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Theoretical analysis of homogeneous catalysis of electrochemical reactions: steady-state current–potential

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Abstract

This article presents a theoretical analysis of homogeneous redox catalysis in electrochemical reactions. A nonlinear differential system is used as a model in which a nonlinear term is linked to homogeneous reactions. The concentration of the mediator and substrate at a planar electrode is computed using an analytical method under pure kinetic conditions and constant substrate concentration. This simplifies the analysis, which can be achieved with slow-scan rates and concentrations in real-world scenarios. The resulting current–potential responses have an S shape and are independent of the scan rate. The impact of two essential parameters on the current is investigated. The derived analytical expressions show high accuracy when compared to numerical results, which show satisfactory agreement. The limiting cases for the concentration characteristics and current–potential response are also investigated.

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Abbreviations

\({C}_{p}^{0},{C}_{A}^{0}\) :

Bulk concentration of species \(P, A\) (\(\text{mol c}{\text{m}}^{-3}\))

\({C}_{SPECIES}\) :

Concentration of the species \(A, B, C, P, Q\) (\(\text{mol c}{\text{m}}^{-3}\))

\(i\) :

Current (A)

\({D}_{p}\) :

Diffusion coefficient of species \(P\)(\({\text{cm}}^{2}{{\text{s}}}^{-1}\))

\(u,v,w, n\) :

Dimensionless concentration of the species \(P, Q, B, C\) (None)

\(\varphi\) :

Dimensionless current (None)

\(x\) :

Dimensionless distance from the (planar) electrode surface (None)

\(\xi\) :

Dimensionless potential (None)

\({v}_{0}\) :

Dimensionless parameters defined in Eq. (13) (None)

\({v}_{1}\) :

Dimensionless parameters defined in Eq. 26 (None)

\({\beta }_{1}, {\beta }_{2}, {\beta }_{3}\) :

Dimensionless parameters defined in Eqs. 19 and 20 (None)

\(y\) :

Distance from the (planar) electrode surface (\({\text{cm}})\)

\(E\) :

Electrode potential (V)

\(F\) :

Faraday constant (C mol–1)

\({\xi }_{1/2}\) :

Half-wave potential (V)

\(\kappa ,\lambda\) :

Dimensionless Intrinsic and operational parameters (None)

\({\varphi }_{pi}\) :

Plateau current (None)

\({E}_{P/Q}\) :

Standard potential of the catalyst couple (V)

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Authors and Affiliations

  1. Department of Mathematics, Meenakshi College of Engineering, West KK Nagar, Chennai, 600078, India

    Ramu Usha Rani

  2. Department of Mathematics, AMET University, Chennai, 603112, India

    Lakshmanan Rajendran

  3. Department of Mathematics and Statistics, American University of Sharjah, Sharjah, United Arab Emirates

    Marwan Abukhaled

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  1. Ramu Usha Rani
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  2. Lakshmanan Rajendran
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  3. Marwan Abukhaled
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Contributions

RUR: Data curation, Formal analysis, Software, Visualization, Writing—original draft. LR: Conceptualization, Methodology, Resources, Supervision, Validation. MA: Methodology, Validation, Resources, Investigation, Supervision.

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Correspondence to Lakshmanan Rajendran or Marwan Abukhaled.

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Rani, R.U., Rajendran, L. & Abukhaled, M. Theoretical analysis of homogeneous catalysis of electrochemical reactions: steady-state current–potential. Reac Kinet Mech Cat 136, 1229–1242 (2023). https://doi.org/10.1007/s11144-023-02407-x

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