Non-Affine Shear Modulus in Entangled Networks of Semiflexible Polymers

We investigate the viscoelastic properties of entangled networks of semiflexible polymers. At intermediate time scales the elastic response of these networks to shear deformation is described by the plateau modulus $G$. Different scaling laws with polymer concentration $c$ have been proposed based on the assumption that the deformation field is affine on all length scales. We develop a numerical approach that allows to calculate the modulus via free energy changes for both affine and non-affine deformations. The non-affine deformation field is obtained by a free energy minimization. Our findings allow for a confirmation of a power law $G\propto c^{7\mathrm{/}5}{l}_p^{-1\mathrm{/}5}$ with polymer concentration $c$ and persistence length $l_p$ and furthermore quantify the systematic deviations due to the affinity assumption.