Non-Hookean statistical mechanics of clamped graphene ribbons

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 $W\times L$ (with $L\ge W$), the macroscopic bending rigidity ${\kappa }_R$ determined from cantilever deformations is independent of the width when $W<{\ell }_{\text{th}}$, where ${\ell }_{\text{th}}$ is a thermal length scale, as expected. When $W>{\ell }_{\text{th}}$, 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 $L>{\ell }_p$, where ${\ell }_p$ is the $W$-dependent thermally renormalized ribbon persistence length, we observe a scaling collapse and the beginnings of large scale random walk behavior.

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• Thermalized buckling of isotropically compressed thin sheets
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• Thermal buckling and symmetry breaking in thin ribbons under compression
• Thermal stiffening of clamped elastic ribbons
• Scale without conformal invariance in membrane theory
• Spontaneous tilt of single-clamped thermal elastic sheets
• Anomalous thermal expansion in Ising-like puckered sheets
• The Föppl-von Kármán equations of elastic plates with initial stress
• A numerical study of the rippling instability driven by electron-phonon coupling in graphene
• Vibrations and tunneling of strained nanoribbons at finite temperature
• Folding pathways to crumpling in thermalized elastic frames
• Flexural phonons in supported graphene: from pinning to localization
• Curvature as an external field in mechanical antiferromagnets
• Stiffening Thermal Membranes by Cutting
• Anomalous curvature evolution and geometric regularization of energy focusing in the snapping dynamics of a flexible body
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