Impedance spectra electrolytes

Introducing the complex notation enables the impedance relationships to be presented as Argand diagrams in both Cartesian and polar co-ordinates (r,rp). The fomier leads to the Nyquist impedance spectrum, where the real impedance is plotted against the imaginary and the latter to the Bode spectrum, where both the modulus of impedance, r, and the phase angle are plotted as a fiinction of the frequency. In AC impedance tire cell is essentially replaced by a suitable model system in which the properties of the interface and the electrolyte are represented by appropriate electrical analogues and the impedance of the cell is then measured over a wide... 

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),... 

In an analysis of an electrode process, it is useful to obtain the impedance spectrum —the dependence of the impedance on the frequency in the complex plane, or the dependence of Z" on Z, and to analyse it by using suitable equivalent circuits for the given electrode system and electrode process. Figure 5.21 depicts four basic types of impedance spectra and the corresponding equivalent circuits for the capacity of the electrical double layer alone (A), for the capacity of the electrical double layer when the electrolytic cell has an ohmic resistance RB (B), for an electrode with a double-layer capacity CD and simultaneous electrode reaction with polarization resistance Rp(C) and for the same case as C where the ohmic resistance of the cell RB is also included (D). It is obvious from the diagram that the impedance for case A is... 

A typical impedance spectrum obtained on LSM microelectrodes is shown in Fig. 42a. The arc represents the impedance due to the electrochemical reaction at the LSM microelectrode. A small ohmic drop caused by the YSZ electrolyte (and partly by the sheet resistance due to the finite electronic conductivity of the LSM electrode) is more than three orders of magnitude smaller than the electrode resistance and not visible in the figure. The impedance spectra for nominally identical microelectrodes turned out to be reproducible with a standard deviation <15%. The data of Fig. 42b display the relation between the electrode resistance Rei and the microelectrode diameter dme several series of experiments with different electrode thicknesses consistently revealed that the resistance Rei is approximately proportional to dmc 2. and hence to the inverse electrode area. 

Fig. 14. (a) Cyclic voltammogram of the reduction of 0.02 M H2O2 on a rotating Ag(pc) in 0.1 M HCIO4 scan rate 50 mV s-1. (b) Impedance spectrum in the complex impedance plane of Ag(pc) in the same electrolyte measured at Asmse = -0.20 V and a rotation speed lower than in (a) where the NDR branch is stable. Numbers indicate the frequency v. (Reproduced from C. Eickes, K. G. Weil and K. Doblhofer, PCCP 2 (2000), 5691-5697 by permission of The Royal Society of Chemistry on behalf of the PCCP Owner Societies.)... 

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.)...

For these reasons, EIS has been explored as an alternative proof test for evaluation of conversion coatings. In these tests, conversion coated surfaces are exposed to an aggressive electrolyte for some period of time during which coating damage will accumulate. An impedance spectrum is collected and evaluated using a suitable equivalent circuit model and complex nonlinear last-squares fitting. 

Figure 37. Nyquist plot of the experimental (solid circles) and simulated (solid Une) impedance spectrum of TRPyPz/CuTSPc film modified ITO electrode, from 1 to 100 kHz, at 0.95 and 0.60 V inset). Electrolyte 0.10 Af lithium trifluoromethane sulfonate aqueous solution.

In LEIS, the full electrochemical impedance spectrum of the sample/electrolyte interface can be obtained at the submillimeter level. The system works by stepping a probe tip across the sample surface (the smallest step size is 0.5 pm) while the sample (connected as the working electrode) is perturbed by an ac voltage waveform (usually about the open-circuit potential with an amplitude typically of 20 mV). The probe tip consists of two separated platinum electrodes, separated by a known distance. Measurement of the potential difference between the two electrodes allows the calculation of the potential gradients above the sample surface, which then give the current density. Comparison of the in-phase and out-of-phase current flow produces the impedance data, as with the regular EIS. The data can be plotted as Bode or Nyquist charts for specific points on the surface, or impedance maps of the sample surface can be obtained. 

Figure 2. Example of the impedance spectrum of a Ag/electrolyte/Ag cell at 350 °C. Separation of the resistance of the electrolyte bulk R uih resistance of grain boundaries Rgi, and polarization resistance of the electrodes R j is shown...

The model to the left in Figure 10.3 is often used to model skin impedance. For instance, R may represent the deeper viable parts and the parallel R and C components represent the poorly conducting stratum corneum (SC). The model to the right may be used for tissue as shown in Figure 10.2. Then G models the extracellular electrolyte, C, the cell membranes, and R the intracellular resistance. Fixed component values in the two models can be found so that they have exactly the same impedance spectrum. 

The applications of impedance spectroscopy are not limited to the characterization of electrode properties. Sometimes it is desirable to investigate the properties of membranes, solutions, or dielectrics. For this kind of appKcation, ur-eiectrode cells provide the best results. Two reference electrodes are placed in the electrochemical cell between counter and working electrodes (Fig. 23c). The impedance measured depends purely on the properties of the electrolyte or membrane between the two reference electrodes, and the electrode properties are completely eliminated from the impedance spectrum. 

Among these electrical elements, and represent the properties of the bulk solution and the diffusion of the redox probe, respectively, whereas Cji and / et depend on the dielectric and insulating features at the electrode/electrolyte interface, respectively. The electrochemical impedance spectrum in Fig. 4d shows a typical Bode plot for the IME system with mixed kinetic and charge transfer control. The agreement between the measured data (solid line) and the fitting spectrum (broken Une) indicates that this... 

The complex impedance plots of these electrolytes recorded at frequencies between 5 Hz and 100 kHz consist of a single spur touching down at the real axis (Figure 3.8). The spectrum corresponds to an equivalent circuit in which a resistor is in series with a capacitor and is consistent with the arguments developed earlier in this chapter for the impedance spectrum of a highly conductive electrolyte in this frequency range. 

Figure 4.1.31. Comparison of admittance and impedance spectra for a zirconia solid electrolyte (TxOii 6 mole % Y2O3) at 240°C (a) Experimental admittance spectrum, (b) Experimental impedance spectrum, (c) Simulated impedance spectrum, using the circuit of Figure 4.1.30 and parameter values given in Table 4.1.5.

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