Time-Domain NMR Observation of Entangled Polymer Dynamics: Analytical Theory of Signal Functions

We present a full analytical treatment of signal functions in time-domain NMR of entangled polymer melts. Our approach is based on the segmental orientation autocorrelation function for entangled chains previously determined experimentally via field cycling NMR, on the one hand, and via analyzing the initial rise of normalized double-quantum buildup curves, on the other hand, which yield consistent data over about 10 decades in time based on time-temperature superposition. The correlation function is similar to but deviates in a few aspects from the predictions of the tube model. We use the Anderson-Weiss approximation to derive formulas for different signal functions for simple transverse relaxation experiments and specifically for the signal functions from multiple-quantum. NMR We demonstrate that our treatment is, for moderate NMR evolution times, in good agreement with proton NMR data of entangled poly(butadiene) samples over large temperature and molecular weight ranges. Our results represent a showcase for the applicability of the Anderson Weiss approximation for the calculation of transverse relaxation phenomena of entangled polymers. Open questions concern the exact form of the autocorrelation function at very short times, where it reflects the local (glassy) dynamics.