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.

The goal of this project is to use the Monte Carlo method to speed up study of graphene hydrogenation. A Monte Carlo simulation requires an absorption probability for each site. In order to obtain reasonable results without an enormous parameter space, a probability for each nearest neighbor(NN) configuration should be determined. Ten possible arrangements of hydrogen atoms attached to the nearest neighbors exist.

#### Calculating Probability

The hard cube model is the theoretical basis for calculating the probability of absorption. This model involves integrating the Maxwell-Boltzmann speed distribution from a minimum to aa maximum velocity and normalizing.

#### Finding Velocities

The minimum and maximum velocities were found using ReaxFF 2, a molecular dynamics program. A Hydrogen atom was 'shot' at the graphene sheet at different velocities, and its impact with the surface was analyzed. After finding a general range, the velocity was incremented slowly to find the maximum and minimum speed which still yielded bonding to the plane.

#### Results

The discovered velocities fall into threeâ€ ranges with a large separation between each range. The underlying cause of this separation is undetermined. Since the Maxwell-Boltzmann Distribution is dependant on temperature it is important to maintain that dependance in thhe probability calculation. The graph below shows this temperature dependence as well as visually showing the grouping effect. Click the graph to see the full size version.

#### Conclusions

- There is in fact a correlation between NN configuration and absorption probability.
- The absorption energy for pristine graphene is larger than results obtained from DFT.
- The probability curves are grouped, which implies a more fundamental relationship.

#### Future Work

- Apply probabilities to Monte Carlo simulation
- Compare ReaxFF results with DFT simulations
- Study graphane clustering with percolation and Monte Carlo simulation
- Use same methods for flourine