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

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.