Atomistic Mechanism of Carbon Nanostructure Self-Assembly as Predicted by Nonequilibrium QM/MD Simulations

Abstract

We review our quantum chemical molecular dynamics (QM/MD)-based studies of carbon nanostructure formation under nonequilibrium conditions that were conducted over the past 10+ years. Fullerene, carbon nanotube, and graphene formation were simulated on the nanosecond time scale, considering experimental conditions as closely as possible. An approximate density functional method was employed to compute energies and gradients on the fly in direct MD simulations, while the simulated systems were pushed away from equilibrium via carbon concentration or temperature gradients. We find that carbon nanostructure formation from feedstock particles involves a phase transition of sp to sp2 carbon phases, which begins with the formation of Y-junctions, followed by a nucleus consisting of pentagons, hexagons, and heptagons. The dominance of hexagons in the synthesized products is explained via annealing processes that occur during the cooling of the grown carbon structure, accelerated by transition-metal catalysts when present. The dimensional structures of the final synthesis products (0D~spheres -- fullerenes, 1D tubes -- nanotubes, 2D sheets -- graphenes) are induced by the shapes of the substrates/catalysts and their interaction strength with carbon. Our work prompts a paradigm shift away from traditional anthropomorphic formation mechanisms solely based on thermodynamic stability. Instead, we conclude that nascent carbon nanostructures at high temperatures are dissipative structures described by nonequilibrium dynamics in the manner proposed by Prigogine, Whitesides, and others. As such, the fledgling carbon nanostructures consume energy while increasing the entropy of the environment and only gradually anneal to achieve their familiar, final structure, maximizing hexagon formation wherever possible.