Thermal crumpling of perforated two-dimensional sheets

Yllanes, David; Bhabesh, Sourav; Nelson, David R.; Bowick, Mark J.

doi:10.1038/s41467-017-01551-y

Cited by 33 publications

(38 citation statements)

References 51 publications

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“…Understanding of the nature of these ripples, their interplay with thermal fluctuations and disorder, and of the statistical properties of the effective gauge fields that they induce for electrons [18] remains unsatisfactory. Finally, the crumpling transition was further studied in a number of works, using NPRG [19] and numerical studies, e.g., see [20] and reference therein, to quote a few.…”

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confidence: 99%

Anomalous elasticity, fluctuations and disorder in elastic membranes

2018

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Motivated by freely suspended graphene and polymerized membranes in soft and biological matter we present a detailed study of a tensionless elastic sheet in the presence of thermal fluctuations and quenched disorder. The manuscript is based on an extensive draft dating back to 1993, that was circulated privately. It presents the general theoretical framework and calculational details of numerous results, partial forms of which have been published in brief Letters [1,2]. The experimental realization atom-thin graphene sheets [3] has driven a resurgence in this fascinating subject, making our dated predictions and their detailed derivations timely. To this end we analyze the statistical mechanics of a generalized D-dimensional elastic "membrane" embedded in d dimensions using a self-consistent screening approximation (SCSA), that has proved to be unprecedentedly accurate in this system, exact in three complementary limits: (i) d → ∞, (ii) D → 4, and (iii) D = d. Focusing on the critical "flat" phase, for a homogeneous two-dimensional (D = 2) membrane embedded in three dimensions (d = 3), we predict its universal roughness exponent ζ = 0.590, length-scale dependent elastic moduli exponents η = 0.821 and ηu = 0.358, and an anomalous Poisson ratio, σ = −1/3. In the presence of random uncorrelated heterogeneity the membrane exhibits a glassy wrinkled ground state, characterized by ζ = 0.775, η = 0.449, η u = 1.101 and a Poisson ratio σ = −1/3. Motivated by a number of physical realizations (charged impurities, disclinations and dislocations) we also study power-law correlated quenched disorder that leads to a variety of distinct glassy wrinkled phases. Finally, neglecting self-avoiding interaction we demonstrate that at high temperature a "phantom" sheet undergoes a continuous crumpling transition, characterized by a radius of gyration exponent, ν = 0.732 and η = 0.535. Many of these universal predictions have received considerable support from simulations. We hope that this detailed presentation of the SCSA theory will be useful to further theoretical developments and corresponding experimental investigations on freely suspended graphene. Contents

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confidence: 99%

Anomalous elasticity, fluctuations and disorder in elastic membranes

2018

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“…Just prior to this anomalous behavior, we find that C(r) is well described by an exponential decay C(r) exp(−r/ p ), where p is a persistence length (see, e.g. [17,25,27]). See the curves with kT /κ ≤ 2.00 in Figure 5.…”

Section: Normal-normal Correlation Functionmentioning

confidence: 72%

“…Our simulations were implemented in the HOOMD-blue package [28,29] and run on Tesla GPUs. Following [17], we use a timestep of ∆t = 0.0025τ , where τ = ma 2 /kT is the Lennard-Jones unit of time (expressed in terms of the particle mass m) and we use natural units with a = m = 1. All energies are measured in units of kT .…”

Section: Modelmentioning

confidence: 99%

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Folding pathways to crumpling in thermalized elastic frames

2019

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The mechanical properties of thermally excited two-dimensional crystalline membranes can depend dramatically on their geometry and topology. A particularly relevant example is the effect on the crumpling transition of holes in the membrane. Here we use molecular dynamics simulations to study the case of elastic frames (sheets with a single large hole in the center) and find that the system approaches the crumpled phase through a sequence of origami-like folds at decreasing length scales when temperature is increased. We use normal-normal correlation functions to quantify the temperature-dependent number of folds.

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“…Slits allow for new configurations that couple bending and stretching deformations [8,23]. The effective spring constant of a sheet with an array of slits is controlled by the number, size, and spacing of the slits [8].…”

Section: Introductionmentioning

confidence: 99%

Stiffening thermal membranes by cutting

2017

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Two-dimensional crystalline membranes have recently been realized experimentally in such systems as graphene and molybdenum disulfide, sparking a resurgence in interest in their statistical properties. Thermal fluctuations can significantly affect the effective mechanical properties of properly thermalized membranes, renormalizing both bending rigidity and elastic moduli so that in particular they become stiffer to bending than their bare bending rigidity would suggest. We use molecular dynamics simulations to examine how the mechanical behavior of thermalized twodimensional clamped ribbons (cantilevers) depends on their precise topology and geometry. We find that a simple slit smooths roughness as measured by the variance of height fluctuations. This counterintuitive effect may be due to the counter-posed coupling of the lips of the slit to twist in the intact regions of the ribbon.

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Thermal crumpling of perforated two-dimensional sheets

Cited by 33 publications

References 51 publications

Anomalous elasticity, fluctuations and disorder in elastic membranes

Anomalous elasticity, fluctuations and disorder in elastic membranes

Folding pathways to crumpling in thermalized elastic frames

Stiffening thermal membranes by cutting

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