Swelling of polymer networks with topological constraints: Application of the Helmis-Heinrich-Straube model

Abstract

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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“…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.…”

“…It is important to mention that the uncertainties [ 44 ] in this experimental approach, mainly caused by the assumed theory of rubber elasticity that does not take the effect of entanglements into the account [ 45 ].…”

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“…Figure 5 shows the effect of solvent on the behavior of the rubber network defects. The release of most of the entanglement effect 37 on the rubber segments increases the measurable fraction of the network defects (reaching a maximum value of 24%) and, because of its increasing mobility, slows the relaxation of this rubber fraction.…”

“…34,35 In addition, it has important uncertainties for determining the cross-link density because of the assumed model for rubber elasticity in swollen samples 36 and the exclusion of entanglement effects. 37 Furthermore, the obtained cross-link density strongly depends on the Flory-Huggins interaction parameter, which is different for each rubber-solvent pair and depends on the solvent fraction and changes for crosslinked or non-cross-linked polymers. 38,39 This is a critical issue for ELT crumb rubber, because it contains different rubber matrices with variable cross-link density when they are subjected to the devulcanization processes.…”

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“…As such, the underlying physical foundation is missing. Some statistical models have also been developed to evaluate the elastic properties of polymer network such as the Rouse model and tube model [16]; however, these models mainly focus on the rubber-stage polymers (melt), and cannot predict the elastic properties of the materials below their glass transition temperatures ( T g ) [17,18].…”