A theory of orientational ordering in uniaxial liquid crystals composed of molecules with alkyl chains

The constituent molecules of thermotropic liquid crystals invariably contain an aromatic core to which is attached one and often two n -alkyl chains. Nuclear magnetic resonance investigations have revealed that the chain does not exist entirely in an all- trans configuration and that the orientational order of the methylene groups varies markedly along the chain. In this paper we develop a theory to explain these variations for a uniaxial phase at a given temperature and pressure. Our theory contains two distinct parts: one is a model for the conformational distribution of the alkyl chains while the other is for the potential of mean torque experienced by a conformer and which is responsible for its alignment with respect to the director. We use the rotameric state model developed by Flory to describe the conformations adopted by the alkyl chain. The potential of mean torque presents a more difficult problem and we assume that it may be represented by a sum of contributions from each rigid group in the molecule. The order parameters for the methylene and methyl groups in the alkyl chains of the 4- n -pentyl and 4- n -octyl-49-cyanobiphenyls predicted by the theory are found to be in good accord with those obtained experimentally. We have also used the theory to predict the conformational distributions for both the isotropic and nematic phases of these mesogens; the calculated distributions are contrasted with those assumed by other models. In addition we have obtained the ordering matrices for the various conformers adopted by the two 4- n -alkyl-49-cyanobiphenyls. The results of these calculations do not support the notion that the orientational order of such molecules can be described by a single, cylindrically symmetric ordering matrix.