Scale dependence in friction: the transition from intimate contact to monolayer lubricated contact
Over the years, nonwear friction with single asperity contact has been examined through experiments using the Surface Force Apparatus (SFA) and the Atomic Force Microscope (AFM). The contact radii in SFA and AFM friction experiments ranged in the order of tens of [mu]m (>10⁵ m) and several nm (< 10⁻⁸ m), respectively. In spite of the fact that the contact radii in these experiments differ by several orders of magnitude, the data from both experiments obey Bowden and Tabor's friction law F = [tau]A , where F is the friction force, [tau] is the frictional shear strength and A is the real contact area. However, there is a crucial difference between the results obtained with the two instruments. The shear strength from the SFA experiments in dry environment is in the tens of MPa, while the shear strength from the AFM measurement is several hundreds of MPa. In the intervening mesoscales, with contact radii ranging from 10⁻⁸ < a < 10⁻⁵, the frictional shear strength must be dependent on contact area in order to link these two extremes. Some models based on dislocation motions have recently been developed to bridge the gap (Hurtado and Kim, 1999a; b). Hitherto, no systematic mesoscale friction experiments to bridge the shear strengths obtained from AFM and SFA have been provided. In addition, this is precisely the range in which MEMS and potential NEMS devices are expected to operate. Therefore, apart from the fundamental challenges involved in resolving the scale dependence of friction, there is a strong technological motivation for studying friction at this scale. In the present work, this transition in shear strength is bridged using a newlydeveloped Mesoscale Friction Tester (MFT) over a wide range of contact radii and relative humidity levels. Since a nonwear and single asperity contact is of interest, novel procedures to fabricate tungsten probes with subnanometer (<0.3nm) surface roughness are initiated. In order to choose an appropriate contact mechanics theory in an ambient environment to obtain the true contact area, a modified Tabor parameter for JKR-DMT transition for capillary force dominant contact is employed. Results from friction experiments show that the transition in shear strength occurred over contact radii of only 20~30nm in both ambient and dry environments. It is hypothesized that shear strengths in the tens of MPa resulted from contact separated by a monolayer of interfacial molecules and shear strengths in hundreds of MPa resulted from intimate contact (no interfacial molecules inside the contact zone). It was the interfacial condition inside the contact zone that governed the transition. Furthermore, there is no continuous spectrum of shear strength, but a "quantized" behavior. A continuum analysis based on Lifshitz theory, which related the shear strength to the estimated strength of van der Waals bonds is proposed to explain the quantized shear strengths obtained from current experiments and both previous AFM and SFA friction experiments.