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1 MOLECULAR DYNAMICS METHOD DEVELOPMENT AND SIMULATIONS OF MOLECULE POLYMER INTERACTIONS By T RAVIS W. K EMPER A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREME NTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2011
2 2011 Travis W. Kemper
3 To my mother and father
4 ACKNOWLEDGMENTS First I would like to thank the Sinnott and Phillpot group members for their support and assistance In particular Dr. Alex Chernatynskiy Dr. Tao Liang and Dr. Bryce Divne provided invaluable guidance and intelligent criticism. Also working with Eric B ucholz, Dr. Donghyun Kim and Dr. Ray Shan has been a great pleasure and working with Dr. Rakesh Behe ra was always entertaining. Also, Dr. Phillpot and his words of wisdom have been priceless. Lastly, I would like to especially thank Prof Sinnott for her constant advice and encouragement has kept me on task and driven throughout my graduate career.
5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 7 LIST OF FIGURES ................................ ................................ ................................ .......... 9 ABSTRACT ................................ ................................ ................................ ................... 11 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 13 2 METHODS ................................ ................................ ................................ .............. 16 2.1 Molecular Dynamics ................................ ................................ .......................... 16 2.2 Classical Atomic Scale Modeling of Materials ................................ .................. 18 2.2 Empirical Potentials ................................ ................................ .......................... 18 2.3 Quantum Mechanical Modeling of Materials ................................ ..................... 28 2.1.1 Molecular Orbital Theory ................................ ................................ ......... 29 2.1.1. 1 Slater determinants ................................ ................................ ........ 29 22.214.171.124 Basis sets ................................ ................................ ....................... 30 126.96.36.199 Self consistent field method ................................ ........................... 31 2.1.2 Density Functional Theory ................................ ................................ ....... 33 188.8.131.52 Hohenberg Kohn theorems ................................ ............................ 34 184.108.40.206 Kohn Sham theorem ................................ ................................ ...... 36 4.3 Post HF, Hybrid and Combinatorial Methods ................................ .................... 37 2.4 Summary ................................ ................................ ................................ .......... 38 3 POTENTIAL DEVELOPMENT ................................ ................................ ................ 40 3.1 REBO Oxygen ................................ ................................ ................................ .. 40 3.1.1 Parameter Fitting Results ................................ ................................ ........ 41 3.2 REBO Sulfur ................................ ................................ ................................ ..... 42 3.2.1 Parameter Fitting ................................ ................................ ..................... 42 3.2.2 Validation and Testing ................................ ................................ ............. 45 3.3 Summary ................................ ................................ ................................ .......... 46 4 COMPARISON OF REBO AND DFT MD DEPOSITION SIMULATIONS ............... 62 4.1 CHF Deposition on Diamond ................................ ................................ ............ 62 4.1.1 Methodology ................................ ................................ ............................ 62 4.1.2 Results ................................ ................................ ................................ .... 63 4.1.3 Discussion ................................ ................................ ............................... 65 4.2 Hydrocarbon Deposition on Polystyrene ................................ ........................... 67
6 4.2.1 Methodology ................................ ................................ ............................ 67 4.2.2 Results ................................ ................................ ................................ .... 68 4.2.3 Discussion ................................ ................................ ............................... 70 4.3 Summary ................................ ................................ ................................ .......... 72 5 SURFCE POLYMERIZATION ION BEAM ASSISTED DEPOSTION ..................... 82 5.1 Methodology ................................ ................................ ................................ ..... 85 5.2 Single trajectory deposition ................................ ................................ ............... 86 5.2.1 Argon 100 ................................ ................................ ............................ 87 5.2.2 Thiophene 100 ................................ ................................ .................... 88 5.2.3 50 Depositions ................................ ................................ ..................... 90 5.2.4 Discussion ................................ ................................ ............................... 91 5.3 Ab initio Reaction Calculations ................................ ................................ ......... 92 5.3.1 Discussion ................................ ................................ ............................... 93 5.4 Summary ................................ ................................ ................................ .......... 94 6 SURFACE MODIFICATION STUDIES ................................ ................................ 107 6.1 Amorphous Polymer Model ................................ ................................ ............. 108 6.2 Methodology ................................ ................................ ................................ ... 112 6.3 Argon Deposition ................................ ................................ ............................ 113 6.3.1 Results ................................ ................................ ................................ .. 114 6.2.2 Discussion ................................ ................................ ............................. 118 6.2.3 Conclusions ................................ ................................ ........................... 119 6.3 Reactive Species ................................ ................................ ............................ 120 6.3.1 Results ................................ ................................ ................................ .. 121 6.3.1 Discussion ................................ ................................ ............................. 125 6.5 Summary ................................ ................................ ................................ ........ 127 7 DEVELOPMENT OF POTENTIALS ................................ ............................ 144 7.1 Density Functional Theory Data ................................ ................................ ...... 145 7.2 Buckingham With Core Shell ................................ ................................ .......... 145 7.3 Empirical Potential for HfO 2 ................................ ................................ ............ 146 7.4 Structure and Phase order ................................ ................................ .............. 146 7.4.1 Elastic Properties ................................ ................................ ................... 147 7.5 Point Defect Energetics ................................ ................................ .................. 148 7.6 Conclusions ................................ ................................ ................................ .... 151 8 CONC LU SIONS ................................ ................................ ................................ ... 156 REFERENCE LIST ................................ ................................ ................................ ...... 159 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 169
7 LIST OF TABLES Table page 3 1 and bond dissociation energies (D O ) and atomization energies ( in ................................ ................................ ................................ ......... 48 3 2 bond dissociation energies (D O ) and atomization energies ( in ...... 49 3 3 and bond dissociation energies (D O ) and atomization energies ( in ................................ ................................ .......................... 50 3 4 Refit spline values for oxygen hydroca rbon interactions ................................ ..... 50 3 5 Pair parameters ................................ ................................ ................................ .. 51 3 6 Angular parameters ................................ ................................ ............................ 51 3 7 Tricubic spline values for the coordination function P ij ................................ ........ 52 3 8 bond dissociation energies (D O ) and atomization energies ( in ...... 53 3 9 bond dissociation energies (D O ) and atomization energies ( in ..... 54 3 10 bond dissociation energies (D O ) and atomization energies ( in ...... 54 3 11 bond dissociation energies (D O ) and atomization energies ( in ...... 55 3 12 and bond dissociation energies (D O ) and atomization energies ( in ................................ ................................ ................................ ......... 56 4 1 Reaction predicted by classical MD simulations using the REBO potential ........ 73 4 2 DFT MD predicted reactions ................................ ................................ ............... 73 4 3 R eaction enthalpies calculate d with the 22 atom carbon cluster ........................ 74 4 4 MD results of radicals deposited on PS ................................ .............................. 74 4 5 Hydrogen interaction with PS monomer ................................ ............................. 75 4 6 Reaction barriers for the interaction of C 2 H + with the polystyrene monomer. ..... 75 4 7 Reaction barriers for the interaction of CH 2 triplet r adical with the polystyrene monomer C4 position. ................................ ................................ ........................ 75 4 8 Reaction barriers for the interaction of CH 2 singlet radical with the polystyrene monomer C4 position ................................ ................................ ...... 75
8 6 1 Coordination analysis of deposition on PE ................................ .................. 128 6 2 Coordination analysis of deposition on PP ................................ .................. 12 8 6 3 Coordination analysis of deposition on PS ................................ .................. 129 6 4 Coordination analysis of atomic oxygen deposition on PE at 25 .................. 129 6 5 Coordination analysis of atomic oxygen deposition on PE at 50 .................. 130 6 6 Coordination analysis of atomic oxygen deposition on PE at 100 ................ 130 6 7 Coordination analysis of atomic oxygen deposition on PP at 25 .................. 131 6 8 Coordination analysis of atomic oxygen deposition on PP at 50 .................. 131 6 9 Coordination analysis of atomic oxygen deposition on PP at 100 ................ 132 6 10 Coordination analysis of atomic oxygen deposition on PS at 25 .................. 132 6 11 Coordination analysis of atomic oxygen deposition on PS at 50 .................. 133 6 12 Coordination analysis of atomic oxygen deposition on PS at 100 ................ 133 6 13 Comparison of probable modifications during argon and atomic oxygen bombardment at ................................ ................................ .................... 134 7 1 Empirical potential parameters of the cubic and tetragonal phases of using the Buckingham formalism with shell model ................................ ........... 152 7 2 Experimental and calculated lattice parameters of the monoclinic, tetragonal and cubic phase s of ................................ ................................ ................ 152 7 3 Elastic constant tensor values for the tetragonal and cubic phases ................. 153 7 4 Elastic moduli for the cubic and tetra gonal phases of HfO 2 .............................. 153 7 5 Defect formation energies from DFT and empirical potential calculations ........ 154
9 LIST OF FIGURES Figure page 2 1 Periodic boundary conditions ................................ ................................ .............. 39 3 1 Dissociation energies of oxygen dataset calculate with G3 plotted as function of values calculated with REBO ................................ ................................ .......... 57 3 2 Bond stretching curves for and bonds. ................................ ....... 58 3 3 Bond energy as a function of bond angle for fitted funct ion .......................... 59 3 4 Dissociation energies of sulfur dataset calculate with G3 plotted as function of values calculated with REBO ................................ ................................ .......... 60 3 5 Atomiza tion energies of test set of molecules, energies boxed in red are included in fitting database ................................ ................................ ................. 61 4 1 Systems used for reaction enthalpies: A) periodic slam of 128 atoms, B) carbon cluster of 22 atoms. ................................ ................................ ................ 76 4 2 Site on diamond (111) surface ................................ ................................ ........... 76 4 3 Transition state geometry of radical on adamantane surface to produce on the surface and an HF molecule ................................ ............................. 77 4 4 Crystalline polystyrene where the black and white atoms are thermostat region, and the blue and gray atoms are active ................................ .................. 78 4 5 PS monomers where carbon is the darker (blue) atoms and hydrogen is the lighter (gray) atoms ................................ ................................ ............................. 78 4 6 Reaction profile of the interaction of H + with the polystyrene monomer .............. 79 4 7 Reaction profile of the interaction of C 2 H + with the polystyrene monomer. The barriers are presented in Table 4 6 ................................ ................................ .... 80 4 8 Reaction pathways for CH 2 triplet radical on C4 the barriers are presented in Table 4 7. ................................ ................................ ................................ ........... 81 4 9 Reaction pathway of singlet radical on C4, the barriers are presented in Table 4 8. ................................ ................................ ................................ ........... 81 5 1 Photoluminescence spectra of 3T and SPIAD films produced with Ar + and Thiopohene (T + ) at 100 and 200 33 ................................ .............................. 96 5 2 Mass spectra data 33 ................................ ................................ ............................ 97
10 5 3 Terthiophene unit cell 135 ................................ ................................ ..................... 98 5 4 Perpendicular and parallel configurations of the 3T films on a hydrogen terminated substrate. ................................ ................................ .......................... 99 5 5 Yield at 100 thiophene and on the surface with 3T in the parallel configuration ................................ ................................ ................................ ..... 100 5 6 Two step process of the removal of a single atom from one 3T (1) and donating it to the set of 3T molecules be low it (2) ................................ ............. 101 5 7 Yield at 100 thiophene and Ar on the surface with 3T in the perpendicular configuration ................................ ................................ ................................ ..... 102 5 8 Molecular analy sis of films resulting from 50 argon and thiophene deposition on 3T in the parallel configuration ................................ ................... 103 5 9 Molecular analysis of films resulting from 50 argon and thiophene deposition on 3 T in the perpendicular configuration ................................ ......... 104 5 10 Reaction pathway of radical and interacting with a thiophene molecule with calculated transition state energies. ................................ ........... 105 5 11 produced by 50 thiophene on parallel ................................ ..... 106 6 1 Initial PE, PP, PMMA and PS substrates with each chain color coded ............. 135 6 2 Pair distribution function for PE, PP and PS ................................ ..................... 136 6 3 Yield of sputtered carbon and hydrogen atoms for at 25 50 and 100 ................................ ................................ ................................ ............... 137 6 4 Molecular mass analysis for deposited at 50 ................................ ........... 138 6 5 Molecular mass analysis for deposited at 100 ................................ ......... 139 6 6 Yields and concentrations of the three most probable groups formed during 100 deposition on PE, PP and PS ................................ ........................... 140 6 7 Yield of sputter ed carbon and hydrogen for atomic oxygen at 25 50 and 100 ................................ ................................ ................................ .............. 141 6 8 Molecular mass analysis of 50 atomic oxygen ................................ .............. 142 6 9 Oxygen bonding in PS for deposition energies at 25 with C (O) C coordinatio n in four possible environments ................................ ...................... 143 7 1 Three low pressure phases of HfO 2 (a) monoclinic, (b) tetragonal, (c) cubi c where oxygen is darkly shaded and hafnium is lightly shaded ......................... 155
11 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Deg ree of Doctor of Philosophy MOLECULAR DYNAMICS METHOD DEVELOPMENT AND SIMULATIONS OF MOLECULE POLYMER INTERACTIONS By Travis W. Kemper December 2011 Chair: Susan Sinnott Major: Materials Science and Engineering Modifying the surface of a material can alter its chemical resistance, frictional properties biocampatability, adhesive proper ties and electrical properties, while maintaining the bulk properties. Treatments utilizing ion beams and plasmas can be employed for a range of modifications from the creation of protective coatings on plastics to the production of complex electronics. However, the complex interaction s between gas molecules and surface s are still not well understood. In order to investigate these interactions atomic scale molecular dy namics simulations using the second generation reactive empirical bond order (REBO) potential are conducted First the second generation REBO potential is modified to improve the previously published oxygen hydrocarbon interactions. Further modification is done to add sulfur interactions with hydrocarbons. Studies of hyperthermal species interacting with surfaces relevant to polymer modification are conducted. The performance of the REBO potential is evaluated by comparing deposition results involving on diamond and and on polystyrene to results
12 obtained with quantum chemical methods. While the second generation REBO potential reproduced reaction enthalpies within reasonable limits, the main deficiency is found to be the short range nature of the potential and the lack of different charge states. However, the comput ational efficiency allows for a greater sampling of possible reactions, and there for is a good initial evaluation tool to allow for further analysis with mor e accurate quantum based methods. Next t he surface polymerization by ion assisted deposition (SPIAD) process is investigated. The SPIAD process involves the deposition of thermal neutrals and hyperthermal ions to produce oligomer films for use in organi c molecule based electronics. In order to study this process thiophene molecules are deposited on thin films of terthiophene. D uring these simulations the differences in argon and thiophene depositions are examined. In order to investigate the effects o f reactivity of the deposited species, argon and atomic oxygen are deposited a set of prototypical polymers. These prototypical polymers polyethylene, polypropylene and polystyrene, are generated using an amorphous polymer model. S tatistical data on pro bable changes in substrate bonding is presented. Thus, atomic scale simulations are conducted to advance the plasma and ion beam treatment s of polymer surfaces. Probable modifications are identified using the second generation REBO potential. Sulfur an d improved oxygen parameters are developed under the second generation REBO potential formalism. Probable modifications are further analyzed using quantum chemical analysis. To identify the mechanism in which ions modify polymer surfaces.
13 CHAPTER 1 INTR ODUCTION Numerous processing methods involve the modification of solid surfaces via exposure to energetic particles. These energetic particles can be photons, electrons, atoms, radicals, or ions produced by a variety of techniques. For example, lasers ar e used to melt surfaces for structural, tribological and corrosion resistance pruposes 1 Chemical vapor deposition (CVD) is used to grow ma terials for a myriad of applications from diamond for electronics to silicon carbide for cutting tools 2 Ion beams can introduce small amounts of dopants to a solid surface thereby altering the mechanical, electrical, optical, magnetic or superconducting properties of the mater ial 3 Non thermal plasmas have been used extensively in the semiconductor industry, primar il y for etching photoresists 4 Plasmas 5 and ion beam 6 treatments have been found to effectively modify polymer surfaces for barrier coatings 7 improving adhesion 5, 8 11 functionalization 12, 13 sterlization 14 and biocompatibility 15 Plasmas and ion beams can modify surfaces without the need for solvents or catalysts, which are not only harmful to the environment 16 18 but can also have negative effects for some applications due to the presence of residual chemicals 19 Low temperature, non thermal plasmas are typically used for materials pro cessing 20 Unlike plasmas used in fusion reactors, plasmas used for surface modification purposes are not in thermodynamic equilibrium, which allows them to exist at or near room temperature. These non thermal low temperature plasmas can be generated in low pressure reactors or in air with an electric field. Direct current (DC) discharges or radio frequency (RF) discharges can be applie d to a parallel plate
14 capacitor to generate the electric field necessary to accelerate electrons into the neutral gas species 4, 20, 21 The collision between free electrons and neutral gas species results in the ionization or exc itation of the neutral gas species 11 This process and subsequent processes, such as the emission of photons due to excitation creates the electrons, ions photons and neutrals which comprise the complex system of the non thermal plasma. Low temperature plasmas have been widely used for etching 22 A range of feed er gases hav e been used including fluorocarbons and air. Fluorocarbon (FC) plasma treatments can not only be used for etching 23 but also to increase hydrophobicity 24 or dielectric constant 25, 26 and to create bearer coatings on polymer surfaces 27 Coatings of diamond like carbon (DLC) can also be grown from FC plasmas at lower temperature than hydrocarbon precursors 28 Oxygen containing plasmas and ion beams 29 can be used for numerous surface modifications, including etching 22 One method that combines plasma and ion beam treatments to produce stable conducting organic films is surface polymerization by ion assisted deposition (SPIAD) 30 33 This method employs the co terthiophene and hyperthermal thiophene cations to induce polymerization at the gas solid interface 30 The production of conjugated higher molecular weight species during the polymerization process is beneficial for photovoltaic devices 30 In particular, the increase in the electron conjugation length produces a red shi ft in the UV/vis absorption spectra 31 which allows for absorption of visible light at longer wavelengths.
15 One of t he primary event s of interest in plasma treatments is the collision of the accelerated ion with the substrate. Hyperthermal ions (1 500 ) have been found to be of particular interest for f ilm growth 34, 35 However, the complex processes involved in the gas surface interactions are still not well understood for the polymer systems. Molecular dynamics (MD) simulations offer a unique opportunity to study these complex interactions. Atomistic MD simulations using reactive empirical potentials can capture events at the ps to ns time scale 36 In particular, these simulations offer a way to model multifaceted chemical reactions due to a single species, while precisely monito ring atomic and molecular c ompositions. In this work the second generation reactive empirical bond (REBO) potential primarily used due to its ability to capture bond dissociation and formation by dynamically evaluating the bonding of atomic pairs dependi ng on the immediate environment 37, 38 The second generation REBO potential for hydrocarbons has been successfully applied to the study of the mechanical properties of graphene 39 tribology 40, 41 and ion beam modification of polymers 42 46
16 CHAPTER 2 M ETHODS The primary motivation of this work is to decouple the effects of relevant ions at various energies interacting with a surface during ion beam and plasma treatments. Experimentally decoupling differ ent factors occurring during treatment is difficult as films are primarily characterized post treatment 47 Computer simulations offer complete control over environmental c onditions, and the ability to limit the interaction of the surface to a single type of particle. The primary focus of this work is the use of molecular dynamics (MD) simulations to evaluate dynamical processes related to the modification of polymer and ol igomer surfaces by energetic atomic and polyatomic species. 2.1 Molecular D ynamics MD describes the evolution of a c scale resolution. Considering t he n uclei of the atoms are at least 2000 times heavier than the electrons orb iting them ; therefore the Born Oppenheimer approximation is usually employed Th is allows the e lectrons to be considered to have instantly relax ed to their ground state in the constant external field created by the nuclei and to produce quantum mechanic al forces that act on the latter. Motion of the nuclei is, in turn controlled by classical Newtonian physics. Newtonian equation s of motion are differential equations that describe the evolution of atomic trajector ies over time. The methods used here to solve the resulting s ystem of differential equations are known as integrators. Various forms with a range of complexity and accuracy exist 48 In this work the Gear third order predictor corrector is
17 primarily used 49, 50 To find the position of the atom at time a Taylor expansion out to the third order about is used: (2 1 ) At the predicted position the forces are calculated at time giving the correct acceleration for an atom at position The error in the prediction step is then be estimated by: (2 2 ) The estimated error can then be used to correct the predicted values: (2 3 ) The coefficients and are and respectively. The value of is known as the time s tep, and has to be on the order of the thermal vibrations of the system. Due to computational limitation s most atomic simulation cells are on the order of nanometers in size. This is rarely representative of a real system ; therefore, periodic boundary conditions are used to artificially extend the simulation cell to make the simulation more realistic, as shown in Figure 2 1 Periodic boundary conditions can be conceptualized as replicating the simulation cell in an infinite pe riod lattice. The results
18 are that for each particle moving along a trajectory in the simulation cell an image particle is moving along the same trajectory in each infinite reproduction. Therefore if a particle exits through one boundary of the simulat ion cell an image will enter through another creat ing an artificially infinite medium. In order to control temperature the velocity of the particles is manipulated through the use of thermostats. In this work the Langevin method is used 51 The fo rce on an atom under thermostat conditions is then governed by the Langevin equation: (2 4 ) Here, is the force felt by the atom, is the velocity of the atom, is friction constant and is a stochastic force chosen in a way to satisfy dissipation fluctuation theorem 52 The friction constant is determined based on the Deb ye temperature of the system and t he stochastic force is dependent on the temperature and the time step. 2.2 Classical Atomic Scale Modeling of Materials In order conduct an MD simulation a description of the inter atomic forces is required The formulation of the physics that governs particles at nanometer scales is q uantum mechanics. approximations is too computationally expensive, or time consuming with regards to CPU time to evaluate the interaction between atoms in dynamical systems on the ps to ns time regi mes. Therefore, empirical potentials are often employed to describe the interactions between particles in a more efficient manner. 2.2 Empirical Potentials Empirical potentials are functions used to represent the quantum mechanical potential energy bet ween particles. This negates the need to solve for the electron wave functions of the system, greatly increasing computational efficiency. For a system
19 of the potential energy can be divided into terms that are dependent on the number of atoms participating in an interaction, (2 5 ) The first term can be considered as t he potential energy due to an external field; while, the subsequent terms are interatomic potential energy functions. The 2 body term is of primary importance for describing a system of atoms; in that, it can describe attraction and repulsion. One of the simplest 2 body or pair potentials is the Lennard Jones (LJ) potential 48 which is often used to describe v an der Waals forces acting between atoms or molecules, (2 6 ) This has met with wide success in the simulation of noble gas interactions where dispersion forces dominate, in particular liquid argon 53 This pair potential is dependent on the interatomic distance The parameters and are depe ndent on the element type of atoms and and are fi t to a dataset of experimental or quantum mechanical data. Furthermore, the LJ potential is divided into two parts : repulsion and attraction The attraction term represents the dec rease in potential energy two atoms experience when coming into bonding proximity of one another. Conversely, the repulsion term captures the increase in potential energy the two atoms impose on each other if too much electron cloud overlap occurs. The s ummation of these terms describes the interatomic potential well between atoms and The features of this well
20 contain information essential to describing the system such as, bond length, bond energy and thermal expansion. In order to capture the ionic bonding in ceramics, particularly oxides, the Buckingham potential has been widely implemented 54 (2 7 ) This pair potential can be seen as a modification of the LJ potential; in that, the term is replaced by an exponential term exponential term The last term is the Coulombic term to take into account the fixed charge of each particle and Furthermore a shell model can be used to c apture atomic polarizability by considering the atom to be composed of a core and shell, with different charges summing to the total charge of the atom. The core and shell are considered to be connected by a spring with a spring constant and displ aced from equilibrium by a distance : (2 8 ) Covalent bonding presents a particular problem in that it has varying bond orders depending on the local environment. To address this Tersoff 55 proposed the use of a bond order term to augment a set of repulsive and attractive terms, based on the work of Abell 56 : (2 9 ) Here the repulsive term is:
21 (2 10 ) and the attractive term is: (2 11 ) The cutoff function: (2 12 ) smoothly reduces the potential to zero between and The bond order term: (2 13 ) contains all the multibody components. The angular function is: (2 14 ) Tersoff successfully parameterized thi s potential to model the covalent nature of silic on and diamond 55, 57 This concept of augmenting the pair terms of a potential with a bond order term has spawned a series of empirical potentials that includes the reactive empirical bond order ( REBO ) potential for hydrocarbons 37 The major modifications made to the Tersoff potential within REBO potential formalism are the additions of coordination and conjugation terms to the bond order term. The details of the first generation REBO potentia l will not be presented; instead we will skip to the second generation REBO 38 potential which is a ma jor focus of this work. However, it should be mentioned that the
22 first generation of REBO potential was success fully applied to CVD growth of diamond 37 frictional properties of diamond surfaces 58 and the mechanical properties o f fullerenes 59 In th e second generation REBO form alism the pair potential shown in Equation (2 9 ) remains unchanged. The attractive and repulsive terms and are slightly modified to: (2 15 ) and (2 16 ) T he cutoff function is modified to: (2 17 ) As mentioned previously, the first generation REBO potential added terms to capture the coordination and the conjugation. The second generation REBO potential kept these modification s and added torsion. The second generation REBO bond order term has the form: (2 18 ) Where captures angu lar and coordination dependence:
23 (2 19 ) Here the coordination function is a bicubic spline dependent on the number of carbon and hydrogen neighbors as defined as: (2 20 ) T he angular term for carbon is a sixth orde r polynomial, (2 21 ) Separate sets of coefficient s are fit for each region : and For the region u nder and over coordinated structures are captured by t he revised angular function: (2 22 ) H ere is another sixth order polynomial. While: (2 23 ) whe re is the total number of neighbors: (2 24 ) The term that captures radicals and co njugation is a tricubic spline:
24 (2 25 ) which is dependent on the total number of neighbors of atom and and the number of conjugate neighbors The number of conjugate neighbors ( ) is dependent on the number of carbon neighbors of a tom and (2 26 ) Here the function is: (2 27 ) and the function is: (2 28 ) To capture the rotation of groups around a carbon carbon bonds a dihedral function is used with the form: (2 29 ) where is the torsional angle between atoms and is the cutoff function and is a tricubic spline. The function is found using the vectors and in th e following way: (2 30 )
25 The second generation REBO potential has successfully modeled mechanical and thermal properties of carbon nanostructures 60 63 a s well as ion beam modification of polymers and nano materials including carbon nanotubes (CNTs) 42, 64 66 While the se cond generation REBO potential is usually only applied to first nearest neighbors, long range interactions are crucial in many systems including polymers and graphite. There have been multiple efforts to extend the REBO formalism beyond the maximum cutoff First, and the most straightforward, is to couple the REBO potential with a LJ potential t o produce a new potential function: (2 31 ) H ere is the pair potential summatio n of Equation (2 9 ) and is the pair potential summation in Equation (2 6 ). I nterpolating between the two functions is done using a cubic spline. Cubic spline coefficients are generated to for m a continuous transition from the REBO potential to the LJ potential between the maximum REBO potential cutoff and The LJ potential cutoff is set at The parameters and are calculated based on the element dependen t parameters using mixing rules where : (2 32 ) a nd (2 33 ) Stuart et al. coupled the first generation REBO potenti al to a Lennard Jones (LJ) potential 48 using a switching function to create the adaptive intermolecular REBO
26 (AIREBO) potential 67 The switching function is added as a term to the LJ potentia l in Equation (2 31 ) and make s the LJ energy component into : (2 34 ) Here is a universal switching function: (2 35 ) and is the Heaviside step function. The function allows for switching to depend on the distance between the pair. The function creates a dependence on a hypothetica l bond order term and depends on the number of neighbors of atom and AIREBO has been shown to more accurately capture the gr aphite to diamond transition tha n the original REBO potential 67 Also the AIREBO potential has been used to model sputtering of molecular solids 44, 68 Recently Pastewka et al. 69 implemented a screening function into the REBO potential in order to efficiently extend the bond d issociation and formation to longer distances. The function used is based on the screening function used in the modified embedded atom method (MEAM) potential 70 Rather tha n extending the potential by coupling the REBO potential to a LJ potential atoms beyond the short range cutoff are included using a modified cutoff function: (2 36 ) H ere is the same as the second generation REBO potential cutoff function Equation (2 17 ) is the same cutoff function applied the edge of the screening
27 region and is the screening function The formalism of remains t he same as except the vales of and for the screening region are given dependencies on the terms in which they appear. In particular different cutoff regions are used for the cutoff functions in the pair ter m angular term and neighbor terms. This modifies in Equation (2 9 ) Equation (2 19 ) and Equation (2 20 ) into separate cutoff functions: and respectively. Where each of the new cutoff functions has the form of Equation (2 36 ) except with different cutoff regions and The sc reening region is similar to the LJ region, in that it extends atomic interactions beyond the first nearest ne ighbor shell. Including atoms in this region is not only computationally inefficient, but also inappropriate for functions dependent on the number of neighbors in Equation (2 20 ). In order to maintain efficiency and the correct number of neighbors, atoms in the screening region can be effectively screened out based on the evaluation of the function: (2 37 ) H ere is an ellipsoidal function that is dependent on the ratios of and to that of The new parameters in the screening function and and in the cutoff function of the screening region and are fit to the interlayer spacing of graphite. This has improved modeling of crack propag ation in diamond and the fracture of CNTs 69
28 Another method is the long range carbon bond order potential II (LCBOPII) 71 w hich includes the long range term as modified Morse potential 72 The primary motivation for the development of these complex long range intera ctions is the proper description of the graphite to diamond transition barrier that is ill defined with the first generation REBO potential. However, these complex modifications come with added computational costs. For example, the AIREBO potential was fo und to be an order of magnitude slower than the first generation REBO potential 73 2.3 Quantum Mechanical Modeling of Materials The particles governing most interatomic interactions in materials are electrons. To determine the behavior of a singl e electron in an external field, one must find its wavefunction by solving the single particle time dependent Schrdinger equation 74 : (2 38 ) H ere is the mass of the electron, is the Laplacian operator, and constant divided by By using separation of variables the time indep endent Schrdinger equation can be found to be: (2 39 ) where is the energy related to time independent wavefunction This can be written more compactly us ing the Hamiltonian operator (2 40 ) The Hamiltonian operator acting on the eigenfunction produces an eigenvalue that is the associated to the energy of the quantum particle.
29 2.1.1 Molecula r Orbital Theory Systems of interest to materials science have multiple electrons interacting with multiple positive nuclei. For these systems the Hamiltonian is a bit more complex: (2 41 ) In this equation and are the number of electrons and nuclei in the system, is the mass of nuclei and is the scalar distance from particle to particle 75 The first and second terms are the kinetic e nergies of the electrons and nuclei, the third, fourth and fifth terms are electron and nuclei, inter electron and inter nuclei Coulombic interactions. Unfortunately, there is no analytical solution to the multi body quantum mechanical system. Consequentl y approximations must be used. The most obvious and powerful is the Born Oppenheimer approximation, which allows the nuclei to be treated as classical particles whose motion is negligible with respect to that of the electrons 76 This removes the second and fifth terms f rom Equation ( 2 41 ) to create the following all electron Hamiltonian: (2 42 ) Here, is the kinetic energy of the electrons, is potential of the electrons interacting with themselves (known as correlation) and is the potential of the electrons and the surrounding environment. This external potential is a generalization of the third term in Equation (2 41 ). 220.127.116.11 Slater d eter minant s Now that the electron Hamiltonian (Equation (2 42 ) ) has been constructed the form of the wa ve function needs to be addressed. This can be done by using a spin dependent wavefunction of electrons where is the
30 position and is the spin state of electron A simple way to construct such a function is as the product of single electron functions (Fock approximation): (2 43 ) Since electrons are fermions the Pauli exclusion princip le applies, whi ch states that the wavefunction of two fermions is: (2 44 ) This stipulates that two electrons cannot have the same state 74 To capture this t he product in Equation (2 43 ) can be replaced by a linear combination of products (Hartree Fock approximation) with alterna ting positive and negative term s over each permutation of and This is conveniently expressed as the determinate of a matr ix know as a Slater determinant: (2 45 ) 18.104.22.168 Basis sets While the Slater determinate provides a form to properly capture the Pauli exclusion princip le it does not provide a form for the individual wavefunction s One approach is to generate molecular wavefunction s as linear combinations of atomic wavefunction s : (2 46 )
31 This is referred to as the linear combination of atomic orbitals (LCAO) basis set. Modern basis sets employ linear combinations of localized function s such as Gaussians, or periodic functions such as plane waves. Localized basis sets used in this work inclu de the 6 31G* basis set, which employs 6 primitive Gaussians and a double zeta polarized basis set for the valence electrons. 2. 1 .1 .3 Self c onsistent f ield m ethod Now that the nature of the electron wavefunction has been established a method to solve for it needs to be determined. The key to this is the variational principle which states that for any set of wavefunction s : (2 47 ) where is the ground state energy of the system. Thi s gives the criterion that the lower energy a set of wavefunction s predicts; the more accurately it describe s the ground state of the system. The Hartree Fock H amiltonian 77 for a single electron in a multi electron system is : (2 48 ) Here the integra ls and are: (2 49 ) and: (2 50 )
32 These integrals are a result of implementing the Sla ter determina nt wavefunction and apply ing it to the electron electron interactions 77 Applying the variational principle to the electron Ham iltonian and the Slater determinate composed of a given basis set yields the following energy expression: (2 51 ) where the coefficient summations can be removed from the integrals to produce: (2 52 ) The integrals in Equation (2 52 ) can be denoted as and for the numerator and denomin ator respectively. As the minimization of this function is the criterion for the ground state energy, setting the first derivative to zero allows one to solve for the coefficients via the secular equation, (2 53 ) Explicitly the element is : 1 2 (2 54 ) Here is the electron density matrix defined by:
33 (2 55 ) wavefunction in the form of the electron density in this equation seems unsolvable. Fortunately, Hartree proposed a solution to this dilem ma in 1928 in the form of iteration. In particular, an initial set of wavefunction s are guessed and used to calculate the predicted energy and iterated wavefunction s The iterated wavefunction s are used to solve for a new set of wavefunction s. This proc ess is repeated until the difference in energy predicted by sequential wavefunction s f a ll s below a predetermined criterion. This process is known as the self consistent field (SCF) method 78 It should be noted that the first computer was not created until 1 1 years after this method was proposed Thus, initial SCF methods were calculated manually which limited its application to relatively simple systems. 2.1.2 Density Functional Theory As is shown in Hartree Fock theory the electron Hamiltonian ( Equation ( 2 48 ) ) of a multi body system consisting of electrons is dependent on the wave equations of the entire system These wavefunction s can be expressed in terms of the electron density Considering this, in 1927 Thomas 79 and Fermi 80 developed an expression for the energy o f the system that was a functional of the electron density, thus establishing the foundation of density functional theory (DFT). It can be seen that the electron nuclei and the electron Coulombic terms Equation (2 41 ) can be expr essed in terms of electron density 75 as follows:
34 (2 56 ) and (2 57 ) Here, and ar e dummy variables running over all space. While this established the concept of a potential as a functional of a charge density distribution it was not until many years later that the DFT was established for practical purposes. 22.214.171.124 Hohenberg Kohn the orems In 1964 Hohenberg and Kohn established two theorems which helped form modern DFT 81 The first theorem is known as the existence theorem and states that the electron s interaction with an external potential is determined by the ground state density 81 Therefore, the ground state density determines the Hamiltonian which determines the ground state wavefunction s, and all excited sates of the wavefunc tion s. Suppose there are two different external potentials and which lead to two different Hamiltonians and and wavefunction s and If it is assumed that each external potential has the sam e ground state density but is not the lowest energy state of then : (2 58 ) where: (2 59 )
35 C onsequently: (2 60 ) However, if the same argument is recast interchanging the labels of and it can be shown that: (2 61 ) Via reductio ad absurdum Equation (2 61 ) shows that there cannot be two different external potentials with the same ground state density. Therefore, the density uniquely determines the external potential. The second theorem shows that the density also obeys a variational principle Equation (2 47 ). In particular as theorem I states, the density determines the external potential, which can be used to calculate the system energy Thus, for a set of densities the one which has the lowest energy is the ground state. Considering a ground state density with a Hamiltonian and a wavefunction evaluating for the energy: (2 62 ) If another density is considered with a wavefunction it follows that must be greater that since: (2 63 ) thus giving a function of the total energy in the form of: (2 64 )
36 Energy can be minimized by varying the electron density. This establishes the gr ound state density. 126.96.36.199 Kohn Sham theorem The theorems of Hohenberg and Kohn established DFT as a valid theory H owever, this is no bette r than Hartree Fock (HF) theory presented in the previous section. Since, all that has been done is replac ing the iterative minimization of the energy with respect to a wavefunction with a n iterative minimization with respect to a charge density. The key to establish ing DFT as an efficient tool was developed by Kohn and Sham 82 body problem by an auxiliary independent particle prob interacting V state of the electron density can be represented by the ground state density of an auxiliary system of non interaction particles. Th e second assumption is to create an auxiliary Hamiltonian of a single non interacting electron with a kinetic energy term and an effective local potential (2 65 ) The energy of the Kohn Sham auxiliary system is: (2 66 ) where the last term contains all the approximations involved in evaluating the energy of the system. Various a pproximations have been made and improved upon.
37 First is the local density approximation ( LDA ). This specifies that the values of at a particular position are approximated by the charge density at that point. Later improvements such as the generalized gradient approximation (GGA) were made that take the gradient of the charge density into account in the term. 4.3 Post HF, Hybrid and Combinatorial Methods Hartree Folk (HF) theory and density functional theory (DFT) are the basis for many of the more complex methods currently being used in the computational materials science community; in that many adaptations are made to improve the accuracy of these methods. HF theory is often used in conjunction with a post Hartree Fock analy sis Post HF methods include configuration interaction (CI). CI takes correlation into account by creating a new wave function based on the results of a HF calculation. The new CI wavefunction is a li near combination of the HF wave function and sets of ex cited configurations in which the occupancy of an occupied orbital is changed to unoccupied (virtual) orbital and a virtual orbital is changed to occupied. An analogous method used in this work is coupled cluster (CC) theory where the set s of CI wave fun ctions are considered. And the theory is noted accordingly CIS singles, CISD singles and doubles etc. Hybrid methods use combinations of HF theory and DFT to calculated the electron wavefunctions a system. to capture method is B3LYP 83 Combinatorial methods give accurate predictions of thermodynamically data. This is done by using a set of predefined calculations with different methods, and a large
38 basis set. These calculations are used to give chemical accurate ( ) enthalpies of formation of molecular systems. Improved variations of these methods have been made and are designated by the suffix number of the G, in the G2 84 and G3 85 methods. 2. 4 Summary In this work the primary focus is on MD simulations using empirical potentials, and empirical potential development. Empirical potentials are a way to bypass explicitly calculating th e electronic structure of a system to determine the system properties. These potentials have developed over the decades to become more complex and accurate The potential formalism focused on in this work is the second generation reactive empirical bon d order (REBO) potential. This potential is well established for use in modeling hydrocarbon systems, and allows for bond breaking and formation. Furthermore, quantum mechanical based methods are used for calculating dataset s for fitting potential paramete rs and by collaborators to calculate reaction enthalpies and transition states. In these calculations hybrid methods and combinatorial methods are often employed. Hybrid methods such as B3LYP 83 use combinations of HF based theory and DFT to calculated the electron wavefunction s a system. Combinatorial methods like the G3 85 method use multiple thermodynamically calculations to achieve accurate predictions of molecular enthalpies.
39 Figure 2 1 Periodic boundary condit ions
40 CHAPTER 3 POTENTIAL DEVELOPMEN T 3 .1 REBO O xygen The second generation REBO potential was parameterized to include oxygen interactions with hydrocarbon s by Ni et al. in 2004 86 There have been some issues with the energetics of this potential and some modifications to the coordination function ha ve been made post publication. Changes include the adjustment of from the pubished value of to to properly capture the atomization energy of the molecule. While this and other corrections were made to address some issues wi th the potential, the effects on other bonding situations were not full y accounted for. Considering the current issues with the implemented form of the second generation REBO potential including oxygen (REBO CHO) the coordination function has been refit. The coordination function used in the REBO CHO potential is modified from Equation (2 19 ) for bonds containing oxygen or oxygen neighbors to the function w here is the summation of carbon and hydrogen nei ghbors. In order to refit the values of this function a dataset of small molecules similar to that used by Ni et al. is considered. Specifically, molecules contain ing the bonds types: , and with each possible coordination of atom is used to find appropriate values of the function While the original dataset used a single molecule to determine each integer value of the coordination function, t he new dataset includes molecules with each possible value of carbon neighbors ( ) and hydrogen neighbors ( ) for the considered bond types. In particular, the dataset includes molecules with all bond types and number of nearest neighbors that satisfy the coordination criterion :
41 (3 1) H ere repre sents the number of neighbors need ed to achieve full coordination of a bonded atom in one of the bonds included in the fitting dataset and are the number of carbons, hydrogen and oxygen neighbors of atom res pectively This is done to find the best value of the coordinat ion function that describes all possible bonding environments. Dissociation energies of each bond type along with the atomization energies are used in the refit of the coordination function a nd these are listed in Table 3 1 Table 3 2 and Table 3 3 3.1.1 Parameter Fitting Results Atomization energies and bond dissociation energies for each of the 64 molecules in t he dataset are calculated using the GAUSSIAN03 87 package. Initial structures are relaxed at the B3LYP 83 /6 31G* level Energies of the subsequent relaxed molecules are calculated using the G3 approach 85 Zero point energy corrections are not used in calculating energies in orde r to be consistent with the previous fitting done by Ni et al. 86 The values of the coordination function are fitted at each point for each bond type using the least squared fitting routine in MATLAB 88 Values of the pair and angular terms a re determine d based on geometries relaxed at the B3LYP/6 31G* level. Weights on the dissociation and atomization energies are adju sted to give the lowest error. The currently implemented coordination values gi ve dissociation energies that differ from ener gies calculated with the G3 method 85 by on average, with crucial bonds energies being too low see Table 3 1 Table 3 2 and Table 3 3 In particular, the hydroxyl carbon bond is too weak by The refit values reduce the average error
42 in dissociation energy to Furthermore, t he hydroxyl dissociation error is improved to be within of G3 energies The refit coordination function values are given in Table 3 4 and the refit bond dissociation energies and atomization energies are in Table 3 1 Table 3 2 and Table 3 3 In Figure 3 1 the predi cted dissociations energies form the updated REBO CHO potential are plotted as a function of energies calculated using the G3 method in order to show relative deviations for each bond type. 3.2 REBO S ulfur Sulfur interactions with hydrocarbons play a cruci al role in processes including the vulcanization of rubber 89 and its reclamation 90 oil processing, gas sensors 91, 92 and batteries 93, 94 Additionally, t hiophene based molecules and polymers are widely used in organic electroni cs 95 97 Therefore, the second generation REBO potential is exte nded to include sulfur. This work thus builds on p revious efforts to extend the potential to include fluorine 43 oxygen 86 and molybdenum di sulfide 98 The parameter fitting of the sulfur hydrocarbon interactions is conducted in a n analogous approach to that of oxygen 86 3.2.1 Parameter Fitting The dataset for the sulfur hydrocarbon interactions con sists of the properties of solid and molecular systems. The properties of the solid systems are determined using density functional theory (DFT) within the Vienna Ab initio Simulation Package (VASP) software package 99, 100 The electron wavefunction s are calculated using projected augmented wave (PAW) psuedopotentials 101 Systems are relaxed with the GGA 102, 103 (PBE) 104 method with an energy cutoff of A k point mesh of and a force convergence criteri on of is also used. The properties of the molecular
43 systems are calculated with GAUSSIAN03 87 Molecular geometries are optimized, and bond stretching and bending curves are determined at the B3LYP/6 31G* level 83 w hile atomization and dissociation energies are calculated with the G3 method 85 The changes in energy due to bond stretching and bending that a re calculated with B3LYP are shifted in energy to have minima that correspond to G3 values. The two body related parameters, Equation (2 15 ) and (2 16 ) for the sulfur car bon, sulfur hydrogen and sulfur sulfur interactions are fit prior to the multi body parameters. In particular, t he pair parameters are fit to molecular bond stretching curves and solid strain curve s, which are illustrated in Figure 3 2 During the fitting of the pair terms the multi body term is left as a fitted parameter and given a range of to This establishes a set of pair parameters capable of capturing a range of values of the bond order term Molecular species are weighted heav i er than solid phases due to the largely molecular nature of the sulfur hydro carbon systems. The fitted pair parameters are given in Table 3 5 Potential cutoff distan ces and are chosen to be between first and second nearest neighbor s within the molecular dataset Once the minimum error for the dataset is established the angular term is then fit A si xth order polynomial Equation (2 21 ) is used for the angular function in congruency with the hydrocarbon angular function. This function also possesses the flexibility to capture the potential energy response to the change in angle while maintaining rea sonable values at angles less than 60. Parameters for each sulfur centered angle type and where is or are fit to the bond bending curves of representative molecules see Figure 3 3 For the parameters the S 3 molecule and the S 8 uded in the fitting
44 dataset The parameters are fit to thiobismethane and the parameters are fit to hydrogen sulfide. Bond energies are fitted to at zero degrees for the sulfur sulfur and sulfur hydrogen terms and for t he sulfur carbon term, to prevent the unphysical stabilization of over coordinated structures. The resulting angular function parameters are displayed in Table 3 6 The coordination function is fit in a similar manner as the refi t of the REBO CHO coordination function. One e xcept ion is that a tricubic spline is used for the coordination function for each bond type: and and the values are given in Table 3 7 The values of the and coordination function where is zero are the same as the bicubic spline values for the second generation REBO potential, and are given in italics in Table 3 7 For hydrocarbon bonds with sulfur neighbors and sulfur hydrocarbon bonds, the coordination func tion values are fit to the dissociation and atomization energies of small molecules. As with the refit of the REBO CHO coordination function the criteria in Equation (3 1) is used in conjunction with considering possible bond order values to establish a dataset of molecules. Dissociation energies and atomization energies are calculated at the G3 level. Atomization energies are included to establish the magnitude of the total cohesive energy of the molecule which ensures reas onable changes in energy while exploring the potential energy space of a system during a MD simulation. Dissociation energies are also included into the fitting database to ensure the best possible capturing of the change in energy during chemical react io ns. The results of the fit to dissociation energies is shown in Figure 3 4 ; t he average deviation from G3 values is 13.7%.
45 3.2.2 Validation and Testing In order to test the performance of the potential under various bonding en vironments, atomization energies of a set of representative molecules are calculated with the modified second generation REBO potential for sulfur (REBO CHS) and compared to G3 values. Characteristic bonding environments include : elemental sulfur molecule s, hydrocarbon molecules with bonds, thials, thiols, sulfides and ring structures that includ e sulfurs. The test set includes molecules, of which are not included in the fitting dataset The average error in the atomization energy is found t o be for the entire set, and for species not included in the fitting dataset The difference in atomization energy between the newly developed REBO CHS potential and atomization energies calculated with the G3 method for molecules containing cha racteristic bonds is show n in Figure 3 5 The ground state of elemental sulfur is cycloo catasulfur, which is an eight membered crown shaped ring 105 The bond length, bond angles and torsion angles of S 8 are predicte d to withi n of corresponding B3LYP geometries. The atomization energy of the ring is predicted within of the G3 energy Other purely sulfur compounds including the sulfur dimer and S 3 and S 4 ring s are found to have an average deviation from G3 energies of However, these small sulfur molecules are included in the fitting dataset C ompounds not in the fitting dataset including the and rings are found to have atomization energies within of G3 energies. The potent ial captured the atomization energies of molecules containing thial and thiol groups well with average errors of approximately for each group. Bond lengths are also well captured C onsidering the prototypical molecules propanethione
46 and methanethi ol have errors in bond lengths of and respectively, when compared to B3LYP geometries. The methanethiol bond angle is also predicated within of the B3LYP geometry. For molecules containing mult iple thiol groups, the hydrogen hydrogen repulsio n from the angular function from the second generation REBO potential 38 where is or is found to be too strong for the case. Specifically it causes dissociation of the molecule during close contact between thiol groups. Therefore, the angular function is set to zero to mitigate th is repulsion. Sulfur bonded to two carbons is considered in the form of sulfide bonds and within ring b onds. Dimethalsulfide is fit to have a bond length within of B3LYP and a bond angle within The atomization energy for dimethalsulfide is within of G3 values, while the average error of the test set is The ring molecules containing sulfur atoms are predicted with the least a ccuracy with an average error in atomization energy of This is due to over binding of conjugate bonds, since the coordination function for this bonding environment is fit to double bonds. 3 3 Summary The coordination function for the oxygen hydrocarbon second generation REBO potential is refit in order to improve bond dissociation energie s. A more extensive dataset is created, including all possible sets of coordination of atom for each bond type The average error in dissociation energy for each molecule in the fitting dataset is reduced from to However the average er ror in atomization energies of the test set is increased from to While undesirable, this error
47 remained under and is found to be unavoidable baring a complete refit of the potential. A similar form of the second generation REBO potential i s developed for the sulfur hydrocarbon system. The differences in formalism are the inclusion of a seventh order polynomial for the angular function which is more consistent with the hydrocarbon second generation REBO potential. Also a tricubic spline i s used in place of the bicubic spline used in the REBO CHO potential as was done for the fluorocarbon REBO potential 43 This increase i n flexibility allowed for the average error in dissociation energies to be and the average error in atomization energy to be
48 Table 3 1 and bond dissociation energies (D O ) and atomization energies ( in Original Refit G3 Molecule D O a D O a D O a H 3 C COH 2.09 26.93 1.80 28.27 3.17 25.67 H 2 C C(OH) 2 4.78 31.74 5.70 35.37 5.38 31.88 H 3 C C(OH)O 2.50 32.53 3.47 34.84 4.05 33.16 H 3 C C(OH) 3 3.80 43.58 3.39 46.97 3.87 42.39 H 2 C C(OH)CH 3 3. 99 39.39 6.17 42.90 6.25 39.62 H 3 C C(CH 3 ) 2 O 2.00 40.44 3.39 41.87 3.54 40.19 H 3 C C(OH) 2 H 3.26 38.76 3.28 41.51 3.68 37.50 H 3 C C(OH) 2 CH 3 3.67 51.52 3.41 54.80 3.79 49.90 H 2 C C(OH)H 5.26 26.96 6.22 29.69 6.49 27.39 H 2 (HO)C C(OH)H 2 3.81 38.66 3.57 40.72 3.53 37.02 H 3 C C(OH)(H)CH 3 4.32 47.57 3.53 48.75 3.66 45.17 H 3 C C(CH 3 ) 2 OH 4.71 60.40 3.37 61.83 3.65 57.39 H 3 C C(H)O 3.24 27.99 3.40 28.62 3.54 27.87 H C(O)OH 3.54 20.19 3.67 21.67 4.29 20.82 H C(OH) 3 4.37 30.79 3.05 33.26 4.15 30.10 H C(O)H 4.17 15. 55 3.52 15.37 3.77 15.52 H C(O)CH 3 2.93 27.99 3.52 28.62 3.81 27.87 H C(OH)CH 2 3.75 26.96 5.24 29.69 4.62 27.39 H C(OH) 2 H 3.85 25.98 3.34 28.20 4.14 25.37 H C(OH) 2 CH 3 4.28 38.76 3.49 41.51 4.11 37.64 H C(OH)H 2 4.46 21.88 3.75 22.33 4.11 20.86 H C(OH) (H)CH 3 4.84 34.72 3.69 35.54 4.06 32.99 H C(CH 3 ) 2 OH 5.26 47.58 3.70 48.78 4.03 45.18
49 Table 3 2 bond dissociation energies (D O ) and atomization energies ( in Original Refit G3 Molecule D O a D O a D O a C O 10.14 10.14 10.17 10.17 11.12 11.12 (CH 3 O) 2 C O 5.96 50.05 5.71 53.04 6.78 48.99 (HO) 2 C O 5.98 24.48 5.77 26.97 7. 11 25.77 (HO)OC OH 3.42 24.48 4.40 26.97 4.81 25.77 HCC OH 4.83 20.81 5.56 21.69 5.25 20.79 HOCH O 6.95 20.19 6.66 21.67 7.77 20.82 OCH OH 4.40 20.19 5.25 21.67 4.63 20.82 HO(CH 3 )C O 5.60 32.53 6.57 34.84 7.64 33.16 O(CH 3 )C OCH 3 0.35 45.32 3.91 47.88 4.35 44.77 HO(CH 2 )C OH 4.10 31.73 6.35 35.37 4.79 31.99 O(CH 3 )C OH 3.05 32.53 5.16 34.84 4.66 33.16 H(OH) 2 C OH 4.25 30.79 3.83 33.26 4.47 30.13 CH 3 (OH) 2 C OH 4.70 43.58 4.38 46.97 4.44 42.39 H 2 C O 7.09 15.55 6.90 15.37 7.67 15.52 CH 3 CH O 3.61 27.99 4 .24 28.62 4.80 27.87 CH 2 CH OH 3.22 26.96 5.79 29.69 4.60 27.39 (CH 3 ) 2 C O 3.77 40.44 5.20 41.87 7.94 40.19 CH 2 (CH 3 )C OH 2.91 39.39 6.27 42.90 4.59 39.62 HOCH 2 OH 4.15 25.98 5.06 28.20 4.19 25.37 HO(CH 3 )CH OH 4.47 38.76 5.09 41.51 4.27 37.64 HO(CH 3 ) 2 C OH 4.79 51.52 5.15 54.80 4.32 49.90 CH 3 OCH 2 OCH 3 1.44 38.77 3.80 41.24 3.75 36.85 CH 3 OH 4.10 21.88 4.39 22.33 3.84 20.86 CH 3 CH 2 OH 3.79 34.72 4.45 35.54 3.97 32.99 CH 3 CH 2 OCH 3 1.08 47.50 3.20 48.58 3.68 44.62 (CH 3 ) 2 CH OH 3.78 47.58 4.82 48.78 4.07 45 .18 (CH 3 ) 3 C OH 3.75 60.40 5.02 61.83 4.13 57.39 CH 2 C O 6.02 21.36 5.96 21.29 7.32 22.27 HO C(OH) 3 3.85 34.68 4.06 38.84 4.49 34.86
50 Table 3 3 and bond dissociation energies (D O ) and atomization energies ( in Orig inal Refit G3 Molecule D O a D O a D O a O C 10.14 10.14 10.17 10.17 11.12 11.12 HOO CH 3 2.33 24.12 4.29 26.81 2.85 22.62 HO CH 3 4.10 21.88 4.39 22.33 3.84 20.86 CH 3 O CH 3 1.38 34.65 3.13 35.36 3.53 32.48 O H 4.41 4.41 4.57 4.57 4.43 4.43 HOO H 3.20 11.61 4.34 13.48 3.71 10.89 HO H 4.69 9.10 4.71 9.28 5.07 9.50 CH 3 O H 1.99 21.88 3.47 22.33 4.50 20.86 O O 5.26 5.26 4.82 4.82 5.07 5.07 O O 2 0.31 5.57 1.11 5.93 1.06 6.13 HO OH 2.79 11.61 4.35 13.48 2.02 10.89 CH 3 O OCH 3 3.18 36.61 2.39 40.11 1.65 34.36 Table 3 4 Refit spline values for oxygen hydrocarbon interactions N C +N H N O P CC P CH P CO P OC P OH P OO 0 0 0.000 0.000 0.500 0.102 0.025 0.032 0 1 0.263 0.336 0.138 0.057 0.022 0.020 0 2 0.182 0.635 0.120 0.000 0.000 0.000 0 3 0.338 0.507 0.193 0.000 0.000 0.000 1 0 0.000 0.000 0.207 0.374 0.013 0.003 1 1 0.007 0.191 0.245 0.000 0.000 0.000 1 2 0.146 0.144 0.075 0.000 0.000 0.000 2 0 0.000 0.000 0.185 0.000 0.000 0.000 2 1 0.188 0.354 0.209 0.000 0.000 0.000 3 0 0. 000 0.000 0.585 0.000 0.000 0.000
51 Table 3 5 Pair parameters S C S H S S A( ) 755.86 1033.73 4489.11 1.90 0.81 1.79 Q() 0.95 0.09 0.16 B1( ) 1423.74 1167.23 4906.07 1.94 0.85 1.78 R min () 2.1 1.5 2.3 R max () 2.4 1.8 2.6 Table 3 6 Angular parameters X S C X S H X S S a 1 6.97E 02 2.95E 03 1.88E 02 a 2 5.80E 02 1.60E 03 6.86E 02 a 3 2.11E 01 1.83E 02 8.07E 02 a 4 1.38E 01 2.74E 02 7.64E 02 a 5 6.63E 02 1.14E 02 5.44E 02 a 6 1.31E 01 1.98E 02 2.54E 02 a 7 2.01E 03 1.20E 02 1.48E 02
52 Table 3 7 Tricubic spline values for the coordination function P ij N C N H N S P CC P CH P CS P SC P SH P SS 0 0 0 0.0 0.0 0.3412 0.2315 0.0018 0.0007 0 0 1 0.0128 0.9398 0.4869 0.2844 0.0052 0.0141 0 0 2 0.1210 0.4464 0.4738 0.0 0.0 0.1089 0 0 3 0.0168 0.2290 0.3476 0.0 0.0 0.0 0 1 0 0.0 0.2093 0.3797 0.2138 0.0063 0.0111 0 1 1 0.0671 0.2899 0.4090 0.0 0.0 0.1028 0 1 2 0.0770 0.4419 0.3480 0.0 0.0 0.0 0 2 0 0.0079 0.0644 0.3389 0.0 0.0 0.1054 0 2 1 0.0126 0.2852 0.4293 0.0 0.0 0.0 0 3 0 0.0161 0.3039 0.4405 0.0 0.0 0.0 1 0 0 0.0 0.0100 0.5200 0.2765 0.01 07 0.0070 1 0 1 0.0950 0.4279 0.4288 0.0 0.0 0.1063 1 0 2 0.1650 0.3032 0.3394 0.0 0.0 0.0000 1 1 0 0.0030 0.1251 0.3142 0.0 0.0 0.1051 1 1 1 0.1282 0.3864 0.3380 0.0 0.0 0.0 1 2 0 0.0063 0.2989 0.4099 0.0 0.0 0.0 2 0 0 0.0 0.1220 0.3175 0.0 0 .0 0.0494 2 0 1 0.0927 0.2156 0.3848 0.0 0.0 0.0 2 1 0 0.0032 0.3005 0.4000 0.0 0.0 0.0 3 0 0 0.0 0.3076 0.3966 0.0 0.0 0.0
53 Table 3 8 bond dissociation energies (D O ) and atomization energies ( in REBO G3 Molecule D O a D O a H 2 C CS 4.82 20.13 5.04 20.81 H 3 C CS 3.42 23.63 2.04 22.85 HC CSH 7.33 21.26 8.34 20.08 H 2 C C(SH) 2 5.33 30.40 5.84 29.55 H 3 C C(SH)S 2.87 30.05 3.75 30.01 HC C(SH) 2 4.31 25.44 5.25 24.37 H 2 C C(SH) 3 3.65 35.06 3.89 33.56 H 3 C C(SH) 3 3.02 39. 34 3.57 38.29 H 2 C CH(SH) 6.30 27.51 6.62 26.95 H 2 C CH(SH) 3.75 27.25 4.30 27.12 HC CH(SH) 5.24 22.52 6.07 21.80 H 2 C C(SH)CH 3 5.61 40.56 6.52 39.88 H 3 C C(CH 3 )S 3.33 40.34 3.91 40.10 HC C(CH 3 )SH 4.59 35.60 5.92 34.67 H 2 C CH(SH) 2 4.06 32.51 4.10 31.09 H 3 C CH(SH) 2 3.47 36.83 3.75 35.78 H 2 C C(SH) 2 CH 3 4.01 45.42 4.11 43.98 H 3 C C(SH) 2 CH 3 3.33 49.64 3.78 48.69 H 2 C CH 2 SH 4.22 29.36 4.20 28.55 (HS)CH2 CH2(SH) 3.13 36.49 3.60 35.71 H 2 C CH(SH)CH 3 4.02 42.39 4.25 41.45 H 3 C CH(SH)CH 3 3.36 46.64 3.89 46.13 H 2 C C(CH 3 ) 2 SH 3.71 55.21 4.24 54.33 H 3 C C(CH 3 ) 2 SH 3.02 59.43 3.88 59.01
54 Table 3 9 bond dissociation energies (D O ) and atomization energies ( in REBO G3 Molecule D O a D O a H CS 3.29 10.13 2.31 9.78 H CSH 3.34 12.75 4. 05 12.10 H C(S)SH 3.33 17.14 4.12 17.04 H C(SH) 3 3.45 26.39 3.98 25.36 H CH(S) 3.89 14.02 4.33 14.12 H CH(SH) 3.93 16.68 4.02 16.05 H C(S)CH 3 3.62 27.25 4.27 27.12 H C(SH)CH 2 4.53 27.51 4.83 26.95 H C(SH) 2 H 3.53 23.52 4.24 22.93 H C(SH) 2 CH 3 3.89 36 .83 4.22 35.79 H CH 2 (SH) 3.80 20.48 4.44 20.49 H CH(SH)CH 3 3.73 33.64 4.38 33.27 H C(CH 3 ) 2 SH 3.62 46.66 4.34 46.13 Table 3 10 bond dissociation energies (D O ) and atomization energies ( in REBO G3 Molecule D O a D O a C S 6.84 6.84 7.48 7.48 SC S 4.17 11.02 4.70 12.18 HSC SH 3.37 16.60 3.55 15.39 (CH 3 S) 2 C S 3.08 47.33 4.43 45.56 (HS) 2 C S 3.37 19.97 4.38 19.80 (HS)SC SH 2.32 19.97 3.09 19.80 (HS) 3 C S 3.24 26.19 2.57 23.95 (HS) 3 C SH 2.45 29.23 2.60 27.76 HC S 5.61 10.13 5.79 9.48 HC SH 4.39 12.75 4.62 12.10 CH 2 C S 4.79 20.13 5.23 20.81 HCC SH 5.86 21.26 4.82 20.08 SHCH S 4.40 17.14 5.01 17.04 SCH SH 3.18 17.14 3.77 17.04 CH 3 (SH)C S 3.57 30.05 4.95 30.01 CH 3 (S)C SCH 3 2.71 43.78 3.51 42.90 CH 2 (SH)C SH 3.57 30.38 3.62 29.52 CH 3 (S)C SH 2.58 30.05 3.38 30.01
55 Table 3 1 1 bond dissociation energies (D O ) and atomization energies ( in REBO G3 Molecule D O a D O a (SH) 2 C S 3.40 23.39 2.78 21.47 (SH) 2 CH SH 2.57 26.39 2.88 25.36 CH 3 (SH) 2 C S 3.39 36.32 2.86 34.43 CH 3 (SH) 2 C SH 2.57 39.34 2.93 38.29 CH 2 C S 5.56 14.02 5.82 14.12 CH 3 CH S 4.40 27.25 6.07 27.12 CH 2 CH SH 4.34 27.51 3.87 26.95 (CH 3 ) 2 C S 3.67 40.34 5.87 40.10 CH 2 (CH 3 )C SH 4.67 40.56 3.80 39.88 HSCH 2 SH 3.75 20.43 2.94 18.99 HSCH 2 S 3.00 23.51 2.97 22.81 HS(CH 3 )C S 4.02 33.93 3.01 31.8 9 HS(CH 3 )CH SH 3.09 36.83 3.12 35.79 HS(CH 3 ) 2 CH S 3.55 46.59 3.04 44.83 HS(CH 3 ) 2 CH SH 2.77 49.64 3.11 48.69 HSCH 2 SH 2.97 37.10 3.05 35.64 CH 3 S 4.07 17.44 3.20 16.54 CH 3 SH 3.28 20.48 3.37 20.49 CH 3 CH 2 S 4.10 30.62 3.20 29.33 CH 3 CH 2 SH 3.28 33.64 3.36 33.27 CH 3 CH 2 SCH 3 3.31 47.28 3.33 46.00 (CH 3 ) 2 CH S 4.24 43.64 3.18 42.15 (CH 3 ) 2 CH SH 3.43 46.66 3.37 46.13 (CH 3 ) 3 C S 4.17 56.41 3.15 55.02 (CH 3 ) 3 C SH 3.35 59.43 3.35 59.01 H 2 C S 4.38 16.68 3.97 16.05
56 Table 3 1 2 and bo nd dissociation energies (D O ) and atomization energies ( in REBO G3 Molecule D O a D O a (CH 3 )C SSH 3.35 24.15 2.82 23.15 (CH 3 )C SH 3.28 20.48 3.37 20.49 CH 3 SCH 3 3.29 34.10 3.34 33.22 S H 3.83 3.83 3.79 3.79 HSS H 3.24 10.66 3.36 10.35 HS H 4.12 7.95 4.10 7.89 CH 3 S H 3.04 20.48 3.95 20.49 S S 4.26 4.26 4.37 4.37 S 8 2.87 22.95 2.75 21.98 S 3 2.77 7.03 2.70 7.07 HS SH 2.99 10.66 2.78 10.35 CH 3 S SCH 3 2.76 37.64 2.87 35.95
57 Figure 3 1 Dissociation energies of oxygen datas et calculate with G3 plotted as function of values calculated with REBO
58 Figure 3 2 Bond stretching curves for and bonds. S C S H S S
59 Figure 3 3 Bond energy as a funct ion of bond angle for fitted function
60 Figure 3 4 Dissociation energies of sulfur dataset calculate with G3 plotted as function of values calculated with REBO
61 Figure 3 5 Atomization energies of test set of molecules, energies boxed in red are included in fitting database
62 CHAPTER 4 COMPARISON OF REBO AND DFT MD DEPOSITION SIMULATIONS 4 .1 CHF Deposition on Diamond In order to better understand the complex processes that occur during the energetic fluorocarbon growth of diamond like carbon ( DLC ) films a multilevel computational analysis is performed. The first involves MD simulation of 300 single trajectory depositions of using with the second generation REBO potential 38 Further analysis was conducted by a colleague Bryce D e v i ne 106 F or comparison 10 complementary depositions a re conducted with the linearly scaling DFT based MD method SIESTA 107 Based on the results of the MD simulations reactions are further analyzed with hybrid DFT methods B3LYP 108 B98 109 and BMK 110 and the multilevel G4MP2B3 method 1 11 4.1.1 Methodology Within the second generation REBO potential formalism electronic excitations and the charge of the atoms is not included. Consequently ions are not explicitly modeled. Rather carbon atoms with dangling bonds are represented by rad icals. Therefore charge related effects, such as the deceleration of the deposited species due to charge accumulation in the substrate are not accounted for. For the empirical MD simulations, hydrogen terminated diamond (111) surfaces of atoms are to t he surface. The has a thermostat applied using the Langevin 51 method e of atoms with a surface area of which is allowed to freely evolve. Molecules of randomly orient ed are deposited with kinetic energies of on the active
63 region. Simulations are run for with a time step using the third order predictor corrector integrator 49, 50 The relatively small active region is used to allow for comparison to DFT MD simulations with the SIESTA software 107 For the DFT MD simulations a by by spurecell of carbon atoms is used, as seen in Figure 4 1 applied in all three dimensions, leaving a vacuum between periodic slabs. Depositions of bot h radicals and cations are simulated. Temperatures are maintained at with the Nose Hoover method 112 114 The Verlet algorithm is used as an integrator, and simulations are run for with a time step. This work was carried out by colleagues Bryce Devine and Inkook Jiang. Higher level quantum chemical calculations are performed using the GASSIAN 03 software 115 Furth er calculations using the hybrid methods are performed using a cluster Figure 4 1 which has been previously determined to be the minimum structure to accurately reproduce hybridization 116 This work was carried out by colleague Bryce Devine. 4.1.2 Results Based on the MD simulations of 300 single trajectory depositions of using the REBO potential reactions are found to depend on the location of the impact and the orientation of the deposited molecule. Given the pyramidal structure of it can either land with carbon or fluorine participating in the initia l impact. The simulations show that fragmentation of the molecule is more likely if the fluorine atoms of the molecule initially impact the diamond surface, rather than the carbon atom.
64 The impact location is also found to affect the products for med during the deposition. In Figure 4 2 the three sites of the (111) diamond surface are shown. The top carbon atom is referred to as the atop site and is labeled (A), the recessed surface carbon is labeled (S) and the hollow site is labeled (H). A majority of deposited radicals (60%) interacted with the atop site, since it is the most exposed. The recessed site is more accessible then the hollow site, and is the primary interaction location of (28%) of the deposited radicals The atop site produced the most reactions; in particular new products are formed 80% of the time when the incident radical impacts this site directly Approximately half of these reactions involved the removal of a hydrogen atom from the surface, and resulted in the bonding to the surface. New products resulted in of the depositions impacting the recessed carbon site (S), with of the reactions leading to surface bound The results of these depositions are summarized in Table 4 1 Ten DFT MD simulations are performed for each charge state, radical and cation, of the molecule. The results of these depositions are summarized in Table 4 2 It can be seen that the radical is more reactive according to DFT than second generation REBO potential as a majority of the DFT MD simulations result in reactions. Similar reactions are observed for the radical and cation, given that is produced in 40% and 30% of the reactions for the radical and the cation respectively in the DFT MD simulations Reactions based on the radical atoms are shown in Table 4 3 The BMK hybrid metho d is used for the comparison of first principles methods and the second generation REBO potential The s econd
65 generation REBO potential does surprising well for an empirical potential at predicting the reaction enthalpies involving the radical radical In order to explore the removal of from the surface the bond ing of and the formation of (reaction (3) Table 4 3 ) a transition state calculation is p er formed. The synchronous transit quasi Newton Raphso n algorithm 117 is used with the B3LYP/6 31G(d) method to find the transition state shown in Figure 4 3 Various initial geometries are used as input structures; however, the same saddle point is found f rom all starting orientations. Based on the saddle point energy and the separate reactants the activation enthalpy is found to be 4.1.3 Discussion The quantum chemical simulations show the differences between the interactions of the ra dical and the cation. It can be seen from reaction (7) in Table 4 3 that the most energetically favorable reaction of the cation is to remove a hydrogen from the surface and produce and While reaction (3) shows that the second most energetically favorable reaction of the radical is to bond to the diamond substrate and produce atomic hydrogen. It can also be seen in Table 4 3 that all reactions that result in film growth involving the cation are energetically unfavorable, reaction (9) by 4.5 and reaction (10) by 10 Conversely, radical interactions that form complexes, as seen in reaction (1 3), are energetically favorable. From the quantum chemical data it can be seen that formation of may be one of the drivers of the bonding of to the substrate. However, is not seen in the second generation REBO results, due to the limit interaction range of the potential. The and cutoff values for the interactions are and where the
66 tra nsition state in Figure 4 3 is found to have an interaction length of This accounts for the lack of during the MD depositions ( see Table 4 1 ) While second generation REBO potential reasonab ly predicts the ground state energetics ( Table 4 1 ), the short range of the potential and the lack of charge are the main draw backs. During the DFT MD simulations, Mullikin population analysis shows that the deposited oxisidizes the carbon substrate producing a radical molecule and a positively charged site on the substrate. This is in part due to an over estimate of the oxidation potential of by SIESTS, Table 4 3 reaction (14). Th is leads to similar results between the second generation REBO and the DFT MD simulations, since both are essentially radical molecules interacting with a surface. However, the DFT MD results using the SIESTA software ( Table 4 2 ) show that reaction s occur with of the radicals and of the cations w hile the second generation REBO potential predicted that of deposited species would react with the surface. While the second generation REBO potential did not accurately ca pture the formation of during the deposition reactions, the bond of a to the diamond surface and the creation of atom and are found to be on e the possible reactions. Therefore, the second generation REBO potential is able to identify t he general form of the most pertinent reaction for the growth of DLC films. While, limit by short cutoff values and the lack of charge states the second generation REBO potential offers a computationally efficient means to guide further study using more a ccurate quantum chemical calculations.
67 4.2 Hydrocarbon Deposition on Polystyrene 4.2.1 Methodology To isolate the most frequently formed products on the surface of polystyrene due to hyperthermal hydro carbon modification a series of MD simulations are p erformed using the second generation REBO potential depositing hydrocarbon molecules with kinetic energies of and on syndiotactic polystyrene, Figure 4 4 In each simulation, particles are randomly oriented and p o sitioned within the surface pla n e D epositions are conducted continuously with impact s every Each beam contain s 300 hundred particles corresponding to fluencies of Following continuous deposition, the systems ar e evolved for an additional until the fluctuations in the potential energy are less than The final surfaces are analyzed to determine the products of the deposition process. Frequently observed products ( ) are subsequently examined using higher order quantum chemical methods with molecules interacting with a PS monomer, Table 4 4 Minimum energy geometries, transition states and intermediates are found with the B3LYP 108 hybrid functional and the 6 31G( d,p) 118 basis set using the GAUSSIAN 03 software pac kage 115 Frequency analysis is preformed to confir m transition states and minima Intrinsic reaction coordinate (IRC) 119 calculations are performed to confirm that an identified transition state corresponds to the reactants and products of interest. The IRC calculatio n s use the transitio n state as an input, and follow the minimum in the potential surface along the saddle by performing geometry optimizations of structures generated at symmetric steps along the negative frequency away from the transition state.
68 While th e B3LYP method is known to produce accurate frequency spectra the magnitude of the energy barriers is less accurate. Therefore, to determine more precisely the energy barriers for the reaction pathways considered, single point couple cluster singles and d oubles (CCSD) 120, 121 calculations are performed on structures optimized at the B3LYP/6 31G(d,p) level. These calculations are performed by Michelle Morton and Joseph Barron of Department of Chemistry, Georgia S outhwestern State University under the guidance of Nedialka Iordanova 122 4.2.2 Results For the 300 atoms deposited at : bond to the backbone carbons, remain in atomic form and bond to the styrene carbons, Table 4 4 In contrast for the atoms deposited at 4 75% percent did not penetrate the sub strate. Of the that did penetrate the substrate, a majority or bonded to the styrene carbons, while only bonded to the backbone. The reaction profile determined using B3LYP and CCSD methods is shown in Figure 4 6 Th e energies for this profile are in Table 4 5 When is in the vicinity of the PS monomer, the attaches directly to one of the carbon atoms of the styrene ring forming a positively charged non aromatic product. The product can isomerize to by a migration of the proton s to another carbon atom via triangular shaped transition state see Figure 4 6 MD simulations of molecule depo sited onto a PS surface result in a majority of the d eposited molecules bonding to the C2, C3 and C4 positions of the styrene ring In pa rticular 17% and 25% of the deposited molecules at and respectively bonded to these carbons Table 4 4 The primary product formed during the
69 deposition is the bonding of the to a sty r ene carbon, while leaving the carbon hydrogen bond intact, Table 4 4 The addition of to a C2, C3 or C4 carbon occurs during and of the bonding reactions of with PS for and deposition energies respecti vely. Therefore the reaction mechanisms of the addition of to the C2, C3 or C4 carbons of the PS monomer are further st udied with quantum chemical methods. Optimized configurations and transition states calculated using B3LYP for the cation are shown in Figure 4 7 The reactions show that the interaction leads to various product minima where the particle is attached to one of the styrene carbon atoms. The minima are connected via transition st ates corresponding to bridged structures where the particle is interacting with two neighboring carbon atoms of the styrene ring. The reactant species and each minimum are directly connected since the bonding between the and the r ing is shown to be barrier less, Table 4 6 The reaction profile shows the single point CCSD calculations as well. The latter are in accordance with the B3LYP calculations and give consistent relative energies between the minima a nd transition states. As with the deposition of the MD simulations using the second generation REBO potential of show the C2, C3 and C4 position on the styrene ring to be more probable than the C5 and C6 positions, as indicated in Table 4 4 Further the pro ducts are a combination of three reactions. The first reaction (i) is the attachment of the particle on one of the styrene ring carbon atoms and the breaking of the aromaticity of the ring The second is the a ttachment of the particle t o one of the styrene ring carbon atoms and subsequent transfer of the hydrogen atom from the styrene ring to
70 the particle to form a methyl group, restoring the aromatic structure of the ring is further identified as reaction (ii) And the third r eaction (iii) is the bonding of the to two of the styrene ring carbons creating a non aromatic ring. The interaction of the radical with the C2, C3 and C4 position on the styrene ring are investigated by quantum chemical calculations Con sidering the radical ground state is a triplet electronic configuration, both the triplet and singlet states are evaluated. For the triplet configuration the first two bonding configurations, (i) and (ii), are found to be stable. The two states are considered within one reaction process, in Figure 4 8 The reaction pathways resulting from the triplet radical deposition and the corresponding barriers are given in Table 4 7 While the initial electron configuration of the radical is a triplet, the ground state of the methyl added to the styrene ring is a singlet. In order to clari fy the reaction pathway of the singlet state is considered separately from the triplet state, se e Figure 4 9 It is determined that a concerted mechanism is more preferable for the formation of a methyl product on the C3, C4, and C5 positions. The energy barriers for the reaction with the C4 position using the B3LYP and CCS D methods are summarized in Table 4 8 4.2.3 Discussion MD simulations of hydrogen deposited on a PS surface resulted in the non preferential bond of atomic to the ring of PS. However, subtle differences are seen in the quantum chemical calculations, Table 4 5 According to these results the ortho and para products are more stable than the meta ones. The para product is 1.12 kc al/mol more stable than the C6 ortho product and 1.19 kcal/mol more stable than the C2 orthoproduct. Relative energies of the C2 and C6 ortho sites show the C6 to be
71 more stable that C2 site, which is counterintuitive considering orientation of the isopro pyl group and its steric effects on the styrene ring. The optimized geometry showed that the isopropyl group rotated significantly to accommodate the incoming particle only when the proton is attaching to the C6 position. The difference between the transition barriers on the left hand and right hand side of the reaction profile ( Figure 4 6 ) are attributed to the presence of the isop ropyl group and its rotation during the reaction. The strong binding of the atom to the styrene ring and relatively small differences between the sites, supports the MD findings of non preferential bonding of to the aromatic carbons. The io n showed similar reactivity with PS. The MD simulations of being deposited at showed C2, C3, and C4 position on the ring to be likely binding sites,. According to the quantum chemical calculations Figure 4 7 the most energetically favorable binding site is the para position (C4), Table 4 6 As with the atom the relative energies of all the bonding sites are within of each other, leading to an assumption of non prefe rential bonding to the styrene ring. This is supported by the depositions which show a more even distribution of bonding to the styrene ring. However, the lack of periodicity of the PS monomer used in gas phase calculations must also be considere d. In the case of the MD simulations the movement of the backbone carbons is restricted. This leads to the C6 being less accessible, which explains the low probability of this bonding site in the MD simulations for For interacting with PS three possible bonds are found to be likely according to the MD simulations. These are the direct bonding to the styrene ring, the formation of a methyl group and the incorporation of the into the ring. According to quantum
72 chemical calculati ons the direct bonding to the ring is found to be stable for the triplet electronic configuration. On the other hand the formation of a methyl group is found to be stable for both the triplet and singlet electronic configurations. 4 3 Summary Based on m ultilevel simulation of the growth mechanism of DLC films of fluorocarbons the production of is found to be one of the key drivers. While formation is not directly observed during the simulations performed with the second generation REBO potential the relevant process of bonding the diamond substrate is identified. From the si mulations of and interactions with PS, non preferential bonding to the styrene ring carbons is found for and However, MD simulations of depositions show that the steric hindrance of the backbone limits the bond ing to the C6 position. For the PS and interactions, the charge and spin state are found to significantly affect the bonding.
73 Table 4 1 Reaction predicted by classical MD simulations using the REBO potential Reaction Probability (%) Reactio n Site (No Rx) 42.0 A ,H,S 13. 7 A 21 .7 A 10.0 A 5.0 A ,S 4.0 A,S 2. 0 S 1. 7 S Table 4 2 DFT MD predicted reactions CF 3 Radical Reactions Probability (%) CF 3 + Reactions Probability (%) (No Rx) 0.0 20 10 10 30 10 10 10 20 10 20 10 10 10 10 10
74 Table 4 3 R eaction enthalpies calculated with the 22 atom carbon cluster Reaction REBO SIESTA a BMK b ZPE 1. 0.28 0.57 0.26 0.20 2. 0.97 1.03 0.92 0.69 3. 0.11 0.05 0.28 0.11 4. 8.41 8.54 8.43 7.98 5. 2.58 2.26 2.60 2.41 6. 4.58 4.17 4.61 4.38 7. -1.44 0.77 1.05 8. -4 .86 4.97 4.83 9. -4.92 5.54 5.31 10. -10.3 10.7 10.3 11. -0.57 1.25 0.92 14. -1.53 0.03 0.30 Mean Absolute Error ( ) 0.05 0.47 --Table 4 4 MD results of radicals deposited on PS Ion: Energy 4 10 4 10 4 10 In substrate 24.67 48.33 39.67 70.89 53.00 74.67 Bonded 15.00 33.67 24.00 58.33 30.67 58.33 Bonded to ri ng 12.67 24.67 17.50 42.00 19.00 35.50 C(2) 2.67 6.67 4.17 12.00 4.00 7.50 C(3) 2.67 3.67 5.67 9.17 5.33 7.83 C(4) 1.33 5.00 5.00 10.50 7.33 9.67 C(5) 2.00 4.67 2.67 6.67 2.00 7.33 C(6) 4.00 4.67 0.00 3.67 0.33 3.17
75 Table 4 5 Hydrogen interaction w ith PS monomer Table 4 6 Reac tion barriers for the interaction of C 2 H + with the polystyrene monomer. B3LYP/6 31G(d,p) kcal/mol CCSD/6 31G(d,p) kcal/mol B3LYP/6 31G(d,p) kcal/mol CCSD/6 31G(d,p) kcal/mol A 12.46 14.16 15.90 17.51 B 10.87 12.08 11.49 13.06 C 11.13 12.56 11 .47 12.74 D 16.12 18.84 16.63 18.56 Table 4 7 Reaction barriers for the interaction of CH 2 triplet radical with the polystyrene monomer C4 position. B3LYP/6 31G(d,p) CCSD/6 31G(d,p) kcal/mol kcal/mol A 4.84 10.52 B 26.69 29.9 C 40.83 44.19 D 40.11 40.99 Table 4 8 Reaction barriers for the interaction of CH 2 singlet radical with the polystyrene monomer C 4 position B3LYP/6 31G(d,p) kcal/mol CCSD/6 31G(d,p) kcal/mol A 76.41 78.09 B 61.13 70.77 C 103.14 108.09 B3LYP/6 31G(d,p) kcal/mol CCSD/6 31G(d,p) kcal/mol B3LYP/6 31G(d,p) kcal/mol CCSD/6 31G(d,p) kcal/mol A 15.46 14.17 15.30 14.32 B 15.95 15.43 16.09 15.75 C 11.47 11.08 12.17 11.92 D 11.50 11.25 11.87 11.45
76 Figure 4 1 Systems used for reaction enthalpies: A) periodic slam of 1 28 atoms, B) carbon cluster of 22 atoms. Figure 4 2 Site on diamond (111) surface a) C 128 Supercell b) C 22 Cluster
77 Figure 4 3 Transition state geometry of radical on adamantane surface to produce on the surface and an HF molecule
78 Figure 4 4 Crystalline polystyrene where the black and white atoms are thermostat region, and the blue and gray atoms are active, a) is a side view along the b ack bone, b) is a top view Figure 4 5 PS monomers where carbon is the darker (blue) atoms and hydrogen is the lighter (gray) atoms C2 C3 C1 C6 C5 C4
79 Figure 4 6 Reaction profile of the interaction of H + with the polystyrene monomer. C1 (C 6 C1) barrier not available because the product where the H atom is attached to the C1 carbon atom could not be localized due to steric hindrance of the C1 carbon atom by the side chain. The barriers are presented in Table 4 4
80 Figure 4 7 Reaction profile of the interaction of C 2 H + with the polystyrene monomer. The barriers are presented in Table 4 6 R T1 A C D 196 kcal/mol 183 kcal/mol B T2 R T4 T3 196 kcal/mol 183 kcal/mol
81 Figure 4 8 Reaction pathways for CH 2 triplet radical on C4 t he barriers ar e presented in Table 4 7 Figure 4 9 Reaction pathway of singlet radical on C4 the barriers are presented in Table 4 8
82 CHAPTER 5 SURFCE POLYMERIZATIO N ION BEAM ASSISTED DEPOSTION Thiophene based molecules possess excellent properties for electronics. They are being used f or photovoltaics 123 field effect transistors 124, 125 biological tags 97 and light emitting diodes 126 While thiophene oligomers and polymers have desirable electrical properties for these applications controlling their morphology under industrial proc essing conditions remains a challenge 124 Various possible alterna tives to wet chemical processing for low cost production of organic electronics are illustrated in a recent Nature article 127 These include the thermal transfer of organic molecules, direct patt erning of organic electronic devices, and variations on chemical vapor deposition (CVD). One attractive feature of vapor phase deposition methods is that they are a a chemical solvent that could have detrimental effect s on device performance 19 A current issue with vapor phase deposition is morphology control of thicker films consisting of species with sufficient conjugation lengths, such as sexithiophene 128 Some success i n controlling morphology th rough the use of energetic particles has been achieved. Podesta et al. used supersonic molecular beam deposition to create ordered layered structures of quaterthiophene 129 However, previou s efforts to use plasmas to polymerize films for organic electronics have meet with little success. For instance, Paterno et al. investigated plasma polymerization of aniline via and 130 While higher molecular weight species were produced they did not consist of conjugated polyaniline and had negligible electric c onductivity. Thiophene based antistatic coatings were created by plasma polymerization 131 However, conductivities in these fi lms were also very low ( ). Poor conductivity is attributed to
83 thiophene fragmentation. Later the same group found that adding substitutional groups onto the ring reduced the fragmentation of the thiophene rings 132 Luke Han l Illinois at Chicago has developed a novel method of producing oligothiohphene thin films This process utilizes the co deposition of thermal neutrals and hyperthermal ions to induce polymerization of the thin film and is referred to as surface polymerization ion assisted deposition (SPIAD) 30 33 In particular thiophene ions and thermal terthiophene ( ) neutrals are found to produce films consisting of polymerized oligomers when deposited with a ratio of Ion beams used in the SPIAD process consist of roughly intact thiophene io ns, as well as and Ion currents of and neutral fluxes of are used. Deposition times are resulting in fluences of and The higher molecular weight species created during this process improve the stability and optical properties of the film. The photolumence spectra of a pure film is compared to films created using the SPIAD proc ess in Figure 5 1 A red shift in the spectra can be seen for SPIAD films produced with thiophene. This red shift is attributed to the presences of higher molecular weight species which have a reduced gap due to an inc rease in conjugation length 133 These higher molecular species are seen in the mass spectra in Figure 5 2 As with other energetic particle surface interactions the polymerization mechanism could not be determined experimentally. The ph otolumences data confirms the existence of conjugated thiophene oligomers in the SPIAD deposited films. However, during the mass spectra analysis large amounts of fragmentation occurs during laser abolition making the exact nature of
84 the molecules diffic ult to deduce. In the mass spectra the species found include , and However whether these molecules are conjugat ed or linear fragments could not be inferred from the data. Many polymerization methods have been proposed to explain the SPIAD process 134 The polymerization process is characterized by initiation, propagation and termination. First cation induced polymerization of the neutrals was proposed; however, the incorporation of the thiophene molecule itself into the molecular structu re suggests that it is directly involved in the process. If the kinetic energy of the hyperthermal ion is the initiator then further reactions need to occur between the deposited molecule and the incident particle for the polymerization to take place. O therwise hyperthermal argon should induce polymerization as well. Given this information, thiophene may act as both an initiator and as a reactant in the polymerization process. Another possible mechanism is reactions that may occur due to the presence o f dissociated species in the system. During hyperthermal interactions with a surface, the ab lation process produces protons as the polymer is oxidized. These loose protons have been proposed to also be involved in the polymerization process. Protons crea ted during the dissociation of polymeric materials have enough kinetic energy transferred to them to allow them to leave the surface. This kinetic energy can be absorbed by the surrounding molecules and it can causes further fragmentation or oxidation le ading to further reactions within the film. Furthermore, the reactivity of the proton itself could be involved in the polymerization of the molecule.
85 5.1 Methodology Giving the complex nature of the SPIAD process MD simulations are conducted of hyperthermal argon and thiophene interac tions with a oligomer surface. The simulations are conducted using the newly parameterized second generation REBO potential for hydrogen, carbon and sulfur. is included via the LJ component of the potential only, as it is not chemically reactive As mentioned previously, ions are not explicitly accounted for within the REBO potential formalism. An initial thin film of is constructed by periodic replications of terthiophene 135 as illustrated in Figure 5 3 Films are created in a simulation cell with periodic boundaries perpendicular to the plane of the film. Films are approximately thick. The substrate is represented by a layer of diamond one unit cell thick, which is hydrogen terminated to limit any substrate oligomer chemical interactions. The bottommost atomic layer of the diamond is held rigid to prevent any rippling of the substrate Thermostats are applied to the rest of the hydrogen terminated diamond using the Langevin method 51 throughout the simulation. Parallel and perpendicular orientations of the terthiophene backbone to the substrate ar e considered Figure 5 4 In particular films are generated with the axis and the axis normal to the substrate surface. The orientation of to the substrate is unknown for SPIAD deposited films. However, both orientations are observed in other work 125, 136 and are found to be correlated with conductivity of the substrate and deposition conditions 137 Thermostats are applied to the films to achieve a temperature of Thermostats are then lifted, and the 3T film is allowed to freely evolve During the relaxation process the temperature of the film
86 is see n to deviate from the initial value. Therefore, thermostats are reapplied and then lifted periodically until the desired temperature of is achieved. 5.2 Single trajectory deposition To investigate the differences between hyperthermal and thiophene interactions with a surface, single traj ectory depositions are conducted at and Experimental results show a difference in yield between and thiophene w ith thiophene producing higher molecular weight species, as indicated in Figure 5 2 Ex perimentally, thiophene ions and neutrals are deposited simultaneously. However, given an ion flux of and a neutral flux of for the ion to neutral ratio 31 and the surface of the simulation cell of this corresponds to and Therefore, single trajectories of hyperthermal ions on films should provide insight into the SPIAD process. The simulations have a duration of which is found to be the necessary time for changes in hybridization to stabilize d The molecular mass distribution of the resulting films are analyzed by grouping carbon and sulfur atoms within the minimum REBO potential cutoff Molecules with a cen ter of mass greater than from the initial height of the 3T surface are considered to be removed into the vacuum. Initial concentrations of each molecular species are subtracted from the finial concentrations to determine the yield of each species. Yields are given in molecules produced per deposited ion. The total yield for each species of a given mass is shown in red, while the yield that remains in the substrate is shown in blue.
87 5.2.1 Argon 100 In order to create a comparison to thiophene de positions, argon is deposited at the same energies on the same two surface orientations as thiophene. In Figure 5 5 the resulting molecular weight distribution for deposition events of argon on the parallel surface configurati on is shown. The primary products are atomic hydrogen, and ; similar molecules with a variance in hydrogen content are also found. The main function of the deposited argon is found to be the fracturing of the thiophene rings of which are predicted to be consumed at an average rate of per event. By comparing the stoichiometry of produced molecules the probable reactions can be deduced. Considering the fact that the individual rings in are thiophenes with variation in hydrogen only, where x= or t he products of and corespond to the removal of a thiophene ring from a molecule However the lack of shows a low probability that once fragmentation occurs due to an impact any se mblance of the original molecule is likely not to be retained. Beyond the destruction, the fusing of dissociated species is predicted to occur in the production of some higher molecular weight species, including While their yield is found to be low the i r existence is investigated due to their relation to a possible polymerization processes. Upon visual analysis of the process it is found that the creation of and are correlated. It is se en that as the deposited argon interacts with the stack of molecules the removal a single carbon from a occur s This ejected carbon atom can be absorbed by an underlying thiophene molecule which can further interact with another thiophene molecul e to create a bridge between two
88 molecules Figure 5 6 This seems to be a direct result of the narrow interaction range of a deposited atom and the stacking of the in the parallel configuration. In the case of perpendic ular alignment of to the substrate, the deposition produces fewer low molecular weight species, as illustrated in Figure 5 7 The yield of species with masses less than that of the thiophene ( ) is found to decrease fr om for the parallel orientation to for the perpendicular orientation. Yields of the primary products of hydrogen, and are reduced by to Furthermore, the formation of and is not predicted due to the different configuration of the with respect to the incident molecule. 5.2.2 Thiophene 100 Sets of single trajectory depositions for each surface orientation are also conducted with thiophene at The mol ecular analysis results are shown in Figure 5 5 and Figure 5 7 The primary low molecular weight products are found to be similar to that of the products of the argon deposition s at the same energy. In particular, the dissociated thiophene rings are predicted to form and Furthermore, the addition of a hydrogen to the molecule to form is predicted. For the thiophene interacting with the parallel configured surface the main difference predicted relative to argon is the lack of dissociated higher molecular weight products. The yields of the primary products of atomic hydrogen, and are predicted to be similar to those produced by argon deposited at the same energy, as shown in Figure 5 5 The increased yield of atomic hydrogen and is found to be about and respectively.
89 The yield of atomic hydrogen and molecules that contain atoms from the deposite d species is found to be about for each molecule A yield of of beam molecules is predicted for the molecules. The average molecular weight of a molecule in the b eam is predicted to be around Therefore the production of atomic hydrogen and is related to the fragmentation of the deposited thiophene, while the production of is mostly due the fragmentation of molecules. This is supported by the relative yield of being similar to that of the argon deposition simulation s. For the perpendicularly aligned the trends predicted in the argon depositions are also predicted to occur for thiophene deposition. However, y ields of the primary products of atomic hydrogen, and are predicted to decrease b y about 50% for all molecules. The yield of molecules with a mass less than the mass of thiophene is predicted to drop as the oligomer orientations change. In particular, the yield varies from for thiophene molecules depositions on the parallel oli gomers, to for thiophene depositions on the perpendicular oligomers. On the other hand, the number average molecular weight of the molecules containing deposited species is predicted to increase from to This indicates an increase in interaction between the deposited species and the modified molecules In fact, the ratio of molecules containing deposited particles in the film and in the vacuum is predicted to be 2:1 for the perpendicular case and 4:1 for the parallel case. Thi s is due to the dissociation products, including the deposited species, being more confined due to the nature of the perpendicular film.
90 5.2.3 50 Depositions As discussed above, there is considerable fragmentation of the deposited thiophene during th e depositions. Therefore, lower energy depositions are also considered I ncident energies are reduced to and the differences in the products is investigated. For the parallel and perpendicular oligomer cases, there are more similaritie s in the products formed at this lower kinetic energy than there are at 100 For the parallel configuration yields of over are not predicted for argon deposition, as indicated in Figure 5 8 The products produced are cons istent with the scission of carbon carbon bonds, which is previously observed to be the primary result of argon deposition at Carbon reduced products including and and carbon increased produc ts such as are produced with yields of less than 0.4. For the perpendicular configuration similar results are predicted, as illustrated in Figure 5 9 with carbon diss ociation playing a primary roll. For thio phene deposited at on the parallel configuration there is a marked difference in products when compared to the argon modification at Figure 5 8 First, the fragmentation of the thiophene molecule is predicted to o ccur even at half the experimental energy. The primary products are found to be atomic hydrogen, and These primary products are predicted to contain deposited species with respective molecul ar yields of and Ad ditional products containing deposited species vary in molecular weight from single carbon and su lfur atoms to modified with an average molecular weight of Similar to the 100 depositions, the ratio of altered molecules that are sputtere d to those that remain in the substrate is found to
91 be 3 .5 :1 Furthermore, the carbon reduced species are not found in the thiophene modified films. The primary modification of intact is the addition of hydrogen. For the 50 argon modification of the perpen dicular oriented films, an in crease in production is predicted when compared to the parallel case for the same energy. However, the other fragments are seen to be better dispersed, as illustrated in Figure 5 8 This coincides with the deposited argon impacting the end of molecule in the perpendicular case This produc es rather than a more random distribution of carbon containing compounds which is seen in the parallel case In t he thiophene modified films with the orientated perpendicular to the substrate a decrease in molecular yield is predicted when compared to the parallel case. However, similar products are seen to form, as shown in Figure 5 9 As with the parallel oligomer case, a notable product is the bonding of hydrogen to a oligomer. This could be the initialization of a polymerization process. Furthermore, argon bombardment at 50 does not produce the same f ound during the thiophene depositions. Visual analysis of the produced films indicates that no conjugated higher molecular weight species are formed during the simulation time of The majority of augmented products are predicted to be linear chai ns of varying molecular mass. 5.2.4 Discussion While the direct observation of the formation of conjugated products is found to not occur during the simulations, numerous facets of the interaction of oligomer films with energetic particles are revealed For all simulations the primary low molecular weight
92 product is predicted to be acetylene ( ) from fracture of a deposited thiophene or fractured ring. Additionally, hydrogen and are produced in most simulations. At 100 both thiophene and argon are predicted to produce similar products via the dissociation of oligomers. Hydrogen, and are produced in the most abundant quantities for both orientations. Furthermore, or is also found to be a probable product of bombardment. Upon visual inspection, is seen to result from a fractured bonding to an extra hydrogen from the environment, see Figure 5 11 Interestingly, is predicted to form more readily in the case of thiophene deposition at when compare d to argon at the same incident energy. This is in part due to the increased yield of atomic hydrogen during the thiophene depositions. In contrast argon is found to principally change of the number of carbon atoms in the molecule. This differs fr om the modification by thiophene at the same energy in that a majority of the modification did not result in changes in carbon content of the 5.3 Ab initio Reaction Calculations Ab intio level calculations carried out by co worker Jasmine Davenport are used to validate the predictions of the classical MD simulations. In this work, Davenport et al. compare d the enthalpies of formation of a set of thiophene and hydrocarbon molecules using six different ab initio methods. The considered set of molecules consist of small hydrocarbon molecules: and ; as well as, thiophene, and thiophene radicals Reactions between thiophene radicals and hydrocarbon molecules are considered, given their possible importance in the polymerization of during the SPIAD process. The GAUSSIAN 03 87 package is used to carry out the
93 calculations. The methods used in comparison of enthalpies of formation are B3LYP 83 BMK 110 B98 110 G2 84 and G3 85 Jasmine found that of the hybrid functional considered B98 gave t he most comparable energies to experimental and the combinatorial methods G2 and G3. The reaction paths and transition states are then calculated using the IRC method and the B3LYP functional with the 6 311+ G(3df, 2p) basis set. In Figure 5 10 the reaction profile of a radical interacting with a thiophene molecule is shown. It can be seen that radical attachment to a thiophene structure is a barrier less reaction with an energy minimum of around l. Howeve r, if the reverse of this reaction is considered a reaction barrier can be seen. The reverse is a thiophene radical with an abstracted hydrogen reacting with an acetylene molecule. This reaction is seen to have a barrier of about 5.3 .1 Discussion The barrier between the thiophene radical and acetylene indicates that one of the primary products of the MD simulations may not play an active role in polymerization processes despite the product being more stable t han the reactants and the quantities of acetylene being produced during the simulation. However, considering the formation of radical thiophene is not readily observed in the MD simulations, further ab inito calculations involving fragmented rings need to be conducted. Accordingly, an initial evaluation of the dissociation energy of a thiophene ring is conducted. Non zero point corrected energies are used to calculate the change in enthalpy of the following reaction: where the is linear and symmetric about the sulfur atom It is found to about or + This is significantly higher
94 than the found with the aromatic thiop hene. However, this reaction involves the scission of two bonds in the aromatic ring and further ab initio calculations need be completed to full y explore the fragmented thiophene reactions with possible reactants including the primary products found in t he MD simulations; atom ic hydrogen, and 5.4 Summary MD simulations using the newly parameterized REBO CHS potential are conducted in conjunction with ab initio calculations to investigate the nature of hyperthermal atomic and polyatomic particles with a conjugated oli gomer surface. Through the use of a set of single trajectory MD simulations the primary products of hyperthermal interactions with a surface are found to be atom ic hydrogen, and Differences are seen between argon and thiophen e depositions at different energies and on oligomers oriented with backbones parallel and perpendicular to the substrate. Ab initio calculations are conducted in order to further illuminate the SPIAD process. Experimentally the SPIAD process is conduc the fracturing due to depositions is balanced by recombination 134 setup, 1 00 is found to be preferred. For our simulations of thiophene and argon at 100 similar products are predicted for both species. While the fusion of dissociated molecules is predicted for argon bombardment, no clear differences between argon a nd thiophene are predicted from the simulations. However, at the lower energy of 50 significant differences in the produced molecules is observed. In particular, more delicate changes to the surface structure are predicted as a result of thiophene
95 dep osition than of argon deposition. This is seen despite the fact that argon produces more variance in carbon content of the modified molecules and While this may lead to the polymerization of the given that broken bonds are seen to reform, one of stipulations for the polymerization of conjugate species is that retention of the base molecule 1 34 And argon deposition is possibly too harsh a treatment to accomplish this. Conversely, thiophene is able to induce small changes in molecular structure of an oligomer film. This is seen through the opening of rings upon impact without the change in molecular mass of the modified To account for the differences in argon and thiophene treatments the difference in mass and the polyatomic nature of the thiophene may be i mportant factors First, the mass ratio of thiophene ( ) and arg on ( ) is about 2.1:1. Thus, for equivalent kinetic energies the momentum of a carbon atom in the thiophene molecule is about of that of the argon atom at the same kinetic energy. Second is the dissociation of the thiophene on impact. T his is found to have an enthalpy of dissociations of about or Therefore, in addition to having less momentum per atom there is also the absorption of energy upon impact in the form of breaking chemical bonds that can play a role in allowing for smaller changes in the oligomer film. Finally, the SPAID processed is found to be a complex interaction involving dissociation of the incident polyatomic molecule, multiple reactions involving ring fragmentation and likely recombination w ith other incident molecules. The combination of MD simulations and ab initio calculations has contributed to the understanding between hyperthermal polyatomic molecules and oligomer films.
96 Figure 5 1 Photoluminescence spectra of 3T and SPIAD films produced with Ar + a nd Thiopohene (T + ) at 100 and 200 33
97 Figure 5 2 Mass spectra data 33
98 Figure 5 3 T erthiophene unit cell 135
99 Figure 5 4 Perpendicular and parallel configurations of the 3T films on a hydrogen terminated substrate. Perpendicular Parallel
100 Figure 5 5 Yield at 100 thiophene and on the surface with 3T in the parallel configuration C 2 H 2 H C 2 HS C 12 H 9 S 3 C 11 H 7 S 3 C 2 HS C 12 H 9 S 3 C 2 H 2 C 25 H 15 S 6 CH H CH CS
101 Figure 5 6 Two step process of the removal of a single atom from one 3T (1) and donating it to the set of 3T molecules below it (2) 1 2
102 Figure 5 7 Yield at 100 thiophene and Ar on the surface with 3T in the perpendicular configuration C 2 H 2 H C 2 H S C 12 H 9 S 3 C 12 H 9 S 3 C 10 H 6 S 3 C 2 H 2 CH H CH
103 Figure 5 8 Molecular analysis of films resulting from 50 argon and thiophene deposition on 3T in the parallel configuration C 2 H 2 C 2 HS C 12 H 9 S 3 H C 13 H 9 S 3 C 11 H 7 S 3 C 2 H 2 H C 7 H 5 S 2
104 Figure 5 9 Molecular analysis of films resulting from 50 argon and thiophene deposition on 3T in the perpendicular configuration C 2 H 2 H C 13 H 9 S 3 C 11 H 7 S 3 C 2 H 2 C 2 HS H C 10 H 6 S 3 C 12 H 9 S 3 C 10 H 6 S 3
105 Figure 5 10 Reaction pathway of radical and interacting with a thiophene molecule with calculated transition state energies of 49 kcal/mol ( a site) and 50 kcal (b site).
106 Figure 5 11 produced by 50 thiophene on parallel
107 CHAPTER 6 SURFACE MODIFICATION STUD IES Plasma and ion beam treatments can involve numerous ionized species being impinged on a polymer surface. These particles have energies in the hyperthermal range of 20, 42 They are produced during c ollisions between accelerated electrons and neutral gas species, such as argon, oxygen, carbon dioxide or water 138 ; however, t he physicochemistry of the plasma and relative concentration of various species that are present is still an active area of re search 139, 140 The concentration of ionized dissociative products is found to be appreciable 4, 141 Interestingly treatments that increase the surface energy of a polymer in order to improve adhesion are less sensitive to the ions involved in the modification processes 138, 142 Other treatments such as the creation of super hydrophic surfaces only occur in a narrow window of processing conditions 143 In order to illuminate the processes in which plasma treatments modify polymer surfaces MD simulations are used to explore the effects of a reactive and non reactive species being deposited on a po lymer surface These simulations allow for the decoupling of these species within the plasma and the negation of environment effects This allow s for the direct analysis of modified surfaces before any subsequent reactions would occur. The archetypal s pecies of argon and atomic oxygen are chosen to represent non reactive and reactive species, respectfully. A representative set of polymer substrates: polyethylene (PE), polyprop ylene (PP) and polystyrene (PS) are considered.
108 6.1 Amorphous Polymer Model In order to represent the faceted nature of an actual polymer surface, a random polymer network model is used. Polymer substrates are created by mapping monomers onto an equilibrated bead spring model 144 The bead spring model consists of randomly created continuous and terminating chains. Continuous chains are created through the perpendicular to the surface, and comprise 10% of t he substrate model These continuous chains are given a length less than the diagonal of the simulation cell to prevent them from migrating to the surface. Once the continuous chains are generated, random chains are added with the following constraints: new beads must be less than a and bond angles, within the bulk, must be greater than 120. The i nitial bead in a chain is positioned randomly, and subsequent beads are pro duced with a randomized translation vector. In order to facilitate the creation of a surface chains are not created though the PBC in the plane. Specifically beads within one bond length of the maximum and minimum of the simulation cell in the direction are angled back into the cell by adjusting the translation vector along the Angles of are accepted during the c reation of surface bead s The bead spring model is evolved under the constant number volume and en ergy (NVE) ensemble using the finite extensible non linear elastic (FENE) model in the LAMMPS package 42, 145 Th e FENE model was developed to study polymer melts and has been shown to compare well to experimental neutron spin echo data 144 The FE NE model has the following energy function: (6 1)
109 The F ENE bond paramete rs of in LJ units, are used with An inter chain LJ potential is also used with a cut off of and parameters and see Equation (2 6 ) A bond angle cosine potential, (6 2) with is used to avoid small bond angles, which are found to be problematic during atomic mono mer addition. Langevin thermostats are applied to the entire system to maintain temperature Once an equilibrated bead spring model is achieved atomic scale mono mers are mapped onto the inter bead bonds. In order to maintain a reasonable density during b ead spring equilibration periodic boundary conditions are enforced in all three dimensions Therefore, chains that have migrated though the PBC s in the plane are cut. However, i n order to avoid small molecular weight segme nts, cut chains with less than mono mers are shifted to connect with ends that are created during the creation of the surface. Atomistic amorphous polymers are created by mappin g atomic scale mono mer structures to the bonds of the reconstructed bead spring model. To achieve this coordinates of compressed forms of each mono mer type are used as initial structures. The monom ers are mapped onto each bond in the bead spring model b y multiplying the fractional coordinates of a mono mer by a set of orthogonal basis vectors. These b asis
110 vectors for the initial monomer in a chain are generated using the bond vector and two other randomly generated vectors as inputs to the Gram Schmidt p rocedure 74 Tacticity of the subsequent monomer is controlled by utilizing a basis vector of the previous mono mer as an input to the orthogonalization procedure, rather than a random vector. By multiplying this basis vector by one or negative one isotactic or syndiotactic polymers can be produced respectively. For atactic polymers the tacticity multiple is randomly selected to be either one or negative one. For both PE a nd PP, the syndiotactic method is used. However, due to the phenyl ring present in PS a random vector method for all monomers had to be used to achieve non overlapping side groups. In order to attain the maximum inter atomic spac ing during the creation o f the atomistic model, a proximity constraint is enforced. The minimum proximity constraint is initialized as During the creation of each mono mer the randomized basis vector is regenerated until this constraint is satisfied. If the threshold guess es for the creation of a n initial mono mer are exceeded the entire model is deleted and restarted. During the creation of each subsequent mono mer if the threshold guess for a mono mer is exceeded, then the entire chain is re started. Furthermore if the t hreshold number of restarts of either the chain or the entire model are exceeded the proximity constraint is decreased. Threshold values of guesses for chain and monomer creation, and restarts before the proximity constraint is decreased are fou nd to efficiently produce well spaced models. If a model is successfully produced the proximity constraint is increased by and the creation of the atomic model is started over. Once an increase is followed by a decrease the model is considered to be at its maximum
111 atomic spacing. Furthermore, if an inter at omic spacing of greater than is not achieved a new bead spring model is generated and equilibrated. Once an atomic model is completed it is evolved with limited interactions to allow fo r equilibrium bond lengths of the compressed monomers to be established. Limitations on the system include : fixed connectivity and limiting inter chain forces to LJ interactions. Langervan thermostats are also applied to the entire system, limiting the system to A dditionally if the kinetic energy of the system surpasses the n the velocit ies of all the atoms are zeroed. After the atomic model undergoes an initial evolution, the system is equilibrated at the desired temperature. To evalu ate the amorphous nature of the constructed polymers the pair distribution function is used: 146 (6 3) Where is the density of the polymer, is the number of atoms in the volume in between spherical shells with radi of and The pair distribution function for the carbon atoms is shown in Figure 6 2 for the equi librated structures using a spherical cutoff of and a of For PE and PP the first and second neighbor peaks are for carbon s. While PS has peaks for both and No long range order can be seen for any of the system s. The initial structures of PE, PP and PS are displayed in Figure 6 1 with individual chains highlighted The surface area of each slab is x with thicknesses of around The densities are measured by usin densities are for PE, for PP and for PS. While the
112 exact densities of the polymers is not precisely achieved the values compare well with experimental values of for PE, for PP and for PS 147 6.2 Methodology Deposition e nergies of and are chosen. Species are deposited with a flux of While this is several orders of magnitude larger than fluxes found in ion beam and plasma experiments, it corresponds to the minimum time necessary ( ) for the fluctuations in k inetic energy due to each individual deposition event to dissipate A total of molecules are deposited on each polymer surface. This corresponds to a fluence of which is of the same magnitude as ion beam tr eatments for similar processes 148 Depositions are conducted with the incid ent species placed normal to the substrate surface. The p osition s of the deposited species within the surface pla n e are randomly chosen. The temperature of the substrat e is controlled by applying thermostats to the bottom 30% of the atoms. During deposi tions of hyperthermal atoms on polymer surfaces, significant energy is imparted onto the surface causing some mixing and allowing for the possibility of a deposited species to come into contact with a thermostat atom. The connectivity of the deposited sp ecies is therefore monitored at the end of the simulation to determine if any species are found to be bond ed to a thermostat atom. In the following work only one such instance is found and the subsequent reaction is not counted in the provided analysis. Molecules that are created during the deposition simulations are characterized by molecular mass. These molecules are considered sputtered from the substrate if they
113 contain less than atoms and have a center of mass greater than from the initial surface maximum. Conversely molecules with greater than atoms that have a center of mass less than for the initial surface maximum are considered to be part of the substrate The change in coordination of a carbon atom in the system is used to establish the probability of different types of modifications t hat occur on the surface of the polymer. The total changes in carbon coordination is divided by the number of deposited species to give the yield of a particular modifica tion. It is also considered that not all modified species remain in the substrate and those that have been removed should not be counted as modified groups with i n the polymer surface. Therefore, the yield of each modification that is found to remain in and is also displayed with the total yield of a modification. The percent of the total yield that is found to remain in the substrate is also displayed. It should also be noted that the second nearest neighbor information is not considered Therefore the bonds that are shown are for connectivity only and the existence of bond order is not taken into account 6.3 Argon Deposition Argon has been involved in plasma research since its discovery in 1928 149, 150 As it is an inexpensive noble gas, it remains prevalent in plasma and ion beam use. Argon modification of polymers 151 F ollowing treatment, polymers can be exposed to atmosphere where the saturation of modified bonds can lead to functionalization 152
114 6. 3 .1 Results First, the number of carbon and hydrogen atoms that are found to be sputtered are a nalyzed. In Figure 6 3 the yield of sputtered carbon and hydrogen is shown due to argon bombardment at 25 50 and 100 A nonlinear response in energy is predicted for all the polymers considered which agrees with the results of experimental studies of polymer etching using argon as a feeder gas Egami et al. found the etching yield (EY) dependence on energy to vary based on the deposited ion 153 For argon, a square root dependence was found Furthermore, this was also shown to be independent of polymer type. For the results of this study the square root relation d oes not completely hold ; rather the resul ts indicate that steady state etching ha s not been achieved. For steady state etching to occur, the ratio of being sputtered should be equal to that of the bulk polymer 154 This ratio is for PE and PP a nd for PS. By measuring the total number of sputtered atoms at the end of the simulations for 100 argon depositions the ratio is found to be for PE, for PP and for PS. This indicates that steady state etching has yet to occur even at the highest considered energy. This is reasonable for fluences on the order of which corresponds to low fluences used for surface modification purposes a s opposed to the higher fluences of used for etching and film growth 152 For argon deposited at 25 in these simulations, negligible sputtering and minimal surface modification is predicted for all considered polymers. For PE a yield of corresponds to changes in carbon coordination from ( ) to ( ) ( Table 6
11 5 1 ) ; this indicates that backbone scission can occur at this energy In addition, minimal sputtering of atomic hydrogen is seen with a yield of No yields over are predicted for the PP surface according to the coordination and molecula r analysis However trace amounts of sputtered methyl groups and broken backbone bonds are predicted to form. Lastly, absolutely no change in surface coordination or molecular content is predicted for PS exposed to argon. In the case of 50 argon on PE, backbone bond scission is predicted to be the primary process to result from the deposition through the creation of ( ) from monomer carbons ( 2 with a yield as indicated in Table 6 1 The creation of ( ) modifications from the monomer shows the propensity for 50 argon to remove hydrogen atoms from the polymer is low for this energy given the yield of This is supported by the lack of mole cular hydrogen in the sputtered particles as illustrated in Figure 6 4 Exposure of PP to argon results in the scission of backbone carbon bonds ( ( ) ( ) ) with a yield of as shown in Table 6 2 The yields of methyl groups are predicted to be approximately equal to the production of atomic and molecular hydrogen see Figure 6 4 Of the modified species the backbone carbons are determined to be the sec ond most susceptible to being sputtered after dissociated methyl groups, with of the 2 ( ) 2 forming sputtered product s. In the case of PS the scission of the styrene ring ( ( ) ( ) ) is predicted to be the most likely consequence of 50 argon exposure with a yield of given in Table 6 3 T he scission of backbone bonds ( 3 ( ) ( ) ) and backbone ring bonds ( 3 ( ) ( ) ) are predicted to be of similar probability with yields of
116 However, the yiel d of dissociated styrene rings ( ) is found to be less than 0.1 as illustrated in Figure 6 4 The sputtering of modified carbon is predicted to be similarly probable for the four most probable modifications with sputtering occurring for of the produced modificati ons. Furthermore, trace amounts of molecules are predicted to be ejected according to the molecular mass analysis given in Figure 6 4 In summation, the primary product of the 50 argon bombardmen t is scission of carbon carbon bonds in the polymer surface and the formation of atomic and molecular hydrogen Specifically atomic and molecular hydrogen are found to comprise and number percent of the sputtered molecules for PE, PP and PS r espectively, as indicated in Figure 6 4 With an increase in kinetic energy from 50 to 100 sputtering and creation of molecular species is predicted to be times greater for deposition s at 100 than at 50 The atomic yield of PE, PP and PS is predicted to increase from to to and to respec tively. Additionally the most probable modifications for are found to remain the most probable for with increased yields. The most probable modification s to the PE monomer due to 100 argon are indicated in Table 6 1 with t he most probable being ( ) 2 ( ) 2 and ( ) 2 ( ) with yields of and respectively. All o ther processes are predicted to occur with yields of and less. Notable modifications are the formation of possib le cross links ( ( ) 2 ( ) ) with a yield of However, bond scission reactions are predicted to dominate with yields of compared to bond forming process with yields of The molecular products of bond break ing are sputtered hydr ogen,
117 molecular hydrogen and single and double carbon containing molecules (see Figure 6 5 ) In Table 6 2 the modification s of PP due to 100 argon are shown. Specifically, the scission of carbon carbon bonds is still the dominate process With backbone bonds breaking with a greater yield of than side group bonds with a yield of Modifications resulting in the dissociation of a single methyl or hydrogen atoms from the back b one are also predicted with yields of around The molecular analysis reveals that the majority of the sputtered species are dissociated atomic and molecular hydrogen and methyl groups Figure 6 5 For PS, the trends for 50 deposition are also observed to be similar to the trends for 100 deposition In particular the four most probable coordination modifications remain the same with increased yields, as shown in Table 6 3 The scission of styrene carbon bonds is the most probable modification and t he formation of is predicted to dominate the carbon species formed with a yield of as illustrated in Figure 6 5 This agrees with previous studies using the second generation REBO potential 45 which predicted that production occurred due to the scission of carbon carbon bonds on the backbone and within the styrene ring According to the coordination analysis conducted in this work the primary production of occurs due to the scission of styrene rings. In particular, the production of ( ) is almost exclusively due to the scission of styrene carbons ( 2 ( ) ), as indica ted in Table 6 3 This may be due to differences in the model used for the simulation. Specifically, Vegh and Graves used vertically aligned chains, while the model used in this work is a faceted surface with the ring more expos ed than the back bone.
118 6.2.2 Discussion The yield of carbon atoms per is found to vary experimentally with system setup 155 ; yet, are usually in the tens of atoms per incident species. This compares well with the simulation results which predict a yield of carbon atoms for PE, carbon atoms for PP and carbon atoms for PS as illustrated in Figure 6 3 Experimental values of steady state etching found yields of carbon atoms per at for a plasma polymerized hydrocarbon film on 156 These values should be considered lower than values obtained by steady state etching in experiments since the : ratio is not equal to the ratio found in the bulk polymer. For a fluence of the resulting concentrations of carbon coordination types due to 100 argon modification are shown in Figure 6 6 For PE and PP, a yield of over per ion is found for both 2 and modifications This corresponds to an even number of modifications involving the scission of carbon carbon backbone bonds and carbon hydrogen bonds within the substrat e for PE. This is supported by the primary concentration of and in the molecular analysis of the sputtered species For PP, a yield of 2 groups is due to a combination of dissociated backbone bonds and oxygenated methyl groups. Meth yl groups are found to have an average removal yield of per deposited ion. For PS the primary modification is to the styrene ring where r ing scission is seen to occur with a yield around and hydrogen removal f rom the ring is seen to occur with a yield of From the molecular analysis the majority of carbon containing molecules that have been sputtered are which agrees with previously published studies using the second generation REBO potential to model deposition on PS 45 Further, the higher
119 molecular weight species that are formed are consistent with the removal of styrene groups and entire monomers. The most probable modifications at 50 are also found to be the most probable at Rate increases for the two most probable modifications of PE and PP are predicted to increase by a facto r of and a factor of and for PS. The difference in products between 50 and reveal the nature of the modification process of argon I n particular, deposition at both of these energies ha s as the primary modification the scission o f carbon carbon bonds. The creation of atomic and molecular hydrogen is predicted to occur at much lower yields than carbon carbon bond scission for argon, while a substantial increase in hydrogen product ion is predicted for argon. This i ndicates that the oxidation of the polymer surface is a secondary interaction while the breaking of carbon carbon bonds is the primary interaction. While these results illuminate the probability of various changes in bond ing to occur during hyperthermal a rgon bombardment, they also provide probable initiation sites for functionalization. Deposition in the simulations is conducted in perfect vacuum, but actual surface modifications occur at low pressure reactors or in air where the surrounding gas phase mo lecules can interact with the modified surface. As with previous studies this MD study will provide the bases for future work involving quantum chemical analysis of possible reactions that can occur with the identified surface modifications. 6.2.3 Conclu sions This work identifies probable modifications of hyperthermal argon on a polymer surface on three prototypical surfaces PE, PP and PS. The magnitude of carbon and
120 hydrogen removal is predicted to be approximately the same as published experimental va lues for similar systems. The most probable modifications for PE, PP and PS are shown in Table 6 1 Table 6 2 and Table 6 3 respectively. Given the simple structure of PE it is not surprising that the most probable modifications are simply chain scission and the removal a single hydrogen atom For PP, the most probable modifications are chain scission, the dissociation of side groups, and the removal of single hydrogen atoms fr om the backbone chain. In the case of PS, c hain scission and ring scission are found to be almost equally probable. While these results are generally predictable based on the structure of the studied polymers they provide a statistical basis for compari son to reactive species such as atomic oxygen. 6.3 Reactive Species The etching of microelectronics using molecular oxygen as a feeder gas in low temperature radio frequency vacuum clamber s has been a focus of study since the 157 and t he ability of oxygen based plasmas to effectively etch surfaces is well established 21 A detailed analysis of reactive species interactions with polymer surface s is necessary to facilitate future development of more complex treatments. These more c omplex treatments including the use of multiple feeder gases and plasma jet system s that operate in air. Plasma treatments us e mixtures of different feeder gases to achiev e increasingly subtle changes to a surface 158 For example, using a combination of and has been attempted to produce functional groups 159 ; h owever, in this work atomic oxygen was reported to degrade the polymer surface More recent stud ies have found atomic oxygen ion concentrations in air jet plasmas 141, 160 Therefore, m ore detailed analysis of atomic oxygen polymer surface interactions using computational
121 methods can offer further insight int o the nature of reactive species and polymer surface interactions of importance for multiple processes Here, s imulations are conducted using the updated hydrocarbon and oxygen coordination function values for the second generation REBO potential. For co mparative analysis to non reactive species (argon deposition ) depositions are conducted at incident energies of 50 and The flux of and fluence of is also equivalent to th e conditions considered in the argon atom depositions. 6.3.1 Results The reactivity of o xygen leads to a lower threshold of kinetic energy to induce modification of a polymer surface relative to non reactive species like argon. This can be seen in the sputtering yield from the simulations given in Figure 6 7 i n th at appreciable sputtering occurs at with hydrogen yields of or greater In contrast only negligible sputtering occurs due to the deposition of argon at th e same energy, Figure 6 3 This phenomenon is known as chemical sputtering 20 Sputtering of carbon atoms is predicted to be less energy dependent compared to argon, with the carbon atoms exhibiting a yield ranging from to fo r PS between 50 and 100 This is a substantially smaller increase than that predicted for argon. Furthermore, the ratio of carbon to hydrogen in Figure 6 7 is predicted to correspond well to the oxidation properties of atomic oxygen fo r PP, PE and PS. By analyzing the molecular mass of the sputtered molecules the primary content is found to be atomic and molecular hydrogen as expect during oxidation of the polymer surface. The molecules produced by 50 atomic oxygen are shown in Figure 6 8 and
122 the yield can be compared to that of argon in Figure 6 4 Yields of a tomic and molecular hydrogen are predicted to be for PE and PP, and for PS These yield s are about 10 times that of the yield for 50 argon. By comparing Figure 6 3 and Figure 6 7 the yields of sputtered hydrogen are seen to be similar in magnitud e for 100 depositions of oxygen and argon. However, the yield of sputtered carb on species is much less dependent on energy for oxygen than for argon. The yields of carbon at 25 50 and 100 are and for PE, and for PP and and for PS. Therefore, sputtering of molecular carbon containing species due to atomic oxygen is predicted to be limited a nd fu rther molecular analysis is not included except for the case of PS. The reflection yield (RY) or number of incident species that bounce off the surface without chemically bonding to it is predicted to have a greater dependence on polymer composition than incident energy. For PS the RY of atomic oxygen is predicted to be zero for all cases, and it is for PE and PP. The number percent of the formed molecular species that conta in deposited oxygen atoms is found to be inversely proportional to the deposition energy. In particular, t he yield of oxygen atoms in the created molecules is rough ly constant for the considered polymers and energies : to for PE to for PP and to for PS T he number of sputtere d molecules increases with the kinetic energy of the deposited species For PE and PP the number yield of created molecules is approximately and for deposition energies of 25 50 and 100 respectively. The total yields for PS are slightly lower at and for the same respective energies.
123 Coordination analysis is conducted on the produced films for all carbon and oxygen atoms. The results of the change s in bonding are shown in Table 6 4 through Table 6 12 for yields greater than For oxygen on PE the monomer carbons are modified with yields of and for 25 50 and 100 respectively. At 25 and 50 chain scission is predicted to be the dominant process with yields of and respectively. In the case of 25 a majority ( ) of the deposited oxygen atoms form a bond with a substrat e carbon causing chain scission ( ( )) This can be seen to correspond to the formation of ( ) and ( ) 2 with yields of and respectively For depositions at the yield of bonded oxygen species is predicted to only increase to a yield of The dominate products of ( ) and ( ) 2 form due to the oxidation of the monomer are the same as with and For the incorporation of deposited oxygen into the substrate is predicted be the s ame as for However, the most probable result of the deposition is predicted to be the oxidation of a monomer to form with a yield of T he second most probable modification being chain scission to produce ( ) 2 The su bstrate modifications due to direct bonding to oxygen are seen to be the incorporation of oxygen as a side group ( ) with a yield and chain scission ( ) 2 with a yield of For atomic oxygen modification of PP the monomer carbons ( ) ( ) 3 and ( ) 2 are modified with yield s of and for and respectively Table 6 7 Table 6 8 and Table 6 9 E ach atom typ e in the PP monomer is predicted to react at approximately the same rate as the others. In the case of depositions at (shown in Table 6 7 ) the primarily bonding of the deposited oxygen
124 atom is to a single carbon with a yi led of The deposited oxygen is seen to bond to the side group, causing the removal of a hydrogen, with a yield of Bonding of the deposited oxygen to backbone carbons is also found to occur resulting in the scission of a carbon carbon bond, wi th a yield of As with the depositions at at the oxidation of the polymer with little chain scission is predicted to occur. The oxidation of the methyl group to form is also predicted to be the most probable reaction with a yield of This is primarily due the bon ding of oxygen to carbon in the substrate with yield s of and for ( ) and ( ) Also limited amounts of water and are predicted to form. At ( Table 6 9 ) the oxidation of the methyl group the scis sion of the backbone chains and the oxidation of the backbone are the most observed reactions in the simulations with yields of and respectively The deposited oxygen is predicted to mainly form ( ) and ( ) bonds with in the subs trate with yields of and respectfully Since a majority of the oxygen modification resulted in yield less than these results are not shown in Table 6 9 The only formed species with a substantial probability is t he attachment of the deposited oxygen to an oxidized methyl group with a yield of For oxygen on PS scission of the styrene ring is seen to be the predominate interaction. This forms ( ) ( ) and ( ) with yields of and respectively. of the deposited species are predicted to bond to the substr ate with ( ) coordinated oxygen being the most likely. The change in coordination of ( ) into ( ) exhibits scission of styrene rings with a yield of In addition, the formation of ( ) coordinated oxygen atoms indicates that th e oxygen is not forming
125 at the end groups in the broken ring structures. Upon visual analysis of the substrate a wide variance of styrene oxygen bond s is predicted to occur. Rather, t he deposited oxygen is found to b oth incorporat e into the ring and for m bridge sites as illustrated in Figure 6 9 At 50 of incident energy the scission and removal of hydrogen from the styrene ring is seen by the change of ( ) to ( ) and ( ) with yields of and respectively. Backbone carbon carbon bonds are predicted to be dissociated by the loss of a carbon neighbor of ( ) with a yield of Again ( ) coordinated oxygen atoms are found to dominat e, consisting of of the deposited species. S ignificant amounts of ( ) yielding ( ) and ( ) show that rin g bridging and incorporation of deposited oxygen is taking place Similar concentrations of ( ) coordinated oxygen and ( ) and ( ) coordinated styrene carbons are predicted to occur for depositions at as indicated in Table 6 12 Increases in ring scission and removal of hydrogen from the ring are also predicted by an increase in the modification of ( ) ( ) and ( ) ( ) with yields of and respectively As with argon deposition processes, the dominate molecular species is predicted to be with a yield of 6.3.1 Discussion Atomic oxygen deposited at and shows a substantial affinity to form bonds wit hin the hydrocarbon polymers PE, PP and PS with uptakes of to Sputtering of carbon containing molecules is predicted to be low for PE and PP. However, greater amounts are seen for PS due to the removal o f portions of the styrene ring.
126 This corre sponds well to experimental findings that atomic oxygen primarily degrade s polymer surfaces during modification i n that atomic oxygen is not found to significantly contribute to etching 161 or functionalization 159 However, it should be noted that due to the short interatomic cutoff of the REBO potential, the probable formation of groups during depositions is likely underestimated. For PE and PP, the products formed with the highest fidelity are predicted to be the scission of a backbone chain and t he removal of a single hydrogen atom from the monomer while leaving the backbone bonds intact. Upon visual analysis these processes are found to be related to the initial interaction with the polymer w hile the subsequent formation of carbon oxygen bonds occur during secondary reactions. The presence of oxygen bonded to a single carbon is predicted to be the most probable configuration with deposition energies of However, the formation of hydroxyl groups and ( ) bonds increases with energy. PS reacts strongly with atomic oxygen to form bonds ( ) within the styrene ring. The scission of the styrene ring can lead to the removal of oxygen and hyd rocarbon containing compounds causing the relative sputtering of carbon containing species to be higher than for PE and PP. Similar results have been seen experimentally with the photo oxidation of PS, where ring opening and ( ) bond formation were also seen to dominate 162 The results of this work do not include the effects of UV radiation; however, th e energy necessary to break styrene ring bonds is provided by the kinetic energy of the atom. A comparison of the most probable modifications due to 100 argon and oxygen depositions on PE, PP and PS are given in Table 6 13 I t can be seen that for PE,
127 despite both atoms having the same kinetic energy the breaking of the backbone bonds due to oxygen is about half that due to argon. Furthermore, the removal of a hydrogen from the backbone is substantially higher for oxygen dep osition For PP, the abstraction of hydrogen is predicted to about twice that of argon while the scission of backbone bonds is found to be similar. For PS, similar values are observed for carbon carbon bond cleavage, but hydrogen abstraction from a styre ne ring is predicted to be about twice as likely to occur. 6 5 Summary Argon a nd atomic oxygen have been deposited on a set of prototypical polymers and the nature over their interactions has been explored with MD simulations. The primary function of energetic particles is predicted to be the cleavage of carbon carbon bonds for PE, PP and PS alike. at 50 produces little oxidation of the surface. However, with an increase to 100 the cleavage of the carbon carbon bonds remain s the primary modification mechanism with oxidation occurring as a secondary process. As expected, atomic oxyge n is found to remove hydrogen from the substrate and produce little etching of the surface. This is due to a combination of preferential removal of hydrogen when compared to argon a nd the bonding of oxygen within the substrate. The bond of atomic oxyge n for the considered polymers is found to be complex especially in the case of PS. In this work changes in the bonding are identified for hyperthermal augmentation of PE, PP and PS by non reactive and reactive particles. The analysis of probable formati ons within the modified structures will hopefully lead to a better understanding of plasma modification of polymer surfaces.
128 Table 6 1 Coordination analysis of deposition on PE Energy Initial coordination Final coordination Total yield Surfac e yield Dissociated (%) Dissociated yield 25 2C CH 2 C CH 2 0.20 0.20 0 0.00 50 2C CH 2 2C CH 0.18 0.18 0 0.00 2C CH 2 C CH 2 1.18 0.92 22 0.26 100 2C CH 2 C C C 0.16 0.14 13 0.02 2C CH 2 C CH 3 0.38 0.28 26 0.10 2C CH 2 3C CH 0.40 0.38 5 0.02 2C CH 2 C CH 0.50 0.14 72 0.36 2C CH 2 2C CH 1.44 1.32 8 0.12 2C CH 2 C CH 2 2.48 1.62 35 0.86 Table 6 2 Coordination analysis of deposition on PP Energy Initial coordination Final coordination Total yield Surface yield Dissociated (%) 25 50 C (C) H 3 C (C) H 2 0.16 0.16 0 C (C) H 3 (C)H 3 0.18 0.00 100 2 C (C) H 2 C (C) H 2 0.40 0.28 30 3 C (C) H 2 C (C) H 0.60 0.52 13 100 2 C (C) H 2 C ( C)H 0.12 0.06 50 C (C) H 3 C ( C)H 0.14 0.06 57 2 C (C) H 2 3 C (C) H 0.14 0.08 43 2 C ( C) H 2 C (C) H 3 0.14 0.10 29 3 C (C) H 3 C (C) 0.16 0.16 0 3 C (C) H C (C) C 0.20 0.10 50 C (C) H 3 2 C (C) H 2 0.34 0.30 12 3 C (C) H C ( C)H 0.34 0.12 65 2 C (C) H 2 2 C (C) H 0.36 0.34 6 C (C) H 3 (C)H 3 0.40 0.00 100 C (C) H 3 C (C) H 2 0.64 0.52 19 2 C (C) H 2 C (C) H 2 0.84 0.54 36 3 C (C) H 2 C (C) H 1.18 0.88 25
129 Table 6 3 Coordination analysis of deposition on PS Energy Initial coordination Final coordination Total yield Surface yield Dissociated (%) 25 50 2C (C)H 3C (C ) 0.12 0.12 0 2C (C)H2 C (C)H2 0.16 0.12 25 3C (C) C (C) C 0.26 0.20 23 3C (C)H 2C (C)H 0.28 0.22 21 2C (C)H C (C)H 0.44 0.32 27 100 2C (C)H (C)H 0.12 0.00 100 2C (C)H C (C) 0.12 0.04 67 3C (C) 2C (C)H 0.16 0.06 63 3C (C)H C (C) C 0.18 0.08 56 2C (C)H 2C (C)H2 0.18 0.16 11 2C (C)H C (C)H2 0.18 0.16 11 3C (C)H 3C (C) 0.22 0.20 9 2C (C)H2 2C (C)H 0.24 0.18 25 2C (C)H 3C (C) 0.32 0.32 0 2C (C)H C (C) C 0.54 0.42 22 2C (C)H2 C (C)H2 0.58 0.32 45 3C (C ) C (C) C 0.58 0.36 38 3C (C)H 2C (C)H 1.00 0.70 30 2C (C)H C (C)H 1.96 0.66 66 Table 6 4 Coordination analysis of atomic oxygen deposition on PE at 25 Initial coordination Final coordination Total yield Surface yield Dissociated (%) 2C (C)H 2 C (C)H 2 O 0.24 0.20 17 2C (C)H 2 C (C)H O 0.28 0.24 14 2C (C)H 2 2C (C)H 0.38 0.36 5 2C (C)H 2 C (C)H 2 0.68 0.48 29 O H (O) H 0.02 0.00 100 O O (O) 0.02 0.02 0 O C (O)H 0.04 0.02 50 O C (O) C 0.06 0.04 33 O ( O ) H 0.08 0.00 1 00 O C (O) O 0.10 0.06 40 O C ( O ) 0.52 0.44 15 O O 0.16 0.00 100
130 Table 6 5 Coordination analysis of atomic oxygen deposition on PE at 50 Initial coordination Final coordination Total yield Surface yield Dissociated (%) 2C (C)H 2 O (C ) 0.12 0.02 83 2C (C)H 2 C (C)H 3 0.14 0.10 29 2C (C)H 2 C (C)H 2 O 0.14 0.12 14 2C (C)H 2 2C (C)H O 0.24 0.22 8 2C (C)H 2 C (C)H O 0.24 0.18 25 2C (C)H 2 C ( C)H 0.30 0.18 40 2C (C)H 2 2C (C)H 0.92 0.90 2 2C (C)H 2 C (C)H 2 1.10 0.88 20 O OH 0.02 0.00 100 O O (O) H 0.04 0.02 50 O H O H 0.06 0.00 100 O C (O) C 0.14 0.12 14 O C (O) O 0.16 0.10 38 O C (O)H 0.24 0.12 50 O C ( O ) 0.26 0.18 31 O O 0.08 0.00 100 Table 6 6 Coordination analysis of atomic oxygen deposition on PE a t 100 Initial coordination Final coordination Total yield Surface yield Dissociated (%) 2C (C)H 2 O (C) H 2 0.14 0.06 57 2C (C)H 2 C (C)H O 0.18 0.18 0 2C (C)H 2 C (C)H 2 O 0.20 0.18 10 2C (C)H 2 2C (C)H O 0.22 0.22 0 2C (C)H 2 C (C)H 3 0.40 0 .36 10 2C (C)H 2 C (C) C 0.44 0.36 18 2C (C)H 2 C ( C)H 0.62 0.36 42 2C (C)H 2 C (C)H 2 1.46 0.86 41 2C (C)H 2 2C (C)H 2.34 2.12 9 O H (O) H 0.04 0.00 100 O ( O ) H 0.04 0.00 100 O C (O) O 0.06 0.04 33 O O (O) H 0.06 0.04 33 O C ( O ) 0.18 0 .04 78 O C (O)H 0.26 0.16 38 O C (O) C 0.28 0.26 7 O O 0.08 0.00 100
131 Table 6 7 Coordination analysis of atomic oxygen deposition on PP at 25 Initial coordination Final coordination Total yield Surface yield Dissociated (%) 3C (C)H 2 C (C)H O 0.12 0.12 0 C (C)H 3 C (C)H 2 0.12 0.12 0 C (C)H 3 C (C)H 2 O 0.16 0.16 0 2C (C)H 2 2C (C)H 0.22 0.22 0 3C (C)H 2C (C)H 0.24 0.24 0 O H (O) H 0.02 0.00 100 O O (O) 0.02 0.02 0 O O (O) H 0.04 0.02 50 O C (O) C 0.06 0.06 0 O ( O ) H 0.08 0.00 100 O C (O)H 0.10 0.10 0 O C (O) O 0.14 0.12 14 O C ( O ) 0.44 0.34 23 O O 0.10 0.00 100 Table 6 8 Coordination analysis of atomic oxygen deposition on PP at 50 Initial coordination Final coordination Total yield Surface yie ld Dissociated (%) 3C (C)H C ( C)H 0.12 0.04 67 C (C)H 3 O (C) H 2 0.12 0.04 67 3C (C)H 3C (C) 0.14 0.14 0 2C (C)H 2 2C (C)H O 0.16 0.14 13 C (C)H 3 C (C)H 2 O 0.16 0.16 0 C (C)H 3 (C)H 3 0.18 0.00 100 2C (C)H 2 C (C)H 2 0.18 0.18 0 3C (C)H 2C (C)H 0.32 0.28 13 2C (C)H 2 2C (C)H 0.34 0.34 0 C (C)H 3 C (C)H 2 0.60 0.58 3 O C (O)H 0.08 0.04 50 O H (O) H 0.10 0.00 100 O ( O ) H 0.12 0.00 100 O C (O) C 0.30 0.26 13 O C ( O ) 0.36 0.22 39 O O 0.04 0.00 100
132 Table 6 9 Coordinatio n analysis of atomic oxygen deposition on PP at 100 Initial coordination Final coordination Total yield Surface yield Dissociated (%) C (C)H 3 (C)H 3 0.12 0.00 100 3C (C)H 2C (C)H 2 0.14 0.10 29 2C (C)H 2 C (C)H 3 0.14 0.12 14 3C (C)H C (C) C 0.14 0.12 14 C (C)H 3 (C)H 4 0.16 0.00 100 C (C)H 3 C (C)H 2 O 0.18 0.18 0 C (C)H 3 C ( C)H 0.22 0.12 45 2C (C)H 2 C ( C)H 0.26 0.12 54 C (C)H 3 2C (C)H 2 0.30 0.30 0 3C (C)H C ( C)H 0.30 0.12 60 2C (C)H 2 C (C)H 2 0.48 0.36 25 3C (C)H 3C (C) 0 .50 0.44 12 2C (C)H 2 2C (C)H 0.80 0.74 8 3C (C)H 2C (C)H 1.00 0.82 18 C (C)H 3 C (C)H 2 1.12 1.02 9 O OH 0.02 0.00 100 O H (O) H 0.04 0.00 100 O O (O) 0.04 0.00 100 O C (O) C 0.20 0.14 30 O C (O) 0.30 0.12 60 O C (O)H 0.32 0.20 38 O O 0.08 0.00 100 Table 6 10 Coordination analysis of atomic oxygen deposition on PS at 25 Initial coordination Final coordination Total yield Surface yield Dissociated (%) 2C (C)H C (C) C 0.12 0.12 0 2C (C)H 2 C (C)H 2 0.16 0.12 25 3C (C )H 2C (C)H 0.22 0.18 18 2C (C)H C ( C)H 0.52 0.38 27 2C (C)H C (C)H O 0.56 0.48 14 2C (C)H 2C (C)H O 0.64 0.60 6 O C (O)H 0.04 0.04 0 O C (O) 0.14 0.08 43 O C (O) C 0.82 0.74 10
133 Table 6 11 Coordination analysis of atomic oxygen dep osition on PS at 50 Initial coordination Final coordination Total yield Surface yield Dissociated (%) 3C (C) 3C (C) O 0.12 0.10 17 2C (C)H 2 2C (C)H 0.12 0.12 0 2C (C)H C (C)H 2 0.12 0.12 0 3C (C) 2C (C) O 0.14 0.06 57 3C (C)H 3C (C) 0. 20 0.20 0 2C (C)H 2 C (C)H 2 0.22 0.20 9 3C (C) C (C) C 0.22 0.18 18 2C (C)H C (C)H O 0.34 0.26 24 3C (C)H 2C (C)H 0.34 0.32 6 2C (C)H C (C) C 0.46 0.44 4 2C (C)H C ( C)H 0.60 0.44 27 2C (C)H 2C (C)H O 0.60 0.56 7 O C (O) 0.10 0.06 40 O C (O)H 0.14 0.10 29 O C (O) C 0.76 0.60 21 Table 6 12 Coordination analysis of atomic oxygen deposition on PS at 100 Initial coordination Final coordination Total yield Surface yield Dissociated (%) 2C (C)H C C 0.12 0.02 83 2C (C)H 3C (C)H 0.18 0.18 0 3C (C)H C (C) C 0.20 0.10 50 3C (C) 2C (C)H 0.20 0.14 30 2C (C)H C (C)H 2 0.22 0.20 9 2C (C)H C (C)H O 0.28 0.28 0 3C (C) C (C) C 0.38 0.36 5 2C (C)H 3C (C) 0.40 0.38 5 3C (C)H 3C (C) 0.42 0.40 5 2C (C)H 2 C (C)H 2 0.50 0.26 48 2C (C)H 2 2C (C)H 0.54 0.54 0 2C (C)H 2C (C)H 2 0.64 0.64 0 2C (C)H 2C (C)H O 0.68 0.68 0 3C (C)H 2C (C)H 0.82 0.70 15 2C (C)H C (C) C 0.96 0.94 2 2C (C)H C ( C)H 1.60 0.86 46 O C (O) 0.06 0.02 67 O C (O)H 0.10 0.10 0 O C (O) C 0.84 0.80 5
134 Table 6 13 Comparison of probable modifications during argon and atomic oxygen bombardment at Ar O Molecule Initial coordination Final coordination Total yield Surface yield Total yield Surface yield PE 2C CH 2 2 C CH 1.44 1.32 2.34 2.12 2C CH 2 C CH 2 2.48 1.62 1.46 0.86 PP C CH 3 C CH 2 0.64 0.52 1.12 1.02 3C CH 2C CH 1.18 0.88 1.00 0.82 PS 2C CH C C C 0.54 0.42 0.96 0.94 3C CH 2C CH 1.00 0.70 0.82 0.70 3C C C C C 0.58 0.36 0.38 0.36 2C CH C CH 1.96 0.66 1.60 0.86
135 Figure 6 1 Initial PE, PP, PMMA and PS substrates wi t h each chain color coded PP PS PE
136 Figure 6 2 Pair distribution function for PE, PP and PS
137 Figure 6 3 Yield of sputtered carbon and hydrogen atoms fo r at 25 50 and 100
138 Figure 6 4 Molecular mass analysis for deposited at 50
139 Figure 6 5 Molecular mass analysis for deposited at 100
140 Figure 6 6 Yields and concentrations of the three most probable groups formed duri ng 100 deposition on PE, PP and PS
141 Figure 6 7 Yield of sputtered carbon and hydrogen for atomic oxygen at 25 50 and 100
142 Figure 6 8 M olecular mass analysis of 50 atomic oxygen
143 Figure 6 9 Oxygen bonding in PS for depo sition energies at 25 with C (O) C coordination in four possible environments: a) in broken ring, b) along broken ring, c) bridge on ring and d) in ring
144 CHAPTER 7 DEVELOPMENT OF POTENTIALS ons is the metal oxide semiconductor (MOS) stack. MOS technology has matured over decades of intense research making it one of the most studied systems. However, a seminal shift is occurring in this industry, with the use of as an insulating ox ide having reached its limit. This is a result of device scaling, necessitating a detrimentally thin layer which allows an unacceptable amount of leakage current through the insolating oxide 163 The a which can trap electrons, as well as unwanted formation 164, 165 Despite these on going issues hafnium dioxide in experimental and quantum computation studies of this material, there exists ample room for further exploration of hafnium dio xide Hafnium dioxide ( ) has become the favored material fo r use as a dielectric layer in MOS applications ; due to it meeting a number of performance metrics, including a high dielectric constant of ~ a large band gap of and conducti on band offset of with respect to 164, 165 is also thermodynamically stable in the presence of silicon, neither reacting or decomposing under annealing conditions 164, 165 With increasing temperature, exhibits three crystalline phases monoclinic tetragonal cubic 166 This is the same phase order as in zirconia. This is not surprising as and occupy the same column of the periodic table
145 7 .1 Density Functional Theory D ata In the absence of a full database for the salient materials properties, electronic structure calculations are used at the density functional theory (DFT) level to provide the necessary materials properties to fit potential parameters. In particular, DFT is used to calculate the elastic prope rties for the cubic and tetragonal phases, and point defect formation energies the cubic phase Calculations are conducted using the VASP software 99, 100 The exchange and correlatio n terms are calculated using the generalized gradient approximation (GGA) 1 02, 103 with the correction of Perdew, Burke and Ernzerhof (PBE) 104 The electron w avefunction s are calculated using projected augmented wave (PAW) psuedopotentials 101 The Monkhorst Pack method of k point meshing is employed 167 ; for the single non p rimitive unit cells used in this study. A 6x6x6 k point mesh is found to give wel l converged results. The conjugant gradient method of geometry optimization i s used. The valence electr on orbitals for hafnium include the and obitials while the and electron orbitals are considered for oxygen. A cut off energy of is used for the elastic constant calculations. Defect formation energies are calculated using non primitive unit cells. 7 2 Buckingham With Core Shell A popular and successful empirical potential for the interatomic interactions for ionic materials is the Buckingham potential Equation (2 7 ) used either with or without a shell model Equation (2 8 ). This potential can be seen to depend on empirical parameters ( ij ij ij and ) that are fit empirically to achieve the desired set of properties. To determine the parameters, a set of properties from either experiment or first principles is specified, such as the equation of st ate and the elastic constants. The
146 set of properties predicted by the potential is then compared to the target set of propert ies and a least squared method routine is used to minimize the error of these properties in parameter space. Considering the lack of experimental data on the high temperature phases of 2 first principles methods are needed to achi eve a full set of properties in order to parameterize a potential. 7 .3 Empirical Potential for HfO 2 In this section, three different potentials are parameterized. One is optimized for the cubic phase (1) one for the tetragonal phase (2) and one for both tetragonal and cubic phases (3) The potentials developed for the two phases separately reproduce more quantitatively the physical properties of the individual phase. The potential that reproduces both the tetragonal and cubic phases inevitably has to make compromises in its ability to capture the materials properties of both phases Based on the values calculated with DFT the lattice parameters and elastic constant parameter sets for the cubic and tetrag onal phases are fitted for the Buckingham potential using the generalized lattice parameter software (GULP) 168 The resulting parameter sets are shown in Table 7 1 where ij ij and ij are the atomic interaction parameters, is the distance after which no interatomic interaction is considered (cut off), is the spring constant and is the shell charge. 7.4 Structure and Phase order In order to ch eck the phase stability each phase of 2 is explored as indicated in Figure 7 1 and t he structural properties are summarized in Table 7 2 The Buckingham form is not able to describe the monoclinic pha se. This is not a surprise since attempts to describe monoclinic zirconia in this manner have not been successful.
147 7 .4 .1 Elastic Properties The two high dielectric constant phases of interest for MOS applications, the cubic and tetragonal phases are furt her analyzed using DFT. The elastic coefficients for these phases are calculated by applying strains under ; the results are given in Table 7 3 together with the elastic constant calculated for the potentials. The compliance tensor is found by calculating the inverse of the elastic coefficient tensor. Then the Reuss and Voigt approximations are used to calculate the bulk ( B ) and shear ( G ) moduli 169 For an isotropic solid (cubic) single crystal the bulk and shear moduli can be found to be : (7 1) (7 2) and (7 3) W here the Voigt and Reuss approximations use s the elastic coefficients and compliance respectively. For tetragonal symmetry these approximations are as fol lows: (7 4) and
148 (7 5) f or the bulk modulus, and (7 6) and (7 7) for the shear modulus. The Hill approximation is found by averaging the Reuss and Voig t approximations 169 an d the is approximated using the Hill values 170 : (7 8) and (7 9) and the results are summarized in Table 7 4 7 .5 Point Defect Energetics For a charge neutral system, the formation of an oxygen vacancy creates a defect site with a 2 + charge, alo ng with two unpaired electrons: (7 10 ) In contrast, the formation o f a hafnium vacancy leaves a defect site with a charge and four holes:
149 (7 11 ) An interstitial oxygen has a charge of requiring two holes to be neutral and an intestinal hafnium has a charge of 4+ requiring four electrons to be neutral. (7 12 ) and (7 13 ) DFT is used to calculate the appropriate range of formation energies of these point defects for limiting cases of the chemical potential 171 The formation of these defects is defined by (7 14 ) w here E perf is energy of the perfect crystal, E def is the energy of the defective system, is the chemical potential of the defective species q is the charge of th e defect and F is the Fermi energy. The range of the chemical potentials is defined first by the stability of the oxide phase compared to the metallic and molecular phases of its constituents In particular the chemical potential of in 2 mus t be less than that of in its hcp metal phase: (7 1 5 )
150 Correspondingly, the chemical potential of oxygen in hafnium oxide must be less than that of oxygen in the molecular p hase for the oxide to be stable: (7 1 6 ) formation where: (7 1 7 ) If the fir st limit of the chemical (Equation (7 1 5 ) ) is considered, then the chemical potential of oxygen in 2 is given as: (7 1 8 ) In contrast, if the first limit of the chemical po tential of oxygen is considered: (7 1 9 ) From Equation ( 7 1 7 ) the enthalpy of formation is calculated to be and per stoichiometric unit for the tetragonal and cubic phases, respectively. In order to properly represent isolated point defects a 2x2x2 super cell consisting of atoms are created. Then single oxygen and hafnium vacancies and i nterstitial point defects were added. These systems were relaxed with a fixed volume, convergence criteria in energy of 0.1 meV and force of 0.02 eV/ U sing Eq uation 7 14 the formation energies are calculated for point defects using the two chemical pot ential extremes, and the results are shown in Table 7 5
151 The defect formation energies are also calculated using the fitted empirical potentials. Defective 4x4x4 super cells are constructed and relaxed at constant volume. However with this method the chemical potential of the constituent species is considered to be the average potential energy associated with the relative element within the oxide system. The results of these calculations are also shown in Table 7 5 7 .6 Conclusion s While the elastic and phase order properties are accurately captured in the fitting the cubic and tetragonal phases are found to be unstable at temperatures above 0K. Therefore, the potential is not considered to be a success ful way to model hafnium oxide in classical molecular dynamics simulations.
152 Table 7 1 Empirical potential parameters of the cubic and tetragonal phases of using the Bucking ham formalism with shell model Parameters Cubic (1) Tetragonal (2) Cubic/Tetragonal (3) A O O (eV) 9547.96 9547.96 9547.96 O O () 0.24 0.27 0.26 C O O (eV 6 ) 170.45 347.94 259.20 A Hf O (eV) 1201.34 975.19 928.75 Hf O () 0.39 0.38 0.39 C Hf O (eV 6 ) 113.22 0.00 6.00 r cut () 12.00 12.00 12.00 k Hf 34.21 34.21 3 4.21 k O 28.80 28.80 28.80 Y Hf (|e|) 3.95 3.95 3.95 Y O (|e|) 2.20 2.20 2.20 Table 7 2 Experimental and calculated lattice parameters of the monoclinic, tetragonal and cubic phases of DFT (PBE) Potentials Potential 3 Expt 169 1 or 2 Tetragonal V ( 3 ) 33.73 33.68 34.38 33.58 a () 5.08 5.08 5.11 5.09 c () 5.23 5.23 5.26 5.18 (g/cm 3 ) 10.36 10.38 10.17 10.41 Cubic V ( 3 ) 32.65 32.53 33.87 32.77 a () 5.07 5.07 5.14 5.08 (g/cm 3 ) 10.70 10.74 10.32 10.67
153 Table 7 3 Elastic constant tensor values for the tetragonal and cubic phases Coefficient (GPa) DFT (PBE) Potential Potential 3 1 or 2 Tetragonal C 11 495.01 625.56 579.81 C 12 151.77 150.36 145.48 C 13 118.76 124.34 117.02 C 33 397.42 422.20 361.98 C 44 89.86 89.41 87.99 C 66 125.12 129.57 121.95 Cubic C 11 560.36 561.19 664.56 C 12 93.20 94.15 111.13 C 44 67.82 68.66 98.43 Table 7 4 Elastic moduli for the cubic and tetragonal phases of HfO 2 Cubic Tetragonal DFT Potential 1 Pote ntial 3 DFT Potential 2 Potential 3 G 114.32 115.14 151.18 122.81 136.05 127.39 B 248.92 249.83 295.61 245.33 269.39 246.54 0.3 0 0.3 0 0.28 0.29 0.28 0.28 E 297.43 299.42 387.48 315.75 349.34 326.01
154 Table 7 5 Defect formation energies from DFT a nd empirical potential calculations Kr ger Vink Defect Potentials notation charge Hf Metal Hf O Molec O2 1&2 3 Tetragonal V O X 0 0.79 6.07 V O +2 4.04 1.23 2.67 0.30 V Hf X 0 16.28 5.73 V Hf '''' 4 12.00 1.45 9.65 10.74 O i X 0 7.54 2.26 O i 2 7.06 1.78 3.79 5.62 Hf i X 0 4.66 15.21 Hf i +4 4.41 6.14 6.65 8.14 Cubic V O X 0 0.82 6.05 V O +2 5.97 0.17 2.38 1.19 V Hf X 0 15.01 4.56 V Hf '''' 4 14.56 2.97 9.65 11.97 O i X 0 9.35 4.13 O i 2 9.32 7.8 9 5.84 7.05 Hf i X 0 3.98 14.43 Hf i +4 5.41 6.17 8.49 11.32
155 Figure 7 1 Three low pressure phases of HfO 2 (a) monoclinic, (b) tetragonal, (c) cubic where oxygen is darkly shaded and hafnium is lightly shaded
156 CHAPTER 8 CONCLUSIONS The p rimary focus of th e work described in this dissertation is to identify the interactions of hyperthermal ions with polymer surfaces. A combination of empirical potential MD simulations and quantum chemical analysis is used to classify the effects of indivi dual ions on polymer surfaces. This method is successfully applied to illuminate fluorocarbon growth of DLC, hydrocarbon modification of PS, the modification of terthiophene during the SPIAD process, and the effects of non reactive and reactive species on PE, PP and PS. In order to study these processes the second generation REBO potential is modified to include sulfur hydro carbon interactions and improve the oxygen hydrocarbon interactions. In particular, the oxygen hydrocarbon second generation REBO p otential is improved by refitting the coordination function. The refit primarily involved fitting to dissociation and atomization energies of an expanded dataset of small molecules that capture all possible coordination. The refit of the coordination fun ction improved the average error in dissociation energy from to for the dataset; however, the average error in atomization energy for a test set is increased from to The sulfur interactions are included in a similar manner as oxygen. Th e pair terms are fit to molecular bond stretching and solid strain curves. The angular function is fit to bond bending curves, and given a dependence on the considered atom types. As with the oxygen coordination function the sulfur coordination function is fit to a dataset of small molecule dissociation and atomization energies. The average error in dissociation energies is predicted to be and the average error in atomization energy to be
157 The multilevel simulation study of fluorocarbon growth of DLC carbon revealed that the creation of may be a key driving force allowing the process to occur at lower temperatures than hydrocarbon growth. The second generation REBO potential is used as an initial guide to probable reactions. DFT MD simulations offer complementary analysis. Subsequ ent reactions are further analyzed with quantum chemical methods. Hydrocarbon interactions with PS are investigated with computational simulations. It is found that the cations and have barrier less interactions with the styrene ring of PS. This results correspond well to MD simulations using the second generation REBO potential, which finds non preferential bond to occur. The reaction path and subsequent barriers of the radical bonding to the styrene ring is found to depend on the spin state However, the final product, a methyl group, is found to be stable for both states. The reaction is also observed during the MD simulations. The difference in the nature of argon and polyatomic thiophene depositions is explored during the S PIAD modification of terthiophene. MD simulations using the newly parameterized REBO potential for sulfur hydrocarbon interactions are conducted in conjunction with ab initio calculations The thiophene is seen to induce fracture of terthiophene rings whil e retaining the chemical structure of terthiophene. Conversely argon is found to alter the number of carbons within the terthiophene during modification. Thiophene is also predicted to produce more reactive species than argon. Reactive hydrocarbon spe cies interacting with a thiophene radical are modeled with quantum chemical methods. These calculations find that thiophene radical readily reacts with small hydrocarbon molecules. Finally, the SPAID process is found to a
158 complex interaction involving di ssociation of the incident polyatomic molecule, multiple reactions involving ring fragmentation and likely recombination with other incident 3T molecules. In order to compare the effect of non reactive and reactive species on polymer surfaces, argon and atomic oxygen are deposited on PE, PP and PS. The primary modifications of each species is identified. Argon is found to break carbon carbon bonds, and remove hydrogen as a secondary process. Atomic oxygen is found to remove hydrogen from the polymer, a nd form chemical bonds within the polymer. The scission of carbon carbon bonds is also found to occur with less frequency for oxygen deposition than argon deposition Lastly, this work illuminates the nature of the of the hyperthermal ion with polymer s urfaces. To this end empirical potentials are developed and implement in order to identify relevant processes. These processes are further analyzed with quantum chemical methods. This work will thus foster further development of plasma and ion beam met hods to modify polymer surfaces.
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169 BIOGRAPHICAL SKETCH Travis Kemper was born in California in 1981. He attended UCSC from 2000 to 2004 and receive d a Bachelor of Science in applied p hysics. From 2005 to 2006 he worked as a Junior S pecialist for Dr. Ali Shakouri in the Electrical E ngineering D epartment at U CSC. After this he traveled the world for one year before starting a PhD program in the Mate rials Science and Engineering Department at the University of Florida in 2007. He receive d a Master of Science in 2010 and his PhD in 2011