Admissible frequency domain response functions of dielectrics

Few empirical formulae produced to represent the complex dielectric constant in the frequency domain are discussed here from the view point of the possibility of their representation in the time domain. Because a generic function of the frequency does not necessarily admit an inverse Fourier transform, it is not always possible to obtain the corresponding time domain representation of the constant defined in the time frequency. With the use of the fractional derivatives, we introduce a tentative model of the dielectric constant including a linear term, the complex dielectric constant with its loss, and the loss of the direct current electrical conductivity. With appropriate values of the parameters, the system reproduces in the frequency domain the K. Cole and R. Cole model, without the contribution of the loss of the direct current electrical conductivity, which is studied by an autonomous constitutive equation. Copyright © 2014 John Wiley & Sons, Ltd.