Dynamic scattering from solutions of semiflexible polymers

Abstract

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 the 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 ℓp, the lateral diameter a of the molecules, and the mesh size ξm of the network) are readily determined by a single scattering experiment with scattering wavelength λ obeying a ≪ λ ≪ ℓp and λ < ξm. 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.

Entropic interactions in suspensions of semiflexible rods: Short-range effects of flexibility

“…However, our values for ℓ p should be contrasted to the often-quoted value, ℓ p = 2.2 µm [16,17]. The latter is based on a fitting of dynamic light scattering data with theoretical models [17,18], whose assumptions may well be questioned in the light of our results. Indeed, smaller values of ℓ p have also been reported based on dynamic structure factor models of semi-flexible filaments [19], and using electron microscopy [20].…”

Self-assembly in aqueous solution of a modified amyloid beta peptide fragment

“…The resulting field correlation function was then fitted to Equation 3. The parameter β   was fixed to 0.75 for all the fittings which is the value expected for a system of semiflexible polymers (β = 3/4) [13]. Figure 3a shows a representative example for g (1) (q,t) calculated for θ =70 o and fitted using Equation Since the diffusion coefficient and the hydrodynamic radius are reciprocally related by the Stokes-Einstein equation, and this D f value is smaller than D= 3.8 x10 -13 m 2 s -1 reported for AAKLVFF nanotubes in methanol [6], the AAKLVFF fibrils in water occupy a larger volume than the nanotubes in methanol.…”

Internal Mechanical Response of a Polymer in Solution

“…In particular, the FCS spectrum is related to (3) and the DLS dynamic structure factor is related to (4) In both cases the correspondence is not exact because the quantities probed by FCS and DLS are dominated by diffusion of the c.m. at long times, while C(r 1 , r 2 , τ) is not.…”

“…The two techniques are complementary in that DLS probes fluctuations at a fixed k vector and FCS at a fixed position vector. Both techniques are also limited in the time scales they can probe: very fast fluctuations occur over distances too short to be detected optically, and very slow fluctuations are masked by translational diffusion.DLS has been used to measure the few longest relaxation times of DNA, and much theory has been devoted to predicting scattering functions for different polymer models [2,3]. FCS has also been used to probe the dynamic fluctuations of fluorescently labeled DNA [4,5].…”

“…DLS has been used to measure the few longest relaxation times of DNA, and much theory has been devoted to predicting scattering functions for different polymer models [2,3]. FCS has also been used to probe the dynamic fluctuations of fluorescently labeled DNA [4,5].…”