Balanced Nucleation and Growth Model for Controlled Crystal Size Distribution

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.

Keywords:

• Crystal
• Crystal nucleation
• Crystal number
• Crystal size
• Crystal size distribution
• Crystallization
• Crystallization batch
• Growth
• Growth rate
• Nucleation
• Nucleation efficiency
• Nucleation period
• Nucleation rate
• Nucleation time
• Reaction condition
• Reaction parameter

Acknowledgments

Notes

¹I am indebted to R. Heist, Manhattan University, New York, NY, for pointing this out and for suggesting the modification of the calculations.