Membrane stress and torque induced by Frank's nematic textures: A geometric perspective using surface-based constraints
arXiv:1903.01419 · doi:10.1103/PhysRevE.100.012704
Abstract
An elastic membrane with embedded nematic molecules is considered as a model of anisotropic fluid membrane with internal ordering. By considering the geometric coupling between director field and membrane curvature, the nematic texture is shown to induce anisotropic stresses additional to Canham-Helfrich elasticity. Building upon differential geometry, analytical expressions are found for the membrane stress and torque induced by splaying, twisting and bending of the nematic director as described by the Frank energy of liquid crystals. The forces induced by prototypical nematic textures are visualized on the sphere and on cylindrical surfaces.
arXiv commentNew version to appear in PRE
References in corpus (18)
- The Geometry of Soft Materials: A Primer
- Two-Dimensional Matter: Order, Curvature and Defects
- Making Faces: Universal Inverse Design of Surfaces with Thin Nematic Elastomer Sheets
- Nematic textures in spherical shells
- Vortices in Superfluid Films on Curved Surfaces
- Stresses in lipid membranes
- Topological Defects in Spherical Nematics
- Membrane geometry with auxiliary variables and quadratic constraints
- Surface free energies for nematic shells
- Defects in nematic membranes can buckle into pseudospheres
- Coarse-Grained Modeling of a Deformable Nematic Vesicle
- Vesicle shape, molecular tilt, and the suppression of necks
- Frustrated order on extrinsic geometries
- Hydrodynamic theory for nematic shells: the interplay among curvature, flow and alignment
- Influence of the Extrinsic Curvature on 2D Nematic Films
- Nematic Films and Radially Anisotropic Delaunay Surfaces
- Stresses in curved nematic membranes
- Dynamics of the molecular orientation field coupled to ions in two-dimensional ferroelectric liquid crystals
Cited by in corpus (5)
- Determination of Elastic Parameters of Lipid Membranes with Molecular Dynamics: A Review of Approaches and Theoretical Aspects
- Morphodynamics of Active Nematic Fluid Surfaces
- Local stress and elastic properties of lipid membranes obtained from elastic energy variation
- Mechanics of nematic membranes: Euler-Lagrange equations, Noether charges, stress, torque and boundary conditions of the surface Frank nematic field
- Passive defect driven morphogenesis in nematic membranes