Ligand Effects in Assembly of Cubic and Spherical Nanocrystals: Applications to Packing of Perovskite Nanocubes

Abstract

We establish the formula representing cubic nanocrystals (NCs) as hard cubes taking into account the role of the ligands and describe how these results generalize to any other NC shapes. We derive the conditions under which the hard cube representation breaks down and provide explicit expressions for the effective size. We verify the results from the detailed potential of mean force calculations for two nanocubes in different orientations as well as with spherical nanocrystals. Our results explicitly demonstrate the relevance of certain ligand conformations, i.e., “vortices”, and show that edges and corners provide natural sites for their emergence. We also provide both simulations and experimental results with single component cubic perovskite nanocrystals assembled into simple cubic superlattices, which further corroborate theoretical predictions. In this way, we extend the Orbifold Topological Model (OTM) accounting for the role of ligands beyond spherical nanocrystals and discuss its extension to arbitrary nanocrystal shapes. Our results provide detailed predictions for recent superlattices of perovskite nanocubes and spherical nanocrystals. Problems with existing united atom force fields are discussed.

Long live(d) CsPbBr3 superlattices: colloidal atomic layer deposition for structural stability

“…Adding too many shells leads to the formation of soer cubes that may deviate from a purely cubic structure with increasingly ligand-rounded edges, perturbed surface ligand graing densities (outside of 1 chains per nm 2 ) and leading to different packing orientations (and the formation of corresponding ligand vortices) not allowing for the formation of purely simple cubic lattices as observed in the 10 c-ALD OLAC samples. 11,25 Signicantly, SEM micrographs also reveal that the c-ALD OLAC treated CsPbBr 3 SLs are much more homogenously sized than the untreated CsPbBr 3 SLs that showed areas of "amorphous" unassembled PNCs around the cubic SLs (Fig. S14 †).…”

“…13,25 Moreover, the inability for c-ALD treated PNCs (without OLAC termination) to form simple cubic SLs may indicate surface shell anisotropy or deviation from a purely cubic shape to one that is becoming spherical that disfavors purely face-to-face packing. 11 Specically, the long carbon chains provided by the OLAC terminated PNCs undergo van der Waals interactions during the slow evaporation process for the SL formation, thus determining the repeating distance between the PNCs within the SL structure while simultaneously controlling the supercrystal shape. 26 In all cases, at room temperature, the solid state PL, and TRPL analyses indicated that SLs assembled from shelled PNCs remained similar to those assembled from untreated PNCs with slight decreases in PLQY and average TRPL lifetimes (Fig.…”

“…8,9 The morphology of the extended structure, as in standard crystal formation, is dictated by a balance of entropy and enthalpic contributions and variations in the constituent "atoms" as well as their surface composition which can lead to different structures and supercrystal stoichiometry (ranging from primary crystal structures such as cubic, BCC, and FCC to more complex binary systems and beyond that are isostructural with known atomic lattices). [9][10][11][12] These are characterized through the observation of crystallographic multilayer diffraction where investigating fundamental structural properties and selfassembly processes remains important to augment our understanding of such superstructures. 8,[12][13][14][15] It is well understood in PNCs that the capping ligands undergo dynamic surface chemistry and therefore can detach from the crystal surface.…”

A multiscale approach to uncover the self-assembly of ligand-covered palladium nanocubes

“…This knowledge gap in fundamental understanding of how ligand-mediated interactions propagate to macroscopic behaviors makes it hard to decouple the role of the ligand shell versus nanoparticle core in driving self-assembly. While there have been computational efforts developed to tackle this key question, 21–23 they are often limited in system size due to the need to simulate the entire ligand shell coating the nanoparticle core and therefore cannot predict, a priori , the emergent self-assembly superlattices. Conversely, thermodynamic perturbation theory based approaches have been successfully employed to design co-assemblies of ligand-functionalized anisotropic nanoparticles, 12,13,15 but these efforts focus on free energy-based phase predictions and do not provide an explanation regarding how ligand–ligand interactions propagate across multiple length scales.…”

High-Precision Calculation of Nanoparticle (Nanocrystal) Potentials of Mean Force and Internal Energies

“…Subsequently, other studies − have reported consistent results. Extensions to other shapes, such as tetrahedra and cubes, and characterization of many-body effects , are also relevant, but extending the results in this study to these more general situations does not raise any new conceptual issues, so we will not discuss them any further.…”