Dielectric decay function

From Equation (3.14) the function vP (f), called the dielectric decay function, is given by... 

Williams, G., Watts, D. C. Non-symmetrical dielectric relaxation behavior arising from a simple empirical decay function, Trans. Farad. Soc., 66, 80 (1970)... 

When an external field is applied to a dielectric, polarization of the material reaches its equilibrium value, not instantaneously but rather over a period of time. By analogy, when the field is suddenly removed, the polarization decay caused by thermal motion follows the same law as the relaxation or decay function of dielectric polarization < >(t) ... 

Relaxation functions for fractal random walks are fundamental in the kinetics of complex systems such as liquid crystals, amorphous semiconductors and polymers, glass forming liquids, and so on [73]. Relaxation in these systems may deviate considerably from the exponential (Debye) pattern. An important task in dielectric relaxation of complex systems is to extend [74,75] the Debye theory of relaxation of polar molecules to fractional dynamics, so that empirical decay functions for example, the stretched exponential of Williams and Watts [76] may be justified in terms of continuous-time random walks. 

As indicated above, exponential relaxation does not generally provide a satisfactory description of experimental data. The response of dielectric materials is instead generally found to be characterized by certain power laws, both in the time and frequency domains (95,96). As observed by Curie and von Schweidler, a long time ago (97,98), the polarization current following the application of a constant electric field typically decays as a power function of time. The same is true for the dielectric response function, since it is proportional to the current oc l/t , where a is a positive constant. This response... 

Williams G, Watts DC, Dev SB, et al. Further considerations of non symmetrical dielectric relaxation behaviour arising from a simple empirical decay function. Trans Faraday Soc 1971 67 1323-1335. 

The SoSoo term corresponds to the instantaneous response of the material to the electric field, whereas the so(s,-8oo) (t) term is related to the slower response assigned to dipolar polarization, where the dielectric function 0(0 describes the temporal development of the dipole orientation. The decay function, < )(0=1-O(0, accoimts for the decrease of polarization after removing the electric field, ( )(0)=1 and < >(oo)=0. In the model of Debye the polarization process follows a first-order kinetics, where its time variation is proportional to the equilibrium value ... 

Here, P is the rapidly stored charge density normalized by the field intensity E P is contributed from the bare capacitor and the distortion of the electron cloud/chemical bonds. AP corresponds to the saturated orientation of dipoles at f = oo, and the factor 1 - (f) (= 0 and 1 at f = 0 and >) is the normalized dielectric retardahon funchon reflecting the molecular motion. The function (t) (= 1 and 0 at f = 0 and °°), referred to as the normalized dielectric relaxation function, is most straightforwardly related to the molecular motion, as explained later for Equation (3.21) (f) specifies the relaxation (or decay) of D(f) on removal of the electric field E after full saturation of the charge density see Figure 3.1c ... 

Williams G, Watts DC (1970) Non-symmetrical dielectric relaxation behavior arising from a simple empirical decay function. Trans Faraday Soc 66 80-85 Williams ML, Landel RR, Ferry ID (1955) The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids. J Am Chem Soc 77 3701-3707 Wood LA (1958) Glass transition temperatures of copolymers. J Polym Sci 28 319-330 Wu SH (1985) Phase structure and adhesion in polymer blends a criterion for rubber toughening. Polymer 26 1855-1863... 

Interfacial or Maxwell-Wagner polarization is a special mechanism of dielectric polarization caused by charge build-up at the interfaces of different phases, characterized by different permittivities and conductivities. The simplest model is the bilayer dielectric [1,2], (see Fig. 1.) where this mechanism can be described by a simple Debye response (exponential current decay). The effective dielectric parameters (unrelaxed and relaxed permittivities, relaxation time and static conductivity) of the bilayer dielectric are functions of the dielectric parameters and of the relative amount of the constituent phases ... 

G. Williams and D. C. Watts [1970] Non-Symmetiical Dielectric Relaxation Behavior Arising from a Simple Empirical Decay Function, Trans. Faraday Soc. 66, 80-85. 

Kerr-effect rise (step-on) and decay (step-off) transients for a rectangular pulse in E(t). Rosato and Williams (87-88) have deduced expressions for the rise and decay functions for the Kerr-effect and for dielectric relaxation for the more general case of a body undergoing reorientational motions (as for equation (19)). They show for a molecule having 2v symmetry that the Kerr-effect decay for the induced part is a weighted sum of correlation functions [Pg.259]

The major advantage of Eq. (208) is that parameters k and n are not involved in the calculation, though n is needed for calculating the dielectric constant. It should be noted that this transient dc current method is only valid for the frequency 10 to 0.1 Hz [I], The reason is obvious The dc current decay function is only valid in a certain time period. 

Moynihan C T, Boesch L P and Laberge N L (1973) Decay function for the electric field relaxation in vitreous ionic conductors, Phys Chem Glasses 14 122-125. Havrihak S Jr and Havriliak S J (1997) Dielectric and Mechanical Relaxation in Materials, Hanser, Munich. 

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