Al Anderson, Case Western Reserve University
Theories for Predicting Reversible Potentials of Reactions Theories for Predicting Reversible Potentials of Reactions on Electrode Surfaces from Internal and Gibbs Energies: Applications to ORR

Abstract

Given a reduction in aqueous electrolyte with standard reversible potential U^o(aq):

                                                  R(aq) + H⁺(aq) + e^- ⇄ P(aq),                           (1)

the corresponding description when reactant and product are adsorbed on the electrode is

                                                  R(ads) + H⁺(aq) + e^- ⇄ P(ads)                         (2)

where R and P stand for reactant and product.  We have found that when these species are adsorbed, the reversible potential U^o(ads) is given to good approximation by

                                                U^o(ads) = U^o(aq) + D_o(P) – D_o(R)                     (3)

where D_o are dissociation energies of the bonds to the surface.  Using eq. 3 for U^o(ads) has the advantage that it does not require calculating solvation energies of charged ions such as hydronium and hydroxyl because they are contained in U^o, which is available from measurement.  For neutral reactants and products, solvation energies are small, allowing eq. 3 to rapidly yield useful predictions based on energy calculations using available commercial codes.

The full Gibbs energy change for a reduction reaction, including potential dependence, is given by

                                          ΔG(U) = {G_Red(U) – G_Ox(U)} + n(φ + FU)             (4)
where -(φ + FU) is the energy of an electron on the vacuum scale, φ being the thermodynamic work function of the standard hydrogen electrode. We have developed a theory that fully implements eq. 4 in a code called Interface 1.0. It uses two-dimensional density functional band theory for periodic systems with linear combinations of pseudo-atomic orbitals, norm-conserving pseudopotentials, and projector expansions. In it the surface potential is adjusted by adding surface charge and a counter charge distribution in the double layer is determined self-consistently using a modified Poisson-Boltzmann theory within a dielectric continuum model.
This presentation shows selected applications of both methods to steps of oxygen reduction over several cathode materials.