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 centimeter length scale, to self-assembled aggregates of lipid molecules or lyotropic liquid crystals on the micron or submicron scale. Theorists have often addressed these structures 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:
* Nematic elastomer films with director gradients in the 2D plane
* Nematic elastomer films with director gradients across the thickness
* Lyotropic liquid crystals with spontaneous curvature (splay)
* Lyotropic liquid crystals with intrinsic chiral twist
* Lyotropic liquid crystals with bend flexoelectricity
In all of these cases, we discuss how the observed shapes can be understood in terms of the target metric and target curvature.