Tube Branch point motion

How can a branch point move The repertoire of polymer movements that we have considered up to now reptation, primitive path fluctuations, and Rouse motion within the tube do not allow for branch-point motion, at least not directly. Yet, clearly, the branch points do move, for if they did not, branched polymers, including stars, would have zero center-of-mass diffusivity. 

Slip-link and other simulation models, that treat entanglements as interactions between two molecules in an ensemble of chains, are producing important insights into the processes of constraint release and branch-point motion, and in some cases yield predictions that are more accurate than tube models. We can expect that considerable progress will be made using such models in the near future. 

Between major branch points, an epicardial artery is modelled as an elastic tube. The flow of blood in each such tube of the network is assummed to be that of an incompressible Newtonian fluid whose motion can be adequately described as... 

Another case where tube contraction is important is the relaxation of branched polymers/as epitomized by star-polymers. Because the branch point is highly immobile, reptation by Brownian motion of an arm as a whole is strongly inhibited. Escape from the tube can only occur by contraction of the primitive path. Any significant contraction has a high free energy (discussed in the exercise above). The time for a fractional contraction i.e. A is... 

This behavior can be understood qualitatively in ter as of the tube model for topological constraints, as pointed out by de Gennes the presence of a branch strongly inhibits the reptation of a molecule along its contour, and motions must be accomplished by tube reorganization. The critical molecular weight for onset of this behavior would be expected to depend on the branch length i.e.. 

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