Dielectric Relaxation in Nematics

In a dielectric relaxation experiment, the linear response of a sample to an oscilating and spatially uniform q=0) electric field is measured. The bulk nematic (non-polar) collective excitations with a nonzero wave-vector q thus cannot contribute to the linear response of a nematic. The exception is here a trivial coupling of an external electric field to the =0 (Goldstone) mode, which represents an uniform rotation of a sample as a whole and is as well non-polar. This leads to the conclusion that the dielectric relaxation experiment will measure the response of individual nematic molecules to an applied electric Beld. Similar to the case of an isotropic liquid, the relaxation rates of the individual molecular motion are expected to be observed in the 100 MHz to GHz frequency region. 

The influence of individual molecular motion on the dielectric relaxation was first considered by Martin, Meier and Saupe [154]. Whereas the onset of the nematic ordering will not drastically influence the rotation around the long molecular axis, the motion around the short molecular axis will be strongly hindered by the nematic order. As a result, we expect four dielectric relaxation mechanisms (see [155]). These are the relaxations of a /tj dipole moment along the long molecuar axis in a direction (1) around the nematic director and (2) perpendicular to the nematic director as well as the relaxations of a H2 dipole moment perpendicular to the long axis, in a direction (3) around 

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Our calculations show that to achieve good accuracy with Eqs. (4.233) and (4.234) in a wide range of temperature and frequency variations, it is necessary to retain at least five (odd k= 1, 3,..., 9) lower modes of the spectrum. We remark that the first three relaxational modes have once been evaluated both numerically [109] and analytically [82] in studies of dielectric relaxation in nematic liquid crystals, where the forms of the potential and of the basic equation coincide with those given by our Eqs. (4.224) and (4.225), respectively. 

Basically the experimental observations of dielectric relaxation in nematics are consistent with Fig.7.14. There are three characteristic modes the rotation of molecules about short molecular axes (the lowest frequency (0i 10 Hz) the precession of long molecular axes about the director n (the middle frequency 2 10 Hz) and the fast rotation of molecules about long molecular axes (the highest frequency 0)3 10 Hz) [6]. The corresponding dielectric spectra are shown in Fig.7.15. The most striking feature is strong retardation of the permittivity component parallel to the director, i.e. S -relaxation, Ty = (DJ" = j Xiso (retardation... 

M. Schadt, Low frequency dielectric relaxation in nematic and dual frequency addressing of field effect. Mol Cryst. Liq. Cryst. 89, 77 (1982). 

The dielectric relaxation in nematics can be conveniently described by the so-called Cole-Cole equation for the complex dielectric constant e (to)... 

A. Axmann, Z. Naturforsch. 1965, 21a, 290. G. Meier, A. Saupe, Dielectric relaxation in nematic liquid crystals. Mol. Cryst. Liq. Cryst. 1966, 7,515-525. 

F. Rondelez, D. Diguets, G. Durand, Dielectric and resistivity measurements on nematic MBBA,Afo7. Cryst. Liq. Cryst. 1971, 15, 183. F. Rondelez, A. Mircea-Roussel, Dielectric relaxation in the radio frequency range for nematic MBBA, Mol. Cryst. Liq. Cryst. 1974,28, 173. 

Effects of Dielectric Relaxation on the Director and Thermal Dynamics 2. DIELECTRIC RESPONSE IN NEMATIC LIQUID CRYSTALS... 

Theories of dielectric relaxation in the nematic phase which considered particular models of the molecular dynamics have assumed the existence... 

To explain these results, Moscicki proposed a qualitative model of the dielectric relaxation in lyotropic LCPs. A main feature of the model was the assumption that each rod can only undergo spatially restricted rotations (hopping between cages) around the nematic director. To rationalize this situation, the theory of small-step rotational diffusion in a was applied, i.e. it was assumed that the free space available... 

A detailed comparative study of dielectric behaviour of smectic and nematic polymers was carried out for polymers of acrylic and methacrylic series, containing identical cyanbiphenyl groups (polymers XI and XII) 137 138>. The difference in structural organization of these polymers consists in a more perfect layer packing of smectic polymer XI (see Chaps. 4.1 and 4.2) with antiparallel orientation of CN-dipoles. This shifts the relaxation process of CN-dipole reorientation to a low frequency region compared to nematic polymer XII. Identification of Arrhenius plots for dielectric relaxation frequencies fR shows that for a smectic polymer the value of fR is a couple of orders lower than for a nematic polymer (Fig. 21). Though the values... 

This chapter is concerned with experimental measurements of flexo-electric coefficients. After a brief introduction to flexoelectricity in nematic liquid crystaJs, some applications exploiting the flexoelectric effect and the influence of this effect on electrohydrodynamic instabilities are pointed out. Flexoelectricity axises in samples with a splay-bend distortion in the director field and as such its measurement is not as direct as for dielectric constants. The theoretical background needed to analyse electro-optic experiments and extract the flexocoefficients is outlined in Section 2.2. Various experimental techniques that have been developed are described in Section 2.3. These involve cells in which the alignment of the nematic director is homeotropic, or planar or hybrid. In the first case, the interdigitated electrode technique is particularly noteworthy, as it has been used to establish several features of flexoelectricity (1) the effect can arise purely from the quadrupolar nature of the medium, and (2) the dipolar contribution relaxes at a relatively low frequency. 

The effect of dielectric relaxation on the frequency dependence of conductivity was already mentioned above. Its experimental confirmation is demonstrated in Fig. 2.8 [9]. The low-frequency conductivity of nematics measured at a relatively weak electric field a c is usually higher for the direction parallel to the director, a, > CTx [18]. 

The alkylcyanobiphenyls are specially suited for the investigation of the dielectric relaxation because the two main modes of dipole relaxation are well separated. The hindered rotation about the short molecular axis is shifted to relatively low frequencies conveniently accessible in impedance bridge measurements. This relaxation process is coupled to the strength of the nematic potential q, which should be sensitive to a variation of the intermolecular distance. Hence a strong pressure dependence is expected for this relaxation process. 

The solutions to the anisotropic diffusion equation can be written as a series expansion, each term of which can be associated with a particular relaxation time. For a harmonic perturbation of the rotational distribution function, as occurs in a dielectric relaxation experiment with an ac electric field, it was found that a single relaxation time was sufficient to describe the relaxation of p, and this could be expressed in terms of the relaxation time Xq) for in the absence of a nematic potential by ... 

In the study of dielectric relaxation, temperature is an important variable, and it is observed that relaxation times decrease as the temperature increases. In Debye s model for the rotational diffusion of dipoles, the temperature dependence of the relaxation is determined by the diffusion constant or microscopic viscosity. For liquid crystals the nematic ordering potential contributes to rotational relaxation, and the temperature dependence of the order parameter influences the retardation factors. If rotational diffusion is an activated process, then it is appropriate to use an Arrhenius equation for the relaxation times ... 

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