Characterization of Molecular Motion in the Solid State by Carbon-13 Spin–Lattice Relaxation Times

Abstract

Relaxation calculations for rapidly spinning samples show that spin–lattice relaxation time (T1Z) anisotropy varies with the angle between the rotor spinning axis and the external field. When the rate of molecular motion is in the extreme narrowing limit, the measurement of T1Z anisotropies for two different values of the spinning angle allows the determination of two linear combinations of the three static spectral densities, J0(0), J1(0), and J2(0). These functions are sensitive to molecular geometry and the rate and trajectory of motion. The utility of these linear combinations in the investigation of molecular dynamics in solids has been demonstrated with natural abundance 13C NMR experiments on ferrocene. In an isolated 13C–1,2H group, the dipole–dipole interaction has the same orientational dependence as the quadrupole interaction. Thus, the spectral densities that are responsible for dipolar relaxation of 13C are the same as those responsible for deuteron quadrupolar relaxation. For ferrocene-d10, deuteron T1Z and T1Q anisotropies and the relaxation time of the 13C magic angle spinning peak provide sufficient information to determine the orientation dependence of all three individual spectral densities.