Impedance semicircle

TSC inhibitor [26], Notice from this Figure 3.11 that the Nyquist impedance semicircles increase with increasing content of the TSC inhibitor. This implies that the polarization resistance (iip) also increases with additions of this inhibitor, which in turn, decreases the corrosion rate (Cji) as indicated in Table 3.3. 

The impedance at the electrochemical reaction interface where reaction occurs can be represented as a parallel combination of charge transfer resistance and a double-layer capacitance. The Nyquist plot for the parallel RC circuit is a characteristic semicircle where the high-frequency intercept of the impedance semicircle is zero and the low-frequency intercept of the semicircle is resistance Rqj. The diameter of the semicircle Rct provides information on the reaction kinetics of the electrochemical reaction interface. A large-diameter semicircle (large Rct) indicates sluggish reaction kinetics while a small-diameter semicircle indicates facile reaction kinetics. 

The Randle cell represents the combination of electrolyte resistance, a double-layer capacitance, and a charge transfer or polarization resistance. The Nyquist plot for a Randle cell is also a semicircle however, the high-frequency intercept of the impedance semicircle is electrolyte resistance Rbl-Thus, electrol5de resistance can be found by reading the real axis value at the high-frequency intercept. This is the intercept near the origin of the plot. The real axis value at the other (low frequency) intercept is the sum of the polarization resistance and the electrolyte resistance. The diameter of the semicircle is therefore equal to the polarization resistance. 

The interfacial phenomena in LiX/PE systems were studied extensively by Scro-sati and co-workers [3, 53, 130]. They found that the high-frequency semicircle in the impedance spectrum of LiC104/ P(EO)8 electrolyte (EO = ethylene oxide),... 

Since this is a new field, little has been published on the LiXC6 /electrolyte interface. However, there is much similarity between the SEIs on lithium and on LixC6 electrodes. The mechanism of formation of the passivation film at the interface between lithiated carbon and a liquid or polymer electrolyte was studied by AC impedance [128, 142]. Two semicircles observed in AC-impedance spectra of LiAsF6/EC-2Me-THF electrolytes at 0.8 V vs. Li/Li+ [142] were attributed to the formation of a surface film during the first charge cycle. However, in the cases of LiC104 or LiBF4 /EC-PC-DME (di-... 

By comparing impedance results for polypyrrole in electrolyte-polymer-electrolyte and electrode-polymer-electrolyte systems, Des-louis et alm have shown that the charge-transfer resistance in the latter case can contain contributions from both interfaces. Charge-transfer resistances at the polymer/electrode interface were about five times higher than those at the polymer/solution interface. Thus the assignments made by Albery and Mount,203 and by Ren and Pickup145 are supported, with the caveat that only the primary source of the high-frequency semicircle was identified. Contributions from the polymer/solution interface, and possibly from the bulk, are probably responsible for the deviations from the theoretical expressions/45... 

Amemiya etal.206 have combined spectroelectrochemical and impedance experiments to probe the origin of high-frequency semicircles in... 

In Fig. 15.9, the impedance spectra of a freshly assembled Li/Cu5.5SiFe4Sni2S32 cell in discharge state and subsequent to it charging are shown. The spectrum is characterized by a high-frequency small semicircle followed by the low-frequency data in the form of an incomplete large semicircle. 

Another coordinate system, plots of capacitive component of impedance X, against the resistive component R was proposed in 1941 by K. S. Cole and R. H. Cole for electric circuits. In 1963 this system (called Cole-Cole plots) was used by M. Sluyters-Rehbach and J. H. Sluyters in electrochemistry for extrapolation of the experimental data. In the case discussed, the resulting impedance diagram has the typical form of a semicircle with the center on the horizontal axis (Fig. I2.I7a). This is readily understood when the term coCp is eliminated from the expressions for R and in Eq. (12.25). Then we obtain, after simple transformations. 

The kinetics of H2 oxidation has been investigated on a Ni/YSZ cermet nsing impedance spectroscopy at zero dc polarization. The hydrogen reaction appears to be very complex. The electrode response appears as two semicircles. The one in the high-freqnency range is assumed to arise partly from the transfer of ions across the TPB and partly from the resistance inside the electrode particles. The semicircle observed at low freqnencies is attributed to a chemical reaction resistance. The following reaction mechanism is suggested ... 

The resulting dependence of Z" on Z (Nyquist diagram) is involved but for values of Rp that are not too small it has the form of a semicircle with diameter Rp which continues as a straight line with a slope of unity at lower frequencies (higher values of Z and Z"). Analysis of the impedance diagram then yields the polarization resistance (and thus also the exchange current), the differential capacity of the electrode and the resistance of the electrolyte. 

There remains the problem of the lowest frequency semicircle. In fact, this is associated with Pt-C),. Under high CP concentrations, Pt-O formation is strongly suppressed, coverage is low and can be maintained reasonably constant within the timescale of an AC impedance run. However, if the chloride concentration is reduced, or if the Pt is not pre-conditioned by holding it at the measured potential for several minutes to stabilise a steady state, then this third semicircle changes drastically. 

Consider the impedance circuit of Fig. 13.6. Show that for Zw = 0 a Nyquist plot gives a semicircle. If Zw / 0 calculate the frequency region in which the semicircle merges into a straight line of unit slope. 

Often a non-blocking interface will behave like a resistance (/ ct) and capacitance (Q,) in parallel. This leads to a semicircle in the impedance plane which has a high frequency limit at the origin and a low frequency limit at Z = (Fig. 10.4). At the maximum of the semicircle if the angular frequency is then ctQin>max = fro which dl can be evaluated. 

The interface impedance for a case such as Ag/Ag4Rbl5 will consist of a capacitance (derived from the Helmholtz formula) in parallel with i et so that in the complex plane impedance a semi-circle will be found from which Qi and can be evaluated. Rq will cause this semicircle to be offset from the origin by a high frequency semicircle due to the bulk impedance between the interface and the reference electrode (Fig. 10.12). There can be no Warburg impedance (a line at 45° to the real axis generally due to diffusion effects) in this case. 

At high frequencies, a semicircle is expected as a result of a parallel combination of R and Cg. At low frequencies a Warburg impedance may be found as part of the interfacial impedance. In some cases it may dominate the interfacial impedance as in Fig. 10.13(a), in which case only the diffusion coefficient of the salt will be determinable. It should be noted that, in the absence of a supporting electrolyte, the electroactive species, in this case Li, cannot diffuse independently of the anions. 

In other cases as in Fig. 10.13(b) the interfacial impedance will show a semicircle due to / <., and Cj, in parallel, with the Warburg impedance becoming apparent at significantly lower frequencies. In such cases R can be evaluated without difficulty. 

Fig. 10.13 Impedance plane diagrams for metal non-blocking electrodes with two mobile species in the electrolyte, (a) Interfacial impedance is only a Warburg impedance. (b) Interfacial impedance shows a charge transfer resistance semicircle.

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.)...

By EIS analysis of the corresponding lithium ion cells, Zhang et al. showed that the impact of SEI resistance on total cell impedance was rather negligible, and hence, they attributed the superior low-temperature behavior of LiBF4-based electrolytes to the lower resistance associated with the so-called charge-transfer processes , which are usually represented in impedance spectra by the semicircle at the lower frequency region. This suggestion could be viewed as a further extension of the conclusion... 

Figure 66. Nyquist plots of the impedance spectra as measured for the fully charged lithium ion cells at —30 °C in which the inset shows the magnified view of the high-frequency part. Electrolytes are 1.0 m LiPFe (hollow) and L1BF4 (solid) in PC/EC/EMC (1 1 3). Note that the semicircles In the inset are almost invisible in the scale of the whole spectra. (Reproduced with permission from ref 134 (Figure 4). Copyright 2002 Elsevier.)...

As has been shown in Eigure 68, since the time constants for these two electrochemical components, Rsei and Ra, are comparable at anode/electrolyte and cathode/electrolyte interfaces, respectively, the impedance spectra of a full lithium ion could have similar features in which the higher frequency semicircle corresponds to the surface films on both the anode and the cathode, and the other at lower frequency corresponds to the charge-transfer processes occurring at both the anode and the cathode. ... 

---