Integral Equation Study of Microstructure and Solvation in Model Attractive and Repulsive Supercritical Mixtures

The Ornstein-Zernike equation with Percus-Yevick closure was used to investigate the local environment around solute molecules in dilute supercritical mixtures and its relationship to solubility. Two binary Lennard-Jones mixtures were studied: one, attractive; the other, repulsive. Both systems were studied at high solute dilution, at supercritical temperature, and over a broad range of reduced densities (0.33 <ρ/ρ_c < 1.6 for the attractive system; 0.33 < ρ/ρ_c 2.3 for the repulsive one). The attractive system exhibited significant short-ranged solvent enrichment around the solute. The difference between the average solvent density within the first, second, and third solvation shells and the bulk solvent density was found to be more pronounced over the approximate range of reduced densities 0.5 < ρ/ρ_c < 0.8. In contrast, the repulsive system exhibited local solvent depletion, but this effect was particularly pronounced at near-critical density. A simple thermodynamic analysis shows that in dilute attractive supercritical systems the solute's chemical potential is necessarily a weak function of bulk density at constant temperature. This was indeed found to be the case. In contrast, the solute's fugacity coefficient (whose reciprocal is a direct measure of solubility enhancement for attractive systems) was found to be a very sensitive function of density. The solute's fugacity coefficient was calculated as a function of a variable distance cutoff, beyond which the mixture was assumed to be uniform. The value of the cutoff beyond which no further change in the fugacity coefficient resulted is thus an unambiguous measure of the size of the local region around solute molecules that is important for solubility. Over the range of densities studied here, this quantity ranged from 3 to 5 solvent diameters for the attractive mixture.