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3.6. Electrochemical Impedance Spectroscopy Figure 3.9: (Left) Illustration of an applied sinusoidal potential and resulting sinusoidal current, with phase shift φ as indicated. (Right) Phasor diagram showing the relationship between impedance in polar and Cartesian coordinates. Ohm’s law, the impedance Z is defined from the alternating voltage and current as Z(ω) = E(t) = E0 sin (ωt) (3.27) I(t) I0 sin(ωt+φ) The phasor diagram in Figure 3.9 (right) shows how the impedance can be expressed in polar and Cartesian coordinates. A simpler way to deal with the impedance is to define it in terms of complex numbers: Z(ω) = ZRe + jZIm (3.28) where j is the imaginary unit, ZRe is the real part of the impedance, and ZIm is the imaginary part of the impedance, which are given as: ZRe = |Z| cos(φ) (3.29) ZIm = |Z| sin(φ) (3.30) The modulus of the impedance, which corresponds to the length of the impedance vector (green line in Figure 3.9 (right)), is defined as |Z| = (ZRe)2 + (ZIm)2 (3.31) Electrochemical impedance data is commonly viewed as a plot of −ZIm against ZRe, which is referred to as a Nyquist (or complex plane) plot. This corresponds to the green line in Figure 3.10, which is a projection of the 3-dimensional impedance onto the ZRe,−ZIm plane. The real and imaginary axes should always be shown with equal scaling on a 31PDF Image | Organic Redox Flow Batteries 2023
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