  We study the dependence of mechanical conformations of graphene sheets
located on flat substrates on the density of unilateral (one-side) attachment
of hydrogen, fluorine or chlorine atoms to them. It is shown that chemically
modified graphene sheet can take four main forms on a flat substrate: the form
of a flat sheet located parallel to the surface of the substrate, the form of
convex sheet partially detached from the substrate with bent edges adjacent to
the substrate, and the forms of single and double rolls on the substrate. On
the surface of crystalline graphite, the flat form of the sheet is lowest in
energy for hydrogenation density p <0.21, fluorination density p<0.20 and
chlorination density p<0.16. The surface of crystalline nickel has higher
adsorption energy for graphene monolayer and the flat form of chemically
modified sheet on such substrate is lowest in energy for hydrogenation density
p<0.47, fluorination density p<0.30 and chlorination density p<0.21. The flat
shape of the graphene sheet remains basic on a substrate also when molecular
groups CH3, CH2-CH3 or rings C6H5 are one-side attached to its outer surface.
At the attachment density p=1/6 (one group per 6 sheet atoms) the sheet becomes
the nanocarpet the basis of which is formed by a sheet of graphene and the pile
of which is formed by the attached molecular groups forming a tightly packed
regular lattice. The addition of hydroxyl groups OH with attachment density
p=1/4 leads to the formation of hexagonal lattices of hydroxyl groups on the
outer surface of graphene sheet on a substrate. In this lattice, the groups can
form various configurations of hydrogen bonds, which turns the chemically
modified sheet into a multistable system.
