Modeling the Precipitation of Polydisperse Nanoparticles Using a Total Interaction Energy Model

A thermodynamic model is presented that can accurately predict, typically within 5%, the average size and size distribution of size-selectively precipitated nanoparticles. A total interaction energy model was developed which accounts for: (1) the interaction of two differently sized ligand-stabilized nanoparticles in a solvent plus antisolvent mixture, (2) the collapsing of the ligand shell as the solvent strength of the mixture decreases, and (3) the variability of the ligand surface coverage of the nanoparticle. A total interaction energy model equates the sum of potential energies for all forces acting on a nanoparticle pair (van der Waals attractive, osmotic repulsive, and elastic repulsive) to that of the Brownian motion energy to predict the nanoparticle size combinations that can be dispersed or would be precipitated under varying solvent conditions. Combining this with simple probabilities describing the frequency of combinations between differently sized nanoparticles leads to average sizes and distributions of precipitated and dispersed nanoparticles at various solvent conditions. The application of this model has been successfully demonstrated by the size-selective fractionation of dodecanethiol-stabilized gold nanoparticles dispersed in hexane and precipitated by the addition of CO2.