Electrochemical Nyquist plot

NonFaradaic electrochemical modification of catalytic activity, NEMCA, see electrochemical promotion NonFaradaic processes, 2 Nyquist plot, 237... 

To learn what a Nyquist plot is, and what such a plot looks like for simple electrical components, plus appreciate that the Nyquist plot for an actual electrochemical cell can be mimicked by constructing an equivalent circuit comprising arrangements of various components. 

At the heart of impedance analysis is the concept of an equivalent circuit. We assume that any cell (and its constituent phases, planes and layers) can be approximated to an array of electrical components. This array is termed the equivalent circuit , with a knowledge of its make-up being an extremely powetfitl simulation technique. Basically, we mentally dissect the cell or sample into resistors and capacitors, and then arrange them in such a way that the impedance behaviour in the Nyquist plot is reproduced exactly (see Section 10.2 below on electrochemical simulation). 

To summarize the impedance discussion so far an electrochemical cell is constructed, and its impedance Z determined as a function of frequency. From these impedance values, the real and imaginary impedances, Z and Z", respectively, are computed and hence a Nyquist plot is drawn. 

Figure 8.14 Huggins analysis of a Warburg element in a Nyquist plot such as that shown in Figure 8.12(a), for the diffusion of Li" ions through solid-state WO3. The traces for Z and Z" against will not be parallel for features other than that of the Warburg. From Ho, C., Raistrick, I. D. and Huggins, R. A., Application of AC techniques to the study of lithium diffusion in tungsten trioxide thin films , J. Electrochem. Soc., 127, 343-350 (1980). Reproduced by permission of The Electrochemical Society, Inc.

Figure 10. Impedance complex plane (Nyquist plots) of lithium electrode in (A) 1.0 M LiPFe/EC/PC and (B) 1.0 M LiC104/EC/PC at initial time (0.0 h) and after 24 h. Re and Im stand for the real and imaginary parts of the impedance measured, respectively. Frequency was indicated in the figure for selected data points. Note that the first semicircle corresponds to SEI impedance. (Reproduced with permission from ref 86 (Figure 2). Copyright 1992 The Electrochemical Society.)...

Electrochemical impedance spectroscopy (EIS) profiles, measured as a function of the interrogating frequency, can be represented on both Bode and Nyquist plots. The two-component Bode plot presents a comprehensive and... 

Fig. 5.6 Equivalent electrical circuit of electrochemical cell (top) and corresponding Nyquist plot containing Warburg impedance W (bottom)...

The same consideration applies to the impedance measurement according to Fig. 8.1b. It is a normal electrochemical interface to which the Warburg element (Zw) has been added. This element corresponds to resistance due to translational motion (i.e., diffusion) of mobile oxidized and reduced species in the depletion layer due to the periodically changing excitation signal. This refinement of the charge-transfer resistance (see (5.23), Chapter 5) is linked to the electrochemical reaction which adds a characteristic line at 45° to the Nyquist plot at low frequencies (Fig. 8.2)... 

Nyquist plots recorded at an electrochemical cell with palladium electrodes or woven, non-woven or knitted textile electrodes with /4=180mm2 and d=103mm for a NaCI concentration of (1) 1x10 2, (2) 1 x10 3 and (3) 1 x10 4mol I- at T=298.0K. Part b is an enlargement of part a. 

In this section, the behaviour of the textile electrodes when used for a longer period in the electrochemical cell is investigated. It is expected that this behaviour can change as a function of time because of uptake of electrolyte solution by the textile electrodes and possible corrosion reactions that can occur. Additionally in this case, the data and results obtained for the textile electrodes will be compared with those obtained for palladium electrodes. Bode and Nyquist plots are recorded for the four types of electrodes and the electrolyte resistance was measured as a function of time for electrolyte concentrations of 1 xlCT1,1 xlO 2,1 xlO 3 and 1 xl(T4moll The values for A and d are 180 mm2 and 103 mm, respectively. For all these concentrations, the resistances are summarised in Tables9.9-9.12. 

Figure 10. Nyquist plot of the impedance spectrum experimentally measured on the ACFCE at an applied potential of 0.1 V (vs. SCE) in a 30 wt % H2SO4 solution. Dotted and solid lines represent the impedance spectra theoretically calculated based upon the transmission line model (TLM) in consideration of pore size distribution (PSD) and pore length distribution (PLD), respectively. Reprinted with permission from G. -J. Lee, S. -I. Pyun, and C. -H. Kim, J. Solid State Electrochem., 8 (2004) 110. Copyright 2003, with kind permission of Springer Science and Business Media.

Different forms of the impedance plots can be obtained for an electrochemical system described by a mixed kinetic/diffusion control process, depending on the parameters of diffusion and charge transfer. An example of a Nyquist plot is presented in Figure 1.21. 

Figure 26 Typical Nyquist plots obtained from impedance spectroscopic measurements of nickel electrodes polarized to different potentials in PC/LiAsF6 1 M solutions. The spectra were measured at the potentials indicated near each plot after the film formation was completed (the current reached a steady low value of Ca. 1 pA/cm2) [34]. (With copyright from The Electrochemical Society Inc.)...

Figure 28 A typical Nyquist plot obtained from a nickel electrode polarized to low potentials (0.2 V versus Li/Li+) in PC solutions (1 M LiBF4 in this case). The equivalent circuit analog of 4 R C circuits in series and their separate Nyquist plots (four semicircles) are also shown. The frame in the lower right represents a typical fitting between the experimental data and this equivalent circuit analog [34]. (With copyright from The Electrochemical Society Inc.)...

Figure 18 Various models proposed for the surface films that cover Li electrodes in nonaqueous solutions. The relevant equivalent circuit analog and the expected (theoretical) impedance spectrum (presented as a Nyquist plot) are also shown [77]. (a) A simple, single layer, solid electrolyte interphase (SEI) (b) solid polymer interphase (SPI). Different types of insoluble Li salt products of solution reduction processes are embedded in a polymeric matrix (c) polymeric electrolyte interphase (PEI). The polymer matrix is porous and also contains solution. Note that the PEI and the SPI may be described by a similar equivalent analog. However, the time constants related to SPI film are expected to be poorly separated (compared with a film that behaves like a PEI) [77]. (With copyrights from The Electrochemical Society Inc., 1998.)...

Generally, the impedance spectrum of an electrochemical system can be presented in Nyquist and Bode plots, which are representations of the impedance as a function of frequency. A Nyquist plot is displayed for the experimental data set Z(Zrei,Zim.,mi), (/ = 1,2,. ..,n) of n points measured at different frequencies, with each point representing the real and imaginary parts of the impedance (Zrei Zim4) at a particular frequency . 

Some typical Nyquist plots for an electrochemical system are shown in Figure 2.38. The usual result is a semicircle, with the high-frequency part giving the solution resistance (for a fuel cell, mainly the membrane resistance) and the width of the semicircle giving the charge-transfer resistance. 

Figure 2.38. Typical Nyquist plots for electrochemical systems 2.6.3 Equivalent Circuit Models...

Figure 4.27. a Ladder structure for electrochemical systems known as Faradaic reactions involving one adsorbed species (Model D23) b Nyquist plot of a ladder structure for the Faradaic reaction involving one adsorbed species, over the frequency range 1 MFIz to 1 mHz (Model D23 Rd = 200 Q, Rct = 400 Q, R3 = 600 Q, Cd, = 0.0001 F, C2 = 0.01 F)... 

Figure 5.4. Nyquist plots obtained at a DC bias potential of 0.2 V versus Ag/AgCl for electrodes with various amounts of catalyst ink applied [2], (Reprinted from Electrochimica Acta, 50(12), Easton EB, Pickup PG. An electrochemical impedance spectroscopy study of fuel cell electrodes, 2469-7, 2005, with permission from Elsevier.)...

Figure 5.20. Calculated Nyquist plot for a single cell with elimination of the transport barrier in the backing [18], (Reproduced with modifications by permission of ECS—The Electrochemical Society, from Springer TE, Zawodzinski TA, Wilson MS, Gottesfeld S. Characterization of polymer electrolyte fuel cells using AC impedance spectroscopy.)...

Figure 6.10. Comparison of Nyquist plots of fuel cells with different Nafion loadings in the catalyst layers of both the cathode and the anode [7], (Reproduced by permission of ECS—The Electrochemical Society, from Guo Q, Cayetano M, Tsou Y, De-Castro ES, White RE. Study of ionic conductivity profiles of the air cathode of a PEMFC by AC impedance spectroscopy.)...

Figure 6.18. Nyquist plots of the sprayed electrode (0.1/0.1 mg Ptcnf2) at different voltages [18], (Reproduced from Abaoud HA, Ghouse M, Lovell KV, Al-Motairy GN, Alternative formulation for proton exchange membrane fuel cell (PEMFC) electrode preparation, Journal of New Materials for Electrochemical Systems 2003 6(3) 149-55, with permission from JNMES.)...

Figure 6.20. Nyquist plots for the electrodes fabricated according to the same preparation procedure [19]. Note NSGA stands for novel silica gel additive, and TNPA stands for traditional Nafion polymer additive. The values in parentheses are the ohmic drop corrected cell potential. (Reproduced from Wang C, Mao ZQ, Xu JM, Xie XF. Preparation of a novel silica gel for electrode additive of PEMFCs. Journal of New Materials for Electrochemical Systems 2003 6(2) 65-9, with permission from JNMES.)...

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