| Abstract: | Studying the mechanics of Bauhinia seeds pod opening we quantified the twisted to helical transition in ribbons with spontaneous negative curvature. Shape selection and shape transitions in this system are well described by the theory of incompatible elastic sheets. We show that the same geometry and mechanics govern 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, therefore, bridging the gap between the molecular and supramolecular structures. Finally, developing a one-dimensional effective description of the ribbons, we combine incompatible 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.
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