Dynamics of wormlike chains

Abstract

The dynamics of free-draining polymers in dilute solution are treated with the Kratky-Porod wormlike chain model. The model consists of differentiable space curves of constant length with bending elasticity. We show that eliminating the stretching elasticity gives an internally consistent model which satisfies the pure bending Langevin equation of motion. The dynamical equation is solved by a normal mode analysis representing the transverse vibrations of an elastic curve with free ends. A time-independent Green's function is used to calculate the pair correlation function, giving all equilibrium properties of the model. The same techniques are applied to the time-dependent case. All properties depend on one parameter, the persistence length, X"1, of the polymer. As an example, the polarized light scattering from a dilute solution of isotropic random coils is calculated in detail. The model requires the separate treatment of the rotational and the internal flexing degrees of freedom of the polymer. Its main area of application will be in the description of the dynamics of dilute solutions of semiflexible macromolecules.

Anisotropic Hydrodynamic Mean-Field Theory for Semiflexible Polymers under Tension

“…7 is that our normal modes incorporate the correct boundary conditions, rather than being based on a Fourier expansion which is strictly valid only far from the chain ends. In fact, at F = 0 the normal modes derived in our way reduce to the expected Aragón and Pecora expressions [41]. The resulting dynamical equations based on U In the case of the longitudinal WBA, the deviations from the simulations at very short times may partially be accounted for by an effect which is not present in our formulation: we do not include corrections for longitudinal friction [31], which are expected to be relevant for times t k B T l p /µ 0 F 2 = 0.25l 2 p /k B T µ 0 , and which are present in more sophisticated implementations of the WBA [9, 11-13] (though these more advanced approaches do not include long-range hydrodynamic interactions, which we incorporate into our version of the WBA).…”

Dynamic scattering from solutions of semiflexible polymers

“…The eigenfunctions of the linear bending equation for the transverse undulations of a weakly bending rod with free ends at s = ±L/2 are given by [13] u(p, s) ∝ cos ν p s/L cos ν p /2 + cosh ν p s/L cosh ν p /2 with ν p ≈ (2p + 1)π/2 for p > 0 odd and by the analoge expression with cos and cosh replaced by sin and sinh, respectively, for p even. Since we will only need the u(p, s) for large p ≫ 1 and s ≪ L (far from the ends), we may drop the hyperbolic terms, which are small of order exp(−pπ/2), and write…”

Diameter-dependent bending dynamics of single-walled carbon nanotubes in liquids

“…1 shows the thermally induced undulations of a SWCNT visualized by this technique. The bending rigidity (persistence length) of each individual SWCNT can be determined from the amplitude of such shape fluctuations (16,22).…”

“…2A). Treating SWCNTs as worm-like chains (22) and following the procedure of Gittes et al (16), the shape of the SWCNT in each image was expressed as a sum of cosine bending modes (which form an orthogonal basis); mode amplitudes were computed by projecting the image shape onto these basis functions.…”