  The mechanical, electrical and chemical properties of chemically modified
graphene (CMG) are intrinsically linked to its structure. Here we report on our
study of the topographic structure of free-standing CMG using atomic force
microscopy and electron diffraction. We find that, unlike graphene, suspended
sheets of CMG are corrugated and distorted on nanometre length scales. AFM
reveals not only long range (100 nm) distortions induced by the support, as
previously observed for graphene, but also short-range corrugations with length
scales down to the resolution limit of 10 nm. These corrugations are static not
dynamic, and are significantly diminished on CMG supported on atomically smooth
substrates. Evidence for even shorter range distortions, down to a few
nanometres or less, is found by electron diffraction of suspended CMG.
Comparison of the experimental data with simulations reveals that the mean
atomic displacement from the nominal lattice position is of order 10% of the
carbon-carbon bond length. Taken together, these results suggest a complex
structure for chemically modified graphene where heterogeneous
functionalisation creates local strain and distortion.
