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

Abstract

INTRODUCTIONThe precipitation and size-selective fractionation of nanoparticles is a crucial and, sometimes, necessary stage of postsynthesis nanomaterial processing to fine-tune the size-dependent properties of nanoparticles for their intended application. Unfortunately, these processes (specifically size-selective fractionation) are somewhat trial-and-error in their application, and predicting the size and size distribution of the recovered nanoparticle fractions is quite difficult. The ability to predict the size and size distributions of the nanoparticles that would disperse and precipitate at different solvent conditions would greatly reduce the need for experimentation and would provide new, physical insights into the underpinning thermophysical phenomena.Traditionally, the size-selective fractionation of nanoparticles has been accomplished through the controlled reduction of solvent strength of a thermodynamically stable nanoparticle dispersion by the addition of an antisolvent 1 (e.g., aliphatic-thiol stabilized nanoparticles dispersed in hexane can be precipitated and fractionated through the addition of ethanol). This liquid-liquid solvent/antisolvent precipitation and fractionation process produces large amounts of organic waste, is very time-intensive, and is capable of producing only monodisperse fractions through repetition. Another method of size-selectively precipitating nanoparticles was developed 2-4 to alievate some of the drawbacks of the liquid-liquid precipitation and fractionation process which makes use of the tunable physicochemical properties of gas-expanded liquids (GXLs): mixtures of an organic solvent and a pressurized gas. An organic solvent (e.g., hexane) dispersion of aliphatic-ligand (e.g., dodecanethiol) stabilized metallic (e.g., gold) nanoparticles can be precipitated when pressured to subvapor pressure levels with CO 2 . The CO 2 partitions (dissolves) into the organic solvent, and as CO 2 is a nonsolvent for the aliphatic ligand tails, the solvent strength of the overall solvent mixture is reduced, thus inducing precipitation of the nanoparticles. The degree to which CO 2 is added to the solvent is simply a function of the applied CO 2 pressure; i.e., CO 2 has a greater solubility at higher applied pressures. Several apparatuses have been developed to make use of this phenomenon to size-selectively fractionate polydisperse nanoparticles. Details on these methods are available elsewhere, 2,4 but in short, if an organic dispersion of nanoparticles is pressurized with CO 2 to a point where only a portion of the nanoparticles precipitate (the largest nanoparticles will precipitate first upon worsening solvent conditions), the nanoparticles which remain dispersed (the smallest nanoparticles) in the solvent mixture can be removed from the precipitated nanoparticles, thereby achieving an effective fractionation.Modeling of these postsynthesis processes involving aqueous nanoparticle dispersions has been successfully accomplished through the use of Derjaguin, Landau, Verwey, and Over...

Classification of Zinc Sulfide Quantum Dots by Size: Insights into the Particle Surface–Solvent Interaction of Colloids

“…Nevertheless, solubility parameters are successfully applied in the field of formulation techniques and also found in the context of SSP. 49,50,55 We think that they are the best solution available at present although from our understanding properly determined solubility parameters for nanoparticulate surfaces do not yet exist or are currently just under determination. 56,57 Regarding the older approach of Hildebrand and Scott, the solubility of a certain molecular compound is connected to its cohesive energy which is approximated by the energy of vaporization.…”

Process Engineering of Nanoparticles Below 20 nm—A Fundamental Discussion of Characterization, Particle Formation, Stability and Post Processing

“…The study was done together with the groups of Prof. Mori (Doshisha University, Kyoto) and Prof. Spiecker (CENEM, FAU Erlangen-Nuremberg). SSP was first reported by the groups of Murray and Weller [45,78] and is often applied not only in the field of QDs but also for noble metal nanoparticles [58,59]. It exploits the effect that after the gradual addition of a poor solvent into a suspension of QDs, larger particles flocculate first [25,61,66].…”

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“…According to the xDLVO framework, the relevant interaction contributions for surface functionalized nanoparticles are van der Waals, electrostatic and steric (osmotic and elastic) interactions (vide infra) as shown in Figure 1.3. [24][25][26] As shown here, the presence of surface functional groups results in additional steric interactions via the mutual interactions of the ligands on each nanoparticles and also the ligands with the nanoparticle cores. Quantification of each interaction above is specific to the type of nanoparticles, Herein, synergistic contributions from a size-dependent Hamaker constant, surface potentials and ligand tilt angles produce an empirically consistent application of the…”

“…51 Calculations use a variety of models including depletion forces, 60 Adapted from Lifschitz theory, 56,61 DLVO, and extended DLVO (xDLVO) theories. [24][25][26]62 According to Lifschitz theory, van der Waals interactions between two nanoparticles arise from the bulk electrodynamic response of one object interacting with a second object, resulting in electromagnetic fluctuations in both objects. 63 These van der Waals attractions are opposed by several repulsive forces including electrostatic repulsions as well as contributions from surface chemistry and the medium.…”

“…26 For functionalized nanoparticles, additional non-classical interactions exist as a result of the surface functional groups sterically interacting with ligands on other nanoparticles as well as other nanoparticle cores themselves. 24,25 According to the xDLVO framework, therefore, the relevant interaction contributions for surface functionalized nanoparticles are van der Waals, electrostatic and steric (osmotic and elastic)…”