Virial series for inhomogeneous fluids applied to the Lennard-Jones wall-fluid surface tension at planar and curved walls

TL;DR

This paper develops a statistical mechanics scheme using virial series for inhomogeneous fluids, analytically evaluating surface tension for Lennard-Jones systems near planar and curved walls, revealing a specific radius-dependent behavior.

Contribution

It introduces a second-order virial expansion approach for inhomogeneous fluids, providing analytical expressions for surface tension in Lennard-Jones systems with curved and planar boundaries.

Findings

Surface tension exhibits a ln(R^{-1})/R^2 dependence for spherical and cylindrical walls.

Analytical second cluster integrals were obtained for Lennard-Jones and 2k-k potentials.

Exact expressions for curvature effects on surface tension were derived.

Abstract

We formulate a straightforward scheme of statistical mechanics for inhomogeneous systems that includes the virial series in powers of the activity for the grand free energy and density distributions. There, cluster integrals formulated for inhomogeneous systems play a main role. We center on second order terms that were analyzed in the case of hard-wall confinement, focusing in planar, spherical and cylindrical walls. Further analysis was devoted to the Lennard-Jones system and its generalization the 2k-k potential. For this interaction potentials the second cluster integral was evaluated analytically. We obtained the fluid-substrate surface tension at second order for the planar, spherical and cylindrical confinement. Spherical and cylindrical cases were analyzed using a series expansion in the radius including higher order terms. We detected a $\ln R^{-1}/R^{2}$ dependence of the surface tension for the standard Lennard-Jones system confined by spherical and cylindrical walls, no matter if particles are inside or outside of the hard-walls. The analysis was extended to bending and Gaussian curvatures, where exact expressions were also obtained.