The hard sphere diameter of nanocrystals (nanoparticles)

Nanocrystal Assemblies: Current Advances and Open Problems

We explore the potential of nanocrystals (a term used equivalently to nanoparticles) as building blocks for nanomaterials, and the current advances and open challenges for fundamental science developments and applications. Nanocrystal assemblies are inherently multiscale, and the generation of revolutionary material properties requires a precise understanding of the relationship between structure and function, the former being determined by classical effects and the latter often by quantum effects. With an emphasis on theory and computation, we discuss challenges that hamper current assembly strategies and to what extent nanocrystal assemblies represent thermodynamic equilibrium or kinetically trapped metastable states. We also examine dynamic effects and optimization of assembly protocols. Finally, we discuss promising material functions and examples of their realization with nanocrystal assemblies.

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

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.

Nanocomposite tectons as unifying systems for nanoparticle assembly

Nanocomposite tectons (NCTs) are nanocomposite building blocks consisting of nanoparticle cores functionalized with a polymer brush, where each polymer chain terminates in a supramolecular recognition group capable of driving particle assembly. Like other ligand-driven nanoparticle assembly schemes (for example those using DNA-hybridization or solvent evaporation), NCTs are able to make colloidal crystal structures with precise particle organization in three dimensions. However, despite the similarity of NCT assembly to other methods of engineering ordered particle arrays, the crystallographic symmetries of assembled NCTs are significantly different. In this study, we provide a detailed characterization of the dynamics of hybridizations through universal (independent of microscopic details) parameters. We perform rigorous free energy calculations and identify the persistence length of the ligand as the critical parameter accounting for the differences in the phase diagrams of NCTs and other assembly methods driven by hydrogen bond hybridizations. We also report new experiments to provide direct verification for the predictions. We conclude by discussing the role of non-equilibrium effects and illustrating how NCTs provide a unification of the two most successful strategies for nanoparticle assembly: solvent evaporation and DNA programmable assembly.

Trade-offs between Translational and Orientational Order in 2D Superlattices of Polygonal Nanocrystals with Differing Edge Count

The goal of this work is to identify factors which modulate structural order in 2D self-assembled superlattices of polygon-shaped colloidal nanocrystals. Using combined experimental and simulation techniques, we quantify order in superlattices of hexagonal prism-shaped CdSe/CdS nanocrystals and cube-shaped CsPbBr₃ nanocrystals. Superlattices derived from cube-shaped nanocrystals display less translational order compared to hexagonal prism-shaped nanocrystals both experimentally and in simulations. This effect can be attributed to geometric considerations inherent to the combined rotational and translational symmetries of different polygonal shapes and their superlattices. Cubes form a simple cubic lattice where nanocrystals can slide without steric overlap, whereas hexagonal prisms interlock, preventing translation. Regarding orientational order, cube assemblies display a narrower orientation distribution. Intuitively, hexagonal prisms are a more "spherical" shape compared to cubes. The results presented here outline a conceptual framework for identifying superlattice structures which favor translationally and orientationally ordered self-assembled superlattices.

Effect of Polymer Chain Length on the Superlattice Assembly of Functionalized Gold Nanoparticles

We report on the assembly of gold nanoparticle (AuNPs) superlattices at the liquid/vapor interface and in the bulk of their suspensions. Interparticle distances in the assemblies are achieved on multiple length scales by varying chain lengths of surface grafted AuNPs by polyethylene glycol (PEG) with molecular weights in the range 2000-40,000 Da. Crystal structures and lattice constants in both 2D and 3D assemblies are determined by synchrotron-based surface-sensitive and small-angle X-ray scattering. Assuming knowledge of grafting density, we show that experimentally determined interparticle distances are adequately modeled by spherical brushes close to the θ point (Flory-Huggins parameter, χ≈12) for 2D superlattices at a liquid interface and a nonsolvent (χ = ∞) for the 3D dry superlattices.

Ligand structure and adsorption free energy of nanocrystals on solid substrates

We present an investigation on the absorption of alkylthiolated nanocrystals on a solid substrate. We calculate adsorption free energies and report a number of effects induced by the substrate. Nearest neighbor distances and bonding free energies are significantly different than for a free floating case, there is a weakening of bonding free energies among nanocrystals, and the adsorption is manifestly anisotropic, i.e., stronger along certain directions of the nanocrystal core. We contend that this last result accounts for the Bain transition (fcc → bcc) observed in experimental results. We report the presence of vortices induced by the substrate, which explain the increased nearest neighbor distance among nanocrystals, which is in excellent quantitative agreement with experimental results and with the predictions of the Orbifold Topological Model. Implications for the assembly of nanostructures and future experiments are also discussed.

The role of ligands in electron transport in nanocrystal solids

We investigate theoretically the transport of electrons and holes in crystalline solids consisting of three-dimensional arrays of semiconductor nanocrystals passivated by two types of organic ligands-linear chain carboxylates and functionalized aromatic cinnamates. We focus on a critical quantity in transport: the quantum-mechanical overlap of the strongly confined electron and hole wavefunctions on neighboring nanocrystals. Using results from density-functional-theory (DFT) calculations, we construct a one-dimensional model system whose analytic wavefunctions reproduce the full DFT numerical overlap values. By investigating the analytic behavior of this model, we reveal several important features of electron transport. The most significant is that the wavefunction overlap decays exponentially with ligand length, with a characteristic decay length that depends primarily on properties of the ligand and is almost independent of the size and type of nanocrystal. Functionalization of the ligands can also affect the overlap by changing the height of the tunneling barrier. The physically transparent analytic expressions we obtain for the wavefunction overlap and its decay length should be useful for future efforts to control transport in nanocrystal solids.

Assembly of nanocrystal clusters by solvent evaporation: icosahedral order and the breakdown of the Maxwell regime

We carry out molecular dynamics simulations of N gold alkylthiolated nanocrystals (0 ≤ N ≤ 29) contained in liquid droplets of octane, nonane and decane coexisting with its vapor. The equilibrium structures that result when all the solvent dries up consist of highly symmetric nanocrystal clusters with different degrees of icosahedral order that are thoroughly characterized. We show that the relaxation times follow two regimes, a first for small nanocrystal packing fraction, dominated by the diffusion of vapor molecules (Maxwell regime, relaxation times independent of N) and another, for larger packing fractions, where the solvent diffuses through the cluster (with relaxation times growing like N2/3). We discuss the connection to the assembly of superlattices, prediction of lattice constants and evaporation models.