A new generalized fractional Maxwell model of dielectric relaxation

Abstract The polarization of dielectric materials in electric field lags behind the external field and the relaxation losses energy. In this paper, the relaxation characteristics of the fractional models established by using a fractional differential operator (cap-resistor) are analyzed. It is found that the cap-resistor just corresponds to the complex impedance used by Cole brothers to represent the dissipation in the dielectrics, and Cole–Cole equation is a special case of the generalized fractional Maxwell model. The fractional models are used to simulate the dielectric relaxation of liquid crystal cells embedded with Pd nanoparticles. The Cole–Cole plot of the relaxation data shows outspread wings in the low frequency range, and the fractional models can represent the relaxation behavior very well.