Investigating the diffusion of an atom on the graphene lattice
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 a was obtained when the atom was restricted to the first six nearest neighbors while the highest diffusion coeffcient Da 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.