Nucleation and growth of metal nanoparticles on a planar electrode: a new model based on iso-nucleation-time classes of particles

An assembly of hemispherical particles continuously nucleating on a planar electrode and growing under mixed kinetic-diffusion control is here considered. A model is derived, from the exact boundary integral formulation of the diffusion equation, to predict the overall current evolution, and the radii distribution of particles nucleating within any prescribed time interval. Iso-nucleation-time classes are introduced in the model, grouping particles (almost) simultaneously nucleating over the underlying substrate. The dynamics of particles belonging to a given iso-nucleation-time class are assumed to be identical. By this approximation, hereby referred to as Averaged Class Approximation (ACA), the computation of the average radius of any iso-nucleation-time class is reduced to the solution of an integro-differential equation, parameterized by the nucleation time. An effective computational method is also presented to solve the model equations, giving predictions that fairly well agree with the results of direct multi-particle numerical simulations.