Topological surprises in channel-confined nematic flow

Chiral order can emerge in intrinsically achiral liquid crystal flows driven by pressure gradients in microfluidic confinement.

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Microscopic structure of materials leaves tell-tale traces in their macroscopic behaviour, which reveal a remarkable wealth of information at a first glance. For solid crystals, the type of the crystal lattice can be deduced from the shape of large monocrystals, without expensive X-ray machinery or microscopes with atomic resolution. In different phases of liquid crystals, the microscopic organization of anisotropic molecules is betrayed by distinctive optical features – defects surrounded by dark brushes in nematic Schlieren texture, fingerprint-like textures of chiral liquid crystals, or focal conic domains in smectics. These features reflect the topological restrictions of the local order: the molecules can arrange in different equally favorable ways (multiple ground states), and defects arise when these ground states cannot be stitched together.

In Emeršič et al. [1], we investigated the flow of a nematic liquid crystal, when pushed through narrow microfluidic channels. In the channels, treated to prefer molecular alignment perpendicular to the surface, the structure is uniformly aligned in the absence of flow, and only when the flow velocity exceeds a certain threshold, the structure changes to a flow-aligned state, which is seen under the polarized light microscope as a separate domain, also the main focus of the study.

Working with liquid crystals, one gets used to visual recognition of domains as different ground states, and domain walls as defect-like structures, which is why this image took us by surprise:

In the oval-shaped flow-aligned domain, observing a Schlieren-like texture with defects and solitons is expected, as this state has a full circle of possible orientations with no way of unwinding full 360-degree turns. Outside the flow-aligned domain, the structure was supposed to be topologically trivial, that is, every point on the picture should be only a smooth continous deformation away from the structure in any other point. And yet, under certain flow conditions, a clearly visible soliton was observed outside the flow-aligned domain, too. Seeing separation of two domains by a visually distinctive domain wall down the middle, contrary to the expectations, indicated existence of two equal-energy ground states. The domain wall between them is energetically unfavourable by the liquid crystal, but is topologically protected and unable to shrink and disappear. Thus, the image not only provided us with a mystery, but gave us the clues to solve it. In our latest study [2], we show this to be a result of chiral symmetry breaking, creating left- and right-handed domains in the flow.

Non-newtonian and anisotropic liquids can adopt new behaviours when set in motion, with transitions between different dynamical regimes closely resembling thermodynamic phase transitions. Many biological liquids and engineered materials are anisotropic in nature, and may also allow this emergent topological separation into topologically protected chiral domains.

This blog was prepared by Simon Čopar and Uroš Tkalec.

[1] T. Emeršič, R. Zhang, Ž. Kos, S. Čopar, N. Osterman, J. J. de Pablo and U. Tkalec, Sculpting stable structures in pure liquids, Science Advances 5, eaav4283 (2019).

[2] S. Čopar, Ž. Kos, T. Emeršič and U. Tkalec, Microfluidic control over topological states in channel-confined nematic flows, Nature Communications 11, 59 (2020).

Uroš Tkalec

Assistant Professor of Physics, University of Ljubljana