Dynamic Critical Phenomena of Polymer Solutions

TL;DR

This paper uses mode coupling theory to predict how the critical divergence of viscosity in polymer solutions diminishes with increasing molecular weight, aligning with recent experimental findings.

Contribution

It introduces a theoretical calculation of kinetic coefficients considering non-linear hydrodynamic interactions, explaining the molecular weight dependence of critical viscosity behavior.

Findings

Critical viscosity divergence decreases as molecular weight increases.

The diffusion constant and dynamic structure factor are explicitly calculated.

Results align with recent experimental observations by Tanaka et al.

Abstract

Recently, a systematic experiment measuring critical anomaly of viscosity of polymer solutions has been reported by H. Tanaka and his co-workers (Phys.Rev.E, 65, 021802, (2002)). According to their experiments, the dynamic critical exponent of viscosity y_c drastically decreases with increasing the molecular weight. In this article the kinetic coefficients renormalized by the non-linear hydrodynamic interaction are calculated by the mode coupling theory. We predict that the critical divergence of viscosity should be suppressed with increasing the molecular weight. The diffusion constant and the dynamic structure factor are also calculated. The present results explicitly show that the critical dynamics of polymer solutions should be affected by an extra spatio-temporal scale intrinsic to polymer solutions, and are consistent with the experiment of Tanaka, et al.