On the calculation of nearest neighbors in activity coefficient models

Guggenheim proposed a theoretical expression for the combinatorial entropy of mixing of unequal sized and linear and branched molecules to improve the Flory-Huggins model. Later the combinatorial activity coefficient equation, which was derived from Guggenheim's model, was applied in the UNIQUAC, UNIFAC, and COSMOSAC models. Here we derive from Guggenheim's entropy theory a new function for the number of nearest neighbors of a compound in a multicomponent mixture for which the knowledge of the coordination number and a reference area are not needed. This new relation requires only the mole, volume and surface fraction of the compounds in the mixture. The benefit of the new relation is that both the combinatorial and the residual term in the aforementioned models can be made lattice-independent. We demonstrate that the proposed relation simplifies the Staverman-Guggenheim combinatorial model and can be applied with success to the UNIQUAC and COSMOSPACE model in the description of vapor-liquid phase equilibria and excess enthalpy. We also show that the new expression for the number of nearest neighbors should replace the relative surface area and the number of surface patches in the residual part of the UNIQUAC and the COSMOSPACE model, respectively. As a result a more rigorous version of the UNIQUAC and the COSMOSPACE model is obtained. This could serve as a better basis for predictive models like UNIFAC, COSMO-RS and COSMOSAC.