Topological soft matter: from liquid crystals to active matter
Gulliver Lab, The French National Centre for Scientific Research (CNRS),
10 Rue Vauquelin 75231 Paris
École Supérieure de Physique et de Chimie Industrielles de Paris (ESPCI)
10 Rue Vauquelin, 75005 Paris
Summary:
The last few decades have witnessed remarkable advances in our understanding of how topological constraints impact biological and soft matter, thanks to the integration of increasingly sophisticated experiments and numerical simulations. Fascinating behaviors have been seen to emerge in ordered systems, where topological constraints and geometrical frustration typically prevent the system from reaching its inherent ground state, resulting in complex organizations in which topological defects play a central role. In this course, I will address these questions in the framework of liquid crystals, a unique type of topological soft matter that exhibits partially ordered states with both fluid and crystalline characteristics. I will start by introducing these systems. I will show you their symmetries, physical properties, and the main models to describe them. Then, I will introduce the concepts of geometrical frustration and topological constraints using the example of a spherical shell of liquid crystal. This experimental system will enable me to introduce a variety of topological defects, with increasing complexity, as well as to study different types of defect-defect interactions and interconversions. Finally, I will talk about active nematics, a new class of liquid crystals combining local orientational order and self-sustained flows. In these out-of-equilibrium materials, topological defects behave not only as singularities structuring the material, but also as self-propelling particles orchestrating the system flows.
