Theoretical Outline - The Reptation or Tube Concept

Tube confinement leads to strong alterations of the mean square segment displacements as compared to the Rouse model. 

A different estimate, which identifies xe with the slowest Rouse mode of a chain with the end-to-end distance, R2 = d2 leads to a quite similar result 

Local reptation regime For times t xe we have to consider curvilinear Rouse motion along the spatially fixed tube. The segment displacement described by Eq. (18) (n = m) must now take the curvilinear coordinates s along the tube into consideration. We have to distinguish two different time regimes. For (t xR), the second part of Eq. (19) dominates - when the Rouse modes 

Diffusion regime For times t xd N3 /4/kBTd2, the dynamics are determined by reptation diffusion. We expect normal diffusive behavior 

The reptation model thus predicts four dynamic regimes for segment diffusion. They are summarized in Fig. 18. 

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