A population balance equation model to predict regimes of controlled nanoparticle aggregation

Prediction of aggregation behavior of submicron-sized particles of praseodymium-doped zirconium silicate in aqueous suspension by population balance model

“…The term cr increases as aggregation proceeds, resulting in a decrease of collision efficiency, which makes the model capable of predicting a stable state of aggregation (Atmuri et al, 2013). Therefore, the parameter c is responsible for the aggregation rate and the final size of the aggregates.…”

“…However, it is still not clear whether it is valid to apply the PBM to a dense suspension for a long time (Kovalchuk & Starov, 2012). To apply the PBM over a long period of time (up to a stable state), aggregates could be considered as large "particles", and thus W could be calculated between primary particles, between aggregates and primary particles, and between aggregates (Atmuri et al, 2013). Through such a modification, the model is able to predict the stable aggregate size and aggregation regimes of charged colloidal particles for a range of salts and particles, despite it overpredicting the aggregate rate (Runkana et al, 2004).…”

“…This seems to be the first PBM that is able to predict the steady state of a system. Furthermore, most previous studies characterized the aggregation process by the mean size of the suspension Lattuada et al, 2004;Runkana et al, 2004; or only predicted the PSD at a stable state (Ahmad, Chong, & Bhatia, 2008;Atmuri et al, 2013;Runkana et al, 2006). Because aggregation is a particle process, the PSD is the most explicit measure of aggregation (Runkana et al, 2004).…”

“…Moreover, most modeling studies (Runkana, Somasundaran, & Kapur, 2005;Runkana et al, 2006;Sandkühler, Lattuada, Wu, Sefcik, & Morbidelli, 2005) focused on the aggregation process leading to gel phases in a short time, thus the finite-size aggregates, while the long-time stability of the suspensions were not discussed. Recently, Atmuri, Henson, and Bhatia (2013) proposed a model considering aggregates as "particles", and consequently allowing the stability ratio to vary as aggregation proceeds. This seems to be the first PBM that is able to predict the steady state of a system.…”

Using hydrolysis of silicon tetrachloride to prepare highly dispersed precipitated nanosilica

“…Theoretically, the reaction system can be seen as a colloidal dispersion system; the degree of dispersion is determined by the total force acting on the particles. The total force is the sum of the hydrogen bonding force, van der Waals force and electrostatic repulsive force [6,7]. Silicon dioxide easily absorbs water due to its molecular structure, leading to hydroxylation.…”