Monte Carlo Simulations of Complete Phase Equilibria for Binary Mixtures

Abstract

The objective of this thesis is to study the phase equilibria ofbinary mixtures using molecular simulation. Vapor-liquid,vapor-solid, liquid-liquid, and liquid-solid coexistence lines arecalculated for binary mixtures of Lennard-Jones spheres using MonteCarlo simulation and the Gibbs-Duhem integration technique. Completephase diagrams, i.e., showing all types equilibrium betweenvapor, liquid, and solid phases are constructed. The calculations presented in this thesismark the first time that molecular simulation hasbeen used to obtain phase diagrams describing all types of equilibriabetween vapor, liquid, and solid phases.We present complete phase diagrams for binary Lennard-Jones mixtureswith diameter ratios ranging from 0.85 to 0.95 and attractivewell-depth ratios ranging from 0.45 to 1.6, at reduced pressuresranging from 0.002 to 0.1. The Lorentz-Berthelot combining rules areused to calculate the cross-species interaction parameters. Wesystematically explore how the complete phase diagrams change as afunction of the diameter ratio, well-depth ratio, binaryinteraction parameter, and system pressure.

We first calculate complete phase diagrams for several binary mixtures at a single pressure and find that for well-depth ratios of unity (equal attractions among species) there is no interference between the vapor-liquid and solid-liquid coexistence regions. As the well-depth ratio increases or decreases from unity, the vapor-liquid and solid-liquid phase envelopes widen and interfere with each other, leading to the appearance of a solid-vapor coexistence region. For diameter ratios of 0.95, the solid-liquid lines have a shape characteristic of a solid solution (with or without a minimum melting temperature); as the diameter ratio decreases the solid-liquid lines fall to lower temperatures until they eventually drop below the solid-solid coexistence region, resulting in either a eutectic or peritectic three-phase line.

We then vary the binary interaction parameter in the Berthelotcombining rule to study the effect of unlike pair attractions onbinary mixture phase behavior. When the binaryinteraction parameter is unity we find a vapor-liquid coexistence region with a eutectic solid-liquidcoexistence region. These two regions are separated by a completelymiscible liquid phase. When the binary interactionparameter is less than unity we find that the vapor-liquid andsolid-liquid coexistence regions interfere. This interference resultsin the appearance of a vapor-solid coexistence region bounded above and below bysolid-liquid-vapor coexistence lines. We also find that when the binary interaction parameter is less than unity, there is a region ofliquid-liquid immiscibility that is metastable with respect to thesolid-fluid phase equilibria.

Next we calcuate temperature versus composition phase diagrams for one mixture at five reduced pressures in order to examine the effects of pressure on complete phase behavior. We observe interference between the vapor-liquid and solid-liquid coexistence regions at the lowest pressure. As the pressure increases, the vapor-liquid coexistence region shifts to higher temperatures, while the solid-liquid coexistence region remains essentially unaffected. Eventually, the vapor-liquid coexistence region lifts off the solid-liquid coexistence region, ending the interference. We then present pressure versus temperature projections for several mixtures to explore how the three-phase loci change with variations in diameter ratio and well-depth ratio. We find that as the diameter ratio decreases, the maximum pressure in the solid-liquid-vapor locus decreases and the characteristic shape of the solid-liquid coexistence region changes from peritectic to eutectic. As the well-depth ratio decreases, the maximum pressure in the solid-liquid-vapor locus increases.