A simple and effective method for the accurate extraction of kinetic parameters using differential Tafel plots

Abstract

Abstract The practice of estimating the transfer coefficient ( $$\alpha$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> ) and the exchange current ( $${i}_{0}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>i</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> ) by arbitrarily placing a straight line on Tafel plots has led to high variance in these parameters between different research groups. Generating Tafel plots by finding kinetic current, $${i}_{k}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>i</mml:mi> <mml:mi>k</mml:mi> </mml:msub> </mml:math> from the conventional mass transfer correction method does not guarantee an accurate estimation of the $$\alpha$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> and $${i}_{0}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>i</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> . This is because a substantial difference in values of $$\alpha$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> and $${i}_{0}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>i</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> can arise from only minor deviations in the calculated values of $${i}_{k}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>i</mml:mi> <mml:mi>k</mml:mi> </mml:msub> </mml:math> . These minor deviations are often not easy to recognise in polarisation curves and Tafel plots. Recalling the IUPAC definition of $$\alpha$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> , the Tafel plots can be alternatively represented as differential Tafel plots (DTPs) by taking the first order differential of Tafel plots with respect to overpotential. Without further complex processing of the existing raw data, many crucial observations can be made from DTP which is otherwise very difficult to observe from Tafel plots. These for example include a) many perfectly looking experimental linear Tafel plots (R 2 &gt; 0.999) can give rise to incorrect kinetic parameters b) substantial differences in values of $$\alpha$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> and $${i}_{0}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>i</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> can arise when the limiting current ( $${i}_{L}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>i</mml:mi> <mml:mi>L</mml:mi> </mml:msub> </mml:math> ) is just off by 5% while performing the mass transfer correction c) irrespective of the magnitude of the double layer charging current ( $${i}_{\mathrm{c}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>i</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:math> ), the Tafel plots can still get significantly skewed when the ratio of $${i}_{0}/{i}_{c}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>i</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo>/</mml:mo> <mml:msub> <mml:mi>i</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:mrow> </mml:math> is small. Hence, in order to determine accurate values of $$\alpha$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> and $${i}_{0}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>i</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> , we show how the DTP approach can be applied to experimental polarisation curves having well defined $${i}_{L}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>i</mml:mi> <mml:mi>L</mml:mi> </mml:msub> </mml:math> , poorly defined $${i}_{L}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>i</mml:mi> <mml:mi>L</mml:mi> </mml:msub> </mml:math> and no $${i}_{L}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>i</mml:mi> <mml:mi>L</mml:mi> </mml:msub> </mml:math> at all.

Topics & Concepts