Balanced Nucleation and Growth Model for Controlled Crystal Size Distribution

Abstract

ABSTRACT Crystal size and size distribution in precision controlled precipitations is modeled using the balanced nucleation-growth (BNG) process model. 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 crystal size distribution, maximum crystal size, L m  , number of crystals, N m  , and nucleation time, t e  , are modeled as a function of molar reactant addition rate during nucleation, R a  , nucleation efficiency, F n  , critical nucleus size, L n  , and crystal maximum growth rate, G m . The model predicts that the maximum crystal size, L m  , is independent of addition rate, R a  , and nucleation efficiency, F n . It increases with nucleus size, L n  , and crystal maximum growth rate, G m . The nucleation time, t e  , is independent of addition rate, R a . It increases with increasing nucleus size, L n  , and decreases with increasing nucleation efficiency, F n  , and growth rate, G m . The crystal size distribution is independent of addition rate, R a  , and growth rate, G m . The small size crystal population increases with increasing nucleus size, L n  , and at low growth rates, G m . The crystal size distribution narrows with increasing nucleation efficiency, F n . In combination of effects, each variable has its own fingerprint and may be experimentally discerned from the others.