Abstract
This study gives the temperature dependence of the two order parameters, namely, polarization P and the tilt angle θ, when there is a biquadratic coupling P 2 θ 2 in the expansion of the Landau free energy. This applies to the electric-field-induced SmA-Ferro-Electric SmC (SmC*) phase transition. From this expansion of the Landau free energy in terms of the polarization and the tilt angle, we obtain the temperature dependence of the electric susceptibility χ and the electric field dependence of the polarization P. These dependences of P, θ and χ are fitted to the experimental data for C7 and their critical behaviour in this liquid crystal is described close to the SmA- ferroelectric SmC (SmC*) phase transition. Also, considering this P 2 θ 2 coupling in the Landau free energy, the temperature dependence of the specific heat C P is obtained and using the experimental data for 2f + 3f, the critical behaviour of C P in this liquid crystal is analyzed close to its SmA- ferroelectric SmC (SmC*) phase transition. Values of the critical exponents which we obtain from our analysis of the SmA- ferroelectric SmC (SmC*) phase tansitions in C7 and 2f + 3f, are in agreement with those predicted by the Landau mean field model.
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