure 3-8. Mass spectra of HT+ and DT+ SPIAD films grown on nanostructured silicon oxide (DIOS) substrate at 50 eV ion energy.

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84 CHAPTER 4 STUDY OF METHANOL MOLECULE ADSORPTION ON COPPER CLUSTER Introduction In this work, the properties of copper clusters (Cun, n=2-9) are determined from density functional theory (DFT) calcu lations. Different approximati on methods for exchange and correlation, and both spin-polari zed/non-spin-polarized wave func tions, are used. The results are then compared with experimental data to verify the validity of the methods. Methanol molecules are then deposited on the copper clusters in DF T molecule dynamics simulations (DFT-MD) and the final equilibrium adsorption structures are analyzed. The results provide insight into how methanol molecules adsorb on copper clusters. Computational Details The calculations and simulations are car ried out using the CASTEP software.68,104 The DFT calculations and DFT-MD simulations make us e of (i) a plane-wave basis to represent the wavefunctions, (ii) pseudopotentials105 that replace the ionic co res, and (iii) the use of fast-Fourier transforms (FFTs). The exchange-c orrelation energy is described by the LDA or the GGA106. Ionic cores are described by ultrasoft pseudopotentials,105 and the valence electrons are described with plane waves that ha ve a kinetic energy cutoff of 270 eV. The calculations include two parts. The firs t part involves the optimization of the Cun clusters, where n=2-9. In these optimization calcula tions, both non-spin -polarized and spin-polarized wave functions are used to compare the effect of spin-polarization on the results. The size of the supercell used in this calculation is 10 The second part involves modeling the collisions of the methanol molecule s with the clusters. Specifically, the methanol molecules have external kinetic energies of 0.5 eV/molecule and are incident on the Cu clusters in each collision. In the case of the collisions, the supercell is increased to 15 in the direction of

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85 molecular motion towards the Cu cluster. The initial distance between a copper cluster and a methanol molecule is around 3-4 The NVT ensemble107-110 is used to maintain the system temperature at 300 K and the time step in the DFT-MD simulations is one femto-second. Each trajectory runs for between 1 and 6 ps, with th e end of the simulation depending on the outcome of the molecule-cluster collision. The potential energy drops when the outcome is adsorption of the methanol to the copper. The total energy c onvergence is tested w ith respect to system supercells as large as 20 k-point meshes up to 3 3, and kinetic energy cutoff up to 320 eV. The results indicate that the differences in Cu cluster absolute total en ergy are about 0.2 eV/atom with the conditions th at are used in this study relativ e to the most computationally expensive conditions, while the differences in copper cluster binding en ergies are about 0.01 eV/atom. Results and Discussion Structure of Neutral Copper Clusters The ground state structure of neutral copper clusters has been investigated by Jaque et al.,32 and Jug et al.33 and the ground-state structures of the clusters examined in this study are constructed based on these published findings. The st ructures of these neut ral copper clusters are then optimized within the DFT calculations using either the LDA or the GGA. The final geometries obtained by optimization with the G GA and non-polarized wave functions are shown in Figure 4-1. As the cluster size increases, the structure of the cluster changes from a linear configuration that is one-dimensional (Cu2), to planar structures that are two-dimensional (Cu3-Cu6), and finally to fully thre e-dimensional structures (Cu7-Cu9). In addition, Table 4-1 provides detailed bond lengths optimized by the LDA and compares the details of the optimized structures to published results. Ex amination of the data indicate s that the average bond lengths predicted in these calculations are around 5% sm aller than those obtained using the LDA method

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86 with Gaussian type basis sets,33 and around 9% smaller than t hose obtained using the B3LPY method with Gaussian type basis sets.32 Figure 4-2 illustrates the aver age bond length versus copper cl uster size as optimized using either the LDA or GGA with and without the in clusion of spin polarization, and Table 4-2 provides the relevant st ructural details. The results show that the average Cu-Cu bond length increases when the cluster size increases and its dimensionality changes. For example Cu2 has the shortest bond length and is a one -dimensional (linear) structure. Cu3 through Cu6 have intermediate bond lengths and are two-dimensional (p lanar) structures. At cluster sizes of seven and greater, three-dimensional clusters are preferred that ha ve the largest Cu-Cu bond lengths. This evolution of the cluster stru cture occurs as a result of the influence of the hybridization of 3d-orbitals, 4s-orbitals and 4p-orbitals.111 In particular, the hy bridization of the 3d-orbitals and 4p-orbitals produces the three-dimensional cluster structures.112 Because these interactions occur over relatively long distances, they result in larger aver age bond lengths in th e clusters. Table 4-2 also shows the coordination number (CN) of the copper atoms in the various clusters. The CN increases as the cluster size increases in a manne r that is illustrative of the changes in the dimensionality of the cluster. One-dimensional clusters have a CN of one, two-dimensional clusters have a CN between two and three, and th ree-dimensional clusters have a CN larger than 4.3. Comparing the results obtained with diffe rent exchange-correlation approximation methods, we find that the LDA predicts smaller copper clusters than the GGA. This is not surprising as it is generally accepted that the GGA predicts longer bond lengths than the LDA.113 Figure 4-2 also indicates that pl ane-wave type basis sets pred ict smaller cluster sizes than Gaussian type basis sets. However, the averag e bond length difference between plane-wave-type

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87 basis sets with the LDA and Gaussian type basis sets with the same approximation33 differ by no more than 3.5%. This proves that using the LDA and plane-wave basis sets is adequate for the study of the copper clusters. Addition ally, Figure 4-2 indicates that the effect of spin-polarization is negligible for the optimization of the structure of th e copper clusters. Figure 4-3 shows the binding energy as a func tion of the cluster size. Here, the binding energy is calculated as n E nE BEnCu Cu/ ) ( (4-1) where n is the number of atoms in the cluster, CuE is the energy of a Cu atom in vacuum, and nCuE is the energy of the Cu cluster containing n copper atoms. The errors associated with self-interaction energies in DFT are large in case s of high localization of electron density, such as occur here in the case of the Cu clusters. Th ese errors are minimized here by the fact that comparable levels of electron localization are presen t in both the initial and final adiabatic states. A similar approach has been successfully used in several comparable studies, such as the catalytic CO oxidati on on Au clusters,114 the interaction of thiolates with Au and Cu clusters,115 and the interaction of S atoms with Au clusters.41 Figure 4-3 illustrates how the binding energy increases monotonically with incr easing cluster size. This indicat es that it is energetically favorable for the copper atoms to form ever larger clusters. Figure 4-3 also provides a comparison of the binding energy calc ulated in this and other studies.32,33,45,116 The larger binding energy (around 38% larger than literature values32) that is predicted here is due to the use of the ultrasoft pseudopotential. Calculations that used the cutoff energy of 600 eV with norm-conserving pseudoupotentials, which is indicated in CASTEP as being the same level of accuracy as using ultrasoft pse udopotentials with a cut-off energy of 270 eV, were tested and the resulting bind energies were si milar to published literature values32 to within 3%. However, the

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88 norm-conserving pseudopotentials ar e about five times more computationally expensive than the ultrasoft pseudopotential in the case of Cu4, and even more expensive for larger clusters. This finding, coupled with the fact th at the ultrasoft pseudopotential gives consistently comparable relative binding energies makes it suitable for use here. If the binding energy per atom is divided by 2CN, then the binding energy per Cu-Cu bond can be obtained. This result is plotted in Figure 4-4, where the dimensionality change of clusters as their size increases is clearly i ndicated. Specifically, the binding energy per Cu-Cu bond decreases as the dimension of the cl usters increases. For the case of Cu2 one-dimensional cluster, the binding energy per Cu-Cu bond is predicted to be 2.73 eV by the GGA approximation. However, it is only around 1.45 eV for the two-dimensional clusters and approximately 1.00 eV for the three-dimensional clusters. Figure 4-4 reveals the effect of spin polarization on the result s. When spin-polarized wave functions are used in the DFT calculations, they predict lower Cu-Cu bond binding energies than do the non-spin polarized wave functions. In Figure 4-3, it is clear that using the GGA with spin polarized wave functions predicts bond energy re sults that are in the best agreement with published experimental data.45,116 It should be mentioned that the experimental data to which the findings are compared is the dissociation energy of anionic and cationic copper clusters rather than the neutral clusters under consideration here. The average bond order versus cluster size is illustrated in Figure 4-5. The average bond order is calculated by averaging the Mulliken overlap population115,117 of the Cu-Cu bonds in the cluster. The bond order value for the Cu2 cluster is around 0.80, but this drops to around 0.35 for the two-dimensional co pper clusters (Cu3-Cu6) and to around 0.25 for the three-dimensional copper clusters (Cu7-Cu9). The bond order is also indicative of the strength of the bonds within

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89 the Cu clusters. Thus the aver age bond order should be dir ectly proportional to the binding energy per Cu-Cu bond. Comparing Fi gure 4-4 and 4-5, it can be s een that they show similar trends and the ratio between the average bond order and the binding energy per Cu-Cu bond is around 0.5. Figure 4-6 indicates the relativ e stability of the different copper clusters. The relative stability is calculated as, n n n nCu Cu Cu CuE E E E21 12 (4-2) where n is the number of atoms in the cluster. A high value of relative stability means that the cluster is more stable. Figure 4-6 shows that the stability oscillates as a function of cluster size. In particular, the clusters compos ed of an even number of atoms have higher relative stabilities than those composed of an odd number of atoms. This is because the Cu atom has an electronic configuration of 3d104s1. When an even number of atoms form a cluster, all the electron orbitals can be fully occupied and form a closed-shell conf iguration, which stabilizes the cluster relative to the odd-numbered clusters. This finding is in agreement with the predictions of the electronic shell jellium model that says that filled-shell clusters with 2, 8, 18, 20, 40, 58, 92, etc. valence electrons have increased stability relative to partially filled she ll clusters. The numbers of atoms that lead to these valence electron va lues are the so-called magic numbers. The relative stabilities obtain ed using different approximati on methods are also compared in Figure 4-6. Typically, spin polarized wave functions and non-spin polarized wavefunctions predict very similar oscillator y behavior; however, the LDA doe s not predict the oscillatory behavior well when the cluster struct ure changes from two-dimensional (Cu6) to three-dimensional (Cu7). Compared to literature results32,33, the GGA is again found to give the most reliable results.

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90 The atomic populations of the copper clusters calculated usin g the GGA are given in Table 4-3. As mentioned before, the electroni c configuration of a Cu atom is [Ar]3d104s1. When Cu atoms form the cluster, the 3d orbital and 4s orbital of each Cu atom became partially occupied. The lost electrons from the 3d and 4s orbitals then occupy the 4p orbital. Thus the interactions between the Cu atoms to form the cluster involve not only 3d and 4s orbitals but also 4p orbitals. Table 4-3 also lists the atomic charge on ever y atom in the cluster. The atomic charge changes on the order of 10-2 but the overall charge on the cluster is zero. It is interesting that the atoms located at the outer cluster sites are more ne gative, while those at the inner cluster sites are more positive. This indicates that the outer atoms, those farthest from the geometric center of the cluster, have higher electron densities than the inner atoms. The outer atoms also have lower CNs than the inner atoms. For example, in the Cu3 clusters shown in Fi gure 4-1, atoms 1 and 2 are separated by a longer distance than atoms 1 and 3 or atoms 2 and 3. Thus, atoms 1 and 2 are located at the outer sites of the Cu3 cluster and are consequently negatively charged, while atom 3 is located at the innermost site and is conseq uently positively charged. Another example is Cu9, where atoms 2, 6 and 7 are closest to the geometri c center of the cluster, at distances of 3.04 0.19 and 3.08 respectively. In contrast, atoms 1, 3, 4, 5, 8 and 9 are farthest away, at around 4-6 from the geometric center of the cluster. This phenomenon illustrates how the electron clouds in small transition metal cl usters are not like those in bu lk metals, which distribute the electron density uniformly. Table 4-3 also indicates that among all the c opper clusters considered in this study, the negatively charged atoms have larger 4s orbital populations than the positively charged atoms. In the one-dimensional cluster (Cu2), the two atoms balance each ot her and are both neutral. In the two-dimensional clusters (Cu3-Cu6), the outer atoms have higher 4s orbital populations and have

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91 lower 4p orbital populations than the inner site atoms. In the three-dimensional clusters (Cu7-Cu9), the outer site atoms have still higher 4s orbital populations than the inner site atoms, but they have almost the same level of 4p orbital population as the inner site atoms. These differences in orbital population are likely responsible for the ch ange in cluster dimensionality that is illustrated in the average bond lengths (Figure 4-1 and Table 4-1), binding energy per Cu-Cu bond (Figure 4-4), a nd bond order (Figure 4-5). Collision of Methanol Molecules with Copper Clusters Figure 4-7 illustrates the initial and final sn apshots from the DFT-MD simulations of the collisions of methanol molecules on the low-c oordination number sites of the various copper clusters. In all the col lisions, the oxygen atom on the methanol molecule adsorbs on the copper clusters, which subsequently distort. The simula tions indicate that adsorption occurs when the molecule and cluster are close enough to one an other, and that their configuration changes immediately following adsorption. The equilibr ium structure is determined after their configuration stops changing and a stable bond has been formed. The Cu4 cluster deforms the most following adsorption of the methanol mol ecule at the low CN site. In particular, the diamond-shaped structure of the Cu4 is broken and it transforms to a triangular structure with an extra Cu atom attached to one corner. Figure 4-8 illustrates the initia l and final snapshots of the collision of methanol molecules with the high-coordination number sites of the copper clusters. In this case, the methanol molecules initially came close to the Cu cluste r and then bounce back. The processes repeats several times until the cluster and molecule reach an equilibrium configuration and distance from one another. The equilibrium structure is once again de termined after their configuration stops changing and a stable bond has b een formed. Again, all the methanol molecules adsorb on the copper cluster through the oxygen atom and the process distorts the clusters.

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92 The simulations indicate that the nearest Cu atom in the cluster to the methanol molecule is attracted to the oxygen atom. This attraction causes the methanol molecule to reorient itself so that the oxygen atom reaches the cluster first. The attraction between the O and Cu atoms make the copper cluster distort toward the methanol molecule. Though the copper cluster distorts in both the collisions on the high CN sites and the low CN sites, the stability of adsorption is different in these two cases. Specifically, molecular adsorption at the low CN site is more stable than at high CN site. The energy evolution curve indicates that it takes longer for the methanol molecule to stably adsorb to the high CN site of the Cu cluster (because it initially bounces off the cluster, as described above) than on the lo w CN site, and there is an obvious energy drop when the methanol molecule adsorbs on the low CN site. Two specific examples for the case of Cu4 and Cu5 are given in Figure 4-9 a) and b) respectively. In the case of Cu4, shown in Figure 4-9 a), adsorption on the higher co ordination site is more stable than on the lower coordination site, which is the opposite of the other cases c onsidered here. Thus the potential energy curve shows a steep drop as a result of adsorp tion on the higher coordination site. The Cu5 case, illustrated in Figure 4-9 b), is more representative of what occurs for the other clusters, where adsorption on the higher coordi nation site is more stable. The equilibrium adsorption structure was an alyzed by averaging all the equilibrium structures and was characterized in terms of the average Cu -O bond length (Figure 4-10), the average O-C bond length (Figure 4-11), the aver age Cu-O-C bond angle, the average Cu-O-H bond angle, and the average C-O-H bond angle (Fi gure 4-12). From those three bond angles, the O solid angle can be characterized by using H O C H O Cu C O Cu o O 360, (4-3)

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93 where Cu-O-C is the average Cu-O-C bond angle, Cu-O-H is the average Cu-O-H bond angle and C-O-H is the average C-O-H bond angle. Since the O, Cu, O and H atoms are able to form a pyramidal shape, Equation (4-3) i ndicates that the pyramid solid an gle at the O atom corner can be described. Though it is not an equation to calculate the real so lid angle at O atom, O still can represent the angular relationshi p between the O atom and its th ree neighbor atoms (Cu, C and H). If O is equal to zero, this means that the O, Cu, C and H atoms are in the same plane. The larger O, the sharper the pyramid solid angle at the O atom corner. In Figure 4-10, the Cu-O bond length is found to generally increase when the cluster size increases. Typically even-numbered clusters have longer Cu-O bond lengths. The three stage trend in dimensionality with clusters size shown in bare copper clusters is not observed here. However, it is found that the Cu-O bond length is l onger if the methanol molecule is adsorbed on the high CN site. The only exception is Cu4CH3OH, which has a shorter Cu-O bond length when the methanol molecule is adsorbed on a high CN site. This is most likely because the Cu4 cluster changed its structure substantially fo llowing adsorption, as discussed above. The resulting C-O bond lengths are shown in Figure 4-11. The C-O bond length trends are the opposite of the Cu-O bond length trend. For exam ple, the high CN site Cu cluster-methanol compounds have a shorter C-O bond length and the lower CN site compounds have longer C-O bond lengths. The only exception is again the Cu4CH3OH. This result indicates that the charge on the O atom is higher when the Cu-O bond length is shorter. From the bare copper cluster calculations discussed in the prev ious section, the low CN Cu site has higher charge than the high CN Cu site. The results imply that to ad sorb a methanol molecule on a neutral copper cluster, there should be electr on cloud transfer between the c opper cluster and the methanol

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94 molecule. Higher electron cloud density provides more opportunity to ach ieve this transfer, which makes the low CN site most favorable for adsorption. Comparing the C-O bond length of bare metha nol and the adsorbed methanol molecule, the C-O bond length of adsorbed methanol is elonga ted when adsorbed at both the high CN site and the low CN site. The amount of elongation is approximately 0.02 (1 .4%) at the low CN site and approximately 0.016 (1 .1%) at the high CN site. This finding further confirms the analysis discussed above. In the isolated meth anol molecule the C-O interaction is through -bonding, while when it is adsorbed on the copper cl uster, part of the O el ectron clouds interact with the Cu atom and part of the Cu at oms electron cloud transfers to the O atom37,118. The net transfer leads the adsorbed Cu atom to have a slight positive charge and the O atom to have a slight negative charge, therefore stabilizing adsorption. The results of O-H bond lengths are also provided in Fi gure 4-11. The O-H bond lengths are all slightly longer than the O-H bond length of an isolated methanol molecule. However there is no obvious trend between the high CN site and the low CN site. For Cu4-Cu6, the high CN site has a longer O-H bond length and for Cu7 and Cu8, the low CN site has a longer bond length. From the electronic calculation of the bare me thanol molecule, the bond order for O-H is 0.78 and for C-O is 0.46. Thus, since the O-H bond is stronger than the C-O bond, the influence of the electron cloud transfer between Cu and O does not affect the O-H bond to any significant degree. Figure 4-12 illustrates the angular relations hip around the O atom after the methanol molecule adsorbs to the Cu clusters. It is inte resting that the C-O-H a ngle does not change much in the different adsorption cases and the angles are almost the same as in the case of the isolated methanol molecule (109.094o). In contrast, the Cu-O-H angle and Cu-O-C angle have more substantial variations. There is no clear trend that indicates that ad sorption at a high CN site or a

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95 low CN site influences the Cu-O-C angle. Howeve r, the Cu-O-H angle typically is larger when methanol is adsorbed at a low CN site than at a high CN site. The pyramid solid angle at an O atom corner ( O) also has larger varia tion and typically the low CN site has a smaller O which indicates a flatter O-Cu-C-H plane. The angular relationships indica te how the methanol molecule adsorbs on the clusters. The small variation in C-O-H angle reveal s that the covalent bonding nature (sp orbital hybridization) between the O-H and O-C is still hold strong af ter adsorption. The larg er variations in the Cu-O-C angle and the Cu-O-H angle show th at the bonding between Cu and O is not purely covalent, but includes donation and back-donation of electrons. This illustrates how the Cu atoms 3d orbitals complicate the bond order th at occur as a resu lt of adsorption. The binding energy between the Cu clusters and methanol molecules are indicated in Figure 4-13. Here the binding en ergy is calculated through: ) (3 3free Cu free OH CH OH CH Cun nE E E BE (4-4) The results show that binding energies increase with increasing cluster size. This may conflict with our intuitiv e sense that with incr easing cluster size the ad sorption behavior should approach the behavior observed on Cu surfaces, which is purely physisorption.21,40 This apparent contradiction is explained by the fact that in the case of the largest cluster, Cu9, considered in this study, the Cu atoms are far from a bulk-like arrangement. The results of binding energy al so indicate that the adsorpti on site influences the binding energy. In particular, binding en ergy is higher when the methanol molecule is adsorbed on a low CN site and is lower when the methanol molecule is adsorbed on a high CN site. This result is consistent with our bond length results and ac companying analysis. The only exception is again Cu4CH3OH. As discussed above, this is because the structure of the Cu4 cluster deforms

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96 significantly when methanol adsorbs on a low CN site. It becomes a Cu3 structure attached to an extra Cu atom on one of its corner. Thus it is difficult to compare the result with the high CN site of Cu4 cluster. Finally it should be mentioned that the spin-p olarized wave function with the GGA is also used in Cu6CH3OH and Cu7CH3OH to verify the result obtaine d by non-spin-polarized function in DFT-MD calculations. The equilibrium struct ures obtained by both met hods are very similar and the differences are within 1%. The results in binding energy also give the same trend and the differences are within 7%. Thus it is believed that non-polarized wave function provide the most reliable results. Conclusions This study has analyzed the structure of sm all bare copper clusters and adsorption of methanol molecule on these cluste rs. It is found that th e structural dimensionality of the bare copper clusters evolves with cluster size in average bond length, binding energy per bond, and bond order. The bond length increases with increasing structural dimensionality. The binding energy per bond and the bond or der, however, decrease with increasing structural dimensionality. These results are explained by the electronic structures of the clusters. The population of 4s and 4p orbitals exhibit different tre nds in the two-dimensional and three-dimensional clusters. It is also found that even numbered Cu clus ters are more stable than odd numbered Cu clusters. The electron density distributions on bare Cu clusters contribute to a significant degree to methanol adsorption. Low CN sites have higher electron densities and provide more opportunity for electron cloud transf er between cluster Cu atoms and molecular O atoms, which makes them the most favorable adsorpti on sites. The complex structure of CunCH3OH compounds prove that the 3d orbital is involved in the interactions.

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97 Table 4-1. Comparison of ground-state st ructure of neutral copper clusters, Cun (n=2-9) Copper Clusters PG This work (LDA Plane-wave type basis set) Jug et al. (LDA Gaussian-type basis set)33 Jaque et al. (B3PW91 Gaussian-type basis set)32 Cu2 D h r12=2.142 r12=2.21 r12=2.254 Cu3 C2v r12=2.246 r13=2.257 r12=2.50 r13=2.26 r12=2.690 r13=2.326 Cu4 D2h r12=2.195 r13=2.282 r12=2.24 r13=2.36 r12=2.574 13=2.293 Cu5 C2v r25=2.243 r24=2.264 r45=2.300 r34=2.289 r25=2.32 r24=2.33 r45=2.36 r34=2.38 r25=2.401 r24=2.415 r45=2.451 r34=2.469 Cu6 D3h r15=2.250 r16=2.316 r34=2.33 r45=2.39 r34=2.404 r45=2.484 Cu7 D5h r34=2.329 r36=2.335 r34=2.39 r36=2.39 r34=2.500 r36=2.500 Cu8 C2v r12=2.302 r28=2.330 r18=2.347 r78=2.300 r23=2.379 r14=3.022 r17=2.333 r67=2.379 r12=2.35 r28=2.38 r18=2.39 r78=2.35 r23=2.47 r14=3.07 r17=2.38 r67=2.47 r12=2.437 r28=2.491 r18=2.512 r78=2.436 r23=2.643 r14=3.225 r17=2.491 r67=2.643 Cu9 Cs r45=2.426 r15=2.350 r56=2.309 r57=2.347 r12=2.342 r16=2.401 r17=2.341 r19=2.353 r23=2.344 r27=2.360 r28=2.341 r67=2.483 r69=2.310 r89=2.426 r45=2.49 r15=2.39 r56=2.35 r57=2.42 r12=2.39 r16=2.46 r17=2.40 r19=2.42 r23=2.39 r27=2.40 r28=2.42 r69=2.35 r45=2.615 r15=2.521 r56=2.463 r57=2.555 r12=2.500 r16=2.555 r17=2.500 r19=2.521 r23=2.650 r27=2.479 r28=2.559 r67=2.650 r69=2.463 r89=2.614 Table 4-2. Average bond length in and mean coordinatio n number (CN) of Cun clusters Copper Clusters LDA LDA+spin GGA GGA+spinJug et al.33 Jaque et al.32 CN Cu2 2.142 2.142 2.180 2.180 2.210 2.254 1.0 Cu3 2.246 2.245 2.326 2.332 2.340 2.447 2.0 Cu4 2.264 2.264 2.328 2.328 2.336 2.418 2.5 Cu5 2.272 2.271 2.348 2.341 2.343 2.429 2.8 Cu6 2.272 2.273 2.338 2.338 2.350 2.431 3.0 Cu7 2.341 2.343 2.413 2.412 2.390 2.500 4.3 Cu8 2.333 2.334 2.407 2.404 2.386 2.501 4.5 Cu9 2.364 2.364 2.430 2.431 2.453 2.534 5.1

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98 Table 4-3. Atomic populations for Cu2-Cu9 using the generalized gradient approximation (GGA) Species Ion 4s1 4p 3d10 4f Total Charge 1 0.99 0.06 9.95 0.00 11.00 0.00 Cu2 2 0.99 0.06 9.95 0.00 11.00 0.00 1 0.94 0.18 9.90 0.00 11.02 -0.02 2 0.93 0.19 9.90 0.00 11.01 -0.01 Cu3 3 0.81 0.24 9.91 0.00 10.97 0.03 1 0.74 0.32 9.90 0.00 10.96 0.04 2 0.74 0.32 9.90 0.00 10.96 0.04 3 1.14 0.02 9.87 0.00 11.04 -0.04 Cu4 4 1.14 0.02 9.87 0.00 11.04 -0.04 1 1.08 0.04 9.89 0.00 11.02 -0.02 2 1.08 0.04 9.89 0.00 11.02 -0.02 3 0.92 0.19 9.88 0.00 10.99 0.01 4 0.92 0.19 9.88 0.00 10.99 0.01 Cu5 5 0.90 0.25 9.84 0.00 10.99 0.01 1 0.90 0.20 9.87 0.00 10.97 0.03 2 0.89 0.18 9.87 0.00 10.94 0.06 3 1.15 0.01 9.89 0.00 11.05 -0.05 4 1.14 0.01 9.89 0.00 11.04 -0.04 5 1.14 0.01 9.89 0.00 11.04 -0.04 Cu6 6 0.90 0.20 9.87 0.00 10.97 0.03 1 0.90 0.29 9.87 0.00 11.06 -0.06 2 0.90 0.28 9.87 0.00 11.05 -0.05 3 0.90 0.29 9.87 0.00 11.06 -0.06 4 0.90 0.28 9.87 0.00 11.05 -0.05 5 0.90 0.28 9.87 0.00 11.05 -0.05 6 0.78 0.26 9.83 0.00 10.87 0.13 Cu7 7 0.78 0.26 9.83 0.00 10.87 0.13 1 0.82 0.28 9.85 0.00 10.95 0.05 2 0.91 0.27 9.87 0.00 11.05 -0.05 3 0.91 0.27 9.87 0.00 11.05 -0.05 4 0.82 0.28 9.85 0.00 10.95 0.05 5 0.82 0.28 9.85 0.00 10.95 0.05 6 0.91 0.27 9.87 0.00 11.05 -0.05 7 0.91 0.27 9.87 0.00 11.05 -0.05 Cu8 8 0.82 0.28 9.85 0.00 10.95 0.05 1 0.81 0.36 9.86 0.00 11.03 -0.03 2 0.78 0.29 9.84 0.00 10.91 0.09 3 0.81 0.36 9.86 0.00 11.03 -0.03 4 0.96 0.24 9.86 0.00 11.05 -0.05 5 0.96 0.24 9.86 0.00 11.056 -0.05 6 0.72 0.45 9.79 0.00 10.96 0.04 7 0.77 0.28 9.84 0.00 10.88 0.12 8 0.95 0.24 9.86 0.00 11.04 -0.04 Cu9 9 0.95 0.24 9.86 0.00 11.04 -0.04

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99 Figure 4-1. The ground state structures of the neutral copper clusters after optimization using the generalized gradient approximation ( GGA) and non-polarized wave function in the calculations. Cu9 r45=2.506 r19=2.433 r15=2.427 r23=2.395 r56=2.366 r27=2.416 r57=2.433 r28=2.436 r12=2.395 r67=2.531 r16=2.459 r69=2.358 r17=2.399 r89=2.519 Cu8 r12=2.363 r23=2.461 r28=2.417 r14=3.119 r18=2.406 r17=2.417 r78=2.363 r67=2.461 1 2 4 5 6 7 8 9 3 1 2 3 4 5 6 7 2.40 2.40 2.52 1 2 3 4 5 6 2.39 2.31 1 2 4 3 2.20 2.35 1 2 2.18 1 2 3 2.44 2.26 1 2 3 4 5 2.39 2.30 2.34 2.37 1 4 2 3 5 6 7 8

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100 Cu2Cu3Cu4Cu5Cu6Cu7Cu8Cu9 2.00 2.05 2.10 2.15 2.20 2.25 2.30 2.35 2.40 2.45 2.50 2.55 Average Bond LengthSize of Copper Clusters LDA LDA+spin GGA GGA+spin LDA (Gaussian) [33] B3PW91 [32] Figure 4-2. Average Cu-Cu bond lengths in the cl usters obtained from the calculations as a function of the level of theory used. Cu2Cu3Cu4Cu5Cu6Cu7Cu8Cu9 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 Binding Energy (eV/atom)Size of Copper Clusters LDA LDA+spin GGA GGA+spin B3PW91[32] LDA (Gaussian)[33] exp1[45] exp2[116] Figure 4-3. Binding energies in the copper clusters obtained from the calculations as a function of the level of theory used and from experimental data.

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101 Cu2Cu3Cu4Cu5Cu6Cu7Cu8Cu9 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 Binding Energy per Cu-Cu Bond (eV) LDA LDA+spin GGA GGA+spin Figure 4-4. Binding energies per Cu-Cu bond in the clusters as a function of the level of theory used in the calculations. Cu2Cu3Cu4Cu5Cu6Cu7Cu8Cu9 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Bond OrderSize of Copper Clusters LDA LDA+spin GGA GGA+spin Figure 4-5. Bond order in the copper clusters as a function of the level of theory used in the calculations.

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102 Cu2Cu3Cu4Cu5Cu6Cu7Cu8 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 Relative StabilitySize of Copper Clusters LDA LDA+spin GGA GGA+spin B3PW91[32] Figure 4-6. Relative stability of the copper cluste rs as a function of the approximations used in the calculations.

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103 Figure 4-7. The initial and final snapshots from the simulations of methanol molecule collisions on low-coordination num ber sites of the copper clusters Figure 4-8. The initial and final snapshots from the simulations of methanol molecule collisions on high-coordination sites of the c opper clusters. Cu8 final Cu8 initial Cu7 final Cu7 initial Cu6 final Cu6 initial Cu5 initial Cu4 final Cu4 initial Cu5 final Cu9 final Cu9 initial Cu8 final Cu8 initial Cu7 final Cu7 initial Cu6 final Cu6 initial Cu5 final Cu5 initial Cu4 final Cu4 initial Cu3 final Cu3 initial Cu2 initial Cu2 final

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104 0500100015002000 -6068.0 -6067.5 -6067.0 -6066.5 -6066.0 -6065.5 PE evolution for low CN site PE evolution for high CN sitePotential Energy (PE) (eV.)number of MD steps PECu4 free+PEmethanol free 050010001500200025003000 -7419.9 -7419.6 -7419.3 -7419.0 -7418.2 -7418.0 -7417.8 PE evolution for low CN site PE evolution for high CN site PECu 5 free+PEmethanol freePotential energy (eV.)number of MD steps Figure 4-9. The potential energy evolution of adsorption of methanol on the a) Cu4 and b) Cu5 cluster. The straight line indicates the approximate potential energy for methanol adsorbed on the high or low coordinati on number site of the Cu clusters. a) b)

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105 2.00 2.01 2.02 2.03 2.04 2.05 2.06 2.07 2.08 2.12 2.13 2.14 2.15 2.16 2.17 2.18 2.19 Cu9C H3OH C u8C H3OH C u7C H3OH Cu6CH3OH Cu5C H3OH C u4CH3OH C u3C H3OH Cu2C H3OH bond length (Angstrom) Cu-O bond length (low CN site) Cu-O bond length (high CN site) Figure 4-10. Cu-O bond length in the copper clus ters. The solid square s represent the binding energy for collision at a low-CN site and hollow circles indicate the binding energy for collision at a high-CN site. 0.970 0.972 0.974 0.976 0.978 1.440 1.445 1.450 1.455 1.460 Cu9C H3OH Cu8CH3OH C u7CH3OH C u6CH3OH Cu5CH3OH C u4C H3OH Cu3C H3OH C u2CH3OH Bond Length (Angstrom) C-O (low CN site) O-H (low CN site) C-O (high CN site) O-H (high CN site) Figure 4-11. The C-O bond lengt h and O-H bond length in the copper clusters. The solid squares and circles represent the binding energy for collis ion at low-CN sites, and hollow squares and circles indicate the binding energy for collision at high-CN sites.

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106 0 5 10 15 20 100 105 110 115 120 125 130 Cu9CH3OH C u8CH3OH Cu7C H3O H C u6CH3OH C u5CH3OH Cu4CH3OH C u3C H3O H Cu2C H3O H Angle (o) Cu-O-C (low CN site) Cu-O-H (low CN site) H-O-C (low CN site) O (low CN site) Cu-O-C (high CN site) Cu-O-H (high CN site) H-O-C (high CN site) O (high CN site) Figure 4-12. Bonding angles in CunCH3OH. The filled symbols represent the binding energy for collision at a low-CN site and empt y symbols indicate the binding energy for collision at high-CN site. -2.4 -2.2 -2.0 -1.8 -1.6 -1.4 -1.2 -1.0 Cu2CH3OH Cu3CH3OH C u4CH3O H Cu5C H3OH Cu6C H3O H C u7CH3O H Cu8CH3OH C u9CH3O H Binding Energy (eV) Figure 4-13. Binding energy in the copper clusters. The solid squares represent the binding energy for collision at low-CN sites and hollow squares indicate the binding energy for collision at high-CN sites.

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107 CHAPTER 5 CHEMICAL MODIFICATIONS OF POLYMER SURFACES BY ION BEAM DEPOSITIONS Here, the chemical modification of polymer surfaces is considered. In particular, two aspects of this process are investigated: (i) co mparison of chemical modi fications on polystyrene (PS) surface by hydrocarbon and fluorocarbon ion b eams and (ii) chemical modification of the poly(vinylidene fluoride-trifluoroethylene) [P(VDF-trFE)] copolymer surface through fluorocarbon ion beam deposition. In the first topic, the focus is on the differences between fluorocarbon and hydrocarbon ions in physics and chemistry. The second topic is focused on the interaction between fluorocarbon ions and fluorinat ed polymer surfaces, and the effect of the size of incident ions on this modification. The computational approach used in these st udies is REBO-MD. Since this approach is empirical, large-size scale simulations can be pe rformed. Thus, extensive information regarding such factors as the accumulativ e effect of ion beam deposition on surfaces can be obtained. The systems of interest here in clude a hydrocarbon system ( PS) and a fluorocarbon system [P(VDF-trFE)], which the REBO-MD appro ach is able to model reasonably well. Comparison of Chemical Modifications of Polystyrene Surface by Hydrocarbon and Fluorocarbon Ion Beams Introduction Here, classical MD simulations are carried out to study the continuous deposition of FC ions (C3F5 + and CF3 +) and HC ions (C3H5 + and CH3 +) onto polystyrene (PS) surfaces at experimental fluences. The goal is to investigat e the differences in the ways in which these polyatomic ion beams chemically modify the PS. Specifically, the chemical products that are produced, their penetration depths into the PS su rface, their reaction with the PS backbone chains and phenyl groups, and the amount of overall cr oss-linking in the PS are determined. These

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108 results are analyzed with respec t to the relative sizes of the ions and the stre ngths of their interatomic bonds. Computational Details A snapshot of the PS surface used in the MD simu lations is shown in Figure 5-1. It is made up of eight layers of syndiotactic PS chains, with six chains per layer. These chains are aligned along the short side of the surface slab (which is 30 ) such that 12 repeat units (-CH2-CHC6H5-) fit within this length. The long si de of the surface slab is 52 wide, the thickness normal to the surface is 56 and the total number of atoms is approximately 10,000. Periodic boundary conditions57 are applied within the surface plane to mi mic an infinite surface. Every PS chain ends at the boundary to effectively wrap around on itself such that there are no surface slab edge effects. In order to maintain the system temperature at 300 K during depositi on, a thermostat is applied to some surface atoms. Specifically, the three bottom layers of the substrate and atoms within 5 from the two long sides of the slab, and 10 from the two sh ort sides of the slab, have Langevin friction and stocha stic forces applied to them.57 This imitates the heat dissipation process of real substrate and prevents the surface from translating in response to polyatomic ion beam deposition. The rest of atoms are active a nd can evolve freely in response to the force fields formed by the surrounding at oms. Before deposition, the PS substrate is relaxed at 300 K for 3 ps at which point the system potentia l energy fluctuates by 0.0033 eV/atom around a constant value as a function of time. Two beams of FC ions, one of C3F5 + and one of CF3 +, and two beams of HC ions, one of C3H5 + and one of CH3 +, are deposited on the ac tive area of the PS substrate in separate simulation studies. Each beam contains a total of 240 C3F5 + or C3H5 + ions, or 400 CF3 + or CH3 + ions, such that the total F/H atom fluence is the same in all cas es. Each ion in the continuously

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109 deposited beam impacts the PS surface at a randoml y selected location within the active area and is randomly orientated relative to the surface. Th e total kinetic energy for each ion is 50 eV, and the incident angle is normal to the PS su rface. The total fluen ce is equal to 1.8 1016 F/H atom/cm2 and is comparable to experimental values.99 The time interval between ion collisions with the surface is around 1.5 ps, and after ev ery 5 ions are deposited the entire system is equilibrated for 3.4 ps to maintain the surf ace temperature at around 300 K. After the ion beam deposition process is complete, each system is fu rther equilibrated for 25 ps at which point the system potential energy again fluctuate by 0.003 3 eV/atom around a constant value with time. The FC ion beam deposition results are the same as those discussed by us previously54 with additional analysis of the chemical modifica tion of the PS surface to better facilitate a comparison with the new HC ion beam depositi on results. The time step used in all the simulations is 0.20 fs. Results and Discussion There are no distinct, new fluorocarbon or hydrocarbon films formed as a result of polyatomic ion beam deposition over the time scales of these classical MD simulations. However, ion fragments and a ggregates of fluorocarbons and hydrocarbons are generated that are consistent with experimentally119-122 observed precursors to the growth of fluorocarbon or hydrocarbon thin films. For example, common expe rimentally observed precursor particles that are predicted to form in these simulati ons are small ion fragments, such as CF2 and CH2, and larger aggregates such as CxFy (x>2, y>1).119-122 While the simulations predict that the C3H5 + ion beam produces the largest number of a ggregate chemical products (such as CnHm where n>3 and m>5), similar aggregates are formed for all the polyatomic ion beams considered here, with the CF3 + beam producing the smallest aggregates (C2Fm, m>1).

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110 Figure 5-2 shows the final structures of the PS surfaces after the depos ition of each of the four polyatomic ion beams. In all cases the PS surfaces swell as a result of the deposition process. However, the resulting structures are significantly different after the deposition of the various ions considered. In pa rticular, in the case of C3H5 + ion beam deposition, chemical products form on and within the PS nearest the topm ost surface layers. In contrast, in the case of the deposition of CH3 + ions, the chemical products are more evenly distributed throughout the PS. For the case of C3F5 + and CF3 + deposition, the penetration profiles of ions and their fragments are similar to each other because CF3 + ions are more reactive with the surface than C3F5 +. The simulations further indicate that the m echanism by which the surface swells depends on whether the incident ions are FCs or HCs. For example, CF3 + ion beam deposition causes much more surface swelling than C3F5 + ion beam deposition because the smaller ion has a larger incident velocity (corresponding to the same inci dent kinetic energy of 50 eV/ion) and, thus, is able to transfer more kinetic energy to the lo cal impact point on the PS surface. This kinetic energy leads to disruption of the PS ordering and causes the distances between the PS chains to increase. The C3F5 + ion has a larger size and mass, and therefore a lower incident velocity. Consequently, it transfers less kinetic energy to th e impact point and lead s to less swelling of PS surface. On the other hand, both C3H5 + and CH3 + ion beam deposition result in substantial surface swelling. The mechanism by which the CH3 + causes swelling is comparable to the mechanism by which the CF3 + ion does so. However, unlike C3F5 +, most of the C3H5 + ions accumulate near the top of the PS surface rather than penetrating into the PS, thus effectively building up the surface.

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111 The depth profiles of incident C, H and F atom ic densities in the PS after each deposition process is complete are illustrat ed in Figure 5-3. The figure indi cates how the overall density of HC products is larger than the overall density of FC products. In other words, the HC ions, or their fragments or products, are most likely to remain in the PS and either form chemical bonds with the polymer chains or simply remain embe dded in the PS surface over the time scales of these simulations. In contrast, the FC ions, or their fragments or produc ts, are more likely to scatter away from the PS surface following de position. The total density of deposited C atoms from the ions is therefore predicted to be higher in the case of HC polyatomic ion beam deposition than in the case of FC polyatomic ion beam deposition. Figure 5-3 also reveals how the depth profile s of the products of the various ion beams differ from one anther. In most cases, the highest density of deposited atoms is at a depth of about 15 and the distribution pr ofile is a symmetric, bell-shape d curve. However, in the case of C3H5 + ion beam deposition, most of the deposited atoms remain very near the top of the PS surface causing the depth profile distribution to be skewed and resemble half of a bell-shaped curve. This result is consistent with the da ta shown in Figure 5-2 and discussed above. Figure 5-4 illustrates the chemical products (including ions and ion fragments) formed after ion-beam deposition. The most plentiful product formed as a result of C3F5 + ion beam deposition is C3F5, and the most plentiful products formed as a result of CF3 + ion beam deposition are CF3 and CF2. These results are explaine d by the strong carbon-fluorine interatomic bonds in the FC ions. The predictio ns for the HC ions are quite different. In particular, the most plentiful products (about 33% of the total products) formed as a result of C3H5 + ion beam deposition are CnHm molecules, where 38>n>3 and 49>m>5 (these numbers only include atoms from incident ions, although some CnHm products bond to the PS chains),

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112 and the most plentiful products formed as a result of CH3 + ion beam deposition are CH, CH2 and C2Hn, where n>1. Thus, the HC ions dissociate or react with other atoms more readily than the FC ions, and the most plentiful products from the larger ions are themselves larger than the most plentiful products from the smaller ions. Another trend indicated in Figure 5-4 is that a higher fraction of the products formed as a result of HC ion beam deposition form chemical bonds with the PS chains on the time scales of these simulations than in the case of FC ion beam deposition. In particular, 50.5% of all of the chemical products form bonds with the PS substrate as a result of C3H5 + ion beam deposition, and 65.4% of all of the chemical products form bonds with the PS substr ate as a result of CH3 + ion beam deposition. In contrast only 19.7% of all the chemical products form bonds with the PS substrate as a result of C3F5 + ion beam deposition, and 25.0% of all of the chemical products form bonds with the PS substrate as a result of CF3 + ion beam deposition. It should be noted that th e quantitative results for C3H5 + deposition differs from the results of our previous study,11 which considered the de position of many individual C3H5 + ions on pristine PS surfaces. That study predicted that the major (about 30% of the total) chemical product to be C3H5, that 50% of the C3H5 products form chemical bonds with the PS, and 90% of the second most commonly formed species, CH2, form chemical bonds with the PS.11 These differences are due to the fact that the previous study considered a statistical analysis of many individual C3H5 + ions deposited onto a pristine PS surf ace rather than the continuous deposition of ions onto the same PS surface. As a result, there were no opportunities for the accumulation of damage or for the chemical products of multiple ion deposition events to interact with one another. In contrast, in this study, it is possible for, e.g., the deposited C3H5 + ions to form bonds with CH2 products on the substrate and thus grow larger species.

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113 While all the polyatomic ions have the same incident kinetic energy of 50 eV, they have different masses and velocities. The simulations indicate how the ions masses and incident velocities influence the results of the deposition pr ocess. Specifically, they show that the ions with higher velocities ca use more damage to the PS surface. Furthermore, the ions mass and overall size affects their collision cross-section with the surface. This too will influence the transfer of energy to the PS and penetration into the surface. Figur e 5-5 illustrates the predicted penetration depths for the va rious chemical products formed by the various ions (zero penetration depth means that the products remain at the top of the PS su rface). In general, the products that form chemical bonds most readily with the PS have shallower penetration depths. In the case of C3H5 + ions, their fragment and resulting products show shallower penetration depths than C3F5 + ions and their products. This is because once the products bond with the PS, they are trapped by the bondi ng and cannot go any deeper. However, in the case of CH3 + ion beam deposition, the ions high velo city and small mass cause them to penetrate deeply into the PS until their kinetic energy is dissipated enough that they are able to form stable bonds. Thus, a large fraction of the resulting products form c ovalent bonds to the PS chains, and do so at a significant penetration depth. Examination and comparison of Figures 5-4 and 5-5 also reveals where the majority of the chemical products formed remain in the PS substrate. For example, in the case of C3F5 + ion deposition, the majority product, C3F5, bonds with the PS about 9 from the top of the PS surface. In the case of CF3 + ion deposition, the majority products, CF3 and CF2, also form bonds with the PS chains around 10 from the top of the PS surface. This suggests that the FC ions effectively fluorinate the PS. In the case of C3H5 + ion deposition, the majority product, CnHm, form bonds with the PS around 5 from the top of the PS surface. Some products, such as

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114 C3Hm, form bonds above the initial PS surface line. This implies that C3H5 + ion deposition is mostly effective for growing HC thin film on the PS substrate. However, in the case of CH3 + ion deposition, the results are quite different. As a result of the fact that the CH3 + ion is the smallest ion and has the largest velocity, mo st of its modifications occur deeper than the other ions at 13 This indicates that CH3 + ions are not as effective as th e other ions considered here at concentrating their chemical modification ne ar the topmost part of the PS surface. The simulations further allow us to examine the details of the PS chain modification as a result of polyatomic ion beam deposition. Table 5-1 shows the percentage of intact PS backbone chains as a function of depth afte r deposition. In general, in the cas e of large ions, damage to the PS chains is shallower than in th e case of small ions. This is becau se the larger ions collide with more atoms in the PS once they im pact the surface. They also ha ve lower velocities relative to the smaller ions. In other words, they have a s horter mean free path within the polymer, a larger scattering cross section, and a slow er incident velocity, which allows them to be scattered easily. The predicted trend in de gree of modification of PS backbone chai ns for the ions considered here is CH3 +>CF3 +>C3F5 +>C3H5 +. Table 5-2 shows the percentage of intact phenyl rings as a function of depth after deposition. The extent of modification of phenyl rings from strong to weak is CH3 +>CF3 +>C3F5 +>C3H5 +, which is the same trend deduced from Table 5-1. However, we should take note of the fact that compared to Table 5-1, the depth of modificatio n of the phenyl rings is significantly shallower than in th e case of the PS backbone chains in general. This result makes sense, as the carbon-carbon conjugate bond is st ronger than the carbon-c arbon single bond, so PS backbone chains are more easily modified, on average, than the car bon-carbon bonds in the phenyl rings.

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115 This point is confirmed in Table 5-3, which shows the number of backbone carbon atoms and phenyl ring carbon atoms that have undergone chem ical reactions with incident ions. At first glance, it appears that the phenyl ring carbon atoms are modifi ed more than the backbone carbon atoms. However, we should notice that there are 2.8 times more phenyl ring carbon atoms than there are backbone carbon atoms prior to ion-beam deposition. If we calculate the occupation volume of both kinds of carbon atoms in the su bstrate, the volume th at the phenyl ring carbon atoms occupy is approximately 9.3 times larg er than the volume occupied by backbone carbon atoms (as determined from a hard sphere model). This means phenyl carbon atoms are 9.3 times more likely to collide with an incoming ion or ion fragment than backbone carbon atoms. Therefore, if the modification strength is th e same for phenyl ring ca rbon atoms and backbone carbon atoms, 9.3 times as many phenyl ring car bon atoms should react as backbone carbon atoms. However, column three in Table 5-3 indicates that the ratio of reacted phenyl ring carbon atoms to backbone carbon atoms ranges from 2.7 to 5.3. Thus, we may conclude that backbone carbon atoms are modified more readily than the phenyl ring carbon atoms. The exact ratio of reacted phe nyl ring carbon atoms to bac kbone carbon atoms also varies among the different incident ions. This indicates that the ability to modify the phenyl ring carbon atoms or the backbone carbon atoms depends to so me extent on the properties of the ions. In particular, the ratio is about 5.3 for C3F5 + ion deposition, 3.1 for CF3 + ion deposition, 4.8 for C3H5 + ion deposition, and 2.7 for CH3 + ion deposition. The larger i ons are better able to modify phenyl ring carbon atoms than small ions. This is especially true in the case of the C3F5 + ion, which is the heaviest ion considered here. It has a larger mass and its carbon-fluorine bonds are stronger than the carbon-hydrogen bonds in the HC ions, and t hus it is more efficient at modifying phenyl rings than other kinds of incident ions. This is because it is able to transfer

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116 more of its kinetic energy to the phenyl ring through elastic collisions and chemical reactions, whereas the HC is more likely to bounce back or dissipate its kinetic energy by breaking apart. On the other hand, the CH3 + ions are less effective at modify ing the phenyl rings but are quite effective at modifying the PS backbone chains. After the ion beam deposition and equilibration processes are complete, the polymer chains or fragments that make up the modified PS surf ace, containing both original PS atoms and atoms from the incident ions, are analyzed and their molecular weights calculat ed individually. Figure 5-6 illustrates the molecular weig ht distribution of chemical produc ts in the PS formed after the polyatomic ion beam deposition processes are co mplete. Prior to deposition, the molecular weight of one PS chain within th e active region of the PS surface (show n in blue in Figure 5-1) is 800-850 g/mole (within each periodic boundary condition cell). Af ter deposition and equilibration, numerous small molecular weig ht chemical products are formed from the dissociation of ions and damage to the PS chains If we look at the high molecular weight region (above 700 g/mole), which corresponds to only mi nor damage to the pristine PS chain, large incident ions, such as C3H5 + and C3F5 +, produce more high molecular weight chemical products that remain in or on the PS surface than the small incident ions. This result is consistent with data shown in Tables 5-1-1 and 5-1-2. It is noted that some large molecular weight species (more than twice as large as one pristine PS chain) are also formed after the HC ion beam deposition processes (see the insets in Figure 5-6). These chemical products are indi cative of the greater cross-linking between PS chains, and greater degree of bonding of chemical products to the PS chains as a result of HC ion beam deposition compared to FC ion beam deposition.

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117 Figure 5-7 displays the density of cross-linked points as a f unction of depth within the PS surface. Here a cross-link point is defined as a new chemical bond that is formed to PS backbone chains, PS backbone fragments, or PS phenyl ring fragments. The results indicate that, overall, HC ion beams produce higher PS cross-link dens ities than FC ion beams. Furthermore, comparison of C3H5 + and CH3 + ion beam deposition processes indicates that C3H5 + ion-produced cross-links are close the top of the PS surface and extend outward from the original surface plane. Thus, these results predict that C3H5 + ion beam deposition on PS surfaces will make these surfaces stronger and more brittle. The CH3 + ion-produced cross-links are located further away from the initial surface of the PS, around the forth and fifth layers. In contrast, the FC ion beam deposition processes only generate slight cr oss-linking within the PS. However, the C3F5 + ions also cross-link the PS on a sh allower level than the CF3 + ions. In short, HC ions are much more efficient at cross-linking the PS than the FC, and in each case the larger ions produce more shallow cross-links, while the smalle r ions produce deeper cross-links. Conclusions We have investigated the process of FC -ion and HC-ion beam deposition on PS surfaces and the way in which these polyatomic ions b eams chemically modify the surface. The amount of resulting modification is influenced by the size of the ions, their velocities, and their intramolecular bond strengths. In pa rticular, the size of the incide nt ions and their velocities affects the depth of the chemical modification with in the PS, such that the larger the size of the ion, and the lower its velocity, the shallower the modification. In the case of the FC ions, the carbon-fluorine bond is strong, and so these ions are not easily broken apart during deposition. However, in the case of the HC ions, the car bon-hydrogen bond is not as strong, and so these ions are more readily broken into fragments on deposition. This causes the HC ions to more readily react with the PS surface than the comparable FC ions. The simulations predict that more

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118 than 50% of the chemical products produced in the HC ion beam deposition processes form chemical bonds with the PS, while less than 25% of the chemical product s produced in the FC ion beam deposition processes form chemical bonds with the PS. The simulations furthermore provide details of how the PS surface is modified by the deposition of these ions, and predict cross-link profiles for the various ion beams considered here. This study thus provides a cl ear understanding of how diffe rences between similarly structured FC and HC ions deposited in beams ch emically modify PS surfaces. It also identifies likely mechanisms that are respons ible for the observed outcomes. Chemical Modification of the Poly(vinylid ene fluoride-trifluoroethylene) Copolymer Surface through Fluorocarbon Ion Beam Deposition Introduction Fluorocarbon ions (CF2 +, CF3 +, CF4 +, C2F6 +, C3F5 +) are the primary components in plasmas used for dry etching of silicon123 and dielectrics124-126 because of the highly reactive nature of the fluorine. At the same time, fluorinated polym er surfaces are highly stable and non-reactive127 because of the strong nature of the C-F bond. It is therefore interesting from a fundamental point of view to examine the surface chemistry that occurs at fluo rocarbon thin film surfaces during the deposition of fluorocarbon ions. It is well-est ablished that the deposition process involves competition between etching and growth. Here, MD simulations are used to indicate the conditions under which etching dominates, and the conditions under which fluorocarbon thin film growth dominates. The partic ular ions under consideration are C3F5 + and CF3 +, which are chosen because they are co mmon in fluorocarbon plasmas128-130 and have the same hybridization of carbon atoms. Therefore they provide a good comp arison of the effect of relatively large and small ions on the deposition outcomes.

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119 The surface onto which the deposi tion takes place poly(vinylidene fluoride-trifluoroethylene), or P(VDF-trF E). This copolymer consists of both C2H2F2 and C2HF3 monomers. The structural formula of the C2H2F2 monomer is -[CH2-CF2]and of the C2HF3 monomer is -[CHF-CF2]-. Due to electronegativity differences between C-H and C-F, there is a dipole moment within these monomers. Conseq uently, P(VDF-trFE) copolymers are termed ferroelectric polymers.131-133 For example, it has b een determined that they can undergo large, longitudinal electrostrictive st rain (of more than 4.5%) unde r certain kinds of electron irradiation.134 These electromechanical properties ma ke P(VDF-trFE) copolymers promising materials for use in a variety of applications, such as actuators,135 sensors,136-138 ultrasonic transducers,139 and dilatometer.140,141 In this study, MD simulations are used to investigate how FC ion beam deposition modifies the P(VDF-trFE) thin film. For example, the deposition process is expected to modify the chemical and/or electromechanical properties of the polymer surface. A systematic approach is employed to identify the effect of different incident ions, C3F5 + and CF3 +, on this modification. In particular, the depth profiles of the incident atoms, the chemical products that are produced, the molecular weight distribution following depo sition, and the products of surface etching are determined. Computational Details Figure 5-8 shows a snapshot of the initial P( VDF-trFE) surface used in the simulations. It consists of twelve layers of P(VDF-trFE) chains and each layer is made up of eight chains of P(VDF-trFE). Every chain c ontains eight monomers w ith the same ratio of C2H2F2 and CHF3 along both the width and the length The monomers are arranged in such a way as to form a random copolymer. The dimensions of the su rface are thus 51.48 39.28 38.40 in depth, width and length, respec tively, and it consists of approximately 8000 atoms. Periodic

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120 boundary conditions57 are applied within the surface plane to mimic an infinite surface. Every P(VDF-trFE) chain ends at the boundary to effectively wrap around on itself such that there are no surface slab edge effects. In order to maintain the system temperature at 300 K during depositi on, a thermostat is applied to some of the atoms in the substrate. The thermostat region (shown in Figure 5-8) consists of the three bottommost layers and atoms within 8.84 from the edges of the width of the surface slab, and atoms with 8.64 from the edges of the length of the surface slab. Thermostat atoms have Langevin friction a nd stochastic forces applied to them.57 This imitates the heat dissipation process of a real copolymer surface and preven ts the surface from translating in response to polyatomic ion beam deposition. The rest of the surface atoms are active and can evolve freely in response to forces fr om the surrounding atoms without any additional constraints. Prior to ion-beam deposition, the P(VDF-trF E) surface is relaxed at 300 K for 20 ps, at which point the system potential energy fluc tuates by 0.0033 eV/atom around a constant value as a function of time. Two beams of FC ions, one of C3F5 + and one of CF3 +, are deposited on the active area of the P(VDF-trFE) substrate in separate simula tions. Each beam contains a total of 190 C3F5 +, or 315 CF3 + ions, such that the total F fluence of 1.8 1016 F atom/cm2 is about the same in both cases and is similar to that used in previous studies.54,142,143 Each ion in the continuously deposited beam impacts the P(VDF-trFE) surface at a randomly selected location within the active area and is randomly orientated relative to the surface. The total kinetic energy for each ion is 50 eV, and the incident angle is normal to the P(VDF-trFE) substrate surface. The time interval between ion collisions with the surface is around 1.5 ps and after every 5 ions are deposited the entire system is equilibrated fo r 4.5 ps to maintain the surface temperature at

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121 around 300 K. After the ion beam deposition pro cess is complete, each system is further equilibrated for 60 ps at whic h point the system potential en ergy again fluctuates by about 0.0033 eV/atom around a constant value as a functi on of time. The time step used in all the simulations is 0.20 fs. Results Figure 5-9 illustrates snapshots of th e final P(VDF-trFE) surface following C3F5 + and CF3 + ion beam deposition. The results show that ther e are numerous chemical products generated near the top of the surface in the case of C3F5 + ion beam deposition, while, in contrast, there are very few chemical products generated near th e top of the surface in the case of CF3 + ion beam deposition. On the whole, more c opolymer chains are modified by CF3 + ion beam deposition than by C3F5 + ion beam deposition, and a statistical breakdown is provided in Table 5-4. The approximate depth of one layer of P(VDF-trFE) chains is 4 Table 5-4 indicates that C3F5 + ion-beam deposition modifies the copolymer surface to the seventh layer, while CF3 + ion-beam deposition modifies the surface to the ninth layer. Overall, th e copolymer chains are 50% less modified by C3F5 + ion-beam deposition than by CF3 + ion-beam deposition. The depth profiles of incident carbon and fl uorine atoms are shown in Figure 5-10. The results indicate that there ar e two peaks in the case of C3F5 + ion-beam deposition. One is higher and sharper at a depth of 0-4 which is near the top of the surface, wh ile the other is smaller and broader at a depth of 4-8 from the top of the surface. Therefore, the depth profile can be roughly resolved into two curves, one of which is sharp and close to the top of the surface, and the other of which is deep and broad, as is common in many deposition or etching processes.144,145 When the C3F5 + ions impact the surface, the copolymer chains near the collision area shift downward in response. This causes the underlying layers to also shift downwards until the energy is dissipated throughout the rest of the copolymer. In some cases, the C3F5 + ions

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122 collide with the copolymer chains move downward with the chains, and then move to the top of the surface. As the deposition process proceeds, more C3F5 + ions or their fragments accumulate near the top of the surf ace through this mechanism. Thus, th e sharp peak observed in the depth profile is due to these products, while the broad peak is due to bond-brea king and other inelastic collision processes that occur during deposition. The depth profile of the CF3 + ion beam deposition exhibits the expected broad shaped curve, as indicated in Figure 5-10. The curve pe ak is located at a depth of 16-20 from the top of the surface. In this case, there is no obvious downward sh ifting of the copolymer chains near the collision sites. This is because the ions pe netrate more deeply due to their smaller size and higher incident velocity (t hat corresponds to the same incident energy as the C3F5 + ion beam). Those incident ions and their fragments that do move toward s the surface following impact usually exit the copolymer surface rather than accumulate near the top of the surface. The total number of carbon and fluorine atom s from the incident ions that embed themselves in, or bond with, th e surface is 71.70 and 122.62 (20/cm3) in the case of C3F5 + ion beam deposition, respectively, and is 26.82 and 93.06 (20/cm3) in the case of CF3 + ion beam deposition, respectively. Since the total intake of fluorine atom fluence is the same for both ion beams, the simulations indicate that the C3F5 + ion beam has higher uptake rate than the CF3 + ion beam. Figure 5-11 shows the density of products th at form from the ion-beam modification process. The products that form as a result of C3F5 + ion-beam deposition include C3F5, F, C2Fn (where n>0), C3Fn (where n>zero and 5), CF2, CnFm (where n>3 and m>5), CnFv (where n>3 and v<5), and CF. The first four of these corres pond to about 74% of all the chemical products, where the breakdown is 23% C3F5, 20% F, 16% C2Fn and 15% C3Fn. The most plentiful products

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123 are thus either the C3F5 + ion itself or its frag ments. Around 13% of the chemical products are larger than the C3F5 + ion, which is indicative of the combination of C3F5 or its fragments with one another and/or with frag ments of the copolymer. The CF2 radical, which is a major building block of FC films47, and is considered by some to the most important precursor to be produced in the plasma deposition of fluorocarbon films,50,146,147 is also predicted to be a majority component of the products at about 12%. The products that are generated by CF3 + ion beam deposition are also shown in Figure 5-11 and include F, CF3, CF4/C2Fn, CF2/F2, and CnFm/CnFv/CF. The dominate chemical product that is generated as a result of deposition is F, whic h makes up about 49% of all the chemical products. The second most dominate product is CF3 at about 26%. Compared with C3F5 + ion beam deposition, there are fewer large chemical products formed in CF3 + ion beam deposition. For example, only about 13% of the chemical produc ts formed are larger than the incident CF3, and only about 3% of the chemical pr oducts formed are larger than C3F5. CF2 is also formed as a result of CF3 + ion beam deposition, but makes up only about 6% of all the chemical products. These results indicate that C3F5 + ion-beam deposition facilitates th e growth of large FC products, while CF3 + ion-beam deposition is more efficient at fluorinating the copolym er. Figure 5-11 also illustrates the percentage of the chemical produc ts that covalently bond with the surface. In particular, about 30% of the chemical products covalently bond with th e surface in the case of C3F5 + ion beam deposition, while about 63% do so in the case of CF3 + ion-beam deposition. The weight fraction molecular weight (WFMW) of the P(VDF-trFE) after C3F5 + and CF3 + ion-beam deposition is presented in Figure 5-12. In the case of the pristine P(VDF-trFE), the WFMW ranges from 500 to 700 g/mol and has a p eak at around 630 g/mol. Following ion-beam deposition, the height of the major peak decrease s and the peak splits into several small peaks.

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124 There are also many new peaks that appear in th e low WFMW region. This is indicative of the fact that some P(VDF-trFE) ch ains are broken as a result of deposition. Figure 5-12 further indicates that the peaks can be broken into three groups: 0-250, 250-500 and 500-700 g/mol. The first group represents small frag ments that consist of less than four carbon atoms. The second group represents medium-sized fragments made up of around four to nine carbon atoms. The last group consists of large fragments or intact P(VDF -trFE) chains. The total weight fraction of each group is 0.51, 0.16 and 0.33 in the case of C3F5 + ion beam deposition, respectively and is 0.59, 0.20 and 0.21 in the case of CF3 + ion beam deposition, respectively. Thus CF3 + ion-beam deposition breaks more P(VDF-trFE) ch ains into small fragments than C3F5 + ion-beam deposition. This finding is consis tent with the results shown in Table 5-4 that indicate that CF3 + ions modify the copolymer more ex tensively and deeply than do the C3F5 + ions. In Figure 5-13, the uptake of carbon and fluorin e atoms is represented. Because the ions are deposited continuously, the up take of these atoms increases monotonically. The inset figures in Figure 5-13 indicate the uptake ratio between fluorine and carbon at oms. It is found that in the case of C3F5 + ion-beam deposition, the F/C ratio is ar ound 1.7, which is essentially the same as the ideal value of 1.667. In the case of CF3 + ion-beam deposition, however, the F/C ratio is 3.3, which is 10.8% more than the ideal value of 3.0. This indicates that when C3F5 + ions collide with the surface, the carbon and fluorine atoms in the ion have the same opportunity to stay in the surface. However, when CF3 + ions collide with the surface, fluorine atoms are more likely to remain on the surface than the carbon atoms. The large deviation of the F/C ratio from the ideal ratio also implies that the CF3 + ions are more likely to dissociate when they collide with the surface than are the larger C3F5 + ions. This finding is in agreement with the results shown in

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125 Figure 5-11 that indicate th at fluorine is the dominate species in the case of CF3 + ion-beam deposition. The yields of the ion-beam deposition processe s are shown in Figure 5-14. Initially (0-12 ps) the C3F5 + ion-beam deposition has very high yi eld, around 76% and 80% for the F and C atoms, respectively. The yield then decreases ra pidly to around 40% after from 12 to 24 ps and gradually converges to around 25% after about 24 ps. The CF3 + ion beam deposition, in contrast, has a yield of around 45% in the first 12 ps. The yield drops slowly to 20% by the end of the simulation and does not appear to stabilize. It is also noted that the yield between the carbon and fluorine atoms is almost the same in the case of C3F5 + ion beam-deposition, while the yield of fluorine atoms is higher than that of carbon atoms in the case of CF3 + ion-beam deposition. Figure 5-15 indicates the number of P(VDF-trFE) atoms that are scattered out from the surface by the ion-beam deposition process. The etch curves tend to saturate in the case of C3F5 + deposition and to maintain a nonzero slope in the case of CF3 + deposition. Combining the results presented in Figures 5-14 and 5-15, in the case of C3F5 + ion-beam deposition the system is undergoing steady yield and saturate d etch by the end of the simula tion. This indicates that the system is approaching a steady-st ate, continuous film growth stag e. In contrast, comparison of Figures 5-13b) and 5-15b) indi cates that the uptake of CF3 + ions is around 4.215/cm2 and 1.215/cm2 for the F and C atoms, respectively, and th at the etch of P(VDF -trFE) substrate is around 5.015/cm2 and 4.115/cm2 for F and C atoms, respectively, in the last steps of the simulation. Overall, the F and C atoms are etched out more than they injected into the film. Figure 5-14b) indicates th at the yield is near steady state at around 20%. Therefore the uptake of F and C atoms will not change much over time unde r these conditions but the etch effect still

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126 increasing (Figure 5-15b)). T hus we concluded that for CF3 + ion beam deposition there is more the surface etching than thin-film growth. The ratios of etched carbon, fluorine, and hydr ogen atoms are close to the ideal ratio of 4:5:3, respectively, throughout both sets of si mulations. In other words, in general, the C2F2H2 and C2F3H monomers in the P(VDF-trFE) chains are m odified to an equal extend by the two sets of incident ion beams. This is, no doubt, because of the similarity in structure and configuration of these two monomers. The chemical products that are etched out of the system during deposition are also analyzed. The importance of this analysis is th at the results can be co mpared directly with experimental, mass spectrometry results. Relate d applications are used in the study of surface-induced dissociation (SID ) that is used to resolv e the structures of large (bio)molecules.148 Figure 5-16 shows the density of particles that form fr om incident ions and are etched away from the P(VDF-trFE) surface. In the case of C3F5 + ion-beam deposition, the majority of the etched species are CF2 and C2Fn, while the second most common etched products are C3F5 and F. In the case of CF3 + ion-beam deposition, the major ity of the etched species are CF2 and F, while the second most etched product is CF3. Combining these findings with the knowledge of those products that remain in the surface (Figure 5-11), CF2 is found to be the most commonly formed product during the deposition process of both sets of incident ions. Thus, C3F5 + has a high probability of undergoing dissociation to C2F3+CF2 during the deposition process, while CF3 + also has a high probability of dissociating to CF2+F. These dissociation products are very reactive. Since th ese two ion beams were designed to have th e same F fluence, and CF2 is more likely to scatter away from the

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127 surface than C2F3, C3F5 + ion-beam deposition thus facilitates th e growth of a FC film more than does CF3 + ion-beam deposition. Figure 5-16 also indicates that about 8% of the etched par ticles scatter away from the surface while bonded to fragments of P(VDF-trFE) chains during C3F5 + ion-beam deposition, while the comparable number for CF3 + ion beam deposition is around 19%. Figure 5-17 indicates the particles that scatter out of the surface that are formed purely from P(VDF-trFE) chains. The most common particles generated from the C3F5 + ions are C3(F/H)n, C2(F/H)n and C(F/H)2, while the most common particles generated from the CF3 + ions are C3(F/H)n, C2(F/H)n, C(F/H)2 and F/H. In both cases the P(VDF-trFE) chains are broken into smaller fragments by the ion beam and gain kinetic energy from the ions that allows the small fragments to scatter away. Figure 5-17 also shows that ther e are large particles (that cons ist of more than three carbon atoms) that scatter away from the surface in the case of CF3 + ion-beam deposition, which is not the case for C3F5 + ion-beam deposition. In order for thes e large particles to scatter away, the incident ions must transfer sufficient kinetic en ergy to the surface to facilitate the process. The CF3 + ion is more efficient at this transfer than the C3F5 + ion because of its smaller size, higher velocity, and fewer vibra tional, rotational or tors ional degrees of freedom. Discussion Due to the bond breaking of the P(VDF-trFE) chains caused by the deposition process, an overall reduction of this polymers electromechan ical properties near the surface is predicted. However, the two ion beams are predicted to ultimately affect the P(VDF-trFE) surface in different ways. For example, the C3F5 + ion beam is predicted to pr oduce more FC film precursors and thus facilitate the growth of FC polymer films that could im prove the wear resistance of the P(VDF-trFE) surface. The CF3 + ion beam, on the other hand, might be used to adjust the electromechanical properties of the polymer near the surface because of its deeper penetration.

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128 Alternating the FC ion beams deposited on the surface might thus be used to tailor the electrochemical properties of adj acent thin layers, building in tr ansverse strain and engineering the surface responses. Comparing these results with our previous study of the deposition of these FC ion-beams on polystyrene (PS) surfaces,54 we note that the relative roles of the C3F5 + and CF3 + ion beams are similar. For example, the most common prod ucts that are generated for each ion beam are comparable. This indicates that the chemical reactions that occu r during deposition are dominated more by the incident ions than by the chemical nature of the surface. In contrast, the final depth prof ile and etching behavior are ve ry different in the deposition on these two polymers. For inst ance, the depth profile of C3F5 + ion-beam deposition in the case of the P(VDF-trFE) surface exhibits two peaks as discussed above, while in the case of the PS surface it exhibits one broad peak. The depth profile of CF3 + ion-beam deposition, however, shows similar depth profiles in the case of both polymers. This is indicative of the fact that the modification of the surface as a result of the C3F5 + ion collision is different for each polymer surface, unlike the modification with CF3 +, which is similar regardless of the nature of the polymer surface. Since the PS chains have a relatively large phenyl side group and the P(VDF-trFE) chain does not, duri ng the ion-impact process there is a higher probability of deposition, as opposed to scattering, on the backb one chain in the case of P(VDF-trFE) than in the case of PS. The number of atoms that are etch ed from the surface is al so higher in the case of P(VDF-trFE) than in the case of PS. This is agai n due to the presence of the large phenyl side group in the PS, which is difficult to etch away from the surface even when it is broken off of the backbone chain.

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129 Conclusions The deposition of FC ion beams on the P(VDF-t rFE), copolymer surface is considered here in classical MD simulations. The results indicate that the C3F5 + ion beam facilitates the growth of FC polymer film, while the CF3 + ion beam promotes the etching of the copolymer chains. These findings might be used to facili tate the engineering of the elec tromechanical properties of the copolymer surface.

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130 Table 5-1. Percentage of int act PS chains as a function of de pth following the deposition of the indicated polyatomic ion beams. Depth ()C3F5 +CF3 +C3H5 +CH3 + 0-702500 7-142525250 14-21752510025 21-281001001000 28-35100100100100 Table 5-2. Percentage of int act phenyl rings as a function of depth following the deposition of the indicated polyatomic ion beams. Depth ()C3F5 +CF3 +C3H5 +CH3 + 0-7232795 7-148636415 14-21100609020 21-2810010010032 28-3510010010050 Table 5-3. The number of backbone carbon at oms and phenyl ring carbon atoms from the PS surface that have undergone chemical reactions with the incident ions or their products. Type of C atoms that have reacted C3F5 +CF3 +C3H5 +CH3 + Backbone C atoms 3151150 Phenyl ring C atoms 164653134 Ratio between phenyl ring C atoms and backbone C atoms 5.33.14.82.7 Table 5-4. Percentage of in tact P(VDF-trFE) chains as a function of depth following the deposition of the indicated polyatomic ion beams Depth () 0-4 4-8 8-1212-1616-2020-2424-2828-32 32-36 C3F5 + 25 0 50002575100 100 CF3 + 0 0 00002525 75

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131 Figure 5-1. Snapshot of the pristine PS surface after equilibration and prior to polyatomic ion beam deposition. The dark blue color repr esents carbon atoms in the active region, the light blue color represent hydrogen atom s in the active region, the dark red color represents carbon atoms in the thermostat region, and the light red color represents hydrogen atoms in the thermostat region.

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132 Figure 5-2. Snapshots of the PS surface after de position and equilibration. a) PS surface after C3F5 + ion beam deposition. b) PS surface after CF3 + ion beam deposition. c) PS substrate surface after C3H5 + ion beam deposition. d) PS surface after CH3 + ion beam deposition. In a) and b) the orange color represents F atoms from incident ions, the green color represents C atoms from incident ions, the gray color represents H atoms from PS surface, and the blue and dark bl ue represent C atoms from the phenyl C atoms and backbone C atoms, respectively, in the PS surface. In c) and d) the pink color represents H atoms from incident ions and all other colors represent the same atom types as in a) and b). The dotted red li ne represents the location of the top of the PS surface prior to ion beam deposition. a) b) c) d)

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133 50 40 30 20 10 0 -10 0102030405060 C3F5 + Density of atoms (1020/cm3)Depth(A) F C 50 40 30 20 10 0 -10 0102030405060 CF3 + Density of atoms (1020/cm3)Depth(A) F C 50 40 30 20 10 0 -10 0102030405060 C3H5 +Density of atoms (1020/cm3)Depth(A) H C 50 40 30 20 10 0 -10 0102030405060 CH3 +Density of atoms (1020/cm3)Depth(A) H C Figure 5-3. The depth profiles of carbon, hydrogen, and fluorine atom densities after ion beam deposition and equilibration. The carbon, hydrogen, and fluorine atoms counted here come from the incident ions only, and th e hydrogen and fluorine atoms counted here are atoms that only bond with carbon atoms. The zero point is the original surface plane, and negative depths are indicative of at oms that stay out of the original surface plane. a) The depth profiles of carbo n and fluorine atomic densities after C3F5 + ion beam deposition. b) The depth profiles of carbon and fluorine atomic densities after CF3 + ion beam deposition. c) The depth profiles of carbon and hydrogen atomic densities after C3H5 + ion beam deposition. d) The depth profiles of carbon and hydrogen atomic densities after CH3 + ion beam deposition. a) d) c) b)

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134 CnFmC3F5C3FnC2FnCF4CF3CF2CF0 10 20 30 40 50 60 70 C3F5 +Density(1013/cm2) Bond Unbond CnFmC3F5C3FnC2FnCF4CF3CF2CF0 10 20 30 40 50 60 70 CF3 +Density(1013/cm2) Bond Unbond CnHmC3H5C3HnC2HnCH4CH3CH2CH0 10 20 30 40 50 60 70 C3H5 +Density(1013/cm2) Bond Unbond CnHmC3H5C3HnC2HnCH4CH3CH2CH0 10 20 30 40 50 60 70 CH3 +Density(1013/cm2) Bond Unbond Figure 5-4. The densities of the various chemical pr oducts formed from the polyatomic ions after deposition and equilibration. The figur e shows the density of chemical products formed after a) C3F5 +, b) CF3 +, c) C3H5 +, and d) CH3 + ion beam deposition. a) d) c) b)

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135 CnFmC3F5C3FnC2FnCF4CF3CF2CF0 10 20 30 40 50 C3F5 +Depth(A) Bond Unbond CnFmC3F5C3FnC2FnCF4CF3CF2CF0 10 20 30 40 50 CF3 +Depth(A) Bond Unbond CnHmC3H5C3HnC2HnCH4CH3CH2CH-10 0 10 20 30 40 C3H5 +Depth(A) Bond Unbond CnHmC3H5C3HnC2HnCH4CH3CH2CH0 10 20 30 40 50 CH3 +Depth(A) Bond Unbond Figure 5-5. The penetration depths of the various chemical products formed after a) C3F5 +, b) CF3 +, c) C3H5 +, and d) CH3 + ion beam deposition. The zer o point is the original surface plane, and negative depths are indica tive of chemical products that locate at out of the original surface plane. a) d) c) b)

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136 01002003004005006007008009001000 0.0 0.1 0.2 01002003004005006007008009001000 0.0 0.1 0.2 01002003004005006007008009001000 0.0 0.1 0.2 300032003400360038004000 0.0 0.1 0.2 100012001400160018002000 0.0 0.1 0.2 01002003004005006007008009001000 0.0 0.1 0.2 After C3F5 + ion beam depositionWeight FractionMolecular Weight (g/mole) After CF3 + ion beam deposition After C3H5 + ion beam deposition After CH3 + ion beam deposition Figure 5-6. The distribution of molecular we ights of chemical products in the PS after CH3 +, C3H5 +, CF3 + and C3F5 + ion beam deposition.

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137 3528211470-7 0 20 40 60 3528211470-7 0 20 40 60 3528211470-7 0 20 40 60 3528211470-7 0 20 40 60 Density of Cross-linked Points (1020/cm3)Depth from PS surface (A)C3F5 + CF3 + C3H5 + CH3 + Figure 5-7. The density of cross-linked points as a function of depth in the PS surface after CH3 +, C3H5 +, CF3 + and C3F5 + ion beam deposition. The depth increment in the direction normal to the plane of the surf ace of 7 corresponds to approximately one layer of PS chains. The zero point is the or iginal surface plane, and negative depths are indicative of PS surface swelling.

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138 Figure 5-8. Snapshots of the (a) side view and (b) top view of th e pristine P(VDF-trFE) substrate after equilibration and prior to polyatomic ion beam deposition. Different types of atoms are marked by different colors as shown in the subset. C in active region F in active region H in active region C in thermostat region F in thermostat region H in thermostat region 51.5 21.1 40.0 21.6 38.4 39.3 (a) (b)

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139 Figure 5-9. Snapshots of P(VDF-trFE) surf ace after depositions and equilibration. a) P(VDF-trFE) surface after C3F5 + ion beam deposition. b) P(VDF-trFE) surface after CF3 + ion beam deposition. The incident ions and substrate atoms are marked by different colors as shown in the subset. C from surface F from surface H from surface C from CF3 + ions F from CF3 + ions C from surface F from surface H from surface C from C3F5 + ions F from C3F5 + ions a) b)

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140 40 36 32 28 24 20 16 12 8 4 0 -4 -8 -12 05101520253035404550 C3F5 + Density of atoms (1020/cm3)Depth (angstrom) F atom depth profile C atom depth profile 40 36 32 28 24 20 16 12 8 4 0 -4 -8 -12 05101520253035404550 CF3 + Density of atoms (1020/cm3)Depth (angstrom) F atom depth profile C atom depth profile Figure 5-10. The depth profiles of carbon a nd fluorine atoms after ion beam deposition and equilibration. The carbon and fluorine atom s counted here are from a) incident C3F5 + ions and b) incident CF3 + ions. The origin 0 in vertical axis represents the origin copolymer surface before deposition, negative values correspond to atoms above the original surface, and positive values correspond to atoms that remain in the substrate. CnFmCnFvC3F5C3FnC2FnC F4CF3C F2CF C F F20 10 20 30 40 50 60 70 80 90 C3F5 +Density(1013/cm2) Bond No-bond CnFmCnFvC3F5C3FnC2FnC F4CF3C F2CF C F F20 10 20 30 40 50 60 70 80 90 CF3 + Density(1013/cm2) Bond No-bond Figure 5-11. The densities of the various ch emical products that formed after ion beam deposition and equilibration. Figures shown here are a) after deposition of C3F5 + ions and b) after deposition of CF3 + ions. The products are as follows: CnFm has n > 3 and m > 5, CnFv, has n > 3 and v < 5, C3Fn has n > 0 and n 5, and C2Fn has n > 0. The chemical products counts here are only active atoms in the simulation. The bond means that the chemical product is bond to the substrate atoms. The no-bond represents that the chemical products is simply embedded in the substrate. a) b) a) b)

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141 0100200300400500600700 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 Weight FractionMolecular Weight (g/mol)C3F5 +0100200300400500600700 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 CF3 + Weight FractionMolecular Weight (g/mol) Figure 5-12. The distribution of molecular weights of the chemical products in the P(VDF-trFE) substrate after ion beam depos itions and equilibration. Figures shown here are a) after C3F5 + ion beam deposition and b) after CF3 + ion beam deposition. The molecular weights of chemical products counts here are only active atoms in the simulation. 02468101214161820 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 02468101214161820 1.6 1.7 1.8 1.9 Fluence (x1015 F atoms/cm2)F/C ratioC3F5 +Fluence (x1015 F atoms/cm2) Uptake (x1015/cm2) F_uptake C_uptake 02468101214161820 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 02468101214161820 3.0 3.2 3.4 3.6 3.8 Fluence (X1015 F atoms/cm2)F/C ratioCF3 +Uptake (x 1015/cm2)Fluence (x 1015 F atoms/cm2) F_uptake C_uptake Figure 5-13. The density of fluorin e and carbon atom uptake during a) C3F5 + and b) CF3 + ion beam deposition. The uptake is calculated fr om the incident ions that stay in the substrate in every ion beams. The inset in figure a) and b) shows the ratio between fluorine atom and carbon at om during the deposition. a) b) a) b)

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142 02468101214161820 20 30 40 50 60 70 80 F_yield C_yield Yield (%)Fluence (X1015 F atoms/cm2)C3F5 +02468101214161820 20 30 40 50 60 70 80 F_yield C_yield Yield (%)Fluence (x 1015 F atoms/cm2)CF3 + Figure 5-14. The deposition yield of fluorine and carbon atoms during a) C3F5 + and b) CF3 + ion beam deposition. The yield is calculated from dividing the incident ions that stay in the substrate by total amount of incident ions. 02468101214161820 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 C3F5 + Fluence (x1015 F atoms/cm2)Etch (x1015/cm2) F_etch C_etch H_etch02468101214161820 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 CF3 +Etch (x1015/cm2)Fluence (x 1015 F atoms/cm2) F_etch C_etch H_etch Figure 5-15. The degree of etch of the P(VDF-trFE) surface during the a) C3F5 + and b) CF3 + ion beam deposition. The degree of et ch is calculated by counting how many substrate atoms that escape from the substrate due to the deposition. a) b) a) b)

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143 CnFmCnFvC3F5C3FnC2FnCF4C F3C F2CF C F F20 40 80 120 160 200 240 280 320 C3F5 +Density(1013/cm2) Bond No-bond CnFmCnFvC3F5C3FnC2FnCF4CF3CF2CF C F F20 40 80 120 160 200 240 280 320 CF3 +Density(1013/cm2) Bond No-bond Figure 5-16. The density of chemical products fo rmed from incident ions that leave the surface for a) C3F5 + and b) CF3 + ion beam deposition. The chemical products are as follows: CnFm has n > 3 and m > 5, CnFv has n > 3 and v < 5, C3Fn has n > 0 and n 5, and C2Fn has n > 0. The bond means that the ch emical products leave the substrate with substrate atoms bonded on them. The no-bond represents that th e chemical products leave the substrate without a ny substrate atom bonded on them. Cn(F/ H)mCn(F /H)vC3( F/H)5C3( F /H )nC2(F/ H )nC ( F / H)4C(F/H)3C(F/ H )2C ( F /H ) C F /H ( F /H )20 10 20 30 40 50 60 70 80 90 100 C3F5 +Density(10 13 /cm 2 ) Cn(F/H)mCn(F / H)vC3(F/H )5C3(F /H)nC2(F/ H )nC(F/H)4C(F / H )3C(F/H)2C(F/H ) C F / H (F/H)20 10 20 30 40 50 60 70 80 90 100 CF3 +Density(10 13 /cm 2 ) Figure 5-17. The density of chemical products formed from P(VDF-trFE) chain fragments that leave the surface for a) C3F5 + and b) CF3 + ion beam deposition. The chemical products are as follows: Cn(F/H)m has n > 3 and m > 5, Cn(F/H)v has n > 3 and v < 5, C3(F/H)n has n > 0 and n 5, and C2(F/H)n has n > 0. a) b) a) b)

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144 CHAPTER 6 GENERAL CONCLUSIONS In this dissertation, collision induced chemi cal reactions in the gas or solid state are investigated. By using atomic-scale simula tion methods, detailed reaction processes and mechanisms are explored. The results provide insights regarding reaction mechanisms and predict how these mechanisms influence the formation of thin films or adsorption of small molecules on metal clusters. Both computational and experimental met hods were used to study the mechanism of surface polymerization of terthiophene oligomers by ion-assisted deposition. The combination of the two strategies vastly improves the mechan istic understanding of th e use of SPIAD for the growth of conducting polymer thin films. E xperiments show that polymerization occurs preferentially under a narrow set of ion energy and ion/neutral ratio conditions. DFT-MD simulations predict that the ideal incident energi es should be balanced within a specific range. The higher incident energies l ead to damage or sputter the -terthiophene on the substrate, while lower incident energies do not produce the necess ary polymerization initia tors. This point thus explains why polymerization only occurs under a narrow set of i on energy and ion/neutral ratio conditions found in experiments. In addition, the simulations pred ict that free protons and other radicals are formed during SPIAD that could potentially survive for long enough timescales to contribute in a significa nt manner to the properties of the conducting polymer. This insight can be used to optimize the SPIAD process for polyt hiophene and other conduc ting polymer systems. In the study of methanol adsorption on copper cl usters, the structure of small bare copper clusters and the strength of adso rption of methanol molecules on these clusters are investigated. As the cluster size increases, the dimensions of the bare copper clusters change along with their average bond length, binding energy per bond, an d bond order. These results are explained by

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145 the electronic structures of the clusters. The population of 4s and 4p orbitals exhibit different trends in the twoand three-dimensional clusters. It is also found that even-numbered copper clusters ar e more stable than odd-numbered copper clusters which follows the conventional je llium model. The electron density distributions on bare copper clusters contri bute to a significant degree to methanol adsorption. Low coordination number sites have higher electr on densities and provide more opportunity for electron cloud transfer between copper atoms and molecular oxygen atoms. This makes low coordination sites favorable for adso rption. The complex structure of CunCH3OH compounds prove that the 3d orbital is involved in the interactions. In the studies of chemical modification on pol ymer surfaces, two different aspects of the modification were considered. In the first, th e chemical modifications of PS surface by FCand HC-ion beam deposition are investigated. The amount of resulting modification is influenced by the size of the ions, their veloci ties, and their intra-molecular bond strengths. The intra-molecular bond strength is higher for FC-ions than HC-ions. Thus the HC-ions react more readily with the PS surface than the FC-ions. The simulations pred ict that chemical pr oducts produced by HC-ion beam deposition form more chemical bonds with PS than the products produced by FC-ion beam deposition. Therefore, crossli nk density is higher in the case of HC-ion beam deposition. This study provides a clear understandi ng of how differences between similarly structured FCand HC-ions chemically modify PS surfaces and identif ies mechanisms that are responsible for the observed outcomes. In the modification of fluorinated polymer su rface, the deposition of FC ion beams on the P(VDF-trFE) copolymer surface is consid ered. The results indicate that the C3F5 + ion beam facilitates the growth of FC polymer film, while the CF3 + ion beam promotes the etching of the

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146 copolymer chains. These findings can be used to facilitate the engineering of the electromechanical propertie s of the copolymer surface.

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PAGE 155

155 BIOGRAPHICAL SKETCH Wen-Dung Hsu is a Ph.D. candidate in th e Department of Materials Science and Engineering, University of Florida, Gainesvi lle. He has completed hi s undergraduate from National Sun Yet-Sen University, Taiwan in Physics and Master degree from National Tsing-Hua Univeristy, Taiwan in Mateirals Sc ience and Engineering. Wen-Dung came to the United States in 2002 for pursing higher educatio n. Since then he has been working in the Computational Materials Science Focus Group (CMSFG) with Dr. Su san B. Sinnott. He has been involved in different projects such as computational modeli ng of surface polymerization of polythiophene thin film by ion-assisted deposi tion, methanol adsorp tion and interaction on copper clusters, and chemical modifications of polymer thin films by fluoro/hydro-carbon ion beam depositions. He has developed the fast and parallel computing code for molecular dynamics simulations by using REBO potential, wh ich could simulate systems with millions of atoms. He also developed many useful analysis codes for the simulation of polymer systems. With the knowledge and experience he inculcated so far he is confiden t to make substantial original contribution to the field of material science.


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Title: Computational Modeling of Collision-Induced Chemical Reactions: Gas Phase and Solid-State Reactions Induced by Ionic or Cluster Impacts
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Copyright Date: 2008

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COMPUTATIONAL MODELING OF COLLISION-INDUCED CHEMICAL REACTIONS:
GAS PHASE AND SOLID-STATE REACTIONS INDUCED BY IONIC OR CLUSTER
IMPACTS




















By

WEN-DUNG HSU


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

2007


































2007 Wen-Dung Hsu



























To my parents and to the Computational Focus Materials Science Group (CMSFG) at the
University of Florida









ACKNOWLEDGMENTS

First of all, I would like to acknowledge Prof Susan B. Sinnott with my sincere gratitude.

Her faith and encouragement helped me handle the difficult times in research. I have learnt the

beauty of simulation under her guidance. Her kindness and scientific expertise have made my

graduate career smooth and enabled me to fulfill my research goal. She was a constant source of

inspiration for me. This study would not have been successful without her support and guidance.

Secondly, I would like to extend my special acknowledgement to Prof. Simon R. Phillpot. His

knowledge in the field of simulation is incomparable. His helpful advice and encouragement has

helped me a lot to expand my exposure to the filed of simulation. Thirdly, I would like to

acknowledge Dr. Sanja Tepavcevic and Prof Luke Hanley from Department of Chemistry,

University of Illinois at Chicago. Their supports in experiments make this study more sound and

meaningful. I would also like to thank Prof Hai-Ping Cheng, Prof. Paul H. Holloway, and Prof

Juan C. Nino for their support throughout the research work.

Besides, I would like to express my appreciation to all of the members in the

computational focus group, especially SeongJun Heo, Rakesh Kumar Behera, Taku Watanabe

and Donghwa Lee who have encouraged and supported me during my hard times and have

brought me a lot of fun throughout my graduate study.









TABLE OF CONTENTS

page

A CK N O W LED G M EN T S ................................................................. ........... ............. .....

L IS T O F T A B L E S ............. ..... ............ ............................................. ............... 8

LIST OF FIGURES ................................. .. ..... ..... ................. .9

A B S T R A C T ............ ................... ............................................................ 1 1

CHAPTER

1 INTRODUCTION ............... .......................................................... 13

General Introduction......................... .... ........ .................. 13
Surface Polymerization of Polythiophene Thin Film..................................................13
Growth of Polythiophene Thin Films................................... ...................13
Surface Polymerization by Ion-Assisted Deposition.................................. ................ 14
Adsorption of Methanol Molecule on Copper Clusters.............................. ...............15
Catalytic Process of M ethanol Oxidation......................................................................15
Collision Reaction of Copper Cluster and Methanol Molecule .....................................16
Chemical M modifications of Polymer Surface .............................................. ............... 18
Modifications of Polymer Surface by Plasma Treatment..............................................18
Polyatom ic Ion B eam D positions ......................................................... ............... 19
Computational Modeling of Collision Induced Reactions ............................................. 20

2 SIM U L A TIO N M E TH O D S ......................................................................... ....................24

M olecular D ynam ics Sim ulations............................................................................. ..... 24
Density Functional Theory Molecular Dynamics (DFT-MD) Simulation..........................25
F first P rin ciple C alcu nation s .................................................................. .....................2 5
Thom as-Ferm i theory .............................................. ...... ................. 27
D en sity functional theory .............................................................. .....................2 8
H ohenberg-K ohn theorem s ........................................................... .....................28
K ohn-Sham form ulation................................................. .............................. 29
Exchange-correlation functional ........................................ ......................... 32
Plane-wave implem entation of DFT ........................................ .......................... 32
T he K -point sam pling ............ .... ........................................................ .... .... ... .34
P seu dopotentials ............................................................................... 34
D FT-M D Sim ulation in CA STEP ........................ .. ......................................... ....36
Molecular Dynamics Simulation Using Reactive Empirical Bond Order (REBO)
P o te n tia l ................................................................................ .. 3 7
Reactive Em pirical Bond Order Potential ............................................ ............... 37
L ennard-Jones Potential .......................................... ................... .... .. .. 41
P eriodic B oundary C conditions ............................................................. .....................4 1
Predictor-Corrector A lgorithm .............................................. .............................. 42









Tem perature Control M ethod .................................................... ................................ 43
Acceleration and Parallelization of REBO-MD Code....................................... ...............44
L ink-C ell T echnique.......... ...................................................................... ...... ........ 45
Spatial D ecom position M ethod ............................................... ............................ 46
M massive P arallelization M ethod ........................................................... .....................47
Dynamic Memory Allocation......................................... 48
R results of Parallel Im plem entation ........................................ ........................... 48

3 MECHANISTIC STUDY OF SURFACE POLYMERIZATION OF TERTHIOPHENE
OLIGOMERS BY ION-ASSISTED DEPOSITION................................... ...............55

In tro d u ctio n ...........................................................................................................5 5
Com putational D details ....................... ........................ .... .. ................... 55
Experimental Methods................................ ........ .................... 57
Sim ulation R results ......... ... ...... ............ ...............................................................58
N neutral Sy stem s .................................................................................................58
C charged Sy stem s ....................................................... 6 1
H ybridization A nalysis................................................... 63
Experimental Results ............... .......... .... ........................................... 65
Discussion .................................. ....... ....... .. ...... ... .............68
Mechanisms Supported by Experimental Data and Simulations ..................................68
Differences between Simulations and Experiments................................ .................. 72
C onclu sions.......... ............................... ................................................74

4 STUDY OF METHANOL MOLECULE ADSORPTION ON COPPER CLUSTER...........84

In tro d u ctio n ................... ...................8...................4..........
Computational Details ......................... ....... ....... ... ................... 84
R results and D iscu ssion .................. ................................................................ ........ .. ... 85
Structure of Neutral Copper Clusters .................................................. 85
Collision of Methanol Molecules with Copper Clusters..............................................91
C onclu sions.......... ............................... ................................................96

5 CHEMICAL MODIFICATIONS OF POLYMER SURFACES BY ION BEAM
DEPO SITION S ............................................................... ...... ..... ........ 107

Comparison of Chemical Modifications of Polystyrene Surface by Hydrocarbon and
F luorocarbon Ion B eam s ............................................... .......................... ....................107
In tro du ctio n ...............................................................10 7
C om putational D etails............ ... .......................................................... ......... ........ 108
R results and D iscu ssion .... ... ...................................................... ................................ 109
C onclu sions ................... ......... ....... ....... ....... ................... ................117
Chemical Modification of the Poly(vinylidene fluoride-trifluoroethylene) Copolymer
Surface through Fluorocarbon Ion Beam Deposition ......................................................118
Introduction ................................................................ ..... ..... ......... 118
Com putational D details .................................................. ...... ................ 119
R e su lts ........................................................................12 1



6









D isc u ssio n ................................................................................................................. 1 2 7
C o n c lu sio n s .............................................................................12 9

6 G EN ER A L C O N C LU SIO N S ........................................................................... ...............144

L IST O F R E F E R E N C E S ..................................................................................... ...................147

B IO G R A PH IC A L SK E T C H ............................................................................... ............... ..... 155















































7









LIST OF TABLES


Table page

3-1 Deposition results predicted by the simulations.. ..................................... ............... 75

3-2 Chemical state of the surface carbon atoms........................... ...... .................. 75

3-3 Relative intensities of the M+1 and M+2 peaks from the mass spectra ..........................75

4-1 Comparison of ground-state structure of neutral copper clusters................................97

4-2 Average bond length and mean coordination number of Cun clusters............................97

4-3 Atom ic populations for Cu2-Cu9 ..................................................................... 98

5-1 percentage of intact PS chains as a function of depth........................................................130

5-2 Percentage of intact phenyl rings as a function of depth................................................130

5-3 Number of backbone and phenyl ring carbon atoms ..................................... ........130

5-4 Percentage of intact P(VDF-trFE) chains as a function of depth...................................130









LIST OF FIGURES


Figure page

1-1 Time and length scale of different types of simulation methods.......................................23

2-1 C concept of pseudopotential............................................................. .............................50

2-2 Periodic boundary conditions ................................................. ............................... 50

2-3 Computational time for running one MD step in different size of the systems ...............51

2-4 Spatial decomposition m ethod .............. ..................................... ............... 51

2-5 Force relationships in REBO potential. ........................................ ........................ 52

2-6 M massive parallelization m ethod. ............................................................. .....................52

2-7 Speedup and time for running thousand steps in 1-D parallelization............................53

2-8 Time for running thousand steps and length of neighbor list in 2-D parallelization.......53

2-9 Time for running thousand MD steps in five chosen cases. ............................................54

3-1 Equilibrium simulation model before deposition.. .....................................................76

3-2 Snapshots of the neutral thiophene depositions. ........................................................77

3-3 Molecular weight distribution of chemical products of neutral depositions................. 78

3-4 Snapshots of the charged thiophene depositions ........................................ ...............79

3-5 Molecular weight distribution of chemical products of the charged depositions ............80

3-6 S/Si elem mental ratio from X PS ................................................. .............................. 81

3-7 Mass spectra (MS) of the SPIAD films. ........................................ ........................ 82

3-8 Mass spectra of HT and DT+ SPIAD films. ............. ............... .......... ...............83

4-1 Ground state structures of the neutral copper clusters................... ..................................99

4-2 Average Cu-Cu bond lengths in the clusters............................................................. 100

4-3Binding energies in the copper clusters ...... ............................................. ............... 100

4-4 Binding energies per Cu-Cu bond......................................................... ............... 101

4-5 Bond order of the copper clusters...................... ......... ...................................101









4-6 Relative stability of the copper clusters. ........ ............................................................ 102

4-7 Snapshots of methanol molecule collisions on low-coordination number sites ............103

4-8 Snapshots of methanol molecule collisions on high-coordination sites. .........................103

4-9 Potential energy evolution of adsorption of methanol on the Cu clusters. ......................104

4-10 Cu-O bond length in the copper clusters ................. ... .............. 105

4-11 C-O bond length and O-H bond length in the copper clusters............... ... .................105

4-12 B ending angles in C unC H 3O H ............................................................................ ....... 106

4-13 Binding energy in the copper clusters........................................ .......................... 106

5-1 Snapshot of the pristine PS surface....................................................... ................... 131

5-2 Snapshots of the PS surface after deposition...............................................................132

5-3 Depth profiles of carbon, hydrogen, and fluorine atoms. ...........................................133

5-4 Densities of various chemical products. ........................................ ....... ............... 134

5-5 Penetration depths of the various chemical products................... ................... ................ 135

5-6 Distribution of molecular weights. .......... ......................................... ................. 136

5-7 D density of cross-linked points. ............................................................ ............... 137

5-8 Snapshots of the pristine P(VDF-trFE) substrate........................................................ 138

5-9 Snapshots of P(VDF-trFE) surface after depositions................... ................... ................139

5-10 Depth profiles of carbon and fluorine atoms. ........................................ 140

5-11 Densities of the various chemical products. .............................................. .............140

5-12 Distribution of molecular weights .......... ......................................... ................. 141

5-13 Density of fluorine and carbon atom uptake.............................................................141

5-14 Deposition yield of fluorine and carbon atoms ............... .............. 142

5-15 Degree of etch of the P(VDF-trFE) surface..............................................................142

5-16 Density of chemical products formed from incident ions that leave the surface............143

5-17 Density of chemical products formed from chain fragments that leave the surface........143









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

COMPUTATIONAL MODELING OF COLLISION-INDUCED CHEMICAL REACTIONS:
GAS PHASE AND SOLID-STATE REACTIONS INDUCED BY IONIC OR CLUSTER
IMPACTS

By

Wen-Dung Hsu

May 2007

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

Collision-induced chemical reactions are fundamental for many science and engineering

applications. The mechanisms responsible for the reactions, however, are difficult to detect or

measure directly using experimental methods. Thus atomistic simulations are important and

complementary approaches to experimental techniques that provide insights into the way

systems reach their final states. In these studies, molecular dynamics (MD) simulations are used

to investigate (i) the surface polymerization mechanism associated with the growth of

polythiophene thin films, (ii) the adsorption of methanol molecules on copper clusters of various

sizes and (iii) the chemical modification of polymer substrate surfaces through polyatomic ion

beam deposition.

Mass-selected beams of thiophene ions are deposited on ca-terthiophene oligomers in

experiments, and density functional theory-molecular dynamics (DFT-MD) simulations are

carried out to determine the dominant mechanisms responsible for the surface polymerization by

ion-assisted deposition (SPIAD) process. The experimental results show that polymerization

occurs preferentially under a narrow set of ion energy and ion/neutral ratio conditions. The

DFT-MD simulations illustrate the manner in which ion energies affect polymerization and









reveal how secondary chemical reactions can substantially modify both the thin film and the

substrate.

In the study of methanol-copper cluster interaction, the preferential structures of small copper

clusters Cu, (n = 2-9) and the adsorption of methanol molecules on these clusters are examined

with DFT-MD simulations. The results indicate that low coordination number sites on the copper

clusters are the most favorable for methanol adsorption and have the greatest localization of

electronic charge. The simulations thus predict that charge transfer between the neutral copper

clusters and the incident methanol molecules is a key process by which adsorption is stabilized.

In the studies of chemical modification of polymer surface through polyatomic ion beam

deposition, two main topics are carried out: the effect of continuous hydrocarbon (HC) and

fluorocarbon (FC) ion beam deposition on a polystyrene (PS) surface and the effects of

continuous FC ion beam deposition on a poly(vinylidene fluoride-trifluoroethylene)

[P(VDF-trFE)] surface. In the first topic, the simulations predict that HC ions dissociate more

readily than FC ions during deposition. Consequently, HC ions are predicted to chemically

modify the polystyrene to a greater extent than FC ions. In the second topic, the differences in

the chemical interactions of C3F5+ ions and CF3+ ions with the P(VDF-trFE) surfaces, a

ferroelectric polymer, are explored. The CF3+ ions are predicted to be more effective at

fluorinating the polymer surface and at the same time, the C3F5+ ions are predicted to be more

effective at growing fluorocarbon thin films. The simulations also reveal how the deposition

process might ultimately modify the electromechanical properties of this polymer surface.

In short, the atomic level, computational simulations used in the studies reported here

reveal important details of the relevant reaction mechanisms and provide predictions to help

guide future experimental work.









CHAPTER 1
INTRODUCTION

General Introduction

Collision induced reactions are widely used in materials engineering. For example

collision-induced reactions play an important role in some thin film growth processes. In these

processes, there is a substrate on which deposition will occur, and a target that contains

functional materials that will ultimately be deposited on the substrate. A hyper-thermal energy

such as using plasma, laser beam, or ion beam, among others then acts on the target. Due to the

absorption of the energy, the target materials translate to the substrate surface. Thus, to tailor

specific thin film properties it is important to control the details of how the target material

approaches the substrate and ultimately reacts. Therefore, it is necessary to study collision

induced reactions in various situations, including in the gas phase and solid phase.

In this dissertation, the study of collision induced reactions are focused on three main

topics: (i) Mechanism studies of surface polymerization of polythiophene thin films by

ion-assisted deposition, (ii) Study of methanol molecular adsorption on copper clusters of

various sizes and (iii) Chemical modifications of polymer surfaces by polyatomic ion beam

deposition.

Surface Polymerization of Polythiophene Thin Film

Growth of Polythiophene Thin Films

Conductive polymers, such as polythiophene, have generated considerable interest in

recent years due to their electrical properties, low cost, light weight, and high processability.

These properties have led to a wide range of applications in electronic and optical devices

including light emitting diodes, field effect transistors, photovoltaics, sensor films, recording

materials and rechargeable batteries.1'2 Properties of conducting polymer thin films such as









charge injection, mobility and recombination efficiency, which are essential to the device

performance, depend on the molecular packing, the extent of grain boundaries and roughness of

the interface with the electrodes. Thus optimization of such devices requires the development of

processing methods that can control film chemistry and morphology on the nanoscale.3'4

Typically conductive polymer thin films are grown by direct thermal deposition or

solution-based growth methods. Direct thermal deposition requires either lower molecular

weight oligomers or polymers that can degrade to produce gaseous species. However, while the

oligomers or gaseous species deposit on the substrate surface, the small molecules sublime back

to the chamber due to low molecular weight. Solution-based growth methods such as printing,

casting or spin coating rely on self-assembly of molecules, but the methods suffer from

inadequate or uncontrolled ordering when the film thickness exceeds a few monolayers. It is also

difficult to control the film thickness by solution-based growth method. All these issues make the

growth of high quality, robust, polymer thin film challenging.

Surface Polymerization by Ion-Assisted Deposition

Surface polymerization by ion-assisted deposition (SPIAD),5-9 which deposit

hyper-thermal polyatomic ions and thermal neutrals in vacuum simultaneously, can avoid the

issues mentioned above in the growth of conducting polymer thin films on substrates. SPIAD

can be performed by using both mass-selected and non-mass-selected ions. Since the kinds of

deposited ions are controlled in the mass-selected ion method, it can be used for mechanistic

studies. On the other hand, the non-mass-selected ion method consists of a broad beam ion

source that is suitable for prototype manufacturing processes. The advantage of SPIAD includes

the fact that ion energy, ion structure, ion kinetic energy, neutral structure, the ion/neutral ratio,

and substrate temperature can all be systematically varied to create libraries of candidate films.10

These film libraries can then be used for optimizing morphology, film thickness, electronic









structure, and target properties in various purposes. ''SPIAD, thus, allows fine tuning of film

optical band gaps and other optoelectronic properties by modifying the chemical and

morphological structure of the film. For example, polythiophene and polyphenyl SPIAD films

display narrower band gaps and reduced barriers to hole injection compared with their

evaporated film counterparts.6'9 SPIAD displays other advantages for the deposition of

conducting polymer films, including the absence of entrained solvent molecules and the

utilization of sustainable (green) production strategies.

Previous experimental work on SPIAD investigated mechanisms of the ion-induced

surface polymerization reactions and found that polymerization occurs for specific ion/neutral

ratios and ion energies. Surface polymerization was also shown to form a distribution of

species and not just a single oligomer.6'8 Contrasting experiments with atomic vs. polyatomic

ions showed that the latter behave both as catalyst and reagent by energetically inducing

polymerization and forming adducts with the neutral reagent, respectively.5 Thus utilization of

SPIAD for combinatorial materials preparation relies on a comprehensive understanding of how

these various mechanisms contribute to the overall film formation event; however, such a

mechanistic understanding remains elusive.

Adsorption of Methanol Molecule on Copper Clusters

Catalytic Process of Methanol Oxidation

Methanol is predicted to be an important component for the next generation of renewable

green fuels and recently there has been interest in the use of methanol in fuel-cells.12 It is

produced using transition metal catalysts. Therefore, there is considerable interest in better

understanding the reactivity of surface intermediates during methanol synthesis13-25 to improve

the efficiency of surface reactions and the heterogeneous catalysis process as a whole.









Current experimental studies propose that methanol oxidation to format (HCO2) through

an intermediate, dioxymethylene (H2C02), is a preferred reaction route on the copper surface.23

At 470 490 K, format decomposes to hydrogen and carbon dioxide (CO2).26 Based on this

experimental data, Gomes and co-workers21 propose a reaction path of methanol with oxygen

preadsorbed on the Cu( 11) surface. The methanol molecule is first physisorbed on the metal

surface. Then it reacts with an oxygen atom to form methoxy (CH30) and water. The methoxy

molecule next gives up one hydrogen atom and forms formaldehyde (H2CO) and hydrogen gas.

The formaldehyde molecule reacts with an oxygen atom and forms dioxymethylene, which

decomposes to format plus hydrogen gas. Finally, the format decomposes to hydrogen gas and

carbon dioxide. The whole reaction contains many sub-steps in which hydrogen gas is the main

product. Thus methanol has been applied as fuel in the fuel cells. A possible mechanism for the

oxidation of methanol is summarized as follows:

+30(d,) -H20(g)
2CH3OH(g) 2CH3OH(ad) 2CH3O(d,) +H20(g) +20(ad,) 2H2CO(ad,) +H2(g) +20(ads)
H2(g) H2(g)
4 2H2CO2(ads) 2HCO2(ads) + H2(g) 2CO2 +H2(g)


Mavrikakis and co-workers24 propose other reaction routes for methanol decomposition on

bare Cu( 11). In their proposal, methanol is also physisorbed on the metal surface, which is

follow by the formation of methoxy, formaldehyde, formyl (HCO), carbon monoxide and atomic

hydrogen in order.

Collision Reaction of Copper Cluster and Methanol Molecule

Atomic clusters effectively connect the atomic scale to the macroscopic scale of bulk

crystals and provide an excellent platform from which one can study the heterogeneous catalysis

process on various surface structures. Experimentally, there has been tremendous progress in









recent years in the production and study of clusters.27-31 There have also been numerous

computational studies32-37 that have provided insight into the structure, stability and reactivity of

clusters that is complementary to the experimental data.

The interaction of methanol molecules with metal clusters changes with the size (number

of the constituent atoms) of the cluster, and has been shown to be quite different from their

interaction with metal surfaces. For instance, experiments find that methanol molecules undergo

chemisorption primarily with clusters that consist of six atoms, demethanation occurs mainly

with clusters that consist of four atoms, and carbide formation occurs with clusters that consist of

seven-eight atoms for nickel cluster ions.38 In contrast, in the case of copper cluster ions

chemisorption occurs at clusters that consist of four atoms with a gradual increase above this size,

demethanation at clusters that consist of six atoms, and HOH formation on clusters that consist

of four-five atoms.39 Note that not only the reaction cross section but also the reaction itself

changes dramatically with the size of the cluster. In contrast, physisorption dominates on metal

surfaces.21'40

The dissociation energy of a bare copper cluster is found to oscillate as the size of the

cluster increases.3233 This oscillation behavior is also found in many other metal clusters.41'42 In

general, clusters with the sizes of "magic" numbers have high dissociation energies and are

considered to be stable. In a typical metal cluster, such as an alkali metal cluster (in a liquid-like

state), this oscillatory behavior can be explained by the jellium model.43'44 In this model, the

delocalized valence electrons of the metal cluster interact with a uniform background built by the

positive core ions to form a spheroidal potential well. This leads to discrete electronic levels

(shells) with angular momentum L and degeneracy 2L+1.45 According to the energy levels of

these shells, the clusters with completely filled shells are more stable and harder to dissociate









than those with partially filled shells. Although the jellium model provides good insight into the

characteristics of metal clusters, its application is limited to qualitative discussion. For instance,

in a theoretical study of the reaction of a methanol molecule on a copper cluster, both the

properties of the cluster and the methanol molecules need to be considered.

Experiments on the collision of a methanol molecule with a metal cluster yield the reaction

products, from which one may infer possible reaction paths. However, it is possible to directly

determine only the mass of the products and not their structures from these experiments. In this

regard, theoretical calculations are helpful in understanding the details of the reactions.

Typically, the electronic structures of various rigid isomers are calculated to determine local

minima on the potential energy surface. These theoretical results may then be compared with the

experimental data to determine which cluster isomers actually emerge in the real reactions.46 An

adduct, i.e., an adsorbed methanol molecule on a metal cluster, can be studied by similar

methods. Of course, the behavior of the adduct is diverse and there are many questions that need

to be solved such as, how does the molecule adsorb (adsorption site and geometry), what is the

nature of the bonding between the molecule and the metal cluster, do the properties of the

adsorbed molecule change as the cluster grows, and so forth.

Chemical Modifications of Polymer Surface

Modifications of Polymer Surface by Plasma Treatment

Plasma is typically an ionized gas. Ionized means at least one electron has been dissociated

from atom, molecule or cluster. Thus an oscillating electric field is usually used to generate the

plasma. Particles in an oscillating electric field are easier to ionize. After ionization, they can be

accelerated by an electric field and generate more collision with other particles. This collision

cascade process is the key process to ignite the plasma. In some cases magnetic fields are also

used to increase the collision frequency and thus enhance the probability to ignite the plasma.









Since there are many energetic ions with high translational energy in the plasma, plasma

treatment is usually used in growing functional thin films or modifying substrate surface. For the

growth of functional thin films, usually there is a target containing the functional material and

the target is put in the plasma environment. Parts of the target material then dissociate from the

target by colliding with the ionized particles in the plasma. These dissociated materials

eventually become part of the plasma and deposit on the surface of the substrate. For the surface

modification, the gas which is expected to have special reaction with the substrate surface, such

as fluorination reaction etc., is used to ionize to form the plasma. Then the substrate is exposed to

the plasma to modify the substrate surface.

Plasma treatment has been widely used to modify the properties of polymer surfaces. For

example, FC plasma deposition has been used to grow fluorinated polymer thin films on various

substrates with high thermal and chemical resistance, high dielectric constant, and low friction

coefficients.47-50 Hydrocarbon plasma deposition has also been used to produce thin films with

high hardness.51'52

Polyatomic Ion Beam Depositions

Despite its use in diverse applications, plasma processing suffers from control and

reproducibility problems during practical implementation. This is due to the complex

environment in the plasma. There are many kinds of possible species that are formed in the

plasma and they are very hard to identify individually. It is already known that the effects of

plasma are highly localized to the topmost layers of the substrate surface. Therefore, if the major

species is identified in the plasma, experimentally the polyatomic ion beam with the major

species can be used to mimic the plasma treatment on the substrate surface.

Improving the fundamental understanding of the physical and chemical interaction of

plasma particles with surfaces is critical to the development of strategies to solve these problems.









Experimental studies of mass-selected polyatomic ion beam deposition of a single type of ion,

which can isolate the effects of the various particles that make up the plasma, have been carried

out to provide insight into the physical and chemical interactions of the ions with the target

surface. Molecular dynamics (MD) simulations have been carried out53'54 to establish an atomic

level understanding of the mechanisms by which surface modification occurs in these

experiments.

Computational Modeling of Collision Induced Reactions

Since collision induced reactions involve many complicated processes, such as

determining reaction paths and reaction mechanisms, it is difficult to understand all the details

associated with a reaction by experimental techniques. Computational modeling can provide

many of the details about atomic interaction and/or electronic-structure information that are

complementary to experimental data, and are thus become useful tool to tailor the details of

collision-induced chemical reactions.

Computational modeling in materials science can be classified into four broad categories

according to the time scales and size scales. Figure 1-1 shows the details of the different

simulation methods at various length and time scales. The continuum methods, such as finite

element methods or finite differential methods which solve differential equations like Fick's law,

Fourier's law numerically are excellent for the simulation of length scales that are over a

micrometer and time scales longer than 10-3 second. However, atomic-scale details cannot be

obtained from these methods.

The mesoscale methods, such as phase-field and kinetic Monte Carlo (KMC) methods, are

suitable for length scales that range from around 20 nm to a micrometer and time scales that are

about 10-9 to 10-3 seconds. The phase-field model is a general name for a class of diffuse

interface models used to examine a wide variety of materials phenomenon. It is usually used to









simulate the evolution of interfaces in materials. In phase field models, microstructure-like

compositional or structural domains and interfaces as a whole are described by a set of field

variables. The total free energy of the system can be obtained by the function of field variables,

which reflect the feature of the system. There are two type of field variables, conserved and

nonconserved. Conserved variables have to satisfy the local conservation condition. The

evolution of field variables can be obtained by solving Cahn-Hilliard equation55 and Allen-Cahn

equation56 for conserved field variables and nonconserved field variables, respectively, in a

numerical manner.

The KMC method uses the Monte Carlo approach, which randomly changes the

configuration of the system, judges if the changes are acceptable or not by comparing the total

energies of the initial and final structures at the temperature of interest, and using a special

algorithm, predicts the evolution of the system with time. The two main ingredients in a KMC

simulation are the identification of all of the possible events and the determination of the rates at

which these events can occur. The occurrence of events is the same as in Monte Carlo methods

and depends on the energy of the system. It is usually used to simulate deposition process over

long time scales. The disadvantage of these meso-scale approaches is the loss of atomic detail as

the system evolves. Thus, these methods cannot be used to determine reaction mechanisms.

Atomistic methods, such as the molecular dynamics (MD) and Monte Carlo (MC)

approaches, are used at smaller length and time scales. Typically the length scale is between 1

nm and 20 nm, and the time scale range is 10-15 to 10-9 seconds. This approach can simulate the

system explicitly at the atomic scale. The MD method integrates Newton's equations of motion

to predict the evolution of systems in which time-step is inherently limited to small scales to

satisfy the accurate requirement. However, with the small time step it can capture the details of









atomic vibrations and movements that occur in the systems. Thus the evolution of the systems

can be investigated in atomic detail and the reaction mechanisms, which are the key point

throughout these studies, also can be explored. The MC method, which does not include time as

a variable in the algorithm, can overcome the time-scale limitation that is inherent to the MD

method. It is therefore useful in obtaining the final equilibrium state of the systems.

Electronic-structure methods, such as quantum mechanical, Hatree-Fock and density

functional theory (DFT), which in concept solve the many-body Schr6dinger equation with some


approximations, are also widely used in the field of materials research. They not only provide

atomic-level information but also provide details of the behavior of the electrons in the system.

They are used to provide information about the system's electronic structure, including band gap,

density of states, and optical properties, among others. This is the biggest advantage over all the

methods mentioned before. Because of their accuracy and ability to model a variety of materials

from first principles, these methods can also act as a database provider for the development of

empirical, atomistic methods. The drawbacks of these kinds of methods are larger simulation

time and smaller system size. To date these methods can only simulate systems consisting of

hundreds of atoms, which are too small to study many interesting issues in materials science,

such as large scale surface modification.

It is also noted that there are overlap areas for different levels of simulation methods.

These overlapped regions provide an avenue to test the validity of the parameters for the more

approximate methods in each case. Consistent predictions at the overlapped regions give more

confidence for the simulation methods. This feature allows multi-scale modeling of materials

ranging from electronic to continuum level.











100 Quantum based calculations Continuum
methods -
finite
differential /
10-2 finite element
~10-~2 Empirical force fields finite element


E 10j -

Mesoscale method
.J1 1o-
Phase field / KMC
.-8 FF with
10 MD/MC

H~' = EY
10-10
1019 10 10 1013 1010 107 104 101
time (second)


Figure 1-1. The approximate range of time and length scale over which simulation methods of
different types can operate.









CHAPTER 2
SIMULATION METHODS

Since the goals of this work are to investigate collision induced chemical reactions in the

gas and solid phases, the methods used in the research should be able to accurately and

predictably model the processes that occur during the reactions. This means that the methods

should be able to appropriately describe the changes in the system in response to changes in the

environment.

Molecular Dynamics Simulations

Molecular dynamics (MD) simulations are an atomic level approach. In this approach, the

evolution of atoms with time are done by numerically integrating Newton's equations of motion

in response to the applied forces.5 Thus, MD simulations are one of the ideal methods to study

collision induced reactions at the atomistic level. The results of MD simulations provide the

positions, velocities and accelerations of all the particles in the system as a function of time.

The accuracy of the MD simulation relies on the way in which the forces are evaluated in

Newton's equations of motion. Typically, this is accomplished using empirical inter-atomic

potentials that contain parameters obtained from quantum based methods or experimental data.

In some cases, the forces are calculated using first principles, electronic structure approaches.

First principles start from the Schrodinger equation and use some approximations and theorems

to reduce the complexity of the equation to make it practically solvable. From the approximate

equations the energies and forces can be obtained. These methods are thus expected to describe

the bonding between the atoms with high accuracy and require only the atomic numbers of the

constituents as input. However, they still require significant computational effort and are limited

to system sizes of hundreds of atoms.









On the other hand, the empirical methods that use special-designed empirical mathematical

equations with fitted parameters to describe the interactions between the atoms are considerably

more efficient than first principles methods to use in MD simulations. For example, systems

consisting of billions of atoms can be examined with empirical potentials if the simulations make

use of special computational technique such as parallel computing.

Density Functional Theory Molecular Dynamics (DFT-MD) Simulation

The DFT-MD simulation used in these studies is the classical MD method that treats the

movement of the ions by Newton's equations of motion and obtains the inter-atomic forces from

first principles calculations. This approximation is based on the Born-Oppenheimer

approximation58 that states that, in most cases, the movement of nuclear and electronic can be

decoupled since the nuclei are of the order of 103 times heavier than the electrons and so are

considered to be stationary with respect to the electrons. The procedure of DFT-MD is as

follows: the ground state of the electron orbitals is first calculated. Then the forces on each

nucleus are calculated from the electron-nuclei and nuclei-nuclei interactions in the system. The

forces on each nucleus are used to calculate the position in the next time steps through MD

algorithm. After that the ground state of the electron orbitals in the new position then is

calculated. The procedure iterates for many steps until the system reaches its equilibration. Then

the analysis of the evolution and final structure will be performed to extract the required

information.

First Principle Calculations

Since the systems of interest contain many atoms, it is inevitable to encounter the solving

of the many-body Schrodinger equation. However, the quantum many-body problem cannot be

solved directly.

The time-independent many-body Schrodinger equation is as follows,










(2.1)


where H is the Hamiltonian, Y(r,,r2,.. .~) is the many-body wave-function and Eis total

energy of the system. The system consists of electrons and nuclei and they interact with each

other via Coulombic interactions. Therefore, the Hamiltonian for the system can be written as,

S 2 N 2 iMM ZZ 1 M Ze N N e2
H =Z-I V V + _-- y+
z=_ 2Mz, R, =2m 4+ o R, -R 4~0o 1 -Rj r, -1r

(2.2)

where M and N are the number of nuclei and electrons in the system. Mz,, Z, and R, are the

mass, charge and position of the nuclei respectively for atom i. me, e and r are the mass,

charge and the position of the electrons, respectively. The first two terms in Equation (2.2) are

the kinetic energy of nuclei and electrons. The rest are Coulombic potential energy terms coming

from the nuclei-nuclei repulsion, nuclei-electron attraction, and the electron-electron repulsion

respectively. Due to the complexity of the Hamiltonian shown in Equation (2.2), the exact

wave-function needed to solve Equation (2.1) is unknown. Thus, the goal of the quantum

many-body problem is to solve the many-body Schrodinger equation with some approximations

that can reduce the complexity of the problem but still maintain the physics of the system.

The first approximation is the Born-Oppenheimer approximation58 that decouples the

electrons and nuclei in the Hamiltonian shown in Equation (2.2). Thus the electron-only

Hamiltonian can be written as,

SN 2 N Ze N N 2
H = h Vz2 _+ e (2.3)
Z 2me 4 ZEO r, -e Rjr, -


H T(r, = ET(r,









However, it is still difficult to solve Equation (2.3) since the electron wave-function has

3N variables for a system with N electrons. This is still a large number of degrees of freedom

and there is no way to obtain the exact solution.

Thomas-Fermi theory

The first breakthrough to solve the many-body Hamiltonian was proposed by Thomas and

Fermi59. In their model the electron density is the main variable instead of the electron

wave-function. This will decrease number of degrees of freedom in the Equation (2.3). In their

model, the exact electronic kinetic energy is assumed equal to the kinetic energy of a

non-interacting electron system in a homogeneous electron gas. The nuclus-electron interaction

is assumed the same as the static Coulomb potential and the electron-electron interaction can be

obtained from the classical Coulomb interaction. Thus all terms in Equation (2.3) are simplified

to what is called Thomas-Fermi energy functional. By applying the constraint that the total

number of electrons is conserved and using the method of Lagrange multipliers, the

Thomas-Fermi energy functional yields the Thomas-Fermi equations which can be solved

directly to obtain the ground-state electron density. The Thomas-Fermi equation is as follow:


5Akn(r) /3+ (r)J n(r) dr' -u = 0 (2.4)
3 r-r


where Ak is a constant n(r) is the electron density and /u is the Lagrange multiplier. In

Equation (2.4) the first term comes from the kinetic energy of the non-interacting electrons, the

second term is from the nuclei-electron interaction and the third term is the electron-electron

interaction.

Though Thomas-Fermi theory was the first breakthrough, it did not give correct

predictions in most cases. The most serious problem is it cannot predict bonding between









atoms6 so molecules and solids are not stable using this theory. The reason for this is first it

assumes that the exact kinetic energy is the same as the kinetic energy in the non-interacting

electron system, which leads to a proportional relationship between electron density and kinetic

energy. The other reason is that it over simplifies electron-electron interactions to only classical

Coulomb interactions, and did not consider additional quantum mechanical behavior, such as

exchange interactions, in which the wave-functions of the system should be anti-symmetric,

between electrons.

Dirac61 later developed an approximation for the exchange interaction based on the

homogeneous electron gas. The results, however, did not improve the Thomas-Fermi theory.

Therefore it is concluded that the electron kinetic energy contributes a large portion to the total

system energy.

Density functional theory

As discussed before, Thomas-Fermi theory was the first breakthrough for solving the

many-body problem based on electron density. Though the result was not satisfactory, the

concept of using the electron density instead of wave-functions as main variables motivated the

generation of density-function theory. In 1964, Hohenberg and Kohn62 had shown that this

concept was indeed workable. They proposed two remarkably powerful theorems in which the

electron density is the main variable. This leads to the formally exact groundstate method -

density functional theory (DFT).

Hohenberg-Kohn theorems

The Hohenberg-Kohn theorems are suitable for any system consisting of electrons that

move in response to the external potential. Here, the external potential mainly arises from the

nuclei. The first Hohenberg-Kohn theorems state as: "The external potential, u, (r), and hence









the total energy, is a unique functional of the electron density n(r) ."62 in other words, the

ground-state density determines the external potential uniquely. Thus, both the external potential

and its electron density completely define the Hamiltonian. The energy functional of the system,

therefore, can be written as,


E[n(r)] = n(r)v, (r)dr + F[n(r)] (2.5)


where, F[n(r)] is a universal function which contain all other interactions in the system.


The second Hohenberg-Kohn theorem states that: "The ground-state energy can be

obtained variationally: the density that minimizes the total energy is the exact ground-state

density."62 Since the intention of this section is only to introduce density functional theory, the

details of the mathematical equations used to prove the theorems are not provided here.

Kohn-Sham formulation

Although the Hohenberg-Kohn theorems are extremely powerful, they do not provide a

way of computing the ground state density of a system in a practical manner. Kohn and Sham63

thus proposed a simpler approach to perform DFT calculations. The method is based on

calculating the full interacting system of the real potential by a fictitious non-interacting system

in which the electrons move in an effective Kohn-Shan single-particle potential, v (r).

The ground state energy of a many-electron system can be obtained by minimizing the

energy functional in Equation (2.5) with the constraint of the total number of electrons. This lead

to the Euler equation as follows,

3F[n(r)]
P = n( + (r) (2.6)
8n(r)









where u/ is the Lagrange multiplier. The idea of Kohn and Sham was to set up a system where

the kinetic energy could be determined exactly and any inconsistencies are included in a

correctional term. This is achieved by invoking a non-interacting system of electrons.

The universal functional, F[n(r)], thus is partitioned into three terms,

F[n(r)] = T [n(r)] + EH [n(r)] + Ex [n(r)] (2.7)

Ts [n(r)] is the kinetic energy of a non-interacting electron with electron density of n(r).

EH [n(r)] is the classical electrostatic energy of the electrons and is given by,


EH [n(r)] (r)n(r drdr' (2.8)
2 [ r-r

These two terms are known exactly. E, [n(r)] is the exchange-correlation energy, a

correctional term, which contains the difference between the exact and non-interacting kinetic

energies and also the non-classical contribution to the electron-electron interactions.

In the Kohn-Sham's method the Euler equation in Equation (2.6) becomes,


8n(r)
S n(r) + vKS(r) (2.9)


where, the Kohn-Sham potential, uS (r) is given by,

UKS (r) = vE (r) + H (r) + vXC (r) (2.10)

.E [n(r)] f n(r)
in which uH (r)= nr = n dr and the exchange-correlation potential,
dn(r) -r'


u, (r) = .[n The main point to understand the Kohn-Sham theory is that Equation (2.9)
5n(r)

is only a rearrangement of Equation (2.6). So the density obtained by solving the non-interacting









Kohn-Sham system is the same as the exact groundstate density. Thus the Schrodinger equation

for this system can be decomposed into N one-electron equations shown as,


- +V2 +Ks(r) V (r) =,(r) (2.11)

where, E, are the Lagrange multipliers for one of the orthonormal N single-particle states.

Equation (2.11) is the Kohn-Sham equation and the Vf, (r) are the Kohn-Sham orbitals. This

decomposability of the Schrodinger equation makes the Kohn-Sham theory useful from a

practical point of view, even as it increases the complexity of the system. For example, when the

number of electrons increases, the problem becomes no more difficult, only the number of

single-particle equations to be solved increases. Since UKS (r) contains the exchange-correlation

potential term that depends on the electron density, n(r), as shown in Equation (2.10), the

Kohn-Sham equations must be solved in a self-consistent manner. Thus, the procedure by which

the equations are solved starts from the initial guess of n(r), which leads to the evaluation of

the exchange-correlation potential term in Equation (2.10). The evaluated value is then used to

obtain the new n(r). This procedure is repeated until the self-consistent condition is achieved.

The issue now is how to determine the exchange-correlation functional, E, [n(r)]. An

implicit definition of E, [n(r)] can be obtained through Equation (2.7) and is shown as,

Exc [n(r)] = T[n(r)] Ts[n(r)]+ E, [n(r)]- EH [n(r)] (2.12)

where T[n(r)] and E, [n(r)] are the exact kinetic and electron-electron interaction energies,

respectively. The intention of Kohn-Sham theory is to make the unknown contribution to the

total energy, contained in the exchange-correlation energy term, as small as possible. However,

in many systems the binding energy has about the same value as the exchange-correlation









energy, E, [n(r)]. Thus it is important to choose a good exchange-correlation approximation

for the system of interest.

Exchange-correlation functional

The first exchange-correlation functional, proposed by Hohenberg and Kohn,62 starts from

the evaluation of the homogeneous electron gas system, are therefore valid for systems with

slowly varying electron density. These functionals only include the density but not the gradient

of the density at a given point and are called local density approximation (LDA) functionals.

Since in real systems the electrons are far from being a homogeneous gas, more elaborate

functionals that include the gradient of the electron density, known as the generalized gradient

approximation (GGA),64 have been proposed. The improvement is achieved by taking the

gradient term from the Tayor series expansion of E [n(r)]. Currently there are numerous

sophisticated exchange-correlation functionals available. However, the LDA and GGA are still

the most popular exchange-correlation functionals in the DFT calculations.

Plane-wave implementation of DFT

If one wants to apply the DFT to a solid-state system, the number of electrons is often

prohibitively large; if they are each treated explicitly, the DFT method is effectively impractical.

Fortunately, most solid state systems can be treated as periodic. According to Bloch's theorem,65

the wave function can be described by the product of a lattice periodic component U, (r) and a

plane-wave-like component e" Kr for a periodic system. Thus,

J,,, (r)= U,(r). eK-r (2.13)

in which the plane-wave wave-vector K is unique only up to the first Brillouin zone in

reciprocal space. For a given wave-vector and potential, there are a number of solutions that are

indexed by j in Equation (2.13). Since U, (r) is also a periodic function with the same









periodicity as the system, it can be expressed as a summation of discrete plane-wave basis sets

with wave-vectors G that are reciprocal lattice vectors of the crystal,

Uj (r) = cj,G er (2.14)
G

In Equation (2.14), c, G is the plane-wave coefficient and G is defined by G = 27an in

which m is an integral and C is the lattice vector. Thus the wave-function can be written as,

'j,K (r) = cG e(K+G) (2.15)
G

The advantages of using plane-wave like wave-function is that their form is

mathematically simple, they can offer a complete basis set that is independent of the type of

crystal, and they treat all areas of space equally. Consequently, the method is quite suitable for

solid-state systems with high accuracy and relatively low computational cost. This is in contrast

to orbital-type wave-functions that are dependent on the positions of the nuclei.

Another advantage of using plane-wave type functions is that when they are used, the

Kohn-Sham equations become relatively simple. For example, substituting Equation (2.15) into

Equation (2.11), gives the Kohn-Sham equation in the following form,


SK+G (G G) + (G G) + (G -G) c ,KG = E, (K) c ,K+G (2.16)
G' 2

In this form it is found that the reciprocal space representation of the kinetic energy is diagonal

and the various potentials can be described in terms of their Fourier components. It is thus easier

to solve mathematically.

For an exact calculation, the dimension of the plane-wave basis set should be infinite.

Fortunately the plane-waves of the lower order terms contribute the most to the kinetic energy,

so a practical solution is obtained by truncating the basis set to a finite number of plane-waves.

This is defined by the kinetic energy cutoff,









K + G < E., (2.17)
2E2 (2.7)

Thus the accuracy of the calculation can be improved systematically by increasing the cutoff

energy, Ecu,, which means including higher order terms (more terms) in the plane-wave basis

set.

The K-point sampling

According to the Bloch's theorem, the wave function for a periodic system can be

described by the product of a lattice periodic part U, (r) and a plane-wave like part e"'r. This

allows the calculation to be performed in reciprocal space. The calculation of the expectation

value that requires solving the integral over all of real space can thus be replaced by solving the

integral in reciprocal-space over only the first Brillouin zone. However, the calculation still

needs to integrate over an infinite number ofK points in reciprocal space. Fortunately, electron

wave-functions do not change appreciably over small distances in reciprocal space. Thus the

integration can be replaced by summations over a finite number ofK points. This gives,


JB F(K)dK j-wF(K ) (2.18)


where, F(K) is the Fourier transform of any integral function, such as the electron density or

total energy, Q is the cell volume, and wi is the weighting factor.

The number of K points that is needed to achieve the desired accuracy can be determined

by testing the total energy convergence with increasing number of K points. This procedure is

termed K-point sampling.

Pseudopotentials

The main drawback of plane-waves is that they require a large number of

plane-wave-function to describe large curvature, such as electron density near the core region









atoms. Consequently, the kinetic energy cutoff, E is very high, which leads to the

unaffordable computational costs. This problem is overcome with the pseudopotential

approximation.66

The pseudo-wave-functions replace the rapidly oscillating wave-functions of electrons in

the core region by a smoother wave-function that leads to a weaker pseudopotential compared to

the strong electron-nuclei interaction potentials. In most cases only the valance electrons are

involved in the interactions. Thus, the idea of the pseudopotential is to replace the strongly

oscillating wave-function that is associated with all-electron wave-functions with smoother

wave-functions in the core region. In this way the pseudopotential not only reduces the amount

of time needed for each calculation, but also maintains the accuracy of the calculation. The

pseudo-wave-functions and the all-electron wave-functions are identical outside a chosen cutoff

radius, but do not have the nodal structure that appears in the all-electron wave-function inside

the cutoff radius (Figure 2-167).

To generate pseudopotentials, the all-electron wave-functions need to be determined first.

Thus, initially, all-electron atomic calculations are performed self-consistently. Then the

pseudopotential is built subject to the following four conventional conditions: (i) the valence

pseudo-wave-function must be the same as all-electron wave-function outside a given cutoff

radius, (ii) the charge enclosed within the cutoff radius must be equal for the two

wave-functions, (iii) pseudo-wave-function must not contain any nodes inside the cutoff radius

and must be continuous at cutoff, including the first and second derivatives, (iv) the valence

all-electron and pseudopotential eigenvalues must be equal.

There are two types of pesudopotentials that are currently most popular that are

implemented in the CASTEP68 software. One is the class of norm-conserving pseudopotentials69









and the other is the class of ultrasoft-pseodopotentials.70 Norm-conserving pseudopotentials are

"harder" in the core region compared to the ultrasoft-pseodopotentials. Here the term "harder"

means that in the core region the pseudopotential is very close to the all-electron potential. In

other words, norm-conserving pseudopotentials have larger curvature in the core region than

ultrasoft-pseudopotentials. Therefore, higher kinetic energy cutoffs are needed and the

calculations are computationally more extensive. Ultrasoft-pseudopotentials attain much

smoother (softer) pseudo-wave-functions, so considerably fewer plane-waves are needed for

calculations of the same accuracy.

DFT-MD Simulation in CASTEP

The DFT-MD used in the simulations discussed in Chapters 3 and 4 treats the movement

of the nuclei by Newton's equations of motion and obtains the inter-atomic forces from first

principle calculations. Therefore, in every MD step the self-consistent field (SCF) procedure

needs to be performed in order to obtain the ground-state electronic structure and the forces on

each nucleus. This process, however, takes an extremely long time to finish the required MD

steps needed to equilibrate the system. Therefore, an alternative approach, termed wave-function

and density extrapolation, is used to accelerate the DFT-MD calculation steps, and this approach

is implemented in the CASTEP68 software. The idea is based on the fact that the nuclei actually

only move a short distance in each MD step. Therefore, the wave-functions at time t + dt will

not be too different from the wave-functions at time t. Thus, the initial guess for the

wave-function associate with the next MD step can be achieved by using the multi-linear

extrapolation approach proposed by Arias et al.71 By using this method, improved initial guesses

for wave-functions at each MD step can be obtained. This procedure decreases the number of

iterations in the SCF procedure, which accelerates the DFT-MD calculation.









Molecular Dynamics Simulation Using Reactive Empirical Bond Order (REBO) Potential

In this section, classical MD simulation are discussed, where the MD procedure is the

same as discussed in the last section, but the inter-atomic force calculations are based on an

empirical, reactive empirical bond-order (REBO) potential. The REBO potential was designed to

predict bond breaking and bond reforming according to changes in the environmental. The

method is used in the studies that will be discussed in chapter 5.

Reactive Empirical Bond Order Potential

The bond-order potential was first proposed by Tersoff72 for modeling silicon systems and

Brenner73 further modified it for the more complicated carbon-based systems. Jang and Sinnott54

later extended the parameterization of the second-generation REBO74 for hydrocarbons to

fluorocarbons. It is capable of predicting new bond breaking and bond formation, both of which

are crucial to accurately model the processes that occur in polyatomic ion beam deposition. Since

this class of bond-order potentials were developed, they have been successfully used to obtain

insight into various processes that involve chemical reactions at surfaces, such as

molecule-surface collisions,75-80 cluster-beam surface deposition,81,82 growth of diamond-like

carbon films by hydrocarbon ion beams,83'84 etching of silicon surfaces by fluorocarbon (FC) ion

beams,53'85'86 and the chemical vapor deposition of diamond.87 However, because of the

empirical and classical nature of the REBO potential, electronic effects, such as electronic

excitations or true charging of the atoms, are not included. Therefore, ions with positive charges

are treated as reactive radicals. Charged ions might be expected to react more readily than the

simulated radicals. However, it is also true that many incident ions are quickly neutralized as

they approach the surface. These potentials are thus expected to provide qualitatively correct

results and important insights in the study of collision induced reactions in solid phases.









The expression of the REBO74 potential used to calculate the binding energy (Eb ) between

atoms i and j is:


Eb =ZZ-VR ()- bU V,Ar] (2.19)

where, VR (y) and VA r,) are repulsive and attractive pairwise potentials, respectively,

between atom i and j, which only depend on the distance r, between the two atoms. They

are given as,


VR()=f() 1+- A-e-a. (2.20)
r3


VA,(r,)= j(r) B -*e Pj (2.21)
n=1

where A, B, Q, a, and 3 are two-body parameters determined by the type of interaction. The


function f (r, ) is a cutoff function that limits the range of the covalent interactions to insure

that the interactions include nearest neighbors only and is written as,

1 if r < D"in
r, D mi
1+ cos -
Dmax mm
f =(r) x 2 i if Dmn 0 if r > Dmax




in which Dm"a Dmln defines the distance over which the function varies from one to zero.
U U

In Equation (2.19) the b, is a many-body empirical bond-order term, which is

characteristic of a Tersoff-type potential. A variety of chemical effects that affect the covalent

bond strength are all accounted for in this term, such as the coordination numbers, bond angles,









torsion angles and conjugation effects. This bond-order term can weigh the bond strength

according to the local environment, which allows the REBO potential to model covalent bond

breaking and reforming with associated changes in atomic hybridization. This term is thus

important for the realistic treatment of chemical reactions that involve changes to the bonding to

carbon atoms. The empirical bond-order term is written as a sum of terms:


b= [b- + +b- ]+b (2.23)
" 2 'J 1

where b' and b'" identical forms but swap the i and j indices. These two terms

depend on the local coordination and bond angles for atoms i and j. The term b,"' is given

as,


b," = 1+ Z fC (rk) G(cos(O k)) -R + P ( N)ek 2 (2.24)
k(#i,j)


where, G(cos(Ojk)) is a polynomial function and controls the influence of the nearest neighbors

to the bond order according to the bond angle among atoms i, j and k, and Ayi is a fitting

parameter used to describe three-body transition states around H-atoms. The function 1P is a


correction term that accounts for the different chemistry around atom i. N, and Nf are the

number of neighboring C- and H-atoms of atom i and are given in the following form,

carbon
N, = Zfc(rk) (2.25)
k(#i,j)

Thus the neighboring atom can be counted according to the distance between atom i and k

and the value is ranged from 0 to 1. This ensures that the changing of bond order is

continuous, and Eb is continuous during bond breaking or reforming. The function PJ is not

defined analytically, but the values are determined by cubic spline interpolation with some









predetermined values that are obtained by fitting to the properties (bond energies, bond lengths)

of known solid-state structures or molecules.

The term b, is further written as a sum of two terms:

bV = R + DH (2.26)

where, HRC is the radical term and nDH is the dihedral term. The value of the nRC term

depends on whether a bond between atoms i and j has radical character or is a part of a

conjugated system. This term is given as

nRC Y(Nt Nt Ncoln ) (2.27)

where, Y, is determined by tricubic spline interpolation and N, and N' are the total number

of neighboring atoms around atom i andj respectively. Nconj can be further written as,

carbon carbon
N,"j =I+ for)-YrF(x,) 1 l()F(xJ), (2.28)
Lk( i,j) '1(.I,J)

where x,= N -f,(rk) (2.29)

1 if x k <2
1+cos[2.t(x 2)]

0 if x,k >3

The HDH term depends on the dihedral angle for carbon-carbon bonds which considers

the torsion effect in the molecule and is given as,

HDH _T t Nt N2 (conk ) f (2.31)
n, T(N,, N', N c-l-cos )). ). ) (2.31)
k(#i,j) l(#i,j)









where Ojk is the torsion angle between atom i,j, k and 1. The function T, is determined by

tricubic spline interpolation. The HDH term has values only when the bond between atom i

and j is a double bond and is zero when atoms i and j are not carbon.

Thus, the second generation REBO potential determines atomic bonding configurations

strictly from the local bonding neighbors and non-local conjugation, which influences the

effective interatomic interactions and the rehybridization of atomic orbitals. Therefore, the

second generation REBO potential predicts covalent bond breaking and reforming within a

classical formalism.

Lennard-Jones Potential

The dispersion effect from long-range interactions is modeled using a Lennard-Jones (L-J)

potential88 that is coupled to the short-range REBO potential with a cubic spline function. The

L-J potential used here is the so-called 12-6 L-J potential that is given as,

1 [ 2 Y6
V,( ;)= 4 (2.32)


where a and E are the L-J parameters for particular types of atoms and r, is the interatomic

distance. For the interaction between different types of atoms, a and e, are determined by


rAB = (7A + 7B) (2.33)
2

EAB = CA "* CB (2.34)

Periodic Boundary Conditions

Periodic boundary conditions (PBCs) are used in the simulations to avoid unphysical edge

effect, since the simulation models are substantially smaller than the actual systems. By applying

PBCs, the models can be effectively extended to infinite sizes. The concept of PBCs is shown in









Figure 2-2.57 The system containing N particles is treated as the primitive cell, and the

primitive cell continuously repeats along each of the periodic boundaries. A given particle A in

figure 2-2 will interact with all other particles in this infinite periodic system, that is, all other

particles in the same periodic cell and all the nearest particle images in all other cells. In practical

systems, the interaction distance is limited to a specific range that depends on the potential setup.

Therefore, particle A only interacts with other particles within the cutoff radius.

Predictor-Corrector Algorithm

The evolution of the system is accomplished by Nordsieck predictor-corrector algorithm,

which is one of the higher order algorithms used to carry out MD simulations. The idea of the

predictor-corrector is that the position, velocity, acceleration, and higher order derivatives of

position with respect to time of each particle at time t + At are predicted by a Taylor expansion

based on the previous time step, then the predicted values are corrected by the interatomic forces

calculated from the interatomic potentials. The REBO-MD simulations used in the study are

performed with the forth order predictor-corrector algorithm. The form of the predictor is,


rp (t + At) = r(t)+ v(t) At + a(t).At2 +- b(t) At3
2 6
v ,(t +At)= v(t) +a(t) At + b(t)- At2

ap(t + At) = a(t)+ b(t). At
b p(t+At) = b(t)


where rp, vp, ap and bp are the predicted position, velocity, acceleration and third

derivative of position with respect to time, respectively, of each atom at t + At. Then the

interatomic forces are calculated based on the predicted position of each atom and the corrected

accelerations, ac (t + At), are obtained. The difference between a (t + At) and a (t + At),










Aa(t + At), is the adjustment parameter that is used to correct the predicted values.. Hence, the

position and other derivatives can be corrected by the following equations,


rc(t + At)= rp(t + At) +-Aa(t + At)
6
> > 5 >
VcC (t + At) = v, (t + At) + A a(t + At)
6 (2.36)
a c(t + At) = a p (t + At) + A a(t + At)
bc (t + At) = b p (t + At) + A a(t + At)
3

These corrected values are used to predict the positions and first n derivatives at the next step

of the simulation, and then the same procedure is repeated. The error for an n th order algorithm

is on the order of At". Higher order derivatives can be used to obtain better accuracy, but this

same level of accuracy can also be achieved using smaller time steps.

Temperature Control Method

In the simplest MD simulation, which calculates the system evolution only by Newton's

equations of motion, the entire system is subjected to the conservation of the total number of

atoms, volume and energy (NVE). Therefore, in this MD simulation, the system properties are

measured in the microcanonical (NVE) ensemble. However, in real cases the properties of the

system is measured in the canonical (NVT/NPT) ensembles. In order to bring the simulations

into better agreement with actual conditions, it is necessary to perform the simulations in the

canonical ensemble.

The way to achieve this requirement is through the control of the system temperature.

There are many methods to control system temperature.89-92 In these studies, the Langevin

thermostat is used to control the system temperature. The Langevin thermostat follows the

Langevin equation of motion instead of Newton's equations of motion. In particular, a friction

force that is proportional to the velocity is added to the conservation force that adjusts the kinetic









energy of the particle so that the temperature matches the set temperature. The Langevin

equation of motion93 is expressed as,

m-a=- v+ f(r)+ f (2.37)


where, m is the mass of the particle, a is the acceleration, f(r) is the conservation force


obtained from interatomic potential, v is the velocity of the particle, E is a friction constant


and f is the random force. The friction force v decreases the temperature of the system,

since is set as a positive value. The random force is randomly determined from a Gaussian

distribution to add kinetic energy to the particle. The random force is a function of the set

temperature and time step. Thus, the system temperature is maintained by balancing the friction

force and random force. The advantage of the Langevin thermostat is that it is simple to

implement and able to mimic real situations accurately.

Acceleration and Parallelization of REBO-MD Code

The MD simulations calculate the information of the system (position, velocity, force on

each atom) at the next time by using the integration of Newton's equations of motion. In order to

maintain the accuracy of the simulation, a small time step (on the order of a femto-second) is

required. Using small time steps in the calculations means that the system will evolve very

slowly because 105-106 time steps are needed to reach the equilibrium state or the state that could

be compared to experimental data. Acquiring forces between the atoms makes the software loop

over all the neighbor atoms of each atom. This increases the computational effort needed to find

the neighbor atoms of each atom. Due to these inherent limitations, in some cases it takes an

unreasonably long computational time to finish one simulation trajectory. It is therefore









necessary to develop certain techniques to overcome these limitations and make MD simulation

practical.

Since the algorithm that allows MD simulations to calculate the system evolution cannot

be changed to a significant degree, the small time step cannot be modified. The efficiency of the

force calculation of each atom in every time step, however, can be improved. Traditional

methods that are used to find the neighbor atoms of each atom require looping over all the atoms

in the system. This method turns out to scale as N2 in the calculation, where Nis the number of

atoms in the system. Figure 2-3 shows the computational time can be perfectly fitted by a second

order polynomial function (red line).

Link-Cell Technique

A new approach combines the neighbor list technique, which is a pre-stored array

containing neighbors of each atom, and the link-cell technique to solve the O(N2) problem

within the REBO MD software. The link-cell technique is described as follows: First the system

is divided into several cells to which the system atoms are sorted. The size of the cell is a little

larger than the potential cut-off, beyond which the interactions are neglected. Thus every atom's

neighboring atoms should be within the same cell as itself and the 26 neighbor cells (9 cells in

the upper level, 9 cells in the lower level and 8 cells in the same level). During the determination

of neighbor atoms, the software loops over only the atoms in the same cell and the 26 neighbor

cells. Therefore, the calculation is scaled down to an O(N) calculation, which means that the

calculation time increases linearly with system size. The result of the implementation of

combination of link-cell and neighbor list is shown in figure 2-3 and can be perfectly fitted by a

linear line (shown in blue).









Though the implementation of the link-cell technique can improve the efficiency of the

MD software, there are additional limitations that must be overcome. For example, in a common

machine the memory is large enough to store position, energy, etc. of approximately 100,000

atoms. A 100,000 atom system is around 10x10x10 nm3 and is too small to many systems of

interest. An additional limitation is the long calculation time for each MD step when the system

size is large. To handle larger system sizes, a parallel computing scheme is required.

Spatial Decomposition Method

The idea behind parallel computing is to divide the system into several blocks such that

each block is computed by a processor independently. The information of the whole system is

then obtained through communication among the processors in a parallel computer cluster.

Ideally, the cost of the calculation will be scaled down to the order of 1M where, M is

number of processors used in the calculation. For example, it will take half the time to finish the

simulation when twice as many processors are used for the same system size. This method also

provides the flexibility of using computer memory effectively by storing part of the information

of the system in each node. This allows for the simulation of larger systems that are more

complex and can be more readily compared to experimental data.

As part of this dissertation, the scalar form of the REBO-MD software was parallelized

using the spatial decomposition method, which can theoretically run efficiently over thousands

of processors. The idea behind the spatial decomposition method is to divide the system into

different cells spatially corresponding to the number of nodes that is used in the calculation.

Figure 2-4 shows the schematic representation of the spatial decomposition in one dimension and

two dimensions that is implemented in the parallel REBO-MD code.









The main issue in the parallelization is to deal with the inter-atomic forces near the node

boundaries. For example, as discussed above, the REBO potential is a many body potential.

Therefore, the forces acting on atom i come from not only the nearest neighbors, j and k,

but also the second neighbors, m and /,and third neighbors, n shown in figure 2-5. If those

atoms are to stay on different nodes, then the information on the neighbor atoms is not complete

on each node. Consequently, some forces will be missed during the calculation. To overcome

this problem, every node is assigned a buffer layer that includes neighboring atoms to that node,

so that during the calculation all the forces can be evaluated. Then the collected forces in the

buffer layer are passed to the neighboring nodes and summed for the corresponding atoms. In

this way all the forces on each atom can be obtained and the total force for each atom can be

calculated correctly.

Massive Parallelization Method

MD simulations allow each atom to move in response to the forces acting on them, so

during the evolution of the system, atoms may move across the node boundary to the

neighboring nodes. In this situation, it is necessary to pass the atom's information, including

position, velocity, acceleration, n derivative, and index number, to the neighboring nodes.

Also, as discussed above for spatial decomposition, it is necessary to pass the forces of the buffer

layer atoms to the neighbor nodes in each MD step. Therefore, passing information is

unavoidable in parallel MD simulations. The data transfer rate, however, is limited by the

hardware of the computer cluster. Consequently, preventing unnecessary communication among

the nodes is key to boosting the efficiency of MD simulations.

The passing method implemented in the parallelized REBO-MD software allows each

node to only communicate with its neighboring nodes, instead of global communication where









each node communicates with the master node sequentially. The local communication thus will

not increase the extent of communication when the number of nodes increases.

Figure 2-6 shows a schematic of how the massive parallelization method works. In every

passing step, all the even nodes pass information to odd nodes and then odd nodes pass

information to even nodes. The process repeats in two directions for one-dimensional spatial

decomposition and eight directions for two-dimensional spatial decomposition in the current

implementation.

Dynamic Memory Allocation

Since the parallelized software will be used for various system sizes, to enhance the

convenience of usage dynamic memory allocation is used to allocate the size of the arrays that

are used to store and pass information about the atoms. The advantages of dynamic memory

allocation are not only convenience in use but also the array size is adjusted automatically

according to the system size (number of atoms in the system). Therefore the array size will not

be too large for the computer to locate the variable address in the memory slots and maintains the

efficiency of the simulation.

Results of Parallel Implementation

Figure 2-7 shows an efficiency test of one-dimensional parallelization implementation. The

test was performed by relaxing a 10,000 atom carbon nanotube. The parallel implementation in

this case is efficient up to 16 processors. The real time for calculating 1000 MD steps is reduced

from 400 seconds to 54 seconds, and the total speedup is 7.4 times faster than serial code.

Figure 2-8 shows the efficiency test of two-dimensional parallelization implementation.

The test was performed by relaxing the alpha-phase of isotactic polypropylene of various system

sizes. The real time for calculating the 1000 MD steps was measured. The algorithm of

parallelization was also tested by measuring the length of the L-J neighbor list. In figure 2-8, the









length of the L-J neighbor list is shown by open symbols. The curves illustrate how the length

decreases linearly as both axes are plotted on a logarithm scale and the curve's slope is close to

-1. This result proves that the parallelization algorithm is correct. The real time of the calculation

(solid symbols shown in figure 2-8) ideally should follow this curve closely. In our results, the

time for 1000 MD steps follows the curve but it shows little deviation when the number of

processors is large. Thus, in general, the two-dimensional, parallel implementation is able to

model systems consisting of millions of atoms.

Implementation is more clear if the number of atoms per node versus calculation time for

1000 MD steps is plotted. In figure 2-9, different combinations of system size and number of

processors used was chosen so that the number of atoms per node is constant. For example, a

system of 15552 atoms with one processor, 62208 atoms with four processors, 248832 atoms

with 16 processors, 559872 atoms with 36 processors, and 995328 atoms with 64 processors

were chosen such that all have 15552 atoms per node. The calculation time should be the same in

these five cases. Figure 2-9, however, shows that the calculation time increases as the system

size increases. The problem may come from the global communication that occurs to calculate

the properties of the entire system during the simulation and the large arrays used in the larger

systems. To solve this problem it will be necessary to check the time spent on passing

information and decrease the number of large arrays used for larger systems.




































Figure 2-1. Schematic illustration of the concept of pseudopotential. The solid lines represent
the all-electron wavefunnction, Y, and the associate all-electron potential, Z/r.
The dashed lines represent the pseudo wavefunnction, pseudo and the associate
pseodopoetntial, Vpeudo,


Figure 2-2. Schematic representation of periodic boundary













1.4-
1.3-
0
o 1.2-
1.1
E 1.0-
S0.9-
0 0.8-
S0.7-
c- 0.6-
O 0.5-
0.4-
0.3-
0.2
3000 4000 5000 6000 7000 8000 9000
Number of atoms



Figure 2-3. The computational time for running one MD step in different size of the systems.
The open symbol represents the code contains only neighbor list technique and the
solid symbol shows that the code which combine the link-cell technique and neighbor
list technique. The red line is fitted by the second order polynomial function. The blue
line is fitted by a linear function.


Node #3


Node #4


Figure 2-4. Schematic representation of spatial decomposition method. a) one-dimensional
decomposition and b) two-dimensional decomposition









m


Figure 2-5. Schematic representation of the force relationships in REBO potential. The circles
mean the cutoff radius for the first neighbors for the center atom.

a)















b) I I I I


Figure 2-6. Schematic representation of the massive parallelization method in a)
two-dimensional spatial decomposition and b) one-dimensional spatial
decomposition.

















450


400
0
8 350

300
(n
2 250
0
0
200

c 150


, 100
0)
E
50


0 2 4 6 8 10 12 14 16 18 20


7


6
V)
(D
5 D
C0

4


3


2

1


0
22


Number of processors




Figure 2-7. Time for running 1000 MD steps and speedup vs. number of processors in

one-dimensional parallelization.








S10 3

v4 i0


v


a,



o
S10
L

a,
E


10
Number of Processors


0

0
-h



106

I-
C-



10"
U)


---15552
-o-62208
248832
-v-559872
995328
-<-1555170


Figure 2-8. The time for running 1000 MD steps (solid symbol) and the length of

Lennard-Jones neighbor list (open symbol) by using various numbers of processors in

different sizes of the systems.


*i


d















S2000

C 1800

a 1600


o
o 1400
1200
0

E 1000

800

600

4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64
Number of Processors



Figure 2-9. The time for running 1000 MD steps in five chosen cases.









CHAPTER 3
MECHANISTIC STUDY OF SURFACE POLYMERIZATION OF TERTHIOPHENE
OLIGOMERS BY ION-ASSISTED DEPOSITION

Introduction

This chapter focuses on surface polymerization mechanisms in ion-assisted deposition

processes. The study is carried out using both experimental and computational methods. The

experiments described here utilize a mass-selected beam of thiophene ions to remove fragment

ions, radicals, and protons (all present in non-mass-selected ion sources) that can contribute to

the film growth process and thereby complicate mechanistic studies of the polymerization event.

They were carried out by Dr. Sanja Tepavcevic and Prof Luke Hanley at Department of

Chemistry, University of Illinois at Chicago. Mass-selected SPIAD experiments are readily

modeled by computer simulations that allow detailed elucidation of mechanistic aspects.

Therefore, DFT-MD simulations are also applied to examine energetic thiophene molecular

deposition on 3T thiophene oligomers. These simulations provide key insights into the complex,

cross-link forming chemical reactions that occur during SPIAD. Comparison of experiments and

computer simulations is a powerful strategy in understanding ion-induced surface processes.9497

Computational Details

The DFT-MD simulations described here are performed using the CASTEP software67'98

with the generalized gradient approximation (GGA-PW91). The core electrons are represented

by ultrasoft pseudopotentials and the valence electrons are described with plane waves that have

a kinetic energy cutoff of 240 eV, and the k-point meshes used in the calculation is 1 x 1 x2. The

convergence of total energy was tested with respective to kinetic energy cutoffs up to 310 eV and

k-point meshes up to 1 x2x2. The results show that the difference in total energy between the

conditions used in the study and the more computationally intensive conditions is within 0.08









eV/atom. This indicates that the conditions used in the DFT-MD simulations represent a good

balance between computational efficiency and accuracy.

The simulation system consists of a supercell that is 13.3 A x 15.4 A x 25 A and contains

three layers of hydrogen-terminated Si (111) covered on one side by a 3T thin film that consists

of four 3T oligomers, two of which are arranged parallel to one another and 3.2 A from the Si

surface, while the other two oligomers are arranged parallel to each other but perpendicular to

the first two. The total number of atoms in the film and substrate is 220 atoms and the setup is

shown in Figure 3-la). The distance between the oligomers in the film is about 3.2 A. The

system is allowed to equilibrate for 200 fs prior to thiophene molecule deposition and the

simulations evolve for about 240 fs/collision event. The NVT ensemble is used in all the

simulations to maintain the system temperature at 300 K and the simulation timestep is 1 fs. This

system configuration mimics the experimental system in which the oligomers are physisorbed on

the silicon surface in random arrangements while at the same time maximizing the contact area

in the relatively small supercell necessitated by the high computational cost associated with the

DFT-MD simulations. Importantly, the simulations should be able to model localized chemical

reactions that occur when ions or neutral molecules collide with the oligomers at locations close

to the substrate surface.

The thiophene incident energies considered in the simulations are 100, 200, 250, and 500

eV/molecule. In the case of the three lowest deposition energies, the effect of charge on the

deposition process is investigated. In particular, both systems that have a +1 charge and that are

neutral are considered. The DFT approach smears the charge throughout the system rather than

localizing it on the incident molecules. However, as the simulations represent only a localized

portion of the actual experimental system over short (nanosecond) time scales, the comparison of









neutral and charged systems is still indicative of what occurs in parts of the experimental system,

especially as the incident molecules approach the surface and are increasingly likely to share

charge with it. The simulations consider the deposition of a single thiophene particle at each

incident energy, except for the 250 eV/molecule deposition case, where two thiophene particles

are deposited to investigate the effects associated with higher fluences.

In all the simulations, the molecules or ions are deposited at the points where the 3T

oligomers cross each other (see Figure 3-lb)) to maximize opportunities for crosslink formation.

This choice ensures that the most energetic phenomena in the SPIAD process will be

investigated in the simulations and shed light on the most complex aspects of polymerization.

Since there are four crossed sites in the model and each of them is slightly different in 3T

oligomer orientation (the thiophene rings tilt to slightly different degrees and in different

directions), in some cases the thiophene molecule or ion is deposited on site #1 in Figure 3-1b),

while in other cases it is deposited on site #2 in Figure 3-1b). Specifically, site #1 is chosen in

the 100 eV deposition case and in the first deposition event at 250 eV for the neutral system,

while site #2 is chosen in the 200 eV deposition case, the first deposition event at 250 eV in the

case of charged-system, the second deposition event at 250 eV for the neutral system, and at 500

eV. The chemical reactions that occur on deposition are then documented and analyzed.

Experimental Methods

SPIAD is performing by combining deposition of thiophene ions with simultaneous dosing of

3T vapor under vacuum. The vacuum apparatus used to perform SPIAD and x-ray photoelectron

spectra (XPS) analysis is only briefly described here.8'99 The apparatus consists of a differentially

pumped ion source, a preparation chamber and analysis chamber. Thiophene (99+%, Aldrich

Chemical Co.) was used as the ion precursor. For the isotopic experiment we used deuterated

thiophene (D4, 97%, Chambridge Isotope Laboratories Inc). Mass-selected beams of C4H4S









(thiophene) ions are produced by electron impact. Terthiophene crystals (2,2':5,2"-Terthiophene,

99%, Aldrich Chemical Co.) are used as received. Terthiophene dosing is accomplished with a

resistively heated homemade source mounted on the preparation chamber whose beam is

incident on the surface during ion bombardment. Different ion/neutral ratios are utilized for ion

energies in the range of 50 200 eV by changing the fluence of neutrals (1 6x 1017neutrals/cm2)

or ions (2 4x1015 ions/cm2). Silicon wafers are used as substrates for deposition, after etching

with 5% HF to produce the hydrogen terminated surface H-Si (100) with a minimum of oxide.

The HF-etched Si surfaces prior to deposition display an elemental content of 10% C, 4% O and

86% Si, as recorded by monochromatic XPS. All XPS of the clean substrates and SPIAD films

are recorded at 44 eV pass energy and normal take-off angle without air exposure following

deposition, as previously described.8'99 SPIAD films are also deposited onto a photopatterned

silicon wafer on which a nanostructured oxide layer has been formed (Mass Consortium Corp.)

for desorption ionization with 337 nm nitrogen laser radiation followed by mass spectral analysis

in a reflection time-of-flight instrument (Voyager-DE PRO 6275, Applied Biosystems).6

Simulation Results

Neutral Systems

Figure 3-2 shows snapshots from the five deposition events considered in the DFT-MD

simulations of the neutral systems, where the incident energy ranges from 100 to 500 eV. The

molecular weight distribution of the chemical products that are generated after these deposition

events are shown in Figure 3-3. As expected, the higher the deposition energy, the greater the

damage to both the incident molecule and the 3T oligomer thin film. In the 100 eV deposition

event, shown in Figure 3-2a), the incident thiophene molecule breaks into two small fragments

(C2H2 and C2H2S) during impact, which chemically modifies only the impacted 3T oligomer.









The resulting chemical products (illustrated in Figure 3-3a)) are formed through bonding

between these fragments and collision induced decomposition of the impacted 3T oligomer to

form a product such as C4H3S2.100 There are also two C2H2 fragments that form, one from the

incident thiophene and the other from the impacted 3T oligomer.

In the 200 eV deposition event, illustrated in Figure 3-2b), however, the incident molecule

breaks into five small fragments (2CH, CH2, C, S) during impact, breaks apart a thiophene ring

within the first layer of the 3T oligomer thin film, and modifies the oligomer chains in the film's

second layer. Polymerization occurs between two 3T oligomers in the bottom layer through

interactions with the collision fragment C3H3, which is generated from an incident thiophene

fragment (CH) and an impacted 3T oligomer fragment (C2H2). The 3T oligomer which adjacent

to the impacted 3T oligomer also undergoes chemical modification, where one H atom is

replaced by CS, where the C atom is from the incident molecule and the S atom is knocked loose

from the impacted thiophene ring. Other chemical products, such as [T][TC] and C2H2, are

formed as a result of bonding between fragments from incident molecules and fragments from

the collision induced decomposition of the 3T oligomer (see Figure 3-3b)).

The first 250 eV event is somewhat similar to the 200 eV deposition event in that the

simulation predicts that the impacting thiophene molecule breaks into six small fragments of

three CH, C, S and H on impact, and breaks the impacted thiophene ring of the 3T oligomer (see

Figure 3-2c)). The incident energy is high enough that the fragments generated by the impact

scatter and modify the oligomers beside and beneath the oligomer at which the initial collision

occurs. Consequently, polymerization is predicted to occur through bonding between the

oligomers beside and beneath the impact site through a (CH)S(CH) fragment, in which the CH

are from the incident molecule and the S is from the impacted thiophene ring. The polymerized









chemical product, [2T][TS][3T]C4H4S2, is also found to form bonds with the Si substrate. Other

chemical products, [3T]C3H3 and [T]C5H3S, are formed by adding 3T oligomer fragments and

incident molecule fragments. Overall, there are two intact 3T oligomers that remain unchanged

following deposition. The majority of the chemical products produced are trapped between the

top and bottom 3T oligomer layers. The molecular weight distribution of these products is

summarized in Figure 3-3c).

A second 250 eV deposition event is performed on the system modified by this first event

that targets a different location on the surface, as shown in Figure 3-2d). This chemically

modifies the targeted oligomer, which polymerized during the course of first deposition event,

and the oligomer beneath it. Thus over the course of these two deposition events, every 3T

oligomer on the surface is chemically modified and fragmentized. Some of the chemical

products, such as [2T][TS][T]2C12HsS6 and C13H11S, evolve from the products formed in the first

collision event, while others, such as C2H and H, are formed from the bonding of small incident

molecule fragments and 3T oligomer fragments. Because of the large extent of modifications of

the 3T oligomers in the film following these two deposition events, simple surface

polymerization between two 3T oligomers is no longer present. Instead, large fragments bond to

one another to create a new chemical product, such as [2T][TS][T]2C12HsS6, with a larger overall

molecular weight. Again, most of the energetic fragments that are produced are ultimately

trapped between the top and bottom oligomer layers. A detailed summary of the chemical

products that are formed after the second deposition event is given in Figure 3-3d).

In the 500 eV deposition event, illustrated in Figure 3-2e), the incident thiophene molecule

breaks into individual atoms or CH fragments when it collides with the surface. The impacted

thiophene ring is also broken into individual atoms of 3C, 3H and S. These products and incident









molecule fragments then collide with the bottom layer of oligomers and break them apart

because of their high kinetic energy. Additionally, some of the fragments form chemical bonds

with the Si substrate by the end of the simulation. In other words, a small collision cascade is

predicted to occur and most of the energetic fragments that are produced are trapped between the

Si surface and the bottom layer of the 3T oligomer thin film or form covalent bonds to the Si

substrate. The chemical products are much smaller than the products produced at the lower

incident energies, as shown in Figure 3-3e), and there are only two 3T oligomers that remain

intact after the deposition process is complete.

Table 3-1 provides a statistical analysis of the chemical products predicted from the

simulations. As expected, the total number of chemical products varies substantially with

deposition energy. In addition, the percentage of chemical products that are covalently bonded to

the underlying Si substrate increases as the deposition energy increases. The percentage of intact

3T oligomer thiophene rings also decreases as the deposition energy increases until 250 eV, after

which this percentage remains essentially unchanged. Furthermore, increasing the number of

deposited thiophene molecules further decreases the percentage of intact 3T oligomer thiophene

rings. Lastly, surface polymerization between 3T oligomers is predicted to occur at incident

energies of 200 and 250 eV.

Charged Systems

Table 3-1 also lists the results of statistical analysis of the chemical products that are

produced in the charged systems. It indicates that the differences in the collision outcomes

between the neutral events and positively charged events are small in most cases. However, a

careful comparison of the forces and velocity variations of the atoms in the system (data not

shown) indicate that the atoms in the +1 charged system experience slightly larger forces and

velocity variations than the atoms in the neutral system. The results further indicate that the









system with the +1 charge makes the potential well between the atoms slightly deeper than in the

case of the neutral system.

In the case of the 100 eV deposition event, the results and mechanisms for the neutral and

charged systems are very similar. The deposited thiophene ion breaks into C3H3 and CHS

fragments during the initial collision. The incident energy is only sufficient enough to modify the

impacted 3T oligomer. Thus, there are two intact 3T oligomers that remain following deposition,

and one 3T oligomer that is beneath the impacted 3T oligomer and has been slightly modified

through the adsorption of a S atom from the impacted thiophene ring. Other chemical products

include a large fragment from the collision induced decomposition of a 3T oligomer, such as

[2T]C2H, and a ring shape molecule (C6H6S) formed from bonding of the incident thiophene

fragments (C4H4S) and a fragment of an impacted 3T oligomer (C2H2). A snapshot of the system

following deposition is shown in Figure 3-4a) and the chemical products are summarized in

Figure 3-5a).

In the case of 200 eV deposition, illustrated in Figure 3-4b), the incident ion breaks into

four fragments, 3CH and CHS, during impact. The 3T oligomer that had a H atom be replaced by

a CS fragment in the neutral case now remains intact. Other chemical products, [3T]C3H2S,

[3T]C3H4, are formed from bonding between the incident molecule fragments and 3T oligomers.

Chemical products, such as [T][TC] and CS, are formed from bonding of 3T oligomer fragments

and thiophene ion fragments (see Figure 3-5b)). There are two major differences between the

neutral and charged cases. The first is that there is a chemical product, [3T]C3H2S, that forms a

bond with the Si substrate in the charged case. In the neutral case, the same fragment, C2H, from

the impacted thiophene ring that forms the [3T]C3H2S bond to the Si substrate is instead bonded

to a H-terminated atom from the Si substrate to produce HCCH. The second is that there is no









surface polymerization observed in the charged case but there is in the neutral case. Additionally,

in the case of the charged system, the fragment that contributes to surface polymerization in the

neutral system instead bonds to a hydrogen atom that is knocked out of the incident thiophene

molecule. This prevents the fragment from forming a bond to another 3T oligomer to polymerize

the film. These differences illustrate how scattered hydrogen atoms can restrain surface

polymerization even when the deposition energy is high enough to trigger the process.

In the case of the 250 eV deposition event (Figure 3-4c)), the incident thiophene ion breaks

into six small fragments (three CH, C, S and H) on impact and breaks a thiophene ring on the

targeted 3T oligomer. Although the target site is different from the target site in the neutral case

(the impacted thiophene ring tilts around 300 towards to Si substrate in this case, while the

impacted thiophene ring tilts only about 10 towards to Si substrate in the neutral case), the same

polymerization mechanism is predicted to occur in both cases. In particular, polymerization

occurs through bonding of the oligomers next to and beneath the impacted oligomer by CS(CH)

fragments, where C and CH are from the incident molecule or ion, and S is from impacted

thiophene ring. This result indicates that the DFT-MD simulations are able to capture the key

mechanisms that contribute to the complicated surface polymerization phenomenon in

ion-assisted deposition. Other chemical products ([T]C5H3S and C3H3) are formed by adding 3T

oligomer fragments and incident ion fragments, and the results are shown in Figure 3-5c). It is

also predicted that some of the products are covalently bonded to the underlying Si substrate and,

overall, there are two intact 3T oligomers that remain unmodified following deposition.

Hybridization Analysis

Examination of the change in the number of sp2-hybridized carbon atoms is another way to

characterize the extent of system chemical modification as a result of deposition. Prior to

deposition all the carbon atoms in the 3T oligomers and incident thiophene molecule are









sp2-hybridized. When the incident thiophene impacts the 3T oligomer, the hybridization of the

carbon atoms change if they are involved in chemical reactions. Transition state carbon atoms,

with temporarily more than four neighbors, are also monitored. Similar transition state hydrogen

and sulfur atoms are also observed in the simulations. The percentages of transition state carbon

atoms that are generated immediately following the thiophene molecule collision range from 4%

in the cases of 100 eV/molecule collisions to 17% in the case of the 500 eV/molecule collision.

Following the initial collision, the transition state atoms move away from the impact side and

modify the 3T oligomers, simultaneously transforming to more stable hybridization states. Most

of the transition-state atoms finish reacting within 30 fs of each collision. In addition, a small

number (< 4%) of new transition state atoms is generated during the equilibration process as part

of additional atomic rearrangements. Importantly, all the transition state atoms have completely

reacted by the end of the equilibration process that follows deposition and are ultimately part of

the chemical products discussed above.

Table 3-2 provides details of the hybridization states and transition states of carbon atoms

in the simulations. The number of transition state atoms is summed from each MD step. The

hybridization states are obtained from the final equilibration. It is found that the sum of the

transition state atoms increases as the deposition energy increase but decreases at the highest 500

eV incident energy. This is because in the 500 eV deposition event the incident energy is high

enough for the fragments to scatter over a large fraction of the supercell and to penetrate into the

Si substarte. Thus the incident energy dissipates more efficiently, which restrains the transition

state atoms from regenerating during equilibration. In the case of the 200 and 250 eV deposition

events, the fragments are generally trapped between the upper layer 3T oligomers and bottom

layer 3T oligomers. Thus, although the transition state atoms are fewer than in the 500 eV









deposition event immediately following impact, more transition state atoms on the whole are

formed at 200 and 250 eV. The number of transition state carbon atoms is slightly smaller in the

neutral case than in the charged case for 100 and 200 eV, while the opposite is true for 250 eV.

In general, after deposition the amount of sp2-hybridization decreases as the deposition

energy increases, which indicates the greater degree of modification of the 3T oligomers at

higher energies. Comparing the neutral and charged system results, Table 3-2 indicates that the

charged systems have less sp-hybridization than the neutral systems. In other words, carbon

atoms in charged systems generally have more neighboring atoms than neutral systems after

equilibration is complete. The result is consistent with the finding that the potential well between

the atoms in the charged-system is slightly deeper than in the neutral system. Thus, carbon atoms

more readily attract and bond to neighboring atoms in charged systems, which results to higher

degrees of hybridization.

Experimental Results

In conjunction with these simulations, experimental SPIAD is performed by combining the

deposition of thiophene ions with the simultaneous dosing of 3T vapor. The vacuum apparatus

and conditions used to perform SPIAD and XPS analysis are similar to those used in previous

studies.8'99 The incident ion energy and the ion/neutral ratio are correlated parameters for

efficient ion-induced surface polymerization. Therefore, experiments are performed in which the

ion energy is varied from 25 to 200 eV and the ion/neutral ratio is varied from 1/50 1/900. The

extent of polymerization is determined from XPS by measuring the S/Si ratio, which increases as

an organic film is formed on the Si substrate from the thiophenic species.

By varying the ion/neutral ratio at a constant ion energy of 200 eV, it is determined that

polymerization occurs in a well-defined region of ion energy and ion/neutral ratio space. Figure

3-6 compares the S/Si ratio from XPS for direct ion deposition at various fluences (empty bars,









no 3T dosing) with SPIAD at similar ion fluences (-1015 ions/cm2) at various ion/neutral ratios

(solid bars). Figure 3-6a) shows that polymerization occurs at 200 eV for ion/neutral ratios of

1/150, 1/450 and 1/900 but not for 1/50. For 200 eV deposition, an ion/neutral ratio of 1/150 is

optimal, as it shows the largest (-10x) increase in S/Si ratio compared to direct ion deposition at

similar ion fluence. By contrast, the 1/50 ratio shows a decrease in S/Si ratio compared to direct

ion deposition (Figure 3-6a)).8'99

Varying both the ion energy and the ion/neutral ratio indicates that lower ion/neutral ratios

are optimal for polymerization at lower ion energies. Figure 3-6 illustrates that the optimal

ion/neutral ratios are 1/100 for ion energies of 100 eV, 1/75 for 50 eV, and 1/50 for 25 eV. This

is likely due to the reduced desorption and sputtering of 3T oligomers at lower ion energies,

which requires less 3T deposition101. All SPIAD films are stable in vacuum for over four hours, a

period during which pure 3T films are observed to completely sublime. The C/S ratio is around

four for all SPIAD and direct ion deposited films, which is consistent with thiophene containing

species.

The mass spectra (MS) of the SPIAD films are shown in Figure 3-7, and are obtained by

laser desorption from films directly deposited onto nanoporous silicon oxide substrates. Previous

work used isotopic distributions to assign the observed mass spectra.6 The ion/neutral ratio used

for MS experiments of each ion energy shown is the optimal value determined by XPS, as

discussed above. Many smaller polymerization products, such as [3T]2 are observed by MS for

all ion energies from 25 to 200 eV. However, the 50 eV SPIAD film displays the highest

molecular weight species, with peaks as large as [3T]4 (see the inset in Figure 3-7c)). Formation

of the polymerization products [3T]x (x=2-4) are indirectly induced by hyperthermal ion impact.

Additionally, a unique series of adduct species displaying loss or pickup of a single sulfur atom









are observed. Sulfur atom loss species include [3T]x-S (x=1-4) while sulfur atom pickup species

include [3T]S By contrast, deposition of only 3T neutrals on the DIOS substrate leads to the

appearance of only 3T+10. Previous results show that most of the ions observed from SPIAD

films display a mixture of protonated and radical cations, indicating the presence of free

hydrogen in the films.5

The mass spectra across 25-200 eV display many similar peaks, but there are other

differences besides those noted above for 50 eV films. 100 and 200 eV SPIAD film mass spectra

are very similar and display peaks up to [3T]2 [3T]T and other adduct-3T species. Higher

mass peaks are occasionally observed in these spectra, including [3T]2CH2+, [3T]2TC3H3+ and

[3T]2T2CHS (data not shown). The 25 eV SPIAD film shows the formation of a strong

[3T]2CH+ signal and only weak [3T]2 signal, in addition to the 3T signal.

To further investigate the mechanism of polymerization, SPIAD is performed with

deuterated thiophene ions combined with the evaporated 3T neutrals and compared with SPIAD

by hydrogenated thiophene ions at otherwise similar conditions. Figure 3-8 shows mass spectra

of the SPIAD films at 50 eV with hydrogenated (a) and c)) and deuterated (b) and d)) thiophene

ions in the mass ranges of 3T and 5T peaks. Deuterated thiophene ion deposition does not shift

the 5T peak at m/z 411 towards higher masses, indicating that only thiophene fragments are

introduced into the film. Table 3-3 shows relative intensities of the M+1 peaks from the mass

spectra prepared from 50 eV hydrogenated and deuterated thiophene ions, normalized to the

parent ion peak intensity of 3T and 5T. Large differences can be seen in the intensity of the

(M+1) peaks of D[5T] vs H[5T] and similar intensity increases are observed for some higher

peaks such as 7T (data not shown). D[5T] and H[5T] show similar values for (M+2) peaks. The

largest deuterated thiophene ion that could have incorporated into the film would be C4D1-2S+,









but this could lead to formation of (M+1) and (M+2) peaks for 5T only if an additional,

non-deuterated thiophene monomer is made available by fragmentation of 3T. However, a more

likely interpretation of the deuterated ion results is that only small deuterated thiophene

fragments incorporated into the films.

Discussion

Mechanisms Supported by Experimental Data and Simulations

Several processes occur during deposition that are both detected in the experiments and

predicted by the simulations shed light on the most important bond dissociation and

polymerization mechanisms that occur during SPIAD. For example, both simulations and

experiments indicate that incident thiophene ions break apart on collision with the 3T film. In

particular, C3H3 is seen experimentally at 200 eV and has previously been observed to result

from the dissociative scattering of thiophene ions from surfaces, in a process referred to as

surface induced dissociation.97

Both experiments and simulations indicate that incident thiophene ions undergo

dissociation during deposition. Comparing SPIAD deposition of deuterated vs. hydrogenated

thiophene ions, the mass spectra do not show any shift (Figure 3-8) expected if there had been

incorporation of an intact, deuterated thiophene unit. This is in agreement with the simulation

results that predict that intact thiophene ions do not survive the collisions with the surface.

Adducts such as [3T]T+ at 25 eV and [3T]2T+ at 50 eV that are seen experimentally might be the

result of dissociation of 3T neutrals upon ion impact. Previous results with non-mass selected ion

deposition show that most of the ions observed from SPIAD films display a mixture of

protonated and radical cations, indicating the presence of free hydrogen in the films5. Comparing

Ar+ and T+ SPIAD films prepared with non-mass selected Ar+ and T ions and 3T neutrals it was









shown that most of the extra hydrogen originates from incident thiophene ions since Ar SPIAD

films did not show a high intensity M+1 peak.

Both the experiments and simulations indicate that incident thiophene ions chemically

modify the structure of the oligomer film by covalently bonding to 3T oligomers. This covalent

bonding occurs primarily via incident thiophene fragments and small 3T fragments to form

adducts such as [3T]C3H4+, [3T]C2H2+, [3T]2TS and [3T]2CH observed in the experiments and

[3T]CS, [3T]CxHy (x=3, y=3,4), [3T]2CxHySz (x=4, y=5,2, z=1,2) in the simulations. The

combination of experiments and simulations provide important information regarding the surface

polymerization of 3T oligomers. Thiophene ion fragments are thought to act as polymerization

initiators. In the simulations, C atoms that come from the incident molecules or broken 3T rings

have high kinetic energy and readily abstract hydrogen atoms from other 3T molecules or

directly add on to other 3T molecules. Once this process occurs on two adjacent 3T molecules, it

is highly likely that these molecules will bond to each other.

Hyperthermal protons also can trigger the formation of polymerization initiators in a

process that is similar to the behavior of hyperthermal organic cations, where the kinematic

nature of proton collisions with simple organic molecules condensed on the substrate is exploited

to preferentially break C-H bonds.102 The simulations also show that hydrogen atoms may,

however, act as restraining agents to prevent surface polymerization. Since polymerization relies

on the bonding of chemical products through carbon atoms, scattered low energy hydrogen atom

may react with terminating carbon atoms and decrease the probability of cross-link formation

between fragments. Importantly, the S atom transfer observed experimentally is also predicted to

occur in the simulations.









The experiments and simulations further indicate that fragmentation of the 3T oligomers is

an important mechanism in SPIAD. Products such as [2T]C4H3S2 in the 100 eV neutral system

deposition event, [2T]C2H, in the 100 eV charged system deposition event, [T][TC] in the 200

eV neutral and charged system deposition events, [T]C5H3S in the first deposition event of the

250 eV neutral and charged systems, [T]C5H2S2 in the 500 eV deposition event, and

[2T][TS][T]2C12HsS6 in the 250 eV second deposition event involve dissociation of a 3T

oligomer through direct impact are predicted to occur in the simulations. Similar products, such

as [T]2C3H3+, [3T]TC3H3 are also observed experimentally by MS at 25 and 50 eV. Analogous

products seen at 100 and 200 eV correspond to [3T]2T2CxHy+. In addition, products such as

3T-S and T2C3H3+ are observed experimentally at 50 eV and the formation of similar (albeit not

identical) species is predicted by the simulations. That similar classes of products form in the

simulations and are observed in the experiments highlights the usefulness of this combined

computational and experimental approach to studying SPIAD, despite the inherent differences in

the systems under consideration.

The simulations also predict that the amount of small fragments (molecular weight < 50

g/mole) increases in the 250 eV second deposition event and in the 500 eV deposition event.

Examples of these products are S, Hx, where x<2, and CxHy, where x <2 and y<2. Some of these

products form bonds with the Si substrate and some of them embed into the thiophene thin film.

These predictions are supported by experimental data that indicates a drop in polymerization

efficiency for higher ion/neutral ratios. It should be pointed out that the experiments require high

neutral fluxes since 3T does not permanently stick to surfaces under vacuum due to very low

binding energy (see below).









The simulations performed here predict that the incident thiophene molecules damage the

structure of the 3T oligomers locally and the incident molecules also break apart on collision

with the surface. They further indicate that the C atoms which come from the incident molecules

or broken 3T oligomers have high kinetic energy. Thus they are energetic and readily abstract

hydrogen atoms from other 3T molecules or adduct on other 3T molecules directly. This is a

polymerization initiation process. Once this process occurs on two adjacent 3T oligomers, it is

highly likely that these molecules will bond to each other. The simulations therefore predict that

in an ideal case where one incident thiophene molecule is in contact with two 3T molecules on

its two sides, the most efficient energy for surface polymerization should be slightly higher than

the C-H bond energy in the thiophene ring. In the experiments it is difficult to ensure this ideal

case. Thus, the incident molecules should generally have enough energy to produce energetic

atoms and/or polyatomic fragments that will subsequently react with 3T molecules and initiate

the polymerization process. This energy should correspond to the energy required to dissociate a

thiophene ring plus the energy that will be dissipated through the film and surface through the

collision process.

Similarly, balance is required for the ion/neutral ratio to generate the proper

polymerization between 3T oligomers. Too many hyperthermal ions (two vs. one) cause a

decrease in polymerization efficiency, more fragmentation, desorption and sputtering. Increasing

the energy/molecule results in more damage to and sputtering of the 3T oligomers, but it also

produces more polymerization initiators. Thus, the amount of energy in the system should be a

balance between damaging or sputtering 3T thiophene oligomers and forming new

polymerization initiators.









Differences between Simulations and Experiments

There are several fundamental differences between the experiments and simulations that

must be taken into account, despite the large area of agreement between the two. The efficiency

of energy transfer during deposition is different in the simulation and experimental systems. This

can be attributed to several factors. There is a difference in effective surface coverage between

the experimental and computational systems: the experimental systems consist of thicker 3T

films than are considered in the simulations. The 3T multilayer present experimental is expected

to recoil more than a 3T bilayer upon thiophene ion impact, as suggested by previous

experiments studying the scattering of thiophene ions off of disparate surfaces.103 Different

surface coverage configurations influence the dissipation of incident energy since the softer

organic layer recoils more upon hyperthermal ion impact than a stiff semiconductor substrate.

Another significant difference can be attributed to the deposition sites chosen for the

simulation are direct impact sites that need higher incident energies to damage the 3T oligomers.

By contrast, the experimental impact sites vary from direct to grazing (i.e., integrated over all

possible impact parameters). Thus, the incident ions might experimentally just graze the 3T

oligomers and generate only minor damage, which could generate fragments with terminated

carbon atoms or transition state atoms to initiate the surface polymerization process. The incident

energy to fulfill this surface polymerization process is much less than the direct impact.

Related to the above differences is that of collision number. The experimental data result

from of multiple ion-surface collision events combined continual redosing of the surface with

3T. The simulations involve either one or two collisions per simulation.

The system size is also confined in the simulation compared with the experiment. Thus the

incident energy can only be dissipated within the supercell. This makes that the higher incident

energy simulations show greater modification of 3T oligomers than the corresponding









experiments. Consequently, direct comparison of incident energies between the simulations and

experiment might not be strictly correct. However, the trends predicted in the simulations and

observed in the experiments are comparable to one another.

The substrates are also not identical in the computational and experimental systems. The

simulations use clean, flat, hydrogen-terminated silicon substrates while the XPS experiments

use flat silicon surfaces and the mass spectra use nanostructured silicon oxide covered substrate.

However, these substrate differences are less relevant here for several reasons. The phenomena

of greatest interest occur between 3T oligomers and incident ions and are therefore largely

independent of the nature of the substrate. The chemical reactions predicted in the simulations to

occur between the surface and the 3T oligomers or the incident ions cannot be directly observed

experimentally by the methods utilized here, as discussed above.

Yet another significant difference between the experimental and computational systems is

their timescales. Specifically, the simulations consider phenomena and relaxation events that

occur on the order of several picoseconds, while the experiments consider phenomena that occur

over hours. Thus, the reactive species formed in simulation (i.e., C or H atoms) may take longer

than simulation timescale to form the polymerization products observed experimentally. In

addition, the experiments allow rearrangement and reorganization over time.

Lastly, the experimental conditions are sufficient to stimulate electronic excitation process

that could influence the chemical reactions that occur. In contrast, the DFT-MD simulations do

not allow electronic excitations to occur.

Despite all of these differences, the simulations are able to provide important insight into

the chemical reactions that occur during deposition. The most significant of which these appear

to occur on the same time scale as the simulations.









Conclusions

The combination of the two strategies vastly improves the mechanistic understanding of

the use of SPIAD for the growth of conducting polymer thin films, despite the significant

differences between the experiments and simulation. Variation of the experimental reaction

conditions indicates that polymerization occurs preferentially under a narrow set of ion energy

and ion/neutral ratio conditions. The first principles MD simulations reported here illustrate the

manner in which ion energies affect polymerization and other chemical reactions that modify the

substrate. Specifically, ideal incident energies should be balanced between values that are too

high and lead to damage or sputtering of the ca-terthiophene on the substrate, and values that are

too low to produce the necessary polymerization initiators. Importantly, this study indicates that

polymerization and fragmentation of ions and/or neutral species are critical steps in the SPIAD

process. In addition, the simulations predict that free protons and other radicals are formed

during SPIAD that could potentially survive for long enough timescales to contribute in a

significant manner to the properties of the conducting polymer. This insight can be used to

optimize the SPIAD process for polythiophene and other conducting polymer systems. More

generally, studies such as this indicate that it should be possible to use computational studies to

guide experiments towards the production of optimized films for particular applications.










Table 3-1. Statistical analysis of deposition results predicted by the simulations. "Intact" means
that the C and S atoms in the thiophene ring maintain the same hybridization as
initial.


Incident energy


Deposition event

Total # of products
% Products bonded to Si
substrate
% Intact 3T rings
# Surface polymerization
reactions


100 eV


200 eV


250 eV


l(neutral) l(charged) l(neutral) l(charged) l(neutral) l(charged) 2(neutral)
(site #1) (site #1) (site #2) (site #2) (site #1) (site #2) (site #2)


500 eV
1 (neutral)
(site #2)


6 5 4 5 3 4 4 14
0 0 0 25 33 33 50 57
75 67 50 42 50 58 17 50
0 0 1 0 1 1 1 0


Table 3-2. Chemical
Incident energy
Deposition event
Sum of transition
state atoms
sp hybridization
sp2 hybridization
sp hybridization
ShybTerminaidiC atomn
Terminal C atom


state of the surface
100 eV
1(neutral) 1(charged)
(site#1) (site #1)


carbon atoms following each deposition event.
200 eV 250 eV 500 eV
1(neutral) 1(charged) 1(neutral) 1(charged) 2(neutral) 1(neutral)
(site #2) (site #2) (site #1) (site #2) (site #2) (site #2)


34 52 117

7.69% 3.85% 7.69%


90.38%
1.92%
0.00%


94.23%
1.92%
0.00%


82.69%
9.62%
0.00%


1.92% 5.77% 3.85% 12.50% 19.23%


88.46%
7.69%
1.92%


90.38%
3.85%
0.00%


84.62%
11.54%
0.00%


69.64%
16.07%
1.77%


75.00%
5.77%
0.00%


Table 3-3. Relative intensities of the M+1 and M+2 peaks from the mass spectra prepared from
50 eV hydrogenated (HT+) and deuterated (DT+) thiophene ions, normalized to 3T and
5T peak intensity (M).


Ion structure


[3T] only (no SPIAD)

H[3T] from SPIAD

D[3T] from SPIAD

H[5T]+ from SPIAD
D[5T]+ from SPIAD


Exp
201%

211%

592%

381%
712%


M+1
Calculated Exp


161%


281%


181%

171%

302%

291%
332%


M+2
Calculated
161%


281%


m/z of M


248
















1'* rt
:;^rl m~c


0 C atom in 3T oliomier'


* S atom il 3T oligomer 0 H atom in 3T oligomer


* H-tenninate atom on Si substrate Si atom

Figure 3-1. a) The equilibrium simulation model before deposition. Two layers of 3T
oligomers sit on the hydrogen-terminated Si (111) substrate surface. b) The top view
of equilibrium simulation model. Two thiophene molecules marked in black represent
the two deposition sites in the simulations.














(t~~mttL


e) 0



0
1O
e ,O


0
,4O


C atom in 3T oligomer
S atom in 3T oligomer
H atom in 3T oligomer
C atom in incident thiophene
S atom in incident thiophene
H atom in incident thiophene


* H-terminate atom on Si substrate

* Si atom


Figure 3-2. Snapshots from the DFT-MD simulations of the neutral system which simulate the
deposition of a thiophene molecule on a terthiophene oligomer thin film and Si
substrate. a) The final snapshot of deposition in the 100 eV deposition event (time =
240 fs). b) The final snapshot of deposition in the 200 eV deposition event (time =
240) fs. c) The final snapshot of the first deposition in the 250 eV deposition event
(time = 240) fs. d) The final snapshot of the second deposition in the 250 eV
deposition event (time = 480) fs. E) The final snapshot of deposition in the 500 eV
deposition event (time = 240) fs.


C)
/ o












.HS [T]C5H2S2


e) 500 eV


4 0 100 200 300
[T]C H3S C13H S(s'"
2 0 10 2HCH ..

0 100 200 300


40 100 200

2 -02H2 [T][TC]
0 I I


400 500 600 700 800
d) 2nd event in 250 eV
[2T][TS][T]2 2H S6(S
I I I L I
400 500 600 700 800
c) 1st event in 250 eV


H3 ,[2T][TS][3T]C4H4S2(S')

300 400 500 600 700 800
,,- b) 200 eV


3 I ]C


L') 1 ]2k-'4rl
I


0 100 200 300 400 500 600 700 800
Molecular Weight (g/mol)



Figure 3-3. The molecular weight distribution of chemical products that are generated after the
neutral deposition events. Chemical products that form bonds with the Si substrate are
marked with a (Si) super script. [TC] and [TS] indicates that there is a C and S atom,
respectively, being included in a thiophene ring.


'^



































0
0


C atom in 3T oligomer
S atom in 3T oligomer
H atom in 3T oligomer
C atom in incident thiophene
S atom in incident thiophene
H atom in incident thiophene
H-terminate atom on Si substrate


* Si atom


Figure 3-4. Snapshots from the DFT-MD simulations of the +1 charged system which simulate
the deposition of a thiophene molecule on a thiophene thin film and Si substrate. a)
The final snapshot of deposition in the 100 eV deposition event (time = 240 fs). b)
The final snapshot of deposition in the 200 eV deposition event (time = 240) fs. c)
The final snapshot of the deposition in the 250 eV deposition event (time =240) fs..











[T]C H3S
[3T]

H r


c) 250 eV
[3T]204H2S2(SI)
[S^^S3


0 100 200 300 400 500 600 700 800


[3T]C3H4

CS [T][TC]3T] ] [3T]C3H2S(s


100 200 300 400 500 600
[3T]
C6H6S [2T]C2H [3T]S


b) 200 eV


700 800
a) 100 eV


I I I I I
100 200 300 400 500
Molecular Weight (g/mol)


600 700 800


Figure 3-5. The molecular weight distribution of chemical products that are generated after the
positively charged deposition events. Chemical products that form bonds with the Si
substrate are marked with a (Si) super script. [TC] and [TS] indicates that there is a C
and S atom, respectively, being included in a thiophene ring.


H C3H3

1 1













a)200 eV C
S C4H48











1/900 1/450 1/150 1/100 1/75 1/50
Thiophene/Terthiophene Ratio


15 -
13 -
o
S11-
re
9-
V 7
E
ID
M 5
3 -
1-



15
13
. 11
9

7


3
1


S3T C4H4S'
S C4H4S


1/900 1/450 1/150 1/100 1/75 1/50
Thiophene/Terthiophene Ratio


b) 100 eV 3T C4H4S+
S C4H4S'










1/900 1/450 1/150 1/100 1/75 1/50
Thiophene/Terthiophene Ratio

d) 25 eV a3T C4H4Sa
0 C4H46S










1/900 1/450 1/150 1/100 1/75 1/50
Thiophene/Terthiophene Ratio


Figure 3-6. S/Si elemental ratio from XPS for direct ion deposition at various fluences (empty
bars) compared with S/Si ratios for SPIAD at similar ion fluences (-1015 ions/cm2)
for various ion/neutral ratios (solid bars). Data recorded at the four ion energies
shown.


c) 50 eV












a) 200 eV [3- + [TiI+
[3T]2+

[3T]S

]+ PTICHIT
C3H3




100 200 300 400 500 600
M/Z


100 200 300 400 500 600
M/Z


b) 100 eV











100 200 300 400 500 600
M/Z


100 200 300 400 500 600
M/Z


Figure 3-7. Mass spectra (MS) of the SPIAD films at four ion energies and the optimal
ion/neutral ratios (from Figure 3-6), obtained by laser desorption of conducting
polymer films that have been deposited directly onto nanoporous silicon oxide
substrates.



















250


260


405 410 415


245 250 255 260 400 405 410 415


M/Z


Figure 3-8. Mass spectra of HT and DT+ SPIAD films grown on nanostructured silicon oxide
(DIOS) substrate at 50 eV ion energy.


a) H[3T]






Si- j









CHAPTER 4
STUDY OF METHANOL MOLECULE ADSORPTION ON COPPER CLUSTER

Introduction

In this work, the properties of copper clusters (Cun, n=2-9) are determined from density

functional theory (DFT) calculations. Different approximation methods for exchange and

correlation, and both spin-polarized/non-spin-polarized wave functions, are used. The results are

then compared with experimental data to verify the validity of the methods. Methanol molecules

are then deposited on the copper clusters in DFT molecule dynamics simulations (DFT-MD) and

the final equilibrium adsorption structures are analyzed. The results provide insight into how

methanol molecules adsorb on copper clusters.

Computational Details

The calculations and simulations are carried out using the CASTEP software.68'104 The

DFT calculations and DFT-MD simulations make use of (i) a plane-wave basis to represent the

wavefunctions, (ii) pseudopotentials105 that replace the ionic cores, and (iii) the use of

fast-Fourier transforms (FFT's). The exchange-correlation energy is described by the LDA or the

GGA106. Ionic cores are described by ultrasoft pseudopotentials,105 and the valence electrons are

described with plane waves that have a kinetic energy cutoff of 270 eV.

The calculations include two parts. The first part involves the optimization of the Cun

clusters, where n=2-9. In these optimization calculations, both non-spin-polarized and

spin-polarized wave functions are used to compare the effect of spin-polarization on the results.

The size of the supercell used in this calculation is 10Ax10Ax 10A. The second part involves

modeling the collisions of the methanol molecules with the clusters. Specifically, the methanol

molecules have external kinetic energies of 0.5 eV/molecule and are incident on the Cu clusters

in each collision. In the case of the collisions, the supercell is increased to 15A in the direction of









molecular motion towards the Cu cluster. The initial distance between a copper cluster and a

methanol molecule is around 3-4 A. The NVT ensemble107-110 is used to maintain the system

temperature at 300 K and the time step in the DFT-MD simulations is one femto-second. Each

trajectory runs for between 1 and 6 ps, with the end of the simulation depending on the outcome

of the molecule-cluster collision. The potential energy drops when the outcome is adsorption of

the methanol to the copper. The total energy convergence is tested with respect to system

supercells as large as 20Ax20Ax20A, k-point meshes up to 3x3x3, and kinetic energy cutoff up

to 320 eV. The results indicate that the differences in Cu cluster absolute total energy are about

0.2 eV/atom with the conditions that are used in this study relative to the most computationally

expensive conditions, while the differences in copper cluster binding energies are about 0.01

eV/atom.

Results and Discussion

Structure of Neutral Copper Clusters

The ground state structure of neutral copper clusters has been investigated by Jaque et al.,32

and Jug et al. 33 and the ground-state structures of the clusters examined in this study are

constructed based on these published findings. The structures of these neutral copper clusters are

then optimized within the DFT calculations using either the LDA or the GGA. The final

geometries obtained by optimization with the GGA and non-polarized wave functions are shown

in Figure 4-1. As the cluster size increases, the structure of the cluster changes from a linear

configuration that is one-dimensional (Cu2), to planar structures that are two-dimensional

(Cu3-Cu6), and finally to fully three-dimensional structures (Cu7-Cu9). In addition, Table 4-1

provides detailed bond lengths optimized by the LDA and compares the details of the optimized

structures to published results. Examination of the data indicates that the average bond lengths

predicted in these calculations are around 5% smaller than those obtained using the LDA method









with Gaussian type basis sets,33 and around 9% smaller than those obtained using the B3LPY

method with Gaussian type basis sets.32

Figure 4-2 illustrates the average bond length versus copper cluster size as optimized using

either the LDA or GGA with and without the inclusion of spin polarization, and Table 4-2

provides the relevant structural details. The results show that the average Cu-Cu bond length

increases when the cluster size increases and its dimensionality changes. For example Cu2 has

the shortest bond length and is a one-dimensional (linear) structure. Cu3 through Cu6 have

intermediate bond lengths and are two-dimensional (planar) structures. At cluster sizes of seven

and greater, three-dimensional clusters are preferred that have the largest Cu-Cu bond lengths.

This evolution of the cluster structure occurs as a result of the influence of the hybridization of

3d-orbitals, 4s-orbitals and 4p-orbitals.111 In particular, the hybridization of the 3d-orbitals and

4p-orbitals produces the three-dimensional cluster structures.112 Because these interactions occur

over relatively long distances, they result in larger average bond lengths in the clusters. Table 4-2

also shows the coordination number (CN) of the copper atoms in the various clusters. The CN

increases as the cluster size increases in a manner that is illustrative of the changes in the

dimensionality of the cluster. One-dimensional clusters have a CN of one, two-dimensional

clusters have a CN between two and three, and three-dimensional clusters have a CN larger than

4.3.

Comparing the results obtained with different exchange-correlation approximation

methods, we find that the LDA predicts smaller copper clusters than the GGA. This is not

surprising as it is generally accepted that the GGA predicts longer bond lengths than the LDA.113

Figure 4-2 also indicates that plane-wave type basis sets predict smaller cluster sizes than

Gaussian type basis sets. However, the average bond length difference between plane-wave-type









basis sets with the LDA and Gaussian type basis sets with the same approximation33 differ by no

more than 3.5%. This proves that using the LDA and plane-wave basis sets is adequate for the

study of the copper clusters. Additionally, Figure 4-2 indicates that the effect of spin-polarization

is negligible for the optimization of the structure of the copper clusters.

Figure 4-3 shows the binding energy as a function of the cluster size. Here, the binding

energy is calculated as

BE= (nEc Ec )/n, (4-1)

where n is the number of atoms in the cluster, ECU is the energy of a Cu atom in vacuum, and

E, is the energy of the Cu cluster containing n copper atoms. The errors associated with

self-interaction energies in DFT are large in cases of high localization of electron density, such

as occur here in the case of the Cu clusters. These errors are minimized here by the fact that

comparable levels of electron localization are present in both the initial and final adiabatic states.

A similar approach has been successfully used in several comparable studies, such as the

catalytic CO oxidation on Au clusters,114 the interaction of thiolates with Au and Cu clusters,115

and the interaction of S atoms with Au clusters.41 Figure 4-3 illustrates how the binding energy

increases monotonically with increasing cluster size. This indicates that it is energetically

favorable for the copper atoms to form ever larger clusters. Figure 4-3 also provides a

comparison of the binding energy calculated in this and other studies.32'33'45'116 The larger binding

energy (around 38% larger than literature values32) that is predicted here is due to the use of the

ultrasoft pseudopotential. Calculations that used the cutoff energy of 600 eV with

norm-conserving pseudoupotentials, which is indicated in CASTEP as being the same level of

accuracy as using ultrasoft pseudopotentials with a cut-off energy of 270 eV, were tested and the

resulting bind energies were similar to published literature values32 to within 3%. However, the









norm-conserving pseudopotentials are about five times more computationally expensive than the

ultrasoft pseudopotential in the case of Cu4, and even more expensive for larger clusters. This

finding, coupled with the fact that the ultrasoft pseudopotential gives consistently comparable

relative binding energies makes it suitable for use here.

If the binding energy per atom is divided by CN then the binding energy per Cu-Cu

bond can be obtained. This result is plotted in Figure 4-4, where the dimensionality change of

clusters as their size increases is clearly indicated. Specifically, the binding energy per Cu-Cu

bond decreases as the dimension of the clusters increases. For the case of Cu2 one-dimensional

cluster, the binding energy per Cu-Cu bond is predicted to be 2.73 eV by the GGA

approximation. However, it is only around 1.45 eV for the two-dimensional clusters and

approximately 1.00 eV for the three-dimensional clusters.

Figure 4-4 reveals the effect of spin polarization on the results. When spin-polarized wave

functions are used in the DFT calculations, they predict lower Cu-Cu bond binding energies than

do the non-spin polarized wave functions. In Figure 4-3, it is clear that using the GGA with spin

polarized wave functions predicts bond energy results that are in the best agreement with

published experimental data.45,116 It should be mentioned that the experimental data to which the

findings are compared is the dissociation energy of anionic and cationic copper clusters rather

than the neutral clusters under consideration here.

The average bond order versus cluster size is illustrated in Figure 4-5. The average bond

order is calculated by averaging the Mulliken overlap population115'117 of the Cu-Cu bonds in the

cluster. The bond order value for the Cu2 cluster is around 0.80, but this drops to around 0.35 for

the two-dimensional copper clusters (Cu3-Cu6) and to around 0.25 for the three-dimensional

copper clusters (Cu7-Cu9). The bond order is also indicative of the strength of the bonds within









the Cu clusters. Thus the average bond order should be directly proportional to the binding

energy per Cu-Cu bond. Comparing Figure 4-4 and 4-5, it can be seen that they show similar

trends and the ratio between the average bond order and the binding energy per Cu-Cu bond is

around 0.5.

Figure 4-6 indicates the relative stability of the different copper clusters. The relative

stability is calculated as,

A2ECu, = ECUn +Ecun, 2Ec (4-2)

where n is the number of atoms in the cluster. A high value of relative stability means that the

cluster is more stable. Figure 4-6 shows that the stability oscillates as a function of cluster size.

In particular, the clusters composed of an even number of atoms have higher relative stabilities

than those composed of an odd number of atoms. This is because the Cu atom has an electronic

configuration of 3do'4s'. When an even number of atoms form a cluster, all the electron orbitals

can be fully occupied and form a closed-shell configuration, which stabilizes the cluster relative

to the odd-numbered clusters. This finding is in agreement with the predictions of the electronic

shell jellium model that says that filled-shell clusters with 2, 8, 18, 20, 40, 58, 92, etc. valence

electrons have increased stability relative to partially filled shell clusters. The numbers of atoms

that lead to these valence electron values are the so-called magic numbers.

The relative stabilities obtained using different approximation methods are also compared

in Figure 4-6. Typically, spin polarized wave functions and non-spin polarized wavefunctions

predict very similar oscillatory behavior; however, the LDA does not predict the oscillatory

behavior well when the cluster structure changes from two-dimensional (Cu6) to

three-dimensional (Cu7). Compared to literature results32'33, the GGA is again found to give the

most reliable results.









The atomic populations of the copper clusters calculated using the GGA are given in Table

4-3. As mentioned before, the electronic configuration of a Cu atom is [Ar]3do'4s'. When Cu

atoms form the cluster, the 3d orbital and 4s orbital of each Cu atom became partially occupied.

The lost electrons from the 3d and 4s orbitals then occupy the 4p orbital. Thus the interactions

between the Cu atoms to form the cluster involve not only 3d and 4s orbitals but also 4p orbitals.

Table 4-3 also lists the atomic charge on every atom in the cluster. The atomic charge

changes on the order of 10-2 but the overall charge on the cluster is zero. It is interesting that the

atoms located at the outer cluster sites are more negative, while those at the inner cluster sites are

more positive. This indicates that the outer atoms, those farthest from the geometric center of the

cluster, have higher electron densities than the inner atoms. The outer atoms also have lower

CNs than the inner atoms. For example, in the Cu3 clusters shown in Figure 4-1, atoms 1 and 2

are separated by a longer distance than atoms 1 and 3 or atoms 2 and 3. Thus, atoms 1 and 2 are

located at the outer sites of the Cu3 cluster and are consequently negatively charged, while atom

3 is located at the innermost site and is consequently positively charged. Another example is Cu9,

where atoms 2, 6 and 7 are closest to the geometric center of the cluster, at distances of 3.04 A,

0.19 A and 3.08 A, respectively. In contrast, atoms 1, 3, 4, 5, 8 and 9 are farthest away, at around

4-6 A from the geometric center of the cluster. This phenomenon illustrates how the electron

clouds in small transition metal clusters are not like those in bulk metals, which distribute the

electron density uniformly.

Table 4-3 also indicates that among all the copper clusters considered in this study, the

negatively charged atoms have larger 4s orbital populations than the positively charged atoms. In

the one-dimensional cluster (Cu2), the two atoms balance each other and are both neutral. In the

two-dimensional clusters (Cu3-Cu6), the outer atoms have higher 4s orbital populations and have









lower 4p orbital populations than the inner site atoms. In the three-dimensional clusters

(Cu7-Cu9), the outer site atoms have still higher 4s orbital populations than the inner site atoms,

but they have almost the same level of 4p orbital population as the inner site atoms. These

differences in orbital population are likely responsible for the change in cluster dimensionality

that is illustrated in the average bond lengths (Figure 4-1 and Table 4-1), binding energy per

Cu-Cu bond (Figure 4-4), and bond order (Figure 4-5).

Collision of Methanol Molecules with Copper Clusters

Figure 4-7 illustrates the initial and final snapshots from the DFT-MD simulations of the

collisions of methanol molecules on the low-coordination number sites of the various copper

clusters. In all the collisions, the oxygen atom on the methanol molecule adsorbs on the copper

clusters, which subsequently distort. The simulations indicate that adsorption occurs when the

molecule and cluster are close enough to one another, and that their configuration changes

immediately following adsorption. The equilibrium structure is determined after their

configuration stops changing and a stable bond has been formed. The Cu4 cluster deforms the

most following adsorption of the methanol molecule at the low CN site. In particular, the

diamond-shaped structure of the Cu4 is broken and it transforms to a triangular structure with an

extra Cu atom attached to one corner.

Figure 4-8 illustrates the initial and final snapshots of the collision of methanol molecules

with the high-coordination number sites of the copper clusters. In this case, the methanol

molecules initially came close to the Cu cluster and then bounce back. The processes repeats

several times until the cluster and molecule reach an equilibrium configuration and distance from

one another. The equilibrium structure is once again determined after their configuration stops

changing and a stable bond has been formed. Again, all the methanol molecules adsorb on the

copper cluster through the oxygen atom and the process distorts the clusters.









The simulations indicate that the nearest Cu atom in the cluster to the methanol molecule is

attracted to the oxygen atom. This attraction causes the methanol molecule to reorient itself so

that the oxygen atom reaches the cluster first. The attraction between the O and Cu atoms make

the copper cluster distort toward the methanol molecule. Though the copper cluster distorts in

both the collisions on the high CN sites and the low CN sites, the stability of adsorption is

different in these two cases. Specifically, molecular adsorption at the low CN site is more stable

than at high CN site. The energy evolution curve indicates that it takes longer for the methanol

molecule to stably adsorb to the high CN site of the Cu cluster (because it initially bounces off

the cluster, as described above) than on the low CN site, and there is an obvious energy drop

when the methanol molecule adsorbs on the low CN site. Two specific examples for the case of

Cu4 and Cu5 are given in Figure 4-9 a) and b), respectively. In the case of Cu4, shown in Figure

4-9 a), adsorption on the higher coordination site is more stable than on the lower coordination

site, which is the opposite of the other cases considered here. Thus the potential energy curve

shows a steep drop as a result of adsorption on the higher coordination site. The Cu5 case,

illustrated in Figure 4-9 b), is more representative of what occurs for the other clusters, where

adsorption on the higher coordination site is more stable.

The equilibrium adsorption structure was analyzed by averaging all the equilibrium

structures and was characterized in terms of the average Cu-O bond length (Figure 4-10), the

average O-C bond length (Figure 4-11), the average Cu-O-C bond angle, the average Cu-O-H

bond angle, and the average C-O-H bond angle (Figure 4-12). From those three bond angles, the

O solid angle can be characterized by using

Qo = 360 cuo-c Cu -OH -Oc H, (4-3)









where Ocu-o-c is the average Cu-O-C bond angle, OCu-O-H is the average Cu-O-H bond angle and

OC-O-H is the average C-O-H bond angle. Since the 0, Cu, O and H atoms are able to form a

pyramidal shape, Equation (4-3) indicates that the pyramid solid angle at the O atom corner can

be described. Though it is not an equation to calculate the real solid angle at O atom, Q0 still can

represent the angular relationship between the O atom and its three neighbor atoms (Cu, C and

H). If Qo is equal to zero, this means that the 0, Cu, C and H atoms are in the same plane. The

larger Qo, the sharper the pyramid solid angle at the O atom corner.

In Figure 4-10, the Cu-O bond length is found to generally increase when the cluster size

increases. Typically even-numbered clusters have longer Cu-O bond lengths. The three stage

trend in dimensionality with clusters size shown in bare copper clusters is not observed here.

However, it is found that the Cu-O bond length is longer if the methanol molecule is adsorbed on

the high CN site. The only exception is Cu4CH30H, which has a shorter Cu-O bond length when

the methanol molecule is adsorbed on a high CN site. This is most likely because the Cu4 cluster

changed its structure substantially following adsorption, as discussed above.

The resulting C-O bond lengths are shown in Figure 4-11. The C-O bond length trends are

the opposite of the Cu-O bond length trend. For example, the high CN site Cu cluster-methanol

compounds have a shorter C-O bond length and the lower CN site compounds have longer C-O

bond lengths. The only exception is again the Cu4CH30H. This result indicates that the charge

on the O atom is higher when the Cu-O bond length is shorter. From the bare copper cluster

calculations discussed in the previous section, the low CN Cu site has higher charge than the

high CN Cu site. The results imply that to adsorb a methanol molecule on a neutral copper

cluster, there should be electron cloud transfer between the copper cluster and the methanol









molecule. Higher electron cloud density provides more opportunity to achieve this transfer,

which makes the low CN site most favorable for adsorption.

Comparing the C-O bond length of bare methanol and the adsorbed methanol molecule,

the C-O bond length of adsorbed methanol is elongated when adsorbed at both the high CN site

and the low CN site. The amount of elongation is approximately 0.02 A (1.4%) at the low CN

site and approximately 0.016 A (1.1%) at the high CN site. This finding further confirms the

analysis discussed above. In the isolated methanol molecule the C-O interaction is through

a-bonding, while when it is adsorbed on the copper cluster, part of the O electron clouds interact

with the Cu atom and part of the Cu atom's electron cloud transfers to the O atom37'118. The net

transfer leads the adsorbed Cu atom to have a slight positive charge and the O atom to have a

slight negative charge, therefore stabilizing adsorption.

The results of O-H bond lengths are also provided in Figure 4-11. The O-H bond lengths

are all slightly longer than the O-H bond length of an isolated methanol molecule. However there

is no obvious trend between the high CN site and the low CN site. For Cu4-Cu6, the high CN site

has a longer O-H bond length and for Cu7 and Cu8, the low CN site has a longer bond length.

From the electronic calculation of the bare methanol molecule, the bond order for O-H is 0.78

and for C-O is 0.46. Thus, since the O-H bond is stronger than the C-O bond, the influence of the

electron cloud transfer between Cu and O does not affect the O-H bond to any significant degree.

Figure 4-12 illustrates the angular relationship around the O atom after the methanol

molecule adsorbs to the Cu clusters. It is interesting that the C-O-H angle does not change much

in the different adsorption cases and the angles are almost the same as in the case of the isolated

methanol molecule (109.0940). In contrast, the Cu-O-H angle and Cu-O-C angle have more

substantial variations. There is no clear trend that indicates that adsorption at a high CN site or a









low CN site influences the Cu-O-C angle. However, the Cu-O-H angle typically is larger when

methanol is adsorbed at a low CN site than at a high CN site. The pyramid solid angle at an O

atom corer (Qo) also has larger variation and typically the low CN site has a smaller Qo which

indicates a flatter O-Cu-C-H plane.

The angular relationships indicate how the methanol molecule adsorbs on the clusters. The

small variation in C-O-H angle reveals that the covalent bonding nature (sp orbital hybridization)

between the O-H and O-C is still hold strong after adsorption. The larger variations in the

Cu-O-C angle and the Cu-O-H angle show that the bonding between Cu and O is not purely

covalent, but includes donation and back-donation of electrons. This illustrates how the Cu

atom's 3d orbitals complicate the bond order that occur as a result of adsorption.

The binding energy between the Cu clusters and methanol molecules are indicated in

Figure 4-13. Here the binding energy is calculated through:

BE = EC CHOH (E fre +Efree (4-4)
-^cu,,CH,OH CH,OH Cu, )V

The results show that binding energies increase with increasing cluster size. This may

conflict with our intuitive sense that with increasing cluster size the adsorption behavior should

approach the behavior observed on Cu surfaces, which is purely physisorption.21'40 This apparent

contradiction is explained by the fact that in the case of the largest cluster, Cu9, considered in this

study, the Cu atoms are far from a bulk-like arrangement.

The results of binding energy also indicate that the adsorption site influences the binding

energy. In particular, binding energy is higher when the methanol molecule is adsorbed on a low

CN site and is lower when the methanol molecule is adsorbed on a high CN site. This result is

consistent with our bond length results and accompanying analysis. The only exception is again

Cu4CH30H. As discussed above, this is because the structure of the Cu4 cluster deforms









significantly when methanol adsorbs on a low CN site. It becomes a Cu3 structure attached to an

extra Cu atom on one of its corner. Thus it is difficult to compare the result with the high CN site

of Cu4 cluster.

Finally it should be mentioned that the spin-polarized wave function with the GGA is also

used in Cu6CH3OH and CuyCH3OH to verify the result obtained by non-spin-polarized function

in DFT-MD calculations. The equilibrium structures obtained by both methods are very similar

and the differences are within 1%. The results in binding energy also give the same trend and the

differences are within 7%. Thus it is believed that non-polarized wave function provide the most

reliable results.

Conclusions

This study has analyzed the structure of small bare copper clusters and adsorption of

methanol molecule on these clusters. It is found that the structural dimensionality of the bare

copper clusters evolves with cluster size in average bond length, binding energy per bond, and

bond order. The bond length increases with increasing structural dimensionality. The binding

energy per bond and the bond order, however, decrease with increasing structural

dimensionality. These results are explained by the electronic structures of the clusters. The

population of 4s and 4p orbitals exhibit different trends in the two-dimensional and

three-dimensional clusters.

It is also found that even numbered Cu clusters are more stable than odd numbered Cu

clusters. The electron density distributions on bare Cu clusters contribute to a significant degree

to methanol adsorption. Low CN sites have higher electron densities and provide more

opportunity for electron cloud transfer between cluster Cu atoms and molecular O atoms, which

makes them the most favorable adsorption sites. The complex structure of CunCH3OH

compounds prove that the 3d orbital is involved in the interactions.









Table 4-1. Comparison of ground-state structure of neutral copper clusters, Cun (n=2-9)

Copper PG This work (LDA Jug eta. (LDA Jaque et al. (B3PW91
Clusters Plane-wave type Gaussian-type basis set)33 Gaussian-type basis et)32
basis set)
Cu2 D.t r12=2.142 r12=2.21 r,=) IA


Cu3 C2v r12=2.246
Cu4 D2h r12=2.195
Cu5 C2v r25=2.243
r24=2.264
Cu6 D3h r15=2.250
Cu7 Da r34=2.329
Cus C2v r12=2.302
r28=2.330
r18=2.347
r78=2.300
Cu9 Cs r45=2.426
r15=2.350
r56=2.309
r57=2.347
r12=2.342
r16=2.401
r17=2.341


r13=2.257
r13=2.282
r45=2.300
r34=2.289
r16=2.316
r36=2.335
r23=2.379
r14=3.022
ri7=2.333
r67=2.379
r19=2.353
r23=2.344
r27=2.360
r28=2.341
r67=2.483
r69=2.310
r89=2.426


Table 4-2. Average bond length in
clusters


Copper
Clusters

Cu2
Cu3
Cu4
Cu5
Cu6
Cu7
CuS
Cu9


LDA LDA+spin GGA


2.142
2.246
2.264
2.272
2.272
2.341
2.333
2.364


2.142
2.245
2.264
2.271
2.273
2.343
2.334
2.364


2.180
2.326
2.328
2.348
2.338
2.413
2.407
2.430


r12=2.50
r12=2.24
r25=2.32
r24=2.33
r34=2.33
r34=2.39
r12=2.35
r28=2.38
r18=2.39
r78=2.35
r45=2.49
r15=2.39
r56=2.35
r57=2.42
r12=2.39
r16=2.46
r17=2.40


r13=2.26 r12=2.690
r13=2.36 r12=2.574
r45=2.36 r25=2.401
r34=2.38 r24=2.415
r45=2.39 r34=2.404
r36=2.39 r34=2.500
r23=2.47 rl2=2.437
r14=3.07 r28=2.491
r17=2.38 r18=2.512
r67=2.47 r78=2.436
r19=2.42 r45=2.615
r23=2.39 r15=2.521
r27=2.40 r56=2.463
r28=2.42 r57=2.555
r12=2.500
r69=2.35 r16=2.555
r17=2.500


r13=2.326
13=2.293
r45=2.451
r34=2.469
r45=2.484
r36=2.500
r23=2.643
r14=3.225
r17=2.491
r67=2.643
r19=2.521
r23=2.650
r27=2.479
r28=2.559
r67=2.650
r69=2.463
r89=2.614


A and mean coordination number (CN) of Cun


GGA+spin

2.180
2.332
2.328
2.341
2.338
2.412
2.404
2.431


Jug et al.33

2.210
2.340
2.336
2.343
2.350
2.390
2.386
2.453


Jaque et al. 32

2.254
2.447
2.418
2.429
2.431
2.500
2.501
2.534


CN

1.0
2.0
2.5
2.8
3.0
4.3
4.5
5.1










Table 4-3. Atomic populations for Cu2-Cu9 using the generalized gradient approximation
(GGA)
Species Ion 4s' 4p 3d10 4f Total Charge
Cu2 1 0.99 0.06 9.95 0.00 11.00 0.00
2 0.99 0.06 9.95 0.00 11.00 0.00
Cu3 1 0.94 0.18 9.90 0.00 11.02 -0.02
2 0.93 0.19 9.90 0.00 11.01 -0.01
3 0.81 0.24 9.91 0.00 10.97 0.03
Cu4 1 0.74 0.32 9.90 0.00 10.96 0.04
2 0.74 0.32 9.90 0.00 10.96 0.04
3 1.14 0.02 9.87 0.00 11.04 -0.04
4 1.14 0.02 9.87 0.00 11.04 -0.04
Cu5 1 1.08 0.04 9.89 0.00 11.02 -0.02
2 1.08 0.04 9.89 0.00 11.02 -0.02
3 0.92 0.19 9.88 0.00 10.99 0.01
4 0.92 0.19 9.88 0.00 10.99 0.01
5 0.90 0.25 9.84 0.00 10.99 0.01
Cu6 1 0.90 0.20 9.87 0.00 10.97 0.03
2 0.89 0.18 9.87 0.00 10.94 0.06
3 1.15 0.01 9.89 0.00 11.05 -0.05
4 1.14 0.01 9.89 0.00 11.04 -0.04
5 1.14 0.01 9.89 0.00 11.04 -0.04
6 0.90 0.20 9.87 0.00 10.97 0.03
Cu7 1 0.90 0.29 9.87 0.00 11.06 -0.06
2 0.90 0.28 9.87 0.00 11.05 -0.05
3 0.90 0.29 9.87 0.00 11.06 -0.06
4 0.90 0.28 9.87 0.00 11.05 -0.05
5 0.90 0.28 9.87 0.00 11.05 -0.05
6 0.78 0.26 9.83 0.00 10.87 0.13
7 0.78 0.26 9.83 0.00 10.87 0.13
Cu8 1 0.82 0.28 9.85 0.00 10.95 0.05
2 0.91 0.27 9.87 0.00 11.05 -0.05
3 0.91 0.27 9.87 0.00 11.05 -0.05
4 0.82 0.28 9.85 0.00 10.95 0.05
5 0.82 0.28 9.85 0.00 10.95 0.05
6 0.91 0.27 9.87 0.00 11.05 -0.05
7 0.91 0.27 9.87 0.00 11.05 -0.05
8 0.82 0.28 9.85 0.00 10.95 0.05
Cu9 1 0.81 0.36 9.86 0.00 11.03 -0.03
2 0.78 0.29 9.84 0.00 10.91 0.09
3 0.81 0.36 9.86 0.00 11.03 -0.03
4 0.96 0.24 9.86 0.00 11.05 -0.05
5 0.96 0.24 9.86 0.00 11.056 -0.05
6 0.72 0.45 9.79 0.00 10.96 0.04
7 0.77 0.28 9.84 0.00 10.88 0.12
8 0.95 0.24 9.86 0.00 11.04 -0.04
9 0.95 0.24 9.86 0.00 11.04 -0.04











2.35

18 2.26 2.20

2.44


=2.461
=3.119
=2.417
=2.461


Cu9
r45=2.506
r15=2.427
r56=2.366
r57=2.433
r12=2.395
r16=2.459
r17=2.399


=2.433
=2.395
=2.416
=2.436
=2.531
=2.358
=2.519


Figure 4-1. Theground state structures of the neutral copper clusters after optimization using
the generalized gradient approximation (GGA) and non-polarized wave function in
the calculations.


Cu8
r12=2.363
r28=2.417
rl8=2.406
r78=2.363


I. DO j b

































Cu2 Cu3 Cu4 Cu5 Cu6 Cu7 Cu8 Cu9
Size of Copper Clusters


- LDA
o- LDA+spin
-- GGA
-v- GGA+spin
SLDA (Gaussian) [33]
B3PW91 [32]


Figure 4-2. Average Cu-Cu bond lengths in the clusters obtained from the calculations as a
function of the level of theory used.


0
4


I I I I I I I


Cu2 Cu3 Cu4 Cu5 Cu6 Cu7
Size of Copper Clusters


Cu8 Cu9


- LDA
-o- LDA+spin
- GGA
-v- GGA+spin
B3PW91[32]
LDA (Gaussian)[331
- exp [45]
- exp2[1161


Figure 4-3. Binding energies in the copper clusters obtained from the calculations as a function
of the level of theory used and from experimental data.


0o


3.2
3.0
2.8
2.6
E
. 2.4
2.2
S2.0
2 1.8
LuJ
1.6
1 1.4
1.2
1.0
0.8