Nemstian systems

FIGURE 6.1. a Dimensionless current (i]/) and charge passed (qe) in the cyclic voltammetry of a Nemstian system, b Construction of the reverse trace from the forward trace. 

Equations (5.83) and (5.84) and the curves in Fig. 5.12 indicate that both peak current and potential of the CV curves change with the scan rate, a feature which is not observed for the peak potential of reversible processes (see Eq. (5.57)). However, the experimental evidence that for a given system the potential peak of the cathodic CV curves shifts to more negative values with increasing scan rate should be used with caution when assigning a non-reversible behavior to the system since, similar displacements can be observed for Nemstian systems when the ohmic drop has an important effect (see Fig. 5.11). Thus, the shift of the CV peak potential with the scan rate is not always a guarantee of a non-reversible charge transfer process. 

Figure 1.4.3 Current-potential curve for a nemstian system involving two soluble species with both forms initially present.

This approximate treatment predicts a diffusion layer that grows with and a current that decays with In the absence of convection, the current continues to decay, but in a convective system, it ultimately approaches the steady-state value characterized by (0 = (Figure 1.4.6). Even this simplified approach approximates reality quite closely equation 1.4.34 differs only by a factor of 2/7t from the rigorous description of current arising from a nemstian system during a potential step (see Section 5.2.1). 

With respect to the heterogeneous electron-transfer process, reversible (nemstian) systems are always at equilibrium. The kinetics are so facile that the interface is governed solely by thermodynamic aspects. Not surprisingly, then, the shapes and positions of reversible waves, which reflect the energy dependence of the electrode reaction, can be exploited to provide thermodynamic properties, such as standard potentials, free energies of reaction, and various equilibrium constants, just as potentiometric measurements can be. On the other hand, reversible systems can offer no kinetic information, because the kinetics are, in effect, transparent. 

Now let us restrict our consideration to a nemstian system in which R is initially absent. The results from Section 5.4.1 show that the surface concentrations during preelectrolysis at potential E are... 

On the other hand, when is negligible compared to the mass-transfer impedance, which is the case for a nemstian system, the following expression applies ... 

Let us consider a completely nemstian system O + R in which R is initially absent. The starting potential for the linear sweep is rather positive with respect to E and the scan direction is negative. Semi-infinite linear diffusion is assumed. The mean surface concentrations, Co(0, Om r(0, exactly those obtained in the analogous linear... 

Figure 14.3.14 Simulated cyclic voltammograms for initial reduction where reactant is strongly adsorbed, = 10. (a) Nemstian reaction, Langmuir isotherm, (b) Nemstian system, Frumkin isotherm, IgTo JRT = -1.5. (c) Irreversible reaction, k%ffl(7rDQvFIRT) = 1, a = 0.5, Frumkin case, 2gToJRT = 0.6. Additional curves in the figure show variation of Fq/Fq,s as a function of E during scan. [Reprinted from S. W. Feldberg in Computers in Chemistry and Instrumentation, Vol. 2, Electrochemistry, J. S. Mattson, H. B. Mark, Jr., and H. C. MacDonald, Jr., Eds., Marcel Dekker, New York, 1972, Chap. 7, by courtesy of Marcel Dekker, Inc.]...

Two groups of methods can be applied to this task equilibrium, which have already been considered above, and non-equilibrium ones. The latter, in turn, can be divided into stationary and nonstationary methods. The non-equilibrium methods can be applied only to Nemstian systems, which means that the electrode equilibrium is attained. Of course, the intervalence equilibria have also to be established. The whole system, however, is non-equilibrium because of the presence of diffusion fluxes of E(/) and B(/). These fluxes are constant at stationary conditions ... 

For non>Nemstian systems the shape of the cyclic voltammogram changes. For the irreversible case the forward peak ceases to be symmetric, and of course there is no reverse peak. For quasi-reversible reactions there will be a reverse peak but both peaks will be asymmetric and the peak potentials will not be coincident. There is insufficient space here to consider these systems more fully, but further details can be found in the literature [12,13]. 

Nemstian systems only avoid scan rates with appreciable nonlinear diffusion should be considered an approximate method... 

Before attempting to measure diffusion coefficients, some basic information regarding the electrochemical behavior of the redox species must be known. This is particularly important for newly prepared compounds. First, one should evaluate the reversibility of the electron transfer reaction. Certain techniques, such as LSV, can only be applied to measure diffusion coefficients for nemstian systems. Second, the presence of any coupled homogeneous reactions should be established. The current for each technique is often dependent on such reactions, thus making measurements of the diffusion coefficient unreliable. Finally, the adsorption of reactants or products can produce faiadaic current that can greatly affect the measurement of the diffusion coefficient. For example, measuronent of the critical time in chronopotentiometry is less reliable when adsorption is present For these reasons, the electrochemical behavior of the compound must be factored into the selection of a technique. 

Linear scan voltammetry (LSV) and cyclic voltammetry (CV) (see Chapter 11) are among the most common electrochemical techniques employed in the laboratory. Despite their utility, however, they are not particularly well suited to careful measurements of diffusion coefficients when using electrodes of conventional size. We will briefly discuss techniques for measuring D with LSV and CV, but the reader should be cautioned that these measurements under conditions of planar diffusion (i.e., at conventional electrodes) are probably useful to only one significant digit, and then only for nemstian systems with no coupled homogeneous reactions and with no adsorption. For more reliable results with LSV and CV, UMEs should be used. 

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