Two-stage kinetic phase transition in a platelet–colloid mixture

Abstract

The semi-grand canonical ensemble theory augmented by the free volume approximation and the scaled particle theory was applied to construct the Helmholtz free energy density function f of a mixture of uncharged colloidal hard spheres and a depletion agent of colloidal hard platelets. The episode of the phase-separation phenomenon is then described by a composite fm which is written as a sum of the coexisting free energy densities fi (i = gas, liquid or solid) and the latter is weighted by Vi/V, Vi and V being the ith spatial volume and total volume, respectively. In this work, we applied the free energy density minimization method to fm [16] and calculated the domains of phases in coexistence instead of delineating coexisting phase-diagram boundaries obtained by computing the pressure and chemical potential in the conventional thermodynamic equilibrium condition. The calculated coexistence domains thus have the same patterns as many colloidal laboratory experiments. We obtained in our calculated platelet–colloid phase diagram the well-known triangular area of triple-phases coexistence. This area, however, has to be realized as some kind of a kinetic process showing coalescence of two sets of coexisting biphases whenever any set of initial input number concentrations of platelets and colloids that falls inside this triangular area. In this kinetic phase-transition process, we find the triple phases of the platelet–colloid system always residing at the same three vertices of the triangle, but their spatial volumes are generally different depending on the initial number concentrations of platelets and colloids. It would be interesting and, a challenge as well, if laboratory experiments at the same quantitative level as that previously reported for the polymer–colloidal mixtures [7] can be carried out to confirm our theoretical findings.