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Research Papers

Algebraic Form and New Approximation of Butler–Volmer Equation to Calculate the Activation Overpotential

[+] Author and Article Information
H. Kazemi Esfeh

Process Systems Engineering
Centre (PROSPECT),
Faculty of Chemical Engineering,
Universiti Teknologi Malaysia, UTM,
Skudai 81310, Johor, Malaysia;
Department of Chemical Engineering,
Mahshahr Branch,
Islamic Azad University,
Mahshahr, Iran
e-mail: h.kazemi.esfeh@gmail.com

M. K. A. Hamid

Process Systems Engineering Centre (PROSPECT),
Faculty of Chemical Engineering,
Universiti Teknologi Malaysia, UTM,
Skudai 81310, Johor, Malaysia
e-mail: kamaruddin@cheme.utm.my

Manuscript received May 6, 2016; final manuscript received August 25, 2016; published online October 11, 2016. Assoc. Editor: William Mustain.

J. Electrochem. En. Conv. Stor. 13(2), 021003 (Oct 11, 2016) (10 pages) Paper No: JEECS-16-1059; doi: 10.1115/1.4034754 History: Received May 06, 2016; Revised August 25, 2016

The Butler–Volmer equation has been widely used to analyze the electron transfer for electrochemical simulation. Although it has been broadly employed with numerous successful applications, the Butler–Volmer equation needs to be solved numerically to find the activation overpotential, which results in the increase of the calculation difficulties. There are also some parameters in Butler–Volmer equation such as exchange current density and symmetry factor that are not always known parameters. In order to avoid the latest mentioned limitation and the numerical calculation which is time consuming and for simplification, there are some approximation equations such as Tafel, linear low polarization, and hyperbolic sine approximation. However, all these equations are only applicable in a specific range of current density or definite condition. The aim of this paper is to present a new form of Butler–Volmer equation using algebraic operation to calculate activation overpotential. The devised equation should be accurate, have a wide application range, able to remove any numerical calculation, and be useful to find exchange current density. In this research, a new form of Butler–Volmer equation and a new approximation equation (called K–J equation) have been successfully derived. The comparison result shows that the new derived form is exactly equal to the Butler–Volmer equation to calculate the activation overpotential, and it removed the necessity of numerical calculation to find the activation overpotential. In addition, the K–J approximation has a good agreement with Butler–Volmer equation over a wide range of current density and is applicable to predict the activation loss.

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Figures

Grahic Jump Location
Fig. 1

Dependence of the electrode current by Butler–Volmer equation on overpotential

Grahic Jump Location
Fig. 2

Comparison of Tafel and low-polarization approximations with Butler–Volmer equation at specific condition (β = 0.5 and T = 800 °C) [28]

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Fig. 3

Comparison of Butler–Volmer equation and its new form at specific condition (β = 0.5 and T = 800 °C)

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Fig. 4

Polarization curves obtained from the model and the experiment data at different pressures

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Fig. 5

Comparison between Butler–Volmer and K–J equation with different symmetry factor in high temperature; (a) β=1/4, (b) β=1/3, (c) β=1/2, and (d) β=3/4

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Fig. 6

Comparison between Butler–Volmer and K–J equation with different symmetry factor in low temperature; (a) β=1/4, (b) β=1/3, (c) β=1/2, and (d) β=3/4

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Fig. 7

R-squared value of K–J and Butler–Volmer equation difference in wide range of symmetry factor

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Fig. 8

Standard deviation between K–J and Butler–Volmer equation in wide range of symmetry factor and temperature

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Fig. 9

The comparison between the K–J equation and other Butler–Volmer approximation in wide range of current density

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Fig. 10

Logarithmic plot of the activation loss against the current density. (a) Layout of the exchange current density prediction and (b) example of exchange current density prediction.

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Fig. 11

Change in activation overpotential by changing the symmetry factor at specific condition (β = 0.5 and T = 800 °C)

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Fig. 12

Change in first-order differential function of activation overpotential in different symmetry factor using new form equation

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Fig. 13

Change in second-order differential function of activation overpotential in different symmetry factor using new form equation

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