Molecular theory of cholesteric liquid crystals and cholesteric mixtures

A molecular theory of cholesteric liquid crystals is presented. By means of symmetry considerations we obtain a general form of the intermolecular potential containing chiral contributions, which are then shown to be responsible for forming the cholesteric phase. The temperature dependence of the cholesteric pitch is calculated. It is found that the pitch depends on temperature through a ratio of orientational order parameters in the form ${\left[\frac{{\sigma }_4\mathrm{}\left(T\right)\mathrm{}}{{\sigma }_2\mathrm{}\left(T\right)\mathrm{}}\right]}^2$. A general mean-field theory for binary cholesteric mixtures is also presented, along with a formula showing how the pitch depends on temperature and concentration. Under certain conditions, the formula reduces at fixed $T-T_c$ to a simple quadratic rational fraction in the concentration. This is consistent with experimental observation.