Solid-liquid phase behavior of ternary mixtures

The Gibbs Duhem integration technique is extended to calculate ternary phase diagrams at constant temperature and pressure. The technique is used to calculate solid-liquid-vapor phase equilibria for a system selected to roughly model a mixture of two diastereomeric molecules of similar melting point and diameter immersed in a solvent with a 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 when the interspecies well-depth is lowered to less than that of either of the diastereomers, the solid phase separates into two solid solutions and consequently there is a region of three-phase coexistence in the ternary phase diagram. We then calculate ternary phase diagrams at a series of temperatures for one set of molecular parameters. 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. (C) 2008 American Institute of Chemical Engineers.