Using molecular dynamics to investigate the energetics and kinetics of graphene fold growth

Experiments [Annett et al., Nature, 2016, 535, 271]. have shown that auto-kirigami structures can grow on the surface of graphene because the graphene-graphene adhesion energy is greater than the graphene-substrate interaction. In this work molecular dynamics (MD) simulations of folded graphene both in vacuum and on a substrate have been performed for a range of different initial geometries and at various temperatures. The final equilibrated configuration for many of these simulations resembles a book with a fold that is at the midpoint of the graphene sheet. We investigate the amount of time it takes to move from an initial, non-equilibrated folded configuration that does not have the fold at the midpoint of the graphene to a book-like configuration that is not necessarily equilibrated. We show that graphene-graphene and graphene substrate-adhesion energies can be extracted from such simulations and that the values obtained are almost always higher than the values of these quantities that are obtained from static calculations. We also show that the rate at which these folded structures grow is affected by differences in these adhesion energies. However, this rate is also affected by factors such as the initial geometry of the graphene that do not change the adhesion energies. Understanding the kinetics of auto-kirigami formation thus requires a description of the system that is more sophisticated than the energy-balance model that is discussed in this paper.