### Abstract

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_{∥}∝ L^{8}L_{p}^{5}required 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;}∝ L^{4}/L_{p}is 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}∝ L^{3}is 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}.

Original language | English (US) |
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Pages (from-to) | 1111-1154 |

Number of pages | 44 |

Journal | Journal of Rheology |

Volume | 46 |

Issue number | 5 |

DOIs | |

State | Published - Jan 1 2002 |

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## Cite this

*Journal of Rheology*,

*46*(5), 1111-1154. https://doi.org/10.1122/1.1501927