Time-dependent electric fields dielectric polarization

B. Dielectric Polarization in Time-Dependent Electric Fields... 

In dielectric spectroscopy the polarization response P(t) of a dipolar material is monitored, which is subject to a time-dependent electric field (Maxwell field), E t). For a linear and isotropic dielectric one can write (e.g., Ref. 34) ... 

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. 

The second approach to the approximate description of the dynamic solvation effects is based on the semiempirical account for the time-dependent electrical polarization of the medium in the field of the solute molecule. In this case, the statistical averaging over the solute-solvent intennolecular distances and configurations is presumed before the solution of the SchrOdinger equation for the solute and correspondingly, the solvent is described as a polarizable dielectric continuum. The respective electrostatic solvation energy of a solute molecule is given by the following equation[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... 

C. J. F. Bottcher and P. Bordewijk, Theory of Electric Polarization, Vol. II, Dielectric in Time-dependent Fields, Elsevier, Amsterdam, 1978. 

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. 

We now analyze a case where we have an instantaneous increase or a reduction of the electric field, E. This will lead to a polarization or depolarization process, which will follow with some delay or retardation due to the increase or reduction of the electric field, respectively. Consequently, in relation with a time-dependent variation of the electric field, E = E(t), the dielectric properties of the materials become dynamic events. In this regard, the time dependency of P = P(t) will not be the same as that of E = E (t), since the different polarization processes have different time delays, with respect to the appearance of the electric field. This delay is obviously related to the time-dependent behavior of the susceptibility % = %(t). 

Refs. [i] Bottcher CJF (1973) Theory of electric polarization Dielectrics in static fields, vol. 1. (1978) Dielectrics in time-dependent fields, vol. 2. Elsevier, Amsterdam [ii] Tide DR (2003) Dipole Moments. In Tide DR (ed) CRC handbook of chemistry and physics, 84til edn. CRC Press, Boca Raton, pp 9-42 - 9-51 [Hi] Miller TM (2003) Atomic and molecular polarizabilities. In Tide DR (ed) CRC handbook of chemistry and physics, 84th edn. CRC Press, Boca Raton, pp 10-163 -10-177 [ivJFred-erikse HPR (2003) Polarizabilities of atoms and ions in solids. In LideDR (ed) CRC handbook of chemistry and physics, 84til edn. CRC Press, Boca Raton, pp 12-17 -12-18... 

When an alternating electric field (a.c.) is applied across an insulator, a time dependent polarization current flow is induced. This is because the electrical charges present in the atoms and molecules in the material respond to the changing directions of the field. This is also referred to as dielectric response of the material. When the frequency of the applied field is well below the phonon frequencies, the dielectric polarization of the bound charges is instantaneous. Therefore, the dielectric constant, e (oo), characterizing the bound charge response, is frequency independent. The frequency dependent part of dielectric constant is by definition related to the frequency dependent conductivity, CT (co) as... 

When a polar solvent is placed in a changing electrical field, the molecules must realign so that their dipole vectors maintain the orientation corresponding to minimum energy. Because of intermolecular forces, this process does not occur infinitely fast but on a time scale which depends on the properties of the medium and which is usually on the order of 1-100 ps. Dielectric relaxation experiments provide very useful information about molecular motion in polar liquids and the ability of the solvent molecules to respond to changing electrical conditions. 

The dielectric permittivity of a medium (relative to the permittivity of free space, 8q = 8.85 X 10 F/m) is given by e and measures the polarization of the medium per unit applied electric field. The dielectric loss factor arises from energy loss during time-dependent polarization and bulk conduction. The loss factor is written as a". The loss tangent or dissipation of the medium, tan<5 is defined by e"/e. The orientation of molecular dipoles has a characteristic time r. Typically is short early in the cure but grows large at the end of the cure. 

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