We study here the tilt angle and the temperature shifts as a function of concentration for the AC* phase transition in a binary mixture, using our mean field model with the biquadratic P2θ2 coupling — and also with the bilinear Pθ and P2θ2 couplings. By expanding the free energy in terms of the tilt angle and polarization, the tilt angle and the temperature shift are evaluated by using the coefficients given in the free energy expansion. By employing a concentration-dependent coefficient, the tilt angle and the temperature shift are calculated as a function of concentration of 10.O.4 for the SmAC* transition in a binary mixture of C7 and 10.O.4. Our calculated values of the tilt angle and the temperature shifts decrease as the concentration of 10.O.4 increases, as confirmed experimentally for the AC* transition in this binary mixture. This indicates that our mean field models studied here are satisfactory to explain the observed behavior of the AC* transition of the binary mixture of C7 and 10.O.4.
We analyze the heat capacity C P for low and high-density amorphous ice below the transition temperature (T C ≈ 140 K) using a power-law formula. The renormalized critical exponent α R is extracted from the observed C P data, which describes similar critical behavior for both low and high-density amorphous ice below T C . Our analysis can also describe a glass transition in the low-density amorphous ice which is made from the high-density amorphous ice at 124 K, as observed experimentally.
The temperature dependence of the tilt angle is studied in the smectic phase near the smectic A-smectic tricritical point for a mixture of 70PD0B in the ferroelectric liquid crystal C7 (). The mean-field models with the biquadratic ( is the spontaneous polarization) and (bilinear) coupling terms in the free energy expansion are used to analyze the experimental data for the tilt angle in this binary mixture. From our analysis, the coefficients given in the free energy expansion of the mean-field models are determined. Our results show that the mean-field theory explains adequately the observed behaviour of the C7-70PD0B mixture near the tricritical point.
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