Entangled polymers

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Abstract
Polymer liquids have fascinating dynamical properties: they flow like conventional viscous liquids when subjected to perturbations slowly varying with time, but behave like elastic solids at higher frequencies. These mechanical properties depend strongly on the molecular structure (linear, branched, flexible, rigid …), but unifying concepts have emerged in the past two or three decades, especially for the easiest case of linear flexible chains, pointing out the crucial role of chain entanglements. The reptation model has provided a fruitful and simple framework to analyse the wide range of available dynamical experiments. The reptation model provides an adequate qualitative description of the dependence of the dynamical properties on the molecular weight of the chains, and yields good estimates of the different time scales involved. The small quantitative discrepancies that remain are the subject of a vigorous debate on the validity of the reptation hypothesis and of a growing number of proposed refinements. In this review, the reptation ideas are presented in their simple version and their application to self-diffusion, viscoelasticity and more local processes is discussed. A critical analysis of the underlying hypothesis is given, and the additional effects which have to be included for a realistic description of the dynamical properties of entangled polymers are mentioned.