Electrical impedance response of gamma irradiated gelatin based solid polymer electrolytes analyzed using a generalized calculus formalism

The electrical impedance response of gelatin based solid polymer electrolyte to gamma irradiation is investigated by impedance spectroscopy. An analysis based on Poisson-Nernst-Plank model, incorporating fractional time derivatives is carried out. A detailed derivation for anomalous impedance function is given. The model involves boundary conditions with convolution of the fractional time derivative of ion density and adsorption desorption relaxation kinetics. A fractional diffusion-drift equation is used to solve the bulk behavior of the mobile charges in the electrolyte. The complex adsorption-desorption process at the electrode-electrolyte interface produces an anomalous effect in the system. The model gives a good fit for the observed impedance data for this biopolymer based solid electrolyte in a wide range of frequencies. We have compared different parameters based upon this model for both irradiated and unirradiated samples. (C) 2015 Elsevier B.V. All rights reserved.