Mechanism and free-energy barrier of the type-57 reconstruction of the zigzag edge of graphene

Abstract

Recent ab initio calculations without spin [P. Koskinen et al., Phys. Rev. Lett. 101, 115502 (2008)] predict that the zigzag edges of graphene should be reconstructed, albeit with an energy barrier to be overcome. After verifying that spin-polarized calculations give qualitatively the same result, we study the mechanism and the free energy of the reconstruction of the zigzag edges from a periodic hexagon structure (zz) to an alternate pentagon-heptagon structure [zz(57)] using the empirical long-range carbon bond order potential II (LCBOPII) potential. The zz(57) edges are stabilized by an almost triple bond similar to that of the armchair edges, and we propose a way to account for this quantum mechanical effect in the LCBOPII potential. Aside from that, the reconstructed edge is flat as a result of tensile edge stress. The reconstruction occurs spontaneously in molecular dynamics simulations at high temperature, leading to the identification of a reaction coordinate for the reconstruction that allows us to calculate the free-energy barrier by using Monte Carlo simulations and umbrella sampling. At room temperature, we find a free-energy barrier of 0.83 eV for the first transformations of two hexagons to a pentagon-heptagon pair that is higher than the one for a fully reconstructed edge and increasing with temperature.

Melting temperature of graphene

“…With an (average) value of γ sv ≃ 1.05 eV/Å for a graphene ribbon from Ref. [21] and taking q ρ ≃ 1 we find γ lv ≃ 0.47 eV/Å . These edge energies, and also γ sl = 0.134 eV/Å from KNT reported above, are physically sound, with γ sv > γ lv > γ sl .…”

Mechanical failure of zigzag graphene nanoribbons under tensile strain induced by edge reconstruction

“…It has been proposed that the zigzag edge is metastable and a planar transition from hexagon-hexagon pairs to pentagon-heptagon pairs (StoneWales defect) spontaneously takes place at room temperature 14 or high temperature. 15 On the other hand, it has been demonstrated that the transition energy barrier is 1.12 eV that is large enough to prevent transition from hexagon-hexagon to pentagon-heptagon pairs. 16 However, the transition can occur under tensile strain larger than about 5% at room temperature.…”

Strain-activated edge reconstruction of graphene nanoribbons

“…3(c) and 3(d). Previous findings indicate that this transition barrier is less than 0.7 eV, 31,32,34 which implies that the reconstruction takes place spontaneously at room temperature. The first step of the reconstruction has the largest barrier (0.8 eV) as compared to further reconstruction steps.…”

“…Also, moleculardynamics calculations show that the zigzag and armchair edges are undulated in the out-of-plane direction, whereas the pentagon-heptagon edge is completely flat. 34 This implies that the reconstruction results in edge stress. A GNR with lattice parameter a 0 is subject to a compressive (tensile) strain of −1.4 (+4.4) nN in the zigzag (FR) edge configuration (for w > 2) [see Fig.…”

“…The first step of the reconstruction has the largest barrier (0.8 eV) as compared to further reconstruction steps. 34 We find a first transition barrier of E 0 = 1.12 eV. Employing transition state theory, we use the relation k = v G exp(−E a /RT ) with frequency v G = 5 × 10 12 s −131 to obtain a rapid transition rate of 7 × 10 −6 s −1 , which suggests that the reconstruction is impossible at room temperature.…”