Neutron-scattering spectra from the hindered rotation of methane in methane + krypton mixtures adsorbed on graphite

Abstract

Incoherent neutron-scattering spectra associated with the hindered rotation of CH₄ in CH₄+ Kr mixtures adsorbed on graphite are described. The spectra, taken over a composition range from 0.3 to 0.9 mole fraction of Kr, indicate partial phase separation into domains of pure CH₄ and krypton-rich domains.

Using the energies, intensities and polarization of the transitions the spectra of CH₄ in the krypton-rich domains have been assigned and found to be consistent with a potential field of trigonal symmetry.

Quantitative calculations of the barriers to rotation have been made using a procedure which uses symmetrized free-rotor functions as a basis set. In the limit when CH₄ is nearly completely surrounded by Kr atoms the barrier heights for threefold rotation about the unique C—H axis normal to the surface and about each of the three equivalent C—H bonds are 31 ± 5 and 79 ± 10 cm^–1, respectively. As the Kr/CH₄ ratio is reduced the unique barrier height increases from 31 (10:1), through 39 (6:1) and 47 (2:1) to 55 cm^–1 for a 1:1 mixture. The other barrier height does not change over the same concentration range.

Atom–atom potential calculations on an ordered CH₄+ Kr₂ mixture with each CH₄ surrounded by six Kr atoms are able to account for the barrier about the equivalent C—H bonds but not for that about the unique axis.