Predicting the Phase Diagram of a Liquid Crystal Using the Convex Peg Model and the Semiempirical PM3 Method

A molecular theory to determine thermodynamic properties of isotropic and nematic phases of liquid crystals is proposed, based on a convex peg model and semiempirical PM3 (Parametrized Method 3) calculations. The Helmholtz-free energy of the molecular system, a convex hard core within an encircling spherical square-well (SW) potential, is obtained from a second-order perturbation theory for SW nonspherical particles, combined with the Parsons decoupling approximation of the translational and rotational degrees of freedom, and a long-range approximation for the evaluation of the perturbation terms. The theory is applied to predict the phase diagram and isotropic?nematic transition of p-azoxyanisole. To do this, an estimation of the volume of a p-azoxyanisole molecule is derived from a minimum-energy geometry, using PM3 calculations; the volume obtained is mapped into a hard ellipsoid revolution volume of a Convex Peg molecule. A very good agreement in the prediction of the thermodynamic properties is obtained when compared with experimental data.