Contact angle determination as a function of solid–liquid molecular characteristics <i>via</i> the Kirkwood–Buff route

The goal of this work is to calculate contact angles as a function of the molecular characteristics of the solid and the liquid. We use Kirkwood-Buff's mechanical route and decompose the normal and transverse components of the pressure tensor into solid and liquid regions. This decomposition leads to the emergence of a new force - the repulsion induced by the liquid displaced by the solid -. We found a neutral state where liquid/wall and displaced-liquid/liquid attractions are balanced. By expanding around this state, we could calculate the density profile within the hard-core van der Waals model at low isothermal compressibility, and establish a relation between the equilibrium contact angle and the microscopic properties of the liquid and solid. This work leads to reformulate Young's equation in a novel manner and sheds new light on the physics of wetting. The density profiles and contact angles obtained theoretically are supported by molecular dynamics simulations using the Lennard-Jones potential.