Helfrich-Hurault elastic instabilities driven by geometrical frustration
arXiv:2109.14668 · doi:10.1103/RevModPhys.95.015004
Abstract
The Helfrich-Hurault (HH) elastic instability is a well-known mechanism behind patterns that form as a result of strain upon liquid crystal systems with periodic ground states. In the HH model, layered structures undulate and buckle in response to local, geometric incompatibilities, in order to maintain the preferred layer spacing. Classic HH systems include cholesteric liquid crystals under electromagnetic field distortions and smectic liquid crystals under mechanical strains, where both materials are confined between rigid substrates. However, richer phenomena are observed when undulation instabilities occur in the presence of deformable interfaces and variable boundary conditions. Understanding how the HH instability is affected by deformable surfaces is imperative for applying the instability to a broader range of materials. In this review, we re-examine the HH instability and give special focus to how the boundary conditions influence the mechanical response of lamellar systems to geometrical frustration. We use lamellar liquid crystals confined within a spherical shell geometry as our model system. Made possible by the relatively recent advances in microfluidics within the past 15 years, liquid crystal shells are composed entirely of fluid interfaces and have boundary conditions that can be dynamically controlled at will. We examine past and recent work that exemplifies how topological constraints, molecular anchoring conditions, and boundary curvature can trigger the HH instability in liquid crystals with periodic ground states. We then end by identifying similar phenomena across a wide variety of materials, both biological and synthetic. With this review, we aim to highlight that the HH instability is a generic and often overlooked response of periodic materials to geometrical frustration.
arXiv comment38 pages, 35 figures, Submitted to Reviews of Modern Physics
References in corpus (34)
- Nematic twist-bend phase with nanoscale modulation of molecular orientation
- The Geometry of Soft Materials: A Primer
- Nematic textures in spherical shells
- Topological Defects in Spherical Nematics
- Twist-bend nematic liquid crystals in high magnetic fields
- Cellulose Photonic Pigments
- Minimal Surfaces, Screw Dislocations and Twist Grain Boundaries
- A change in stripes for cholesteric shells via anchoring in moderation
- Topological defects in cholesteric liquid crystal shells
- Waltzing route towards double-helix formation in cholesteric shells
- The Effect of Shear Flow on the Helfrich Interaction in Lyotropic Lamellar Systems
- Geometric Theory of Columnar Phases on Curved Substrates
- Extrinsic Curvature, Geometric Optics, and Lamellar Order on Curved Substrates
- Hydrodynamic instabilities in active cholesteric liquid crystals
- Active cholesterics: odder than odd elasticity
- Temperature-driven anchoring transitions at liquid crystal / water interfaces
- Undulation instabilities in the meniscus of smectic membranes
- Shaping nanoparticle fingerprints at the interface of cholesteric droplets
- Coiling Instabilities in Multilamellar Tubes
- Smectic blue phases: layered systems with high intrinsic curvature
- Instability patterns in ultrathin nematic films: comparison between theory and experiment
- Swelling cholesteric liquid crystal shells to direct colloids at the interface
- Spherical nematics with a threefold valence
- The Geometry of the Cholesteric Phase
- Undulation instabilities in cholesteric liquid crystals induced by anchoring transitions
- Elastic interactions between topological defects in chiral nematic shells
- Second harmonic light scattering induced by defects in the twist-bend nematic phase of liquid crystal dimers
- Contact Topology and the Structure and Dynamics of Cholesterics
- Elastocapillary driven assembly of particles at free-standing smectic-A films
- Thin nematic films: anchoring effects and stripe instability revisited
- Mesoscale structure of wrinkle patterns and defect-proliferated liquid crystalline phases
- Thick smectic shells
- The weirdest martensite: Smectic liquid crystal microstructure and Weyl-Poincaré invariance
- Defect-driven shape instabilities of bundles