Thermodynamic model for the investigation of phase transition properties of homologous series ofnALandnHLferroic mesogens

Abstract

The thermodynamic model, developed by us previously (Singh S, Singh S. Application of thermodynamic model to study the ferroelectric properties of nAL and nHL homologous series. Phase Transit. 2013;86:531-540), has been modified to investigate the phase transition properties of SmC* phase and SmA-SmC* phase transition. As usual, in this approach, the free energy density of a system is written as an expansion series in powers of order parameters (tensor orientational order Q ij , scalar smectic order c and polarization vector order P) and the couplings between these order parameters. Since Q ij governs the tilt vector ξ, no term is included in the free energy density involving only ξ. The coupled equations for these order parameters are obtained by the minimization of the free energy density with respect to respective order parameters. A detailed analysis of the relative contribution of each individual term of the expansion series and the values of spontaneous polarization (P 0 ), tilt angle (u 0 ) and pitch (p) as a function of temperature for the two homologous series nALðn ¼ 9; 10; 12Þ and nHLðn ¼ 9; 10; 12; 14; 16Þ of ferroic mesogens is presented. The influence of the alkyl chain length on the ferroelectric properties has been analysed and found to be substantial. A close agreement between theory and experiment for all the mesogens has been observed.

Effect of Alkyl Chains Length on Ferroelectric Properties of Km/n and KLLm/n Homologous Series

“…In conclusion, we would like to mention that all the phenomenological model (9-18) based on the two degrees of freedom P and ξ ij order parameters, are insufficient and do not incorporate the physical reality and that the thermodynamic model developed by us (6) in terms of Q ij , ψ and P order parameters is conceptually correct and takes account of the real situation and is capable of explaining the characteristic features of Sm C * phase and Sm C * -Sm A transition properties.…”

“…The temperature dependences of the spontaneous polarization and tilt angle for Km/n (m = 8; n = 4, 5, 6,8,9) series is shown in Fig. 3 P 0 with the temperature is more pronounced as compared to θ 0 .…”

“…Defining the wave vector q of the pitch as q = 2π p , we assume following ansatz of the P and ξ order parameters: ξ 1 = θ 0 cos(qz), ξ 2 = θ 0 sin(qz) P x = −P 0 sin(qz), P y = P 0 cos(qz) (6) Here, P 0 and θ 0 are the magnitude of the polarization and tilt angle, respectively. The azimuthal angle φ describes the average position of molecules on the cone changes with the coordinate z as φ = qz.…”

“…(13)] in terms of f 0 , α 1 , β, e 1 , h 0 , δ * 1 , and δ * 2 . (18) for the S, these coefficients have been determined for the five members of Km/n (m = 8; n = 4, 5, 6,8,9) series and six members of KLLm/n (m = 6, 8; n = 4, 5, 6) series by carrying out the least square fitting, based on MATLAB software, to the experimental data (1, 2) of P 0 , θ 0 , and p. The values of these coefficients are given in Tables 1 and 2. (18) for the S, these coefficients have been determined for the five members of Km/n (m = 8; n = 4, 5, 6,8,9) series and six members of KLLm/n (m = 6, 8; n = 4, 5, 6) series by carrying out the least square fitting, based on MATLAB software, to the experimental data (1, 2) of P 0 , θ 0 , and p. The values of these coefficients are given in Tables 1 and 2.…”

“…A number of ferroelectric liquid crystal (FLC) series having the same rigid core containing a keto group and various numbers of lactate group in the chiral segment were synthesized and characterized by Hamplova et.al. These authors (1, 2) measured the basic characteristics, mesomorphic properties, and the temperature dependances of P 0 , θ 0 , and p for both the homologous series Km/n (m = 8; n = 4, 5, 6,8,9) and KLLm/n (m = 6, 8; n = 4, 5, 6). Two homologs of these series containing one and two lactate units with a keto group in the core are abbreviated in short as Km/n and KLLm/n, respectively (Figures 1 and 2).…”