Rouse and Zimm Short-Time Exponents When Subtracting the Solvent Contribution in Semidilute Polymeric Solutions

Optical trapping interferometry measures the Brownian motion of an optically trapped microsphere inside a fluid, allowing access to the short-time/high-frequency power-law behavior appearing in the complex modulus of polymeric aqueous suspensions, which is characteristic of the individual dynamics of the macromolecules. The short-time behavior is shaped by the hydrodynamics and inertia effects because of the solvent, whose influence in the complex modulus we analyze through inertia-corrected expressions and by removing the contribution of the solvent. We detect that the classic Zimm and Rouse models in the high-frequency region reproduce the experimental results for aqueous suspensions of poly-(ethylene oxide) and of worm-like micelles in the semidilute regime when the water contribution is adequately subtracted. Our results reflect the incompleteness of the Zimm-Rouse model for including full hydrodynamic interactions but also reveal how the transition between different dynamic behaviors of the polymers in suspension depends on the network interconnection.