  Using the molecular dynamics method, dynamics of hydrogen bond (HB) networks
emerging on the surface of a graphene sheet during its functionalization with
hydroxyl groups OH are simulated. It is demonstrated that two OH groups form an
energetically more advantageous structure when they are covalently attached on
one side of the sheet to carbon atoms forming opposite vertices of one hexagon
of valence bonds of the sheet. Attaching of OH groups to carbon atoms located
at the opposite vertices of hexagons of valence bonds leads to the emergence of
hydroxygraphene C$_4$(OH). In such sheet lying on a flat substrate, attached
oxygen atoms on its outer surface form a hexagonal lattice, and hydroxyl groups
due to their turns can in various ways form chains of hydrogen bonds. The
modification of the sheet from two sides results in forming of hydroxygraphene
C$_2$(OH) with HB networks on both sides of the graphene sheet. Simulation of
the dynamics of these sheets shows that their heat capacity at low temperatures
$T<T_0$ increases monotonously when the temperature rises, reaches its maximum
at $T=T_0$ and then decreases monotonically. The initial growth is caused by
the accumulation of orientational defects in the lattice of hydrogen bonds
whereas the decrease at $T>T_0$ is explained by the "melting" of the lattice.
For one chain of OH groups connected to the outer side of a nanoribbon the
melting temperature is $T_0=500$K, while for a graphene sheet C4(OH) modified
on one side $T_0=260$K, and for a graphene sheet C$_2$(OH) modified on both
sides $T_0=485$K.
