(58e) Modeling the Dispersability of Polydisperse Nanoparticles In Gas-Expanded Liquids

Controlling nanoparticle dispersability is crucial for most processing methods and applications, including size-selective fractionation, thin film deposition, and nanoparticle composite formation.  While nanoparticle dispersability has been well studied in aqueous systems, organic dispersions have seen very little investigation.   Ligand stabilized nanoparticles will disperse in an organic solvent when the combined repulsive forces, an osmotic repulsive force (due to the solvation of the stabilizing ligand by the solvent) and an elastic repulsive force (due to steric interactions between the stabilizing ligands of two interacting nanoparticles) is greater than or equal to the inherent van der Waals attractive force. Thermodynamically, when the sum of the potential energies (i.e. the total interaction energy) is greater than the Boltzmann threshold energy necessary for Brownian motion (-3/2 k_bT) the nanoparticles will remain dispersed in a solvent.   The degree to which nanoparticles disperse is a function of nanoparticle size, ligand shell thickness, surface coverage of the ligand, solvent strength and solvent composition.   By accounting for two-body interactions of differently sized nanoparticles, it can be demonstrated that a certain distribution of sizes can be stabilized at a given set of conditions.   A model has been developed to examine the dispersability of nanoparticles in various gas-expanded liquid mixtures (CO₂ + hexane) and the results of these modeling efforts will be compared to experimental measurements of a size-selective fractionation of 1-dodecanethiol stabilized gold nanoparticles in order to provide a greater physical understanding.