Dynamic properties of molecular chains with variable stiffness

Abstract

The dynamics of a free-draining chain of variable stiffness in a dilute solution is investigated. The chain is considered as a differentiable space curve with stretching and bending elasticity. Second moments, like the mean square end-to-end distance, the radius of gyration, and the pair correlation function of the equilibrium distribution exactly agree with those of the well-known Kratky–Porod wormlike chain. The equation of motion of the chain is derived and solved by a normal mode analysis. In the limit of a flexible chain the model exhibits the well-known Rouse dynamics, whereas in the rod limit the eigenfunctions correspond to bending motion only. In addition, the rotational motion in the latter limit is naturally obtained within the model. The relaxation times obtained by the model are compared with experimental transient birefringence and dynamic light scattering data. In addition, electric dichroism measurements are interpreted in terms of the model. All of these experiments are in good agreement with the theoretical predictions.

From Rouse dynamics to local relaxation: A neutron spin echo study on polyisobutylene melts

“…II A we started basically from a RIS description of the chain statistics, we now course grain and introduce the chain stiffness more generally in terms of a local rigidity which is exhibited by locally stiff chain molecules of Gaussian segments. Harnau et al 7 have shown that by a maximum entropy principle the partition function for such a chain can be formulated. Its evaluation leads to the correct average static properties of the Kratky-Porod wormlike chain.…”

“…5,6 The second approach models the stiffness in terms of bending elasticity-fourth-order derivative with respect to the contour coordinate-in the Rouse equation. 7 Again we give solutions for this modified Rouse equation and discuss the modifications of the dynamic structure factor.…”

“…L relates to the number of chain bonds N and the bond length l 0 by LϭNl 0 sin(/2), where is the bond angle. 7 From that analysis characteristic relaxation times are obtained as…”

Self-Diffusion and Cooperative Diffusion in Semidilute Polymer Solutions As Measured by Fluorescence Correlation Spectroscopy

“…In order to examine the influence of internal chain motions such as bending and stretching on the dynamics (see refs [37][38][39][40] and references therein), one may trace out the internal degrees of freedom of a polymer chain by studying the monomer mean square displacement B s (τ ) in eq 4 in detail. Various theoretical predictions on the time dependence of the monomer mean square displacement of both continuously and single labeled DNA molecules in aqueous solution have been verified using FCS measurements.…”

Dynamic scattering from solutions of semiflexible polymers

“…It renders awkward any general theory [11,13,14] which tries to represent this property faithfully. On the other hand, models that relax the constraint too much -as e.g., the so-called Harris-Hearst-Beals model [15] and its latest descendants [16][17][18][19] -include artificial stretching modes and find a Gaussian distribution for all spatial distances along the contour; i.e., the essence of semiflexibility has obviously been lost. The correct radial distribution function of a semiflexible polymer with L ≈ ℓ p is actually very different from a Gaussian distribution [20].…”