Chemomechanics control of tearing paths in graphene

Xu Huang, Hui Yang, Adri C. T. van Duin, K. Jimmy Hsia, and Sulin Zhang

Phys. Rev. B 85, 195453 – Published 25 May 2012

Abstract

Owing to its molecular membrane structure, tearing is the predominant fracture mode for a monolayer graphene. Yet, the tearing mechanics of monolayer graphene as a two-dimensional (2D) crystal remains poorly understood. Here, we performed molecular dynamics simulations with reactive force field to determine the fracture path of monolayer graphene under tearing. Our simulations revealed that the chemomechanical tearing conditions play a regulatory role on the edge structures of graphene nanoribbons (GNRs) produced by tearing. In vacuum, the resulting GNR features the armchair edge, whereas in the presence of chemical additives (such as oxygens) to the fracture surface, the resulting GNR edge changes from armchair to zigzag. In addition, due to the large in-plane stretching to out-of-plane bending stiffness ratio of monolayer graphene, tearing causes local bending at the crack tip, giving rise to a fracture mode mixity that also modulates the fracture path. In addition to provide an atomistic understanding of tearing mechanics of 2D crystal membranes, our findings shed light on chemomechanical engineering of GNRs with controlled edge structures.

Received 6 September 2011

DOI:https://doi.org/10.1103/PhysRevB.85.195453

Authors & Affiliations

Xu Huang¹, Hui Yang¹, Adri C. T. van Duin², K. Jimmy Hsia³, and Sulin Zhang^1,*

¹Department of Engineering Science and Mechanics, Pennsylvania State University, University Park, Pennsylvania 16802, USA
²Department of Mechanical and Nuclear Engineering, Pennsylvania State University, University Park, Pennsylvania 16802, USA
³Department of Mechanical Science and Engineering, University of Illinois, Urbana, Illinois 61801, USA

^*suz10@psu.edu

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Vol. 85, Iss. 19 — 15 May 2012

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Images

Figure 1
The simulation models. (a) The finite-sized crack model. Edge atoms in gray are fixed and subjected to out-of-plane pulling with directions denoted by circled dot (outward, for the edge atoms on the left) and circled cross (inward, for the edge atoms on the right), respectively. (b) The semi-infinite crack model. Atoms at the outer layer (in gray) are held fixed, while the remainder of the atoms are free.Reuse & Permissions
Figure 2
Fracture paths in graphene determined by direct MD simulations, where red dots represent oxygens and green dots represent carbons. Tearing in vacuum or in the presence of hydrogens (not shown) causes notch extension along the armchair direction (a), but along the zigzag direction in the presence of oxygens (b). GNRs with edge orientations [(c) and (d)] corresponding to different chemical additives are produced by tearing off a graphene sheet with two initial notches.Reuse & Permissions
Figure 3
Energetics and kinetics analyses of the unit bond-breaking process illustrate crack-kinking mechanisms in graphene. (a) A schematic description of the energy landscape for bond breaking at the crack tip. The energy difference between the filled black circle and the open circle gives rise to the thermodynamic driving force ( $Δ E$ ) for bond breaking, while the energy difference between the filled yellow circle and the open circle to the kinetic barrier. (b) State A with two bonds (1 and 2) highlighted at crack tip, showing two possible crack-extending directions (blue: armchair direction; pink: zigzag direction) by breaking each of the bonds; (c), (d) state B (or C) is a replica of state A, but with bond 1 (or 2) broken. A $\to$ B (or A $\to$ C) thus forms a unit bond-breaking process.Reuse & Permissions
Figure 4
Numerical determination of the Griffith load along different crystographic directions. Figures (a) to (c) plot the energy differences in vacuum, in the presence of hydrogens, and in the presence of oxygens on the fracture surfaces, respectively, for an initial armchair notch. Figures (d) to (f) plot the energy differences in vacuum, in the presence of hydrogens, and in the presence of oxygens on the fracture surfaces, respectively, for an initial zigzag notch. Black curves: $Δ E_{1}$ ; red curves: $Δ E_{2}$ .Reuse & Permissions
Figure 5
Crack-tip stress ( $σ_{13}$ ) distribution suggests mode mixity. Red (blue) color represents positive (negative) stresses. (a) Continuum asymptotic solution of pure mode III; (b) the finite-size tearing model; (c) the size-reduced model with pure mode-III loading.Reuse & Permissions
Figure 6
A map of the preferred fracture paths in the plane of chemical condition and crack-tip mode mixity $φ$ . The preferred fracture paths are shaded differently (slashed for zigzag direction, and cross-hatched for armchair).Reuse & Permissions

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