The liquid-vapour interface of the restricted primitive model (RPM) of ionic fluids

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Abstract
The liquid-vapour interface of the restricted primitive model (RPM) of ionic fluids is investigated within a square-gradient theory. We compute density profiles and interfacial tensions for different temperatures using Debye-Hückel (DH) theory and its recent extension for ion-pair formation and interactions between the dipolar ion pairs and free ions developed by Fisher and Levin. This Fisher-Levin (FL) theory is known to give an accurate description of the coexistence curve of the RPM. To account for the inhomogeneities in the interfacial region, the local free-energy density is expanded in terms of the density gradient. For small gradients, e.g. reasonably close to the critical point, such an expansion can be truncated after the square-gradient term. The coefficient of the latter is calculated from the direct correlation function using an approximate (quadratic) hypernetted-chain (AHNC) relation and, alternatively, from an extended van der Waals approach in conjunction with different approximations to the local density. The results from the AHNC relation and various local density approximations in the thermodynamic framework of DH theory and FL theory, respectively, are compared, and it is asserted that the AHNC relation in conjunction with FL theory predicts reliably the interfacial properties of the RPM even within this simple square-gradient theory. In contrast to the situation for simple fluids, the local density approximation must be chosen carefully for ionic fluids since properties such as the interfacial thickness and the surface tension may vary by a factor of three or four depending on the applied local density approximation.