Silica nanoparticle formation in the TPAOH-TEOS-H2O system:: A population balance model

A model describing the kinetics of silica nanoparticle formation in the TPAOH-TEOS-H2O system is presented. These nanoparticles are an important intermediate in the clear-solution synthesis of silicalite-1, so understanding the mechanisms by which they are formed and stabilized is a key step in determining the crystallization behavior of pure-silica zeolites. The model presented here is based on the mass-conserving form of the Becker-Doring population balance equations, describing growth and fragmentation by addition or removal of monomeric units, and modified to account for rapid equilibration of small silicate species and electrostatic and/or template stabilization of nanoparticles. The model predictions compare favorably with the experimental results. It is found that nanoparticle evolution exhibits distinct time regimes consisting of TEOS hydrolysis, condensation, nanoparticle formation, Ostwald ripening, and a self-sharpening mechanism in particle size distribution toward equilibrium due to stabilization during which no apparent changes in average particle size and pH are observed. Finally, the model provides an alternative, to a recent hypothesis, kinetics point of view to explain the enhanced stability of nanoparticles over extended periods of time.