Unified equation of state based on the lattice fluid theory for phase equilibria of complex mixtures part I. Molecular thermodynamic framework

Consistent calculation of fugacities of fluid mixtures remains as one of the most important subjects in contemporary molecular thermodynamics. In practice, equations of state (EOSs) and g^E-models have been used. However, most EOSs are erroneous for condensed phases at high densities and g^E-models are inapplicable for pressuresensitive systems. Recently to remedy the shortcomings in both approaches, there has been a surge of new g^E-EOS mixing rules. By equating any set of EOS and g^E-models, the limitations in both approaches could be resolved significantly. However, the self-consistency in the underlying concept of those mixing rules remains controversial. During the last several years, the present authors proposed a new lattice-fluid EOS and its simplification relevant to phase equilibrium calculations. Without employing any g^E-EOS mixing rule and with only two parameters for a pure component and one adjustable interaction energy parameter for a binary mixture, results obtained to date demonstrated that the EOSs are quantitatively applicable to a great variety of phase equilibrium properties of mixtures, especially, for complex and/or macromolecular systems. In the present article we summarize the EOSs and extended the applications to liquid-liquid Equilibria. In part I, we discussed briefly the molecular thermodynamic aspects of general derivation of the EOS and a brief discussion of applying the EOSs to pure fluids while the illustrative application to various real mixture systems is discussed in part II.