On the theory of deuteron NMR free induction decay of reptating polymer chains: Effect of end segment dynamics

A self-consistent approximation beyond the Redfield limit and without using the Anderson-Weiss approximation for the Free Induction Decay (FID) of deuteron spins belonging to polymer chains undergoing reptation is formulated. The dynamical heterogeneity of the polymer segments created by the end segments is taken into account. Within an accuracy of slow-changing logarithmic factors, FID can be qualitatively described by a transition from an initial pseudo-Gaussian to a stretched-exponential decay at long times. With an increase in observation time, the contribution from end effects to the FID increases. In the regime of incoherent reptation, contributions to the FID from central segments yield an exponent of 1/4 for the stretched decay and contributions from end segments yield an exponent of 3/16. In the regime of coherent reptation, the central segments generate a stretching exponent of 1/2, whereas the end segments contribute with an exponent of 1/4. These predictions are shown to be in qualitative agreement with the experimental FIDs of perdeuterated poly(ethylene oxide) with molecular masses of 132 kg/mol and 862 kg/mol.