Phase equilibria in polydisperse fluids

The Gibbs simulation technique has been extended to calculate the phase equilibria of fluids of particles exhibiting variable polydispersity, such as micellar solutions. The density-temperature sections of the phase diagrams and the distribution of particle sizes in the coexisting phases have been calculated for two very simple model fluids. In the first model of size polydispersity, spherical particles of different additive diameters interact through a Lennard–Jones potential and the underlying, or low-density, distribution of particle sizes is a Gaussian characterized by a standard deviation, s. In the second model the well depth associated with each particle is additionally correlated with the diameter. In the case of size polydispersity, with s=0.03 and 0.05 (typical of the degree of polydispersity in spherical micelles close to the critical micelle concentration), we observe no change in the phase envelope from that of the monodisperse fluid. At s=0.2 there is a significant shift in the coexisting ‘‘liquid’’ density to smaller values. On average the particles in the liquid phase are larger than those in the ‘‘vapor’’ phase. The balance of attractive and repulsive forces causes particles in the coexisting liquid phase to increase their average size, and then decrease, in moving from the critical point to the triple point. For size polydispersity the packing fraction of the coexisting phases is independent of the degree of polydispersity. Inclusion of the energy correlation in the model magnifies the effects observed with pure size polydispersity. Moreover, the packing fraction at coexistence is now a strong function of polydispersity. These results constitute the first simulations of phase equilibria in polydisperse fluids.