Quantitative Tube Model Predictions for the Linear Viscoelasticity of Linear Polymers

Tube models derived from the basic ideas of De Gennes and Doi & Edwards on reptation of entangled chains have made tremendous progress in the past 30 years and have now reached a quantitative level for the prediction of linear viscoelasticity of linear polymers. After a concise reminder of key experimental features of dynamic moduli, we first review the fundamental ingredients of quantitative tube models: reptation, contour length fluctuations and constraint release, as well as some important modifications that are proving essential in difficult cases, such as the “StruglinskiGraessley criterion” or the “constraint release Rouse” regime. The main models published since the origin of the theory are next briefly described and compared. They can be classified in two major categories, those derived from the Doi-Edwards theory built on the original reptation concept and those derived from the Milner-McLeish theory, which considers linear chains as two-arms stars able to reptate. We further review published comparisons between experimental data and model predictions for various systems, comprising monodisperse, polydisperse and bidisperse polymers. The latter are the most difficult to predict because they emphasize complex interactions between the relaxation mechanisms. Hence they highlight the current limitations of the models, in particular the influence of constraint release mechanisms on reptation and fluctuations.