Elastic nonchiral smectics

A further element of formalism in this argument is the arbitrary insistence on right-handed coordinates. Unless the molecules are enantiomorphic (i.e., chiral) or enantio-morphically arranged, this condition may also be relinquished. This is the case provided the phase is composed of nonchiral molecules. Thus we can cancel further terms contributing to the elastic moduli in both nematic and nonchiral smectic liquid crystals. 

In this expression only the coefiBcient of the term quadratic in the primary parameter is temperature dependent, whereas the coefficient of the P term is constant this is so because it is not the interaction between the electric polarization that leads to a phase transition. The coefficient is of the form = Aq T - Tqa), where Tqa is the smectic-C-smectic-A transition temperature, Kj is the elastic constant, and A is the coefficient of the so-called Lifshitz term responsible for the helicoidal stmcture. p and C are the coefficients of the flexoelectric and piezoelectric bilinear couplings between the tilt and the polarization. The coefficients A and C are dependent on the chiral character of the molecules. For nonchiral molecules, A and C are zero minimization of the free energy given in Equation (4.94) yields a system where the director axis is homogeneously tilted below the transition temperature T. There is no linear coupling between the tilt and the polarization, and thus, P. For temperatures... 

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