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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 freestanding graphene cantilevers, we combine the statistical mechanics of thin elastic plates and largescale 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 Wdependent thermally renormalized ribbon persistence length, we observe a scaling collapse and the beginnings of large scale random walk behavior.
Original language  English 

Article number  104109 
Pages (fromto)  17 
Number of pages  7 
Journal  Physical Review B: Condensed matter and materials physics 
Volume  95 
Issue number  10 
DOIs  
Publication status  Published  22 Mar 2017 
ASJC Scopus subject areas
 Electronic, Optical and Magnetic Materials
 Condensed Matter Physics
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Dive into the research topics of 'NonHookean statistical mechanics of clamped graphene ribbons'. Together they form a unique fingerprint.Projects
 2 Finished

Dry Active Matter on a Sphere (First Grant Scheme)
Engineering and Physical Sciences Research Council
1/05/15 → 31/10/16
Project: Research