Liquid-crystalline transitions in homologous p-phenylenes and their mixtures. Part 2.—Theoretical treatment

Abstract

The lattice theory of nematic fluids is modified to take into account the presence of unoccupied sites representing the free volume which, according to results of the preceding paper, may constitute a substantial fraction of the sites of the lattice. A reduced volume [graphic omitted] > 1 (where [graphic omitted] is the ratio of the actual volume V to the ‘hard-core’ volume V^*) increases the combinatory factor in the partition function; the magnitude of the orientation-dependent intermolecular attractions is simultaneously decreased by the factor [graphic omitted]. The former effect dominates the latter. The theory is applied to the nematic → isotropic transitions in homologous p-phenylenes, H—(C₆H₄)_n—H, with n= 4–6. Axial ratios may be calculated from crystallographic data on members of this series. Results of the previous paper furnish values for [graphic omitted]. A single parameter T^*, characterizing the intensity of the orientation-dependent interactions, is required to determine the nematic → isotropic transition temperature T_NI. The same value, T^*= 483 K, reproduces the transition temperatures for all three homologues within a few degrees. Biphasic equilibrium in the three binary systems formed from these homologues are in excellent agreement with predictions of theory throughout experimentally accessible ranges of composition, the same value of T^* being used for these comparisons.