Dynamic structure factor of a stiff polymer in a glassy solution

TL;DR

This paper reviews the theoretical understanding of the dynamic structure factor of stiff polymers in solutions, extending models with numerical precision and addressing hydrodynamic interactions, including the glassy wormlike chain extension.

Contribution

It provides exact numerical coefficients for the dynamic MSD of a free polymer and compares hydrodynamic interaction approximations, resolving a controversy and extending the WLC model to the GWLC.

Findings

Exact numerical coefficients for dynamic MSD

Comparison of hydrodynamic interaction approximations

Prediction of power-law and logarithmic tails in GWLC

Abstract

We provide a comprehensive overview of the current theoretical understanding of the dynamic structure factor of stiff polymers in semidilute solution based on the wormlike chain (WLC) model. We extend previous work by computing exact numerical coefficients and an expression for the dynamic mean square displacement (MSD) of a free polymer and compare various common approximations for the hydrodynamic interactions, which need to be treated accurately if one wants to extract quantitative estimates for model parameters from experimental data. A recent controversy about the initial slope of the dynamic structure factor is thereby resolved. To account for the interactions of the polymer with a surrounding (sticky) polymer solution, we analyze an extension of the WLC model, the glassy wormlike chain (GWLC), which predicts near power-law and logarithmic long-time tails in the dynamic structure factor.