The Phase Behavior of Nanoparticle Superlattices in the Presence of a Solvent

Abstract

Superlattices of nanoparticles coated by alkyl-chain ligands are usually prepared from a stable solution by evaporation, therefore the pathway of superlattice self-assembly critically depends on the amount of solvent present within it. This work addresses the role of the solvent on the structure and the relative stability of the different supercrystalline phases of single-component superlattices (simple cubic, body-centered cubic (BCC), face-centered cubic (FCC), and hexagonal close-packed). The study is performed with a molecular theory for nanoparticle superlattices introduced in this work, which predicts the structure and thermodynamics of the supercrystals explicitly treating the presence and molecular details of the solvent and the ligands. The theory predicts a FCC–BCC transition with decreasing solvent content due to the competition between the translational entropy of the solvent and the entropy and internal energy of the ligands. This result provides an explanation for recent experimental observations by in situ X-ray scattering, which reported a FCC–BCC transition during solvent evaporation. The theory also predicts the effects of the length and surface coverage of the ligands and the radius of the core on the phase behavior in agreement with experimental evidence and previous molecular dynamics simulations. These results validate the use of the dimensionless softness parameter λ (ratio of ligand length to core radius) to predict the phase behavior of wet superlattices. Our results stress the importance of explicitly considering the presence of the solvent in order to reach a complete picture of the mechanisms that mediate the self-assembly of nanoparticle superlattices.

On the Thermodynamic Stability of Binary Superlattices of Polystyrene-Functionalized Nanocrystals

“…Although there is supporting experimental evidence, additional studies will be necessary to rigorously establish this issue. On the theory side, self-consistent calculations , and further simulations with other APS force fields will be necessary. Other possible effects to consider may include dipolar forces, or solvent interactions, but given the magnitude of the free energy differences, those are not of sufficient magnitude to tilt these balances for all cases.…”

On the Formation of Honeycomb Superlattices from PbSe Quantum Dots: The Role of Solvent-Mediated Repulsion and Facet-to-Facet Attraction in NC Self-Assembly and Alignment

“…In three-dimensional structures (3D), a similar effect is observed in several NC systems, where it is described as the Bain deformation. 23 , 27 , 28 , 40 − 46 In all experiments presented below, the TEM samples were placed under vacuum immediately after sampling, “freezing” the superstructures as they have formed on the liquid substrate. The next step is to synthesize PbSe superstructures on the mixtures of BD and EG, to tune the superstructure attachment.…”

“…In experiments, this was achieved using nearly solvent-saturated conditions, which swell the ligand corona. 27 , 28 , 48 , 50 , 57 Previous works on the self-assembly of NCs show that this causes a larger NC–NC separation and more repulsion. 27 , 28 , 48 , 57 − 59 The results of time-monitoring reported here, supported by large-scale simulations with compressive and slow solvent evaporation, show that honeycomb formation is driven by the formation of hexagonal bilayers in a confined quasi-2D space.…”

“… 27 , 28 , 48 , 50 , 57 Previous works on the self-assembly of NCs show that this causes a larger NC–NC separation and more repulsion. 27 , 28 , 48 , 57 − 59 The results of time-monitoring reported here, supported by large-scale simulations with compressive and slow solvent evaporation, show that honeycomb formation is driven by the formation of hexagonal bilayers in a confined quasi-2D space. NCs not (yet) aligned with the ⟨111⟩ axis upwards, in the hexagonal bilayer, are able to reorient, allowing for maximal attraction between opposing (100) facets and eventually neck formation.…”

“… 24 − 26 To form structures with other nanogeometries, i.e., honeycomb structures, the continued presence of the residual solvent in the ligand shell or additional unbound ligands was found to be essential. 23 , 27 , 28 …”