Valence-free open nanoparticle superlattices

TL;DR

This work addresses the challenge of assembling open, diamond-like nanoparticle superlattices without directional bonding. It demonstrates that valence-free, oppositely charged PEG ligands on isotropic AuNPs enable self-assembly into ZnS-like, NaCl-like, diamond, simple cubic, and CsCl-like lattices by tuning the hydrodynamic size ratio $\gamma$ and the ligand MW ratio $\theta$, as well as solution pH. SAXS experiments, phase diagrams, and all-atom MD simulations with an electrostatic-correlations-based free-energy model reveal how A–B attraction and B–B repulsion stabilize open lattices and shift phase boundaries, enabling precise lattice control and tunable lattice constants. The approach is generalizable to other NP–ligand systems and scalable to larger NPs, offering a versatile route for photonic, catalytic, and other functional nanomaterials.

Abstract

A cornerstone of advanced materials design is establishing a framework for assembling nanoparticle superstructures with tailored symmetries. A longstanding challenge has been assembling diamond-like superstructures for photonic devices. Traditionally, such open superstructures require functionalized nanoparticles with directional or anisotropic interactions, reminiscent of valence bonding in a diamond. Here, we present a robust strategy for assembling valence-free nanoparticles into a broad array of cubic superstructures. By grafting nanoparticles with oppositely charged, end-functionalized water-soluble polymers of adjustable molecular weight, we gain control over electrostatic interactions and conformational constraints. This unified approach yields lattices analogous to rock salt, CsCl, zinc-blende, diamond, and the rare simple cubic phase, with tunable lattice constants. Theoretical models and simulations elucidate the underlying interactions, providing a framework for engineering valence-free nanoparticle superlattices.

Figures (5)

• Figure 1: Strategy to construct valence-free ionic-like NP superlattices. (a) Depiction of gold nanoparticles (AuNPs) with core diameters ($D_{\rm core}$) of 5 nm (yellow) and 10 nm (blue) are functionalized with poly(ethylene glycol) (PEG) terminated with either -NH2 (blue) or -COOH (green). The surface charges on the blue ($+$) and the green ($-$) PEG corona are indicated consistently. $D_A$ and $D_B$ denote the actual hard sphere diameters of grafted AuNPs, with their ratio defined as $\gamma = \frac{D_B}{D_A}$. $\Delta q_A$ and $\Delta q_B$ account for local charge correlations, and the parameter $\alpha$ measures their combined effect on stabilizing the lattice. $\theta$ represents the molecular weight (MW) ratio of the grafted PEG chains. $\delta = \frac{r_c }{D_A}$ represents the normalized cut-off distance for nearest electrostatic interactions. (b) Legend for identifying the various NPs used to assemble the reported superlattices. The spheres on the right depict the effective hard sphere diameter after grafting AuNP with 2, 5, and 10 kDa PEG. (c) (Top) Normalized $\zeta$-potential as a function of pH for PEG-AuNPs, with PEG terminated by either -NH2 (squares) or -COOH (circles). Dashed and dash-dotted lines, representing predictions from electrostatic model calculations (detailed in the SI), are also shown. Long-range ordered (LRO) superlattices form optimally at pH 3–4, while higher pH values lead to short-range order (SRO) assembly. (Bottom) Ideal zinc-blende and diamond structures derived from X-ray analysis are presented alongside the corresponding actual grafted-AuNP assemblies depicted in b. In the zinc-blende structure, distinct colors highlight the two different particle types, whereas in the diamond structure, the spheres are shown in a uniform color, reflecting that the X-ray pattern arises predominantly from identical AuNP cores. Henceforth, structures with uniform core sizes (e.g., diamond, simple cubic, and body-centered cubic) are depicted with their actual grafted PEG using the symbols from b. (d) (Top) (110) plane view of a rock-salt lattice for different $\gamma$ values, illustrating ideal hard sphere contacts at $\gamma = \gamma_c$. (Bottom) A proposed phase diagram based on geometrical constraints and electrostatic interactions that guide the assembly of various superlattices. The dashed lines indicate the region that aligns with our experimental observations.
• Figure 2: Transition from Zinc-Blende to Diamond Superstructure. (a) SAXS diffraction pattern ($I(Q)$ vs. $Q$) for COOH-PEG5k-Au5 and NH2-PEG10k-Au10 at pH 3 (4:1 mixing ratio), fitted using a ZnS-like structural model. The solid line overlaid on the experimental data points (open circles) represents the fitted structure factor corresponding to each lattice. The modeled intensity profile (blue solid line) is shown below, with individual structure-factor contributions indicated by shaded colors. The corresponding Miller indices for each shaded contribution are provided below the plot. This ZnS-like structure can also be formed from the same binary system with mixing ratios of 1:1, 2:1, and 4:1, as shown in Fig. S7. (b) SAXS diffraction pattern for a 2:1 mixture of COOH-PEG5k-Au10 and NH2-PEG10k-Au10 at pH 3, fitted to a diamond-like structural model. The only change from A to B is that the 5 nm NPs are replaced with 10 nm. This diamond structure can also form with mixing ratios of 1:1 and 4:1 for the same system, as shown in Fig. S9. (c) SAXS diffraction pattern for a 2:1 mixture of COOH-PEG5k-Au5 and NH2-PEG10k-Au10 at pH 4, fitted to a NaCl-like structural model. This NaCl-like structure can also form with mixing ratios of 1:1 and 4:1 for the same system, as shown in Fig. S8. (d) SAXS diffraction pattern for a 1:1 mixture of COOH-PEG5k-Au10 and NH2-PEG10k-Au10 at pH 4, fitted to a simple cubic structural model (blue solid line). This simple cubic structure arises from the identical core sizes (10 nm) of both grafted NPs, differentiating it from the binary NaCl-like structure. Illustrations of the ZnS-like, NaCl-like, diamond-like, and simple cubic superstructures are provided adjacent to their respective diffraction patterns, with the lattice constant ($a_{L}$) of each structure indicated in the illustrations. The SAXS intensity profiles, $I(Q)$, are normalized individually for each dataset and displayed on a linear scale. The $\gamma$ value for each mixture is indicated in the plot. The symbol $\ast$ represents the $\gamma$ value estimated from the nearest neighbor (NN) distance.
• Figure 3: Simple Cubic and Cesium-chloride–like Superstructures. (a) SAXS diffraction pattern ($I(Q)$ vs. $Q$) for a 1:1 mixture of COOH-PEG10k-Au10 and NH2-PEG2k-Au10 at pH 3, consistent with a simple cubic structural model. This simple cubic structure is effectively equivalent to the NaCl-like arrangement; however, due to the similar core sizes of the NPs, X-ray scattering detects it as a simple cubic structure. (b) SAXS diffraction pattern for a 1:1 mixture of COOH-PEG2k-Au10 and NH2-PEG10k-Au10 at pH 3, consistent with a diamond-like structural model. This diamond structure is achieved by swapping the grafted PEG terminal groups in panel (a). The observed fluctuations in $\gamma$ arise from changes in the $D_{\rm H}$ of the -NH2-terminated NPs. (c) SAXS diffraction pattern for a 1:2 mixture of COOH-PEG10k-Au10 and NH2-PEG5k-Au10 at pH 3, consistent with a KCl-like structural model. Although a simple cubic arrangement derived from the NaCl-like structure might be expected, NP fractionalization favors the KCl-like structure. (d) SAXS diffraction pattern for a 1:2 mixture of NH2-PEG5k-Au10 and COOH-PEG5k-Au5 at pH 3, consistent with a CsCl-like structural model. Experimental data are shown as open circles; structure-factor-Lorentzian fits are drawn as solid black lines through the data; and modeled intensity profiles from structural models are plotted below as blue solid lines with individual peak contributions shaded in color. The corresponding Miller indices for each shaded contribution are provided below the plot. Illustrations of the NaCl-like, diamond-like, CsCl-like, and simple cubic superstructures are provided adjacent to their respective diffraction patterns, with the $a_{\rm L}$ indicated in each illustration. The SAXS intensity profiles, $I(Q)$, are normalized individually for each dataset and displayed on a linear scale. The $\gamma$ value for each mixture is given in the plots, and the symbol $\#$ denotes the $\gamma$ value estimated from $D_{\rm H}$ as described in the SI.
• Figure 4: Experimental, Theoretical Phase Diagrams and Molecular Simulations. (a) SAXS-derived experimental phase diagram of cubic superstructures plotted as a function of $\theta$ versus $\gamma$. Larger cube symbols indicate binary mixtures containing 10 nm core NPs, whereas smaller symbols represent mixtures incorporating both 10 nm and 5 nm cores. (b) Calculated phase diagram of $\alpha$ versus $\gamma$ at a fixed $\delta = 0.07$, which shows agreement with the experimental data. (c) Pair distribution function from simulations of PEG-functionalized flat walls with charged end groups illustrates electrostatic correlations. The prominent peak in the black curve reflects the hydrogen-bond-mediated attraction between COO$^{-}$ and NH$_3^{+}$ groups (inset: typical hydrogen bonding geometry). The blue and green curves lack peaks, indicating strong repulsion between like-charged groups. (d) Simulation snapshot highlighting the attractive interaction between NH$_3^{+}$ and COO$^{-}$ groups. (e) Simulation snapshot showing the repulsive interaction among NH$_3^{+}$ groups.
• Figure 5: Schematic illustration of the standard procedure for creating and characterizing superstructures by SAXS. (1) Prepare the binary system using specified mixing ratios. (2) Adjust the pH of the mixture. (3) Thoroughly mix and incubate the suspension. (4) Load the mixture into a capillary and expose it to a monochromatic X-ray beam, resulting in a ring-like diffraction pattern characteristic of polycrystalline samples. (5) Convert the ring pattern to 1D $I(Q)$ versus $Q$ scattering plots and assign the corresponding superlattice structure.