Audible sound-controlled spatiotemporal patterns in out-of-equilibrium systems


Naturally occurring spatiotemporal patterns typically have a predictable pattern design and are reproducible over several cycles. However, the patterns obtained from artificially designed out-of-equilibrium chemical oscillating networks (such as the Belousov–Zhabotinsky reaction for example) are unpredictable and difficult to control spatiotemporally, albeit reproducible over subsequent cycles. Here, we show that it is possible to generate reproducible spatiotemporal patterns in out-of-equilibrium chemical reactions and self-assembling systems in water in the presence of sound waves, which act as a guiding physical stimulus. Audible sound-induced liquid vibrations control the dissolution of atmospheric gases (such as O2 and CO2) in water to generate spatiotemporal chemical patterns in the bulk of the fluid, segregating the solution into spatiotemporal domains having different redox properties or pH values. It further helps us in the organization of transiently formed supramolecular aggregates in a predictable spatiotemporal manner.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Sound-controlled spatiotemporal patterns.
Fig. 2: Sound-controlled redox-specific domains and spatiotemporal patterns.
Fig. 3: Sound-controlled pH-specific domains and spatiotemporal patterns.
Fig. 4: Sound-controlled organization of supramolecular aggregates in spatiotemporal patterns.

Data availability

The authors declare that the data supporting the findings of this study are available within the paper and its Supplementary Information files.


  1. 1.

    Tsuji, K. & Müller, S. C. Spirals and Vortices: in Culture, Nature, and Science (Springer, 2019).

  2. 2.

    Mandelkow, E., Mandelkow, E. M., Hotani, H., Hess, B. & Muller, S. C. Spatial patterns from oscillating microtubules. Science 246, 1291–1293 (1989).

    CAS  Article  Google Scholar 

  3. 3.

    Kondo, S. & Miura, T. Reaction-diffusion model as a framework for understanding biological pattern formation. Science 329, 1616–1620 (2010).

    CAS  Article  Google Scholar 

  4. 4.

    Halatek, J. & Frey, E. Rethinking pattern formation in reaction–diffusion systems. Nat. Phys. 14, 507–514 (2018).

    CAS  Article  Google Scholar 

  5. 5.

    Vecchiarelli, A. G. et al. Membrane-bound MinDE complex acts as a toggle switch that drives Min oscillation coupled to cytoplasmic depletion of MinD. Proc. Natl Acad. Sci. USA 113, 1479–1488 (2016).

    Article  Google Scholar 

  6. 6.

    Agladze, K. I., Krinsky, V. I. & Pertsov, A. M. Chaos in the non-stirred Belousov-Zhabotinsky reaction is induced by interaction of waves and stationary dissipative structures. Nature 308, 834–835 (1984).

    CAS  Article  Google Scholar 

  7. 7.

    Ashkenasy, G., Hermans, T. M., Otto, S. & Taylor, A. F. Systems chemistry. Chem. Soc. Rev. 46, 2543–2554 (2017).

    CAS  Article  Google Scholar 

  8. 8.

    Ragazzon, G. & Prins, L. J. Energy consumption in chemical fuel-driven self-assembly. Nat. Nanotechnol. 13, 882–889 (2018).

    CAS  Article  Google Scholar 

  9. 9.

    van der Zwaag, D. & Meijer, E. W. Fueling connections between chemistry and biology. Science 349, 1056–1057 (2015).

    Article  Google Scholar 

  10. 10.

    Boekhoven, J., Hendriksen, W. E., Koper, G. J. M., Eelkema, R. & van Esch, J. H. Transient assembly of active materials fueled by a chemical reaction. Science 349, 1075–1079 (2015).

    CAS  Article  Google Scholar 

  11. 11.

    Jain, A., Dhiman, S., Dhayani, A., Vemula, P. K. & George, S. J. Chemical fuel-driven living and transient supramolecular polymerization. Nat. Commun. 10, 450 (2019).

    CAS  Article  Google Scholar 

  12. 12.

    Choi, S. et al. Fuel-driven transient crystallization of a cucurbit[8]uril-based host–guest complex. Angew. Chem. Int. Ed. 58, 16850–16853 (2019).

    CAS  Article  Google Scholar 

  13. 13.

    Leira-Iglesias, J., Tassoni, A., Adachi, T., Stich, M. & Hermans, T. M. Oscillations, travelling fronts and patterns in a supramolecular system. Nat. Nanotechnol. 13, 1021–1027 (2018).

    CAS  Article  Google Scholar 

  14. 14.

    Zhang, Y., Tsitkov, S. & Hess, H. Complex dynamics in a two-enzyme reaction network with substrate competition. Nat. Catal. 1, 276–281 (2018).

    Article  Google Scholar 

  15. 15.

    Heuser, T., Steppert, A.-K., Lopez, C. M., Zhu, B. & Walther, A. Generic concept to program the time domain of self-assemblies with a self-regulation mechanism. Nano Lett. 15, 2213–2219 (2015).

    CAS  Article  Google Scholar 

  16. 16.

    Grzybowski, B. A., Fitzner, K., Paczesny, J. & Granick, S. From dynamic self-assembly to networked chemical systems. Chem. Soc. Rev. 46, 5647–5678 (2017).

    CAS  Article  Google Scholar 

  17. 17.

    Pelling, A. E., Sehati, S., Gralla, E. B., Valentine, J. S. & Gimzewski, J. K. Local nanomechanical motion of the cell wall of Saccharomyces cerevisiae. Science 305, 1147–1150 (2004).

    CAS  Article  Google Scholar 

  18. 18.

    Martorell, A. J. et al. Multi-sensory gamma stimulation ameliorates Alzheimer’s-associated pathology and improves cognition. Cell 177, 256–271 (2019).

    CAS  Article  Google Scholar 

  19. 19.

    Zhou, Q., Sariola, V., Latifi, K. & Liimatainen, V. Controlling the motion of multiple objects on a Chladni plate. Nat. Commun. 7, 12764 (2016).

    CAS  Article  Google Scholar 

  20. 20.

    Westra, M. T., Binks, D. J. & van de Water, W. Patterns of Faraday waves. J. Fluid Mech. 496, 1–32 (2003).

    Article  Google Scholar 

  21. 21.

    Suslick, K. S. Sonochemistry. Science 247, 1439–1445 (1990).

    CAS  Article  Google Scholar 

  22. 22.

    Margulis, M. A. & Maximenko, N. A. in Advances in Sonochemistry Vol. 2 (ed. Mason, T. J.) Ch. 7 (JAI Press, 1991).

  23. 23.

    Chambers, L. A. & Flosdorf, E. W. The denaturation of proteins by sound waves of audible frequencies. J. Biol. Chem. 114, 75–83 (1936).

    CAS  Google Scholar 

  24. 24.

    Cravotto, G. & Cintas, P. Molecular self-assembly and patterning induced by sound waves the case of gelation. Chem. Soc. Rev. 38, 2684–2697 (2009).

    CAS  Article  Google Scholar 

  25. 25.

    Tsuda, A. et al. Spectroscopic visualization of sound-induced liquid vibrations using a supramolecular nanofiber. Nat. Chem. 2, 977–983 (2010).

    CAS  Article  Google Scholar 

  26. 26.

    Miura, R., Ando, Y., Hotta, Y., Nagatani, Y. & Tsuda, A. Acoustic alignment of a supramolecular nanofiber in harmony with the sound of music. ChemPlusChem 79, 516–523 (2014).

    CAS  Article  Google Scholar 

  27. 27.

    Hotta, Y., Fukushima, S., Motoyanagi, J. & Tsuda, A. Photochromism in sound-induced alignment of a diarylethene supramolecular nanofiber. Chem. Commun. 51, 2790–2793 (2015).

    CAS  Article  Google Scholar 

  28. 28.

    Chen, P. et al. Microscale assembly directed by liquid-based template. Adv. Mater. 26, 5936–5941 (2014).

    CAS  Article  Google Scholar 

  29. 29.

    Saylor, P. & Handler, R. A. Gas transport across an air/water interface populated with capillary waves. Phys. Fluids 9, 2529–2541 (1997).

    CAS  Article  Google Scholar 

  30. 30.

    Jeon, W. S., Kim, H.-J., Lee, C. & Kim, K. Control of the stoichiometry in host–guest complexation by redox chemistry of guests: Inclusion of methylviologen in cucurbit[8]uril. Chem. Commun. 1828–1829 (2002).

  31. 31.

    Trabolsi, A. et al. Radically enhanced molecular recognition. Nat. Chem. 2, 42–49 (2010).

    CAS  Article  Google Scholar 

  32. 32.

    Tsuda, A. et al. Spectroscopic visualization of vortex flows using dye-containing nanofibers. Angew. Chem. Int. Ed. 46, 8198–8202 (2007).

    CAS  Article  Google Scholar 

  33. 33.

    Limpanuparb, T., Ruchawapol, C., Pakwilaikiat, P. & Kaewpichit, C. Chemical patterns in autoxidations catalyzed by redox dyes. ACS Omega 4, 7891–7894 (2019).

    CAS  Article  Google Scholar 

  34. 34.

    Agrawal, P., Gandhi, P. S. & Neild, A. Particle manipulation affected by streaming flows in vertically actuated open rectangular chambers. Phys. Fluids 28, 032001 (2016).

    Article  Google Scholar 

  35. 35.

    Helfrich, W. Orienting action of sound on nematic liquid crystals. Phys. Rev. Lett. 29, 1583–1586 (1972).

    CAS  Article  Google Scholar 

  36. 36.

    Xing, W. et al. in Rotating electrode methods and oxygen reduction electrocatalysts (eds Waly, M. & Rahman, M.) Ch. 1 (Elsevier, 2014).

  37. 37.

    Pazos, E., Novo, P., Peinador, C., Kaifer, A. E. & García, M. D. Cucurbit[8]uril (CB[8])-based supramolecular switches. Angew. Chem. Int. Ed. 58, 403–416 (2019).

    CAS  Article  Google Scholar 

  38. 38.

    Draper, E. R. et al. pH-Directed aggregation to control photoconductivity in self-assembled perylene bisimides. Chem 2, 716–731 (2017).

    CAS  Article  Google Scholar 

  39. 39.

    Hariharan, P. S., Pitchaimani, J., Madhu, V. & Anthony, S. P. A halochromic stimuli-responsive reversible fluorescence switching 3, 4, 9, 10-perylene tetracarboxylic acid dye for fabricating rewritable platform. Opt. Mater. 64, 53–57 (2017).

    CAS  Article  Google Scholar 

  40. 40.

    Buck, A. T., Paletta, J. T., Khindurangala, S. A., Beck, C. L. & Winter, A. H. A noncovalently reversible paramagnetic switch in water. J. Am. Chem. Soc. 135, 10594–10597 (2013).

    CAS  Article  Google Scholar 

  41. 41.

    Douady, S. Experimental study of the Faraday instability. J. Fluid Mech. 221, 383–409 (1990).

    Article  Google Scholar 

Download references


We thank I.S. Kang (POSTECH) and S. Shin (Hongik University) for helpful discussions on fluid dynamics and the Faraday instability. This work was supported by the Institute for Basic Science (IBS) [IBS-R007-D1].

Author information




I.H., R.D.M. and K.K. conceived the idea and designed the experiments. S.-Y.K., I.H., P.D. and S.C. synthesized the materials. P.D., R.D.M., S.C. and I.H. participated in pattern generation and other associated experiments. Y.H.K. helped in NMR experiments. K.B. performed cryo-transmission electron microscopy experiments. All authors discussed the results, analysed the data and commented on the manuscript. K.K. supervised the overall research.

Corresponding authors

Correspondence to Ilha Hwang or Rahul Dev Mukhopadhyay or Kimoon Kim.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Synthesis and characterization of compounds, Supplementary Figs. 1–20 and references.

Supplementary Video 1

Pattern generation with the MV2+/MV•+ redox couple at 40Hz. The video is played 20 times faster than real time.

Supplementary Video 2

Pattern generation with the SF0/SF+ redox couple at 40Hz. The video is played two times slower than real time.

Supplementary Video 3

Pattern generation experiments under the inert atmosphere and in air. No pattern was observed in an inert atmosphere, but a spatiotemporal pattern was generated from air exposure.

Supplementary Video 4

Slow motion video of surface wave pattern at 40Hz. The video was recorded at 960 frames per second and is played 128 times slower than real time.

Supplementary Video 5

Self-healing behaviour of the pattern. The preformed pattern was disturbed with a syringe needle while keeping the sound source on and the collapsed pattern was recovered after a while.

Supplementary Video 6

Dynamic interchange between patterns. As the vibration frequency of the solution changes, the resulting patterns also change accordingly.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Hwang, I., Mukhopadhyay, R.D., Dhasaiyan, P. et al. Audible sound-controlled spatiotemporal patterns in out-of-equilibrium systems. Nat. Chem. 12, 808–813 (2020).

Download citation

Further reading


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