The constituent particles of soft matter systems typically exhibit variation in terms of some attribute such as their size, charge, etc. Examples of these so-called “polydisperse” systems are everywhere, including colloids, liquid crystals, and polymers. Understanding the physical consequences of polydispersity, however, is a considerable challenge. We explore qualitative aspects of polydisperse phase behaviour on two fronts. We first study the dynamics of phase separation in polydisperse colloidal systems by developing, analysing, and simulating a dynamical mean-field theory for the Polydisperse Lattice-Gas (PLG) model. In particular we test effects of fractionation, where mixture components are distributed unevenly across coexisting phases. Our results provide strong theoretical evidence that, due to slow fractionation, (i) dense colloidal mixtures phase-separate in two stages and (ii) the denser phase contains long-lived composition heterogeneities. We also provide a practical method to determine whether such heterogeneities are indeed present in a given phase-separating mixture. Moreover, we study colloidal mixtures phase separating after a secondary temperature quench into the two- and three-phase coexistence regions. We found several interesting effects (mostly associated with the extent to which crowding effects can slow down composition changes), including long-lived regular arrangements of secondary domains; interrupted coarsening of primary domains; wetting of fractionated interfaces by oppositely fractionated layers; ‘surface’-directed spinodal ‘waves’ propagating from primary domain interfaces; and filamentous morphologies arising out of secondary domains. Secondly, we analyse the critical gas-liquid phase equilibrium behaviour of arbitrary fluid mixtures in the coexistence region, focussing on settings which are relevant for polydisperse colloids. Our analysis uses Fisher’s complete scaling formalism and thus includes ‘pressure mixing’ effects in the mapping from the fluid’s thermodynamic fields to the 3D Ising effective fields. Because of fractionation, the behaviour is remarkably rich. We give scaling laws for a number of new and conventional important loci in the phase diagram. In particular we identify new suitable observables for detecting pressure mixing effects. Our predictions are checked against numerics by using mapping parameters fitted to Lennard- Jones simulation data, allowing us to highlight crossovers where pressure mixing becomes relevant close to the critical point.
Phase separation of polydisperse fluids
de Castro, P. (Author). 1 Apr 2019
Student thesis: Doctoral Thesis › Doctor of Philosophy