Morphological thermodynamics for hard bodies from a controlled expansion

TL;DR

This paper derives the morphometric approach for hard bodies as an exact resummation of virial series terms, offering insights into its accuracy and potential extensions to mixtures of convex shapes.

Contribution

It provides a fundamental derivation of the morphometric approach from virial series, clarifying its accuracy and guiding inclusion of higher-order terms.

Findings

Derived the morphometric approach as an exact virial resummation.

Provided insights into the inclusion of higher-order terms.

Extended the theory to mixtures of convex bodies.

Abstract

The morphometric approach is a powerful ansatz for decomposing the chemical potential for a complex solute into purely geometrical terms. This method has proven accuracy in hard spheres, presenting an alternative to comparatively expensive (classical) density functional theory approaches. Despite this, fundamental questions remain over why it is accurate and how one might include higher-order terms to improve accuracy. We derive the morphometric approach as the exact resummation of terms in the virial series, providing further justification of the approach. The resulting theory is less accurate than previous morphometric theories, but provides fundamental insights into the inclusion of higher-order terms and to extensions to mixtures of convex bodies of arbitrary shape.