The Polymer Chain in a Tube Model and Similar Ones

1 The Polymer Chain in a Tube Model and Similar Ones 

The first phenomenological model for description of polymer dynamics in concentrated solutions and melts was proposed in 1971 by P.de Gennes [50]. In this classical work, it was assumed that due to entanglements, the chain motions in the direction normal to the chain contour are blocked up and only tangential ones are possible. This kind of chain motion in the effective tube was called reptation. In the absence of external fields, the chain can escape from the tube by either of the free tube ends. 

In the course of investigation of polymer dynamics, all topological states of chains are equivalent due to the presence of their free ends and it is not necessary to construct the topological invariant. However, for every instantaneous chain configuration, its topological state is definite and is determined by the topological invariant - the primitive path. 

The development of the polymer chain in a tube model by M. Doi and S.F. Edwards [51] allowed them to describe on the molecular level a set of hydrodynamic and viscoelastic properties of concentrated polymer solutions and melts. 

The polymer chain in a tube model and its modifications are widely used for investigation of the rubber elasticity of polymer networks with topological constraints. The detailed review on that problem one can find in the monograph 

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