Subject tunneling into

Redox ions in solution are subject to chaotic Brownian movement. In principle, a certain range of tunneling distances between the metal and the redox species should be taken into account in a kinetic theory. The tunneling probability decays exponentially with increasing distance between the metal and the redox ion. Only redox ions nearest to the metal surface are, therefore, taken into account. Then, the inner solvation shell of the ion contacts the Helmholtz layer. There is no penetration of the reacting system into the electrochemical double layer (See Section 4.7.2). 

The two models have recently come into sharp contrast since they have both been applied to the analysis of the same INS spectrum of benzoic acid [51,53]. The molecular structure of this system is shown in Fig. 9.13. These are the only INS data on O-H-O bonds to be fully analysed using the phonon assisted tunnelling model. However, it is probable that the INS spectra of most systems could be subjected to a similar analysis. 

The two chief experimental criteria for tunneling in chemical reactions are an abnormal isotope effect (the tunnel effect is much more pronounced for hydrogen than for deuterium), which does not concern us here, and a curved Arrhenius plot. The reason for this is that the effect becomes most marked at low temperatures, when the fraction of systems which are able to cross the barrier becomes considerably higher than that calculated from classical considerations. As a result, the rate decreases with decreasing temperature less than expected, and the Arrhenius plot becomes concave upward. We cannot go into the quantum-mechanical details, and refer the reader to the literature on the subject. (See, e.g., Refs. 2b, 23, 77, 99, 105.)... 

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