Inner-double layer, electron transfer

Hence, reductive electrochemistry converts electrons (e ) via the solution matrix at the interface to atoms and anions. The solution outside the inner double layer never is exposed to an electron. Some examples of such inner-doublelayer electron transfer include... 

In the treatment of the kinetics of the electron transfer illustrated in Section 4.1, it has been assumed that the propulsive force for the electron transfer was the electrochemical potential E i.e. a quantity directly related to 4>M — < >s). However, since the solvated ions cannot enter the inner layer of the double layer (IHP), the true propulsive force should be < )M — standard rate constant, k°, and the exchange current, i0, should become respectively ... 

For the electron transfer of hydrated redox particles (the outer-sphere electron transfer), the electrode acts merely as a source or sink of electrons transferring across the compact double layer so that the nature of the electrode hardly affects the reaction kinetics this lack of influence by the electrode has been observed for the ferric-ferrous redox reaction. On the other hand, the electron transfer of adsorbed redox particles (the inner-sphere electron transfer) is affected by the state of adsorption so that the nature of the electrode exerts a definite influence on the reaction kinetics, as has been observed with the hydrogen electrode reaction where the reaction rate depends on the property of electrode. 

The crucial point is that the difference of potential available to effect electrode reactions and surmount activation barriers is not simply the difference between the Galvani potential (i.e. the Fermi energy) and the potential in solution. On the side of the solid it is the Volta potential and on the side of the solution it is the potential at the inner Helmholtz plane, where species have to reach to in order for electron transfer to be possible. Corrections to rate constants for the latter are commonly carried out using the Gouy-Chapman model of the electrolyte double layer and will be described in Section 6.9. 

Therefore, for most experimental conditions, the transfer coefficient for the electron-transfer step, aet, is predicted to approximate 0.5 with deviations from this value at moderate driving forces expected most often for processes featuring large inner-shell structural changes [55]. By and large, these expectations are borne out by experiment work-corrected transfer coefficients in the range ca. 0.35-0.65 are commonly observed for simple one-electron redox couples, although the extraction of ae, values is often impeded by uncertainties in the double-layer corrections. 

In the context of the present discussion, it is worth noting that virtually all the experimental systems that exhibit such "anomalous temperature-dependent transfer coefficients are multistep inner-sphere processes, such as proton and oxygen reduction in aqueous media [84]. It is therefore extremely difficult to extract the theoretically relevant "true transfer coefficient for the electron-transfer step, ocet [eqn. (6)], from the observed value [eqn. (2)] besides a knowledge of the reaction mechanism, this requires information on the potential-dependent work terms for the precursor and successor state [eqn. (7b)]. Therefore the observed behavior may be accountable partly in terms of work terms that have large potential-dependent entropic components. Examinations of temperature-dependent transfer coefficients for one-electron outer-sphere reactions are unfortunately quite limited. However, most systems examined (transition-metal redox couples [2c], some post-transition metal reductions [85], and nitrobenzene reduction in non-aqueous media [86]) yield essentially temperature-independent transfer coefficients, and hence potential-independent AS orr values, within the uncertainty of the double-layer corrections. 

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