Why, and when, does dynamic tube dilation work for stars?

The anzatz known as "dynamic dilution" or "tube dilation," introduced by Marrucci [Marrucci, G., J. Polym. Sci. Polym. Phys. Ed. 23, 159-177 (1985)] and employed by Ball and McLeish [Ball, R. C., and T. C. B. McLeish, Macromolecules 22, 1911-1913 (1989)] in the case of star polymers, has been criticized, in spite of its success, for its apparent lack of controlled renormalization at different timescales of the effective diffusion constant of the retracting star arm. Here we show that the dynamic dilution hypothesis, and the "Ball-McLeish equation," may in some circumstances generate a-close approximation to a less heurustic approach in which arm retraction procedes by a nested set of constraint-release "supertubes." This more complex picture, consistent with the current treatment of constraint release in linear entangled polymers, provides a way in which to understand recent results on diffusion, dielectric relaxation, and slip-link simulations of star polymer melts. (C) 2003 The Society of Rheology.