Ferromagnetic Liquid Crystals

Liquid crystals are stable only over limited temperature ranges. The degree of orientation decreases with increasing temperature. There is a critical temperature, Tc, at which s drops to zero, as shown in Figure 16.8. This is analogous to Curie temperature, 7 in ferromagnetic materials, at which the material ceases to be ferromagnetic. 

Unlike ferromagnets, where G((p) = G(-(f), the free energy of nematic liquid crystals exhibits an asymmetry G(S) G(-5), as discussed previously and shown in Fig. 3b. To reproduce this behavior, a term that is an odd power of the order parameter S is needed in the Landau expression for the free energy of a nematic liquid crystal. A term linear in 5 is not allowed since the equilibrium condition dQdS = 0 could not then be satisfied in the disordered isotropic phase where 5=0. The presence of a cubic term will lead to the desired asymmetry in G as a function of 5 and to the emergence on cooling of a second minimum in G at a finite 5 value. 

It is demonstrated in [8] that the transport coefficients (thermal diffusivity, diffusion coefficient, fluidity, etc.) considered in the Fourier approximation are proportional to the stability coefficients. This makes it possible to determine whether we are dealing with a critical transition or a limited phase transition of the second kind and, in the latter case, which of the parameters are characteristic. In critical transitions, the transport coefficients decrease strongly, whereas in limited transitions of the second kind they tend to infinite values. This criterion shows that phase transitions of the second kind which occur in binary alloys, polymers, ferromagnets, ferroelectrics, liquid crystals, etc., are essentially transcritical transitions, which are sometimes close to the critical conditions because the values of the transport coefficients decrease strongly at the transition point. The occurrence of superfluidity in He H demonstrates that, even in the absence of a coordinate or a derivative which tends to zero, this substance is a superphase in the kinetic sense. 

The hydrodynamic description of complex condensed matter systems like superfluids, ferromagnets, polymeric solutions, etc. has been possible thanks to the deep understanding of the role played by the symmetries and thermodynamic properties of the system (Kadanoff and Martin P.C. 1963, Hohenberg and Matin P.C., Kalatnikov 1. M. 1965). The extension of this linear hydrodynamic to liquid crystals has been started in the seventies, (Parodi 0.1970, Forster D. 1975), and in recent years it has been generalized to the nonlinear case and to more complex liquid crystal phases (Brand H. R. Pleiner H. J. 1980). 

The ferroelectric effect was discovered in 1920 by Valasek, who obtained hysteresis curves for Rochelle salt analogous to the B-H curves of ferromagnetism [5.5], and studied the electric hysteresis and piezoelectric response of the crystal in some detail [5.6]. For about 15 years thereafter, ferroelectricity was considered as a very specific property of Rochelle salt, until Busch and Scherrer discovered ferroelectricity in KH2PO4 and its sister crystals in 1935. During World War II, the anomalous dielectric properties of BaTiOs were discovered in ceramic specimens independently by Wainer and Solomon in the USA in 1942, by Ogawa in Japan in 1944, and by Wul and Goldman in Russia in 1946. Since then, many ferroelectrics have been discovered and research activity has rapidly increased. In recent decades, active studies have been made on ferroelectric liquid crystals and high polymers, after ferroelectricity had been considered as a characteristic property of solids for more than 50 years. 

Strong short-range orientational correlations can be conveniently taken into account in the cluster approximation. The simplest version of the cluster approximation in the theory of liquid crystals was proposed by Ypma et al. [26] who used the general approach of Callen and Strieb developed in the theory of ferromagnetism. 

Can liquids in which the constituents are dipoles be ferroelectric For instance, if we could make a colloidal solution of small particles of the ferroelectric BaTi03, would this liquid be ferroelectric The answer is no, it would not. It is true that such a liquid would have a very high value of dielectric susceptibility and we might call it superparaelec-tric in analogy with the designation often used for a colloidal solution of ferromagnetic particles, which likewise does not show any collective behavior. An isotropic liquid cannot have polarization in any direction, because every possible rotation is a symmetry operation and this of course is independent of whether the liquid lacks a center of inversion, is chiral, or not. Hence we have at least to diminish the symmetry and go to anisotropic liquids, that is, to liquid crystals, in order to examine an eventual appearance of pyroelectricity or ferroelectricity. To... 

A physical system in which phase transition(s) can occur is usually characterized by one or more long range order parameters (order parameter for short). For example, in nematic liquid crystals the order parameter is the quantity S = (P2(cos 0)) as defined in previous chapters " in ferromagnets the order parameter is the magnetization in a single domain and in liquid-gas systems the order parameter is the density difference between the liquid and gas phases. In each of the above cases the state of the system, at any fixed temperature, can be described by an equilibrium value of the order parameter and fluctuations about that value. A phase transition can be accompanied by either a continuous or a discontinuous change in the equilibrium value of the order parameter when the system transforms from one phase to the other. (For simplicity we will consider temperature as the only thermodynamic variable in this paper the pressure depedence of the various phenomena will be neglected). 

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