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Amonton's law states that the sliding friction force increases linearly with the load. We show that this result is expected for stiff enough solids, even when the adhesional interaction between the solids is included in the analysis. As a function of the magnitude of the elastic modulus E, one can distinguish between three regions: (a) for E > E 2 , the area of real contact (and the friction force) depends linearly on the load, (b) for E 1 < E < E 2 , the area of real contact depends nonlinearly on the load but vanishes for zero load, and (c) for E < E 1 the area of real contact depends nonlinearly on the load and is non-vanishing at zero load. In this last case a finite pull-off force is necessary in order to separate the solids. Based on molecular dynamics calculations, we also discuss the pressure dependence of the frictional shear stress for polymers. We show that the frictional shear stress is independent of the normal pressure p 0 as long as p 0 is much smaller than the adhesional pressure p ad , which depends on the atomic corrugation of the solid surfaces in the sliding interface. Finally, we discuss the origin of why the contact area between a soft elastic solid (e.g. rubber) and a flat substrate decreases from the JKR (adhesive contact) limit at zero or small sliding velocities, to the Hertz (non-adhesive) limit at high sliding velocities.

The properties of alkane lubricants confined between two approaching solids are investigated by a model that accounts for the curvature and the elastic properties of the solid surfaces. We consider linear alkane molecules of different chain lengths, C 3 H 8 , C 4 H 10 , C 8 H 18 , C 9 H 20 , C 10 H 22 , C 12 H 26 , and C 14 H 30 confined between smooth gold surfaces. In most cases we observe well defined molecular layers develop in the lubricant film when the width of the film is of the order of a few atomic diameters. An external squeezing-pressure induces discontinuous, thermally activated changes in the number n of lubricant layers. We find that with increasing alkane chain length, the transition from n to nϪ1 layers occurs at higher pressure, as expected based on the increasing wettability ͑or spreading pressure͒ with increasing chain length. Thus, the longer alkanes are better boundary lubricants than the shorter ones, and this should result in less wear. We obtain good correlation between our theoretical results and wear experiments.

We present molecular dynamics friction calculations for confined hydrocarbon solids with molecular lengths from 20 to 1400 carbon atoms. Two cases are considered: a) polymer sliding against a hard substrate, and b) polymer sliding on polymer. In the first setup the shear stresses are relatively independent of molecular length. For polymer sliding on polymer the friction is significantly larger, and dependent on the molecular chain length. In both cases, the shear stresses are proportional to the squeezing pressure and finite at zero load, indicating an adhesional contribution to the friction force. The friction decreases when the sliding distance is of the order of the molecular length indicating a strong influence of molecular alignment during run-in. The results of our calculations show good correlation with experimental work.

The properties of butane (C4H10) lubricants confined between two approaching solids are investigated by a model that accounts for the curvature and elastic properties of the solid surfaces. We consider the linear n-butane and the branched isobutane. For the linear molecule, well defined molecular layers develop in the lubricant film when the width is of the order of a few atomic diameters. The branched isobutane forms more disordered structures which permit it to stay liquidlike at smaller surface separations. During squeezing the solvation forces show oscillations corresponding to the width of a molecule. At low speeds (<0.1 ms) the last layers of isobutane are squeezed out before those of n-butane. Since the (interfacial) squeezing velocity in most practical applications is very low when the lubricant layer has molecular thickness, one expects n-butane to be a better boundary lubricant than isobutane. With n-butane possessing a slightly lower viscosity at high pressures, our result refutes the view that squeeze-out should be harder for higher viscosities; on the other hand our results are consistent with wear experiments in which n-butane were shown to protect steel surfaces better than isobutane.

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We present molecular dynamics friction calculations for confined hydrocarbon "polymer" solids with molecular lengths from 20 to 1400 carbon atoms. Two cases are considered: (a) polymer sliding against a hard substrate and (b) polymer sliding on polymer. We discuss the velocity dependence of the frictional shear stress for both cases. In our simulations, the polymer films are very thin (approximately 3 nm), and the solid walls are connected to a thermostat at a short distance from the polymer slab. Under these circumstances we find that frictional heating effects are not important, and the effective temperature in the polymer film is always close to the thermostat temperature. In the first setup (a), for hydrocarbons with molecular lengths from 60 to 1400 carbon atoms, the shear stresses are nearly independent of molecular length, but for the shortest hydrocarbon C(20)H(42) the frictional shear stress is lower. In all cases the frictional shear stress increases monotonically with the sliding velocity. For polymer sliding on polymer (case b) the friction is much larger, and the velocity dependence is more complex. For hydrocarbons with molecular lengths from 60 to 140 C atoms, the number of monolayers of lubricant increases (abruptly) with increasing sliding velocity (from 6 to 7 layers), leading to a decrease of the friction. Before and after the layering transition, the frictional shear stresses are nearly proportional to the logarithm of sliding velocity. For the longest hydrocarbon (1400 C atoms) the friction shows no dependence on the sliding velocity, and for the shortest hydrocarbon (20 C atoms) the frictional shear stress increases nearly linearly with the sliding velocity.

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