Viscoelasticity of Concentrated Isotropic Solutions of Semiflexible Polymers. 1. Model and Stress Tensor

The viscoelastic behavior of entangled solutions of semiflexible chains is discussed. After identifying the different possible regimes of concentration and chain length in such a solution, attention is focused on a “tightly-entangled” regime in which the polymer is confined to a tube of diameter less than its persistence length. A tube model analogous to the Doi−Edwards model is introduced to describe this regime. A general expression for the stress tensor of a solution of wormlike chains is derived, which may be applied to any concentration regime, and three intramolecular stress contributions are identified: a curvature contribution arising from forces that oppose transverse deformation or rotation of chain segments, a tension contribution arising from tangential forces that resist stretching or compression of the chain, and an orientational contribution that reduces in the appropriate limit to the Brownian stress of a rigid-rod solution. Intermolecular stress contributions are also calculated. A qualitative discussion is given of the high-frequency viscoelastic response of any solution of wormlike chains, which is dominated by the tension contribution and exhibits a characteristic power law dependence on frequency.