Spontaneously Twisted Nonchiral Nematic Liquid Crystals

Miroscopic theories of nematic liquid crystals allow us to calculate from a few molecular parameters a number of macroscopic and static properties, such as the equation of state, the short and long-range order parameters and the visco-elastic coefficients. An attempt to provide such a microscopic theory which, for the more common nematics, fits the experimental data for the elastic constants and the long-range order parameters simultaneously, was introduced in [1]. From this theory it is possible to derive the microscopic potential which leads to a negative elastic constant K2. The equilibrium state of the system described by such a potential would exhibit a spontaneously broken symmetry of the twist-type. Experimental evidence of this property can be obtained by the investigation of the Freederiks effect. Due to the negative value of K 2 , a Freederiks effect would occur even for an arbitrary weak magnetic field. The purpose of this paper is to investigate this phenomenon from the microscopic point of view. All the results have been obtained by the constant curvature approximation (CCA) derived from the mean-field theory; therefore this technique is described in Chapter 2. In order to test the CCA, we derived in Chapter 3 the formulas for the elastic constants K1, K2, and K3. As K2 can be negative, contrary to K1 and K 3 , we have to consider higher order terms in the free energy expansion for the twist deformation. Expansion coefficients occurring in the higher order