Tribology Letters

, Volume 39, Issue 1, pp 49–61

Atomistic Insights into the Running-in, Lubrication, and Failure of Hydrogenated Diamond-Like Carbon Coatings

Authors

    • Fraunhofer-Institut für Werkstoffmechanik IWM
    • Physikalisches InstitutUniversität Freiburg
  • Stefan Moser
    • Fraunhofer-Institut für Werkstoffmechanik IWM
  • Michael Moseler
    • Fraunhofer-Institut für Werkstoffmechanik IWM
    • Physikalisches InstitutUniversität Freiburg
    • Freiburger Materialforschungszentrum
Original Paper

DOI: 10.1007/s11249-009-9566-8

Cite this article as:
Pastewka, L., Moser, S. & Moseler, M. Tribol Lett (2010) 39: 49. doi:10.1007/s11249-009-9566-8

Abstract

The tribological performance of hydrogenated diamond-like carbon (DLC) coatings is studied by molecular dynamics simulations employing a screened reactive bond-order potential that has been adjusted to reliably describe bond-breaking under shear. Two types of DLC films are grown by CH2 deposition on an amorphous substrate with 45 and 60 eV impact energy resulting in 45 and 30% H content as well as 50 and 30% sp3 hybridization of the final films, respectively. By combining two equivalent realizations for both impact energies, a hydrogen-depleted and a hydrogen-rich tribo-contact is formed and studied for a realistic sliding speed of 20 m s−1 and loads of 1 and 5 GPa. While the hydrogen-rich system shows a pronounced drop of the friction coefficient for both loads, the hydrogen-depleted system exhibits such kind of running-in for 1 GPa, only. Chemical passivation of the DLC/DLC interface explains this running-in behavior. Fluctuations in the friction coefficient occurring at the higher load can be traced back to a cold welding of the DLC/DLC tribo-surfaces, leading to the formation of a transfer film (transferred from one DLC partner to the other) and the establishment of a new tribo-interface with a low friction coefficient. The presence of a hexadecane lubricant leads to low friction coefficients without any running-in for low loads. At 10 GPa load, the lubricant starts to degenerate resulting in enhanced friction.

Keywords

Running-inCoatingsFriction-reducingBoundary lubricationFriction mechanismsUnlubricated frictionCarbon

1 Introduction

The amorphous hydrocarbon (a-C:H) material family falls into the class of materials known as diamond-like carbon (DLC) [1]. By tuning the sp2/sp3 ratio and the hydrogen concentration of a-C:Hs to obtain the desired mechanical and electrical properties [1], these materials can easily be tailored to specific applications. Examples of the wide-spread technological use of a-C:H include wear-resistant low-friction coatings [2] for the protection of magnetic and optical storage discs [3], bearings [4], or micro-electro-mechanical-systems (MEMS) [5]. Even the building of complete MEMS devices out of DLC [6] has been reported.

In addition to their technological importance, a-C:H coatings are scientifically exciting since these simple two-elemental materials exhibit already many tribological features of much more complex multi-elemental metallic tribo-systems. Therefore, insights into processes that govern the performance of sliding a-C:H interfaces can pave the path to a deeper understanding of general tribological phenomena, such as running-in, lubrication, the formation of transfer films, wear, and final failure.

For instance, during the sliding of a-C:H against a-C:H, friction coefficients can approach values as low as 0.001 [79]. This “superlubricity” is sometimes linked to another remarkable property of these films, their ultrasmoothness [10]. Interestingly, the ultralow friction coefficient requires some time to develop [7] a phenomenon that is called running-in. An initially high friction coefficient (>0.1) decreases over a couple of hundred frictional cycles until a low steady-state value is established. Although running-in occurs in many tribo-contacts (including most metallic systems), the details of the underlying mechanisms are not even understood for simple a-C:H contacts.

Molecular dynamics (MD) simulations are ideally suited to gain insight into the processes that govern the performance of a-C:H tribo-contacts. Previous theoretical investigations in the tribology of hydrocarbons have focused on systems in which the surfaces were completely saturated with hydrogen and no chemical reaction or just single hydrogen abstraction events occurred (for reviews see the recent articles by Harrison et al. [11, 12]). Examples include the friction between self-assembled monolayers [13, 14] as well as amorphous carbon films [15]. The latter work considered hydrogen-free DLC films sliding with 100 m s−1 against a hydrogen-terminated diamond (111) surface. During the sliding over a distance of 12 nm, the number of bond-breaking and bond-formation events within the amorphous carbon film was monitored. The frequency of structural rearrangements decreased over time and dropped to zero after approximately 60 ps. Although no accompanying decrease in the friction coefficient was reported in Ref. [15], this observation was interpreted as a manifestation of running-in.

Recently, we found a different running-in mechanism in our MD simulations [16]. Two a-C:H surfaces were slid at 50 m s−1. We observed that the decrease in friction coefficient was exactly correlated with a reduction of chemical bonding between the two surfaces. The bonding even vanished after around 3–4 ns corresponding to a sliding distance of 150–200 nm. We validated our simulations by comparing the increase in sp2 hybridization to experimental data obtained from Raman measurements yielding reasonable agreement. The difference in time-scale observed in Refs. [15, 16] already indicates that different relaxation processes might occur during running-in, an observation that will be discussed in this study.

In this article, we make a further step into the direction of realistic sliding friction simulations. In order to reproduce the experimental conditions as close as possible, the whole process chain ranging from the growth of a-C:H surfaces to the final failure of the tribo-system is covered. Our surfaces are grown by subsequent CH2 deposition (see Sect. 3). After preparation of two sliding systems with 30 and 45% hydrogen by pairing grown surfaces with the respective hydrogen content (see Sect. 4), these are slid at 20 m s−1. Note, that this reduced sliding velocity brings our simulations closer to experimental conditions than previous works [15, 16], since 20 m s−1 represents a characteristic velocity of a piston in a race car engine. Two load regimes are investigated in our dry sliding simulations: 1 (see Sect. 5) and 5 GPa (see Sect. 6). Finally, in Sect. 7, we investigate lubricated sliding in the boundary lubrication regime.

2 Simulation Model

The most direct approach to model materials’ properties on nanometer length scales is MD [17] where the motion of each individual atom is traced by solving Newton’s equations of motion. A reliable description of interatomic interactions can be obtained by solving the electronic Schrödinger equation directly. Density functional theory [18, 19], for example, is a very accurate approximation to the full solution of the electronic structure problem and has become one of the materials scientist’s workhorses. However, the accessible system sizes are currently limited to around 1,000 atoms. Since the computational time required for the exact solution of the Kohn–Sham equations [19] scales with the cube of the number of electrons, it is difficult to push that limit further. Even more importantly for tribology, the accessible timescale is also limited to a couple of picoseconds.

By systematically simplifying the interatomic interactions, one arrives at tight-binding models and finally at bond-order potentials [18] which we use in this study. In bond-order potentials, the electronic degrees of freedom have been integrated out, leading to an effective short-ranged description of the interatomic forces. This allows computations to scale linearly with the number of atoms. The typical total energy expression for a second-moment bond-order potential is given by [18, 20, 21]
$$ E = \sum\limits_{i<j} ( V_{\rm R}(r_{ij}) + b_{ij} V_{\rm A}(r_{ij}) ) f_{\rm C}(r_{ij}) $$
(1)
where the sum extends over pairs ij of atoms, and rij is the distance of atoms i and j. The term VR(rij) is purely repulsive and the strength of the attractive part VA(rij) is modulated by the bond-order bij which is determined by the chemical environment of each bond. Finally, the cut-off function fC(rij) drops from unity to zero somewhere between the first- and second-neighbor shell of atoms and thus forces the potential to only act between nearest-neighbors. A well-tested parametrization for hydrocarbons is the interaction potential of Brenner [22], also known as the reactive empirical bond-order potential (REBO), whose revised incarnation is used here [23].

Although this potential has also been employed in previous studies on hydrocarbon tribology [1315], one should be extremely cautious to use it in its original formulation for mechano-chemical simulations. Bond-order potentials, like the REBO, are typically fitted to ground-state energies and force constants, such as solid-state structures and their respective elastic constants as well as molecules and their respective vibration frequencies. While these fitted properties are excellently reproduced, such a construction does not guarantee transferability to other equilibrium structures and thus extensive testing is necessary. The situation becomes even worse if systems are driven by an external force to configurations far from equilibrium—this is for example the case in tribology and fracture, where in the latter case these potentials severely fail to reproduce the experimentally observed brittle behavior [24].

The reason for this can be traced back to the cut-off function fC(rij). In situations where an external driving force does not play a role, such as thermally driven chemical reactions, a faithful representation of respective energy levels and barriers leads to a proper description of the system’s behavior. After including an external driving force, not only energies need to be correct, but also forces. The cut-off function fC(rij) drives the interatomic bond energies to zero in a narrow interval. Since the forces are the derivative of the energies, this rather steep drop leads to an artificial force contribution which overestimates the correct forces by as much as a factor of 4 to 5 in the case of the REBO [25]. It has been proposed that in these situations the forces should be cut-off instead of the energies [26]. This, however, also changes the respective energy landscape, and worse, it is not even clear that such a force can be expressed as the derivative of a potential energy expression.

We showed in Ref. [25] that these artifacts can be avoided by using a cut-off function that is based on screening concepts [27]. We allowed a bond between two atoms to persist over long distances provided that no third atom moves into the bonding region. The resulting-modified REBO shows drastically improved fracture behavior, and coincidentally, also fixes problems with the sp2-to-sp3 ratio obtained in quenched amorphous carbon [28]. An approach identical to ours was later presented in Ref. [29] with the sole purpose to fix the amorphous cabon’s microstructure.

3 Growth of Representative a-C:H Surfaces

Our a-C:H surfaces are grown according to a standard protocol [10, 28]. The ions are incident normal to the surface, a circular region of 0.6 nm radius around the impact position evolves unperturbed, and the rest of the system is thermalized using a Langevin thermostat with a dissipation constant of 0.15 fs−1 to remove the impact energy. We quench the initial substrate from around 1,000 molten carbon and hydrogen atoms, where the hydrogen-to-carbon ratio and the overall density are chosen to roughly match that of the final grown films. Subsequently, the trajectories of 1,300 single CH2 impacts are propagated for 15 ps each.

The atomic configuration of the final samples and the fraction of hydrogen and carbon are shown in Fig. 1. On average, around 30 and 45% hydrogen is obtained for impact energies of 60 and 45 eV, respectively. Close to the surface, the hydrogen fraction increases, indicating a hydrogen termination of the surfaces. The hydrogen concentration in the bulk film is smaller than the hydrogen content of the impinging species since during each impact a fraction of hydrogens is ejected from the surface. The surface hydrogen atoms, however, have not experienced as many impacts resulting in a larger hydrogen concentration at the film/vacuum interface.
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Fig. 1

Final samples after 1,300 impacts at projectile energies of a 60 eV and b 45 eV. The fraction of hydrogen (circles) and carbon (squares) is shown as a function of position within the thin film

The morphologies of our samples agree well with samples used in recent experiments. In Ref. [7], two model samples with 34 and 40% hydrogen and sp2-to-sp3 ratios of 70:30 and 65:35, respectively, were used in ultra-high vacuum (UHV) tribology experiments. Our samples with 30 and 45% hydrogen show reasonable agreement at sp2-to-sp3 ratios of 65:35 and 50:50, respectively.

4 Setup of the Sliding System and Boundary Conditions

In our sliding simulations, we pair surfaces from our growth simulations with the same hydrogen content. The two sliding partners are taken from different snapshots of the growth process to provide slightly different surface morphologies. By cutting off the bottom part of the grown films, we construct final simulation cells with a total height of about 6.0 nm, a length in sliding direction of 2.0 nm, and a width of 1.4 nm. Our 30% H system contains 1,811 carbon atoms, whereas the number of C in the 45% H system is 1,630. An example snapshot of such a setup is shown in Fig. 2.
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Fig. 2

Total simulation cell and boundary conditions of the MD simulations. The inset shows the estimate of the transfer function giving the response of the separation of the rigid slabs as a function of normal force. See Appendix for more information

In order to impose a constant sliding velocity on the system, the position of the 0.3 nm top- and bottommost atoms is frozen to their initial values. While the bottom-fixed atoms stay immobile during the whole simulation, the block of top-fixed atoms is allowed to move. A normal force is added to this rigid block providing the respective normal load. Furthermore, we add a dampening force and increase its total mass to mimic the response of the bulk of the sliding partners which is not explicitly included in our MD simulation cell. For more information on this barostat and the choice of parameters, see Appendix. The next 0.3 nm above and below the rigid atoms is thermalized using a Langevin thermostat [17, 30]. We only thermalize the motion perpendicular to the plane of sliding in order to avoid contamination of the friction coefficients by the Langevin dissipation. We checked that despite thermalizing only one Cartesian direction, equipartition is re-established in close vicinity of the Langevin layer. Therefore, our approach establishes reasonable energy transport to the boundaries of our simulational volume, mimicking the thermal behavior of a macroscopic tribo-system.

Sliding is started instantly at 20 m s−1 from samples that were equilibrated at the respective load (pressure normal to the sliding surface) without sliding. The sliding direction is slightly tilted by 10° with respect to the coordinate axis to avoid periodic encounters of the same surface structures. Our pressure coupling algorithm and the tilting of the sliding direction are designed to avoid finite-size effects introduced by the finite simulation cell in sliding friction simulations.

5 Dry Sliding at Low Loads

Figure 3a displays the temporal evolution of the friction coefficient for the 30 and 45% H tribo-contacts during sliding at a load of 1 GPa. We compute this friction coefficient under the assumption of equal real and apparent contact area, i.e., we calculate the ratio of shear stress to normal pressure (both averaged over time intervals of 10 ps). Linear elastic modeling of measured DLC surfaces shows that the ratio of real-to-apparent surface area is about 1% when pressures average at around 5 GPa [16]. This estimate depends on the detailed topology of the sample under consideration and should be considered an order of magnitude evaluation only. Nevertheless, it should be clear that our friction coefficients represent an overestimation of the corresponding experimental values.
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Fig. 3

Dry sliding at a load of 1 GPa for a H-depleted (30% H) and a H-rich (45% H) a-C:H sample. a The friction coefficient under the assumption of equal real and apparent surface area, b the amount of time a chemical bond exists between the sliding partners in an interval of 0.5 ns, c the sp2 and sp3 content in a region ±1 nm around the sliding interface, and d the number of atoms transferred between the sliding partners. Quantities a, c, and d are averaged over an interval of 10 ps

For both, the H-rich and H-depleted system, the friction coefficient μ (Fig. 3a) starts at values of above 1.0 and then drops to a value of around 0.1. This manifestation of running-in is much faster for the H-rich sample where the saturated value of the friction coefficient establishes already after 5 ns.

The friction coefficient directly correlates with the amount of time the two sliding partners stay chemically connected (Fig. 3b). We define two carbon atoms to be bound if their distance is closer than 1.85 Å. By following the network of carbon bonds, it is straightforward to determine if a connection between the two sliding partners exists. As a measure of connectivity, we compute the relative amount of time the two surfaces exhibit chemical bonding during time intervals of 0.5 ns. In the H-depleted case, we observe a steady decrease in the connected time reaching zero after approximately 30 ns. In the H-rich case, the surfaces are also chemically connected during the first 10 ns, but the total time this chemical connection persists is much smaller than in the 30% hydrogen case. After running-in, the two sliding partners remain disconnected in both cases, leading to a steady and low friction coefficient. The fact that chemical bonding and friction coefficient are directly correlated is nicely demonstrated at around 20 ns in the H-rich case. Here, a connection is established for a short time which instantly raises the friction coefficient to a value of 0.3.

During sliding, the local structure of the a-C:H changes slightly. Figure 3c shows the sp2 and sp3 content in the interface region. In the H-depleted as well as the H-rich sample, sp2 increases by a few percent accompanied by a corresponding decrease in sp3. This “phase-transformation” is another manifestation of running-in and is presumably also reflected in the bond-formation and bond-breaking process observed in Ref. [15]. As already stressed in our earlier publication [16], this “graphitization” reflects a minor rearrangement in the amorphous carbon’s local network structure and not the formation of graphitic sheets.

This microscopic running-in, which is evident in the friction coefficient, sample connection, and hybridization, is also seen in the rate at which atoms are transferred from one sliding partner to the other. Figure 3d shows the difference in the number of atoms belonging to the two sliding partners, shifted to zero at t = 0. Each jump corresponds to a transfer of atoms between the two slabs. Initially, the transfer rate is large as indicated by frequent jumps in Fig. 3d; however, it drops to zero around the time the friction coefficient saturates in both the H-depleted and the H-rich cases.

Let us summarize our main observation. The strong reduction of friction during the first few nanoseconds is accompanied by a drop in chemical connectivity of the two tribo-surfaces. Such a lowering of the surface reactivity requires some kinds of passivation mechanism. Figure 4 shows a sample trajectory of such a passivation event. Typically, a reactive surface has unsaturated carbon atoms exposing dangling bonds into the sliding contact. These are marked in red and blue in Fig. 4a. When the atoms approach each other a bond is established, linking the two sliding partners (Fig. 4b). In general, this bond or one of the neighboring bonds has to break again during further sliding. The weakest bond is determined by the chemical environment of the atoms and to some extend by thermal fluctuations that can carry an atom over energy barriers. The bonds are already strained in the snapshot shown in Fig. 4b and after breaking (Fig. 4c) the CH2 group (red) has moved to the other sliding partner. An unsaturated carbon is still exposed to the sliding interface. Subsequently, this exposed unsaturated carbon finds a binding partner within the surface (Fig. 4d). Note that this passivation process can only occur if a suitable binding partner within the tribo-surface is available. However, once passivated such an atom is unlikely to become unsaturated again.
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Fig. 4

Typical trajectory of a passivation event. a The methylene group (red atoms) bound to the upper surface (green atom) binds to the lower sliding surface (blue atom) in (b). Movement of the upper surface strains the carbon–carbon bonds that connect the methylene to the top and bottom surface. The weaker bond to the top surface finally breaks (c) and subsequently, the methylene finds a binding position (d) within the bulk of the bottom surface leading to passivation. In ad, carbon atoms are displayed by large grey spheres, whereas hydrogens are smaller white spheres

6 Dry Dliding at High Loads

At a load of 5 GPa, the difference between the H-depleted and the H-rich sample becomes more pronounced. Now, the H-depleted sample shows no running-in. The friction coefficient μ (Fig. 5a) stays at an average value of 0.5 in stark contrast to the H-rich system which still exhibits a behavior similar to that at 1 GPa. For both loads, the friction coefficient has dropped to about 0.1 after 5 ns.
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Fig. 5

Dry sliding at a load of 5 GPa for a H-depleted (30% H) and a H-rich (45% H) a-C:H samples. a The friction coefficient under the assumption of equal real and apparent surface area, b the amount of time a chemical bond exists between the sliding partners in an interval of 0.5 ns, c the sp2 and sp3 contents in a region ±1 nm around the sliding interface, and d the position of the interface, obtained from the position where the velocity drops from 20 m s−1 to 0. Quantities a, c, and d are averaged over an interval of 10 ps

Again, this behavior correlates with the amount of time the samples stay chemically connected (Fig. 5b). The H-depleted sample maintains bonds between the two sliding partners during the whole simulation, while in the H-rich sample the surfaces passivate after about 20 ns. Subsequently, only minimal re-connection between the two sliding partners is observed.

The evolution of the hybridization in the high load H-rich system is practically identical to the corresponding low load case: the sp2 contents jumps initially by about 5% and saturates at this final value (Fig. 5c). On the other hand, the change in hybridization is more pronounced in the high load H-depleted case. Here the increase in sp2 is about 15%—considerably higher than the 2% increase in the corresponding low load simulation (Fig. 3c).

Let us characterize the structural transition in the 5 GPa H-rich sample in more detail. Figure 6a displays the ring statistics [31] of the sample computed in the region ±1 nm around the sliding interface initially and after 40 ns sliding. The structure is dominated by rings of length 3, 5, 6, and 7. A slight change in structure (a shift of the majority of rings from 7 to 5) occurs during sliding.
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Fig. 6

Microstructure of the initial sliding system with 45% hydrogen (thick blue lines), and the system after running-in at 40 ns and 5 GPa load (thin red lines). a The ring statistics and b the distribution of the orientations of these rings, all computed within ±1 nm of the sliding interface. The angle θ is defined between the surface normal of the sliding interface and the normal of the surface which minimizes the distance to each atom within a ring. The solid black line in b shows the distribution obtained for a random orientation of rings (given by sin θ). The graphs have been obtained by averaging over a 1-ns time interval

An even more pronounced rearrangement can be observed in the orientation of the rings. For each ring, the plane minimizing the distances perpendicular to all atoms in the ring is determined using a least squares fit. The distribution of angles of the plane’s normal vector with respect to the normal vector of the sliding interface is then computed (Fig. 6b). Already at the beginning of the simulation the rings are slightly oriented parallel to the sliding plane (at an angle of 0). After 40 ns, this orientation becomes more pronounced indicating a rotation of the rings. Also this process contributes to the passivation of the surfaces since dangling bonds are less exposed to the sliding interface and thus less likely to weld the two sliding surfaces by chemical bonding.

In the H-depleted case (30% hydrogen), the two sliding partners stay chemically connected during most of the time. This is reminiscent of a cold welding of the two samples. The velocity profile, however, shows a clear sliding interface where the velocity jumps from 0 to 20 m s−1 from which the interface position can be inferred. Figure 5d shows the time evolution of this position which is not fixed but fluctuates at a width of approximately ±1 nm. Each time the interface jumps to a new position, material is transferred from one sliding partner to the other. This is the formation of a nanoscopic transfer film.

In Fig. 7 the atomic configuration, density, and velocity profile at three different times are displayed in order to further analyze the formation of this transfer film. The density profile shows the number-density of carbon and hydrogen. Initially (Fig. 7a), the carbon density is lower than the bulk value in the interface region. The hydrogen density, however, is constant over the whole sample, indicating hydrogen termination of the sliding surface.
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Fig. 7

Atomic configuration, hydrogen nH, and carbon nC number-densities and velocity v at a 16.7 ns, b 17.2 ns, and c 18.9 ns (30% hydrogen, 5 GPa load). ac The sliding interface jumps by about 1 nm. The red broken lines show the interface region whose properties are displayed in Fig. 8. Densities and velocities are averaged over 0.1 ns

When the two sliding surfaces weld together (Fig. 7b), the velocity profile changes and becomes Couette-like. The velocity drops almost linearly between the initial interface position and the prospective one. This indicates that at the new interface position the a-C:H is structurally different from its bulk, already before the two surfaces weld—a behavior reminiscent of a predetermined breaking point. Furthermore, the interface does not jump instantaneously. Rather, film transfer is accompanied by the establishment of the intermediate Couette-like behavior. The final sliding interface (Fig. 7c) again shows a sharp step in the velocity profile and a pronounced density minimum.

During film transfer, the Couette velocity profile is accompanied by structure formation in the Couette region. The carbon density in Fig. 7b shows density peaks reminiscent of fluid layering in confined channels and near surfaces [32, 33]. A further analysis of the transfer region in terms of the pair-distribution function and ring-statistics is reported in Fig. 8. The data are collected over the transfer region only (indicated by the red broken lines in Fig. 7). While the nearest-neighbor carbon–carbon peak in the pair-distribution function exhibits only a slight increase during the transfer of the film (Fig. 8a), the ring-statistics (Fig. 8b) shows a pronounced shift of the initial maximum at 8-membered rings to 6-membered rings, under Couette flow conditions already.
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Fig. 8

Microstructure change in the transfer region (30% hydrogen, 5 GPa load). a The nearest-neighbor peak of the pair-distribution function, b the ring statistics. Both histograms are averaged over 0.1 ns

7 Lubricated Sliding and Lubricant Degeneration

In order to simulate lubricated sliding in the boundary lubrication regime, we add nine hexadecane molecules to the sliding contact formed by the two H-depleted samples (30% hydrogen), since those samples show higher friction coefficients and more dominant transformation under dry sliding. For these simulations, the a-C:H surfaces are duplicated in one lateral dimension resulting in a simulation cell with 2.0 nm × 2.8 nm cross section. The sliding direction is chosen along the longer side. For simplicity, we do not include long-ranged van der Waals interactions, as for example included in the AIREBO potential [34], since we are operating at very high pressures where the interaction between molecules is mainly repulsive and thus included in our description. As shown by Gao et al. [15], van der Waals interaction mainly influences the equilibrium separation at constant load. For systems held at the same separation distance, the behavior obtained using the REBO and the AIREBO potential was identical.

The lubricated systems are equilibrated at the respective load and sliding is started instantaneously as in our simulations of dry sliding. In contrast to dry sliding, no running-in is observed in the friction coefficient. Figure 9a shows the friction coefficient which stays almost constant for the first 10 ns at loads of 1, 5, and 10 GPa. In contrast to dry sliding without welding of the surfaces, the value of the friction coefficient depends on the load. Values of around 0.05, 0.15, and 0.20 are obtained at loads of 1, 5, and 10 GPa, respectively. After 10 ns, the friction coefficient in the 5 GPa case starts to rise slowly.
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Fig. 9

Lubricated sliding at 1, 5, and 10 GPa (left to right). a The friction coefficient under the assumption of equal real and apparent surface area, b the amount of time a chemical bond exists between the sliding partners in an interval of 0.5 ns, c the sp2 and sp3 content in a region ±1 nm around the sliding interface, d the number of hydrocarbon fragments remaining in the lubrication region, e the total number of hydrogen and carbon belonging to these fragments, and f the diffusion coefficient D(t) of the hydrocarbon fragments (see text). The increase in D(t) over time in the 1 GPa case can be explained by a superimposed lateral drift due to the external motion. Quantities a, c, d, and e are averaged over 10 ps

In the dry sliding simulations, the increase in friction was correlated to the chemical bonding across the sliding interface. The proportion of time such inter-surface bonds exist is displayed in Fig. 9b for the lubricated case. Although the friction coefficients differ, in both the 1 and 5 GPa cases, no chemical bond connects the two sliding surfaces during the first 10 ns. Therefore, the difference in μ during this time interval is most likely caused by an increased viscosity of the lubricant at higher pressures. After about 10 ns, the friction coefficient at 5 GPa starts to increase. At the very same time, first chemical inter-surface bonds appear. When increasing the load to 10 GPa, the sliding partners exhibit chemical connection right from the beginning of the simulation.

Although no running-in is observed in the friction coefficient, the hybridization exhibits pronounced variations for all three loads (Fig. 9c) . The fraction of sp2 sites increases as the fraction of sp3 sites decreases over the first 5 ns and then saturates at the respective values as in the dry sliding cases. The strong increase in sp2 at 10 GPa is related to lubricant degeneration since intact hexadecane contributing exclusively with sp3 sites partly hybridizes to sp2 upon reaction with the surfaces.

For a further analysis of the lubricant degeneration, the total number of free hydrocarbons is monitored. Initially at nine (i.e., the nine hexadecanes), this number remains constant if the lubricant is not transformed. In addition, the total number of hydrogen and carbon atoms in the lubricant layer were recorded in order to detect H or C abstraction. These quantities are shown in panels d and e of Fig. 9. At 1 GPa and the first 10 ns of the 5 GPa simulation, the lubricant remains in its molecular form. The onset of degeneration starts at a load of 5 GPa, where after 10 ns the number of free hydrocarbons, the number of carbon, and the number of hydrogen atoms in the lubricant layer decreases. The hydrogen and carbon content decays almost monotonically, while the number of free hydrocarbons jumps back to nine at about 11 ns. This can be explained by the cracking of a single hydrocarbon chain leading to two fragments, without incorporation of either one in the sliding surfaces.

At 10 GPa, the number of free hydrocarbons in the lubrication layer decreases monotonically from the beginning, indicating continuous incorporation of lubricant into the sliding surfaces. This is accompanied by a rise in sp2. Since the hexadecane is purely sp3 bonded, the degeneration leads to formation of sp2 coordinated carbons, probably because each CH2 segment is straightforwardly incorporated at a dangling bond site as sp2 carbon.

An example trajectory of how lubricant degeneration proceeds is shown in Fig. 10. Under stress a hexadecane carbon–carbon bond breaks (plotted green in Fig. 10a, b). The chains now end with methylene (CH2) groups, both of which subsequently bind to a methylene in the a-C:H surfaces (colored blue in Fig. 10c, d). Thus, the hexadecane is removed from the lubrication region and bound to the sliding surfaces.
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Fig. 10

Sample trajectory of a degenerating lubricant molecule at 10 GPa load where large spheres are carbon and small spheres hydrogen atoms. Gray atoms belong to the sliding surfaces, lubricant atoms are red. A carbon–carbon bond, marked green in a, breaks due to strain (b). The remaining methylene endgroups attach to the surfaces (marked blue in c and d)

The pair-distribution function g2(r) also carries a signature of lubricant degeneration. We compute the pair-distribution function of the bulk by summing up pair-distribution functions individually computed for the top and the bottom sliding partners, all within ±1 nm around the sliding interface. This avoids counting neighbors across the sliding interface whose distance represents no measure of the local microstructure but of the surface separation and would thus lead to spurious peaks in g2(r). Additionally, we compute the pair-distribution function between the individual hydrocarbon atoms—or between fragments if the lubricant has started degenerating. These distribution functions are displayed in Fig. 11 where panels a–c show the results at different pressures.
https://static-content.springer.com/image/art%3A10.1007%2Fs11249-009-9566-8/MediaObjects/11249_2009_9566_Fig11_HTML.gif
Fig. 11

Carbon–carbon pair-distribution function g2(r) for lubricated sliding, initially (at 0 ns, left panels) and after 20 ns (10 ns at 10 GPa—right panels). The different panels show the results for (from top to bottom) loads of a 1 GPa, b 5 GPa, and c 10 GPa. Blue thick lines show the pair-distribution function in the bulk of the materials, red thin lines gives the pair-distribution of the hydrocarbon fragments

The carbon–carbon nearest-neighbor distance is slightly larger for the lubricant molecules than in the bulk of the material. This can be explained by the local bonding structure, which is mainly sp2 in the bulk and sp3 in the hexadecane. In graphite, the nearest-neighbor distance is around 1.4 Å, being slightly larger in diamond at around 1.5 Å. From LDA-PAW-DFT calculations [35], we obtain the hexadecane’s ground-state carbon–carbon bond-length to be as well 1.504 Å. These results are in excellent agreement with the nearest-neighbor peaks in Fig. 11. At 1 GPa, the initial and final pair-distributions are almost identical. The final bulk nearest-neighbor peak is slightly increased compared to the initial one. This has also been seen in dry sliding simulation and is related to the sp2 to sp3 transformation.

At 5 GPa, where lubricant degeneration starts, the hydrocarbons’ pair-distribution function remains unchanged while the bulk function develops a bimodal first nearest-neighbor peak. The location of the right sub-peak corresponds to the nearest-neighbor distance of the lubricant molecules, indicating that the hydrocarbons are incorporated into the surface in their sp3-coordinated chain structure. The sample trajectory in Fig. 10 shows exactly this situation, where a hexadecane chain splits and binds essentially unmodified to the surfaces.

At 10 GPa, in addition to the bulk peak, the hydrocarbon nearest-neighbor peak becomes bimodal (Fig. 11c). This bimodality is more pronounced than for the bulk, indicating a severe deformation of the hydrocarbon fragments. While at 5 GPa, chain rupture is the main degeneration mechanism, at 10 GPa single atoms are abstracted leading to sp2 bonded carbons—which have a smaller bond-length than sp3 bonded carbon—within the lubrication layer.

This mechanical degeneration of the lubricant occurs preferably at higher load since the hexadecane molecules are confined in the pressurized tribo-contact. To quantify this confinement, we compute the diffusion coefficient of the hexadecane atoms from their root mean square displacements. The reference coordinates are taken after 1 ns of sliding to ensure initial relaxation. We only compute the displacement \(\Updelta r\) perpendicular to the sliding direction and the sliding surface normal to avoid a contamination with the sliding drift. Figure 9f shows the time evolution of \(D(t)={\frac{1}{2}}(t-t_0)^{-1} \langle \Updelta r^2\rangle(t)\) where the average 〈·〉 is taken over all atoms belonging to a hydrocarbon fragment, i.e., all hexadecanes if no lubricant degeneration has occurred. The mobility D(t) of the chain segments decreases with increasing load, leading to a solid-like behavior at 10 GPa where the lubricant molecules are pinned to their respective locations and only minimal rearrangement is allowed.

8 Conclusions

Our results clearly demonstrate that the hydrogen concentration is crucial for the running-in behavior and the resulting steady-state friction coefficient of a-C:H tribo-contacts. Films with lower H-concentration require longer for the running-in and even weld together at higher loads. This theoretical observation correlates with UHV experiments of Ref. [7] that revealed a steady-state friction coefficient of 0.003 and 0.53 for an a-C:H with 40 and 34% hydrogen, respectively. Fontaine et al. [7] explained the anti-correlation between μ and H concentration by the increased viscoplasticity of the H-rich films, leading to weaker intra-film interactions and hence different relaxation of the asperities. Our simulations indicate that not only the bulk response of the DLC to shearing is important, but also the ability of the surfaces to passivate.

Two passivation mechanisms can be extracted from our simulations. First, dangling bonds are saturated by finding a binding partner with other dangling bonds, within the surface. If this is not possible, single radicals can be abstracted from the surface and moved to a location where such a passivation is possible. Second, the carbon-bonded rings forming the a-C:H’s glassy network rotate parallel to the sliding direction within the surface. This exposes fewer dangling bonds and leads to sp2-coordinated sites since a tetrahedral sp3 site would require bonds perpendicular to the surface. This could be a possible explanation of the observed sp3 to sp2 transformation, which is seen under dry as well as lubricated sliding. Since no chemical modification of the surfaces occurs in the latter case, and the overall magnitude of the phase change is similar in both cases, the change in hybridization seems to be mediated by the shear stress experienced by the samples. Ultra-low friction is also seen in (also sp2-bonded) graphite and sometimes termed superlubricity [36]. The mechanisms of superlubricity should, however, not be naïvely transferred from graphite to a-C:H, since “graphitization” during running-in is a mere sp3 to sp2 transformation which does not necessarily lead to graphitic surface morphologies.

Similar observations on running-in have been made previously by Gao et al. [15]. They observed bond-breaking events within the amorphous carbon film which saturated on a time-scale an order of magnitude below the saturation of surface termination chiefly discussed in this study. Bond-breaking within the film is related to the transformation of sp3 to sp2 which is most pronounced during the first 5 ns of sliding in our simulations. The timescale clearly depends on the specific structure of the films and the sliding velocity explaining the slight discrepancy to the work of Gao et al. [15]. However, the presence of two timescales for surface and bulk relaxation indicates that tribology in general, and running-in in particular, is a multi-timescale problem. At longer times and lengths, for example, the surface roughness typically flattens as observed in experiments (e.g., diamond, Ref. [37]; Al, Ref. [38]). As already mentioned above, also in a-C:H viscoplastic topography evolution seems to be of importance. The underlying processes are clearly suppressed by the small simulation cell size used here and in previous works [15, 16], and most probably not observable on the timescales accessible in MD simulations. We expect in general that a multitude of different processes occur during sliding, defining a hierarchy of relaxation times. The typical time-acceleration approach namely the separation of fast and slow processes and subsequent integration over the fast degrees of freedom [3941] might therefore be not straightforwardly applicable to friction.

It will be extremely hard to disentangle the (slow) topography evolution and the (fast) local chemistry on the asperities. Let us come back to the lubricated a-C:H tribo-system. At low pressures where no lubricant degeneration occurs, we still see a change in microstructure of the two sliding surfaces, however, no running-in in the sense of a decreasing friction coefficient. On the other hand, a drop in friction coefficient under lubrication conditions has been experimentally observed for amorphous hydrocarbons [42] and is typically believed to be related to a change in surface roughness and thus a smooth transition from boundary lubrication to mixed lubrication and finally to elastohydrodynamic behavior. Due to the confined nature of our simulation setup such a change cannot occur. In future it will be of crucial importance to extend the atomistic simulations to length and timescales that allow for topographic variations either by brute force massive parallelization of MD or by concurrent multiscale atomistic–continuum coupling [43].

Acknowledgment

We thank the BMBF for funding this study within project OTRISKO. Computations were carried out on the clusters Hercules (Fh-ITWM), O2 (Fh-EMI), and Joe1 (Fh-IWM) within the Fraunhofer Society.

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© Springer Science+Business Media, LLC 2010