Does Young's equation hold on the nanoscale? A Monte Carlo test for the binary Lennard-Jones fluid

When a phase-separated binary (A+B) mixture is exposed to a wall, that preferentially attracts one of the components, interfaces between A-rich and B-rich domains in general meet the wall making a contact angle θ. Young's equation describes this angle in terms of a balance between the A-B interfacial tension γ_AB and the surface tensions γ_wA, γ_wB between, respectively, the A- and B-rich phases and the wall, γ_ABcos θ=γ_wA−γ_wB. By Monte Carlo simulations of bridges, formed by one of the components in a binary Lennard-Jones liquid, connecting the two walls of a nanoscopic slit pore, θ is estimated from the inclination of the interfaces, as a function of the wall-fluid interaction strength. The information on the surface tension difference γ_wA−γ_wB are obtained independently from a new thermodynamic integration method, while γ_AB is found from the finite-size scaling analysis of the concentration distribution function. We show that Young's equation describes the contact angles of the actual nanoscale interfaces for this model rather accurately and the location of the (first-order) wetting transition is estimated.