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A molecular-statistical theory of the temperature-dependent pitch in cholesteric liquid crystals van der Meer, B. W.; Vertogen, G.; Dekker, A. J.; Ypma, J. G. J.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 multi pole 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. multi pole expansion are discussed.

The elastic-distortion free-energy density of biaxial nematics is derived with use of the formalism of tensor analysis. The macroscopic description of biaxial nematics involves 12 bulk elastic constants. The appearance of chirality introduces an additional number of 5 twist terms.

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The generalized Landau-de Gennes theory for uniaxial and biaxial nematic liquid crystals is analyzed using tensor analysis. In this way all terms allowed by symmetry appear in the free-energy expression. This improves the quantitative shortcomings of the commonly used theory. It appears that uniaxial nematic liquid crystals are described by 12 independent generalized elastic terms and that biaxial nematic liquid crystals are described by 48 independent generalized elastic terms. For practical purposes, several approximations based on symmetry arguments are discussed. The theory is applied to describe the variation in order and orientation near a surface. The relevance of the theory to the debate on the surface elastic constant K 13 is pointed out.