A Balanced Nucleation and Growth Model for Controlled Precipitations

Abstract

This paper describes the balanced nucleation-growth (BNG) process during nucleation in controlled precipitations. This model is distinct from the classical nucleation model by including the growth of the newly formed nuclei. This allows modeling of the population nucleation rate, maximum growth rate, and supersaturation as a function of time, molar addition rate during nucleation, initial nucleation rate, fraction of supersaturation converted to nuclei (nucleation efficiency), and crystal maximum growth rate. The model predicts that increasing the initial nucleation rate or the crystal growth rate reduces the time during which new crystals are formed (nucleation time). Increasing the addition rate increases the nucleation time. The BNG model predicts the experimental result that many crystallization processes lead to a limited number of crystals during a nucleation period followed by growth. The model also predicts that factors like diffusion and kinetically controlled growth process, Ostwald ripening agents and growth restrainers that affect the growth rate will affect the nucleation outcome. The extension of the BNG mechanism to model the nucleation period leads to new insights for the control of nucleation processes.