Models of transient networks

If one end of an active chain dissociates from a junction due to thermal motion, or a tension caused by the external force, the chain becomes dangling and relaxes to an equilibrium state after the single-chain relaxation time r, which is of the order of the Rouse relaxation time tr = /()7t k T)n in the unentangled regime. We 

Let f (r) be the tension of a bridge chain with the end-to-end vector r working on the micelle at its end. The tension is a function of the vector r. Similarly, let f (y = 1,2,3.) be the tensions given by the other chains connected to the same micelle. Then, the random motion of the micelle is described by the Langevin equation 

For the average movement of the micellar junction, we follow the assumption JGl in Section 4.3, and assume an affine deformation 

We also assume as for JG2 in Section 4.3 that the random force has Gaussian white noise 

Similarly, the equation of motion of the free end of a dangling chain is given by 

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