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In 2007, we predicted the compound Graphane: a graphene-like structure with a 1:1 composition of Carbon and Hydrogen with stability better than mixtures of cyclohexene and graphite. In January of 2009, Elias et al. published evidence of graphene’s reversible hydrogenation by exposure to hydrogen plasma [D. C. Elias et al., Science 323, 610 (2009)] though full hydrogenation of the sample did not seem readily apparent. In contrast, CF, a fluorinated analog of graphane, forms much more easily. Our current work aims to explain the true barriers of adsorption for Graphene-H and Graphene-F as well as model the random process of graphene’s exposure to hydrogen plasma. With this knowledge, we can find the most energetically favorable reaction pathways and hope to engineer the barrier of adsorption to facilitate graphane’s formation further.

Graphene’s π band is formed with the same orbitals used for bonding with H as well as F. In both cases, the p_z electron of the interacting carbon is ‘cut’ from the π band to sp3 hybridize with its adsorbate. Through DFT calculations we have adiabatically probed the Graphene-H and Graphene-F interactions in detail, finding a 0.2eV barrier of adsorption for Hydrogen and no barrier for Fluorine. We attribute this barrier difference to the electronegativity of Fluorine (3.98 in the Pauling scale) compared to Hydrogen (2.20 in the Pauling scale) relative to Carbon (2.55 in the Pauli scale). Fluorine’s extra negativity allows for charge to transfer from the Graphene sheet, weakening the π band and allowing for electrostatic attraction. In the case of the Hydrogen, the π band is only weakened by the puckering and subsequent sp3 hybridization of the bonding carbon, which costs 0.2eV before bonding and gaining 0.78eV overall. Our current work involves charging the graphene plane by removing electrons from our DFT simulation to probe the effect of charge on this adsorption barrier.  To analytically support our DFT results, we are also studying a 3-electron tight binding model which takes into account the distance dependence of hopping integrals between the bonding Carbon and the graphene π band, as well as the bonding Carbon and the Hydrogen. Coulombic terms are also taken into account to observe the charge transfer influence on bonding for Hydrogen compared to Fluorine. These results are the contents of a manuscript currently under preparation. We have also carried out lattice relaxations of graphene cells under varying amounts of hydrogenation. Relaxations yield relatively stable averaged lattice constants up to ~40% hydrogenation, which is close to the percolation threshold of 30.3% for an infinite hexagonal lattice [P. N. Suding, and R. M. Ziff, Physical Review E 60, 275 (1999)] . Beyond this point, the lattice constant depends on the hydrogenated topology, reaching 2.54Å for full hydrogenation.

The dynamic process of hydrogenation is also of interest. In the experiment by Elias et al, graphene was exposed to cold hydrogen plasma while on a SiO₂ substrate as well as suspended within a TEM grid to allow for single and double sided exposure, respectively. We are using a version of the reactive force field molecular dynamics code ReaxFF [A. C. T. van Duin et al., The Journal of Physical Chemistry A 105, 9396 (2001)] , modified by its creator, Adri van Duin, to simulate the dynamic interactions between a “plasma” of H atoms and a graphene plane. With this code, we can model the hydrogenation process on a relatively large scale (1000+ atom) and much quicker than a similar simulation using DFT.

Due to the quick nature of the ReaxFF plasma simulations, probabilities of adsorption have been constructed for a Hydrogen atom nearing a Carbon atom with its nearest neighbors in all possible hydrogenated or dehydrogenated configurations. From these probabilities, a random site Monte Carlo approach to hydrogenation can be run on 10^6 atom graphene cells. These simulations reveal the topology of a cell under hydrogenation on a near macroscopic scale, which is of great value to experiment. Current results show that adsorption probabilities are highest when two or three of the bonding Carbon’s nearest neighbors are hydrogenated on the opposite side, and  lowest for pristine neighbors of the bonding site, giving further evidence of a clustering of hydrogenation around a seed site.