A novel analysis for the NMR magic sandwich echo in polymers: application to the ?-relaxation in polybutadiene

On the basis of a method to describe the relaxation dynamics in an ensemble of spin pairs, an analytical expression is derived for the magic sandwich echo refocusing efficiency of H-NMR signals from systems where dipolar interaction dominates. At the sake of illustration the method is applied to the analysis of the ?-relaxation in poly(butadiene). The Vogel-Fulcher-Tammann behaviour of the central relaxation rates, derived by fitting the refocusing efficiency as a function of the temperature, follows very well independent measurements performed with stimulated echo H-NMR experiments. Comparison with literature data worked out by broad band dielectric spectroscopy also shows very good agreement. In the framework of an Havriliak-Negami representation of the distribution of correlation times, information about width and asymmetry of the frequency profile is also provided by the analysis. This novel method is believed to represent a suitable path to extract basic information on the motional distribution in a variety of similar systems.