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Physics  2010 

Statistical Mechanics of Developable Ribbons

DOI: 10.1103/PhysRevLett.104.238104

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We investigate the statistical mechanics of long developable ribbons of finite width and very small thickness. The constraint of isometric deformations in these ribbon-like structures that follows from the geometric separation of scales introduces a coupling between bending and torsional degrees of freedom. Using analytical techniques and Monte Carlo simulations, we find that the tangent-tangent correlation functions always exhibits an oscillatory decay at any finite temperature implying the existence of an underlying helical structure even in absence of a preferential zero-temperature twist. In addition the persistence length is found to be over three times larger than that of a wormlike chain having the same bending rigidity. Our results are applicable to many ribbon-like objects in polymer physics and nanoscience that are not described by the classical worm-like chain model.


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