Understanding the Formation of PbSe Honeycomb Superstructures by Dynamics Simulations

Abstract

Using a coarse-grained molecular dynamics model, we simulate the self-assembly of PbSe nanocrystals (NCs) adsorbed at a flat fluid-fluid interface. The model includes all key forces involved: NC-NC shortrange facet-specific attractive and repulsive interactions, entropic effects, and forces due to the NC adsorption at fluid-fluid interfaces. Realistic values are used for the input parameters regulating the various forces. The interface-adsorption parameters are estimated using a recently introduced sharpinterface numerical method which includes capillary deformation effects. We find that the final structure in which the NCs self-assemble is drastically affected by the input values of the parameters of our coarsegrained model. In particular, by slightly tuning just a few parameters of the model, we can induce NC selfassembly into either silicene-honeycomb superstructures, where all NCs have a f111g facet parallel to the fluid-fluid interface plane, or square superstructures, where all NCs have a f100g facet parallel to the interface plane. Both of these nanostructures have been observed experimentally. However, it is still not clear their formation mechanism, and, in particular, which are the factors directing the NC self-assembly into one or another structure. In this work, we identify and quantify such factors, showing illustrative assembled-phase diagrams obtained from our simulations. In addition, with our model, we can study the self-assembly dynamics, simulating how the NCs' structures evolve from few-NCs aggregates to gradually larger domains. For example, we observe linear chains, where all NCs have a f110g facet parallel to the interface plane as typical precursors of the square superstructure, and zigzag aggregates, where all NCs have a f111g facet parallel to the interface plane as typical precursors of the silicene-honeycomb superstructure. Both of these aggregates have also been observed experimentally. Finally, we show indications that our method can be applied to study defects of the obtained superstructures.

Unravelling three-dimensional adsorption geometries of PbSe nanocrystal monolayers at a liquid-air interface

“…Hanrath et al showed that large cubic PbSe NCs with an edge length of 25 nm do align a [111] axis perpendicular to the toluene-air interface, but there the NCs formed 3-D body-centered cubic superlattices 25 . This is also the orientation that PbSe NCs are required to have before silicene-type honeycomb superlattices can form 7,22 . We will show in the section below that the full adsorption geometry of the PbSe NCs studied here is determined by an interplay between the adsorption energy, mostly dictated by the NC size, and the degree of truncation of the NCs.…”

“…Which factors determine the amount of disorder on both atomic and NC length scales and how can we reduce this 10,[15][16][17][18][19][20][21] ? A recently introduced simulation model to predict the self-assembly of NCs at fluid-fluid interfaces provided fundamental insights that will help to answer these questions 22,23 .…”

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

“…Further details on this model are reported in Supporting Information 6 and a recent publication. 53 In the simulations presented here, up to 10 4 NCs are initially randomly dispersed in a cubic box of side L aligned with a Cartesian coordinate system x , y , z and with periodic boundary conditions. The external force −d U 2D ( z c )/d z c is applied to each NC center of mass, with z c the z coordinate of the NC center of mass, to model the effect of the evaporating solvent, which compresses the NCs in a 2D plane.…”

“…The parameter u z is 10 –19 J, in line with predicted solvent–air adsorption potentials of NCs. 53 During the first 0.1 μs of simulation, the beads of different NCs interact with each other only by a soft repulsive pair potential, mimicking the effect of ligand molecules chemisorbed on the NC surface where r is the bead–bead center-of-mass distance, ϵ R is the magnitude of the repulsive potential, and σ R is the ligand length. After 0.1 μs, the attractive pair potentials between beads belonging to NCs’ {100} facets are (gradually) turned on, mimicking ligands detaching from {100} facets (thus allowing the facet–facet interaction).…”

The Role of Dimer Formation in the Nucleation of Superlattice Transformations and Its Impact on Disorder

“…Several different MD approaches have been used to study the formation of lead chalcogenide superstructures. , Recent work by Wang et al used MD simulations to study superlattice phase transitions for small 1D structures, focusing on the deformability of PbSe NCs during the phase transition and its impact on disorder. The force field used in that study considered only nonbonded interactions, namely, a short-ranged Lennard-Jones part and a long-ranged Coulombic part.…”