Electrode redox reactions with polarizable molecules.

A theory of redox reactions involving electron transfer between a metal electrode and a polarizable molecule in solution is formulated. Both the existence of molecular polarizability and its ability to change due to electron transfer distinguish this problem from classical theories of interfacial electrochemistry. When the polarizability is different between the oxidized and reduced states, the statistics of thermal fluctuations driving the reactant over the activation barrier becomes non-Gaussian. The problem of electron transfer is formulated as crossing of two non-parabolic free energy surfaces. An analytical solution for these free energy surfaces is provided and the activation barrier of electrode electron transfer is given in terms of two reorganization energies corresponding to the oxidized and reduced states of the molecule in solution. The new non-Gaussian theory is, therefore, based on two theory parameters in contrast to one-parameter Marcus formulation for electrode reactions. The theory, which is consistent with the Nernst equation, predicts asymmetry between the cathodic and anodic branches of the electrode current. They show different slopes at small electrode overpotentials and become curved at larger overpotentials. However, the curvature of the Tafel plot is reduced compared to the Marcus-Hush model and approaches the empirical Butler-Volmer form with different transfer coefficients for the anodic and cathodic currents.