Thermodynamic Equilibrium of Binary Nanocrystal Superlattices

Abstract

We present a detailed investigation of nanoparticle binary superlattices. We characterize the properties of given superlattices and characterize the splayed ligand conformation, that is, vortices that determine bonding among nanoparticles. We show that the overall structure is accurately predicted by the orbifold topological model (OTM). Our explicit free energy calculations show that binary superlattices reported in experiments are dominated by many-body effects and are marginally stable or unstable, with a priori subleading effects, such as dipole–dipole or van der Waals core attraction being critical for the overall stability. We discuss vortices as fundamental bonding mechanisms, implications for actual experiments, as well as for future developments.

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

“…The spherical NC we considered is Au 4033 (SC 18 ) 533 . The core diameter is D = 5.452 (nm) and from eq 12 (n = 18) it is L = 2.28 nm, 19 so that λ = 0.836. The grafting density was such that ξ = 0.85.…”

“…16 Lattice free energies were calculated following our previous work. 17,19 Basically, the nearest neighbors are connected by harmonic springs and the reversible work is calculated by quasistatically compressing the system; see the Supporting Information for explicit formulas. In all cases, rotation of NC cores were not allowed, implemented in HOOMD-blue by including rotation false in the rigid body degrees of freedom.…”

“…Yet, this is an exceedingly ambitious goal, so in this paper we consider a simpler problem: Given a number of NC types and assuming they arrange into a known lattice, predict its structure: lattice constant, density, ligand arrangements, etc. For systems consisting of two types of spherical NCs, the Orbifold Topological Model (OTM) , provides a complete solution to this problem, as it has been validated from both simulations − and experiments. ,, Basically, the OTM describes NCs as hard spheres, whose diameter is given by the Optimal Packing Model (OPM) . However, when the number of nearest neighbors (coordination) is small (less than 6), large deformations of the ligands, i.e., vortices, are possible, breaking down the hard sphere (OPM) description and enabling closer NC separation, with detailed formulas derived by optimizing the packing fraction.…”

Modeling of effective interactions between ligand coated nanoparticles through symmetry functions

“…These effective interactions are computed from fully atomistic molecular simulations of nanoparticles. In this regard there have been a number of studies previously reported [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] that have computed effective inter-particle interactions. These studies looked at various aspects of interactions between nanoparticles including length of ligand chains, role of solvent, three-body interactions, etc.…”

“…Recently, Travesset 16,17 developed the Orbifold Topological Model (OTM) that has improved upon both OPM and OCM. The predictions of the OTM were shown to be quite accurate for Binary Nanocrystal Superlattices (BNSLs) by Zha and Travesset 18 .…”