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

## TL;DR

This paper introduces a new model for electrolytic systems that explains how memory effects influence ion movement and electrical impedance.

## Contribution

The novel contribution is a generalized Poisson–Nernst–Planck model with memory effects to describe nonlocal ionic transport and anomalous diffusion.

## Key findings

- The model shows that memory effects can cause non-Debye relaxation and fractional-like scaling in impedance.
- The model accurately fits experimental impedance data from NH4Cl-glycerol solutions.
- Memory-driven transport is shown to govern transitions between normal and anomalous diffusion regimes.

## Abstract

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.