Permittivity components, temperature

Dielectric spectroscopy is concerned with the dependence of complex permittivity on temperature and frequency. The relatively low level of d.c. conduction in polycarbonate ensures that the principal relaxations associated with polycarbonate s active C 0 dipole can be observed over a useful range of frequency and temperature. In multi-phase or multi-component polymers charge accumulation at the sub-structure interfaces leads to Maxwell-Wagner-Sillars (MWS) contributions to the overall polarization. 

Figure 6.4. Generic behavior of temperature dependence of permittivity components (e, 8") recorded for an amorphous polymer with considerable ionic conductivity. The higher the relaxation time of the mechanism, the higher the temperature range at which the corresponding signal appears in this isochronal recording. The signals present in this spectrum will shift to lower temperatures by decreasing the frequency of the alternating electric field.

For other substances the parallel permittivity component, e,, is only known. Figure 11 shows a typical behavior of the static permittivity e n in the nematic and isotropic phase of 7PCH at constant temperatures, while the pressure was successfully reduced from the points close to the nematic-solid transition line. Figure 12 presents the dependencies of e, on the reduced pressure, p —Pni, for different substances studied. It is... 

Figure 12. Parallel permittivity component, e,, as a function of the reduced pressure, p - Pm, for different substances in the nematic phase. The temperatures correspond to a few Kelvins above the clearing points at ambient pressure.

When applying an alternating electric field to a polymer placed between two electrodes, the response is generally attenuated and the output current is out of phase compared with the input voltage. This response stems from the polymer s capacitive component and its conductive or loss component, as represented by a complex dielectric permittivity measured frequencies f, and temperatures T ... 

From the value of the resonant frequency and its change with temperature or other external parameters the permittivity of a dielectric sample and its temperature or field dependence can be determined. In case of superconductors, the temperature dependence of the magnetic field penetration depth can be determined [8], Since the mode spectrum of a resonator is controlled both its physical dimensions and by the material properties, the physical dimensions of all resonator components have to be known with tight tolerances. Relative changes of permittivity or penetration depth can be determine with much higher accuracy than absolute values. 

The principal components of the relative permittivity tensor, measured parallel to the crystal axes, a, b and c, at 1 kHz and room temperature, are (Orczyk, 1990) ... 

Electrical conductivity, permittivity (dielectric constant) and loss angle are the most important electrical properties of glass at low temperatures. These properties are important when glass is used as an insulating material or as a functional component of electrotechnical devices and instruments. 

For pure liquids, the Debye equation suggests that the molar polarization should be a linear function of the reciprocal temperature. Furthermore, one should be able to analyze relative permittivity data for a polar liquid like water as a function of temperature to obtain the dipole moment and polarizability from the slope and intercept, respectively. In fact, if one constructs such a plot using data for a polar solvent, one obtains results which are unreasonable on the basis of known values of p and ocp from gas phase measurements. The reason for the failure of the Debye model in liquids is the fact that it neglects the field due to dipoles in the immediate vicinity of a given molecule. However, it provides a reasonable description of the dielectric properties of dilute polar gases. In liquids, relatively strong forces, both electrostatic and chemical, determine the relative orientation of the molecules in the system, and lead to an error in the estimation of the orientational component of the molar polarization. 

This anisotropy, illustrated by refractive index, extends to other properties, and common properties of interest would be the anisotropy in linear polarizability (Aa), dielectric permittivity (Ae), and diamagnetism (Ax). In the nematic phase, these properties are quite strongly temperature dependent the order parameter, S, increases as samples cool away from the N-I transition. This is illustrated in Figure 19 where it is also seen that the parallel component has the stronger temperature dependence as it is the orientational correlations that increase on cooling. 

On the other hand, miscibility is, in one sense, one of the characteristic properties in liquid crystals. Miscibility in liquid crystals is a well-known macroscopic property where one can see two mesogens exhibiting a thermodynamically identical liquid crystalline phase are mixed to show its phase at arbitrary component ratio. This has already been applied to liquid crystals for LCDs to control some properties such as temperature range of nematic phase. A diversity of functional properties such as temperature range, anisotropic electrical permittivity, viscosity etc. can be controlled in nematic blends and non-mesogenic molecules also can be a component which contributes to the resultant properties as they behave like a solute in liquid solution. However, charge transport property has not yet been well studied in terms of molecular blends with liquid crystalline materials, while thin film organic photovoltaics have been so extensively studied in recent years as molecular blends. 

Fig. 1. Temperature dependences of the principal components of the electric permittivity tensor in monomer and fully polymerized pTS (e ). The numbers correspond to the indices of the components, the symbols "M and "P" refer to monomer and polymer, respectively. Results obtained for pFBS are also shown for comparison curves "A" and "B" refer to the measurements carried out along the a and b directions of pFBS, respectively. Note the different scales of e in Figs, la and lb.

A computer automated system, shown schematically in figure 5, has been developed to yield results for permittivity and dielectric loss over a range of temperatures. A real dielectric is considered to have an admittance, Y=j(oC. In practice, the measured admittance is found to have a conductive as well as a capacitive component, Y = G + jcoC. In order to account for this, the capacitance of the dielectric, C, is considered to be characterised by a complex relative permittivity, r ... 

In mixed solvent, CCI4-C6H5CI, universal relation to acetic acid (because the mixed solvent components do not enter into specific solvation with the acid), the dimerization constant dependence on the temperature and permittivity in accordance with [9.52.a] and [9.56] is described by equation ... 

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