Resolving high-frequency dynamics in semidilute polymer theta-solutions: Scaling behavior in polyacrylamide

We investigated the high-frequency dynamics of semidilute entangled polymer solutions under θ-solvent conditions using diffusing-wave spectroscopy (DWS) microrheology. By analyzing the complex specific viscosity of polyacrylamide solutions, we experimentally identified the hierarchical crossover between Zimm, Rouse, and entanglement dynamics predicted by polymer dynamics theory. Time-concentration superposition successfully extended the accessible frequency range and yielded shift factors that exhibit the expected power-law concentration dependences. The frequency scaling of the complex specific viscosity and the concentration dependences of the characteristic relaxation times are both consistent with theoretical predictions. Furthermore, we demonstrated that the two-parameter scaling behavior characteristic of semidilute entangled polymers under θ-solvent conditions can be extracted solely through dynamic rheological measurements, without complementary static characterization. These results provide direct experimental validation of high-frequency polymer dynamics in semidilute entangled solutions under θ-solvent conditions and establish DWS microrheology as a powerful tool for probing hierarchical polymer dynamics beyond the frequency range accessible by conventional rheometry.