Order–disorder phenomena. Part 1.—Theory of order–disorder phase equilibria in D- and L-systems of quasiglobular compounds

Abstract

The Kirkwood approximation for substitutional disorder in a binary equicomponent system in the superlattice model is generalised to cover the case of unequal composition. Another model, the domain model is developed. It is shown that the binary system has a choice of two mixing modes by which to interact, i.e., the domain or the superlattice modes, and chooses the mode that minimises the free energy of the system. Statistical mechanical models based on the two mixing modes are developed by which the symmetric binary phase diagrams associated with orientational disordering in crystals of optically active quasi-globular molecules can be interpreted. The key parameters in the theory are Δ[graphic omitted] and Δ[graphic omitted] which are the change in the chiral substitutional discrimination energy and the change in the square of the chiral substitutional discrimination energy at the solid-state orientational transition. The former gives a depression on the transition temperature leading to a minimum at the 50 % composition on the phase diagram, and the latter is associated with short-range order effects which may produce a submaximum or maximum on the phase diagram if both the rotator and non-rotator phases are substitutionally disordered. Some pretransitional phenomena detectable by calorimetric and relaxation studies are predicted for low temperature transitions. It is also shown that if the orientational transition occurs simultaneously with substitutional disordering the transition temperature may rise to a maximum at x_D=½ on the binary phase diagram. The phenomenon associated with compound formation in a symmetric binary phase diagram without eutectic features may be attributed to short-range order effects and the coupling between orientational and substitutional transitions. A model for eutectic transitions involving orientational disorder is also presented. Finally a scheme of classification of symmetric binary phase diagrams based on the dependence of both the transition energy and temperature on composition is proposed.