Dynamic scattering from solutions of semiflexible polymers

The dynamic structure factor of semiflexible polymers in solution is derived from the wormlike chain model. Special attention is paid to the rigid constraint of an inextensible contour and to he hydrodynamic interactions. For the cases of dilute and semidilute solutions exact expressions for the initial slope are obtained. When the hydrodynamic interaction is treated on the level of a renormalized friction coefficient, the decay of the structure factor due to the structural relaxation obeys a stretched exponential law in agreement with experiments on actin. We show how the characteristic parameters of the system (the persistence length l(p), the lateral diameter a of the molecules, and the mesh size xi(m) of the network) are readily determined by a single scattering experiment with scattering wavelength lambda obeying a much less than lambda much less than l(p) and lambda < xi(m). We also find an exact explicit expression for the effective (wave-vector-dependent) dynamic exponent z(k)<3 for semiflexible polymers and thus an enlightening explanation for a longstanding puzzle in polymer physics.