A novel analysis for the NMR magic sandwich echo in polymers: application to the α-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 1H-NMR signals
from systems where dipolar interaction dominates. At the sake of illustration the method is applied to
the analysis of the α-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 2H-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.