Landau expansion for the critical point of a polydisperse system

Weakly polydisperse systems: perturbative phase diagrams that include the critical region

The phase behavior of a weakly polydisperse system, such as a colloid with a small spread of particle sizes, can be related perturbatively to that of its monodisperse counterpart. I show how this approach can be generalized to remain well behaved near critical points, avoiding the divergences of existing methods and giving access to some of the key qualitative features of polydisperse phase equilibria. The analysis explains also why in purely size-polydisperse systems the critical point is, unusually, located very near the maximum of the cloud and shadow curves.

Polydisperse lattice-gas model

We describe a lattice-gas model suitable for studying the generic effects of polydispersity on liquid-vapor phase equilibria. Using Monte Carlo simulation methods tailored for the accurate determination of phase behavior under conditions of fixed polydispersity, we trace the cloud and shadow curves for a particular Schulz distribution of the polydisperse attribute. Although polydispersity enters the model solely in terms of the strengths of the interparticle interactions, this is sufficient to induce the broad separation of cloud and shadow curves seen both in more realistic models and experiments.

Phase behavior and particle size cutoff effects in polydisperse fluids

We report a joint simulation and theoretical study of the liquid-vapor phase behavior of a fluid in which polydispersity in the particle size couples to the strength of the interparticle interactions. Attention is focused on the case in which the particle diameters are distributed according to a fixed Schulz form with degree of polydispersity delta = 14%. The coexistence properties of this model are studied using grand canonical ensemble Monte Carlo simulations and moment free energy calculations. We obtain the cloud and shadow curves as well as the daughter phase density distributions and fractional volumes along selected isothermal dilution lines. In contrast to the case of size-independent interaction [N. B. Wilding et al., J. Chem. Phys. 121, 6887 (2004)], the cloud and shadow curves are found to be well separated, with the critical point lying significantly below the cloud curve maximum. For densities below the critical value, we observe that the phase behavior is highly sensitive to the choice of upper cutoff on the particle size distribution. We elucidate the origins of this effect in terms of extremely pronounced fractionation effects and discuss the likely appearance of new phases in the limit of very large values of the cutoff.

Liquid-vapor interface of a polydisperse fluid

We report a grand canonical Monte Carlo simulation study of the liquid-vapor interface of a model fluid exhibiting polydispersity in terms of the particle size sigma. The bulk density distribution, rho0(sigma), of the system is controlled by the imposed chemical potential distribution mu(sigma), the form of which is specified such that rho0(sigma) assumes a Schulz form with associated degree of polydispersity approximately = 14%. By introducing a smooth attractive wall, a planar liquid-vapor interface is formed for bulk state points within the region of liquid-vapor coexistence. Owing to fractionation, the pure liquid phase is enriched in large particles, with respect to the coexisting vapor. We investigate how the spatial variation of the density near the liquid-vapor interface affects the evolution of the local distribution of particle sizes between the limiting pure phase forms. We find [as previously predicted by density-functional theory, Bellier-Castella, Phys. Rev. E 65, 021503 (2002)] a segregation of smaller particles to the interface. The magnitude of this effect as a function of sigma is quantified via measurements of the relative adsorption. Additionally, we consider the utility of various estimators for the interfacial width and highlight the difficulty of isolating the intrinsic contribution of polydispersity to this width.

Liquid-gas coexistence and critical point shifts in size-disperse fluids

Specialized Monte Carlo simulations and the moment free energy (MFE) method are employed to study liquid-gas phase equilibria in size-disperse fluids. The investigation is made subject to the constraint of fixed polydispersity, i.e., the form of the "parent" density distribution rho(0)(sigma) of the particle diameters sigma, is prescribed. This is the experimentally realistic scenario for, e.g., colloidal dispersions. The simulations are used to obtain the cloud and shadow curve properties of a Lennard-Jones fluid having diameters distributed according to a Schulz form with a large (delta approximately 40%) degree of polydispersity. Good qualitative accord is found with the results from a MFE method study of a corresponding van der Waals model that incorporates size dispersity both in the hard core reference and the attractive parts of the free energy. The results show that polydispersity engenders considerable broadening of the coexistence region between the cloud curves. The principal effect of fractionation in this region is a common overall scaling of the particle sizes and typical interparticle distances, and we discuss why this effect is rather specific to systems with Schulz diameter distributions. Next, by studying a family of such systems with distributions of various widths, we estimate the dependence of the critical point parameters on delta. In contrast to a previous theoretical prediction, size dispersity is found to raise the critical temperature above its monodisperse value. Unusually for a polydisperse system, the critical point is found to lie at or very close to the extremum of the coexistence region in all cases. We outline an argument showing that such behavior will occur whenever polydispersity affects only the range, rather than the strength of the interparticle interactions.

Triple points in solutions of polydisperse semiflexible polymers

When a mother solution of semiflexible polymers with differing molecular weights is forced to undergo phase transition, cloud and shadow curves emerge instead of a coexistence curve. For the first time, we calculate the cloud and shadow curves for an isotropic-nematic transition coupled to polydispersity and predict novel triple points. Because of the emergence of new triple points, polydispersity allows the occurrence of anisotropic phases at much lower polymer concentrations than for the monodisperse solutions.