Two dimensional nuclear magnetic resonance relaxation spectroscopy of molecular solids

Abstract

Molecular motions in solids cover a broad dynamic range, extending from the fast rotational to the ultraslow motional regime. Two dimensional (2D) NMR relaxation spectroscopy is designed to follow these motions and to differentiate the various motional modes. The method employs the pronounced anisotropy of the nuclear spin relaxation times, observed for polycrystalline or multidomain samples. Generally, 2D NMR relaxation spectra are obtained by recording the time signals S(t2) after the last pulse as a function of successive incremented time intervals t1, corresponding to the relaxation period of the particular sequence. A Fourier transformation in both time domains transforms S(t1,t2) into a 2D representation S(ω1,ω2) of the relevant relaxation experiment. The normalized contour plot then displays the change of the corresponding relaxation rate 1/Ti along the frequency spectrum. It turns out that this variation is very dependent upon the character of the molecular motion. Model calculations for deuterons, involved in planar motions, demonstrate the potential of 2D NMR relaxation techniques. Generally, the type of motion can reliably be deduced from the shape of the contour plots. A model independent analysis provides the geometrical parameters of the dynamic process, including the jump angle ΔψK and the orientation ϑK of the rotation axis in the magnetic frame. In addition, from the separation of the contour lines the motional correlation times can be determined. The techniques are employed in the dynamical characterization of L-alanine, specifically deuteriated at the methyl group. From an analysis of 2D quadrupole echo spectra geometrical parameters of ΔψK=(120±1)° and ϑK=(70.5±1)° have been determined. Apparently, methyl group reorientation in L-alanine occurs via three-site jumps about a rotation axis, tilted by an angle of ϑK=70.5° relative to the C–2H bond direction. Computer simulations of 2D quadrupole echo and inversion recovery experiments provide the correlation times for this motion. The values range from τJ=5×10−10 s at T=353 K to τJ=3×10−5 s at T=140 K. An Arrhenius plot for these correlation times is linear over the entire dynamic range. From the slope of the straight line an activation of Ea=20 kJ/mol has been determined.