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Molecular dynamics simulations of C60 nanobearings
Chemical Physics Letters 386 (2004) 425–429 www.elsevier.com/locate/cplett
Molecular dynamics simulations of C60 nanobearings q Sergio B. Legoas *, Ronaldo Giro, Douglas S. Galv~ ao Instituto de Fısica ÔGleb WataghinÕ, Universidade Estadual de Campinas, C.P. 6165, 13083-970 Campinas SP, Brazil Received 18 December 2003; in final form 28 January 2004 Published online:
Abstract Recently was reported an ultra-lubricated system based on C60 molecules deposited over graphite layers. In that work a stick-slip rolling model for C60 molecules was proposed to explain the observed ultra-low friction force. In this Letter, we report the first molecular dynamics studies for these systems. Our results show that the AB stacking is not observed and the main experimental features can be explained without invoking stick-slip motions. Ó 2004 Elsevier B.V. All rights reserved.
1. Introduction Nanotribology has recently emerged [1,2] as a new research field, focused on the understanding of tribological properties at molecular and atomic scale. The interaction between two surfaces when one is moved with respect to the other is ultimately determined by atomic interactions. For two sliding surfaces the atomic spatial arrangement and their relative degree of commensurability play a critical role in the energy dissipation, and are fundamental to determine the friction coefficient values [3–5]. With the coming of the nanotechnology era, advances in the tribology field become crucial for the design and engineering of mechanical components at different scales [6,7]. Much of the recent progresses on the understanding of the atomistic processes of friction were made possible by the invention of experimental techniques, such as atomic force microscopy. These techniques permitted for the first time measurement of friction forces at atomic scale [8,9]. Recently, using such techniques, Miura et al. [10] have reported the experimental realization of a type of molecular bearings using C60 molecules deposited on highly oriented pyrolytic graphite. They measured latq Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.cplett.2004.01.096. * Corresponding author. Fax: +55-19-37885376. E-mail address: slegoas@ifi.unicamp.br (S.B. Legoas).
0009-2614/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2004.01.096
eral forces of over-positionated graphite flakes and observed an effective ultra-low friction regime of C60 monolayers in contact with graphite flakes under different axial load regimes. Since their discovery fullerene compounds (such as C60 ) have been recognized as promising novel materials. C60 has attracted a great deal of attention and debate in order to determine whether it has potential as a lubricant [11–15]. It has been demonstrated that the dissipation energy and shear strength of fullerenes films are one order of magnitude lower than typical values for boundary lubricants [13]. However, fullerene films have been proved to be stickier than anticipated. The ingenious experimental set up of Miura et al. [10], with the experimental realization of an ultra-lubricated system, opens new and interesting perspective for tribological applications. In order to explain the ultra-low friction regime, they proposed a model based on stick-slip and rotational molecular motions. Their model assumes that the observed AB stacking between a C60 molecule and graphite would be preserved when a C60 monolayer is formed. In this work we report the first molecular dynamics simulations for these systems. Our results show that the AB stacking is not preserved and the frustrated AB stacking can easily explain the main experimental features (force profile, commensurability patterns, frictional load dependence) without the necessity of invoking stick-slip rotational motions.
426
S.B. Legoas et al. / Chemical Physics Letters 386 (2004) 425–429
2. Methodology We have carried out molecular dynamics simulations in the framework of classical mechanics with a standard molecular force field [16], which includes van der Waals, bond stretch, bond angle bend, and torsional rotation terms. We have considered structures containing up to thousands of carbon atoms, which precludes the use of quantum methods. This methodology has been proven to be very effective in the study of dynamical properties of carbon structures [17,18]. For all simulations, the following convergence criteria were used: maximum root mean square (RMS) force of 0.005 kcal/mol A, energy differences of deviations of 0.001 kcal/mol A, 0.0001 kcal/mol, maximum atomic displacement of and RMS displacement of 0.00001 A. After 0.00005 A, initial minimization procedures selective microcanonical (constant number of particles, volume, and total energy) impulse dynamics was used. Time steps of 1 fs were used for all simulations.
3. Results and discussions In Fig. 1, we show the obtained equilibrium configurations for the cases of an isolated C60 molecule and one C60 monolayer (ML) deposited on a graphite plane. For the case of an isolated C60 molecule we observed an AB stacking type between one of their six-membered rings and the graphite hexagons. This is the same type of stacking arrangement observed among graphite planes. The distance between the center of a C60 molecule and the graphite plane is 6.38 A. We have calculated the formation energy dE of a C60 / graphite-plane system using the following relation: dE ¼ ES EC60 EG ;
Fig. 1. Equilibrium arrangements for C60 deposited over a graphite sheet. (a) Isolated C60 molecule forming AB stacking with graphite. (b) A C60 monolayer forms frustrated AB stacking with the graphite plane.
ð1Þ
where ES , EC60 , and EG refer to the total energy for the system C60 /graphite-plane (S), isolated molecule (C60), and isolated graphite-plane (G), respectively. The formation energies for an AB (eclipsed configuration) stacking and frustrated AB stacking are )29.89 and )28.98 kcal/mol, respectively. These results indicate that for an isolated C60 molecule deposited on a graphite plane the AB stacking configuration is the most stable situation, which is in agreement with other theoretical results [19]. A video version of the optimization results is show as a complementary material (Movie 1) [20]. The fact that the AB stacking is energetically favorable can be understood as a direct consequence of the symmetry configuration that maximizes the van der Waals interactions. This is better illustrated in Fig. 2 where we have acene molecules (benzenoid types – graphitic segments) around a C60 molecule. Our results show that the most stable arrangement is obtained when the acene molecules are benzenoid/benzenoid eclipsed
Fig. 2. Equilibrium arrangements for three acene molecules around a C60 molecule. The most stable configuration is reached for an AB stacking between acenes and C60 molecules, e.g., for an eclipsed arrangement of acene and C60 six-membered rings.
stacked (AB configuration). Complementary information of the optimization process can be obtained from the Movie 2 [20]. This arrangement is about 0.5 kcal/mol
S.B. Legoas et al. / Chemical Physics Letters 386 (2004) 425–429
more stable than when the acenes are arranged over the five-membered rings of the C60 molecule. However, the situation is completely different when a C60 monolayer is formed. In this case we have a competition between the energetic gain from the molecule–molecule versus molecule–graphite interactions. Contrary to the Miura et al. [10] expectations, our results show that the molecule–molecule interactions dominate the van der Waals contributions and the AB stacking is then frustrated. The most stable configuration is reached when only one atom of C60 molecule faces the geometrical center of a six-membered ring of graphite plane (orthogonal projection line passing by the middle of a graphite hexagon) (Fig. 1b). The distance between the center of the C60 molecule and the graphite The C60 monolayer (ML-C60 ) has hexplane is 6.39 A. agonal symmetry, with a distance between two neigh (Fig. 1b), in excellent boring molecules of 9.86 A agreement with the available experimental data [10,21, 22]. The frustrated AB stacking configuration is almost 3.0 kcal/mol more stable than the AB stacked one. In Fig. 3 we illustrate a three-dimensional representation of a C60 monolayer deposited on a graphite surface. We observe that in the frustrated AB stacking the C60 molecules lie in the intersections of h1 2 3 0i directions (center of the graphite hexagons). A video version of the optimization process is show in Movie 3 [20]. Miura et al. [10] also observed very unique friction force loop patterns (no hysteresis), with positive and negative regimes, but with mean frictional forces equal to zero. The observed patterns repetition has a period of Miura et al. [10] proposed the stick-slip about 10 A. mechanism based in part in the existence of these force patterns.
427
We can explain these patterns in terms of the force profiles generated by the frustrated AB stacking, without the necessity of invoking the stick-slip movements. In order to demonstrate this we have carried out simulations were flakes of graphite are moved at constant mean height with relation to the C60 /graphite arrangement (thus simulating the experimental set up). The obtained force profiles are showed in Fig. 4. There are positive and negative regions but with mean zero values, along the h1 and with a spatial periodicity of 9.86 A 1 0i, exactly the observed experimental features. Using rigid models, Miura et al. [10] were unable to reproduce the frictional force map. Another very interesting aspect observed by Miura et al. [10] was the frictional force map behavior as a function of the applied load. They observed that increasing the load values (up to a certain limit) the frictional force values presented little changes. One possibility for this behavior is that the multiple graphite layers are absorbing much of the applied compression. In order to test this hypothesis we built supercells, c-axis perpendicular to graphite planes and fullerene monolayer, a and b angles equal to 90° with different numbers of graphite layers and one C60 monolayer. We then reduced the equilibrium c-axis value by 5% and fully reoptimized the structures. Analyzing the geometrical changes for the graphite–graphite and graphite–C60 interdistances we can determine the regions presenting the principal geometric deformations. In Fig. 5, we present these results. We can observe, as supposed, that the graphite interlayers are absorbing much of the compression, which can explain the observed experimental behavior.
17.5 Å
0.4
9.8 Å
Force (nN)
0.2 0.0 -0.2 --
<112>
-0.4
C60 molecule
<110> <112>
--
<110>
-0.6 0
5
10
15
20
25
30
Displacement (Å) Fig. 3. Three-dimensional illustration of a C60 monolayer deposited on a graphite surface. C60 molecules are arranged in frustrated AB stacking. Arrows show main symmetry directions of the graphite plane.
Fig. 4. Force profiles in directions h1 1 0i and h1 1 2i. In the inset are indicated the main symmetry directions of a C60 monolayer over graphite. These directions correspond to the displacement lines of the graphite flakes along which we have mapped the forces.
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S.B. Legoas et al. / Chemical Physics Letters 386 (2004) 425–429
Compression absorbed by graphite planes (%)
100 90 80 70 60 50 40 30 0
10
20
30
40
50
60
Number of graphite planes Fig. 5. Percentual compression absorbed by graphite planes as a function of number of graphite planes. In this simulation we have considered a unit cell with a monolayer of C60 between variable numbers of graphite planes. In all the studied cases we have compressed by 5% the c-axis value of the unit cell (perpendicular to graphite planes and fullerene monolayer). When the number of graphite layers is increased they almost absorbed all the deformations induced by mechanical compression.
In order to analyse the different frictional behavior of graphite/graphite and graphite/C60 /graphite systems, we have carried out further simulations. Our results for the case of sliding a graphite flake over a graphite surface show the expected zigzag movement of the flake (see [10]). These movements are a natural consequence of the minima energy paths (e.g., the AB stacking) and are not dependent on the initial sliding direction. On the other hand, when a graphite flake is sliding over an ML-C60 /graphite-surface system, the flake movement is always in rectiline directions and not dependent on the initial movement of the flake. We observed the movement of the C60 molecules as being different of a stick-slip model proposed by Miura et al. [10]. The C60 molecules move in complex patterns, spending most of the time oscillating around their initial positions. This rotational behavior was also observed for C60 single crystal surfaces [23]. The different sliding behaviors for the two cases, and the fact that the graphite/C60 van der Waals interactions are significantly lower than graphite/graphite ones, can explain the experimentally observed ultra-low frictional regime. Video version of our dynamics simulations can be observed as complementary material in Movie 4 and Movie 5 [20].
4. Conclusions Using dynamical molecular simulations we have investigated the experimentally observed ultra lubricated system based on C60 molecules deposited on highly
oriented pyrolitic graphite reported by Miura et al. [10]. Our results show that (in contrast with models proposed in the literature) the most energetically stable configuration of a C60 monolayer deposited over graphite surface is obtained for a frustrated AB stacking. Also, the movement of graphite flakes over a ML-C60 does not correspond to the stick-slip rolling model proposed by Miura et al. [10]. We show that the energy profiles generated by the frustrated AB stacking can easily explain the main experimental features (force regime, commensurability patterns, frictional loading dependence) without the necessity of invoking stick-slip rotational motions. The ultra-low frictional behavior of C60 molecules and graphite sheets can be explained due to the decreasing of the van der Waals interaction between the C60 monolayer and the graphite sheets, as well as to the characteristic movement of the graphite flakes over C60 monolayer.
Acknowledgements This work was supported in part by the Brazilian agencies CNPq, IMMP/MCT, and FAPESP. The authors also wish to acknowledge support from Accelrys, Inc. for helpful assistance.
References [1] S. Granick, MRS Bull. 16 (1991) 33. [2] B. Bhushan (Ed.), Handbook of Micro/Nanotribology, CRC, Boca Raton, FL, 1995. [3] H. Hirano, K. Shinjo, R. Kaneko, Y. Murata, Phys. Rev. Lett. 67 (1991) 2642. [4] P.E. Sheehan, C.M. Lieber, Science 272 (1996) 1158. [5] G. He, M.H. Muser, M.O. Robbins, Science 284 (1999) 1650. [6] B. Bhushan, J.N. Israelachvilli, U. Landman, Nature (London) 374 (1995) 607. [7] B.N.J. Persson, Sliding Friction: Physical Properties and Applications, Springer, Berlin, 1998. [8] G. Binnig, C.F. Quate, C.H. Gerber, Phys. Rev. Lett. 56 (1986) 930. [9] C.M. Mate, G.M. McClelland, R. Erlandsson, S. Chiang, Phys. Rev. Lett. 59 (1987) 1942. [10] K. Miura, S. Kamiya, N. Sasaki, Phys. Rev. Lett. 90 (2003) 055509. [11] B. Bhushan, B.K. Gupta, G.W. Van Cleef, G. Capp, J.V. Coe, Tribol. Trans. 4 (1993) 573. [12] B. Bhushan, J. Ruan, J. Mater. Res. 8 (1993) 3019. [13] R. L€ uthl, E. Meyer, H. Haefke, L. Howald, W. Gutmannsbauer, H.-L. G€ untherodt, Science 266 (1994) 1979. [14] T. Thundat, R.J. Warmack, D. Ding, R.N. Compton, Appl. Phys. Lett. 63 (1993) 891. [15] R. L€ uthl, E. Meyer, H. Haefke, L. Howald, W. Gutmannsbauer, M. Gugglsberg, M. Bammerlin, H.-L. G€ untherodt, Surf. Sci. 338 (1995) 247. [16] UNIVERSAL1.02 Molecular Force Field, available from Accelrys, Inc. as part of Materials Studio and CERIUS 2 program suites. Available from http://www.accelrys.com.
S.B. Legoas et al. / Chemical Physics Letters 386 (2004) 425–429 [17] R.H. Baughman, D.S. Galv~ao, Nature (London) 365 (1993) 735. [18] S.B. Legoas, V.R. Coluci, S.F. Braga, P.Z. Coura, S.O. Dantas, D.S. Galv~ ao, Phys. Rev. Lett. 90 (2003) 055504. [19] P.A. Gravil, M. Devel, Ph. Lambin, X. Bouju, Ch. Girard, A.A. Lucas, Phys. Rev. B 53 (1996) 1622.
429
[20] See EPAPS Document for movies, in AVI and MOV formats, of simulations discussed in the Letter. [21] S. Okita, K. Miura, Nano Lett. 1 (2001) 101. [22] B. Bhushan, J. Ruan, B.K. Gupta, J. Phys. D: Appl. Phys. 26 (1993) 1319. [23] Q. Liang, O.K.C. Tsui, Y. Xu, H. Li, X. Xiao, Phys. Rev. Lett. 90 (2003) 146102.
Molecular dynamics simulations of C60 nanobearings q Sergio B. Legoas *, Ronaldo Giro, Douglas S. Galv~ ao Instituto de Fısica ÔGleb WataghinÕ, Universidade Estadual de Campinas, C.P. 6165, 13083-970 Campinas SP, Brazil Received 18 December 2003; in final form 28 January 2004 Published online:
Abstract Recently was reported an ultra-lubricated system based on C60 molecules deposited over graphite layers. In that work a stick-slip rolling model for C60 molecules was proposed to explain the observed ultra-low friction force. In this Letter, we report the first molecular dynamics studies for these systems. Our results show that the AB stacking is not observed and the main experimental features can be explained without invoking stick-slip motions. Ó 2004 Elsevier B.V. All rights reserved.
1. Introduction Nanotribology has recently emerged [1,2] as a new research field, focused on the understanding of tribological properties at molecular and atomic scale. The interaction between two surfaces when one is moved with respect to the other is ultimately determined by atomic interactions. For two sliding surfaces the atomic spatial arrangement and their relative degree of commensurability play a critical role in the energy dissipation, and are fundamental to determine the friction coefficient values [3–5]. With the coming of the nanotechnology era, advances in the tribology field become crucial for the design and engineering of mechanical components at different scales [6,7]. Much of the recent progresses on the understanding of the atomistic processes of friction were made possible by the invention of experimental techniques, such as atomic force microscopy. These techniques permitted for the first time measurement of friction forces at atomic scale [8,9]. Recently, using such techniques, Miura et al. [10] have reported the experimental realization of a type of molecular bearings using C60 molecules deposited on highly oriented pyrolytic graphite. They measured latq Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.cplett.2004.01.096. * Corresponding author. Fax: +55-19-37885376. E-mail address: slegoas@ifi.unicamp.br (S.B. Legoas).
0009-2614/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2004.01.096
eral forces of over-positionated graphite flakes and observed an effective ultra-low friction regime of C60 monolayers in contact with graphite flakes under different axial load regimes. Since their discovery fullerene compounds (such as C60 ) have been recognized as promising novel materials. C60 has attracted a great deal of attention and debate in order to determine whether it has potential as a lubricant [11–15]. It has been demonstrated that the dissipation energy and shear strength of fullerenes films are one order of magnitude lower than typical values for boundary lubricants [13]. However, fullerene films have been proved to be stickier than anticipated. The ingenious experimental set up of Miura et al. [10], with the experimental realization of an ultra-lubricated system, opens new and interesting perspective for tribological applications. In order to explain the ultra-low friction regime, they proposed a model based on stick-slip and rotational molecular motions. Their model assumes that the observed AB stacking between a C60 molecule and graphite would be preserved when a C60 monolayer is formed. In this work we report the first molecular dynamics simulations for these systems. Our results show that the AB stacking is not preserved and the frustrated AB stacking can easily explain the main experimental features (force profile, commensurability patterns, frictional load dependence) without the necessity of invoking stick-slip rotational motions.
426
S.B. Legoas et al. / Chemical Physics Letters 386 (2004) 425–429
2. Methodology We have carried out molecular dynamics simulations in the framework of classical mechanics with a standard molecular force field [16], which includes van der Waals, bond stretch, bond angle bend, and torsional rotation terms. We have considered structures containing up to thousands of carbon atoms, which precludes the use of quantum methods. This methodology has been proven to be very effective in the study of dynamical properties of carbon structures [17,18]. For all simulations, the following convergence criteria were used: maximum root mean square (RMS) force of 0.005 kcal/mol A, energy differences of deviations of 0.001 kcal/mol A, 0.0001 kcal/mol, maximum atomic displacement of and RMS displacement of 0.00001 A. After 0.00005 A, initial minimization procedures selective microcanonical (constant number of particles, volume, and total energy) impulse dynamics was used. Time steps of 1 fs were used for all simulations.
3. Results and discussions In Fig. 1, we show the obtained equilibrium configurations for the cases of an isolated C60 molecule and one C60 monolayer (ML) deposited on a graphite plane. For the case of an isolated C60 molecule we observed an AB stacking type between one of their six-membered rings and the graphite hexagons. This is the same type of stacking arrangement observed among graphite planes. The distance between the center of a C60 molecule and the graphite plane is 6.38 A. We have calculated the formation energy dE of a C60 / graphite-plane system using the following relation: dE ¼ ES EC60 EG ;
Fig. 1. Equilibrium arrangements for C60 deposited over a graphite sheet. (a) Isolated C60 molecule forming AB stacking with graphite. (b) A C60 monolayer forms frustrated AB stacking with the graphite plane.
ð1Þ
where ES , EC60 , and EG refer to the total energy for the system C60 /graphite-plane (S), isolated molecule (C60), and isolated graphite-plane (G), respectively. The formation energies for an AB (eclipsed configuration) stacking and frustrated AB stacking are )29.89 and )28.98 kcal/mol, respectively. These results indicate that for an isolated C60 molecule deposited on a graphite plane the AB stacking configuration is the most stable situation, which is in agreement with other theoretical results [19]. A video version of the optimization results is show as a complementary material (Movie 1) [20]. The fact that the AB stacking is energetically favorable can be understood as a direct consequence of the symmetry configuration that maximizes the van der Waals interactions. This is better illustrated in Fig. 2 where we have acene molecules (benzenoid types – graphitic segments) around a C60 molecule. Our results show that the most stable arrangement is obtained when the acene molecules are benzenoid/benzenoid eclipsed
Fig. 2. Equilibrium arrangements for three acene molecules around a C60 molecule. The most stable configuration is reached for an AB stacking between acenes and C60 molecules, e.g., for an eclipsed arrangement of acene and C60 six-membered rings.
stacked (AB configuration). Complementary information of the optimization process can be obtained from the Movie 2 [20]. This arrangement is about 0.5 kcal/mol
S.B. Legoas et al. / Chemical Physics Letters 386 (2004) 425–429
more stable than when the acenes are arranged over the five-membered rings of the C60 molecule. However, the situation is completely different when a C60 monolayer is formed. In this case we have a competition between the energetic gain from the molecule–molecule versus molecule–graphite interactions. Contrary to the Miura et al. [10] expectations, our results show that the molecule–molecule interactions dominate the van der Waals contributions and the AB stacking is then frustrated. The most stable configuration is reached when only one atom of C60 molecule faces the geometrical center of a six-membered ring of graphite plane (orthogonal projection line passing by the middle of a graphite hexagon) (Fig. 1b). The distance between the center of the C60 molecule and the graphite The C60 monolayer (ML-C60 ) has hexplane is 6.39 A. agonal symmetry, with a distance between two neigh (Fig. 1b), in excellent boring molecules of 9.86 A agreement with the available experimental data [10,21, 22]. The frustrated AB stacking configuration is almost 3.0 kcal/mol more stable than the AB stacked one. In Fig. 3 we illustrate a three-dimensional representation of a C60 monolayer deposited on a graphite surface. We observe that in the frustrated AB stacking the C60 molecules lie in the intersections of h1 2 3 0i directions (center of the graphite hexagons). A video version of the optimization process is show in Movie 3 [20]. Miura et al. [10] also observed very unique friction force loop patterns (no hysteresis), with positive and negative regimes, but with mean frictional forces equal to zero. The observed patterns repetition has a period of Miura et al. [10] proposed the stick-slip about 10 A. mechanism based in part in the existence of these force patterns.
427
We can explain these patterns in terms of the force profiles generated by the frustrated AB stacking, without the necessity of invoking the stick-slip movements. In order to demonstrate this we have carried out simulations were flakes of graphite are moved at constant mean height with relation to the C60 /graphite arrangement (thus simulating the experimental set up). The obtained force profiles are showed in Fig. 4. There are positive and negative regions but with mean zero values, along the h1 and with a spatial periodicity of 9.86 A 1 0i, exactly the observed experimental features. Using rigid models, Miura et al. [10] were unable to reproduce the frictional force map. Another very interesting aspect observed by Miura et al. [10] was the frictional force map behavior as a function of the applied load. They observed that increasing the load values (up to a certain limit) the frictional force values presented little changes. One possibility for this behavior is that the multiple graphite layers are absorbing much of the applied compression. In order to test this hypothesis we built supercells, c-axis perpendicular to graphite planes and fullerene monolayer, a and b angles equal to 90° with different numbers of graphite layers and one C60 monolayer. We then reduced the equilibrium c-axis value by 5% and fully reoptimized the structures. Analyzing the geometrical changes for the graphite–graphite and graphite–C60 interdistances we can determine the regions presenting the principal geometric deformations. In Fig. 5, we present these results. We can observe, as supposed, that the graphite interlayers are absorbing much of the compression, which can explain the observed experimental behavior.
17.5 Å
0.4
9.8 Å
Force (nN)
0.2 0.0 -0.2 --
<112>
-0.4
C60 molecule
<110> <112>
--
<110>
-0.6 0
5
10
15
20
25
30
Displacement (Å) Fig. 3. Three-dimensional illustration of a C60 monolayer deposited on a graphite surface. C60 molecules are arranged in frustrated AB stacking. Arrows show main symmetry directions of the graphite plane.
Fig. 4. Force profiles in directions h1 1 0i and h1 1 2i. In the inset are indicated the main symmetry directions of a C60 monolayer over graphite. These directions correspond to the displacement lines of the graphite flakes along which we have mapped the forces.
428
S.B. Legoas et al. / Chemical Physics Letters 386 (2004) 425–429
Compression absorbed by graphite planes (%)
100 90 80 70 60 50 40 30 0
10
20
30
40
50
60
Number of graphite planes Fig. 5. Percentual compression absorbed by graphite planes as a function of number of graphite planes. In this simulation we have considered a unit cell with a monolayer of C60 between variable numbers of graphite planes. In all the studied cases we have compressed by 5% the c-axis value of the unit cell (perpendicular to graphite planes and fullerene monolayer). When the number of graphite layers is increased they almost absorbed all the deformations induced by mechanical compression.
In order to analyse the different frictional behavior of graphite/graphite and graphite/C60 /graphite systems, we have carried out further simulations. Our results for the case of sliding a graphite flake over a graphite surface show the expected zigzag movement of the flake (see [10]). These movements are a natural consequence of the minima energy paths (e.g., the AB stacking) and are not dependent on the initial sliding direction. On the other hand, when a graphite flake is sliding over an ML-C60 /graphite-surface system, the flake movement is always in rectiline directions and not dependent on the initial movement of the flake. We observed the movement of the C60 molecules as being different of a stick-slip model proposed by Miura et al. [10]. The C60 molecules move in complex patterns, spending most of the time oscillating around their initial positions. This rotational behavior was also observed for C60 single crystal surfaces [23]. The different sliding behaviors for the two cases, and the fact that the graphite/C60 van der Waals interactions are significantly lower than graphite/graphite ones, can explain the experimentally observed ultra-low frictional regime. Video version of our dynamics simulations can be observed as complementary material in Movie 4 and Movie 5 [20].
4. Conclusions Using dynamical molecular simulations we have investigated the experimentally observed ultra lubricated system based on C60 molecules deposited on highly
oriented pyrolitic graphite reported by Miura et al. [10]. Our results show that (in contrast with models proposed in the literature) the most energetically stable configuration of a C60 monolayer deposited over graphite surface is obtained for a frustrated AB stacking. Also, the movement of graphite flakes over a ML-C60 does not correspond to the stick-slip rolling model proposed by Miura et al. [10]. We show that the energy profiles generated by the frustrated AB stacking can easily explain the main experimental features (force regime, commensurability patterns, frictional loading dependence) without the necessity of invoking stick-slip rotational motions. The ultra-low frictional behavior of C60 molecules and graphite sheets can be explained due to the decreasing of the van der Waals interaction between the C60 monolayer and the graphite sheets, as well as to the characteristic movement of the graphite flakes over C60 monolayer.
Acknowledgements This work was supported in part by the Brazilian agencies CNPq, IMMP/MCT, and FAPESP. The authors also wish to acknowledge support from Accelrys, Inc. for helpful assistance.
References [1] S. Granick, MRS Bull. 16 (1991) 33. [2] B. Bhushan (Ed.), Handbook of Micro/Nanotribology, CRC, Boca Raton, FL, 1995. [3] H. Hirano, K. Shinjo, R. Kaneko, Y. Murata, Phys. Rev. Lett. 67 (1991) 2642. [4] P.E. Sheehan, C.M. Lieber, Science 272 (1996) 1158. [5] G. He, M.H. Muser, M.O. Robbins, Science 284 (1999) 1650. [6] B. Bhushan, J.N. Israelachvilli, U. Landman, Nature (London) 374 (1995) 607. [7] B.N.J. Persson, Sliding Friction: Physical Properties and Applications, Springer, Berlin, 1998. [8] G. Binnig, C.F. Quate, C.H. Gerber, Phys. Rev. Lett. 56 (1986) 930. [9] C.M. Mate, G.M. McClelland, R. Erlandsson, S. Chiang, Phys. Rev. Lett. 59 (1987) 1942. [10] K. Miura, S. Kamiya, N. Sasaki, Phys. Rev. Lett. 90 (2003) 055509. [11] B. Bhushan, B.K. Gupta, G.W. Van Cleef, G. Capp, J.V. Coe, Tribol. Trans. 4 (1993) 573. [12] B. Bhushan, J. Ruan, J. Mater. Res. 8 (1993) 3019. [13] R. L€ uthl, E. Meyer, H. Haefke, L. Howald, W. Gutmannsbauer, H.-L. G€ untherodt, Science 266 (1994) 1979. [14] T. Thundat, R.J. Warmack, D. Ding, R.N. Compton, Appl. Phys. Lett. 63 (1993) 891. [15] R. L€ uthl, E. Meyer, H. Haefke, L. Howald, W. Gutmannsbauer, M. Gugglsberg, M. Bammerlin, H.-L. G€ untherodt, Surf. Sci. 338 (1995) 247. [16] UNIVERSAL1.02 Molecular Force Field, available from Accelrys, Inc. as part of Materials Studio and CERIUS 2 program suites. Available from http://www.accelrys.com.
S.B. Legoas et al. / Chemical Physics Letters 386 (2004) 425–429 [17] R.H. Baughman, D.S. Galv~ao, Nature (London) 365 (1993) 735. [18] S.B. Legoas, V.R. Coluci, S.F. Braga, P.Z. Coura, S.O. Dantas, D.S. Galv~ ao, Phys. Rev. Lett. 90 (2003) 055504. [19] P.A. Gravil, M. Devel, Ph. Lambin, X. Bouju, Ch. Girard, A.A. Lucas, Phys. Rev. B 53 (1996) 1622.
429
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