Mechanics Interpretation on the Bending Stiffness and Wrinkled Pattern of Graphene

Abstract

In this paper we attempt to answer two questions on graphene from a mechanic's viewpoint: why does this one-atom-thick monolayer have finite bending stiffness to ensure its stability? and what is its wrinkle mechanism? As for the first question, it is found that the repulsive residual internal moment in the bond angle can lead to a nonzero bending stiffness, which makes the graphene fiat. Together with long-range attraction among atoms, such as van der Waals forces, a graphene prefers to have a self-buckling wrinkled configuration with many waves.

Geometry and Self-stress of Single-Wall Carbon Nanotubes and Graphene via a Discrete Model Based on a 2nd-Generation REBO Potential

“…Remark 2 In [53], graphene's bending stiffness is presumed to be related to a bond-angle nanostress, and Geometry and Prestress of Single-Walled CNTs 19 than r 0 , a result which disagrees with the DFT calculations in [29].…”

“…In [53], graphene's bending stiffness is presumed to be related to a bond-angle nanostress, and it is argued that, if such a nanostress were actually present, then the bending stiffness would be equal to τ g /2, that is, the value the bending stiffness should have in the absence of a dihedral contribution, according to the computations reported in [34].…”

“…In our opinion, recognizing that both CNTs and FGSs are self-stressed structures and, morever, qualifying and quantifying their self-stress state is the main element of novelty of our study. Accounting for self-stress is crucial to produce reliable predictions whenever a harmonic approximation of the interatomic potential is accepted [16]; see also [53], where it is shown that bond-angle self-stress can contribute to the bending stiffness of monolayer FGSs. We find that the dihedral contribution to self-energy is large, about half of the total for CNTs of large radius, a result consistent with those in [34]; we also find that the dihedral contribution is less important in small-radius CNTs, a fact that can be justified by the large change of bond angles when curvature is large.…”

Wrinkling Instability of Graphene on Substrate-Supported Nanoparticles

“…Graphene is a flexible, atomically thin membrane with remarkable electronic, mechanical, and chemical properties [1][2][3]. The two-dimensional nature of graphene renders its extra-large surface-to-volume ratio, giving rise to morphological varieties such as intrinsic ripples, extrinsic wrinkles and folds [4][5][6][7][8][9][10][11], and other folded carbon nanostructures [8,[12][13][14][15][16][17][18][19]. In particular, the wrinkling formation in graphene has received considerable attention, largely due to its potential in manipulating the electronic properties of graphene [20][21][22][23].…”

The mechanical characterization of stacked, multilayer graphene cantilevers and plates

“…This approach assumes that the few-layer graphene stack behaves as a pure membrane, without bending stiffness. However, as the graphene stack reaches 3 or 4 layers, the bending stiffness cannot be neglected and a plate model is needed [3,4]. A plate model assuming infinitely small beam bending rotations has been implemented for experimental characterization of a graphene flake 69 layers thick, although this approach is not applicable to few-layer graphene for which significant rotations during loading are expected [5].…”