Adhesive contact based on the Lennard-Jones potential: a correction to the value of the equilibrium distance as used in the potential.

A Lennard-Jones type surface law is commonly used in adhesive contact modeling; however, one of its parameters, namely the equilibrium distance z0, is not well defined. In this paper, a self-consistent method is used to derive the Lennard-Jones surface law from the interatomic Lennard-Jones potential. The parameters of the surface law are directly related to the material lattice parameter and surface energy, and the equilibrium distance z0 values are obtained for various materials. The effect of using the z0 proposed in the present work is demonstrated via the study of adhesive contact behavior for a single sphere and a flat surface, as well as the contact between planar rough surfaces. For pull-off force prediction of the contact between a single sphere and a flat surface, the error of using the z0 suggested in previous studies could be as large as 10% at intermediate ranges of a dimensionless adhesion parameter. For the contact between planar rough surfaces, the error of using the previously proposed z0 is larger for smoother cases, and the prediction of pull-off force could be different by as much as a factor of 5.