Equilibrium swelling is a feasible and simple experiment to determine the cross-link density of networks. It is the most popular and useful approach; however, in most of the cases, the given values are highly uncertain if not erroneous. The description of the complex thermodynamics of swollen polymer networks is usually based on the Flory-Rehner model. However, experimental evidence has shown that both the mixing term described by the Flory-Huggins expression and the elastic component derived from the affine model are only approximations that fail in the description and prediction of the rubber network behavior. This means that the Flory-Rehner treatment can only give a qualitative evaluation of cross-link density because of its strong dependence on the thermodynamic model. In this work, the uncertainties in the determination of the cross-link density in rubber materials by swelling experiments based on this model are reviewed. The implications and the validity of some of the used approximations as well as their influence in the relationship of the cross-link densities derived from swelling experiments are discussed. Importantly, swelling results are compared with results of a completely independent determination of the cross-link density by proton multiple-quantum NMR, and the correlation observed between the two methods can help to validate the thermodynamic model.

In this study, we focus on qualitative differences in the network structure and dynamics of natural as well as poly(butadiene) rubber in dependence of the cure system (sulfur/accelerator or organic peroxide) used in the vulcanization process. The spatial homogeneity of the distribution of chemical and physical cross-links in the network is assessed via the quantitative measurement of proton-proton residual dipolar couplings as measured by static multiple-quantum (MQ) NMR spectroscopy at low field. The experiment also provides information on the apparent correlation time of fast segmental fluctuations that dominate chain relaxation processes at lower temperature, for which we also find characteristic differences. Vulcanization via a radical mechanism (using organic peroxides) leads to networks with a high content of nonelastic defects (loops or dangling chains), a rather inhomogeneous distribution of cross-links, and modified (slower) local dynamics, as compared to networks obtained by sulfur vulcanization. These microstructural factors can be related with the well-known differences in the macroscopic properties of diene rubbers vulcanized with different cure systems.

In this work we present an improved approach for the analysis of (1)H double-quantum nuclear magnetic resonance build-up data, mainly for the determination of residual dipolar coupling constants and distributions thereof in polymer gels and elastomers, yielding information on crosslink density and potential spatial inhomogeneities. We introduce a new generic build-up function, for use as component fitting function in linear superpositions, or as kernel function in fast Tikhonov regularization (ftikreg). As opposed to the previously used inverted Gaussian build-up function based on a second-moment approximation, this method yields faithful coupling constant distributions, as limitations on the fitting limit are now lifted. A robust method for the proper estimation of the error parameter used for the regularization is established, and the approach is demonstrated for different inhomogeneous elastomers with coupling constant distributions.