NMR Studies of Secondary Relaxation Processes

Probing highly hindered motion by 2H NMR theoretical background and random walk simulations 

Due to the dead time, the correlation functions Fcos,sin(rm rp) for short tp cannot be measured with three-pulse sequences, but a further pulse is necessary to refocus the stimulated echo, leading to four-pulse sequences such as (tc/2)x — tp — (n/2) x - tm - (n/2)x - A - (rc/2)y, where the echo forms at a time tp + A after the last pulse.6,102 So far, we assumed x tp so that molecular dynamics during the evolution time can be neglected. In the studies of relaxation processes in glasses, this assumption is not justified since very broad distributions of correlation times G( 1 n x) exist. Then, it is necessary to explicitly calculate the phases (h, tf) according to Eq. (8) so that, in general, correlation functions resulting from the above four-pulse sequence can be written as 

In the field of the glass transition, the molecular orientation/position is often considered as a stochastic process and the dynamics is described in the framework of the Ivanov model, i.e., the molecular orientation/position is assumed to be constant 

In general, three steps are required to create trajectories by means of RW simulations,76,84 (i) determination of an initial orientation/position so that the equilibrium distribution is obeyed, (ii) random selection of a waiting time tw between two subsequent jumps from a suitable distribution and (iii) calculation of the new orientation/position after the jump. After step (i), the steps (ii) and (iii) are performed alternately until a trajectory of sufficient length in time is obtained. While the time scale of the motion is determined by the distribution of waiting times g(tw) in step (ii), the geometry of the motion comes into play in step (iii). For example, the new orientation 0i+ after a -degree-rotational jump of a C-2H bond can be obtained from the old orientation 0, according to 

RW simulations were performed to demonstrate that the use of suited inter-pulse delays tp in 2H NMR solid- and stimulated-echo experiments allows one to resolve spatially highly restricted reorientations.76 For this purpose, it was assumed that C-2H bonds (t] — 0) show rotational random jumps (cf Fig. 25) where all possible 

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We review nuclear magnetic resonance (NMR) studies of secondary relaxation processes in glasses. The main focus is work on molecular glasses, where the secondary relaxation is usually associated with spatially highly restricted motion. 

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