ABSTRACT:Reductions of molecular weight dependences of the zero-shear viscosity IJo and the steady-state compliance for multi-branched star polystyrenes with different numbers (P=7 -40) and molecular weights (M, = 1.3-20 x 10 4 ) of branches as well as those of smallnumber (six or less) branched polystyrenes and linear ones have been investigated. The reduction methods of IJo and ever established both theoretically and experimentally for small-number branched star polymers could not be applied to multi-branched star polymers. We tried to reduce the data of IJo and for multi-branched star polymers by corrected molecular weights by considering the expansion of molecules. In the course of discussions we proposed a new method to estimate the unperturbed dimensions of star polymers from the rheological measurements.KEY In the terminal or flow zone, the viscoelastic behavior of polymer melts can be characterized by the zero-shear viscosity rJo and the steady-state compliance A lot of experimental studies on the viscoelastic properties for star-shaped polymers having the number of branches six or less have been carried out 3 -20 and have established the molecular weight dependences of rJo and which quantitatively agree with recent theories. 21 -23 In the previous paper, 24 the viscoelastic properties of multi-branched star polystyrenes having a variety of number (P) and molecular weight (M 5 ) of branches were measured in wide ranges of temperature and frequency, and the effects of temperature, total molecular weight M, M,, and P were investigated. In this paper, the multi-branched star polymer means that having more than seven branches in a molecule.Mean square radius of gyration of multi-1 Rheological Properties of Anionic Polystyrenes XII.* To whom all correspondences should be addressed.branched star polystyrene prepared by coupling narrow-distribution polystyryl anions with divinylbenzene (DVB) was found to be larger than that the random-walk model predicts, 25 • 26 because of a microgel nodule at the center of molecule. 25 • 27 -31 In recent studies, 32 • 33 however, it was found that the extra expansion of multi-branched star polymer is due to the effect of increased segment density near its center. The non-Gaussian distribution of the chain segments not only makes the molecules expanded but also reduces flexibility of chain near the central branch point. This effect gives rise to a core formed at the center of molecule, which behaves rheologically like a nodule. Both the extra expansion and the reduced flexibility at the center of multi-branched star molecule necessarily affect the rheological properties of the melts. This paper describes reduction of the mo-337