Hindered rotation of diatomic molecules in the adsorbed phase

• Main Author: MacRury, Thomas Bernard
• Language: English
• Published: University of British Columbia 2011
• Subjects: Molecular rotaiton
• Online Access: http://hdl.handle.net/2429/35607

The hindered rotation of diatomic molecules in the adsorbed phase is investigated using two models: 1) the adsorbent is considered to be a planar continuum and the out-of-plane rotations of the admolecule are hindered by a potential of the form V’ = ʎcos²Ф; 2) the adsorbent is now considered to be a square lattice and the admolecule localised half-way between two lattice sites. The in-plane rotations of the admolecule are hindered by a potential of the form W’ = μ(l-cos2Ф) and the out-of-plane rotations are hindered by a potential of the same form as in the first model. Using spherical harmonics as the basis set for the free rotator, a variational solution is presented for finding the eigenvalues of the out-of-plane hindered rotator. Then treating the in-plane hindrance as a perturbation on the out-of-plane hindered rotator, the eigenvalues of the out-of-plane and in-plane hindered rotator are found using variation. The out-of-plane hindrance removes all the 2ℓ+l m degeneracy of the free rotator except the ±m degeneracy. The in-plane perturbation then removes this ±m degeneracy leaving all eigenstates non-degenerate. The eigenvalues found for the two models are then used to calculate the hindered rotational heat capacities and entropies of the various nuclear spin species of hydrogen and deuterium. The heat capacities and entropies of equilibrium hydrogen (equilibrium deuterium) and orthohydrogen (pai-adeuterium) are found to be quite sensitive to the barrier heights ʎ and μ. In contrast, the thermodynamic properties of parahydrogen (orthodeuterium) are rather insensitive to rotational hindrance. Theoretical ortho-para separation factors are then compared with those measured experimentally for hydrogen adsorbed on doped alumina and for hydrogen and deuterium adsorbed on alumina. However, due to large uncertainties in the experimental data, no definitive conclusions can be drawn. Finally, the Henry's law data for hydrogen and deuterium adsorbed on graphitic carbon are analysed using the quantum corrected gas-surface configurational integral and the out-of-plane hindered rotational model. The best-fit parameters are found to be very sensitive to the rotational barrier and thus there appears to be good justification for incorporating hindered rotations in the hydrogen (deuterium)-graphite system. === Science, Faculty of === Chemistry, Department of === Graduate