Eur. Phys. J. E (2007) 24: 35-46
https://doi.org/10.1140/epje/i2007-10208-2

Regular Article

Quantitative tube model for semiflexible polymer solutions

Arnold Sommerfeld Center for Theoretical Physics and Center of NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, D-80333, München, Germany

^* e-mail: frey@lmu.de

Received: 3 March 2007
Accepted: 13 July 2007
Published online: 3 September 2007

Abstract

We develop an analytical and quantitative theory of the tube model concept for entangled networks of semiflexible polymers. The absolute value of the tube diameter L _⊥ is derived as a function of the polymers' persistence length l _p and mesh size ξ of the network. To leading order, we find L _⊥ = 0.31ξ^6/5 l _p ^-1/5 , which is consistent with known asymptotic scaling laws. Additionally, our theory provides finite-length corrections that can account for effects of polydispersity. 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.