Dielectric relaxation static electric fields

Now we consider an experiment in which a static electric field is suddenly applied to a dilute polypeptide solution. If the rates of interconversions between helix and random-coil units are much faster than those of rotational motions of the entire dissolved polymer molecule as well as of local segments of it, there will be an increase in the dielectric constant which approaches a constant value (ds)ch with time t. This relaxation process is a kind of chemical relaxation, because the helix-coil interconversions responsible for it may be regarded as chemical reactions. Its detailed study should provide information about such elementary processes as those illustrated in Eqs. (E-13) and (E-15). This is Schwarz s basic idea. 

In this section, a simple description of the dielectric polarization process is provided, and later to describe dielectric relaxation processes, the polarization mechanisms of materials produced by macroscopic static electric fields are analyzed. The relation between the macroscopic electric response and microscopic properties such as electronic, ionic, orientational, and hopping charge polarizabilities is very complex and is out of the scope of this book. This problem was successfully treated by Lorentz. He established that a remarkable improvement of the obtained results can be obtained at all frequencies by proposing the existence of a local field, which diverges from the macroscopic electric field by a correction factor, the Lorentz local-field factor [27],... 

As shown in Figure 11.1, to obtain a complex TSC spectrum, a static electric field E is applied to the sample at a polarization temperature labeled Tp for a time tp, which is necessary to obtain polarization saturation, i.e., the equilibrium polarization. Afterward, the sample is cooled down to a temperature T0 in such a way that the dielectric relaxation proceeds extremely slowly, so that after removal of the field the sample retains a frozen-in polarization. The depolarization current, Id, caused by the return to equilibrium of dipolar units, is then recorded by increasing the temperature at a constant rate from T0 up to the final temperature Tf, where Tf > Tp. The plot of Id as a function of temperature is a complex TSC spectrum. 

Since 1875, thanks to Kerr s discovery [ 1], it is known that a static electric field can induce a modification of the optical properties of a liquid. Many years later researchers found out that also an optical electromagnetic field was capable of producing a measurable modification of the dielectric properties, inducing a hirefiringence effect the first experimental observation of the optical Ken-effect (OKE) was reported in 1963 [2]. After few years, with the introduction of the first pulsed lasers, spectroscopists discovered the chance to induce in a material a transient birefringence and to measure its relaxation toward the equiUhrium [3]. They also realized that this could be a relevant new spectroscopic tool able to collect new information on the dynamical processes present in the material. The spectroscopic research, worked out in the following years, confirmed this forecast beyond the expectations. Two important experimental improvements of this spectroscopic technique have been made. On one hand, the pulsed laser sources have become able to produce very short pulses of high... 

The dielectric constant (permittivity) tabulated is the relative dielectric constant, which is the ratio of the actual electric displacement to the electric field strength when an external field is applied to the substance, which is the ratio of the actual dielectric constant to the dielectric constant of a vacuum. The table gives the static dielectric constant e, measured in static fields or at relatively low frequencies where no relaxation effects occur. 

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]. 

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... 

Notably, the use of the macroscopic dielectric constant s = Sq in the last formula is justified only when the lifetime of the solute molecule in a given (v-th) state is much longer than the rotational-vibrational relaxation time of the solvent at given temperature. This is not a valid assumption in the case of the Franck-Condon states, which have the lifetime much shorter than the rotational-vibrational relaxation time of the solvent. Therefore, the solvent is only partially relaxed for these states and the corresponding reaction field is characterized by the dielectric constant at infinite frequency of external electric field, 8 . By inserting the expression for the reaction field [11.1.36] into the equation [11.1.18] and assuming that the static polarizability of the solute molecule is approximately equal to the one third of the cube of Onsager s cavity radius... 

Besides frequency, time is another critical parameter for the description of dielectric phenomena in polymers. The mathematical analysis of the time-dependent response is based largely on the (macroscopic) relaxation function 0(r), which describes the change of the system after the removal of an applied stimulus (in the present case, the electric field, in the case of DMA, the stress). Dipole orientation, which follows the application (at time r = 0) of a static... 

In this section we wish to consider all the possible contributions to the electric permittivity of liquid crystals, regardless of the time-scale of the observation. Conventionally this permittivity is the static dielectric constant (i.e. it measures the response of a system to a d.c. electric field) in practice experiments are usually conducted with low frequency a.c. fields to avoid conduction and space charge effects. For isotropic dipolar fluids of small molecules, the permittivity is effectively independent of frequency below 100 MHz, but for liquid crystals it may be necessary to go below 1 kHz to measure the static permittivity polymer liquid crystals can have relaxation processes at very low frequencies. 

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 dielectric contribution of each of these modes has been worked out using the extended Landau free energy expansion of Sec. 2.5.11. The static electric response of each mode is obtained by minimizing the free energy in the presence of an electric field. The relaxation frequency of the fluctuations in the order parameter is obtained by means of the Landau-Khalatnikov equations, which control the order parameter dynamics. 

The switching memory effect is a reflection of the fact that the electric displacement, being the function of both the applied field and the material s properties, needs some finite time to adjust to the value of the electric field. The widely accepted model of the instantaneous relationship between the electric displacement and the electric field in the NLC is invalid when the characteristic times of the director dynamics are close to the relaxation times for molecular permanent dipoles. This time scale is typically in the submillisecond range which is of great interest for modem fast-switching devices. The electric displacement (as well as the dielectric torque density) becomes a function of the static dielectric properties of the NLC, the present and past electric field, and the present and past director. We discussed the recently proposed theory and experimental verification of the phenomenon [11]. The model in Ref [11] should be applicable to dynamic reorientation of other LC phases in the appropriate range of times/frequencies. In the case of ferroelectric LCs, the theory should be supplemented by the consideration of spontaneous electric polarization. A similar approach should be also... 

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