Frequency-dependent dielectric analysis

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. 

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. 

A detailed analysis of the dielectric response of PMMA has been performed [75]. The frequency dependence of the dielectric loss, e"y at a few temperatures is shown in Fig. 108. An increase in temperature is associated with a shift towards higher frequency, as expected, but also with quite a significant increase in the height of the peak maximum. 

The analysis of the dynamics and dielectric relaxation is made by means of the collective dipole time-correlation function (t) = (M(/).M(0)> /( M(0) 2), from which one can obtain the far-infrared spectrum by a Fourier-Laplace transformation and the main dielectric relaxation time by fitting < >(/) by exponential or multi-exponentials in the long-time rotational-diffusion regime. Results for (t) and the corresponding frequency-dependent absorption coefficient, A" = ilf < >(/) cos (cot)dt are shown in Figure 16-6 for several simulated states. The main spectra capture essentially the microwave region whereas the insert shows the far-infrared spectral region. 

Dielectric relaxation of complex materials over wide frequency and temperature ranges in general may be described in terms of several non-Debye relaxation processes. A quantitative analysis of the dielectric spectra begins with the construction of a fitting function in selected frequency and temperature intervals, which corresponds to the relaxation processes in the spectra. This fitting function is a linear superposition of the model functions (such as HN, Jonscher, dc-conductivity terms see Section II.B.l) that describes the frequency dependence of the isothermal data of the complex dielectric permittivity. The temperature behavior of the fitting parameters reflects the structural and dynamic properties of the material. 

In recent years, great attention has been paid to the analysis of the dependence of the properties of metal-insulator composites on frequency [91-109], which is related to the difficulties in describing the anomalous behavior of dielectric properties in the low-frequency limit. The nature of the anomalous behavior of the frequency dependence of the dielectric properties can be clarified if we consider a model medium consisting of small spherical metallic particles described by the Drude dielectric function... 

These authors noted that the intermediate power law (i.e., t l+y, with a small positive 7) of the OKE data was formally equivalent to the excess wing in the frequency-dependent susceptibility, the latter discussed in the dielectric literature since 1951. Brodin and Rossler argued that the intermediate power law observed in the OKE data was in essence a manifestation of the excess wing of the corresponding frequency-domain data, known long since from broadband dielectric spectroscopy and anticipated from DLS studies of supercooled liquids [83]. More recently, these authors showed that the excess wing was an equally common feature of the DLS data and discussed the merits of the Mode coupling theory analysis of the time and frequency-domain data [84]. 

For the analysis of the reflection spectra, we consider as usual the frequency-dependent complex dielectric tensor s (co). We restrict ourselves here to the case that the direction of polarisation is parallel to the stacking axis, and denote the real and imaginary parts of the complex dielectric function as usual s (jo) = i(co) -i- is2(co). It is related to the complex index of refraction, n = ni -i-in2, via n = The real part of... 

The principles of time-temperature superposition can be used with equal success for dielectric measurements as well as dynamic mechanical tests. Analysis of the frequency dependence of the glass transition of the adhesive in the system described above shows that it follows a WLF type dependence whereas the transition of PET obeys Arrhenius behaviour. This type of study can be used to distinguish between different types of relaxation phenomena in materials. 

Inelastic Scattering Cross Section. The inelastic scattering cross section that defines the probability that an electron loses energy T per unit energy loss and per unit path length traveled is one of the key parameters in quantitative peak shape analysis. In the dielectric response formalism of solid electron interaction, the cross section may be evaluated from the wave vector and frequency dependent complex dielectric function ( , [Pg.42]

Equations 5.30 through 5.33 are termed the Debye equations and contain the basic framework used for the analysis of the frequency dependence of polymer dielectrics [2]. Thus, for example, integration of equation 5.33 assuming a single relaxation time yields... 

Schwan emphasized the concept of dispersion in the field of dielectric spectroscopic analysis of biomaterials. Dispersion has already been introduced in Section 3.4.1 dispersion means frequency dependence according to relaxation theory. Biological materials rarely show a single time constant Debye response as described in Section 3.4.2. Knowing how complex and heterogeneous living tissue is, the concept of a distribution of... 

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