ANALYSIS OF THE FORMATION OF MONODISPERSE POPULATIONS BY HOMOGENEOUS NUCLEATION

A mathematical analysis of the precipitation of monodisperse populations of particles, governed by homogeneous nucleation from solution, is presented. The model incorporates a "hydrolysis" reaction step, homogeneous nucleation of the population, and size-independent linear growth of the particles once formed. The population balance formalism is used to describe the particulate phase, and material balances are developed to account for changes in the solute concentrations in the precursor phase and the active phase. Any statistical parameters of the particulate population may be predicted. It is shown that the success of forming monodisperse populations depends on the magnitude of the interfacial energy of the solution/particulate system. It is also shown that separating the nucleation and growth steps of the process is not an essential feature in the formation of monodisperse populations; however, the length of time the solution concentration is above the nucleation threshold is important. The rate at which the intermediate active solute species is generated affects the induction time significantly, but has little to do with the success of forming a monodisperse particle population, at least in the cases shown here. © 1991 Academic Press, Inc. All rights reserved.