  The instability of a free-standing one sided hydrogenated/fluorinated
graphene nano-ribbon, i.e. graphone/fluorographene, is studied using ab-initio,
semiempirical and large scale molecular dynamics simulations. Free standing
semi-infinite arm-chair like hydrogenated/fluorinated graphene (AC-GO/AC-GF)
and boat like hydrogenated/fluorinated graphene (B-GO/B-GF) (nano-ribbons which
are periodic along the zig-zag direction) are unstable and spontaneously
transform into spiral structures. We find that rolled, spiral B-GO and B-GF are
energetically more favorable than spiral AC-GO and AC-GF which is opposite to
the double sided flat hydrogenated/fluorinated graphene, i.e.
graphane/fluorographene. We found that the packed, spiral structures exhibit
unexpected localized HOMO-LUMO at the edges with increasing energy gap during
rolling. These rolled hydrocarbon structures are stable beyond room temperature
up to at least $T$=1000\,K.
