Low-frequency permittivities

E,o and are the low- and high-frequency values of the permittivity for the relaxation process with relaxation time t,. The static permittivity is equal to the low- frequency permittivity for the first relaxation process Sjo. In addition, the high-frequency permittivity for the th relaxation is equal to the low-frequency permittivity for the (i + l)th relaxation Ep+po- Thus, for a liquid having n relaxation processes, there are n values of e,o which must be specified together with n different relaxation times, t, and finally the high-frequency permittivity for the last relaxation process, e oq. 

Figure 4 shows typical variations of the dielectric relaxation with water content as recorded along a line stretched across I( /o) and directed towards the 100% water vertex of the pseudo-ternary phase diagram, that is for systems characterized with a fixed ratio of combined surface-active agents to hexadecane and enriched gradually with water. While dielectric relaxation phenomena are hardly detectable at low water contents, systems characterized with higher water contents exhibit striking dielectric relaxations, the dielectric increment (e - e ) increasing drastically as p approaches the critical value corresponding to the transparent-to-turbid transition. The increase in (G - e ) results from the drastic increase in the low frequency permittivity whose variations with p are plotted in Figure 5a. While at low water contents, increases slowly and almost linearly with p, it displays a divergent behavior in the vicinity of the border line F. Simi-...

Fig. 5. Variations of the low frequency permittivity and conductivity observed upon increasing water content in water-in-hexadecane systems. Specifications identical to those of Figure 4. (a) versus p curve (b) versus...

Fig. 7. Variations of the low frequency permittivity with increasing water mass fraction in water-hexadecane systems using potassium oleate and 1-hexanol combined with the mass ratio 3/5, for different values of p, the hexa-decane mass fraction. Temperature T = 25°C.

Applying an electric field reduces the thermal fluctuations and hence light scattering.Therefore, tj could be raised by increasing The applied electric field introduces an energy term E Ae/2, where Ac is the low-frequency permittivity anisotropy. This term is added to... 

The decreases in permittivity when ions are added to a polar solvent were traditionally interpreted in terms of saturation or solvation of local ionic environments (76) until Hubbard and Onsager (77) (78) worked out a continuum theory of the kinetic depolarization effect. This arises from the fact that part of the electric field solvent dipoles near an ion is from the moving ion and similarly for the ion in the field of reorienting dipoles with the consequences that both responses are delayed in proportion to the relaxation time of the solvent polarization. The remarkably simple Hubbard-Onsager expression for the resulting decrement of static (or better limiting low frequency) permittivity can be written... 

The reduced symmetry of chiral phases results in additional contributions to the low frequency permittivity. Tilted chiral phases such as smectic C, F and I lack a centre of symmetry, and it is possible for these materials to be ferroelectric. The resulting spontaneous polarization is directed along the C2 symmetry axis, and is perpendicular to the tilt plane it also depends di-... 

The theory of the dielectric properties of chiral smectic liquid crystals is far from complete, particularly with respect to a molecular statistical approach. Simple Landau theory [31 ] gives expressions for the contributions of soft modes (jj g) and Goldstone modes (Xo) to the low frequency permittivity as ... 

The Debye circuit has been described in the dielectric literature using the complex permittivity notation. The circuit serves as an expression for a "single dielectric relaxation" system, where transition occurs from high-frequency permittivity (or in this example capacitance Cj) to low-frequency permittivity Eij. (capacitance C,). As was shown above, in the Debye circuit the response is completely capacitive at high- and low-frequency extremes, making e = e (real permittivity) for both e and ,j. = -Ae (Section 1-2). 

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