Frequency dependence polymer electricity

The temperature and frequency dependence of the complex dielectric permittivity a for both 2-chlorocydohexyi isobutyrate (CCHI) and poly(2-chlorocyclohexyl acrylate) (PCCHA) is reported. The analysis of the dielectric results in terms of the electric modulus suggests that whereas the conductive processes in CCHI are produced only by free charges, the conductivity observed in PCCHA involves both free charges and interfacial phenomena. The 4x4 RIS scheme presented which accounts for two rotational states about the CH-CO bonds of the side group reproduces the intramolecular correlation coefficient of the polymer. 

The electrical properties of polyelectrolyte complexes are more closely related to those of biologically produced solids. The extremely high relative dielectric constants at low frequencies and the dispersion properties of salt-containing polyelectrolyte complexes have not been reported for other synthetic polymers. Neutral polyelectrolyte complexes immersed in dilute salt solution undergo marked changes in alternating current capacitance and resistance upon small variations in the electrolyte concentration. In addition, their frequency-dependence is governed by the nature of the microions. As shown in... 

Frequency characteristics — Polymer dielectrics typically show signification frequency dependence in their electrical characteristics. For example, many polymers show significant roll-off in their... 

For a long time the finite oligomer approach was the only method available for determining linear and nonlinear polarizabilities of infinite stereoregular polymers. Recently, however, the problem of carrying out electronic band structure (or crystal orbital) calculations in the presence of static or frequency-dependent electric fields has been solved [115, 116]. A related discretized Berry phase treatment of static electric field polarization has also been developed for 3D solid state systems... 

Implications. These results have an important implication concerning the use of Fourier analysis of DC transients in polymeric materials to extract the frequency-dependence of the dielectric response (12)- In order for the principle of superposition to apply the electric field inside the material being measured must be time- and space-invariant. This critical condition may not be met in polymers which contain mobile ionic impurities or injected electrons. Experimentally, we can fix only the average of the electric field. Moreover, our calculations demonstrate that the bulk field is not constant in either time or space. Thus, the technique of extracting the dielectric response from the Fourier components of the transient response is fundamentally flawed because the contribution due to the formation of ionic and electronic space-charge to the apparent frequency-dependent dielectric response can not generally be separated from the dipole contribution. 

Generally, the literature shows that for pol)timides the dielectric constant decreases gradually with increasing frequency. This variation is attributed to the frequency dependence of the polarization mechanisms which include the dielectric constant. The magnitude of the dielectric constant is dependent on the ability of the polarizable emits in a polymer to orient fast enough to keep up with the oscillations of an alternating electric field. At optical frequencies (approx. 10 Hz), only the lowest mass species, the electrons, are efficiently polarized. At lower frequencies, the atomic polarization of nuclei, which move more slowly, also, contribute to the dielectric constant. Atomic polarization of induced... 

The Nature and Application of Electrical Phenomena in Polymers 2.2 TTie Frequency Dependence of Pemuttivity... 

A typical example for the frequency- and temperature-dependent dielectric properties of a piezoelectric polymer is given in Fig. 7 that displays the a-relaxation, related the dynamic glass transition, of a polyvinylidene fluoride (PVDF) film along with an upswing of the dielectric loss at low frequencies due to electrical conduction. 

If a mechanical or an electric field is applied to a polymer sample and remains suSiciently small, then the reaction, as given by the deformation and the polarization respectively, can be described by linear equations. We shall deal first with the linear viscoelasticity, which can be specified by various mechanical response functions, and then with the linear dielectric behavior, as characterized by the time- or frequency dependent dielectric function. 

An example of polymer solutions is P(VDF/TrFE)/DMF solution [49] (Fig. 11). Poly(vinylidene-co-trifluoroethylene) (P(VDF/TrFE)) is known as a strong dielectric polymer. It possesses a permanent dipole moment in the main chain. The electric field frequency dependence of the relative viscosity was measured by a capillary rheometer. The result showed a positive ER effect at 10 Hz whereas it showed a negative ER effect at 1 kHz. 

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