Nemstian reaction

The diffusion of the electroactive ions is both physical and due to electron transfer reactions.45 The occurrence of either or both mechanisms is a function of the electroactive species present. It has been observed that the detailed electrochemical behaviour of the electroactive species often deviates from the ideal thin film behaviour. For example, for an ideal nemstian reaction under Langmuir isotherm conditions there should be no splitting between the anodic and cathodic peaks in the cyclic voltammogram further, for a one-electron charge at 25 °C the width at half peak height should be 90.6 mV.4 In practice a difference between anodic and cathodic potentials may be finite even at slow scan rates. This arises from kinetic effects of phase formation and of interconversion between different forms of the polymer-confined electroactive molecules with different standard potentials.46... 

Figure 1.4.2 (a) Current-potential curve for a nemstian reaction involving two soluble species... 

Semiempirical Treatment of Nemstian Reactions with Coupled Chemical Reactions 37... 

Rearrangement of equation 1.4.16 yields the following expression for i as a function of E, which is convenient for calculating i—E curves for nemstian reactions ... 

Figure 6.1.1 (a) A portion of the i-t-E surface for a nemstian reaction. Potential axis is in units of... 

Figure 6.2.2 Effect of scan rate on cyclic voltammograms for an ultramicroelectrode (hemispherical diffusion) with 10 jxm radius. Simulations for a nemstian reaction with = 1,...

The difference between and often symbolized by AEp, is a useful diagnostic test of a nemstian reaction. Although A "p is slightly a function of E, it is always close to 23RTInF (or 59/n mV at 25°C). Actual values as a function of E are shown in Table... 

In addition, one needs the appropriate i-E characteristic (i.e., for a reversible, totally irreversible, or quasireversible reaction). The resulting nonlinear integral equation must be evaluated numerically. Alternatively, the problem can be addressed by digital simulation techniques. Figures 8.3.1 and 8.3.2 illuminate the effects of different relative contributions of double-layer charging on if (at constant /) and on the E-t curves of a nemstian reaction. The charging contribution is represented there by the dimensionless parameter, K, defined as... 

For a nemstian reaction, combination of the Nemst equation for the 0,R couple with the equations for the various currents yields the familiar voltammetric wave equation ... 

In the periodically modulated version of this experiment (32), the laser heating is carried out sinusoidally at a frequency of 5 to 20 Hz, and the resulting sinusoidally varying current, is detected with a lock-in amplifier, as in hydrodynamic modulation. The variation of A/q with E is called thermal modulation voltammetry (TMV). Near, A/p shows a peak whose magnitude for a nemstian reaction is a function of the ratio of the en-tropic energy of the electrode reaction divided by the activation energy of the mass transport process. While the method is capable of extracting thermodynamic information about a reaction, both the theory and the experimental set-up is sufficiently complex that it has not yet found widespread use. 

Figure 10.6.4 Theoretical second-harmonic responses for a nemstian reaction as a function of phase angle (solid line) and at that same angle plus 90° (dashed line). The horizontal axis is — RT/F) E — E ) and the vertical axis is the second harmonic current normalized to the maximum response. The calculation assumes Dq = Dr and AD = 25 mV. [Reprinted with permission from C. P. Andrieux, P. Hapiot, J. Pinson, and J.-M. Saveant, /. Am. Chem. Soc., 115, 7783 (1993). Copyright 1993, American Chemical Society.]...

The extent or degree of completion of a bulk electrolytic process can be predicted for nemstian reactions from the applied electrode potential and a suitable form of the Nernst equation. 

Figure 11.7.3 Cyclic current-potential curve for a nemstian reaction with n = 1, V = 1.0 fjiL, i = 1 mV/s, CS = 1.0 mM, T = 298 K. [From A. T. Hubbard and F. C. Anson, Electroanal. Chem.,4, 129(1970), by courtesy of Marcel Dekker, Inc.]...

The peak current, and indeed the current at each point on the wave, is proportional to V, in contrast to the dependence observed for nemstian waves of diffusing species. The proportionality between i and v is the same as that observed for a purely capacitive current [see (6.2.25)], and this fact has led to some treatments of adsorption in terms of pseudocapacitances (32, 34). The area under the reduction wave, corrected for any residual current, represents the charge required for the full reduction of the layer, that is, nFATQ. The anodic wave on scan reversal is the mirror image of the cathodic wave reflected across the potential axis. For an ideal nemstian reaction under Langmuir isotherm conditions, and the total width at half-height of either the cathodic or anodic... 

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.]...

Because of the different dependency of the current on time for t < and t > the i-t curve at potentials of the adsorption prewave can have an unusual appearance for Wx m- The current increases until t then falls off with a dependence. For a nemstian reaction, both the prewave and the main wave will have the usual reversible shapes (33). Note also, from the dependence of m and t on the corrected mercury column height, /zcorr [i- - Kon and t oc (see Section 7.1.4)] that is directly proportional to /icon- [see (14.3.32)], compared to the dependence for... 

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