Exceptional properties (electronic spectrum and transport, thermal conductivity, high Young’s modulus) of 2D materials are at the forefront of current research thanks to the recently discovered graphene and other 2D materials (e.g., hexagonal boron nitride (h-BN), fluorographene (FG), MoS2, silicene, etc.).

The vibrational properties of graphene nano-flakes (GNFs) with and without H-passivation were investigated using classical molecular dynamics simulations. The frequency of the normal modes as a function of the number of atoms for GNFs and H-passivated GNFs were investigated. The phonon density of states of different GNFs were compared with theoretical results for graphene and found to be in good agreement. The melting temperature of small GNFs was found to be lower than those for graphene and graphene nano-ribbons, and on average increases versus the number of atoms in GNFs. The melting temperature of defective GNFs are found to be lower than defect free nanoflakes. H-passivated GNFs have a higher melting temperature than the non H-passivated GNFs with the same number of C-atoms. Using density functional theory, the electronic properties of GNFs were reported for two different atoms (H and F) of edge termination. The n-fold symmetry causes no net dipole in GNFs. Breaking the n-fold symmetry by heptagon and pentagon defects and reducing the symmetries to mirror symmetry enhances the polarization. We found that larger the dipole moment, lower the energy gap for both type of saturated atoms.

The thermal properties of h-BN and FG sheets were studied using large scale atomistic simulations. The scaling properties of a h-BN sheet follows closely the results of membrane theory and hence the thermal excited ripples are not characterized by any particular wave-length. An increasing trend of bending rigidity of h-BN with temperature is found which is smaller than the one of graphene. The different stiffness between the GE and h-BN sheets leads to different patterns of deformations in the presence of either uniaxial or shear stress. Fluorographene remains a flat sheet similar to graphane even at high temperature, i.e. up to 900 K. The bending rigidity of FG is found to be independent of temperature and its Young's modulus is in good agreement with experiment. The melting temperature for fully fluorinated graphene (FFG) was found to be 2800 K which is twice lower than melting of graphene (5500 K).