Deuteron NMR studies of guest motion in alkanoic acid urea inclusion compounds

The orientation dependence of deuteron relaxation times of Zeeman $(T1Z)$ and quadrupole $(T1Q)$ order have been measured in the temperature range $−30$ to $+45 °C$ for polycrystalline urea inclusion compounds containing alkyl deuterated octanoic acid-$d18,$ dodecanoic acid-$d23,$ and hexadecanoic acid-$d31.$ These data were fitted to a model, based on Redfield relaxation theory, which incorporates rapid rotation about the long molecular axis and slower, limited angle libration of individual CD bonds about a perpendicular axis. The activation energies for rotational diffusion about the long axis are $17.4±0.8 kJ/mol$ for octanoic acid-$d18,$ $14.4±0.6 kJ/mol$ for dodecanoic acid-$d23,$ and $22.5±0.4 kJ/mol$ for hexadecanoic acid-$d31$ guests. These values are larger than those for alkane guests with the same number of carbon atoms, and they increase more rapidly with increasing chain length. Quadrupole coupling constants, determined at room temperature from measurements on large single crystals, are consistent with a small gauche population near the methyl end of the alkanoic acid chains. Analytic models which relate the measured quadrupole coupling constants and relaxation times to conformational probabilities and dynamics require the assumption that rotations about individual C–C bonds are uncorrelated. Newtonian molecular dynamics simulations reveal that this incorrect assumption introduces significant error.