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.

Novel information on filler−elastomer interactions is obtained by combining solid-state 1H low-field NMR spectroscopy and equilibrium swelling experiments. Multiple-quantum (MQ) NMR experiments provide detailed quantitative molecular information on the cross-link density of the elastomer matrix in a variety of filled systems, indicating generally weak filler effects on the overall cross-link density and on the network homogeneity. Swelling experiments, as well as mechanical data, are additionally influenced by the matrix−filler and filler−filler interactions. Our approach is based on comparing cross-link densities from NMR and (Flory−Rehner) swelling experiments, for which a masterline is always found in unfilled elastomers. In filled elastomers two different scenarios are observed. If there are no interactions between the polymer chains and the filler surface, no deviations from the masterline are detected because the swelling capacity of the composite is governed by the bulk polymer. Deviations from the masterline (reduced swelling) are exhibited by those composites that have strong rubber−filler interactions. In these cases, some fraction of the polymer is connected to the filler surface, which thus behaves like a giant cross-link, and the overall degree of swelling is thus reduced as compared to the bulk polymer. The novel experimental approach was used to evaluate filler−elastomer interactions in different composites and nanocomposites.

The network structure and chain dynamics of ionic elastomers based on carboxylated nitrile rubber (XNBR) cross-linked with different content of magnesium oxide (MgO) have been studied by different low-field time-domain NMR experiments. Ionic contacts created during the vulcanization tend to aggregate trapping some polymer segments that show restricted mobility as it was quantified by analyses of refocused free induction decays. Increasing the MgO content above the stoichiometric fraction has no effect on the amount of trapped polymer segments, but it increases the network cross-link density as measured by multiple-quantum (MQ) NMR experiments. The central finding of this work is that MgO addition above the stoichiometric content enhances the mechanical properties by creating a larger number of smaller ionic clusters, which act as dynamic cross-links, but are not readily seen by other techniques. Changes in the network structure and morphology of segregated thermolabile ionic domains have an impact on the ionic rearrangement dynamics and, in consequence, on the thermoplastic behavior of these materials at elevated temperatures.

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