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Precise Electrochemical Sizing of Individual Electro-Inactive Particles

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Voltammetry based on fractional diffusion.

Valentin Mirceski¹, Zivorad Tomovski

¹Institute of Chemistry, Faculty of Natural Sciences and Mathematics, Ss Cyril and Methodius University, P.O. Box 162, 1000 Skopje, Republic of Macedonia. valentin@iunona.pmf.ukim.edu.mk

The Journal of Physical Chemistry. B

|February 27, 2009

Summary

Fractional calculus models anomalous diffusion in cyclic voltammetry. The study reveals how fractional order (alpha) influences voltammogram shape and peak currents, offering new insights into electrochemical systems.

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Area of Science:

Electrochemistry
Physical Chemistry
Theoretical Chemistry

Background:

Anomalous diffusion deviates from traditional Fickian models.
Fractional calculus provides a framework for describing complex diffusion processes.
Cyclic voltammetry is a key technique for studying electrochemical reactions.

Purpose of the Study:

To theoretically analyze cyclic voltammetry under anomalous diffusion using fractional calculus.
To derive mathematical solutions for electrochemical systems with fractional time derivatives.
To investigate the physical significance of the fractional parameter (alpha) on voltammogram characteristics.

Main Methods:

Application of fractional calculus to model diffusion mass transfer.
Derivation of rigorous solutions using the Wright function for reversible electrode reactions.
Simulation of cyclic voltammetric experiments under varying conditions.
Analysis of concentration profiles and Cottrell-like equations for different alpha values.

Main Results:

The shape of cyclic voltammograms is strongly dependent on the fractional order (alpha).
Voltammograms transition from sigmoid (alpha --> 0) to peak-like (alpha --> 1) shapes.
Peak currents are proportional to the sweep rate raised to the power of alpha/2.
Midpeak potential remains independent of the alpha parameter.

Conclusions:

Fractional calculus offers a powerful tool for understanding anomalous diffusion in electrochemistry.
The fractional parameter alpha provides a quantitative measure of diffusion behavior.
This work elucidates the impact of anomalous diffusion on cyclic voltammetric responses.