39 research outputs found
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
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