Time-dependent diffusion coefficient electron-transfer reactions

In the case of irreversible reactions, the polarographic half-wave potential also depends on the standard potential (formal potential) however, the kinetics of the electrode reaction lead to strong deviation as an overpotential has to be applied to overcome the activation barrier of the slow electron transfer reaction. In the case of a totally irreversible electrode reaction, the half-wave potential depends on the standard rate constant ks of the electrode reaction, the transfer coefficient a, the number e- of transferred electrons, the diffusion coefficient T>ox, and the drop time t [7] as follows ... 

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. 

Dogonadze et al. have commented on the possibility of obtaining experimental information about the transmission coefficient x [equation (1)]. Referring again to equation (2), if the reactants A+ and B can be generated suddenly, and if the subsequent electron-transfer reaction is rapid compared with the rate of diffusion (which requires that electron transfer can occur over long distances), then the dependence of reaction rate upon time can be shown to be related to the dependence of transition... 

Formula (II.2.5) states that the NPV current is proportional to the bulk substrate concentration, C, the number of electrons transferred, n, the square root of the substrate diffusion coefficient, D, the electrode area, A, and is inversely proportional to the pulse time, tp. In fact, the formula should contain the sampling time, ts y especially when the sampling is not performed exactly at the end of the pulse. Formula (II.2.5) is valid for electrodes of regular size (radius in the range of a few mm) and for processes where the transport of the substrate to the electrode surface is done only by diffusion. Chemical reactions involving the substrate that either precede or follow the electron transfer will also lead to different currents. The height of NPV waves does not depend on the electron transfer rate, so this technique is considered as a very reliable one for the determination of diffusion coefficients of the examined compounds. 

The ratios given in Eq. (4.66) are only dependent on the electrode shape and size but not on parameters related to the electrode reaction, like the number of transferred electrons, the initial concentration of oxidized species, or the diffusion coefficient D. For fixed time and size, the values of f or Qf2 are characteristic for a simple charge transfer (see Fig. 4.4 for the plot of Qf2 calculated at time (ti + T2) for planar, spherical, and disc electrodes) and, as a consequence, deviations from this value are indicative of the presence of lateral processes (chemical instabilities, adsorption, non-idealities, etc.) [4, 32]. Additionally, for nonplanar electrodes, these values allow to the estimation of the electrode radius when simple electrode processes are considered. 

The current-potential relationship of the totally - irreversible electrode reaction Ox + ne - Red in the techniques mentioned above is I = IiKexp(-af)/ (1+ Kexp(-asteady-state voltammetry, a. is a - transfer coefficient, ks is -> standard rate constant, t is a drop life-time, S is a -> diffusion layer thickness, and

logarithmic analysis of this wave is also a straight line E = Eff + 2.303 x (RT/anF) logzc + 2.303 x (RT/anF) log [(fi, - I) /I -The slope of this line is 0.059/a V. It can be used for the determination of transfer coefficients, if the number of electrons is known. The half-wave potential depends on the drop life-time, or the rotation rate, or the microelectrode radius, and this relationship can be used for the determination of the standard rate constant, if the formal potential is known. 

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