Adiabaticity reactant-electrode separation

Relatively little attention has been given in the literature to the electronic transmission coefficient for electrochemical reactions. On the basis of the conventional collisional treatment of the pre-exponential factor for outer-sphere reactions, Kel has commonly been assumed to equal unity, i.e. adiabatic reaction pathways are followed. Nevertheless, as noted above, the dependence of xei upon the spatial position of the transition state is of key significance in the "encounter pre-equilibrium treatment embodied in eqns. (13) and (14). Thus, the manner in which Kel varies with the reactant-electrode separation for outer-sphere reactions will influence the integral of reaction sites that effectively contribute to the overall measured rate constant and hence the effective electron-tunneling distance, Srx, in eqn. (14). 

Fn in Eq. (33) takes into account the fact that the electron transfer can also occur for reactant molecules without fully overcoming the energy barrier. At normal temperatures for electrode reactions F approaches 1 [131]. Therefore Eq. (33) is often used without the F term, in this equation was estimated to have a value of the order of 60 pm [138]. However, the quantitative estimation of depends on the adiabaticity factor k (see Eq. (24)), which varies with the reactant-electrode separation distance. It was suggested [139] that the electrode reactions should be more adiabatic than the corresponding homogeneous redox reactions. But as the reaction site, for outer-sphere systems, is probably separated from the electrode surface by a layer of solvent molecules [129], k may drop below 1 since the reaction may become less adiabatic. These problems were more extensively discussed in [131]. 

Since k depends on the distance of the reaction site from the electrode, for outer-sphere electrode reactions where the reactant is separated from the electrode by a layer of solvent molecules [128], the adiabaticity of such reactions may also be dependent on the nature of the solvent. 

In electrochemical kinetics, this model corresponds to the Butler-Vohner equation widely used for the electrode reaction rate. The latter postulates an exponential (Tafel) dependence of both partial faradaic currents, anodic and cathodic, on the overall interfacial potential difference. This assumption can be rationalized if the electron transfer (ET) takes place between the electrode and the reactant separated by the above-mentioned compact layer, that is, across the whole area of the potential variation within the framework of the Helmholtz model. An additional hypothesis is the absence of a strong variation of the electronic transmission coefficient", for example, in the case of adiabatic reactions. 

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