Nonlocal Response in Electrolytic Cells: A Generalized Poisson-Nernst-Planck Model with Memory Effects

We present an extension of the standard Poisson-Nernst-Planck model by incorporating temporal memory effects to describe the spectroscopy impedance response in electrolytic systems. This model yields a modified current-density relation in which the ionic flux depends nonlocally on the applied electric field. The resulting electrical impedance may exhibit non-Debye relaxation and fractional-like scaling at low frequencies, providing a basis for anomalous diffusion in confined electrolytes. We analyze impedance spectroscopy data from NH₄Cl-glycerol solutions for various concentrations to validate the model. The comparison demonstrates how the memory kernel governs the transition between normal and anomalous diffusion regimes, enabling accurate fits to experimental data. These results evidence the relevance of memory-driven transport in complex fluids and suggest a pathway to unify standard and fractional impedance models.