On dynamic scaling theories of polymer solutions at nonzero concentrations

Publisher Website
Google Scholar
Abstract
A scaling theory is presented for the translational diffusion coefficient of a tagged chain and for the specific viscosity of polymer solutions at nonzero concentration. The derivations employ the full diffusion equation including unaveraged hydrodynamic interactions for the dynamical motion of continuous Gaussian coils with excluded volume. The effects of screened excluded volume and hydrodynamic interactions at nonzero polymer concentrations are introduced through an effective excluded volume strength, v (c), and draining strength, h (c), c being the monomer concentration. For c[η]≲O (1), [η] is the intrinsic viscosity, the hydrodynamics of the polymer solution is treated using effective medium arguments, resulting in exponential forms for v (c) and h (c) (e.g., h (c) =h (0) exp[constant c[η]]). Towards the concentrated end of the semidilute regime, c[η]≳O (1), a bloblike picture of chain dynamics is seen to appear. An application of the results derived herein is also presented for polyelectrolyte solutions at nonzero concentrations in the presence of added salt.