Segmented hydrodynamic characteristics

Comparing Eqs. (83), (84) and Eqs. (21), (22) it follows immediately that Rouse and Zimm relaxation result in completely different incoherent quasielastic scattering. These differences are revealed in the line shape of the dynamic structure factor or in the (3-parameter if Eq. (23) is applied, as well as in the structure and Q-dependence of the characteristic frequency. In the case of dominant hydrodynamic interaction, Q(Q) depends on the viscosity of the pure solvent, but on no molecular parameters and varies with the third power of Q, whereas with failing hydrodynamic interaction it is determined by the inverse of the friction per mean square segment length and varies with the fourth power of Q. 

A high segment length value A of rigid chain polymers leads to many characteristic hydrodynamic properties of their solutions differing from those of flexible polymers. 

Here, the average distance Rsui from the end segments of the arms to the center of the star is taken as a measure of the characteristic size of the star polymer. Within the scaling approximation, the mean-square gyration radius (Rp i and the hydrodynamic radius Rh,sar of the star exhibit the same power-law dependence on N, r, and/as Rstaj. 

---