Predicting phase equilibria in polydisperse systems

Many materials containing colloids or polymers are polydisperse: They comprise particles with properties (such as particle diameter, charge, or polymer chain length) that depend continuously on one or several parameters. This review focusses on the theoretical prediction of phase equilibria in polydisperse systems; the presence of an effectively infinite number of distinguishable particle species makes this a highly nontrivial task. I first describe qualitatively some of the novel features of polydisperse phase behaviour, and outline a theoretical framework within which they can be explored. Current techniques for predicting polydisperse phase equilibria are then reviewed. I also discuss applications to some simple model systems including homopolymers and random copolymers, spherical colloids and colloid-polymer mixtures, and liquid crystals formed from rod- and plate-like colloidal particles; the results surveyed give an idea of the rich phenomenology of polydisperse phase behaviour. Extensions to the study of polydispersity effects on interfacial behaviour and phase separation kinetics are outlined briefly.Comment: 48 pages, invited topical review for Journal of Physics: Condensed Matter; uses Institute of Physics style file iopart.cls (included

Projected free energies for polydisperse phase equilibria

A `polydisperse' system has an infinite number of conserved densities. We give a rational procedure for projecting its infinite-dimensional free energy surface onto a subspace comprising a finite number of linear combinations of densities (`moments'), in which the phase behavior is then found as usual. If the excess free energy of the system depends only on the moments used, exact cloud, shadow and spinodal curves result; two- and multi-phase regions are approximate, but refinable indefinitely by adding extra moments. The approach is computationally robust and gives new geometrical insights into the thermodynamics of polydispersity.Comment: 4 pages, REVTeX, uses multicol.sty and epsf.sty, 1 postscript figure include