Application of the Theory of Absolute Reaction Rates to Overvoltage

Abstract

It is shown by means of the theory of absolute reaction rates that the current density I at an electrode is related to the overvoltage V by the expression I = I0eαVF/RT where I0 is a constant for a given electrode, representing the current passing in each direction at the reversible potential, and α is the fraction of the added potential V operating between the initial and activated states. Since α is about 0.5 for many electrodes, it appears that the energy barriers at the electrode surface is a symmetrical one. The quantity I0 is equal to Be—ΔH1‡/RT, where ΔH1‡ is the heat of activation of the rate-determining process responsible for overvoltage, and B is C1(kT/h)F/N·eΔS1‡/R, where k, h, F, N and R are universal constants, T is the temperature, ΔS1‡ is the entropy of activation and C1 is the concentration, per unit area, of the species involved in the slow process. Since ΔH1‡ and I0 can be obtained from experimental data, it is possible to evaluate B, which is found to be independent of the nature of the cathode or the hydrogen ion concentration of the solution, and hence it appears that C1 is almost constant for all electrodes in aqueous solutions. This suggests that the rate-determining step in the discharge of a hydrogen ion involves a water molecule, for only in this way could C1 remain constant, and the slow process is believed to consist in the transfer of a proton from a molecule of water attached to the solution to another water molecule attached to the electrode surface. The suggested prototropic mechanism permits of an approximate estimate of ΔS1‡, and taking C1 as 1015 molecules of water per sq. cm, the value of B calculated is in satisfactory agreement with experiment. The mechanism suggested immediately leads to the expectation of a symmetrical barrier at the electrode surface and so accounts for the value of 0.5 for α. The linear rate of attainment of overvoltage and the effect of changes in zeta-potential are readily explained, and it is shown that metals which form strong M—H bonds should have low overvoltages, as found in practice. The hydrogen-deuterium electrolytic separation factor is considered from the standpoint of the prototropic theory of overvoltage, and an explanation is proposed for the influence of the cathode material and of temperature. Oxygen overvoltage is attributed to a proton transfer in the opposite direction, i.e., from a water molecule on the electrode to one in a layer associated with the solvent, and so the striking similarities between cathodic and anodic phenomena can be readily understood. The high overvoltage accompanying the discharge of H3O+ and OH— but not other ions is attributed to the fact that these ions are comfortably built into the structure of the solvent water.