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Nonlocal Response in Electrolytic Cells: A Generalized Poisson-Nernst-Planck Model with Memory Effects
Gabriel G da Rocha1, Michely P Rosseto2,3, Rodrigo J Jaronski1
1Graduate Program in Science, State University of Ponta Grossa, Ponta Grossa 84030-900, PR, Brazil.
The Journal of Physical Chemistry. B
|December 21, 2025
Summary
This study introduces a new model for electrolyte spectroscopy impedance by including temporal memory effects, explaining anomalous diffusion and non-Debye relaxation in confined systems.
Area of Science:
- Physical Chemistry
- Electrochemical Systems
- Theoretical Modeling
Background:
- Standard Poisson-Nernst-Planck models are widely used for electrolytic systems.
- Electrochemical impedance spectroscopy (EIS) is crucial for characterizing these systems.
- Understanding anomalous diffusion in confined electrolytes requires advanced modeling.
Purpose of the Study:
- To extend the standard Poisson-Nernst-Planck model by incorporating temporal memory effects.
- To describe the spectroscopy impedance response in electrolytic systems with memory.
- To provide a theoretical basis for anomalous diffusion in confined electrolytes.
Main Methods:
- Developed a modified Poisson-Nernst-Planck model with temporal memory.
- Derived a nonlocal current-density relation accounting for ionic flux memory.
- Analyzed impedance spectroscopy data from NH4Cl-glycerol solutions.
Main Results:
- The extended model predicts non-Debye relaxation and fractional-like scaling in electrical impedance.
- Demonstrated the transition between normal and anomalous diffusion regimes governed by the memory kernel.
- Achieved accurate fits to experimental impedance spectroscopy data.
Conclusions:
- Temporal memory effects are relevant for understanding transport in complex fluids.
- The memory kernel effectively governs diffusion behavior in confined electrolytes.
- The model offers a pathway to unify standard and fractional impedance models.
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