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Computational Modeling of Atomistic Phenomena at the Interface

Permanent Link: http://ufdc.ufl.edu/UFE0024892/00001

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Title: Computational Modeling of Atomistic Phenomena at the Interface
Physical Description: 1 online resource (150 p.)
Language: english
Creator: Chiu, Patrick
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: dynamics, molecular, tribology
Materials Science and Engineering -- Dissertations, Academic -- UF
Genre: Materials Science and Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: As the design of devices and applications becomes increasing complex, the interfaces of advanced materials have a pervasive influence on a variety of engineered properties. In functional ceramics, the electronic conductivity is strongly impacted by the ion arrangement at grain boundaries. Interlayer dielectric materials such as thin films with nanoscale porosity require structure with precisely controlled interfaces. In addition, the environment in which surfaces are coated is often very different from the environment they are subjected to in tribological application. To engineer materials with desired properties, it is thus important to understand these interfaces at the atomic level. In this dissertation, ab initio calculations and molecular dynamics (MD) simulations were carried out toward the understanding of different interfaces. Defects in titanium dioxide (TiO2) grain boundaries are investigated where the bulk properties are largely determined by these internal interfaces. Defect formation energies in TiO2 grain boundaries are calculated using density functional theory (DFT) and are compared to corresponding energies in bulk TiO2. In particular, various Schottky and Frenkel defects complexes are considered. The morphology and mechanical properties of surfactants, which are surface active agents that are used as organic templates in mesoporous silica thin films and in the synthesis of other emerging technologies, are investigated. Classical molecular dynamics simulations with empirical potentials are used to compare the structures and mechanical properties of cationic surfactant micelles that are being indented with carbon nanotubes and silica nanowires at the silica-water interface. The findings are compared to the results of bulk indentation with graphite and silica surfaces, and the influence of nanometer-scale curvature on the results is described. A tribological study of polyethylene (PE), a widely used polymer with great wear resistance and other advantageous tribological properties, was carried out to gain insight into the atomic-level origins of friction. The role of sliding orientation, surface loading, temperature, crosslinking, and composite sliding on the tribological behavior of PE is investigated using classical molecular dynamics simulations. At various temperatures, oriented crosslinked PE surfaces are slid in different sliding directions and applied normal loads. The tribological behavior of different crosslinked PE surfaces is compared, and the differences and similarities are discussed.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Patrick Chiu.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Sinnott, Susan B.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2010-02-28

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0024892:00001

Permanent Link: http://ufdc.ufl.edu/UFE0024892/00001

Material Information

Title: Computational Modeling of Atomistic Phenomena at the Interface
Physical Description: 1 online resource (150 p.)
Language: english
Creator: Chiu, Patrick
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: dynamics, molecular, tribology
Materials Science and Engineering -- Dissertations, Academic -- UF
Genre: Materials Science and Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: As the design of devices and applications becomes increasing complex, the interfaces of advanced materials have a pervasive influence on a variety of engineered properties. In functional ceramics, the electronic conductivity is strongly impacted by the ion arrangement at grain boundaries. Interlayer dielectric materials such as thin films with nanoscale porosity require structure with precisely controlled interfaces. In addition, the environment in which surfaces are coated is often very different from the environment they are subjected to in tribological application. To engineer materials with desired properties, it is thus important to understand these interfaces at the atomic level. In this dissertation, ab initio calculations and molecular dynamics (MD) simulations were carried out toward the understanding of different interfaces. Defects in titanium dioxide (TiO2) grain boundaries are investigated where the bulk properties are largely determined by these internal interfaces. Defect formation energies in TiO2 grain boundaries are calculated using density functional theory (DFT) and are compared to corresponding energies in bulk TiO2. In particular, various Schottky and Frenkel defects complexes are considered. The morphology and mechanical properties of surfactants, which are surface active agents that are used as organic templates in mesoporous silica thin films and in the synthesis of other emerging technologies, are investigated. Classical molecular dynamics simulations with empirical potentials are used to compare the structures and mechanical properties of cationic surfactant micelles that are being indented with carbon nanotubes and silica nanowires at the silica-water interface. The findings are compared to the results of bulk indentation with graphite and silica surfaces, and the influence of nanometer-scale curvature on the results is described. A tribological study of polyethylene (PE), a widely used polymer with great wear resistance and other advantageous tribological properties, was carried out to gain insight into the atomic-level origins of friction. The role of sliding orientation, surface loading, temperature, crosslinking, and composite sliding on the tribological behavior of PE is investigated using classical molecular dynamics simulations. At various temperatures, oriented crosslinked PE surfaces are slid in different sliding directions and applied normal loads. The tribological behavior of different crosslinked PE surfaces is compared, and the differences and similarities are discussed.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Patrick Chiu.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Sinnott, Susan B.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2010-02-28

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0024892:00001


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1 COMPUTATIONAL MODELING OF ATOMISTIC PHENOMENA AT THE INTERFACE By PATRICK Y. CHIU A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF D OCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2009

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2 2009 Patrick Y. Chiu

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3 To my family with love and gratitude

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4 ACKNOWLEDGMENTS I would like to express my sincer e gratitude and respect to my advisor, Professor Susan B. Sinnott for investing her expertise, guidance and patience I feel very fortunate to be given the opportunity by her to learn and explore the world of computational materials science. I would like to extend my sincere appreciation to Profe ssor Simon R. Phillpot for his helpful advice and encouragement I have deep respect for h is knowledge in the fie ld of simulation I also would like to thank Professors W. Gregory Sawyer, Scott S. Perry, Anthony B. Brennan, and Aravind Asthagiri for invalu able collaborations and discussions. Great thanks go to all members past and present, of the Computational Materials Science Focus Group I especially thank working with Dr. Kunal Shah Dr. Jun He, Dr. SeongJun Heo, and Peter R. Barry, one half of the gru esome twosome. I am especially blessed to have my wife Melanie, and am very thankful for her constant love and support I would not have persevered without her M y heartfelt appreciation goes out to my parents, for their belief in me through their love an d support

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS .................................................................................................................... 4 LIST OF TABLES ................................................................................................................................ 7 LIST OF FIGURES .............................................................................................................................. 9 ABSTRACT ........................................................................................................................................ 12 CHAPTER 1 INTRODUCTION ....................................................................................................................... 14 General Introduction ................................................................................................................... 14 Titanium Dioxide ........................................................................................................................ 15 Structure of TiO2 .................................................................................................................. 16 Defect Formation in TiO2 .................................................................................................... 17 Grain Boundary Structures .................................................................................................. 18 Surfactants ................................................................................................................................... 20 Structure of Surfactants ....................................................................................................... 21 Thermodynamics of Surfactant Adsorption at Solid Liquid Interfaces ........................... 21 Atomic Force Microscopy................................................................................................... 22 Templating of One Dimensional Materials ........................................................................ 24 Polyethylene ................................................................................................................................ 25 Structure of Polyethylene .................................................................................................... 26 Crosslinking ......................................................................................................................... 27 Tribological Studies of Polymers ....................................................................................... 28 2 COMPUTATION AL METHODS ............................................................................................. 35 Density Functional Theory ......................................................................................................... 35 Kohn -Sham Theory ............................................................................................................. 35 E xchange -Correlation .......................................................................................................... 36 Pseudopotential .................................................................................................................... 38 Molecular Dynamics ................................................................................................................... 38 Statistical Ensemble ............................................................................................................. 39 Periodic Boundary Conditions ............................................................................................ 39 MicelleMD ........................................................................................................................... 40 Velocity Verlet ..................................................................................................................... 41 Velocity Rescaling ............................................................................................................... 41 REBO ................................................................................................................................... 42 Predictor Corrector Algorithm ............................................................................................ 44 Langevin Thermostat ........................................................................................................... 46

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6 3 AB INITIO CALCULATIONS OF DEFECT FORMATION ENERGIES AT TITANIUM DIOXIDE GRAIN BO UNDARIES ..................................................................... 48 Computational Details ................................................................................................................ 48 Results .......................................................................................................................................... 50 Schottky and Fre nkel Defects at the Grain Boundary ....................................................... 50 Comparison of Defects at the Grain Boundary and in the Bulk ....................................... 54 Sources of Error ................................................................................................................... 54 Conclusions ................................................................................................................................. 55 4 MORPHOLOGY AND MECHANICAL PROPERTIES OF SURFACTANT AGGREGATES WITH NANOTUBES AND NANOWIRES USING MOLECULAR DYNAMICS SI MULATIONS ................................................................................................... 65 Computational Details ................................................................................................................ 65 Results .......................................................................................................................................... 66 Surfactant Stru ctures at Solid Liquid Interfaces ................................................................ 66 Mechanical Properties of Surfactants ................................................................................. 68 Conclusions ................................................................................................................................. 71 5 TRIBOLOGY OF POLYETHYLENE USING MOLECULAR DYNAMICS SIMULATIONS .......................................................................................................................... 78 Computational Details ................................................................................................................ 78 Results .......................................................................................................................................... 79 Sliding Orientation ............................................................................................................... 79 Normal Load ........................................................................................................................ 82 Temperature ......................................................................................................................... 83 Crosslinking ......................................................................................................................... 85 Composite Sliding ............................................................................................................... 87 Conclusions ................................................................................................................................. 89 6 GENERAL CONCLUSIONS .................................................................................................. 103 APPENDIX RANDOMIZED CROSSLINKING CODE ............................................................ 106 LIST OF REFEREN CES ................................................................................................................. 141 BIOGRAPHICAL SKETCH ........................................................................................................... 150

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7 LIST OF TABLES Table page 1 1 Classification of polyethylene by density. ............................................................................ 31 3 1 Comparison between calculated structural lattice parameters and experimental values of TiO2. ................................................................................................................................... 57 3 2 Comparison of the grain boundary energy with a smaller bulk region and with a larger bulk region. .................................................................................................................. 57 3 3 Number of overcoordinated and undercoordinated atoms and defect formation energy (DFE) of each grain boundary system with Schottky defects. ................................ 57 3 4 Number of overcoordinated and undercoordinated atoms and energy (DFE) of each grain boundary system with Frenkel defects. ....................................................................... 57 3 5 Number of overcoordinated and undercoordinated atoms and defect formation energy (DFE) of each bulk system with Schottky defects. .................................................. 58 3 6 Number of overcoordinated and undercoordinated atoms and defect formation energy (DFE) of each bulk system with Frenkel defects. .................................................... 58 3 7 Comparison of calculated Frenkel and Schottky DFEs with publi shed theoretical values for rutile TiO2. ............................................................................................................. 58 5 1 Friction coefficient and adhesive force for all sliding orientations of PE. ......................... 90 5 2 Calculation of crosslinking density using the ratio of crosslinked CH2 units over total CH2 units. Values are for one PE surface. ............................................................................ 90 5 3 Friction coefficient and adhesive force for all crosslinking densities of PE in perpendicular sliding. ............................................................................................................. 90 5 4 Friction coefficient and ad hesive force for all crosslinking densities of PE in violin sliding. ..................................................................................................................................... 90 5 5 Friction coefficient and adhesive force for all sliding orientations of PE -PTFE sliding. ..................................................................................................................................... 90 5 6 Friction coefficient and adhesive force of PE PE, PE -PTFE, and PTFE -PTFE systems for perpendicular sliding. ......................................................................................... 90 5 7 Friction coefficient and adhesive force of PE PE, PE -PTFE, and PTFE -PTFE systems for violin sliding. ...................................................................................................... 91

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8 5 8 Friction coefficient and adhesive force of PE PE, PE -PTFE, and PTFE -PTFE systems for parallel sliding. ................................................................................................... 91

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9 LIST OF FIGURES Figure page 1 1 Phase diagram of TiO2. .......................................................................................................... 32 1 2 Model of u nit cell structure of rutile TiO2 ............................................................................ 32 1 3 Construction of 2 ..................................... 33 1 4 Model of C12TAB (n dodecyltrimethylammoniumbromide) surfactant ............................. 33 1 5 S napshots of s urfactant structures at high concentrations ................................................... 34 1 6 Diagram of AFM apparatu s ................................................................................................... 34 1 7 Model of polyethylene chain ................................................................................................. 34 2 1 Illustration of periodic boundary conditions applied in simulation. ................................... 47 3 1 Pristine bulk unit cell of TiO2 ................................................................................................ 59 3 2 Plot of total energy of perfect bulk TiO2 unit cell versus cutoff energy of PAW PBE pseudopotential. ...................................................................................................................... 59 3 3 Model of 5 (210) tilt grain boundary with two grain boundaries of opposite direction with no vacuum ...................................................................................................... 59 3 4 Modle of 5 (210) tilt grain boundary system with larger bulk region .............................. 60 3 5 Plot of energy of the grain boundaries as a function of the separation between them for ZrO2 2 GB systems .............................. 60 3 6 Snapshots of Schottky and Frenkel defects in the grain boundaries ................................... 61 3 7 Overlay of relaxed TiO2 defects on the Z -contrast image. ............................................................................................ 61 3 8 Overlay of Schottky (mixed1) defect grain boundary structure on the Z -contrast image ....................................................................................................................................... 62 3 9 Overlay of Schottky (clustered) defect grain boundary structure on t he Z -contrast image ....................................................................................................................................... 62 3 10 Snapsho ts of Schottky and Frenkel defects in the bulk ....................................................... 63 3 11 Graph of DFE (eV) of different Schottky spatial arrangements for grain boundary and bulk systems .................................................................................................................... 64

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10 4 1 Adsorbed micelle of C12TAB surfactants in between carbon nanotubes on silica in aqueous medium ..................................................................................................................... 73 4 2 Adsorbed micelle of C12TAB surfa ctants in between silica nanowires on silica in aqueous medium ..................................................................................................................... 74 4 3 Snapshots of silica nanowire indentation at a rate of 25 m/s at various indenter separation distances. ............................................................................................................... 75 4 4 Total force felt by the indenter as a function of separation distance between the surface and indenter for silica indenters in surface and nanowire forms. .......................... 76 4 5 Snapshots of carbon nanotube indentation at a rate of 25 m/s at various indenter separation distances. ............................................................................................................... 77 5 1 Model of t he unit cell s tructure of PE ................................................................................... 92 5 2 Schematic diagram of the PE polymer chain alignment ...................................................... 92 5 3 Sliding orientations of PE co nsidered ................................................................................... 93 5 4 Graph of frictional and normal forces as functions of sliding distance for perpendicula r, parallel, and violin sliding ............................................................................ 94 5 6 Friction force as a function of normal force for perpendicular sliding at various temperatures. ........................................................................................................................... 96 5 7 Friction force as a function of normal force for parallel sliding at various temperatures. ........................................................................................................................... 96 5 8 Friction force as a function of normal force for violin sliding at various temperatures. ... 97 5 9 Friction coefficient as a function of temperature for the different sliding orientations. .... 97 5 10 Adhesive force as a function of temperature for t he different sliding orientations. .......... 98 5 11 Top down view of PE system with an extended surface. .................................................... 98 5 12 Fricti on force as a function of normal force for perpendicular sliding at various crosslinking densities. ............................................................................................................ 99 5 13 Friction force as a function of normal force for parallel sliding at variou s crosslinking densities. ............................................................................................................ 99 5 14 Friction force as a function of normal force for violin sliding at various crosslinking densities. ............................................................................................................................... 100 5 15 Histogram of surface chain movement normalized by the sliding surface distance for perpendicular sliding of PE surfaces with 19% randomized crosslinking density .......... 101

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11 5 16 Side view of PE PTFE system ............................................................................................ 102 5 17 Friction force as a function of normal force for all sliding orientations of the PE PTFE system. ........................................................................................................................ 102

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12 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy COMPUTATIONAL MODELING OF ATOMISTIC PHENOMENA AT THE INTERFACE By Patrick Y. Chiu August 2009 Chair: Susan B. Sinnott Major: Materials Science and Engineering As the design of devices and applications becomes increasing complex, the interfaces of advanced materials have a pervasive influence on a variety of engi neered properties. In functional ceramics the electronic conductivity is strongly impacted by the ion arrangement at grain boundaries. Interlayer dielectric materials such as thin films with nanoscale porosity require structure with precisely controlled i nterfaces. In addition, t he environment in which surfaces are coated is often very different from the environment they are subjected to in tribological application To engineer materials with desired properties, it is thus important to understand these int erfaces at the atomic level. In this dissertation, a b initio calculations and molecular dynamics (MD) simulations were carried out toward the understanding of different interfac es Defects in titanium dioxide (TiO2) grain boundaries are investigated where the bulk properties are largely determined by these internal interfaces. Defect formation energies in TiO2 grain boundaries are calculated using density functional theory (DFT) and are compared to corresponding energies in bulk TiO2. In particular, various Schottky and Frenkel defects complexes are considered.

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13 The m orphology and mechanical properties of surfactants, which are surface active agents that are used as organic templates in mesoporous silica thin films and in the synthesis of other emerging techn ologies, are investigated. Classical molecular dynamics simulations with empirical potentials are used to compare the structures and mechanical properties of cationic surfactant micelles that are being indented with carbon nanotubes and silica nanowires at the silica -water interface. The findings are compared to the results of bulk indentation with graphite and silica surfaces, and the influence of nanometer -scale curvature on the results is described. A tribological study of polyethylene (PE), a widely use d polymer with great wear resistance and other advantageous tribological properties, was carried out to gain insight into the atomic level origins of friction. The role of sliding orientation, surface loading, temperature, crosslinking, and composite slidi ng on the tribological behavior of PE is investigated using classical molecular dynamics simulations. At various temperatures, oriented crosslinked PE surfaces are slid in different sliding directions and applied normal loads. The tribological behavior of different crosslinked PE surfaces is compared, and the differences and similarities are discussed.

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14 CHAPTER 1 INTRODUCTION General Introduction Interface science is the study of physical and chemical phenomena that occur at the interface of two phases suc h as grain boundaries, solidliquid in terfaces, and sliding surfaces. As advanced materials become increasing ly multifunctional there is a concerted focus on the influence i nterfaces have on targeted properties such as electrical conductivity, impact str ength, and wear resistance To tailor the properties of materials, it is therefore significant to have a solid fundamental understand ing of atomistic phenomena at the interfa ce For many electronic and structural materials, bulk properties are mainly deter mined by internal interfaces such as grain boundaries. Therefore, the first system to be addressed in my dissertation is the study of grain boundaries in TiO2, which is o ne of the most widely used transition metal oxides because of its use in heterogeneous catalysis, as gas sensor s as photocatalyst s and as o ptical and protective c oati ngs to name a few1. There has been tremendous interest in gaining k nowledge of the atomic structure at TiO2 grain boundaries in relation to its electronic properties and how these properties are influenced by the presence of impurities and imperfections at these boundaries The second system that is investigated is micelles at the solid -liquid interface. Micel les consist of surfactants which are surface active agents that are traditionally used as emulsifiers in detergents, inks, and paints2. Surfactant systems are also used in emerging technologies such as controlled drug delivery, abrasives for precision polishing, and synthesis of thin films with nanoscale porosity3. Understanding the morphology and mechanical properties of surfactants and micelle s at solid liquid interfaces at the molecular level is of great interest in both scientific and industrial fields.

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15 The third and last area that I discuss in this dissertation is tribology, which is the study of surfaces in relative motion; it plays an incr easingly important role in the development of new products in electronics sensors and by extens ion for all mode rn technology4. Polyethylene is one of the most widely used polymers because of its versatility and manufacturability5. It has excellent wear resistance, toughness, and other advantageous tribologica l properties5. For this reason, PE is increasingly used in applications for its tribological performance such as thin coatings for microelectromechanical systems ( MEMS ), artificial joints, and sports equipment. Understanding the atomic -level origins o f friction is important in PE and polymer surfaces in general. Ti tanium Dioxide T iO2 is used in a broad spectrum of technological applications such as white pigments in the dye industry oxygen transfer catalysts, and protective coating s1. It has also been analyzed in great detai l b ecause sample surfaces can be readily prepared and characterized6. In particular, well -characterized bicrystals of titanium dioxide can be grown and examined by a variety of experimental techniques such as high resolution electron microscopy (HREM)7 and Z -contrast scanning transmission electron microscopy (STEM)8. It is wellestablished that the grain boundaries (GBs) in polycrystalline materials influence their electronic properties6 8, and determining pre dictive structure property relationships for these internal interfaces is of significant technological importance. The first step in achieving this overall understanding is to determine the structure of GBs through both experimental techniques and compute r simulations and establish how the stability of defects in GBs compare to the stability of defects in bulk environments

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16 Structure of TiO2 TiO2 naturally occurs in three primary crystal structures: rutile (tetragonal, 14 4 hD P42/mnm, a=b =4.594 c=2.959 )9, anatase (tetragonal, 19 4 hD I41/amd, a=b=3.7 82 c=9. 502 )1, and brookite (rhombohedral, 15 2 hD Pbca, a=5.436 b=9.166 c=5.135 )10. A structural study of rutile and anatase was originally investigated by Vegard11 in 1916 and accurate measurements of the lattice parameters have been reported by others1, 9. The crystal structure of brookite was initially verified by Pauling and Sturdivant12 in 1928, with subsequent findings by Baur13 in 1961 and Meagher and Lager14 in 1979. Among these structures, only rutile and anatase are used in applications and are the focus of research studies. The p hase diagram of TiO2 is shown in Figure 1 1 The most common form of TiO2 is rutile, which also is the most stable15; it is the crystal structure considered in this dissertation. The unit cell of r utile TiO2, illustrated in Figure 1 2 c onsists of a titanium atom surrounded by s ix oxygen atoms in a distorted octahedral configuration with two distinct bond lengths B etween the titanium and the oxygen atoms the length of the two apical bonds along the linear, twofold coordination is slightly longer than that of the four bonds alon g the rectangular, fourfold coordinati on. The nonstoichiometric states of TiO2 ha ve been of great research interest16. It has been mostly thought of as an ntype semiconductor16, 17. The n type properties have been regarded with oxygen vacancies as the majority defects and titanium interstitials as the minority defects16. However, recent stud ies have brought to light the fact that oxidized TiO2 may also have p type properties in the form ation and transport of titanium vacancies as acceptor -type defects18. Thus, nonstoichiometric formula TiO2x (redu ced specimen) or Ti1xO2 (oxidized specimen) can be considered

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17 Defect Formation in TiO2 Experimental techniques, such as thermogravimetry and electrical conductivity measurements, have been used to study deviations from stoichiometry in bulk TiO2. Individual defects an d impurities in oxides can be analy zed by HR EM19, Z contrast imaging, and electron energy loss spectroscopy (EELS) in STEM20. All these techniques are proven to be most sensitive to the heavier el ements in the crystal structure. However the oxygen atom, which is the element that in many cases plays the largest role in determining the electronic properties in oxides, is the least well characterized in these experiments. Most computational determinations o f defect formation in metal oxides such as TiO2 use one of three classes of theoretical approaches: empirical and semiempirical methods such as tight binding21, classical molecular dynamics simulations using empirical potentials22, and first principles calculations that are based on quantum mechanical principles First principles methods can be further classified as being either based on Hartree-Fock (HF) methods density functional theory (DFT) methods or hybrids of each23. Most of these methods have been applied to defect studies of TiO2. For example, Catlow et al.22, 24, 25 performed an extensive series of Mott Littleton calculations26 using classical potentials on TiO2 and found that the Schottky defect was energetically more stable than the Frenkel defect in rutile and that vacancy disorder will predominate in TiO2. In addition, Yu and Halley calculated the electronic structure of point defects in reduced rutile using a tight binding method21. They predicted the presence of defect clustering in nearly stoichiometric rutile with multiple defects. Several DFT studies have also been done to examine defect structures and stabilities27, 28. He et al. used DFT calculations to obtain electronic structure energy information about pristine and defective atomic -scale systems and then used thermodynam ic calculations to

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18 determine defect formation energies The ordering on the relative stabilities of the point defects studied was titanium vacancy, oxygen vacancy, and titanium interstitial. As stated earlier, t he chemical and electronic properties of TiO2 are connected to point defects at the surface. Experimental methods such as scanning tunneling microscopy (STM) and transmission electron microscopy (TEM) have been used to examine surface structures and defect diffusion on the TiO2 surface. For instance, Diebold et al.29 31 reported STM studies combined with theoretical calculations to determine the image contrast in STM analysis of the oxygen -deficient rutile TiO2 (110) surface. They found in scanning tunneling sp ectroscopy (STS) that oxygen-deficient defects do give rise to defect states within the band gap. Furthermore, Schaub et al.32 examined the oxygen mediated diffusion of oxygen vacancies on the TiO2 (110) surface b y HREM. They tracked a dsorbed oxygen molecules that mediate d vacancy diffusion through the loss of an oxygen atom to a vacancy leading to an anisotropic oxygen vacancy diffusion pathway perpend icular to the bridging oxygen rows. Grain Boundary Structures The photocatalytic properties of TiO2 were discovered by Fujishima and Honda33 in 1972. They showed TiO2 immersed in water and exposed to sunlight results in the evolution of oxygen from the anode and hydrogen from the cathode The discovery was made for single -c rystal TiO2. However, the application of TiO2 as a photoelectrode is made of polycrystalline TiO2 because it is less expensive than single -crystal TiO2. The difference between single crystals and pol ycrystalline materials is that GBs are formed and their structural formation largely determines the local properties rather than the structure of the bulk phase. Therefore, there is a need to understand the effect of GB s on the functional properties such as electrical conductivity through charge carrier mobility, which are vital for

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19 application performance. This understanding may lead to the develop ment of processing polycrystalline materials with controlled bulk properties through GB engineering The noti on of a coincident site lattice (CSL) misorientation has been widely used when discussing grain boundary character34. T he CSL model serves as a primary means of categorizing boundary types The CSL is a geometrical construction based on the geometry of the lattice. Any CSL orie ntation may be expressed a s a product of elementary operations in which lattice onto lattice points of explained as: 2 2 2l k h if 2 2 2l k h is odd 2 / ) (2 2 2l k h if 2 2 2l k h is even (1 1 ) and was first described by Ranganathan35. If a fixed fraction of lattice sites are coincident, then the expectation is that the boundary structu re will be more regular than a general boundary. A boundary that contains a high density of lattice points in a CSL is expected to have low ene rgy because of good atomic fit In many materials, certain low numbers correlate with these special boundaries which may have different strengths, chemical resistances, or impurit y segregation properties compared to random boundaries. In this grain boundary from rutile TiO2 is studied. The GB is derived from two TiO2 rutile crystal lattice cleaved in the (210) plane with the second lattice tilted in a 36.8 rotation to bring a lattice point into coincidence with every fifth point in the first lattice. The geometry is such that the rota ted and the superimposed point are related by a mirror plane in the unrotated state. Construction of the pronounced grain boundary is illustrated in Figure 1 3

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20 To provide insights into the atomic structure, Dahmen et al.7 (210) grain boundary in rutile TiO2 using HREM. The structure was prepared using a laser float zone method where a TiO2 bicrystal seed wa s grown from the melt using a laser. Experimental obse rvations surprisingly found rigid -body contractions leading to conclusions that the structure has a high density of defects and/ or nonstoichiometry from an excess of Ti ions with 3+ valence. Equally, Wallis et al.8 analyzed the atomic structure of 5 (210) grain boundary in rutile TiO2 using Z -constrast imaging and collecting EELS with STEM. It was found that the structure preserves bulk stoichiometry and ionic charge at the grain boundary. It is important to note that the grain boundaries of relate d ceramics, such as NiO and SrTiO3, have been carried out to better understand the atomic structure of these internal interfaces. An 10) grain boundary in NiO19 has found a distinct tendency for faceting and regular arrays of dislocations. It was hypothesized that the volume expansion at the interface was far smaller than predicted by lattice statics calculations. In contrast, a n HREM 10) grain boundary in SrTiO3 did not observe volume expansion 36. It w as concluded that the Ti ions in the interface had the same 4+ valence as in the bulk. The step structure of the interface was not determined in great detail. Although much information about grain boundary structure has been accumulated from studies of met als and semiconductors37, comparatively little is known about the atomic structure of grain boundaries in oxides. Further progress in the field of grain boundary engineering aims to improve material properties through the control of the types and structures of grain boundaries in ceramics Surfactants Surfactant systems are of great interest to researchers in the field of surface science. They exist in solution, usually with water, and their presence at solid -liquid interfaces are important in a wide range of applica tions, from c hemical mechanical p olishing (CMP)38 to organic templates

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21 in the synthesis of inorganic materials with nanoscale porosity such as mesoporous silica thin films39, 40. Structure of Sur factants Surfactants are amphiphilic ; they have a hydrophobic group, the tail, and a hydrophilic group, the head Depending on the nature of the hydrophilic group, they are classified as: cationic (positively charged), anionic (negatively charged), zwi tterionic (both positively and negatively charged), and nonionic (not charged). Figure 1 4 illustrates C12TAB (n dodecyltrimethylammoniumbromide), the catonic surfactant investigated in this dissertation. In aqueous media, surfactants aggregate and, above the critical micelle concentration (cmc), form a self assembled structure called a micelle. At the solid liquid interface, the self assembly is influenced by surfactant -surface interactions and surrounding water -surface interactions; the process depends on the nature of the surface, the properties of the type of surfactant, and concentration of electrolytes present in the aqueous medium. The self assembled structure of the surfactants is a function of the concentration of surfactants in the system. At low c oncentrations, surfactants adsorb randomly; at moderate concentrations hemi micelle structures may form; at high concentrations, monolayers, bilayers, spherical micelles, or cylindrical micelles are seen in aqueuous media41. Figure 1 5 illustrates structures at high concentrations. It is known that at solid liquid interfaces, the self assembly of surfactants occurs at lower concentrations than in the aqueous bulk media41. The cmc values are lower at the interface than in the bulk due to adsorption of surfactants through hydrophobic or hydrophilic interaction. Thermodynamics of Surfactant Adsorption at SolidLiquid Interfaces The adsorption free energy of surfactants at the solid-ads, is: ads elec h h chem C C C S solv/desolv (1 2 )

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22 elec hh represents the cont ribution from chem represents the contribution from any chemical interaction between the C C represents the contribution from any lateral interactions C S r epresents contributions from the interaction of solv/desolv represents energy from the solvation/desolvation of the surface and surfactant species upon adsorption42. From the nature of the surfactant, surface properties, solution properties, and electrolyte concentration, these terms change in their importance in influencing the adsorption of surfactants on a solid surface and consequently the self assembly process. Generally, the electrostatic elecC C) energi es are the major factors in determining the structure and morphology of surfactant aggregates on solid surfaces42. For example, in the case of a cationic surfactant adsorbed on a negatively charged hydrophilic surface, the hydrophilic interaction between the cationic head group of t he surfactant and the negatively charged sites on the solid surface dominate at first. Beyond a certain amount of adsorption, chain -chain interaction (hydrophobic interaction) becomes the dominant factor for the adsorption process to continue. Conversely, in the case of a surfactant on a hydrophobic surface, the hydrophobic interactions between the surfactant tail and surface dominant. Atomic Force Microscopy Figure 1 6 diagrams the apparatus of an atomic force microscope (AFM). AFM involves controlling the interaction between a tip attached to a cantilever and a flat substrate mounted on a piezoelectric crystal. The piezoelectric crystal allows movement of the substrate in the vertical and lateral directions. The cantilever is made up of silicon or silicon nitride and typically has a bypyramidal tip with a radius on the order of 10 nm43. Force measurements on hard surfaces are obtained using static contact mode. In this mo de, the substrate is brought to the AFM tip.

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23 Through the interaction between the surface and the tip, the cantilever either bends away, recording repulsive forces, or bends towards the surface, recording attractive forces. This deflection of the cantilever is recorded through position sensitive photodiode detectors. These measurements are repeated in all directions to get an entire image. Imaging adsorbed surfactant aggregates on solid substrates is done using dynamic noncontact mode44. In this mode, the interaction between surfactant aggregate adsorbed on the substrate and AFM tip is determined. Since its invention 45, great progress in the study of surfactant adsorption at the solid liquid interface has been made. In particular, the ability to establish a physical connection between the macroscopic and individual nanoscale structures has become increasingly evident. For instance, AFM aids in studying the periodicity of disc rete adsorbed aggregates on the surface through in situ images of the adsorbed surfactant aggregates on the surface. These images allow adsorption isotherms to be analyzed to gain knowledge of the morphology of surfactant aggregates. However, there are lim itations to AFM. This technique is only valid when head groups of surfactants are aligned, when the concentration of surfactant is above the cmc, to provide repulsive forces. AFM does not offer measurements about surface excess or density of adsorption bet ween aggregates. Therefore, several morphologies can be consistent with AFM images. When AFM results, though, are analyzed with other forms of adsorption data, the most probable structure can be justified with reasonable evidence. AFM experiments are very valuable in trying to understand the different morphologies of surfactant aggregate under various surface modifications or solution conditions. AFM imaging provides knowledge of the size, shape, and spacing of the adsorbed self assembled structure and thus about the intermolecular and surfactant -substrate interactions46.

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24 Templating of One Dimensional Materials One dimensional (1D) nanoscale materials, such as nanotubes and nanowire s, have been the focus of considerable research efforts in recent years due to their sizedependent physical and chemical properties. These intriguing properties make them suitable for use as functional and structural nanobuilding blocks in nanoscale elect ronic, optical, and nanoelectromechancial systems applications. Single -walled carbon nanotubes (SWNTs)47 and multi -wall carbon nanotubes (MW NTs)48 are being explored for use as reinforcing fibers for nanocomposites49, 50, interconnects for nanometer -scale electric devices51, 52, components in nanoelectromechanical systems53, 54, and for use in a wide range of other applications where their orderin g is of significant importance55. More recently, the synthesis and properties of inorganic nanotubes and nanowires have been of interest56, 57. For example, t he ordered alignment of silica nanowires (SNWs) is integral for their use in synthesis of low dielectric consta nt mesoporous silica films58, 59, high resolution optical heads of scanning near -field optical microscopy60, and nan ointerconnects in integrated optical electronic devices61. One dimensional nanoscale materials, such as SWNTs and SNWs, tend to form aggregates, which has a negative effect on their properties. Good dispersion between the nanostructures is a prerequisite for their use in most applications. Surfactants play a well documented role in enabling the dispersion of nanoparticles62, 63. For instance, they are important processing aids for the dispersion of CNTs that is necessary to obtain CNT polymer composites with uniform structures50, 64. In addition, nanofiber -reinforced composites treated with surfactants have been shown to have improved mechanical properties For example, Loo et al.64 investigated cetyltrimethyl ammonium bromide (CTAB) surface MWNT -reinforced sol -gel silica composite to have increases in modulus and in hardness compared to pure sol -gel silica composite. In addition, Jinwei et al.50 found that CTAB treated CNT reinforced silica composites had greater

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25 fracture toughness values because the tubes were adequ ately dispersed. However, our understanding of surfactant CNT interactions is not well understood at the molecular level. Mesoporous silica thin films39, 40 are utili zed as hosts in fabricating ordered arrays of nanomaterials. Syntheses with surfactants as templates, such as sol -gel processing65, 66 and vapor -phase synthesis67, 68, has been performed in order to generate various mesoporous geometries to fit application designs. Successful surfactant removal is crucial in upholding the mechanical properties of the film. Chemin et al.69 applied different template removal processing to mesoporous silica thin films and concluded that the silica structure evolved differently, and that these differences affected film hardness and elastic modulus. Additionally, Wahab et al.3 suggested that trapped surfactant molecules inside the pore channels of periodic mesoporous organosilica films reduces their hardness. Molecular -scale morphology of surfactant aggregates on silica nanostructures could provide insight in to the molecular level processes associated with surfactant removal methods. Polyethylene Polyethylene is a heavily u sed polymer with its material properties varying greatly depending on its percent crystallinity, structure, and molecular weight70. PE was first used clinically in the manufacture of components for total joint replacement prosthese s in 1962 by Sir John Charnley71. Compared to other polymers, the superior toughness and low wear rate of PE made it an attractive orthopaedic implant material choice to be used as a bearing surface in both total joint replacements for the knee, hip, and spine. PE has been the focus of many tribological studies as it is increasingly used for novel (MEMS coatings) as well as established (artificial joints) applications71. In addition, t here has been considerable effort spent search ing for effective methods to apply organic or inorganic lubricating coatings onto silicon MEMS components which are three -dimensional and intricate in shap e72. Dip -coating to apply a thin

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26 polyethylene/ perfluoropolyether film onto a silicon surface is a novel method reported to have greatly reduced the coefficient of friction of the silicon surface72. Structure of Polyethylene Polyethylene has the simplest form among hydrocarbon polymers; it has th e following structure: [ -CH2CH2]n. Figure 1 7 illustrates a polyethylene chain. It was first synthesized by Hans von Pechmann by accident while heating diazomethane in 1898 and first industrially produced by in 1933 by polymerizing the ethylene monomer. Polyethylene can be classified into two main types : low density polyethylene (LDPE) that consists of branched molecules and high density polyethylene (HDPE) that has a linear structure. Depending on the molecular weight, structure, and type of branching, P E can also be categorized into several other categories as shown in Table 1 1. In this dissertation, ultra high molecular weight polyethylene (UHMWPE) is studied. UHMWPE has extremely long chains with a molecular weight ranging in the millions of grams pe r mol. The longer chains align in the same direction strengthening the intermolecular interactions allowing for a more effective transfer load to the polymer backbone5. This creates a material with high toughness and high impact strength. Wear of UHMW PE is low but has continued to be a concern particularly in its applied use in artificial joints73. Because UHMWPE has no bulky side groups, it has a smooth molecular profile. This gives rise to unique surface and chemical properties. UHMWPE does not absorb water easily because there are no pola r side groups to bond to water5. It has been observed that UHMWPE has low frictional properties such as a low friction coefficient due to the smooth molecular profile rather than the chemical composition74.

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27 Crosslinking In the bulk, atoms are b onded to neighboring atoms and are in a low energy state. At the surface, atoms are exposed and are in a higher energy state. Crosslinks in polymers are bonds that link one polymer chain to another, including surface chains to bulk chains. Crosslinking is used to promote a difference in a polymer's physical properties Surface cross linking may considerably affect the frictional and adhesive properties of polymers Pristine polymer surfaces for the most part have a weak surface layer of low molecular weight chains. This is often detrimental to the interfacial adhesion strength75, 76. Cross linking the surface layer can provide a diffusion barrier against solvents and moisture that negatively affect polymer bonding to other surfaces76. Augmentation of the polymer surface strength by cross linking is due to the formation of three dimensional molecular chain networks77. Bulk treatments such as gamma ray and x ray treatments may degrade the fracture toughness78 an d other me chanical polymer properties. Consequently, surface -specific methods that crosslink the polymer surface and preserve the bulk properties are more effective than bulk treatments. Research on polymer surface cross linking by an inert gas plasma75 have been important in analyzing the m echanisms responsible for cross linking. S urface cross linking involves three main process steps79, 80. First, h ydrogen atoms are hindered from molecu lar chains by energetic species suc h as ions, photons, and uncharge d particles. Second, t his leads to radical formation at hydrogen obstruction sites Lastly, r eaction s between radicals lead to the formation of a crosslinked surface layer. E valuation into the mechanical properties of crossl inked polymer surfaces call for techniques with nanometer depth resolution. Surface force microscopy is used for nanomech anical testing and nanoscratching of surface -cross linked polymers. T he

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28 nanoindentation response is measured to determine the surface me chanical properties of polymer surfaces modified by ion beam and plasma techniques81 82. T he shear resistance of the crosslinked polymer surface s can be evaluated by nanoscratching83. Tribological Studies of Polymers Efforts to improve the wear performance of UHMWPE for applications such as total knee replacements (TKRs) have led to numerous tribological studies of this polymer8491. In TKRs, e ven a little wear can generate large number of particulate debris which could get in the periprosthetic tissue leading in to periprosthetic osteolysis, a major problem in arthroplasty92. This often requires revision surgery. If the resulting bone l oss is substantial, there is a risk of component loosening or fracture. Because of the complex kinematics of the knee joint, there is particular interest in understanding the effect of polymer chain orientation on friction and wear Vinograd ov et al.89 investigated the frictional properties of oriented crystalline polymers Microhardness and dilatometric measurements were made and it was found that oriented polyethylene showed lower friction coeff icients and higher shear modulus than non-oriented poly ethylene. An important factor in the wear of UHMWPE is the sliding direction. In an experimen tal study by Sambasivan et al.91, it was found that there was more wear on UHMWPE pins that underwent a cross -shear motion versus a unidirectional sliding because more chains are not aligned with the sliding direction. N ondestructive X ray absorption spectroscopy measurements were used to characterize the chain alignment. The results exhibited a strong correlation between sliding motion and the resulting molecular orientation of UHMWPE UHMWPE is also observed to be sensitive to roughness. In an experimental study by Turell et al.93, counterface roughness had a substantial effect on the wear rate of UHMWPE where a series of six different wear path geometry patterns were tested. On the rough and smooth tests, the wear rates for most of the wear path geometry pattern s were statistically different. The

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29 rough counterface tests showed wear rates that were much bigger than the smooth counterface tests. Because of surface roughness, the initial area of contact between surfaces occurs on asperities Similar to fractals, these asperities span all length scales which Archard94 conceptualized as protuberances on protuberances on protube rances. T hese contact locations make up a real area of contact that is inaccessible to most measurement techniques that obtain an apparent area of contact Computational studies have been done to help elucidate wear mechanisms on this scale. In a computat ional study by Suhendra and Stachowiak95, a two dimensional finite element model was developed to predict possible mechanisms of UHMWPE wear particle formation. The model is on the micrometer scale. A single cobalt -chromium alloy asperity was slid on a single UHMWPE asperity of the same roughness. Reported possible mechanism include particle curling up due to stress differences between surfaces, thin sheet particle detaching off, and large particle breaking down into smaller particles. Other polymer ic systems, such as polytetrafluoroethylene (PTFE), have been investigated using MD simulations96, 97 to better understand the way in which t ribology can induce anisotr opy Atomic s imulations by Jang et al.96 showed that molecular profile and structural orientation at the interface of sliding PTFE surfaces strongly influence friction and wear Sliding of oriented PTFE chains paralle l to the chain backbone re sulted in low friction al forces. S liding of oriented PTFE chains perpendicular to the chain backbones resulted in high friction al forces and there was molecular reorientation and chain scission. Subsequent a tomic simulations by Barry et al.97 demonstrate d how the relative chain orientation changes their responses at low and high normal loads. It was found that the magnitude of the interfacial atomic displacements exhibits little dependence on load over the range considered (5 to 30 nN) The predicted fricti on

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30 coefficients are also found to vary with chain orientation and are in great agreement with experimental values96. Microtribological measurements on PTFE aligned films showed a strong anisotropy in friction and wear where the parallel sliding of oriented films produce d low friction while perpendicular sliding produced higher friction. PTFE has shown promising tribological behavior as solid lubricants which are used at the high and low ends of the temperature range. Experiments of orie nted transfer films of PTFE at diff erent temperatures (173 to 317 K) by McCook et al.98 found that there was an increase in friction coefficient as the sample surface temperature was decreased The disruptions of van der Waals interactions between adjacent PTFE molecules are responsible f or the friction forces.

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31 Table 1 1 Classification of polyethylene by density Polyethylene classification Density range (g/cm 3 ) Very low density polyethylene (VLDP E) 0.880 0.915 Low density polyethylene (LDPE) 0.910 0.940 Linear low density polyethylene (LLDPE) 0.915 0.925 Medium density polyethylene (MDPE) 0.926 0.940 High density polyethylene (HDPE) 0.941 or greater Ultra high molecular weight polyethylene (U HMWPE) 0.930 0935

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32 Figure 1 1 Phase diagram of TiO2 99. Figure 1 2 Unit cell structure of rutile TiO2. Titanium atoms are represented by gray atoms. Oxygen atoms are represented by re d atoms

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33 Figure 1 3 2: a) Mirror (210) cleaved planes of rutile TiO2. Green and blue circled titanium atoms follow same lattice vector with green circles highli ghting every fifth lattice point. b) Overlapping of structures illustrate coincident site lattice on every fifth lattice point (green circle). c) T he constructed after carrying out the necessary rotations and removing all ions that were within 0.5 of one another The color scheme is the same as in Figure 1 1. Figure 1 4 C12TAB (n -dodecyltrimethylammoniumbromide) surfactant consisting of a hydrophilic cationic head group of trimethyl ammonium (N+(CH3)3), a hydrophobic tail of twelve hydrocarbon units (CH3, CH2), and an anionic counter ion of bromide (Br-). Carbon is represented by gray atoms. Hydrogen is represented by white atoms. Nitrogen is represented by blue atom. Bromide is represented by r ed atom.

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34 Figure 1 5 Surfactant structures at high concentrations: a) monolayer, b) bilayer, and c) micelle. Figure 1 6 Diagram of AFM apparatus Probe tip at end of cantilever is used to scan the s ample surface. F orces between the tip and the sample lead to a deflection of the cantilever according to Hooke's law. Photodetector measures deflection of cantilever from laser beam reflection. Image is produced through feedback electronic system. F igure 1 7 Model of polyethylene chain. Carbon atoms are represented by blue atoms. Hydrogen atoms are represented by gray atoms

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35 CHAPTER 2 COMPUTATIONAL METHODS Density functional theory (DFT) methods have become a significa nt part of materials research. DFT has become more pervasive in computational studies with the development of sufficiently accurate functionals, efficient algorithms and improvements in computing capabilities. Researchers in this field can be divided into three groups: those who developed the fundamentals of the theory for more accurate functionals; those who developed the numerical implementation for more efficient algorithms, and those who use the software to study materials for different research areas. Computer simulation s have become an extremely powerful tool not only to aid in understanding and interpret ing the experimental data but to provide details that are lacking through experiments The progress of high speed computers has added to capabilities of atomistic simulations and thus the demand for accuracy of the models. Molecular dynamics (MD) is an atomistic or pseudoatomistic computational approach that has benefited greatly from the advancements in computing power. Now large systems on the order of ten to hundreds of thousands of atoms are routinely simulated with upper limits pushed up to millions of atoms. It is important that researchers should have understanding of both the theory and the applied use of these computational methods to know the ir capabilities and limitations. In this chapter, an overview of density functional theory and molecular dynamics is provided. Density Functional Theory Kohn-Sham Theory At the electronic level, s olid -state systems are described as a combination of positively charged nuclei and negatively charged electrons. If t he electronic motion and the nuclear motion can be separated and th ere are only time independent interactions in the system, the much

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36 heavier nuclei can be considered to be static relative to the ele ctrons. Based on these assumptions, a solid -state system can be thought of as electrons interacting in the nuclei potential and electron -electron interactions This is the premise behind the Born -Oppenheimer approximation23 which is used to simplify the classic Schrdinger equation a s : E H (2 1 ) where is the wave function, H is the Hamiltonian operator and E is the total ground -state energy The Hamiltonian and total energy functional is given by: U VT H (2 2 ) N j i ij N i i N i ir r v U V T E 1 2 11 1 2 (2 3 ) In these equations, t he first term, T is the electron kinetic energy The second term V is the potential energy of the electron -nucleus attraction. T he third term, U is the potential energy of the electron -electron interactions. A number of method s have been developed to simplify the Hamiltonian in equation (2 3 ), such as the Thomas F ermi Dirac method, the Hartree Fock (HF) method, and the density functional theory (D FT) approach The ab initio simulations in this dissertation implemented the DFT method. Exchange -Correlation The exchange -correl ation (xc) potential, xcE is the sum of the exchange energy and correlation energy and is expressed as: c x xcE E E (2 4 ) The exchange energy, xE, is taken as the energy dif ference between true electron electron potential energy, eeV, and direct Hartree energy, U The correlation energy,

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37 cE is described as the difference between the ground state Kohn -Sham energy, and the sum of the Thomas Fermi energy, direct Hartree energy, U and exchange energy, xE From the second Hohenberg-Kohn theorem100, there should be an exact form of the exchange -correlation functional, xcE to calculate the ground state energy. The explicit form of this functional is unknown because to independently verify if a new functional is the one and only exact form cannot be done. When a new functional is developed it is evaluated by how comparable the predicted properties, such as lattice parameters, bulk properties, and band structure, are with the experimental data. The local -density approximation (LDA) was proposed by Kohn and Sham101 in 1965 and is expressed as: r r d EHEG LDA xc 3 (2 5 ) where rHEG is the xc energy per unit volume of the homogenous electron gas (HEG) of density and can be calculated using the Monte Carlo method by Ceperley and Alder102. LDA has been shown to be more apt for systems with slowly -varying densities. It does, however, under estimate the exchange energy and o verestimates the correlation energy due to error in electron density. LDA usually agree s well with experimental stru ctural and vibrational data, but overestimates bonding energies and predicts shorter equilibrium bond lengths compared to experimental findings The generalized gradient approximation (GGA) has a similar form as LDA, but HEG depends on the density and its gradient and is expressed as: f r r d EHEG GGA xc13 (2 6 )

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38 where f is a Taylor expansion of gradient This gradient correction can help describe systems where the electron density is not slowly varying. For spatially inhomogeneous systems such as surfaces, crystals with internal surfaces, and small molecules, GGA is generally more accurate than LDA. GGA shows good agr eement with Hartree-Fock quantum chemical methods. However, it usually overestimates cell parameters due to the cancellation of exchange energy error in LDA. Pseudopotential The electron wave fun ctions can be expanded using a series of plane waves. Because the wave functions of valence electrons fluctuate strongly near the nuclear core, a very large plane wave basis set would be needed for an all -electron calculation. Since the inner electrons are strongly bonded to the nuclear core and do not have a signif icant role in bonding, an atom can be described from its valence electrons. The core electrons and nucleus can be replaced by a pseudopotential that includes both the nuclear attraction and the repulsion of the inner electrons The valence electron that ef fective interact with the pseudopotential can be described by a set of modified wave functions that are nodeless and maximally smooth within some core radius. The se pseudowavefunctions can now be expanded in a much smaller plane wave basis set saving much computational time. Molecular Dynamics Classical MD simulations solve Newtons equation of motion to predict the motion of a system of particles. The particles are allowed to evolve over time in response to the forces that act on them. Newtons second law states that the force vector, iF applied on particle i is the product of mass mi and acceleration ia as shown by: i i ia m F (2 7 )

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39 In MD simulatio ns, Newtons equation of motion is numerically integrated; the trajectory of particles can be solved, determining the positions, velocities, and accelerations. From this, the properties of a system can be calculated. Statistical Ensemble MD simulates a sys tem of atoms and the average properties are obtained. Often, the system simulated is a representation of a more complex system; the justification for this simplification is, in part that an appropriate ensemble is used. An ensemble is a collection consist ing of a large number of copies of a system, each of which represents a possible state t hat the real system might be in The principle is that a ll possible states appear with an equal probability. Thus in an ensemble, the macroscopic or thermodynamic properties are the same but the microscopic properties differ. Ensembles are divided by keeping three thermodynamic quantities constant. Microcanonical, or NVE ensemble, keeps the number of particles (N), volume (V), and total energy (E) constant. Isobaric isot hermal, or NPT, ensemble keeps the number of particles, pressure (P), and temperature (T) constant. Grand canonical, or VT, ensemble keeps the chemical potential ( ), volume, and temperature constant. Canonical, or NVT, ensemble keeps the number of particles, volume, and temperature constant. All MD simultations performed in this dissertation follow a canonical ensemble. P eriodic Boundary Conditions At current computing power, MD simulations are done usually on system sizes on the order of several nanometers. However, they are useful in showing atomic -scale details related to experimentally observed macroscopic systems. To mimic materials in the bulk or at surfaces, periodic boundary conditions (PBCs) are applied. PBCs are used for simulating a part of a bulk system with no surfaces present. In simulations dealing with planar surfaces, two dimensions are

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40 simulated with periodic boundari es; the third direction typically includes a vacuum region In general, large systems can be simulated with smaller systems through the use of PBCs to predict macroscopic behavior of the system. Figure 2 1 illustrates PBCs in two dimensions. The system cell is repeated to have no edges and mimic an infinite lattice. During the simulation when a particle moves in the system cell, the corresponding particle in each neighboring periodic cell moves in the same manner. If a particle leaves the system cell, say through the left boundary, one of its periodic images enters through the opposite side, the right boundary. In this scheme, the number of particles in the system cell stays constant. To prevent self interaction, system sizes in each direction ar e usually larger than a cutoff distance, a radial distance criteria. MicelleMD MicelleMD103 is a molecular dynamics code that can model C12TAB surfacta nt in an aqueous medium in the presence of negatively charged silica surface and/or graphitic surface. C12TAB is comprised of a hydrophobic 12 carbon chain and a trimethylammonium head group that is hydrophilic. The CH3, CH2, and trimethylammonium molecule s are treated as single units, or pseudoatoms. Negatively -charged bromide ions serve as the counter ions in solution The intra -molecular interaction, ra E int,104 of the surfactant is represented as the sum of the following terms: LJ torsion bend stretch raE E E E E int (2 8 ) where stretchE is the bond stretching term, bendE is the bending potential term, torsionE is the torsion term, and LJE is the Lennard Jones (LJ) potential term for long range interactions. To model the water molecules, a simple point charge model (SPC) is used. The intermolecular interactions between two water molecules are determined by a Lennard Jones

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41 potential between two oxygen atoms of different water molecules and a Coulombic electrostatic potential. To model the interactions between surfactants water molecules, and surface present (silica and/or graphite), empirical Lennard Jones potentials are implemented. Ewald summation is computed to simulate the long rang e electrostatic interactions of the surfactant system with PBCs. Velocity Verlet The Velocity Verlet algorithm is implemented to integrate Newtons equation of motion in the MicelleMD simulations in this dissertation. The acceleration of the particle is ca lculated from the force acting on the particles in the system. The velocity is determined from the temperature of the system. This iterative algorithm computes the position and velocity of the particles after time step t depending on the value of the acceleration and velocity at time t and is expressed as follows: t t t a t t a t v t t v t t a t t v t r t t r 2 1 2 1 2 12 (2 9 ) The forces and linear momentum of the particles are conserved. No integration algorithm will provide an exact solutio n over a n extended period of time because of the truncation of the Taylor expansion and the round off errors when recording the data values during the computer simulation However, greater accuracy can be achieved by using a smaller time step, t Velocity Rescaling Velocity rescaling is the temperature control method for the MicelleMD simulations in this disseration. The Berendsen method105 is applied. In this approach, t he velocity of the particles is

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42 2 / 11 1 ins TT T t (2 10) where t is the time step, T is the coupling time constant, T is the desired temperature, and insT is the instantaneous temperature. The velocity of the particles is adjusted such that the instantaneous temperature of the system insT approaches the desired temperature T. Exchange of the thermal energy and fluctuation in the energy of the system is controlled by the coupling time constant T REBO The bond order potential was developed by Tersoff106 to model the energetics and dynamic s of covalently -bonded materials such as carbon and silicon. It was based on the formalism by Abell107, where the binding energy of a many-body system can be described with pair -wise nearest neighbor interactions that are influenced by the local atomic environment. The Tersoff potenti al can describe the carbon -carbon single, double, and triple bond lengths and energies for hydrocarbons. It cannot, however, describe bonding situations intermediate between single and double bonds. To correct this, Brenner108 developed an improved form of the Tersofftype potenti al for hydrocarbons. However, the Morse type functions for pair interactions used in the Tersoff potential go to finite values as the distance between atoms decreases. Brenner et al.109 modified the expressions for intra -molecular interactions and expanded the fitting database. The second generation reactive bond order (REBO) potential provides more a ccurate bond lengths, energies, and force constants for hydrocarbon molecules. In the REBO potential, the total binding energy is as follows: i i j j i b i i totr E E E ) ( (2 11)

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43 where iE is the energy of atom i and ) (j i br E is the binding energy between atom i and its nearest neighbors, j expressed as: i i j ij vdw ij A ij ij R ij br V r V b r V r E ) ( (2 12) The function ij Rr V is the pair -wise repulsive potential representing th e core -core and electron -electron interactions the function ij Ar V is the attractive pair -wise potential representing the core -electron interactions and the function ) (ij vdwr V is the contribution from the van der Waals int eractions These functions depend on the interatomic distance, rij, between atom i and atom j The analytic forms of these functions are : ijr j i ij c ij Re A r Q r f r V 1 ) ( (2 13) ij nr n n ij c ij Ae B r f r V 3 1) ( (2 14) 6 124ij ij ij vdwr r r V (2 15) The repulsive term, ij Rr V goes to infinity as the interatomic distance, ijr ,approaches zero. The attractive term ij Ar V has flexibility to s imultaneously fit the bond properties. The variables A, B, Q, and are two -body parameters that are determined by the type of interaction. The van der Waals term ) (ij vdwr V is a Lennard Jones 6 12 potential110 that takes into account long range interactions. The parameter is the depth of the pote ntial well and is the dis tance at which the potential is zero.

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44 The bond -order term, ijb is a many body empirical feature of the Tersoff type potential It accounts for various chemical effects such as coordi nation numbers, bond angles, torsion angles, and conjugation effects It determines the bond strength depending on the local atomic environment and thus can describe covalent bond formation and br eakage The formalism of this term i s expressed by : ij ji ij ijb b b b 2 1 (2 16) The terms ijb and jib depend on the local coordination and bond angles for atoms i and j The term ijb is written as a sum of two terms: DH ij RC ij ijb (2 17) where the term RC ij depends on whether a bond between atoms i and j has radical character and is part of a conjugated system and the term DH ij depends on the dihedr al angle for carboncarbon double bonds. Predictor-Corrector Algorithm T he predictor -corrector algorithm is one of the high order algorithms and is used in the REBO simulations in this dissertation The scheme of predictor -corrector is that the positions, velocities, accelerations, and higher order derivatives of position at are predicted by a Taylor expansion about t in the condition of continuous trajectory. The REBO simulations used in this dissertation are performed with the fourth order Nor dsieck Gear predictor -corrector algorithm. The predictor forms are:

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45 t b t t b t t b t a t t a t t b t t a t v t t v t t b t t a t t v t r t t rp p p p 2 3 22 1 6 1 2 1 (2 18) where pr pv pa and pb are the predicted posi tion, velocity, acceleration and third derivative of position w ith respect to time, respectively, of each atom at time t t After calculating the correct ed accelerations t t ac based on the predicted positions r t t ac the difference of the corrected accelerations with the predicted accelerations can estimate the er ror size of the prediction step: t t a t t a t t ap c (2 19) From this error and the predicted values the p ositions and other derivatives can be corrected. The expressions are as follows: t t a t t b t t b t t a t t a t t a t t a t t v t t v t t a t t r t t rp c p c p c p c 3 1 6 5 6 1 (2 20) The corrected values are then used to predict the positions and first n derivatives at the next time step. The algor ithm is reiterated for the entire simulation trajectory. Although higher order derivatives can be used, greater accuracy can be achieved by using a smaller time step, t

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46 Langevin Thermostat T he Langevin th ermostat is used to control the temperature of the system in the REBO simulations in this disseration. Instead of Newtons equations of motion this thermostat follows the Langevin equation of motion: f r f v a m (2 21) where, m is the mass of the particle, a is the acceleration of the particle is a friction constant, v is the velocity of the particle, r f is the conservation force, and f i s the random force. The first term on the right side of the equation is the friction force that is coupled to the velocity corresponding to the frictional dragging between particles; it serves to impede motion and acts to remove excess energy. The seco nd term is the conservation force obtained from the interatomic potential The third term is the random force that is determined randomly from a Gaussian distribution to add kinetic energy to the particle. The temperature of the system is thus maintained b y balancing the friction force and the random force.

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47 Figure 2 1 Illustration of periodic boundary conditions applied in simulation.

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48 CHAPTER 3 AB INITIO CALCULATIONS OF DEFE CT FORMATION ENERGIE S AT TITANIUM DIOXIDE GRAIN BOUNDARIES The formation of Schottky and Frenkel defects at this grain boundary were considered Experimental studies of the symmetric tilt grain boundaries found that the grain boundary core region incorporates point defects as half -filled columns20, 111. Previous static lattice energy minimization calculations found that the arrangement of vacancies into half -fill ed columns of atoms at the grain boundary core region is favored slightly over a combination of completely filled and completely empty columns112. In addition, semi -empirical self -consistent calculations21 found that the distribution of defects in TiO2 may not be random but instead spatially clustered. Here the grain boundary systems are considered to investigate the existence of point defects and their arrangement into half -filled columns at the grain boundary core region. Even though experimental studies7, 8 do not exclude the possibility of 25% or 75% occupancy of the cation columns at the grain boundary core region, only half -occupation is being considered here. T his specification of the defect concentration to be 50% is thus purely arbitrary and is based only on experimental findings a lthough therm odynamic calculations support point defects at the grain boundary core region. No thermodynamic or kinetic a r guments are implied. I n order to preserve charge neutrality, Schottky and Frenkel defects are considered. Computational Details T he ab initio calcu lations were performed using density functional theory (DFT)100, 101 within the Vienna Ab Inito Simulation Package (VASP)113, 114. The Perdew -Burke Ernzerhof (PBE)115 exchange -correlation functional was used. The projector augmented-wave method (PAW) was performed to treat valen ce -core interactions, with a core of [Ne] for Ti and 3s23p64s23d2 electrons as valence and with a core of [He] for O and 2s22p6 electrons as valence. The valence electron states are described within a plane wave basis set, with a cutoff of 500 eV.

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49 Test cal culations of the perfect bulk unit cell, see Figure 3 1, were performed to check the accuracy of the calculations. The results are summarized in Table 3 1 and Figure 32. They show that the structural lattice parameters calculated by PAW PBE pseudopotentia l are in good agreement with experimental values and the total energy stabilizes at a cutoff energy of 500 eV. Real space projection was utilized for the PAW functions, with projection operators optimized to an energy criterion of 1x105 eV and a force cri teria of 0.02 eV/. A k point mesh of 1x2x4 was implemented. The grain boundary structure was constructed by bringing two (210) surfaces together and removing duplicate atoms using coincident site lattice theory. The grain boundary system matches the grain boundary system published in Refs. 116. As shown in Figure 3 3, t he model contains two boundaries that are 180 in rotation relative to each other. This removes the influence of edge effects on the results, a s the system is a periodic, supercell structure without any vacuum regions The grain boundary energy is calculated to be 0.926 J/m2 and was obtained from the following equation: A nE E Ebulk tot GB2 ) ( (3 1 ) where totE is the total energy of the grain boundary supercell n is the number of TiO2 units in the grain boundary supercell bulkE is the TiO2 bulk energy per formula unit and A is the area o f the grain boundary plane Another grain boundary system used to model the 5 (210) tilt grain boundary was constructed where a larger bulk region was simulated as shown in Figure 3 -4, to investigate the effect of self interaction between grain boundary regions. In the system with a larger bulk region,

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50 atoms that comprise the extended bulk region are fixed while the all the atoms in system with the smaller bulk region have no such constraint. The energy of this grain boundary structure is calculated to be 1.097 J/m2 (s ee Table 3 2 ). The atoms in the grain boundary region for both systems relaxed in a similar manner in both structures despite the fact that the system with the larger bulk region has a higher grain boundary energy. Mao et al.117 exami ned ZrO2 ab initio calculations. To determine the effect of grain boundary/grain boundary interactions from periodic boundary conditions, t he energy of the grain boundaries as a function of the separation between them w as calculated. Figure 3 5 compares the TiO2 GB systems with the ZrO2 GB systems by Mao et al.117. It is seen that the grain boundary energy increases as the distance between the two grain boundaries increases. T here is c onsiderable interaction be tween the grain boundaries that needs to be take n into account when calculating the grain boundary energy. This is most important for grain boundary separations smaller than 10.43 in the ZrO2 GB systems The grain boundary energy was calculated for two TiO2 and has a comparable increase in grain boundary energy. To balance t he need for an adequate separation between the grain boundaries and a reasonable system size to decrease the computatio nal effort involved in the calculations a system size where the separation betwe en the grain boundaries is 10.5 is used for TiO2 Results Schottky and Frenkel Defects at the Grain Boundary Here, the TiO2 grain boundary systems i nvestigated have Schottky defect complexes where several spatial arrangement s of th e titanium and oxygen vacancies that comprise them are considered These vacancies form half -filled columns. Mao et al.117 examined ZrO2 grain boundaries with half -f illed columns and maintained stoichiometry. Their models were not

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51 explicitly called grain boundaries with Schottky defects as the approach was model development to determine the most stable structure that most agreed with experimental image data. The TiO2 grain boundary model without defects considered here are based on Ref. 116 where the pristine grain boundary system is modeled from Z -contrast imaging. This system, as illustrated in Figure 3 3, is the most en ergetically favorable structure compared to the TiO2 grain boundary systems with defects. It is assumed this model is the pe rfect grain boundary structure for TiO2 tilt grain boundary. High angled tilt grain boundaries and amorphous grain boundary structures are not considered as they are regarded as less energetically favorable structures118. Figure 3 6 shows the different defect systems considered These models were used as representative configurations of the different possible combinations: a distributed Schottky defect where the titanium and oxygen vacancies are farther apart, a clustered Schottky defect where the vacancies are arranged as nearest neighbors, and a mixed c onfiguration where some vacancies are nearest neighbors and some are farther apart. Cationic Frenkel and anionic Frenkel defect systems are also considered. The zero -Kelvin defect formation energies, presented in Table s 3 3 through 3 6 were calculated fro m the following equation: pristine defect pristine defectn n E E DFE (3 2 ) whe re defectE is the total energy of TiO2 supercell with defects pristineE is the total energy of TiO2 supercell without defects defectn is the number of TiO2 units in supercell with defects and pristinen is the number of TiO2 units in supercell without defects The vacancies of the Schottky defect create undercoordinated atoms. It is seen that the systems with low er DFEs have fewer undercoordinated atoms. Schottky (mixed1) is the most

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52 stable Schottky configuration with a DFE of 3.11 eV and Schottky (distributed) is the least stable Schottky configuration with a DFE of 6.02 eV. The difference between the various def ect systems is the arrangement of the vacancies, which have different numbers of undercoordinated atoms. The trend of lowest to highest DFEs ( see Table 3 3 ) matches the trend of lowest to highest number of total under -coordinated atoms for the grain bounda ry systems with different Schottky defect arrangements Schottky (mixed1) had the lowest DFE of 3.11 eV while Schottky (clustered) had the second lowest DFE of 3.19 eV. The DFE difference between Schottky (mixed1) and Schottky (clustered) is relatively sma ll compared to Schottky (mixed2) with a DFE of 5.72 eV and Schottky (distributed) with a DFE 6.02 eV. In both the Schottky (mixed1) and Schottky (clustered) systems, the atoms move along the boundary to areas that have more free volume. In the Schottky (mi xed2) and Schottky (distributed) systems, the atoms in the bulk region move to areas along the boundary creating more undercoordinated atoms in the grain boundary and bulk regions Figure 3 7 shows the overlay of the defect -free relaxed structure of TiO2 5 (210) tilt grain boundary on the Z -contrast image from Dahmen et al.7 Figure s 3 8 and 3 9 illustrate the overlay of Schottky (mixed1) and Schottky (clustered) defect grain boundary struct ure on other areas of said experimental image. The agreement with the experimental image is good a s the relative Ti4+ cation positions match the Z -contrast image along the boundary. Thus, t he calculations predict that the atoms along the boundary move to t he areas that have more free volume. These defect containing grain boundary structures, Schottky (mixed1) and Schottky (clustered), demonstrated atoms moving along the boundary to areas of more free volume whereas this was not the case in

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53 the Schottky (mix ed2) and Schottky (distributed) structures and the overlay of these structures indicated that they are not consistent with the experimental data When the titanium and oxygen vacancies of the Schottky defects are introduced, local nonstoichiometric region s are created. Depending on the location of the vacancies, th e nonstoichiometric region s may affect a fewer or greater number of atoms. In the Schottky (distributed) system, the vacancies are most spread out and undercoordinate the majority of the ato ms in the grain boundary region thus creating a large nonstoichiometric region. As a result, this system has the highest DFE and is predicted to be the least stable. It should be expected then that the Schottky (clustered) system would have the least number of undercoordinated atoms. However, the clustering of vacancies in that region of the grain boundary affect s the neighboring bulk region and undercoordinate s bulk atoms. The Schottky (mixed1) system has the vacancies located in the grain boundary that do not affect the bulk region as much as the Schottky (clustered) system and thus has the lowest DFE. It was also found that the cationic Frenkel co nfiguration is a lower energy structure than the anionic Frenkel configuration ( see Table 3 4 ) The cationic Frenke l configuration (DFE of 3.05 eV) is the most stable among all the grain boundary systems, with Schottky or Frenkel defects This suggests that titanium interstitials may form preferentially at GBs. This finding agrees with the experimental results of Nowot ny et al.6 who considered that donor type defects, such as oxygen vacancies and/or Ti interstitials, may enrich GBs in TiO2. This may provide additional und er standing of the charact er ization of atomic grain boundary structures from experimental imaging (Z -contrast imaging)8 where there is more sensitivity toward the heavier elements (Ti interstitals).

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54 Comparison of Defects at the Grain Boundary and in the Bulk The formation of Schottky and Frenkel defects in the bulk were considered for comparison to the grain boundary systems The bulk systems investigated here use the VASP program and PAW pseudopotentials to enable a direct numerical comparison to the grain boundary systems In the simulations discussed in this dissertation, t he titanium and oxygen vacancies of the Schottky defects were spatially arranged to match the corresponding Schottky defects at the grain boundary as shown in Figure 3 10. The same spatial arrangement setup was constructed for the Frenkel defects in the bulk to compare the Frenkel de fects at the grain boundary. The trend of lowest to highest DFEs, see Table 3 5 and Table 3 6 matches the trend of lowest to highest number of total under -coordinated atoms for the grain boundary systems with different Schottky defect arrangements and Frenkel def ects in the bulk as in the grain boundary systems. Schottky (distributed) and Schottky (mixed1) have lower DFEs in the grain boundary than in the bulk while Schottky (clustered) and Schottky (mixed2) have higher DFEs in the grain boundary than in the bulk ( see Figure 3 11). It is expected that the Schottky DFE would be lower in the grain boundary than in the bulk. However, the Schottky (clustered) and Schottky (mixed1) systems undercoordinate atoms in the bulk region resulting in higher DFEs. T itanium and o xygen vacancies located in grain boundary area s that affect the stoichiometry of atoms in the bulk region are relatively less stable in these simulations. Sources of Error T here are differences between the DFT calculations and experimental measurements suc h as temperature, defect concentration, and impurities The DFT calculations are carried out a t 0 K. Frenkel defects are predicted to be more likely to occur than Schottky defects in the grain boundaries However, this could change at high temperatures. Fo r a Schottky defect, the change in entropy would be calculated for three vacancies, while for a Frenkel defect, there are only two

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55 contributions to the change in entropy. Schottky defects may be preferentially stabilized at high temperatures by entropic co ntributions than the Frenkel defect s T here are no impurities in the TiO2 systems considered whereas there are likely impurities present in experimental TiO2 samples that may influence the results. The high concentration of defects is also a consideration as there may be an effect of self interaction among defects, as seen in Figure 3 5. The simulations investigated employ a constant volume constraint. Response of the system to Schottky and Frenkel defects are through atomic movement in the grain boundary and bulk regions and do not consider volume changes of the system to try to mimic the experimental dilute limit Allowing the system to relax through volume expansion or contraction may have a lower concentration of defects and may more closely mimic exper imental sample structures of TiO2 grain boundaries. Table 3 7 shows a c omparison of the c alculated Frenkel and Schottky DFEs in this dissertation with published theoretical values from He et al.27 for bulk rutile TiO2. The trend of Schottky (cluster ed), Frenkel (distributed), and Schottky (distributed) as the most to least energetically favorable defect structure is consistent. The DFE values are not the same as different pseudopotentials and DFT program s are used for the calculations Conclusions Th e results indicate that different arrangements of the vacancies for Schottky defect grain boundary systems create different numbers of undercoordinated atoms. Lower DFEs have fewer undercoordinated atoms for all Schottky and Frenkel defect systems The siz e of the nonstoichiometric region in the system depends on t he location of the Schottky defect vacancies Cationic Frenkel defects in the GB system were found to have the lowest DFE. Consequently, titanium interstitals may form preferently at the GB and gi ve insight into the characterization of atomic grain boundary structures from experimental imaging (Z -contrast imaging)8 that is more

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56 sensitivity toward the heavier elements. Titanium and oxygen vacancies locations in grain boundary area affect the stoichiometry of atoms in the bulk region.

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57 Table 3 1 Comparison between ca lculated structural lattice parameters and experimental values of TiO2. Approach a ( Difference C ( Difference Experiment 9 4.594 2.959 PAW PBE 4.647 1.154% 2.977 0.6 0 8 % Table 3 2 Comparison of the grain boundary energy with a smaller bulk region and with a larger bulk region. Grain boundary system G rain boundary energy (J/m 2 ) S maller bulk region 0.926 L arger bulk region 1.097 Table 3 3 Number of overcoordin ated and undercoordinated atoms and defect formation energy (DFE) of each grain boundary system with Schottky defects. Grain boundary system Over coordinated oxygen Under coordinated oxygen Under coordinated titanium Under coordinated total DFE (eV) Schottky (mixed1) 0 14 14 28 3.11 Schottky (clustered) 0 18 16 34 3.19 Schottky (mixed2) 2 25 15 40 5.72 Schottky (distributed) 0 22 22 44 6.02 Table 3 4 Number of overcoordinated and undercoordinated atoms and energy (DFE ) of each grain boundary system with Frenkel defects. Grain boundary system Over coordinated oxygen U nder coordinated oxygen Under coordinated titanium Under coordinated total DFE (eV) Cationic Frenkel 2 18 10 28 3.05 Anionic Frenkel 2 16 16 32 12.30

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58 Table 3 5 Number of overcoordin ated and undercoordinated atoms a nd defect formation energy (DFE) of each bulk system with Schottky defects. Bulk system Under coordinated oxygen Under coordinated titanium Under coordinated total DFE (eV) Schottky (clustered) 4 4 8 2.55 Schottky (mixed1) 5 5 10 3.66 Schottky (mixed2) 5 5 10 4.18 Schottky (distributed) 8 6 14 6.79 Table 3 6 Number of overcoordin ated and undercoordinated atoms and defect formation energy (DFE) of each bulk system with Frenkel defects. Bulk system Over coordinated oxygen Un der coordinated oxygen Under -coordinated titanium Under coordinated total DFE (eV) Anionic Frenkel 0 0 0 0 0.00 Cationic Frenkel 5 6 1 7 3.62 Table 3 7 Comparison of c alculated Frenkel and Schottky DFEs with published theor etical values from He et al.27 for rutile TiO2. Bulk system DFEs from VASP (eV) DFE s from CASTEP by He et al.27 (eV) Schottky (clustered) 2.55 3.01 Frenkel (distributed) 3.62 3.84 Schottky (distributed) 6.79 5.47

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59 Figure 3 1 Pristine bulk unit cell of TiO2. Titanium atoms are represented by gray atoms. Oxygen atoms are represented by red atoms -58.83 -58.78 -58.73 -58.68 -58.63 -58.58 400 450 500 550 600 Cutoff Energy (eV) Total Energy (eV) Figure 3 2 Plot of total energy of perfect bulk TiO2 unit cell versus cutoff ener gy of PAW PBE pseudopotential Figure 3 3 5 (210) tilt grain boundary with two grain boundaries of opposite direction with no vacuum. Unit cell dimensions are 23.157 x 10.477 x 6.057 Color scheme same as Figure 3 1.

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60 Figure 3 4 5 (210) tilt grain boundary system with larger bulk region. Atoms in the bulk region inside the green box were held fixed. Unit cell dimensions are 43.950 x 10.477 x 6.057 Color scheme same as Figure 3 1 Figure 3 5 T he energy of the grain boundaries as a function of the separation between them for ZrO2 et al.117 and TiO2 studied in this dissertation. The energies are normalized with respect to the lowest energy GB energy to enable the direct comparison.

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61 a) b) c) d) e) f) Figure 3 6 a) Schottky defects (clustered) b) Schottky defects (distributed) c) Schottky defects (mixed1) d) Schottky defects (mixed2) e) cationic Frenkel defects f) anionic Frenkel defects in the grain boundaries. Green circles show locations of titanium and oxygen vacancies and blue c ircles show locations of titanium and oxygen interstitials. Figure 3 7 Overlay of relaxed TiO2 defects on the Z -contrast image from Dahmen et al.7 Color scheme same as Figure 3 1.

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62 Figure 3 8 Ov erlay of Schottky (mixed1) defect grain boundary structure on the Z -contrast image from Dahmen et al.7 Color scheme same as Figure 3 1. Figure 3 9 Overlay of Schottky (clustered) defect grain boundary structure on the Z -contrast image from Dahmen et al.7 Color scheme same as Figure 3 1.

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63 a) b) c) d) e) f) Figure 3 10. a) Schottky defects (clustered) b) Schottky defects (distributed) c) Schottky defects (mixed1) d) Schottky defects (mixed2) e) cationic Frenkel defects f) anionic Frenkel defects in the bulk. Green circles show locations of titanium and oxygen vacancies and blue circles show locations of titanium and oxygen interstitials.

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64 0 1 2 3 4 5 6 7 Schottky (clustered) Schottky (distributed) Schottky (mixed1) Schottky (mixed2) DFE (eV) GB Bulk Figure 3 11. Graph of DFE (eV) of different Schottky spatial arrangements for grain boundary and bulk systems.

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65 CHAPTER 4 MORPHOLOGY AND MECHANICAL PROPERTIE S OF SURFACTANT AGGR EGATES WITH NANOTUBES AND N ANOWIRES USING MOLEC ULAR DYNAMICS SIMULATIONS Surfactants are important for a wide range of applications dealing with one -dimensional nanoscale materials, including dispersion of carbon nanotubes, as organic templates in mesoporous silica thin films, and for the fabrication of silica nanowires. There is therefore great interest in better understanding the structure and properties of surfactant aggregates at the solidliquid interface. Here, classical molecular dynamics simulations with empirical potentials are used to compare the structures and mechanical properties of cationic surfactant micelles that are being indented with carbon nanotubes and silica nanowires at the silica -water interface The findings are compared to the results of bulk indentation with graphite and silica surfaces, and the influence of nanometer -scale curvatu re on the results is described. Computational Details The MD simulations numerically integrate Newtons equation of motion such that all the atoms or pseudoatoms in the system are allowed to evolve over time in response to the forces that act on them. Here we use an MD program that we developed using published parameters that is extensively described in Ref. 103. The water molecules, the silica surfaces, and the graphite surfaces are treated in an a tomistic manner, while the surfactant head groups, counter ions, and CH3/CH2 tail units are treated in a pseudoatomistic manner. The full details of the force -fields and the associated parameters for the surfactants, water, silica and graphite are provide d in Ref. 103. The velocity Verlet algorithm119 is used as the integrator and the velocity rescaling algorithm is applied to all the atoms in the system to keep the temperature of the system constant at 300 K. An Ewald summation120, 121 is used to maintain charge neutrality over the simulations,

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66 where periodic boundary conditions122 are applied in all directions. The program has been parallelized with the atom decomposition method22. The time step used is 1 femtosecond and e very simulation trajectory runs for a few hundred picoseconds to few tens of nanoseconds. Although these times scales are too short to entirely understand the true dynamic properties of micelles and surfactants as changes and fluctuations in the shape of micelles and micelle aggregation number can vary with time scales of milliseconds to seconds123, the simulations provide information which is representative of the processes occurring at the dyn amic level. Results Surfactant Structures at Solid-Liquid I nterfaces Surfactant structures have been employed as processing aids in the dispersion of CNTs for CNT reinforced silica composites. Loo et al.64 employed positive cationic surfactants that adsorbed MWCNTs where the interactions of the like cationic charges resulted in steric repulsion. This repulsion between the nanotubes due to the cationic ions exceeded the van der Waals forces of attraction, thus improving dispersion64. In addition, Hwang et al.124 reported that surfactant molecules can form co -mice lle structures with CNTs through strong van der Waals forces. To shed more light on the role of morphology of surfactant structures in the dispersion of CNTs, we examined the case where an adsorbed micelle is between two CNTs on silica in aqueous media, as illustrated in Figure 4 1a. In particular, a CTAB micelle with a diameter that varies between 3.4 and 4.0 nm that is comprised of 48 surfactants, is placed between two (24,0) zigzag CNTs that are 3.8 nm in length and 2.0 nm in diameter. A silica surface is placed some distance from the nanotubes in the system to ensure the same boundary conditions as in the nanoindentation simulations. Both silica surfaces have dimensions of 9.0 nm by 3.8 nm within the plane of the surface and a slab thickness of 5.0 nm. One CNT is moved towards the other

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67 CNT at a constant rate of 25 m/s (0.00025 /fs) such that it compresses the micelle structure between the two nanotubes The force felt by the CNT is calculated with respect to the distance between the CNTs, and is illustrated in Figure 4 1b The simulation predicts that the surfactants adsorb onto the CNT surface with the cationic head groups of the surfactants shielding the CNTs from each other as they approach one another. During this process the micelle does not remai n intact as a single aggregate. Rather, it acts as an active reservoir of surfactants facilitating monomer adsorption onto the CNT surface. The micelle completely dissociates at a separation distance between CNTs of 2.5 nm. From 1.3 nm to 0.5 nm, the total force of the surfactants felt by the CNT increases sharply from 3.5 nN to 44 nN, as indicated in Figure 4 1b. This is because of increased steric repulsion between the catonic head groups of adsorbed surfactants as the CNTs approaches one another. Specifi cally, the dissociation of the micelle leads to adsorbed surfactants on the CNTs where the tails of the adsorbed surfactants lie along the CNT walls. This results in a region between the CNTs where the cationic head groups repel each other. These repulsive interactions exceed the van der Waals forces of attraction between the nanotubes; the result is improved CNT dispersion It should be noted, however, that the total force and separation distance values are dependent on the specifics of the simulation setu p. If the micelle was composed of more surfactants, the separation distance at which the total force sharply rises would be greater, as would the total value of the peak force. In the next MD simulation, SNWs of the same dimensions replace the CNTs, as ill ustrated in Figure 4 2a, to compare the same 1D nanoscale structure with a hydrophilic surface. The molecular -scale morphology of surfactant aggregates on silica nanostructures influences surfactant removal. In this instance, the micelle does not dissociat e by monomer adsorption to the SNW. Rather, the micelle changes from a dense aggregate to a loose aggregate, and the

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68 cationic head groups adsorb onto all the surrounding surfaces. In particular, most of the cationic ions are adsorbed onto a silica surface, SNW or substrate, and are not forced to cluster together. There is thus no strong steric repulsion between the SNWs and thus the force as a function of distance between the nanowires (Figure 4 2b) remains essentially invariant until the van der Waals inte ractions between the surfactant tails are maximized which leads to a slight drop in the force. This is followed by a slight increase in the force as the surfactants are compressed together. Further e xamination of Figure 4 2a indicates that a higher densi ty of cationic head groups are present in the region between the SNWs and the silica surface than are present elsewhere in the system. Because of their curvature, the compressive forces on the surfactants from the SNWs in this region are minimized. In addi tion, the non periodicity of the surface region creates a higher density of adsorption sites at which surfactant monomers may be trapped, making surfactant removal more difficult. This region is representative of jagged edges of channels within mesoporous silica thin films that are predicted to preferentially trap surfactants. Mechanical Properties of Surfactants Several atomic force microscopy (AFM) experiments125127 have been carried out to examine the mechanical properties of adsorbed micel les at liquid/silica interfaces. As a result, two primary hypotheses have been formulated for the response of micelles to nanoindentation. The first is that the AFM tip breaks the adsorbed micelle structure and the measured force is the force required to f acilitate this breakup. The second is that the micelle structure slips out from between the tip and the surface such that the measured force is due to the tip indenting the substrate. Experimental force curves do not contain many data points at tip-surface separation distances of 2.6 0.5 nm that correspond to the mechanical response of the surfactant aggregates. This is because the AFM tip jumps into contact with the substrate127. In our previous work103, a

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69 silica surface was used as an indenter on an adsorbed micel le structure on silica. The simulations predicted that the micelle structure breaks apart on indentation and, once the structure is broken, surfactant monomers are still present between the indenter and the surface and are unable to escape. As a result, th e force increases after the micelle breaks apart due to the monolayer of surfactants trapped between the indenter and substrate. To better understand these interpretations, a n MD simulation was carried out where the same adsorbed micelle structure on silic a in aqueous media103 was indented by a SNW, as shown in Figure 4 3a, to determine the effect of tip geometry on the results. The SNW is lowered at a c onstant rate of 25 m/s (0.00025 /fs) and compresses the micelle. The force on the indenter is calculated with respect to the distance between the indenter (SNW) and substrate (silica surface). The simulation predicts that the micelle structure breaks apar t when the distance between the indenter and the surface is 2.85 nm, as indicated in Figure 4 3a. This result is in good agreement with published experimental and computational findings103, 127. The simulation also predicts that the indentation process breaks the micelle structure. The surfactant monomers that have broken away then creep up the SNW indenter. Experimental data shows that the force required to break the micelle structure is 1.5 nN127 while the MD simulation predicts the force required to break apart the micelle to be 1.6 nN (see Figure 4 3b). These results are in excellent agreement with each other. The small difference in the quantitative values can be explained by the smaller AFM tip (about 2 nm in diameter) used in the simulation relative to the much larger experimental AFM tips (about 15 nm in diameter)127 and the fact that the SNW is held rigid in the simulation. It is expected that a nonrigid surface, which would be covered with hydroxyl g roups, would have more attractive interactions with the micelle than the surface under

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70 consideration here and would also lead to a higher force being required to break apart the micelle. A comparison of this result to our previous work103, where a silica surface was used to mimic a micro indenter is given in Figure 4 4. In t he case of the silica surface indentation the micelle is not indented by the prof ile of the indenter. As a result, the adso rbed micelle is intact until it is compressed to such an extent that it breaks apart and the flat indenter easily traps the entire aggregate between the substrate and the indenter103. When the micelle breaks apart, the force decreases, at around 0.9 nm (see Figure 4 4). In contrast, in the case of t he silica nanowire, the indentation process is dominated by the c urvature of the indenter T he micelle dissociates at around 4 nm of separation because of the attraction of the micelle head groups for the approaching silica nanowire. In addition, the SNW is not large enough in diameter to trap the aggregate on the subst rate Consequently the force on the SNW steadily increases at values that are comparable to those predicted for the silica microindenter between 1 and 2 nm of separation, but does not decrease at a separation of 0.9 nm Rather, the forces keep increasing as the SNW begins compressing the bare silica substrate as the surfactants adhere to its walls. An additional MD simulation was carried out where a carbon nanotube is used to indent the same adsorbed micelle structure on silica, and the results are illustra ted in Figure 4 5a. The goal is to compare the same indenter tip geometry with a hydrophobic indenter. In this case, the simulation again predicts that the micelle structure breaks apart, although this does not occur until the separation distance between t he tip and the surface is 2.50 nm. The surfactants that have broken away then climb up the CNT indenter more rapidly than was the case during indentation with the SNW. The surfactant head groups interacted with the hydrophilic SNW as well as the water mole cules, which caused them to be more dispersed in the aqueous media than is the case

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71 with the CNT indenter. However, the separation distance to break the micelle is smaller than in the case of the indentation with the SNW due to the stronger hydrophobic att raction between the surfactant tails and the CNT walls compared to the hydrophilic attraction between the surfactant head groups and the SNW walls. The predicted force required to break apart the micelle during CNT indentation is 6 nN. This is higher than the force predicted to break the micelle structure with the SNW (1.6 nN). The forces during CNT indentation also have a steeper slope and a higher peak force value (see Figure 4 5b) than the SNW indentation. This is due to several factors. The first is tha t the micelle dissociates slightly more rapidly in the case of SNW indentation than in the case of CNT indentation. The second important factor is that the hydrophobic attraction between the tails of the surfactants and CNT surface, which exceeds the hydro philic attraction between the head groups of the surfactants and the silica substrate. Thus, as the CNT moves closer to the adsorbed micelle, the micelle dissociates monomer by monomer as the hydrophobic attraction to the CNT surface becomes greater than t he hydrophobic attraction to the tails of the surfactant in the micelle. Conclusions The classical MD simulations reported here provide predictions about the morphology of surfactant aggregates at hydrophobic and hydrophilic solid liquid interfaces As two CNTs were brought together, the dissociation of the micelle was the source of adsorbed surfactants on the CNTs, creating steric repulsion between the nanotubes that exceed the van der Waals forces of attraction The results should provide insight into impr oved dispersion of CNTs. As two SNWs were brought together, surfactant monomers became trapped where there was a higher density of adsorption sites from the non periodicity of the structures. The results should provide insight in surfactant removal during synthesis of mesoporous silica thin films.

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72 The classical MD simulations reported here also provide predictions about the responses of surfactant aggregates to nanoindentation with AFM tips. The predicted findings agree well with available experimental and simulation data. Importantly, significant differences in the force curves for these systems are predicted and an explanation for these differences is provided. Silica surface indentation with a flat profile tip had a force peak at the breaking of the micel le, showed the force decreases as surfactant monomers escape and then increases when only a few become trapped in between the indenter and surface. Nanoindentation with a tip of sharp curvature showed no surfactants trapped in between the indenter and surf ace and no decrease in force when surfactants escaped but a steady rise in force as the escaped surfactant monomers climbed up the SNW. The results should help in the experimental analysis of future AFM indentation data on surfactants relating changes in f orce curves to surfactant aggregate failure mechanisms.

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73 Figure 4 1 Adsorbed micelle of C12TAB surfactants in between carbon nanotubes on silica in aqueous medium. (a) Snapshots at different carbon nanotube separation distances: 4.20 nm: Initial configuration of an adsorbed micelle on silica between two carbon nanotubes. 4.10 nm: Surfactant monomers leave the adsorbed micelle to the carbon nanotubes. 3.75 nm: The shape of the micelle is no longer intact as many surfactant mon omers break away and adsorb on the carbon nanotubes. Smaller surfactant aggregates result. 1.7 nm: Most of the surfactants adsorb onto the carbon nanotube surface with the cationic head groups of the surfactants shielding the carbon nanotubes from each other. 0.8 nm: Total force felt by a carbon nanotube is at the highest (48 nN) where all the surfactants are trapped in between. (b) Total force felt by a carbon nanotube as a function of separation distance between the carbon nanotubes. Dark blue represents the head group N+(CH3)3 and green represents the tail molecules CH3/CH2. Silica atoms (Si and O) are represented by yellow (Si) and red (O). The carbon nanotube C atoms are shown in gray. The water molecules are not shown for clarity.

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74 Figure 4 2 Adsorbed micelle of C12TAB surfactants in between silica nanowires on silica in aqueous medium. (a) Snapshots at different silica nanowire separation distances: 4.00 nm: Initial configuration of an adsorbed micelle on silica between t wo silica nanowires. 3.85 nm: Surfactant monomers start to separate from the adsorbed micelle. 2.90 nm: The adsorbed micelle is being compressed. 2.00 nm: The shape of the micelle is no longer intact as the cationic head groups adsorb onto the silica nanow ires. 1.00 nm: The cationic head groups of the surfactants stay adsorbed on the silica nanowires with repulsion from the surfactant tails shielding the silica nanowires from each other. The color scheme is the same as in Figure 4 1. The water molecules are not shown for clarity. (b) Total force felt by the indenter as a function of separation distance between the silica nanowires.

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75 Figure 4 3 (a) Snapshots of silica nanowire indentation at a rate of 25 m/s at various indente r separation distances: 4.90 nm: Initial configuration prior to the indentation of an adsorbed micelle on silica. 4.05 nm: The adsorbed micelle starts feeling the presence of the indenter as the structure begins to break. 2.85 nm: The shape of the micelle is no longer intact as surfactant monomers break away and creep up the SNW indenter. 1.75 nm: Some surfactants stay adsorbed on the silica surface while some surfactants climb further up the SNW indenter. 0.25 nm: The SNW indenter is in contact with the si lica surface with surfactants surrounding the indenter and a couple surfactant monomers above the indenter. The color scheme is the same as in Figure 4 -1. The water molecules are not shown for clarity. (b) Total force felt by the indenter as a function of separation distance between the surface and indenter.

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76 Figure 4 4 Total force felt by the indenter as a function of separation distance between the surface and indenter for silica indenters in surface and nanowire forms.

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77 Figure 4 5 (a) Snapshots of carbon nanotube indentation at a rate of 25 m/s at various indenter separation distances: 4.90 nm: Initial configuration prior to the indentation of an adsorbed micelle on silica. 4.20 nm: The ads orbed micelle starts feeling the presence of the indenter as a few surfactant monomers break away and adsorb onto the indenter. 2.50 nm: The shape of the micelle is no longer intact as more surfactant monomers break away and climb up the CNT indenter. 1.95 nm: Some surfactants stay adsorbed on the silica surface while more than half the surfactants adsorb onto the CNT indenter and climb further up. 0.25 nm: The CNT indenter is in contact with the silica surface with all the surfactants completely adsorbed o n the indenter. The color scheme is the same as in Figure 4 1. The water molecules are not shown for clarity. (b) Total force felt by the indenter as a function of separation distance between the surface and indenter for both the SNW and CNT indenters.

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78 CHAPTER 5 TRIBOLOGY OF POLYETHYLENE USING MOLECULAR DYNAMICS SIMULATIO NS P E surfaces with oriented chains are slid against one another in the different sliding directions over a range of normal loads. The objective is to elucidate the effect of PE PE surfac e loadi ng on frictional anisotropy. These sliding simulations are done over a range of temperatures and crosslinking density to investigate the effect of these system conditions and structural differences PTFE composites have exhibited favorable tribologi cal performance as solid lubricants. Composite sliding of a PE surface and a PTFE surface is in vestigated to compare with the sliding of PE surfaces Computational Details The classical MD simulations carried out here numerically integrated Newton's equati on of motion with a third -order Nordsieck predictor correc tor using a time step of 0.2 fs. The short range inter atomic forces are calculated using the second-generation, carbon -hydrogen -fluorine many -body, REBO potential Long range van der Waals interact ions between polymer chains are calculated in the form of a Lennard Jones potential T he orthorhombic unit cell128 of crystalline PE considered in the simulations is shown in Figure 5 1. The simulation setup is shown schematically in Figure 5 2. There are 17 ethene (C2H4) monomers in each polymer chain with a chain length of 4.4 nm. Each chain is connected to its four nearest chains with two cross link units Crosslinks are added to simulate the entanglement of PE found in physical samples. The two crosslinked aligned films of PE each contain seven layers of chains, 84 total chains, for a thickness of 3.4 nm and a sliding surface area of 4.4 nm 4.4 nm. Periodic boundary conditions are applied within the planes of the surfaces to remove edge effects and to mimic infinite PE surfaces. The simulation is comprised of opposing regions of rigid atoms, thermostated atoms, and active atoms. The bottom l ayer of

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79 the lower film is fixed. T he top layer of the upper film moves as a rigid unit to pro duce compression and sliding. The structure is equilibrated with a 1.5 nm gap between the films. The rigid atoms of the top film are then lowered toward the bottom film. This compression process entails incrementally compressing and equilibrating the syste m at a rate of 10 m/s until the target normal load is reached. Additional equilibration of the system is done to preclude a prearranged interface before sliding. The sliding process entails the films sliding against each other by moving the top film agains t the stationary bottom film. Results Sliding Orientation Three different sliding orientations of the PE films are considered at a constant system temperature of 300K. As shown in Figure 53, when the P E chains in the two films are aligned in the same direction to each other, parallel sliding occurs when the sliding direction is parallel to the chain alignment and perpendicular sliding occurs when the sliding direction is perpendicular to the chain alignment. When the P E chains in the two films are aligned perpendicular to each other and slid violin sliding occurs. Figure 5 4 shows the frictional and normal forces of the perpendicular, parallel, and violin sliding configurations as functions of the sliding distance of the top PE film. The frictional forces were measured as the lateral force in the same direction of sliding and the normal forces were measured normal to the direction of sliding. During the initial stages of sliding, the forces change rapidly as the PE chains go through an initial relaxation. After about 2.5 to 4.0 nm of sliding these forces attain steady state during sliding and are relatively constant with fluctuation in a narrow range Therefore, the tribological properties of PE are analyzed after th is initial relaxation.

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80 During sliding, s tick -slip phenomenon is observed in all sliding orientations. In each sliding orientation, there is a barrier the interfacial chains must overcome. As the surfaces move relative to each other, pinning of the surfaces occurs before the interfacial chains ov ercome the barrier; the surfaces stick. After the interfacial chains overcome the barrier, the surfaces slip and slide past one another. In the perpendicular sliding, the chains at the interface slide over the corrugation of the chain alignment. In par allel sliding, the chains at the interface slide along the atomic profile of the chain. In violin sliding, the chains at the interface slide over the spots of chain intersection. The pinning of the surfaces distorts the chains to a significant extent in the case of perpendicular sliding, and to a much smaller extent in the case of parallel and violin sliding; the barrier that must be overcome is bulkier in perpendicular sliding than in parallel or violin sliding because of the interfacial structure. As the surface moves, the chains elastically strain in response to the applied shearing forces. This pinning of the surfaces to each other builds up the elastic strain until some critical force is reach. In Figure 5 4, snapshot B for each sliding shows the bending of the vertical stripe region to illustrate the elastic deformation of the films; the corresponding point B on the graph is at a maximum of the frictional force. When the surfaces slide past one another, the shear strain energy is released. In Figure 5 4 snapshot C for each sliding shows the stripe region becomes relatively vertical illustrating release of the built up shear strain energy; the corresponding point C on the graph is at a minimum frictional force. The pattern of pinning and sliding repeats continuously. In perpendicular sliding, the relative frictional force maxima and minima range from about 7.5 nN down to about 1 nN for a large difference of 6.5 nN. In parallel sliding, the relative frictional force maxima and minima have the smallest diff erence of 1 nN with a range from about 1 nN down to about 0.0 nN. In violin sliding, the relative frictional force maxima and

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81 minima range from about 2.5 nN down to about 1.0 nN; the absolute difference is in between the perpendicular sliding and parallel sliding cases. This comparison matches the distortion of the films shown in the corresponding snapshots (Figure 5 4). The bending of the stripe region is greatest in perpendicular sliding, smallest in parallel sliding, and in -between for violin sliding. T he opposite bending direction seen in snapshot C of violin sliding corresponds to the frictional force minima of 1.0 nN. The three sliding simulations all start from an initial normal force of 5 nN; however, evolution of the normal forces in each case dif fers. After the initial relaxation period, the normal force during perpendicular sliding has a median value of 7.5 nN, which is 50% higher than the initial normal force. The normal force during parallel sliding evolves to a median value of 2.5 nN, which is 50% lower than the initial normal force. The normal force during violin sliding has a median value equal to the initial normal force of 5 nN. These differences can be attributed to the change in the interfacial structure during relaxation. As the chains a t the interface slide over the corrugation of the chain alignment in perpendicular sliding, the films are compressed when the chains of the upper film reach the peaks of the chains in the lower film. The normal forces thus increase. When the interfacial ch ains of the upper film move to the depressions between the interfacial chains of the lower film, they are not able to fully optimize to a commensurate position because of the sliding. Therefore, overall the normal forces increase slightly du ring perpendicu lar sliding. In parallel sliding t he interfacial chains of the upper film move into the depressions between the chains to establish a commensurate configuration. Thus the normal forc es of parallel sliding decrease and stay constant In violin sliding, the interfacial chains are not aligned in the same direction but intersect at right angles. This interfacial chain configuration

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82 does not have features of peaks or depressions that overall change the evolution of the normal force. Normal Load The value of the frictional force calculated is dependent on the applied normal load. Here, PE films are slid against one another in the perpendicular, parallel, and violin directions at 300K over a range of normal loads from about 4 to 33 nN. This corresponds to a range in pressure of about 200 to 1650 MPa. In Figure 5 5, the normal load ramps show almost linear increase of the frictional force for all sliding directions. By plotting frictional force as a function of normal force, the friction coefficient is calculated by taking the slope value of the least -squares fit and the adhesive force is calculated by taking the xintercept of the least-squares fit. Table 5 1 has the friction coefficient and adhesive force values for each sliding orientation. The predicted adhesive force values for parallel and violin sliding are close to zero but are negative because of the extrapolation of the x intercept from the least -squares fit. Parallel and violin sliding have almost the same friction coefficient with perpendicular sliding having the highest friction coefficient. Strain of the system was greatest in perpendicular sliding as seen from the considerable elastic distortion of the chains in Figure 5 4. When the surfaces become pinned during sliding, build up of the shear strain ener gy becomes greater and greater at higher and higher applied normal loads. In Figure 5 5, the series of snapshots for perpendicular sliding at a 33 nN load illustrates the build up of shear strain energy to the point of chain breakage at the interface creat ing debris. As the surfaces chains agglomerated, sub-surface chains became exposed at the interface. From Figure 5 5, a part of a sub -surface chain at 7.224 nm of sliding is seen being dragged along the direction of sliding. At a sliding distance of 7.248 nm, the sub -surface chain breaks creating debris. The debris continues to move in the sliding direction.

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83 Perpendicular sliding has a large adhesive force (12 nN) compared to violin and parallel sliding, which have adhesive force values that are close to ze ro. A dhesion between two surfaces depends on the area over which the two are in contact The violin configuration has the smallest real contact area as the two surfaces are in contact only at the junctions of the interfacial chains. This low commensurabili ty at the interface would seem to be reflected in the adhesive force value. In constrast, the parallel configuration has the maximum possible real area of contact because of the uninterrupted interlocking of chains at the interface during sliding. This doe s not explain the essentially zero adhesive force; the two surfaces, though, are the same material and bringing them together in near perfect registry makes the interface almost indistinguishable from the bulk. The perpendicular sliding configuration has t he interlocking of chains interrupted during sliding. A possible contribution to the large adhesive force value is the increase in normal force when the chains of the upper film reach the peaks of the chains in the lower film during sliding. Interestingly, parallel and violin sliding have nearly same linear fit of frictional force versus normal force. While the interfacial structure is different from the alignment of the interfacial chains, the barrier of the chains during sliding that must be overcome is t he same, the atomic corrugation of the opposing surface chains. However, this is at a temperature of 300K. Temperature Frictional force as a function of normal force at various temperatures for perpendicular (Figure 5 6), parallel (Figure 5 7), and violin (Figure 5 8) sliding are plotted. The temperatures range from 25K to 300K. The normal load ramps show almost linear dependence of the frictional force for all sliding directions at all temperatures. At any applied normal force, the frictional force increas es as the temperature decreases for all sliding orientations.

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84 Below 200K and for the same normal force, the frictional force for parallel sliding is less than for violin sliding which, in turn, is less than for the perpendicular case. Interestingly at 200K and 300K, parallel and violin sliding have nearly same linear fit of frictional force versus normal force. According to glass transition studies for PE70, 129132, the experimental values of the glass transition temperature (Tg)are in the range of 130250K. If sliding in the parallel and violin directions at 200K and 300K are above the Tg, it is possible the average kinetic energy of the interfacial chains is enough to move and respond dur ing sliding over the atomic profile of the other interfacial chains similarly. At sliding simulations below 200K, the distortion of the interfacial chains is more exaggerated in the violin direction than in the parallel direction but less than in the perpe ndicular direction. For all sliding orientations, the friction coefficient increases overall as the temperature decreases. The friction coefficient for perpendicular sliding was higher than parallel and violin sliding as plotted in Figure 5 9. For perpendi cular sliding, the friction coefficient ranges from 0.23 to 0.45 at temperatures of 300K down to 25K. For parallel sliding, the friction coefficient ranges from 0.08 to 0.20 at temperatures of 300K down to 25K. For violin sliding, the friction coefficient ranges from 0.07 to 0.31 at temperatures of 300K down to 25K. For all sliding orientations, the adhesive force increases overall as the temperature decreases. Friction coefficients of PE reported for all sliding directions are found to be dependent on temperature. For all sliding orientations, the adhesive force increases overall as the temperature decreases. The adhesive force for perpendicular sliding was higher than parallel and violin sliding as plotted in Figure 5 10. For perpendicular sliding, the adhesive force ranges from 11.44 to 19.32 nN at temperatures of 300K down to 25K. For parallel sliding, the adhesive force ranges from 2.11 to 4.71 nN at temperatures of 300K down to 25K. For violin sliding, the adhesive

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85 force ranges from 2.45 to 6.97 nN at temperatures of 300K down to 25K. Adhesive force predictions of PE reported for all sliding directions are found to be dependent on temperature. Crosslinking Surface crosslinking may affect the frictional and adhesive properties of polymers. In these simu lations, crosslinks are used to mimic the effects of entanglement, which takes place on a longer length scale than is available for atomistic scale study Detailed crosslinking implementation is given in the Appendix. This gives the PE films sufficient sti ffness to effectively transfer the load to the tribological surfaces, while still maximizing the freedom of motion of the individual PE chains The influence of crosslinking density is examined. The crosslinking density was changed by varying the number of crosslinks in a PE surface. Calculation of the crosslink density is tabulated in Table 5 2. For the 19% and 12% crosslinking density, each PE chain is crosslinked to all four of its nearest neighbor chain. For the 6% crosslinking density, each PE chain is crosslinked to two of its nearest neighbor chain. For the 3% crosslinking density, each PE chain is crosslinked to one of its nearest neighbor chain. Also, an extended system where the chain lengths are twice as long (8.8 nm) compared to the other systems (4.4 nm) is considered with a 6% crosslinking density. The effect of normal load on the frictional force for perpendicular sliding is shown in Figure 5 12 for all the crosslinking densities. The ordered 19% crosslinking density is where the crosslinks wer e arranged in an ordered manner. This structure was used for the simulations to study the effect of sliding orientation, normal loading, and temperature. All other crosslinking densities are where the crossslinks were arranged randomly. Generally at the sa me normal load, the frictional force increases with increased randomized crosslinking density. The friction coefficients of the various crosslinking densities during perpendicular sliding are comparable as shown in Table 5 3 The frictional force is not a s linear a function of normal

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86 force for the randomized crosslinking densities as the ordered crosslinking density. There is less of an increase in frictional force at lower and intermediate normal forces of 5 to 19 nN. Because the chains are not crosslinke d in an ordered manner, the chains in the randomly crosslinked structures have more freedom of motion to respond as the surfaces slid. At higher normal forces, the motion of the chains is more restricted and the effect of varying the crosslinking density i s not as obvious. There is more distortion of the surface chains with the randomized crosslinking densities. Figure 5 15 illustrates th e different surface chain movements during perpendicular sliding for 19% randomized crosslinking density films. During the initial stages of sliding, bunching together of chains at the surface occur. This leads to rolling over of adjacent chains. The chains, interestingly, does not reorient in the perpendicular sliding direction but maintains the initial chain alignment dire ction. One chain, the white chain in Figure 5 15, experiences bowing because two crosslinks anchor one end of the chain. In parallel sliding, due to the randomized arrangement, the crosslinks do not transfer the frictional forces at the interface, which ar e the inner layers of the chains in the system, to the outer layer of the chains in the system where the forces are recorded. At high normal load of 26 to 31 nN, some of the frictional force at the interface is imparted down through the thickness of the fi lm to the outer chains where the forces are recorded. The frictional force of 19% randomized crosslinking density ( 0.6 nN) is greater than the frictional force of 12% randomized crosslinking density (0.4 nN) following the trend of increased frictional forc e as the crosslink density increases. In the violin direction, the friction coefficients of the various crosslinking densities are comparable, as shown in Table 5 4. In this case, the frictional force as a function of normal force

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87 is linear for the randomi zed crosslinking densities similarly as for the ordered crosslinking density. At about same normal load, t he 19% ordered crosslinking density has a frictional force value that is higher than 3% and 6% randomized crosslinking and 12% and 19% randomized cros slinking. Composite Sliding Very few materials exhibit both low friction and low wear Polymer and polymer composites are frequently used as solid lubricants because of its adv antages including simplicity, cleanliness, ease of implementation, and range of operational temperature PTFE and PTFE composites have shown promising tribological behavior as solid lubricants wh ere the use of fluid lubricants are precluded133, 134. PTFE -filled polyetheretherketone (PEEK) is available commercially because of its ultralow wear. PTFE is a high wear material but is lubricating, while PEEK a polymer resistant to wear, may have fillers added to it to reduce the friction coefficient Bijwe et al.135 investigated PTFE inclusions in PEEK and found a decrease in friction coefficient and wear rate as the PTFE content i ncreased. Burris et al.133, 134 examined PEEK /PTFE composite s and found the composite material had a friction coefficient and wear rate lower than unfilled PTFE and unfilled PEEK. Here, c omposite sliding of a PE film sliding against a PTFE film was investigated At the interfaces, the chains are not interlocked because of different lattice parameter spacing between chains, as illustrated in Figure 5 1 6 For PE, this spacing is 0.7417 nm between the chain centers and 0.873 nm for PTFE. Both PE and PTFE films are crosslinked randomly for a 12% crosslink ing density. Perpendicular, parallel, and violin sliding directions were considered at 300 K In Figure 5 17, the frictional forces plotted against corresponding normal force follow a l east square linear fit for all sliding directions. At the same normal l oad, the frictional force for

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88 parallel sliding is less than for violin sliding, which in turn is less than perpendicular sliding. This trend is consistent with the sliding simulations of two PE surfaces. The friction coefficient and adhesive forces are com pared to PE -PE sliding systems investigated in this dissertation and PTFE PTFE sliding systems investigated by Peter R. Barry. For perpendicular sliding, the friction coefficient of PE PTFE sliding is slightly greater than the friction coefficient of PE-PE sliding and less than the friction coefficient of PTFE -PTFE sliding as shown in Table 5 6. The adhesive force is much greater in the PE -PTFE sliding than both PE -PE sliding and PTFE -PTFE sliding. This is because the sliding surfaces are dissimilar to eac h other. For violin sliding, the friction coefficient of PE -PTFE sliding is in between that of PE-PE sliding and that of PTFE PTFE sliding, as shown in Table 5 7. The adhesive force is greater in the PE -PTFE sliding than both PE -PE sliding and PTFE -PTFE sl iding. Interestingly for parallel sliding, the friction coefficient of PE-PTFE sliding is greater than the friction coefficient of both PE PE sliding and PTFE -PTFE sliding, as indicated in Table 5 8. This is because the PE and PTFE chains at the interface are not interlocked. The adhesive force is the lowest in PE -PTFE sliding compared to both PE PE sliding and PTFE -PTFE sl iding. Burris et al.133 attributes the interlocking of phases in the PEEK/PTFE composite as the likely source of ultralow wear. The friction coefficient and wear rate are lower in the composite material than in the unfilled PEEK and unfilled PTFE samples. In these simulations, the interfacial chains are not interlocked and the friction coefficient value is in between (for perpendicular and violin sliding) or highest (parallel sliding), consistent with the influence of molecular profile observed in the simulations of PE surface sliding.

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89 Conclusions In general, the frictional force linearly increases as a function of increasing normal force. The tribological properties of PE show frictional anisotropy. Perpendicular sliding, in particular, has a greater frictional coefficient and adhesive force compared to the parallel and violin sliding directions. Overall, increasing the crosslinking density inc reases the frictional forces at the same normal forces. However, the frictional coefficients are comparable. Composite sliding of PE and PTFE surfaces exhibit tribological properties such as frictional coefficient and adhesive forces values that are in bet ween PE -PE sliding and PTFE -PTFE sliding.

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90 Table 5 1 Friction coefficient and adhesive force for all sliding orientations of PE Sliding orientation F riction coefficient Adhesive force (nN) P erpendicular 0.24 12.1 P arallel 0 .07 2.11 V iolin 0.08 2.45 Table 5 2 Calculation of crosslinking density using the ratio of crosslinked CH2 units over total CH2 units. Values are for one PE surface. Crosslinks C rosslinked CH 2 units Chains CH2 units per ch ain T otal CH2 units Crosslink ing density 237 474 72 34 2448 19% 144 288 72 34 2448 12% 72 144 72 34 2448 6% 36 72 72 34 2448 3% Table 5 3 Friction coefficient and adhesive force for all crosslinking densities of PE in perpendicular sliding C rosslinking density F riction coefficient A dhesive force (nN) 19% (ordered) 0.23 11.4 19% (randomized) 0.20 22.3 12% (randomized) 0.19 17.6 6% (randomized) 0.14 17.3 Table 5 4 Friction coefficien t and adhesive force for all crosslinking densities of PE in violin sliding C rosslinking density F riction coefficient Adhesive force (nN) 19% (ordered) 0.80 4.2 19% (randomized) 0.12 4.4 12% (randomized) 0.10 4.6 6% (randomized) 0.05 1.6 Table 5 5 Friction coefficient and adhesive force for all sliding orientations of PE -PTFE sliding Sliding orientation Friction coefficient Adhesive force (nN) Perpendicular 0.245 25.65 Violin 0.188 0.89 Parallel 0.134 1.23 Table 5 6 Friction coefficient and adhesive force of PE -PE, PE -PTFE, and PTFE PTFE systems for perpendicular sliding. System Friction coefficient Adhesive force (nN) PE 0.242 12.06 PE PTFE 0.245 25.65 PTFE 0.450 1.64

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91 T able 5 7 Friction coefficient and adhesive force of PE -PE, PE -PTFE, and PTFE PTFE systems for violin sliding. System Friction coefficient Adhesive force (nN) PE 0.080 4.18 PE PTFE 0.189 0.89 PTFE 0.301 1.88 Table 5 8 Friction coefficient and adhesive force of PE -PE, PE -PTFE, and PTFE PTFE systems for parallel sliding System Friction coefficient Adhesive force (nN) PE 0. 059 0.37 PE PTFE 0. 134 1.23 PTFE 0. 085 7.94

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92 Figure 5 1 The unit cell structure of PE Carbon atoms are in blue and hydrogen atoms are in gray. Figure 5 2 S chematic diagram of the PE polymer chain alignment. Regions of rigid, thermostated, and active ato ms are indicated.

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93 Figure 5 3 Sliding orientations of PE considered. Top film is in blue and bottom film is in green. Blue and green lines denote chain alignment of film.

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94 a) 0 5 10 15 0 5 10 15 C Perpendicular Normal FrictionalForce (nN)Sliding Distance (nm) B A b) 0 5 10 15 0 5 10 15 B Parallel Normal FrictionalForce (nN)Sliding Distance (nm) C A c) 0 5 10 15 0 5 10 15 Violin Normal FrictionalForce (nN)Sliding Distance (nm) A B C Figure 5 4 Graph of frictional and normal forces as functions of sliding distance for a) perpendicular, b) parallel, and c) violin sliding. Snapshots A, B, and C of PE system correspond to points A, B, and C on graph. Vertical stripe regions not by specific chains but by distance emphasis stick -slip motion. Arrow follows same stripe region for each snapshot. Direction of sliding is from right to left. Snapshot A is the system just before sliding. Snapshot B illustrates sticking of the surfaces. Snapshot C is the system after the surfaces slip.

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95 0 5 10 15 20 25 30 35 40 0 5 10 15 perpendicular parallel violinFf (nN)Fn (nN) Figure 5 5 Frictional force plotted against normal force for perpendicular, parallel, and violin sliding. Snapshots of the top interfacial chains of the lower film at various sliding distances for perpendicular sliding at a 33 nN load are shown above. Direction of sliding is from right to left. Hydrogen atoms are in gray. Carbon atoms of s ub-surface chains are in yellow. Carbon atoms of surface chains one through six are different colors. Atoms in black are from sub-surface chain where chain broke creating debris.

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96 0 5 10 15 20 25 30 35 40 45 0 4 8 12 16 20 24 28 25K 50K 75K 100K 200K 300KFf (nN)Fn (nN) Fi gure 5 6 Friction force as a function of normal force for perpendicular sliding at various temperatures. 0 5 10 15 20 25 30 35 40 45 0 2 4 6 8 10 12 14 25K 50K 75K 100K 200K 300KFf (nN)Fn (nN) Figure 5 7 Friction force as a function of normal force for parallel sliding at various temperatures.

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97 0 5 10 15 20 25 30 35 40 45 0 2 4 6 8 10 12 14 25K 50K 75K 100K 200K 300KFf (nN)Fn (nN) Fi gure 5 8 Friction force as a function of normal force for violin sliding at various temperatures. 0 50 100 150 200 250 300 0.0 0.1 0.2 0.3 0.4 0.5 0.6 perpendicular parallel violinTemperature (K) Figure 5 9 F riction coefficient as a function of temperature for the different sliding orientations.

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98 0 50 100 150 200 250 300 -5 0 5 10 15 20 25 30 perpendicular parallel violinAdhesive Force (nN)Temperature (K) Figure 5 10. Adhesive force as a function of temperature for the different sliding orientations. Figure 5 11. Top down view of PE system with an extended surface inp lane dimension of 8.8 nm, twice the length of the PE systems considered for all other simulations The chain lengths are doubled compared to the other systems.

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99 0 4 8 12 16 20 24 28 32 36 40 0 4 8 12 16 3% (randomized) 6% (randomized) 12% (randomized) 19% (randomized) 19% (ordered)Ff (nN)Fn (nN) 6% (extended) Figure 5 12. Friction force as a function of normal force for perpendicular sliding at various crosslinking densities. 0 4 8 12 16 20 24 28 32 36 40 0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0 3% (randomized) 6% (randomized) 12% (randomized) 19% (randomized) 19% (ordered)Ff (nN)Fn (nN) 6% (extended) Figure 5 13. Friction force as a function of normal force for paral lel sliding at various crosslinking densities.

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100 0 8 16 24 32 40 48 56 0 1 2 3 4 5 6 7 8 3% (randomized) 6% (randomized) 12% (randomized) 19% (randomized) 19% (ordered)Ff (nN)Fn (nN) Figure 5 14. Friction force as a function of normal force for violin sliding at various crosslinking densities.

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101 0.0 0.2 0.4 0.6 0.8 1.0 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 chain sliding / surface sliding Figure 5 15. Histogram of surface chain movement normalized by the sliding surface distance for perpendicular sliding of PE surfaces with 19% randomized crosslinking density. Snapshots illustrate chain movement of surface chains.

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102 Figur e 5 16. Side view of PE -PTFE system. Top film is PE and botto a m film is PTFE. Carbon atoms are in blue, hydrogen atoms are in gray, and fluorine atoms are in green. 0 8 16 24 32 40 48 56 0 4 8 12 16 20 24 perpendicular sliding violin sliding parallel slidingFf (nN)Fn (nN) Figure 5 17. Friction force as a function of normal force for all sliding orientations of the PE PTFE system.

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103 CHAPTER 6 GENERAL CONCLUSIONS In this dissertation, a b initio calculations and molecular dynamics (MD) simulations were carried out toward the unders tanding of different interfaces. Grain boundary defects were investigated in titanium dioxide where the bulk properties are largely determined by these internal interfaces. The m orphology and mechanical properties of surfactants, which are surface active a gents used in synthesis of emerging technologies, were studied. A tribological study of polyethylene, a widely used polymer with great wear resistance and other advantageous tribological properties, was done to gain insight into the atomic level origins of friction The different arrangements of the vacancies for Schottky defect grain boundary systems create different numbers of undercoordinated atoms. Lower DFEs have fewer undercoordinated atoms for all Schottky and Frenkel defect systems. The size of the nonstoichiometric region in the system depends on the location of the Schottky defect vacancies. Cationic Frenkel defects in the GB system were found to have the lowest DFE. Consequently, titanium interstitals may form preferently at the GB. The Schottky defect arrangements that agreed with the experimental imaging predict ed that the atoms along the boundary move to the areas that have more free volume. The classical MD simulations reported here provide predictions about the morphology of surfactant aggrega tes at hydrophobic and hydrophilic solid liquid interfaces As two CNTs were brought together, the dissociation of the micelle was the source of adsorbed surfactants on the CNTs, creating steric repulsion between the nanotubes that exceed the van der Waals forces of attraction The results should provide insight into improved dispersion of CNTs. As two SNWs were brought together, surfactant monomers became trapped where there was a higher density of

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104 adsorption sites from the non periodicity of the structures The results should provide insight in surfactant removal during synthesis of mesoporous silica thin films. The classical MD simulations reported here also provide predictions about the responses of surfactant aggregates to nanoindentation with AFM tips. The predicted findings agree well with available experimental and simulation data. Importantly, significant differences in the force curves for these systems are predicted and an explanation for these differences is provided. Silica surface indentation wit h a flat profile tip had a force peak at the breaking of the micelle, showed the force decreases as surfactant monomers escape and then increases when only a few become trapped in between the indenter and surface. Nanoindentation with a tip of sharp curvat ure showed no surfactants trapped in between the indenter and surface and no decrease in force when surfactants escaped but a steady rise in force as the escaped surfactant monomers climbed up the SNW. The results should help in the experimental analysis of future AFM indentation data on surfactants relating changes in force curves to surfactant aggregate failure mechanisms. In general, the frictional force linearly increases as a function of increasing normal force. The tribological properties of PE show f rictional anisotropy. Perpendicular sliding, in particular, has a greater frictional coefficient and adhesive force compared to the parallel and violin sliding directions. Overall, increasing the crosslinking density increases the frictional forces at the same normal forces. However, the frictional coefficients are comparable. Composite sliding of PE and PTFE surfaces exhibit tribological properties such as frictional coefficient and adhesive forces values that are in between PE -PE sliding and PTFE -PTFE sli ding. Simulations that can model the different interfaces of materials will give direct insight into the whole experimental characterization of the atomic interfacial structures Hence the

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105 computational simulations mentioned have shown themselves to be pr omising materials science and engineering tools that are worth further exploration and development

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106 APPENDIX RANDOMIZED CROSSLINK ING CODE MODULE coorddmod INTEGER*8, PARAMETER :: NPMAX=1010000 INTEGER*8 :: KTYPE(NPMAX) REAL*16 :: R0(3,NPMAX) INTEGER*8 :: INDEX INTEGER*8 :: MNP END MODULE coorddmod MODULE buildchainmod REAL*16 :: LENGTHcc, LENGTHch REAL*16 :: pi, ANGLEcc, ANGLEch REAL*16 :: LPa, LPb, LPc END MODULE buildchainmod MODULE sysparamsmod INTEGER*8 :: FIXED,THERMO,ACTIVE INTEGER*8 :: LOWERorUPPER REAL*16 :: DIMx, DIMy, DIMz REAL*16 :: BUILDERx, BUILDERy END MODULE sysparamsmod MODULE rotationmod REAL*16 :: THETA REAL*16 :: LENGTHccx,LENGTHccy,LENGTHchx,LENGTHchy REAL*16 :: CTOPclockx,CTOPclocky,CTOPcwisex,CTOPcwisey REAL*16 :: CBOTclockx,CBOTclocky,CBOTcwisex,CBOTcwisey REAL*16 :: HTOPclockx,HTOPclocky,HTOPcwisex,HTOPcwisey REAL*16 :: HBOTclockx,HBOTclocky,HBOTcwisex,HBOTcwisey REAL*16 :: ROTATECx,ROTATECy REAL*16 :: ROTATEHx,ROTATEHy INTEGER*8 :: ROTATIONi END MODULE rotationmod MODULE countermod INTEGER*8, PARAMETER :: NPMAX=1010000 INTEGER*8 :: LABEL(7,NPMAX),COUNTER(3),MAXLABEL(3) INTEGER*8 :: XLABEL(7,NPMAX) END MODULE countermod MODULE xlinkingmod INTEGER*8, PARAMETER :: NPMAX=1010000 INTEGER*8 :: XLINK REAL*16 :: PERCENTAGE INTEGER*8 :: QUOTA

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107 INTEGER*8 :: Aflag,Bflag,Cflag,Dflag INTEGER*8 :: SITESperLAYER INTEGER*8 :: XLINKKTYPE(NPMAX) REAL*16 :: XLINKR0(3,NPMAX) INTEGER*8 :: NHR INTEGER*8 :: XNP END MODULE xlinkingmod c+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ PROGRAM pe c Program to build randomized crosslinked polyethylene chains c+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ c Programmer: c Patrick Chiu c Department of Materials Science and Engineering c University of Florida c choochoo@ufl.edu c Version 1.0 3/4/07 Patrick Chiu c Version 2.0 10/1/07 Patrick Chiu c Version 3.0 3/4/08 Patrick Chiu c+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ c This is main code & requires subroutine files (see INCLUDE statements at end) c+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ c+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ IMPLICIT none INTEGER*8, DIMENSION(1) :: seed CALL random_seed CALL random_seed (get=seed(1:1)) c OPEN (UNIT=10,FILE='.xyz',status='unknown') OPEN (UNIT=20,FILE='a0label.out',status='unknown') CALL initialize CALL constructlayers CALL xlinking CALL writeout STOP END PROGRAM pe c+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ c+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

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108 INCLUDE 'initialize.for' INCLUDE 'constructlayers.for' INCLUDE 'xlinking.for' INCLUDE 'writeout.for' c+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ c+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ SUBROUTINE initialize c Initializes constants and variables USE coorddmod ,ONLY: NPMAX USE coorddmod ,ONLY: KTYPE USE coorddmod ,ONLY: R0 USE coorddmod ,ONLY: INDEX USE coorddmod ,ONLY: MNP USE buildchainmod ,ONLY: LENGTHcc,LENGTHch USE buildchainmod ,ONLY: pi,ANGLEcc,ANGLEch USE buildchainmod ,ONLY: LPa,LPb,LPc USE sysparamsmod ,ONLY: FIXED,THERMO,ACTIVE USE sysparamsmod ,ONLY: LOWERorUPPER USE sysparamsmod ,ONLY: DIMx,DIMy,DIMz USE sysparamsmod ,ONLY: BUILDERy USE rotationmod ,ONLY: THETA USE rotationmod ,ONLY: LENGTHccx,LENGTHccy,LENGTHchx,LENGTHchy USE rotationmod ,ONLY: CTOPclockx,CTOPclocky USE rotationmod ,ONLY: CTOPcwisex,CTOPcwisey USE rotationmod ,ONLY: CBOTclockx,CBOTclocky USE rotationmod ,ONLY: CBOTcwisex,CBOTcwisey USE rotationmod ,ONLY: HTOPclockx,HTOPclocky USE rotationmod ,ONLY: HTOPcwisex,HTOPcwisey USE rotationmod ,ONLY: HBOTclockx,HBOTclocky USE rotationmod ,ONLY: HBOTcwisex,HBOTcwisey USE rotationmod ,ONLY: ROTATECx,ROTATECy USE rotationmod ,ONLY: ROTATEHx,ROTATEHy USE rotationmod ,ONLY: ROTATIONi USE countermod ,ONLY: LABEL,COUNTER,MAXLABEL,XLABEL USE xlinkingmod ,ONLY: XLINK,PERCENTAGE,QUOTA USE xlinkingmod ,ONLY: Aflag,Bflag,Cflag,Dflag USE xlinkingmod ,ONLY: SITESperLAYER USE xlinkingmod ,ONLY: XLINKKTYPE,XLINKR0,NHR,XNP IMPLICIT none INTEGER*8 i local variable

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109 c initialize coorddmod DO i=1,NPMAX KTYPE(i)=999 999 is red flag number ENDDO DO i=1,NPMAX R0(1,i)=999 R0(2,i)=999 R0(3,i)=999 ENDDO INDEX=0 MNP=0 matrix number of particles c initialize buildchainmod c PE LENGTHcc=1.54 in Angstroms LENGTHch=1.09 in Angstroms pi=ACOS(1.0) ANGLEcc=113.5*(pi/180) in radians ANGLEch=106.0*(pi/180) in radians LPa=7.298 in Angstroms LPb=4.945 in Angstroms LPc=2*COS(pi/2ANGLEcc/2)*LENGTHcc in Angstroms [2*COS(pi/2ANGLEcc/2)*LENGTHcc] or 2.57576136 c PTFE c LENGTHcc=1.54 in Angstroms c LENGTHch=1.34 in Angstroms c c pi=ACOS(1.0) c ANGLEcc=116.0*(pi/180) in radians c ANGLEch=109.0*(pi/180) in radians c c LPa=8.73 in Angstroms c LPb=5.69 in Angstroms c LPc=2*COS(pi/2ANGLEcc/2)*LENGTHcc in Angstroms [2*COS(pi/2ANGLEcc/2)*LENGTHcc] or 2.61198814 c c initialize sysparamsmod FIXED =1 number of fixed layers THERMO =2 number of thermostat layers ACTIVE =4 number of active layers LOWERorUPPER=1 1 for lower substrate, 0 for upper substrate DIMx=11*LPa/2 in Angstroms (1+2*n) 131

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110 DIMy=13*LPb/2 in Angstroms (1+2*n) 39 DIMz=34*LPc/2 in Angstroms (2+4*n) 94 BUILDERy=0.0 in Angstroms c initialize rotationmod THETA=45*(pi/180) rotation angle is 45 degrees LENGTHccx=0 rotation point at (0,LENGTHccy/2) LENGTHccy=(LENGTHcc*SIN(pi/2ANGLEcc/2))/2 LENGTHchx=LENGTHch*COS(pi/2ANGLEch/2) LENGTHchy=LENGTHch*SIN(pi/2ANGLEch/2) c set C rotation length increments CTOPclockx =COS(1*THETA)* 1*LENGTHccxSIN(1*THETA)* 1*LENGTHccy CTOPclocky =COS(1*THETA)* 1*LENGTHccy+SIN(1*THETA)* 1*LENGTHccx CTOPcwisex =COS( 1*THETA)* 1*LENGTHccxSIN( 1*THETA)* 1*LENGTHccy CTOPcwisey =COS( 1*THETA)* 1*LENGTHccy+SIN( 1*THETA)* 1*LENGTHccx CBOTclockx =COS(1*THETA)*1*LENGTHccxSIN(1*THETA)*1*LENGTHccy CBOTclocky =COS(1*THETA)*1*LENGTHccy+SIN(1*THETA)*1*LENGTHccx CBOTcwisex =COS( 1*THETA)*1*LENGTHccxSIN( 1*THETA)*1*LENGTHccy CBOTcwisey =COS( 1*THETA)*1*LENGTHccy+SIN( 1*THETA)*1*LENGTHccx c set H rotation angle increments HTOPclockx =1*THETA HTOPclocky =1*THETA HTOPcwisex = 1*THETA HTOPcwisey = 1*THETA HBOTclockx =1*THETA HBOTclocky =1*THETA HBOTcwisex = 1*THETA HBOTcwisey = 1*THETA c initialize rotate variables ROTATECx =999 ROTATECy =999 ROTATEHx =999 ROTATEHy =999 ROTATIONi=999

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111 c initialize countermod DO i=1,3 COUNTER in x,y,z COUNTER(i)=999 ENDDO DO i=1,NPMAX LABEL(1,i)=999 chain id along x layer LABEL(2,i)=9 99 chain id along y layer LABEL(3,i)=999 atom id within chain along z LABEL(4,i)=999 empty LABEL(5,i)=999 empty LABEL(6,i)=999 empty LABEL(7,i)=999 remove hydrogen flag ENDDO DO i=1,3 MAXLABEL(i)=999 ENDDO DO i=1,NPMAX XLABEL(1,i)=999 chain id along x layer XLABEL(2,i)=999 chain id along y layer XLABEL(3,i)=999 atom id within chain along z XLABEL(4,i)=999 chain id along x layer of matrix carbon attached to XLABEL(5,i)=999 chain id along y layer of matrix carbon attached to XLABEL(6,i)=999 atom id within chain along z of matrix carbon attached to XLABEL(7,i)=999 crosslink type (A=210,B=220,C=230,D=240) ENDDO c initialize xlinkingmod XLINK=2 1 is for 100% crosslinking, 2 is for 50%, 3 is for 33%, etc. PERCENTAGE=38.72 calculated percent crosslinked (38.72%,23.52%,11.76%, 5.88%) QUOTA=237 crosslink quota ( 237, 144, 72, 36) Aflag=1 actual percent crosslinked (19.36%,11.76%, 5.88%, 2.94%) Bflag=1 Cflag=1 Dflag=1 SITESperLAYER=((DIMz/(LPc/2))2)/4 n DO i=1,NPMAX XLINKKTYPE(i)=999 999 is red flag number

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112 ENDDO DO i=1,NPMAX XLINKR0(1,i)=999 XLINKR0(2,i)=999 XLINKR0(3,i)=999 ENDDO NHR=0 number of hydrogens removed XNP=0 crosslink number of particles RETURN END SUBROUTINE initialize c+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ c+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ c+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ SUBROUTINE constructlayers c Constructs uncrosslinked layers of polyethylene chains USE coorddmod ,ONLY: INDEX USE coorddmod ,ONLY: MNP USE buildchainmod ,ONLY: LPa,LPb USE sysparamsmod ,ONLY: DIMx,DIMy USE sysparamsmod ,ONLY: BUILDERx,BUILDERy USE countermod ,ONLY: LABEL,COUNTER,MAXLABEL IMPLICIT none INTEGER*8 i,j local variables COUNTER(2)=1 set y counter to 1 100 IF(BUILDERy.LE.DIMy) THEN BUILDERx=0.0 COUNTER(1)=1 reset x counter to 1 IF(MOD((BUILDERy/LPb*10),10.0).EQ.5.0) THEN BUILDERx=BUILDERx+LPa/2 ENDIF 200 IF(BUILDERx.LE.DIMx) THEN CALL buildchain BUILDERx=BUILDERx+LPa increment x by lattice parameter a COUNTER(1)=COUNTER(1)+1 increment x counter GOTO 200 ENDIF BUILDERy=BUILDERy+LPb/2 increment y by lattice parameter b COUNTER(2)=COUNTER(2)+1 increment y counter GOTO 100

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113 ENDIF DO i=1,MNP DO j=1,3 IF(LABEL(j,i).GT.MAXLABEL(j)) THEN MAXLABEL(j)=LABEL(j,i) ENDIF ENDDO ENDDO RETURN END SUBROUTINE constructlayers INCLUDE 'buildchain.for' c+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ c+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ c+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ SUBROUTINE buildchain c Builds polyethylene chain USE coorddmod ,ONLY: KTYPE USE coorddmod ,ONLY: R0 USE coorddmod ,ONLY: INDEX USE coorddmod ,ONLY: MNP USE buildchainmod ,ONLY: LENGTHcc,LENGTHch USE buildchainmod ,ONLY: pi,ANGLEch,ANGLEcc USE sysparamsmod ,ONLY: FIXED,THERMO,ACTIVE USE sysparamsmod ,ONLY: LOWERorUPPER USE sysparamsmod ,ONLY: DIMz USE sysparamsmod ,ONLY: BUILDERx,BUILDERy USE rotationmod ,ONLY: THETA USE rotationmod ,ONLY: ROTATECx,ROTATECy USE rotationmod ,ONLY: ROTATEHx,ROTATEHy USE rotationmod ,ONLY: ROTATIONi USE countermod ,ONLY: LABEL,COUNTER IMPLICIT none INTEGER*8 i,j,k local variables REAL*16 BUILDERz j=0 reset to 0 the C backbone counter of chain to be built COUNTER(3)=0 reset z counter to 0 BUILDERz=1*LENGTHcc*COS(pi/2ANGLEcc/2) =0 after first increment

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114 100 IF(BUILDERz+LENGTHcc*COS(pi/2ANGLEcc/2).LE.DIMz0.5) THEN 0.5 arbitrary for not adding extra GOTO 200 ELSE GOTO 300 ENDIF c build CH2 200 INDEX=INDEX+1 DO i=INDEX,INDEX+2 IF(MOD(i,3).EQ.1) THEN COUNTER(3)=COUNTER(3)+1 increment z counter KTYPE(i)=6 backbone C atom DO k=1,3 LABEL(k,i)=COUNTER(k) set x,y,z label of matrix atom ENDDO IF(LOWERorUPPER) THEN lower substrate IF(LABEL(2,i).LE.(FIXED)*2) THEN LABEL(7,i)=102 set label as stationary fixed matrix atom ELSE IF(LABEL(2,i).LE.(FIXED+THERMO)*2) THEN LABEL(7,i)=101 set label as thermostat matrix atom ELSE LABEL(7,i)=100 set label as active matrix atom ENDIF ELSE upper substrate IF(LABEL(2,i).GE.(THERMO+ACTIVE)*2+1) THEN LABEL(7,i)=103 set label as moving fixed matrix atom ELSE IF(LABEL(2,i).GE.ACTIVE*2+1) THEN LABEL(7,i)=101 set label as thermostat matrix atom ELSE LABEL(7,i)=100 set label as active matrix atom ENDIF ENDIF ROTATIONi=i CALL rotation set rotation components R0(1,i)=BUILDERx+ROTATECx x marker + x rotation R0(2,i)=BUILDERy+ROTATECy y marker + y rotation & +LENGTHcc*SIN(pi/2ANGLEcc/2) & *MOD(j,2) y increment by C counter:0,1,0,1,etc

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115 R0(3,i)=BUILDERz & +LENGTHcc*COS(pi/2ANGLEcc/2) j=j+1 increment C backbone counter ENDIF IF(MOD(i,3).EQ.2) THEN COUNTER(3)=COUNTER(3)+1 increment z counter KTYPE(i)=1 corresponding 1st H atom DO k=1,3 LABEL(k,i)=COUNTER(k) set x,y,z label of matrix atom ENDDO IF(LOWERorUPPER) THEN lower substrate IF(LABEL(2,i).LE.(FIXED)*2) THEN LABEL(7,i)=102 set label as stationary fixed matrix atom ELSE IF(LABEL(2,i).LE.(FIXED+THERMO)*2) THEN LABEL(7,i)=101 set label as thermostat matrix atom ELSE LABEL(7,i)=100 set label as active matrix atom ENDIF ELSE upper substrate IF(LABEL(2,i).GE.(THERMO+ACTIVE)*2+1) THEN LABEL(7,i)=103 set label as moving fixed matrix atom ELSE IF(LABEL(2,i).GE.ACTIVE*2+1) THEN LABEL(7,i)=101 set label as thermostat matrix atom ELSE LABEL(7,i)=100 set label as active matrix atom ENDIF ENDIF R0(1,i)=R0(1,i1) start from x of backbone C atom & +LENGTHch*COS(pi/2ANGLEch/2ROTATEHx) cos shift R0(2,i)=R0(2,i1) start from y of backbone C atom & +LENGTHch*SIN(pi/2ANGLEch/2ROTATEHy) sin shift & *(MOD(j1,2)*21) 1 if C counter is odd otherwise 1 R0(3,i)=R0(3,i1) use z of backbone C atom ENDIF IF(MOD(i,3).EQ.0) THEN COUNTER(3)=COUNTER(3)+1 increment z counter KTYPE(i)=1 corresponding 2nd H atom

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116 DO k=1,3 LABEL(k,i)=COUNTER(k) set x,y,z label of matrix atom ENDDO IF(LOWERorUPPER) THEN lower substrate IF(LABEL(2,i).LE.(FIXED)*2) THEN LABEL(7,i)=102 set label as stationary fixed matrix atom ELSE IF(LABEL(2,i).LE.(FIXED+THERMO)*2) THEN LABEL(7,i)=101 set label as thermostat matrix atom ELSE LABEL(7,i)=100 set label as active matrix atom ENDIF ELSE upper substrate IF(LABEL(2,i).GE.(THERMO+ACTIVE)*2+1) THEN LABEL(7,i)=103 set label as moving fixed matrix atom ELSE IF(LABEL(2,i).GE.ACTIVE*2+1) THEN LABEL(7,i)=101 set label as thermostat matrix atom ELSE LABEL(7,i)=100 set label as active matrix atom ENDIF ENDIF R0(1,i)=R0(1,i2) start from x of backbone C atom & LENGTHch*COS(pi/2ANGLEch/2+ROTATEHx) cos shift R0(2,i)=R0(2,i2) start from y of backbone C atom & +LENGTHch*SIN(pi/2ANGLEch/2+ROTATEHy) sin shift & *(MOD(j1,2)*21) 1 if C counter is odd otherwise 1 R0(3,i)=R0(3,i2) use z of backbone C atom ENDIF INDEX=INDEX+1 ENDDO INDEX=INDEX1 BUILDERz=R0(3,INDEX2) GOTO 100 300 MNP=INDEX RETURN END SUBROUTINE buildchain

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117 INCLUDE 'rotation.for' c+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ c+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ c+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ SUBROUTINE rotation c Rotates polyethylene chain 45 degrees clockwise or counterclockwise USE rotationmod ,ONLY: LENGTHccy,LENGTHchx,LENGTHchy USE rotationmod ,ONLY: CTOPclockx,CTOPclocky USE rotationmod ,ONLY: CTOPcwisex,CTOPcwisey USE rotationmod ,ONLY: CBOTclockx,CBOTclocky USE rotationmod ,ONLY: CBOTcwisex,CBOTcwisey USE rotationmod ,ONLY: HTOPclockx,HTOPclocky USE rotationmod ,ONLY: HTOPcwisex,HTOPcwisey USE rotationmod ,ONLY: HBOTclockx,HBOTclocky USE rotationmod ,ONLY: HBOTcwisex,HBOTcwisey USE rotationmod ,ONLY: ROTATECx,ROTATECy USE rotationmod ,ONLY: ROTATEHx,ROTATEHy USE rotationmod ,ONLY: ROTATIONi USE countermod ,ONLY: LABEL IMPLICIT none IF(MOD(LABEL(2,ROTATIONi),2).EQ.1) THEN odd layer IF((MOD((LABEL(3,ROTATIONi)1)/3,2)+1).EQ.1) THEN odd C atom in chain ROTATECx= CBOTclockx ROTATECy= CBOTclocky ROTATEHx= 1*HBOTclockx ROTATEHy= 1*HBOTclocky ENDIF ENDIF IF(MOD(LABEL(2,ROTATIONi),2).EQ.1) THEN odd layer IF((MOD((LABEL(3,ROTATIONi)1)/3,2)1).EQ.0) THEN even C atom in chain ROTATECx= CTOPclockx ROTATECy= CTOPclocky2*LENGTHccy ROTATEHx=1*HTOPclockx ROTATEHy=1*HTOPclocky ENDIF ENDIF IF(MOD(LABEL(2,ROTATIONi),2).EQ.0) THEN even layer

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118 IF((MOD((LABEL(3,ROTATIONi)1)/3,2)+1).EQ.1) THEN odd C atom in chain ROTATECx= CBOTcwisex ROTATECy= CBOTcwisey ROTATEHx= 1*HBOTcwisex ROTATEHy= 1*HBOTcwisey ENDIF ENDIF IF(MOD(LABEL(2,ROTATIONi),2).EQ.0) THEN even layer IF((MOD((LABEL(3,ROTATIONi)1)/3,2)1).EQ.0) THEN even C atom in chain ROTATECx= CTOPcwisex ROTATECy= CTOPcwisey2*LENGTHccy ROTATEHx=1*HTOPcwisex ROTATEHy=1*HTOPcwisey ENDIF ENDIF RETURN END SUBROUTINE rotation c+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ c+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ c+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ SUBROUTINE xlinking c Constructs crosslinks for polyethylene system USE coorddmod ,ONLY: MNP USE buildchainmod ,ONLY: LENGTHch USE buildchainmod ,ONLY: pi,ANGLEch USE buildchainmod ,ONLY: LPa,LPb,LPc USE sysparamsmod ,ONLY: FIXED,THERMO,ACTIVE USE sysparamsmod ,ONLY: LOWERorUPPER USE sysparamsmod ,ONLY: DIMx,DIMy,DIMz USE countermod ,ONLY: LABEL,MAXLABEL,XLABEL USE xlinkingmod ,ONLY: XLINK,PERCENTAGE,QUOTA USE xlinkingmod ,ONLY: Aflag,Bflag,Cflag,Dflag USE xlinkingmod ,ONLY: SITESperLAYER USE xlinkingmod ,ONLY: XLINKKTYPE,XLINKR0,NHR,XNP IMPLICIT none INTEGER*8 b,e,i,j,n,m local variables INTEGER*8 PBCx,PBCy,PBCz local variables

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119 INTEGER*8 SETxlink,XSHIFT,YSHIFT,ZSHIFT local variables INTEGER*8 KEEP local variables REAL*16 x, RANDOM local variables INTEGER*8 XLABELtemp(3,2) local variables INTEGER*8 QUOTALABEL(MAXLABEL(1),MAXLABEL(2),2,SITESperLAYER) local variables INTEGER*8 QUOTAxcounter(MAXLABEL(1)) local variables INTEGER*8 RANDOMsite,RANDOMrowx,RANDOMcoly,RANDOMlayz local variables INTEGER*8 QUOTAperLAYER local variables INTEGER*8 QUOTAleftover local variables INTEGER*8 XLINKSperLAYER local variables PBCx=DIMx/(LPa/2) PBCy=DIMy/(LPb/2) PBCz=DIMz/(LPc/2) SETxlink=0 XSHIFT=0 YSHIFT=0 ZSHIFT=0 DO n=1,MAXLABEL(2) initialize crosslink sites in QUOTALABEL to zero DO m=1,MAXLABEL(1) DO j=1,2 DO i=1,SITESperLAYER QUOTALABEL(m,n,j,i)=0 ENDDO ENDDO ENDDO ENDDO IF(LOWERorUPPER) THEN lower substrate b=FIXED*2 e=MAXLABEL(2)1 ELSE upper substrate b=1 e=MAXLABEL(2)FIXED*2 ENDIF

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120 IF(QUOTA/((MAXLABEL(1)*2)*(MAXLABEL(2)FIXED*2)).LT.1) THEN not all crosslinked DO n=b,e DO i=1,MAXLABEL(1) QUOTAxcounter(i)=0 ENDDO DO i=1,(MAXLABEL(1)*2)/ & (((MAXLABEL(1)*2)*(MAXLABEL(2)FIXED*2))/QUOTA) 1 00 CALL random_number(x) x is random number between 0 and 1 m=x*MAXLABEL(1)+1 IF(QUOTAxcounter(m)) THEN GOTO 100 ELSE QUOTAxcounter(m)=1 ENDIF IF(QUOTA.EQ.72) THEN IF(n.EQ.e) THEN j=2 ELSE CALL random_number(x) j=x*2+1 ENDIF ENDIF 200 CALL random_number(x) RANDOMsite=x*SITESperLAYER+1 IF(QUOTALABEL(m,n,j,RANDOMsite).EQ.0) THEN QUOTALABEL(m,n,j,RANDOMsite)=1 ELSE GOTO 200 ENDIF ENDDO ENDDO ELSE all crosslinked at least once QUOTAperLAYER=QUOTA/((MAXLABEL(1)*2)*(MAXLABEL(2)FIXED*2)) minimum quota DO n=b,e turn on randomly minimum number of crosslink sites per layer DO m=1,MAXLABEL(1) DO j=1,2 DO i=1,QUOTAperLAYER 300 CALL random_number(x) RANDOMsite=x*SITESperLAYER+1 IF(QUOTALABEL(m,n,j,RANDOMsite).EQ.0) THEN QUOTALABEL(m,n,j,RANDOMsite)=1 ELSE

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121 GOTO 300 ENDIF ENDDO ENDDO ENDDO ENDDO QUOTAleftover=QUOTAQUOTAperLAYER* & ((MAXLABEL(1)*2)*(MAXLABEL(2)FIXED*2)) leftover amount DO i=1,QUOTAleftover add one extra crosslink site to layer randomly 400 CALL random_number(x) RANDOMrowx=x*MAXLABEL(1) +1 500 CALL random_number(x) RANDOMcoly=x*MAXLABEL(2) +1 IF(RANDOMcoly.LT.b) THEN IF(RANDOMcoly.GT.e) THEN GOTO 500 ENDIF ENDIF CALL random_number(x) RANDOMlayz=x*2 +1 CALL random_number(x) RANDOMsite=x*SITESperLAYER+1 XLINKSperLAYER=0 DO j=1,SITESperLAYER XLINKSperLAYER=XLINKSperLAYER & +QUOTALABEL(RANDOMrowx,RANDOMcoly,RANDOMlayz,j) ENDDO IF(XLINKSperLAYER.LT.QUOTAperLAYER+1) THEN IF(QUOTALABEL(RANDOMrowx,RANDOMcoly,RANDOMlayz,RANDOMsite) & .EQ.0) THEN QUOTALABEL(RANDOMrowx,RANDOMcoly,RANDOMlayz,RANDOMsite)=1 ELSE GOTO 400 ENDIF ENDIF ENDDO ENDIF m=0 no crosslinking for top layer DO n=1,MNP IF(LABEL(2,n).LT.MAXLABEL(2)) THEN m=m+1

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122 ENDIF ENDDO i=0 counter for XLINKRO DO n=1,m KEEP=0 reset KEEP c CALL random_number(x) x is random number between 0 and 1 c RANDOM=x*100+1 c IF(RANDOM.LE.PERCENTAGE) THEN c KEEP=1 c ENDIF IF(MOD(LABEL(3,n)0,(XLINK*6)).EQ.0) THEN crosslink A criteria IF(MOD(LABEL(2,n),2).EQ.1) THEN C2 multiple (for C2H2) IF(QUOTALABEL(LABEL(1,n),LABEL(2,n),2, & (LABEL(3,n)+0)/(XLINK*6)).EQ.1) THEN KEEP=1 crosslink A ENDIF ENDIF ENDIF IF(MOD(LABEL(3,n)9,(XLINK*6)).EQ.0) THEN crosslink B criteria IF(MOD(LABEL(2,n),2).EQ.1) THEN C2 multiple (for C2H2) IF(QUOTALABEL(LABEL(1,n),LABEL(2,n),1, & (LABEL(3,n)+3)/(XLINK*6)).EQ.1) THEN KEEP=1 crosslink B ENDIF ENDIF ENDIF IF(MOD(LABEL(3,n)11,(XLINK*6)).EQ.0) THEN crosslink C criteria IF(MOD(LABEL(2,n),2).EQ.0) THEN C2 multiple (for C2H2) IF(QUOTALABEL(LABEL(1,n),LABEL(2,n),1, & (LABEL(3,n)+1)/(XLINK*6)).EQ.1) THEN KEEP=1 crosslink C ENDIF ENDIF ENDIF IF(MOD(LABEL(3,n)8,(XLINK*6)).EQ.0) THEN crosslink D criteria IF(MOD(LABEL(2,n),2).EQ.0) THEN C2 multiple (for C2H2) IF(QUOTALABEL(LABEL(1,n),LABEL(2,n),2, & (LABEL(3,n)+4)/(XLINK*6)).EQ.1) THEN KEEP=1 crosslink D ENDIF ENDIF

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123 ENDIF IF(KEEP) THEN IF(Aflag) THEN IF(MOD(LABEL(7,n+((PBCx+1)/2)*PBCz*3*LOWERorUPPER),100) & .NE.2) THEN IF(MOD(LABEL(7,n+((PBCx+1)/2)*PBCz*3*LOWERorUPPER),100) & .NE.3) THEN IF(MOD(LABEL(3,n)0,(XLINK*6)).EQ.0) THEN crosslink A criteria IF(MOD(LABEL(2,n),2).EQ.1) THEN C2 multiple (for C2H2) NHR=NHR+2 increment number of H2 hydrogens removed counter LABEL(7,n)=9 turn on remove hydrogen flag XLABELtemp(1,1)=LABEL(1,n) XLABELtemp(2,1)=LABEL(2,n) XLABELtemp(3,1)=LABEL(3,n)2 DO j=1,MNP IF(LABEL(1,j).EQ.LABEL(1,n)+0) THEN IF(LABEL(2,j).EQ.LABEL(2,n)+1) THEN IF(LABEL(3,j).EQ.LABEL(3,n)+0) THEN LABEL(7,j)=9 turn on remove hydrogen flag XLABELtemp(1,2)=LABEL(1,j) XLABELtemp(2,2)=LABEL(2,j) XLABELtemp(3,2)=LABEL(3,j)2 ENDIF ENDIF ENDIF ENDDO SETxlink=1 set crosslink flag true XSHIFT=LABEL(1,n)1 set x shift of crosslink C atom YSHIFT=LABEL(2,n)1 set y shift of crosslink C atom ZSHIFT=((LABEL(3,n)0)/(XLINK*6)0)*XLINK set z shift of crosslink C atom ENDIF ENDIF ENDIF ENDIF ENDIF ENDIF IF(SETxlink) THEN i=i+1 XLINKKTYPE(i)=6 1st C atom of crosslink A XLINKR0(1,i)= 1.169575321 & + LPa *XSHIFT x shift

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124 XLINKR0(2,i)= 1.569987196 & +(LPb/2)*YSHIFT y shift XLINKR0(3,i)=1.582750859 & + LPc *ZSHIFT z shift XLABEL(1,i)=XLABELtemp(1,1) XLABEL(2,i)=XLABELtemp(2,1) XLABEL(3,i)=i XLABEL(4,i)=XLABELtemp(1,1) XLABEL(5,i)=XLABELtemp(2,1) XLABEL(6,i)=XLABELtemp(3,1) IF(LOWERorUPPER) THEN lower substrate XLABEL(7,i)=210+MOD(LABEL(7,n2+((PBCx+1)/2)*PBCz*3),100) A type crosslink ELSE upper substrate XLABEL(7,i)=210+MOD(LABEL(7,n2 ),100) A type crosslink ENDIF i=i+1 XLINKKTYPE(i)=1 corresponding 1st H atom XLINKR0(1,i)= 1.856652929 & + LPa *XSHIFT x shift XLINKR0(2,i)= 1.394171843 & +(LPb/2)*YSHIFT y shift XLINKR0(3,i)=2.443122049 & + LPc *ZSHIFT z shift XLABEL(1,i)=XLABELtemp(1,1) XLABEL(2,i)=XLABELtemp(2,1) XLABEL(3,i)=i XLABEL(4,i)=XLABELtemp(1,1) XLABEL(5,i)=XLABELtemp(2,1) XLABEL(6,i)=XLABELtemp(3,1) IF(LOWERorUPPER) THEN lower substrate XLABEL(7,i)=210+MOD(LABEL(7,n2+((PBCx+1)/2)*PBCz*3),100) A type crosslink ELSE upper substrate XLABEL(7,i)=210+MOD(LABEL(7,n2 ),100) A type crosslink ENDIF i=i+1 XLINKKTYPE(i)=1 corresponding 2nd H atom XLINKR0(1,i)= 0.921911340 & + LPa *XSHIFT x shift XLINKR0(2,i)= 2.647137168 & +(LPb/2)*YSHIFT y shift XLINKR0(3,i)=1.435660991 & + LPc *ZSHIFT z shift XLABEL(1,i)=XLABELtemp(1,1)

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125 XLABEL(2,i)=XLABELtemp(2,1) XLABEL(3,i)=i XLABEL(4,i)=XLABELtemp(1,1) XLABEL(5,i)=XLABELtemp(2,1) XLABEL(6,i)=XLABELtemp(3,1) IF(LOWERorUPPER) THEN lower substrate XLABEL(7,i)=210+MOD(LABEL(7,n2+((PBCx+1)/2)*PBCz*3),100) A type crosslink ELSE upper substrate XLABEL(7,i)=210+MOD(LABEL(7,n2 ),100) A type crosslink ENDIF i=i+1 XLINKKTYPE(i)=6 2nd C atom of crosslink A XLINKR0(1,i)= 2.334647584 & + LPa *XSHIFT x shift XLINKR0(2,i)= 1.880984265 & +(LPb/2)*YSHIFT y shift XLINKR0(3,i)=0.624895271 & + LPc *ZSHIFT z shift XLABEL(1,i)=XLABELtemp(1,1) XLABEL(2,i)=XLABELtemp(2,1) XLABEL(3,i)=i XLABEL(4,i)=XLABELtemp(1,2) XLABEL(5,i)=XLABELtemp(2,2) XLABEL(6,i)=XLABELtemp(3,2) IF(LOWERorUPPER) THEN lower substrate XLABEL(7,i)=210+MOD(LABEL(7,n2+((PBCx+1)/2)*PBCz*3),100) A type crosslink ELSE upper substrate XLABEL(7,i)=210+MOD(LABEL(7,n2 ),100) A type crosslink ENDIF i=i+1 XLINKKTYPE(i)=1 corresponding 1st H atom XLINKR0(1,i)= 2.068637381 & + LPa *XSHIFT x shift XLINKR0(2,i)= 0.987284534 & +(LPb/2)*YSHIFT y shift XLINKR0(3,i)=0.013532708 & + LPc *ZSHIFT z shift XLABEL(1,i)=XLABELtemp(1,1) XLABEL(2,i)=XLABELtemp(2,1) XLABEL(3,i)=i XLABEL(4,i)=XLABELtemp(1,2) XLABEL(5,i)=XLABELtemp(2,2) XLABEL(6,i)=XLABELtemp(3,2)

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126 IF(LOWERorUPPER) THEN lower substrate XLABEL(7,i)=210+MOD(LABEL(7,n2+((PBCx+1)/2)*PBCz*3),100) A type crosslink ELSE upper substrate XLABEL(7,i)=210+MOD(LABEL(7,n2 ),100) A type crosslink ENDIF i=i+1 XLINKKTYPE(i)=1 corresponding 2nd H atom XLINKR0(1,i)= 1.924276914 & + LPa *XSHIFT x shift XLINKR0(2,i)= 2.841739245 & +(LPb/2)*YSHIFT y shift XLINKR0(3,i)=0.235317592 & + LPc *ZSHIFT z shift XLABEL(1,i)=XLABELtemp(1,1) XLABEL(2,i)=XLABELtemp(2,1) XLABEL(3,i)=i XLABEL(4,i)=XLABELtemp(1,2) XLABEL(5,i)=XLABELtemp(2,2) XLABEL(6,i)=XLABELtemp(3,2) IF(LOWERorUPPER) THEN lower substrate XLABEL(7,i)=210+MOD(LABEL(7,n2+((PBCx+1)/2)*PBCz*3),100) A type crosslink ELSE upper substrate XLABEL(7,i)=210+MOD(LABEL(7,n2 ),100) A type crosslink ENDIF XNP=i SETxlink=0 set crosslink flag false ENDIF IF(KEEP) THEN IF(Bflag) THEN IF(MOD(LABEL(7,n+((PBCx+1)/2)*PBCz*3*LOWERorUPPER),100) & .NE.2) THEN IF(MOD(LABEL(7,n+((PBCx+1)/2)*PBCz*3*LOWERorUPPER),100) & .NE.3) THEN IF(MOD(LABEL(3,n)9,(XLINK*6)).EQ.0) THEN crosslink B criteria IF(MOD(LABEL(2,n),2).EQ.1) THEN C2 multiple (for C2H2) c IF( LABEL(1,n) .NE.1) THEN C2 multiple (for C2H2) c NHR=NHR+2 increment number of H2 hydrogens removed counter LABEL(7,n)=9 turn on remove hydrogen flag

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127 NHR=NHR+1 increment number of H2 hydrogens removed counter XLABELtemp(1,1)=LABEL(1,n) XLABELtemp(2,1)=LABEL(2,n) XLABELtemp(3,1)=LABEL(3,n)2 DO j=1,MNP IF(LABEL(1,n).NE.1) THEN PBCB check IF(LABEL(1,j).EQ.LABEL(1,n)1) THEN IF(LABEL(2,j).EQ.LABEL(2,n)+1) THEN IF(LABEL(3,j).EQ.LABEL(3,n)+0) THEN LABEL(7,j)=9 turn on remove hydrogen flag NHR=NHR+1 increment number of H2 hydrogens removed counter XLABELtemp(1,2)=LABEL(1,j) XLABELtemp(2,2)=LABEL(2,j) XLABELtemp(3,2)=LABEL(3,j)2 ENDIF ENDIF ENDIF ELSE PBCB check IF(LABEL(1,j).EQ.MAXLABEL(1)) THEN PBCB check IF(LABEL(2,j).EQ.LABEL(2,n)+1) THEN PBCB check IF(LABEL(3,j).EQ.LABEL(3,n)+0) THEN PBCB check LABEL(7,j)=9 turn on remove hydrogen flag NHR=NHR+1 increment number of H2 hydrogens removed counter XLABELtemp(1,2)=LABEL(1,j) XLABELtemp(2,2)=LABEL(2,j) XLABELtemp(3,2)=LABEL(3,j)2 ENDIF ENDIF ENDIF ENDIF PBCB check ENDDO SETxlink=1 set crosslink flag true XSHIFT=LABEL(1,n)1 set x shift of crosslink C atom YSHIFT=LABEL(2,n)1 set y shift of crosslink C atom ZSHIFT=((LABEL(3,n)9)/(XLINK*6)0)*XLINK set z shift of crosslink C atom c ENDIF ENDIF ENDIF ENDIF ENDIF ENDIF

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128 ENDIF IF(SETxlink) THEN i=i+1 XLINKKTYPE(i)=6 1st C atom of crosslink B XLINKR0(1,i)=1.179924515 & + LPa *XSHIFT x shift XLINKR0(2,i)= 0.930209154 & +(LPb/2)*YSHIFT y shift XLINKR0(3,i)= 2.876735764 & + LPc *ZSHIFT z shift XLABEL(1,i)=XLABELtemp(1,1) XLABEL(2,i)=XLABELtemp(2,1) XLABEL(3,i)=i XLABEL(4,i)=XLABELtemp(1,1) XLABEL(5,i)=XLABELtemp(2,1) XLABEL(6,i)=XLABELtemp(3,1) IF(LOWERorUPPER) THEN lower substrate XLABEL(7,i)=220+MOD(LABEL(7,n2+((PBCx+1)/2)*PBCz*3),100) B type crosslink ELSE upper substrate XLABEL(7,i)=220+MOD(LABEL(7,n2 ),100) B type crosslink ENDIF i=i+1 XLINKKTYPE(i)=1 corresponding 1st H atom XLINKR0(1,i)=1.806598723 & + LPa *XSHIFT x shift XLINKR0(2,i)= 0.181020162 & +(LPb/2)*YSHIFT y shift XLINKR0(3,i)= 3.414528001 & + LPc *ZSHIFT z shift XLABEL(1,i)=XLABELtemp(1,1) XLABEL(2,i)=XLABELtemp(2,1) XLABEL(3,i)=i XLABEL(4,i)=XLABELtemp(1,1) XLABEL(5,i)=XLABELtemp(2,1) XLABEL(6,i)=XLABELtemp(3,1) IF(LOWERorUPPER) THEN lower substrate XLABEL(7,i)=220+MOD(LABEL(7,n2+((PBCx+1)/2)*PBCz*3),100) B type crosslink ELSE upper substrate XLABEL(7,i)=220+MOD(LABEL(7,n2 ),100) B type crosslink ENDIF i=i+1 XLINKKTYPE(i)=1 corresponding 2nd H atom XLINKR0(1,i)=1.459645484

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129 & + LPa *XSHIFT x shift XLINKR0(2,i)= 1.882302773 & +(LPb/2)*YSHIFT y shift XLINKR0(3,i)= 3.385163764 & + LPc *ZSHIFT z shift XLABEL(1,i)=XLABELtemp(1,1) XLABEL(2,i)=XLABELtemp(2,1) XLABEL(3,i)=i XLABEL(4,i)=XLABELtemp(1,1) XLABEL(5,i)=XLABELtemp(2,1) XLABEL(6,i)=XLABELtemp(3,1) IF(LOWERorUPPER) THEN lower substrate XLABEL(7,i)=220+MOD(LABEL(7,n2+((PBCx+1)/2)*PBCz*3),100) B type crosslink ELSE upper substrate XLABEL(7,i)=220+MOD(LABEL(7,n2 ),100) B type crosslink ENDIF i=i+1 XLINKKTYPE(i)=6 2nd C atom of crosslink B XLINKR0(1,i)=2.345996836 & + LPa *XSHIFT x shift XLINKR0(2,i)= 1.241206282 & +(LPb/2)*YSHIFT y shift XLINKR0(3,i)= 1.918880122 & + LPc *ZSHIFT z shift XLABEL(1,i)=XLABELtemp(1,1) XLABEL(2,i)=XLABELtemp(2,1) XLABEL(3,i)=i XLABEL(4,i)=XLABELtemp(1,2) XLABEL(5,i)=XLABELtemp(2,2) XLABEL(6,i)=XLABELtemp(3,2) IF(LOWERorUPPER) THEN lower substrate XLABEL(7,i)=220+MOD(LABEL(7,n2+((PBCx+1)/2)*PBCz*3),100) B type crosslink ELSE upper substrate XLABEL(7,i)=220+MOD(LABEL(7,n2 ),100) B type crosslink ENDIF i=i+1 XLINKKTYPE(i)=1 corresponding 1st H atom XLINKR0(1,i)=2.884330292 & + LPa *XSHIFT x shift XLINKR0(2,i)= 0.355275128 & +(LPb/2)*YSHIFT y shift XLINKR0(3,i)= 1.508333418 & + LPc *ZSHIFT z shift

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130 XLABEL(1,i)=XLABELtemp(1,1) XLABEL(2,i)=XLABELtemp(2,1) XLABEL(3,i)=i XLABEL(4,i)=XLABELtemp(1,2) XLABEL(5,i)=XLABELtemp(2,2) XLABEL(6,i)=XLABELtemp(3,2) IF(LOWERorUPPER) THEN lower substrate XLABEL(7,i)=220+MOD(LABEL(7,n2+((PBCx+1)/2)*PBCz*3),100) B type crosslink ELSE upper substrate XLABEL(7,i)=220+MOD(LABEL(7,n2 ),100) B type crosslink ENDIF i=i+1 XLINKKTYPE(i)=1 corresponding 2nd H atom XLINKR0(1,i)=1.400311954 & + LPa *XSHIFT x shift XLINKR0(2,i)= 1.331049675 & +(LPb/2)*YSHIFT y shift XLINKR0(3,i)= 1.335071615 & + LPc *ZSHIFT z shift XLABEL(1,i)=XLABELtemp(1,1) XLABEL(2,i)=XLABELtemp(2,1) XLABEL(3,i)=i XLABEL(4,i)=XLABELtemp(1,2) XLABEL(5,i)=XLABELtemp(2,2) XLABEL(6,i)=XLABELtemp(3,2) IF(LOWERorUPPER) THEN lower substrate XLABEL(7,i)=220+MOD(LABEL(7,n2 +((PBCx+1)/2)*PBCz*3),100) B type crosslink ELSE upper substrate XLABEL(7,i)=220+MOD(LABEL(7,n2 ),100) B type crosslink ENDIF XNP=i SETxlink=0 set crosslink flag false ENDIF IF(QUOTA.EQ.144) THEN IF(Bflag.EQ.0) THEN IF(LOWERorUPPER) THEN IF(LABEL(2,n).EQ.2) THEN Cflag=1 ENDIF ENDIF IF(LOWERorUPPER.EQ.0) THEN IF(LABEL(2,n).EQ.MAXLABEL(2)2) THEN Cflag=1

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131 ENDIF ENDIF ENDIF ENDIF IF(KEEP) THEN IF(Cflag) THEN IF(MOD(LABEL(7,n+((PBCx+1)/2)*PBCz*3*LOWERorUPPER),100) & .NE.2) THEN IF(MOD(LABEL(7,n+((PBCx+1)/2)*PBCz*3*LOWERorUPPER),100) & .NE.3) THEN IF(MOD(LABEL(3,n)11,(XLINK*6)).EQ.0) THEN crosslink C criteria IF(MOD(LABEL(2,n),2).EQ.0) THEN C2 multiple (for C2H2) NHR=NHR+2 increment number of H2 hydrogens removed counter LABEL(7,n)=9 turn on remove hydrogen flag XLABELtemp(1,1)=LABEL(1,n) XLABELtemp(2,1)=LABEL(2,n) XLABELtemp(3,1)=LABEL(3,n)1 DO j=1,MNP IF(LABEL(1,j).EQ.LABEL(1,n)+0) THEN IF(LABEL(2,j).EQ.LABEL(2,n)+1) THEN IF(LABEL(3,j).EQ.LABEL(3,n)+0) THEN LABEL(7,j)=9 turn on remove hydrogen flag XLABELtemp(1,2)=LABEL(1,j) XLABELtemp(2,2)=LABEL(2,j) XLABELtemp(3,2)=LABEL(3,j)1 ENDIF ENDIF ENDIF ENDDO SETxlink=1 set crosslink flag true XSHIFT=LABEL(1,n)1 set x shift of crosslink C atom YSHIFT=LABEL(2,n)2 set y shift of crosslink C atom ZSHIFT=((LABEL(3,n)11)/(XLINK*6)0)*XLINK set z shift of crosslink C atom ENDIF ENDIF ENDIF ENDIF ENDIF ENDIF IF(SETxlink) THEN i=i+1

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132 XLINKKTYPE(i)=6 1st C atom of crosslink C XLINKR0(1,i)= 2.44295175 & + LPa *XSHIFT x shift XLINKR0(2,i)= 3.872443921 & +(LPb/2)*YSHIFT y shift XLINKR0(3,i)= 3.367800539 & + LPc *ZSHIFT z shift XLABEL(1,i)=XLABELtemp(1,1) XLABEL(2,i)=XLABELtemp(2,1) XLABEL(3,i)=i XLABEL(4,i)=XLABELtemp(1,1) XLABEL(5,i)=XLABELtemp(2,1) XLABEL(6,i)=XLABELtemp(3,1) IF(LOWERorUPPER) THEN lower substrate XLABEL(7,i)=230+MOD(LABEL(7,n1+((PBCx+1)/2)*PBCz*3),100) C type crosslink ELSE upper substrate XLABEL(7,i)=230+MOD(LABEL(7,n1 ),100) C type crosslink ENDIF i=i+1 XLINKKTYPE(i)=1 corresponding 1st H atom XLINKR0(1,i)= 3.270839892 & + LPa *XSHIFT x shift XLINKR0(2,i)= 4.540839718 & +(LPb/2)*YSHIFT y shift XLINKR0(3,i)= 3.034524066 & + LPc *ZSHIFT z shift XLABEL(1,i)=XLABELtemp(1,1) XLABEL(2,i)=XLABELtemp(2,1) XLABEL(3,i)=i XLABEL(4,i)=XLABELtemp(1,1) XLABEL(5,i)=XLABELtemp(2,1) XLABEL(6,i)=XLABELtemp(3,1) IF(LOWERorUPPER) THEN lower substrate XLABEL(7,i)=230+MOD(LABEL(7,n1+((PBCx+1)/2)*PBCz*3),100) C type crosslink ELSE upper substrate XLABEL(7,i)=230+MOD(LABEL(7,n1 ),100) C type crosslink ENDIF i=i+1 XLINKKTYPE(i)=1 corresponding 2nd H atom XLINKR0(1,i)= 2.000271211 & + LPa *XSHIFT x shift XLINKR0(2,i)= 3.438050878 & +(LPb/2)*YSHIFT y shift

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133 XLINKR0(3,i)= 2.441214395 & + LPc *ZSHIFT z shift XLABEL(1,i)=XLABELtemp(1,1) XLABEL(2,i)=XLABELtemp(2,1) XLABEL(3,i)=i XLABEL(4,i)=XLABELtemp(1,1) XLABEL(5,i)=XLABELtemp(2,1) XLABEL(6,i)=XLABELtemp(3,1) IF(LOWERorUPPER) THEN lower substrate XLABEL(7,i)=230+MOD(LABEL(7,n1+((PBCx+1)/2)*PBCz*3),100) C type crosslink ELSE upper substrate XLABEL(7,i)=230+MOD(LABEL(7,n1 ),100) C type crosslink ENDIF i=i+1 XLINKKTYPE(i)=6 2nd C atom of crosslink C XLINKR0(1,i)= 1.374908471 & + LPa *XSHIFT x shift XLINKR0(2,i)= 4.287750146 & +(LPb/2)*YSHIFT y shift XLINKR0(3,i)= 4.403968203 & + LPc *ZSHIFT z shift XLABEL(1,i)=XLABELtemp(1,1) XLABEL(2,i)=XLABELtemp(2,1) XLABEL(3,i)=i XLABEL(4,i)=XLABELtemp(1,2) XLABEL(5,i)=XLABELtemp(2,2) XLABEL(6,i)=XLABELtemp(3,2) IF(LOWERorUPPER) THEN lower substrate XLABEL(7,i)=230+MOD(LABEL(7,n1+((PBCx+1)/2)*PBCz*3),100) C type crosslink ELSE upper substrate XLABEL(7,i)=230+MOD(LABEL(7,n1 ),100) C type crosslink ENDIF i=i+1 XLINKKTYPE(i)=1 corresponding 1st H atom XLINKR0(1,i)= 1.883563849 & + LPa *XSHIFT x shift XLINKR0(2,i)= 5.194187081 & +(LPb/2)*YSHIFT y shift XLINKR0(3,i)= 4.000400369 & + LPc *ZSHIFT z shift XLABEL(1,i)=XLABELtemp(1,1) XLABEL(2,i)=XLABELtemp(2,1) XLABEL(3,i)=i

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134 XLABEL(4,i)=XLABELtemp(1,2) XLABEL(5,i)=XLABELtemp(2,2) XLABEL(6,i)=XLABELtemp(3,2) IF(LOWERorUPPER) THEN lower substrate XLABEL(7,i)=230+MOD(LABEL(7,n1+((PBCx+1)/2)*PBCz*3),100) C type crosslink ELSE upper substrate XLABEL(7,i)=230+MOD(LABEL(7,n1 ),100) C type crosslink ENDIF i=i+1 XLINKKTYPE(i)=1 corresponding 2nd H atom XLINKR0(1,i)= 0.926738341 & + LPa *XSHIFT x shift XLINKR0(2,i)= 3.772408170 & +(LPb/2)*YSHIFT y shift XLINKR0(3,i)= 3.52261062 & + LPc *ZSHIFT z shift XLABEL(1,i)=XLABELtemp(1,1) XLABEL(2,i)=XLABELtemp(2,1) X LABEL(3,i)=i XLABEL(4,i)=XLABELtemp(1,2) XLABEL(5,i)=XLABELtemp(2,2) XLABEL(6,i)=XLABELtemp(3,2) IF(LOWERorUPPER) THEN lower substrate XLABEL(7,i)=230+MOD(LABEL(7,n1+((PBCx+1)/2)*PBCz*3),100) C type crosslink ELSE upper substrate XLABEL(7,i)=230+MOD(LABEL(7,n1 ),100) C type crosslink ENDIF XNP=i SETxlink=0 set crosslink flag false ENDIF IF(QUOTA.EQ.144) THEN IF(Bflag.EQ.0) THEN Cflag=0 ENDIF ENDIF IF(KEEP) THEN IF(Dflag) THEN IF(MOD(LABEL(7,n+((PBCx+1)/2)*PBCz*3*LOWERorUPPER),100) & .NE.2) THEN IF(MOD(LABEL(7,n+((PBCx+1)/2)*PBCz*3*LOWERorUPPER),100) & .NE.3) THEN IF(MOD(LABEL(3,n)8,(XLINK*6)).EQ.0) THEN crosslink D criteria

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135 IF(MOD(LABEL(2,n),2).EQ.0) THEN C2 multiple (for C2H2) c NHR=NHR+2 increment number of H2 hydrogens removed counter LABEL(7,n)=9 turn on remove hydrogen flag NHR=NHR+1 increment number of H2 hydrogens removed counter XLABELtemp(1,1)=LABEL(1,n) XLABELtemp(2,1)=LABEL(2,n) XLABELtemp(3,1)=LABEL(3,n)1 DO j=1,MNP IF(LABEL(1,j).EQ.LABEL(1,n)+1) THEN IF(LABEL(2,j).EQ.LABEL(2,n)+1) THEN IF(LABEL(3,j).EQ.LABEL(3,n)+0) THEN LABEL(7,j)=9 turn on remove hydrogen flag NHR=NHR+1 increment number of H2 hydrogens removed counter XLABELtemp(1,2)=LABEL(1,j) XLABELtemp(2,2)=LABEL(2,j) XLABELtemp(3,2)=LABEL(3,j)1 ENDIF ENDIF ENDIF ENDDO IF(MOD(PBCx,2).EQ.1) THEN PBCD check IF(LABEL(1,n).EQ.(PBCx1)/2+1) THEN PBCD check IF(MOD(LABEL(2,n),2).EQ.0) THEN PBCD check DO j=1,MNP IF(LABEL(1,j).EQ.1) THEN IF(LABEL(2,j).EQ.LABEL(2,n)+1) THEN IF(LABEL(3,j).EQ.LABEL(3,n)+0) THEN IF(LABEL(4,j).EQ.0) THEN LABEL(7,j)=9 turn on remove hydrogen flag NHR=NHR+1 increment number of H2 hydrogens removed counter XLABELtemp(1,2)=LABEL(1,j) XLABELtemp(2,2)=LABEL(2,j) XLABELtemp(3,2)=LABEL(3,j)1 ENDIF ENDIF ENDIF ENDIF ENDDO ENDIF ENDIF ENDIF IF(MOD(PBCy,2).EQ.1) THEN PBCD check

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136 IF(LABEL(2,n).EQ.PBCy+1) THEN PBCD check DO j=1,MNP IF(LABEL(1,j).EQ.LABEL(1,n)+1) THEN IF(LABEL(2,j).EQ.1) THEN IF(LABEL(3,j).EQ.LABEL(3,n)+0) THEN IF(LABEL(4,j).EQ.0) THEN LABEL(7,j)=9 turn on remove hydrogen flag NHR=NHR+1 increment number of H2 hydrogens removed counter XLABELtemp(1,2)=LABEL(1,j) XLABELtemp(2,2)=LABEL(2,j) XLABELtemp(3,2)=LABEL(3,j)1 ENDIF ENDIF ENDIF ENDIF ENDDO ENDIF ENDIF SETxlink=1 set crosslink flag true XSHIFT=LABEL(1,n)1 set x shift of crosslink C atom YSHIFT=LABEL(2,n)2 set y shift of crosslink C atom ZSHIFT=((LABEL(3,n)8)/(XLINK*6)0)*XLINK set z shift of crosslink C atom ENDIF ENDIF ENDIF ENDIF ENDIF ENDIF IF(SETxlink) THEN i=i+1 XLINKKTYPE(i)=6 1st C atom of crosslink D XLINKR0(1,i)= 5.183034896 & + LPa *XSHIFT x shift XLINKR0(2,i)= 2.971996009 & +(LPb/2)*YSHIFT y shift XLINKR0(3,i)= 3.149029796 & + LPc*ZSHIFT z shift XLABEL(1,i)=XLABELtemp(1,1) XLABEL(2,i)=XLABELtemp(2,1) XLABEL(3,i)=i XLABEL(4,i)=XLABELtemp(1,1) XLABEL(5,i)=XLABELtemp(2,1) XLABEL(6,i)=XLABELtemp(3,1)

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137 IF(LOWERorUPPER) THEN lower substrate XLABEL(7,i)=240+MOD(LABEL(7,n1+((PBCx+1)/2)*PBCz*3),100) D type crosslink ELSE upper substrate XLABEL(7,i)=240+MOD(LABEL(7,n1 ),100) D type crosslink ENDIF i=i+1 XLINKKTYPE(i)=1 corresponding 1st H atom XLINKR0(1,i)= 5.759724129 & + LPa *XSHIFT x shift XLINKR0(2,i)= 3.631679704 & +(LPb/2)*YSHIFT y shift XLINKR0(3,i)= 3.838574616 & + LPc *ZSHIFT z shift XLABEL(1,i)=XLABELtemp(1,1) XLABEL(2,i)=XLABELtemp(2,1) XLABEL(3,i)=i XLABEL(4,i)=XLABELtemp(1,1) XLABEL(5,i)=XLABELtemp(2,1) XLABEL(6,i)=XLABELtemp(3,1) IF(LOWERorUPPER) THEN lower substrate XLABEL(7,i)=240+MOD(LABEL(7,n1+((PBCx+1)/2)*PBCz*3),100) D type crosslink ELSE upper substrate XLABEL(7,i)=240+MOD(LABEL(7,n1 ),100) D type crosslink ENDIF i=i+1 XLINKKTYPE(i)=1 corresponding 2nd H atom XLINKR0(1,i)= 4.671226179 & + LPa *XSHIFT x shift XLINKR0(2,i)= 3.639558655 & +(LPb/2)*YSHIFT y shift XLINKR0(3,i)= 2.417157509 & + LPc *ZSHIFT z shift XLABEL(1,i)=XLABELtemp(1,1) XLABEL(2,i)=XLABELtemp(2,1) XLABEL(3,i)=i XLABEL(4,i)=XLABELtemp(1,1) XLABEL(5,i)=XLABELtemp(2,1) XLABEL(6,i)=XLABELtemp(3,1) IF(LOWERorUPPER) THEN lower substrate XLABEL(7,i)=240+MOD(LABEL(7,n1+((PBCx+1)/2)*PBCz*3),100) D type crosslink ELSE upper substrate

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138 XLABEL(7,i)=240+MOD(LABEL(7,n1 ),100) D type crosslink ENDIF i=i+1 XLINKKTYPE(i)=6 2nd C atom of crosslink D XLINKR0(1,i)= 6.246364979 & + LPa *XSHIFT x shift XLINKR0(2,i)= 3.442141966 & +(LPb/2)*YSHIFT y shift XLINKR0(3,i)= 2.127134462 & + LPc *ZSHIFT z shift XLABEL(1,i)=XLABELtemp(1,1) XLABEL(2,i)=XLABELtemp(2,1) XLABEL(3,i)=i XLABEL(4,i)=XLABELtemp(1,2) XLABEL(5,i)=XLABELtemp(2,2) XLABEL(6,i)=XLABELtemp(3,2) IF(LOWERorUPPER) THEN lower substrate XLABEL(7,i)=240+MOD(LABEL(7,n1+((PBCx+1)/2)*PBCz*3),100) D type crosslink ELSE upper substrate XLABEL(7,i)=240+MOD(LABEL(7,n1 ),100) D type crosslink ENDIF i=i+1 XLINKKTYPE(i)=1 corresponding 1st H atom XLINKR0(1,i)= 7.053621030 & + LPa *XSHIFT x shift XLINKR0(2,i)= 2.742605282 & +(LPb/2)*YSHIFT y shift XLINKR0(3,i)= 2.44683932 & + LPc *ZSHIFT z shift XLABEL(1,i)=XLABELtemp(1,1) XLABEL(2,i)=XLABELtemp(2,1) XLABEL(3,i)=i XLABEL(4,i)=XLABELtemp(1,2) XLABEL(5,i)=XLABELtemp(2,2) XLABEL(6,i)=XLABELtemp(3,2) IF(LOWERorUPPER) THEN lower substrate XLABEL(7,i)=240+MOD(LABEL(7,n1+((PBCx+1)/2)*PBCz*3),100) D type crosslink ELSE upper substrate XLABEL(7,i)=240+MOD(LABEL(7,n1 ),100) D type crosslink ENDIF i=i+1 XLINKKTYPE(i)=1 corresponding 2nd H atom

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139 XLINKR0(1,i)= 6.384230825 & + LPa *XSHIFT x shift XLINKR0(2,i)= 3.594260896 & +(LPb/2)*YSHIFT y shift XLINKR0(3,i)= 1.031197455 & + LPc *ZSHIFT z shift XLABEL(1,i)=XLABELtemp(1,1) XLABEL(2,i)=XLABELtemp(2,1) XLABEL(3,i)=i XLABEL(4,i)=XLABELtemp(1,2) XLABEL(5,i)=XLABELtemp(2,2) XLABEL(6,i)=XLABELtemp(3,2) IF(LOWERorUPPER) THEN lower substrate XLABEL(7,i)=240+MOD(LABEL(7,n1+((PBCx+1)/2)*PBCz*3),100) D type crosslink ELSE upper substrate XLABEL(7,i)=240+MOD(LABEL(7,n1 ),100) D type crosslink ENDIF XNP=i SETxlink=0 set crosslink flag false ENDIF ENDDO RETURN END SUBROUTINE xlinking c+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ c+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ c+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ SUBROUTINE writeout c Writes xyz and label files USE coorddmod ,ONLY: KTYPE USE coorddmod ,ONLY: R0 USE coorddmod ,ONLY: MNP USE buildchainmod ,ONLY: LPa,LPb,LPc USE countermod ,ONLY: LABEL,MAXLABEL,XLABEL USE xlinkingmod ,ONLY: XLINK,Aflag,Bflag,Cflag,Dflag USE xlinkingmod ,ONLY: XLINKKTYPE,XLINKR0,NHR,XNP IMPLICIT none I NTEGER*8 i,N local variables WRITE(*,104) MNPNHR+XNP NP WRITE(*,*)

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140 DO i=1,MNP print matrix atoms IF(LABEL(7,i).NE.9) THEN crosslink criteria WRITE(*,101) KTYPE(i),(R0(N,i),N=1,3) ENDIF ENDDO DO i=1,XNP print crosslinking atoms WRITE(*,101) XLINKKTYPE(i),(XLINKR0(N,i),N=1,3) ENDDO IF(1) THEN print labeling WRITE(20,104) MAXLABEL(1)*MAXLABEL(2)*MAXLABEL(3)+XNP, & MNPNHR+XNP NL,NP WRITE(20,104) MAXLABEL(1)*MAXLABEL(2)*MAXLABEL(3),XNP ML,XL WRITE(20,104) (MAXLABEL(N),N=1,3) WRITE(20,105) LPa,LPb,LPc WRITE(20,105) MAXLABEL(1)*LPa,MAXLABEL(2)/2*LPb,MAXLABEL(3)/6*LPc DO i=1,MNP WRITE(20,104) ( LABEL(N,i),N=1,7) ENDDO DO i=1,XNP WRITE(20,104) (XLABEL(N,i),N=1,7) ENDDO ENDIF 101 FORMAT(I4,3E20.11) xyz position format 104 FORMAT(7I10) NP or label line 1 05 FORMAT(3E20.11) coord.d PBC line RETURN END SUBROUTINE writeout c+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

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150 BIOGRAPHICAL SKETCH Patrick Chiu graduated from Nova High School in Davie, Florida in June of 2000. He started his undergraduate studies at the Universi ty of Florida that fall. In the spring of 2003, he joined the Sinnott group where he began his studies in computational materials science. He received his bachelors degree in materials s c ience and e ngineering from the University of Florida in 2005. That s ame year, h e started his doctorate studies in computational materials s cience.