On the thermodynamic consistency of non-random hydrogen bonding lattice-fluid model for multicomponent mixtures

Compressible lattice-fluid Equation of State (EoS) models have been widely used to interpret phase equilibria and related properties of pure fluids and their mixtures, including polymer solutions. One of the first models of this family has been proposed by Sanchez and Lacombe (SL), providing useful expressions for EoS and chemical potentials for both pure components and mixtures. The assessment of the thermodynamic consistency of the expressions provided by these models for the chemical potential of each component in a mixture is a relevant issue, to which has seldom been devoted the attention it deserves. In fact, it has been demonstrated in the literature that the equations provided by the SL theory for the equilibrium chemical potential of a component in a mixture exhibits a thermodynamic inconsistency emerging from the adopted mixing rules for the close packed volume. Consequently, these expressions do not converge to the proper form in the limit of ideal gas mixtures. Later, the Non-Random Hydrogen Bonding (NRHB) lattice-fluid model was introduced to overcome some limitations of the SL model, by accounting for possible presence of strong specific intermolecular interactions, such as hydrogen bonding, as well as for non-random distribution of intermolecular contacts. In the present work, using a thermodynamic framework endowed with internal state variables, it is shown that the expressions of the chemical potential provided by the NRHB model for a multicomponent mixture at equilibrium, converge consistently to the correct form in the limit of ideal gas mixtures, thus overcoming the inconsistency implicit in the most common corresponding formulations of the SL model. We demonstrate that this feature is essentially related to the assumption of a constant value of the segmental volume, v*, that takes the same ‘universal’ value (9.75/NA cm3/molecular segment, where NA is the Avogadro number) for all pure fluids as well as for their mixtures. In addition, we have re-examined also the inconsistency issue of the SL model proving that this model recovers the thermodynamic consistency if it is assumed again a constant value of v* or if a particular type of mixing rule is assumed for v*.