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Shape Transitions and Fluctuations of Helical Ribbons – from Cold Seed Pods to Thermal Chiral Macromolecules

Banff International Research Station for Mathematical Innovation and Discovery

Studying the mechanics of Bauhinia seeds pod opening we quantified the twisted to helical transition in ribbons with spontaneous negative curvature. Such ribbons appear in pre-stressed materials, nematic ellastomer sheets and various fibrous plants tissues. The intrinsic negative curvature results from active deformation, oriented at different directions on opposite faces of the ribbon. We show that the same geometry governs shape selection in nano-scale self assembled ribbons, made of lipids and peptides with chiral head groups. We find that the ribbon’s configurations are well described by the elastic theory and suggest how the parameters in the theory are determined from the molecular interactions. Finally, developing a one-dimensional effective description of the ribbons, we combine elasticity with statistical mechanics to derive predictions for various statistical properties of ribbon shapes at finite temperature. Some of the predictions are quantitatively verified by analyzing experimental data.

Mathematics; Mechanics of deformable solids; Statistical mechanics, structure of matter; Mathematical physics

video/mp4

Author affiliation: The Hebrew University of Jerusalem

2017-03-10

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/60851

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/