Modelling Activity and Durability of Electrocatalysts from a Statistical Perspective

We develop a theory to investigate how energetic nonhomogeneity of active sites determines the overall activity of an electrocatalyst and how the evolution of the nonhomogeneity determines the overall durability. The simple theory is amenable to exact analytical solutions and thus fosters an in-depth transparent analysis. It is revealed that nonhomogeneity does not necessarily diminish the electrocatalytic activity; instead, the highest overall activity is obtained with a suitable level of nonhomogeneity that is commensurate with the mean property. The evolution kinetics of nonhomogeneity is described by using the Fokker-Planck theory. Exponential decay of the activity is predicted theoretically and confirmed experimentally. The present work represents a first step toward closing the gap between model and practical electrocatalysts using statistical considerations.