Multiple relaxations of concentration fluctuations in entangled polymer solutions

We have investigated by dynamic light scattering the dynamics of semidilute polymer solutions in a good solvent, specifically polystyrene in benzene. We have shown that, using state-of-the-art instrumentation and data analysis techniques, it is possible to identify in the spectra. of relaxation times three very weak slow modes with a combined amplitude of less than 5%, in addition to the dominant cooperative diffusion component (first mode). The results are compared with the predictions of Semenov's theory of dynamics of semidilute solutions in good solvents. The slowest component (fourth mode) was identified as the diffusion of clusters with characteristic size in the range of 100 nm. The third, broad mode corresponds to the reptation process, and finally the second mode is diffusive, with a decay time independent of molecular weight. It is about an order of magnitude slower than the cooperative diffusion and is tentatively assigned to dynamics corresponding to the interentanglement spacing. The three slow relaxation processes only appear for solutions having their concentration or molecular weight above the entanglement limit, c(e) or M-e,M-c. For M = 770 000 we obtain c(e) congruent to 4.0c*, with c* being the usual overlap concentration and for a fixed concentration, of 0.05 g/mL we obtain M-e,M-c congruent to 12M(c)*, with M-c* being the overlap molecular weight for this concentration.