Dielectric relaxation time-dependent electric field

For small electric field strength, the dielectric relaxation can he described in the framework of the linear response theoiy (Landau and Lifschitz 1979). The relevant materials equation which links the time-dependent polarization P(t) with the time-dependent electric field E(t) is given by (Schonhals and... 

Dielectric relaxation means the adjustment of dielectric displacement (D) or polarization ( ) to the time-dependent electrical field (E). Relative permittivity (e) characterizes the capacitance ratio of a condenser filled with an insulating material and with vacuum. If the field is sinusoidal, the permittivity becomes a complex number ... 

On the contrary, when the time-dependent electric field varies on a time scale faster than the relaxation time of one or more molecular degrees of freedom there is not time to reach at any moment a time-dependent polarization which is in equilibrium with the electric field. In this regime, which is called non-equilibrium polarization, the actual value of polarization will also depend values of the electric field at previous time, and the relation between the polarization of a dielectric medium and the time-dependent polarizing field is phenomenologically described in terms of the whole specuiim of the dielectric permittivity as a function of the frequency co of the oscillating electric field. 

There are several complications in using this technique for a-Si H, first of which is the frequency dependence. The capacitance is measured by the response to a small alternating applied electric field. The depletion layer capacitance is obtained only when the free carriers within the bulk of the semiconductor can respond at the frequency of the applied field, dielectric relaxation time. 

V. The curves in Figure 1 were calculated by using the static value of the dielectric constant for each liquid. However, the dielectric constant of a medium is time dependent, because it requires a certain amount of time for the medium to attain its new polarization equilibrium after the sudden application of an electric field. In a polar liquid the permanent molecular dipoles require a certain time to rotate to line up with the electric field. When the value of tgn is in the vicinity of or smaller than that of the dielectric relaxation time t of the liquid—i.e., when tgn S 10t,— then a time-averaged complex dielectric constant should be used in Equations II, IV, and V. At a time t after the instantaneous application of a d.c. electric field, the dielectric constant of the medium in the field is given approximately by... 

At 2450 MHz, the field oscillates 4.9 x 10 times per second and sympathetic agitation of the molecules generates heat. The quantity of heat produced by dipole rotation is dictated by the dielectric relaxation time of the sample, which in turn, is affected by temperature and viscosity. Ionic conduction on the other hand, occurs by migration of dissolved ions with the oscillating electric field. Heat is generated by frictional losses that depend on the size, charge and conductivity of the ions and on their interactions with the solvent. 

Na = Avogadro s number = 6.02x10 /mole D(t) = the time dependent electric displacement E(t) = corresponding electric field t = dielectric relaxation time. 

Under a changing electric field, a dielectric adjusts its properties over a certain period of time. Because of a finite speed of this dielectric relaxation process, the electric displacement D(f) depends not only on the current electric field E(f) but also the past electric field E(f ), where -oo electric field is not very strong, then D(r) can be represented using the superposition rule [13],... 

Relaxation processes are probably the most important of the interactions between electric fields and matter. Debye [6] extended the Langevin theory of dipole orientation in a constant field to the case of a varying field. He showed that the Boltzmann factor of the Langevin theory becomes a time-dependent weighting factor. When a steady electric field is applied to a dielectric the distortion polarization, PDisior, will be established very quickly - we can say instantaneously compared with time intervals of interest. But the remaining dipolar part of the polarization (orientation polarization, Porient) takes time to reach its equilibrium value. When the polarization becomes complex, the permittivity must also become complex, as shown by Eq. (5) ... 

Dielectric relaxation study is a powerful technique for obtaining molecular dipolar relaxation as a function of temperature and frequency. By studying the relaxation spectra, the intermolecular cooperative motion and hindered dipolar rotation can be deduced. Due to the presence of an electric field, the composites undergo ionic, interfacial, and dipole polarization, and this polarization mechanism largely depends on the time scales and length scales. As a result, this technique allowed us to shed light on the dynamics of the macromolecular chains of the rubber matrix. The temperature as well as the frequency window can also be varied over a wide... 

This longitudinal relaxation time differs from the usual Debye relaxation time by a factor which depends on the static and optical dielectric constants of the solvent this is based on the fact that the first solvent shell is subjected to the unscreened electric field of the ionic or dipolar solute molecule, whereas in a macroscopic measurement the external field is reduced by the screening effect of the dielectric [73]. 

The objective of this monograph is to describe and interpret the time dependence of the electrical response of dielectrics. Interpretation is difficult because the observable relationship between polarization and field is simple in the cases relevant for dielectric relaxation and because the measurements have relatively little information content. The response of the dielectric can be described by a set of linear differential equations and many models can be described which correspond to the same differential equations. When the dielectric relaxation of a given material has been measured the investigator is in the position of a man presented with a black box which has two terminals. He may apply alternating fields of various kinds and he may heat the box but he is not allowed to look inside. And he finds that the box behaves as if it contained a combination of capacitors and resistors. 

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