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Shape Selection in thin films: from liquid-crystal elastomers to self-assembled aggregates

Banff International Research Station for Mathematical Innovation and Discovery

Throughout the science of soft matter, there are many examples of thin films that form complex curved structures. Examples range from liquid-crystal elastomers on the cen- timeter length scale, to self-assembled aggregates of lipid molecules or lyotropic liquid crystals on the micron or submicron scale. Theorists have often addressed these struc- tures through separate approaches that are applicable to each case. In recent years, there has been extensive theoretical and experimental work on elastic sheets, which has led to a unified approach to describe shape selection problems. This approach is based on a target metric tensor for 3D bodies, which implies target metric and curvature tensors for thin (effectively 2D) sheets. The purpose of this talk is to apply that unified approach to liquid crystals. In particular, we consider: (1) Nematic elastomer films with director gradients in the 2D plane, (2) Nematic elastomer films with director gradients across the thickness, (3) Lyotropic liquid crystals with spontaneous curvature (splay), (4) Lyotropic liquid crystals with intrinsic chiral twist, (5) Lyotropic liquid crystals with bend flexo- electricity. In all of these cases, we discuss how the observed shapes can be understood in terms of the target metric and target curvature.

Mathematics; Mechanics of deformable solids; Statistical mechanics, structure of matter; Mathematical physics

video/mp4

Author affiliation: Kent State University

2017-03-08

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/60817

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/