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5 Single fibre electrode measurements - a versatile strategy for assessing the non-uniform kinetics where π is the radius of the electrode, πΆ is the concentration of the oxidised species at the π π,π electrode surface, πΆπ ,π is the concentration of the reduced species at the electrode surface., π0 is the rate constant, πΌ is the charge transfer coefficient, π is the number of electrons exchanged (equal to one for this reaction), πΉ is the Faraday constant, π is the universal gas constant, π is the absolute temperature, π is the activation overpotential and π· is the average diffusion coefficient of the redox species. This boundary condition was also applied to the flux of the oxidised species to the surface, where ππΆπ | is replaced by β ππΆπ| in Eq. (5.3). In this work only one parameter, k0 was altered in order to obtain an accurate fit for the single carbon fibre electrodes. The electrode length was measured and the fibre diameter was assumed to be equal to the average from SEM imaging. The diffusion coefficients were calculated from LSV measurements and the temperature recorded during the experiment, thus the only two variables that were unknown were Ξ± and k0. With this redox couple it can be seen that the peak currents for the forward and reverse sweeps are very similar, thus Ξ± is likely to be close to 0.5. For ease of fitting Ξ± was fixed at 0.5 and only k0 was manipulated, which is similar to the approach used by McCreery, where Ξ± was also assumed to be 0.5 [89]. In this work the fitting was carried out using an automated and simple bisection root finding method in Matlab. The initial upper and lower k0 values for the solver were set to 0.1 cm s-1 and 0.0001 cm s-1 respectively, with the difference between the experimental and the simulated peak potential separations minimised to within a tolerance of 0.5 mV. Obtaining an accurate fit by minimizing the difference in peak separation is the logical choice in this work due to the correlations previously reported by Aoki and Kaneko [142] and Neudeck and Dittrich [181]. 56 ππ π=ππ ππ π=ππPDF Image | Electron Transfer Kinetics in Redox Flow Batteries
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