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

FABIAN VACA CHAVEZ; KAY SAALWAECHTER

MACROMOLECULES

AMER CHEMICAL SOC

Lugar: Washington; Año: 2011 vol. 44 p. 1560 - 1569

0024-9297

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 protonNMRdata 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. I. INTRODUCTION Since de Gennes presented the reptation model almost 40 years ago,1 the experimental study of polymer dynamics and its theoretical understanding has been an active focus of polymer physics. The reptation model describes the motion of an entangled polymer chain through a net of immobile obstacles representing the other polymer chains, creating a ?tube? which the chain is confined to. A combination with the Rouse theory for unentangled chains2 resulted in what is today referred to as the tube model of polymer dynamics.3 This model describes entangled melt rheology qualitatively well, yet the improvements? or the necessity for an entirely new theoretical approach? needed to achieve a truly quantitative understanding are a matter of active debate.4 While the melt rheology, ideally in the form of mechanical spectroscopy, stands at the very heart of any serious endeavor to understand polymer melt properties,5 the understanding of the data requires the use of theoretical models. In turn, actual, critical tests of model ingredients are the domain of molecular techniques, where dielectric spectroscopy6 and scattering techniques7 stand out in that they have entered the realm of textbook knowledge.8 NMR, while offering a rich toolbox of multiple techniques to study polymer structure and dynamics,9,10 is not yet on par with its competitors as to its reception in the polymer physics community, mainly owing to its utter complexity. We here hope to improve on this aspect, stressing the use of a simple segmental orientation autocorrelation function (OACF) as a descriptor of polymer dynamics