Phase separation in solutions of large spherical particles
The effect of large size ratios of solute to solvent on the critical properties and phase behaviour of binary mixtures of spherical particles is investigated using an "augmented van der Waals" equation of state. The equation used is essentially a van der Waals equation with an improved hard sphere repulsive term. Molecular dynamics and constant-pressure Monte Carlo simulations of binary mixtures of hard spheres with different diameter ratios and mole fractions are undertaken to check the adequacy of the hard sphere equation. Good agreement is found, even for systems with large differences in size. Furthermore, many of the hard sphere mixtures exhibited a transition from a fluid to a solid phase at high densities. Phase boundaries are calculated for model mixtures comprising spheres of different sizes between which there are long-ranged attractive forces. Particular attention is paid to the case in which the ratio of sizes is infinite. The systems show a wide variety of behaviour that includes liquid-liquid and gas-gas immiscibility, and the formation of negative azeotropes. Calculations investigating the effect of different attractive interactions between the small and large spheres show that as the magnitude of this interaction is increased, liquid-liquid immiscibility becomes the dominant feature of the phase diagram at moderate temperatures. The extent of liquid-liquid coexistence is greatest at large size differences. These model systems are shown to reproduce some of the behaviour of aqueous solutions of surfactants if it is assumed that the large spheres are models of the micelles and the small spheres models of the solvent molecules. The properties of binary lattice mixtures of bifunctional molecules whose ends are chosen to mimic surfactant and solvent molecules are also briefly investigated, to determine the effect of the asymmetric surfactant molecule on the phase separation. Closed-loops emerge in the phase diagrams as the surfactant character of one of the species is increased.