Potential perturbation, electrode—solution interface

With any electrochemical technique to study kinetics, the electrode-solution interface is perturbed from its initial situation. The initial conditions may be such that the system is in a chemical equilibrium and this usually means that the interfacial potential difference is determined by Nernst s law holding for the two components O and R of a redox couple being present... 

Figure 3.37 illustrates the Nernst diffusion layer in terms of concentration-distance profiles for a solution containing species O. As pointed out previously, the concentration of redox species in equilibrium at the electrode-solution interface is determined by the Nernst equation. Figure 3.37A illustrates the concentration-distance profile for O under the condition that its surface concentration has not been perturbed. Either the cell is at open circuit, or a potential has been applied that is sufficiently positive of Eq R not to alter measurably the surface concentrations of the 0,R couple. 

Composition. While the average environment of a molecule in solution is well represented by the bulk concentrations of the various constituents of a reaction mixture, the environment of a molecule bound to a heterogeneous interface may be strongly perturbed. The properties of the motionally restricted phase may dictate. rather large deviations in the local concentrations of ions, reactants, and other mobile species from their respective bulk concentrations. The most important examples of this have been demonstrated for electrode-solution interfaces where, for example, the pH in the electrical double layer may differ significantly from its value in the bulk solution and can change with applied potential (1). A similar, though less extreme,example involves the interface between aqueous solutions and hydrophobic polymers. 

The rapid temperature change of the electrode perturbs the equilibrium at the electrode-solution interface and causes a change in the potential of the electrode measured with respect to a reference electrode. The change in the open-circuit potential, A t, and its relaxation with time are used to obtain kinetic information about the electrode reaction. A number of different phenomena come into play to cause the potential shift with temperature (e.g., temperature dependence of the double-layer capacitance and the Soret potential arising from the temperature gradient between the electrode and the bulk electrolyte), but the response can be treated by a general master equation (40) ... 

In most theory concerning the electron transfer at the electrode-solution interface, the electronic transition probability is generally kept unevaluated or determined in terms of the WKB treatment. The WKB treatment is applicable for situations where the potential at the interface does vary fairly slowly. This situation is rare. Use of time dependent perturbation theory is needed to have a proper evaluation of the transition probability, Pr, of electrons at the interface. One attempt of calculation of electronic transition probability T E) from electrode Fermi level to an available redox ion, e.g., Fe (H20)e, state is given. 

The EIS technique is based on a transient response of an equivalent circuit for an electrode/solution interface. The response can be analyzed by transfer functions due to an applied smaU-amphtude potential excitation at varying signals or sweep rates, hi turn, the potential excitation yields current response and vice verse, hi impedance methods, a sine-wave perturbation of small amphtude is employed on a corroding system being modeled as an equivalent circuit (Figure 3.8) for determining the corrosion mechanism and the polarization resistance. Thus, a complex transfer function takes the form... 

Two limiting cases for the description of an electrode are the ideally polarizable electrode and the ideally nonpolarizable electrode [8, 9, 14], The ideally polarizable electrode corresponds to an electrode for which the Zfaiadaic element has infinite resistance (i.e., this element is absent). Such an electrode is modeled as a pure capacitor, with Cdi = Aq 6V (equation 26), in series with the solution resistance. In an ideally polarizable electrode, no electron transfer occurs across the electrode/electrolyte interface at any potential when current is passed rather all current is through capacitive action. No sustained current flow is required to support a large voltage change across the electrode interface. An ideally polarizable electrode is not used as a reference electrode, since the electrode potential is easily perturbed... 

In conventional EIS experiments the electrode response to a perturbation signal corresponds to a measurement averaged across the whole electrode surface area. However, electrochemical systems show nonuniform current and potential distributions, resulting in CPE behavior. Such distributions can be studied bythe local EIS method, which employs in situ probing of local current density distribution in the vicinity of the working electrode surface. Local EIS (LEIS) relies on the fact that AC current density in the solution very near the working electrode is proportional to the local impedance properties of the electrode [22]. The AC current spreads in the solution as a funchon of the distance from the electrode surface, and as a consequence the LEIS results depend on the distance between the probe and the surface. That allows for spatially resolved LEIS measurements of the surface topography and kinetics at the electrochemical interface. 

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