A competitive aggregation model for flash nanoprecipitation

Flash NanoPrecipitation (FNP) is a novel approach for producing functional nanoparticles stabilized by amphiphilic block copolymers. FNP involves the rapid mixing of a hydrophobic active (organic) and an amphiphilic di-block copolymer with a non-solvent (water) and subsequent co-precipitation of nanoparticles composed of both the organic and copolymer. During this process, the particle size distribution (PSD) is frozen and stabilized by the hydrophilic portion of the amphiphilic di-block copolymer residing on the particle surface. That is, the particle growth is kinetically arrested and thus a narrow PSD can be attained. To model the co-precipitation process, a bivariate population balance equation (PBE) has been formulated to account for the competitive aggregation of the organic and copolymer versus pure organic-organic or copolymer-copolymer aggregation. Aggregation rate kernels have been derived to account for the major aggregation events: free coupling, unimer insertion, and aggregate fusion. The resulting PBE is solved both by direct integration and by using the conditional quadrature method of moments (CQMOM). By solving the competitive aggregation model under well-mixed conditions, it is demonstrated that the PSD is controlled primarily by the copolymer-copolymer aggregation process and that the energy barrier to aggregate fusion plays a key role in determining the PSD. It is also shown that the characteristic aggregation times are smaller than the turbulent mixing time so that the FNP process is always mixing limited.