Phase equilibria of model ternary mixtures: Theory and computer simulation

Isomolar semigrand ensemble molecular dynamics: Development and application to liquid-liquid equilibria

An extended system molecular dynamics method for the isomolar semigrand ensemble (fixed number of particles, pressure, temperature, and fugacity fraction) is developed and applied to the calculation of liquid-liquid equilibria (LLE) for two Lennard-Jones mixtures. The method utilizes an extended system variable to dynamically control the fugacity fraction xi of the mixture by gradually transforming the identity of particles in the system. Two approaches are used to compute coexistence points. The first approach uses multiple-histogram reweighting techniques to determine the coexistence xi and compositions of each phase at temperatures near the upper critical solution temperature. The second approach, useful for cases in which there is no critical solution temperature, is based on principles of small system thermodynamics. In this case a coexistence point is found by running N-P-T-xi simulations at a common temperature and pressure and varying the fugacity fraction to map out the difference in chemical potential between the two species A and B (mu(A)-mu(B)) as a function of composition. Once this curve is known the equal-distance/equal-area criterion is used to determine the coexistence point. Both approaches give results that are comparable to those of previous Monte Carlo (MC) simulations. By formulating this approach in a molecular dynamics framework, it should be easier to compute the LLE of complex molecules whose intramolecular degrees of freedom are often difficult to properly sample with MC techniques.

Amphiphilic hard body mixtures

In order to study ternary amphiphilic mixtures, we introduce a simplistic model of hard spheres corresponding to water and hard needles corresponding to oil and amphiphilic particles, where the hydrophilic head is modeled as a hard sphere and the hydrophobic tail as an infinitely thin needle attached radially to the sphere. For this system, we construct a geometry-based density functional and perform Monte Carlo computer simulations. The equation of state derived from the theory is found to be in remarkable agreement with our simulation results. We investigate the theoretical demixing phase diagram, and find that the predicted trends strongly support the amphiphilic character of the model.