Flexoelectricity is a coupling between orientational deformation and electric polarization. We present a direct method for measuring the flexoelectric coefficients of nematic liquid crystals (NLCs) via the electric current produced by periodic mechanical flexing of the NLC's bounding surfaces. This method is suitable for measuring the response of bent-core liquid crystals, which are expected to demonstrate a much larger flexoelectric effect than traditional, calamitic liquid crystals. Our results reveal that not only is the bend flexoelectric coefficient of bent-core NLCs gigantic (more than 3 orders of magnitude larger than in calamitics) but also it is much larger than would be expected from microscopic models based on molecular geometry. Thus, bent-core nematic materials can form the basis of a technological breakthrough for conversion between mechanical and electrical energy.

Using both experiments and finite element simulations, we explore the shape evolution of off-axis twist nematic elastomer ribbons as a function of temperature. The elastomers are prepared by cross-linking the mesogens with planar anchoring of the director at top and bottom surfaces with a 90° left-handed twist. Shape evolution depends sensitively on the off-axis director orientation at the sample midplane. Both experiments and theoretical studies show that when the director at midplane is parallel to either the ribbon's long or short axes, ribbons form either helicoids or spirals depending on aspect ratio and temperature. Simulation studies show that if the director at midplane is off-axis, ribbons never form helicoids, instead evolving to distorted spiral shapes. Experimental studies for two samples with off-axis geometry show agreement with this prediction. Samples in all these geometries show a remarkable transition from right- to left-handed chiral shapes on change of temperature. Simulations predict off-axis samples also change their macroscopic chirality at fixed temperature, depending on the angular offset. These results provide insight into the mechanisms driving shape evolution and macroscopic chirality, enabling engineering design of these materials for future applications.

We study, analytically and theoretically, defects in a nematically-ordered surface that couple to the extrinsic geometry of a surface. Though the intrinsic geometry tends to confine topological defects to regions of large Gaussian curvature, extrinsic couplings tend to orient the nematic in the local direction of maximum or minimum bending. This additional frustration is unavoidable and most important on surfaces of negative Gaussian curvature, where it leads to a complex ground state thermodynamics. We show, in contradistinction to the well-known effects of intrinsic geometry, that extrinsic curvature expels disclinations from the region of maximum curvature above a critical coupling threshold. On catenoids lacking an "inside-outside" symmetry, defects are expelled altogether.PACS numbers: 61.30. Dk, 61.30.Jf,61.30.Hn The intrinsic curvature of a surface frustrates the order of materials living upon it, making defects necessary even in the ground state [1]. This frustration derives from the incompatibility of straight and parallel directions on surfaces with Gaussian curvature. A nematic texture on a sphere, for example, must have a net topological charge of +2 [2-4], as do, for example, lines of latitude on the globe. On more complex surfaces with non-uniform intrinsic curvature, the ground-state organization of defects is well-described theoretically by competition between defect-defect interactions, which favor separation of like-charged defects, and curvature-defect interactions, which favor the localization of defects in regions of relatively high Gaussian curvature [5,6]. This picture is far from complete, however, as real surfaces are endowed with an extrinsic geometry that depends in detail on how they sit in space [7][8][9]. Stripes on a curved surface, for example, tend to orient along"flat" directions to minimize their bending energy, an effect observed in block copolymer films [10].In this Letter, we demonstrate that the extrinsic geometry of a surface generates a strong and previously unstudied source of frustration which controls the ground state of anisotropically-ordered surfaces. While the intimate relationship between topological defects and intrinsic curvature is well-established, we show that the coupling between the spatial organization of defects and extrinsic geometry is as important, and in some cases more important, than intrinsic geometry for determining the ground state of nematic order on anisotropic surfaces. Away from umbilics, extrinsic geometry gives rise to symmetry-breaking fields in regions of high curvature that favor uniform order most strongly in precisely those regions where the intrinsic geometry favors the locally "isotropic" textures generated by defects. The frustration between textures favorable to intrinsic and extrinsic energies becomes particularly pronounced on surfaces of negative Gaussian curvature. As prototypical example this frustration, we study the ground state of nematic order on the surface of catenoid (see Fig. 1). While the intrinsic curvature favors...

Liquid crystal elastomers are cross-linked polymer networks covalently bonded with liquid crystal mesogens. In the nematic phase, due to strong coupling between mechanical strain and orientational order, these materials display strain-induced instabilities associated with formation and evolution of orientational domains. Using a three-dimensional finite element elastodynamics simulation, we investigate one such instability, the onset of stripe formation in a monodomain film stretched along an axis perpendicular to the nematic director. In our simulation, we observe the formation of striped domains with alternating director rotation. This model allows us to explore the fundamental physics governing dynamic mechanical response of nematic elastomers and also provides a potentially useful computational tool for engineering device applications.

Non-spherical emulsion droplets can be stabilized by densely packed colloidal particles adsorbed at their surface. In order to understand the microstructure of these surface packings, the ordering of hard spheres on ellipsoidal surfaces is determined through large scale computer simulations. Defects in the packing are shown generically to occur most often in regions of strong curvature; however, the relationship between defects and curvature is nontrivial, and the distribution of defects shows secondary maxima for ellipsoids of sufficiently high aspect ratio. As with packings on spherical surfaces, additional defects beyond those required by topology are observed as chains or "scars". The transition point, however, is found to be softened by the anisotropic curvature which also partially orients the scars. A rich library of symmetric commensurate packings are identified for low particle number. We verify experimentally that ellipsoidal droplets of varying aspect ratio can be arrested by surface-adsorbed colloids.