Graphene is a conductor with extremely high electron mobility. This high electron mobility will lead to an increase in the speed of electronic devices through a reduction of the heat dissipation. Due to the increase in operating speed, graphene will possibly replace silicon in the next generation of electronic devices. However, graphene is a two dimensional sheet of carbon atoms. To create conducting channels and devices we need to embed graphene into an insulating matrix. Our group found that by hydrogenation a gap larger than 3.5 eV can be produced in graphene, forming a compound called graphane. The problem is the creation of this 100% hydrogenated graphene, graphane, has yet to be verified.

My project is to use a Monte Carlo approach to analyze the hydrogenation of graphene. The first task is to calculate the probabilities of an atom sticking to the sheet of graphene. The probability is derived from the Maxwell-Boltzmann speed distribution of a hydrogen atom moving towards a sheet of graphene. Atoms with too low velocity cannot overcome the formation barrier while atoms with too large velocity bounce back. This sets the upper and lower velocity are used as the limits of integration. The minimum kinetic energy, and consequently the minimum velocity, required for absorption is related to the energy barrier of the reaction. The maximum velocity is derived from a hard cube model of the collision.

Once reasonable probabilities are calculated analysis of the hydrogenation can begin. Cluster size, number of clusters, shape of clusters, and percent hydrogenation are some of the variables of interest. These variables will be used to measure defects and help determine how close the product of the simulation is to ordered graphane. This work can also be applied to fluorine. These results will be compared to molecular dynamics simulations performed by other group members. The probabilistic approach is advantageous because it runs much faster, while providing similar results.