Becker–Döring rate equations for heterogeneous nucleation, with direct vapour deposition and surface diffusion mechanisms

Abstract

We develop a set of microscopic rate equations describing the growth and decay of molecular clusters adsorbed onto a seed particle. Such Becker–Döring equations are fundamental to descriptions of homogeneous nucleation, but do not appear to have been developed for the rather more complicated case of heterogeneous nucleation. We show that the familiar Fletcher theory of heterogeneous nucleation emerges from such a Becker–Döring description, but only if the concentration of adsorbed single molecules on the surface is estimated in a rather rudimentary manner. For small seed particles, this approach fails and one needs a proper Becker–Döring approach to provide a better estimate. The change in predicted nucleation rate can be several orders of magnitude for nanometre-size seed particles. We go on to include into the Becker–Döring treatment the processes of growth and decay of clusters by monomer surface diffusion on the seed. We use recent high quality experimental data to show that the latter process can make only a small contribution to the nucleation current for nanoparticle seeds. We also use the data to demonstrate that the traditional Fletcher theory fails to account for critical sizes and nucleation currents correctly, and that a modification to the implied underlying cluster properties is necessary.