Interaction Potentials of Anisotropic Nanocrystals from the Trajectory Sampling of Particle Motion using in Situ Liquid Phase Transmission Electron Microscopy

Abstract

We demonstrate a generalizable strategy to use the relative trajectories of pairs and groups of nanocrystals, and potentially other nanoscale objects, moving in solution which can now be obtained by in situ liquid phase transmission electron microscopy (TEM) to determine the interaction potentials between nanocrystals. Such nanoscale interactions are crucial for collective behaviors and applications of synthetic nanocrystals and natural biomolecules, but have been very challenging to measure in situ at nanometer or sub-nanometer resolution. Here we use liquid phase TEM to extract the mathematical form of interaction potential between nanocrystals from their sampled trajectories. We show the power of this approach to reveal unanticipated features of nanocrystal-nanocrystal interactions by examining the anisotropic interaction potential between charged rod-shaped Au nanocrystals (Au nanorods); these Au nanorods assemble, in a tip-to-tip fashion in the liquid phase, in contrast to the well-known side-by-side arrangements commonly observed for drying-mediated assembly. These observations can be explained by a long-range and highly anisotropic electrostatic repulsion that leads to the tip-selective attachment. As a result, Au nanorods stay unassembled at a lower ionic strength, as the electrostatic repulsion is even longer-ranged. Our study not only provides a mechanistic understanding of the process by which metallic nanocrystals assemble but also demonstrates a method that can potentially quantify and elucidate a broad range of nanoscale interactions relevant to nanotechnology and biophysics.

Figure 1

In situ liquid phase TEM imaging of tip-to-tip assembly of Au nanorods. (A) The liquid flow TEM setup, with Si₃N₄ windowed microchips. Well-dispersed Au nanorods self-assemble under the illumination of electron beam. (B) Representative TEM image (left) and schematics (right) showing the final assembled structures. (C) A time series of TEM images showing how nanorods approach and attach to each other. Red arrows highlight the trajectories of nanorods before they attach to the cluster of growing rod assemblies. Scale bar is 100 nm.

Figure 2

Spatial mapping of pairwise interaction potentials from in situ dynamics of Au nanorods. (A) A TEM image highlighted with tracked positions of Au nanorods at their tips (red and green stars), and their centroids (yellow stars). In this pair, the bottom rod was chosen to be the reference rod, and the top rod was simplified as a blue line and chosen to be the repositioned rod. (B) rod density plot, where the blue lines are the observed positions of other rods relative to the vertical reference rod (yellow rod drawn to scale). The data was obtained from ∼10000 pairs of rods, but for simplicity, only 1/8 randomly chosen data was plotted in this figure. (C) The color-coded counts of total number of rods in the 2D plane of 5 nm by 5 nm pixels. Color bar shows the counts. (D) g(r) vs r plot. (E) u(r) vs r plot with its exponential fitting (red line). The inset shows the exponential decay relation of u(r) by illustrating the resultant linear relationship of ln(u(r)) vs r.

Figure 3

Comparison of experimental data and theoretical modeling of electrostatic interactions. (A) The rod position plot from ∼300 rod–rod attachments. The symbol and color scheme are based on what is shown in Figure 2B. (B) The observed density of rods in the attached configuration where the reference rod is also sitting vertically at the center. It is clear that the rods have a preference to align roughly parallel with each other (see the dark red pixels). (C) Energy contour plot showing calculated lowest potential for a pair of nanorods, where one rod stays vertically at the center and the other samples all the possible rod orientations at each pixel. The potential at each pixel is color-coded: red for larger values and blue for smaller values. At the rod side position, the potential energy is ∼2 times higher than at the rod tip. (D) Calculated orientation of rods for the lowest energy at each pixel, with blue color meaning parallel and red color meaning perpendicular as shown in the schematics on the left.

Figure 4

Suppression of Au nanorod assembly at low ionic strength. (A) Plot of different rod configurations (each rod as a purple line) relative to the central reference rod. The yellow dashed circle indicates the depleted zone. (B) TEM image of electrostatically stabilized Au nanorods overlaid with yellow dotted depleted zone. (C) Trajectories of all eight rods in panel B. Scale bar is 50 nm.