Entropy-driven phase transition in binary mixtures

Based on the principle of entropy maximum, a transparent method to study the phase separation is proposed. The excluded volume effects of binary mixtures of hard spheres with two different diameters are analyzed and the role of entropy is emphasized. As a result of the entropy variation caused by the packing of large spheres, there is a critical volume fraction to denote the phase boundary. It is shown that the variation of free volume fraction is influenced by the ratio α=d_L/d_S of large to small sphere diameters and the ratio x=η_L/(η_L+η_S) of large-sphere volume fraction to the total volume fraction of large- and small-spheres. We introduce a modification factor β to describe the overlap degree of two large spheres excluded volumes when they pack together. The critical volume fractions for large-sphere packing with different values of α and x are calculated, and the corresponding phase boundaries are determined. Our results are in quite good agreement with previous experimental measurements.