EIS Equivalent Circuits

As discussed in Chapter 3, the electrolyte/interface and associated electrochemical processes can be treated as an electric circuit consisting of electrical elements, including resistance, capacitors, constant phase elements, and so on. Although the commonly used electrical elements have already been described in Chapters 2 and 3, the following section provides a brief review to preface the ensuing discussion of EIS equivalent circuits and their related PEM fuel cell processes. 

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. 

Other Useful Information Obtained by Probes Both EIS and electrochemical noise probes can be used to determine information about the reactions that affect corrosion. Equivalent circuit analysis, when properly applied by an experienced engineer, can often give insight into the specifics of the corrosion reactions. Information such as corrosion product layer buildup, or inhibitor effectiveness, or coating breakdown can be obtained directly from analysis of the data from EIS or indirectly from electrochemical noise data. In most cases, this is merely making use of methodology developed in the corrosion laboratory. 

FIGURE 7.3 Simplified equivalent circuit of an original (unmodified) EIS structure (a) and EIS biosensor functionalized with charged macromolecules (b). Cj, Cx and CML are capacitances of the gate insulator, the space-charge region in the semiconductor, and the molecular layer, respectively / u is the resistance of... 

Figure 5.10 is EIS of marmatite electrode in O.lmol/L KNO3 solution with different pH modifiers at open circuit potential. This EIS is very complicated. Simple equivalent circuit can be treated as the series of electrochemical reaction resistance R with the capacitance impedance Q == (nFr )/(icR ) resulting fi-om adsorbing action, and then parallel with the capacitance Ca of double electric... 

EIS data is generally interpreted based on defining an appropriate equivalent circuit model that best fits the acquired data. The elements of the circuit model involve a specific arrangement of resistors, capacitors, and inductors that tacitly represent the physicochemical reality of the device under test. Under these circumstances the numerical value for chemical properties of the system can be extracted by fitting the data to the equivalent circuit model. Impedance measurements are typically described by one of two models ... 

Electrochemical impedance measurements of the physical adsorption of ssDNA and dsDNA yields useful information about the kinetics and mobihty of the adsorption process. Physical adsorption of DNA is a simple and inexpensive method of immobilization. The ability to detect differences between ssDNA and dsDNA by impedance could be applicable to DNA biosensor technology. EIS measurements were made of the electrical double layer of a hanging drop mercury electrode for both ssDNA and dsDNA [34]. The impedance profiles were modeled by the Debye equivalent circuit for the adsorption and desorption of both ssDNA and dsDNA. Desorption of denatured ssDNA demonstrated greater dielectric loss than desorption of dsDNA. The greater flexibility of the ssDNA compared to dsDNA was proposed to account for this difference. 

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. 

Generally, depending on the bias potential, the EIS leads to RC equivalent circuit loops representing both the space charge and the interface impedance components. The complete set of imaginary versus real impedance data leads to the construction of a semicircle that can be... 

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.

Eventually, as pores increase in size, additional equivalent circuit elements are required to account for the detection of these pores as discrete time constants in the low frequency end of the spectrum, Fig. 19C. As frequencies are scanned to lower values in recording the EIS spectrum, the frequency at which the decrease in phase shift (i.e., a decrease in absolute value of the phase angle) commences provides an indication of either the number density of fine pores or the dimensions of a smaller number of larger pores. The value of the pore resistance (/ pore) is a more direct indication of pore dimension. The interfacial capaci-... 

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. 

Equivalent circuit analysis is well suited for analysis of EIS measurements of conversion coatings and is the primary method for interpreting EIS spectra from conversion coated metal surfaces. A widely accepted generalized equivalent circuit model for the EIS response of pitted conversion coatings is shown in Fig. 22a (66,67). Several related models discussed below are also shown. In the gener-... 

Figure 25 (a) Bode plot for CeCl3-treated 7075-T6 during immersion in 0.5 M NaCl solution, (b) Results of the equivalent circuit modeling of the EIS data from Fig. 25 using the generalized equivalent circuit model in Figure 22a. (From F. Mansfeld, S. Lin. S. Kim. H. Shih. Corrosion 45, 615 (1989).)... 

Breakdown of anodic films is yet another phenomenon for which EIS is well suited. Equivalent circuit analysis has been used to analyze EIS spectra from corroding anodized surfaces. While changes in anodic films due to sealing are detected at higher frequencies, pitting is detected at lower frequencies. Film breakdown leads to substrate dissolution, and equivalent circuit models must be amended to account for the faradaic processes associated with localized corrosion. 

Figure 41 Example of simulated EIS data from the equivalent circuit model shown with circuit element values indicated in the plot. (From M. Kendig, J. Scully. Corrosion 46, 22 (1990).)...

Figure 43 Equivalent circuit model for a degraded polymer coating on a metal substrate and the corresponding EIS data presented in Bode plot format. The breakpoint frequency is indicated as/b in the plot. (From C. H. Tsai, F. Mansfeld. Corrosion 49, 726 (1993).)...

EIS data analysis is commonly carried out by fitting it to an equivalent electric circuit model. An equivalent circuit model is a combination of resistances, capacitances, and/or inductances, as well as a few specialized electrochemical elements (such as Warburg diffusion elements and constant phase elements), which produces the same response as the electrochemical system does when the same excitation signal is imposed. Equivalent circuit models can be partially or completely empirical. In the model, each circuit component comes from a physical process in the electrochemical cell and has a characteristic impedance behaviour. The shape of the model s impedance spectrum is controlled by the style of electrical elements in the model and the interconnections between them (series or parallel combinations). The size of each feature in the spectrum is controlled by the circuit elements parameters. 

When investigating an electrochemical system using EIS, the equivalent circuit model that has been constructed must be verified. An effective way to do so is to alter a single cell component and see if the expected changes in the impedance spectrum occur, or to keep adding components to the circuit to see if a suitable circuit can be achieved, until reaching a perfect fit. Nevertheless, empirical models should use as few components as possible. 

The rapid development of computer technology has yielded powerful tools that make it possible for modem EIS analysis software not only to optimize an equivalent circuit, but also to produce much more reliable system parameters. For most EIS data analysis software, a non-linear least squares fitting method, developed by Marquardt and Levenberg, is commonly used. The NLLS Levenberg-Marquardt algorithm has become the basic engine of several data analysis programs. 

Research Solutions Resources (2008) Fitting EIS data to equivalent circuits. http //www.consultrsr.com/resources/eis/eiscrkts.htm. Accessed 1 December 2008... 

When we begin to investigate an electrochemical system, we normally know little about the processes or mechanisms within the system. Electrochemical impedance spectroscopy (EIS) can be a powerful approach to help us establish a hypothesis using equivalent circuit models. A data-fitted equivalent circuit model will suggest valuable chemical processes or mechanisms for the electrochemical system being studied. From Chapter 1, we know that a fuel cell is actually an electrochemical system involving electrode/electrolyte interfaces, electrode reactions, as well as mass transfer processes. Therefore, EIS can also be a powerful tool to diagnose fuel cell properties and performance. 

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