The generalized van der Waals partition function as a basis for excess free energy models

The important insight of J. D. van der Waals in developing the equation of state that bears his name was the analysis of the separate contributions of the attractive and hard-core repulsive interactions to the equation of state. This insight led him to important advances in understanding fluids and their phase transitions. This same separation of attractive and hard core interactions have been used in statistical mechanics in the form of perturbation theory, and also as here in a form referred to as the Generalized van der Waals partition function. This partition function has been used in the literature to understand the assumptions that underlie equations of state, and to develop equations with a better theoretical basis. Here, we demonstrate how the generalized van der Waals partition function can be used to elucidate the assumptions inherent in all of the commonly used correlative activity coefficient models.