Spontaneous Twist and Intrinsic Instabilities of Pristine Graphene Nanoribbons

In pristine graphene ribbons, disruption of the aromatic bond network results in depopulation of covalent orbitals and tends to elongate the edge, with an effective force of f e ~ 2 eV/Å (larger for armchair edges than for zigzag edges, according to calculations). This force can have quite striking macroscopic manifestations in the case of narrow ribbons, as it favors their spontaneous twisting, resulting in the parallel edges forming a double helix, resembling DNA, with a pitch t of about 15 20 lattice parameters. Through atomistic simulations, we investigate how the torsion~1/ t decreases with the width of the ribbon, and observe its bifurcation: the twist of wider ribbons abruptly vanishes and instead the corrugation localizes near the edges. The length-scale (e) of the emerging sinusoidal " frill " at the edge is fully determined by the intrinsic parameters of graphene, namely its bending stiffness D=1.5 eV and the edge force f e with e ~D/f e. Analysis reveals other warping confi gurations and suggests their sensitivity to the chemical passivation of the edges, leading to possible applications in sensors. The special physical properties of monoatomic sp 2-carbon sheets and ribbons have been described previously [1, 2]. However, experimental testing and exploration have been hampered by the difficulty in singling out these nanoscale objects, until it was shown [3] to be possible through a direct mechanical lift-off from crystalline graphite. This has inspired further interest and multiple efforts in synthesis, chemical modifications, measurements, and theoretical models, focusing mainly on their electronic and magnetic properties [4 6]. Many of these fascinating and important phenomena depend on the geometrical structure of the flat monoatomic s h e e t m e m b r a n e , a n d c a n b e a l t e re d b y i t s deformation. Deformations can be caused by various factors, including thermal fluctuations or chemical functionalization [7], such as oxidation [8, 9]. In contrast to relatively stiff carbon nanotubes, graphene ribbons are very fl exible, " fl imsy " objects. To quantify this characteristic, one can compare the bending stiffness K of a nanotube of diameter d with the bending stiffness of a ribbon of equivalent cross section mass, that is of width w=πd. For this, the most straightforward way is to circumvent the details of atomistic calculations and apply a well parameterized shell model [10 12], …