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electrode, and Q2 is given according to Equation 3.50: (ρe + ρi)bAt 3.6. Electrochemical Impedance Spectroscopy Porous carbon electrode Electrolyte filled pore Ri Ri Ri Current collector Re Re Re To membrane and opposite electrode Figure 3.16: Schematic of the transmission line ladder network inside a single pore of a flooded porous electrode contacted to a membrane and current collector. Ri, Re, and ζ represent the electrolyte ionic resistance, electrode electronic resistance, and surface impedance, respectively, of a small element of the pore. Adapted from [70]. Q2 = Aζ (3.50) where At is the internal electrode surface area. It can be calculated from the fibre diameter d and porosity ε using a cylindrical pore model [74]: At = d4(1−ε) (3.51) The definition of the surface impedance depends on the absence or presence of faradaic reactions. In the absence, the surface impedance is modelled by a CPE, i.e.: ζblocking = ZQ(ω) = 1 (3.52) (jω)qQ0 An example of the impedance response of such a system is shown in Figure 3.17 (black line). The Nyquist plot displays a straight line with a 45° phase at high frequencies, followed by a CPE-like behaviour at low frequencies. The behaviour can be explained as follows: At high frequencies, the AC signal penetration length λ is much smaller than the pore length l (λ ≪ l), which means the pore appears as semi-infinite, giving the initial 45° line. At low frequencies, the AC signal penetration length becomes much larger than the pore length (λ ≫ l), and the signal can reach the bottom of the pore, which results in the CPE-like behaviour of the impedance [67]. 39PDF Image | Organic Redox Flow Batteries 2023
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