Smectic blue phases: layered systems with high intrinsic curvature

Abstract

We report on a construction for smectic blue phases, which have quasi-long range smectic translational order as well as three dimensional crystalline order. Our proposed structures fill space by adding layers on top of a minimal surface, introducing either curvature or edge defects as necessary. We find that for the right range of material parameters, the favorable saddle-splay energy of these structures can stabilize them against uniform layered structures. We also consider the nature of curvature frustration between mean curvature and saddle-splay.

15 pages, 11 figures

References in corpus (4)

• The Geometry of Soft Materials: A Primer
• Stresses in lipid membranes
• Smectic Phases with Cubic Symmetry: The Splay Analog of the Blue Phase
• Scaling of the buckling transition of ridges in thin sheets

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• Ground state of a large number of particles on a frozen topography
• Geometrical Frustration in Two Dimensions: Idealizations and Realizations of a Hard Disc Fluid in Negative Curvature
• Focussing frustration for self-limiting assembly of flexible, curved particles
• Smectic Liquid Crystals: Materials with One-Dimensional, Periodic Order
• Escape configuration lattice near the nematic-isotropic transition: Tilt analogue of blue phases
• Compactness and sharp lower bound for a 2D smectics model