Reptation Mechanism and the Tube Model

In the tube model, the chains can stretch and contract along the tube or slide along the tube as a whole. The former motion equilibrates the fluctuation in the density of the chain segment along the tube, and the latter motion is related to the diffusion of the 

we are left with a single parameter a, which depends on the statistical nature of the network. As shown below, a is related to by 

However, whether or not there indeed exists such a critical length a is an important question yet to be answered. 

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