Statistical Mechanics of Thin Spherical Shells

Košmrlj, Andrej; Nelson, David R.

doi:10.1103/physrevx.7.011002

Cited by 44 publications

(79 citation statements)

References 91 publications

(213 reference statements)

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“…In spherical shells thermal fluctuations produce effective negative surface tension, which can be interpreted as an effective external pressure. As a result thermal fluctuations reduce the critical buckling pressure for spherical shells up to a point, that shells, which are larger than some temperature dependent critical radius, become crushed even when the pressure difference between the inside and outside of the shell is zero [50]. A similar result was observed in numerical simulations of carbon nanotubes [51], where thermal fluctuations reduced the critical axial load.…”

Section: Discussionsupporting

confidence: 69%

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Non-Hookean statistical mechanics of clamped graphene ribbons

et al. 2017

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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.

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Section: Discussionsupporting

confidence: 69%

“…The spontaneous curvature of sheets also leads to new surprising phenomena as was demonstrated in recent Monte Carlo simulations [22] and in a theoretical study [50] of thermalized spherical shells. In spherical shells thermal fluctuations produce effective negative surface tension, which can be interpreted as an effective external pressure.…”

Section: Discussionmentioning

confidence: 92%

Non-Hookean statistical mechanics of clamped graphene ribbons

et al. 2017

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“…These values are obviously only indicative and are in no way supposed to provide a quantitatively accurate prediction in D = 2. However, one can note that the twoloop correction moves the value of η 4 towards the right direction if one refers to the generally accepted numerical data that lie in the range [0.72, 0.88] [55][56][57][58][59][60][61][62][63][64][65].…”

Section: Two-loop Ordermentioning

confidence: 99%

Flat phase of quantum polymerized membranes

Coquand

Mouhanna

2016

Phys. Rev. E

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We investigate the flat phase of quantum polymerized phantom membranes by means of a nonperturbative renormalization group approach. We first implement this formalism for general quantum polymerized membranes and derive the flow equations that encompass both quantum and thermal fluctuations. We then deduce and analyze the flow equations relevant to study the flat phase and discuss their salient features: quantum to classical crossover and, in each of these regimes, strong to weak coupling crossover. We finally illustrate these features in the context of free-standing graphene physics.

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“…It is known [36,39] that the anomalous elasticity of membrane affects the stability of spherical membrane shells. The renormalization of the bending rigidity and Young's modulus decreases the pressure induced tension towards a negative value which is enough for developing the buckling instability.…”

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confidence: 99%

Effect of anomalous elasticity on bubbles in van der Waals heterostructures

2020

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It is shown that the anomalous elasticity of membranes affects the profile and thermodynamics of a bubble in van der Waals heterostructures. Our theory generalizes the non-linear plate theory as well as membrane theory of the pressurised blister test to incorporate the power-law scale dependence of the bending rigidity and Young's modulus of a two-dimensional crystalline membrane. This scale dependence caused by long-ranged interaction of relevant thermal fluctuations (flexural phonons), is responsible for the anomalous Hooke's law observed recently in graphene. It is shown that this anomalous elasticity affects dependence of the maximal height of the bubble on its radius and temperature. We identify the characteristic temperature above which the anomalous elasticity is important. It is suggested that for graphene-based van der Waals heterostructures the predicted anomalous regime is experimentally accessible at the room temperature.

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Statistical Mechanics of Thin Spherical Shells

Cited by 44 publications

References 91 publications

Non-Hookean statistical mechanics of clamped graphene ribbons

Non-Hookean statistical mechanics of clamped graphene ribbons

Flat phase of quantum polymerized membranes

Effect of anomalous elasticity on bubbles in van der Waals heterostructures

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