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1 ELUCIDATION OF ATOMIC SCALE MECHANISMS FOR POLYTETRAFLUOROETHYLENE TRIBOLOGY USING MOLECULAR DYNAMICS SIMULATION By PETER R. BARRY A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2009
2 2009 Peter R. Barry
3 To he who like s to take risky chances To she who make s lots of mistakes To he who truly enjoy s learning To she who dares to live life fully as she sees fit
4 ACKNOWLEDGMENTS I thank my thesis advisor Prof. Simon Phillpot first for taking a chance on me and second for his attentive, conscious, proactive, strategic guidance in helping me to grow through this PhD process and to successfully complete this phase of my educationally life and career. I thank Prof. Susan Sinnott for close research collaboration and for complementing seamlessly Dr. Phillpots efforts with me throug h this process. It made for a unique, r ewarding experience to have had two thesis advisors and to obtain first hand observation into the dynamics of what makes a successful team. I also tha nk Prof. Wallace Gregory Sawyer for being Greg. That basically me ans 1) for being extremely passionate about what he does, 2) for his willingness to go 10,000 miles if necessary with students who are motivated to work hard to get things done properly and 3) for taking the time to help and inspire other s including myself I also thank Prof. Scott Perry for his high standards as a scientist and for holding me accountabl e to those high standards in my early days Some professors may not have taken the time to emphasize the importance of performing thorough and careful analy sis prior to presentation; so, I thank him for emphasizing tha t important point. In conjunction, I also thank my two other committee members Prof. Elliot Douglas for making sure I was up to snuff with regard to polymer understandings (i.e. through the poly mer course and thesis proposal defense) and Prof. Curtis Taylor for agreeing, on relatively short notice with respect to th e oth er committee members, to serve on my defense committee. Additionally, I thank Dr. Tao Liang for his technical expertise with th e REBO code and his continuous willingness to help. I would like to acknowledge Dr. Inkook Jang who laid a significant part of the foundation from a potential and code development standpoint so that a graduate student such as me cou ld have come into the gr oup, generation different types of fluorocarbon systems and focus strictly on conducting scientific investigation s I would also like
5 to thank Dr. Patrick Chiu for the use of his codes to obtain much improved versions of PTFE cross -linked structures to sim ulate and for ideas and critical feedback. Much thanks to Dr. Seongjun Heo for his help in the early days when I was getting started on this project and to Drs. Rakesh K. Bahera, Damian M. Cupid and David Hor ton for critical discussions of ideas. Finally, countless thanks to family, friends and everyone who Ive crossed paths with so far for making the journey worthwhile. Merci tout le monde!
6 TABLE OF CONTENTS page ACKNOWLEDGMENTS .................................................................................................................... 4 LIST OF TABLES ................................................................................................................................ 8 LIST OF FIGURES .............................................................................................................................. 9 ABSTRACT ........................................................................................................................................ 12 CHAPTER 1 INTRODUCTION ....................................................................................................................... 14 1.1 Tribology ............................................................................................................................... 14 1.2 Lubrication in Tribology ...................................................................................................... 15 1.3 Solid vs Grease vs Liquid vs Gas Lubrication (overview) ................................................. 16 1.4 Polytetrafluoroethylene (PTFE) ........................................................................................... 17 1.4.1 General Properties and Applications ......................................................................... 17 1.4.2 Synthesis, Polymerization and Fabrication............................................................... 19 1.4.3 Structure ...................................................................................................................... 21 188.8.131.52 Characterization ............................................................................................... 21 184.108.40.206 Proposed deformation mechanisms ................................................................ 22 1.4.4 Proposed Theories of Wear ....................................................................................... 23 1.5 Motivations and Objectives .................................................................................................. 27 2 SIMULATION METHODOLOGY ........................................................................................... 29 2.1 Molecular Dynamics Simulation Overview ........................................................................ 29 2.2 Calculation of Inter atomic Forces ...................................................................................... 31 2.2.1 Reactive Empirical Bond Order (REBO) Potential .................................................. 31 2.2.2 Lennard Jones (LJ) 126 Potential ............................................................................ 33 2.3 Integration Method................................................................................................................ 33 2.4 Thermostat Method ............................................................................................................... 35 2.5 Periodic Boundary Conditions ............................................................................................. 36 2.6 Benefits of Atomic -level Simulation ................................................................................... 37 3 FOUNDATIONAL APPROACHES TO SYSTEM SPECIFICATION, SIMULATION CONDITIONS AND DATA ANALYSIS ................................................................................ 41 3.1 Building of Crystalline PTFE Surfaces ............................................................................... 41 3.2 Approaches to Cross link Distribution ................................................................................ 43 3.3 Effect of Cross link Morphology and Density on Crystalline PTFE -PTFE sliding ......... 44 3.4 Effect of Sliding Velocity on Crystalline PTFE PTFE Sliding ......................................... 47 3.5 Least Squares Fitting for Calculating Friction Coefficients and Adhesive Forces ........... 51 3.6 Summary................................................................................................................................ 54
7 4 EFFECT OF SLIDING ORIENTATION .................................................................................. 64 4.1 Perpendicular vs. Parallel ..................................................................................................... 65 4.2 Violin (Combination of Perpendicular and Parallel) .......................................................... 67 4.3 Microscopic Processes of Friction and Wear ...................................................................... 68 4.3.1 Bowing and Bunching Together of Chains .............................................................. 69 4.3.2 Chain Entanglement ................................................................................................... 70 4.3.3 Chain Scission ............................................................................................................ 71 4.3.4 Chain and Chain -Segment Reorientation .................................................................. 73 4.4 Summary................................................................................................................................ 73 5 EFFECT OF TEMERATU RE .................................................................................................... 82 5.1 Frictional Response ............................................................................................................... 83 5.2 Adhesive Component of Temperature Dependent Friction ............................................... 87 5.3 Influence of Normal Load on Amonton Friction ................................................................ 90 5.4 Interfacial Wear ..................................................................................................................... 91 5.5 Summary................................................................................................................................ 92 6 EFFECT OF FLUOROCARBON MOLECULES AT THE SLIDING INTERFACE ........ 102 6.1 Monolayer of Molecular Fluid ........................................................................................... 104 6.1.1 Frictional Response .................................................................................................. 105 6.1.2 Wear Response ......................................................................................................... 107 6.2 Four Monolayers of Molecular Fluid ................................................................................ 109 6.2.1 Frictional Response .................................................................................................. 109 6.2.2 Shearing of fluid layers ............................................................................................ 110 6.2.3 Reorientation of Fluid Molecules ............................................................................ 110 6.3 Overall Reduction in Friction Coefficient and Wear ........................................................ 114 6.4 Summary.............................................................................................................................. 116 7 CONCLUSIONS ....................................................................................................................... 135 LIST OF REFERENCES ................................................................................................................. 138 BIOGRAPICAL SKETCH .............................................................................................................. 144
8 LIST OF TABLES Table page 2 1 Lennard Jones parameters used carbon and fluorine atoms utilized for the simulations described in this work. ....................................................................................... 40 3 1 Effect of different boxcar siz e averaging on Ff and Fn values. ............................................ 63 3 2 Friction coefficient based on reduced and unreduced force averages ................................ 63 5 1 The lowest and highest frictional forces for the three sliding configurations explored at the two extreme temperatures investigated. ................................................................... 101 6 1 Breakdown of the number of molecules, carbon atoms and total number of atoms for the various fluid systems studied. ....................................................................................... 133 6 2 Densities of the PTFE surface with and without cross links. ............................................ 133 6 3 Diffusion coefficients for the fluorocarbon fluids used in this study ............................... 133 6 4 Quantification of friction coefficient and adhesive force using least squares fitting for perpendicular sliding. ........................................................................................................... 134 6 5 Quantification of friction coefficient and adhesive force using least squares fitting for parallel sliding. ..................................................................................................................... 134
9 LIST OF FIGURES Figure page 1 1. Schematic of a contact point of two rough surfaces and the separation of these contact points or asperity peaks by a fluid ....................................................................................... 28 2 1. Flow chart of the major components of a simple MD program. ............................................. 39 2 2. Schematic representation of a four particle system employing periodic boundary conditions. ............................................................................................................................... 40 3 1. Simulation cell of two aligned, cross -linked PTFE surfaces ................................................... 56 3 2. Schematic of the PTFE surface chain arrangement ................................................................. 57 3 3. Comparison of the Amonton friction coefficient (i.e = ff/fn) for perpendicular and parallel sliding at 300K with sliding velocity of 10 m/s for two different polymer cross -link morphologies. ........................................................................................................ 58 3 4. Illustration of the friction response with respect to normal load for perpendicular and parallel sliding at different cross -li nk densities and distribution ........................................ 58 3 5. Evolution of temperature during sliding for different sliding rates in the perpendicular direction and parallel sliding di rection ................................................................................. 59 3 6. Normal (FN) and frictional (FF) forces for the perpendicular and parallel sliding configurations, respectively, at sliding rates of 10 m/s and 20 m/s. ................................... 59 3 7. Coefficient of friction for the sliding of PTFE surfaces at 5m/s and 20m/s in the perpendicular and parallel configurations, res pectively ...................................................... 60 3 8. Edge on view for perpendicular sliding. ................................................................................... 61 3 9. Graph of the normal distribution for the frictional force data generated using the Monte Carlo method ......................................................................................................................... 62 3 10. Illustration of the series of Monte Carlo least -squares fitting car ried on the simulation data .......................................................................................................................................... 62 4 1. The simulations are initially compressed to a load of 5nN before sliding is commenced .... 76 4 2. A sequence of molecular snapshots of the upper 25 PTFE chains from the bottom stationary PTFE surface ......................................................................................................... 77 4 3. A histogram of the displacements along the sliding direction for the carbon atoms in the surface PTFE chains highlighted in Figure 4 2 .............................................................. 78
10 4 4. Comparison of frictional response for the three sliding configuration for comparable normal loads at 300K. ............................................................................................................ 79 4 5. Illustration of the various microscopic molecular processes at work in the sliding of crystalline PTFE surfaces during perpendicular sliding. ..................................................... 80 4 6. Molecular snapshots at select stages of the various microscopic processes for the violin slidin g configuration taken at 25K at an average normal load of ~ 32nN .......................... 81 5 1. Friction force (Ff) vs. Normal force (Fn) at various temperatures and normal loads for cry stalline PTFE -PTFE sliding ............................................................................................. 95 5 2. Depiction of the friction coefficient ( determined by taking the average of a series of least square fits to the respective temperature data points in Figure 5 1 ............................ 96 5 3. Schematic diagramming the experimental derivation of the pull -out or adhesive force ....... 97 5 4. An alternative perspective of friction and wear for perpendicular sliding at low temperature which includes an arbitrarily chosen low friction, low normal load data pair not obtained from simulation ......................................................................................... 98 5 5. Friction coefficient, without reference to adhesion, as a function of normal load at various temperatures for the three sliding configuration. .................................................... 99 5 6. Displacement of the bottom surface inter facial carbon atoms are measured with respect to their initial positions prior to sliding of the top PTFE surface ...................................... 100 6 1. MD snapshot of the PTFE system without molecular fluid. ................................................. 119 6 2. MD snapshot of the two surface PTFE system set up with a separating fluid monolayer .. 120 6 3. MD snapshot of the crystalline PTFE PTFE system setup with four monolayers of molecular fluid at the interface. ........................................................................................... 121 6 4. Illustration of the effect of one fluid layer of hexafuoroethane(C2F6) and perfluorooctane (C8F18) on crystalline PTFE PTFE friction. ............................................ 122 6 5. Illustration of the interfacial displacement of various components in response to the sliding of the top PTFE surface .......................................................................................... 122 6 6. Carboncarbon bond length distribution for the one monolayer of the two fluid types both before and after sliding of the top PTFE surface ...................................................... 123 6 7. Carbon-fluorine bond length distribution for the one monolayer of fluid for both fluid types before and after sliding of the top PTFE surface ..................................................... 123 6 8. Illustration of the effect of four fluid layers of hexafuoroethane(C2F6) and perfluorooctane (C8F18) on crystalline PTFE PTFE friction. ............................................ 124
11 6 9. Illustration of the displacement of various interfacia l system components in response to the sliding of the top PTFE surface ..................................................................................... 124 6 10. Interfacial planar displacement of fluid layers perpendicular to the sliding direction of top PTFE surface with the1st layer being closest to the bottom PTFE surface ............... 125 6 11. Reorientation of molecular fluid molecules towards the sliding direction (i.e. xdirection) for the perpendicular sliding of C8F18 fluid system at 300K ............................ 126 6 12. Ori entation behavior of molecular fluid for C8F18 viewed along the alignment of the surface chains and perpendicular to the surface chains within the sliding interface ...... 127 6 13. Quantification of the orientation order of the C2F6 molecular fluid for perpendicular PTFE PTFE sliding configuration at 300K ........................................................................ 128 6 14. Quantification of the orientation order of molecular fluid C2F6 for the perpendicular PTFE P TFE sliding configuration at 300K ........................................................................ 129 6 15. Graph of Ff vs Fn for perpendicular and parallel PTFE -PTFE sliding at 300K for wet and dry sliding ...................................................................................................................... 130 6 16. Molecular snapshots of the interfacial polymer chain of the bottom PTFE surface (top down view) ........................................................................................................................... 131 6 17. Mol ecular snapshots for additional sliding of the C8F18 4 monolayer fluid system described in Figure 6 16. ..................................................................................................... 132
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 ELUCIDATION OF ATOMIC SCALE MECHANISMS FOR POLYTETRAFLUOROETHYLENE TRIBOLOGY USING MOLECULAR DYNAMICS SIMULATION By Peter R. Barry December 2009 Chair: Simon R. Phillpot Major: Material s Science and Engineering Polytetrafluoroethylene (PTFE) is a polymer that has been widely exploited commercial ly as a result of its low friction non-stick properties The polymer has found usage as non -stick chemically resistant coatings for bearings, valves, rollers and pipe linings with applications in indus tries ranging from food and chemical processing to construction, automotive and aerospace The major drawback of PTFE in low friction applications involves its excessive wear rate. For decades, scientist s and engineers have sought to improve the polymers wear resistance while maintaining its low sliding friction by reinforcing the polymer matrix with a host of filler materials ranging from fibril to particulate In this study, a different approach is taken in which the atomic scale phenomena between two c rystalline PTFE surfaces in sliding contact are examined. The goal is to obtain atomic -level insights into PTFEs low friction and high wear rate to aid in the designing of effect ive polymer based tribological composites for extreme condition application s To accomplish this, several tribological condit ions were varied. These included sliding direction of the two polymer surface s with re spect to their chain alignment, sliding velocity degree of crystalline phase rigidity
13 interfacial contact pressure, samp le t emperature and the presence of fluorocarbon fluids between the two crystalline PTFE surfaces. From these studies, it was found that crystalline PTFE -PTFE sliding demonstrate s friction anisotropy Low friction and molecular wear was observed when slidin g in the direction of the chain alignment with high friction and wear behavior dominating when sliding in a direction perpendicular to the chain alignment. For the range of cross link density (average linear density of 6 .2 to 11.1 ) and sliding rate (5 m/ s to 20 m/s) explored, a significant change in friction behavior or wear mechanisms was not observed. Under conditions of increased normal load or low temperature however, the frictional force increased linearly. Additional ly the inclusion of fluorocarbon molecular fluids at the sliding interface between the two crystalline PTFE surfaces resulted in a significant decrease in both the friction and wear of the surfaces.
14 CHAPTER 1 IN TRODUCTIO N 1.1 Tribology Defined simply, tribology is the science and technology of solid, interacting surfaces in relative motion1 The scientific aspect is often the direct concern of researchers at universities and national laboratories while the technological perspective, involving more of a finish ed product or system implemented for a specific task, is often the focus of design engineers in the field. In this work, the scientific aspect is highlighted from a material s standpoint without strong e mphasis placed on the technological aspect as it relates to system desi gn for a specific application. Be fore delving into the material aspect s of tribology however, it is necessary to establish why tr ibology is an important subject. The answer may be found in the fact that we live in a mechanical world. Much of the work performed in todays industrialized countries i s done by motorized machinery. These machines appear in the form of a host of automotive vehicles such as heavy trucks, large construction mach inery and expensive vehicles for space exploration. T he manufacturing plants us ed to build these machines are equally complex mechanical entities The interaction of surfaces for a high number of moving parts in these mechanical systems play s a significant role i n their operational ef ficiency Scientific studies by various researchers both in the United States and United Kingdom have estimated the economic impact of tribology to be in the range of billions of dollars. For example, for the year 1974, Jost2 estimated tha t the United States could save between $12 and $16 billion per year by investing in tribology research and utilizing the insights gained to both improve efficiency and increase material usage lifetime. Subsequent estimates for the year 1977 were even higher, to the tune of $40 billion per year.3,4 Rabinowic z s5 calculations also predicted the tri bological, economic impact to be in the billion dollar range wit h friction and wear account ing for approxim ately 10 and 100 billion dollars respectively. These studies were
15 conducted over three decades ago. Since then, the world has grown substantially from a technological s tandpoint with the advent of information technology. The relentless miniaturization of integrate d circuits to build more powerful computers and other small sophisticated electronic devices have given more relevance to surface interactions and associated phenomena such as stiction. Undoubtedly, the importance of tribolgy has likewise grown en ormously. Given the high cost of wear in tribology, the phenomena is often address ed through the use of a lubricating materials such as solid film, semi -solid grea se or fluids such as oil s and gas es 1.2 Lubrication in Tribology When two material surfaces in contact move wit h respect to each other, there is always an opposing force to this movement. This resistance or opposing force is referred to as friction. The friction force may be broken up into two components: an adhesive component a nd a deformation c omponent.6 The adhesive component is a result of the f act that the surface s are in contact. Atoms at a surface, as opposed to those within the bulk of a material, are under coordinated and thus, are not in the ir thermodynamically favorable energy state. This cause s interactions that foster proper coordination betwee n the atoms of the surfaces in contact. The higher the relative surface energies, the stronger the surface inter action will be This inte raction accounts for adhesion. The deformation component of friction st ems from the fact that surfaces, from the nano to the macro -scale, are not flat. Most surfaces are composed of a large number of rough, jagged peaks (i.e. asperities) and valleys. When two surfaces are pressed together, the contact pressure at the interface is supported by these mountain top asperity peaks ( see Figure 1 1 -A ). The number of asperity peaks in contact dynamically changes with increasing contact pressure ( e.g. some peaks plastically deform and become part of large peaks that, in turn ma y support more of
16 the pressure ). From the deformation perspective, a lubricant place d betw een the two material surfaces functions by providing a relatively low shear strength interface for sliding while ensuring that the asperity peaks of the two surfaces do not phys ically interact with each other (see Figure 1 1 B). From an adhesive perspective, the lubricant lowers the surface inte rface energy by pacifying, to some extent, the need to achieve proper coordination of the surface atoms. 1.3 Solid vs Grease vs Liquid vs Gas Lubrication (overview) The four basic categories of lubricants are oils, g reases, dry lubricants and gases.7 Oils and gases are a form of fluid lubrication where oils refer to liquid lubricants and gases refer to any gas that does not attack or decompose the bearings on which it is used. Greases are basically oils with an added thickening agent that renders them as semi -solids while dry lubricants take on the properties of a solid as paint like coatings, loose powders and bulk solids. Both their advantages and disadvantages stem from the basic properties suggested by the form that each take s For example, oils, owing to their fluid nature, may be used for cooling and can be easily fed into a bearing via pumping or peri odically dripping and simply drained when they are no longer usabl e. Greases are not as easily fed into a bearing compared to oils and they provide almost no cooling; yet they will no t migrate away from bearings into surrounding surfaces or volatilize as easily as oils would.7 Similarly, dry or solid lubrication may support a substantially high er load compared to gas lubrication; however, since solid lubricants do not flow, they offer significantly less potential cooling of the bearings and cannot accommodat e velocities that are as high as gases. In addition to these advantages and disadvantages, there are added considerations of lubricant cost, the complexity associated with administer ing the lubricant and also the compatibility of the lubricant with the ma t erial system in question.
17 In general, for bearings where high conta ct pressure is the main requirement a solid lubricant would be the first choice, followed by greases, oils and finally gas es This order ing of the lubricant class es for high contact pres sure applications represents one of decreasing viscosity. For a case where high bearing speed is the main criteria, the reverse order, beginning with a gas would be appropriate Additional c onsideration for gas bearings including the need for precise contr ol of the surface finish (the requirement is usually one of very high smoothness), clean gas supply and rather complex system design.7 With regard to the four lubricant classes, thermal and chemical stability, compat ibility with bearing materials, maintenance of lub r icant in bearings toxicity, environmental effects, availability and price are additional fa ctors to be considered when making a choice for impro ving tribological performance. 1.4 Polytetrafluoroethylene (PTFE) 1.4.1 General Properties and Applications PTFE is a semicrystalline, fluoropolymer consisting of tetrafluoroethylene (C2F6)n mers ; it has a m elting temperature of ~ 327 8 The polymer is widely used in engineering applications for its low friction,9 relatively high temperature stability chemical resistance,10 and dielectric properties.11 PTFE is often the top polymer choice for handling aggressive acids (e.g. HF, H2SO4) at high temperatures (e.g. 28045012 PTFEs superior engineering properties compared to other common polymers (e.g. polyethylene, po lystyrene or polypropylene ) is due to a combination of its strong C F bond energy which is among the highest known (~ 481 kJ/mol) and low inter -chain attractive forces which conversely, is among the lowest at ~ 3 kJ/mol. As a result of the mutual repulsion of its fluorine atoms, PTFE s chain conformation ta kes on a helical nature in three of its four well characterized phases13 where the fluori ne atoms twist and are staggered around the carbon mo lecular backbone.14 This arrangement shields the carbon -based core from attack; hence, the polymer s high chemical resistance. The mutual fluorine -fluorine
18 repulsion simultaneously accounts for the low inter -chain attractive force. In conjunction with its smooth molecular profile, the rod like polymer chains are to a ble to easily slide past each other, thus enabling PTFEs low friction. U nfortunately, though, this property accounts for its high wear rate as well .15 Owing to its strong covalent bonding, PTFE acts an electrical insulator The polymers low dielect ric strength is a direct result of its highly symmetrical chains conformation where its electrical dipoles (i.e. the polar C F bonds) balance each other.12 The polymers outstanding electrical properties could be compromised however by the presence of voids and micro -cracks in its structure that may arise during processing. Given its array of unique physical, chemical and electrical properties, PTFE finds usage in a wide range of engineering applications. PTFE finds usage in the automotive industry and in the area of office equipment due to its low friction and for its mechanical and chemical resistance. It is used as seals and rin gs in automotive power steering and transmission s and in air conditioning. It is used as rollers for office equipment and as coverings for food processing equipment.10 PTFE coated bearings pins and other bearing parts may be used in aircraft and aerospace vehicle control systems an d office machines. PTFE is also used in sliding bearings or bea ring pads for support systems such as bridges and buildings to accommodate thermal and seismic movement without damage t o the structures they support. Additionally, bearing pads made with PTFE fibers are used in packaging machinery and pulp and paper proce ssing equipment. Valves, pumps and other components can be lined with or made from PTFE through i sostatic molding. Unlined valves fabricated f r o m stainless steel and other metals will often have PTFE components, for instance, s eats, packings and diaphragms In addition to providing chemical resistance, PTFE in seats and packings provide conformability to mating surface s for good sealing and low friction for ease of operation.10 The main disadvantages of PTFE are its high sensitivity to ionizing
19 radi ation and it s tendency to creep (i.e. to experience cold flow). With regard to sliding applications, the unfilled polymer matrix exhibits a high wear rate. 1.4.2 S ynthesis Polymerization and Fabrication PTFE is made from the polymerization of the tetraflu oroethylene (TFE) mer (C2F4) which is a colorless, odorless, tasteless, nontoxic gas that boils at 76.3 142. 5 10 Works referring to c ommercially relevant techniques ,1618 in the preparation of TFE, mention CaF2, hydrofluoric acid and chloroform as starting ingredients. The polymerization of TFE to for m fluoropolymers such as PTFE is often carried out through a process of free radical polymerization .19 Typical initiators used at high temperatures are bisulfite or persulfate. PTFE homopolymers polymerize linear ly withou t any detectable b ranches, contrary to the situation for polyethylene (PE). Owing to its symmetric structure and the mutual inter and intra chain repulsion of its fluorine atoms, PTFE exhibits low surface energy. Thus, the PTFE chains interact minimally with each other. In order to en sure good mechanical properties in the presence of van der Waals interactions between the polymer chains, very high molecular weights (i.e. degree of polymerizations of 106107) are required where the long chains have an incr eased probability of becoming entangled in the melt state An undesirable effect of such high molecular weights is PTFEs extremely high melt viscosity of ~ 10 GPa (i.e. 1011 poise) at 380 T his viscosity is millions of times too high to allow for me lt processing via extrusion or injection molding techniques.10 The fact that the polymer does not flow upon melting creates additional challenges from the standpoint of voids (giving rise to mechanical and permeability issues) that are not easily clo sed within parts made of PTFE. Addressing this problem requires a reduction in the polymers viscosity without significant increases in re -crystallization. The solution has been to polymerize small amounts of a co -monomer with TFE to disrupt PTFEs crystal line structure.20-
20 23 This polymerization process is done through two techniques: suspension and dispersion. The suspension technique10 employs little or no dispersion agent in conjunction with vigor ous agitation of the polymer at elevated temperature and pressure. This yields a granular polymer which may be processed as a molding powder. In t he dispersion technique,10 a high purity aqueous medium (to minimize retardation effects on the radica l polymerization process) is often used to produce dispersion and fine powder PTFE pr oducts. The approach is different from that of the suspension technique in that ample dispersing agent is combined with mild agitation at elevated temperature and pressure In its granular, dispersion and fine powder forms, different fabrication techniques are used to make a variety of PTFE products. The properties of the desired fi nish part often dictate the starting form of the polymer used for fabrication. Granular PTFE is often used to make relatively simple shapes and objects that do not require extensive machi ning to produce fine details. The t echniques used include some form of moldi ng (e.g. compression, iso s tatic or automatic ) or ram extrusion.10 PTFE disper sions are aqueous, milky mixtures comprised of small particles (< 0.25 m) of resin suspended in water. These dispersions are characterized by high fluidity and are amenable to fluid coating techniques. Thus, applications are primarily coating s and films for stadium roofs, conveyor belts, bearings, automobile gaskets and many other parts. Fine powders are usually pa ste extruded to commercial form parts such as rods, tape, tubing, electrical insulation and other profiles. Paste extrusion is a tec hnique adapted from ceramic processing where PTFE powder is blended with a hydrocarbon lubricant (i.e. paste) which serves as an extrusion aid. It may then be formed into a cylindrical preform at relatively low pressure (e.g. 1 8 MPa) and transferred to th e barrel of a ram extruder for shaping.10 The extrudate may be dried in an oven prior to sintering to rem ove the hydrocarbon lubricant.
21 1.4.3 Structure The actual manner in which semi -crystalline polymers, such as PTFE, deform in response to stre ss is currently not completely understood. The reason lies in the fact that details of the polymer st ructure are still being debated. The general accepted model of a semi -crystalline polymer is one consisting of two distinct phases: a crystalline phase and an amorphous phase. In the crystalline phase, the chains loop back on themselves with each loop being approximately 100 carbon atoms long.19 The folded chain pattern extends in three dimensions to produce thin plates or lamellae. These lamellae or crystals take on different forms (e.g. spherulitic shape s ) and orientations The amorphous transition zones are assumed t o reside between the thin plates 220.127.116.11 Characterization The c haracterization of polymers involve s the u se of many different techniques and depends on the property of interest. A comm on property, average molecular weight is measured in different ways; hence, the three common averages: the number average molecular weight (Mn), the weight average molecular weight (Mw) and the viscosity average molecular weight (Mv). For relatively low molecular weights (e.g. Mn < 25,000 g/mol), special end-groups (e.g. hydroxyl or carboxyl) left at one or both ends of the polymer chains after synthesis may be titrated or ana lyzed instrumentally using infrared methods to obtain Mn measurements.24 A second method used for the determination of Mn involves osmotic pressure experiments and solution thermodynamics theory which has a practical limit of approximately 500,000 g/mol.24,25 The principle method used for determining Mw is light scattering. For the bulk state, small angle neutron scattering is becoming more widely used and X ray scattering is sometimes utilized.24 Gel permeation or size exclusion chromatography may be used to determine either Mn or Mw while intrinsic viscosity measurem ents may be used to determine Mv.24
22 In conjunction, a vari ety of spectroscopy techniques may be employed to identify and obtain distribution information regarding major polymer components while highlighting f undamental features of the polymers vibrational motions.26 Infrared s pectra are obtained by passing infrared radiation through a polymer sample and recording the wavelength of the absorption peaks. These peaks, which are caused by the absorption of the electromagnetic radiation, are correlated to specific molecular motion o f different species, such as C -F bond stretching.24 Raman scattering works similarly in that the net result is an increase or decrease in a specific molecular motion. In addition X ray and electron diffraction m ethods may be used to identify repeat units in crystalline po lymers, inter and intra -molecular spacings, chain conformation and configurations and so forth.24 Ultraviolet and visible light spectroscopy may be used to determine sequence lengths and obtain information regarding conformational and spatial order while electron spectro scopy may be applied for microstructure analysis at the polymer surface. Yet another method is found in nuclear magnetic resonance (NMR) where the magnetic field of atomic nuclei is manipulated to obtain information about its environment. NMR may be used t o obtain informati on such as steric configuration, chemical function ality, structural, geometric, substitutional isomerism and so forth.24 18.104.22.168 Proposed deformation mechanisms There are different theories regarding deformation process es experienced by semi crystalline polymers A typical stress -strain diagram for a semi crystalline polymer features Hookean elastic type behavior at small deformations with irreversible deformation occurring beyond the yield point where the curve transitions into a plateau region charact eristic of a necking process before rising again right before fracture.27 It is often suggest ed that this behavior is related to the complex process of slip between lamellar planes of the crystal and unfolding of the polymer chains.25 In the ir studies of PTFE in tension, Rae and Brown28
23 identified two mechanisms. Above 196 egions were assumed to orient along with simultaneous slip of the thin plates within the crystalline regions. In addition to the slip of the thin plates, the crystalline regions themselves also tend to orient by rotation so that the long slip axis of the constituent thin plates become parallel to the pulling direction. At even higher strains, the crystals were observed to bow or kink (i.e. the long slip axes of the thin plates were no longer parallel to the pulling direction). For PTFE compression behavior, Rae and Dattelbaum13 observed that for a strain rate of 102 s1 at a temperature of 198 allowed greater ductility than the crysta lline regions. This conclusion was drawn as a result of stress -strain curves for low and high crystallinity PTFE showing significantly different behavior with the high crystallinity sample experiencing breakage with less than 40% true strain while the low crystallinity sample withstood 50% true strain and did not break. Additionally, based on the intersection of the initial tangent modulus and a straight line fit to the stress -strain curves at 10 and 20% strain at temperatures of 50, 24 and 0 e a strength parameter, Rae and Dattelbaum13 suggested that at around room temperature, t he stress required to deform PTFE changes at the same rate in the crystalline and amorphous domains. 1.4. 4 Proposed Theories of Wear PTFE is an exceptional polymer in that it exhibits a low coefficient of friction under a variety of conditions. Compared to other polymeric systems, however, the unfilled polymer shows a very high wear rate under most sliding conditions. In general, the wear coefficient of PTFE in sliding contact against a hard surface is often two orders of magnitude higher than a ceramic -ceramic material pair and at least one order of magnitude higher than a ceramic -metal pair .15 Compared to other polymers, the results are also unfavorable. According to Bhushan,15 unfilled PTFE has a wear coefficient of approximately 4000 x 107 mm3/(Nm) under dry sli ding
24 conditions against steel. Comparatively, the wear coefficient of acetal, polyamide, polycarbonate and pol yimide are 9.5, 38.0, 480 and 30.0 107mm3/(Nm) respectively. Consequently, many researchers have sought to understand the mechanism s by which PTFE so readily wears Since the early 1960s,29,30 scientists h ave sought to elucidate the nature of PTFEs low friction properties. Their efforts have results in the hypothesis that PTFE friction is governed largely by molecular scale as opposed to asperity scale interactions. Since then, a number of publications h ave surfaced in the literature to supp ort this early hypothesis.31 35 Over the last 20 years in particular, many studies have been geared specifically towar ds understanding the atomic or mole cular origins of friction.36 39 Researchers have presented both computational36 40,41 and experimental42 44 evidence of frictional anisotropy in a variety of polymeric systems and in the case of PTFE, have attributed such phenome na to its smooth molecula r profile .33 With regard to PTFE wear however, a number of hypotheses have also been put forth in the tribology literature These hypotheses may be roughly placed into th ree main categories: i ) the prevention of the large scale destruction of PTFE s banded structure ; ii) the fostering of adhesion of PTFE composite transfer films to the counterface material; iii) preferential support of the load imposed on the matrix. Associated with these hypotheses are a host of fillers, both particulate and fibril that have been successfully used to varying degrees, to reduce the sliding wear and/or frictional coefficient of PTFE systems. Bunn et al.45 proposed a banded structure of PTFE consisting of fine parallel striations that run per pendicular to the band length. Speerschneider and Li46 improved on this model by suggesting that the banded PTFE structure consists of two phases with crystalline striations or platelets separated from one another by a viscous, amorphous phase. From this model, Tanaka et al.31 proposed that easy slipping of crystalline slices leads to the destruction of PTFEs banded
25 structure wit hout any melting of the sliding surfaces and that a film of about 300 in thickness is produce d on the counterface material. In contrast to the assertions of Makinson and Tabor ,29 Tanaka et al.31 found no evid ence for the existence of bands in material transferred to the counterface material and proposed the occurrence of crystalline intra band slipping as opposed to slippage via the amorphous regions to explain the deve lopment of PTFE transfer film. The very h igh wear rate of PTFE was attributed to the easy detachment of the se films from the counterface. Their results further showed that the wear of PTFE is apparently affected by the w idth of these band structures. Based on the results of electron microscopy an d diffe rential thermal analysis Kar and Bahadur47 suggested that the crystalline lamellae interspersed with the amor phous phase and contributed to inter lamellar shear. Gong et al.48 reasoned that the incorporation of fillers into a PTFE matrix would reduce wear by retarding large scale destruction of PTFEs banded structure. A somewhat related idea was proposed by Blanchet and Kenned y32 who asserted that fillers reduce wear in PTFE by interrupting subsurface deformation and crack propagation which would otherwise lead to large wear sheets several microns in thickness. Second, it is often proposed in the literature that the wear behavior of PTFE has much to do with the adhesion of the PTFE and PTFE copolymer transfer film s to the counterface ma terial. Based on their experiments on PTFE sliding on abraded counterfaces, Bahadur and Tabor49 suggest ed that unfilled PTFE wears as fragmented sheets that are approxi mately 3 microns in thickness. The sheets mechanically lock into the rough s urface in discrete locations so that they appear as loose films on the wear track. Filled PTFE, however wear s as particles that easily lock into the crevices of asperities which allowed for the development of a coherent fil m on the mated steel surfaces The bond between the transfer film and the steel counterface was
26 deem ed to be mechanical in nature. Brainard and Buckley50 found that the bonding of PTFE transfer film s on clean, activ e metal counterfaces was stronger than van der Waals forces and may be of a chemical type. Cadman and Gossedge51 who conducted studies involving the rubbing of PTFE on metal under ultrahigh vacuum also suggested a physical or c hemical interaction between PTFE and the metal counterface and later conclud ed from observation of metallic fluorides at the metal -polymer interface that bonding at the interface is through chemical means. Correspondingly, Wheeler52 observed metal fluorides on both clean and oxidized metal surfaces after sliding of PTFE but concluded that it is difficult to completely marry the notion of chemical interaction to PTFE film -metal interactions since fluorine is monovalent. Gong et al.48,53,54 a lso agreed that the binding between the first PTFE transferred film and active metal surfaces is not of a van der Waals nature but rather of a chemical nature via the fluorine atoms. In spit e of this chemical bonding, the wear rates of PTFE rubbing against different metallic counterfaces (i.e. active an d inert) were nearly the same. This phenomenon was explained by Gong et al.55 on the basis of poor adhesion between the second, third, etc. layers of the transfer film which allow s for a low shear strength sliding int erface compared to the stronger bonded interface between the metal and the first layer of the transfer film. A third hypothesis generally present ed in the literature involves fillers preferentially supporting the load during compressing and sliding of the PTFE composite. From his experiments on the dry sliding of carbon fiber reinforced PTFE, Lancaster56 found that fibers are exposed at the sliding surface and thus, su pport part of the applied load. Additionally, the fibers smooth the surface of the counterface, thereby reducing the localized stre sses at the asperit y contacts. Likewise, Arkles et al.57 emphasized the necessi ty of exposing the filler, which bears most of the load, thus protecting the PTFE matrix from wear c ontact to the sliding surface. Gong
27 et al.58 also supported the previous hypotheses that the load -supporting action of fillers may be the main mechanism in reducing wear of PTFE based composites, although the presence of the filler may change the mechani sm of formation of wear debris. 1.5 Motivations and Objectives In the previous sections, many important engineering propertie s of PTFE have been discussed. Exploitation of these properties has led to widespread usage in a variety of applications and indu stries. With regard to tribology, t he major drawback of PTFE is its excessive wear. For demanding applications requiring extreme conditions (i.e. large temperature ranges, high sliding rate high contact pressures, long service life etc.), improvement of PTFEs wear behavior is need ed while maintaining its low friction response. Section 1.4 .4 discussed various approaches from the literature that have tried to address this need. In work discussed here a different approach is taken in which the atom ic s cale phenomena between two PTFE crystalline surfaces in sliding contact are examined. The idea is to obtain molecular insights into PTFEs low friction and high wear rate by examining the process of crystalline displacement using atomic level simulation T o accomplish this, several trib ological conditions were varied A few questions to be answered are: (i) Is crystalline PTFE -PTFE sliding behavior representative of the tribological behavior of the overall semi -crystalline bulk polymer? (ii) What are the do minant microscopic mechanisms associated with the destruction of PTFE surfaces (i.e. PTFE transfer films)? (iii) Are these mechanisms affect ed by the mechanical rigidity of the crystalline phase or by temperature, sliding velocity and contact pressure? (iv ) Will a molecular, fluorocarbon fluid at the interface between the two crystalline surfaces significantly alter the tribological behavior of the polymer surfaces ? If so, how and by what mechanisms is the behavior altered?
28 Figure 1 1. Schematic of a contact point of two rough surfaces (a) and the separation of these contact points or asperity peaks by a fluid (b).
29 CHAPTER 2 SIMULATION METHODOLOGY 2.1 Molecular Dynamics Sim u lation Overview Molecular Dynamics ( MD) simulation is a numerical t echnique used to determine the equilibrium and transport properties of a classical many -body system.59 The system being simulated is classical from the standpoint that its particl es (e.g. atoms, molecules ) are treated as obeying the laws of classical mechanics. In MD simulation, Newtons second law of motion is solved as atoms interact among themselves via an inter atomic potential. The relation is as follow s : i i i iE dt d m r r F 2 2 (2 1) where Fi is the force vector, mi is the mass and ri the position vector of atom i ; t is time and E is the potential energy of atom i Th e technique is a very useful one for a wide range of materials. Quantum effects are usually neglected and are considered only when deal ing with the translational or rotational motions of light atoms or molecules (e.g. He, H2, D2) or vibration motion with a frequency such that h > kbT.59 An MD program is made up of three major essential components or sections coupled with auxiliary methods or techniques used to achieve a variety of simulation or experimental conditions. The flow of a simple MD program may read as follows: initialize the simulation at time equals zero then w hile time is less than the maximum desired simulation time, evaluate the forces on all t he particles in the system, advance the position of the particles with time based on the force s acting on them, increment the simulation time counter and sample averages for properties of importance (see F igure 2 1 ). The three indispensible components, whi ch may be deduced from the previous description, are: 1) initialization, 2) determining of the forces and 3)
30 advancement of the system with time. The initialization step requires the definition of a material system. This is often given in the form of a mat hematical structure file that relates the type, starting position, velocities and accelerations of the particle s in the material system to be explored. For proper initialization of the simulation program, additional information may be specified. These incl ude but are not limited to length of time to simulate, how often to advance the system with time (i.e. size of the time step), parameters for potentials energy expressing being used and setting options for the thermostat or barostat method being used. A no ther important component of MD simulation is evaluation of the forces which is accomplished via the manipulation of a material specific inter atomic potential This portion is arguably the heart and soul of the simulation program as it deals directly with the degree of accuracy to which the material s ystem can be describe d An inter atomic potential that does not describe the essential physical and chemical phenomenon of the material system under inve stigation will give nonsensical simulation properties. Thu s, simulation results are only as good as the inter atomic potential used to capture the science of the material system The inter atomic potentials used in this work are discussed in S ection 2.2. In conjunction, an accurate and efficient method for advanc ing the position of the particles in the system with time is necessary to achieve correct, thermodynamic equilibrium properties. The integration method used in this work is th e predictor -corrector algorithm. It is described in detail in S ection 2.3. There are a number of factors to consider in choosing an integration algorithm.60 The algorithm should be fast and require minimal amounts of memory. It should a llow for the use of a reasonably long time step. This would allow for faster computing of material averages over relatively larger times. It s hould replicate the classical trajectory of the
31 system particles as closely as possible while satisfying known conservation laws for energy and momentum. Additionally, it should be time reversible and relatively simple to program. 2.2 Calculation of Inter -atomic Forces 2.2.1 Reactive Emp i rical Bond Order (REBO) Potential A carbon -hydrogen -fluorine (C H -F) many body empirical potential ,61 based on Brenners secondgeneration reactive empirical bond-order (REBO)62 potential for hydrocarbons was used for a ll simulations in this study. The C H version of the REBO potential developed by Brenner was based on the Abell Tersoff bond-order potential which has been used to explore cluster surface impacts, chemical vapor deposition of diamond films and surface collisions.6366 To develop the potential used for the simulations in this work, two -body parameters for carbon fluorine (C -F) and fluorine -fluorine (F F) interactions was used from a version of the Br enner potential customized by Grave et al .67,68 with H -F interactions obtained from semi -empirical AM1 calculations .68 70 The total binding energy for the atomic potential is given by i i j ij vdw ij A ij ij R ij br V r V b r V r E ) ( (2 2 ) VR(rij) and VA(rij) are pair -wise additive interactions that represent respectively inter atomic repulsion and attraction due to electron -electron and nuclear -nuclear repulsion and electron nuclear attractions. The functions rely strictly on distance between pairs of nearest neig hbor atoms i and j which is noted by the term rij. The term bij signifies a bond-order term to account for many -body interactions between atoms i and j and thus, incorporates nearest neighbors and angular interactions. The Vvdw(rij) term denotes the van de r Waals long range interactions and are used to describe the dispersion force s within the polymeric system. The Vvdw(rij) term was implemented using a Len nard Jones potential an d is discussed in detail in S ection 2.2.2 The
32 functions employed for the repul sive and attractive interactions are identical to those developed by Brenner et al .62 The terms take the following forms: ijr j i ij c ij Re A r Q r f r V 1 ) ( (2 3 ) ij nr n n ij c ij Ae B r f rV 3 1) ( (2 4 ) -body parameters and were adopted from the previous versions of the REBO potential.62,68 A detail ed listing of all the parameters used for the C H -F version of REBO used herein is given in the publication by Jang and Sinnott.61 The function fc(rij) limits the range of the covalent interactions. This ensures that only nearest neighbo r interactions are considered. The bond-order function is given by: ij ji ij ijb b b b 2 1 (2 5 ) The terms ijb and jib respectively represent the local coordination an d bond angles of atom i and j. The term ijb is used to describe radical character, influence of dihedral angles on C C double bonds and also conjugated systems.62 Its form is given by DH ij RC ij ijb (2 6 ) where RC ij describes whether the bond between atoms i and j is part of a conjugated system or is radical in character while DH ij is for dihedral angles in C -C double bonds.62 Additional detailed functional expre ssions, parameter values etc. are noted in the references given herein.
33 2.2.2 Len nard Jones (LJ) 12-6 Pote ntial The Leonard Jones potential60 was use d in this work to describe the long range van der Waals interactions in the fluorocarbon system Of the various forms of the potential, the 12 6 form was for the work in this dissertation. The form is given by 6 124ij ij ij vdwr r r V (2 7 ) where ) (ij vdwr V represents the cohesive energy with rij being the distance between atoms i and j. The parameters and represent respectively the depth of the potential well and the distance at which the potential energy function is zero (0). The te rm 1/r12 denotes the short ranged repulsive interaction between atoms according to the Pauli Exclusion Principle which asserts that strong electron cloud overlap results in an abrupt increase in energy. Conversely, the term 1/r6 corresponds to the relative ly long ranged attractive interaction due to van der Waals dipoledipole interaction. The Lorentz Ber th elot combinatio n rule was to calculate the para meters and for the interaction of different atoms types. For example, given that the parameters and of the same atoms type may be given by aa and aa, and parameters for atoms X and Y are given by xy = ( xx + yy) (2 8 ) xy = ( xx yy)1/2 (2 9 ) Parameters CC FF CC and FF used for the simulation described herein are given in T able 2 1 2.3 Integration Method The finite difference approach is a standard method used with atomic level simulations to advance the system with time One of the assumptions of the finite difference approach is that if
34 the atomic positions, velocities and other dynamic system information at time t are known these values may be determine d at time t + t with a good level of accuracy. For the simulations described herein, a third order Nordsieck Gear predictor corrector59,60 algorithm was used. The predictor corrector algorithm works as follows. Given the dynamics of the system at time t and assumi ng a continuous classical trajectory of the particles (e.g. atoms), an estimate of the positions, velocities, accelerations etc. at time t + t may be predicted using a Taylor expansion about time t: 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 10) pr pv pa and pb are respectively the predicted (hence the subscript p) position, velocity, acceleration and third derivative of the position of a particle (e.g. atom) in the system. Equation 2 10 represents a truncated form of the Taylor expansion, after the 3rd derivative. Greater accuracy in the determination of atomic trajectories may be achieved by using higher order nth derivatives or by using a smaller time step, t. The aforementioned trunc ations, in addition to the finite representation of numerical digits within computer systems introduce errors which are compounded for long simulation times. Given that no integration algorithm can provide an exact solution, a compromise must be made to ac hieve a reasonable balance between accurate prediction of atomic trajectories and computational speed. The prediction system dynamics are now to be corrected, as the name of the algorithm suggests. This is predicted by evaluating the forces and hence the accelerations (i.e. a, = fi/mi).
35 This yields the correct ed accelerations t t ac at time t + t. The correct accelerations are then compared with the predicted accelerations from equations (2 10) to estimate the size of the error in the prediction step: t t a t t a t t ap c (2 11) The size of the error given in equations (2 11) is then used with the predicted positions, velocities and other derivat ives of position (see equation 2 10) to obtain a more accurate approximation of these values The new or correct ed values are given by equation (2 12). 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 12) These corrected values are in turn used to predict the next n derivations for the following iteration for the advancement of the system with time. This co rrector step may be iterated to obtain even new er correct ed accelerations from the correct positions of equations ( 2 12). This results in a further refining of the positions, velocities and other time derivatives with respect to the atomic positions. T he evaluation of the accelerations and hence the forces are the most time consuming portion of molecular dynamics simulations; thus, usually one or two corrector steps are implemented. 2.4 Thermostat Method In order t o control the temperature of a system, a thermostat is typically applied. In this study, a Langevin thermostat was employed where the thermostated atoms obeyed Langevins equations of motion71,72 (see equation 2 13) instead of Newtons second law :
36 f r f v a m (2 13) where m, a v are respectively the particles mass, acceleration and velocity. r f and f are the frictional constant, conservative force and the random force respectively. is a fixed positive value. The negative sign is used since friction acts against sliding. Thus, the term s v on the right hand side of equation (2 13) maybe referred to as a frictional force as it removes excess energy from the system and consequently serves to decrease the temperature. The conservative force is obtained from the inter atomic potential. The random force is dependent on the required system temperature and the time step t used for advancing the system with time. It is randomly obtained from a Gaussian distribution and adds kinetic energy to an atom. As a result, the systems temperature is mai ntained by balancing the frictional force and the random force. 2.5 Period ic Boundary Conditions Atomic level simulations, including molecular d ynamics attempt to provide useful information about macroscopic properties of materials systems. Due to current limitations in computer speed and memory/storage capacity, the number of atomic interactions considered range from a co uple of hundred to a few million. This number is very far from the thermodynamic limit Additionally, for a three -dimensional system with free boundaries consisting of N number of atoms, the fraction of all molecules located at the surface is proportional to N1/3. Hence, for a simple cubic crystal consisting of 1000 atoms, approximately 49% of the atoms are loca ted at the surface. For a 106 atoms system, this number drops only to 6%.59 Consequently, to obtain more accurate macroscopic behavior, pe riodic boundaries which allow for an N atom system to be surrounded by an infinite bulk of si milar atoms were employed (see F igure 2 2 ).
37 In Figure 2 2 the highlighted simulation box with four (4) particles is replicated in space to construct an infinite lattice. As the system evolves, particles move within the system (noted by the highlighted cell). The particles in the other cells, representing the periodic image of the highlighted cell, mov e in exactly the same way Thus, if a particle were to migrate ou t of the highlighted cell through a particular edge (e.g. particle 1 leave via the top edge), one of its periodic images would enter the highlighted cell in the same manner through an opposite edge (e.g. particle 1 enters via the bottom edge). In this fash ion, the number of particles in the highlighted cell (i.e. the system) is conserved. 2.6 Benefits of Atomic -level Simulation The true power of MD simulation can be realized when the technique is used to complement find ing s from experiment and /or theory. MD allows for the specification of and the tracking of the time dependent position of every atom in a given material system. T his feature provides the capability to directly manipulate the microstructure and corresponding chemistry for a given material sys tem. As a result, features that are inextricably intertwined during the performing of an experiment may be isolated. For example, for the tribological simulation of a semi -crystalline polymer, a system consisting of a 100% crystalline phase may be specifie d to determine its friction and wear contribution to the overall semi -crystalline polymer while potential mechanisms for the amorphous phase s are isolated. A similar approach may be applied to polycrystalline ceramics or metals where the effect of dislocat ions may be separated to highlight that of grain boundaries and vice versa. Such control over a systems microstructure may also help to quickly clarify trends. For instance, the thermal conductivity of a given material may be affect ed when it is doped wit h atoms of a given element. To clari fy the source of the effect of the dopant atom, a systematic test of characteristically similar dopant atoms may be easily specific to determine any potential radii, valance or mass effects. In addition to these
38 capabilities, MD provides to ability to clarify atomic level process and mechanisms which are often difficult, if not impossible to capture during experiments. In addition, atomic level simulation results may be compared directly with theory. Given a parti cular scientific problem, exact model s may be constructed. From these models, approximate theories may be devised, from which in turn, theoretical predictions may be made. Simulation results on the exact model s may be compared to theoretical predictions f rom the exact model s in order to identify any potential faulty assumption in either the theoretical predictions or approximate theories. In this work, atomic -level simulations are used to provide insights into areas that may be problematic for experimenta l approaches to capture. Specifically, the tribological properties of PTFE are address with emphasis placed on the atomic level processes associated with the polymers high wear rate. The e ffects of the amorphous phase of this semi -crystalline polymer are isolated by simulating a 100% crystalline structure.
39 Figure 2 1. Flow chart of the major components of a simple MD program. start initialization force calculation integrate equations of motion is time up? end yes no
40 Figure 2 2. Schematic representation of a four particle system employing periodic boundary conditions. Table 2 1. LennardJones parameters used carbon and fluorine atoms utilized for the simulations described in this work. Atom ) b C 3.35 51.2 F 2.81 62.4
41 CHAPTER 3 FOUNDATIONAL APPROAC HES TO SYSTEM SPECIFICATION SIMULATION CONDITIONS AND DATA ANALYSIS 3.1 Building of Crystalline PTFE Surfaces The process of building crystalline PTFE surfaces for the simulations described in this work may be described as an endeavor character ized by an equal mixture of artistry and science As mentioned in S ection 1.4.1, there are four well -characterized solid phases of PTFE .13,73 Construction of the crystalline PTFE surfaces started with building of a hexagonally packed, high pressure non -helical phase. The model system simulated in this work was a fully crystalline PTFE phase with no amorphous regions Figure 3 1 illustrates the system setup. Each PTFE surface contains seven layers of chains for a total thickness of 4.0 nm and a sliding surface area of 4.5 nm x 4.5 nm. The PTFE chains in the bottom layer of the bottom surface were held fixed, while the PTFE chains in the top layer of the top surface moved as a rigid unit to compress and slide the top surface against the bottom surface. Sliding was carried out in the direction along the chain alignment and perpendicular to the chain alignment in both surfaces (i.e. parallel and perpendicular sliding respectively). A combination of parallel and perpendicular sliding (i.e. the violin configuration) was also explored (see Figure 3 1). Each surface is divided into a thermostat region for administer ing of the systems temperature and an active region in which atoms evolve without constraint under the inf luence of dynamic system f orces Given current limitations in the number of atoms that may be reasonably simulated using MD simulations two approximations were made. First, periodic boundary conditions (see S ection 2.5) were used to simulation an infinite sliding interface between the two crystalline PTFE surfaces. Second, fluorocarbon cross links were introduced between chains in the hexagonal structure to simulate the rigidity and mechanical integrity of the polymers crystalline phase.
42 T he second approximation proved to be more difficult to implement. Cross linking was accomplished by utilizing two to three linked branches of (CF2) units to form a fluorocarbon branch between the polymer chains to establish rigidity, stability and inter chain load transfer pathways The carbon atoms in the PTFE chain to which the fluorocarbon branch was to be attached was unsaturated in that one of its fluorine atoms (on the side of the chain to which the cross -link were to be attached) was removed. Thus, upon attachment of the cross -link, the c ha in carbon atom in question beca me saturated with a coordination number of four (i.e. by two PTFE matrix carbon atoms within the linear chain, one carbon atom from the adjoining cross link and one fluorine atom on the side of the chain opposite to that of the cross link). Two to three linked ( CF2) units were chosen for forming cross -link braches due to the proximity of their total length to that of the equilibrium distance between adjacent PTFE chains. The fluorocarbon branch when considered as part of a polymer chain segment normally maintains an average C C -C dihedral bond angle of ~ 116 with a total end -to -en d carbon distance of ~ 2.62 This consideration, when combined with the equilibrium spacing of the PTFE chains, did not make for an exact fi t of the rotated fluorocarbon branch within the PTFE chain structure to act as an unstrained cross -link. The problem stems f r o m the fact that given the equilibrium constraints ( see F igure 3 2 ), t he bond length between the end carbon atom of the cross -linking branch and that of the unsaturated PTFE matrix chain carbon were either too long or too short (i.e. longer or shor ter than the C C bond length of 1.54 ). Additionally, the C C C dihedral bond angles were significantly different from the equi librium value. Utilizing these constraints led to structures that, once relaxed in an MD simulation contained a significant number of carbon atoms with defects with respects to both over and under coordination due to cross -link breakage resulting from exc essive strain In some case, high energy configurations in
43 which fluorine atoms w ere too close to each other beca me dislodged from the ir respective carbon atoms during the simulation s Ultimately, a modified approach was taken in which the fluorocarbon cro ss-link branch was slightly altered to fit between the hexagonally packed PTFE chains with minimal st rain on the overall structure. This was achieved by introducing small strains in each of the cross link branch atomic bonds (i.e. C -C and C F ) and als o by arbitrarily orienting the C -F bonds in space to maximize distance between fluorine atoms on neighboring carbon atoms, especially those from carbon atoms within the linear chain of PTFE matrix The C C C dihedral bond angle between the cross link branch and the PTFE matrix polymer chain were also modified slightly from their equilibrium values These concession s were made in order to ensure that cross links remain bonded to the PTFE hexagonal matrix during simulation. These modifications were explored by hand in the Chemcraft visualization program prior to testing with our in house MD simulation code For the res ults to be discussed in S ection 3.3, two different types of cross -link ed approaches from a construction standpoint were explored. In the modified, cr osslink ed approach, much effort was taken to reduce the strain on the cross -links to ensure proper coordination using the Chemcraft visualization program as previously described. In the unmodified cross -link ed approach, the cross links were built without careful attention paid to the induced strain on the equilibrium structure spacing. 3.2 Approaches to Cross-link Distribution For the crystalline PTFE surfaces simulated in the work, two general approaches to cross link distribution were implemented. The fi rst may be classified as a symmetrical approach whi le the second was more random or nonsymmetrical in nature. In both approaches, the system size was the same; thus, the periodic chain length over which the cross links were distributed was ~45 Four different cross -link branches were built to establish linkage between a given chain
44 and the four surrounding, neighboring chains in the hexagonal lattice (see F igures 3 1 -A and 3 2 ). Two cross-link branches of each type ( i.e of the four types ) were placed at a rbitrary sites al ong each chain molecular axis. Thus, each chain had eight branches attached to its molecular axis. This arrangement was replicated in the three dimension ed space ; hence, the notion of a symmetrical cross linked structure as the cross l inks w ere placed at symmetrically identical lattice or chain positions in space For the nonsymmetrical cross -linked structure, a particular target linear cross linked density was chosen prior to building the structure. Every other carbon atom along the PTFE m atrix molecular chain axis was deemed to be a potential cross -link site. A random number gener ator with a uniform probability distribution was then used to determine if a given si te was to be cross linked based on the chosen linear cross linking density (e.g. 10% coverage of po tential cross -link sites along a given chain backbone ). In this manner, random distribution of the cross links with in the PTFE surfaces was achieved as the cross links placements yielded a structure whi ch was nonsymmetrical 3. 3 Effect of Cross -link Morphology and D ensity on Crystalline PTFE PTFE sliding Since the structural integrity of the polymer surface was provided for by cross link branches, the rigidity of the crystalline surfaces and hence, thei r tribological properties will, of course, depend on the density and distribution of cross links. However, even for a given nominal cross -link density, it is important to assess how the microscopic details of the cross linking affect the frictional behavio r. We have therefore generated two different cross linked structures, each with a density of 8 cross links per ~ 4.5 nm of chain length. In the unmodified, symmetrically cross -linked structure the cross links were introduced without any attention to the s trains that they produce in the system. Consequently, after compression and equilibration of this structure, we find that 85% of the atoms in the system are four -fold coordinated (assumed to be sp3
45 hybridized), 13% three -fold coordinated (assumed to be sp2 hybridized), and 2% two-fol d coordinated (assumed to be sp hybridized). In the modified, symmetrically cross linked structure, considerable care was taken to cross link in a manner that reduces the strain in the system. For this structure, after compressi on and equilibration, there were 78% sp3 hybridized, 22% sp2 hybridized and 0.08% sp hybridized carbon atoms in the system. This difference between the hybridizations of the two systems is actually quite large because only 25% of the carbon atoms is in the cross -links. Figure 3 3 compares the friction coefficient for perpendicular and parallel sliding configuration for the two different cross link branch morphologies. Reassuringly, the frictional coefficients predicted by the simulations are very sim ilar, indicating that the variations in microscopic details of the cross -linking explored here do not significantly affect tribological behavior. Using an approach similar to that taken for making the modified nonsymmetrical cross linked structures, the s ensitivity of aligned PTFE PTFE sliding to cro sslink density was explored. Two different linear cross -link densities, where there is between 6.8 and 11.2 on average, between cross links were considered. The frictional response, as a function of normal lo ad was probed at 300K. Figure 3 4 illustrates the frictio n behavior for the two modified nonsymmetrical cross link structures in addition to that for the unmodified, symmetric cross link structure with cross -link spacings of ~ 6.2 on average between cr osslinks The graph shows that for the perpendicular s liding configuration (F igure 3 4 -A ), the behavior of the PTFE systems are almost identical for the two modified nonsymmetrical cross -link implantation with average spacing s of 6.8 and 11.2 By contrast the friction response for the PTFE system with the unmodified, symmetrical cross link implementation (with average linear intercross link spacing of 6.2 ) was more varied and followed a more stair step pattern, as opposed one of
46 steady, monotoni c friction increase with increasing normal load. Correspondingly, the latter experienced a greater degree of interfacial molecular rearrangement (confirmed visually through molecular movies) than the modified, nonsymmetrical cross linked system. The more s evere wear behavior of the unmodified symmetrical cross link system may be due to the non uniformity of stress distribution through the system which may have led to more systematic and catastrophic failures The amount of energy required to deform and rea rrange the interfacial chains resulted in a higher frictional forces for normal loads greater tha n 10 nN; thus, a higher friction coefficient was observed. For the parallel sliding configuration, minimal wear and relatively low frictional forces were observed for all three cross link densities. Given the minimal amount of molecular rearrangement at the sliding interface, it is no t surprising that the unmodified symmetrical cross linked and the modified, nonsymmetrical cross linked system s (6.2 and 6.8 o n average between cross links respectively) displayed almost identical behavior. At first glance, it may be s omewhat surprising that modified, nonsymmetrical cross linked system showed superior friction behavior than the more highly cross linked ones Careful inspection of F igure 3 4 B reveals that for load s less than approximately 10 nN, the relatively low cross linked PTFE system (i.e average of 11.2 between cross links) shows frictional responses that mirror that of the more densely cross -link ed syste ms For normal loads greater than ~ 10 nN, the less crosslinked structure clearly outperforms the more highly cross linked ones. This behavior may have much to do with the relative stiffness of the systems with the idea being that the polymer chains for the more highly cross linked systems experience greater restrictions. This is in contrast to a similar PTFE system with a lesser degree of cross linking. In the latter case, interfacial chains are less restricted and thus may be able to more effectively undergo relaxation in response to
47 normal and shear forces; hence, the more favorable frictional response at the higher normal loads explored for the less densely cross link PTFE system Such interplay involving spacing between the cross li nk and natural backbone rela xation processes has been noted in other polymeric systems.74 Nonetheless, beneath a critical crosslink density and high enough normal load, a lightly cross linked crystalline polymer surface, as those previously described for these simulations would sustain catastrophic level s of damage under sliding conditions as the structure may not have the strength to support loading as a cohesive solid 3.4 Effect of Sliding Velocity on Crystalline PTFE PTFE Sliding Experimental sliding rates in tribology generally range from millimeters per second to about ten meters per second (in, for example, computer hard dri ves) .75 MD simulation models full atomistic motion, including atomic vibrations that occur on femtosecond timescales, and involve the step -wise solution of Newtons equation of motion; it is therefore only computationally poss ible to usefully simulate sliding rates at the high end of this range. Numerous comparisons of experimental data to MD simulation results, however, indicate that important physical insights can be obtained from simulations that enhance understanding of the experimental re sults even if the sliding rates are significantly faster than experimental values Although it has been noted that the friction coefficient of self -mated PTFE increases with sliding rates spanning four orders of magnitude,76 a considerably narrow er range is considered here. The main objective is to establish that the simulation rates accessible to simulation (>5 m/s) yield reliable information on the tribological behavior of this crystalline PTFE system. A second objective is to identify the fastest sliding rate that will give phy sically reasonable results thereby maximizing the computational efficiency of the simulations. The focus in this section then is on two aspects of the effects of sliding rate: its effect on the temperature of the system and on the compressive and frictional forces, or friction coefficient.
48 To examine the effect of slid ing rate on the frictional behavior of the crystalline PTFE surfaces two scenarios are considered: (i) a sliding direction that is perpendicular to the direction of chain orientation in both the top and bottom surfaces ( perpendicular sliding, Figure 3 1 B), and (ii) the sliding direction is parallel to the direction of chain orientation in both the top and bottom surfaces ( parallel sliding Figure 3 1 D ). In these sliding velocity studies, the unmodified, symmetrica l PTFE surfaces were used (see S ect io ns 3 1 and 3 -2 ). The corrugation of the chains leads to large energy bar riers to slidin g in the perpendicular configuration ; this is very disruptive to the materials structure. For parallel sliding the chains can slide without any significant local structu ral rearrangements. The focus of this section is not on the physical interpretation of the results, but simply on establishing the effect of simulation conditions on the results. The frictional work generates a substantial heat flux that must be rapidly dissipated in order to prevent excessive temperatures in the contact (e.g. for 100MPa pressure, =0.1, and v =10 m/s the heat flux is order 100 MW/m2).15 Since the heat flux is stationary from the point of view of the simulation, the dissipation mechanisms require that this energy is removed from t he interior of t he surface through the thermostated regions. If this heat transfer is too slow, then a substantial temperature rise can take place at the interface, leading to morphological changes within the polymer surface changes in the friction coefficient, and anoma lous changes in the wear rate at the sliding surfaces. In simulation, we can expect to observe similar undesirable effects if excess heat generated at the surface is not adequately transported to the thermostated regions and dissipated. It is therefore imp ortant to establish that the system temperature is maintained despite the energy added by friction and wear at the interface.
49 Figure 3 5 illustrates the average temperature in the simulation as a function of sliding distance for sliding rates in the range of 5 100 m/s. For both parallel and perpendicular sliding, the temperature remains very close to the target of 300 K for sliding rates ranging from 5 m/s to 20 m/s. However, at higher sliding rates of 50 m/s (for perpendicular sliding) and 100 m/s (for bo th parallel and perpendicular sliding) there is substantial system heating with the extent of heating increasing as the sliding rate increases. This heating of the system arises from a combination of two effects. First, the heat itself must be transported from the sliding surfaces as lattice vibrations mediated by both the van der Waals interactions b etween the chains and the cross -links; there is a limit as to how much heat can be conducted through the relatively low density of cross -links in this system. Second, the thermostat itself has a limited ability to regulate the temperature of the system and can be overloaded if too much heat arrives too rapidly. Our conclusion is thus that for this polymer morphology and thermostat, the sliding rate should be 20 m/s or less. Having established that there is no excessive heating for rates up to 20 m/s, it is also important to establish the range of sliding rates over which the frictional behavior is unchanged. In particular, for computational efficiency, we would like to establish the maximum viable sliding rates Fig ur e 3 6 illustrates the normal and tangential or frictional forces associated with the perpendicular and par allel configurations at sliding rates of 10 and 20 m/s averaged over 0.01 ns intervals : these fixed time averages correspond to different sliding distances depending on the rate. In analogy with the usual Amonton macroscopic definition, t he microscopic coefficient of friction, is defined as the ratio of the change in the frictional forc e to the normal force: = FF/FN. For both parallel and perpendicular sliding the normal force is consistently higher than
5 0 the frictional force, thus giving coefficients of friction that are less than unity. Furthermore, although the values of the normal forces for both the perpendicular and parallel sliding configurations are initially identical (approximately 5 nN), the normal force for the perpendicular sliding fluctuates while that for parallel sliding remains fairly constant after an initial gradual d rop. This differing behavior arises because in the perp endicular sliding configuration the normal force is larger when the interfacial chains from the top PTFE surface are directly on top of the interfacial chains in the bottom PTFE surface and somewhat smaller when the chains from the top PTFE surface fit in to the inter -chain grooves of the bottom surface In the case of the parallel configuration the chains from the top PTFE surface remain in the inter -chain grooves of the bottom surface throughout slid ing; he nce, there are weaker fluctuations in the normal force with sliding distance. Similar force curves are obtained at sliding rates of 5 and 15 m/s. Fi gu re 3 7 illustrates the evolution of the friction coefficient ( with sliding distance at the slowest and fasted sliding rates investigated: 5 m/s and 20 m/s Here is determined from the sliding distance a veraged forces shown in Figure 3 6 ; using this ratio of the averages, rather than the ratio of the instantaneous forces, significantly redu ces the noise in the calculated values. Although there are small variations among the data sets at all four sliding rates (data for 10 m/s and 15 m/s are not shown for the sake of clarity) the overall trends are remar kably similar at all four sliding rate s which suggest that the microscopic process es are also similar. To establish that the microscopic behavior is indeed similar at different sliding rates, we examine the evolution of the structure of the films in detail; Figure 3 8 shows three snapshots from perpendicular sliding simulations Each is an edge -on view of the system in which the top layer of the top surface is sliding to the left at a fixed rate To clarify the atomic level processes that are occurring, only three init ially vertical slices of atom s are visualized. The positions of the
51 same atoms in their in itial positions are shown in panel a and are shown after 10 nm of sliding at 5 m/s a nd 20 m/s in panels b and c respectively While there are clearly some microscop ic differences between the two systems, the general level of damage (e.g., number of small polymeric fragments) and the roughness of the tribological surface are similar. The results and analyses in this section establish that simulations with sliding rate s ranging from 5 m/s to 20 m/s yield physically reasonable results with no apparent simulation artifacts. 3.5 Least Squares Fitting for Calculating Friction Coefficients and Adhesive Forces The approach to analysis for frictiona l data reported in C hapters 5 and 6 are explained in this section. The data analyzed using the approach described here were taken from simulations consisting of 24 to 36 nm of sliding, carried out at 10 m/s with a 0.2 fs time steps. Data points were taken every 1000 steps (eq uivalent to 200 fs of time and 2 pm of sliding); which yields approximately 12,000 to 18,000 instantaneous values for the frictional and normal force pairs. Here, a concise explanation is given to describe the process used to reduce this large data set to scientifically and statistically meaningful results. First, this large number of data points was reduced using boxcar averaging of 100 data points corresponding to 0.2 nm of simulated sliding. This distance was chosen as it is comparable to the spatial res olution of microscopic tribological experiments. For the ith boxcar, the average force is fi and its standard deviation is i. The standard deviation of the mean, i point data sets was also determined. These 0.2 nm averaged forces and were then used for the calculation of the average forces. The quantification of the forces were calculated using a weighted average:77
52 N i 1 wifi fbest = ___________ (3 1) N i 1 wi where wi = 1/ i 2. The uncertainty in the weighted average force was then calculated in the standard way as: best = ( N i 1 wi)1/ 2 (3 2) The process defined above is not unique, in that different choices of the size of the boxcars would yield slightly different final results ( see T able 3 1). The nonuniqueness of the analysis notwithstanding, we justify the particular choice of the size of the boxcars as being representative of the spatial resolution achievable in atomic force microscopy experiment s The first 2.4 nm of sliding was omitted from the calculation of all averages so as to exclude the initial ela stic response of the two polymer system s to shear stress. For many tribological situations, the friction coefficient is defined as = ff / fn where ff is the frictional or lateral force and fn is the normal force. In this work, simulations were carried out such that the different fric tional forces were determined for a number of different normal loads; similar normal loads were used for perpe ndicular and parallel sliding. The related uncertainties for each ff and fn were calculated as described above. A Monte Carlo method was used to determine the friction coefficient from the force data. In particular, for each of the (ff, f) and (fn, n) pairs, approximately 2,000 statistical justifiable possible friction and normal forces were generated in Microsoft Excel using a one -dimensional
53 ra ndom walk where the (n+1)t h value for ff is determined from the nth value according to ff (n+1) = ff (n) + f, where is a ran dom number between 0.5 and 5. This process leads to a statistically normal distribution in ff as is illustrated in F igu re 3 9 A least -squares fit was then calculated for each set of the new data (ff(n) and fn(n) and their uncertainties) generated. The average slope of these least square fits we re taking as our best approximation of the friction coefficient. The standard deviati on of the mean was taken as the uncertainty in the measurement. Fi gu re 3 10 illustrates a few examples of the least square fits calculated from the generated data Calculation of friction coefficients in this manner also allows for the determination of th e adhesive contribution to sliding friction which may be approximated as the value of the x inter cept of the least squares fits. As in the case of the coefficient of friction, the average of the x intercepts of the least square fits and the corresponding s tandard deviations of the mean were taken as the best approximation of the adhesive force an d uncertainty respectively. This approach to determining the friction coefficient and adhesive forces yields results that are almost identical to that obtained fro m the original, unreduced data set for ff and fn. Averages for ff and fn for the original data set were computed by taking the ari thmetic mean of the data sets. The uncertainty for each mean is given as the s tandard deviation of the mean. Table 3 2 gives numerical values for friction coefficient and adhesive force based on reduced and u nreduced force averages. The numerical values obtained were identical except for the adhesive force for the p arallel sliding configuration. The difference in the adhe sive force for the parallel sliding configuration is accounted for by the fact that the y intercepts of the least sq uare fits are between 1 and 0. As a result, small variations in this value leads to what appears to be significant changes in the x intercep ts which corresponds to the adhesive force. The uncertainties in and
54 fa, determined from the standard deviation of the mean and the propagation of uncertainties ,77 are not shown since the values are significantly smaller than the calc ulated averages. 3.6 Summary The approach taken in the building of crystalline PTFE surfaces for MD simulation was described. Fluorocarbon cross link bra n ches were employed within the PTFE surfaces to simulate the rigidity and mechanical integrity of the c rystalline polymer phase. The effect of two different cross link morphologies, along with random and non-random cross link distribution in the context of sliding configuration, was explored. Results showed similar tribological trends for both cross link morphologies. With regard to cross -link distribution s the random cross link distribution showed more favora ble tribological responses from both a friction and wear standpoint, especially for the perpendicular sliding configuration. Additionally, the effect of cross -link density was considered. The results showed that for the perpendicular sliding configuration, the friction response for PTFE surfaces with averages spacing of 6.8 and 11.2 between cross links were essentially identical. For the parallel slid ing configuration, the PTFE surfaces with an average of 11.2 between cross links demonstrated lower friction. In addition the effect of sliding rate on the tribological performance of crystalline self mated PTFE was investigated. It was found that signi ficant frictional heating occurred for sliding rates in excess of 20 m/s for both sliding configurations while the overall tribological behavior remain fairly consistent for sliding rates in the range of 5 20 m/s. Finally, the approach used for calculating average forces, friction coefficient and adhesive forces was explained. The foundational results obtain from this study are related to the studies of C hapters 4, 5 and 6 as follows. A sliding velocity of 10 m/s was chosen for all remaining studies For the study in C hapter 4 on sliding orientation and also for the effect of normal load and temperatur e in Chapter 5, the symmetrical, unmodified PTFE cross -link surfaces were employed to maintain
55 strict consistency and continuity with the PTFE samples that w ere already in used at the beginning of t hose studies. For the work in C hapter 6 on the effect of fluorocar bon molecular fluids at the sliding interface between the two crystalline surfaces, the nonsymmetrical, modified cross -link PTFE surfaces at a linear cross link density of 11.2 were utilized.
56 Figure 3 1. (a) Simulation cell of two al igned, cross linked PTFE surfaces. Each surface is ~ 4.0 nm think with rigid, thermostat and active regions of approximately 0.6, 1.2 and 2.2 nm thickness respectively. The system is periodic along the x and z directions. Schematic views of the x -z plane at the sliding interface for (b) perpendicular, ( c ) violin an d (d) parallel sliding are shown The dark colored polymer chains are at the interface of the top PTFE surface while the light ly colored chains are at the interface of the bottom PTFE surface
57 Figure 3 2. Schematic of the PTFE surface chain arrangement. The figure highlights the physical barriers to smooth sliding for the three sliding configurations considered.
58 Figure 3 3. Comparison of the Amonton friction coefficient (i.e = ff/fn) for perpendicular (a) and parallel (b ) sliding at 300K with sliding velocity of 10 m/s for two different polymer cross link morphologies. Figure 3 4. Illustration of the friction respons e with respect to nor mal load for perpendicular (a) and parallel (b ) sliding at different cross li nk densities and distribution. The op en symbols represent unmodified symmetrical cross link implementations whereas the fill symbols denote modified, nonsymm etrical cross -links implementation Sliding was carried out at a temperature of 300K.
59 Figure 3 5. Evolution of temperature during sliding for different sliding rates in the perpendicular direction (a) and parallel sliding direction (b). The data for 5, 10, 15 and 20m/s (bottom four curves) all show good temperature stability. Sliding rates of 50 and 100 m/s (top two curves) show increasing levels of heating. Figure 3 6. N ormal (FN) and frictional (FF) fo rces for the perpendicular (a ) and parallel sliding (b ) configurations, respectively, at slidi ng rates of 10 m/s and 20 m/s.
60 Figure 3 7. C oefficient of friction for the sliding of PTFE surfaces at 5m/s and 20m/s in the perpendicular (a) and parallel (b ) configurations, respectively. The results for 10 m/s and 15 m/s are very similar.
61 Figure 3 8. Edge on view for perpendicular sliding. Panel (a) shows the initial configuration with only three vertical stripes of atoms shown. After 10 nm of sliding at 5 m/s (b) and 20 m/s (c ) of sliding, the surface has roughened to approximately the same degree.
62 Figure 3 9. Graph of the normal dist ribution for the frictional force data generated using the Monte Carlo method. The yaxis shows the fraction value of the generated data that were within a given frictional force value. Figure 3 10. Illustration of the series of Monte Carlo least -squar es fitting carried on the simulation data. The averages of these fits were used in determining the coefficient of friction and adhesive force for the data sets involving several normal loads.
63 Table 3 1. Effect of different boxcar size averaging on Ff and Fn values. Table 3 2. Friction coefficient based on reduced and unreduced force averages Perpendicular Reduced Perpendicular unreduced Parallel reduced Parallel unreduced 0.28 0.28 0.09 0.09 F a 12.0 12.0 2.8 8.1 size of boxcar average 1 (original data) 10 50 100 500 1000 distance (nm) 0.002 0.02 0.1 0.2 1 2 F n 13.8 0.06 9.6 0.1 11.7 0.4 11.6 0.6 11.8 1.3 11.8 1.9 F f 1.6 0.02 (6 6) x 10 5 0.4 0.04 1.6 0.3 1.7 0.3 1.8 0.4
64 CHAPTER 4 EFFECT OF SLIDING OR IENTATION In their efforts to clarify the atomic/molecular origins of friction, scientists have found experimental evidence of frictional anisotropy for a variety of polymeric tribological systems. For example, Liley et al.43 investigated the frictional response of a lipid monolayer on mica in the wear less regime using lateral force microscopy. The lipid monol ayer consisted of condensed domains with long range orientational order. The domains not only displayed non -negligible friction asymmetries but also strong frictional anisotropies. The molecular tilt causing this frictional res ponse was less than 15 thus demonstrating that even small molecular tilts can contribute significantly to friction. Similarly, Carpick et al.78 reported frictional anisotropy in their study of polydiacetylene monolayer films where maximum friction was observed when sliding occurred in a direction that was perpendicular to the oriented polymer backbone. This anisotropic behavior was attributed to inherent anisotropy in the film stiffness. Of special significance is molecular dynamics simulation and its manipulation by a number of studies to clarify potential atomic level process es associated with the way in which the inherent structural anisotropy of polymeric systems can lead to corresponding anisotropies in the tribological behavior, or, inversely, the way in which tribology can induce structural anisotropy in polymeric systems. In one such study, Harris on and co -workers36 predicted low friction coefficients for self assembled, n alkane chains when sliding occurs in the direction of chain tilt; in co ntrast, when sliding occurs in the direction opposing chain tilt, they determined that friction forces would be high until the chains reorient and tilt in the direction of sliding. This is consistent with the findings of Liley et al.,43 mentioned above. In a second study, Landman et al.40 used MD simulations to examine the sliding of two gold surfaces with linear hydrocarbon chain molecule s trapped between them. The forces generated by the sliding caused the hydrocarbon molecules to
65 align and form layers. A third related MD study has predicted significant changes in the frictional properties of carbon nanotubes that were aligned in the hori zontal and vertical directions, with the horizontal nanotubes showing a substantially lower friction coefficient due to their ability to compress in response to applied loads.79 These predictions are in excellent agreement with experimental results for aligned nanotube films.44 Although there is considerable evidence in the literature that molecular -scale interactions may dominate the observed macroscale friction response of polytetrafluoroethylene PTFE tribosystems,29,3135,80 there have been few or no molecular -scale investigations of PTFE to substantiate this hypothesis. In s tudies of friction for various thermoplastics, Pooley and Tabor concluded that the smooth molecular profile of PTFE is responsible for its low friction coefficients;33 further, results from McL aren and Tabor suggest that adhesion processes were dominated by molecular -scale interactions rather than by asperity -scale interactions.30 Discussions on the intrinsic lubricity of PTFE have proposed that the disruption of van der Waals interactions between adjacent PTFE molecules are responsible for the frict ion forces.81 Her e, we p resent the results of crystalline PTFE -PTFE sliding in three distinct sliding configurations: sliding perpendicular to the chain alignment in both surfaces (i.e. perpendicular sliding), sliding parallel to chain alignment in both surfaces (i.e. parallel sliding) and simultaneous sliding both perpendicular and parallel to the bottom and top PTFE surfaces resp ectively (i.e. violin sliding). The atomic level mechanisms responsible for the distinct frictional responses associated with each of these sliding co nfigurations are discussed. 4.1 Perpendicular vs Parallel The simulations showed sliding behaviors that were both qualitatively and quantitatively different for the perpendicular and p arallel sliding configuration. Figure 4 1 shows the normal and tangenti al (i.e frictional) forces (relative to the sliding direction of the top PTFE surface),
66 along with the computed Amonton friction coefficients after 40 nm of sliding fo r both sliding configurations. These simulations were initiated from the same structure under norm al load of approximately 5 nN. During sliding, the interfacial chains of both configurations experienced structural changes, the more pronounced of which occurr ed for the perpendicular case. Here, the normal force increased from 5 nN to a median v alue of 9nN. Correspondingly, the frictional or tangential forces achieved a median value of 5.7 nN and appear to be closel y coupled to the normal force. Spatial frequency analysis of the force data gives a value of 4.5 nm for the periodic contact, which i s consistent with the size of the simulation cell in the sliding direction. For the parallel configuration, additional relaxation of the structure occurred such that the normal load decayed from 5nN to a median value of 2.3 nN. Interestingly, the associated frictional force across the interface maintained a steady median value of 0.8 nN. A series of interfacial images of the top 25 chains from the bo ttom PTFE surface are shown in Figure 4 2 The fluctuating behavior of the normal and tangential or frictional forces for the perpendicular sliding configuration is conf irm ed by the corresponding images which show that the aligned structural integrity becomes progressively less well defined after 2, 5, 10 and 40 nm of sliding. Particularly, the highlighted chains that constituted the topmost part of the interface for the bottom PTFE surface mixed into the bulk. This mixing and deformation is dilatant, resulting in an increased normal force. Additionally, in the vi ews of the carbon atoms along the backbones of the topmost interfacial chains of the bottom PTFE surface, which are labeled 1 5, chain scission is visible. Moreover, one of the broken chains ali gns with the sliding direction. Figure 4 3 also confirms that there is gross motion of the chains during sliding in the perpendicular configuration. As Figure 4 3 shows, this rate of motion sharply decreases after about ~ 20 nm of sliding; this abrupt decrease occurs at the time that portions of the chains begin
67 to r ea lign in the sliding direction. This gross structural reorganization is characteristic of microscopic wear, which might be expected to be accelerated by the explicit inclusion of electrostatic interactions. We anticipate that further sliding would lead to further chain scissions, further chain ali gnments and further wear. In the stark contrast to the perpendicular case, the parallel sliding configuration retains the aligned structure of the PTFE over the forty (40) nm of sliding (see F igure 4 2). As F igure 4 3 shows, the chains in the parallel configuration move by a maximum of ~2.5% (~ 1 nm over 40 nm) of the sliding distance, indicative of alm ost complete interfacial slip. Spatial periodicity analyses of these histograms give strong periodic content at 0. 21, 0.16, and 0.11 nm, which is close to the lattice spacing along the PTFE backbone (~0.13 nm carbon-carbon bond length along the sliding direction). The peak widths do not appreciably change during the simulation, which is also con sistent with interfacia l slip. These results are all consistent with parallel sliding friction being dominated by van der Waals interactions, and it is not expected that the explicit inclusion of electrostatic interactions would signi ficantly alter this behavior. 4.2 Violin (C o mbination of Perpendicular and Parallel) In the violin sliding configuration ( see F igure 3 1 C), the top PTFE surface was rotated 90 from the starting configuration for the perpendicular and parallel cases, resulting in a perpendicular alignment of the ch ains in the top and bottom surface within the plane of the sliding interface. The resulting configuration is one where sliding is rougher than that for the parallel configuration but initially smoother than the perpendicular case Figure 3 2 captures the p otential surface topography to be traversed by three differently sliding configurations From F ig ure 3 2 -A it is clear to see that upon compression, the top and bottom PTFE surface would interpenetrate by a fraction of an For the violin configuration, this distance would be a little less than 0.82 based on trigonometric analysis. From the actual simulations described herein
68 for various loads at a temperature of ~ 300K, the number s range from 0 0.5 and 2.432.72 for violin and perpendicular/paralle l configurations, respectively. For the high friction, high wear sliding configurations (i.e. perpendicular and violin), these range values represent a significant physical barrier to sliding. The effect ive barrier is even greater for the perpendicular case where the cha ins in both surface are aligned, thus maximizing the real area of contact. The parallel slid ing configuration is different compared to the other two configurations even though the top and bot tom surface interpenetration depth remains fairly constant during sliding and is comparable to that for the starting perpendicular configuration. This is because the interpenetration depth of the two PTFE surface s is not physically overcome during parallel sliding. Instead, the physically roughness for the parallel sliding configuration is governed mostly by the length of the C F bonds which easily rotate and w hose equilibrium value is ~ 1.34 The simulation results at comparable normal loads with regard to the frictional forces for the sliding configurations confirm the reasoning from the previous paragraph. Figure 4 4 compares the frictional forces for PTFE -PTFE sliding at 300K as a function of distance at comparable normal loads. The results show that t he frictional response for the violin sliding configuration is indeed intermediate with respect to that for the perpendicular and parallel ca ses with a steady increase for increased sliding distance. The steady increase in frictional force with sliding dis tance may have to do with the force required to deform and rearrange the slidi ng interface 4.3 Microscopic Processes of Friction and Wear Our simulations manifested a series of microscopic processes that foster surface damage which eventually led to high friction. The processes ranged from the bowing and bunching together of adjacent chains to the rolling of chains on top of and around each other, in a manner
69 similar to that by which fibril strands of rope are rolled together in a clockwise or counterclo ckwise fashion. More severe wear processes involved chain scission and the reorientation and translation of molecular debris and chain fragments in the direction of sliding. The occurrence, extent and sequencing of these events were highly dependent on the complex interplay of sliding orientati on and load transferability. In this section, the mechanisms underlying the tribological behavior are dissected and their origins are identified. The discussion which follows in this section pertains mostly to the high wear sliding configurations (i .e. perpendicular and violin). The parallel sliding configuration, which showed minimal wear, is treated separately. 4.3.1 Bowing and Bunching Together of C hains For the perpendicular sliding configuration at relatively low normal loads (i.e., less than 10 nN), surface chains in the bottom PTFE surface bowed as a result of the shear forces imposed by the mov ement of the top PTFE surface. No other significant movements of the interfacial polymer chains for the bottom PTFE surface were observed. This is later shown by the quantification of their displacements in C hapter 5 on the effects of normal load and temperature. In particular the lower the normal load, the smaller the displacement of the ch ains on the surface of the bottom PTFE surface. As the load was in creased beyond approximately 10 nN, breakage of cross links between the PTFE chains at the interface and adjacent sub -interfacial layer of chains occurred. This was evidenced by the subsequent bunching together of the bottom surface interfacial chains to form a regular continuous layer without the normal PTFE lattice spacing. Fi gure 4 5 captures this phenomenon. In moving from the position in Figure 4 5 B to Figure 4 5 C, the top PTFE surf ace was slid ~ 4.5 nm at 300 K. During this interval, chain #s 1, 4 and 5 were displaced between 3.5 and 4.5 nm, such that they effectively bunched together while still maintaining their initial alignment. At lower temperatures, this behavior was even more marked,
70 with all five ch ains on the bottom surface bunching together as will be discussed in C hapter 5 This process began after only a few nanometers of sliding; the chains were displaced at different rates, causing bunching and concomitant gaps to appear between adjacent chains in the group. These gaps yielded space into which other chains were able to bow. For some chains, these points of bowing facilitated the partial roll up of the chains along their molecular axes (i.e., perpendicular to the sliding direction of the top PTFE surface) in response to the constant rate of displac ement of the top PTFE surface. This process of polymer chain roll up along the molecular axes often occurred without scission of the chain into separate fragments. This process is highli ghted in panels c and d of Figure 4 5 by the behavior of chains #2 and 3 which, under conditions of high contact pressure, bow almost immediatel y in response to shear stress. The violin sliding configuration, by comparison, demonstrated similar behavior to the perpendicul ar case at low no rmal forces (i.e., less than 10 nN) in that the chains remain relatively unresponsive to the shear stress. There were two exceptions which occurred at relatively low temperatures however, in which bowing of one chain was observed after pr olonged sliding (100 K at Fn ~ 3.7 nN and 25 K at Fn ~ 3.6 nN). As the normal force was increased, bowing of the bottom surface interfacial chains increased somewhat, albeit not before having experienced significant sliding of the top PTFE surface. In gene ral, the chains bowed to a lesser extend in comparison to the perpendicular sliding case (see Figure 4 6 -E ). Interestingly however, at relatively high temperature and normal load (e.g., 300 K and ~ 35 nN) even before significant shear stress was imposed (i.e., less than 0.02 nm of violin sliding), the chains appeared somewhat strain ed as they were bowed in multiple points along their axes. 4.3.2 Chain E ntanglement Due to the extensive bowing of the polymer chains at random sites along the molecular back bone, a process was initiated between adjacent chains where a severely bowed segment of
71 one chain intertwined to a limited degree with a s egment of a neighboring chain. As the temperature was lowered to 25 K, a few of the chains showed a tendency to break under the tensile component of the shear force imparted by the moving top PTFE surface. Most of the entanglement exper ienced by these chains segments, however, was brought on by their motion (i.e., reorientation and/or displacement of fragments in the sliding direction of the top PTFE surface). This process was especially prevalent for the perpendicular sliding configuration, in which displacement led to the bunching of aligned chains, as descr ibed in S ection 4.3.1. The bunching initiated the entanglem ent p rocess by providing the opportunity for chains to slide and roll over each other. This resulted in the interlocking of the zigzag (C -C C) molecular axes of the chains (see Figure 4 5 -F and 4 6 -F ). Initially, this process occurred while the chains molecu lar axes remained largely unbroken. Regardless of mechanism of its initiation, the resulting entanglement led to severe strain as different segments of the polymer chains were displaced at different rates; thus, causing additional bowing. In some cases th is resulted in immediate chain scission and reorientation of chain segments. The segments of the polymer chains molecular axes that became intertwined, whethe r from severe bowing or displacement occurred at both cross -linked and uncross -linked sites Thu s, the location of the onset of cha in entanglement appears to be random, with the specific atomic mechanisms involved incorporating the effect of load transferability (both normal and shear) through the structure. 4 .3.3 Chain Scission For the perpendicul ar sliding conf iguration, a few chain scission events occurred at cross l inked locations along a chains (C C C) molecular backbone due to the effects of normal load. The majority, however, occurred at random locations along the chain molecular axis and r esult ed from extensive bowing, displacement and reorientation of chai n segments due to shear forces. F igure 4 5 B, taken after 0.98 nm of sliding by the top surface, captures the breakage of chain #3
72 precisely at a carbon atom where the chain was cross linked to an adjacent chain. The actual breakage, however, occurred almost instantaneo usly, after 0.52 nm of sliding. Chain #5 in Figure 4 5 C showed evidence of partial breakage as carbon atoms from its molecular backbone were left in the wake of its dis placement in the sliding direction of the top PTFE surface Chain #2 which was displaced in the direction of sliding of the top PTFE surface, significantly bowed at multiple points along its molecular axis and eventually reoriented along the direction of s liding of the top PTFE surface (see Figure 4 5 E ). The reorientation process led directly to the breakage of chain #s 4 and 5 while also further widening the scission gap between the fragments for chain #1. Chain scission for the perpendicular sliding geom etry, similar to that of entanglement as described in S ection 4.3.2, occurred randomly alo ng the chains molecular axes. It appears that the complex interplay of the processes of chain bowing, breakage of cross links and chain displacement contributed to t he randomness in stress distribution throughout the interface and the system. This, in turn, influenced the dynamics of the chains breakage process. Chain scission, in the violin sliding configuration, resulted from the sawing effect of perpendicularly re oriented chains or broken chain segments being dragged across another chains molecular axis. F igure 4 6 illustrates that on several occasions, chain scission was initiated precisely in the region of the molec ular axes in which both the aligned chains from the top and bottom PTFE surfaces intersect perpendicularly. The sawing motion experienced by these perpendicularly oriented chains caused scission to occur in chains for both surfaces. F igure 4 6 A depicts the initial sta ges of sliding, after 1.32 nm. Int erfacial chains for the bottom surface are oriented vertically and are labeled 1 5 while those in the top surface are horizonta lly oriented and are labeled 6 10. After almost 10 nm of sliding, the first onset of scission is shown in Figure 4 6 B in chain # 2 after it has been displacement in the sliding direction of the top PTFE surface next
73 to chain #1. B reakage was initiated at the point where chains #2 and 7 intersect perpendic ularly. Figure 4 6 C highlights this scission to a greater extent while also illustrating additional similar cases. Figure 4 6 D shows the evolution of these broken chain links. The breakage of these chains allow for significant movement and reorganization of the interfacia l structure as shown in Figures 4 6 E and 4 6 F respectively. As may b e ascertained from the sequence of images, neither the chains cross link sites nor extensive initial bowing of the chains played a significant role in bringing about chain breakage. 4.3.4 Chain and Chain-Segment R eorientation Chain or segment reorientation was usually (but not in all cases) the last event that led to significant molecular wear. In some rare instances, small segments of chains were reoriented in the sliding direction without being severed from the main chain molecula r axis. In general, segments of chains, after having broken off, translated and reoriented in the sliding direction of the top PTFE surface. The reorientation of chains and their segments did not lead to lower friction but instead served to further damage and disrupt the regular ordering of the interfacial chains as illustrated in Figure 4 5 -F 4.4 Summary Simulations results of crystalline PTFE -PTFE sliding were reported. Three different sliding configurations were explored: 1) sliding perpendicular to the chain orientation in both PTFE mating surfaces (i.e. perpendicular sliding) 2) sliding parallel to the chain orientation in both PTFE surfaces (i.e. parallel sliding) and 3) simultaneous sliding both perpendicular to the chain orientation in one surface and parallel with respect to the other (i.e. violin sliding) The quantitative results showed that perpendicular sliding demonstrated the highest frictional forces, friction coefficient and associated interfacial wear while the parallel sliding configurat ion correspondingly showed the lowest values. The frictional force, friction coefficient and
74 associated molecular wear for the violin sliding configuration were intermediate with respect to the perpendicular and parallel configurations. The frictional forc es and molecular wear for the violin configuration however showed a gradual tendency to increase steadily with sliding distance. Additionally, microscopic p rocesses associated with behaviors were described in detail. Four major microscopic processes were observed: 1) the bowing and bunching together of the polymer chains, 2) the entanglement of polymer chains, 3) the scission of the chains and 4) the reorientation of polymer chains and the severed fragments. The bowing of the polymer chains occurred with t he cross links sites playing the role of anchor points for bowing The bunching together of the interfacial ch ains resulted from their displacement due to the breaking of shared cross -links with chains from the sub-surface. This resulted in the disruption of the equilibrium spacing of the aligned chains thus allowing for the mechanical entanglement of their C -F bonds and also intertwining of the C -C molecular axes. Chain scission resulted from extensive bowing of the polymer chains and also occurred at the junctions with the perpendicularly aligned interfacial chains for the top a nd bottom PTFE surfaces meet in the violin sliding configuration. Scission occurred at these junctions due to the sawing effect the chains experience at these contact points du ring sliding. Reorientation of chains and chain fragments in the direction of sliding of the top PTFE surface also occurred. It was rare that an entire chain expe rience reorientation. The majority of the species experiencing this process usually had already undergone scission due to the reorienting force. Furthermore, the microscopic processes described were associated with the relatively high friction, high wear sliding configurations (i.e. perpendicular and violin).
75 The results from thi s stu dy may be used as a foundational part of efforts geared towards tailoring the crystalline microstructure of polymeric solid lubricant surfaces, specifically PTFE for applications requiring long wear lifetimes Such an undertaking may prove to be mostl y beneficial for applications involving unidirectional sliding where sli di ng may be design to occur along the chain alignment. Findings from this study may also be useful as part of efforts for the intelligent incorporation of reinforcing filler material into the PTFE matrix from that standpoint microscopic wear process to be prevented or inhibited during sliding.
76 Figure 4 1. The simulations are init ially compressed to a load of 5 n N before sliding is commenced. Friction coefficients were computed from t he corresponding normal and frictional force. For parallel sliding, the average normal force decayed with sliding distance due to compressive stress relaxation whereas the frictional or tangential force remain ed steady. F or perpendicular sliding the average normal force increased due to dilation of the system with sliding; the lateral forces for this configuration were comparatively higher and less stable.
77 Figure 4 2. A sequence of molecular snapshots of the upper 25 PTFE chains from the bottom s tationary PTFE surface. The five surface chains are highlighted with blue (carbon ) and orange (fluorine) atoms. The structure and alignment of these chains appear to maintain during sliding for the parallel configuration whereas the perpen dicular sliding configuration produces gross chain motions and mixing within the highlighted region. The snapshots are taken at approximately 2, 5, 10 and 40 nm of sliding. The top view of the carbon atoms for the five surface chains are shown at the same ti mes for perpendicular sliding. Chain scission and realignment is apparent in the 40 nm view.
78 Figure 4 3. A histogram of the displacements along the sliding direction for the carbon atoms in the surface PTFE cha ins highlighted in Figure 4 2. The carbon atoms in the parallel configuration move very little (~2%) during the 40 nm of simulation sliding; the distribution suggests that the chains ar e moving in a discrete fashion. In contrast, the perpendicular configur ation has substantial chain motion over the first 10 nm of sliding (moving over 3 nm on average durin g the first 10 nm of sliding). The sliding distance, means and standard deviations of the parallel and perpendicular are tabulated and plotted in the inset
79 Figure 4 4. Comparison of frictional response for the three sliding configuration for comparable normal loads at 300K.
80 Figure 4 5. Illustration of the various microscopic molecular processes a t work in the sliding of crystalline PTFE surfaces during perpendicular sliding. The interfacial chains for the bottom PTFE surface are shown. Snapshots were taken from simulation carried out at 300K and an average normal load of 25nN. In panel a, the initial configuration for the interfacial, bottom surface chains is shown. The top surface chains, not shown, move at an average rate of 10 m/s in the x direction.
81 Figure 4 6. Molecular snapshots at select stages of the various microscopic processes for the violin slidin g configuration taken at 25K at an average normal load of ~ 32nN. Panel a shows the early stage of sliding with the vertically orientated chains labeled 1 5 and the horizontal ones 6 10. Panels b and c show that chain scission was initiated mainly in regions where the interfacial chains of the top and bottom PTFE surfaces intersected perpendicularly. Panel d captures the propagation of the chain scission process and the direct results which may be des cribed as severe chain bowing and entanglement (panels e and f respectively).
82 CHAPTER 5 EFFECT OF TEMERATURE Polytetrafluoroethylene (PTFE), due to its low friction coefficient, relatively high temperature stability and chemical resistance is widely used either as a solid lubricant or as a key component in composite solid lubricants for dry sliding applications. Recently, it has been proposed that the friction behavior of solid lubricants such as PTFE, graphite and molybdenum disulphide (MoS2) is thermall y activated. McCook et al.81 reported on the temperature effects of PTFE and PTFE composites in pin -o n -disk tribometry experiments. Their findings, which also incorporated appropriate data from the literature, showed a monotonic increase in friction with decreasing sur face temper ature down to 173 K. The data set was modeled to an adjusted Arrhenius equation which yielded an activation energy of 3.7 kJ/mol (0.038 eV), suggesting the breaking of van der Waals bonds as the key mechanism to the observed frictional behavior. Burris et al.82 whose experimental approach was fundamentally different from that of McCook et al.,81 reported similar results for PTFE under macroscopic pin on-disk testing over the temperature range 200 400 K and calculated an activation energy of 5 kJ/mol. Results, on the length scales ranging from macro to nanometers have been reported for other system in which friction increased exponential ly with decreasing surface temperature .8385 For polymer polymer contacts, the main mechanisms of friction and wear invol ve either adhesion, deformation (i.e. elastic or plastic) or both.6 Consequently n ormal load or contact pressure plays a significant role on a polymers tribological performance. As in the case involving the effect of temperature, scientists have sought to understand the effects of normal load on PTFE and its composites during sliding under various conditions. For example, in their friction studies carried out on pin -on-disc wear test rigs at room temperature under dry co nditions, Unal et al.86 found that for pure PTFE and its composites, the friction coefficient
83 decreased with increasing normal load. Taking into account the visco -elastic nature of polymers, the variation of the friction coefficient in their study was modeled using the equation87 = kN(n 1) where is the coefficient of friction, N is the load and k and n are constants w ith the value of n being 2/3 < n < 1. Accordingly, the friction coefficient decreases with increasing load up to the limit load values of the polymer where friction and wear will increase due to the critical surface energy of the polymer. Conversely howeve r, the specific wear rate of pure PTFE increased with increasing normal load. This behavior was in stark contrast to the PTFE composites. Similar results were report ed by Jia et al.88 in their tribological study of polymer -polymer sliding a lso carried out under dry conditions. The ir findings revealed that all polymer -polymer sliding combinations tested (including PTFE -PTFE) showed a decrease in friction coefficient with increasing applied load for dry slidin g conditions. Under the same conditions though, the wear of PTFE increased slightly with increasing load. Other studies on PTFE composites have revealed similar trends. Unal et al.89 macroscopic pin -on -disc sliding wear tests however, showed somewhat different results. F or several thermoplastic polymers and polymer composites (including PTFE + 17% glass fiber reinforcement and PTFE + 25% bronze ) sliding against a 15% glass fiber reinforced unsaturated polyester polymer, the friction coefficien t and wear rate were not signific antly affected by normal load. Herein, the effect of normal load on the friction coefficient is also examined, although outside of the context of adhesion based on the unmodified Amonton definition of friction coefficient. 5.1 Frictional Response Figure 5 1 shows the dependence of the friction force on normal force at a number of different tempe ratures for the perpendicular (F igure 5 1 -A ), violin (F igure 5 1 B) and parallel (F igure 5 1 C) sliding configurations The error ba rs on the normal load and frictional forces
84 were determined using the previously outlined protocol ( see S ection 3 5 ). We observed a number of general trends in these results. First, for all three sliding configurations and at all temperatures, there was an almost linear dependence of the frictional force on the normal force. This was a strong indication of the internal consistency of the simulation results, and allowed a reliable estimate of the friction coefficient to be extracted from the slope. Second, for any fixed normal force, the frictional force increased as the temperature decreased; however, the temperature dependence did appear to significantly weaken below 100 K. Third, for the same normal force the frictional force for parallel sliding was less than for the violin case which, in turn, was less th an for the perpendicular case. A s previously discussed in detail in Section 4 3 significant structural damage occurred especially for the high friction sliding configurations. This led to gross rearrang ements of the structure at the sliding interface The perpendicular sliding configuration showed a dependence on temperature with friction forces ranging from 2.1 to 10.7 nN at 300 K, and from 13.2 to 26.6 nN at 25 K. The friction coefficient for the perpendicular sliding configuration was consistently higher than that for the violin and parallel cases and was accompanied by significantly more molecular wear. As a result, the temperature dependence was not as strong or as uniformly changing: there was relatively little difference between the frictional forces at 75 K and 100 K, or between those at 150 K and 200 K (Figure 5 1 -A ). As we shall see, this weaker temperature dependence is due to the higher friction and greater associated structural damage. Un like the perpendicular sliding configuration, the frictional force in the violin sliding configuration showed strong temperature dependence, with the friction increasing with decreasing temperature. Over a comparable range of normal loads, the frictional f orces for the violin sliding configuration were higher than those for the parallel sliding configuration and ranged from 1.7 to 10.4 n N at 300 K, and from 6.9 to 21.0nN at 25 K. In the parallel sliding
85 configuration, the simulations also showed a clear tre nd of increasing frictional forces with decreasing temperat ure (F igure 5 1 C ). Over the range of normal loads considered, the frictiona l forces ranged from 1.3 to 3.3 nN at 300 K and from 7.2 to 10.3 nN at 25 K. For all three sliding configurations, the a forementioned respective range of the frictional forces measured at various loads (see Table 5 1) widened with a decrease of temperature from 300K to 25K. At both temperature extremes, the range or the difference between the highest and lowest recorded fri ctional force was largest for the violin sliding configuration, followed very closely by that for perpendicular configuration while the parallel configuration was significantly lower at approximately one quarter of the value of the previous two. Of all the frictional forces measured, those for the perpendicular sliding configuration were the highest. The slopes of the respective data sets shown in Figure 5 1 were taken as an approximation of the friction coefficients for each temperature.90 The temperature dependence of the friction coefficient is shown in Figure 5 2 -A The friction coefficient for the perpendicular sliding configuration were relatively high even at high temperatures, and remained fairly unchanged as the temperature was decreased, a result of the significant molecular wear seen over the entire temperature range. Sliding in the perpendicular configuration required the polymer chains to continuously move between a somewhat interdigitated ge ometry to one that is not. In every sliding case carried out for the perpendicular configuration, the original interfacial corrugations were destroyed. Thus, it was reasoned that the high friction may be largely accounted for by the resistive force s requir ed to rearrange and extensively alter the molecul ar chain arrangement at the sliding interface. Under such conditions where the interfacial chains were essentially plowing each other, the contribution of the forces from atomic positional fluctuations were dwarfed by
86 comparison; hence, the apparently temperature insensitivity of the friction coefficient for the perpendicular sliding configuration. The violin sliding configuration, by contrast however, showed a more complex dependence of the friction coeffic ient with temperature. Above 200K the interfacial sliding occurred with minimal amount of damage to the structure of the chain alignment. There was a dramatic increase in the friction coefficient with decreasing temperature from 200 to 100 K. As the temperature was lowered below 100K, the friction coefficient, like that for the perpendicular case, became essentially temperature independent. These changes seemed to be correlated to a marked decrease in the rate of atomic positional fluctuations during sliding at the interface. Visual inspection of our atomic movies of the crystalline PTFE -PTFE sliding interface provided unmistakable, qualitative evidence of this, pr imarily for the fluorine atoms. Above 200 K, the interfacial chain atomic positions fluct uated more vigorously with sliding than at lower temperatures. Such behaviors based on temperature have been noted in studies of fluorocarbon, monolayer coatings, accompanied by a change in adhesion energy hysteresis per unit area.91 Prolonged sliding under such conditions led to chain scission, which eventually led to the large scale destruction of the crystalline chain structure. These structural damages, in turn, resulted in relatively high friction coefficients, on a level comparable to that which was observe d for the perpendicular sliding configuration. The parallel sliding configuration showed a steady increase in friction coefficient with decreasing temperature with a very small drop in friction at 75 K. The sl iding interface remained intact with the excep tion of one case where one chain rolled up in the sliding direction. This is in stark contrast to the p erpendicular and violin cases. Hence, we hypothesize that the temperature
87 dependence of the friction coefficient in this case may be almost exclusively a ccounted for by changes in the rate of positional atomic fluctuations at the sliding interface. 5.2 Adhesive Component of Temperature Dependent Friction The frictional forces for the various loads (see Figure 5 1 ) did not intercept the load axis at zero f orce upon extrapolation. Instead, an extrapolation of a linear fit would cross the yaxis at a value greater than zero. This value, within the assumption of a linear model for the friction behavior, corresponds to the offset C, based on a modified definiti on of Amonton s law for friction coefficient, f = N + C where N is the total load across the interface (i.e. N = Next + Nint, where Next is the externally applied load and Nint is the surface adhesion).90 The value of this C offset represents the residual friction force at zero applied external load. A portion of this offset value contributes to the adhe sive load across the interface. The larger the C offse t, the stronger the adhesion usually is for sliding situations exhibiting minimal or very l ow wear The frictional force (Ff) may be thought to consist of an adhesive component (Fad) and a deformation component F(def) (i.e. Ff = Fad + Fdef).6 Thus, the likelihood of adhesion dominated friction is more likely as the real area of contact increase s or is maintain ed at a relatively high value For defor mation controlled friction, surfaces in general may experience extensive damage; thus resulting in the formation and evolu tion of sharp asperity peaks. The initial PTFE interface topography for the perpendicular configuration was identical to that f or the parallel configuration. Sliding perpendicular to the chain orientations however resulted in behavior characteristic of defor mation dominated friction (see F ig ur e 4 5) although the interfacial contact area remained constant throughout A s Figure 5 2 B shows, the value of the C offset increases with decreasing temperature; thus, suggesting that adhesion makes a more significant contribution to frict ion at the lower
88 temperatures. This trend was observed for all three sliding configuration with the parallel and perpendicular configuration demonstr ating the highest C offsets at 300K and 25 K respectively. In the parallel sliding configuration, the chains remain ed in their interdigitated geometry. This allowed for maximum contact area between the interfacial chains of th e top and bottom PTFE surface. As the temperature was lowered, molecular rearrangement at the interface became more pronounced for the perpendicular and especially the violin slidi ng configuration, thus leading to rough sliding. The calculated adhesive force (see Figure 5 2 C), taken as the average value of the x intercept for the series of least -squares fi ts for the data in F igure 5 1, confirmed what was suggested from the interpre tation of the C offset values. The method used here to calculate the adhesive force is different from the experimental approach.84,91 In experiment, an Atomic Force Microscopy may be used to measure friction due to sliding while simultaneously increasing the normal load after the completion of predetermined numbe r of scans. The average frictional and normal load pairs obtained upon completion of a given number of scans at a par ticular normal load corresponds roughly to the procedure conducted to generat e the simulation data shown in Figure 5 1. Upon achieving a desired number of Ff, Fn pairs at increasing higher normal loads, the normal load is then consistent ly reduced with the rev erse process being carried out. As the applied normal force approaches zero, a residual frictional force is observed if adhesion occ urred between the two surfaces. The continual backing out of the probe tip eventually leads to its brea king away from th e counterface material. The force required to separate the probe tip and the counterface material is referred to experimentally as the pull -out or adhesive force (Fad) and is noted by the magnitude of the distance on the x axis between zero and where the f rictional force finally decays to zero A schematic representation of this force is shown in Figure 5 3
89 As Figure 5 2 C illustrates, the calculated adhesive force for the parallel sliding configuration is consistently and significantly higher than that for the perpendicular and violin configuration. This result is consistent with the reasoning given previously; that is, intimate sliding contact of the two PTFE surface for the perpendicular and violin is more intermittent compared to the parallel case. This reasoning is consistent with the notion of a slightly smaller real area of interfacial contact for the perpendicular and violin configurations; hence, their smaller adhesive force compared to the parallel configuration even though the PTFE surface were ma intained in continuous sliding contact. The results show that the high friction, high wear configurations demonstrated less adhesion while the low friction configuration consistently showe d higher adhesion. This is consistent with what is known about the r elatively low shear strength of and high wear rate of PTFE.10 The adhesion force for the perpendicular sliding configuration was consistently the lowest of the three for the temperatures 30075 K. At 25 K however, the calculated adhesive force app ear to increase to a level, almost comparable to that fo r the parallel configuration. It may be that theres significant uncertainty in this particular adhesion value considering the substantial amount of molecular wear and resulting rough sliding expe rienced at the interface for this temperature. To test this hypothesis, a fictitious data point was added to the 25 K perpendicular sliding data at approximately 5 nN. A least squares fit was then plotted to the altered data set. The results gave a frictio n coefficient of ~ 0.64 and an adhesive force of ~ 7.1 nN (see Figure 5 4). These values continue the trends observed for all three sliding configurations between 300 K and 75 K in that the friction coefficient gap between the perpendicular and the violin configuration was lessened while the adhesive force for the perpendicular configuration remained slightly beneath that of the violin configuration This analysis shows the source of the
90 error in determining the adhesive force for 25 K perpendicular sliding data set and highlights the difficulty of obtaining very low normal loads for the perpendicular sliding configuration as the polymer chains became extremely rigid at 25 K. Regardless the trend of increasing adhesive force with decreasing temperature for the various sliding confi gurations fits accepted models.81,82,84 5.3 Influence of Normal Load on Amonton Friction Figure 5 5 illustrates the relationship between friction coefficient and normal load with the friction coefficient being defined using the Amontons relationship = Ff / Fn 92 At 300 K, the friction coefficient for the violin and parallel sliding configuration remains fairly constant with normal load. For the perpendicular case, the friction coefficient showed more variability, probably owing to the higher degree of associated molecular wear. At ~ 10 nN, the friction coefficient dropped to a level more comparable to that o f the violi n and parallel configurations. As the temperature was decreased, the friction coefficient experienced an overall increase for the three sli ding configuration considered. The violin configuration showed interesting behavior in that the friction c oefficient may be viewed as bein g segregated into two regimes: one of relatively low friction coefficient at temperatures 150 K, 200 K and 300 K ; the other relatively high friction coefficient for temperatures of 25 K, 75 K and 100 K. This particular obser vation for the violin configuration, taken from a strictly Amontons perspective, is in agreement with the modified Amonton approach illustrated in Figures 5 1 B and 5 2 -A where there was a significant increase in friction coefficient for the violin configuration with temperature change from 150 K to 100 K. With respect to normal load, there was a significant increase in friction coefficient for temperatures lower than 300 K. In some cases, especially for the violin
91 configuration, the friction coefficient s howed an exponential rise at the lower normal loads. The results ar e in good agreement with experimental studies.86,88,89 5.4 Interfacial Wear F igure 5 6 captures the relationship between int erfacial chain displacement and normal load. Chain displacement in the direction of sliding of the top PTFE surface was calculated for carbon atoms in the bottom PTFE surface at the interface (see Figures 4 2, 4 5 & 4 6 for illustrations of these carbon atoms). The il lustration relates that chain displacement a form of molecular wear, increases with higher normal load for the perpendicular and violin sliding configuration. For the perpendicular sli ding configuration, there was almost no chain displacement at low normal loads. As the normal load approached ~ 10 nN however, significant displacement occurred due to the breakage of cross links between the PTFE chains at the interface and adjacent su b i nterfacial layer of chains. The displacements of these interfacial chains were temperature independent with the mean remaining within the range of roughly 5 8 nm at relatively high normal loads. Chain displacement for the violin configuration also showed significant increases at high normal load; however, the transition was not as pronounced in comparison t o the perpendicular case. The increase in displacement with increas ing load was a steadier more gradu al process and while there was not a clear overall temperature dependence, the displacements obtained for the three (3) lower temperatures were noticeably larger than those of the three (3) higher ones. Again, this correlates to what was described previous in regards to the friction b ehavior illustrated i n Figures 5 1 B and 5 2 -A .; a segregation of molecular scale wear behavior into two temperature regimes (one of high wear at relatively low temperatures and one of low wear at relatively high temperatures).
92 5.5 Summary Crystalline PTFE -PTFE sliding showed a significant increase in friction as a function of both temperature and normal load for the three sliding configurations considered. The friction values were highest for the perpendicular sliding configuration, intermediate for the violin configuration and lowest for the parallel sliding configuration. The friction coefficient, calculated from the average of a series of least squares fits to the ff,fn pairs at various loads for the different temperatures, showed a clear temperature dependence for the violi n and parallel configurations. A sharp increase in the friction coefficient was observed for the violin sliding configuration between 100 and 150 K. At temperatures lower than 100 K, the friction coefficient of the violin sliding configuration was comparable to that of the perpendicular configuration. The parallel sliding configuration showed a slow, graduate increasing in friction coefficient with decreasing temperature and remained comparably low. The friction coefficient for the perpendicular sliding conf iguration was largely athermal and did not change significantly with temperature. The adhesive force between the two crystalline PTFE surfaces increased with decreasing temperature with the parallel sliding configuration consistently showing the highest v alue, followed by intermediate values for the violin configuration and lowest, the perpendicular configuration. The gap in values between the parallel configuration and the other two configurations was substantial and increase d with decreasing temperature. The gap between the values for the violin and perpendicular configurations was comparatively much smaller and significantly narrowed with decreasing temperature. The results show that the relatively high friction, high wear sliding configurations (i.e. pe rpendicular and violin) demonstrated relatively low adhesion while the low friction, low wear sliding configuration (i.e parallel) showed
93 comparably high adhesive forces It follows logically that friction for crystalline PTFE -PTFE sliding is not adhesion dominated. Consistent with the findings of many polymer tribological studies (introduction to current chapter), a decrease in friction coefficient (using the basic Amonton definition without regard to adhesion) with increasing normal load was observed This behavior was most pronounced for the violin and parallel sliding configurations. The perpendicular configuration showed less of a clear dependence on normal load except in a few cases at extremely low normal loads. In the three sliding configuration however, there was a clear difference or increase in friction coefficient from a load standpoint with a change in temperature from 300 to 25 K. In conjunction, with respect to interfacial wear, displacement of the polymer chains increase with higher normal loads. For the perpendicular configuration, a significant increase was observed at approximately 10 nN for the temperature range probed. A more gradual increase was observed for the violin configuration while the parallel configuration showe d lower values with an even lower rate of increase with load. There was no clear temperature dependence for any of the sliding configuration. Overall, the perpendicular sliding configuration showed significantly more interfacial chain displacement than the other two configurations. Similar to the case with the behavior of the friction coefficient, the violin values were intermediate while the parallel configuration showed the lowest values. Finally, the thermally activated friction observed in many tribolog ical systems (and probably in PTFE as well) was not observed, in this study, to the extent that is has been reported in the literature. The violin sliding configuration demonstrated temperature dependent friction behavior that appears to be the result of t hermally mediated molecular wear. Its friction coefficient range, however, did not completely bridge the friction gap between the athermal
94 regime (i.e. perpendicular sliding configuration) and that of the thermally affected one (i.e the parallel sliding c onfiguration). There may be a variety of reasons why more convincing evidence was not brought forth. It may be that a wide r range of sliding configurations ought to be explored while allowing the volume of the system to expand and contract naturally (as op posed to constraining the volume of the simulation box by keeping it constant) in response to the tribological forces It may also be that the amorphous phase of the polymer holds the key to its temperature dependent behavior; the entangled polymer chains of the amorphous phase, which was not modeled, probably responds more readily than the crystalline regions to changes in temperature. While there is room for expansion on the work presented herein, a firm foundation has been laid from which additional mechanistic studies may be launch in pursuit of revealing the mysteries of PTFEs low friction and high wear rates.
95 Figure 5 1. Friction force (Ff) vs. Normal force (Fn) at various temperatures and normal loads for crystalline PTFE -PTFE sliding. Res ults are shown for the perpendicular (a), violin (b) and parallel (c) sliding configurations.
96 Figure 5 2. (a) Depiction of the friction coefficient ( determined by taking the average of a series of least square fits to the respective temperature data points in Figure 5 1. Panel (b) gives the average C offset value (i.e. the residual friction at 0 applied normal load or the y intercept) from the extrapo lation of the aforementioned least squares fits. Panel (c) illustrates the adhesive forces obtained by taking the average of the x intercept of the extrapolation of the previously mentioned least squares fits.
97 Figure 5 3. Schematic diagramming the experimental derivation of t he pull -out or adhesive force. The filled symbols denote the systematic increasing of the normal force with sliding while the open symbols denote the subsequent decreasing of the load towar ds s eparation of the two surfaces. The blue line represents a linear fit of the closed symbols and denotes the method used to es timate the adhesive force in the simulations results presented
98 Figure 5 4. An alternative perspective of friction and w ear for perpendicular sliding at low temperature which includes an arbitrarily chosen low friction, low normal load data pair not obtained from simulation. The recalculated adhesive force is ~ 7.1 nN while the friction coefficient is ~ 0.64. 0 5 10 15 20 25 30 35 40 45 0 5 10 15 20 25 30 35 Ff (nN) Fn (nN) 25K perpendicular linear fity = A + B X 4.55+/0.31 0.64+/-0.01 data point not simulated
99 Figure 5 5. Friction coefficient, without reference to adhesion, as a function of normal load at various temperatures for the three sliding configuration.
100 Figure 5 6. Displacement of the bottom surface i nterfacial carbon atoms are measured with respect to their initial positions prior to sliding of the top PTFE surface. The median displacement values are plotted with the standard error in the mean taken as the uncertainty. The median was taken over a slid ing distance of ~ 24 nm.
101 Table 5 1. T he lowest and highest frictional forces for the three sliding configurations explored at the two extreme temperatures investigated. The range between the lowest and highest frictional forces increased with decreasing temperature. 300K 25K Configuration F f (low) F f (high) difference F f (low) F f (high) difference Perpendicular 2.1 10.7 8.6 13.2 26.6 13.4 Violin 1.7 10.4 8.7 6.9 21.0 14.1 Parallel 1.3 3.3 2 7.2 10.3 3.1
102 CHAPTER 6 EFFECT OF FLUOROCARB ON MOLECULES AT THE SLIDING INTERFACE Polymers and polymer composites have experienced high demand as solid lubricants and as coatings fo r various sliding applications .93 In many cases the combination of polymer polymer sliding via the formation of transfer films is the critical factor for achieving low friction. For some of these polymer -polymer sliding combination s, t he associated wear may be high; this is especially true for PTFE.94,95 Various ap proaches have been tried to address PTFEs excessive wear (see S ec t i on 1.4.4 ). A less well -developed approach involves the incorporation of fluids at the sliding interface. As Jia and co -workers88 discovered through their investigation of polymer polymer sliding combinations under liquid paraffin conditions using pin-on -disc tribometry, both the friction coefficient and wear rate of self -mated PTFE were reduced significantly (i.e by a factor of ~ 14 and ~2 respectively). Additionally both the friction coefficient and wear rate remain low and fairly constant with increased sliding velocity and applied load. In a somewhat different tribological study Zappone et al.96 examined the effect of nanometer roughness on the adhesion and friction of a rough polymer surface against a molecularly smooth mica surface under hydrocarbon oil conditions using the surface force apparatus. The polymer used was polyurethane replicas of different substrate roughness. The introduction of the hydrocarbon oil between the sliding surface s resulted in a decrease in friction coefficient while eliminating the adhesive force. In yet another polymer polymer sliding example, the introduction of silicone oil in Acrylonitrile -Butadie ne Styrene (ABS) polymer was found to lower friction values and required higher normal loads to cause frictional instabilities than without the oil.97 Raviv et al.98 also found very low friction coefficients (i.e. ~ 0.003) for adsorbed layers of poly(ethylene oxide) in the solvent toluene sheared against a smooth, curved solid mica surface for loads up to 100 MPa. The behavior was attributed t o a combined system effect of being able to
103 accommodate relatively large loads due to osmotic repulsion between the compressed layers in the solvent medium and simultaneously maintaining the fluidity of the sheared interfacial zone within which the frictio nal dissipation occurred. For t he work to be described in the following sections, the typical Stribeck behavior that is characteristic of many oil lubricated systems including polymer -polymer systems99 in which the friction coefficient increase s with either an increase in oil viscosity or sliding rate and decreases with applied load was not observed as in the previously described study since only a single sliding velocity was considered. In the work to be described fluorocarbon molecules were placed at the sliding interface between two crystalline PTFE surf aces. A snapshot of t he two crystalline surface s of PTFE without fluid at the interface is illustrated in Figure 6 1. The effect of two different species was investigated: perfluorooctane (C8F18) and hexafluoroethane (C2F6). Perfluorooctane (C8F18) is a clear, colorless, fully -fluorinated liquid that is the rmally and chemically stable, nonflammable and practically non -toxic. Its excellent material compatibility and high dielectric strength makes it a good choice for applications involving lubricant deposition, process solvents and heat transfer. The liquid c omprise s of units having an average molecular weight of ~ 438 g/mol, boils at 101 30100 Hexafluoroethane (C2F6) is a colorless, odorless, nonflammable gas composed of the elements carbon and fluorine with a molecular weight of 138.02 g/mol. The gas has melting and boiling temperatures of 101 78.2, respectively. Its density is 4.8 times that of air and 1.23 that of water. Hexafluoroethane has a vapor pressure of 30 bar at 20 the electronics industry as an etchant for many substrates in semiconductor manufacturing. With oxygen, it strips photoresist and is used for selective etching of silicides and oxides (e.g. silicon) over their metal substrates.101 With regard to material compatibility, it is purported to have a
104 slight risk of corrosion in water and causes significant lost of mass by extraction or chemical reactions with hydrocarbon and fluorocarbon based lubricants. It behaves satisfactor ily however with some plastics such as PTFE, polypropylene and polyamide, metals (e.g. aluminum, brass, copper, carbon and stainless steel) and elastomers (e.g. chloroprene, nitrile rubber and buthyl rubber). 101 Two different fluid film thicknesses were also considered: one monolayer (see Figure 6 2) and four monolayers (see Figure 6 3). Additional detail s regarding the two fluid film thicknesses are given in Table 6 1. The simulation fluid densities (see T able 6 2 ) were significantly higher than the ir experimental values due to the substantial contact pressure (hundreds of MPa) imparted by the compression of the two crystalline PTFE surface s T he mean square displacement of carbon atoms within the fluid atoms was cal culated under these high contact pressures during the equilibration stages of the simulation prior to the commencement of sliding. Calculation of the diffusion coefficient102 based on t he mean square displacement gave values on the order of 106 cm2/s for the four monolayer C2F6 systems which is about one order of magnitude lower than that for many fluorocarbon and hydrocarbon species (e.g C2F6) in water at 25C103(see T able 6 3 ). The diffusion coefficient for the monolayer fl uid systems for both species was one to two orders of magnitude smaller than the experimental values A s S ection 6.1 will rev eal, the monolayer systems represent essentially boundary layer lubrication with respect to the PTFE surface s Overall, the C8F18 species showed lower simulation diffusion coefficients than those for C2F6. In spite of the relatively low simulation diffusion coefficients, the values are still order s of magnitude faster than that for solid diffusion. 6.1 Monolayer of Molecular F luid Figure 6 1 shows a snapshot of the simulation se tup for the aligned, self -mated, crystalline PTFE setup for sliding without the fluorocarbon molecules The carbon atoms in the top and
105 bottom surfaces are colo red red and blue respectively. For emphasis, the carbon atoms of the interfacial chains of the bottom PTFE surface are colored in black. As shown before in Figures 4 2, 4 3 and 5 6 displacement of these inter facial chain atoms due to sliding of the top PTFE surface was used as the main metric for determining wear or damage of the system. Figure 6 2 shows a similar snapshot with one monolayer of molecular fluid (depicted by violet carbons and silver fluorines ) between the two crystalline PTFE surfaces. The interfacial chains previously mentioned were enhanced for emphasis since the behavior of these interfacial atoms are expected to be influenced by the pre sence of the molecular fluid. In this chapter, the prima ry emphasis will be on the perpendicular sliding configuration due to its associated high friction and wear; however, a few cases for parallel sliding will be briefly examined. 6.1.1 Frictional Response Figure 6 4 compares the frictional response of the perp endicular sliding configuration with the three different interfacial conditions (i.e. crystalline PTFE PTFE sliding:1. without fluorocarbon molecules, 2. with a monolayer of C2F6 molecules and 3. with a monolayer of C8F18 molecules) at roughly the sam e normal load. For the simulations with fluorocarbon molecules, the number of carbon atoms was conserved for both case s ( see T able 6 1 ). A comparison of the normal forces in Figure 6 4 shows a significant evolution of the normal force (from ~ 6 nN to 15 nN ) for system the without the fluid monolay er. This phenomenon is correlated to the corresponding fri ctional force in the form of a large peak between at 1 2 nm, followed by a series of smaller peaks. The first large peak in the fri ctional force incorporate s the response of the surfaces to shear and signifies the transition from static to kinetic friction while the latter ones denote the run in period to steady state friction and is characterized by the rearrangem ent of the interfacial chains. This behavior is in contrast to the systems with molecular fluid between the crystalline sliding PTFE surfaces where no substantial upward evolution or increase in the
106 normal forces were observed As a result, the normal forces remained fairly constant, with in a narrow range for the duration of sliding. Accordingly, the initial frictional response (i.e. transition from static to kinetic friction) was much smoother than the scenario with no molecular fluid ; as a result, the first pe ak being significantly reduced. This res ulted in lower friction for the simulations with fluoroc arbon fluids at the interface. Focusing on the frictional responses for the simulations involving the fluorocarbon fluids, a close inspection of the forces reveal that the normal force (see Figure 6 4 ) for the C2F6 system is slightly but consistently higher than that for the for C8F18 system. The frictional force for the C2F6 system however remained slightly lower than that for the C8F18 system for approximately the first 11 nm of sliding and again for the last 4 n m of sliding. As will be shown later as a function of normal load for the monolayer systems, the C2F6 case consistently showed lower frictional response than the C8F18 case. Al so to be noted is the fairly sinusoidal, periodic undulation of the normal forces for the systems with molecular fluid compared with the more random, irregula r form for the fluid -less case. This behavior is highlighted even more for the molecular fluid sys tems with fou r (4) monolayers where the normal lo ads more consistently oscillate around a constant value and also with larger but very consistent amplitude (range of ~ 3 nN for four (4) monolayer systems compared to ~ 2 nN initially and t hen ~ 3 nN for mon olayer case). The load at the interface of the two crystalline PTFE surfaces is transferred through the surfaces via cross links. The normal and frictional forces, as mentioned previously, are measured on the rigid moving layer ( see F igure 3.1). The distan ce between the rigid moving layer and the sliding interface is shortest for an interfacial position directly on top of an interfacial chain o f the bottom PTFE surface (see F igure 6 2) and longest for interfacial positions that are in bet ween two bottom sur face interfacial chains. Given that these simulations were carried out at constant surface displacement,
107 it is reasonable that the normal load felt will be somewhat higher when the interfacial chains in both surfaces are directly on top of each other and correspondingly, somewhat lower when both surfaces interlock as illustrated in Figure 6 1. I n the case of no molecular fluid, these interfacial corrugations were quickly destroyed dur ing perpendicular sliding, which resulted in the randomness and irregul arity in the evolution of the associated normal force. 6.1.2 Wear Response The displacement of the interfacial atoms with respect to their initial positions for the non fluid PTFE system and that for the fluid case are shown in F igure 6 5 Here, we quantify the extensive damage for the former while showing a clear reduction in molecular w ear for the latter. The displacement in response to sliding of the top PTFE surface was calculated for various i nterfacial components. In F igure 6 5 the bl ack solid line represents the movement of the top PTFE surface which is th e baseline to which the displacement of the bottom surface interfacial chains and the monolayer of molecular fluids were compared The graph compares displacement of the bottom surfa ce in terfacial chains for the two systems (filled, solid symbols) to that for the corr esponding fluid (open symbols). As the graph relates, the interfacial chains (solid squares) for the non -fluid system were displace d by a little more than five nm aft er a pproximately twenty six nm of sliding by the top PTFE surface. The addition of either the C2F6 or C8F18 monolayer of molecular fluid reduced the displacement of the interfacial chains to a value roughly half that for the non-fluid case f or the same amount of sliding. Consequently, this reduction was accounted for by extensi ve displacement of the molecules in the monolayer of fluid. A priori it may seem surprising that the fluid with the larger molecular weight (i.e. C8F18) w as displaced to a larger extent than the fluid with the small, seemingly more mobile molecules (i.e. C2F6). The answer may have to do with the ability of the C2F6 molecules to roll to a much greater degree in
108 comparison to the more linear, longer C8F18 molecules. Detailed analysis in thi s regard will be covered in the next section with respect to the four monolayer systems. Considering that substantial interfacial displacement occurred within the fluid in order to reduce the fri ction and molecular wear, analysis was focu sed on this sacrif icial layer. Figure s 6 6 and 6 7 show resp ectively a distribution of the C -C and C F bond lengths of the two types of molecular fluids at the sliding interface both before and after sliding. The graphs show no significant change in the distribution of bonds within the sheared molecular fluids; however, a slight elongation or stretching of both types of bonds w as observed for the two cases. Not surprisingly the coordination of the carbon atoms ( taken over a range of 1.7 to 2.0 ) within the fluid layers determined before an d after sliding was identical. Consequently, a more stringent approach and requirement to ascertain ing breakage and formation of bonds both before and after sliding was undertaken. In this approach, each molecule was individually consi dered separately instead of calculating over the fluid as a whole. Additionally, a bond length change of 10% or more was arbitrarily chosen to determine breakage. The findings of this more stringent approach were consistent with that of the former For the C8F18 system, 16% of the molecules had experienced breakage of the mole cular chains (i.e. C -C bonds). The breakages occurred prior to sliding and thus occurred during the compression and normal force and temperature equilibration phases of setting up the system (see C hapter 3 on the various methods employed to achieve desirable initial system conditions). In addition to probing the initial and final system configurations, the configuration at 50% of the total sliding distance was examined with identical br eakage statistics. The only difference in the three configurations probed at the various sliding distances was the increase in physical separation between the carbon atoms whic h had broken prior to sliding. In comparison, the C2F6 system was examined with the same approach
109 previously used to describe the C8F18 system The results were different in that no b reakage of C C bonds observed. Nonetheless, 5% of the carbon atoms constituting the C2F6 molecules were under coordinated due to the detachment of a fluorine atom. A s in the case of the C8F18 system the separation of the two detached atoms increas ed with sliding distance. 6.2 Four Monolayers of Molecular F luid Figure 6 3 shows an MD snapshot of the simulation setup for the 4 monolayer fluid systems, simi lar to that for the monolaye r systems (Figures 6 2). In this system, there are four times as many carbon atoms within the fluid layer compared to the monolayer system (see Table 6 1). The differently colors (blue, red, orange and purple) denote the carbon atoms within the fluid layers in order of increasing distance from the top PTFE surface (i.e. layers 4, 3, 2 and 1 respective ly). The snaphot was taken after physical and thermal equi libration of the system and at 0 nm of sl iding by the top PTFE surface. Consistent with the behavior of a fluid molecules from the different layers int ermixed during equilibration. 6.2.1 Frictional Response Similar to Figure 6 4 F igure 6 8 compares the f rictional response of the non-fluid system against that of the two fluid systems albeit this time with four times the amount of fluid between the two PTFE surfaces. The results show an even more dramatic response compared to t hat for the monolayer systems The normal force for the two fluid systems are roughly the same while that for the non -fluid lags just beneath the former two. The frictional response for the C8F18 system, however, was consistently beneath that of the non-fluid case with the C2F6 system demonstrating far superior frictional behavior of the three (i.e. frictional force, C2F6 on average ~ five times lower than the frictional force the C8F18 case and eight times lower than the frictional force for the non -fluid case).
110 6.2.2 Shearing of flui d layers Fi gure 6 9 compares the relative displacements of interfacial component s resulting from the shear force imposed by the sliding of th e top PTFE surface. For both fluid systems, the fluid layers closest to the moving top PTFE surface experienced the largest displacement while those further from the surface were progressive ly displaced to a lesser degree. The solid square and circle symbols denote the displacement of the interfacial chains for th e non -fluid and fluid systems respectively For both flu id systems, the interfacial chains of the bottom PTFE surface experienced no displacement as a result of sliding by the top PTFE surface. Basically, the fluid layers account for all of the molecular rearrangements due to the shear force impos ed by the top sliding surface. It is intere sting to note that fluid layer 4 (i.e. the layer closet to the moving top PTFE surface) was displaced to roughly the same degree as that for the monolayer described previously (compare F igure s 6 5 & 6 9). Thus, th e remaining three fluid layers accounted for both the reduction in friction and the amount of energy required to rearrange the interfacial chains that experienced displacement in the monolayer systems. The figure shows that surprisingly bot h fluid systems experienced roughly the same degree of interfacial displacement for the same components (i.e. interfacial chains of the bottom PTFE surface and the respective fluid layers). Considering the significant difference in the measured frictional fo rce as a func tion of load (see F igu re 6 8 ), this was indeed striking. 6.2.3 Reorientation of Fluid Molecules Given the simila rities in the degree of displacement in the sliding direction for the interfacial components of the C8F18 and C2F6 fluid systems, additional exp lanations were required to account for their drastic difference in frictional response at roughly the same normal load Figure 6 10 quantifies the degree of displacement of the fluid layers perpendicular to the direction of sliding for both the C8F18 and C2F6 systems. The median displacement value for each
111 layer is reported along with the associated standard deviation. The graphs paint a consistent pict ure of a wider range of displacement perpendicular to the direction of sliding of the top PTFE surface fo r the C2F6 fluid system. This behavior was highlighted for the intermediate layers (i.e layers 2 and 3) where the molecules were less likely to become attached to or be influenced by the top or bottom PTFE surfaces. The graph suggests that C2F6 molecular fluid was more likely than the C8F18 fluid to spread and traverse over the entire sliding interface This result is not unexpected given that the C2F6 fluid has a low er density and high er diffu sion coefficient (see Tables 6 2 and 6 3 ) compared t o the C8F18 fluid. Figure 6 11 considers the amount of rotation experienced in the plane of the sliding interface by molecules in the C8F18 fluid while sliding. The figure shows a top down view of the bottom PTFE surface onto the plane of the sliding inter face. For clarification, only one C8F18 molecule is shown; however, the four histograms give a snapshot view of the orientation of the four fluid layers both before and after sliding. As the figure indicates the sliding direction is the x direction and th e orientation angle of the molecular axis was measured with respect to the z axis. Thus, for the top simulation snapshot shown between the histograms for layers 1 and 2 ( see F igure 6 11), the lone C8F18 molecules makes a shallow angle (0 25) with the z axis. Similarly, the bottom simulation snapshot, taken after significant sliding of the top PTFE surface shows the same C8F18 molecule which is now orientate d in the direction of sliding. The molecule forms roughly a 90 angle with the z axis as is indicated by the arrow. Viewed collec tively, the four histograms of F igure 6 11 relate that at zero nm of sliding by the top PTFE surface, the C8F18 molecular axis orientation is fairly random with no obvious trend. After significant sliding of the top PTFE surfa ce, the orientation of the C8F18 fluid molecules within each of the layers become less random and more oriented along the x axis (i.e. the sliding direc tion of the top
112 PTFE surface). This is evidenced by two striking feature s of the graphs: the sharp reduction in the number of molecular orientation at low angles with respect to the z axis and the steady and sometimes large increases at progressively larger angles. Figure 6 12 attempts to further clarify the orientation behavior of the C8F18 molecules from the side vie ws (i.e. along the z axis which is parallel to PTFE chain alignment in both surface and also along the x axis which is perpendicular to the chain alignment of both PTFE surfaces but along the sliding direction). The orientation behavior of the C8F18 molecules, when viewed along the z axis, was similar to that shown previou sly for the topdown view (see Figure 6 11). This result suggests that as the top PTFE surface moves from right to left along the plane of the page, the majorit y of the C8F18 molecules tend to align horizontally or at an angle closer t o being parallel to the x axis. The reverse trend was observed when viewed along th e sliding direction or x axis in that more C8F18 molecules tend to align along relatively s maller angles due to sliding. This finding is consistent with the results of the top-down view (F ig ure 6 11) and the previous side view along the z axis Horizontal orientation within the plane of the sliding interface implies that the C8F18 molecules, when viewe d in the sliding direction or along the x axis, would appear as a point molecule or a short line segment. Given the orientation of the former two views, it makes sense that the latter would demonstrate a te ndency towards smaller angles. The molecular snaps hot labeled c captures a single molecule from both view s and with the approximate orientation angle denoted in both histograms by the same letter. The various histo grams depicting interfacial displacement (both perpendicular to and in the direction of sl iding), along with those capturing the relative orientation of C8F18 molecules as a function of sliding distance indicate that the molecules tend to align along a given direction and are dragged in that direction. The data shows little evidence to suggest si gnificant rolling and
113 alignments cha racteristic of rolling motion. This hypothesis was confirmed visually by various molecular simulation movies highlighting the behavior of the C8F18 f luid molecules during sliding. The previous orientation analysis described for the C8F18 4 -monolayer system was also carried out for the C2F6 4 -monolayer system. The results for the top-down view (i.e. along the y axis) onto the plane of the sliding interface are given in Figure 6 13. Examination o f the figure indicates that no significant changes in the alignment of the C2F6 molecules in all fou r fluid layers due to sliding. At various angles, there was a small increase in the alignment towards the sliding direction (i.e. x direction) while at othe r, there was a small decrease. Still, at other angles, there was no change in the alignment due to sliding. Additionally, the significant drop -off in small angle alignment experienced by the C8F18 molecules (see F igure 6 11) was not observed for the C2F6 s ystem. Figure 6 14 captures the orientation behavior from the two side views Irrespective of the view, whether it was either along the zaxis and hence parallel to the chain orientation in both PTFE surface or along the sliding direction (i.e. in the slid ing direction of the top PTFE surface which is perpendicular to the chain orientation in both surfaces), the results showed a random distri bution of molecular alignment. The results regarding the orientation of the C2F6 molecule due to sliding with respect to the three orthogonal views, in addition to the results of F igure 6 10 which showed the relatively greater tendency of the C2F6 molecules to spread over the sliding interface in a direction perpendicular to that of moving top PTFE surface suggest that theres likely a strong rolling component to the mo tion of the C2F6 molecules in comparison to that for the C8F18. Given the ir resp ective molecular shapes, one would expect that the smaller, less linear molecule (i.e. C2F6) would show a greater tendency to roll. Indeed, side -
114 by -side comparison of molecular movies highlighting various C2F6 and C8F18 molecules visually showed a higher d egree of rolling motion (in the presence of sliding motion) for the C2F6 system 6.3 Overall Reduction in Friction Coefficient and Wear Using the least-squar es fitting method described in S ection 3 5, quantitative values of the friction coefficient and adh esi ve force was determined for some of the da ta plotted in F igure 6 15 (see T ables 6 4 and 6 5 ). The table s indicate a clear decrease in friction coefficient when the fluid layers were placed between the crystalline PTFE -PTFE sliding interfaces. The reduction was most dramatic when more fluid (i.e. four instead of one monolayer) was used. This is confirmed by the low friction value for the C8F18 4 monolayer system given in Table 6 2 and the relatively low slope for th e C2F6 4 monolayer system shown in F igure 6 15. Also inter esting to note is the apparent correlation between the friction coefficient of the fluid systems and the density of the fluid placed between the PTFE sliding surfaces with the less dense fluid showi ng lower friction values A significant reduction in friction did not always correspond to a substantial decrease in the adhesive force as a comparison of the respective values for the C2F6 monolayer and C8F18 4 monolayer systems would confirm. While this behavior was consistent with what has been reported for PTFE -PTFE sliding ( see S ection 5 2 ) where PTFE -PTFE adhesion plays a lesser role in the friction response compared to PTFE deformation (probably owing to the polymers low surface energy), o ther syst ems (see the literature review in the introduction of this chapter) in which fluids were added to interface between two sliding polymer surfaces have shown reductions in the adhesions of the two surfaces. The same general adhesion behavior was observed in three out of the four applicable cases (see Table 6 2 for two of those cases: C2F6 monolayer and C8F18 4 monolayer) as the C2F6 4 monolayer system further confirms ( value not
115 quantified but ded uced from visual inspection of F igure 6 15) with the lone exception being the C8F18 monolayer system (i.e showing relatively high adhesion) The reduction in friction coefficient was also accompanied by a reduction in molecula r wear of the PTFE surfaces as Figures 6 5 and 6 9 quantitatively demonstrated Figure 6 1 6 provides representative simulation snapshots of the PTFE top and bottom surfaces after approximately 21 nm of sliding for each of the fluid systems. Sliding of the top PTFE surface was done from right to left horizontally across the plane of the page o r in the x direction. A careful c omparison of Figure 6 16-E and 6 16 G shows that for the monolayer systems, the interfacial chains of the bottom PTFE surface experienced a higher degree of displacement for the C2F6 fluid system compared to the C8F18 case This may be confirmed by noticing the placement of the yellow carbon and the b lack carbon interfacial chains. In Figure 6 16 E, the yellow carbon chain is further along the slidi ng direction that in Figure 6 16G. The b lack carbon chain in Figure 6 16-E has already crossed the periodic boundary. Quantifica tion of the interfacial displacement of the interfacial chains of the same monolayer systems (see Figure 6 5) captures this observation as the C2F6 systems showed a slightly small degree of displacment b etween approximately 7 and 18 nm of sliding. The resulting interfacial wear of the C2F6 fluid system also seem to expose comparative more of the interface for the bottom PTFE surface. The four monolayer molecular fluid systems also showed somewhat different behaviors. Comparison of Figures 616 B and 6 16-F reveals very little change in the positions of the interfacial chains of the bottom PTFE surface for the C2F6 fluid system with the exception of a slight bow of one of the chains. In contrast, the C8F18 fluid system (see Figures 6 16D and 6 16H) shows a slight shift of the interfacial chains of the bottom PTFE surface to the left or in the x direction (i.e. the sliding direction of the top PTFE surface). This shift represents the initial
116 response of the bottom surface to the shear force imposed by the sliding of the top surface. The response was not seen for the C2F6 4 monolayer fluid system as its frictional force was substantially low (see the corresponding force graphs in Figure 6 8). Additional sliding showed chain scission for the C8F18 case (see Figure 6 17) while none was seen for the C2F6 4 monolayer fluid system up to ~ 24 nm of sliding. Given the extremely how friction and the associated smooth sliding, no wear in the form of chain scission is expect for extensive sliding at the given normal load. 6.4 Summary Incorporation of a layer of molecular fluid between the two crystalline PTFE surfaces made a noticeable impact on the measured friction and wear of the surfaces For a normal load of approximately 15 nN, both the C8F18 and the C2F6 monolayer of fluid reduced the friction by a range of 10 30%. A significant drop in the static friction was observed with the incorporation of the molecular fluids between the sliding surfaces. For wear, the interfacial chains of the bottom PTFE surface exp erienced a 50% reduction in displacement due to sliding when the fluorocarbon molecules were introduced between the surfaces. The monolayer fluid experienced a higher degree of displacement (more so in the C8F18 case) to compensate for this reduction. The amount of molecular wear was still excessive however as usage of a monolayer of fluid did not result in sliding conditions essentially diff erent from that of boundary layer with respect to the PTFE surfaces The normal force for the 4 monolayer fluid systems remained more consistent and showed even more defined undulation than in the monolayer cases. The frictional response of the non fluid s ystem dropped substantially with sliding distance to a level almost comparable to that of the C8F18 fluid system at a normal load of ~ 17nN The C2F6 system showed by far the lowest frictional response. Surprisingly, all interfacial components for the flui d systems were displaced
117 to roughly the same degree. Fluorocarbon molecules of the C8F18 system showed a tendency to oriented and align parallel to the sliding direction of the top PTFE surface. This was not the case for the C2F6 fluorocarbon molecules whi ch consistent showed random alignment. The large difference in friction between the C2F6 and the other two cases was due to the large amount of rolling experienced by the C2F6 fluid molecules during sliding of the top PTFE surface. No wear in the form of i nterfacial chain rearrangement was observed for the 4 monolayer C2F6 fluid system The C2F6 4 -monolayer system, which was sle d in the perpendicular configuration showed friction that was lower than that for the fluid -less, parallel sliding configuration. The addition of either a monolayer or even 4 monolayers of C8F18 molecular fluid did not result in a change in friction or wea r for the parallel sliding configuration. Sliding in the parallel configuration for the C2F6 monolayer system showed friction that was equivalent to that of the C2F6 4 monolayer slid ing in the perpendicular sliding configuration. The C2F6 4 monolayer syste m sliding in the parallel sliding configuration showed the lowest friction of all the systems considered The C2F6 molecular fluid was less dense and showed diffusion coefficients higher than that for C8F18. More importantly, the friction and wear results overall, were more favorable for the C2F6 systems for the perpendicular and even parallel sliding configuration. As a result, one may speculate that given proper material compatibility, less viscous fluids may provide superior friction and wear response compared to more viscous ones when inserted at the sliding interface between two relatively smooth polymer surfaces (e.g. PTFE). Considering that a less viscous fluid would comparably carry lower load s than a more viscous one, the fluid inserted at the slidi ng interface, may be externally pressurized. Although solid and fluid lubrication represent two distinct categories of lubricants which usually function under competing conditions where
118 on category of lubricant is more favorable than the other, a combined approach, when applicable, could lead to superior performance over substantially increase service times.
119 Figure 6 1. MD snapshot of the PTFE system without molecular fluid. The PTFE chains oriented normal to the plane of the page are color separated into the top (red carbons) and bottom (blue carbons) surf aces with green fluorine atoms. T he interfacial chains (with black carbons) of the bottom PTFE surface are highlighted. These interfacial chains will be characterized in detail to elucidate phenomena resulting from sliding.
120 Figure 6 2. MD snapshot of the two surface PTFE system set up with a separating fluid monolayer. The inter facial chains of the bottom surface, noted in Figure 6 1 are enhanced for emphasis. The monolayer of fluid is denoted by violet carbon atoms and silver fluorine atoms.
121 Fig ure 6 3. MD snapshot of the crystalline PTFE PTFE system set up with four monolayer s of molecular fluid at the interface. The inter facial chains, noted in Figure 6 1 are enhanced for emphasis. The colors in the fluid denote the different layers and represent carbon atoms.
122 Figure 6 4. Illustration of the effect of one fluid la yer of hexafuoroethane(C2F6) and perfluorooctane (C8F18) on crystalline PTFE PTFE friction. Figure 6 5. Illustration of the interfacial displacement of various components in response to the slidi ng of the top PTFE surface. The figure indicates that interfacial chains of the b ottom PTFE surface (see Figure 6 1 black carbon atoms) were displaced a little more than 5 nm in response to ~ 25 nm of s liding by the top PTFE surface. The fluids C2F6 and C8F18 reduced the interfacial wear of the bottom PTFE by roughly the same amount at the expense of intra -fluid molecular displacement
123 Figure 6 6. Carbon-carbon bond length distribution for the one monolayer of the two fluid types both before and after sliding of the top PTFE surface. The graphs indicate a small stretching and a slight shifting of the C -C bonds to larger bond lengths due to sliding. Figure 6 7. Carbon-fluorine bond length distribution for the one monolayer of fluid for both fluid t ypes before and after sliding of the top PTFE surface. The graphs show a small stretching and a slight shifting of the C -F bonds to larger bond lengths due to sliding.
124 Figure 6 8. Illustration of the effect of four fluid layer s of hexafuoroethane(C2F6) and perfluorooctane (C8F18) on crystalline PTFE PTFE friction. Figure 6 9. Illustration of the displacement of various interfacial system components in response to the sliding of the top PTFE surface. The figure shows that interfacial chains of the b ottom PTFE surface (see Figure 6 1 black carbon atoms) were displaced a little more than 5 nm in re sponse to ~ 25 nm of sl iding by the top PTFE surface. The fluids C2F6 and C8F18 reduced the interfacial wear of the bottom PTFE by roughly same amount at the expense of roughly the same degree of intra -fluid molecular displacements
125 Figure 6 10. Interfacial planar displacement of fluid layers perpendicular to the sliding direction of top PTFE surface with the1st layer being closest to the bottom PTFE surface. The distribution was calculated after 21.4 nm of top surface sli ding. The bin size used was 0.02 nm. For all the fluid layers, C2F6 showed a wider range and larger standard deviation of planar molecular displacement.
126 Figure 6 11. Reorientation of molecular fluid molecules towa rds the sliding direction (i.e. x direction) for the perpendicular sliding of C8F18 fluid system at 300K. Bin size is 15 The snapshots represent a top down view of the sliding interface. The histograms indicate that the molecular fluid C8F18 prefers to align with the sliding direction.
127 Figure 6 12. Orientation behavior of molecular fluid for C8F18 viewed along the alignment of the surface chains and perpendicular to the surface chains within the sliding interface. The histogram result is consistent with those from Figure 6 11 in that the molecules prefer to align in a fairly horizontal manner withi n the sliding interface. Rotating the view to along the line of the x axis or sliding direction, the reverse trend was observed in that there are increases in smaller angles as a result of sliding.
128 Figure 6 13. Qua ntification of the orientation order of the C2F6 molecular fluid for perpendicular PTFE PTFE sliding configuration at 300K. Bin size used was 15 represent a top down view of the sliding interface. The histograms indicate that the C2F6 molec ular fluid did not align with the sliding direction in contrast to the C8F18 system (see Figures 6 11 and 6 12).
129 Figure 6 14. Quantification of the orientation order of molecular fluid C2F6 for the perpendicular PTFE P TFE sliding configuration at 300K. Bin size used was 15 indicate that the molecular fluid C2F6 does not align with the sliding direction in contrast to that for C8F18 (see Figures 6 11 and 6 12). The combination of Figures 613 and 6 14, when viewed together, supports the hypothesis that the C2F6 molecules roll to a greater extent than their C8F18 counterparts.
130 Figure 6 15. Graph of Ff vs Fn for perpendicular and parallel PTFE PTFE sliding at 300K for wet and dry sliding. The effect of two different fluorocarbons, C2F6 and C8F18 were explored. 0 5 10 15 20 25 30 35 40 45 50 0 1 2 3 4 5 6 7 8 9 10 Ff(nN) Fn (nN)perpendicular no fluid C8F18 monolayer C2F6 monolayer C8F18 4 monolayers C2F6 4 monolayers ----------------parallel no fluid C8F18 monolayer C8F18 4 monolayers C2F6 monolayer C2F6 4 monolayers
131 Figure 6 16. Molecular snapshots of the interfacial polymer chain of the bottom PTFE surface (top down view). The remainder of the bottom surface, the molecular fluid and the top surface are not shown. The snapshots were taken from sliding system within a narrow load range of 15 17 nN (see Figure 6 15).
132 Figure 6 17. Molecular snapshots for additional sliding of the C8F18 4 monolayer fluid system described in Figure 6 16.
133 Table 6 1 Breakdown of the number of molecules, carbon atoms and total number of atoms for the various fluid systems studied. monolayer: number of molecules carbons atoms 4 monolayers: number of molecules carbons atoms C 2 F 6 120 240 960 480 960 3840 C 8 F 18 30 240 780 120 960 3120 Table 6 2. Densities of the PTFE surface with and without cross -links. The range for the experimental PTFE value denotes the amorphous and crystalline phase respectively.104 The individual fluids densities, apart from that for the PTFE surfaces are also given. The experimental value for the C2F6 the solid phase105 is denoted by the superscript a and the liquid100 experimental value for C8F18 by the superscript b. d ensity (g/cm3) PTFE surface c ross links C 2 F 6 fluid monolayer C 2 F 6 fluid 4 monolayers C 8 F 18 fluid monolayer C 8 F 18 fluid 4 monolayers with without simulation 3.20 2.74 2.05 2.40 2.25 3.07 experiment 2.00 2.302* 1.8786 a 1.77 b Table 6 3. Diffusion coefficients for the fluorocarbon fluids used in this study. Experimental/calculated theoretical values, denoted by *, in water at 25 hexafluoroethane is given. The simulation values were obtained from mean square displacement m easures during thermal and physical equilibration of the surfaces prior to sliding at 300K. Diffusion Coefficient (cm 2 /s) C 2 F 6 fluid monolayer C 2 F 6 fluid 4 monolayers C 8 F 18 fluid monolayer C 8 F 18 fluid 4 monolayers simulation 1.08 x 10 7 1.28 x 10 6 4.30 x 10 8 2.14 x 10 7 experiment/ calculation 5.47 x 10 5
134 Table 6 4 Quantification of friction coefficient and adhesive force using least squares fit ting for perpendicular sliding. P erpendicular sliding F ad No fluid 0.21 11.6 +/ 0.14 C 8 F 18 monolayer 0.16 16.8 +/ 0.13 C 2 F 6 monolayer 0.20 2.9 +/ 0.05 C 8 F 18 4 monolayers 0.14 8.9 +/ 0.10 Table 6 5 Quantification of friction coefficient and adhesive force using least squares fit ting for parallel sliding. Parallel sliding F ad No fluid 0.06 7.09 +/ 0.14
135 CHAPTER 7 CONCLUSIONS The sliding of crystalline self -mated PTFE surfaces showed friction anisotropy. Sliding perpendicular to the chain orientation in both surfaces reveal ed very high friction and molecular wear compared to sliding parallel to the chain alignment in both surfaces. Sliding in a configuration where the chain were oriented perpendicular within the plan e of the sliding interface (i.e. sliding parallel to the chai n orientation in one surface and perpendicular to the chain orientation in the counter -surface) yielded comparatively intermediate friction and wear behavior. The tendency of both the friction and wear behavior for the latter configuration (i.e. the violin configuration) was towards that of the perpendicular sliding configuration with increased sliding distance. As the normal load was increased, the frictional response due to sliding increase d linearly for the three sliding configuration. There was a significant increase in interfacial molecular wear with increasing normal load, especially for the high wear, high friction sliding configurations (i.e. perpendicular and violin sliding configurations). The Amonton friction coefficient (i.e. = ff/fn) generally decreased with increasing normal load for the three sliding configurations explored. The frictional force for the three sliding configurations considered increase d with decreasing temperature. The associated wear behavior did not show clear systematic temperature dependence; however, calculated wear values over a temperature range of room temperature down to 25 K demonstrated a significant difference. As the temperature was decreased, the modified, Amonton friction coefficient (i.e. = ff/fn + C) remained high and largely unchanging with small variations for the perpendicular sliding configuration. The violin sliding configuration showed a sharp increase in friction coefficient to a level comparable to that
136 of the perpendicular configuration between the temperatures of 100 and 150 K. The parallel sliding configuration showed a small steady increase in friction coefficient with decreasing temperature but remain substantially lower than the perpendicular and violin configurations. Additio nally, the adhesion of the two crystalline PTFE surfaces increase with decreasing temperature, with the parallel configuration being significantly higher than the perpendicular and violin configurations. The incorporation of molecular fluorocarbon fluid be tween the two crystalline PTFE surfaces resulted in a drastic reduction in both friction and wear of the surfaces for the perpendicular sliding configuration The su rfaces separated by a monolayer of molecular fluid showed lower friction for the C2F6 fluor ocarbon fluid compared to the C8F18 fluid; however, the rate of frictional increase with increasing normal load was higher for the system incorporating the C2F6 fluid. Additionally, the associated wear was slightly higher for the C2F6 fluid system. For the systems separated by four monolayers of molecular fluid, a much large reduction in friction and wear of the PTFE surfaces was achieved for perpendicular sliding with the C2F6 system demonstrating extremely l ow frictional forces (i.e approximately half that of the parallel sliding configuration without molecular fluid). The systems separated by a monolayer of fluid did not significantly affect the friction and wear for the parallel sliding configuration while the four monolayer C2F6 fluid system showed the lowest friction behavior of all with slightly lower friction that its perpendicular sliding counterpart. While the trends in friction behavior of crystalline PTFE may be identified and the mechanisms explaine d, the wear behavior, which may be viewed as involving stochastic processes is more complex. To gain further insights into the tribological behavior of PTFE, with an emphasis on wear, enhanced models that take into account the amorphous domain of the
137 poly mer structure are need ed This would allow for a richer description of the overall tribological behavior of PTFE with consideration given to mechanisms of the amorphous phases. Such an undertaking would continue to add to the foundational insights for the effective design of extreme conditions composite lubricants such as carbon nanotube reinforced PTFE. Viewed holistically, the findings of this work are significant from three different perspectives with regard to PTFE tribology. 1) The establishment and cl arification of micro processes associated with PTFEs friction anisotropic suggests that the polymer may be exploited in a variety of applications in such a manner as to provide low friction and to delay the onset of prohibitive wear by sliding along the p olymer s chain alignment. Specifically, tribological applications involving unidirectional sliding would benefit the most. 2) As mentioned in the introduction to this chapter, it has been recently proposed that PTFE exhibits thermally activated friction with a transition from relatively low to high friction with decreasing and relatively temperatures The results f or the violin sliding configuration described in Chapter 5, show thermally mediated friction behavior with a significant increase from relativel y intermediate to high between the temperature s of 100 K and 150 K. This demonstrates that the exploration of PTFEs friction anisotropy with regard to different sliding configurations is the key to clarifying the mechanisms of its thermally activated fric tion. MD simulation has proven to be a unique and powerful technique that may be exploited in such an undertaking. 3) The combination of PTFE with a compatible fluid lubricant, where applicable, represents a strong, alternative approach (compared to filler incorporation into the polymer matrix) for sustained low friction and polymer wear.
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144 BIOGRAPICAL SKETCH Peter R. Barry received a Bachelor of Science in computer science from Claflin University in 2002 and a Master of Science in computer engineering from the University of Florida in 2004. By utilizing the thinking strategies and increase mental frame of reference he has acquired throughout his educational career as a university student, he has lost hundreds of illusions about life as it relates to our planet and the interactions among people of different cultures who inhabit it. As a result, he has developed a strong interest in the interactions among people of different cultures, more specifical ly, interpersonal multicultural interactions as a nanoscopic form of social intercourse. It is his quest to actively cultivate new illusions each day by directly engaging in an d postulating new theories regarding nanoscopic multicultural social intercourse with the idea of not only gaining deeper insight into the scientific aspects of our physical world from various viewpoints (e.g. chemical, geological, pharmacological, biological etc.) but to develop a profound understanding of people in general; that i s, their thinking and motivations (both conscious and subconscious), actions in response to stimuli (environmental and social ), their fears, hidden secrets, hopes and aspirations with the ultimate personal goal being to not just simply survive or exist but to truly live.