Warburg impedance Bode plot

Figure 19 Schematic Bode plots from EIS measurements and equivalent circuits that could be used to fit them for various possible corrosion product deposit structures (A) nonporous deposit (passive film) (B) deposit with minor narrow faults such as grain boundaries or minor fractures (C) deposit with discrete narrow pores (D) deposit with discrete pores wide enough to support a diffusive response (to the a.c. perturbation) within the deposit (E) deposit with partial pore blockage by a hydrated deposit (1) oxide capacitance (2) oxide resistance (3) bulk solution resistance (4) interfacial capacitance (5) polarization resistance (6) pore resistance (7) Warburg impedance (8) capacitance of a hydrated deposit.

In a situation where a charge transfer is also influenced by diffusion to and from the electrode, the Warburg impedance will be seen in the impedance plot. This circuit model presents a cell in which polarization is controlled by the combination of kinetic and diffusion processes. The equivalent circuit and the Nyquist and Bode plots for the system are all shown in Figure 2.40. It can be seen that the Warburg element is easily recognizable by a line at an angle of 45° in the lower frequency region. 

Figure ll(b-d) also shows complex plane and Bode plots for the total electrode impedance in the presence of slow charge-transfer kinetics. It should be stressed that the Warburg impedance caimot be represented by... 

Figure 5.7 Warburg impedance for semi-infinite diffusion, (a) Nyquist plot and (b) Bode plot.

Figure 5.10 Representation of the impedance spectrum of the equivalent circuit in Figure 5.8 for when Warburg impedance is much larger than the charge transfer resistance = 1000 Mil, IZ I = 1 Mil s , Cj, = 100 nF, = 10 il. (a) Nyquist plot and (b) Bode plot.

In the case of the impedimetric IME sensor, the two sets of electrodes of the IME can be two poles in a two-electrode configuration for electrical impedance measurements. Figure 4 shows 4a a picture, 4b a schematic, 4c the equivalent circuit model for the IME device, and 4d the Bode plot of the electrochemical impedance spectram obtained in aqueous 0.01 M phosphate-buffered saline containing 10 mM ferricyanide at room temperature. The equivalent circuit for the IME device in Fig. 4c consists of an ohmic resistance (/ s) of the electrolyte between two sets of electrodes and the double-layer capacitance (Cdi), an electron transfer resistance (Ret), and Warburg impedance (Z, ) around each set of electrodes [2], Rs and the two branch circuits are connected... 

Figure 3. (a) Nyquist plot and (b) Bode plot, obtained from the equivalent circuit of Figure 2. The impedance spectra were theoretically determined by arbitrarily taking Rq=5 Q, Rj=20 Q, Cj=10 jjF, Rc=35 Q, and C =2 mF. The diffusion impedance is expressed as Zji AjJa>) hanh[5(ja)f ] (where, Sis defined as L/D , a is the angular frequency, and A is the Warburg coefficient expressed as Ri/5). Rd=400 Q, L=I0 /am, and D=10 cm /s were taken for the calculation of The elemental resistance r and capacitance c in the TML were estimated to be 4x10 and 2.5x10 s C2 m respectively.

On a Nyquist plot, the infinite Warburg impedance appears as a diagonal line with a slope of 1. On a Bode plot, the Warburg impedance exhibits a phase shift of 45°. 

A line of 45° versus the coordinate axis represents the Warburg impedance in the complex plain presentation (Nyquist plot. Figure 5.7a). The representation in the Bode diagram is shown in Figure 5.7b. The phase shift has a constant value of 45°, whereby the modulus of the impedance, IZI is linearly decreasing with increasing frequency. 

When a range of frequencies is applied to the DUT, both El and ECI techniques are called spectroscopies, i.e., electrical impedance spectroscopy and electrochemical impedance spectroscopy. Electrochemical impedance spectroscopy (EIS) profiles, measured as a function of the interrogating frequency, can be presented by two popular plots complex plane impedance diagrams, sometimes called Nyquist or Cole-Cole plots, and Bode (I Z I and 6) plots (Fig. 2). As the impedance, Z, is composed of a real and an imaginary part, the Nyquist plot shows the relationship of the imaginary component of impedance, Z" (on the Y-axis), to the real component of the impedance, Z (on the X-axis), at each frequency. A diagonal line with a slope of 45° on a Nyquist plot represents the Warburg... 

An overview on the topic of IS, with emphasis on its application for electrical evaluation of polymer electrolytes is presented. This chapter begins with the definition of impedance and followed by presenting the impedance data in the Bode and Nyquist plots. Impedance data is commonly analyzed by fitting it to an equivalent circuit model. An equivalent circuit model consists of elements such as resistors and capacitors. The circuit elements together with their corresponding Nyquist plots are discussed. The Nyquist plots of many real systems deviate from the ideal Debye response. The deviations are explained in terms of Warburg and CPEs. The ionic conductivity is a function of bulk resistance, sample... 

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