Calculation of a generalised smectic–hexatic phase diagram in liquid crystals

Abstract

This study gives a generalised smectic-hexatic phase diagram calculated by the Landau mean field theory. Our calculated phase line equations are fitted to the experimental phase lines, which represent first-order transition for the liquid crystals studied here. The temperature-and concentrationdependent phase lines calculated in this study describe the observed T-X phase diagram for the smectic-hexatic transitions. This indicates that the method of calculating the phase line equations from the mean field theory is general and it can be applied to other phase transitions in liquid crystals.

Temperature Dependence of the Tilt Angle for the Smectic A-Smectic Transition in a Mixture of C7-70PDOB Ferroelectric Liquid Crystals near the Tricritical Point

“…On the basis of our earlier meanfield models with the biquadratic coupling (P 2 θ 2 ), recently we have calculated tilt angle and the temperature shifts 2 Advances in Condensed Matter Physics as a function of concentration for a mixture of 10.04+C7 [16] and the temperature dependence of the spontaneous polarization and the tilt angle for a mixture of SCE9+SCE10 [17,18] for the AC * transition. Very recently, we have studied the dielectric constant as a function of temperature for the AC * transition in 4-(3-methyl-2-chlorobutanoyloxy)-4 -heptyloxybiphenly (A7) [21] and we have calculated a generalized smectic-hexatic phase diagram in various mixtures of liquids crystals [22].…”

“…The experimental data for the dielectric constant of A7 [24] was then analyzed according to the expression derived from the mean-field model [21]. Similarly, we have used our mean-field model with the quadratic couplings Ψ 2 θ 2 (Ψ is the orientational order parameter and θ is the tilt angle) for the smectichexatic phase transitions in various mixtures of liquid crystals in our recent study [22]. By expanding the free energy in terms of the order parameters (Ψ and θ), we derived the phase line equations and calculated a generalized phase diagram (T-X) on the basis of the experimental data [25].…”

Critical behaviour of the dielectric constant for the smectic AC* transition under the electric field in ferroelectric liquid crystals

“…These bilinear coupling P [10,11] and the biquadratic coupling P 2 2 [12][13][14][15] between the spontaneous polarisation P and the tilt angle have been considered in the mean field models for various liquid crystalline systems. Regarding the biquadratic P 2 2 coupling, we have studied the mean field models for the AC* transition in A7 [3,16,17], in binary mixtures [18][19][20][21][22] and also for the C* phase of SCE9 and SCE10 [23].…”