Mechanism of nanoparticle formation in self-assembled colloidal templates: Population balance model and Monte Carlo simulation

Modeling the nanoparticle formation mechanism in water-in-oil microemulsion, a self-assembled colloidal template, has been addressed in this paper by two formalisms: the deterministic population balance equation (PBE) model and stochastic Monte Carlo ( MC) simulation. These are based on time-scale analysis of elementary events consisting of reactant mass transport, solid solubilization, reaction, coalescence-exchange of drops, and finally nucleation and growth of nanoparticles. For the first time in such a PBE model, realistic binomial redistribution of molecules in the daughter drops ( after coalescence-exchange of two drops) has been explicitly implemented. This has resulted in a very general model, applicable to processes with arbitrary relative rates of coalescence-exchange and nucleation. Both the deterministic and stochastic routes could account for the inherent randomness in the elementary events and successfully explained temporal evolution of mean and variance of nanoparticle size distribution. This has been illustrated by comparison with different yet broadly similar experiments, operating either under coalescence ( lime carbonation to make CaCO3 nanoparticles) or nucleation (hydride hydrolysis to make Ca(OH)(2) nanoparticles) dominant regimes. Our calculations are robust in being able to predict for very diverse process operation times: up to 26 min and 5 h for carbonation and hydrolysis experiments, respectively. Model predictions show that an increase in the external reactant addition rate to microemulsion solution is beneficial under certain general conditions, increasing the nanoparticle production rate significantly without any undesirable and perceptible change in particle size.