Electrochemical stability of metal nanoparticles: The role of size-distribution broadness

In this article, we develop a thermodynamic and an electrochemical kinetic model to study the stability of metal nanoparticles (MNPs) supported on an inert substrate and in contact with an electrolyte. Regardless of the model, we find that the redox potential is a property of the entire MNPs' size distribution, which has to be characterized by, at least, its mean and variance. The thermodynamic model, which considers only the excess free energy due to the increased surface-to-volume ratio on MNPs, predicts an increase in surface effects as the size distribution becomes broader. On the other hand, the electrochemical kinetic approach models the MNPs as reactive systems considering the changes in the heterogeneous-rate constants due to surface effects. This allows the use of the mixed potential theory to evaluate the electrode potential, which would be experimentally accessible, showing a tendency contrary to that predicted by the thermodynamic model for closed systems. Then, the electrochemical boundary conditions -i.e., charge conservation- have to be considered rather than just the thermodynamic criteria. Also, it is analyzed under which circumstances the charge-transfer processes control the electrode potential, instead of mass-transfer. Hence, it is shown that the electrochemical kinetic approach is applicable to the study of the electrochemical Ostwald ripening among many other processes.