Tube theory of entangled polymer dynamics

The dynamics of entangled ¯exible polymers is dominated by physics general to many chemical systems. It is an appealing interdisciplinary ®eld where experimentaland theoretical physics can work closely with chemistry and chemical engineering. The role of topological interactions is particularly important, and has given rise to a successful theoretical framework: the `tubemodel’. Progress over the last 30 years is reviewed in the light of specially-synthesized model materials, an increasing palette of experimental techniques, simulation and both linear and nonlinear rheological response. Our current understandingof a series of processes in entangled dynamics: `reptation’, `contour length ¯uctuation ’ and `constraint-release ’ are set in the context of remaining serious challenges. Especial attention is paid to the phenomena associated with polymers of complex topology or `long chain branching’.