Electrostatically Assembled Open Square and Checkerboard Superlattices

TL;DR

The study tackles the challenge of assembling open 2D square lattices at a liquid–air interface by using PEG-grafted gold nanoparticles with opposite terminal charges. By tuning three parameters—core size, PEG molecular weight, and pH—the authors control the effective size ratio $\gamma$ and electrostatic interactions to program binary NP superlattices into checkerboard, simple square, or honeycomb motifs, with pH-driven transitions between lattice types. In situ GISAXS and XRR confirm monolayer interfacial ordering, reveal reversible lattice transitions, and map how polymer conformation and interfacial adsorption govern structure. This work provides a versatile, broadly applicable method for programmable fabrication of colloidal superstructures with tailored architectures for plasmonic and photonic applications.

Abstract

Programmable assembly of nanoparticles into structures other than hexagonal lattices remains challenging. Assembling an open checkerboard or square lattice is harder to achieve compared to a close-packed hexagonal structure. Here, we introduce a unified, robust approach to assemble nanoparticles into a diverse family of two-dimensional superlattices at the liquid-air interface. Gold nanoparticles are grafted with pH-responsive, water-soluble poly(ethylene glycol) chains terminating in -COOH or -NH2 end groups, enabling control over interparticle interactions, while the grafted polymer's molecular weight dictates its conformation. This combined control crystallizes checkerboard, simple-square, and body-centered honeycomb superlattices. We find that even for identical nanoparticle core sizes, the polymer's molecular weight dictates superlattice symmetry and stability. Furthermore, tuning pH induces structural transitions between different lattice types. This method opens new avenues for the programmable fabrication of colloidal superstructures with tailored architectures.

Figures (7)

• Figure 1: Schematic of Size‐ and Charge‐Tunable PEG‐Grafted AuNPs. AuNP cores of 5 nm (yellow) and 10 nm (blue) diameter are functionalized with thiol‐PEG chains (2, 5, or 10 kDa) terminating in –NH2 (blue) or –COOH (green). Positively and negatively charged PEG coronas are marked with “$+$” and “$-$” symbols. The resulting hard‐sphere diameters, $D_A$ and $D_B$, define the size ratio $\gamma = D_B/D_A$. As PEG MW increases, the hydrodynamic diameter grows, as depicted in the Figure.
• Figure 2: Checkerboard and Square Superlattices Revealed by GISAXS. Grazing‐incidence small‐angle X‐ray scattering line-cuts, $I(Q)$, for nanoparticle mixtures as a function of pH. (a–c) A 1:1 mixture of COOH‐PEG2k–Au5 and NH2‐PEG5k–Au10: (a) at pH 6, a well‐defined checkerboard superlattice arises from complementary electrostatic interactions; (b) at pH 4, checkerboard order is distorted; and (c) at pH 3, a body‐centered honeycomb (quasi‐stoichiometric A$_2$B) superlattice forms. (d–f) Core‐matched AuNPs (10 nm) with identical polymer ligands to those in (a-c): (d) at pH 6, a perfect simple square lattice is formed; (e) at pH 4, improved square lattice ordering is induced; and (f) at pH 3, a square lattice diffraction pattern with a shoulder at lower $Q$ value indicative of partial core‐particle fractionalization. The solid line through the data points (open circles) is a fit to the structure factor of each lattice. Colored lines below represent the calculated structure factors, with shaded regions indicating individual peak contributions. Calculated structure factors are identical for all instances of a given structure type and are shown to illustrate the structural motifs that are intended as a qualitative guide rather than a quantitative fit to the diffraction data. The inset shows a schematic of the ideal superlattice geometry. PEGylated polymers act as scaffolds to direct nanoparticle placement into these targeted architectures.
• Figure 3: X-ray Reflectivity Confirming Monolayer Formation and Coverage Normalized X-ray reflectivity curves and corresponding electron density profiles, corresponding to the same samples shown in Fig. \ref{['fig:Checkerboard_Square_1']}. (a) X-ray reflectivity curves for a 1:4 mixture of COOH‐PEG2k–Au5 and NH$_2$‐PEG5k–Au10 (corresponding to the samples in Fig. \ref{['fig:Checkerboard_Square_1']}(a-c)) at three different pH values (6, 4, and 3). Solid lines through the experimental data (symbols as indicated) represent the best fit. (b) The electron density (ED) profiles derived from the fits in panel (a). The characteristic thickness of the excess ED layer, on the order of 10 nm, confirms that the films giving rise to the 2D diffraction patterns in Fig. \ref{['fig:Checkerboard_Square_1']}(a-c) consist of a single layer of AuNPs. The lower electron density observed at pH 6 and 4 compared to pH 3 indicates incomplete surface coverage, where crystallites coexist with bare water regions, forming a 'crystal-moat' morphology. (c) X-ray reflectivity curves for the core-matched binary system of COOH‐PEG2k–Au10 and NH$_2$‐PEG5k–Au10 (corresponding to samples in Fig. \ref{['fig:Checkerboard_Square_1']}(d-f)), also at three pH values (6, 4, and 3). (e-f) Schematic illustration depicting the interfacial morphology: an intact, densely packed AuNP monolayer formed at pH 3 (bottom), contrasting with dispersed crystallites coexisting with bare water 'moats' at pH 4 and 6 (top).
• Figure 4: pH‐Dependent Lattice Transformations in PEG‐Chain‐Swapped AuNP Mixtures. Grazing‐incidence small‐angle X‐ray scattering line-cuts, $I(Q)$, of PEG‐chain‐swapped nanoparticle systems as a function of pH. (a–c) A 1:1 mixture of COOH‐PEG5k–Au5 and NH2‐PEG2k–Au10 (PEG chains swapped relative to Fig. \ref{['fig:Checkerboard_Square_1']}): (a) at pH 6, an ill‐defined body‐centered honeycomb superlattice; (b) at pH 4, short‐range ordering with two dominant Bragg reflections indicative of a disordered binary arrangement; (c) and at pH 3, a transition to an almost perfect checkerboard superlattice. (d–f) Core‐matched AuNPs (10 nm) functionalized with the same swapped ligands form a robust, simple square lattice across the entire pH range: (d) at pH 6, (e) pH 4, and (f) pH 3. Solid lines through the open‐circle data are fits to the corresponding structure factors; colored lines below represent the calculated structure factors, with shaded regions highlighting individual peak contributions. Calculated structure factors are identical for all instances of a given structure type and are shown to illustrate the structural motifs that are intended as a qualitative guide rather than a quantitative fit to the diffraction data. The insets illustrate the ideal superlattice geometry.
• Figure 5: From single-nanoparticle hexagonal lattice to checkerboard square lattice 1D GISAXS line-cuts for a binary mixture of COOH-PEG5k-Au5 and NH$_2$-PEG10k-Au10 at three different pH values. Panels (a-c) display results for a nominal 1:1 ratio of the two components, while panels (d-f) show results for a nominal 4:1 ratio (COOH-PEG5k-Au5: NH$_2$-PEG10k-Au10). (a-c) At a 1:1 nominal mixing ratio, the upper panels indicate that the interface is predominantly populated by a single component from the suspension, which self-assembles into a hexagonal lattice. This observation is consistent with the preferential formation of a unitary crystal by the NH$_2$-PEG10k-Au10 nanoparticles. (d-f) As the nominal concentration of the COOH-PEG5k-Au5 is increased to a 4:1 ratio, the system adopts a checkerboard-square superlattice at both pH 6 and pH 4. However, upon lowering the pH further to 3, the interface becomes populated by a coexistence of the original unitary hexagonal superstructure and the checkerboard lattice. Solid lines through the open‐circle data are fits to the corresponding structure factors; colored lines below represent the calculated structure factors, with shaded regions highlighting individual Bragg peaks. Calculated structure factors are identical for all instances of a given structure type and are shown to illustrate the structural motifs that are intended as a qualitative guide rather than a quantitative fit to the diffraction data. The insets illustrate the ideal superlattice geometry.