Mean field theory of the orientational properties of (<i>J</i> = 1) hydrogen molecules on the surface of Grafoil

A mean field theory is developed which is applicable to the orientational behavior of (J = 1) hydrogen molecules on the surface of Grafoil. The hydrogen molecules are assumed to form a triangular lattice in a weak, axially symmetric crystal field, Vc. perpendicular to the substrate and to interact via the electric quadrupole–quadrupole interaction with nearest-neighbor coupling constant Γ. Free energy calculations for the various possible ordered phases are presented, and a Landau expansion is used to investigate the phase boundary between the disordered and ordered phases. A computer calculation, based on the iterative method of James, is used to determine the lines of transition between ordered phases. For almost all values of Vc < 22.5Γ, the disordered to ordered state phase transition is continuous. Four distinct types of ordered phases are found — a four-sublattice phase, two two-sublattice phases, and a one-sublattice phase which resembles an X–Y model. Comparison is made to the recent nmr data of Kubik and Hardy for H2 and D2 on Grafoil.

Mean field theory of the orientational properties of (J = 1) hydrogen molecules on the surface of Grafoil Journal Articles