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

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.

6 pages, 6 figures

References in corpus (4)

• Conceptual aspects of line tensions
• Curvature Dependence of Surface Free Energy of Liquid Drops and Bubbles: A Simulation Study
• Static and Dynamic Critical Behavior of a Symmetrical Binary Fluid: A Computer Simulation
• Critical Dynamics in a Binary Fluid: Simulations and Finite-size Scaling

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• Simulation of fluid-solid coexistence in finite volumes: A method to study the properties of wall-attached crystalline nuclei
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