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Langmuir 1997, 13, 1718-1722
Effects of Molecular Structure on Frictional Properties of Langmuir-Blodgett Monolayers A. Koike* and M. Yoneya Hitachi Research Laboratory, Hitachi, Ltd., 7-1-1 Omika-cho, Hitachi, Ibaraki 319-12, Japan Received July 2, 1996. In Final Form: December 27, 1996X Molecular dynamics simulations have been used to study shear friction in Langmuir-Blodgett monolayers of carboxylic acids. The effects of partial fluorination of hydrocarboxylic acids, of introduction of ether linkages into perfluorocarboxylic acids, and of chain length on frictional properties such as frictional mechanism and frictional coefficients were investigated. The frictional coefficient of the semifluorocarboxylic acid monolayer changed with the fluorination ratio of the hydrocarboxylic acid. Furthermore, the frictional coefficients of hydrocarboxylic acids with a carbon chain length from 12 to 20 were found to be independent of this length. The qualitative aspects of the simulation results were consistent with reported experimental results. The simulation results were discussed in relation to excess root mean square fluctuations of the potential energy under shear from the equilibrium energy value.
1. Introduction Thin organic films are widely used as lubricant molecules to reduce friction between two surfaces. With development of sophisticated technological devices, such as magnetic storage devices, demands are increasing for a lubricant film which is thinner, is more durable, and has low friction. Therefore it is necessary to elucidate the tribological mechanism of thin organic films. Availability of high precision apparatuses such as a SFA (surface force apparatus)1 and SFM (scanning force microscope)2 allows measurements of frictional forces with atomic resolution. Microscopic behavior of molecules has been studied in relation to the tribology of various kinds of thin organic films.3-6 In particular, Langmuir-Blodgett (LB) films, which are highly ordered, minute films, have been widely used not only in experiments7-14 but also in computer simulations15,16 to investigate the frictional mechanism and effects of the load, temperature, shear rate, and relative humidity on frictional behavior. However, the frictional mechanism and the relationship between frictional force and molecular structures remain elusive. X Abstract published in Advance ACS Abstracts, February 15, 1997.
(1) Israelachivili, J. N.; McGuiggan, P. M.; Homola, A. M. Science 1988, 8, 189. (2) For review of AFM: Overney, R. M.; Meyer, E. MRS Bull. 1993, May 26. (3) Gee, M. L.; McGuiggan, P. M.; Israelachvili, J. N.; Homola, A. M. J. Chem. Phys. 1990, 93, 1895. (4) Ru¨he, J.; Novotony, V. J.; Kanazawa, K. K.; Clarke, T.; Street, B. Langmuir 1993, 9, 2383. (5) Bhushan, B.; Israelachvili, J. N.; Landman, U. Nature 1995, 374, 607. (6) Homola, A. M.; Israelachvili, J. N.; McGuiggan, P. M.; Gee, M. L. Wear 1990, 136, 65. (7) Yoshizawa, H.; Chen, Y.-L.; Israelachvili, J. N. Wear 1993, 168, 161. (8) Chen, Y.-L.; Israelachvili, J. N. J. Phys. Chem. 1992, 96, 7752. (9) Meyer, E.; Howald, L.; Overney, R.; Heinzelmann, H.; Frommer, H; Gu¨therodt, H.-J.; Wagner, T.; Shier, H.; Roth, S. Nature 1991, 349, 398. (10) Overney, R. M.; Meyer, E.; Frommer, J.; Gu¨therodt, H.-J.; Decher, G.l Reibel, J.; Sohling, U. Langmuir 1993, 9, 341. (11) Overney, R. M.; Meyer, E.; Frommer, J.; Brodbeck, D.; Lu¨thi, R.; Howald, L.; Gu¨therodt, H.-J.; Fujihira, M.; Takano, H.; Gotoh, Y. Nature 1992, 359, 133. (12) Overney, R. M.; Meyer, E.; Frommer, J.; Gu¨therodt, H.-J.; Fujihira, M.; Takano, H.; Gotoh, Y. Langmuir 1994, 10, 1281. (13) Overney, R. M.; Takano. H.; Fujihira, M.; Meyer, E.; Gu¨therodt, H.-J. Thin Solid Films 1994, 240, 105. (14) Briscoe, B. J.; Evans, D. C. Proc. R. Soc. London A 1982, 380, 389. (15) Glosli, J. N.; McClelland, G. M. Phys. Rev. Lett. 1993, 70, 1960. (16) Tupper, K. J.; Brenner, D. W. Thin Solid Films 1994, 253, 185.
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In our previous paper,17 we simulated the friction between a SiO2 slider and an LB film on SiO2 and discussed the cause of the higher frictional coefficients in perfluorocarbons than hydrocarbons. Although the frictional coefficients of fluorocarbons are higher than those of hydrocarbons, fluorocarbons are good lubricants from the viewpoint of their low reactivity and good hydrophobic properties. In this article, we investigated the effects of partial fluorination of hydrocarboxylic acids and the introduction of ether linkages into perfluorocarboxylic acids on frictional properties such as frictional mechanism and frictional coefficients. Additionally, we investigated the effects of chain length on the frictional coefficients. 2. Molecular Model and Simulation Methods 2.1. Molecular Model. The molecular model and parameters for the simulations were the same as those previously used.17 We employed the CVFF (consistent valence force field).18 Though some kinds of force fields which regard CF2 and CF3 groups as isotropic19-22 and anisotropic23 spherical united atoms have been developed recently, we expected that the atoms would become too close to be represented as pseudoatoms under the shear condition in the present simulation. Thus we explicitly simulated all fluorine and hydrogen atoms. The quartz type SiO2(001) surface composed of 510-714 atoms was used as base and slider surfaces and SiO2 surfaces were simulated as two rigid layers. Simulated monolayers were composed of 36 chains of each kind of molecule adsorbed on the SiO2 surface. The cell sizes of C18F37COOH, C12F25C6H12COOH, C8F17C10H20COOH, C5F11C13H26COOH, C3F7OCF2OC12F24COOH, and C13F27OCF2OC2F4COOH monolayers were 3.437 × 3.246 nm2 (the area per molecule was 0.310 nm2). The C3F7C15H30COOH monolayer was 2.946 × 3.246 nm2 (the area per molecule was 0.265 nm2). The C20H41COOH, C18H37COOH, C14H29COOH, and C12H25COOH monolayers were 2.946 × 2.705 nm2 (the area per molecule was 0.221 nm2). These areas per molecule correspond to those (17) Koike, A.; Yoneya, M. J. Chem. Phys. 1996, 105, 6060. (18) Dauber-Osguthorpe, P.; Roberts, V. A.; Osguthorpe, D. J.; Wolff, J.; Genest, M.; Hagler, A. T. Protein: Struc., Funct. and Genetics 1988, 4, 31. (19) Shin, S.; Collazo, N.; Rice, S. A. J. Chem. Phys. 1992, 96, 1352. (20) Collazo, N.; Shin, S.; Rice, S. A. J. Chem. Phys. 1992, 96, 4735. (21) Shin, S.; Collazo, N.; Rice, S. A. J. Chem. Phys. 1993, 98, 3469. (22) Shin S.; Rice, S. A. Langmuir 1994, 10, 262. (23) Schmidt, M. E.; Shin, S.; Rice, S. A. J. Chem. Phys. 1996, 104, 2101.
© 1997 American Chemical Society
Frictional Properties of LB Monolayers
Figure 1. Variation with time of the frictional force (solid line) and potential energy (dashed line): (a) C18F37COOH; (b) C8F17C10H20COOH; (c) C18H37COOH.
at 20-40 mN/m experimental surface pressures.24,25 Under these pressures, hardly any defects exist in the film and the collapse which is caused by high pressure does not occur. In the close packed condition which we considered in the simulations, there are almost no gauche defects in any molecular films.19 Then initial configurations of the molecules were all assumed to be trans. 2.2. Simulation procedure. A simulation was carried out in three steps. First the monolayer film was equilibrated for 50 ps. Next the slider was compressed to the 〈001〉 direction at a constant velocity 0.1 nm/ps from the point at which the distance between the slider and base was 1.0 nm. Finally the slider was moved into the 〈010〉 direction at a constant velocity 0.1 nm/ps under a constant load 6.0 nN for 4.0 nm (40 ps). The load was calculated as a sum of the normal forces to the slider surface. A leapfrog algorithm26 was used to integrate Newton’s equations of motion. In the equilibrium step, we used a time step of 0.5 fs and in the compression and sliding steps, 0.4 fs. Periodic boundaries were imposed in the in-plane direction, and the minimum image convention was employed. The cut-off length of the nonbonding interaction was set at 0.9 nm. The average temperature was maintained at 300 K by use of a weak coupling to an (24) Barton, S. W.; Goudot, A.; Bouloussa, O.; Rondelez, F.; Lin, B.; Novak, F.; Acero, A.; Rice, S. A. J. Chem. Phys. 1992, 96, 1343. (25) Kato, T.; Kameyama, M. Private communications, 1995. (26) Hockney, R. W. Methods Comput. Phys. 1976, 20, 136.
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Figure 2. Variation with time of the averaged collective tilt angle: (a) C18F37COOH; (b) C8F17C10H20COOH, hydrocarbon part (dashed line) and flurocarbons part (solid line); (c) C18H37COOH.
external bath, i.e., Berendsen’s thermostat.27 The initial velocities of each atom were sampled from MaxwellBoltzmann distributions. The particle positions were stored every 125 time steps and then analyzed. 3. Results and Discussions 3.1. Molecular Behavior. Figure 1 shows the time evolution of frictional force and potential energy of C18F37COOH, C8F17C10H20COOH, and C18H37COOH. The frictional force is the total lateral force needed for the slider to move a constant velocity. Figure 1 indicates that a periodic change of the frictional force and potential energy is almost absent in semifluorocarboxylic and hydrocarboxylic acids, although fluorocarboxylic acid has the periodic change. Figure 2 shows the time evolution of collective tilt angles. Figure 2b separates the collective tilt angles in the hydrocarbon and fluorocarbon parts. We defined the collective tilt angle as the average of the angles between the vectors perpendicular to the base surface and the vectors that connect the carbon atoms as in our previous study.17 Figure 2 shows that a periodic change of the tilt angle of the semiflurocarboxylic and hydrocarboxylic acids is almost absent. Although it is not clear compared to the periodic change of the frictional force, (27) 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 3. Root mean square fluctuations of the carbon atom positions. The values are averages of the rms fluctuations calculated at intervals of 0.5 ps for 20-40 ps. The atom number of the end atom of the carboxylic group is 18. The other end atom of the molecule is 1.
the periodic change of tilt angles is seen in fluorocarboxylic acid. In other semifluorocarbons, the frictional force, potential energy, and collective tilt angle do not change periodically, except for C12F25C8H16COOH. As noted by Glosli and McClelland,15 these periodical changes of frictional force and potential energy correspond to discontinuous energy dissipation, i.e., a plucking mechanism. We have observed the plucking mechanism elsewhere in similar systems, C14F29COOH and C14H29COOH.17 Consequently we can assume that the plucking mechanism does not occur in a long chain hydrocarboxylic acid, since the disorder of the molecular movement increases with increasing chain length because of the flexibility of the hydrocarbons. In semifluorocarbon molecules in which the partially fluorinated part is shorter than a certain length, the plucking mechanism also does not occur. We expect that if the hydrocarbon chains are long enough, the hydrocarbons act like a cushion and it is hard to save strain energy as potential energy, since the hydrocarbon part is more flexible than the fluorinated part. Figure 3 shows averaged root mean square (rms) fluctuations of carbon atom positions in each molecule. In order to decrease the influence of the plucking mechanism, we calculated the rms fluctuations of atomic positions for 0.5 ps intervals and averaged these values for 20-40 ps. The fluctuations of the hydrocarbon parts in the semifluorocarboxylic acids are larger than those of the corresponding parts of the hydrocarboxylic acid, though those of fluorocarbon parts in semifluorocarboxylic acids are roughly as large as the corresponding parts of perfluorocarboxylic acid. For the semifluorocarboxylic acids increased fluctuations in the hydrocarbon parts are attributed to (1) the difference in the van der Waals radii between fluorine and hydrogen atoms and (2) easier strain energy conservation for the hydrocarbon parts because there is a mixture of two kinds of molecular stiffness parts, fluorocarbons and hydrocarbons. 3.2. Frictional Coefficient. The simulated frictional coefficients of LB films of C18F37COOH, C10F21C8H16COOH, C8F17C10H20COOH, C5F11C13H26COOH, C3F7C15H30COOH, and C18H37COOH are 0.31, 0.31, 0.26, 0.26, 0.18, and 0.12, respectively. The experimental frictional coefficients of LB films of C17F35COOH, C8F17C10H20COOH, and C18H37COOH obtained with the repeating sliding apparatus, using a sapphire slider and a glass base, are 0.16, 0.13, and 0.06, respectively.25 By SFM, in which the slider is Si3N4 and the base is Si, the frictional coefficients of
Koike and Yoneya
Figure 4. Relation between the frictional force and the averaged rms fluctuations of total potential energy difference 〈E〉 between shear and equilibrium conditions. The filled circles 〈E2〉 represent the differences of averaged rms fluctuations of potential energies calculated at intervals of 0.5 ps for 20-40 ps and open circles 〈E1〉 represent the differences of the standard deviations of potential energies for 20-40 ps.
C9F19C2H4OC2H4COOH and C19H39COOH are 0.4 and 0.1, respectively.13 In both simulated and experimental results, the decreasing order of size of the frictional coefficients is perfluorocarboxylic acid, semifluorocarboxylic acid, and hydrocarboxylic acid. Thus we conclude that the experimental frictional coefficients are qualitatively reproduced by the simulations. 3.3. Relation between Frictional Force and Root Mean Square Fluctuations of Potential Energy. In our previous simulations,17 we found that the rms fluctuations of potential energy difference under shear and equilibrium conditions were roughly proportional to the frictional force. In order to confirm whether this relation is valid for the present simulations, we plotted rms fluctuations of potential energy difference and frictional force in Figure 4. The equilibrium condition was calculated as follows. The initial structure in the sliding procedure was the final structure of the shear condition and the slider was kept with a constant load 6.0 nN for 40 ps without sliding. In order to investigate the influence of the plucking mechanism, we used two calculation methods. The open circles were calculated to include the influence of the plucking mechanism. Thus they represent the values which subtracted the rms fluctuations of the potential energy for 20-40 ps in the equilibrium condition as thermal fluctuations from those in the shear condition. The black circles were calculated so as to reduce the influence of the plucking mechanism. That is, they represent the differences which subtracted the averaged rms fluctuations of the potential energy for 0.5 ps intervals during 20-40 ps in the equilibrium condition from those in the shear condition. From Figure 4, we conclude that the relationship, that rms fluctuations of potential energy difference between shear and equilibrium conditions are roughly proportional to the frictional force, also holds true in the present simulations, although for the open circles the data are not so clear. We interpreted this relation in the previous paper as follows. The frictional energy accompanying the frictional force dissipates as thermal energy after being saved once as potential energy (which consists of film potential energy and interfacial interaction between the slider). Then fluctuations of the potential energy are related to frictional force. If we regard this frictional energy as the energy
Frictional Properties of LB Monolayers
Figure 5. Averaged rms fluctuations of each potential energy difference 〈E〉 between shear and equilibrium conditions. Interfacial interaction means the nonbonded interaction between slider and LB film. The other energy terms represent each term for the LB film. The values are the differences of the averaged rms fluctuations calculated at intervals of 0.5 ps for 20-40 ps.
needed for the deformation of the film under the shear condition and regard the fluctuations of interfacial interaction energy as overcoming the local maximum of the interfacial interaction, the frictional force represents the energy needed for deformation of the film and overcoming the local maximum of the interfacial interaction when the slider moves. Here we use the term film deformation to mean small elastic film deformations. The reasons why the relationship between the frictional force for the open circles is unclear are that (1) almost no plucking mechanism is observed for semifluorocarboxylic and hydrocarboxylic acids and (2) disorder in molecular behavior cannot be ignored in long term calculations of rms fluctuations. 3.4. Influence of Partial Fluorination on Root Mean Squares Fluctuations of Potential Energy. Figure 5 shows the averaged rms fluctuations of each potential energy difference between shear and equilibrium conditions. The averaged rms fluctuations represent the averaged difference of rms fluctuations of the potential energy for 0.5 ps intervals during 20-40 ps between equilibrium and shear conditions as noted above. Figure 5 shows that the fluctuations of the interfacial interaction for all molecules are small compared to the other energy fluctuations. This indicates that the energy needed for overcoming the local maximum of the interfacial interaction when the slider moves is small compared to that of the other energy terms. Consequently we conclude that the difference in interfacial interaction in each molecule makes scarcely any contribution to the frictional coefficient difference. The data show that the energy fluctuations of the Lennard-Jones (L-J) terms are the largest in perfluorocarboxylic and semifluorocarboxylic acids. The fluctuation of the intramolecular L-J term in C18F37COOH is 25.8 kJ/mol and that of the intermolecular L-J term is 8.8 kJ/mol. The values show that the fluctuations of L-J terms are dominated by the intramolecular interaction. It seems reasonable to conclude that the 1-4, L-J (1-4 van der Waals) interaction mainly contributes to the high frictional coefficient of C18F37COOH, as was found previously,17 since intramolecular interaction is dominated by 1-4, nonbonded interaction. Figure 5 shows that the magnitudes of the energy fluctuations of C18F37COOH and C12F25C6H12COOH are comparatively similar. On the other hand, the fluctuations of each energy decrease significantly between C12F25C6-
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H12COOH and C8F17C10H20COOH. Since the van der Waals radius of the hydrogen atom is smaller than that of the fluorine atom and it is easy for softer parts, i.e., hydrocarbons, to move due to the mixture of two kinds of molecular stiffness parts, fluorocarbons and hydrocarbons, it becomes easy for the hydrocarbons to move a lot as shown in Figure 3. Then the atomic fluctuations and the energy fluctuations of the hydrogen parts in semifluorocarboxylic acids are larger than those of perhydrocarboxylic acid. Thus we expect that for C12F25C6H12COOH, the effect of the decrease of the energy fluctuations due to replacement of fluorine atoms by hydrogen atoms is almost the same as the effect of increasing the energy fluctuation of the hydrogen parts. On the other hand, when comparing the semifluorocarboxylic acids, except C12F25C6H12COOH, since the hydrogen parts are long, the effect of replacing fluorine atoms by hydrogen atoms is larger than the effect of increasing the energy fluctuations of the hydrogen parts. Furthermore, Figure 5 shows that the differences between C8F17C10H2COOH, C5F11C13H26COOH, and C3F7C15H3COOH are small. This may be due to film deformation, which causes the high frictional coefficient, occurring mainly in the surface of the film, as the atomic fluctuations are large in the surface parts of the molecules (cf. Figure 3). Thus if the hydrocarbon parts in the semifluorocarboxylic acids are long enough, there is a tendency for the magnitude of each energy fluctuation in one molecule to resemble that of the others. The reason why the differences in each energy fluctuation for C5F11C13H26COOH and C3F7C15H30COOH are small, although the frictional coefficient of C3F7C15H3COOH is smaller than that of C5F11C13H26COOH, is as follows. Since the frictional mechanism for C3F7C15H3COOH and C5F11C13H26COOH is similar, the energy needed for the slider to move is not large enough to clarify the difference of each energy fluctuation in the two molecules. If we simulated these molecules by a heavier load, the energy needed for the slider to move would increase and the differences between the two molecules would become clear. 3.5. Effect of Ether Linkages on Frictional Coefficient. In the previous section, we concluded that the film deformation, which is considered to cause the high frictional coefficient, mainly occurred in the surface of the film. Consequently we expect that the frictional coefficient will decrease by decreasing the film surface deformation through introduction of ether linkages to lower the torsion energy barrier and to move flexible groups close to the film surface. We simulated frictional coefficients of C3F7OCF2OC12F24COOH and C13F27OCF2OC2F4COOH to allow a comparative study. The frictional coefficients of C3F7OCF2OC12F24COOH and C13F27OCF2OC2F4COOH are 0.25 and 0.28, respectively. Figure 6 shows that the ether parts of the atomic rms fluctuations of C3F7OCF2OC12F24COOH and C13F27OCF2OC2F4COOH are larger than those of the corresponding cabon parts in C18F37COOH. We cannot identify the reason for the increase in the atomic rms fluctuations; it may be caused by molecular deformation or by easier movement of surface atoms due to the greater space available by replacing fluorocarbons with the ether linkages. Consequently whether the introduction of the ether linkage close to the film surface has an effect on the surface film deformation decrease or if it only removes the corresponding cabon parts of the molecular deformation is also not clear. In either case, we know that the frictional coefficient decreases with the introduction of the ether linkages close to the film surface. 3.6. Relation between Frictional Coefficient and Chain Length. The frictional coefficients of C12H25COOH,
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Koike and Yoneya
Figure 6. Root mean square fluctuations of the carbon atom positions of each fluoroethercarboxylic acid. The values are averages of the rms fluctuations calculated at intervals of 0.5 ps for 20-40 ps. The atom number of the end atom of the carboxylic group is 18. The other end atom of the molecule is 1.
Figure 7. Root mean square fluctuations of the carbon atom positions of each hydrocarboxylic acid. The values are averages of the rms fluctuations calculated at intervals of 0.5 ps for 2040 ps. The atom number of the end atom of the carboxylic group is the largest one in the molecule. The other end atom of the molecule is 1.
C14H29COOH, C18H37COOH, and C20H41COOH are 0.12, 0.11, 0.12, and 0.12, respectively. Though there are some discrepancies, the frictional coefficients are almost the same without regard to the molecular length. In some experiments, it was found that the molecular length did not influence the frictional coefficient.13,14 As noted above, the frictional force is related to the energies needed for the film conformational change and for overcoming the local maximum barrier of the interfacial interaction. As regards hydrocarboxylic acid, the energy need for overcoming the local maximum barrier of the interfacial interaction is small compared to that of film conformational change as noted in section 3.3. Accordingly the energy needed for the deformation of the film is related to the largeness of the frictional force (frictional coefficient). Furthermore for hydrocarboxylic acid, probably the energy fluctuations correspond to atomic fluctuations. Figure 7 shows the atomic rms fluctuations. In order to decrease the influence of the plucking mechanism, we calculated these atomic rms fluctuations for 0.5 ps intervals and averaged them for 20-40 ps. From the figure we conclude the following. Since the atomic rms fluctuations decreased inverse proportion to the chain length, the energy needed for molecular deformation, when the slider is moving, is unchanged and independent of the chain length. Accordingly the frictional coefficient is independent of the chain length.
found that the frictional coefficients of the semifluorocarboxylic acids differed depending on the fluorination ratio of the hydrocarboxylic acid. In the case of much fluorination of the hydrocarboxylic acid, the frictional mechanism and frictional coefficients of semifluorocarboxylic acids did not differ from those of perfluorocarboxylic acid. On the other hand for little fluorination, the frictional mechanism and frictional coefficients were similar to those of hydrocarboxylic acid. We also found that the frictional coefficients decreased with introduction of ether linkages into perfluorocaboxylic acid. In particular the introduction of ether links had an effect of decreasing the frictional coefficient, when the ether links were close to the film surface. These findings indicated that there are possibilities for getting molecules which have low reactivity and good hydrophobic and low frictional properties by partial fluorination of hydrocarboxylic acids and by introduction of ether linkages into perfluorocarboxylic acids. Furthermore we found that the frictional coefficients were almost the same for carbon chain lengths of 12-20 carbons. This was interpreted as follows. Since the atomic fluctuations decreased in inverse proportion to the chain length, the energy needed for molecular deformation when the slider was moving was unchanged and independent of the chain length.
4. Conclusion We carried out molecular dynamics simulations of the hydrocarboxylic acid, semifluorocarboxylic acids, fluoroethercarboxylic acids, and perfluorocarboxylic acids. We
Acknowledgment. We are grateful for helpful discussions with T. Kato and M. Kameyama of Utsunomiya University and Y. Tomioka and Y. Ito of Hitachi Research Laboratory. LA9606557
