This article deals with recent work on the theory of entanglement effects in polymer rheology, in particular, the reptation idea of deGennes and the tube model of Doi — Edwards. Predictions which depend on the independent alignment approximation are omitted. Attention is focussed primarily on linear viscoelastic properties, macromolecular diffusion, relaxation following step strains and network properties. Theoretical predictions and experimental observations are discussed for monodisperse linear and star-branched polymer liquids. Effects due to chain length distribution, relaxation behavior of unattached chains in networks, and the equilibrium elasticity of networks are also considered. The results suggest a need to consider relaxation mechanisms in addition to simple reptation as well as certain modifications in the tube model itself. The effect of fluctuations in chain density along the tube is probably quite important in branched chain liquids. Considerations about lifetimes of the tube defining constraints seem necessary to account for polydispersity effects and for differences between relaxation rate of chains in liquids and in networks. A modified tube model is proposed which gives a somewhat better description of elasticity in entangled networks while still producing the Doi-Edwards expression for stress in entangled liquids. Experimental results so far are qualitatively consistent with the picture which is presented here. Much work needs to be done however to test for quantitative consistency.

Entangled linear, branched and network polymer systems — Molecular theories

Soft polymer networks have seen an explosion of recent developments motivated by new high tech applications in the biomedical field or in engineering. We present a candid and critical overview of the current understanding of the relation between the structure and molecular architecture of polymer networks and their mechanical properties, restricting ourselves to soft networks made of flexible polymers and displaying entropic elasticity. We specifically review and compare recent approaches to synthesize swollen hydrogels with enhanced toughness, resilient but tough unfilled elastomers and self-healing networks containing dynamic bonds. The purpose is less to draw a comprehensive catalogue of approaches than to identify and unify the underlying principles controlling toughening mechanisms and mechanical self-healing behavior and to point out remaining challenges.

50th Anniversary Perspective: Networks and Gels: Soft but Dynamic and Tough

Model networks based on `endlinking' processes: synthesis, structure and properties

The present state of development of the statistical mechanics of rubber elasticity is reviewed and analysed, starting from some problems and controversial results drawn from recent experimental progress in this area. Attention is focused on the tube model as a mean field approach to the statistical mechanics of polymer systems with topology conservation. In particular, a new model for simulating the topological constraints in polymer networks and melts is presented which allows the order and the deformation dependence of the tube dimensions to be calculated. Conclusions resulting from the description of large-strain and small-strain behaviour of dry, completely crosslinked networks are discussed and compared with experimental data where all modes of deformation usually employed can be described with similar accuracy. Further, the concept of relaxed microscopic deformation much smaller than the macroscopic deformation of the sample is introduced, which allows explanation of mechanical and thermodynamic properties as well as the scattering results for networks at higher swelling degrees. Similarly, constraint release effects are expected to be responsible for the different experimental results collected for end-linked networks and for networks prepared by cross-linking of long primary chains. The different degrees of completeness of crosslinking have to be considered as the main reason for these differences.

G. S. Benjamin

Papers

Equilibrium Modulus of Model Poly(dimethylsiloxane) Networks

Large strain behavior of model silicone networks.