The precipitation technique to formulate drug nanoparticles has recently been used to encapsulate a broad range of hydrophobic drug molecules (Horn & Rieger, 2001; Hu et al., 2004; Johnson & Prud'homme, 2003). The governing principle behind this kinetically driven process is the stabilization of the aggregates formed by the solutes by the block copolymer. Though particles of the desired size can be obtained by the addition of inert filler, a more detailed study needs to be performed to fully understand the factors controlling the nanoparticles size. The estimation of particle size for gold colloid stabilized by PEG-b-PCL was recently studied (Gindy et al., 2008) based on the assumption that the sticking probability between two colliding gold particles is unity. However a more unified approach needs to be developed to estimate the nanoparticle size for solutes with weaker interparticle interaction. The aggregation kinetics for colloids have already been theoretically analyzed for both the diffusion and reaction limited regime (Smoluchowski, 1916; Weitz et al., 1984; Ball et al., 1987).

In this study, the particle size is first tuned by the addition of inert filler during the formulation. By varying the amount of PCL homopolymer, the size of the gold nanoparticle changed from 60 to above 200 nm. However, estimation of the particle size for any given solute and need for the formulation of even smaller particles make it imperative to fully understand the aggregation kinetics of the solutes. The study provides a starting point for the development of a correlation between the aggregation kinetics of the colloids and their surface properties. We tuned the sticking probability of the gold colloids by using both ionic and non-ionic surfactants. Ionic surfactants including SDS and TDTAB have been used to characterize the surface properties of the gold colloid. The anionic surfactant, SDS, was found to be better stabilizing agent compared to the cationic surfactant. The nanoparticle size is then tuned by varying the concentration of the surfactant and thereafter the stabilizing effect of the block copolymer, PEO-b-PS (3k-b-1k) on the assembly has been analyzed.

The experiments are analyzed by comparing them with an aggregation model that solves the population balance equations (PBEs) as functions of mixing time and physical properties of the inlet streams. In this work, a multivariate population balance model is developed to account for the copolymer arresting and stabilizing particle growth mechanisms in the NanoPrecipitation process. In order to achieve more economical computation, the quadrature method of moments (QMOM) is applied to solve PBEs in this model. The QMOM transforms the PBE into a set of lower moment equations, which contain useful information regarding the particle size, surface area, solid volume, and mean particle size. As a result, instead of solving the particle size distribution (PSD), QMOM requires less computation and has proven a good numerical approach in terms of its efficiency and accuracy.