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

• An irradiated polymer electrolyte with gelatin is studied.
• Ion conductivity shows normal as well as anomalous diffusion.
• Anomalous behavior of the motion of ions is analyzed by generalized calculus.
• Both the experimental and theoretical values give a satisfactory agreement.

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.