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Multistable polar textures in geometrically frustrated nematic liquid crystals

Abstract

The ability to manipulate polar entities with multiple external fields could enable functionalities and applications in spin systems, photonics, metamaterials and soft matter. Liquid crystals that exhibit both a crystalline structure and liquid fluidity represent a promising platform for manipulating phases with polar molecular order, notably ferroelectric ones. However, achieving a polar symmetry is challenging with rod-shaped liquid crystal molecules, which form predominantly apolar nematic phases. Here we report an approach in which a geometric lattice confinement of nematic liquid crystals is used to induce planar polar order on the scale of a mesoscopic metamaterial. We confine the nematic liquid crystal in a micropillar array, forming topological defect–pillar pairs of elastic dipoles with a free top interface in contact with an immiscible fluid. The resulting dipole lattice configurations can be programmed rheologically by flowing the top fluid and maintained even after flow cessation, a phenomenon attributed to orientational multistability of the dipoles. This multimemory effect enables the encoding and reconfiguration of directional information. Overall, these results advance our understanding of topological dipoles under confinement and shear flow, enabling the detection, tracking and recording of flow profiles and could facilitate the development of stimuli-responsive materials.

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Fig. 1: Elastic dipoles in micropillar-array-confined LCs.
Fig. 2: Elastic dipole configuration induced by droplet placement and removal.
Fig. 3: Dipole reorientation induced by interfacial droplet motion.
Fig. 4: Microcantilever encoding of dipole orientation.

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The data presented in this Article are available from the corresponding authors upon reasonable request.

Code availability

Simulation code is available from the corresponding authors upon reasonable request.

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Acknowledgements

This work is supported by NSF CMMI-2227991 (X.W.), the start-up fund of The Ohio State University (OSU) (X.W.) and OSU Materials Research Seed Grant Program, funded by the Center for Emergent Materials, an NSF-MRSEC, grant number DMR-2011876, the Center for Exploration of Novel Complex Materials, and the Institute for Materials Research (X.W.). S.Č. and U.T. acknowledge the support of the Slovenian Research and Innovation Agency (ARIS) through grant numbers P1-0055, P1-0099, J1-50006, J2-50092 and BI-US/24-26-087. R.L.B.S. acknowledges support from the United States–Israel Binational Science Foundation through grant number 2022197.

Author information

Authors and Affiliations

Authors

Contributions

U.I.K., B.C., S.Č., U.T. and X.W. conceived and designed the experiments, as well as lead the paper writing. U.T. and X.W. supervised the experiments. S.L. and Y.Y. fabricated the Si microstructure arrays, U.I.K., B.C., R.M., Y.X., A.H.W., E.B. and Z.Y. conducted microstructure functionalization, polarized light microscopy characterization and data collection. S.Č. conducted the numerical modelling of the nematic LC director profile and accessible polar states. R.L.B.S. conducted numerical simulation of the simplified XY model of dipole relaxation to metastable states. All authors contributed to data interpretation, discussions and paper preparation. U.I.K., B.C. and S.Č. contributed equally to this work.

Corresponding authors

Correspondence to Uroš Tkalec or Xiaoguang Wang.

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Nature Physics thanks Jordan Hobbs, Liana Lucchetti and Victor Reshetnyak for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Orientation of LCs confined in unfunctionalized Si micropillar arrays.

a,b, Polarized light micrographs of unfunctionalized micropillar array-confined LCs for (a) air (homeotropic) and (b) water (planar) on the top interface. LCs exhibit degenerate planar anchoring on unfunctionalized Si surfaces. Dewetting of LCs by water was observed in the bottom right region of panel (b). (c) Polarized light micrograph (transmission mode) showing Schlieren textures of LCs confined within a Cu grid on a dimethyl-octadecyl [3-(trimethoxysilyl) propyl] ammonium chloride (DMOAP) silane-functionalized glass slide under pure water, confirming degenerate planar anchoring at the water−LC interface. Crossed, double-headed arrows indicate the direction of the crossed polarizers.

Extended Data Fig. 2 Elastic dipole orientation underneath water films.

a, Color wheel indicating the six distinct orientations of elastic dipoles. Each color corresponds to a specific location of point defects in relation to the micropillar area. b, c, Percentage distribution of elastic dipole orientation beneath a water film (b) after the nematic−isotropic−nematic transition of LCs following the introduction of the water film and (c) after sliding the water film towards 6 o’clock, with the LC in its nematic phase. The histogram colors correspond to the elastic dipole orientations as defined in (a). Insets in (b) and (c) depict the distribution of micropillars in terms of defect association: no associated defects (vacancies), one associated defect, and two associated defects (double occupancy). The displayed percentages are based on analyses of 1,012 micropillars in (b) and 586 micropillars in (c) across 6 independent experiments. Error bars represent standard deviations from 6 independent measurements.

Extended Data Fig. 3 Effect of micropillar spacing on the orientation of elastic dipoles.

Polarized light micrographs showing LCs confined in a micropillar array with pillar pitch of (a–c) 50 µm and (d–i) 100 µm, observed (a, d) in the air and (b,c,e-i) under a water droplet. Micrographs were captured (b,f) after the nematic−isotropic−nematic transition, (e) immediately after water droplet placement, and (c,g-i) after sliding the water droplet towards (c,g) 6 o’clock, (h) 8 o’clock and (i) 7 o’clock. Single-headed arrows indicate the orientation of elastic dipoles, with the arrow color representing the orientation defined in Extended Data Fig. 2a. White disks represent the vacancies (micropillars without an associated defect). In (b), yellow single-headed arrows indicate half-integer charge defects. In (e,i), white single-headed arrows show elastic dipole orientation towards 3, 7 and 9 o’clock, not covered by the six orientations defined in Extended Data Fig. 2a. Crossed double-headed arrows indicate the direction of the crossed polarizers.

Extended Data Fig. 4 Orientation of elastic dipoles in a square lattice micropillar array.

Polarized light micrographs alongside a numerical model sketch showing LCs confined within a square lattice micropillar array (a) in the air or (b-d) under a water droplet. Micrographs were captured (b) after the nematic−isotropic−nematic transition, (c) immediately after water droplet placement, and (d) after sliding the water droplet towards 6 o’clock. Single-headed arrows indicate the orientation of elastic dipoles, with the arrow color representing the orientation: blue, 3 o’clock; red, 6 o’clock; orange, 9 o’clock; and green, 12 o’clock. White disks indicate the vacancies. Crossed, double-headed arrows indicate the direction of the crossed polarizers.

Extended Data Fig. 5 Effect of water droplet sliding angle on elastic dipole orientation.

a, Percentage distribution of elastic dipole orientation under a sliding water droplet at different angles (θ) relative to the hexagonal lattice. The percentages in (a) were calculated from the analysis of at least 800 micropillars per measurement in 21 independent measurements. Each error bar represents standard deviations from 3 independent measurements. b, Representative polarized light micrograph depicting elastic dipoles underneath a water droplet as it slides at a 30° deviation from the hexagonal lattice, revealing a polydomain pattern with dipoles orienting towards the two nearest lattice angles. Sliding at other intermediate angles results in a monodomain, where dipoles align with the nearest lattice angle. Single-headed arrows indicate the orientation of elastic dipoles, with the arrow color representing the orientation as defined in Extended Data Fig. 2a. Crossed, double-headed arrows indicate the direction of the crossed polarizers. The color of the histogram indicates the elastic dipole orientation as defined in Extended Data Fig. 2a.

Extended Data Fig. 6 Dipole reorientation induced by air bubble sliding.

Schematic and polarized light micrographs showing the creation of striped domains by a sliding air bubble underwater on an LC surface with uniformly aligned dipoles. Bubble sliding in the direction of the dipole alignment leads to net zero total rotation from left to right while sliding against the dipolar alignment causes a full 360o rotation (a double Néel wall). Single-headed arrows indicate the orientation of elastic dipoles, with the arrow color representing the orientation as defined by Extended Data Fig. 2a. Crossed, double-headed arrows indicate the direction of the crossed polarizers.

Extended Data Fig. 7 Repeatability and hysteresis in dipole reorientation.

a, Scheme illustrating the conceptual framework for information writing and erasing. b,c, Percentage distribution of dipole orientation beneath a water film, analyzed based on (b) the number of isotropic−nematic LC transitions and (c) isotropic−nematic transition of LCs, followed by the directional sliding of the water film towards 6 o’clock with the LC in its nematic phase. d, Scheme illustrating the conceptual framework for information overwriting. e, Sliding distance of the top glass plate to align dipoles towards a 6 o’clock orientation, depending on their initial orientation. f, Percentage distribution of dipole orientation beneath a water film after alternating the direction of the water film sliding between 6 and 12 o’clock. The dipole orientation in (b,c,e,f) is indicated by the color of the histogram as defined in Extended Data Fig. 2a. The displayed percentages are based on analyses of at least 480 micropillars per cycle in (b,c,f). Error bars represent standard deviations from 3 independent measurements.

Extended Data Fig. 8 Microfluidic flow-induced reorientation of elastic dipoles.

a, Design and dimension of microfluidic chamber. b, Polarized light micrographs showing elastic dipoles of micropillar array-confined LCs in a microfluidic chamber. A water flow towards 3 o’clock is applied. Single-headed arrows indicate the orientation of elastic dipoles, with the arrow color representing the orientation as defined by Extended Data Fig. 2a. White single-headed arrows represent the orientation of elastic dipoles towards 3 o’clock, excluding the six regions defined in Extended Data Fig. 2a. Crossed, double-headed arrows indicate the direction of the crossed polarizers.

Extended Data Fig. 9 Dipole reconfiguration induced by underwater streaming.

a, Schematic depiction of the underwater streaming experiment. b, Polarized light micrographs of the domain walls created by underwater streaming. Single-headed arrows indicate the orientation of elastic dipoles, with the arrow color representing the orientation as defined in Extended Data Fig. 2a. Crossed, double-headed arrows indicate the direction of the crossed polarizers. In this experiment, a global underwater flow was first applied to pre-align the dipoles, followed by a localized underwater streaming to selectively reorient dipoles in specific regions. This approach resulted in the formation of bidomain structures that cannot be achieved through droplet collision alone, notably without the emergence of Ising or Néel walls, as discussed in Fig. 3b of the main text.

Extended Data Fig. 10 Cantilever encoding of dipole orientation.

a, Polarized light micrograph and numerical model illustrating spiral-pattern dipole orientation. b, Polarized light micrographs show representative straight-line arrays of dipoles (Supplementary Movie 6). Dipoles are preset to 6 o’clock. Single-headed arrows indicate the orientation of elastic dipoles, with the arrow color representing the orientation as defined in Extended Data Fig. 2a. White disks indicate the vacancies (micropillars without an associated defect). Crossed, double-headed arrows indicate the direction of the crossed polarizers.

Supplementary information

Supplementary Information

Supplementary Notes 1–4 and captions for Supplementary Movies 1–7.

Supplementary Movie 1

Randomizing dipole orientations through nematic-to-isotropic phase transition.

Supplementary Movie 2

Numerical simulation of simplified XY model for dipole relaxation.

Supplementary Movie 3

Soliton-directed monopole migration.

Supplementary Movie 4

Monopole migration and annihilation via soliton pathways.

Supplementary Movie 5

Monodomain alignment via water film shearing.

Supplementary Movie 6

Water flow-induced dipole alignment in microfluidics.

Supplementary Movie 7

Cantilever-driven dipole manipulation in LC systems.

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Kara, U.I., Chen, B., Čopar, S. et al. Multistable polar textures in geometrically frustrated nematic liquid crystals. Nat. Phys. 21, 1404–1411 (2025). https://doi.org/10.1038/s41567-025-02966-x

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