Prandtl–Tomlinson-Type Models for Coupled Molecular Sliding Friction: Chain-Length Dependence of Friction of Self-assembled Monolayers

Abstract

Previous work (Manzi et al. in Tribol Lett 69:147, 2021) proposed a tip–molecular interaction for calculating the friction of organic overlayers that consisted of a parabolic potential that extended to some cut-of distance when the energy reached a value of E0 sld, which represents an activation barrier for the detachment of the tip from the molecular terminus. A proposed advantage of such a potential was that it could be coupled to other degrees of freedom of the system. A method for accomplishing this is described here for the interaction between a tip and a compliant molecular chain to model the velocity, temperature, and chain-length dependences of the friction force. Analytical equations are derived for constant force sliding, such as in a ball-on-fat tribometer, and for compliant sliding, such as in an atomic force microscopy (AFM) experiment. The analytic models provided good fts to the chain-length dependence of the friction of carboxylate self-assembled monolayers (SAMs) on copper measured in an ultrahigh vacuum tribometer as part of this work and for alkyl thiolate SAMs on gold measured by an AFM taken from the literature. The results indicate that the commonly observed decrease in friction with increasing chain length has a component that is due to geometrical efects, as well as the possible participation of interchain van der Waals’ interactions that are commonly invoked as being responsible for the friction reduction.