Homogeneous quadratic expression

Let us consider the situation [44] where an external stationary homogeneous electric field is applied along the 2-axis, Fig. 5.3. We will use the quadratic Stark effect energy expression in the form of (5.15), supposing 0q = 7t/4. The choice of azimuth angle (p value needs more discussion. First, one must remember that the Ir — Ii signal only appears if the orientation component along the direction of observation possesses non-zero... 

The smoothed density functional, p, is expanded to a quadratic series to make the homogeneous fluid match the Percus-Yevick using the expression... 

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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