Macromolecules, Vol.51, No.5, 2076-2088, 2018
Revisiting Segmental Order: A Simplified Approach for Sulfur-Cured Rubbers Considering Junction Fluctuations and Entanglements
The use of modern multiple-quantum proton NMR experiments for the determination of cross-link density requires precise knowledge of several model-dependent physical and structural quantities, like the dipolar static frequency or the definition of vector segmental order. In this paper, different models for describing segmental order of the polymer backbone, based on different assumptions about the contribution of cross links and entanglements, are critically reviewed and applied for the analysis of unfilled natural rubber samples with average mass between cross-links and entanglements determined from network tube model fittings of stress-strain data. A recent theoretical model developed by Lang and Sommer, which allows for the consideration of junction fluctuations, is adapted for the analysis of NMR experimental results. After having verified the correlation between the calculations with this enhanced theoretical treatment and the residual dipolar coupling from multiple-quantum NMR experiments carried out in a low-field spectrometer, a new simplified approach to determine the segmental order parameter is proposed for sulfur-cured rubbers.