Electric polarization time-dependent dielectric constant

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) ... 

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... 

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... 

A time-dependent polarization P (0 due to the orientation of dipoles in the electric field. If the field remains in place for an infinitely long time, the resulting total polarization Pj defines the static dielectric constant e/. 

Whether CT is possible depends on the polarity of the solvent, as measured by the dielectric constant. There are essentially two important dielectric constants one for slow processes or the static dielectric constant (Cj) and the other for very fast processes (faster than any reorganization process), referred to as or the dielectric constant at infinite frequency. of a compound can be obtained by measuring the capacitance of a condensator where the compound is used as a dielectricum. is obtained by measuring molecular polarizability. The higher the frequency of the applied electric field, the slower are the motions in the medium to follow the variations in the field. For example, a water molecule has a certain rotation time and when the field frequency is too fast, the water molecule no longer moves with the field. When the frequencies applied correspond to UV frequencies, (for all practical purposes) is measured. One may show that = n, where n is the refractive index. 

The role of inherent polarization and ionic transport effects in actuation mechanism of EAPap actuators are investigated. To physically investigate the actuation mechanism, several tests are performed. X-ray diffraction (XRD) spectra are compared before and after electrical activation and the possibility of crystalline structure change is observed. Dielectric property measurement indicates a dependence of the dielectric constant on fiber direction, as well as on frequency, humidity, and temperature. Thus, we conclude that piezoelectric effect and ionic migration effect are in the EAPap at the same time associated with dipole moment of cellulose paper ingredients. The amount of these effects may depend on environmental condition. 

Molecules consisting of atoms with different values of the electronegativity are polar. The dipole moment of a chemical bonding is a vector and therefore, a compensation or increase of the bond moments in a molecule can be observed [1, 2], Furthermore, the overall dipole moment of a molecule depends on the life time of different conformations. By the dielectric method, only a very small orientation of the molecular dipoles and the time for its reorientation can be measured as static dielectric constant and relaxation time T, respectively. Thereby the static dielectric constant can be produced by switching off an external electrical field in different steps as demonstrated in Fig. 1. 

The permittivity discussed so far depends only on frequencies and, through the relaxation times, on the particle size. It is well-known that the dielectric response of materials, in particular metal, is non-local, i.e. the polarization vector induced at a certain point depends on the values of the electric field in all other points. In the reciprocal space language, we can say that e(plane-waves in which the probing electric field can be decomposed. The permittivity of metals such as Ag, Au and Cu at optical frequencies mainly depends on the behavior of both the valence electrons, which is close to that of a free-electron gas, and the core of the metal. As we did before, the total dielectric constant of the metal ([Pg.239]

A dipole in a cavity in a polarizable solvent will polarize the medium and create an electric field at its own position. The simplest model is that of a dipole ]1 at the center of a spherical cavity of radius a embedded in a dielectric. We already encountered its results in Section 9.5. The way Nee and Zwanzig [16] came to their results is as follows Outside the cavity there is a dielectric with dielectric constant c (o)), and inside the cavity we assume only electronic polarization C or vacuum (fj = 1). The frequency dependence of the outside dielectric constant derives from the fact that the molecules in the solvent can rotate to change the polarization. This rotation is diffusional, so the dipoles need time to adjust to a new situation. This does not have an effect on the solution of the boundary value problem. At the boundary, the usual boundary conditions apply the transverse component of the electric field is continuous, as is the normal component of the displacement field. Using these boundary conditions, it is possible to find the fields inside and outside the cavity. Solving this problem gives the electric and displacement fields inside and outside the cavity. The important field is the field created by the outside polarization inside the cavity, the so-called Onsager reaction field [23] E ... 

As already mentioned, each of the contributing parts of the electric polarization corresponds to motions of different microscopic species. In order to observe each of these motions, the experimental time available for the observation must be correlated with the speed of the motion under study. Therefore, as a consequence of different timescales of the motions, the frequency dependence of (cu) features different dispersion regions, as shown schematically in Fig. 4.1. If the frequency is sufficiently low, all contributions to polarization have enough time to build up and the net polarization is in equilibrium with the electric field. s oj) is then equal to the static dielectric constant Sq, and s"(a)) = 0. 

Orientational polarization is not a resonant process since the molecular dipoles have inertia. The response of the orientational polarization to a charge of the electric field is, therefore, always retarded. This process is called dielectric relaxation. The characteristic time constant of such a relaxation process—this is the time for reaching new equilibrium after changing the excitation—is called relaxation time (r). It is strongly temperature dependent, since it is closely related to the viscosity of the material. At room temperature, the relaxation times of the orientational polarization in crystals are of 10 -10 s. In amorphous solids and polymers, however, they can reach a few seconds or even hours, days, and years, depending on the temperature. 

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