Theory and Background of Dielectric Analysis

Frequency-Dependent Response of Dielectrics Basic Aspects 

Careful measurement and analysis of dielectric data necessitates a well-defined environment and configuration of the material under study, along with the use of the appropriate mathematical formulation for effective data analysis. The 

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 

Dielectric experiments that involve studies of the relaxation function l (r) are denoted as time-domain experiments, while those related to the complex permittivity function e (co) are considered dynamic experiments. The latter have the advantage of introducing an experimental timescale ( l/(o), which, when compared to the different intrinsic timescales of the system (the relaxation time x), provides useful information on the molecular level. In terms of the single-relaxation-time model of Debye (1921,1929), the complex permittivity for a dipolar mechanism can be written as follows  

Direct-current (DC) conductivity contributes only to the imaginary part of permittivity, by a term Odc/eoCO, where Odc is the specific DC conductivity of the material. The difference in the frequency dependence of the dipolar and the DC conductivity terms allows their experimental separation. The analysis of simple permittivity plots provides estimates for the dielectric strength (Ae = r - u) and the relaxation time of each relaxation process, along with the value for Odc at the temperature of the experiment. 

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