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Emergence of an enslaved phononic bandgap in a non-equilibrium pseudo-crystal

Nature Materials volume 16, pages 808–813 (2017)Cite this article

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Abstract

Material systems that reside far from thermodynamic equilibrium have the potential to exhibit dynamic properties and behaviours resembling those of living organisms. Here we realize a non-equilibrium material characterized by a bandgap whose edge is enslaved to the wavelength of an external coherent drive. The structure dynamically self-assembles into an unconventional pseudo-crystal geometry that equally distributes momentum across elements. The emergent bandgap is bestowed with lifelike properties, such as the ability to self-heal to perturbations and adapt to sudden changes in the drive. We derive an exact analytical solution for both the spatial organization and the bandgap features, revealing the mechanism for enslavement. This work presents a framework for conceiving lifelike non-equilibrium materials and emphasizes the potential for the dynamic imprinting of material properties through external degrees of freedom.

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Figure 1: Bandgap emergence in a non-equilibrium material.
Figure 2: Pseudo-crystal formation.
Figure 3: Theoretical prediction of bandgap emergence out of equilibrium.
Figure 4: Position and momentum phase-space collapse.

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References

  1. Bhat, H. L. Introduction to Crystal Growth: Principles and Practice (CRC Press, 2014).

    Book  Google Scholar 

  2. Kalsin, A. M. et al. Electrostatic self-assembly of binary nanoparticle crystals with a diamond-like lattice. Science 312, 420–424 (2006).

    Article  CAS  Google Scholar 

  3. Dong, A., Chen, J., Vora, P. M., Kikkawa, J. M. & Murray, C. B. Binary nanocrystal superlattice membranes self-assembled at the liquid–air interface. Nature 466, 474–477 (2010).

    Article  CAS  Google Scholar 

  4. van Blaaderen, A., Ruel, R. & Wiltzius, P. Template-directed colloidal crystallization. Nature 385, 321–324 (1997).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  6. de Nijs, B. et al. Entropy-driven formation of large icosahedral colloidal clusters by spherical confinement. Nat. Mater. 14, 56–60 (2014).

    Article  Google Scholar 

  7. Grzybowski, B. A., Wilmer, C. E., Kim, J., Browne, K. P. & Bishop, K. J. M. Self-assembly: from crystals to cells. Soft Matter 5, 1110–1128 (2009).

    Article  CAS  Google Scholar 

  8. Karsenti, E. Self-organization in cell biology: a brief history. Nat. Rev. Mol. Cell Biol. 9, 255–262 (2008).

    Article  CAS  Google Scholar 

  9. Shimoyama, N., Sugawara, K., Mizuguchi, T., Hayakawa, Y. & Sano, M. Collective motion in a system of motile elements. Phys. Rev. Lett. 76, 3870–3873 (1996).

    Article  CAS  Google Scholar 

  10. Couzin, I. D. & Franks, N. R. Self-organized lane formation and optimized traffic flow in army ants. Proc. R. Soc. B 270, 139–146 (2003).

    Article  CAS  Google Scholar 

  11. Mateus, A. M., Gorfinkiel, N. & Arias, A. M. Origin and function of fluctuations in cell behaviour and the emergence of patterns. Semin. Cell Dev. Biol. 20, 877–884 (2009).

    Article  CAS  Google Scholar 

  12. Mora, T. et al. Local equilibrium in bird flocks. Nat. Phys. 12, 1153–1157 (2016).

    Article  CAS  Google Scholar 

  13. Whitesides, G. M. & Grzybowski, B. Self-assembly at all scales. Science 295, 2418–2421 (2002).

    Article  CAS  Google Scholar 

  14. Kondepudi, D. & Prigogine, I. Modern Thermodynamics: From Heat Engines to Dissipative Structures (John Wiley, 2014).

    Book  Google Scholar 

  15. Fialkowski, M. et al. Principles and implementations of dissipative (dynamic) self-assembly. J. Phys. Chem. B 110, 2482–2496 (2006).

    Article  CAS  Google Scholar 

  16. Osterman, N. et al. Field-induced self-assembly of suspended colloidal membranes. Phys. Rev. Lett. 103, 228301 (2009).

    Article  CAS  Google Scholar 

  17. Grzybowski, B. A., Stone, H. A. & Whitesides, G. M. Dynamic self-assembly of magnetized, millimetre-sized objects rotating at a liquid–air interface. Nature 405, 1033–1036 (2000).

    Article  CAS  Google Scholar 

  18. Snezhko, A., Aranson, I. S. & Kwok, W.-K. Surface wave assisted self-assembly of multidomain magnetic structures. Phys. Rev. Lett. 96, 078701 (2006).

    Article  CAS  Google Scholar 

  19. Snezhko, A. & Aranson, I. S. Magnetic manipulation of self-assembled colloidal asters. Nat. Mater. 10, 698–703 (2011).

    Article  CAS  Google Scholar 

  20. Lehn, J.-M. Toward self-organization and complex matter. Science 295, 2400–2403 (2002).

    Article  CAS  Google Scholar 

  21. England, J. L. Dissipative adaptation in driven self-assembly. Nat. Nanotech. 10, 919–923 (2015).

    Article  CAS  Google Scholar 

  22. Perunov, N., Marsland, R. A. & England, J. L. Statistical physics of adaptation. Phys. Rev. X 6, 021036 (2016).

    Google Scholar 

  23. Snezhko, A., Belkin, M., Aranson, I. S. & Kwok, W.-K. Self-assembled magnetic surface swimmers. Phys. Rev. Lett. 102, 118103 (2009).

    Article  CAS  Google Scholar 

  24. Boekhoven, J. et al. Dissipative self-assembly of a molecular gelator by using a chemical fuel. Angew. Chem. 122, 4935–4938 (2010).

    Article  Google Scholar 

  25. Bricard, A., Caussin, J.-B., Desreumaux, N., Dauchot, O. & Bartolo, D. Emergence of macroscopic directed motion in populations of motile colloids. Nature 503, 95–98 (2013).

    Article  CAS  Google Scholar 

  26. Palacci, J., Sacanna, S., Steinberg, A. P., Pine, D. J. & Chaikin, P. M. Living crystals of light-activated colloidal surfers. Science 339, 936–940 (2013).

    Article  CAS  Google Scholar 

  27. Martinez-Pedrero, F., Ortiz-Ambriz, A., Pagonabarraga, I. & Tierno, P. Colloidal microworms propelling via a cooperative hydrodynamic conveyor belt. Phys. Rev. Lett. 115, 138301 (2015).

    Article  Google Scholar 

  28. Solis, K. J. & Martin, J. E. Complex magnetic fields breathe life into fluids. Soft Matter 10, 9136–9142 (2014).

    CAS  Google Scholar 

  29. Maiti, S., Fortunati, I., Ferrante, C., Scrimin, P. & Prins, L. J. Dissipative self-assembly of vesicular nanoreactors. Nat. Chem. 8, 725–731 (2016).

    Article  CAS  Google Scholar 

  30. 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 

  31. Hynninen, A.-P., Thijssen, J. H. J., Vermolen, E. C. M., Dijkstra, M. & van Blaaderen, A. Self-assembly route for photonic crystals with a bandgap in the visible region. Nat. Mater. 6, 202–205 (2007).

    Article  CAS  Google Scholar 

  32. Lemoult, F., Kaina, N., Fink, M. & Lerosey, G. Wave propagation control at the deep subwavelength scale in metamaterials. Nat. Phys. 9, 55–60 (2012).

    Article  Google Scholar 

  33. Alonso-Redondo, E. et al. A new class of tunable hypersonic phononic crystals based on polymer-tethered colloids. Nat. Commun. 6, 8309 (2015).

    Article  CAS  Google Scholar 

  34. Beatus, T., Tlusty, T. & Bar-Ziv, R. Phonons in a one-dimensional microfluidic crystal. Nat. Phys. 2, 743–748 (2006).

    Article  CAS  Google Scholar 

  35. Timonen, J. V. I., Latikka, M., Leibler, L., Ras, R. H. A. & Ikkala, O. Switchable static and dynamic self-assembly of magnetic droplets on superhydrophobic surfaces. Science 341, 253–257 (2013).

    Article  CAS  Google Scholar 

  36. Tretiakov, K. V., Bishop, K. J. M. & Grzybowski, B. A. The dependence between forces and dissipation rates mediating dynamic self-assembly. Soft Matter 5, 1279–1284 (2009).

    Article  CAS  Google Scholar 

  37. Joannopoulos, J. D., Johnson, S. G., Winn, J. N. & Meade, R. D. Photonic Crystals: Molding the Flow of Light 2nd edn (Princeton Univ. Press, 2011).

    Book  Google Scholar 

  38. Dholakia, K. & Zemánek, P. Gripped by light: optical binding. Rev. Mod. Phys. 82, 1767–1791 (2010).

    Article  Google Scholar 

  39. Karásek, V. et al. Long-range one-dimensional longitudinal optical binding. Phys. Rev. Lett. 101, 143601 (2008).

    Article  Google Scholar 

  40. Frawley, M. C., Gusachenko, I., Truong, V. G., Sergides, M. & Chormaic, S. N. Selective particle trapping and optical binding in the evanescent field of an optical nanofiber. Opt. Express 22, 16322–16334 (2014).

    Article  CAS  Google Scholar 

  41. Strogatz, S. H. Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering (Westview Press, 2001).

    Google Scholar 

  42. von Freymann, G., Kitaev, V., Lotsch, B. V. & Ozin, G. A. Bottom-up assembly of photonic crystals. Chem. Soc. Rev. 42, 2528–2554 (2013).

    Article  CAS  Google Scholar 

  43. Prather, D. W. Photonic Crystals, Theory, Applications and Fabrication (John Wiley, 2009).

    Google Scholar 

  44. Martyushev, L. M. & Seleznev, V. D. Maximum entropy production principle in physics, chemistry and biology. Phys. Rep. 426, 1–45 (2006).

    Article  CAS  Google Scholar 

  45. Ross, J., Corlan, A. D. & Müller, S. C. Proposed principles of maximum local entropy production. J. Phys. Chem. B 116, 7858–7865 (2012).

    Article  CAS  Google Scholar 

  46. Martyushev, L. M. & Seleznev, V. D. The restrictions of the maximum entropy production principle. Phys. Stat. Mech. Appl. 410, 17–21 (2014).

    Article  Google Scholar 

  47. Deplazes, A. & Huppenbauer, M. Synthetic organisms and living machines. Syst. Synth. Biol. 3, 55–63 (2009).

    Article  Google Scholar 

  48. Deplazes, A. Piecing together a puzzle. EMBO Rep. 10, 428–432 (2009).

    Article  CAS  Google Scholar 

  49. Szostak, J. W., Bartel, D. P. & Luisi, P. L. Synthesizing life. Nature 409, 387–390 (2001).

    Article  CAS  Google Scholar 

  50. Haken, H. Principles of Brain Functioning: A Synergetic Approach to Brain Activity, Behavior and Cognition (Springer Science & Business Media, 2013).

    Google Scholar 

Download references

Acknowledgements

The experimental part of this work is supported by the Office of Naval Research (ONR) MURI program under Grant No. N00014-13-1-0631; the numerical calculation and energy analysis is supported by the ‘Light-Material Interactions in Energy Conversion’ Energy Frontier Research Center funded by the US Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number DE-AC02-05CH11231.

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Author notes

  1. Nicolas Bachelard and Chad Ropp: These authors contributed equally to this work.

Authors and Affiliations

  1. NSF Nanoscale Science and Engineering Center, 3112 Etcheverry Hall, University of California, Berkeley, California, 94720, USA

    Nicolas Bachelard, Chad Ropp, Marc Dubois, Rongkuo Zhao, Yuan Wang & Xiang Zhang

  2. Materials Sciences Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California, 94720, USA

    Yuan Wang & Xiang Zhang

  3. Department of Physics, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Xiang Zhang

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  1. Nicolas Bachelard
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Contributions

N.B. and C.R. designed and conducted experiments and performed the theoretical investigation; M.D. performed COMSOL simulations; R.Z. provided theoretical guidance; X.Z. and Y.W. guided the research. All authors contributed to writing the manuscript.

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Correspondence to Xiang Zhang.

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Bachelard, N., Ropp, C., Dubois, M. et al. Emergence of an enslaved phononic bandgap in a non-equilibrium pseudo-crystal. Nature Mater 16, 808–813 (2017). https://doi.org/10.1038/nmat4920

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