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Molecular Dynamics Studies of the Frictional Properties of Hydrocarbon Materials† Martin D. Perry and Judith A. Harrison* Department of Chemistry, U.S. Naval Academy, Annapolis, Maryland 21402 Received October 17, 1995X This essay discusses the importance of friction and wear and the necessity to understand these processes on the atomic level. Because of the unique friction and wear characteristics of diamond, molecular dynamics simulations were used to examine the friction and wear properties of diamond. These simulations have complemented available experimental data obtained with an atomic force microscope and that obtained with instruments which yield more macroscopic data. In particular, it was shown that the presence of methane molecules, trapped between diamond (111) surfaces, significantly reduces the calculated friction coefficients in agreement with experiment [Hayward and Field, Proc. Inst. Mech. Eng., IMechE Conf. 1987, 1, 205]. In addition, the limitations of molecular dynamics simulations and possible future directions for this type are research are discussed.
I. Introduction and Importance Understanding and ultimately controlling friction, the force which opposes the motion of two bodies in sliding contact, has long been recognized as being central to optimizing many areas of technology.1,2 This is due, in large part, to the results of the friction, namely, heating of the contacting materials, plastic deformation, and wear. In engineering applications, such as automobile engines, the natural outcomes of friction can lead to catastrophic failure of equipment and machines. If the origins of friction and its natural outcomes were understood, these catastrophic failures might be avoided and equipment lifetimes extended. Historically, trial and error and empirical observation were used to examine the macroscopic effects of friction.1 However, this approach has left many unanswered questions. For instance, because all surfaces are rough on the atomic level, the interactions that dominate friction and wear might be atomic-level interactions.3 What are the nature and identity of these atomic-level interactions? How do these atomic-level interactions govern the macroscopically observed phenomena? The answers to these, and other, questions have taken on even greater significance with the advent of miniaturization, where microscale and even nanoscale contacts are becoming commonplace. In an effort to ascertain the atomic-level origins of friction and wear, new experimental techniques such as the atomic force microscope (AFM),3-6 the surface force apparatus,7,8 and the quartz crystal microbalance9,10 have * To whom correspondence should be addressed. † Presented at the Workshop on Physical and Chemical Mechanisms in Tribology, held at Bar Harbor, ME, August 27 to September 1, 1995. X Abstract published in Advance ACS Abstracts, Sept. 15, 1996. (1) Rabinowicz, E. Friction and Wear; John Wiley and Sons: New York, 1965; p 52. (2) Bhushan, B. In Handbook of Micro/Nanotribology; Bhushan, B., Ed.; CRC Press: Boca Raton, FL, 1995; p 1. (3) Mate, M. In Handbook of Micro/Nanotribology; Bhushan, B., Ed.; CRC Press: Boca Raton, FL, 1995; p 167. (4) Mate, C. M.; McClelland, G. M.; Erlandsson, R.; Chiang, S. Phys. Rev. Lett. 1987, 59, 1942. (5) Meyer, E.; Overney, R.; Brodbeck, D.; Howald, L.; Luthi, R.; Frommer, J.; Guntherodt, H.-J. Phys. Rev. Lett. 1992, 69, 1777. (6) German, G. J.; Cohen, S. R.; Neubauer, G.; McClelland, G. M.; Seki, H.; Coulman, D. J. Appl. Phys. 1993, 73, 163. (7) Israelachvilli, J. N.; McGuiggan, P. M.; Homola, A. M. Science 1988, 240, 189. (8) Van Alsten, J.; Granick, S. Phys. Rev. Lett. 1991, 16, 33. (9) Krim, J.; Solina, D. H.; Chiarello, R. Phys. Rev. Lett. 1991, 66, 181.
all been used to examine atomic-scale friction. Advances in computer technology have allowed for complementary theoretical investigations of experimentally determined atomic-scale phenomena.11-23 Theoretical techniques which have been employed to examine the atomic-scale origins of friction include first principles calculations12,13 and molecular dynamics (MD) simulations.14-23 With this in mind, we have used MD simulations to examine the atomic-scale origins of friction and wear in diamond and related hydrocarbon systems. We have investigated diamond because of its unique friction and wear properties. Historically, these unique properties spawned a large number of studies.24 Developments in scientific instrumentation and chemical vapor deposition (CVD) techniques for diamond growth have recently renewed the interest in the frictional properties of diamond.25-29 (10) Watts, E. T.; Krim, J.; Windom, A. Phys. Rev. B 1990, 41, 3466. (11) Hirano, M.; Shinjo, K. Phys. Rev. B 1984, 41, 11837. Hirano, M.; Shinjo, K.; Kaneko, R.; Murata, R. Phys. Rev. Lett. 1991, 67, 2642. (12) Sokoloff, J. B. Surf. Sci. 1984, 144, 267; Phys. Rev. B 1990, 42, 760. (13) Zhong, W.; Tomanek, D. Phys. Rev. Lett. 1990, 64, 3054. (14) McClelland, G. M.; Glosli, J. N. NATO ASI Proceedings on Fundamentals of Friction: Macroscopic and Microscopic Processes; Singer, I. L., Pollock, H. M., Eds.; Kluwer Academic Publishers: Dordrect, The Netherlands, 1992; pp 405-426. (15) Landman, U.; Luedtke, W. D. J. Vac. Sci. Technol. B 1991, 9, 414. Landman, U.; Luedtke, W. D.; Burnham, N. A.; Colton, R. J. Science 1990, 248, 454. (16) Thompson, P. A.; Robbins, M. O. Science 1990, 250, 792. Cieplak, M.; Smith, E. D.; Robbins, M. O. Science 1994, 265, 1209. (17) Harrison, J. A.; Brenner, D. W. Handbook of Micro/Nanotribology; Bhushan, B., Ed.; CRC Press: Boca Raton, FL, 1995; p 397 and references therein. (18) Harrison, J. A.; White, C. T.; Colton, R. J.; Brenner, D. W. Phys. Rev. B 1992, 46, 9700. (19) Harrison, J. A.; White, C. T.; Colton, R. J.; Brenner, D. W. J. Phys. Chem. 1993, 97, 6573; Wear 1993, 168, 127. (20) Harrison, J. A.; White, C. T.; Colton, R. J.; Brenner, D. W. Thin Solid Films 1995, 260, 205. (21) Perry, M. D.; Harrison, J. A. J. Phys. Chem. 1995, 99, 9960. (22) Harrison, J. A.; Brenner, D. W. J. Am. Chem. Soc. 1994, 116, 10399. (23) Perry, M. D.; Harrison, J. A. Tribol. Lett. 1995, 1, 109. (24) Tabor, D.; Field, J. E. In The Properties of Natural and Synthetic Diamond; Field, J. E., Ed.; Academic Press: London, 1992; p 547 and references therein. (25) Tsuda, M.; Nakajima, M.; Oikawa, S. J. Am. Chem. Soc. 1986, 108, 5780. (26) Frenklach, M.; Wang, H. Phys. Rev. B 1991, 43 (2), 1520. (27) Belton, D. N.; Harris, S. J. J. Chem. Phys. 1992, 96, 2371. (28) Goodwin, D. G.; Gavillet, G. G. J. Appl. Phys. 1990, 68 (12), 6393.
S0743-7463(95)00895-X This article not subject to U.S. Copyright. Published 1996 by the American Chemical Society
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Figure 1. (a) Initial configurations at low load for the diamond (111) lattices with two methane molecules trapped at the interface viewed along the [1 h 10] direction. Large gray spheres represent carbon atoms of the diamond lattices, large white spheres represent carbon atoms of the methane molecules, and small white spheres represent hydrogen atoms. (b) The lower lattice and methane molecules viewed along the [111] direction.
Our work began with an investigation of the atomicscale friction between two atomically-flat, hydrogenterminated diamond (111) and (100) surfaces.17,21 Hydrocarbon chains were chemisorbed to one of the diamond (111) surfaces to roughen the surfaces, making them more realistic, and the friction was investigated.19 More recently, third-body effects on friction and wear of diamond surfaces have been investigated. Third-body particles are mobile particles which may or may not be made of the same material as the contacting surfaces. Examples of third-body particles include debris particles originally present between surfaces, particles formed during the sliding, and contamination particles. Our studies of the effects of third-body particles on friction and wear have begun with hydrocarbon molecules trapped between two hydrogen-terminated diamond (111) surfaces. II. Methodology The molecular dynamics sliding experiments are briefly described below, the details having been given elsewhere.17,19 A typical simulation starting configuration, showing two methane molecules trapped between the two diamond (111) lattices, is depicted in Figure 1. Friction is investigated by moving the topmost two layers of the upper surface, or the rigid layers (Figure 1a), in the chosen sliding direction. The atoms were allowed to dynamically evolve in time according to Newton’s equations of motion with the forces governing their motion derived from a reactive empirical-bond-order potential.30 A thermostat was applied to the middle five layers of each lattice to (29) Perry, M. D.; Raff, L. M. J. Phys. Chem. 1994, 98, 4375. (30) Brenner, D. W. Phys. Rev. B 1990, 42, 9458. Brenner, D. W.; Harrison, J. A.; White, C. T.; Colton, R. J. Thin Solid Films 1991, 206, 220.
maintain the temperature of the system at 300 K.31 The outermost layers of each lattice were held rigid; thus, their relative position was used to define the distance between the two inner surfaces. (It should be noted that this rigidity of the outermost layers more closely simulates an AFM experiment rather than a surface force apparatus experiment where lateral movement in the direction perpendicular to sliding is allowed.) The normal load was increased by decrementing the distance between the rigid layers. The sliding direction and speed were [112 h] crystallographic direction (from left to right in Figure 1a) and 100 m/s, respectively. Periodic boundary conditions were applied in the XY plane (Figure 1b) to simulate an infinite interface. The friction coefficient µ for an individual sliding run was taken to be the average frictional force on the rigid layers of the upper lattice divided by the average normal force on those same rigid layers. Average friction coefficients were obtained by averaging the individual friction coefficients from a number of different starting configurations.19 III. Results and Discussion In Figure 2, friction coefficients are plotted as a function of average normal load per rigid-layer atom for two systems. Friction coefficients in the upper panel are those obtained for two hydrogen-terminated diamond (111) lattices with methane-debris molecules trapped between the diamond surfaces (Figure 1a). For comparison, the lower panel contains data for a methyl-terminated system. Methyl-terminated systems are constructed by starting with two hydrogen-terminated diamond (111) surfaces and randomly replacing 1/8 of the hydrogen atoms on the upper surface with methyl (CH3) groups.19 (31) Berendsen, H. J. C.; Postma, J. P. M.; van Gunsteren, W. F.; DiNola, A.; Haak, J. R. J. Chem. Phys. 1984, 81, 3684.
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Figure 2. Average friction coefficient µ as a function of average normal load per rigid-layer atom for sliding in the [112 h] crystallographic direction for the methyl-terminated (CH3) and methane-debris (CH4) systems. Simulation conditions are described in the text.
Substituting methyl groups for hydrogen atoms on one of the diamond surfaces does not significantly affect the behavior of µ with load compared to that of the strictly hydrogen-terminated system.19 That is, the values of µ generally increase as a function of load with µ becoming independent of load at high loads. The magnitude of the calculated µ is directly related to the amount of vibrational excitation introduced into the lattice as a result of the sliding.20 In the case when two hydrogen-terminated diamond (111) surfaces are in sliding contact, the vibrational excitation arises from the interaction of the hydrogen atoms on opposing surfaces. This interaction is not altered significantly by the presence of the small methyl groups. Thus, the amount of vibrational excitation, and hence the friction, is approximately the same.19 In contrast, the behavior of µ with load is markedly different when methane molecules are physically trapped between two hydrogen-terminated diamond (111) surfaces. The value of µ is independent of load and significantly smaller than it was in the previous case, over almost the entire load range examined. Visualization of the MD simulations gives some insight into how the presence of the methane molecules affects µ. Unlike the chemisorbed methyl groups, the motion of the methane molecules is not restricted by attachment to the upper surface; therefore, the methane molecules are free to move anywhere over the lower surface. As a result, they are able to avoid interaction with the hydrogen atoms on the opposing surface. This is also apparent from examination of the center-of-mass trajectories of the methane molecules during the course of a simulation. These trajectories are shown on a potential energy contour plot of the hydrogenterminated diamond (111) lower surface in Figure 3. (High regions of potential energy correspond to the hydrogen atoms on the lower diamond surface.) The unattached methane molecules are able to avoid regions of high potential energy when sliding (Figure 3). In fact, these molecules are able to stay in the potential energy valleys for the majority of the simulation. In contrast, chemicallybound methyl groups, because they are attached to the upper surface and the surfaces are not permitted to move
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Figure 3. Center-of-mass trajectories (dark lines) of the methane molecules plotted on a potential-energy contour map of a hydrogen-terminated diamond (111) surface. The sliding direction is from the bottom of the figure to the top of the figure. Due to the periodic boundary conditions, trajectories which disappear off the plot at large Y reappear at the bottom of the figure (near Y ) 0). This contour map was generated by rastering a hydrogen atom, which is approximately 0.6 Å above the diamond surface, across the diamond (111) surface. The filled triangles and squares represent the starting points of the individual methane molecules. The average normal force per atom on the rigid layers of the upper surface is 0.70 nN. The contour values are 0.271, 0.771, 1.271, 1.771, and 2.271 eV.
laterally, are constrained to move over the regions of high potential energy. That is, they are interacting significantly with hydrogen atoms on the opposing diamond surface. Therefore, the amount of vibrational energy excitation caused by the sliding, and hence the friction, is lower when methane molecules are present rather than the chemisorbed methyl groups.23 The fate of the debris molecules might also have some effect on the friction and wear of the diamond surfaces. For instance, if the sliding process caused a hydrogen atom to be worn from the methane molecule, the nascent -CH3 radical could chemically bind to one of the diamond surfaces. Continued sliding would result in significantly higher friction coefficients compared to the case where only the methane debris is present. With this in mind, we have examined the fate of the methane molecules and the partitioning of internal energy within the molecules as the sliding progresses. This was done at a number of applied loads. For all the loads examined, the methane molecules remained intact during the course of the simulation. Consequently, wear of the molecules and subsequent tribochemical reactions are not an issue in this system. However, preliminary work on debris molecules other than methane indicates that this is not always the case. Varying the load does have a significant effect on the partitioning of energy within the methane molecules. At the start of the simulations, the molecules are rotationally and translationally cold. The vibrational modes of the molecules are all populated, and the vibrational temperature of the molecules is approximately 300 K. The sliding motion of the diamond surfaces does not induce a great deal of translation or rotation in the methane molecules regardless of the applied load. However, the potential energy of the methane molecules is dependent upon load. At low loads, there is very little fluctuation in the potential energy of the methane molecules (Figure 4a). As the normal load is increased, however, significant fluctuations in the potential energy of methane begin to occur (Figure 4b). Animation of these molecular dynamics sequences reveals the molecular motions responsible for these
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(b)
(a)
Figure 4. Potential energy of one of the methane molecules as a function of sliding distance. (The other molecule exhibits similar behavior.) In panel a (lower) the average normal load and µ are 0.16 nN/atom and 0.11, respectively. In panel b (upper) the average normal load and µ are 0.66 nN/atom and 0.079, respectively. Other simulation conditions are given in the text.
fluctuations. As the upper surface slides, the methane molecules are slowly swept along by the hydrogen atoms attached to the upper surface. When the methane molecules begin to encounter hydrogen atoms on the lower surface, increases in the potential energy are observed (Figure 4b). While the debris molecules do not have to pass directly over these hydrogen atoms of the lower surface, they become distorted due to the close proximity of the surfaces at high loads. Peaks in the potential energy of the methane molecule occur as the molecule is squeezed between these opposing sets of hydrogen atoms. Once the debris molecules have navigated this region, the potential energy of the molecule returns to its base line value. The vibrational motion of the methane molecules can be analyzed by examining power spectra32 of these molecules under differing load conditions. The power spectra (Figure 5) are obtained by computing the fast Fourier transform of the vibrational velocities of a methane molecule as a function of time. The results are compared to the power spectrum of an isolated methane molecule (Figure 5a) to determine which particular vibrational modes are becoming enhanced or dampened during a given sliding simulation. The peaks between 1100 and 1300 cm-1 correspond to bending modes while those between 3000 and 3500 cm-1 correspond to stretching modes of methane.33 The data represented in Figure 5b,c are from sliding runs carried out under low- and high-normal-load conditions, respectively.34 Most noticeably, the spectra are noisy with the peaks shifted in frequency and broadened compared with the spectrum from the isolated case (Figure 5a). Given that the molecule is distorted by the pressure of the two surfaces and that this distortion changes with time during sliding, these results are not surprising. Methods and procedures to filter and reduce the noise are currently under investigation. Even from (32) The fast Fourier transform routines were developed at Oak Ridge National Labs. (33) Herzberg, G. Molecular Spectra and Molecular Structure; D. Van Nostrand Company, Inc.: New York, 1945; pp 100 and 307. (34) These power spectra were filtered using a standard Gaussian filter.
Figure 5. Power spectra for methane: (a) isolated molecule; (b) low-load sliding simulation corresponding to data in Figure 4a; (c) high-load sliding simulation corresponding to data in Figure 4b. The spectra in panels b and c have been filtered using a Gaussian filter.
these current spectra, it is obvious that the bending modes present under low-load conditions (Figure 5b) have become damped out under high-load conditions (Figure 5c) while the stretching frequencies remain essentially the same. It could be argued that the methane-debris molecules reduce the interaction of the terminal hydrogen atoms on opposing surfaces simply by providing a boundary layer between the two hydrogen-terminated diamond (111) surfaces. Indeed, under similar load conditions, the distance separating the terminal hydrogen atoms on opposing diamond surfaces is approximately 0.5 Å greater for the methane-debris system than for a methylterminated system. However, it should be noted that even at comparable surface separations µ is still lower for the methane-debris system that it is for the methyl-terminated system.23 This confirms the importance of the motion of the methane molecules in reducing friction in addition to their role as a boundary layer. While larger and bulkier hydrocarbon-debris molecules could also act as a boundary layer between opposing surfaces, they might not be able to avoid the areas of higher potential energy as easily as methane. Thus, they might not lower the friction as significantly. The effects of larger hydrocarbon-debris molecules on the friction of diamond (111) surfaces are currently under investigation. The present calculations are in qualitative agreement with experimental friction studies where debris and boundary lubricants present during sliding reduce the observed friction.35,36 For example, friction experiments performed by Hardy and Doubleday35 on glass and steel have shown that as the concentration of ethyl alcohol vapor increases, the coefficient of friction decreases from the dry contact level of 0.74-0.93 to about 0.45-0.65. Experiments on diamond and diamond-like surfaces have yielded similar results. Hayward and Field36 noted that when debris was formed between diamond surfaces during sliding experiments, the result was lower friction. They (35) Hardy, W. B.; Doubleday, I. Proc. R. Soc. London, Ser. A 1922, 101, 487; 1922, 100, 550; 1923, 104, 25. (36) Hayward, I. P.; Field, J. E. Proc. Inst. Mech. Eng., IMechE Conf. 1987, 1, 205.
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also cited a direct correspondence between the amount of debris and friction; thus, as the surface became more and more contaminated with debris, friction was reduced until boundary lubrication eventually took place. IV. Limitations and Future Directions Direct comparison of theoretically obtained data with atomic-level experimental data is not possible because the inherent time and length scales of MD simulations are still orders of magnitude smaller than atomic-level experimental time and length scales. Most current MD simulations last for times on the order of picoseconds to a few nanoseconds while typical AFM experiments range in time from milliseconds to seconds. The disparity in the length scales is not as large. Typical AFM experiments examine samples on the nanometer to micrometer scale while MD simulations typically use calculation cells which are tens or hundreds of angstroms in length. At present, this is a limitation of molecular dynamics. Given the current rate of computer speed and data storage evolution, it should not be long before this hurdle is cleared. The reader is referred to Harrison and Brenner17 for a more complete discussion of the limitations of theoretical techniques. Despite this mismatch of time and length scales, MD simulations have yielded a great deal of insight, which is generally in good agreement with currently available experimental data, into atomic-scale processes. Landman et al.15 used MD to simulate the indentation of a gold substrate using a nickel tip. Force curves obtained from these simulations qualitatively agreed with experimental AFM data. Robbins and co-workers have recently used MD simulations to model the friction between an adsorbate (Kr) and a substrate (Au).16 These simulations showed quantitative agreement between the experimentally measured values of τ, the slip time, and those values obtained from the simulations. Harrison and co-workers have shown that the atomic-scale friction between two diamond (111) surfaces is approximately the same as it is between
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two diamond (100) surfaces.21 This observation has also been made experimentally using an AFM to measure the frictional force. In addition, MD simulations, which have modeled the wear of diamond surfaces, and the subsequent tribochemical reactions have demonstrated that the debris formed is consistent with experimental observations.22 Heartened by the agreement between MD simulations and experiments, we intend to continue to use them to model friction, wear, and lubrication between hydrocarbon surfaces. We will continue to look at how the presence of the third bodies, or debris particles, affects friction. The major focus of this work will be to identify the mechanisms by which the particles affect friction and to identify the fate of the debris particles. For instance, which vibrational modes of the debris particles become hot and which become cold during the sliding? Will the excitation of some modes eventually lead to the decomposition of the particles? If so, what effect will this have on the frictional properties of the system? There are many other questions which could be addressed with regard to the debris molecules. The reader is referred to Hiller37 for more information regarding the effects of third bodies on friction and wear and additional references. Acknowledgment. This work was supported by the U.S. Office of Naval Research under contracts N0001495-WR-20014 and N00014-96-WR-20008. The authors also thank Donald W. Brenner, Susan B. Sinnott, Frederick H. Streitz, James J. C. Barrett, Richard J. Colton, and Carter T. White for many helpful discussions and Eric I. Altman for writing the Gaussian filter program. Some of the figures were generated with the program XMol (XMol, Version 1.3.1, Minnesota Supercomputer Center, Inc., Minneapolis, MN, 1993). LA9508957 (37) Hiller, B. In Handbook of Micro/Nanotribology; Bhushan, B., Ed.; CRC Press: Boca Raton, FL, 1995; p 505.
