Depletion-Driven Solid–Solid Coexistence in Colloid–Polymer Mixtures

Abstract

Hard spheres mixed with penetrable hard spheres display an isostructural solid–solid transition. This phase transition is fully driven by the entropy gain of the depletants without invoking explicit pair potentials between the colloidal particles. The solid–solid phase coexistence exists for size ratios \(q\equiv \delta /R \lesssim 0.09\), with \(\delta \) the penetrable hard sphere radius and R the hard sphere radius. This coexistence is revealed using a modified free volume theory, where the free volume fraction for depletants in the solid phase is calculated on geometrical grounds. Due to a better account of the small depletant partitioning, the fluid branch of the fluid–solid coexistence also decreases with decreasing q. Colloid–polymer mixtures are an excellent candidate for the experimental realization of this intricate solid–solid transition, first predicted by Bolhuis and Frenkel for hard spheres with short range pair attractions [PRL 72, 2211–2214 (1994)].