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Topology-driven surface patterning of liquid spheres


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.

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

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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.


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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.

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

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Correspondence to Eli Sloutskin.

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

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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).

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Das, S., Butenko, A.V., Mastai, Y. et al. Topology-driven surface patterning of liquid spheres. Nat. Phys. 18, 1177–1180 (2022).

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