Surface tension of molecular liquids: Lattice gas approach

TL;DR

This paper develops a lattice gas approach based on the global isomorphism with the Ising model to derive an expression for the surface tension of Lennard-Jones fluids across temperatures, matching literature results without fitting parameters.

Contribution

It introduces a novel theoretical method linking fluid surface tension to the Ising model, applicable in 2D and 3D, with no fitting parameters needed.

Findings

Derived an expression for surface tension valid in 2D and 3D.

Theoretical estimates agree with existing literature.

Demonstrated methodology using exact 2D Ising solution.

Abstract

The approach of global isomorphism between the fluid and the Ising model is applied to obtain an expression for the surface tension of the Lennard-Jones fluid on the basis of the information about the Ising model. This is done in a broad interval of temperatures along the phase coexistence, and is valid both in 2D and 3D. The relation between the critical amplitudes of the surface tension of the fluid and the Ising model is derived in the vicinity of the critical point. The obtained theoretical estimates agree well with the literature results for the surface tension. The methodology is demonstrated for the 2D LJ fluid on the basis of the exact solution of the 2D Ising model and is tested for the 3D LJ fluid. As a result, an expression for the surface tension without any fitting parameter is derived.