A molecular-statistical theory of the temperature-dependent pitch in cholesteric liquid crystals

An interaction between chiral molecules is derived in terms of the orientations of their long molecular principal axes. In analogy with Maier–Saupe and Goossens the derivation is based on the electric multipole expansion. The molecules are assumed to behave as if they were cylindrically symmetric, i.e., the system is locally nematic. As an example the chiral molecules are represented by Kuhn models, and the relevant coupling constants are calculated explicitely. An expression for the free energy is obtained in the molecular field approximation. It is shown that, if only the induced dipole–dipole and the dipole–quadrupole dispersion energies are taken into account, a temperature-independent cholesteric pitch is obtained. This result is traced back to the symmetric character of the interaction. In order to explain the experimental situation one has to introduce, in analogy with Keating, an asymmetry producing interaction. The proposed model is discussed and its thermodynamic properties are calculated in the molecular field approximation. It is found that the magnitude of the reciprocal pitch varies nearly linearly with temperature in agreement with experiment. Interpretational difficulties related to the use of the multipole expansion are discussed.