E. Kilit

Temperature Dependence of the Polarization and Tilt Angle Under an Electric Field Close to the Smectic AC* Phase Transition in a Ferroelectric Liquid Crystal

The temperature dependence of the polarization P and the tilt angle θ is calculated here in the presence of a constant electric field near the smectic AC* phase transition of a ferroelectric liquid crystal using a mean field model. We demonstrate here the temperature dependence of P and θ under some fixed electric fields for the ferroelectric liquid crystal of 4-(3-methyl-2-chlorobutanoyloxy)-4′-heptyloxybiphenyl. Our predicted values of P and θ at various temperatures under fixed electric fields, follow similar critical behaviour as predicted for zero electric field from the mean field model near the smectic AC* phase transition in 4-(3-methyl-2-chlorobutanoyloxy)-4′-heptyloxybiphenyl.

Calculation of the Dielectric Constant as a Function of Temperature Near the Smectic AC* Phase Transition in Ferroelectric Liquid Crystals

We calculate here the dielectric constant ϵ as a function of temperature for the AC* phase transition of a ferroelectric liquid crystal using a mean field model. Using the values of the polarization P and the tilt angle θ, calculated from the mean field model with the P2θ2 coupling for 4-(3-methyl-2-chlorobutanoyloxy)-4′-heptyloxybiphenyl, the dielectric constant ϵ is calculated in the smectic C* phase of this ferroelectric liquid crystal at various temperatures at constant electric fields. Our calculated ϵ values predict the critical behaviour of the experimental dielectric constant measured at 15, 30, 45 and 60 V for 4-(3-methyl-2-chlorobutanoyloxy)-4′-heptyloxy-biphenyl, as reported in the literature.

Critical Behaviour of the Polarization, Tilt Angle, Electric Susceptibility and the Specific Heat Close to the SmA- Ferroelectric SmC (SmC*) Phase Transitions

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.

Analysis of the specific heat of p-azoxyanisole (PAA) near the phase transitions

The analysis of the experimental data for the specific heat Cp at various temperatures is given here near the nematic-isotropic liquid (TNI = 133.9°C) and the solid-nematic (TSN = 117.6°C) transitions in p-azoxyanisole (PAA). The analysis of the specific heat Cp is performed according to a simple power-law formula and a renormalisation-group expression. The values of the critical exponent α are extracted above and below the transition temperatures of TNI and TSN for this liquid crystalline material. Our exponent values are compared with the predictions of a three-dimensional Ising model and XY model for liquid crystals. Using the specific heat Cp , the temperature dependence of the enthalpy H and the entropy S is calculated in the nematic phase (T > TSN ) of p-azoxyanisole.

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

The temperature dependencies of the dielectric constant and the tilt angle (order parameter) are calculated under the electric field for the smectic A–smectic C* (AC*) transition in 4-(3-methyl-2-chlorobutanoyloxy)-4′-heptyloxybiphenyl (A7). The dielectric constant is fitted to the experimental data by using our mean field model with the biquadratic coupling between the spontaneous polarisation P and the tilt angle . Our results show that the mean field model with the coupling describes satisfactorily the observed behaviour of the AC* transition in A7. It is indicated here that a first-order AC* transition occurring at low electric fields changes its character towards a second order as the electric field increases in A7.

Analysis of the Specific Heat in the Supercooled Solid Phase of Liquid Crystals

The specific heat Cp is analyzed using the experimental data at various temperatures in the solid phase of cholesteryl myristate according to a power-law formula for the rapidly and slowly cooled solid in the stability limit. We also analyze the temperature dependence of the Cp using the experimental data for the supercooled solid phase of p-azoxyanisole in the stability limit and the stability temperatures are determined for both cholesteryl myristate and p-azoxyanisole. Our results show that the method of analysis given here is adequate to describe the observed behaviour of the Cp at low temperatures in the solid phase.

Calculation of the Dielectric Constant of a Ferroelectric Liquid Crystal From a Mean Field Model

The static dielectric constant ϵ⊥ of the ferroelectric liquid crystal 4-(3-methyl-2-chlorobutanoyloxy)-4′-heptyloxybiphenyl (A7) with high spontaneous polarization is calculated as a function of temperature using a mean field model. This calculation is performed close to the smectic A-isotropic liquid (SmA-I) transition for pure optically active compound (Tc = 81.6°C). For this calculation of ϵ⊥, the free energy of the SmA phase is expanded in terms of the orientational order parameter ψ and spontaneous polarization P with P2ψ2. It is shown here that our model describes adequately the observed behaviour of the temperature dependence of ϵ⊥ close to the SmA-I transition for A7.

A First-Order Transition of the Smectic A-Smectic C* in Ferroelectric Liquid Crystals

The static dielectric constant is calculated as a function of temperature using a mean field model close to the smectic A-smectic C* transition for the ferroelectric liquid crystal 4-(3-methyl-2-chlorobutanoyloxy)-4′-heptyloxybiphenyl (A7). This calculation of the dielectric constant is performed for the pure optically active compound (Tc = 73.4°C) and the temperature range is determined for a first-order smectic A-smectic C* transition from the mean field model. Our predicted values describe adequately the observed behaviour of the dielectric constant close to the smectic A-smectic C* transition and also the temperature range in the smectic A phase of A7.

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 () is calculated close to the smectic A-smectic B () transition ( = 71.3°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 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 transition of B5. Our results show that the observed behaviour of the dielectric constant close to the transition in B5 can be described satisfactorily by our mean field model.

Temperature Dependence of the Dielectric Constant Calculated Using a Mean Field Model Close to the Smectic A - Isotropic Liquid Transition

Various transitions among the phases of isotropic liquid (I), nematic (N) and smectic (SmA, SmC and SmC*) in liquid crystals have been studied extensively. The nematic-smectic A (NA) and the smectic Asmectic C (AC) or the smectic A-smectic C* (AC*) transitions are usually continuous and they are considered to belong to the three-dimensional XY universality class for the critical fluctuations (de Gennes, 1973). Experimentally, this requires a wide range of the nematic phase (Garland & Nounesis, 1994) for the NA transition, whereas at the AC transition the critical fluctuations are very large (Safinya et al., 1980). Ferroelectric liquid crystals exhibiting transitions from the isotropic liquid (I) to the nematic (N), smectic A and the smectic C or smectic C* (with optically active molecules), have also been studied extensively, in particular, those with high spontaneous polarization such as 4(3-methyl-2-chlorobutanoyloxy)4′ -heptyloxybiphenyl (A7). Experimental studies on the ferroelectric liquid crystals with high spontaneous polarization (Bahr & Heppke, 1986Mercuri et al., 2003) have been reported in the literature. The AC (or AC*) transitions in the ferroelectric liquid crystals (Bahr & Heppke, 1990Denolf et al., 2006) and in the antiferroelectric liquid crystals (Ema,, et al., 1996) have also been studied experimentally. Theoretical studies on the AC and AC* transitions have been reported in the literature (Musevic et al.,. 1983Mukherjee, 2009). We have also studied the AC and AC* transitions in the ferroelectric liquid crystals (A7 and C7) theoretically by using the mean field models in our previous works (Salihoglu et al., 1998Yurtseven 2011). Among the various physical properties of the ferroelectric liquid crystals, the dielectric properties have been studied extensively close to the AC (or AC*) transitions (Bahr et al., 1987, Musevic et al., 1983, Yurtseven & Kilit, 2008, Kilit & Yurtseven, 2008, Benguigui, 1984). In an another ferroelectric liquid crystal known as DOBAMBC which shows a second order transition (Zeks, 1984, Indenbom et al., 1976, Carlsson & Dahl, 1983), the AC* transition is associated with an increase in the dielectric constant e⊥ with decreasing temperature, as observed experimentally (Bahr et al., 1987). This increase in the e⊥ has been attributed to the contributions from a soft mode and also a Goldstone mode of this ferroelectric material with