Dielectric relaxation frequency

The dramatic slowing down of molecular motions is seen explicitly in a vast area of different probes of liquid local structures. Slow motion is evident in viscosity, dielectric relaxation, frequency-dependent ionic conductance, and in the speed of crystallization itself. In all cases, the temperature dependence of the generic relaxation time obeys to a reasonable, but not perfect, approximation the empirical Vogel-Fulcher law ... 

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... 

Physical Mechanisms. The simplest interpretation of these results is that the transport coefficients, other than the thermal conductivity, of the water are decreased by the hydration interaction. The changes in these transport properties are correlated the microemulsion with compositional phase volume 0.4 (i.e. 60% water) exhibits a mean dielectric relaxation frequency one-half that of the pure liquid water, and ionic conductivity and water selfdiffusion coefficient one half that of the bulk liquid. In bulk solutions, the dielectric relaxation frequency, ionic conductivity, and self-diffusion coefficient are all inversely proportional to the viscosity there is no such relation for the thermal conductivity. The transport properties of the microemulsions thus vary as expected from simple changes in "viscosity" of the aqueous phase. (This is quite different from the bulk viscosity of the microemulsion.)... 

Interestingly, it had been suggested that the dispersion interaction energy between the solute and the solvent eould be accounted for, in principle, in the framework of this approach as related to the full distribution of dielectric relaxation frequencies of the solvent. Thus, the formula for the MC SCRF solvation energy has been expressed as follows... 

The dielectric relaxation frequency (/,) of 5CB at room temperature is in the order of 10 Hz [43], whereas/c of the neat LCE (without solvent) corresponding to SNE-7 (unpublished results from this laboratory) and/c of an uncross-linked side-chain EC polymer with the similar mesogen [44] are in the order of 10 Hz at 70°C (above the glass transition temperatures of ca. 50°C). The significantly lower values of /c for the neat LCE and the side-chain EC polymers are due to the constraint effect of the network and polymer backbone on the motion of the dangling... 

Fig. 2.3 The splitting of the peak dielectric relaxation frequency of a chlorobenzene/cis-decalin mixture into two separate relaxations. Figure reproduced from Debenedetti and Stillinger [15], Reprinted by permission from Macmillan Publishers Ltd ...

The conductivity of one-dimensional metal complexes has been reviewed. The influence of structure is emphasized, as are the interesting structural changes which occur when the fractional oxidation state is varied. Measurements of dielectric relaxation frequency have been used to obtain ac and dc conductivities, the latter of which lead to the rate of hopping ( site-transfer ) conductivity. In the double salt K3(Mn04)2, these data give the rate of the outer-sphere electron transfer reaction (35). A... 

The relaxation time constant 0 would also influence the parameter A, finally p substantially. From either Eq.(73) and (75), one will find that p increases as 0 increases, that is, the ER effect will be stronger if the dielectric relaxation is slower. However, too slow relaxation time (tlien the slow response time) would make FR fluids useless. Generally, the FR response time around 1 millisecond is favorable, thus requiring the relaxation time be of the same time scale, i.e., the dielectric relaxation frequency around lO llz. Block presumably thought the polarization rate would be important in the ER response process, and too fast or too slow polarization is unfavorable to the ER effect [7J. Ikazaki and Kawai experimentally found that the FR fluids of the relaxation frequencies within the range 100-10 Hz would exhibit a large ER effect [21,31], supporting the derivation from Eq. (69). 

Changes in the dielectric relaxation frequency at the SmA-SmB transition have also been reported to correlate with the appearance of a librational peak, suggesting a hardening of the potential [78]. 

Figure 20. Dielectric relaxation frequencies of the solute A-D as function of the length-to-width relation r (thereby the flexible alkyl chain was neglected), T=313 K tl5 ].

Figure21. Dielectric relaxation frequencies of a mixture with high glass temperature for the parallel direction. The conductivity was only given for 2, the second high frequency relaxation only for 1. 1 315.6 K, 2 331.1 K, 3 339.2K, 4 346.5 K, 5 351.6 K, 6 359.6 K [14].

Figure 33. Dielectric relaxation frequencies of the mixtures at different concentrations [159].

Fig. 1—Field effect (lateral electrode geometry). The change in optical orientation properties with frequency is a result of changing field penetration. The dielectric relaxation frequency is 80 Hz. This material of positive dielectric anisotropy does not show any turbulent flow (R.A. SoreP).

In the storage effect/ on the other hand, a write mode is obtained below the dielectric relaxation frequency. This is a hydrodynamically produced turbulent flow that disturbs the (cholesteric) order. An erase mode is produced at high frequencies, where the ordered structure is restored by dielectric reorientation forces. 

Fig. 4—Retardation as a function of voltage. The continuing reorientation of the structure (left side) with increasing voltage results in an ever increasing retardation, i.e., birefringence. The retardation A0 continues to increase unless another electro-optic regime ensues viz, below the dielectric relaxation frequency, domains, and above, chevron distorions (M. Hareng, et al ).

At frequencies above the dielectric relaxation frequency, another diffraction with a threshold makes its appearance (see Fig. 4). This is the chevron regime, which is not hydrodynamic in origin but depends on interaction between the anisotropic dielectric properties of the fluid and the field. It represents a sinusoidal modulation of the... 

Measurements of conductance are usually made using alternating voltage of a frequency that falls between the dielectric relaxation frequency (see Ref. 1, Chap. 4, Sec. 1), above which ions cannot contribute to the current, and the inverse transit time, below which, as will be seen later, there are complications due to polarization of the electrodes. 

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