Two-dimensional exchange nuclear magnetic resonance of powder samples. III. Transition to motional averaging and application to the glass transition

Abstract

The two‐dimensional (2D) exchange nuclear magnetic resonance (NMR) experiment is applied to study ultraslow as well as faster motions in powdered solids. The theoretical framework required for the simulation of 2D exchange of the faster motions, and for the evaluation of the experimental data, is developed. Calculations are presented for two standard models: two‐site jump and isotropic rotational diffusion. For discrete jump motion, anisotropic spin‐lattice relaxation during the mixing time is also considered. The resulting, simulated 2D line shapes show new characteristics in the intermediate dynamic range. Experimental data are presented for two‐site exchange in the model compound polycrystalline dimethylsulphone. The technique is then applied to study the chain dynamics of linear polystyrene in the glass transition range. Close to T_g the correlation times extracted from 2D exchange NMR exhibit strong non‐Arrhenius behavior. This data together with correlation times obtained at higher temperatures from conventional T₁ data follows the WLF equation over 11 orders of magnitude, from 10⁻⁶ to 1000 s. It is shown that 2D exchange NMR and spin‐lattice relaxation probe the α and the β process, respectively, of the chain dynamics in the glass transition region.