# Molecular heterogeneity drives reconfigurable nematic liquid crystal drops

## Abstract

With few exceptions1,2,3, polydispersity or molecular heterogeneity in matter tends to impede self-assembly and state transformation. For example, shape transformations of liquid droplets with monodisperse ingredients have been reported in equilibrium4,5,6,7 and non-equilibrium studies8,9, and these transition phenomena were understood on the basis of homogeneous material responses. Here, by contrast, we study equilibrium suspensions of drops composed of polydisperse nematic liquid crystal oligomers (NLCOs). Surprisingly, molecular heterogeneity in the polydisperse drops promotes reversible shape transitions to a rich variety of non-spherical morphologies with unique internal structure. We find that variation of oligomer chain length distribution, temperature, and surfactant concentration alters the balance between NLCO elastic energy and interfacial energy, and drives formation of nematic structures that range from roughened spheres to ‘flower’ shapes to branched filamentous networks with controllable diameters. The branched structures with confined liquid crystal director fields can be produced reversibly over areas of at least one square centimetre and can be converted into liquid crystal elastomers by ultraviolet curing. Observations and modelling reveal that chain length polydispersity plays a crucial role in driving these morphogenic phenomena, via spatial segregation. This insight suggests new routes for encoding network structure and function in soft materials.

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## Data availability

The authors declare that the data supporting the findings of this study are available within the text, including the Methods section, and Extended Data files. Raw data are available from the corresponding author upon reasonable request.

## Code availability

Custom computer codes associated with modelling in this study are available on GitHub (https://github.com/wei-shao-wei/Molecular-heterogeneity-induces-reconfigurable-nematic-liquid-crystal-drops).

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## Acknowledgements

We thank the following for discussions: K. B. Aptowicz, C.-C. Chang, P. J. Collings, A. de la Cotte, Z. S. Davidson, R. Dreyfus, P. Habdas, A. Hill, Y.-Y. Ho, R. D. Kamien, J. Jeong, T. C. Lubensky, X. Ma, A. Martinez, C. K. Mishra and P. Palffy-Muhoray. A. Soleymannezhad and J. Timmons (Tosoh Bioscience) assisted with SEC operation and analysis. We acknowledge financial support from the National Science Foundation (grant no. DMR16-07378), the Materials Research Science & Engineering Center (MRSEC) at University of Pennsylvania (grant no. DMR-1720530) including MRSEC’s Optical Microscopy and Electron Microscopy Shared Experimental Facility, and NASA (grant no. 80NSSC19K0348).

## Author information

W.-S.W., Y.X., S.Y. and A.G.Y. conceived the idea and designed the experiments. W.-S.W., Y.X. and S.E. initiated and performed the experiments. W.-S.W., Y.X., S.E., S.Y. and A.G.Y. worked on different facets of the data analysis. W.-S.W. and A.G.Y. wrote the paper, and all authors contributed to the final manuscript.

Correspondence to Wei-Shao Wei.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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

Peer review information Nature thanks Kari Dalnoki-Veress, Stoyan Smoukov and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

## Extended data figures and tables

### Extended Data Fig. 1 Distribution of chain length and molecular weight of NLCO samples measured by size exclusion chromatography.

a, The NLCO source samples are shown by size exclusion chromatography (SEC) to be a mixture of monomers, dimers, trimers, tetramers and other oligomers (blue solid line; peaks appearing at longer retention times represent shorter chain lengths). In step-polymerization processes, when the extent of reaction is less than 0.9, monomers dominate the overall molar fraction. For comparison, liquid crystal (LC) macromers (used in the supporting experiment in Methods) synthesized following the schemes of Ware et al.10 are also included in the plot; these show longer mean chain length and very few (if any) short-chain components (red dashed line). Furthermore, since our system is made in an aqueous solution, the polymerization rate is expected to be slower. For reference, the black dotted line shows the peak for pure RM82 monomer. b, Calculated from SEC data (example in a), the number-average molecular weight ($${\bar{M}}_{{\rm{n}}}$$, blue solid squares) and polydispersity index (PDI, red filled circles) of the NLCOs are shown as function of oligomerization time. Both $${\bar{M}}_{{\rm{n}}}$$ and PDI increase with oligomerization time. The dotted (for $${\bar{M}}_{{\rm{n}}}$$) and dashed (for PDI) curves are to guide the eye. (For comparison, the LC macromer synthesized following the schemes of Ware et al.10 and used in Methods section ‘Macromer–monomer mixing experiments’ has $${\bar{M}}_{{\rm{n}}}\approx \text{6,900}\,{\rm{D}}{\rm{a}}$$ and PDI ≈ 1.3.) Bars indicate the spread in $${\bar{M}}_{{\rm{n}}}$$, which mainly arises from our inability to detect the longer-chain components.

### Extended Data Fig. 2 Bright-field optical microscopy images showing reversible shape transitions of NLCO drops during temperature cycling.

ac, When temperature is increased from room temperature (20 °C) to a higher value (here 90 °C), the NLCO filamentous structures reversibly evolve into spherical microdroplets. ce, When cooled from 90 °C to 20 °C, the spherical microdroplets reversibly evolve back into filamentous structures. The drop morphology can be transformed repeatedly, remaining quantitatively similar. Here, multiple small drops evolve in the field of view; data shown earlier (Fig. 1c–h) showed only one large evolving drop. Scale bar in a (for all panels), 20 μm.

### Extended Data Fig. 3 Macroscopic interfacial tension of NLCO pendant drops as function of temperature and NLCO oligomerization time.

The NLCO drop has homeotropic anchoring at the interface in an aqueous solution consisting of 0.1 wt% SDS. The interfacial tension γ decreases with decreasing temperature and increasing NLCO mean oligomer chain length (consult Fig. 2f for the relation between oligomerization processing time and ). Inset, optical image of a NLCO pendant drop hanging from a flat-tip syringe needle (1.26 mm outer diameter) in a 0.1 wt% SDS aqueous solution. The dashed curves are to guide the eye.

### Extended Data Fig. 4 Bright-field optical microscopy images of drop morphologies obtained from mixtures of macromers (⟨ℓ⟩ ≈ 9) and monomers (RM82) at different weight ratios in a 0.1 wt% SDS aqueous solution after cooling.

ae, Images for monomer:macromer weight ratios of 1:0.3, 1:0.5, 1:0.7, 1:0.9 and 1:1, respectively. With a fixed amount of RM82, increasing the concentration of macromers in the drop leads to longer , larger bulk elasticity and lower interfacial tension. The last two factors favour interfacial roughening and filament formation. Images are taken at room temperature after cooling. Scale bar in a (for all panels), 50 μm.

### Extended Data Fig. 5 Bright-field optical microscopy images of NLCO structures in aqueous solutions of different surfactants as a function of the mean oligomer chain length, ⟨ℓ﻿⟩.

af, NLCO drops in aqueous solutions with different surfactants, that is, with either cationic (ac; hexadecyltrimethylammonium bromide, C16TAB) or nonionic (df, Polysorbate 20, Tween 20) surfactants. These systems exhibit a drop morphology evolution similar to that resulting from SDS, that is, with respect to cooling and an increase of . After cooling from 90 °C to 20 °C, a representative NLCO drop in a 0.5 mM C16TAB aqueous solution (below the CMC; ac) and a representative NLCO drop in a 0.03 mM Tween 20 aqueous solution (below the CMC; df). Both evolve with increasing (left to right; consult Fig. 2f for the relation between the oligomerization time (shown at bottom left in all panels) and ). For this behaviour to be shown, it is important that NLCOs should favour homeotropic anchoring at the drop interface. Images are taken at room temperature. Scale bars in af, 20 μm.

### Extended Data Fig. 6 Bright-field optical microscopy image of aggregated NLCO filamentous structures for an SDS concentration above the CMC.

In a 1 wt% SDS aqueous solution (shown here), the NLCO drops exhibit a similar but more complicated shape transition behaviour than that which occurs below the CMC, after cooling from 90 °C to 20 °C. For example, aggregated filamentous structures form and sometimes stick to the substrate due, in part, to micelle-induced depletion. (For comparison, expanded filamentous structures form in aqueous solutions below the CMC, see example in Fig. 1h.) Scale bar, 20 μm.

### Extended Data Fig. 7 Self-assembled NLCE fibrous mat.

NLCE fibres can be densely packed into centimetre-wide and few-micrometres-thick, non-woven, free-standing mats by sedimentation. Here we show an image of such a mat (mounted on a hollowed holder) with a diameter greater than 1 cm. Corresponding high-magnification SEM images of this mat are shown in Fig. 4e, f.

## Supplementary information

### Supplementary Video 1 | Spontaneous shape transition of NLCO drop during cooling

At high temperature (~40 °C, 00:00:00), the suspended NLCO drop is spherical. Upon cooling, the drop destabilizes and spontaneously evolves from a sphere to a filamentous structure (01:00:00 roughening starts at ~37 °C; 11:00:00 short filaments form at ~30 °C; 26:00:00 long filaments form at ~26 °C). Images are taken between crossed-polarizers with a full-wave retardation plate. This scheme permits visualization of director fields (yellow indicates northwest–southeast alignment; cyan indicates northeast–southwest alignment). Scale bar is 15 μm. The video is sped up by 100×. The focal plane is occasionally adjusted to keep filaments in focus.

### Supplementary Video 2 | Reversible shape transitions of small NLCO drops during temperature cycling

Multiple small NLCO drops are shown in the field-of-view in bright-field microscopy. At the beginning of the video, equilibrium NLCO filamentous structures are intertwined with their neighbors at low temperature (~25 °C). As the temperature increases to 60 °C, the NLCO filamentous structures reversibly evolve back into spherical micro-droplets. Then, during recooling, the micro-droplets evolve back into filamentous structures. The temperature cycling and corresponding morphology changes are repeatable. Scale bar is 20 μm. The video is sped up by 20×.

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Wei, W., Xia, Y., Ettinger, S. et al. Molecular heterogeneity drives reconfigurable nematic liquid crystal drops. Nature 576, 433–436 (2019). https://doi.org/10.1038/s41586-019-1809-8