Elasticity and Fluctuations of Frustrated Nano-Ribbons

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.