Viscoelasticity of dilute solutions of semiflexible polymers

We show using Brownian dynamics simulations and theory how the shear relaxation modulus $G\left(t\right)\mathrm{}$ of dilute solutions of relatively stiff semiflexible polymers differs qualitatively from that of rigid rods. For chains shorter than their persistence length, $G\left(t\right)\mathrm{}$ exhibits three time regimes: At very early times, when the longitudinal deformation is affine, $G\left(t\right)\mathrm{}\sim t^{-3/4}.$ Over a broad intermediate regime, during which the chain length relaxes, $G\left(t\right)\mathrm{}\sim t^{-5/4}.$ At long times, $G\left(t\right)\mathrm{}$ mimics that of rigid rods. A model of the polymer as an effectively extensible rod with a frequency dependent elastic modulus $B\left(\omega \right)\sim (i\omega {)}^{3/4}$ quantitatively describes $G\left(t\right)\mathrm{}$ throughout the first two regimes.