Correlations in the isotropic phases of chiral liquid crystals: The role of helicity modes

Abstract

The phenomenological theory of chiral liquid crystals is further developed by generalizing the model of self-consistent correlations [J. Englert, L. Longa, H. Stark, and H.-R. Trebin, Phys. Rev. Lett. 81, 1457 (1998)]. In the present approach, not only a leading helicity mode of the tensor order parameter is retained but also the remaining four modes. By considering a full fluctuating spectrum of the order parameter, the role of correlations between helicity modes in the isotropic phases is studied. Additionally, an exact form of the two-point correlation function in real space is derived and its properties are thoroughly discussed. It is shown that for chiral isotropic liquids purely chiral modes could be identified that do not exist for an ordinary liquid. Detailed results of the numerical calculations are compared with those obtained from the earlier model and these show regions where the coupling between the modes becomes important, in agreement with the available experimental data. Though the analysis up to first-order cumulant expansion does not predict a direct phase transition between the blue phase III and the isotropic phase, it is fairly easy to identify two differently correlated regions in a temperature-chirality plane. Various structural quantities, such as optical activity and specific heat, also reveal a behavior characteristic of two isotropic phases with different correlation lengths.