Revisiting Segmental Order: A Simplified Approach for Sulfur-Cured Rubbers Considering Junction Fluctuations and Entanglements

Abstract

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.

Sulfur-Modified Carbon Nanotubes for the Development of Advanced Elastomeric Materials

“…As shown in Figure 13 , the storage modulus of filled rubber compounds showed a decrease in the applied deformation (this is named the “ Payne effect ”), while it remained practically constant in the unfilled composites. This non-linear behavior is amplified with an increasing filler volume fraction, being interpreted as the rupture of the filler network when rubber samples are subjected to high deformations and the subsequent liberation of trapped rubber in filler aggregates as well as rubber–filler bonding and debonding mechanisms [ 64 , 65 , 90 , 91 , 92 , 93 , 94 , 95 ]. Following this concept, the significant reduction of the Payne effect for NR/TCNT and NR/CCNT samples compared to the non-modified CNT filled samples should be related to important differences in the filler networking and/or the rubber fraction affected by the existence of filler aggregates.…”

“…In this work, 1 H DQ-NMR experiments were performed in a low field spectrometer to obtain detailed information about the structure of the NR compounds and how the functionalization of CNT affects the rubber network structure. Figure 18 shows the obtained distributions of the residual dipolar couplings, D res , which is proportional to the molecular weight distributions between constraints (i.e., entanglements, cross-links and filler–rubber interactions) [ 60 , 65 , 95 , 103 ].…”

“…Thus, this signal is used to realize a point-by-point normalization of DW intensity, I DQ . The analysis of the so-obtained normalized DQ build-up curve ( I nDQ = I DQ / I ΣMQ ) by using a numerical inversion procedure based on fast Tikhonov regularization is used to obtain the actual distribution function of residual couplings [ 64 ], D res , which is directly related to the spatial distribution of rubber network constraints in the sample [ 60 , 65 ]. More details about the 1 H DQ-NMR measurement and analysis procedure applied to the CNT-NR samples are given in the Supporting Information section in the reference [ 20 ].…”

Poly(acrylonitrile-co-butadiene) as polymeric crosslinking accelerator for sulphur network formation

“…Finally, it should be noticed that rubber networks are not perfect and they contain elastically inactive defects such as dangling chain ends and unentangled loops, which are attached to the rubber network and therefore un-extractable, and also free (uncrosslinked) rubber chains that is commonly associated to the sol-content of the network. Thanks to recent studies, these network defects (including the non-extractable fraction) are accessible by DQ-NMR spectroscopy [ 45 , 46 , 49 , 54 ] because they show slower relaxation processes as compared to the faster decay of the network segments. According to the non-coupled network defects fraction obtained from Figure 4 b (e.g.…”

“…crosslinks ( N c ) and entanglements ( N e ), being that dependence defined by the applied model of rubber elasticity [ 49 ]. Considering the Lang-Sommer model [ 48 ] and assuming that (assumption valid for most of the technological valuable rubber compounds), it is possible to obtain the widely used simplified expression [ 49 ] and to apply the defined relationship for the cis-BR matrix [ 46 ]. Some particular details about the analysis procedure applied in this work will be described in the following sections.…”