Model of the evolution of nanoparticles to crystals via an aggregative growth mechanism

A mechanistic mathematical model is presented that describes the evolution of precursor nanoparticles (PN) to crystals. The model treats PN as pseudospecies evolving through an arbitrary number of reversible first-order steps and having the ability to contribute to growth by aggregation with existing crystals after they evolve beyond a certain stage. The number concentration of any of the intermediate PN is small compared to the initial number concentration of PN. If quasi-steady-state (QSS) is assumed for these intermediate PN, the model can be solved analytically. The analytical solution can be used to obtain initial parameter estimates for the full, dynamic model. DLVO interactions between coalescing PN are accounted for in the model through the coalescence kernel, which is shown to be very sensitive to the size of the particles and to the surface potential of the particles. Modifications are made to the mechanism to increase the likelihood of older PN to coalesce and to decrease the likelihood of older PN to dissolve. The maxima in the simulated crystal size distributions (CSD) propagate to larger sizes over time in a propagating front manner and, in some cases, a peaked population can form.