Electrochemical nucleation and three-dimensional growth of metal nanoparticles under mixed kinetic-diffusion control: model development and validation

A model is derived to compute the current transient generated by electrochemical nucleation and three-dimensional growth of metal nanoparticles under mixed kinetic diffusion control. The model can describe the dependence of the current transient on nucleation rate, number of active sites and charge transfer kinetic constant. A numerical algorithm is proposed to solve the model and an analytical expression is derived for the current transient predicted in the limit of instantaneous nucleation. As the ratio between diffusion and charge transfer characteristic times is greater than one, model predictions are in satisfactory agreement with the results of direct numerical simulations of electrochemical nucleation and growth.