Quantitative Tube Model for Semiflexible Polymer Solutions

TL;DR

This paper presents a comprehensive analytical and simulation-based theory for the tube model in entangled semiflexible polymer networks, deriving the tube diameter as a function of polymer properties and validating it with simulations.

Contribution

It introduces a new quantitative theory for the tube diameter in semiflexible polymers, including finite length corrections, supported by extensive computer simulations.

Findings

Derived tube diameter formula L_perp = 0.32 xi^{6/5} l_p^{-1/5}

Confirmed theoretical predictions with simulation data

Provided distribution functions for tube widths

Abstract

We develop a analytical and quantitative theory of the tube model concept for entangled networks of semiflexible polymers. The absolute value of the tube diameter L_perp is derived as a function of the polymers' persistence length l_p and mesh size xi of the network. To leading order we find L_\perp = 0.32 xi^{6/5} l_p^{-1/5}, which is consistent with known asymptotic scaling laws. Additionally, our theory provides corrections to scaling that account for finite polymer length effects and are dominated by the mesh size to polymer length ratio. We support our analytical studies by extensive computer simulations. These allow to verify assumptions essential to our theoretical description and provide an excellent agreement with the analytically calculated tube diameter. Furthermore, we present simulation data for the distribution function of tube widths in the network.