  Meyer et al (2007) found that free-standing graphene sheets, just one atom
thick, display spontaneous ripples. The ripples are of order 2-20 {\AA} high
and 20-200 {\AA} wide. The sheets in which they appear are only one atom thick,
and extend for around 5000 {\AA} through vacuum between metal struts that
support them. Other groups have since created free-standing graphene as well
(Garcia-Sanchez 2008 ; Bolotin et al. 2008), and similar ripples have been
found for graphene on a glass substrate (Geringer et al. 2008). Here we show
that these ripples can be explained as a consequence of adsorbed molecules
sitting on random sites. The adsorbates cause the bonds between carbon atoms to
lengthen slightly. Static buckles then result from a mechanism like the one
that leads to buckling of leaves; buckles caused by roughly 20% coverage of
adsorbates are consistent with experimental observations. We explain why this
mechanism is more likely to explain rippled than thermal fluctuations or the
Mermin-Wagner theorem, which have previously been invoked.
