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

TL;DR

This study uses Monte Carlo simulations to test if Young's equation accurately predicts contact angles at the nanoscale in a binary Lennard-Jones fluid, revealing good agreement and estimating the wetting transition point.

Contribution

The paper introduces a new thermodynamic integration method to independently determine surface tensions and tests Young's equation at the nanoscale using Monte Carlo simulations.

Findings

Young's equation holds accurately at the nanoscale for the model.

Surface tensions are measured independently via thermodynamic integration.

The wetting transition location is estimated from the simulations.

Abstract

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 $\theta$. Young's equation describes this angle in terms of a balance between the $A-B$ interfacial tension $\gamma_{AB}$ and the surface tensions $\gamma_{wA}$, $\gamma_{wB}$ between, respectively, the $A$- and $B$-rich phases and the wall, $\gamma _{AB} \cos \theta =\gamma_{wA}-\gamma_{wB}$. 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, $\theta$ is estimated from the inclination of the interfaces, as a function of the wall-fluid interaction strength. The information on the surface tensions $\gamma_{wA}$, $\gamma_{wB}$ are obtained independently from a new thermodynamic integration method, while $\gamma_{AB}$ 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 location of the (first order) wetting transition is estimated.