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.
