A comparison of the stochastic and deterministic approaches in a nucleation-growth type model of nanoparticle formation

Abstract

In response to the suggestion of James Martin,12 which called for a consideration of single nucleation events, and then the suggestion of Finke,13 which called for considering the stochastic nature of those single nucleation events, in nanoparticle formation models, a comparison of the stochastic (continuous time discrete state) and the more common deterministic approaches was presented here in two nucleation-growth type nanoparticle formation models. Detectable fluctuations in reaction time were found, which are very similar to those demonstrated in simple autocatalytic reactions50 and are by no means specific to nanoparticle formation. The results showed that even at initial monomer molecule numbers as low as 107 , the stochastic and deterministic approaches predict almost identical particle size distributions. This comparison validates the deterministic kinetic approach and calculations for the size distribution in such systems.