Calculation of the Dielectric Constant as a Function of Temperature Close to the Smectic A-Smectic B Transition in B5 Using the Mean Field Model

The temperature dependence of the static dielectric constant (epsilon) is calculated close to the smectic A-smectic B (S-A-S-B) transition (T-c = 71.3 degrees C) for the liquid crystal compound B5. By expanding the free energy in terms of the order parameter in the mean field theory, the expression for the dielectric susceptibility (dielectric constant) is derived and is fitted to the experimental data for epsilon which was obtained at the field strengths of 0 and 67 kV/cm from literature. Coefficients in the free energy expansion are determined from our fit for the S-A-S-B transition of B5. Our results show that the observed behaviour of the dielectric constant epsilon close to the S-A-S-B transition in B5 can be described satisfactorily by our mean field model