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Article

Mathematical Modeling of the Limiting Current Density from Diffusion-Reaction Systems

by
Stephan Daniel Schwoebel
*,
Markus Mueller
,
Thomas Mehner
and
Thomas Lampke
Materials and Surface Engineering Group, Institute of Materials Science and Engineering, Chemnitz University of Technology, D-09107 Chemnitz, Germany
*
Author to whom correspondence should be addressed.
Axioms 2022, 11(2), 53; https://doi.org/10.3390/axioms11020053
Submission received: 26 November 2021 / Revised: 19 January 2022 / Accepted: 26 January 2022 / Published: 28 January 2022
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Abstract

The limiting current density is one of to the most important indicators in electroplating for the maximal current density from which a metal can be deposited effectively from an electrolyte. Hence, it is an indicator of the maximal deposition speed and the homogeneity of the thickness of the deposited metal layer. For these reasons, a major interest in the limiting current density is given in practical applications. Usually, the limiting current density is determined via measurements. In this article, a simple model to compute the limiting current density is presented, basing on a system of diffusion–reaction equations in one spatial dimension. Although the model formulations need many assumptions, it is of special interest for screenings, as well as for comparative work, and could easily be adjusted to measurements.
Keywords: modeling; electroplating; limiting current density; current density; diffusion boundary layer; systems of diffusion reaction equations; three-component system; thermodynamic equilibrium modeling; electroplating; limiting current density; current density; diffusion boundary layer; systems of diffusion reaction equations; three-component system; thermodynamic equilibrium

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MDPI and ACS Style

Schwoebel, S.D.; Mueller, M.; Mehner, T.; Lampke, T. Mathematical Modeling of the Limiting Current Density from Diffusion-Reaction Systems. Axioms 2022, 11, 53. https://doi.org/10.3390/axioms11020053

AMA Style

Schwoebel SD, Mueller M, Mehner T, Lampke T. Mathematical Modeling of the Limiting Current Density from Diffusion-Reaction Systems. Axioms. 2022; 11(2):53. https://doi.org/10.3390/axioms11020053

Chicago/Turabian Style

Schwoebel, Stephan Daniel, Markus Mueller, Thomas Mehner, and Thomas Lampke. 2022. "Mathematical Modeling of the Limiting Current Density from Diffusion-Reaction Systems" Axioms 11, no. 2: 53. https://doi.org/10.3390/axioms11020053

APA Style

Schwoebel, S. D., Mueller, M., Mehner, T., & Lampke, T. (2022). Mathematical Modeling of the Limiting Current Density from Diffusion-Reaction Systems. Axioms, 11(2), 53. https://doi.org/10.3390/axioms11020053

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