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Electron Transfer Kinetics in Redox Flow Batteries

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Electron Transfer Kinetics in Redox Flow Batteries ( electron-transfer-kinetics-redox-flow-batteries )

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4 EIS at carbon fiber cylindrical microelectrodes Fitting failed to converge using the Bessel function expression Eq. (4.2), probably because the numerical evaluation of the real and imaginary parts is subject to error. Therefore, the expression was replaced by the approximation 𝑧 = ln (1 + √𝑖𝜔𝜏𝑑) (4.13) √𝑖𝜔𝜏𝑑 or which the real and imaginary parts have analytical expressions known to Maple. It matches the logarithmic dependence on frequency of the real part and constant imaginary part − 𝜋/4 at low frequencies and (𝑖𝜔)−1/2 dependence at high frequencies [148] and interpolates between them. The relative errors (with respect to Eq. (4.2)) in the real and imaginary parts do not exceed 4%. For the fitted data, the resulting systematic error in the parameters can be estimated by individually varying the parameters to find the minimum in the residual sum of squares. For example, for the 0 V case below, these errors were about 2% for 𝜓, 9% for 𝜏𝑑 and 1% for 𝑅𝑐𝑡. The statistical errors given below used the fitted function, but in the plots comparing the experimental and theoretical values, the full Eq. (4.2) is shown. The data were analyzed without regard to the electrode area, but Figure 4.1 presents data relative to the area, which was estimated from the length and the radius determined from 𝜏𝑑 as described below. 45

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