Molecular Simulation of Liquid Crystals: Phase Equilibrium and the Solubility of Gases in Ordered Fluids

Monte Carlo simulations were performed in the NPT ensemble and in an expanded version of the Gibbs ensemble. The phase behavior of single-phase hard-sphere chain fluids was determined using NPT ensemble simulations, while the isotropic-nematic phase equilibrium of single-component and binary mixtures of hard-sphere and Lennard-Jones fluids was calculated using expanded Gibbs ensemble simulations. Fluid properties such as packing fractions (hard-sphere fluids), densities and temperatures (Lennard-Jones fluids), order parameters, pressures, and gas solubilities (Henry coefficients) were obtained for chain fluids with different degrees of elongation and flexibility. The study of single-component athermal (hard-sphere) systems showed that larger chain lengths increase the potential for the formation of nematic phases, decreasing monotonically the pressure and packing fractions at which the isotropic-nematic phase transition takes place. However, a maximum in the isotropic-nematic packing fraction difference was observed as a function of chain length. Flexibility reduces the anisotropy of the molecule, which increases the isotropic-nematic transition pressure and decreases the packing fraction difference between both phases. It was shown that the solubility of a single-segment hard-sphere gas molecule does not depend on molecular order, being determined only by the packing fraction of the system. The solubility difference at the isotropic-nematic phase transition is therefore determined by the packing fraction difference at coexistence. The effect of connectivity was studied by considering relative Henry coefficients, defined as the Henry coefficient of the gas in the chain fluid divided by the Henry coefficient of the gas in the monomer fluid at same density. A linear relationship between relative Henry coefficients and packing fraction was obtained. Binary mixtures of hard-sphere chain fluids showed a phase split and fractionation between a nematic phase concentrated in the longest component and an isotropic phase richer in the shortest component. Fractionation is a consequence of the larger tendency to align of the long chains compared to the short chains. This tendency increases with the difference in chain length between both components forming the mixture. A larger fractionation leads to a larger isotropic-nematic packing fraction difference, which was found to be always larger for the mixture than for the constituting pure components. Flexibility of the longest component reduces fractionation, increasing the pressure and packing fraction at which the isotropic-nematic transition takes place for a specific composition of the fluid. As in the case of pure components, a linear relationship between relative Henry coefficients and packing fraction independent of the molecular order was observed. The isotropic-nematic phase equilibria of Lennard-Jones chains was determined for: linear chain molecules with different lengths, a partially-flexible chain molecule, and a binary mixture of linear chains. Increasing chain lengths displaces the isotropic-nematic coexistence of linear Lennard-Jones chain fluids to larger equilibrium densities and lower equilibrium pressures, increasing at the same time the isotropic-nematic density difference. Flexibility reduces the anisotropy of the molecule shifting the isotropic-nematic equilibrium to larger pressures and densities, reducing at the same time the density difference between both phases. In a binary mixture of linear Lennard-Jones chains, fractionation between an isotropic phase richer in the short chains and a nematic phase richer in the long chains was observed. The isotropic-nematic density difference was found to be always larger in the mixture than for pure components, with a maximum at a certain mole fraction. The solubility of a single-segment Lennard-Jones gas molecule was calculated for linear Lennard-Jones chain fluids and for a binary mixture of them. A linear relationship between solubility difference and density difference at coexistence was identified for all linear chain systems. Furthermore, it was shown that the solubility of a Lennard-Jones gas in linear Lennard-Jones chain fluids is independent of the molecular order of the fluid at coexistence. The isotropic-nematic solubility difference in the binary mixture was observed to be always larger in the mixture than for the pure components, with an observed maximum at the mole fraction corresponding to the maximum in the isotropic-nematic density difference. Simulation results for the isotropic-nematic transition were compared to theoretical predictions obtained from the analytical equation of state developed by van Westen et al.. Excellent agreement between simulation and theoretical results were observed. A rescaled Onsager theory was used in the description of hard-sphere systems showing an accurate prediction compared to simulation results. A perturbed theory approach was used in the treatment of Lennard-Jones fluids, whereby orientation dependent attractions were not considered explicitly in the development of the dispersion term. A reliable description of the isotropic-nematic phase equilibrium of Lennard-Jones fluids was obtained using this approach. The simulation data presented in this work represents a large contribution to the liquid crystal phase behavior of chain fluids. The effect of molecular properties on the phase behavior of liquid crystals was determined using linear and partially-flexible molecules with different elongations and flexibility, for purely repulsive (hard-sphere) and soft-attractive (Lennard-Jones) interactions. Predictions obtained from the equation of state of van Westen et al. showed an excellent agreement with simulation data, validating the assumptions made in the development of this theory