Leader: Gareth Alexander, University of Warwick, United Kingdom

Co-leader: Slobodan Zumer, University of Ljubljana, Slovenia

General overview. Topological defects in a bulk orientational field in liquid crystals (LC) appear as unstable structural imperfections in the form of defect points, lines, or closed loops. They are stabilized by a frustration due to the competing effect of chirality (blue phases), or by the presence of complex confining geometries like colloidal dispersions or by the inclusion of the LC in confining matrices (thin layers, drops, shells). From the materials perspective, a recent major result in liquid crystals is that multiple micro, sub-micro, and nano-structures with unique properties have been experimentally realised, including 1D, 2D, 3D nematic colloidal crystals, disclination entangled structures, field and material micro-knots, optically imprinted states, and confinement & chirality conditioned defect structures. These new soft superstructures based on LCs are fundamentally topological in nature and their stability is based on minimization of elastic deformations of the LC’s molecular order. This supports self-assembly properties and high resistance of micron scale structures against thermal fluctuations. Such complex constructs in liquid crystals are strongly birefringent and are characterized by the spatial variation of their birefringence, typically at optical wavelengths. All this has triggered immense interest and potential for soft photonic applications.

General objectives of WG5. Understanding how to design and build topological superstructures in liquid crystals will have a deep and broad impact both in general physics, for example by solving the problem of the appearance of skyrmions, and in multidisciplinary applications like photonics, sensorics, fluidics, and biophysics. This is however a quite hard problem, and emphasis on the simplest model systems will be crucial here, as well as the seamless integration of simulation, theory and experiments.

Within the EUTOPIA COST Action this ambitious challenge can be achieved by pursuing the following goals:

1. Find the physical conditions that drive the formation of knotted/linked defects in blue phases.
2. Understand how molecular anchoring at the surfaces can control the amount and topology of defects (e.g. skyrmions) in thin layers.
3. Combine the topology and geometry of defects with more general frustration effects in LCs to design multi-scale tunable photonic superstructures.
4. Understand the formation and the dynamics of complex topological structures in active structured fluids such as cell extracts, cytoskeletal gels and microtubule-kinesin suspensions.

Specific tasks of WG5.
 This WG aims to systematically examine possible mechanisms that lead to the formation and stabilization of complex topological soft matter superstructures in passive and active complex fluids (e.g. liquid crystals). In order to achieve these goals, the following tasks have been identified:

1. Establish a unified definition and characteristics of topological superstructures generated and stabilized in the molecular orientational field of complex fluids by frustration. Map analogies and differences between topological structures from various experiments and theoretical models, and investigate their transitions and reconfiguration kinetics.
2. Cross-fertilization of ideas and knowledge exchange regarding topological aspects of liquid crystals between the research groups working on passive and active liquid crystals.
3. Stabilization of particular inhomogeneous ordering patterns (including defects) in chiral and achiral liquid crystals for potential use in photonics.
4. Promote the understanding of highly frustrated superstructures with numerous metastable states and convoluted energy landscapes, by bringing together analytical and modelling approaches.
5. Design optical and electrical fields and flows to directly induce complex defect structures, including linking and knotting in nematic fluids.

Deliverables: STSMs within the WG and to other WGs. At least one article with 3 international members per each task. Establishment of collaborations with industrial partners.