Publisher Summary This chapter discusses field of ferroelectricity. It deals with selected salient properties and associated physics. The chapter reviews the phenomenological, soft mode, and first-principles theories of ferroelectrics. There are similarities between spin glasses and dielectric dipolar glasses. The dipolar interaction in both a normal, or ordinary, polarizable medium leads to the formation of a dipolar glass at low temperatures, and in a highly polarizable medium that leads to either long-range ferroelectric order or to a glass-like relaxor state. The properties of relaxor ferroelectrics and the contrast between properties and normal ferroelectrics have also been discussed in the chapter. Discoveries coupled with the scientific challenges of the many facets of ferroelectric phenomena and the technological importance of the field ensure health and vitality of research in ferroelectricity.

Ferroelectricity revisited—Advances in materials and physics

Electro-optic properties of polymer stabilized ferroelectric liquid crystal (PSFLC) systems are examined as a function of varying concentrations of either a linear or crosslinked thiol-ene polymer. The thiol-ene method of polymer stabilization is a drastic change from previous studies designed to avert the problem of polymer phase separation. FLC rise time and tilt angle measurements were used to determine the effects of the polymer network on the optical properties of the system. The addition of monomer impurities to both systems demonstrated a reduction in tilt angle, which translated into decreased switching speeds in both systems prior to polymerization. The crosslinked thiol-ene system showed increased switching times due to the creation of polymer in the interlayer spacing of the FLC, but exhibited minimal increase in the rotational viscosity of the system. In addition, the crosslinked polymer systems resulted in an increase in the liquid crystalline order, which produced an increase in the contrast...

Electro-optic properties of thiol-ene polymer stabilized ferroelectric liquid crystals

Smectic Liquid Crystals: Ferroelectric Properties and Electroclinic Effect

Four members of a homologous series of diarylethane α-chloroester ferroelectric liquid crystals [1] have been synthesized and characterized by polarizing optical microscopy and DSC measurements. Two of the compounds exhibit a twist grain boundary structure (TGB A* phase) or twisted smectic A* phase, shortly before reaching the smectic to cholesteric phase transition. The temperature dependence of the optical tilt angle θ, the spontaneous polarization P s and the effective rotational viscosity γo were investigated for the ferroelectric S*C, S*I and S*F phases. It was found that especially the spontaneous polarization and the rotational viscosity increased with decreasing length of the alkyl chain for all three ferroelectric phases. At the phase transition from S*C to S*I, all material parameters determined showed a discontinuous change, giving evidence for a first order transition. At the transition from the S*1 to the S*F phase, the material parameters show only small, rather continuous changes.

Properties of higher-ordered ferroelectric liquid crystal phases of a homologous series

Dielectric Properties of Liquid Crystals Under High Pressure

We report the results of dielectnc studies on three ferroelectnc liquid crystals exhibiting the A-C* transition Two relaxation modes viz , the soft mode and the Goldstone mode have been observed in the frequency domain covered Careful measurements have allowed us to obsirve the soft mode relaxation in the C* phase, even in'the absence ofa bias field, over a larger temperature range than in any previous study The results are discussed in the light of the predictions of the generahsed mean-field model 1. Inboduction. The temperature and frequency dependence of the complex dielectric constant of ferrielectnc liquid crystals has been siudied quite extensively~[1-4]. The results of these studies may be briefly summansed as follows When the sample is cooled the'loW frequency static dielectric constant increases steeply as the temperature approaches the smectic A-smectic C* (A-C*) transition and reaches a broad maximum a few degrees below the transition point (T~). The dispersion regtme\"exhibits tWo'important relaxation modes, viz., the Goldstone mode and the soft~ mode The former, appearing only in the C* phase, owes its existence to the presence of phase (or azimuthal) fluctuations of the tilt order parameter. The latter is due to the amplitude fluctuations of the tilt angle and exists, in the absence of any bias field, only very close to the transition. Most of these studies have been done on compounds having low spontaneous polansation (P~). In order to study the effect of the magnitude of P~ on dielectric properties, We have carried out static and dispersion studies on materials Which are structurally similar, but exhibit Varying magnitudes of P~. The results are discussed in the light of the predictions of the generalised Landau model [4-6]. The effect of bias field on the soft mode relaxation is also studied 2. Experimental. The structural formulae and phase transition temperatures of the substances [7] investigated for convenience referred to as I, II and III are given below. 172 JOURNAL DE PHYSIQUE II N 2 The P~ values measured [8] at T~-10 °C are 500 ~CC/m2, 720 ~CC/m2 and 370 ~CC/m2 for I, II and III respectively. Cl CH3 C~H~~O~hCH=CHCOO§OOC(H(HCH?CH3 CompoUnd 615 C* 68 5 A 88 0 CH 950 Cl CH3 IOH~~O~hCH=CHCOO~OOC(HCH?~HCH3 CompoUnd Ii 690 C* 78 0 A 92 5 Cl CH3 C~~H?30~hCH=CH COO ~ COOCH2 H H CH2CH3 CompoUnd III * * K 62 5 C* 68 5 A 88 0 The preparation of the sample cell (typical thickness ~ 20 ~cm) has been descnbed in an earlier paper [8] The ITO treated glass plates Were coated with a polymer solution and rubbed unidirectionally to get planar onentation of the molecules The samples Were aligned by cooling from the isotropic phase at a slow rate (~ l °C/h) and the alignment was checked by optical microscopy The capacitance and the dielectric loss were measured using an Impedance Analyser ~HP4192A). During any dispersion measurement the temperature of the cell was maintained to a cinstancy of ± 5i1~K The data acquisition was handled by a microcomputer which was also used for storage and analysis of the data. 3. Results and discussion. As mentioned earlier, in the C* phase onentational fluctuations of the director gtve nse to two relaxation modes, the Goldstone and soft modes Thus the complex dielectric constant can be written as Ae~ A~S + e~ (I) ~~~f) \" ~'~~~~ ~ l + of/fG)~~~~~ l + bf/fS)~~~~ where f~_ and f~ are the Goldstone and soft mode relaxation frequencies, Ae~ and Ae~ their respective strengths, e' and e\" are the real and imaginary parts and e~ represents the sum of the dielectric strengths of all other high frequency modes, h is the distnbution parameter of the mode. In the A phase the amplitude and phase fluctuations are degenerate and hence only the second and third terms on the right hand side of equation (I) remain Before presenting the results of our expenments, it may be relevant to recall some of the predictions Of the generalised Landau model [5] A phase ~2 ~2 Ass ~ 2 2 (2) a (TT~) + (K~ ep ) qo fs = ~ la (T T~) + (K~ ep 2) qjj (3) Is Ass = ~ /~ E~ C~ (4) N 2 DIELECTRIC STUDIES OF GOLDSTONE MODE AND SOFT MODE 173 C* phase neglecting the ep2 term, p 2 ~~~ 2K~ q8 '~~~ K~ ~ ~~ 2 aryi ~ ~~~ i p 2 fG AEG = ~ ~~ ~ (?) where the subscripts s and G denote soft mode and Goldstone mode respectively f and he are the relaxation frequency and dielectnc strengths of the mode, K~ is the elastic constant, e represents the high temperature dielectric susceptibility, p and C are the coefficients of the flexoelectnc and piezoelectnc bilinear coupling, a is the coefficient of the temperature dependent term in the Landau expansion, P, 8 and q are respectively the polansation, tilt angle and inverse pitch in the C* phase, and qo = q at T~ yi represents the rotational viscosity of the modes. The experimental data of (e*(f), f) was fitted to equation (I) using a non-linear least square technique by varying the parameters Ae~, e~, f~ and h~ (here i represents different modes Golflstone and soft mode) [9] The distribution parameter h, was found to be small (= 0,I Figure la-c shows Cole-Cole diagrams, for the compound II figure la in the A phase, figure16 in the C* phase close to T~ and figure lc in the C* phase away from T~ Plots in figure la and lc exhibit single relaxation behaviour and are due to soft mode and Goldstone modes respectively But figure16 shows the presence of relaxations due to both the modes Normally it is very difficult to resolve the soft mode from the Goldstone mode because as seen in these figures the strength of the former is small compared to the latter. Also~ as will be discussed later, the strength of the soft mode rapidly decreases as T~ T( is increased However owing to the large polarization in compound I we have been able to resolve the two over a temperature range of 0.8 °C in the C* phase For the same reason the soft mode could be studied up to 3 °C above the transition. In fact, this point is quite clear when we note that for the three materials these ranges are 0.8, 3 0 for1, 0 5, 5 for II and 0 07, 0 5 for III respectively Temperature variation of the soft mode dielectric strength ind relaxation frequency are plotted m figures 2-4 The salient features seen are (i) f~ decreases linearly with reduced temperature (TT~), the value of f~ at T~~fo) is considerably different for different materials ~fo)~~ (fo)jj~-(fo)nj. (ii) the inverse dielectric strength llie~, unlike f~, is non-linear in the A phase, indeed it appears to have a power-law behavlour, but has a linear temperature dependence in the C* phase Most of the earlier experiments have also shown the linear behaviour of f~, but only a few observations of non-linear variation of I/Ae~ exist From equation (2j we see that I/Ae~ will linearly decrease with temperature only if temperature dependence of the piezoelectnc coefficient C, elastic constant K~ and the flexoelectnc term p~ are negligible Experimentally it is known that the value of the piezoelectnc coefficient C remains constant in the A phase in materials possessing low as well as high polarization [10] Thus one possible explanation for a non-linear vanation of I/Ae~ could be that the twist to piezo energy ratio may be changing with temperature ~'Afe will see later that this is true in the C* phase ) But if the ratio of elastic to viscosity terms is weakly temperature dependent ill ], then only the term (a (T T~)/2 ar y i ) will influence the thermal variation of f~. This could be the reason for the linear behavlour of f~. Multiplying equations (2) and (3) to el1mlnate the elastic term, we get equation (4). Based on the arguments presented above we can expect the product AeJ~ to be non-linear only in the immediate prox1mlty of the transition Thls is indeed the expenmental behaviour as seen in 174 JOURNAL DE PHYSIQUE II N 2 20 T-Tc = -0.12°C (b) ~ (a) T-Tc = ° °8° C ~~ o.ikHz ~ii ~° i0kHz 11 ~ ° ~_~ __~~~o~ 45 90 15 C~

Dielectric studies of Goldstone mode and soft mode in the vicinity of the A-C* transition

Several methods have been employed to determine the rotational viscosity γφ in the smectic C* phase associated with the molecular motion around the cone about the layer normal. We have measured this parameter using four different techniques and show that the values are in good agreement with each other. We have also studied the effect of chain length on γφ in the C* phase and γφ the viscosity associated with tilt angle fluctuations, in the A phase. The results suggest that the activation energy associated with these motions is basically controlled by the rigid core and not by the chain length of the molecule.

Measurement of rotational viscosity in the Smectic Cphase

In contrast to the wealth of data available on ferroelectric liquid crystals at atmospheric pressure, only a few reports of studies at high pressure exist. We have undertaken systematic high pressure studies of the properties of these materials. In this paper the results of detailed measurements of spontaneous polarisation and transverse static dielectric constant as functions of pressure for two different compounds exhibiting low and high values of polarisation are presented.

High pressure studies on ferroelectric liquid crystals

We report here the results of systematic measurements of spontaneous polarization and rotational viscosity on four structurally related homologous series derived from trans-p-n-alkoxycinnamic acids. The influence of alkyl chain length on the magnitude and temperature dependence of the polarization, and the effect of subtle structural changes on the rotational viscosity are discussed.

Spontaneous polarization and rotational viscosity measurements on ferroelectric liquid crystals derived from trans-p-n-alkoxycinnamic acids

We have studied the soft mode and Goldstone mode relaxations in a ferroelectric liquid crystal compound (referred to as C6 for short) exhibiting a high value of spontaneous polarisation. The results show that the relaxation frequency fs as well as the dielectric strength Δϵ S can be described by a simple power law, but gives non-mean field exponents. However, fitting done to the Δϵ s data using an expression given by the generalised mean field theory, not only yields the mean field susceptibility exponent γ but also helps in determining the Landau coefficients a and C (where a is the electroclinic coefficient and C the polarisation-tilt coupling constant) as well as the soft mode viscosity. We also present the Goldstone mode viscosity and the relevant elastic torque data. Measurements on C7 and C8, the higher homologs of C6, bring out the effect of chain length on the relaxation parameters.

B. Shivkumar

Papers

Dielectric studies of Goldstone mode and soft mode in the vicinity of the A-C* transition

Measurement of rotational viscosity in the Smectic Cphase

High pressure studies on ferroelectric liquid crystals

Spontaneous polarization and rotational viscosity measurements on ferroelectric liquid crystals derived from trans-p-n-alkoxycinnamic acids

Dielectric studies in the vicinity of the A-C* transition