The temperature dependence of the dielectric constant is studied under some fixed electric fields for the smectic G- (tilted-) smectic A (orthogonal) transition of the ferroelectric liquid crystal of compound A6. For this study, a mean field model with the quadrupole-quadrupole interactions is introduced. By fitting the inverse dielectric susceptibility from the mean field model to the experimental data from the literature, the observed behaviour of the dielectric constant is described satisfactorily for the smectic AG transition in A6. The transition temperature induced by an external electric field is also discussed for this ferroelectric compound. 1. Introduction Ferroelectric liquid crystals have been the subject of various experimental and theoretical studies [1–12]. As a function of temperature under fixed pressures or concentrations, the physical quantities such as the spontaneous polarization, tilt angle, dielectric constant, specific heat, and so forth. have been studied for their phase transitions between the smectic phases of A and C (or ) in particular. Under the electric field, some of those quantities have also been investigated and the first order or second order nature of the transitions between the smectic phases has been clarified. Among the smectic phases, smectic C (or ) and also smectic G phases are tilted since the long axes of the molecules make an angle with the director, whereas smectic A, B, and E phases are orthogonal ( ). In the presence of the chiral molecules, the smectic tilted phases possess a spontaneous polarization [1]. In the chiral-racemic systems, as the spontaneous polarization increases, the ferroelectric transition temperatures are shifted. Similarly, increasing the applied electric field causes the ferroelectric transition temperatures to shift [7]. Increasing the amount of spontaneous polarization or the external electric field then changes the phase transition from a first order towards a second order in ferroelectric liquid crystals. In some ferroelectric materials, a tricritical transition [12, 13] occurs which exhibits both the features of first order and second order transitions. The nature of the transition among the smectic phases can be investigated by considering the coupling between the order parameters (tilt angle, spontaneous polarization, orientational order parameter, etc.) in the mean field models. A bilinear coupling between the spontaneous polarization and the tilt angle ( coupling) [5, 7] and the biquadratic coupling ( coupling) [3, 4] have been considered in the mean field models mainly for
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