One long chain in a melt of shorter chains

To understand the dynamics of one chain in a melt, it is convenient to start from a slightly different problem. We consider one test chain of Ni monomers, embedded in a monodisperse melt of the same chemical species, with a number N of monomers per chain. We consider three types of motion for the test chain reptation, tube renewal, and Stokes-Einstein friction. We first describe tube renewal and show that this is probably negligible for most practical purposes. Then we discuss competition between reptation and Stokes-Einstein friction. 

The basic process associated with this word was introduced in Ref. 14 and is shown in Fig. VIII. 10, where we see one entanglement constraint being altered when one of the ambient chains (F) has an extremity in the immediate vicinity of the test chain (F,), the relative positions of (F) and (Fj) may change qualitatively in a very short time. This may be viewed as a modification of the tube. 

We then try to picture the tube itself as a Rouse chain, following early ideas of Edwards. The basic parameter in this description is the microscopic jump frequency of one unit of tube—the analog of the con- 

In an early attempt, the present author assumed that IV was simply reduced by a factor equal to the fraction of tube sites which are near the extremity of a F chain 

A more detailed justification of eq. (Vin.27) has been given recently by Daoud and the present author (to be published in J. Polym. Set.). The frequency W is very low. For example, it leads to a diffusion coefficient of Ae long chain 

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