Non-Hookean statistical mechanics of clamped graphene ribbons

Bowick, Mark J.; Košmrlj, Andrej; Nelson, David R.; Sknepnek, Rastko

doi:10.1103/physrevb.95.104109

Cited by 67 publications

(47 citation statements)

References 51 publications

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“…In Ref. [44], it was shown that this simplified dual model gives results consistent with graphene simulations [45] that incorporate explicitly the energetics of carbon-carbon bonds. As for anharmonic contributions to the free energy we emphasize that our model incorporates nonlinearities through the nonlinear strain tensor u ij , which leads to a critical nonlinear stretching term once in-plane phonons are integrated out.…”

Section: Simulation Methodsmentioning

confidence: 73%

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Thermal stiffening of clamped elastic ribbons

2017

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We use molecular dynamics to study the vibrations of a thermally fluctuating two-dimensional elastic membrane clamped at both ends. We directly extract the eigenmodes from resonant peaks in the frequency domain of the time-dependent height and measure the dependence of the corresponding eigenfrequencies on the microscopic bending rigidity of the membrane, taking care also of the subtle role of thermal contraction in generating a tension when the projected area is fixed. At finite temperatures we show that the effective (macroscopic) bending rigidity tends to a constant as the bare bending rigidity vanishes, consistent with theoretical arguments that the large-scale bending rigidity of the membrane arises from a strong thermal renormalization of the microscopic bending rigidity. Experimental realizations include covalently-bonded two-dimensional atomically thin membranes such as graphene and molybdenum disulfide or soft matter systems such as the spectrin skeleton of red blood cells or diblock copolymers.

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Section: Simulation Methodsmentioning

confidence: 73%

“…[25] and the non-Hookean statistical mechanics of thermalized ribbons clamped at one end only, with the associated scale-dependent stiffening of the bending rigidity, studied in Ref. [44].…”

Section: Fig 2 (Color Online) (A)mentioning

confidence: 99%

Thermal stiffening of clamped elastic ribbons

2017

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“…Following refs. 25 , 32 , we will use . This corresponds to a Young’s modulus about an order of magnitude lower than for real graphene 33 , 34 , in order to facilitate equilibration in our computer simulations.…”

Section: Resultsmentioning

confidence: 99%

Thermal crumpling of perforated two-dimensional sheets

et al. 2017

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Thermalized elastic membranes without distant self-avoidance are believed to undergo a crumpling transition when the microscopic bending stiffness is comparable to kT, the scale of thermal fluctuations. Most potential physical realizations of such membranes have a bending stiffness well in excess of experimentally achievable temperatures and are therefore unlikely ever to access the crumpling regime. We propose a mechanism to tune the onset of the crumpling transition by altering the geometry and topology of the sheet itself. We carry out extensive molecular dynamics simulations of perforated sheets with a dense periodic array of holes and observe that the critical temperature is controlled by the total fraction of removed area, independent of the precise arrangement and size of the individual holes. The critical exponents for the perforated membrane are compatible with those of the standard crumpling transition.

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“…However, physically, the maximum value of the γ FvK number is γ FvK ≈ 10 14 . This value does not occur for shells since it describes the behavior of a 200 µm square sheet of graphene [48]. Graphene is one-atom thick membrane with high in plane Young's modulus (Y = 500 GPa).…”

Section: Quantification Of Bending Versus Stretching Deformationmentioning

confidence: 99%

Effect of Gravity on the Scale of Compliant Shells

Charpentier

Adriaenssens

2020

Biomimetics

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Thin shells are found across scales ranging from biological blood cells to engineered large-span roof structures. The engineering design of thin shells used as mechanisms has occasionally been inspired by biomimetic concept generators. The research goal of this paper is to establish the physical limits of scalability of shells. Sixty-four instances of shells across length scales have been organized into five categories: engineering stiff and compliant, plant compliant, avian egg stiff, and micro-scale compliant shells. Based on their thickness and characteristic dimensions, the mechanical behavior of these 64 shells can be characterized as 3D solids, thick or thin shells, or membranes. Two non-dimensional indicators, the Föppl–von Kármán number and a novel indicator, namely the gravity impact number, are adopted to establish the scalability limits of these five categories. The results show that these shells exhibit similar mechanical behavior across scales. As a result, micro-scale shell geometries found in biology, can be upscaled to engineered shell geometries. However, as the characteristic shell dimension increases, gravity (and its associated loading) becomes a hindrance to the adoption of thin shells as compliant mechanisms at the larger scales-the physical limit of compliance in the scaling of thin shells is found to be around 0.1 m.

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Non-Hookean statistical mechanics of clamped graphene ribbons

Cited by 67 publications

References 51 publications

Thermal stiffening of clamped elastic ribbons

Thermal stiffening of clamped elastic ribbons

Thermal crumpling of perforated two-dimensional sheets

Effect of Gravity on the Scale of Compliant Shells

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