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.

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While an equation of state (EOS) plays a critical role in estimating thermodynamic properties, employing it in the determination of binary interaction parameters is extremely important. In general, these parameters can be determined from phase equilibrium data. However, data collection from experiments is a time-consuming and tedious process. In this study, after measuring the excess enthalpies of binary systems containing CO 2 by high-pressure flow isothermal microcalorimetry (IMC), we determined the EOS binary interaction parameters, specifically, the Peng-Robinson EOS binary interaction parameters. These binary interaction parameters obtained by IMC were compared with those obtained by vapor-liquid equilibrium (VLE) experiments. Hence, high-pressure flow IMC appears to be an effective method for the determination of interaction parameters that are used in the estimation of thermodynamic properties. Further, the Flory-Huggins interaction parameters of a binary mixture CO 2 containing with various mole compositions were also estimated by employing high-pressure IMC.

A new riogorous equ;,tion of state (EOSI and its simplified version have been proposed by the present authors based on the full Guggenheim combinatorics of the nonrandom lattice hole theory. The simplified EOS. with the introduction of the concept of local composition, becomes similar to the density-dependent UNIQUAC model. However. in the present approach we have a volumetric EOS instead of the excess Gibbs function. Both EOSs were tested for their applicability in correlating the ph~ise equilibria behavior of pure components and complex mixtures. Comparison of both models with experiment includes such systems as nonpolar nonpolar, nonpolar polar, and polar,,polar hydrocarbons, supercritical systems, and polymer solutions. With two parameters Ibr each pure component and one binary interaction energy parameter, results obtained to date demonstrate that both formulations are quantitatively applicable to complex systems oer a wide range of temperatures, pressures, and concentrations.KEY WORDS: complex mixtures: equation of state: multiphase equilibria: nonrandom lattice theory; polymer solutions: supercritical fluids.