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.

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.

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We study the impact of excluded volume interactions on the orientation statistics of chain segments in polymer gels, and show that nuclear magnetic resonance (NMR) experiments provide a direct and unique measure of excluded-volume effects on the chain statistics. In particular we consider the tensor order parameter, which can be expressed as the second Legendre polynomial of the segment orientation with respect to a fixed end-to-end distance vector and which is directly related to the residual coupling constant obtained in NMR experiments. We provide analytical results for the case of single chains in a good solvent and for semidilute solutions. Computer simulations using the bond fluctuation model are applied to compare with the analytical predictions. Considering polymer gels at the equilibrium state of swelling we predict a unique relation between the tensor order parameter and the correlation length (blob size) of the gel. Experiments applying multiple-quantum NMR methods to both end-linked and randomly cross-linked polymer networks are in excellent agreement with this prediction. The initial decay of the tensor order parameter as observed in experiments at low and intermediate degrees of swelling can be explained as a solvent effect without making additional assumptions about constraint release processes during swelling.

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The network structure of poly(vinyl alcohol) (PVA) hydrogels obtained by freezing−thawing cycles was investigated by solid-state 1H low-field NMR spectroscopy. By the application of multiple-quantum NMR experiments, we obtain information about the segmental order parameter, which is directly related to the restrictions on chain motion (cross-links) formed upon gelation. These measurements indicate that the network mesh size as well as the relative amount of nonelastic defects (i.e., non-cross-linked chains, dangling chains, loops) decrease with the number of freezing−thawing cycles but are independent of the polymer concentration. The formation of the PVA network is accompanied by an increasing fraction of polymer with fast magnetization decay (∼20 μs). The quantitative study of this rigid phase with a specific refocusing pulse sequence shows that it is composed of a primary crystalline polymer phase (∼5%), which constitutes the main support of the network structure and determines the mesh size, and a secondary population of more imperfect crystallites, which increase the number of elastic chain segments in the polymer gel but do not affect the average network mesh size appreciably. Correspondingly, progressive melting of the secondary crystallites with increasing temperature does not affect the network mesh size but only the amount of network defects, and melting of the main PVA crystallites at ∼80 °C leads to the destruction of the network gel and the formation of an isotropic PVA solution.