1 Introduction

Polytetrafluoroethylene (PTFE) is widely used as a solid lubricant and as a key component in composite solid lubricants for dry sliding applications. Since the early 1960s, attempts have been made to elucidate the nature of PTFE’s low-friction properties [1, 2]. These efforts have resulted in the hypothesis that PTFE friction is governed largely by molecular-scale interactions, as opposed to asperity-scale interactions. Subsequent work has supported this early hypothesis [3–7]. Over the last 20 years, many studies have been geared specifically toward understanding the atomic or molecular origins of friction [8–11]. Both simulation [10, 12, 13] and experimental evidence [14–17] of frictional anisotropy in a variety of systems, including PTFE, have been obtained. Interestingly, the low-friction behavior in PTFE has been attributed to chain mobility and a molecular profile lacking in local corrugation as a result of the well-known helical confirmation taken by PTFE chains [4].

Recently, based on nanoscale and macroscale experiments [18–20], it has been proposed that the friction behavior of certain classes of solid lubricants such as PTFE, graphite and molybdenum disulfide (MoS2) are thermally activated. The general hypothesis of thermally activated friction involves the notion that local potential barriers on contacting surfaces may be overcome thermally, thereby facilitating slippage [18, 21]. A logical extension of this hypothesis suggests a reduction in friction with increasing temperature. Additionally, in studies ranging from macro- to nanoscale tribometry to numerical simulations [19, 20, 22], peak-like enhancement of nanoscale friction at cryogenic temperatures has been demonstrated for different classes of hard materials, including amorphous, crystalline and layered surfaces [23]. For example, Brukman et al. [24] reported a combined AFM and molecular dynamics study of friction between diamond and diamond junctions as a function of temperature. Their findings showed a slight decrease in friction with increasing temperature. Barel et al. [25] reported similar findings in their study involving atomic force microscopy (AFM) nanoscale friction in the wearless regime as a function of temperature under clean ultrahigh vacuum conditions. Systems probed included silicon, silicon carbide, sodium chloride and highly oriented pyrolytic graphite. An increase in friction with decreasing temperature was reported with a maximum friction at relatively low temperatures; this was followed by a significant and steady drop in friction at even lower temperatures. Trends for the corresponding adhesive force between the surfaces were less clear. Other findings by the same authors [23] showed that in non-polymeric systems, temperature-independent friction below 220 K was related to the onset of wear process. Other sources [26, 27] suggested that for polymeric systems, nanoscale friction depends strongly on the relaxation dynamics of the polymer chains close to the glass transition temperature.

In the context of polymeric systems, McCook et al. [20] reported on the effects of cryogenic temperatures on the friction coefficient in PTFE and PTFE composites using pin-on-disk tribometry experiments performed in vacuum. Their findings, which also incorporated appropriate data from the literature, showed a monotonic increase in friction with decreasing surface temperature down to 173 K. The data were modeled to a modified Arrhenius equation, which yielded an activation energy of 3.7 kJ/mol (0.038 eV), suggesting that van de Waals interactions are key to the frictional behavior. Later, Burris et al. [21] 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. Similar results, on length scales ranging from macroscale to nanometers, showing an exponential increase in friction, have been reported for other systems [18, 19, 28].

Primarily, two theoretical models have been proposed in the literature to explain the aforementioned variations in mean friction force as a function of temperatures: (1) the Prandtl–Tomlinson model [29, 30] and (2) the mechano-kinetic model which describes friction through a thermally activated rupture and formation of molecular contacts [23, 25]. In the former, there is pronounced stick–slip behavior in the mean friction force over a large temperature range. The “slip length” changes markedly with variation in temperature. The mechano-kinetic model predicts the cessation of stick–slip oscillation in the friction force response for temperatures above a given peak temperature with resulting chaotic motion at the interface, which has been likened to the sliding across a blurred potential surface as a result of the thermal energy.

Previously [31], we have reported on the effect of normal load on self-mated PTFE sliding at 300 K for perpendicular and parallel sliding (Fig. 1). Our simulation results showed an increase in friction with normal load with the increase being more pronounced for the high-friction, high-wear perpendicular sliding configuration. The current study builds on the previous findings by elucidating the effect of temperature and characterizing the new “violin” sliding configuration which, being a combination of the perpendicular and parallel sliding (Fig. 1), is a representative of a typical sliding direction. In this study, molecular dynamics (MD) simulations are used to address the issue of thermally activated friction in PTFE. In particular, both thermally activated and athermal behaviors are seen. The molecular-level processes that are responsible for these behaviors in the simulation are identified and characterized, and its dependence on polymer type is determined.

Fig. 1
figure 1

a Schematic representation of two aligned cross-linked PTFE surfaces. Each surface is 4.5 × 4.5 × 4.0 nm in length (x direction), width (z direction) and thickness (y direction). The rigid, thermostat and active regions are approximately 0.6, 1.2 and 2.2 nm in thickness, respectively. The system is periodic along the x and z directions. The aligned chains in the bottom surface (i.e., the lightly colored chains in panel b, c and d) are oriented along the z direction. Schematic top-down views of the x–z plane at the sliding interface are shown for b perpendicular, c parallel and d violin sliding. The dark colored polymer chains represent those in the top PTFE surface at the interface, while the light colored chains denote those in the bottom PTFE surface at the sliding interface. The arrows denote the sliding direction of the top PTFE surface (Color figure online)

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The details of our simulation approach are given in Sect. 2. In Sect. 3, the effects of temperature on friction and wear are presented with respect to variation in both the sliding configuration and normal load. Section 4 gives detailed descriptions of the microscopic processes associated with the tribological behavior described in the previous section. Section 5 compares the findings for PTFE to those of comparable PE systems. Finally, Sect. 6 presents an overall discussion and conclusions.

2 Methods

The simulated conformation of PTFE [32] was generated by equilibrating a non-helical form of the polymer at 300 K. Experimentally, PTFE takes on a helical conformation with turns of 180° every 13–15 –CF2– units (i.e., the “helical length”) on average depending on the polymer’s phase [33]. For the simulations described here, this “helical length” is somewhat shorter on average and varies according to the length between cross-links. Our level of cross-linking was chosen to impart some level of structural integrity in the form of entanglement in order to effectively simulate self-mated sliding of the system under the influence of an externally applied load. An in-depth analysis of the effects of the degree of cross-linking on friction behavior for our simulated PTFE and PE systems was conducted by Chiu et al. [34]. That study showed that the friction force increases with cross-link density for fixed, constant normal load; however, for the range of normal load considered in that particular study, similar to that used here, a substantial change in friction coefficient was not observed. Potential artifacts of shorter helical lengths are shorter corrugated “slip lengths” along the polymer chain backbone with respect to each other during sliding which, on average (in the wearless sliding regime), would imply a higher level of friction, as was observed. With prolonged sliding, this may lead to a faster transition to the sliding wear regime and consequently even higher friction responses.

As in a number of previous studies of fluorocarbons, partial charges resulting from charge separation in the C–F bond are not explicitly accounted for using Columbic interaction but are implicitly treated by the short-ranged REBO potential [35] which is parameterized to capture the energetics and confirmations of fluorocarbons, in conjunction with the somewhat weaker, long-ranged van der Waals interactions. This implicit treatment of charge may lead to a slight overestimation of friction forces; nonetheless, the qualitative, overall trends of friction with respect to load and temperature should be adequately captured. The simulated system consists of two, initially crystalline slabs of PTFE that are equilibrated and then slid against each other under an applied external normal load. Each PTFE slab is individually cross-linked; this cross-linking ensures sufficient rigidity to effectively impart the applied load to the tribological surfaces, while still maximizing the freedom of motion of the individual polymer chains across the shearing interface. The artificially high cross-link density within each PTFE layer is approximately 2.83 nm−3, which corresponds to an average of one cross-link per every 5 CF2 units along any given chain. Physically, this cross-linking is intended to mimic the effects of the structural reinforcement in semicrystalline polymers arising from entanglement, which takes place on a longer length scale than those accessible to these atomic-level simulations. The effects of changing this cross-link density are discussed elsewhere [34]. Each PTFE crystal or slab contains seven layers of chains for a total thickness of 4.0 nm and a sliding surface area of 4.5 nm × 4.5 nm. The PTFE chains in the bottom layer of the lower slab are held fixed, while the PTFE chains in the top layer of the upper slab move as a rigid unit to compress and slide the top surface against the bottom surface. Periodic boundary conditions are applied in the two in-plane directions to remove edge effects in the sliding surfaces and to more closely mimic real systems (see Fig. 1).

The interatomic potential includes both covalent interactions, calculated using the second-generation, many-body, reactive empirical bond-order (REBO) potential [35, 36], and long-ranged van de Waals interactions, calculated using standard Lennard–Jones (LJ) potentials [37]. Classical molecular dynamics (MD) simulations are used in which Newton’s equations of motion were numerically integrated with a third-order Nordsieck predictor corrector. The MD simulations are carried out with a constant number of atoms, temperature and simulation cell size. The time step is 0.2 fs.

It is well established that the REBO potential does poorly when bonds are systematically expanded [38]. In addition, it is known that REBO-type potentials often tend to somewhat overestimate critical loads and shear stress when applied to fracture mechanics and tribology [38]. This may lead to somewhat higher estimates of the forces required for bond breaking. As a result, the degree of interfacial damage in the form of microscopic wear processes described below for the high-friction, high-wear sliding configurations may be underestimated. Likewise, the minimal amount of wear obtained for the parallel sliding configuration may also be underestimated. In spite of this limitation, the qualitative results should be reliable. Moreover, additional credibility comes from the consistency of the major atomic processes of wear in PTFE with our previous experimental results [14].

In order to maintain the system at the desired temperature and to provide thermal dissipation, Langevin frictional and stochastic forces are applied in the two directions normal to the direction of sliding to the two layers of chains closest to the fixed or rigid moving regions of both the top and bottom PTFE slabs; these are marked as the thermostat region in Fig. 1. The temperature at the sliding surfaces themselves (marked as the active region) is not constrained. A constant sliding velocity of 10 ms−1 is employed. The frictional and normal forces, measured at the rigid moving region on the top PTFE slab, are recorded and analyzed.

Prior to sliding, the two PTFE slabs are equilibrated at the desired temperature with a 1-nm gap between them until the system energy fluctuates in a narrow range around a fixed value. The top slab is then incrementally compressed and equilibrated against the bottom slab to establish a distinct contact pressure, fluctuating within a narrow range. Upon achieving the target contact pressure, the system is further equilibrated for 106 time steps prior to initiating sliding. During this equilibration period, the spatial separation of slabs is fixed; in some cases, the internal equilibration leads to a further decrease in the load. During the tribological simulations, the upper layer of atoms is slid unidirectionally. When the compressed PTFE chains in the two slabs are initially parallel to each other, the top PTFE slab is slid either parallel to the PTFE chains (parallel sliding) or perpendicular to the PTFE chains (perpendicular sliding), as shown in Fig. 1b, d. When the PTFE chains in the two slabs are initially perpendicular to each other, i.e., crossed, the sliding configuration comprises a combination of parallel sliding with respect to one PTFE surface and perpendicular sliding with respect to the other; we refer to this as “violin” sliding, which is shown in Fig. 1c. The simulations for all sliding configuration are carried out at constant surface displacement with continuous and constant interfacial contact maintained during sliding. Short-time fluctuations in the load are observed because the force is determined at some distance from the inherently corrugated sliding interface. However, the overall trend in the forces remains constant and experiences significant evolution only when the interfacial chains undergo gross damage and rearrangements due to sliding.

These simulation studies are carried out over temperatures ranging from 25 to 300 K. The normal loads considered range from 0 to 40 nN, which corresponds to pressures from 0 to 2 GPa. Sliding distances of 14–50 nm are examined, and the lateral forces and normal forces are monitored throughout. The average of each is then calculated over the entire sliding event, excluding the first 2 nm of motion during which the system accumulates shear strains largely without slip across the interface. The friction coefficient and a projected adhesive force for each sliding geometry (perpendicular, violin and parallel) and for each temperature are then determined from a least-square fits to three or four well-spaced frictional forces/normal forces pairs [31].

3 Effects of Temperature, Load and Sliding Direction

Figure 2 shows the dependence of the friction force on the normal force at a number of different temperatures for the perpendicular (Fig. 2a), violin (Fig. 2b) and parallel (Fig. 2c) sliding geometries. The error bars on the normal load and frictional forces are determined using the previously outlined protocol [31]. As discussed in the previous study, the raw data set from the simulations yields in excess of 18,000 points for each simulate run. Weighted boxcar averaging is used to reduce this large data set to a scientifically and statistically meaningful result. The results of each boxcar window size sampled (i.e., 10, 50, 100, 500 and 1000 data points representing spatial distances of 0.02, 0.1, 0.2, 1 and 2 nm, respectively) correspond to force averages that are almost identical to the original data set. A number of general trends can be seen in these results. First, for all three sliding geometries, and at all temperatures, there is an almost linear dependence of the frictional force on normal force. This is a strong indication of the internal consistency of the simulation results and allows reliable estimates of the friction coefficient to be extracted from the slopes. Second, for any fixed normal force, the frictional force increases as the temperature decreases; however, the temperature dependence does appear to significantly weaken below 100 K. Third, for the same normal force, the frictional force for parallel sliding is less than for the violin case which, in turn, is less than for the perpendicular case. As discussed in detail in Sect. 4, in some simulations, there is structural damage leading to gross rearrangements of the structure at the sliding interface.

Fig. 2
figure 2

Friction force (F f) versus normal force (F n) at various temperatures and normal loads for PTFE–PTFE sliding under a perpendicular, b violin and c parallel sliding configurations

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The perpendicular sliding configuration exhibits 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 is consistently higher than that for the violin and parallel cases and is accompanied by significantly more molecular wear (discussed in detail below). As a result, the temperature dependence is not as strong or as uniformly changing: as Fig. 2a shows, there is relatively little difference between the frictional forces at 75 and 100 K or between those at 150 and 200 K. As we shall see, this weaker temperature dependence is due to the higher friction and greater associated structural damage.

Unlike the perpendicular sliding configuration, the frictional force in the violin sliding configuration shows strong temperature dependence, with the friction increasing as the temperature decreases. Over a comparable range of normal loads, the frictional forces for the violin sliding configuration are higher than those for the parallel sliding configuration and range from 1.7 to 10.4 nN at 300 K and from 6.9 to 21.0 nN at 25 K.

In the parallel sliding configuration, the simulations also show a clear trend of increasing frictional forces with decreasing temperature, as shown in Fig. 2c. Over the range of normal loads considered, the frictional forces range from 1.3 to 3.3 nN at 300 K and from 7.2 to 10.3 nN at the 25 K.

For all three sliding configurations, the respective ranges in the frictional forces at various loads widen when the temperature decreases from 300 to 25 K. At both temperature extremes, the difference between the highest and lowest recorded frictional force is largest for the violin sliding configuration, followed very closely by that for the perpendicular configuration; the parallel configuration displays only about one-fourth the range. Of all the frictional forces obtained, those for the perpendicular sliding configuration are the highest.

The slopes of the respective data sets shown in Fig. 2 are our best estimates of the friction coefficients for each temperature. The temperature dependence of the friction coefficients is shown in Fig. 3a. The friction coefficient for the perpendicular sliding configuration is relatively high even at ambient temperatures and remains relatively constant as the temperature decreases, a result of the significant molecular wear seen over the entire temperature range; this is described in detail in Sect. 4.3. The comparatively high friction coefficient may be largely a result of the forces required to rearrange and extensively alter the molecular chain arrangement of the sliding interface, which is likely a molecular-scale wear process reordering the sliding interface. Interestingly, under the molecular-scale wear process in which the surface chains are dynamically rearranging as a result of bond breaking, the frictional forces (though higher) are almost completely temperature insensitive.

Fig. 3
figure 3

a Friction coefficient (μ) determined by taking the average of a series of least-square fits to the respective temperature data points in Fig. 2. b Average C offset value (i.e., the residual friction at 0 applied normal load or the y-intercept) from the extrapolation of the least-squares fits. c Adhesive forces obtained by taking the average of the x-intercept of the extrapolation of the least-squares fit

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The violin sliding configuration, by contrast, shows a complex dependence of friction coefficient with temperature. Above 200 K, the interfacial sliding produces a minimal amount of damage to the structure of the chain alignment. There is a dramatic increase in the friction coefficient from 200 to 100 K. As the temperature decreases below 100 K, the friction coefficient becomes essentially temperature independent, as for the perpendicular sliding configuration. This crossover correlates with a marked decrease in the rate of atomic positional fluctuations during sliding at the interface. Interestingly, this friction transition temperature range between 100 and 200 K corresponds nicely to the suggested glass transition temperature of approximately −100 °C [39, 40] for PTFE. Prolonged sliding at low temperatures leads to scission of the stiff chains, which eventually leads to the large-scale destruction of the aligned chain structure (see Sect. 4). This structural damage, in turn, results in relatively high friction coefficients, comparable to those for perpendicular sliding. Parallel sliding shows a steady increase in friction coefficient with decreasing temperature throughout; in this case, the sliding interface remains completely intact. It thus appears that the temperature dependence of the friction coefficient for frictional sliding may be almost exclusively accounted for by changes in the temperature dependence of the strength of the intermolecular forces at the sliding interface.

The extrapolations of the frictional forces in Fig. 2 to zero load do not go to the origin, but intersect the y-axis at values less than zero. These values, within the assumption of a linear model for the friction behavior, correspond to the offset C, in f = μF s + C where F s is the total load across the interface and C = μF a, with F a being typically interpreted as the adhesive surface forces, i.e., those other than dynamical friction [41, 42]. A portion of this C offset accounts for the residual friction force at zero applied external normal load (see Fig. 3b). The offset C also incorporates effects from confinement of the system under an externally applied load, the resulting stiffness of the interfacial contacts, and possibly effects from periodic boundary conditions [42]. Notwithstanding these possible effects, the fact that the value of the C offset increases with decreasing temperature suggests that adhesion may make a more significant contribution to friction at the lower temperatures. This trend is observed for all three sliding configurations. As Fig. 3c shows, the calculated adhesive force for the parallel sliding is by far the largest of the three configurations, even though its friction is the lowest. For deformation-controlled friction, the surface may experience extensive damage. The perpendicular and violin sliding configurations experience gross molecular rearrangement and damage at the sliding interface. Their associated frictional behavior may be deemed to be significantly deformation controlled; however, the evolution of asperity peaks is not apparent even for these two relatively high-friction, high-wear configurations, because the top and bottom PTFE surfaces remain in continuous contact during sliding. However, the perpendicular and violin sliding configurations are inherently rougher relative to the parallel sliding configuration, since molecular chains have to ride over each other. As a result, intimate sliding contact of the two PTFE surfaces for the perpendicular and violin configurations is more intermittent than for 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 somewhat smaller adhesive force compared to the parallel configuration. The inference from Fig. 3 that the high-friction, high-wear configurations manifest less adhesion than the low-friction configuration is consistent with what is known experimentally about the low shear strength of PTFE [43].

An obvious feature of Fig. 3c is the sharp increase in adhesion for the perpendicular sliding configuration at 25 K. This may be a computational artifact because, while there is a significant amount of molecular wear for the perpendicular sliding configuration at all the temperatures explored, there is a considerable variability in results from MD trajectories under the same conditions of load and temperature. This is a particular problem at small loads, for which rare deformation events can dominate the response of the system.

4 Microscopic Processes of Friction and Wear

Our simulations manifest a series of microscopic surface damage processes that eventually lead to high friction. The processes range from the bowing and bunching together of adjacent chains, to the rolling of chains on top of and around each other in a manner similar to the entanglement process by which fibril strands are rolled together to form rope. More severe wear processes involve chain scission, and the reorientation and translation of molecular debris and chain fragments along the direction of sliding. The occurrence, extent and sequencing of these events are highly dependent on the complex interplay of sliding orientation, load transfer and temperature. In this section, the mechanisms underlying these processes are dissected and their origins are identified. This discussion pertains mostly to the high-wear sliding configurations (i.e., perpendicular and violin). The parallel sliding configuration, which shows minimal wear, will be treated separately in Sect. 5.

4.1 Bowing and Bunching of Chains

For the perpendicular sliding configuration at relatively low normal loads (i.e., <10 nN), surface chains in the lower PTFE slab bow as a result of the shear forces imposed by the motion of the top PTFE slab. No other significant movements of the interfacial polymer chains for the lower PTFE slab are observed. In particular, Fig. 4 shows that for the perpendicular sliding configuration, as the normal load decreases, the displacement of the chains on the surface of the lower slab decreases. The displacements are temperature independent with the mean within the range of approximately 5–8 nm at high normal loads. As the load is increased beyond approximately 10 nN, breakage of cross-links between the PTFE chains at the interface and adjacent sub-interfacial layer of chains occurs, which is evidenced by the subsequent bunching together of the bottom surface interfacial chains to form a regular continuous layer without the normal PTFE lattice spacing. In moving from Fig. 5b to c, the top PTFE surface slides ~4.5 nm at 300 K. During this interval, chains #1, #4 and #5 are displaced between 3.5 and 4.5 nm, such that they effectively bunch together while still maintaining their initial alignment. At lower temperatures, this behavior is even more marked, with all five chains on the bottom surface bunching together. This process begins after only a few nanometers of sliding with the chains slipping at different rates. For some chains, these points of bowing facilitate 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 displacement of the top PTFE surface. This process of rolling of the chains around their axes often occurs without scission of the chain into separate fragments, as has been note previously [31].

Fig. 4
figure 4

Displacement of the bottom surface interfacial carbon atoms with respect to their initial positions. The mean is taken over a sliding distance of ~24 nm

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Fig. 5
figure 5

Various microscopic molecular processes at work in the sliding of aligned, cross-linked PTFE surfaces during perpendicular sliding taken from simulations carried out at 300 K and an average normal load of 25 nN. The evolution of the interfacial chains for the bottom PTFE slab or surface is shown as a function of sliding distance

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The violin sliding configuration demonstrates similar behavior to the perpendicular case at low normal forces (i.e., <10 nN) in that the chains remain relatively unresponsive to the shear stress, albeit with smaller displacements. Although there is no clear temperature dependence, the displacements at the three lower temperatures are noticeably larger than those at the three higher temperatures. Consequently, the chains bow less than in the perpendicular sliding case, as indicated in Fig. 6e. Interestingly, however, at relatively high temperature and normal load (e.g., 300 K and ~35 nN), the chains bow at multiple points along their axes even before a significant amount of sliding takes place (<0.02 nm).

Fig. 6
figure 6

Molecular snapshots of various microscopic processes for the violin sliding configuration taken at 25 K for an average normal load of ~32 nN. a Starting configuration with the vertical orientation chains labeled 1–5 and the horizontal ones for 6–10. b, c Chain scission is initiated mainly in regions where the chains in the top and bottom surfaces intersect perpendicularly. d Propagation of the chain scission process leads to e severe chain bowing and f distortion. The corresponding sliding distance in nm is shown for each panel

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4.2 Entanglement of Chains

Due to the extensive bowing of the polymer chains at random sites along the molecular backbone, a process is initiated between adjacent chains by which a severely bowed segment of one chain intertwines with a segment of a neighboring chain. As the temperature is lowered to 25 K, scission takes place first on chains that are aligned perpendicular with the direction of lateral motion. This leads to entanglement brought on by their motion (i.e., reorientation and/or displacement of fragments in the sliding direction of the top PTFE surface).

This process is especially prevalent for the perpendicular sliding configuration, in which slippage leads to the bunching together of aligned chains, as described in Sect. 4.1. This bunching initiates the entanglement process by providing a means for chains to slide and roll over each other. This results in the interlocking of the zigzag –(C–C–C)– molecular axes of the chains, as shown in Figs. 5f and 6f. Initially, molecular backbones remain largely unbroken during this process. Regardless of the mechanism of its initiation, the resulting entanglement leads to severe strain and dilatation across the interface. In some cases, this results in immediate chain scission and reorientation of chain segments. The location of the onset of chain entanglement appears to be random, with the specific atomic mechanisms involved incorporating the effect of load transfer (both normal and lateral or shear) through the structure.

4.3 Chain Scission

For the perpendicular sliding configuration, the effects of the normal load cause chain scissions at random cross-links. Figure 5b, taken after 0.98 nm of sliding, shows the breakage of chain #3 at a carbon atom where the chain is cross-linked to an adjacent chain. The actual breakage, however, occurs after only 5.52 nm of sliding. Chain #5 in Fig. 5c shows evidence of bond breakage as carbon atoms from its molecular backbone (some of which were attached to backbone carbons within a few carbons of cross-linked sites) are left in the wake of its displacement in the sliding direction of the top PTFE surface. Chain #2, which is displaced in the direction of sliding of the top PTFE surface, significantly bows at multiple points along its molecular axis and finally, in Fig. 5e, reorients along the direction of sliding of the top PTFE surface. This reorientation process leads directly to the breakage of chains #4 and 5 , also further widening the scission gap between the fragments of chain #1 (see Fig. 5e). Chain scission for the perpendicular sliding geometry, like that for entanglement described in Sect. 4.2, occurs at random positions along the backbones. It thus appears that this complex interplay of processes feeds back into the dynamics of the chain breakage process.

Chain scission, in the violin sliding configuration, is found to have two independent origins: high stresses generated along a molecular axis when a reoriented chain segment is dragged across the molecular axis, and prior scission of chains aligned in the perpendicular direction. Figure 6 shows that on several occasions, chain scission is initiated precisely in the region at which aligned chains in the top and bottom PTFE surfaces meet. Figure 6a shows the initial stages of sliding after 1.32 nm. Interfacial chains in the bottom surface are oriented vertically and are labeled 1–5, while those in the top surface are horizontally oriented and are labeled 6–10. The scission shown in Fig. 6b takes place after almost 10 nm of sliding, with the breakage taking place at the point where chains #2 and #7 meet perpendicularly. Figure 6c shows this scission even clearer, also illustrating additional similar events. Figure 6d shows the evolution of these broken chain links. The breakage of these chains allows significant movement and reorganization of the interfacial structure as shown in Fig. 6e, f, respectively. As may be ascertained from the sequences of images, in this case, neither the chain cross-link sites nor extensive initial bowing of the chains plays a significant role in bringing about chain breakage.

4.4 Chain and Chain-Segment Reorientation

Chain or segment reorientation usually occurs after prolonged sliding and often is the last major event that leads to significant molecular wear for the perpendicular sliding configuration [14]. At higher temperatures (150–300 K), chains that bow at multiple positions usually experience partial reorientation. However, it is rare for an entire aligned polymer chain to experience complete reorientation. In several instances, unsevered chain segments that bow extensively to the point of reorientation brake and subsequently translate in the sliding direction of the top PTFE slab. At lower temperatures (25–100 K), the polymer chains, being more rigid, experience extensive entanglement. This often leads to a metastable, entangled mass where several small chain segments reorient in the direction of sliding for the top PTFE surface. In this sliding configuration, particularly at the lower temperatures, many small segments of chains are created and translate with their new orientations in the sliding direction of the top PTFE slab or surface. The reorientation of chains and their segments do not act as lubricants leading to lower friction, but instead serve to further damage and disrupt the regular ordering of the interfacial chains, as shown in Fig. 5f.

For the violin sliding configuration, the reorientation of chain segments at the sliding interface for the bottom PTFE slab takes place quite rapidly and often within the first 10 nm of sliding. Chain scission, as described above, allows broken chain segments additional freedom to easily bow and realign in the sliding direction of the top PTFE surface. As the temperature is lowered, this process becomes noticeably more staccato as significant bowing of the chains’ molecular axes often precedes chain scission.

5 Comparison of PTFE and Polyethylene

Samples from our earlier study [12] of polyethylene (PE) were examined under similar sliding conditions as PTFE for a variety of normal load and temperatures. Figure 7 shows the friction coefficient with respect to temperature for PE–PE sliding. A comparison of Figs. 3a and 7 reveals that the perpendicular and violin sliding configurations show lower friction coefficient values for PE–PE sliding than for PTFE–PTFE sliding. The high frictional forces for these configurations have different origins in the two materials: For PTFE, it arises from the extensive wear described above, while for PE, it arises from the greater stiffness of polymer, which far more effectively transmits load to the interfaces. For the parallel configuration, PE–PE and PTFE–PTFE sliding show approximately equal friction at high temperatures; however, as the temperature is lowered, the PTFE friction increases less and settles at a lower relative value. The similarity in the frictional response with temperature nonetheless is consistent with the idea that the initial chain alignment at the sliding interface is largely maintained during sliding for both systems. For PTFE, there is a clear distinction between parallel and violin sliding: At low temperatures, the interfacial violin configuration degrades into a state characterized by significant molecular wear comparable to that of the perpendicular configuration. In the case of PE, however, the friction coefficient behavior of the violin cases more closely follows that of the relatively low friction parallel sliding configuration. Visual inspection of the respective sliding interface confirms that there is a minimal amount of molecular wear for both violin and parallel configurations in PE. Comparison of comparable PTFE and PE sliding configurations indicates that the stiffness of the polymer also plays an important role in determining the extent of system wear.

Fig. 7
figure 7

a Friction coefficient for PE–PE sliding obtained by taking the average of a series of least-squares fit to a graph of multiple F f, F n data pairs. b The adhesive forces were calculated by taking the average of the x-intercept for a series of least-squares fits alluded to in a

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6 Discussion and Conclusions

Molecular dynamics simulation of aligned PTFE–PTFE sliding for a range of normal loads and temperatures was carried out for three different sliding configurations, spanning the range of microstructural and stress environments likely to be experienced in aligned PTFE systems. In each case, friction increases with decreasing temperature. The friction coefficient, as defined by the slope of a least-squares fit to the frictional and normal force pairs for the respective temperatures, is highest for perpendicular sliding configuration, intermediate for violin sliding and least for parallel sliding. The trend for the adhesive force is almost opposite of that for the friction coefficient in that the parallel sliding configuration displayed the highest adhesion, followed by the violin sliding configuration and then the perpendicular sliding configuration. These trends indicate that the frictional anisotropy experienced by aligned PTFE self-mated surfaces is not dominated by adhesion.

Also of particular significance is the low-wear, low-friction parallel sliding configuration. The stability of the parallel sliding configuration is attributed to the relatively smooth self-mated sliding topography and the alignment of the shearing forces along the chain backbone; this interface remained largely intact for all the temperatures explored. As mentioned in the Introduction, there is strong evidence in the literature to suggest that PTFE experiences thermally activated friction. Such friction is only likely to occur under conditions of very low wear, hence the importance of the parallel sliding configuration. While an exponential increase in friction with decreasing temperature is not observed in our simulations, a significant increase in friction is demonstrated. This phenomenon appears to be correlated with the marked decrease in the rate of atomic positional fluctuations with decreasing temperature. Visual inspection of the PTFE–PTFE sliding interface provides clear, qualitative evidence of this, primarily for the fluorine atoms. It is likely that at relatively higher temperatures, additional, low-barrier pathways for interfacial molecular motion are available, whereas these pathways disappear at lower temperatures due to the increased bond stiffness associated with the interfacial atoms. In cases of significant wear, these molecular pathways become less well defined or unavailable, and thus, their influence by temperature becomes less significant.

As discussed in the Introduction, PTFE manifests low friction. The main drawback of PTFE is its excessively high wear, the origin of which has been the subject of much discussion. There are three main hypotheses associated with reducing this high wear rate: i) the prevention of the large-scale destruction of PTFE’s banded structure [6, 44, 45]; ii) the fostering of adhesion of PTFE composite transfer films to the counterface material [46–49]; and iii) preferential support of the load imposed on the matrix [50–52]. A host of fillers, both particulate and fibril, have been used, with varying degrees of success to reduce the sliding wear and/or frictional coefficient of PTFE systems. It is hard to systematically design such composite systems without a molecular-scale understanding of the processes associated with friction and wear of these interfaces. This study is aimed at developing such insights. It can be expected that the relative rate of occurrence and duration of these microscopic processes in real systems will depend on system morphology, temperature and deformation history. Thus, the understanding of the fundamental mechanisms of PTFE tribology developed here accounts for only the first, but also very crucial, step in successfully designing PTFE composites for low friction, low wear and long serve lifetime under a wide range of temperature and loading conditions.