  We analyze the electrostatic interactions between a single graphene layer and
a SiO$_2$ susbtrate, and other materials which may exist in its environment. We
obtain that the leading effects arise from the polar modes at the SiO$_2$
surface, and water molecules, which may form layers between the graphene sheet
and the substrate. The strength of the interactions implies that graphene is
pinned to the substrate at distances greater than a few lattice spacings. The
implications for graphene nanoelectromechanical systems, and for the
interaction between graphene and a STM tip are also considered.
