Imaging the polymerization of multivalent nanoparticles in solution

Abstract

Numerous mechanisms have been studied for chemical reactions to provide quantitative predictions on how atoms spatially arrange into molecules. In nanoscale colloidal systems, however, less is known about the physical rules governing their spatial organization, i.e., self-assembly, into functional materials. Here, we monitor real-time self-assembly dynamics at the single nanoparticle level, which reveal marked similarities to foundational principles of polymerization. Specifically, using the prototypical system of gold triangular nanoprisms, we show that colloidal self-assembly is analogous to polymerization in three aspects: ensemble growth statistics following models for step-growth polymerization, with nanoparticles as linkable "monomers"; bond angles determined by directional internanoparticle interactions; and product topology determined by the valency of monomeric units. Liquid-phase transmission electron microscopy imaging and theoretical modeling elucidate the nanometer-scale mechanisms for these polymer-like phenomena in nanoparticle systems. The results establish a quantitative conceptual framework for self-assembly dynamics that can aid in designing future nanoparticle-based materials.Few models exist that describe the spontaneous organization of colloids into materials. Here, the authors combine liquid-phase TEM and single particle tracking to observe the dynamics of gold nanoprisms, finding that nanoscale self-assembly can be understood within the framework of atomic polymerization.

Fig. 1

Chains assembled from gold prisms via step-growth polymerization. a Schematics showing a single gold triangular prism coated with negatively charged thiols and labeled with spots at the three triangular tips. The spots are black when the prisms are in deionized water, meaning the repulsive cloud (red) envelopes the prism tips and renders the prisms non-reactive. Once the prism solution is illuminated by the electron beam at the appropriate dose rates (9.8–25.8 e⁻ Å⁻² s⁻¹), the prisms are rendered attachable at the tips (two spots changing to red) with the repulsive cloud shrunken inwards. b Stepwise tip-to-tip assembly schematic representing the connection scheme of the prisms highlighted in c. c Time-lapse liquid-phase TEM images showing the growth of a prism chain at a dose rate of 16.3 e⁻ Å⁻² s⁻¹ (see details on image processing in Supplementary Fig. 3 and Supplementary Note 3). We overlay outlines on the prisms: dotted red lines for monomeric prisms before attachments, solid red lines for assembled prisms, and solid purple lines for prisms newly attached to the chain. The yellow arrows show the direction of prism attachment. d Distribution of x-mer, chains comprising x prisms, fraction changing over time (black: t = 0 s, green: t = 322 s, light emerald: t = 1349 s), which shows a shift toward higher aggregation number x. e The graph showing ${\overline{X}}_{\mathrm{n}}$ (squares to the left y axis), the number-average degree of polymerization, growing linearly with time t, and the total number of prisms n (both unreacted and reacted, blue circles to the right y axis) remaining constant over time. The gray dotted line is the linear fitting of ${\overline{X}}_{\mathrm{n}}-t$ relation, while the blue dotted line is a guide to the eye. f A semi-log plot showing how the fraction of x-mers ($n_x∕N_{\mathrm{L}}$) is distributed at different assembly times (black circle: t = 0 s, light green up triangle: t = 808 s, emerald down triangle: t = 1078 s). The lines are the corresponding fit based on the Flory−Schulz distribution. Error bars denote standard deviations from counting. Scale bars: 50 nm

Fig. 2

Temporal traces showing the selection of tip-to-tip attachments through long-range repulsion. a Schematics defining d, the center-to-center distance, d _g, the gap distance between two approaching prism tips, and α, the relative orientation of two close prisms. The α angle is defined as supplementary to the angle formed by two intersecting straight lines each connecting the closest tip and midpoints of the remote prism side. Based on this definition, the angle is independent of the distance d. b–d Three representative types of time-lapse liquid-phase TEM images of two prisms approaching each other, and corresponding temporal traces characterizing changes in their center-to-center distance d (black circles) and relative orientation α (blue circles) over time. In the case of “Align and attach” b, the green arrow in the graph corresponds to the time for the TEM image boxed in green, when the tip-to-tip orientation is selected; the magenta arrow in the graph corresponds to the time for the TEM image boxed in magenta, when the prisms are attached. Scale bars: 50 nm

Fig. 3

Statistical analysis of tip-to-tip attachments due to long-range repulsion. a A scattered map showing the distances and relative orientations sampled by two approaching prisms based on experimental liquid-phase TEM observations. Each data point color corresponds to a single trace of prism pairs. We see three regions in the map, non-interacting (I), pre-align (II), and attach (III), which correspond to distinct relative orientation distributions shown in b. b The relative orientation (α) distributions obtained from the scattered map in a, changing from wide distribution (I), narrowing toward one single peak (II), to peaking at 60° for these data series (III). c The isoenergetic contour plots of electrostatic repulsion E _el surrounding a single prism at 160 µM ionic strength. d The graph of calculated electrostatic repulsion between two approaching prisms in the side-by-side (olive) and tip-to-tip (emerald) configurations vs. gap distance d _g at 160 µM ionic strength. Scale bar: 50 nm

Fig. 4

Optimal bond angle determined by prism tip curvature. a The bond angle (α) distribution in the prism chains based on liquid-phase TEM observations has two peaks at 0° and 60°. The schematics show the two bonding motifs for 0° (gray bar) and 60° (green bar) bond angle connections. b TEM images and corresponding schematics of dimeric and trimeric chains growing out of the two bonding motifs. c Representative TEM images of prisms overlaid with edge contour curvature plots showing two typical curvatures (1/r, r being the radius of the fitted circle) of the triangular prism tips. The schematics highlight the difference in tip geometry at these two bond angle configurations. d The dependence of total interaction energy of attached prisms (d _g = 0.5 nm) as a function of bond angles and tip curvatures. The two lines highlighted in black on the energy map show the energy curves at curvatures of 0.2 and 0.026 nm⁻¹, respectively. Scale bars: 50 nm for b, 5 nm for c and 30 nm for the inset in c

Fig. 5

Colloidal polymer topology determined by prism coordination geometry. a The calculated electrostatic repulsion (E _el) maps showing that the increase in the ionic strength leads to an increase in the number of bonds, i.e., valency, of prisms (ionic strength: 129 µM, 160 µM, and 205 µM from left to right). The red spots in the prism schematics indicate reactive sites that determine the connection scheme and final assembly structure. b Time-lapse liquid-phase TEM images of the cyclic assemblies at a dose rate of 39.5 e⁻ Å⁻² s⁻¹. The black arrows show the direction of assembly (Supplementary Movie 4). Scale bars: 100 nm