Adsorption impedance Resistance

All three elements can scarcely be identified from impedance spectra of systems with adsorption for example, in many cases the adsorption resistance is masked by the diffusional element. In addition, whenever electrodes of inhomogeneous surfaces (e.g., poly crystalline electrodes) are measured, the resistance-diffusional element - capacitance terms of the adsorption impedance are smeared out yielding a CPE-like impedance. 

Equations (II.5.46) and (II.5.47) correspond to an equivalent circuit in which the capacity Chf is in parallel with the adsorption impedance Z. This impedance represents a series of an adsorption resistance (determined by the rate of adsorption) and a Warburg-like complex impedance (corresponding to diffusion of the surfactants) and a pure capacity Clf The electrolyte resistance is already eliminated here. For very high frequencies it follows that and... 

Adsorption impedance Z may be represented by a parallel combination of resistance R and CPE p, which represents pseudocapadtance created by charge accumulation at the electrode surface. The adsorbed spedes become involved in complex surface-mediated kinetics, such as temperature-driven complexation of the surface-active oil additives [7]. The experimental and modeled data confirmed the presence of two facile adsorption-driven processes—adsorption of at least two different groups of surface-active oil additives (likely to be detergents and antwear agents), and their mutual complexation. 

Variations of resistance with frequency can also be caused by electrode polarization. A conductance cell can be represented in a simplified way as resistance and capacitance in series, the latter being the double layer capacitance at the electrodes. Only if this capacitance is sufficiently large will the measured resistance be independent of frequency. To accomplish this, electrodes are often covered with platinum black 2>. This is generally unsuitable in nonaqueous solvent studies because of possible catalysis of chemical reactions and because of adsorption problems encountered with dilute solutions required for useful data. The equivalent circuit for a conductance cell is also complicated by impedances due to faradaic processes and the geometric capacity of the cell 2>3( . 

Fig 29. A simple equivalent circuit for the artificial permeable membrane. Physical meaning of the elements C, membrane capacitance (dielectric charge displaceme-ment) R, membrane resistance (ion transport across membrane) f pt, Phase transfer resistance (ion transport across interface) Zw, Warburg impedance (diffusion through aqueous phase) Ctt, adsorption capacitance (ion adsorption at membrane side of interface) Cwa, aqueous adsorption capacitance (ion adsorption at water side of interface). From ref. 109. 

By the method of introducing Pt into the DLC, the platinum metal is assumed to be distributed over the carbonaceous material bulk as discrete atoms or clusters [154], Essentially, Pt is not a dopant in the DLC, in the sense that the term is used in semiconductor physics. Nor is the percolation threshold surpassed, since the admixture of Pt (not exceeding 15 at. %) did not affect the a-C H resistivity, as was shown by impedance spectroscopy tests p 105 Q, cm, like that of the undoped DLC (see Table 3). It was thus proposed that the Pt effect is purely catalytic one Pt atoms on the DLC surface are the active sites on which adsorption and/or charge transfer is enhanced [75], (And the contact of the carbon matrix to the Pt clusters is entirely ohmic.) This conclusion was corroborated by the studies of Co tetramethylphenyl-porphyrin reaction kinetics at the DLC Pt electrodes [155] redox reactions involving the Co central ion proceed partly under the adsorption of the porphyrin ring on the electrode. 

The detailed derivation leads to an impedance function, having an equivalent circuit where serially to the adsorption capacitance there are a resistance and a -> Warburg impedance [1]. Important points are as follows ... 

The above formulas may become inapplicable for systems with adsorption processes or/and coupled chemical steps in solution whose characteristic times are comparable with the inverse frequency within the impedance measurement interval. In this case the charge-transfer resistance, Rct, must be replaced by a complex charge-transfer impedance, Zct. Another restriction of this treatment is its assumption of the uniform polarization of the m s interface which requires to ensure a highly symmetrical configuration of the system. Refs. [i] Sluyters-Rehbach M, Sluyters JH (1970) Sine wave methods in the study of electrode processes. In Bard A/ (ed) Electroanalytical chemistry, vol. 4. Marcel Dekker, New York, p 1 [ii] Bard A], Faulkner LR (2001) Electrochemical methods, 2nd edn. Wiley, New York [iii] Retter U, Lohse H (2005) Electrochemical impedance spectroscopy. In Scholz F (ed) Electroanalytical methods. Springer, Berlin, pp 149-166 [iv] Bar-soukov E, Macdonald JR (ed) (2005) Impedance spectroscopy. Wiley, Hoboken... 

Two impedance arcs, which correspond to two relaxation times (i.e., charge transfer plus mass transfer) often occur when the cell is operated at high current densities or overpotentials. The medium-frequency feature (kinetic arc) reflects the combination of an effective charge-transfer resistance associated with the ORR and a double-layer capacitance within the catalyst layer, and the low-fiequency arc (mass transfer arc), which mainly reflects the mass-transport limitations in the gas phase within the backing and the catalyst layer. Due to its appearance at low frequencies, it is often attributed to a hindrance by finite diffusion. However, other effects, such as constant dispersion due to inhomogeneities in the electrode surface and the adsorption, can also contribute to this second arc, complicating the analysis. Normally, the lower-frequency loop can be eliminated if the fuel cell cathode is operated on pure oxygen, as stated above [18],... 

High r factors are, however, not without some other complications since they imply porosity of materials. Porosity can lead to the following difficulties (a) impediment to disengagement of evolved gases or of diffusion of elec-trochemically consumable gases (as in fuel-cell electrodes 7i2) (b) expulsion of electrolyte from pores on gas evolution and (c) internal current distribution effects associated with pore resistance or interparticle resistance effects that can lead to anomalously high Tafel slopes (132, 477) and (d) difficulties in the use of impedance measurements for characterizing adsorption and the double-layer capacitance behavior of such materials. On the other hand, it is possible that finely porous materials, such as Raney nickels, can develop special catalytic properties associated with small atomic metal cluster structures, as known from the unusual catalytic activities of such synthetically produced polyatomic metal clusters (133). 

On an Au/ITO electrode, Hb exhibited similar electrochemical behavior to Mb if Hb was immobilized on the electrode surface by casting the Hb solution thereon. However, when Hb was immobilized on Au/ITO by adsorption of Hb on a modified electrode, no direct voltammetric response for Hb could be seen. This was because the adsorption of Hb on the modified electrode did not provide a sufficient amount of protein. However, the adsorptive immobilization of Hb on a gold nanoparticle-modified ITO electrode could be observed by electrochemical impedance measurements using an [Fe(CN)6]37[Fe(CN)6]4 redox probe (Figure 14) [46], By the simulation program, the charge transfer resistance (Rt) value of bare ITO is estimated to be 77.43 kQ, which is decreased to 15.97 kQ after the gold nanoparticles... 

The above analysis shows that in the simple case of one adsorbed intermediate (according to Langmuirian adsorption), various complex plane plots may be obtained, depending on the relative values of the system parameters. These plots are described by various equivalent circuits, which are only the electrical representations of the interfacial phenomena. In fact, there are no real capacitances, inductances, or resistances in the circuit (faradaic process). These parameters originate from the behavior of the kinetic equations and are functions of the rate constants, transfer coefficients, potential, diffusion coefficients, concentrations, etc. In addition, all these parameters are highly nonlinear, that is, they depend on the electrode potential. It seems that the electrical representation of the faradaic impedance, however useful it may sound, is not necessary in the description of the system. The systen may be described in a simpler way directly by the equations describing impedances or admittances (see also Section IV). In... 

III.l [see also Eq. (17) and Fig. 2], and that in the presence of a faradaic reaction [Section III. 2, Fig. 4(a)] are found experimentally on liquid electrodes (e.g., mercury, amalgams, and indium-gallium). On solid electrodes, deviations from the ideal behavior are often observed. On ideally polarizable solid electrodes, the electrically equivalent model usually cannot be represented (with the exception of monocrystalline electrodes in the absence of adsorption) as a smies connection of the solution resistance and double-layer capacitance. However, on solid electrodes a frequency dispersion is observed that is, the observed impedances cannot be represented by the connection of simple R-C-L elements. The impedance of such systems may be approximated by an infinite series of parallel R-C circuits, that is, a transmission line [see Section VI, Fig. 41(b), ladder circuit]. The impedances may often be represented by an equation without simple electrical representation, through distributed elements. The Warburg impedance is an example of a distributed element. 

Experiments carried out on monocrystalline Au(lll) and Au(lOO) electrodes in the absence of specific adsorption did not show any fre-quency dispersion. Dispersion was observed, however, in the presence of specific adsorption of halide ions. It was attributed to slow adsorption and diffusion of these ions and phase transitions (reconstructions). In their analysis these authors expressed the electrode impedance as = R, + (jco iJ- where is a complex electrode capacitance. In the case of a simple CPE circuit, this parameter is = T(Jcaif. However, an analysis of the ac impedance spectra in the presence of specific adsorption revealed that the complex plane capacitance plots (C t vs. Cjnt) show the formation of deformed semicircles. Consequently, Pajkossy et al. proposed the electrical equivalent model shown in Fig. 29, in which instead of the CPE there is a double-layer capacitance in parallel with a series connection of the adsorption resistance and capacitance, / ad and Cad, and the semi-infinite Warburg impedance coimected with the diffusion of the adsorbing species. A comparison of the measured and calculated capacitances (using the model in Fig. 29) for Au(lll) in 0.1 M HCIO4 in ths presence of 0.15 mM NaBr is shown in Fig. 30. 

Fast scan voltammetry, in particular on microinterfaces, can be used for determination of charge-transfer rate constants. Impedance analysis can be used not only in analytical applications, but also to obtain a better understanding of surface phenomena (48) and adsorption (32). Microinterfaces, with their high own resistance, are well suited for impedance analysis derived from measurements of noise generated by electrochemical systems (49, 50). Understanding the phenomena peculiar to microinterfaces is essential to future studies of the electrochemistry of small domains. 

PDEIS is a new technique based on fast measurements of the interfacial impedance with the virtual instruments [3] that benefits from the efficient synchronization of direct hardware control and data processing in the real-time data acquisition and control [4], The built-in EEC fitting engine of the virtual spectrometer divided the total electrochemical response into its constituents those result from different processes. Thus, just in the electrochemical experiment, we come from the mountains of raw data to the characteristics of the constituent processes - the potential dependencies of the electric double layer capacitance, charge transfer resistance, impedance of diffusion, adsorption, etc. The power of this approach results from different frequency and potential dependencies of the constituent responses. Because of the uniqueness of each UPD system and complex electrochemical response dependence on the frequency and electrode potential, the transition from the PDEIS spectrum (Nyquist or Bode plot expanded to the 3D plot... 

Among the various models ° " proposed in order to explain two-arc behavior in the Nyquist plot for the insertion electrode, the simple equivalent circuit " depicted in Figure 10(b) was used to analyze the impedance spectra. Flere, / ,. is the sum of the electrolyte and conducting substrate resistances Ream is the resistance associated with the particle-to-particle contact among the oxide particles Ccom is the contact capacitance due to the accumulation of charged species at the surface of the oxide particles Rat is the resistance associated with the absorption reaction of adsorbed lithium into the oxide and Cad represents the capacitance arising from the adsorption of lithium in the near-surface region of the oxide. 

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