Slow β process in simple organic glass formers studied by one and two-dimensional H2 nuclear magnetic resonance. II. Discussion of motional models

Applying random walk simulations we analyze results of one- (1D) and two-dimensional (2D) H2 nuclear magnetic resonance (NMR) experiments carried out to study the slow β process of toluene-d5 below the glass transition temperature Tg. In this way, we reveal amplitude and mechanism of rotational jumps involved in the secondary relaxation of a rigid molecule. It is shown that essentially all toluene molecules take part in the β-process. In the glass, nearly independent of temperature, the attributed reorientation is restricted to small solid angles of typically 4°–5° for the majority of particles. Only 10%–20% of the molecules exhibit amplitudes χ>10°. Concerning the mechanism of this highly restricted motion we demonstrate that the reorientation takes place step-by-step via several elementary rotational jumps one after the other. Assuming thermally activated jumps within energy landscapes which are, first, attributed to a small section of the unit sphere for each respective molecule and, second, chosen in accordance with the distribution of energy barriers g(Eβ) found in dielectric spectroscopy we succeed in reproducing the results of 1D and 2D H2 NMR experiments on toluene below Tg.