Selective assemblies of giant tetrahedra via precisely controlled positional interactions

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Science  24 Apr 2015:
Vol. 348, Issue 6233, pp. 424-428
DOI: 10.1126/science.aaa2421

Creating unusual nanostructures

Self-assembly often occurs when dissimilar molecular fragments are forced together by covalent bonding. Surfactants or block copolymers are two common examples. Huang et al. grafted four different nanoparticles, based on polyhedral oligomeric silsesquioxanes with slightly different compositions, onto a single tetrahedal core (see the Perspective by Yang). Depending on the type of nanoparticle, they assembled into a range of defined, ordered supramolecular lattices similar to a range of metal alloys. These include phases that have higher coordination numbers than usually found in the packing of spherical objects.

Science, this issue p. 424; see also p. 396


Self-assembly of rigid building blocks with explicit shape and symmetry is substantially influenced by the geometric factors and remains largely unexplored. We report the selective assembly behaviors of a class of precisely defined, nanosized giant tetrahedra constructed by placing different polyhedral oligomeric silsesquioxane (POSS) molecular nanoparticles at the vertices of a rigid tetrahedral framework. Designed symmetry breaking of these giant tetrahedra introduces precise positional interactions and results in diverse selectively assembled, highly ordered supramolecular lattices including a Frank-Kasper A15 phase, which resembles the essential structural features of certain metal alloys but at a larger length scale. These results demonstrate the power of persistent molecular geometry with balanced enthalpy and entropy in creating thermodynamically stable supramolecular lattices with properties distinct from those of other self-assembling soft materials.

Self-assembled hierarchical structures in soft materials have been intensely studied. Among them, assemblies of building blocks with specific geometric shapes and symmetry are of particular interest. As the simplest case, ordered structures constructed from packing of spherical motifs have been a classic yet dynamic research field that can be traced back to the study of metals and metal alloys. Most metal atoms, viewed as congruent spheres, typically tend to hold 12 neighbors (the coordination number, CN, is thus 12) in local environments, forming the most efficient packing scheme with tetrahedral interstices (1). This type of structure allows three possible variations: face-centered cubic (the cuboctahedron), hexagonal close-packed (the twinned cuboctahedron), and the topologically close-packed icosahedron (or “icosahedral coordination”).

In metal alloys, different metal atoms with various sizes and electronic states are involved. Frank and Kasper (2) studied the stability of icosahedral lattices and proved that distorted icosahedra could be accommodated with topologically close-packed Kasper polyhedra, which allow even higher coordination numbers (CN = 14, 15, and 16) in metal alloy crystals. This class of metal alloy crystal structures is referred as the “Frank-Kasper” phases, including the A15 phase (with an A3B stoichiometry such as Cr3Si), the Friauf-Laves phase (with an A2B stoichiometry such as Zn2Mg), the σ phase (with an AB stoichiometry such as CrFe), and others (3). Some Frank-Kasper phases are viewed as periodic approximates of aperiodic “quasicrystals.” Therefore, they provide a platform to understand how to fill in space with different spherical motifs and how to achieve properties related to their characteristic structural features of low lattice symmetry and high coordination numbers.

A typical cubic unit cell of the A15 phase (Fig. 1A) consists of six A units (pale red spheres) in 14-fold Kasper polyhedra and two B units (dark red spheres) in 12-fold icosahedral coordination (Fig. 1B) with a space group of Embedded Image (Embedded Image). The projection view along the 〈001〉 direction (Fig. 1C) displays a regular two-dimensional (2D) 44 tiling pattern (4). Recently, examples of the A15, σ, and quasicrystalline phases constructed by nano- and micrometer-sized “deformable” spheres, micelles, and colloids were reported in many systems, including spherical dendrimers (58), ABC star-triblock copolymers (9), micelles of linear diblock or tetrablock copolymers in the bulk (1012) or in solution (13), binary nanoparticle lattices (14), and mesoporous silica produced from surfactant micelles (15). In particular, formation of the A15 phase in dendrimers has been attributed to the presence of soft “squishy surface layers” composed of alkyl chains, which can deform to minimize steric interactions (5, 16) and surface contact area among the spheres (the Weaire-Phelan structure) (17, 18).

Fig. 1 Schematic illustration of the A15 phase.

(A) In an A15 cubic unit cell, the dark red and pale red colors represent different coordination environments. (B) Schemes of CN = 12 and CN = 14 coordination environments in the A15 lattice. (C) 2D-projected view of the A15 lattice along the 〈001〉 direction. The inset shows a 2D 44 tiling pattern along the z axis. The spheres at the sparse layers (z/4 and 3z/4) are represented by gray circles; the spheres at the dense layers are shown by black and white circles (z/2 and z).

Constructing ordered phases with the use of shaped building blocks other than spheres has yet to be demonstrated. Recent computer simulation results revealed possible crystalline and liquid crystalline structures from the packing of polyhedra (19). Among all the polyhedra, the tetrahedron is the simplest. Rigid tetrahedron building blocks have been shown to form quasicrystalline and crystalline phases with high packing fractions (20). However, related experimental investigation remains largely unexplored in terms of both observations of ordered structures and their formation mechanisms. Shape-persistent molecular nanoparticles, such as derivatives of POSS (21), fullerenes (22), polyoxometalates (23), and proteins (24), offer great opportunities to construct nanosized giant tetrahedra with atomic precision (25, 26).

Here, we present an experimental study of giant tetrahedra constructed by attaching four POSS cages with different functional groups to a rigid tetrahedral core (Fig. 2). They are distinguished from the reported dendrimer and block copolymer systems (12) by the absence of any flexible alkyl or polymeric chains. Self-assembly of these giant tetrahedra is mediated by interactions among the POSS nanoclusters and the overall molecular symmetry. Various ordered supramolecular lattices, including the Frank-Kasper A15 phase, are observed in this system by tuning the numbers of hydrophilic or hydrophobic POSS cages in each molecule and the functional groups on the hydrophilic POSS cages.

Fig. 2 Chemical structures and molecular models (shown in shadow) of the four categories of giant tetrahedra.

Cartoons in the boxes are corresponding simplifications of the giant tetrahedra, in which blue spheres represent hydrophilic POSS cages and red spheres represent hydrophobic BPOSS cages.

Giant tetrahedra 1 to 4 with different partitions of hydrophobic and hydrophilic POSS cages were synthesized by sequentially applying two “click” reactions (fig. S1): the copper-catalyzed azide-alkyne [3+2] cycloaddition reaction and the thiol-ene reaction (27, 28). The hydrophobic POSS cages have seven isobutyl groups (BPOSS) and the hydrophilic POSS cages have either hydroxyl or carboxylic acid groups (Fig. 2). Incorporation of different POSS cages results in competing interactions (i.e., collective hydrogen-bonding interactions among the hydrophilic POSS cages and the crystallization of BPOSS cages) to drive self-assembly; tuning the number of hydrophobic or hydrophilic POSS cages systematically varies molecular symmetry of the giant tetrahedra. Nuclear magnetic resonance and mass spectroscopy results (figs. S2 and S3) confirmed their structural precision and high purity. We expect that geometric and interactional factors jointly determine their self-assembly behaviors.

Giant tetrahedron 1 contains four identical BPOSS cages. A crystalline structure with a triclinic unit cell and a space group of P1 has been determined (fig. S4 and table S1), based on the combination of selected-area electron diffraction (SAED; fig. S4A) data from its single crystals and wide-angle x-ray diffraction (WAXD; fig. S4B) data from the bulk sample (28). In the simulated molecular packing, the tetrahedral cores adopt an interpenetrated stacking manner to form geometrically locked columns, which are surrounded by a shell of crystalline BPOSS cages (fig. S4, D and E). To maximize the contacts among the crystalline BPOSS cages, the lattice is distorted from hexagonally packed cylinders toward lower symmetry.

Replacing one BPOSS cage with a hydrophilic POSS cage in 1 lowers the molecular symmetry to C3v and results in giant tetrahedra 2a to 2c. At 25°C, density-frustrated lamellar supramolecular structures with a three-layer packing periodicity are observed in 2a to 2c, as supported by the combined small-angle x-ray scattering (SAXS) and WAXD results (Fig. 3A) with a scattering vector (q) value ratio of 1:2:3. Besides, the strongest diffraction peak at 1.09 nm in the WAXD pattern is attributed to the characteristic diffraction of crystalline BPOSS domains (29). A bright-field (BF) transmission electron microscope (TEM) image of microtomed thin-sectioned 2a samples (Fig. 3B) and its fast Fourier transform (FFT) pattern (Fig. 3B, inset) also confirm the lamellar structure. The measured periodicities of 4.3 to 4.7 nm (Table 1) can only accommodate two layers of BPOSS and one interdigitated layer of the hydrophilic POSS cages (Fig. 3G) (estimated ~4.5 nm). Despite the unmatched numbers of hydrophobic and hydrophilic POSS cages, crystallization of BPOSS cages dominates and preferentially creates flat interfaces (30), leading to the formation of frustrated supramolecular lamellae.

Fig. 3 Selectively assembled structures of 2a.

(A) Combined SAXS and WAXD profiles of 2a evaporated from tetrahydrofuran-acetonitrile (THF/MeCN) mixed solvents at 25°C. (B) BF TEM image and corresponding FFT pattern (inset) of a microtomed thin-sectioned 2a sample. (C) SAXS pattern of 2a after the sample was heated to above its Tm and annealed at 140°C for 12 hours. (D) A {100} plane of an A15 supramolecular lattice was identified by the BF TEM image after the thin-sectioned sample was stained by RuO4. The inset is the FFT pattern of this image. (E) Fourier filtering of the image shown in (D) revealed a clear view of the 2D 44 tiling along the 〈100〉 direction. (F) Inverse colored and magnified image of (E). White spheres represent the hydrophilic POSS domains with different sizes. The inset shows a simulated projection view along the 〈100〉 direction. Spheres in the red-dot circles correspond to the dark red ones shown in Fig. 1A. (G) Schematic illustrations of the selective assembly mechanism and molecular packing in the A15 lattice.

Table 1 Supramolecular lattice analysis of the giant tetrahedra with different symmetry.

Lattice I structures were formed by slow evaporation of the sample solutions in THF/MeCN mixed solvents at 25°C; lattice II structures were formed after annealing treatment. dI is the determined periodicity of the lamellar structures.

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After 2a was heated to 180°C (above its melting point Tm; Table 1) and immediately cooled to and annealed at 140°C for 12 hours, an entirely different SAXS pattern was observed (Fig. 3C). The WAXD pattern indicates that BPOSS cages were amorphous in this structure (fig. S5A). Both 2b and 2c exhibited virtually identical SAXS patterns upon the same thermal treatment (fig. S5, B and C). The observed q value ratios (Fig. 2C and fig. S5, B and C) are Embedded Image:Embedded Image:Embedded Image:Embedded Image, which is characteristic of the A15 phase (5). A cubic unit cell with a = 13.2 nm can be deduced for 2a. The lattice assignment is further validated by TEM images of the microtomed, RuO4-stained thin-sectioned samples of 2a (∼80 nm thick). The BF TEM image in Fig. 3D exhibits the arrangement of spheres along the 〈100〉 direction of the A15 phase in real space. Its FFT pattern is shown in the inset of Fig. 3D (also in fig. S5D) with major diffractions assigned. Fourier filtering treatment provides a clear view of the regular 2D 44 tiling pattern along the 〈100〉 direction (Fig. 3E). From this image, the measured distance between two closest neighboring squares is 13.2 nm, which is consistent with the value calculated from the SAXS result. Setting Fig. 3E in inverse contrast makes it easier to identify the fine features of the spherical packing (Fig. 3F). It is observed that spheres in the red-dot circles (Fig. 3F), which correspond to the dark red spheres in Fig. 1A with CN = 12, are smaller relative to their neighbors (pale red spheres in Fig. 1A with CN = 14). On the basis of the average size ratio between these two types of spheres (1.1 ± 0.06), we estimate that these two types of spheres contain 38 and 50 giant tetrahedra, respectively (28). These results support the existence of two types of spheres with different coordination environments in a single-component system, in contrast to metal alloys with different types of atoms. Moreover, the number of giant tetrahedra in each sphere is found to increase with increasing strength of the collective hydrogen-bonding interactions and the molecular masses from 2a to 2c (Table 1). The formation mechanism of the A15 phase is illustrated in Fig. 3G. When the frustrated lamellar crystals melt, the hydrophilic POSS cages form spherical aggregates via collective hydrogen bonding, while BPOSS cages originally located in the neighboring top and bottom lamellar layers undergo a 2D scrolling to form the shell. The self-assembled spheres finally pack into the A15 supramolecular lattice.

Dendrimers with a poly(benzyl ether) core and a dodecyl corona are known to form spheres that further pack into A15 lattices (5, 7), which can be explained by the soft “squishy surface layers” that promote deformation of the spheres to maximize entropy and minimize interfaces (17, 18, 31, 32). The molecular geometry of giant tetrahedra 2a to 2c also prefers the formation of spheres in the first step. Without any flexible chains, it is proposed that extra degrees of freedom (such as the excluded volume of BPOSS cages and the nonclose packing of the hydrophilic POSS cages via hydrogen bonding) contribute to the size differentiations of the assembled spherical motifs, which entropically favor more space and looser packing to form the A15 phase. Furthermore, it is believed that the deformability is associated with the size of the spheres, because the interstitial gaps become larger as the size of spheres increases (16).

To prove this assumption, we synthesized 2d (Fig. 2 and fig. S6A) containing a hydrophilic POSS cage with the weakest hydrogen-bonding interaction and the smallest molar mass among 2a to 2d. After similar thermal treatment, a body-centered cubic (bcc) lattice composed of only one type of spheres was found (fig. S6). Each sphere contains 44 giant tetrahedra 2d. This number provides a reasonable estimation of the upper size limit of nondeformable spheres assembled from this series of giant tetrahedra, because a small fraction of the A15 phase can also be identified from the TEM image of thin-sectioned 2d samples (fig. S6F). Any spheres larger than this size would deform as the result of nonclose packing of the hydrophilic POSS cages at the spherical center (33) to better fit into the supramolecular lattice-packing requirements with lower symmetry.

Giant tetrahedra 3a to 3c are more symmetric in terms of both volume fractions and interactions. “Double-layered” lamellar supramolecular lattices (30, 34) are observed for 3a to 3c at 25°C, due to the dominating BPOSS crystallization (fig. S7A). Layer thicknesses of these lamellar structures were determined from SAXS results (Table 1 and fig. S7B), and they match the estimated values from molecular packing models (28). Their high-temperature structures were obtained by annealing above their Tm at 180°C for 3 hours and subsequent quenching into liquid nitrogen to suppress crystallization of BPOSS cages (fig. S7C). SAXS and TEM results (Fig. 4, A and D) indicate that the lamellar structures of 3b and 3c remain but have increased lamellae d-spacings relative to their room-temperature structures; this is mainly attributed to the disordered BPOSS packing and thermal expansion. On the other hand, a highly ordered double-gyroid supramolecular lattice (space group Embedded Image) forms in 3a after similar treatment (Fig. 4, B and E, and fig. S7D). In the TEM image (Fig. 4E), the darker regions are hydrophilic POSS domains embedded in the hydrophobic matrix composed of BPOSS cages and the tetrahedral cores. Formation of such a double-gyroid phase from the rigid and symmetric giant tetrahedron 3a reflects the ubiquity of the gyroid structure, implying the subtle influence of the slightly different volume fractions and interactions on the selective assembly of these giant tetrahedra (Fig. 4G).

Fig. 4 Selectively assembled structures from giant tetrahedra 3 and 4.

(A to C) SAXS patterns of 3c (A), 3a (B), and 4b (C) were taken at 25°C after corresponding thermal treatments. (D) BF TEM image of thin-sectioned 3c confirms the lamellar lattice deduced from the SAXS result shown in (A). (E) BF TEM image of thin-sectioned and RuO4-stained 3a confirms the double-gyroid lattice deduced from the SAXS result shown in (B). (F) BF TEM image of thin-sectioned 4b confirms the honeycomb-like hexagonal lattice deduced from the SAXS result shown in (C). In (D) to (F), the insets are the FFT patterns of the TEM images. (G) Schematic illustration of the selective assembly mechanisms and packing models of 3a to 3c. (H) Schematic packing models of 4a to 4c.

Giant tetrahedra 4a to 4c failed to crystallize in similar solvent evaporation processes because of the low volume fraction of BPOSS cages that does not favor the formation of continuous 2D flat crystals (fig. S8). At such a volume fraction, an inverse spherical phase such as bcc or A15 was expected. However, after thermal annealing at 130°C, only ordered hexagonal cylinder phases were observed in 4a to 4c, as revealed by the q value ratio of 1:Embedded Image:Embedded Image in their SAXS patterns (fig. S8B, Fig. 4C, and fig. S8C for 4a, 4b, and 4c, respectively) and the honeycomb-like hexagonal structure observed in BF TEM images (Fig. 4F). In the proposed schematic packing model of 4a to 4c (Fig. 4H), BPOSS cages are wrapped into centers of the columns while hydrophilic POSS cages with strong collective hydrogen bonding form the continuous matrix. In sharp contrast to the packing of 2a to 2c at higher temperatures, 4a to 4c tend to maximize the contacts of hydrophilic POSS cages (and thus the extent of collective hydrogen-bonding formation), which substantially minimizes the overall free energy of the system.

Symmetry breaking on accurately controlled positional interactions of nanosized giant tetrahedra has been used to construct the Frank-Kasper A15 phase and other ordered supramolecular lattices. The diverse self-assembly behaviors of these giant tetrahedra reveal that rigid, single-component soft-matter systems offer potential for building supramolecular “metal alloy analogs.” The subtle competition between the persistent molecular geometry and the deformability driven by interaction terms dictates the selective assembly of the giant tetrahedra. Because of the “click” synthesis, this system is highly tunable in terms of core structure, nanoparticle functionality, and feature size. The concepts and formation mechanisms of these supramolecular structures could be extended to other giant-polyhedra molecules with different topologies and chemical compositions.

Supplementary Materials

Materials and Methods

Supplementary Text

Figs. S1 to S8

Table S1

References (3538)

References and Notes

  1. See supplementary materials on Science Online.
  2. Acknowledgments: Supported by NSF grant DMR-1408872. We thank B. Lotz for helpful discussion. The MALDI-TOF MS analysis was assisted by K. Guo, C. Shi, and C. Wesdemiotis. Use of the Advanced Photon Source at Argonne National Laboratory was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under contract DE-AC02-06CH11357.

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