Anisotropic solute–solvent interactions in liquid crystals: An analysis of dipolar and quadrupolar couplings of methane in nematic solvents

Abstract

The most complete sets of available dipolar and quadrupolar couplings obtained from the NMR spectra of methane and its deuterated analogs dissolved in two different liquid crystals are analyzed. The analyses are based on a generalized theory for the correlation between the vibration and rotation of partially oriented molecules, which retains the quadratic terms in the Taylor series describing the functional dependence of the orienting forces on the vibrational normal coordinates. These quadratic terms are essential for the cases where vibrational effects (e.g., isotope effects) on the molecular orientation are of importance. In both liquid crystals all the 17 couplings can be reproduced by three adjustable parameters which describe the forces acting on the CH or CD bonds. However, the resulting forces are unexpectedly strong, and physically more plausible solutions are obtained by allowing for an additional parameter Bdp+Bext. Bdp and Bext are contributions to quadrupolar couplings arising from direct perturbations of the molecular electron distribution and external electric field gradient due to the neighboring molecules, respectively. The values of Bdp+Bext corresponding to plausible solutions can be rationalized in terms of (1) orientation dependent direct perturbations of the order of 0.5% on the quadrupole coupling constant of the deuteron, or (2) an external field gradient produced by the quadrupole moments of the liquid crystal molecules surrounding a cylindrical cavity which encloses the methane molecule. Independent values of Bext, estimated previously by the quadrupolar couplings of the hydrogen molecule, are strikingly similar to the present values of Bdp+Bext. The results appear to be consistent with two different physical interpretations: the anisotropic forces experienced by the methane molecule may be dominated by (1) the van der Waals forces acting on its atoms, or (2) the interaction between its quadrupole moment and the external field gradient. The results also lend support to the assumption that the molecular distortions due to a liquid crystal environment are normally dominated by bond-bending deformations.