Viscosity and terminal time

The viscosity t) is very sensitive to chain length. Both t) and T( increase as a power of N 

The exponent ntr, represents one of the major unsolved problems of polymer physics. An early attempt to derive ntr, is due to Bueche and is based on the notion of one chain dragging other chains. His analysis led to r) N -, which is good, but to a value of the terminal time N -, which is clearly ruled out by the experiments. More refined discussions along similar lines were analyzed and criticized by Graessley.  

Another work, by Edwards and Grant, attempted to give a self-consistent description of a chain trapped in a tube due to neighboring chains. This calculation gave i) It suffered, however, from two defects  

Another group of m( els is based on the notion of a transient network, introducing a finite lifetime for crosslinks into the classical rubber elasticity. This contains some excellent physical points. However, the dependence of Tt on the molecular mass is not attacked and remains unexplained in this picture. Thus, we do not describe the transient network models. 

A different approach, based on the reptation concept, was initiated by the present author and was recently augmented by Edwards and Doi. As explained in the next section, it leads to tj — N , and there is no 

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