Computational modelling of multi-phase equilibria of mesogenic mixtures

A computational study of phase equilibrium and phase diagrams of binary mixtures involving nematic liquid crystals and flexible polymers or monomeric solvents is performed using classical numerical integration schemes, and classical liquid crystalline thermodynamic models. A unique characteristic of these mixtures is the presence of isotropic–isotropic, isotropic–nematic, and/or nematic–nematic phase equilibrium. In addition, mixtures of nematic polymers and monomeric solvents are characterized by the ubiquitous bi-phasic chimney in the phase diagram. Also, the order parameter in the nematic phase is a highly non-linear function of temperature and concentration. The impact of integration schemes and asymptotic models on all these features is quantitatively determined. It is found that low order numerical quadrature schemes lead to poor order parameter predictions which in turn lead to inaccurate phase diagrams. It is also found that the classical Landau-de Gennes asymptotic expansion model fails to predict important phase equilibrium features, such as the above-mentioned bi-phasic chimney, and nematic–nematic phase coexistence. This paper establishes computational modelling guidelines on integration schemes and thermodynamic models of liquid crystalline materials that ensure a high accuracy in the predicted phase diagrams.