Theory of Melting of Molecular Crystals: The Liquid Crystalline Phase

The theory of melting of molecular crystals developed by Pople and Karasz, which takes into account order-disorder processes in both the positions and orientations of the molecules, is discussed in a slightly modified form. The theory is an extension of the two-lattice model of Lennard-Jones and Devonshire so as to allow the molecules to take up two orientations on any site. It is assumed in this paper that the energy required for a molecule to diffuse to an interstitial site varies as V −4, as in the original formulation, but that the orientational barrier varies as V −3, in conformity with recent calculations of the orientational potential energy in nematic liquid crystals. The thermodynamic properties of the disordered system are evaluated relative to those of the perfectly ordered one using the Bragg-Williams approximation. For small orientational barriers, the theory predicts two transitions, a solid state rotational transition followed by a melting transition. For larger orientational barriers, the two transitions coalesce and there is a corresponding increase in the entropy of fusion. For even larger orientational barriers, the positional melting precedes the rotational melting and there occurs an intermediate phase, similar to the nematic mesophase, that has orientational order but no positional order. The predicted entropies of transition from the liquid crystal to the isotropic phase for a certain range of orientational barriers are comparable to those observed in nematic compounds. Theoretical curves are drawn for the degree of orientational order, the anomalous specific heat and thermal expansion as functions of temperature in the liquid crystalline range, and for the variation of the transition temperatures with pressure. The curves reproduce the trends in the physical properties of nematic liquid crystals.