Identifying the Mechanisms of Polymer Friction through Molecular

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Identifying the Mechanisms of Polymer Friction through Molecular Dynamics Simulation Ling Dai, M. Minn, N. Satyanarayana, Sujeet K. Sinha, and V. B. C. Tan* Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore S117576, Singapore ABSTRACT: Mechanisms governing the tribological behavior of polymer-onpolymer sliding were investigated by molecular dynamics simulations. Three main mechanisms governing frictional behavior were identified. Interfacial “brushing” of molecular chain ends over one another was observed as the key contribution to frictional forces. With an increase of the sliding speed, fluctuations in frictional forces reduced in both magnitude and periodicity, leading to dynamic frictional behavior. While “brushing” remained prevalent, two additional irreversible mechanisms, “combing” and “chain scission”, of molecular chains were observed when the interfaces were significantly diffused.

’ INTRODUCTION The development of new experimental techniques in the last 2 decades, such as the microbalance technique, surface force apparatus, and atomic force microscopy (AFM), has brought about renewed research interest in nanotribology.1,2 In 1987, Mate el al. reported periodic stick slip motion of a tungsten tip sliding on a graphite surface3 and measured the coefficient of friction (COF) to be 0.012. The periodicity of the stick slip was determined by the lattice structure of the graphite surface. Similarly, periodic stick slip was also observed for a silicon tip sliding on a mica surface.4 Subsequently, several tip substrate friction studies were reported by Bhushan’s group. Frictional studies involving surfaces of Si, SiO2, Si3N4, and diamond were conducted, and very low COFs were recorded, with most below 0.1.5 8 Polymer tribology was reported by Maeda et al.,9 who found that a cross-linked polymer (polystyrene and polyvinyl benzyl chloride) has a significantly lower COF than a noncross-linked polymer because of the diffusion of polymer end segments. At the nanometer scale, force measurement is a challenge and experimental works are still very limited. Numerical approaches, such as molecular dynamics (MD) simulations, are establishing themselves to be effective tools for analyzing nanotribological mechanisms.10 Robbins’s group11,12 conducted pioneering and important nanotribology numerical investigations in the early 1990s. They modeled a block of atomic film sandwiched between two rigid walls. When one wall was dragged with a spring while the other wall was kept fixed, the motion of the atomic film at the wall film interface was observed to display a stick slip phenomenon. The wall was initially stuck to the solid film via atomic interactions. The drag force increased gradually until it exceeded the critical shear stress to melt the film surface, at which point the wall surged forward for a distance. As the wall slipped, the sliding r 2011 American Chemical Society

force decreased. The wall then quickly became stuck to the refrozen film again before the next cycle of stick slip. At higher sliding rates, the stick slip behavior changed to dynamic frictional sliding. Fluctuations of the friction force during dynamic frictional sliding were lower than in the case of stick slip sliding. It was proposed that dynamic fiction was due to insufficient structural reordering after sticking occurs. A super-kinetic friction phenomenon with continually instantaneous ultra-low friction force at very high sliding rates was later reported by Yoshizawa et al.13 More recent works from Robbins’ group were extended to crystalline materials.14,15 They found that two clean contacting crystalline surfaces have little static friction force unless there were “third body” contaminations at the interface because mobile atoms of the third body would cause the two surfaces to be pinned together. MD simulations are increasingly being used as an analytical tool for studying tribology of polymer interfaces. Notably, Bitsanis and Pan simulated the equilibration of an oligomer film sandwiched between two solid cubic walls and found that polymer chains that adhered to the wall need more time to relax than those in the film bulk.16 Tsolou et al. reported that structures with longer polymer chains led to a higher COF because of the diffusive entanglement.17,18 Sivebaek et al. found that the friction force was much higher for polymer polymer interfaces than polymer metal interfaces using coarse grain models because of weak interactions between polymer and metal units.19 It has also been reported that, at sufficiently high sliding rates, the surface of the polymer film shows flow characteristics beyond which the shear stress increases monotonically with the sliding rate.20 Received: July 19, 2011 Revised: October 29, 2011 Published: November 01, 2011 14861

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Figure 1. Front views of polymer models: (a) slider for model I and substrate model, (b) slider for model II, and (c) slider for model III. The substrates for all three models are the same. The width of the cell is 32 Å. Gray dots indicate C atoms, and white dots indicate H atoms.

The effect of the sliding rate was also studied via the coarse grain model by Farrow et al., who claimed that the COF increases linearly and then logarithmically with the increase of the sliding rate.21 In other publications, the tribology of the polymeric interface was reported to be also dependent upon the sliding direction22 and degree of cross-linking in the polymer bulk.23 Interestingly, Tanaka and Kato reported that the COF dropped as the normal load increased in their perfluoropolyether-lubricated interface model.24 Recently, the tribology of organic films has seen many investigations into the self-assembled mononlayer (SAM) deposited on rigid substrates. Glosli and McClelland proposed two mechanisms for the stick slip friction between two SAM surfaces:25 a plucking mechanism associated with the sudden release of shear strain via molecular deformation and a more continuous viscous mechanism arising from continuous collisions of atoms from opposite films. The effects of the molecule chain length and sliding velocity were studied by Chandross et al.,26 who found that the friction force was independent of the chain length at 2 GPa contact pressure. The friction force was weakly correlated to the sliding velocity only when the pressure dropped to 0.2 GPa. The tribology of SAMs was recently reviewed by Harrison’s group.27 Materials of current interest are those with noncrystalline structures, such as amorphous polymers. Tribological behaviors and, more importantly, their underlying mechanisms remain an area of active research for amorphous polymers. In this report,

MD simulations were carried out to study the tribological phenomena of amorphous polyethylene interfaces to determine the governing mechanisms.

’ EXPERIMENTAL SECTION Two atomistic polyethylene film models, a 50 Å thick substrate film and a 20 Å thick slider film, containing 10 116 atoms are constructed for this investigation. The amorphous films have the same density of 0.94 g/cm3 as standard commercial polyethylene and are constructed with linear polyethylene chains containing 50 ethylene monomers each. The amorphous structure is constructed following the procedure used by the commercial Materials Studio software.28 Individual polymer chains were randomly placed in a cell one at a time until the target density is obtained. Their atomic positions were adjusted to avoid overlapping or overclosing of any pair of atoms. The Monte Carlo method was then used to locate the minimum energy state as the starting structure. Three slider substrate models, with the same substrate film but different conditions imposed on the slider, were built, as shown in Figure 1. A layer of molecules at the bottom of the substrate was spatially fixed. Another layer of thermally quenched atoms lies above them and is topped by a layer of free atoms to form the substrate. Model I has a rigid slider, whereas in model II, a thin layer of atoms at the bottom of the slider is free, with the rest of the slider remaining rigid. The slider in model III has the same layered structure as the substrate. Periodic boundary conditions were applied in the plane of the substrate and slider. MD simulations were carried out using the LAMMPS code29 with the PCFF interatomic forcefield30 and a 10 Å cutoff distance. Atoms in the 14862

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Figure 2. Views of interfaces. (a) Schematic of interface types: A, nondiffused; B, slightly diffused but non-entangled; and C, diffused and entangled. Equilibrated interfacial configurations of three models: (b) model I, (c) model II, and (d) model III. The slider atoms were marked differently in red (C atoms) and pink (H atoms) to highlight the level of interfacial diffusion. rigid region of the slider were set to move as a block. Periodic scaling of the atomic velocities was performed every 0.1 ps to maintain a temperature of 300 K for the thermal quench layer. The remaining atoms were not constrained. The position, velocity, and acceleration of all of the individual atoms were updated every 1 fs.

’ RESULTS AND DISCUSSION The simulations started with the slider at a position more than the cutoff distance above the substrate. The slider was then moved downward and brought in contact with the substrate. A constant contact pressure of 1 GPa was applied on the top of the slider throughout the sliding simulation. As the slider approached the substrate, slider and substrate atoms interacted to create an interface. The interface would initially oscillate before becoming stable. The equilibrated interface configurations of the three models gave rise to different types of interface conditions, as shown in Figure 2a, and have similar features, with interface conditions described by Maeda et al.9 Type A has a distinct interface, with atoms from the two films located distinctly on opposite sides of the interface. Friction for the type-A interface is often expected to be weak. In type B, the end segments of the polymer chains from both sides diffuse slightly across the interface. The tribological interaction is moderately stronger than type-A interfaces because of stearic barriers posed by the diffused polymer chain ends during sliding. The type-C interface represents interfaces with strong interdiffusion accompanied by chain entanglement of molecules from both the slider and substrate. The interfacial interactions would be the strongest of the three. Panels b d of Figure 2 are snapshots of the equilibrated interfacial structures of three models. Obvious differences in the level of interfacial diffusion induced by different slider conditions are seen. The interfacial structures almost entirely resemble type A in model I, whereas mainly type-B with some type-A and a small fraction of type-C interactions are found in model II. In model III, a combination of type-C and type-B interactions are present.

After the interface has stabilized, a constant horizontal sliding velocity was applied to the rigid layer of atoms in the slider. The friction force was taken to be the reaction force of the substrate acting on the slider in the sliding direction, and the normal force was the constant normal pressure applied on the top of the slider. Figure 3 presents the simulation results for model I at sliding rates of 0.1, 1, and 10 m/s, for a total sliding distance of 10 nm. The charts show the time histories of the COF between the slider and substrate (Figure 3a), the instantaneous average velocities of atoms on the surface of the substrate (Figure 3b), and the average horizontal displacements of these surface atoms from their original positions (Figure 3c). Surface atoms are defined as substrate atoms, which lie within the interatomic forcefield cutoff distance from slider atoms. For sliding at 0.1 m/s, an obvious periodic stick slip phenomenon is observed. The cause of stick slip is interpreted in Figure 4. Figure 4a shows the initial equilibrated interfacial configuration prior to sliding. The polymer chains within the substrate are entangled in the bulk with a few end segments protruding loosely out at the interface. Figure 4b is a schematic of the relative interfacial deformation. It shows atom A from the surface of the slider interacting with the end atom of a substrate polymer chain as the slider is dragged across the substrate. During the periods of sticking, the force on the substrate near atom A increased until it attains a threshold value corresponding to the peak interatomic attractive force from atom A. The peak friction force is attained at intervals of 4.1 nm (Figure 3) sliding distance, the intervals at which the substrate polymer chain detached abruptly from atom A and retracted upon being released. The low sliding speed provides ample time for the molecules to relax almost completely before they are stretched again. Because of the high degree of entanglement of the polymer chains in the bulk and the low sliding speed, the release of a single molecule triggered the release of a series of other surface atoms within a stick slip cycle. This concurrent deformation and full relaxation of a significant number of atoms led to the abrupt drops in the COF (Figure 3) between “stick” and “slip”. 14863

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Figure 3. Time histories of simulation data for model I: (a) COF between the slider and substrate (top), (b) instantaneous average velocities of atoms on the surface of the substrate closest to the slider (middle), and (c) average horizontal displacements of substrate surface atoms from their original positions (bottom), for sliding velocities of 0.1 m/s (left), 1 m/s (center) and 10 m/s (right).

Figure 5. Schematic description of interfacial polymer chain deformation mechanisms for diffused interfaces. The dark and light gray lines represent polymer chains from the slider and substrate, respectively. Figure 4. (a) Initial interface configuration, (b) illustration of full relaxation, and (c) incomplete relaxation during “brushing” deformation. Unfilled circles denote substrate atoms, and filled circles denote atoms in the slider.

Because the slip of surface atoms on the substrate was in the opposite direction to the sliding, the average of their instantaneous velocity was negative at the commencement of slip (Figure 3). From the thermodynamics of individual surface atoms Ek = 3/2kBT (where Ek is the kinetic energy, kB is the Boltzmann constant, and T is the temperature), the instantaneous temperature of the surface atoms at the onset of slip was determined to have reached the regime of melting (417 425 K), an observation in congruence with the Debye Waller factor analysis from Robinson’s model.11 With sufficient time to relax, the surface atoms returned close to their original positions before they are stuck to and dragged along by the next slider atom (atom B in Figure 4b) to commence the next cycle of stick slip. It can

seen from Figure 3 that all of the results for sliding at 0.1 m/s show a regular periodicity of 4.1 nm sliding distance because of simultaneous relaxation of polymer chains under such slow sliding. At a higher sliding velocity of 1 m/s, the spatial frequency of the stick slip is higher. The reduced relaxation time meant that the polymer chain end segments of the substrate have insufficient time to relax substantially between periods of sticking. During slip, no clear concurrency of polymer chain deformations was observed because of the insufficient time to trigger slippage of many molecular chains within a stick slip cycle. Therefore, the periodicity of stick slip cycles became irregular, and fluctuations in the COF (Figure 3) are of a smaller magnitude. The higher sliding speed also brought more frequent and stronger atomic collisions at the interface, leading to a higher instantaneous speed of surface atoms. As illustrated in Figure 4c, the surface atoms of the substrate collided repeatedly with the slider atoms, providing no opportunity for complete relaxation. This is similar to the “viscous mechanism” reported in Glosli’s work.25 In comparison 14864

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Figure 6. Time histories of simulation data for model II: (a) COF between the slider and substrate (top), (b) instantaneous average velocities of atoms on the surface of the substrate closest to the slider (middle), and (c) average horizontal displacements of substrate surface atoms from their original positions (bottom), for sliding velocities of 0.1 m/s (left), 1 m/s (center), and 10 m/s (right).

to the simulations of 0.1 m/s sliding velocity, the surface atoms were dragged along further, i.e., rebounded less during slip, for 1 m/s sliding velocity. These atoms at the interface made irreversible displacement in the sliding direction even after removal of the slider, indicating the existence of plastic surface deformation. When the sliding velocity was increased to 10 m/s, the tribological characteristics conformed to pure dynamic frictional sliding (Figure 3). It is noted that the maximum velocity recorded for the surface atoms is much lower than the slider velocity, indicating that the surface no longer adheres to the slider. This also suggests that there is a limiting sliding velocity beyond which sticking is not observed and the stick slip phenomenon will switch to dynamic frictional sliding. The simulations using model I suggest that tribological behavior is dependent upon the sliding velocity. Regular periodic stick slip is characteristic of slow sliding, but with increasing sliding speed, the polymer substrate no longer showed evidence of periodic relaxation because of the absence of sufficient molecular reconfiguration. Instead, the frequency of the stick slip cycles becomes higher, and fluctuations in the COF are smaller in magnitude, as shown in Figure 3. Beyond a critical sliding speed, characteristics of dynamic frictional sliding were observed. Because of the significant interfacial diffusion, the sliding tribology in models II and III was dominated by the interactions of the chain segments that have diffused across the interface. As shown in Figure 5, three mechanisms of deformations, “brushing”, “combing”, and “chain scission”, were identified for the substrate polymer chains. Brushing occurs when the substrate chains only interfered with a small segment of the slider chains [no more than the length of three polyethylene (PE) monomers]. The substrate chain segments are likely to be bent and pressed down by the collisions from the sliding units (Figure 5a) as they brush across the opposite surface. At low sliding velocities (e.g., 0.1 m/s), the substrate chain end segments were observed to repeatedly bend and straighten and diffuse back into the slider region again, giving rise to periodic tribological characteristics (Figure 4b). However, in the case of fast sliding, such as

at 10 m/s, the chain segments were pressed down throughout the sliding process because the continuous atomic collisions did not allow for appreciable straightening of substrate chain end segments (Figure 4c). When the diffused substrate segments did not directly obstruct the sliding chains, the substrate chains will normally follow zigzag motions as they weave and squeeze in between neighboring slider chains (Figure 5b); i.e., the molecular chains from opposite surfaces “combed” through one another. “Combing” requires little interface deformation and, therefore, does not contribute much to frictional forces. Besides the widely observed “brushing”, “combing” was more noticeable in model III than model II because of the deeper surface diffusion in model III. Very rarely did scission of molecular chains occur. During the sliding process, the lengths of individual bonds were monitored. Once a bond extended beyond a cutoff distance as defined by the PCFF potential in LAMMPS,29 the chemical binding was considered to be weak enough to ignore and bond breakage was assumed to have taken place. “Chain scission” (Figure 5c) only happened when the substrate chains were deeply diffused into the slider and, more importantly, almost completely blocked the path of the sliding units. Some chains were even entangled with others. During sliding, the diffused substrate chains were held tightly in place and dragged along in the sliding direction. The diffused chains would then fully straighten before being finally sheared in two. “Chain scission” only appeared in model III and only for fast sliding speeds of 1 10 m/s. After breakage, the sheared-off segment further diffused into the slider and joined the sliding units of the slider. The cropped substrate chains were not long enough to diffuse deep into the slider again and experienced “brushing” with continued sliding. There was significant reconfiguration of the interfacial structure following the scission of molecular chains, resulting in reduced fiction. Figures 6 and 7 present the time histories of COF, surface atom velocities, and surface atom displacement for models II and III, respectively. At 0.1 m/s, periodic stick slip was still observable but much less defined than that in model I. 14865

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Figure 7. Time histories of simulation data for model III: (a) COF between the slider and substrate (top), (b) instantaneous average velocities of atoms on the surface of the substrate closest to the slider (middle), and (c) average horizontal displacements of substrate surface atoms from their original positions (bottom), for sliding velocities of 0.1 m/s (left), 1 m/s (center), and 10 m/s (right).

Regular periodic stick slip is the manifestation of the deformation and relaxation of molecular chains “brushing” over one another, a dominant feature of slow sliding for model I. While “brushing” continued to be widespread for models II and III, the additional phenomena of “combing” and “chain scission” masked the stick slip cycles. This is because “brushing” is largely a reversible deformation and relaxation of molecular chains, whereas there is no recovery from “combing” and “chain scission” during sliding. Hence, the surface atoms in models II and III displaced further and further away from their original positions even after each stick slip cycle, as compared to model I. With increasing sliding speeds, the COF curves became irregular and gradually transformed to dynamic frictional sliding. It is noticed that the surface atoms of interfaces with stronger surface diffusion displaced significantly in the sliding direction at the initial stage and then oscillated about some equilibrium configuration without moving any further, as shown by the plots of surface atom displacements in Figures 6 and 7. “Brushing” continued to be the most prevalent interface deformation and the main cause of the fluctuations in Figures 6 and 7. The lower amplitude of the fluctuations for models II and III compared to model I (Figure 3) is again due to the presence of “combing” and the occasional “chain scission”. Higher sliding rates brought about more chain scission. At 10 m/s sliding in model III, the scission of chains stopped after a certain sliding distance (5.2 nm), as reflected by a reduction in the fluctuations of the COF plot (Figure 7). Figure 8 shows the time-averaged COF of the three models as a function of the sliding rate. As expected, models with stronger interfacial diffusion had higher COF and required higher sliding speeds to induce the transformation from stick slip to dynamic frictional sliding because of the denser and stronger interfacial locking. It is also observed that the COF increased during the transformation from periodic stick slip to irregular stick slip but dropped when pure dynamic frictional sliding occurred. This was due to the lower relative percentage increase in friction forces to normal forces during the transformations, although both

Figure 8. Time-averaged COF of three models as a function of the sliding speed.

frictional and normal forces increased. For all three models, the COF became independent of the sliding velocity in the pure dynamic frictional sliding regime, in agreement with Glosli’s model.25

’ CONCLUSION In conclusion, the tribology of the polymer polymer interface has been studied by MD simulations and several friction mechanisms were observed. Interfacial configuration determines the characteristics of the tribological behavior. Three mechanisms, namely, “brushing”, “combing”, and “chain scission”, govern interfacial deformations during frictional sliding. Three regimes of velocity-dependent tribological behavior were also identified: periodic stick slip, irregular stick slip, and dynamic frictional sliding. 14866

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’ AUTHOR INFORMATION Corresponding Author

*Telephone: +65-65168088. Fax: +65-67791459. E-mail: mpetanbc@ nus.edu.sg.

’ ACKNOWLEDGMENT The authors acknowledge the financial support given to this work by the National Research Foundation (NRF), Singapore (Award NRF-CRP 2-2007-04). ’ REFERENCES (1) Kaneko, R.; Umemura, S.; Hhirano, M.; Andoh, Y.; Miyamoto, T.; Fukui, S. Recent progress in microtribology. Wear 1996, 200, 296. (2) Persson, B. N. J. Sliding friction. Surf. Sci. Rep. 1998, 33, 83. (3) Mate, C. M.; McClelland, G. M.; Erlandsson, R.; Chiang, S. Atomic-scale friction of a tungsten tip on a graphite surface. Phys. Rev. Lett. 1987, 59, 1942. (4) Akamine, S.; Barrett, R. C.; Quate, C. F. Improved atomic force microscope images using microcantilevers with sharp tips. Appl. Phys. Lett. 1990, 57, 316. (5) Ruan, J. A.; Bhushan, B. Frictional behavior of highly oriented pyrolytic graphite. J. Appl. Phys. 1994, 76, 8117. (6) Bhushan, B.; Kulkarni, A. V. Effect of normal load on microscale friction measurements. Thin Solid Films 1996, 278, 49. (7) Bhushan, B.; Li, X. D. Micromechanical and tribological characterization of doped single-crystal silicon and polysilicon films for microelectromechanical systems devices. J. Mater. Res. 1997, 12, 54. (8) Bhushan, B.; Sundararajan, S. Micro/nanoscale friction and wear mechanisms of thin films using atomic force and friction force microscopy. Acta Mater. 1998, 46, 3793. (9) Maeda, N.; Chen, N. H.; Tirrell, M.; Israelachvili, J. N. Adhesion and friction mechanisms of polymer-on-polymer. Science 2002, 297, 379. (10) Gao, J. P.; Luedtke, W. D.; Gourdon, D.; Ruths, M.; Israelachvili, J. N.; Landman, U. Frictional forces and Amontons law: From the molecular to the macroscopic scale. J. Phys. Chem. B 2004, 108, 3410. (11) Thompson, P. A.; Robbins, M. O. Origin of stick slip motion in boundary lubrication. Science 1990, 250 (4982), 792. (12) Robbins, M. O.; Thompson, P. A. Critical velocity of stick slip motion. Science 1991, 253 (5022), 916. (13) Yoshizawa, H.; McGuiggan, P.; Israelachvili, J. Identification of a second dynamic state during stick slip motion. Science 1993, 259 (5099), 1305. (14) He, G.; Muser, M. H.; Robbins, M. O. Adsorbed layers and the origin of static friction. Science 1999, 284, 1650. (15) Muser, M. H.; Robbins, M. O. Conditions for static friction between flat crystalline surfaces. Phys. Rev. B: Condens. Matter Mater. Phys. 2000, 61, 2335. (16) Bitsanis, I. A.; Pan, C. M. The origin of “glassy” dynamics at solid oligomer interfaces. J. Chem. Phys. 1993, 99, 5520. (17) Tsolou, G.; Mavrantzas, V. G.; Theodorou, D. N. Detailed atomistic molecular dynamics simulation of cis-1,4-poly(butadiene). Macromolecules 2005, 38, 1478. (18) Tsolou, G.; Stratikis, N.; Baig, C.; Stephanou, P. S.; Mavrantzas, V. G. Melt structure and dynamics of unentangled polyethylene rings: Rouse theory, atomistic molecular dynamics simulation, and comparison with the linear analogues. Macromolecules 2010, 43, 10692. (19) Sivebaek, I. M.; Samoilov, V. N.; Persson, B. N. J. Frictional properties of confined polymers. Eur. Phys. J. E: Soft Matter Biol. Phys. 2008, 27, 37. (20) Sivebaek, I. M.; Samoilov, V. N.; Persson, B. N. J. Velocity dependence of friction of confined hydrocarbons. Langmuir 2010, 26, 8721. (21) Farrow, M. R.; Chremos, A.; Camp, P. J.; Harris, S. G.; Watts, R. F. Molecular simulations of kinetic-friction modification in nanoscale fluid layers. Tribol. Lett. 2011, 42, 325.

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