Theory of linear viscoelasticity of semiflexible rods in dilute solution

We present a theory of the linear viscoelasticity of dilute solutions of freely draining, inextensible, semiflexible rods. The theory is developed expanding the polymer contour about a rigid rod reference state, in a manner that respects the inextensibility of the chain, and is asymptotically exact in the rodlike limit where the polymer length L is much less than its persistence length L_p. In this limit, the relaxation modulus G(t) exhibits three time regimes: At very early times, less than a time τ_∥∝ L⁸L_p⁵required for the end-to-end length of a chain to relax significantly after a deformation, the average tension induced in each chain and G(t) both decay as t^-3/4. Over a broad range of intermediate times, τ_∥≪ t ≪ τ_⊥, where τ_perp;∝ L⁴/L_pis the longest relaxation time for the transverse bending modes, the end-to-end length decays as t^-1/4, while the residual tension required to drive this relaxation and G(t) both decay as t^-5/4. As later times, the stress is dominated by an entropic orientational stress, giving G(t) ∝ e^-t/τrod, where τ_rod∝ L³is a rotational diffusion time, as for rigid rods. Predictions for G(t) and G* (ω) are in excellent agreement with the results of Brownian dynamics simulations of discretized free draining semiflexible rods for lengths up to L = L_p, and with linear viscoelastic data for dilute solutions of poly-γ-benzyl-L-glutamate with L ∼ L_p.