Tunable three-dimensional architecture of nematic disclination lines.

Disclination lines play a key role in many physical processes, from the fracture of materials to the formation of the early universe. Achieving versatile control over disclinations is key to developing novel electro-optical devices, programmable origami, directed colloidal assembly, and controlling active matter. Here, we introduce a theoretical framework to tailor three-dimensional disclination architecture in nematic liquid crystals experimentally.

Energetics of topographically designed Smectic-A oily streaks.

A thin Smectic-A liquid crystal (LC) film is deposited on a polymer vinyl alcohol-coated substrate that had been scribed with a uniform easy axis pattern over a square of side length ≤ 85 μm. The small size of the patterned region facilitates material distribution to form either a hill (for a thin film) or divot (for a thick film) above the scribed square and having an oily streak (OS) texture. Optical profilometry measurements film thickness suggest that the OS structure aims to adopt a preferred thickness that depends on the nature of the molecule, the temperature, and the surface tension at the air interface.

Shape Morphing of Planar Liquid Crystal Elastomers.

We consider planar liquid crystal elastomers: two-dimensional objects made of anisotropic responsive materials that remain flat when stimulated, however change their planar shape. We derive a closed form, analytical solution based on the implicit linearity featured by this subclass of deformations. Our solution provides the nematic director field on an arbitrary domain starting with two initial director curves.

Curved Geometries from Planar Director Fields: Solving the Two-Dimensional Inverse Problem.

Thin nematic elastomers, composite hydrogels, and plant tissues are among many systems that display uniform anisotropic deformation upon external actuation. In these materials, the spatial orientation variation of a local director field induces intricate global shape changes. Despite extensive recent efforts, to date there is no general solution to the inverse design problem: How to design a director field that deforms exactly into a desired surface geometry upon actuation, or whether such a field exists.

Twist renormalization in molecular crystals driven by geometric frustration.

Symmetry considerations preclude the possibility of twist or continuous helical symmetry in bulk crystalline structures. However, as has been shown nearly a century ago, twisted molecular crystals are ubiquitous and can be formed by about 1/4 of organic substances. Despite its ubiquity, this phenomenon has so far not been satisfactorily explained.

Universal inverse design of surfaces with thin nematic elastomer sheets.

Programmable shape-shifting materials can take different physical forms to achieve multifunctionality in a dynamic and controllable manner. Although morphing a shape from 2D to 3D via programmed inhomogeneous local deformations has been demonstrated in various ways, the inverse problem-finding how to program a sheet in order for it to take an arbitrary desired 3D shape-is much harder yet critical to realize specific functions. Here, we address this inverse problem in thin liquid crystal elastomer (LCE) sheets, where the shape is preprogrammed by precise and local control of the molecular orientation of the liquid crystal monomers.

The smectic order of wrinkles.

A thin elastic sheet lying on a soft substrate develops wrinkled patterns when subject to an external forcing or as a result of geometric incompatibility. Thin sheet elasticity and substrate response equip such wrinkles with a global preferred wrinkle spacing length and with resistance to wrinkle curvature. These features are responsible for the liquid crystalline smectic-like behaviour of such systems at intermediate length scales.

Composite Dislocations in Smectic Liquid Crystals.

Smectic liquid crystals are characterized by layers that have a preferred uniform spacing and vanishing curvature in their ground state. Dislocations in smectics play an important role in phase nucleation, layer reorientation, and dynamics. Typically modeled as possessing one line singularity, the layer structure of a dislocation leads to a diverging compression strain as one approaches the defect center, suggesting a large, elastically determined melted core.

Internal Stresses Lead to Net Forces and Torques on Extended Elastic Bodies.

A geometrically frustrated elastic body will develop residual stresses arising from the mismatch between the intrinsic geometry of the body and the geometry of the ambient space. We analyze these stresses for an ambient space with gradients in its intrinsic curvature, and show that residual stresses generate effective forces and torques on the center of mass of the body. We analytically calculate these forces in two dimensions, and experimentally demonstrate their action by the migration of a non-Euclidean gel disc in a curved Hele-Shaw cell.

Geometry and mechanics of two-dimensional defects in amorphous materials.

We study the geometry of defects in amorphous materials and their elastic interactions. Defects are defined and characterized by deviations of the material's intrinsic metric from a Euclidian metric. This characterization makes possible the identification of localized defects in amorphous materials, the formulation of a corresponding elastic problem, and its solution in various cases of physical interest.

Geometry of thin nematic elastomer sheets.

A thin sheet of nematic elastomer attains 3D configurations depending on the nematic director field upon heating. In this Letter, we describe the intrinsic geometry of such a sheet and derive an expression for the metric induced by general nematic director fields. Furthermore, we investigate the reverse problem of constructing a director field that induces a specified 2D geometry.

Shape selection in chiral ribbons: from seed pods to supramolecular assemblies.

We provide a geometric-mechanical model for calculating equilibrium configurations of chemical systems that self-assemble into chiral ribbon structures. The model is based on incompatible elasticity and uses dimensionless parameters to determine the equilibrium configurations. As such, it provides universal curves for the shape and energy of self-assembled ribbons.

Emergence of spontaneous twist and curvature in non-euclidean rods: application to Erodium plant cells.

We present a limiting model for thin non-euclidean elastic rods. Originating from the three-dimensional (3D) reference metric of the rod, which is determined by its internal material structure, we derive a 1D reduced rod theory. Specifically, we show how the spontaneous twist and curvature of a rod emerge from the reference metric derivatives.

Direct observation of the temporal and spatial dynamics during crumpling.

Crumpling occurs when a thin deformable sheet is crushed under an external load or grows within a confining geometry. Crumpled sheets have large resistance to compression and their elastic energy is focused into a complex network of localized structures. Different aspects of crumpling have been studied theoretically, experimentally and numerically.