Negative Poisson's ratio in periodic porous graphene structures

Ho, Viet Hung; Ho, Duc Tam; Kwon, Soon‐Yong; Kim, Sung Youb

doi:10.1002/pssb.201600061

Cited by 53 publications

(42 citation statements)

References 41 publications

(43 reference statements)

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“…2D materials can also be tailored extrinsically to exhibit NPR. This has been accomplished through cutting and patterning of graphene [78], buckling of 2D boron (borophene) sheets [79], rippling through introduction of vacancies in graphene [80], and via edge stress-induced warping in graphene nanoribbons [81]. A common feature underlying these extrinsic mechanisms is that they lead to a reference configuration that involves out-of-plane deformation.…”

Section: Theoretical Predictionsmentioning

confidence: 99%

A review on mechanics and mechanical properties of 2D materials—Graphene and beyond

Akinwande

Brennan

Bunch

et al. 2017

Extreme Mechanics Letters

1,056

649

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Since the first successful synthesis of graphene just over a decade ago, a variety of twodimensional (2D) materials (e.g., transition metal-dichalcogenides, hexagonal boron-nitride, etc.) have been discovered. Among the many unique and attractive properties of 2D materials, mechanical properties play important roles in manufacturing, integration and performance for their potential applications. Mechanics is indispensable in the study of mechanical properties, both experimentally and theoretically. The coupling between the mechanical and other physical properties (thermal, electronic, optical) is also of great interest in exploring novel applications, where mechanics has to be combined with condensed matter physics to establish a scalable theoretical framework. Moreover, mechanical interactions between 2D materials and various substrate materials are essential for integrated device applications of 2D materials, for which the mechanics of interfaces (adhesion and friction) has to be developed for the 2D materials. Here we review recent theoretical and experimental works related to mechanics and mechanical properties of 2D materials. While graphene is the most studied 2D material to date, we expect continual growth of interest in the mechanics of other 2D materials beyond graphene.

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Section: Theoretical Predictionsmentioning

confidence: 99%

A review on mechanics and mechanical properties of 2D materials—Graphene and beyond

Akinwande

Brennan

Bunch

et al. 2017

Extreme Mechanics Letters

1,056

649

View full text Add to dashboard Cite

show abstract

“…(38) and (39) for the differential response in the case of an isotropic stress σ can be obtained from Eqs. (28) and (29) for the absolute response to an uniaxial stress σ by the replacement…”

Section: Differential Poisson Ratiomentioning

confidence: 99%

“…It is seen from Eqs. (29) and (79) that for σ σ * the Young modulus and the PR are given, to the leading order, by their bare values. On the other hand, for σ σ * anomalous terms dominate and we find…”

Section: Absolute Prmentioning

confidence: 99%

Stress-controlled Poisson ratio of a crystalline membrane: Application to graphene

et al. 2018

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We demonstrate that a key elastic parameter of a suspended crystalline membrane-the Poisson ratio (PR) ν-is a non-trivial function of the applied stress σ and of the system size L, i.e., ν = νL(σ). We consider a generic two-dimensional membrane embedded into space of dimensionality 2 + dc.(The physical situation corresponds to dc = 1.) A particularly important application of our results is to free-standing graphene. We find that at a very low stress, when the membrane exhibits linear response, the PR νL(0) decreases with increasing system size L and saturates for L → ∞ at a value which depends on the boundary conditions and is essentially different from the value ν = −1/3 previously predicted by the membrane theory within a self-consisted scaling analysis. By increasing σ, one drives a sufficiently large membrane (with the length L much larger than the Ginzburg length) into a non-linear regime characterized by a universal value of PR that depends solely on dc, in close connection with the critical index η controlling the renormalization of bending rigidity. This universal non-linear PR acquires its minimum value νmin = −1 in the limit dc → ∞, when η → 0. With the further increase of σ, the PR changes sign and finally saturates at a positive non-universal value prescribed by the conventional elasticity theory. We also show that one should distinguish between the absolute and differential PR (ν and ν diff , respectively). While coinciding in the limits of very low and very high stress, they differ in general: ν = ν diff . In particular, in the non-linear universal regime, ν diff takes a universal value which, similarly to the absolute PR, is a function solely of dc (or, equivalently, of η) but is different from the universal value of ν. In the limit of infinite dimensionality of the embedding space, dc → ∞ (i.e., η → 0), the universal value of ν diff tends to −1/3, at variance with the limiting value −1 of ν. Finally, we briefly discuss generalization of these results to a disordered membrane.

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“…[11][12][13][14] The search for nanomaterials with negative Poisson's ratio (NPR) and the search for new mechanisms for NPR of nanomaterials have been significant. [15] Inspired by some existing mechanisms for bulk materials, some nanostructures involving defects or some specific engineered structures can show auxetic behavior such as patterned graphene structures based on rigid rotating unit model, [16] and wrinkled graphene structures based on de-wrinkling and unfolding mechanism. [17][18][19] In addition, auxeticity has been also found in nanoscale materials due to specific nanoscale physical properties that were not observed in materials and structures at macroscale.…”

Section: Introductionmentioning

confidence: 99%

Negative In‐Plane Poisson's Ratio for Single Layer Black Phosphorus: An Atomistic Simulation Study

Park

et al. 2017

Physica Status Solidi (b)

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We utilized molecular statics (MS) simulations to investigate the auxeticity of single layer black phosphorus (SLBP). Our simulation results show that the SLBP has a negative in‐plane Poisson's ratio in the zigzag direction when the applied strain along the armchair direction exceeds 0.018. We show that the interplay between bond stretching and bond rotating modes determines the in‐plane Poisson's ratio behavior. While the bond stretching mode always tends to increase the in‐plane auxeticity, the bond rotating mode might increase or decrease the in‐plane auxeticity. Furthermore, we show that graphite also exhibits an in‐plane negative Poisson's ratio at finite strains due to a similar mechanism.

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Negative Poisson's ratio in periodic porous graphene structures

Cited by 53 publications

References 41 publications

A review on mechanics and mechanical properties of 2D materials—Graphene and beyond

A review on mechanics and mechanical properties of 2D materials—Graphene and beyond

Stress-controlled Poisson ratio of a crystalline membrane: Application to graphene

Negative In‐Plane Poisson's Ratio for Single Layer Black Phosphorus: An Atomistic Simulation Study

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