We studied, both theoretically and by multiscale modeling methods, the synthesis processes, structure and thermodynamics of Graphanes CH_θ (0 < θ ≤ 1), diverse polymorphous modifications of the innovative Graphene-based functional material different in stoichiometry, energy and symmetry of the long-range order of the ground state. All of them are obtained by deposition of atomic hydrogen fluxes under conditions of competition of single-layer chemisorption and desorption.

  The systematics of the ordered phases of Graphane on the basis of the simple fractions expressed degrees of coverage θ = 1/4, 1/3, 1/2, 2/3 and 3/4 of Graphene by hydrogen was introduced. It has been shown that the existence of at least one of these phases (paragraphane С₄Н, θ = 1/4) is confirmed experimentally.

 Phase diagrams of Graphanes in the variables «temperature – chemical potential» and «temperature – degree of coverage θ» have been built for the first time (see Figure 1). They manifested a second order phase transition of the «order–disorder» type with a critical temperature Tc dependent on the coverage θ and on the symmetry of the ordered low-temperature phase.

 For the thermodynamic interpretation of the phase diagrams of Graphanes, an effective phenomenological Hamiltonian of an Ising-type lattice model was proposed and a corresponding mean-field theory was constructed.

 Analytic formulas for the critical temperature T_c of the phase transition, the expression for the Gibbs free energy and the Equation of State of Graphanes were obtained. They agree quantitatively with the data obtained by means of the kinetic Monte Carlo simulation method. This allows numerical and analytical calculations of their susceptibilities (heat capacity, compressibility, etc.) valuable for prediction of their properties for Graphane applications as a functional material of modern nanoelectronics.