Electrochemical impedance spectroscopy model

Keywords Electrochemical Impedance Spectroscopy, modeling, Li-ion cell, inner resistance, voltage step response, Constant Phase Element... 

Electrochemical impedance spectroscopy was used to determine the effect of isomers of 2,5-bis( -pyridyl)-l,3,4-thiadiazole 36 (n 2 or 3) on the corrosion of mild steel in perchloric acid solution <2002MI197>. The inhibition efficiency was structure dependent and the 3-pyridyl gave better inhibition than the 2-pyridyl. X-ray photoelectron spectroscopy helped establish the 3-pyridyl thiadiazoles mode of action toward corrosion. Adsorption of the 3-pyridyl on the mild steel surface in 1M HCIO4 follows the Langmuir adsorption isotherm model and the surface analysis showed corrosion inhibition by the 3-pyridyl derivative is due to the formation of chemisorbed film on the steel surface. 

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. 

The state of charging, mainly of sealed cells, can be studied using galvanos-tatic methods [353] and electrochemical impedance spectroscopy [354-356] (see reviews [357, 358]). The battery behavior was analyzed using electronic network modeling [359, 360]. 

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. 

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. 

Brunetto C, Tina G, Squadrito G, Moschetto A (2004) PEMFC diagnostics and modelling by electrochemical impedance spectroscopy. Proceedings of the 12th IEEE Mediterranean electrochemical conference. IEEE Cat. No. 04CH37521, 3 1045-50... 

Wang X, Hsing IM, Leng YJ, Yue PL (2001) Model interpretation of electrochemical impedance spectroscopy and polarization behavior of H2/CO mixture oxidation in polymer electrolyte fuel cells. Electrochim Acta 46(28)4397-405... 

Agarwal P, Orazem ME, Garcia-Rubio LH (1992) Measurement models for electrochemical impedance spectroscopy. J Electrochem Soc 139(7) 1917-27... 

Remember 5.2 Kinetic expressions of the law of mass action provide the foundation for modeling the charge-transfer resistance commonly encountered in electrochemical impedance spectroscopy. 

P. Agarwal, M. E. Orazem, and L. H. Garcia-Rubio, "Measurement Models for Electrochemical Impedance Spectroscopy I. Demonstration of Applicability," Journal of The Electrochemical Society, 139 (1992) 1917-1927. 

I. Frateur, C. Deslouis, M. E. Orazem, and B. Tribollet, "Modeling of the Cast Iron/Drinking Water System by Electrochemical Impedance Spectroscopy," Electrochimica Acta, 44 (1999) 4345-4356. 

The kinetics and mechanisms of 3D Me deposition have been intensively studied by electrochemical impedance spectroscopy (EIS) as well as classical electrochemical techniques during the last two decades. Different simplified models of 2D nucleation and growth were theoretically treated in terms of their impedance behavior by Armstrong and Metcalfe [6.72] and Eppelboin et al. [6.73]. Later, a more realistic model of a partially blocked electrode surface was developed and analyzed by Schmidt, Lorenz et al. [6.75-6.78]. 

Model study investigating the role of interfacial factors in electrochemical impedance spectroscopy measurements. Corrosion 2000, (7),... 

Concerning the two-layer model, the thickness and properties of each layer depend on the nature of the electrolyte and the anodisation conditions. For the application, a permanent control of thickness and electrical properties is necessary. In the present chapter, electrochemical impedance spectroscopy (EIS) was used to study the film properties. The EIS measurements can provide accurate information on the dielectric properties and the thickness of the barrier layer [13-14]. The porous layer cannot be studied by impedance measurements because of the high conductivity of the electrolyte in the pores [15]. The total thickness of the aluminium oxide films was determined by scanning electron microscopy. The thickness of the single layers was then calculated. The information on the film properties was confirmed by electrical characterisation performed on metal/insulator/metal (MIM) structures. 

Electrochemical impedance spectroscopy (EIS) simplest electrical-circuit model... 

Membrane structures that contain the visual receptor protein rhodopsin were formed by detergent dialysis on platinum, silicon oxide, titanium oxide, and indium—tin oxide electrodes. Electrochemical impedance spectroscopy was used to evaluate the biomembrane structures and their electrical properties. A model equivalent circuit is proposed to describe the membrane-electrode interface. The data suggest that the surface structure is a relatively complete single-membrane bilayer with a coverage of 0.97 and with long-term stability/... 

Membranes containing the visual pigment rhodopsin, a G-protein-linked receptor, were chosen as a model system for this work. Rhodopsin was one of the first integral membrane proteins whose amino acid sequence was determined (16-18). More than 40 receptors have been reported to have structural and functional homologies with rhodopsin (19). This chapter describes the use of electrochemical impedance spectroscopy to evaluate lipid bilayer membranes containing rhodopsin formed on electrode surfaces. 

Electrochemical impedance spectroscopy provides a sensitive means for characterizing the structure and electrical properties of the surface-bound membranes. The results from impedance analysis are consistent with a single biomembrane-mimetic structure being assembled on metal and semiconductor electrode surfaces. The structures formed by detergent dialysis may consist of a hydrophobic alkyl layer as one leaflet of a bilayer and the lipid deposited by dialysis as the other. Proteins surrounded by a bound lipid layer may simultaneously incorporate into pores in the alkylsilane layer by hydrophobic interactions during deposition of the lipid layer. This model is further supported by the composition of the surface-bound membranes and by Fourier transform infrared analyses (9). 

With modern computerized frequency-analysis instrumentation and software, it is possible to acquire impedance data on cells and extract the values for all components of the circuit models of Figure 2.>7, This type of analysis, w hich is called electrochemical impedance spectroscopy, reveals the nature t>f the faradaic processes and often aids in the investigation of the mechanisms of electron-transfer reactions. In the section that follows, we explore the processes at the electrode-solution interface that give rise to the faradaic impedance. 

Electrochemical impedance spectroscopy EIS Impedance of coated metal Modeling 95, 96... 

Finally, electrochemical impedance spectroscopy (EIS) can be used to quantify the impedance characteristics of a CP. The vast majority of literature has shown that CP coating of conventional electrode materials can reduce the interface impedance by several orders of magnitude [12,52,79,139]. This has widely been attributed to the increase in surface area available for charge transfer when CPs are employed. Importantly, EIS is also used to model the electrode interface. CPs reportedly alter the capacitive behavior of conventional electrode materials to produce a predominantly resistive interface with significantly smaller phase angles at low frequencies [12,51,139,140]. 

Mansfeld, F. 1995. The Use of Electrochemical Impedance Spectroscopy for the Evaluation of the Properties of Passive Films and Protective Coatings. ACH-Model Chem., 132 (4), 619. 

Electric Double Layer and Fractal Structure of Surface Electrochemical impedance spectroscopy (EIS) in a sufficiently broad frequency range is a method well suited for the determination of equilibrium and kinetic parameters (faradaic or non-faradaic) at a given applied potential. The main difficulty in the analysis of impedance spectra of solid electrodes is the frequency dispersion of the impedance values, referred to the constant phase or fractal behavior and modeled in the equivalent circuit by the so-called constant phase element (CPE) [5,15,16, 22, 35, 36]. The frequency dependence is usually attributed to the geometrical nonuniformity and the roughness of PC surfaces having fractal nature with so-called selfsimilarity or self-affinity of the structure resulting in an unusual fractal dimension... 

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