Self-diffusion with dynamic dilution in star polymer melts

We use a recent theory of arm retraction in star polymer melts to calculate the self-diffusion constant of symmetric stars. Star polymers can only take a diffusive step when an arm fully retracts to the center. Because of the wide separation of relaxation times along the star arms, star polymers obey dynamic dilution, in which the effective entanglement network dilutes as portions of the star arms relax. This implies a picture of self-diffusion in which the junction point hops a distance of order the dilated tube diameter a(d) associated with the diluted network, rather than a distance of order the original "skinny" tube diameter a(0) defined by the entanglement molecular weight. The difference is substantial, since a(d) scales with arm length N as a(0)N(2/7). However, comparing our results to self-diffusion data of Bartels et al.,(1) we find that the data are more consistent with diffusive hops of a length scale a(0) rather than a(d).