Dielectric relaxation nonexponential

The dielectric relaxation properties in a sodium bis(2-ethylhexyl) sulfosuc-cinate (AOT)-water-decane microemulsion near the percolation temperature threshold have been investigated in a broad temperature region [47,143,147]. The dielectric measurements of ionic microemulsions were carried out using the TDS in a time window with a total time interval of 1 ps. It was found that the system exhibits a complex nonexponential relaxation behavior that is strongly temperature-dependent (Figure 8). 

In order to explain the non-Debye response (134) it is possible to use the memory function approach [22,23,31,266-268]. Thus, the normalized dipole correlation function k(f) (22) corresponding to a nonexponential dielectric relaxation process obeys the equation... 

In the following section the power of the fractional derivative technique is demonstrated using as example the derivation of all three known patterns of anomalous, nonexponential dielectric relaxation of an inhomogeneous medium in the time domain. It is explicitly assumed that the fractional derivative is related to the dimension of a temporal fractal ensemble (in the sense that the relaxation times are distributed over a self-similar fractal system). The proposed fractal model of the microstructure of disordered media exhibiting nonexponential dielectric relaxation is constructed by selecting groups of hierarchically subordinated ensembles (subclusters, clusters, superclusters, etc.) from the entire statistical set available. 

Analysis of the enthalpy relaxation the enthalpy relaxation time and the activation energy were calculated by KWW in accordance with the previous work (Kawai et al., 2004). The KWW theory was originally proposed in dielectric relaxation study by Williams and Watts (1970), then applied in the form of nonexponential function such as the enthalpy relaxation. In KWW theory, the enthalpy relaxation, AH eiax/ which corresponds to the peak area given from the enthalpy relaxation is expressed by the equation... 

For many of the systems being studied, the relationship above does not sufficiently describe the experimental results. The Debye conjecture is simple and elegant. It enables us to understand the nature of dielectric dispersion. However, for most of the systems being studied, the relationship above does not sufficiently describe the experimental results. The experimental data are better described by nonexponential relaxation laws. This necessitates empirical relationships, which formally take into account the distribution of relaxation times. 

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