Attachment efficiency of nanoparticle aggregation in aqueous dispersions: modeling and experimental validation.

To describe the aggregation kinetics of nanoparticles (NPs) in aqueous dispersions, a new equation for predicting the attachment efficiency is presented. The rationale is that at nanoscale, random kinetic motion may supersede the role of interaction energy in governing the aggregation kinetics of NPs, and aggregation could occur exclusively among the fraction of NPs with the minimum kinetic energy that exceeds the interaction energy barrier (E(b)). To justify this rationale, we examined the evolution of particle size distribution (PSD) and frequency distribution during aggregation, and further derived the new equation of attachment efficiency on the basis of the Maxwell-Boltzmann distribution and Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. The new equation was evaluated through aggregation experiments with CeO(2) NPs using time-resolved-dynamic light scattering (TR-DLS). Our results show that the prediction of the attachment efficiencies agreed remarkably well with experimental data and also correctly described the effects of ionic strength, natural organic matter (NOM), and temperature on attachment efficiency. Furthermore, the new equation was used to describe the attachment efficiencies of different types of engineered NPs selected from the literature and most of the fits showed good agreement with the inverse stability ratios (1/W) and experimentally derived results, although some minor discrepancies were present. Overall, the new equation provides an alternative theoretical approach in addition to 1/W for predicting attachment efficiency.