Dynamic structure factor of a stiff polymer in a glassy solution

Abstract

Abstract. We provide a comprehensive overview of the current theoretical understanding of the dynamic structure factor of stiff polymers in semidilute solution based on the wormlike chain (WLC) model. We extend previous work by computing exact numerical coefficients and an expression for the dynamic mean square displacement (MSD) of a free polymer and compare various common approximations for the hydrodynamic interactions, which need to be treated accurately if one wants to extract quantitative estimates for model parameters from experimental data. A recent controversy about the initial slope of the dynamic structure factor is thereby resolved. To account for the interactions of the polymer with a surrounding (sticky) polymer solution, we analyze an extension of the WLC model, the glassy wormlike chain (GWLC), which predicts near power-law and logarithmic long-time tails in the dynamic structure factor.

Fluctuations of Stiff Polymers and Cell Mechanics

“…This is accomplished by prescribing a modified relaxation time τ λ for collective excitations of wavelength λ by , exp[ ( / 1)], . of stiff polymer solutions (Kroy & Frey, 1997;Glaser et al, 2008) yields excellent agreement of the model predictions with the data (Fig. 6, right, red curves).…”

“…To distinguish between contour length and time derivatives, we use primes and dots, respectively. Improved approximations for the viscous drag lead to logarithmic corrections to the linearized dynamics of a WBR (Granek, 1997;Glaser et al, 2008). The external and the stochastic thermal force per unit length are denoted by g and ξ, respectively.…”

Binding branched and linear DNA structures: From isolated clusters to fully bonded gels

“…This functional form is observed also in glass-forming systems when different competing arrest mechanisms are present [57][58][59][60] . Logarithmic decays have also been reported in mixtures of polymeric systems 61 and in glassy wormlike chain polymers 62 . Finally, in the fully bonded case we observe a clear two-step relaxation process.…”

Micro-rheological behaviour and nonlinear rheology of networks assembled from polysaccharides from the plant cell wall

“…In order to understand the time and length-scale dependent rheological properties of such systems, the central task is to understand how the interactions interfere with the dynamics of the individual constituents. Inspired by the underlying similarity of constraint release in these systems and the thermally-activated jumping between local traps in soft glasses [13,14], the glassy worm-like chain (GWLC) model [15][16][17] addresses this problem by exponentially stretching the relaxation spectrum for single-chain motions involving wavelengths beyond a characteristic backbone length, . While the exponential form of the stretching is not microscopically derived, the model builds on the known mesostructure of the polymer network, and introduces a single 'stickiness' parameter that intuitively corresponds to the characteristic depth of the potential well that a cross-linked chain section must escape in order to dissociate.…”