Lattice-Fluid Models derived from Density Functional Theory

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.