Influence of the Molecular Level Structure of Polyethylene

Tribol Lett (2011) 42:193–201 DOI 10.1007/s11249-011-9763-0

ORIGINAL PAPER

Inﬂuence of the Molecular Level Structure of Polyethylene and Polytetraﬂuoroethylene on Their Tribological Response

Patrick Y. Chiu • Peter R. Barry • Scott S. Perry • W. Gregory Sawyer • Simon R. Phillpot • Susan B. Sinnott

Received: 15 September 2010 / Accepted: 23 February 2011 / Published online: 11 March 2011 Ó Springer Science+Business Media, LLC 2011

Abstract Crosslinks occur in polymers following irradi- 1 Introduction ation and are used in computational simulations to mimic the effects of chain tangling. Here, the effect of crosslink Approximations are often needed when materials are density on the tribological behavior of atomic-scale models modeled at the atomic-scale in molecular dynamics (MD) of polyethylene and polytetrafluoroethylene is determined or similar types of simulations. For example, periodic using classical molecular dynamics simulations. In the boundary conditions [1] are used to remove edge effects, simulations, oriented crosslinked surfaces are slid in dif- thermostats [2] are used to regulate temperature, and inter- ferent directions over a range of applied normal loads. The atomic interactions are described by empirical potentials. results indicate that, at the same normal load, the friction In the case of modeling, the tribological behavior of force increases with increased crosslink density. In addi- polymers with chains oriented in the plane of sliding, tion, the influence of randomized versus ordered cross- crosslinks have been used to provide structural integrity to linking on the simulated tribological behavior is each polymer surface and to mimic the effects of chain investigated. Finally, the influence of crosslink density on entanglement and the resulting increased interaction among the simulated wear mechanisms of polyethylene and the polymer chains that occur in the experimental system polytetrafluoroethylene is elucidated. The results have [3–5]. important implications for the atomic-scale modeling of Experimentally, the actual crosslinking of polymer sur- friction at the interfaces of polymers that have been irra- faces can be achieved through plasma and irradiation diated or contain entangled chains. treatments [6, 7], with the treated surfaces often displaying more resistance to wear. For instance, chemically cross- Keywords Dynamic modeling Á Nanotribology Á Friction linked and radiation-crosslinked polyethylene (PE) bear- mechanisms Á Wear mechanisms Á Polymers (solid) Á ings [8] have reduced abrasive and adhesive wear relative Fluorocarbons Á PTFE to untreated bearings. This resistance has been shown to be heavily influenced by surface topography [9, 10]; the changes in surface topography as a result of crosslinking have been proposed as a possible method to reduce wear and friction coefficients [11]. Since the surfaces in the atomic-scale MD simulations typically have areas on the order of hundreds of nanometers squared, they effectively P. Y. Chiu Á P. R. Barry Á S. S. Perry Á W. G. Sawyer Á model the experimental tribological responses of chains S. R. Phillpot Á S. B. Sinnott Department of Materials Science and Engineering, University of that are confined by either entanglement with other chains Florida, Gainesville, FL 32611, USA or by actual crosslinks [12, 13]. Surface topography and surface kinematics are expected & W. G. Sawyer Á S. B. Sinnott ( ) to depend on the properties of the individual polymer under Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611, USA consideration. For example, one hypothesis for the low e-mail: [email protected]fl.edu friction of polytetrafluoroethylene (PTFE) and its 123 194 Tribol Lett (2011) 42:193–201 composites is that the long chains orient during sliding, empirical bond order (REBO) [21] potential. Long range making a low shear-strength interface [14]. As a solid van der Waals interactions between polymer chains are lubricant, transfer films of PTFE are thus thought to calculated in the form of a Lennard-Jones potential [22]. facilitate the primary mechanism of low friction [15]. Although electrostatic interactions play a prominent role in While it is known that the wear resistance of PTFE modeling fluoropolymers, the effect of these interactions is increases with increasing crystallinity, the atomic-scale somewhat diminished by the high contact pressures mechanisms by which this occurs are unknown [16]. The explored in our simulations. The orthorhombic unit cell distance between crosslinks is one material property that [23] of crystalline PE or PTFE is considered in the simu- has been proposed to describe the wear behavior [17]; in lations, and the simulation setup is shown schematically in particular, Muratoglu et al. [17] reported that the wear rate Fig. 1a. There are 17 monomers in each polymer chain, decreases linearly with crosslink density. leading to a chain length of 4.4 nm for PE and 4.5 nm for The effect of polymer chain orientation on tribological PTFE. properties has also been investigated. For instance, In test simulations of PTFE aligned films without Scho¨nherr and Vancso [18] used scanning force micros- crosslinks, where the chains experienced only van der copy and scanned both parallel and perpendicular to highly Waals interactions with one another, there is little transfer oriented PE and PTFE chains. They found that the friction of externally imposed forces to the tribological surfaces; as during a perpendicular scan was about four times larger a result, sliding occurred between multiple polymer chains than that during a parallel scan. Dunn et al. [19] analyzed both within the slabs and between the slab surfaces. ultrahigh molecular weight polyethylene (UHMWPE) Crosslinks between the chains allow each slab to move as a friction coefficient measurements using a multi-directional single unit in the simulations with a distinct interface tribometer and found that the friction coefficient depended between them. This approach gives each polymer surface on the sliding direction. In addition, Sambasivan et al. [20] sufficient structural rigidity to effectively impart the determined through non-destructive X-ray absorption applied normal load to the tribological interface while still spectroscopy that a cross-shear motion from pin-on-disk maximizing the freedom of motion of the individual motion created more wear on UHMWPE samples than polymer chains. unidirectional sliding. Jang et al. [3] demonstrated with Periodic boundary conditions are applied within the MD simulations that the polymer orientation at the sliding planes of all the surfaces to remove edge effects and to interface of PTFE strongly influences friction and wear, mimic infinite surfaces. Each simulation is composed of consistent with microtribological measurements on bulk two slabs, each containing regions of rigid atoms, PTFE that produced aligned transfer films and strong thermostatted atoms, and active atoms, as illustrated in anisotropy in friction and wear. Fig. 1a. The thermostat is turned off in the direction of In this article, the effect of crosslink density on the tri- sliding to prevent the introduction of numerical artifacts bological behavior of atomic-scale models of PE and PTFE into the predicted frictional forces. Thus, in the case of is investigated using classical MD simulations. In partic- parallel sliding, the thermostat is turned off in the z direc- ular, oriented crosslinked surfaces are slid in different tion, while in the case of perpendicular sliding, the ther- directions over a range of applied normal loads and the mostat is turned off in the x direction. The bottom-most influence of crosslink density on the simulated wear layer of the lower surface is fixed, while the top-most layer mechanisms of PE and PTFE is determined. Additionally, of the upper surface moves as a rigid unit to produce the influence of randomized versus ordered crosslinking on compression and sliding. The forces are recorded on the the simulated tribological behavior is investigated because, rigid topmost layer and smoothed and averaged with while ordered crosslinks are more readily created in com- weighted boxcar averaging in the same way as in [5]. putational systems with periodic boundary conditions, The two PE slabs in sliding contact each contain six randomized crosslinks are more representative of entangled layers for a total of 72 chains. The top six chains of the or experimentally crosslinked systems. bottom slab and the bottom six chains of the top slab form the interface. The thickness of each surface slab is 3.4 nm and the sliding surface area is 4.4 nm 9 4.4 nm. The two 2 Computational Details PTFE slabs also each contain six layers for a total of 60 chains. In this case, the topmost five chains of the bottom The classical MD simulations carried out here numerically slab and the bottom five chains of the top slab form the integrate Newton’s equation of motion with a third-order interface. The thickness of each surface slab is 3.4 nm and Nordsieck predictor corrector using a time step of 0.2 fs. the sliding surface area is 4.5 nm 9 4.5 nm. In addition, an The short range inter-atomic forces are calculated using the extended PE system is considered in order to investigate second-generation, carbon–hydrogen many-body, reactive the effect of surface area on the results. In this case, 123 Tribol Lett (2011) 42:193–201 195

Fig. 1 a Simulation cell of two aligned cross-linked polymer thermostat and active regions of approximately 0.6, 1.2, and 2.2 nm surfaces. Each PE surface is 3.4 nm thick with rigid, thermostat and thickness, respectively. The system is periodic along the x and active regions of approximately 0.5, 1.0 and 1.9 nm thickness, z directions. Schematic views of the x–z plane at the sliding interface respectively. Each PTFE surface is 4.0 nm thick with rigid, for b parallel, c perpendicular, and d violin sliding although a lower crosslink density is used, all the chains schematically in Fig. 1b–d. The predicted friction and fully connect within a given surface to one another because normal forces for each established contact pressure are then the chains are longer. In this system, the chain lengths are recorded. These values are used to quantitatively determine 8.8 nm, and the cell width and depth are 4.4 and 3.4 nm, the friction coefficients and adhesive forces for the differ- respectively. ent sliding configurations for each polymer system. In All systems are equilibrated at a temperature of 300 K. particular, the friction in most cases is found to change Langevin dissipative and stochastic forces are applied to linearly with the applied load in agreement with Amon- the atoms in the thermostatted regions to maintain the tons’ First Law. The slope of the friction force versus temperature at 300 K. The active regions are not con- normal force is the friction coefficient, and the intercept of strained and can evolve freely under the forces produced this line is the adhesive force. across the tribological surface. Each tribological system is initially equilibrated with a 1.5 nm gap between the two surfaces, which is beyond the range of any interatomic 3 Results interactions in the system. The rigid atoms of the top slab of chains are then lowered toward the bottom surface. This We first investigate the influence of crosslink density on compression process entails incrementally compressing simulated friction coefficients and adhesive forces. Table 1 and equilibrating the system at a rate of 10 m/s until the lists the numbers of crosslinks present in the PE and PTFE target normal load is reached. The compression rate used is systems considered and the corresponding crosslink den- consistent with the rate used by us previously [3–5] for the sities. The crosslink density percentage is determined using tribological study of similar PE and PTFE tribological the ratio of crosslinked CH2 or CF2 units to the total systems. Additional equilibration of the system is done to number of units within an individual polymer slab. A PE preclude a predetermined interface before sliding and to crosslink density of 19%, which corresponds to an average ensure that the system is in equilibrium prior to sliding. of one crosslink per every 5.16 CH2 units along any given The sliding process involves moving the top polymer slab chain, and a PTFE crosslink density of 19%, which cor- against the stationary bottom polymer slab. There are three responds to an average of one crosslink per every 5.16 CF2 sliding configurations: in parallel sliding, the chains slide units along any given chain, have the same densities as that parallel to their axes; in perpendicular sliding, the chains used in previous studies [3–5]. However, there are some slide perpendicular to their axes; in violin sliding, the axes differences in the arrangement of the crosslinks in the of the chains of the two sides of the interface are perpen- systems under consideration here and in the systems pre- dicular to each. These sliding scenarios are indicated viously considered. Specifically, the crosslinks considered

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Table 1 Crosslink density using the ratio of crosslinked CH2 units per total CH2 units or crosslinked CF2 units per total CF2 units

Crosslinks Crosslinked Chains CH2 units Total CH2 units Crosslink density Crosslink -3 CH2 units per chain percentage density (nm )

118 236 72 17 1224 19% 3.60 72 144 72 17 1224 12% 2.19 72 144 72 34 2448 6% (extended) 1.09

Crosslinks Crosslinked Chains CF2 units Total CF2 units Crosslink density Crosslink -3 CF2 units per chain percentage density (nm )

98 196 60 17 1020 19% 2.81 60 120 60 17 1020 12% 2.43

Values are for one PE or PTFE surface here are randomly oriented in two directions, while those considered previously had a higher degree of order. As we shall see, the degree of randomness inﬂuences the frictional behavior in some cases. A crosslink density of 12% corresponds to an average of one crosslink per every 8.5

CH2 or CF2 units along any given chain, and represents the minimum number of crosslinks needed to fully connect all the chains within a given surface to one another for this system size. As a result of these crosslink density differences, each polymeric system has an inherently different degree of structural integrity and rigidity. Figure 2 sum- marizes the systems considered and the nomenclature used to refer to these different polymeric tribological systems. The dependence of the friction force on normal force for PE at all crosslink densities is given in Fig. 3 for perpendicular sliding. The polymer chains at the interface slide over each other and compress the polymer slabs when the chains of the upper surface are directly on top of the chains of the lower surface. Thus, during sliding, the normal forces increase as do the friction forces. For all crosslink densities, the friction force at the same normal load is the same to within 2 nN, which, in most cases, is within the standard deviation of the data for a given crosslink density. The friction force is recorded from the forces at the sliding interface that are transferred through the chains of the substrate. Thus, the crosslinking densities simulated are sufficient to capture the evolution of the friction force at Fig. 2 Schematic views of the x–z plane at the sliding interface and naming abbreviation for all systems considered. The first part of the different induced normal loads. The 6% randomized nomenclature designates the polymer system (PE or PTFE), the extended system (PE-6ER-PER in Fig. 2), where the sur- second designates the crosslink density and ordered (O), randomized face has been doubled in the direction of sliding, has the (R), or extended randomized (ER) system, and the last part designates same number of crosslinks as PE-12R-PER (see Table 1). the sliding configuration (PAR for parallel, PER for perpendicular, and VIO for violin) The longer chains in the extended system can be fully connected to one another at the lower crosslink density force (of about 1 nN) is within than the standard deviations such that in both the PE-6ER-PER and PE-12R-PER cases, for the randomized systems, and so is not significant. each chain is crosslinked to its nearest neighbor only once. The dependence of the friction force on normal force for The friction force in the PE-6ER-PER system is lower as a PTFE at all crosslink densities is given in Fig. 3 for per- result of the greater degree of freedom of the longer chains pendicular sliding. Among all crosslink densities, the in this extended system. However, the difference in friction friction force at the same normal load again does not

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Fig. 3 Friction force as a PE-19O-PER PTFE-21O-PER function of normal force for PE 16 PE-19R-PER 16 and PTFE perpendicular sliding PE-12R-PER PTFE-19R-PER at various crosslink densities 14 PE-6ER-PER 14 PTFE-12R-PER 12 12 10 10 8 8 (nN) f (nN) f F

F 6 6 4 4 2 2 0 0 0 5 10 15 20 25 30 35 40 45 50 55 60 0 5 10 15 20 25 30 35 40 45 50 55 60 F (nN) Fn (nN) n deviate more than 2 nN except in the case of PTFE-19O- Table 2 Friction coefficient and adhesive force for all crosslink PER at loads greater than 22 nN. This is due to the fact that densities of PE in perpendicular sliding when high loads are applied to ordered crosslink densities, Crosslink density Friction coefficient Adhesive force (nN) the crosslinks between the PTFE chains at the interface break. As a result, the friction force is much higher (by PE-19O-PER 0.23 ± 0.014 12.3 ± 0.32 about 3 nN) than for all the randomized crosslink densities PE-19R-PER 0.22 ± 0.066 12.7 ± 1.45 at the same normal load. PE-12R-PER 0.20 ± 0.044 13.6 ± 0.92 The friction coefficients for the PE system during perpendicular sliding as a function of crosslink density are given in Table 2. It can be seen that the friction coefficients chains occurs. The simulations yield a higher friction at the various crosslink densities are very similar to one coefficient for PE than PTFE under perpendicular sliding another. This indicates that once all the chains are con- for the randomized crosslink densities [4]. The two ran- nected to one another, small increases in crosslink density domized crosslink densities investigated for PTFE show do not lead to appreciably different behavior. The adhesive very similar force plots. This is because these crosslink forces increase slightly as the crosslink density decreases densities have all the polymer chains connected to their or the amount of order increases, both of which increase nearest neighbors. Consequently, there is efficient load the amount of overlap between atoms at the sliding inter- transfer at these crosslink densities. face. The friction coefficients for the PTFE system during The results for PE sliding in the parallel configuration perpendicular sliding as a function of crosslink density are are given in Fig. 4 and Table 4. At low normal loads given in Table 3. The friction coefficients for the two (5–16 nN), the friction forces are predicted to be close to randomized crosslink densities are nearly the same; the zero due to the commensurate sliding interface; the parallel friction coefficient for the ordered crosslink density is sliding configuration has inherently low friction because nearly twice as high. This indicates the extent to which the interfacial chains of the upper surface move into and ordered crosslinks influence predicted friction coefficients, then remain in the depressions, so the crosslinks do not an effect that will be discussed in more detail in the next transfer the loading efficiently through the surface slab. In section. In this case, the adhesive force increases as the perpendicular sliding, the friction force is higher at low amount of order decreases. This is due to the greater normal loads. At high normal loads of 26–31 nN, the amount of wear that takes place in the ordered crosslink interfacial chains of the top surface are compressed more system relative to the randomized crosslinked systems. when they slide over the interfacial chains of the bottom During perpendicular sliding, the PTFE surface undergoes surface causing a greater friction force. At these higher high molecular wear, as illustrated by widespread chain loads, the friction force for PE-19R-PAR (0.6 nN) is scission and molecular reorientation [5]. The extent of wear greater than the friction force for PE-12R-PAR (0.4 nN), is significantly greater in the case of ordered crosslinks following the trend of increased friction force as the because the ordered array of junctions act as stress con- crosslink density increases. As in the perpendicular sliding centrators along the plane normal to the surface, while in configuration, PE-6ER-PAR has a friction force closest to the case of random crosslinks, the non-ordered array of PE-12R-PAR because of similar load transfer. The friction junctions distributes the stress more evenly. In contrast, force is slightly lower (0.2 nN) because of the greater during perpendicular sliding of PE, stick–slip motion is structural flexibility of the extended chains, as in the per- predicted for all crosslink densities and no rupture of the pendicular case. Not surprisingly, the predicted friction

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Table 3 Friction coefficient and adhesive force for all crosslink Table 4 Friction coefficient and adhesive force for all crosslink densities of PTFE in perpendicular sliding densities of PE in parallel sliding Crosslink density Friction coefficient Adhesive force (nN) Crosslink density Friction coefficient Adhesive force (nN)

PTFE-19O-PER 0.31 ± 0.089 7.8 ± 1.83 PE-19O-PAR 0.077 ± 0.002 -0.1 ± 0.04 PTFE-19R-PER 0.17 ± 0.008 20.2 ± 0.19 PE-19R-PAR 0.021 ± 0.009 -0.2 ± 0.18 PTFE-12R-PER 0.15 ± 0.013 26.3 ± 0.27 PE-12R-PAR 0.015 ± 0.006 -0.5 ± 0.11 coefficients are uniformly low, as are the adhesive forces. The negative values of the adhesive forces are indicative of Table 5 Friction coefficient and adhesive force for all crosslink the repulsion within the Lennard-Jones potential between densities of PTFE in parallel sliding the chains that are in close registry while they slide. Crosslink density Friction coefficient Adhesive force (nN) The results for PTFE sliding in the parallel configuration are given in Fig. 4 and Table 5. For all crosslink densities, PTFE-19O-PAR 0.085 ± 0.006 7.9 ± 0.11 the friction forces at all the normal loads compare very PTFE-19R-PAR 0.083 ± 0.002 20.1 ± 0.03 well, deviating by at most 1 nN from each other. The PTFE-12R-PAR 0.032 ± 0.007 21.8 ± 0.08 friction and normal forces for the PE-19O-PAR are very similar to the forces all the PTFE crosslink densities. This similarity is because the initial chain alignment at the In the parallel configuration, the friction force for PTFE sliding interface is mostly maintained during sliding in is higher than for PE at the same normal force; the adhesive both material cases. PTFE parallel sliding exhibits low force is also higher (by one order of magnitude) in PTFE friction coefficients compared to PTFE perpendicular than in PE. Within the overlapped range of friction coef- sliding. The parallel sliding configuration is inherently low ficients (PTFE ranges from 0.032 to 0.085 and PE ranges friction when the interfacial chains remain in a commen- from 0.015 to 0.077), linearly extrapolating frictional force surate configuration. There is no chain scission or molec- versus normal force yields the higher adhesive force for ular reorientation. The interfacial chains of one surface PTFE. slide over the molecular profile of the interfacial chains of The results for PE sliding in the violin configuration are the other surface. The friction forces and the friction given in Fig. 5 and Table 6. In this case, the friction coefficients are higher for PTFE than for PE, but are still coefficients of the various crosslink densities are again low (less than 0.1). Unlike PE, PTFE shows substantial comparable to one another. The friction coefficients in this adhesive forces, even larger in the case of the randomized configuration are an order of magnitude higher than in the crosslinked systems. This is because the ordered crosslink case of the parallel sliding, but about a factor of two less system stiffens the PTFE and prevents the chains from than the perpendicular case. This is because of the motion interacting as strongly as in the randomized systems, where of the chains, which are not in registry as in the parallel the chains are more flexible. These points are described in case. In particular, the nature of the violin motion, where more detail in the next section, but, in general, the simu- the interfacial chains align perpendicular to each other, lations indicate that adhesion is strongest for more flexible keeps the chains further apart than in the other cases, which systems. is reflected in the significant negative values of the

Fig. 4 Friction force as a PE-19O-PAR PTFE-21O-PAR function of normal force for PE 16 PE-19R-PAR 16 PTFE-19R-PAR and PTFE parallel sliding at PE-12R-PAR PTFE-12R-PAR 14 14 various crosslink densities PE-6ER-PAR 12 12 10 10 8

8 (nN) f (nN) f F F 6 6 4 4 2 2 0 0 0 5 10 15 20 25 30 35 40 45 50 55 60 0 5 10 15 20 25 30 35 40 45 50 55 60 F (nN) Fn (nN) n

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PE-19O-VIO coefficients. In the case of perpendicular sliding in the PE 16 PE-19R-VIO system, PE-19R-PER behaves in a manner that is very PE-12R-VIO 14 similar to that of PE-12R-PER. This is because the chains in the randomly crosslinked structures have more freedom 12 of motion to respond as the surfaces slide relative to the 10 system with ordered crosslinks. This increased flexibility is 8 shown in Fig. 6a by the surface chain movements during (nN) f perpendicular sliding for PE-19R-PER. During the initial F 6 stages of sliding, crosslinks rupture and cause chain 4 bunching but no chain scission. This bunching causes 2 surface chains to roll over adjacent chains. The chains, interestingly, do not reorient in the perpendicular sliding 0 0 5 10 15 20 25 30 35 40 45 50 55 60 direction but rather maintain their initial alignment. There Fn (nN) is no chain scission in either PE-12R-PER or PE-19R-PER. The lightly colored chain in Fig. 6a experiences bowing Fig. 5 Friction force as a function of normal force for PE violin because two crosslinks anchor one end of the chain. sliding at various crosslink densities Crosslink breakage prevents the formation of a stable sliding interface, and the entanglement of the polymer at Table 6 Friction coefficient and adhesive force for all crosslink the surface negatively influences the integrity of the densities of PE in violin sliding interface. Over the time scales considered here, no debris

Crosslink density Friction coefficient Adhesive force (nN) (molecules of CH2 units in the case of PE or molecules of CF2 units in the case of PTFE as a result of bond breakage) PE-19O-VIO 0.13 ± 0.001 -2.5 ± 0.001 forms for any randomized crosslink density system. PE-19R-VIO 0.12 ± 0.011 -2.8 ± 0.394 The friction coefficients predicted by the simulations of PE-12R-VIO 0.10 ± 0.006 -2.9 ± 0.208 PE perpendicular sliding increase slightly with increased crosslink densities; there are variations in the microscopic adhesive forces in this case, which is indicative of the details of the cross-linking explored here that affect tribo- repulsion between the two sliding surfaces. logical behavior. At higher normal forces, the motion of the chains is more restricted because the two surfaces are pressed together, and so the effect of varying the crosslink 4 Discussion density is not as large. Figure 6b illustrates breakage of sub-surface chains in The simulation results indicate a significant influence of PE-19O-PER. A sub-surface chain is exposed to the crosslink ordering on the predicted forces and friction sliding interfacial region and a part of it, two CH2 units,

Fig. 6 a Snapshots illustrate chain movement for PE-19R- PER. The normal load is 30 nN. b Snapshots illustrate chain movement for PE-19O-PER. The normal load is 33 nN

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Fig. 7 Snapshots illustrate chain movement for PTFE-19O- PER. The normal load is 25 nN

is dragged along the sliding direction. The sub-surface 5 Conclusions chains continue to be pulled out until failure, creating debris comprised of these two CH2 units. On the whole, The two polymeric systems investigated here with various these simulations predict that the formation of debris is a crosslink densities have inherently different degrees of random event. It occurs under extreme conditions under structural integrity and rigidity. During the initial stages of the highest applied load (34 nN) with the highest friction sliding, PE crosslinks rupture, which leads to chain force (11 nN) during perpendicular sliding where the bunching. In contrast, certain configurations of PTFE chains are in their least commensurate configuration. It is undergo extensive chain scission. In general, PE chains do under these extreme conditions that debris formation in not experience chain scission under the conditions explored PE with the highest randomized crosslink density is seen; here and are thus predicted to be lower wearing than PTFE, it is not observed in any other randomized crosslink in agreement with experimental observations of the high density in perpendicular sliding or any other sliding wear resistance of UHMWPE [24] and the self-mated configuration. transfer films of PTFE [25]. For both PE and PTFE sys- Figure 7 illustrates breakage of crosslinks between the tems, the friction force increases linearly as a function of PTFE chains at the interface. First, chain scission of the increasing normal force. Overall, increasing the crosslink bottom surface interfacial chains takes place. This is fol- density increases the friction forces at the same normal lowed by chain bunching while still maintaining their ini- forces. The friction coefficients also increase with tial alignment. As the surfaces continue to slide, some increasing crosslink density. chains bow and roll in the sliding direction. Similar wear Taken in its totality, this work indicates that random occurs at all normal loads for PTFE-19O-PER where the crosslinks can be successfully used to model polymer tri- ordered arrays of crosslinks act as stress concentration bology over nanometer-scale regions of the sliding inter- sites. face as long as the density is sufficiently high to transfer the For both materials, breakage of crosslinks occurs only in applied loads and there are no uncrosslinked chains where the ordered crosslink structures. Since the ordered crosslink chain entanglement or physical crosslinks may occur. arrangement has regular spacing between the crosslinks, chain movement is restricted. This restriction of the motion Acknowledgments This was supported by an AFOSR-MURI grant of the polymer chains creates a greater ‘‘stiffness’’. Hence, FA9550-04-1-0367. Any opinions, findings, conclusions, or recom- mendations expressed in this material are those of the authors and do comparison of PE and PTFE perpendicular sliding con- not necessarily reflect the views of the Air Force Office of Scientific figurations illustrates the way in which the stiffness of the Research. The University of Florida High-Performance Computing polymer plays an important role in determining the extent Center is acknowledged for providing computational resources and of wear. support.

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