Robust quantitative cross-link density characterization becomes necessary for the complete understanding of the structure and optimization of final properties of rubber compounds for industrial applications. A combination of different experimental techniques have been used to establish the quantitative consistency on the correlations between the results obtained by the individual methods within a reliable unique (physically based) platform reclined on the concept of rubber elasticity that considers the impact of entanglements in technical rubbers. The contribution of cross-links and elastically active entanglements to mechanical properties has been quantified by the analysis of uniaxial stress–strain measurements by means of the extended tube model of rubber elasticity. In a complementary manner, rubber network structure has also been investigated by state-of-the-art multiple-quantum low-field NMR experiments and classical T1 and T2 relaxation measurements. In addition, equilibrium swelling data were analyzed by the classical phantom and Flory–Rehner limits as well as by applying the theoretical approach proposed by Helmis, Heinrich, and Straube that takes into account topological constraints during swelling. Correlations among these complementary techniques have been reported, and the interpretation of the obtained differences is addressed. The baseline study focuses on unfilled NR, setting the basis for the investigation of unfilled SBR matrices and filled rubbers.

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.

Immiscible blends of elastomers present high technological interest, and the selection of the vulcanization system is important for the optimization of properties for different technical applications. In particular, the effect of the curing agents on the distribution of cross-links in each phase is key for the full comprehension of the structure−property relationships. Aiming at the understanding of the phase-specific network structure in rubber blends, this work presents an innovative strategy for the quantitative characterization of the local viscoelastic properties of immiscible rubber blends by atomic force microscopy (AFM) measurements. A systematic study on the quantitative nanomechanical characterization by AFM of unfilled single natural rubber (NR) matrixes with different degrees of cross-link densities ultimately allows for the estimation of the phase-specific cross-link density of the NR phase in NR/butadiene rubber (BR) blends, prepared with varying vulcanization systems. Complementary chemical information by highresolution secondary ion mass spectrometry imaging is able to reveal differences in sulfur contents in each elastomeric phase of the blends.

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For the first time since its formulation in 1986, the theoretical approach proposed by Helmis, Heinrich and Straube (HHS model), which considers the contribution of topological restrictions from entanglements to the swelling of polymer networks, is applied to experimental data. The main aspects and key equations are reviewed and their application is illustrated for unfilled rubber compounds. The HHS model is based on real networks and gives new perspectives to the interpretation of experimental swelling data for which the entanglement contributions are usually neglected by considering phantom network models. This investigation applies a reliable constrained-chain approach through a deformation-dependent tube model for defining the elastic contribution of swollen networks, which is one of the main limitations on the applicability of classical (affine) Flory-Rehner and (non-affine) phantom models. This short communication intends to provide a baseline for the application and validation of this modern approach for a broader class of rubber materials.

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