Quantitative tube model for semiflexible polymer solutions

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 perpendicular is derived as a function of the polymers' persistence length lp and mesh size xi of the network. To leading order, we find L perpendicular = 0.31xi 6/5 lp (-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.