Elasticity and Fluctuations of Frustrated Nano-Ribbons

Abstract

We derive a reduced quasi-one-dimensional theory of geometrically frustrated elastic ribbons. Expressed in terms of geometric properties alone, it applies to ribbons over a wide range of scales, allowing the study of their elastic equilibrium, as well as thermal fluctuations. We use the theory to account for the twisted-to-helical transition of ribbons with spontaneous negative curvature, and the effect of fluctuations on the corresponding critical exponents. The persistence length of such ribbons changes non-monotonically with the ribbon's width, dropping to zero at the transition. This and other statistical properties qualitatively differ from those of non-frustrated fluctuating filaments.

References in corpus (4)

• The structure of suspended graphene sheets
• Elastic theory of unconstrained non-Euclidean plates
• Shape Selection in Chiral Self-Assembly
• Statistical Mechanics of Developable Ribbons

Cited by in corpus (12)

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• Building blocks of non-Euclidean ribbons: Size-controlled self-assembly via discrete, frustrated particles
• Ligand-Induced Incompatible Curvatures Control Ultrathin Nanoplatelet Polymorphism and Chirality
• Hierarchy of Geometrical Frustration in Elastic Ribbons: shape-transitions and energy scaling obtained from a general asymptotic theory
• Shape and Fluctuations of Positively Curved Ribbons
• A ribbon model for nematic polymer networks
• On the Packing of Stiff Rods on Ellipsoids Part I -- Geometry
• Asymptotic rigidity for shells in non-Euclidean elasticity