SOME CONSIDERATIONS ON THE ROLE OF PROTON TUNNELING IN CERTAIN CHARGE TRANSFER PROCESSES

Quantum mechanical tunneling of H atoms in certain reactions can have a rate comparable with that of the corresponding classical reaction. Proton tunneling appears to be the mechanism of proton transport in ice. Further studies of this mechanism have been made by determination of the a-c. and d-c. conductance of D2O (and H2O) ice under rigorous conditions of purification. Pre-electrolysis techniques have been applied to the ultrapurification of the D2O and H2O used for the conductance determinations. Isotopic ratios of conductance in solid H2O and D2O are obtained and discussed in terms of the mechanism of H+ or D+ transport in the solid and liquid substances. The theory of proton tunneling previously given is improved by using a quantal distribution function in the calculation of tunneling rates and better agreement with experiment is then obtained. The theoretical isotopic ratio of conductances by the tunneling mechanism in the ices is similar to that found experimentally and smaller than that predicted classically.Since the proton tunneling theory is quantitatively successful in the case of conductance of ice, its examination for other electrochemical processes involving H is necessary. A favorable case for investigation is the electrochemical hydrogen evolution reaction for which the barrier height for tunneling can be varied. Tunneling probabilities are calculated for proton and deuteron discharge at mercury from acid solutions using the theory of Eckart. At intermediate overpotentials the Tafel equation is still obeyed; at low overpotentials a linear current–potential relation is found as in the classical theory. H/D separation factors are calculated for the tunneling mechanism and it is shown that at intermediate and high overpotentials, tunneling leads to values of the separation factor comparable with those deduced classically. Only at low electrochemical rates of H or D production are high separation factors predicted. The tunneling mechanism, however, is distinguishable from the classical mechanism by a new criterion: the Tafel slopes for the tunneling process would be considerably larger (0.2–0.3) than those arising classically (0.12) for a simple discharge mechanism assuming a symmetry factor of 0.5. It is concluded that in certain cases proton tunneling may occur simultaneously with the classical reaction in electrochemical proton discharge and lead to anomalous Tafel 'b' values which are sometimes observed experimentally.