(217ba) Precise Simulation of Fluid-Solid Transitions in Colloid-Polymer Systems

In simulation studies of fluid-solid transitions, the constrained cell model is defined by dividing the simulation volume, V, into N Wigner-Seitz cells, each of volume V/N, appropriate for the solid phase under consideration, and confining a single particle per cell. Constant-pressure simulations indicate that the pressure vs. density curve of the constrained cell model exhibits an anomaly (inflection point) at a density which is approximately 60-70% of the density at close packing. Although the presence of such an instability or anomaly does not affect free energy calculations, it is the main reason for which the constrained cell model has not been very popular in simulation studies of fluid-solid transitions. In previous work, a generalized cell model was devised by adding a homogenous external field that controls the relative stability of the solid versus the fluid phase. High field values force single occupancy configurations with one particle per Wigner-Seitz cell and thus favor the solid phase. Normal (unconstrained) system behavior is restored in the limit of vanishing field. The generalized cell model can be used to link the fluid with the solid phase on a constant-density (or pressure) path by gradually increasing the strength of the field. Constant-pressure simulations results indicate that as the strength of the field is reduced, the transition from the solid to the fluid phase is smooth and continuous at low and moderate pressures. In contrast, at high pressures, the passage from the solid to the fluid occurs via a discontinuous first-order phase transition. The special point that separates continuous from discontinuous behavior is very close to the inflection point of the solid phase, as modeled through the constrained cell model. The fluid-solid transition of pure-component systems at fixed temperature can be determined by analyzing the field-induced, order-disorder transition of the corresponding generalized cell model in the high-pressure, vanishing-field limit using flat-histogram techniques.

In the present work, these cell-based simulation techniques for fluid-solid equilibria are extended to binary systems. The binary system investigated is the Asakura-Oosawa model, appropriate for colloid-polymer systems. The parameter that determines the resulting type of phase diagram is the colloid-to-polymer size ratio. The solid phase is characterized by an ordered arrangement of the colloidal particles with a random distribution of the polymers. The simulations are implemented at constant pressure and polymer activity. The simulation results indicate that the osmotic pressure vs. colloid density curve of the solid phase (as modeled through the constrained cell model) exhibits an inflection point analogous to that seen in simulation of pure species. As anticipated, simulations of the corresponding generalized cell model indicate that the transition of the fluid to the solid is continuous at low and moderate osmotic pressures and discontinuous at high osmotic pressures. Fluid-solid coexistence of the Asakura-Oosawa model at fixed polymer activity is obtained by analyzing the order-disorder transition of the corresponding generalized cell model. The entire phase diagrams have also been determined for different values of the colloid-to-polymer size ratio. At small size asymmetries, the phase diagram contains a stable critical/consolute point, on which first-order coexistence between a colloidal gas and a colloidal liquid phase terminates, as well as a triple point between a colloidal gas, liquid and a solid phase. As the colloid-to-polymer size ratio increases, the critical point becomes metastable against crystallization. At even higher-colloid-to-polymer size asymmetry, a solid-solid type of coexistence emerges. The two coexisting phases are expanded and compressed solid structures of the same symmetry. The results obtained from this work are in good qualitative accord with previous theoretical and simulation approaches that were mostly based on mapping the binary system to a one-component, colloid-only model with effective interactions.