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3.6. Electrochemical Impedance Spectroscopy response is shown in Figure 3.15. Figure 3.15 also shows that for a system with well- defined kinetic and diffusion impedances, the series and charge transfer resistances can be determined graphically as the high-frequency intercept with the real axis and as the diameter of the charge transfer arc, respectively. Q0, q Rs W Rct σ Figure 3.14: Schematic of the Randles equivalent circuit, which consists of a series resistor Rs, a constant-phase element Q, a charge transfer resistor Rct, and a Warburg diffusion element W. The associated parameters are shown above or below the elements. Applying the definition of series and parallel impedances leads to the following equation for the Randles circuit impedance: ZRandles(ω) = ZRs + 1 = ZRs + ZQ (ZRct + ZW) (3.45) 1+ 1 ZQ+ZRct+ZW Figure 3.15: Nyquist plot of the simulated impedance of a Randles circuit. The figure also shows how the series and charge transfer resistances can be found graphically, and which part of the impedance is controlled by kinetics and mass transfer, respectively. Simulation parameters: fmax = 1 MHz, fmin = 0.1 Hz, Rs = 1 Ω, Rct = 5 Ω, Q0 = 1 × 10−5 S sq, q = 0.95, σ = 20 Ω s−1/2, and A = 1 cm2. For an electrochemical system that can be modelled by the Randles circuit, information about the kinetic and mass transfer parameters can be extracted from the parameters associated to the circuit elements. The standard rate constant is determined through the ZQ ZRct +ZW 37PDF Image | Organic Redox Flow Batteries 2023
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