Electrochemical impedance spectroscopy resistance circuit

Most often, the electrochemical impedance spectroscopy (EIS) measurements are undertaken with a potentiostat, which maintains the electrode at a precisely constant bias potential. A sinusoidal perturbation of 10 mV in a frequency range from 10 to 10 Hz is superimposed on the electrode, and the response is acquired by an impedance analyzer. In the case of semiconductor/electrolyte interfaces, the equivalent circuit fitting the experimental data is modeled as one and sometimes two loops involving a capacitance imaginary term in parallel with a purely ohmic resistance R. 

Rational optimization of performance should be the main goal in development of any chemical sensor. In order to do that, we must have some quantitative tools of determination of key performance parameters. As we have seen already, for electrochemical sensors those parameters are the charge-transfer resistance and the double-layer capacitance. Particularly the former plays a critical role. Here we outline two approaches the Tafel plots, which are simple, inexpensive, but with limited applicability, and the Electrochemical Impedance Spectroscopy (EIS), based on the equivalent electrical circuit model, which is more universal, more accurate, and has a greater didactic value. 

The second meaning of the word circuit is related to electrochemical impedance spectroscopy. A key point in this spectroscopy is the fact that any -> electrochemical cell can be represented by an equivalent electrical circuit that consists of electronic (resistances, capacitances, and inductances) and mathematical components. The equivalent circuit is a model that more or less correctly reflects the reality of the cell examined. At minimum, the equivalent circuit should contain a capacitor of - capacity Ca representing the -> double layer, the - impedance of the faradaic process Zf, and the uncompensated - resistance Ru (see -> IRU potential drop). The electronic components in the equivalent circuit can be arranged in series (series circuit) and parallel (parallel circuit). An equivalent circuit representing an electrochemical - half-cell or an -> electrode and an uncomplicated electrode process (-> Randles circuit) is shown below. Ic and If in the figure are the -> capacitive current and the -+ faradaic current, respectively. 

Transmission line — This term is related to a more general concept of electric -> equivalent circuits used frequently for interpretation of experimental data for complex impedance spectra (-> electrochemical impedance spectroscopy). While the complex -> impedance, Z, at a fixed frequency can always by obtained as a series or parallel combinations of two basic elements, a resistance and a capacitance, it is a much more compli-... 

Electrochemical corrosion techniques are essential to predict service life in chemical and construction industries. The following direct current (dc) electrochemical methods are used in corrosion engineering practice linear polarization technique, Tafel extrapolation, and open circuit potential vs. time measurements. The alternating current (ac) technique is electrochemical impedance spectroscopy (EIS). This technique uses alternating current to measure frequency-dependent processes in corrosion and estimates the change of polarization resistance as a function of time. 

Electrochemical methods are well adapted for characterizing the corrosion behavior of coated metals in solution. Because of the high resistance of organic coatings, ac methods are generally more suited than dc polarization methods. In electrochemical impedance spectroscopy (EIC) one measures the response of the coated electrode to a small amplitude ac perturbation as a function of frequency (Chapter 5). The interpretation of the measured frequency response, in principle, requires a physical model. However, for coated metals useful information is more easily obtained by representing the metal-coating-electrolyte interface by an electrical circuit (equivalent circuit). 

Analysis based on electrochemical impedance spectroscopy (EIS also called AC impedance spectroscopy) allows estimation of frequency behavior, quantification of resistance, and the ability to model equivalent circuits (ECs) of ES systems. The fundamental EC for a double-layer circuit, as discussed in Chapter 2, contains series resistance and double-layer capacitance. In addition, there is often a faradic parallel resistance from impurities in the carbon. In the pseudocapacitive case, the faradic resistance is a related reciprocal of the overpotential-dependent charge transfer [2,21]. 

ABSTRACT State determination of Li-ion cells is often accomplished with Electrochemical Impedance Spectroscopy (EIS). The measurement results are in frequency domain and used to describe the state of a Li-ion cell by parameterizing impedance-based models. Since EIS is a costly measurement method, an alternative method for the parameterization of impedance-based models with time-domain data easier to record is presented in this work. For this purpose the model equations from the impedance-based models are transformed from frequency domain into time domain. As an excitation signal a current step is applied. The resulting voltage step responses are the model equations in time domain. They are presented for lumped and derived for distributed electrical circuit elements, i.e. Warburg impedance, Constant Phase Element and RCPE. A resulting technique is the determination of the inner resistance from an impedance spectrum which is performed on measurement data. 

As discussed above, the corrosion current density (Icorr), the critical current density (Icri), and the passive current density (Ipass) were obtained from potentiodynamic polarization. The capacitance (Qf) and the resistance (Rf) of oxide layer were obtained from electrochemical impedance spectroscopy (EIS) equivalent circuits. And the weight-loss rate (Wbss) was obtained from weight-loss immersion test. All these data were taken from experiments at ambient temperature (25°C) in 0.5 M H2SO4. 

The electrochemical impedance spectroscopy (EIS) method is very useful in characterizing an electrode corrosion behavior. The electrode characterization includes the determination of the polarization resistance (/J ), corrosion rate (Cfl), and electrochemical mechanism [1,4,6,19-28]. The usefulness of this method permits the analysis of the alternating current (AC) impedance data, which is based on modeling a corrosion process by an electrical circuit. Several review papers address the electrochemical impedance technique based on the AC circuit theory [22-24,29-30]. 

In Chapter 1, Figure 1.4 shows a typical polarization curve of a PEM fuel cell. The voltage loss of a cell is determined by its OCV, electrode kinetics, ohmic resistance (dominated by the membrane resistance), and mass transfer property. In experiments, the OCV can be measured directly. If the ohmic resistance (Rm). kinetic resistance (Rt, also known as charge transfer resistance), and mass transfer resistance (Rmt) are known, the fuel cell performance is easily simulated. As described in Chapter 3, electrochemical impedance spectroscopy (EIS) has been introduced as a powerfiil diagnostic technique to obtain these resistances. By using the equivalent circuit shown in Figure 3.3, Rm, Rt, and R t can be simulated based on EIS data. 

Electrochemical impedance spectroscopy is useful in the evaluation of coatings, the elucidation of transport phenomena in electrochemical systems, and the determination of corrosion mechanisms and rates. Bode and Nyquist plots are the most common data output formats, and an example of each for a simple parallel-connected resistance-capacitance circuit are shown in Figs. 31.3, and 31.4, respectively. The Bode plot format shows the... 

Figure 11. (a) A commonly used circuit model representing resistive and capacitive elements in a corrosion cell, and (b) graphical derivation of values for / s and from a Bode plot of the modulus and phase angle values as a function of applied sweep frequency in an electrochemical impedance spectroscopy experiment. 

Corrosion behavior of uncoated and Ti02 deposited Ti6A14V was evaluated by Karpagavalli et al. (2007) in freely aerated Hank s solution at 37°C by the measurement and analysis of open circuit potential variation with time, Tafel plots and electrochemical impedance spectroscopy. The electrochemical results indicated that nano Ti02 coated Ti6A14V showed a better corrosion resistance (Table 5.7, Fig. 5.14) in simulated biofluid than uncoated Ti6A14V. 

---