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Solid liquid crystals

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The Mathematics of Liquid Crystals

Liquid crystals can become solids when they form glasses or when liquid crystalline polymers are crosslinked to form rubber. They can show properties richer than solids and liquid crystals separately. Glasses have high moduli and their directors are not mobile with respect to the solid matrix. Rubber maintains the molecular mobility of a liquid; it can be deformed hugely, has a low modulus, and its director is mobile. Both can have their order reduced by heat, light and solvent, and then mechanically contract along the director by a few percent (glasses) and by 100s% (rubber). Topological defects in their director fields means that such mechanical response generates Gaussian curvature or topology changes.

Mobile directors respond to imposed strains by reapportioning natural length in directions required by distortions, rendering their energetic cost zero or very small. If necessary textures of such low cost deformations are required to comply with boundary conditions in much the same way as in Martensite. Indeed such techniques of quasi-convexification have been extended by DeSimone et al to complete and generalise the soft mechanics discovered theoretically and experimentally by physicists and chemists.

I shall sketch some of these phenomena and present recent results on the mechanical and topological effect of disclinations in nematic solids, and on how polydomain nematic solids can be super-soft.

This talk is part of the Isaac Newton Institute Seminar Series series.

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