Solubility Limits in Lennard-Jones Mixtures: Effects of Disparate Molecule Geometries

In order to better understand general effects of the size and energy disparities between macromolecules and solvent molecules in solution, especially for macromolecular constructs self-assembled from smaller molecules, we use the first- and second-order exact bridge diagram extensions of the HNC integral equation theory to investigate single-component, binary, ternary, and quaternary mixtures of Lennard-Jones fluids. For pure fluids, we find that the HNCH3 bridge function integral equation (i.e., exact to third order in density) is necessary to quantitatively predict the pure gas and pure liquid sides of the coexistence region of the phase diagram of the Lennard-Jones fluid. For the mixtures, we find that the HNCH2 bridge function integral equation is sufficient to qualitatively predict solubility in the binary, ternary, and quaternary mixtures, up to the nominal solubility limit. The results, as limiting cases, should be useful to several problems, including accurate phase diagram predictions for complex mixtures, design of self-assembling nanostructures via solvent controls, and the solvent contributions to the conformational behavior of macromolecules in complex fluids.