Dynamic Scattering from Solutions of Semiflexible Polymers

TL;DR

This paper derives the dynamic structure factor of semiflexible polymers in solution using the wormlike chain model, providing exact expressions and insights into structural relaxation, hydrodynamic interactions, and parameters determination through scattering experiments.

Contribution

It introduces a comprehensive theoretical framework for analyzing the dynamics of semiflexible polymers, including explicit formulas and a new understanding of the dynamic exponent z(k).

Findings

Exact expressions for initial slope in dilute solutions.

Decay of structure factor follows a stretched exponential law.

Explicit formula for the dynamic exponent z(k)<3.

Abstract

The dynamic structure factor of semiflexible polymers in solution is derived from the wormlike chain model. Special attention is paid to the rigid constraint of an inextensible contour and to the hydrodynamic interactions. For the cases of dilute and semidilute solutions exact expressions for the initial slope are obtained. When the hydrodynamic interaction is treated on the level of a renormalized friction coefficient, the decay of the structure factor due to the structural relaxation obeys a stretched exponential law in agreement with experiments on actin. We show how the characteristic parameters of the system (the persistence length \ell_p, the lateral diameter a of the molecules and the mesh size \xi_m of the network) are readily determined by a single scattering experiment with scattering wavelength \lambda obeying a << \lambda <<\ell_p and \lambda<\xi_m. We also find an exact explicit expression for the effective (wave vector dependent) dynamic exponent z(k)<3 for semiflexible polymers and thus an enlightening explanation for a longstanding puzzle in polymer physics.