Understanding the Formation of Pbse Honeycomb Superstructures by Dynamics Simulations
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PHYSICAL REVIEW X 9, 021015 (2019) Understanding the Formation of PbSe Honeycomb Superstructures by Dynamics Simulations Giuseppe Soligno* and Daniel Vanmaekelbergh Condensed Matter and Interfaces, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, Utrecht 3584 CC, Netherlands (Received 28 October 2018; revised manuscript received 28 January 2019; published 23 April 2019) 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 short- range 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 sharp- interface 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 coarse- grained model. In particular, by slightly tuning just a few parameters of the model, we can induce NC self- assembly 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. DOI: 10.1103/PhysRevX.9.021015 Subject Areas: Computational Physics, Materials Science, Nanophysics I. INTRODUCTION superstructure: (i) synthesis of the NCs, i.e., the super- structure building blocks, from their atomic precursors Nanoparticle self-assembly is an emerging route with [48–60], and (ii) self-assembly of the NCs into ordered tremendous potential to build novel nanostructured materi- structures [61–66]. Typically, NCs are, after their synthesis, als [1,2]. In the past two decades, increasing interest has dispersed in solution and fully covered by organic molecules been devoted toward the formation of 3D [3–20] and 2D (ligands), chemically attached (chemisorbed) at the NC [21–32] nanogeometric materials for optoelectronic appli- surface, which largely screen NC-NC attractive interactions. cations [33–47]. These nanomaterials are formed by the The NC self-assembly can be induced, for example, by self-assembly of semiconductor nanocrystals (NCs) with solvent evaporation (i.e., by increasing the NC density). In the size of a few nanometers, and often with a roughly this case, a close-packed NC superstructure is obtained, spherical shape, into various types of superstructures. whose geometry is dictated mainly by entropic factors, i.e., Two main stages are required for the formation of a the shape and size of the NCs [67–71]. NC-NC attractive interactions can be activated (e.g., by ligand-exchange [72] *Corresponding author. or facet-specific ligand-detachment [73] reactions), inducing [email protected] NC self-assembly in different types of superstructures. A special class of NC superstructures, referred to as NC Published by the American Physical Society under the terms of superlattices, is formed when NC self-assembly is followed the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to by crystal-structure alignment and oriented attachment the author(s) and the published article’s title, journal citation, [74–83] of close-by NCs, resulting in atomically coherent and DOI. nanogeometric materials. The formation process of NC 2160-3308=19=9(2)=021015(32) 021015-1 Published by the American Physical Society GIUSEPPE SOLIGNO and DANIEL VANMAEKELBERGH PHYS. REV. X 9, 021015 (2019) superlattices can be confined in 2D when the NCs are superstructures obtained with our MD model present the adsorbed at a fluid-fluid interface [84]. The NCs self- same kind of defects observed in the experimental super- assemble in ordered monolayers at the fluid-fluid interface, lattices, indicating that our MD model can also be used to and subsequently perform oriented attachment [73,85–88], study the formation and stability of defects in these resulting in 2D atomically coherent nanogeometric materi- structures. als. In this last class of processes, in addition to NC entropy and NC-NC interactions, also the different interactions of the II. COARSE-GRAINED MD MODEL NCs with the different molecules of the two fluids forming First, we briefly illustrate our simulation model (more the interface (i.e., interface-adsorption effects) are involved details are provided in Appendix A). in the superlattice formation mechanism. First experimentally observed a few years ago [73,85,86,88], the PbSe silicene-honeycomb 2D super- A. Outline lattice is expected to exhibit a Dirac-type band structure, We model a PbSe NC using a polybead structure. The with the semiconductor band gap preserved [89–91]. beads forming the NC are disposed to reproduce a Hence, such a material would combine the properties of rhombicuboctahedron of size 6 nm, that is a typical semiconductors with those of graphene, making it very experimental shape [76,92]. We simulate the dynamics interesting for optoelectronic applications. This superlattice of the NCs using the position-Verlet algorithm [94] to is formed by PbSe NCs, approximately having a 5-nm size compute the bead’s motion. Bead-bead pair potentials are and a rhombicuboctahedron shape, disposed as in the used to reproduce NC-NC short-range facet-specific attrac- silicene lattice, i.e., in a periodically buckled honeycomb tive and repulsive interactions. The distance between beads lattice, and all oriented with a f111g facet parallel to the belonging to the same NC is kept fixed by constraint forces superlattice plane. The PbSe NCs, before the self-assembly, [95]. The solvent is treated implicitly by modeling the NC i.e., when still dispersed in solvent, are fully covered by Brownian motion. External potentials are applied to the NC oleic acid ligands, which are strongly attached at the f111g, beads to mimic the interface-adsorption forces experienced f110g facets and weakly bonded at the f100g facets [92]. by NCs at a fluid-fluid interface. The formation process of the PbSe silicene-honeycomb superlattice typically occurs at the solvent-air interface. B. NC-NC interactions During the process, ligands desorb from the NC f100g facets, allowing oriented attachment between PbSe NCs The polybead structure representing each NC is formed by opposite f100g facets [73]. In similar experiments by 144 beads (shell beads) disposed to represent the NC [73,85,87], self-assembly of NCs into square superlattices surface, see Fig. 1, plus seven beads (core beads) used, see was observed, with all NCs oriented with a f100g facet later, for the Brownian motion of the NCs. To model parallel to the superlattice plane, and with oriented attach- van der Waals and electrostatic-chemical atomic inter- ment between PbSe NCs by opposite f100g facets also actions between NCs at almost-contact distance, shell performed. Although the relevant forces involved in the beads of different NCs interact with each other by the formation of these superlattices are known [93], the precise Lennard-Jones pair potential, mechanisms are far from understood. In particular, it is not σ 12 σ 6 clear yet why the PbSe NCs form square superlattices in U ¼ 4ϵ − ; ð1Þ some cases and silicene-honeycomb superlattices in others. LJ r r In this work, we shed light on this, introducing a new coarse-grained molecular dynamics (MD) model to study truncated and shifted in r ¼ 2.4σ [see Eq. (A3)], where r is the self-assembly of NCs at fluid-fluid interfaces. By the center-to-center bead-bead distance, σ ¼ 1 nm, and ϵ presenting simulations with our MD model, we illustrate sets the interaction strength for the bead pair. PbSe NCs are, how the intricate interplay between interface-adsorption after their synthesis, dispersed in solution, and ligands, forces orienting and keeping the NCs at the interface and typically oleic acid molecules, are chemisorbed at the NC attractive forces only between f100g facets of close-by facets. At this stage, ligands largely screen NC-NC attrac- NCs drive the self-assembly of PbSe NCs into either square tive interactions and prevent NC assembly. In the experi- or silicene-honeycomb superstructures. As a confirmation ments of interest [73,85–88], the NC self-assembly is that our model correctly captures the key features of the activated by chemically inducing the detachment of ligands NC self-assembly, in our simulations we observe, in the from the PbSe NC f100g facets, i.e., where the bonding formation of both the silicene-honeycomb and square energy between ligand molecules and NC surface atoms is superstructures, the same few-NCs precursors observed lowest [73,92]. Hence, during the self-assembly, NCs experimentally, that is zigzag aggregates, where all NCs attract (and attach to) each other only by f100g facets, have a f111g facet parallel to the interface plane, and while NC-NC bonds by f110g and f111g facets are linear chains, where all NCs have a f110g facet parallel prevented by ligands.