Liquid-vapour equilibrium in the restricted primitive model for ionic liquids

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Abstract
We study the thermodynamic equilibrium between liquid and vapour for the restricted primitive model (charged hard spheres of equal diameters) of a two component ionic liquid. We point out that physical clustering of ions will have a crucial effect on this equilibrium. The calculations presented are based on the representation of the vapour as a mixture of clusters of different types, the interactions between clusters being neglected. The relative proportions of the different types are governed by the law of mass action. We show that neglect of interactions yields a lower bound to the true vapour pressure. The internal free energies of the clusters in the vapour are obtained from a combination of analytic and Monte Carlo calculations and the thermodynamic properties of the liquid phase are derived from Larsen's published Monte Carlo results. We present numerical results for the densities of different cluster types in the vapour phase, for the overall liquid and vapour densities and for the vapour pressure. A comparison with the predictions of the mean spherical approximation and of Larsen's empirical equation show that these yield vapour pressures which are far below our lower bound and are therefore erroneous. We point out that Larsen's equation implies a weak subsidiary critical point on the liquid branch of the coexistence curve, an effect which we suggest is spurious. Finally, we discuss the relation between our work and that of Stell, Wu and Larsen.