Anisotropic nanocrystal shape and ligand design for co-assembly

Abstract

The use of nanocrystal (NC) building blocks to create metamaterials is a powerful approach to access emergent materials. Given the immense library of materials choices, progress in this area for anisotropic NCs is limited by the lack of co-assembly design principles. Here, we use a rational design approach to guide the co-assembly of two such anisotropic systems. We modulate the removal of geometrical incompatibilities between NCs by tuning the ligand shell, taking advantage of the lock-and-key motifs between emergent shapes of the ligand coating to subvert phase separation. Using a combination of theory, simulation, and experiments, we use our strategy to achieve co-assembly of a binary system of cubes and triangular plates and a secondary system involving two two-dimensional (2D) nanoplates. This theory-guided approach to NC assembly has the potential to direct materials choices for targeted binary co-assembly.

Fig. 1. Schematic of design workflow.

Illustration of design strategy, demonstrating how lattice prediction methods (purple) lead to a feasible set of parameters for co-assembly, which are verified by computation (pink) and then realized experimentally (green). (Top left quadrant) Nanocrystals and ligands tested in the theoretical screening, serving as input to TPT. (Top right quadrant) Representative phase diagram for system computed from using TPT. (Bottom left quadrant) Phase diagram guides selection of phase space for Monte Carlo simulation. (Bottom left quadrant) Experimental realization of the designed system from both theory and MC validation. Scale bar in TEM image, 50 nm.

Fig. 2. Theoretical prediction of co-assembly phase space.

Phase diagram for cube and triangular plate co-assembly for (A) OA ligand and (B) PCL, with ligand structures shown above. (C) Representative snapshots of the crystal structures used in construction of the phase diagrams. Border coloring corresponds to each respective phase.

Fig. 3. Differences in interparticle interactions for different ligands drive enhanced co-assembly.

(A) Computed PMF for CC, PP, and CP interactions. (B) Radial distribution function (black lines show peak locations) for CC, g_CC(r), overlaid with PMF for CC. (C) Radial distribution function for CP, g_CP(r), overlaid with PMF for CP. (D) Radial distribution function for PP, g_PP(r), overlaid with PMF for PP. All PMFs shown are for relative orientation between NCs shown in the inset for (B) to (D). For all panels, dashed lines indicate PMF for OA and solid line is PMF for PCL.

Fig. 4. Results of Monte Carlo simulations for various (ϕ_plate, ε).

The theoretical phase diagram is overlaid by diamonds representing the matching phase (top left). We include snapshots of the bottom layer of the simulation box (right) representing state points of (0.8, 7.0) (A), (0.8, 8.0) (B), (0.6, 7.0) (C), and (0.2, 8.0) (D). Gray NCs indicate NCs not included in the bottom layer. Colored outlines represent the phases that best match the snapshot. We demonstrate that the radial distribution function can identify peaks corresponding to PP, CP, and CC interactions (green, magenta, and purple peaks) [g(r) shown for (0.6, 7.0)].

Fig. 5. Phase classification using relative peak heights.

We demonstrate the various contributions to the final assembly by computing the contribution of contacts (peak height) for PP, CP, and PP, respectively, at various (ϕ_plate, ε). Dominant phases are identified by comparing their relative contributions to the sum of peak heights.

Fig. 6. Single-component NCs self-assembled with OA as the capping ligand.

TEM images of (A) PbTe with selected-area electron diffraction (SAED) inset in the lower right corner, (B) LaF₃ assembled on tetraethylene glycol, and (C) LaF₃ assembled on ethylene glycol forming lamella morphology. Scale bars, 100 nm. FFT images are upper right corner insets.

Fig. 7. Successful co-assembly of PbTe and LaF₃.

(A and B) TEM images at various magnifications. Scale bars, 100 nm (with FFT insets in the upper right corners and small-angle SAED in the lower right corners). (C) EDS spectroscopy overlay, with each element listed. Scale bars, 20 nm.

Fig. 8. Comparison of experiments with the predicted phase diagram.

Corresponding TEM images for a series of points are labeled within the diagram. (A) Co-assembly with highest uniformity and a bullseye within the phase diagram, with FFT and small-angle SAED as insets in the upper and lower right corners. Lamellar morphologies in domains with fewer cubes than triangles can be clearly seen in (B) to (D), which match well with predicted phases. Scale bars, 100 nm (A) and 50 nm (B to D).

Fig. 9. Co-assembly of GdF₃ rhombic plates with LaF₃ triangular plates.

(A and B) Co-assembly with appropriate edge-length matching, where assembly can be dictated by the concentrations of each component. (C and D) Smaller triangular plates are used in assembly for substitutional doping into film morphologies of the rhombic plates. FFTs are upper right insets. Scale bars, 50 nm. False coloring has been added to (C) and (D) to highlight the doping.