  We show that charge doping can induce transitions between three distinct
adsorbate phases in hydrogenated and fluorinated graphene. By combining ab
initio, approximate density functional theory and tight binding calculations we
identify a transition from islands of C$_8$H$_2$ and C$_8$F$_2$ to random
adsorbate distributions around a doping level of $\pm 0.05$ e/C-atom.
Furthermore, in situations with random adsorbate coverage, charge doping is
shown to trigger an ordering transition where the sublattice symmetry is
spontaneously broken when the doping level exceeds the adsorbate concentration.
Rehybridization and lattice distortion energies make graphene which is
covalently functionalized from one side only most susceptible to these two
kinds of phase transitions. The energy gains associated with the clustering and
ordering transitions exceed room temperature thermal energies.
