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Assembling molecular Sierpiński triangle fractals

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Abstract

Fractals, being “exactly the same at every scale or nearly the same at different scales” as defined by Benoit B. Mandelbrot, are complicated yet fascinating patterns that are important in aesthetics, mathematics, science and engineering. Extended molecular fractals formed by the self-assembly of small-molecule components have long been pursued but, to the best of our knowledge, not achieved. To tackle this challenge we designed and made two aromatic bromo compounds (4,4″-dibromo-1,1′:3′,1″-terphenyl and 4,4‴-dibromo-1,1′:3′,1″:4″,1‴-quaterphenyl) to serve as building blocks. The formation of synergistic halogen and hydrogen bonds between these molecules is the driving force to assemble successfully a whole series of defect-free molecular fractals, specifically Sierpiński triangles, on a Ag(111) surface below 80 K. Several critical points that govern the preparation of the molecular Sierpiński triangles were scrutinized experimentally and revealed explicitly. This new strategy may be applied to prepare and explore various planar molecular fractals at surfaces.

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Figure 1: Typical individual molecular STs at the surfaces.
Figure 2: The whole family of the observed B4PB molecular STs.
Figure 3: Chirality propagation of the molecular STs.
Figure 4: Kinetic optimization of the B4PB-ST-3 structure.

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References

  1. Mandelbrot, B. B. The Fractal Geometry of Nature (W. H. Freeman, 1982).

    Google Scholar 

  2. Newkome, G. R. & Shreiner, C. Dendrimers derived from 1→3 branching motifs. Chem. Rev. 110, 6338–6442 (2010).

    Article  CAS  Google Scholar 

  3. Sugiura, K-I., Tanaka, H., Matsumoto, T., Kawai, T. & Sakata, Y. A mandala-patterned bandanna-shaped porphyrin oligomer, C1244H1350N84Ni20O88, having a unique size and geometry. Chem. Lett. 28, 1193–1194 (1999).

    Article  Google Scholar 

  4. Newkome, G. R. et al. Nanoassembly of a fractal polymer: a molecular ‘Sierpinski hexagonal gasket’. Science 312, 1782–1785 (2006).

    Article  CAS  Google Scholar 

  5. Fujibayashi, K., Hariadi, R., Park, S. H., Winfree, E. & Murata, S. Toward reliable algorithmic self-assembly of DNA tiles: a fixed-width cellular automaton pattern. Nano Lett. 8, 1791–1797 (2007).

    Article  Google Scholar 

  6. Sarkar, R. et al. One-step multicomponent self-assembly of a first-generation Sierpiński triangle: from fractal design to chemical reality. Angew. Chem. Int. Ed. 53, 12182–12185 (2014).

    Article  CAS  Google Scholar 

  7. Wang, M. et al. Hexagon wreaths: self-assembly of discrete supramolecular fractal architectures using multitopic terpyridine ligands. J. Am. Chem. Soc. 136, 6664–6671 (2014).

    Article  CAS  Google Scholar 

  8. Conversano, E. & Lalli, L. T. Sierpinski triangles in stone, on medieval floors in Rome. J. Appl. Math. 4, 114–122 (2011).

    Google Scholar 

  9. Devaney, R. L. Chaos and Fractals: the Mathematics behind the Computer Graphics (American Mathematical Society, 1989).

    Book  Google Scholar 

  10. Wolfram, S. A New Kind of Science (Wolfram Media, 2001).

    Google Scholar 

  11. Alfonseca, M. & Ortega, A. Determination of fractal dimensions from equivalent L systems. IBM J. Res. Dev. 45, 797–805 (2001).

    Article  Google Scholar 

  12. Pawin, G., Wong, K. L., Kwon, K. Y. & Bartels, L. A homomolecular porous network at a Cu(111) surface. Science 313, 961–962 (2006).

    Article  CAS  Google Scholar 

  13. Bui, T. T. T., Dahaoui, S., Lecomte, C., Desiraju, G. R. & Espinosa, E. The nature of halogen···halogen interactions: a model derived from experimental charge-density analysis. Angew. Chem. Int. Ed. 48, 3838–3841 (2009).

    Article  CAS  Google Scholar 

  14. Walch, H., Gutzler, R., Sirtl, T., Eder, G. & Lackinger, M. Material- and orientation-dependent reactivity for heterogeneously catalyzed carbon–bromine bond homolysis. J. Phys. Chem. C 114, 12604–12609 (2010).

    Article  CAS  Google Scholar 

  15. Chung, K-H. et al. Polymorphic porous supramolecular networks mediated by halogen bonds on Ag(111). Chem. Commun. 47, 11492–11494 (2011).

    Article  CAS  Google Scholar 

  16. Wang, W., Shi, X., Wang, S., Van Hove, M. A. & Lin, N. Single-molecule resolution of an organometallic intermediate in a surface-supported Ullmann coupling reaction. J. Am. Chem. Soc. 133, 13264–13267 (2011).

    Article  CAS  Google Scholar 

  17. Fasel, R., Parschau, M. & Ernst, K-H. Amplification of chirality in two-dimensional enantiomorphous lattices. Nature 439, 449–452 (2006).

    Article  CAS  Google Scholar 

  18. Blüm, M-C., Ćavar, E., Pivetta, M., Patthey, F. & Schneider, W-D. Conservation of chirality in a hierarchical supramolecular self-assembled structure with pentagonal symmetry. Angew. Chem. Int. Ed. 44, 5334–5337 (2005).

    Article  Google Scholar 

  19. Hauptmann, N. et al. Surface control of alkyl chain conformations and 2D chiral amplification. J. Am. Chem. Soc. 135, 8814–8817 (2013).

    Article  CAS  Google Scholar 

  20. Nieckarz, D. & Szabelski, P. Understanding pattern formation in 2D metal–organic coordination systems on solid surfaces. J. Phys. Chem. C 117, 11229–11241 (2013).

    Article  CAS  Google Scholar 

  21. Nieckarz, D. & Szabelski, P. Simulation of the self-assembly of simple molecular bricks into Sierpiński triangles. Chem. Commun. 50, 6843–6845 (2014).

    Article  CAS  Google Scholar 

  22. Röder, H., Hahn, E., Brune, H., Bucher, J-P. & Kern, K. Building one- and two-dimensional nanostructures by diffusion-controlled aggregation at surfaces. Nature 366, 141–143 (1993).

    Article  Google Scholar 

  23. Brune, H., Romainczyk, C., Röder, H. & Kern, K. Mechanism of the transition from fractal to dendritic growth of surface aggregates. Nature 369, 469–471 (1994).

    Article  CAS  Google Scholar 

  24. Otero, R. et al. Elementary structural motifs in a random network of cytosine adsorbed on a gold(111) surface. Science 319, 312–315 (2008).

    Article  CAS  Google Scholar 

  25. Barth, J. V., Costantini, G. & Kern, K. Engineering atomic and molecular nanostructures at surfaces. Nature 437, 671–679 (2005).

    Article  CAS  Google Scholar 

  26. Libbrecht, K. G. The physics of snow crystals. Rep. Prog. Phys. 68, 855–895 (2005).

    Article  Google Scholar 

  27. Gross, L. et al. Bond-order discrimination by atomic force microscopy. Science 337, 1326–1329 (2012).

    Article  CAS  Google Scholar 

  28. de Oteyza, D. G. et al. Direct imaging of covalent bond structure in single-molecule chemical reactions. Science 340, 1434–1437 (2013).

    Article  CAS  Google Scholar 

  29. Chiang, C-L., Xu, C., Han, Z. & Ho, W. Real-space imaging of molecular structure and chemical bonding by single-molecule inelastic tunneling probe. Science 344, 885–888 (2014).

    Article  CAS  Google Scholar 

  30. Blake, M. M. et al. Identifying reactive intermediates in the Ullmann coupling reaction by scanning tunneling microscopy and spectroscopy. J. Phys. Chem. A 113, 13167–13172 (2009).

    Article  CAS  Google Scholar 

  31. Fan, Q. et al. Surface-assisted organic synthesis of hyperbenzene nanotroughs. Angew. Chem. Int. Ed. 52, 4668–4672 (2013).

    Article  CAS  Google Scholar 

  32. Horcas, I. et al. WSXM: a software for scanning probe microscopy and a tool for nanotechnology. Rev. Sci. Instrum. 78, 013705 (2007).

    Article  CAS  Google Scholar 

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Acknowledgements

This work was jointly supported by National Natural Science Foundation of China (51121091, 21133001, 21333001, 21261130090, 61321001, 913000002) and Ministry of Science and Technology (2011CB808702, 2013CB933404), China, with partial support from the Singapore National Research Foundation CREATE-SPURc. We thank X. Ma at the School of Mathematics in Peking University for his assistance and discussions on the fractal structure analysis.

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J.S., Y.F.W., J.M.G. and K.W. designed the experiments. J.S., M.C., J.X.D. and X.Z. performed the experiments. J.K. and G.H. synthesized the precursors. J.S., Y.F.W., X.S. and K.W. analysed the data and wrote the manuscript. All the authors discussed the results and commented on the manuscript.

Corresponding authors

Correspondence to Yongfeng Wang, J. Michael Gottfried or Kai Wu.

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The authors declare no competing financial interests.

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Shang, J., Wang, Y., Chen, M. et al. Assembling molecular Sierpiński triangle fractals. Nature Chem 7, 389–393 (2015). https://doi.org/10.1038/nchem.2211

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