Effects of spatial disorder in modelling the anomalous diffusion of tracer particles on a graphene lattice


Modern microscopic techniques such as high resolution transmission electron microscopy have been developed by experimentalists in order to track the anomalous diffusion of tracer particles. By using the site percolation model, this paper investigated the effects of spatial disorder on a graphene lattice and how parameters such as the percolation threshold contributes to a significant deviation from the linear diffusion equation. In order to obtain the numerical percolation threshold, a cluster-identifying algorithm was developed. This value was found to be 0.7139 which has a theoretical deviation of 2.542%. After establishing this, simulations of the particle diffusing on the percolating system with p=0.7139 were done and its mean squared displacement (MSD) at each time step t was extracted. After analysis of the log-log plot of the MSD vs. number of steps taken, it was found that the particle exhibited subdiffusive behavior for the different cases tested because it violated Einstein's third condition for linear diffusion.