Methane adsorbed on graphite. III. The bilayer and trilayer

Models for the monolayer, bilayer, and trilayer of methane (${\mathrm{CH}}_4$ and ${\mathrm{CD}}_4$) adsorbed on the basal plane of graphite are studied using the quantum-mechanical cell model. The calculations are made for a range of temperatures from the ground state to near the two-dimensional triple line. This microscopic finite-temperature model gives quantitative results for structural and thermodynamic properties. The results include the following: the equilibrium structure for the system, the conditions for monolayer-bilayer and bilayer-trilayer coexistence, comparisons to three-dimensional bulk solids, incommensurability to the substrate, and the chemical potential for the entire temperature range for a stable solid film. The results show that the bilayer and trilayer films are significantly compressed at coexistence. The planar nearest-neighbor distance (at coexistence) is less than that of the corresponding bulk solid. However, the chemical potential of the film is still below that of bulk value.