Establishment of nucleation and growth model of silica nanostructured particles and comparison with experimental data

A mathematical model is developed for the calculation of the nucleation and growth process of silica nanostructured particles prepared by using the drop-by-drop method, and the calculation results of the proposed model is compared with the experimental value obtained from SAXS data. The model provides a non-ideal improvement in the supersaturation calculation and considers the impact of both mass transfer and surface reaction on the particle growth rate. The nucleation and growth rates are coupled depending on the change in monomer concentration over time, based on which the particle size and distribution are calculated. The growth curve of the silica particles from 3 nm to 20 nm and the change in particle number from 0 to over 10²⁰ are calculated, which are consistent with the experimental values, establishing the reliability of the model. The calculations of the growth rate reveal that mass transfer controls the growth of silica particles before 10 min and the surface reaction is the rate-determining step after 10 min. The changes in the model parameters obtained by fitting with the SAXS data under different reaction conditions indicate the sensitivity of the corresponding process to different conditions. Moreover, the relationship between the particle growth rate and monomer concentration change is analyzed using the proposed model.