Monte Carlo Simulation of Solid-Fluid Phase Equilibria in Binary and Ternary Mixtures

Abstract

The objective of this research is to study the solid-fluid phase equilibria of binary and ternary mixtures using molecular simulation. Solid-fluid phase equilibria plays an important role in many chemical processes, especially crystallization. This research provides insight into the underlying phenomena that govern these processes.

We first calculate complete phase diagrams, that is showing the solid, liquid, and vapor phases, for 29 binary mixtures of Lennard-Jones molecules characterized by different sets of interaction parameters using the Gibbs Duhem integration technique. The impact of including the possibility of a solid phase on the global phase behavior of such mixtures is investigated by comparing the complete phase behavior calculated by simulation to the global phase diagram calculated from a fluid-phase-only equation of state. Complete phase diagrams from each region of the global phase diagram are presented and compared with the fluid-phase-only phase behavior for the same mixture. It is found that for mixtures in which the components have greatly dissimilar critical temperatures, the presence of the solid phase significantly alters the fluid phase equilibria. In those cases, the phase behavior classification based on experimental observations should differ from that predicted by an equation of state approach.

The Gibbs Duhem integration technique is then extended to calculate ternary phase diagrams at constant temperature and pressure. We calculate solid-fluid phase equilibria for ternary mixtures of Lennard-Jones molecules. The simulation parameters were selected to roughly model a mixture of two diastereomeric molecules in a solvent, where the two 'diastereomer' molecules are of similar melting point and diameter and the solvent has a considerably lower melting point and a slightly smaller diameter. The cross-species well-depth and diameter between the two diastereomers are varied to determine their impact on the phase equilibria. We find that increasing the interspecies diameter up to the diameter of the larger diastereomer results in a slight increase of the solubility of the solid phase. We find that when the interspecies well-depth is lowered to less than that of either of the diastereomers, an immiscibility is formed in the solid phase and consequently there was a region of three-phase coexistence in the ternary phase diagram. Finally we calculate ternary phase diagrams at a series of temperatures for one set of molecular parameters. As the temperature increases, we find that the three-phase region decreases in size until it eventually disappears. For an equimolar mixture of diastereomers, there is a range of temperature and solvent concentration at which only one of the diastereomers will precipitate, thus effecting a separation of the diastereomers. As the temperature is decreased the purity of the precipitate increases.