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Publication Title | Assembly of reconfigurable one-dimensional colloidal superlattices due to a synergy of fundamental nanoscale forces

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depletion force to be maximized. Colloidal nanoprisms are highly tunable anisotropic structures that exhibit size- and shape-depen- dent plasmon resonances (30) and are predicted to exhibit unique collective optical properties (5, 9).

In our system, the synergy of depletion and electrostatic forces causes triangular nanoprisms to naturally assemble into one- dimensional lamellar colloidal crystals with interparticle spacings greater than four times the thickness of the nanoprism building blocks. Forces that inherently have no directionality are made to prefer specific interaction modes via particle anisotropy, consis- tent with previous reports of directional entropic interactions (31). Both types of interactions arise from the presence of the surfactant CTAB: In solution, the CTAB molecules form micelles that act as depletants, driving the entropic association of prisms, whereas the presence of the CTAB bilayer leads to a positive charge on the surface of the prisms (32, 33), causing an electro- static repulsion between them. The combination of extremely anisotropic particles and charged depletant molecules leads to the formation of robust crystals with interparticle spacings that are significantly larger than the particle size, which, to the best of our knowledge, is an unprecedented example of achieving such large spacings between particles using interparticle forces alone (13). We demonstrate that the lattice parameters are reversibly tunable in situ by manipulating the balance of the forces via a change in surfactant concentration, temperature, or ionic strength. Additionally, we propose a simplified model that explains the large lamellar d spacings observed experimentally by minimizing the free energy of the system, taking into account the relevant interactions. Finally, we utilize the fundamental knowledge gained in this study to develop a procedure to purify the anisotropic triangular gold nanoprisms from the spherical gold nanoparticles formed conco- mitantly during their synthesis, which has proven to be a challenge to date (29).

Results and Discussion

Gold nanoprisms (henceforth also referred to as prisms) were synthesized according to literature methods with minor modifica- tions (29) (SI Appendix). A typical synthesis produces a mixture of triangular gold nanoprisms (thickness of 7.5 ` 1 nm and three congruent edges) and spherical gold particles (SI Appendix, Fig. S1). Nanoprism edge length was varied from 40–210 nm by changing the ratio of the gold seeds to the gold salt precursor (34). The cationic surfactant CTAB serves as the stabilizing agent in our system. CTAB forms a bilayer structure around the gold nanoprisms, with the inner layer binding to the gold surface via its charged headgroups (32). The adsorbed bilayer has an approx-

imate thickness of 3.2 nm (35, 36) and leads to a net positive charge on the surface of the prisms (32, 33). Because the synthesis of the prisms is carried out at a CTAB concentration of 50 mM, which is 50 times the critical micelle concentration (1 mM) (36), charged CTAB micelles are also present in solution. At a CTAB concentration of 50 mM, the fractional charge of the micelles is approximately 0.26 (37).

Immediately after their synthesis and without further modifi- cation, the 7.5-nm-thick prisms (145-nm edge length) naturally assemble into 1D lamellar superlattices in solution with the prisms aligned face-to-face with a center-to-center spacing (d spa- cing) of 29.9 nm (Fig. 1 A and B). These lamellar nanoprism crys- tals were characterized by small angle X-ray scattering (SAXS) using the Advanced Photon Source at Argonne National Labora- tory. The two-dimensional scattering images were radially aver- aged over all orientations to produce plots of scattered intensity IðqÞ versus scattering vector q, where q 1⁄4 4π sin θ∕λ. The SAXS profile for 145-nm edge length prisms (Fig. 1D) features four re- solvable diffraction peaks at integer spacings with respect to the first-order peak (q 1⁄4 0.021, 0.042, 0.063, 0.084 Å−1), consistent with a highly ordered lamellar structure (38, 39). Although the scattering from the spherical gold particles (form factor) can be seen in the SAXS patterns (39), they were not found to have an effect on the formation of the lamellar nanoprism crystals and, as a result, were disregarded for the remainder of this study (SI Appendix, Fig. S2). Using the Scherrer equation (40), the crystal- lites were determined to contain a total of 10–15 prisms. Cryoe- lectron microscopy images of the nanoprism superlattices provide further evidence of the lamellar structure (Fig. 1C). However, it is important to note that the appearance of hexagonal ordering between 1D nanoprism columns and the reduced interparticle spacings observed in the image are likely consequences of the microscopy preparation procedure, as these features are not sup- ported by the SAXS data.

A d spacing of approximately 30 nm between 7.5-nm-thick prisms corresponds to a solvent layer (dw) of approximately 16 nm when the CTAB bilayer on the prisms is taken into account (Fig. 1B). A 1D electron density profile ρðzÞ was derived from the SAXS data using a Fourier synthesis method to confirm the large interparticle spacing (39) (SI Appendix, Fig. S3). Anomalous SAXS studies at the X-ray absorption edges of Au and Br re- vealed that the majority of the Br− species are located outside of the lamellar superstructures, as opposed to between the nano- prisms that make up the superlattices, suggesting that the major- ity of the micelles are located outside of the lamellar crystals (SI Appendix, Fig. S4).

Fig. 1. Columnar superlattices of anisotropic gold nanoprisms. (A) Nanoprisms form 1D lamellar crystals in solution with an average of 10–15 prisms per crystal. (B) A zoomed in edge-on view of two nanoprisms within a lamellar superlattice where d is the d spacing, dw is the water region, tprism is the thickness of the nanoprism, tbCTAB is the thickness of the CTAB bilayer, and dCTAB is the diameter of the CTAB micelles. (C) Cryoscanning transmission electron microscopy image of the lamellar crystals. The outlined region highlights an edge-on view of the nanoprism crystals. (Scale bar: 200 nm.) (D) One-dimensional SAXS profile of the as-synthesized Au nanoprisms (145-nm edge length) in solution. The sharp diffraction peaks at q 1⁄4 0.021, 0.042, 0.063, and 0.084 1∕Å indicate a periodic lamellar structure.

Young et al. PNAS ∣ February 14, 2012 ∣ vol. 109 ∣ no. 7 ∣ 2241


Image | Assembly of reconfigurable one-dimensional colloidal superlattices due to a synergy of fundamental nanoscale forces

depletion maximized colloidal nanoprisms highly tunable anisotropic structures exhibit plasmon
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