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Chapter 3. Characterisation Methods Figure 3.13: Nyquist plots of the simulated impedance of semi-infinite (black line), transmissive (red line), and reflective (green line) linear diffusion elements. Simula- tion parameters: fmax = 1MHz, fmin = 0.1Hz, σ = 20Ωs−1/2, δ = 4×10−4cm, D = 1×10−6 cm2 s−1, and A = 1cm2. where δ is the diffusion layer thickness. 3.6.2 Equivalent Circuits In order to model the processes occurring in an electrochemical system, the basic elements are combined in series and/or parallel to create an equivalent circuit model. The impe- dance of such circuits is defined from the impedances of the individual elements, with the series and parallel combinations defined in the same way as resistors, i.e.: Zseries =Z1 +Z2 +...+ZN (3.43) 1 = 1 + 1 +...+ 1 (3.44) Though helpful for the interpretation of EIS data, one has to remember that these equiv- alent circuits are only an electrical representation of the real processes, and that resistors, capacitors etc. do not exist physically in electrochemical systems [67]. 3.6.2.1 Three-Electrode Systems: Randles Circuit The Randles circuit is used to model the impedance of a heterogeneous charge transfer under semi-infinite linear diffusion conditions, which are the conditions assumed to be valid for a standard three-electrode setup using a stationary flat disk WE. A schematic of the equivalent circuit model is shown in Figure 3.14 and an example of the impedance 36 Zparallel Z1 Z2 ZNPDF Image | Organic Redox Flow Batteries 2023
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