Theory of the intermediate tilted smectic phases and their helical rotation

Abstract

A molecular-statistical theory for the entire sequence of the chiral tilted smectic phases is derived. Uniaxial and biaxial subphases were found to be stable in different temperature ranges depending on the molecular parameters. The model of a chiral molecule possessing a strong transverse terminal dipole moment and a quadrupole moment located in the molecular core was used. Direct dispersion and electrostatic interactions (modulated by shape) between molecules located in the same or in the neighboring smectic layers are taken into account. An effective long-range interaction arises after the minimization of the free energy with respect to polarization vectors. If the molecular quadrupole moment is small, only uniaxial phases with different periodicities arise. Their periodicity may be tens and hundreds of layers (Sm-C*), or approximately two layers (Sm-C*)(Sm-C*A), or several layers (Sm-C*alpha). In the presence of the nonpolar biaxial ordering (in addition to polarization) there is a cap-shaped border in the phase diagram that separates Sm-C*A, Sm-C*, and Sm-C*alpha. If the molecules are nonchiral, Sm-CA, Sm-C, and the de Vries's phases arise instead of the three phases mentioned above. If the molecular quadrupole moment is large, the left "arm" of the border breaks into two lines, and a sequence of biaxial subphases arises in the area between these two lines. Among these biaxial subphases, the one with periodicity of three smectic layers appears to be the broadest in the temperature range. In addition, the subphases with different periodicities were found to be stable in narrow temperature ranges. The long helical rotation in every biaxial subphase is calculated. It is found to change sign between the three-layer subphase and Sm-C*, and may diverge in the four-layer subphase if it arises. All calculations are done with help of (A)FLC Phase Diagram Plotter software developed by the first author and available at his web-page.