Effects of gradient of polarization on dielectric relaxation

We present a non-equilibrium thermodynamic model to describe diffusion effects in dielectric materials with spatial inhomogeneities in the polarization vector and with local viscoelastic effects. The model presented here is a generalization of the Debye relaxation equation including inertial effect, and contributions from the spatial inhomogeneities of the polarization vector, together with a contribution from the antisymmetric stress tensor via the divergence operator. At the same time, a Maxwell viscoelastic-relaxation type equation for the antisymmetric stress tensor is proposed to describe the time evolution of this tensor. On the other hand, a generalized hydrodynamics model for the dielectric memory for short wave length and high frequencies is obtained, by considering the linearized complete set of differential equations of the model. By working in the Fourier–Laplace space, the dielectric susceptibility is obtained and their main features are described and compared with π and α dielectric relaxation