Universal behavior of crystalline membranes: Crumpling transition and Poisson ratio of the flat phase

Cuerno, Rodolfo; Gallardo‐Caballero, Ramón; Gordillo‐Guerrero, A.; Monroy, Pedro; Ruiz‐Lorenzo, J. J.

doi:10.1103/physreve.93.022111

Cited by 16 publications

(31 citation statements)

References 43 publications

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“…To understand the mechanism of the J-shaped diagram, we first calculate the frame tension τ of cylindrical surfaces using the canonical surface model of Helfrich and Polyakov (HP) [38,47,48]. From the Monte Carlo data of the HP model, we find that τ is J-shaped.…”

Section: Discussionmentioning

confidence: 99%

J-shaped stress-strain diagram of collagen fibers: Frame tension of triangulated surfaces with fixed boundaries

Takano

Koibuchi

2017

Phys. Rev. E

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We present Monte Carlo data of the stress-strain diagrams obtained using two different triangulated surface models. The first is the canonical surface model of Helfrich and Polyakov (HP), and the second is a Finsler geometry (FG) model. The shape of the experimentally observed stressstrain diagram is called J-shaped. Indeed, the diagram has a plateau for the small strain region and becomes linear in the relatively large strain region. Because of this highly non-linear behavior, the J-shaped diagram is far beyond the scope of the ordinary theory of elasticity. Therefore, the mechanism behind the J-shaped diagram still remains to be clarified, although it is commonly believed that the collagen degrees of freedom play an essential role. We find that the FG modeling technique provides a coarse-grained picture for the interaction between the collagen and the bulk material. The role of the directional degrees of freedom of collagen molecules or fibers can be understood in the context of FG modeling. We also discuss the reason for why the J-shaped diagram cannot (can) be explained by the HP (FG) model. *

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Section: Discussionmentioning

confidence: 99%

J-shaped stress-strain diagram of collagen fibers: Frame tension of triangulated surfaces with fixed boundaries

Takano

Koibuchi

2017

Phys. Rev. E

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“…We have seen that cutting holes in a membrane can induce crumpling at much lower temperatures. We have yet to show, however, that this phenomenon quantitatively corresponds to the standard crumpling transition that has been extensively studied for full sheets 7 , 9 , 16 , 17 , 29 , 31 , 35 – 41 . This can be accomplished by performing a finite-size scaling (FSS) study 42 and finding the universality class of the phase transition.…”

Section: Resultsmentioning

confidence: 93%

“…Normally, when performing a numerical study (see, e.g., refs. 9 , 31 ) one chooses natural units where = 1 and is varied. To better approximate the behavior of materials such as graphene or MoS 2 , however, we will instead fix the ratio and vary temperature by changing the ratio.…”

Section: Resultsmentioning

confidence: 99%

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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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“…techniques [8,9]. In contrast, it is reported that the order of transition is of second-order on the free boundary lattices [22,23]. Therefore, this continuous transition combining the above mentioned first-order one indicates that the order of transition depends on the surface topology; spheres or free boundary planer disks.…”

Section: Introductionmentioning

confidence: 91%

Parallel Tempering Monte Carlo Studies of Phase Transition of Free Boundary Planar Surfaces

Shobukhov

Koibuchi

2018

Preprint

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We numerically study surface models defined on hexagonal disks with a free boundary. 2D surface models for planer surfaces have recently attracted interest due to the engineering applications of functional materials such as graphene and its composite with polymers. These 2D composite meta-materials are strongly influenced by external stimuli such as thermal fluctuations if they are sufficiently thin. For this reason, it is very interesting to study the shape stability/instability of thin 2D materials against thermal fluctuations. In this paper, we study three types of surface models including Landau-Ginzburg (LG) and Helfirch-Polyakov models defined on triangulated hexagonal disks using the parallel tempering Monte Carlo simulation technique. We find that the planer surfaces undergo a first-order transition between the smooth and crumpled phases in the LG model and continuous transitions in the other two models. The first-order transition is relatively weaker compared to the transition on spherical surfaces already reported. The continuous nature of the transition is consistent with the reported results, although the transitions are stronger than that of the reported ones.

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Universal behavior of crystalline membranes: Crumpling transition and Poisson ratio of the flat phase

Cited by 16 publications

References 43 publications

J-shaped stress-strain diagram of collagen fibers: Frame tension of triangulated surfaces with fixed boundaries

J-shaped stress-strain diagram of collagen fibers: Frame tension of triangulated surfaces with fixed boundaries

Thermal crumpling of perforated two-dimensional sheets

Parallel Tempering Monte Carlo Studies of Phase Transition of Free Boundary Planar Surfaces

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