Rheology of dilute polymer solutions with time-dependent screening of hydrodynamic interactions

TL;DR

This paper develops a bead-spring model to study how time-dependent hydrodynamic screening influences the dynamics and viscosity of dilute polymer solutions, revealing a transition between Rouse and Zimm behaviors over time.

Contribution

A novel theoretical framework incorporating time-dependent hydrodynamic screening in polymer solutions, bridging Rouse and Zimm dynamics dynamically.

Findings

Hydrodynamic interactions are dynamically screened, affecting polymer relaxation and diffusion.

Solution viscosity and internal modes transition between Rouse and Zimm regimes over time.

The model predicts a long-time return to Rouse behavior after initial Zimm-like dynamics.

Abstract

The screening of hydrodynamic interactions (HI) essentially affects macroscopic properties of polymeric solutions. This screening depends not only on the polymer concentration but has a dynamic nature. In the present work, a bead-spring theory is developed, in which this phenomenon is described for solutions of nonentangled polymer coils. The equation of motion for the beads of a test polymer is solved together with the Brinkman's equation for the solvent velocity that takes into account the presence of other coils in solution. The time correlation functions for the polymer normal modes are found. A tendency to the screening of HI is demonstrated on the coil diffusion as well as on the relaxation of its internal modes. With the growing concentration of the coils they both show a transition to the exact Rouse behavior. The viscosity of the solution and some other observable quantities are calculated. As the time increaes, the time-dependent quantities change their behavior from the Rouse regime through the Zimm one again to the Rouse dynamics at long times.