Effect of Polydispersity on the Phase Diagram of Colloid Systems

Abstract

A theoretical model is proposed that describes the experimentally observed phase diagram of colloidal dispersions of disk-shaped polydisperse particles. In the framework of the phenomenological theory of phase transitions, it is shown that if disk-shaped particles have polydispersity comparable in thickness and disk diameter, then the following sequence of phase transitions should be expected with increasing volume fraction of ϕ particles: an isotropic liquid (I); a nematic liquid crystal (N), in which the director n sets the preferred orientation of the disk normal; and the discotic (columnar) phase (C), in which the disklike molecules aggregate into liquid columns, and the latter form a two-dimensional hexagonal crystal consisting of liquid columns. However, when the particles forming the colloidal dispersion do not have any polydispersity in thickness (but the polydispersity in the particle diameter is preserved), another sequence of phase transitions takes place, in which the columnar phase is replaced by a smectic liquid crystal (S); that is, particles form a system of equidistant liquid layers. This work proposes and discusses the mechanisms of this behavior and new predictions that follow from this consideration.