Free energy landscapes and volumes of coexisting phases for a colloidal dispersion

Abstract

Treating the repulsive part of a pairwise potential by the hard-sphere form and its attractive part by the effective depletion potential form, we calculate using this model potential the colloidal domains of phase separation. Differing from the usual recipe of applying the thermodynamic conditions of equal pressure and equal chemical potential where the branches of coexisting phases are the ultimate target, we employ the free energy density minimization approach [G. F. Wang and S. K. Lai, Phys. Rev. E 70, 051402 (2004)] to crosshatch the domains of equilibrium phases, which consist of the gas, liquid, and solid homogeneous phases as well as the coexistence of these phases. This numerical procedure is attractive since it yields naturally the colloidal volume of space occupied by each of the coexisting phases. In this work, we first examine the change in structures of the fluid and solid free energy density landscapes with the effective polymer concentration. We show by explicit illustration the link between the free energy density landscapes and the development of both the metastable and stable coexisting phases. Then, attention is paid to the spatial volumes predicted at the triple point. It is found here that the volumes of spaces of the three coexisting phases at the triple point vary one dimensionally, whereas for the two coexisting phases, they are uniquely determined.

Phase diagram of colloid-rod system

“…We should perhaps digress at this point to remark that there is an alternative to the free energy density minimization. It consists in plotting the free energy density landscapes 49,50 for the fluid ͑where the low density fluid is gas and the higher density fluid is liquid͒ and solid phases as functions of C and r and construct all sets of common tangents for two phases. The one with the lowest energy tallies with the minimized f m and it corresponds to stable equilibrium phases in contrast to the higher energy common tangent for two phases describing the metastable equilibrium.…”