  We consider the effect of atomic hydrogen exposure to a system of two undoped
sheets of graphene grown near a silica surface (the first adsorbed to the
surface and the second freestanding near the surface). In the absence of atomic
hydrogen the van der Waals force between the sheets is attractive at all
separations causing the sheets to come closer together. However, with addition
of atomic hydrogen between the sheets the long range van der Waals interaction
turns repulsive at a critical concentration. The underlying triple layer
structure (SiO2 -Atomic Hydrogen Gas -Air) gives rise to a long range repulsion
that at large enough separations dominates over the more rapidly decaying
attraction between the two-dimensional undoped graphene sheets (and between the
outer graphene sheet and SiO2). This may be an avenue to tune the separation
between two graphene sheets with the gas concentration. Doping of the graphene
layers increases the attractive part of the interaction and hence reduces the
net repulsive interaction.
