Thermodynamic Analysis of Nanoparticle Size Selective Fractionation Using Gas-Expanded Liquids

A thermodynamic model was developed for the size-selective fractionation of ligand-stabilized nanoparticles by a CO2 gas-expanded liquid precipitation process. The tunable solvent strength of gas-expanded liquids, via CO2 pressurization, results in an effective method to fractionate nanoparticles, based on the size-dependent dispersibility of the particles. Specifically, the thermodynamic model is used to estimate the size of dodecanethiol-capped Ag nanoparticles that can be dispersed at a given CO2 pressure by equating the total interparticle interaction energy to the Boltzmann threshold stabilization energy (−3/2 k B T). The ligand−solvent interaction is found to have the greatest impact on the total interaction energy. This model illustrates that the entire length of the ligand is not accessible to the solvent, and three phenomenological model variations were developed to vary the ligand−solvent interaction.