Dynamics of pull and release of graphene nanoribbons

A Singh and RC Batra, COMPUTATIONAL MATERIALS SCIENCE, 197, 110568 (2021).

DOI: 10.1016/j.commatsci.2021.110568

The pull and release molecular dynamics simulations of graphene nanoribbons (GNR) lead to their length dependent several folded conformations in the ground states at finite temperatures. The folding occurs when the potential energy of the stretched GNR is sufficient to overcome the energy barriers between the flat GNR and its folded conformations. We explore the dynamics of GNRs during their pull and release as the flat GNR develops intrinsic ripples as soon as thermal fluctuations are introduced and rich mechanical phenomena are found even before the folding process starts. Nudged elastic band calculations were performed to understand the nature of energy barriers and the minimum energy paths between the flat and the rippled nanoribbons. The potential and the kinetic energies of nanoribbons show strong oscillatory characters with attenuation in amplitudes at the start and the end of the pulling process, but as soon as the release process starts the oscillatory nature becomes weak giving rise to small fluctuations. Both thermostatted and unthermostatted nanoribbons were studied with some important observations. Different equivalent continuum models were analyzed which can mimic these experiments. It has been found that the pull and release of the GNRs without any intrinsic rippling can be successfully simulated with a thin plate continuum model using Hooke's law which does not account for geometric nonlinearities and therefore is aptly able to capture small deformations of the flat GNR. This relation fails when the GNR develops ripples and then undergoes through the pull and release experiments. The rippled GNR was modeled by introducing ripples in the flat continuum GNR by nonlinear curve fitting of the atomistic z-coordinates with a sinusoidal function. Then three different constitutive relations were tried and it was found that modeling GNRs as St. Venant-Kirchhoff materials, which assume a linear relation between the second Piola-Kirchhoff stress tensor and the Green-St. Venant strain tensor correctly reproduce the atomistic behavior before the folding starts. The temperature results were also reproduced by solving the energy balance equation where a thermoelastic constitutive relation between the second Piola-Kirchhoff stress tensor and the Green-St. Venant strain tensor subtracted by the thermal strain tensor was assumed.

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