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Chapter 3. Characterisation Methods Figure 3.17: Nyquist plots of impedance simulated from Equation 3.49 for a blocking (black line, surface impedance given in Equation 3.52) and non-blocking (red line, surface impedance given in Equation 3.53) porous electrode. Simulation parameters: A = 5 cm2, At = 320cm2, a = 1×10−3 cm, b = 0.035cm, cOx = cRed = 1×10−4 molcm−3, DOx = DRed = 7×10−6 cm2 s−1, f = 0.3, i0 = 0.01Acm−2, Q0 = 5×10−3 Ssq cm−2, q = 0.97, T = 298.15K, ρe = 0.14Ωcm, and ρi = 5Ωcm. In the presence of faradaic reactions, the charge transfer and diffusion processes of the redox-active material must be taken into account. The non-blocking surface impedance is defined in Equation 3.53 [73] (the nomenclature is modified from the reference and includes the number electrons transferred, which was assumed to be 1 in the reference): tanha jω DRed RTa DOx q +fgn2F2cOxDOx a jω + (jω) Q0 DOx ζnon-blocking=nFi+fn2F2c D 0 g Red Red tanha jω −1 −1 RT RTa jω a DRed (3.53) where a is the average diffusion layer thickness and fg is the geometric scale factor. The former is an average over the distribution of Nernstian diffusion layer thicknesses in the pores, while the latter is a unitless factor that accounts for the geometric form and distribution of the pores. An example of the impedance response of a non-blocking porous electrode is shown in Figure 3.17 (red line). The non-blocking porous electrode impedance can be resolved into contributions from distributed ohmic (which is the parallel combination of electrode electronic and electrolyte ionic resistances throughout the porous electrode), charge transfer, and finite diffusion processes. The resistances Rdist, Rct, and Rfd are calculated from Equations 3.54–3.56 40PDF Image | Organic Redox Flow Batteries 2023
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