Revisiting the Concept of Relaxation/ Retardation of Electric Modulus Dielectric Permittivity and Determination of Normalized Electric Field Decay Function (with Several Detailed Derivations of Formulas)

This chapter contains several derivations of formulas for the Relaxation/Retardation of Electric Modulus, Dielectric Permittivity and analytical method of determination of Electric Field Decay Function from the Frequency Dispersion experiments. Here we explain and revise/recall the relaxation or retardation process, where the dielectric permittivity or the electric modulus responds in time to external perturbation (excitation). The relaxation is phenomena where the response to the external perturbation decays monotonically, and retardation is phenomena where there is monotonic increase of the response to the stimulus. The phenomena are governed by the normalized decay function. We also revise the concept of AC analysis i.e. the sinusoidal or steady state analysis, where the excitation is in the form of sinusoidal harmonic function. In this process one obtains the frequency dispersion data and generates various diagrams of frequency dispersion by plotting the real and imaginary parts of the response function vis-à-vis the frequency. This AC analysis is Impedance Spectroscopy or Dielectric Spectroscopy. The chapter deliberates on how to extract the decay function (that is function in time) from these frequency dispersion experimental data (of the dielectric permittivity and or the electric modulus). This chapter also derives in detail the various important expressions pertaining to dispersion of the dielectric permittivity and electric modulus. In general physics the response is said to be relaxation dynamics whether it is decay (relaxation) or growth (retardation) phenomena. This chapter primarily focuses on Debye type relaxation that enables understanding of various other types of complex-relaxation processes of non-Debye types. The detailed derivations of this chapter give insight of the classical concept of Electric Field relaxation/retardation process.