F. V. Chávez, K. Saalwächter.
Time-Domain NMR Observation of
Entangled Polymer Dynamics: Analytical Theory of Signal Functions.
Macromolecules 44, 1560–1569 (2011). DOI 10.1021/ma102571u.
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