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.

Self-assembly route for photonic crystals with a bandgap in the visible region

Nature Materials volume 6, pages 202–205 (2007)Cite this article

Abstract

Three-dimensional photonic crystals, or periodic materials, that do not allow the propagation of photons in all directions with a wavelength in the visible region have not been experimentally fabricated, despite there being several potential structures and the interesting applications and physics that this would lead to1. We show using computer simulations that two structures that would enable a bandgap in the visible region, diamond and pyrochlore, can be self-assembled in one crystal structure from a binary colloidal dispersion. In our approach, these two structures are obtained as the large (Mg) and small (Cu) sphere components of the colloidal analogue of the MgCu2 Laves phase2, whose growth can be selected and directed using appropriate wall patterning. The method requires that the particles consist of different materials, so that one of them can be removed selectively after drying (for example, by burning or dissolution). Photonic calculations show that gaps appear at relatively low frequencies indicating that they are robust and open for modest contrast, enabling fabrication from more materials.

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

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Get just this article for as long as you need it

$39.95

Learn more

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

Figure 1: Binary Laves crystal structures.
Figure 2: Phase diagram of binary hard spheres with a small-to-large size ratio of 0.82.
Figure 3: Density profile and a snapshot of the simulation along the z direction.
Figure 4: Calculated relative width of the gap between bands 2 and 3 as a function of the dielectric contrast.

References

  1. Soukoulis, C. M. (ed.) Photonic Crystals and Light Localization in the 21st Century (NATO Science Series (C): Mathematical and Physical Sciences, Kluwer Academic, Dordrecht, 2001).

  2. Pearson, W. B. The Crystal Chemistry and Physics of Metals and Alloys (Wiley-Interscience, New York, 1972).

    Google Scholar 

  3. Maldovan, M., Ullal, C. K., Carter, W. C. & Thomas, E. L. Exploring for 3D photonic bandgap structures in the 11 f.c.c. space groups. Nature Mater. 2, 664–667 (2003).

    Article  CAS  Google Scholar 

  4. Moroz, A. Metallo-dielectric diamond and zinc-blende photonic crystals. Phys. Rev. B 66, 115109 (2002).

    Article  Google Scholar 

  5. Garcia-Adeva, A. J. Band gap atlas for photonic crystals having the symmetry of the kagome and pyrochlore lattices. New J. Phys. 8, 86 (2006).

    Article  Google Scholar 

  6. Ngo, T. T., Liddell, C. M., Ghebrebrhan, M. & Joannopoulos, J. D. Tetrastack: colloidal diamond-inspired structure with omnidirectional photonic band gap for low refractive index. Appl. Phys. Lett. 88, 241920 (2006).

    Article  Google Scholar 

  7. Li, Z.-Y. & Zhang, Z.-Q. Fragility of photonic band gaps in inverse-opal photonic crystals. Phys. Rev. B 62, 1516–1519 (2000).

    Article  CAS  Google Scholar 

  8. Tkachenko, A. V. Morphological diversity of DNA-colloidal self-assembly. Phys. Rev. Lett. 89, 148303 (2002).

    Article  Google Scholar 

  9. Zhang, Z., Keys, A. S., Chen, T. & Glotzer, S. C. Self-assembly of patchy particles into diamond structures through molecular mimicry. Langmuir 21, 11547–11551 (2005).

    Article  CAS  Google Scholar 

  10. Manoharan, V. N. & Pine, D. J. Building materials by packing spheres. Mater. Res. Soc. Bull. 29, 91–95 (2004).

    Article  CAS  Google Scholar 

  11. Velikov, K. P., Christova, C. G., Dullens, R. P. A. & van Blaaderen, A. Layer-by-layer growth of binary colloidal crystals. Science 296, 106–109 (2002).

    Article  CAS  Google Scholar 

  12. Vlasov, Y. A., Bo, X. Z., Sturm, J. C. & Norris, D. J. On-chip natural assembly of silicon photonic bandgap crystals. Nature 414, 289–293 (2001).

    Article  CAS  Google Scholar 

  13. Frenkel, D. & Smit, B. Understanding Molecular Simulations (Academic, New York, 2002).

    Google Scholar 

  14. Mansoori, G. A., Carnahan, N. F., Starling, K. E. & Leland, T. W. Jr. Equilibrium thermodynamic properties of the mixture of hard spheres. J. Chem. Phys. 54, 1523–1525 (1971).

    Article  CAS  Google Scholar 

  15. Speedy, R. J. Pressure and entropy of hard-sphere crystals. J. Phys. Condens. Matter 10, 4387–4391 (1998).

    Article  CAS  Google Scholar 

  16. Hasaka, M., Nakashima, H. & Oki, K. Structure of the Laves phase observed in polystyrene latexes. Trans. Japan Inst. Met. 25, 65–72 (1984).

    Article  Google Scholar 

  17. Yoshimura, S. & Hachisu, S. Order formation in binary mixtures of monodisperse latices. Prog. Colloid Polym. Sci. 68, 59–70 (1983).

    Article  CAS  Google Scholar 

  18. Ma, G. H., Fukutomi, T. & Morone, N. Preparation and analysis of ordered structure of binary-mixtures composed of poly(4-vinylpyridine) and polystyrene microgels. J. Colloid Interface Sci. 168, 393–401 (1994).

    Article  CAS  Google Scholar 

  19. Shevchenko, E. V., Talapin, D. V., Kotov, N. A., O’Brien, S. & Murray, C. B. Structural diversity in binary nanoparticle superlattices. Nature 439, 55–59 (2006).

    Article  CAS  Google Scholar 

  20. Polson, J. M., Trizac, E., Pronk, S. & Frenkel, D. Finite-size corrections to the free energies of crystalline solids. J. Chem. Phys. 112, 5339–5342 (2000).

    Article  CAS  Google Scholar 

  21. Pusey, P. N. et al. Structure of crystals of hard colloidal spheres. Phys. Rev. Lett. 63, 2753–2756 (1989).

    Article  CAS  Google Scholar 

  22. Hoogenboom, J. P., Vossen, D. L. J., Faivre-Moskalenko, C., Dogterom, M. & van Blaaderen, A. Patterning surfaces with colloidal particles using optical tweezers. Appl. Phys. Lett. 80, 4828–4830 (2002).

    Article  CAS  Google Scholar 

  23. Hoogenboom, J. P., van Langen-Suurling, A. K., Romijn, J. & van Blaaderen, A. Hard-sphere crystals with hcp and non-close-packed structure grown by colloidal epitaxy. Phys. Rev. Lett. 90, 138301 (2003).

    Article  CAS  Google Scholar 

  24. Biswas, R., Sigalas, M. M., Subramania, G. & Ho, K.-M. Photonic band gaps in colloidal systems. Phys. Rev. B 57, 3701–3705 (1998).

    Article  CAS  Google Scholar 

  25. Johnson, S. G. & Joannopoulos, J. D. Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis. Opt. Express 8, 173–190 (2001).

    Article  CAS  Google Scholar 

  26. Wang, X., Zhang, X.-G., Yu, Q. & Harmon, B. N. Multiple-scattering theory for electromagnetic-waves. Phys. Rev. B 47, 4161–4167 (1993).

    Article  CAS  Google Scholar 

  27. Moroz, A. Density-of-states calculations and multiple-scattering theory for photons. Phys. Rev. B 51, 2068–2081 (1995).

    Article  CAS  Google Scholar 

  28. Busch, K. & John, S. Photonic band gap formation in certain self-organizing systems. Phys. Rev. E 58, 3896–3908 (1998).

    Article  CAS  Google Scholar 

  29. Miguez, H. et al. Control of the photonic crystal properties of fcc-packed submicrometer SiO2 spheres by sintering. Adv. Mater. 10, 480–483 (1998).

    Article  CAS  Google Scholar 

  30. Eiden-Assmann, S., Widoniak, J. & Maret, G. Synthesis and characterization of porous and nonporous monodisperse colloidal TiO2 particles. Chem. Mater. 16, 6–11 (2004).

    Article  CAS  Google Scholar 

  31. Velikov, K. P. & van Blaaderen, A. Synthesis and characterization of monodisperse core-shell colloidal spheres of zinc sulfide and silica. Langmuir 17, 4779–4786 (2001).

    Article  CAS  Google Scholar 

  32. Leunissen, M. E. et al. Ionic colloidal crystals of oppositely charged particles. Nature 437, 235–240 (2005).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

We thank M. Megens for the MPB patch file and A. Moroz for useful discussions on KKR calculations and for providing the FORTRAN KKR code. This work is part of the research program of the ‘Stichting voor Fundamenteel Onderzoek der Materie (FOM)’, which is financially supported by the ‘Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO)’. The work of E.C.M.V. is supported by NanoNed, a nanotechnology program of the Dutch Ministry of Economic Affairs. This work has been carried out within the framework of the SFB TR6 Collaborative Research Centre. On its inducement, it has been printed under appropriation of funds that were set at disposal by the DFG.

Author information

Authors and Affiliations

  1. Department of Chemical Engineering, Princeton University, Princeton, New Jersey 08544-5263, USA

    Antti-Pekka Hynninen

  2. Soft Condensed Matter, Debye Institute, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands

    Antti-Pekka Hynninen, Job H. J. Thijssen, Esther C. M. Vermolen, Marjolein Dijkstra & Alfons van Blaaderen

Authors
  1. Antti-Pekka Hynninen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Job H. J. Thijssen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Esther C. M. Vermolen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Marjolein Dijkstra
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Alfons van Blaaderen
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

A.-P.H. did the MC simulations under the supervision of M.D., J.H.J.T and E.C.M.V did the photonic bandgap calculations and A.v.B. initiated and supervised the project.

Corresponding authors

Correspondence to Antti-Pekka Hynninen or Alfons van Blaaderen.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Hynninen, AP., Thijssen, J., Vermolen, E. et al. Self-assembly route for photonic crystals with a bandgap in the visible region. Nature Mater 6, 202–205 (2007). https://doi.org/10.1038/nmat1841

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nmat1841

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