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4 EIS at carbon fiber cylindrical microelectrodes Materials and Methods Single carbon fibers were extracted from a carbon felt sample (GFE1, Ceramaterials, USA) and glued to electrical wire using carbon glue. The wire was housed in a glass capillary tube and the end sealed with epoxy resin, leaving only the carbon fiber exposed to the electrolyte. Data were collected at 23 ± 1°C. SEM images of the felt showed fiber diameters averaging 10 μm with a standard deviation of 1 μm. Detailed EIS data were collected for two fibers, but the results are here reported for a single 3.4 mm long fiber, which had lower EIS noise. The solution was 1 mol dm−3 KNO3 with 10.0 mmol dm−3 each of K3Fe(CN)6 (Vickers Laboratories Ltd) and K4Fe(CN)6 (BDH AnalaR). The diffusivities in 1 mol dm−3 KNO3 were calculated from the limiting current reached during steady state polarisation curves on a polished gold rotating disk electrode (5 mm diameter, Pine Research Instrumentation), rotated at speeds from 100 to 600 rpm. The Levich equation was applied to relate the limiting current to the diffusivities, which were found to be 8.6 × 10-6 cm2 s−1 for Fe(CN)4− and 8.37 × 10-6 cm2 s−1 6 for Fe(CN)3−. Here we use the mean value 8.50 ± 0.05 × 10-6 cm2 s−1, where the quoted 1𝜎 6 error is somewhat arbitrarily estimated so that ± 2𝜎 spans the two measured diffusivities. This is similar to the literature mean value in 0.5 mol dm−3 K2SO4 of 8.45 × 10-6 cm2 s−1 [152]. Potentiostatic EIS data were collected with a Gamry 3000 potentiostat, and were fitted to the impedance expression Eq. (4.12) for the Randles circuit for cylindrical diffusion and with a CPE replacing the double-layer capacitance. 𝑍 = 𝑅𝑢 + 1 (4.12) 𝑌 (𝑖𝜔)∅ + 1 The complex nonlinear least squares fitting was done using Maple’s NLPSolve routine using the nonlinearsimplex option, with a custom calling program that also derives the standard errors in the usual way, i.e., from the values of the derivatives of the impedance with respect to the parameters at the minimum [153]. No weighting was used. 44 0 𝑅𝑐𝑡(1 + 𝜓√𝜏𝑑𝑧)PDF Image | Electron Transfer Kinetics in Redox Flow Batteries
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