Phase Diagram and Structure Map of Binary Nanoparticle Superlattices from a Lennard-Jones Model

Abstract

A first principle prediction of the binary nanoparticle phase diagram assembled by solvent evaporation has eluded theoretical approaches. In this paper, we show that a binary system interacting through Lennard-Jones (LJ) potential contains all experimental phases in which nanoparticles are effectively described as quasi hard spheres. We report a phase diagram consisting of 53 equilibrium phases, whose stability is quite insensitive to the microscopic details of the potentials, thus giving rise to some type of universality. Furthermore, we show that binary lattices may be understood as consisting of certain particle clusters, i.e. motifs, which provide a generalization of the four conventional Frank-Kasper polyhedral units. Our results show that meta-stable phases share the very same motifs as equilibrium phases. We discuss the connection 1 with packing models, phase diagrams with repulsive potentials and the prediction of likely experimental superlattices.

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

“…Still, as clear from our study, the considerable magnitude of many body effects shows that the characterizations in terms of pair potentials require further analysis on the structure of the ligand shell. An approach based on motifs, 44 i.e., many body clusters, may provide the appropriate way to circumvent these issues. In any case, the obvious presence of metastability highlights that the full determination of the pathways leading to the assembly holds the key to programmable matter.…”

“…Our study selected most of the common BNSLs and computed their free energies and structural properties, and therefore makes no attempt to predict what is the optimal, i.e., the absolute free energy minimum superlattice. There has been significant progress in this regard from studies with simpler potential models , such as inverse power laws or Lennard-Jones, , which have successfully identified many putative new BNSLs. Still, as clear from our study, the considerable magnitude of many body effects shows that the characterizations in terms of pair potentials require further analysis on the structure of the ligand shell.…”

Thermodynamic Equilibrium of Binary Nanocrystal Superlattices

“…There are, however, obvious limitations: in our recent characterization of the phase diagram for binary LJ particles, we have identified 53 equilibrium phases. 21 Even (wrongly) assuming that the true equilibrium for given external conditions is always among these 53 phases (note that the reported Li 3 Bi 4 phase, e.g., is not an equilibrium LJ), simulations are costly and challenging to perform with high precision, so consideration of these 53 phases for all relevant conditions (and OTM branches) requires hefty computer capabilities. For these reasons, in this paper, we will restrict our study to a smaller subset: BNSLs that have been reported in experiments.…”

“…The OTM provides a quantitative description of the structure of a given BNSL but does not, however, provide an actual free energy from which the actual phase diagram can be predicted. Other attempts to establish phase diagrams using simpler binary systems such as optimization of packing fraction, − finite temperature HS, binary inverse power law potentials, − or Lennard-Jones (LJ) potentials provide some guidance but lack truly predictive power as they contain many BNSLs not observed experimentally, and other phases that are observed are not thermodynamically stable in these models. Describing the stability of BNSLs in terms of effective pair potentials is not possible since “vortices” induce a dependence on particle coordination and lead to a free energy dominated by many-body effects.…”

Discovery of Two-Dimensional Binary Nanoparticle Superlattices Using Global Monte Carlo Optimization

“…The task of obtaining globally stable NP structures is thus a global optimization problem, akin to protein folding. Although some computational efforts have been devoted to exploration of BNSLs [24][25][26][27] , none of them have focused on 2D BNSLs formed at interfaces.…”