Lattice-Fluid Models derived from Density Functional Theory

TL;DR

This paper rederives key lattice-fluid models from a continuum functional, clarifies their limitations, and proposes a more consistent theoretical foundation based on molecular density functional theory.

Contribution

It provides a unified derivation of UNIQUAC, UNIFAC, and COSMO-RS from a density functional perspective, highlighting the importance of particle geometry and Coulomb interactions.

Findings

Wilson ansatz is not physically valid for grand potential minimization

Larsen-Rasmussen equation offers a consistent foundation for COSMO-RS

Analysis of approximation methods within a molecular density functional framework

Abstract

In the current article, we rederive the lattice-fluid excess models UNIQUAC, UNIFAC, and COSMO-RS from a continuum functional. The calculation explains the missing dependence on the particle geometry and how to include the Coulomb interaction, problems that are common to all three models. It is then shown that the Wilson ansatz, used in UNIQUAC and UNIFAC to minimize the grand potential, is not a physically valid solution of the Euler-Lagrange equation. A consistent approach is the Larsen-Rasmussen equation, which forms the foundation of COSMO-RS. We then analyze the various approximation methods and interpret them in the framework of a molecular density functional.