Curvature Dependence of Surface Free Energy of Liquid Drops and Bubbles: A Simulation Study

TL;DR

This simulation study investigates how the surface free energy of liquid droplets and bubbles depends on curvature, revealing differences in Tolman correction signs and confirming the absence of Tolman length in symmetric binary mixtures.

Contribution

The paper extends previous analysis to quantify curvature dependence of surface free energy for droplets and bubbles, and compares simulation results with density functional theory.

Findings

The Tolman correction sign differs for droplets and bubbles.

Surface free energy deviates from planar value by ~1/R^2.

Symmetric binary mixtures show no Tolman length.

Abstract

We study the excess free energy due to phase coexistence of fluids by Monte Carlo simulations using successive umbrella sampling in finite LxLxL boxes with periodic boundary conditions. Both the vapor-liquid phase coexistence of a simple Lennard-Jones fluid and the coexistence between A-rich and B-rich phases of a symmetric binary (AB) Lennard-Jones mixture are studied, varying the density rho in the simple fluid or the relative concentration x_A of A in the binary mixture, respectively. The character of phase coexistence changes from a spherical droplet (or bubble) of the minority phase (near the coexistence curve) to a cylindrical droplet (or bubble) and finally (in the center of the miscibility gap) to a slab-like configuration of two parallel flat interfaces. Extending the analysis of M. Schrader, P. Virnau, and K. Binder [Phys. Rev. E 79, 061104 (2009)], we extract the surface free energy gamma (R) of both spherical and cylindrical droplets and bubbles in the vapor-liquid case, and present evidence that for R -> Infinity the leading order (Tolman) correction for droplets has sign opposite to the case of bubbles, consistent with the Tolman length being independent on the sign of curvature. For the symmetric binary mixture the expected non-existence of the Tolman length is confirmed. In all cases {and for a range of radii} R relevant for nucleation theory, gamma(R) deviates strongly from gamma (Infinity) which can be accounted for by a term of order gamma(Infinity)/gamma(R)-1 ~ 1/R^2. Our results for the simple Lennard-Jones fluid are also compared to results from density functional theory and we find qualitative agreement in the behavior of gamma(R) as well as in the sign and magnitude of the Tolman length.