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.

  • Letter
  • Published:

Topology-driven surface patterning of liquid spheres

Nature Physics volume 18, pages 1177–1180 (2022)Cite this article

Subjects

Abstract

Surfaces of classical spherical liquid droplets are isotropic, promoting the random distribution of surface-adsorbed molecules1. Here we demonstrate a counterintuitive temperature-controlled self-assembly of well-defined and highly ordered patterns of surface-adsorbed fluorescent molecules on the surfaces of water-suspended spherical oil droplets. These patterns are induced by precisely self-positioned, topology-dictated structural defects in a crystalline monolayer covering these droplets’ surfaces over a wide temperature range. We elucidate the pattern formation mechanism, visualize the defects’ positions and map the stress fields within the surface crystal. The observed phenomena provide insights into the interfacial freezing effect on curved surfaces, enable precise positioning of functional ligands on droplets for their self-assembly into higher-hierarchy structures2,3,4,5,6 and may also play an important role in vital protein positioning on cell membranes7 and morphogenesis8,9,10,11,12.

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

Fig. 1: Self-assembly of ordered patterns on liquid spheres.
Fig. 2: Surface transition temperatures.
Fig. 3: Scars and mazes.

Similar content being viewed by others

Data availability

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

Code availability

To ensure accurate use, codes to perform computer simulations and three-dimensional confocal data are available only upon request from the corresponding author.

References

  1. Berg, J. C. An Introduction to Interfaces & Colloids: The Bridge to Nanoscience (World Scientific, 2010).

  2. Nelson, D. R. Toward a tetravalent chemistry of colloids. Nano Lett. 2, 1125–1129 (2002).

    Article  ADS  Google Scholar 

  3. DeVries, G. A. et al. Divalent metal nanoparticles. Science 315, 358–361 (2007).

    Article  ADS  Google Scholar 

  4. Jacobs, H. O., Tao, A. R., Schwartz, A., Gracias, D. H. & Whitesides, G. M. Fabrication of a cylindrical display by patterned assembly. Science 296, 323–325 (2002).

    Article  ADS  Google Scholar 

  5. Marin, O., Deutsch, M., Zitoun, D. & Sloutskin, E. Nanoparticle positioning on liquid and polymerized faceted droplets. J. Phys. Chem. C 123, 28192–28200 (2019).

    Article  Google Scholar 

  6. Liber, S. R. et al. Precise self-positioning of colloidal particles on liquid emulsion droplets. Langmuir 35, 13053–13061 (2019).

    Article  Google Scholar 

  7. García-Lara, J. et al. Supramolecular structure in the membrane of staphylococcus aureus. Proc. Natl Acad. Sci. USA 112, 15725–15730 (2015).

    Article  ADS  Google Scholar 

  8. Hoffmann, L. A., Carenza, L. N., Eckert, J. & Giomi, L. Theory of defect-mediated morphogenesis. Sci. Adv. 8, eabk2712 (2022).

  9. Maroudas-Sacks, Y. et al. Topological defects in the nematic order of actin fibres as organization centres of Hydra morphogenesis. Nat. Phys. 17, 251–259 (2021).

    Article  Google Scholar 

  10. Marin, O., Tkachev, M., Sloutskin, E. & Deutsch, M. Polyhedral liquid droplets: recent advances in elucidation and application. Curr. Opin. Colloid Interface Sci. 49, 107–117 (2020).

    Article  Google Scholar 

  11. Gordon, R., Hanczyc, M. M., Denkov, N. D., Tiffany, M. A. & Smoukov, S. K. Emergence of polygonal shapes in oil droplets and living cells: the potential role of tensegrity in the origin of life. Habitability of the Universe before Earth 427–490 (2018).

  12. Cholakova, D. et al. Rechargeable self-assembled droplet microswimmers driven by surface phase transitions. Nat. Phys. 17, 1050–1055 (2021).

  13. Rajabi, M., Baza, H., Turiv, T. & Lavrentovich, O. D. Directional self-locomotion of active droplets enabled by nematic environment. Nat. Phys. 17, 260–266 (2021).

    Article  Google Scholar 

  14. Olzmann, J. E. & Carvalho, P. Dynamics and functions of lipid droplets. Nat. Rev. Mol. Cell Biol. 20, 137–155 (2019).

    Article  Google Scholar 

  15. Guttman, S. et al. How faceted liquid droplets grow tails. Proc. Natl Acad. Sci. USA 113, 493–496 (2016).

    Article  ADS  Google Scholar 

  16. Liber, S. R. et al. Polyhedral water droplets: shape transitions and mechanism. J. Am. Chem. Soc. 142, 8672–8678 (2020).

    Article  Google Scholar 

  17. Guttman, S. et al. Nanostructures, faceting, and splitting in nanoliter to yoctoliter liquid droplets. Nano Lett. 19, 3161–3168 (2019).

    Article  ADS  Google Scholar 

  18. Tokiwa, Y. et al. Effect of surface freezing on stability of oil-in-water emulsions. Langmuir 34, 6205–6209 (2018).

    Article  Google Scholar 

  19. Guerra, R. E., Kelleher, C. P., Hollingsworth, A. D. & Chaikin, P. M. Freezing on a sphere. Nature 554, 346–350 (2018).

    Article  ADS  Google Scholar 

  20. Meng, G., Paulose, J., Nelson, D. R. & Manoharan, V. N. Elastic instability of a crystal growing on a curved surface. Science 343, 634–637 (2014).

    Article  ADS  Google Scholar 

  21. Bausch, A. et al. Grain boundary scars and spherical crystallography. Science 299, 1716–1718 (2003).

    Article  ADS  Google Scholar 

  22. Zandi, R., Dragnea, B., Travesset, A. & Podgornik, R. On virus growth and form. Phys. Rep. 847, 1–102 (2020).

    Article  ADS  MathSciNet  Google Scholar 

  23. Euler, L. Elementa doctrinae solidorum. Comment. Acad. Sci. Imp. Petropol. 4, 109–140 (1758).

    Google Scholar 

  24. Sengupta, A., Bahr, C. & Herminghaus, S. Topological microfluidics for flexible micro-cargo concepts. Soft Matter 9, 7251–7260 (2013).

    Article  ADS  Google Scholar 

  25. García-Aguilar, I., Fonda, P., Sloutskin, E. & Giomi, L. Faceting and flattening of emulsion droplets: a mechanical model. Phys. Rev. Lett. 126, 038001 (2021).

    Article  ADS  MathSciNet  Google Scholar 

  26. Giarritta, S. P., Ferrario, M. & Giaquinta, P. V. Statistical geometry of hard particles on a sphere: analysis of defects at high density. Physica A 201, 649–665 (1993).

    Article  ADS  Google Scholar 

  27. Wales, D. J., McKay, H. & Altschuler, E. L. Defect motifs for spherical topologies. Phys. Rev. B 79, 224115 (2009).

    Article  ADS  Google Scholar 

  28. Cholakova, D., Denkov, N., Tcholakova, S., Lesov, I. & Smoukov, S. K. Control of drop shape transformations in cooled emulsions. Adv. Coll. Interf. Sci. 235, 90–107 (2016).

    Article  Google Scholar 

  29. García-Aguilar, I., Fonda, P. & Giomi, L. Dislocation screening in crystals with spherical topology. Phys. Rev. E 101, 063005 (2020).

    Article  ADS  MathSciNet  Google Scholar 

  30. Li, S., Zandi, R., Travesset, A. & Grason, G. M. Ground states of crystalline caps: generalized jellium on curved space. Phys. Rev. Lett. 123, 145501 (2019).

    Article  ADS  MathSciNet  Google Scholar 

  31. Yadav, N., Sen, P., Ghosh, A. Bubbles in superfluid helium containing six and eight electrons: soft, quantum nanomaterial. Sci. Adv. 7, eabi7128 (2021).

  32. Kohyama, T. & Gompper, G. Defect scars on flexible surfaces with crystalline order. Phys. Rev. Lett. 98, 198101 (2007).

    Article  ADS  Google Scholar 

  33. Chen, Y. et al. Morphology selection kinetics of crystallization in a sphere. Nat. Phys. 17, 121–127 (2021).

    Article  Google Scholar 

  34. Gómez, L. R., Garcia, N. A., Vitelli, V., Lorenzana, J. & Vega, D. A. Phase nucleation in curved space. Nat. Commun. 6, 6856 (2015).

    Article  ADS  Google Scholar 

  35. Li, S., Matoz-Fernandez, D. A. & de la Cruz, M. O. Effect of mechanical properties on multicomponent shell patterning. ACS Nano 15, 14804–14812 (2021).

    Article  Google Scholar 

  36. Michina, Y. et al. Absence of lateral phase segregation in fatty acid-based catanionic mixtures. J. Phys. Chem. B 114, 1932–1938 (2010).

    Article  Google Scholar 

  37. Schelero, N., Stocco, A., Möhwald, H. & Zemb, T. Pickering emulsions stabilized by stacked catanionic micro-crystals controlled by charge regulation. Soft Matter 7, 10694–10700 (2011).

    Article  ADS  Google Scholar 

  38. Dlamini, N., Prestipino, S. & Pellicane, G. Self-assembled structures of colloidal dimers and disks on a spherical surface. Entropy 23, 585 (2021).

    Article  ADS  Google Scholar 

  39. Marin, O. et al. Self-faceting of emulsion droplets as a route to solid icosahedra and other polyhedra. J. Colloid Interf. Sci. 538, 541–545 (2019).

    Article  ADS  Google Scholar 

  40. Duclos, G. et al. Topological structure and dynamics of three-dimensional active nematics. Science 367, 1120–1124 (2020).

    Article  ADS  Google Scholar 

  41. Lei, D. et al. Single-molecule 3D imaging of human plasma intermediate-density lipoproteins reveals a polyhedral structure. BBA-Mol. Cell Biol. L. 1864, 260–270 (2019).

    Google Scholar 

  42. Wei, W.-S., Xia, Y., Ettinger, S., Yang, S. & Yodh, A. G. Molecular heterogeneity drives reconfigurable nematic liquid crystal drops. Nature 576, 433–436 (2019).

    Article  ADS  Google Scholar 

  43. Guttman, S., Ocko, B. M., Deutsch, M. & Sloutskin, E. From faceted vesicles to liquid icoshedra: where topology and crystallography meet. Curr. Opin. Colloid Interface Sci. 22, 35–40 (2016).

    Article  Google Scholar 

  44. Wu, X. Z. et al. Surface tension measurements of surface freezing in liquid normal alkanes. Science 261, 1018–1021 (1993).

    Article  ADS  Google Scholar 

  45. Tamam, L. et al. Modification of deeply buried hydrophobic interfaces by ionic surfactants. Proc. Natl Acad. Sci. USA 108, 5522–5525 (2011).

    Article  ADS  Google Scholar 

  46. Ocko, B. M. et al. Surface freezing in chain molecules: normal alkanes. Phys. Rev. E 55, 3164–3182 (1997).

    Article  ADS  Google Scholar 

  47. Guttman, S., Sapir, Z., Ocko, B. M., Deutsch, M. & Sloutskin, E. Temperature-tuned faceting and shape-changes in liquid alkane droplets. Langmuir 33, 1305–1314 (2017).

    Article  Google Scholar 

  48. Brakke, K. A. The surface evolver. Exp. Math. 1, 141–165 (1992).

    Article  MathSciNet  MATH  Google Scholar 

  49. Yong, E. H., Nelson, D. R. & Mahadevan, L. Elastic platonic shells. Phys. Rev. Lett. 111, 177801 (2013).

    Article  ADS  Google Scholar 

  50. Bowick, M. J. & Giomi, L. Two-dimensional matter: order, curvature and defects. Adv. Phys. 58, 449–563 (2009).

    Article  ADS  Google Scholar 

  51. Lidmar, J., Mirny, L. & Nelson, D. R. Virus shapes and buckling transitions in spherical shells. Phys. Rev. E 68, 051910 (2003).

    Article  ADS  Google Scholar 

  52. Azadi, A. & Grason, G. M. Neutral versus charged defect patterns in curved crystals. Phys. Rev. E 94, 013003 (2016).

    Article  ADS  Google Scholar 

  53. Sloutskin, E., Sirota, E. B., Wu, X. Z., Ocko, B. M. & Deutsch, M. Surface and bulk interchange energy in binary mixtures of chain molecules. Eur. Phys. J. E 13, 109–112 (2004).

    Article  Google Scholar 

Download references

Acknowledgements

This research is supported by the Israel Science Foundation (grant no. 2205/21 (E.S.)). We thank the Kahn Foundation for the funding of the equipment.

Author information

Authors and Affiliations

  1. Chemistry Department, Bar-Ilan University, Ramat-Gan, Israel

    Subhomoy Das & Yitzhak Mastai

  2. Bar-Ilan Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan, Israel

    Subhomoy Das, Alexander V. Butenko, Yitzhak Mastai, Moshe Deutsch & Eli Sloutskin

  3. Physics Department, Bar-Ilan University, Ramat-Gan, Israel

    Alexander V. Butenko, Moshe Deutsch & Eli Sloutskin

Authors
  1. Subhomoy Das
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alexander V. Butenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yitzhak Mastai
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Moshe Deutsch
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Eli Sloutskin
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All the authors contributed to the setup of the experiment, data acquisition, data analysis and writing of the manuscript.

Corresponding author

Correspondence to Eli Sloutskin.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Physics thanks Giuseppe Pellican and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

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

Extended data

Extended Data Fig. 1

Synthesis of the fluorescent compound 3.

Extended Data Fig. 2

1H NMR spectrum of 3 (CDCl3, 400 MHz).

Extended Data Fig. 3

13C{1H} NMR spectrum of 3 (CDCl3, 100 MHz).

Extended Data Fig. 4 Line-tension effects in temperature-dependence of fluorescent patterns.

a, The subtle differences in the temperature-increasing droplets’ fluorescence for different-length alkanes (see legend), are magnified on a semi-logarithmic plot, showing a steeper A/AT growth with increasing alkanes length. The lines are guides to the eye. Standard deviation is ≈ 5 × 10−3. b, Similarly, the semi-logarithmic scale allows the difference between computer simulations corresponding to different γL values, to be magnified. The curves are spline-smoothed for clarity of representation. The error bars show the typical standard deviations between simulations carried out with different random number generator seeds. The sizes of the error bars rapidly decrease from the left of the plot to its right. Importantly, the comparison between the A(T) trends observed in (a) and in (b) suggests that the line tension can be directly varied in these experiments.

Supplementary information

Supplementary Video 1

A cooling temperature scan (from ~34 to ~23 °C), demonstrating the desorption of the fluorescent dye from the surfaces of the C16 alkane droplets suspended in an aqueous SHS solution. The fluorescent patterns formed during the desorption of the dye on cooling are disordered, contrasting with the highly ordered icosahedrally symmetric patterns forming in the heating scans. Once dye desorption from the droplets’ surfaces is complete, we turn on white-light illumination, demonstrating the droplets’ self-faceting transition10,15,17 (see the labels). In this regime, the droplets appear dark on a brighter background. The scanning rate is ~0.8 °C min–1; note the pauses in the video. The cooling scan transitions occur at slightly lower temperatures than Tu and Tp, demonstrating a possible barrier for dye desorption.

Supplementary Video 2

A confocal microscopy scan along the optical axis (‘z stack’), demonstrating optical slices through the pattern-decorated droplet at different heights (see the labels). A 3D reconstruction is shown in the inset, where the z position of the current slice is shown for each frame. Since the fluorescent dye adsorbs only to the 12 icosahedrally positioned patches, the spherical oil droplet (drawn in blue in the inset) is invisible by fluorescence microscopy. The 12 fluorescent patches are maximally separated on the surface of the droplet with their centres positioned at the vertices of an imaginary sphere-inscribed icosahedron. The five-fold symmetry of the pattern, which is clearly visible at z = 9.9 and 24.3 μm, is the fingerprint of such an arrangement. The scales in the inset are in micrometres. Note that due to the elongation of the confocal point-spread function along the z axis, the reconstructed fluorescent patches appear substantially elongated along this axis, whereas their true shape is rounded. The oil is the C16 alkane, fluorescent dye is flC12OH and continuous phase is 40% (w/w) glycerol in aqueous SHS solution. The introduction of glycerol considerably slows down the droplets’ spatial diffusion, providing better z-stack collection. Although the addition of glycerol does not change the patterns, it slightly shifts all the transition temperatures.

Supplementary Video 3

Heating temperature scan, demonstrating the transitions in flC12OH-stained C16 alkane droplets suspended in an aqueous SHS solution. At low T, the droplets are faceted, with two triangular platelet-like and several rod-like liquid droplets clearly visible10,15,17. In this regime, the fluorescent dye resides in the aqueous phase, its concentration being too low to observe by fluorescence microscopy. To visualize the droplets, we turn on white-light illumination and carry out the imaging employing transmitted light, yielding slightly darker droplets than the background. On heating to T ≈ 29 °C, where the dye starts adsorbing onto the droplets, the white light is turned off and only the fluorescent patches are visible. On further heating, the icosahedrally symmetric 12 patch patterns are formed on all the droplets, then grow and finally coalesce at T = Tu, yielding uniform fluorescence of the full droplet’s surface. Note the slight variation in the focus depth at T ≈ 31 °C.

Supplementary Video 4

Computer simulations of pattern formation on spherical droplets. The left panel shows the zero line tension (γL = 0); right panel, γL/YR = 2.3 × 10−4, where R is the radius of the droplet and Y is the 2D extensional Young modulus. The surface-adsorbing fluorophore is coloured in orange and the droplet, black. The frames show the simulated minimum-energy state for each value of the adsorption energy Δγ/Y (see the label on top).

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Das, S., Butenko, A.V., Mastai, Y. et al. Topology-driven surface patterning of liquid spheres. Nat. Phys. 18, 1177–1180 (2022). https://doi.org/10.1038/s41567-022-01705-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41567-022-01705-w

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