Theory of Melting of Molecular Crystals: The Liquid Crystalline Phase

Abstract

The theory of melting of mol. crystals developed by Pople and Karasz, which takes into account order-disorder processes in both the positions and orientations of the mols., is discussed in a slightly modified form. The theory is an extension of the 2-lattice model of Lennard-Jones and Devonshire so as to allow the mols. to take up 2 orientations on any site. It is assumed that the energy required for a mol. 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 calcns. of the orientational potential energy in nematic liq. crystals. The thermodynamic properties of the disordered system are evaluated relative to those of the perfectly ordered system using the Bragg-Williams approxn. For small orientational barriers, the theory predicts 2 transitions, a solid state rotational transition followed by a melting transition. For larger orientational barriers, the 2 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 liq. crystal to the isotropic phase for a certain range of orientational barriers are comparable to those obsd. in nematic compds. Theoretical curves are drawn for the degree of orientational order, the anomalous sp. heat, and thermal expansion as functions of temp. in the liq. cryst. range, and for the variation of the transition temp. with pressure. The curves reproduce the trends in the phys. properties of nematic liq. crystals. [on SciFinder(R)