Analytical Models for the Chain-Length- and Velocity-Dependent Tribochemical Reaction Rates of Molecular Monolayers on Copper

Abstract

Previous work proposed a model potential for the interaction between a contact and the outermost surface of an organic overlayer that could be integrated into a Prandtl–Tomlinson model to analyze the velocity and temperature dependences of the friction force. The potential consisted of a parabola that extended to some cut-off distance when the energy reached a value of E^0_sld , which represents an activation barrier for the detachment of the tip from the molecular terminus. In addition to its simplicity, an advantage was that the potential also lent itself to being coupled to other degrees of freedom of the system. This feature was implemented by analyzing the friction of an interacting system between the tip-surface contact and a compliant molecular chain to yield velocity, temperature and chain-length dependences of the friction force that agreed well with experimental measurements of self-assembled monolayers (SAMs). This approach is extended here to allow the potential between the SAM and the surface to result in a chemical reaction by cleaving the bond between the hydrocarbon chain and the anchoring group, thus further emphasizing the versatility of this approach. The theory predicts that the tribochemical reaction rate should decrease with increasing chain length, in agreement with experimental results. Similar trends are seen for alkyl species that are used to cap lubricant additives such as in zinc dialkyl dithiophosphate (ZDDP). Measurements of the velocity dependence of the reaction of methyl thiolate species on copper showed little variation in accord with a lack of velocity dependence of the friction force.