Investigating the diffusion of an atom on the graphene lattice

Abstract

Atomic-scale surface diffusion in graphene is of recent interest to determine the viability of single-atom catalysts in functionalized graphene materials. To model such behavior, we study the random walk behavior of an atom in graphene using mean square displacement (MSD). Without the presence of a driving force, the atom performing a random walk on the graphene lattice would expect to follow linear Brownian motion. We confirm this linear behavior by measuring its mean square displacement (MSD). As the atom was given a driving force, the relationship between MSD and time steps begin to follow the properties of anomalous diffusion. The highest values of α was obtained when the atom was restricted to the first six nearest neighbors while the highest diffusion coeffcient D_α was obtained when the atom is free to move to all lattice sites. The power-law relationship between MSD and time step can be controlled and serve as a precursor in understanding how the metal atom diffuses on graphene-oxide support.