Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Assembling molecular Sierpiński triangle fractals

Nature Chemistry volume 7, pages 389–393 (2015)Cite this article

Subjects

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.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

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.

Similar content being viewed by others

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 

Download references

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.

Author information

Authors and Affiliations

  1. SKLSCUSS, BNLMS, College of Chemistry and Molecular Engineering, Peking University, Beijing, 100871, China

    Jian Shang, Jingxin Dai, Xiong Zhou & Kai Wu

  2. Department of Electronics, Key Laboratory for the Physics and Chemistry of Nanodevices, Peking University, Beijing, 100871, China

    Yongfeng Wang

  3. Fachbereich Chemie, Philipps-Universität Marburg, Hans-Meerwein-Strasse, Marburg, 35032, Germany

    Min Chen, Julian Kuttner, Gerhard Hilt & J. Michael Gottfried

  4. Department of Chemical Physics, School of Chemistry and Materials Science, University of Science and Technology of China, Hefei, 230026, China

    Xiang Shao

  5. SPURc, 1 CREATE Way, #15-01, CREATE Tower, Singapore, 138602, Singapore

    Kai Wu

Authors
  1. Jian Shang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yongfeng Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Min Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jingxin Dai
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Xiong Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Julian Kuttner
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Gerhard Hilt
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Xiang Shao
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. J. Michael Gottfried
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. Kai Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

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.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary information (PDF 1204 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nchem.2211

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing