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Non-Hookean statistical mechanics of clamped graphene ribbons

Author(s): Bowick, Mark J; Košmrlj, Andrej; Nelson, David R; Sknepnek, Rastko

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Abstract: Thermally fluctuating sheets and ribbons provide an intriguing forum in which to investigate strong violations of Hooke's Law: Large distance elastic parameters are in fact not constant but instead depend on the macroscopic dimensions. Inspired by recent experiments on free-standing graphene cantilevers, we combine the statistical mechanics of thin elastic plates and large-scale numerical simulations to investigate the thermal renormalization of the bending rigidity of graphene ribbons clamped at one end. For ribbons of dimensions W×L (with L≥W), the macroscopic bending rigidity κR determined from cantilever deformations is independent of the width when W<th, where th is a thermal length scale, as expected. When W>th, however, this thermally renormalized bending rigidity begins to systematically increase, in agreement with the scaling theory, although in our simulations we were not quite able to reach the system sizes necessary to determine the fully developed power law dependence on W. When the ribbon length L>p, where p is the W-dependent thermally renormalized ribbon persistence length, we observe a scaling collapse and the beginnings of large scale random walk behavior.
Publication Date: Mar-2017
Electronic Publication Date: 22-Mar-2017
Citation: Bowick, Mark J, Košmrlj, Andrej, Nelson, David R, Sknepnek, Rastko. (2017). Non-Hookean statistical mechanics of clamped graphene ribbons. Physical Review B, 95 (10), 10.1103/PhysRevB.95.104109
DOI: doi:10.1103/PhysRevB.95.104109
ISSN: 2469-9950
EISSN: 2469-9969
Type of Material: Journal Article
Journal/Proceeding Title: Physical Review B
Version: Author's manuscript

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