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Dodecagonal tiling in mesoporous silica


Recent advances in the fabrication of quasicrystals in soft matter systems have increased the length scales for quasicrystals1 into the mesoscale range (20 to 500 ångströms). Thus far, dendritic liquid crystals2, ABC-star polymers3, colloids4 and inorganic nanoparticles5 have been reported to yield quasicrystals. These quasicrystals offer larger length scales than intermetallic quasicrystals (a few ångströms)1,6, thus potentially leading to optical applications through the realization of a complete photonic bandgap induced via multiple scattering of light waves in virtually all directions7,8,9. However, the materials remain far from structurally ideal, in contrast to their intermetallic counterparts, and fine control over the structure through a self-organization process has yet to be attained. Here we use the well-established self-assembly of surfactant micelles to produce a new class of mesoporous silicas, which exhibit 12-fold (dodecagonal) symmetry in both electron diffraction and morphology. Each particle reveals, in the 12-fold cross-section, an analogue of dodecagonal quasicrystals in the centre surrounded by 12 fans of crystalline domains in the peripheral part. The quasicrystallinity has been verified by selected-area electron diffraction and quantitative phason strain analyses on transmission electron microscope images obtained from the central region. We argue that the structure forms through a non-equilibrium growth process, wherein the competition between different micellar configurations has a central role in tuning the structure. A simple theoretical model successfully reproduces the observed features and thus establishes a link between the formation process and the resulting structure.

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Figure 1: The three basic crystal structures and their packing geometries.
Figure 2: Mesoporous particles with dodecagonal morphology and associated electron microscopy.
Figure 3: Diffraction patterns and tilings indicating fine quasicrystallinity.
Figure 4: Three tilings, each containing 1,500 vertices, simulated using different input parameters.


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We thank K. Niizeki, T. Dotera, A. E. Garcia-Bennett, S. Che and C. Gao for discussions, O. M. Yaghi and M. O’Keeffe for critical reading of the manuscript, and J. Shen for encouragement and support. This work was supported by the Swedish Research Council (VR), the Japan Science and Technology Agency (JST) and Berzelii EXSELENT. SEM and TEM studies were performed at the Electron Microscopy Center (EMC) at Stockholm University, which is supported by the Knut and Alice Wallenberg Foundation. Support from the WCU programme, Korea (R-31-2008-000-10055-0; K.M. and O.T.), Grants-in-Aid for Young Scientists (B) of JSPS (no. 23710132; Y.S.), and Special Coordination Funds for Promoting Science and Technology of MEXT, Japan (Y.S.) is also acknowledged.

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C.X. synthesized the materials and carried out electron microscopy observations. C.X. and N.F. analysed the tilings obtained experimentally. N.F. developed the theoretical part, including the modelling of the energetics and the growth process. K.M. and Y.S. contributed early TEM observations and data analysis. C.X. and N.F. wrote the manuscript with inputs from all co-authors. O.T. initiated and led the project. All authors discussed the results and commented on the manuscript.

Corresponding author

Correspondence to Osamu Terasaki.

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The authors declare no competing financial interests.

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Xiao, C., Fujita, N., Miyasaka, K. et al. Dodecagonal tiling in mesoporous silica. Nature 487, 349–353 (2012).

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