A simple molecular statistical treatment of a model for cholesterics

The cholesteric state is discussed in terms of a model consisting of the Maier-Saupe and a twist interaction. The model can be easily solved in the mean field approximation. In the practical case of a large pitch analytical expressions are obtained for relevant quantities like the order parameters and the free energy. Then it appears that the pitch is temperature independent, which is a general result, and does not influence the discontinuity of the main (nematic) order parameter at the isotropic-cholesteric transition. Interactions giving rise to a temperature-dependent pitch are discussed briefly.