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

Abstract

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.