Effects of stiffness on the flow behavior of polymers

Dua, Arti; Cherayil, Binny J.

doi:10.1063/1.1324710

Cited by 16 publications

(12 citation statements)

References 36 publications

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“…This is in accordance with theoretical work [20,38,39] and numerical simulations for flexible polymers [40][41][42][43][44][45][46]. It is commonly argued that the relaxation time in the Weissenberg number should be that of the slowest modes [34,42,47]. While for a flexible polymer these clearly are internal modes, it will eventually become the global rotation with increasing polymer stiffness.…”

Section: Introductionsupporting

confidence: 86%

Dynamics of a semiflexible polymer or polymer ring in shear flow

2014

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Polymers exposed to shear flow exhibit a remarkably rich tumbling dynamics. While rigid rods rotate on Jeffery orbits, a flexible polymer stretches and coils up during tumbling. Theoretical results show that in both of these asymptotic regimes the corresponding tumbling frequency f(c) in a linear shear flow of strength γ scales as a power law Wi(2/3) in the Weissenberg number Wi = γτ, where τ is a characteristic time of the polymer's relaxational dynamics. For a flexible polymer these theoretical results are well confirmed by a large body of experimental single molecule studies. However, for the intermediate semiflexible regime, especially relevant for cytoskeletal filaments like F-actin and microtubules, the situation is less clear. While recent experiments on single F-actin filaments are still interpreted within the classical Wi(2/3) scaling law, theoretical results indicated deviations from it. Here we perform extensive Brownian dynamics simulations to explore the tumbling dynamics of semiflexible polymers over a broad range of shear strength and the polymer's persistence length l(p). We find that the Weissenberg number alone does not suffice to fully characterize the tumbling dynamics, and the classical scaling law breaks down. Instead, both the polymer's stiffness and the shear rate are relevant control parameters. Based on our Brownian dynamics simulations we postulate that in the parameter range most relevant for cytoskeletal filaments there is a distinct scaling behavior with f(c) τ* = Wi(3/4)f(c)(x) with Wi = γτ* and the scaling variable x = (l(p)/L)(Wi)(-1/3); here τ* is the time the polymer's center of mass requires to diffuse its own contour length L. Comparing these results with experimental data on F-actin we find that the Wi(3/4) scaling law agrees quantitatively significantly better with the data than the classical Wi(2/3) law. Finally, we extend our results to single ring polymers in shear flow, and find similar results as for linear polymers with slightly different power laws.

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Section: Introductionsupporting

confidence: 86%

Dynamics of a semiflexible polymer or polymer ring in shear flow

2014

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“…The studies reach beyond those of Ref. 28, where the Harris-Hearst model 68 is adopted to describe semiflexible polymers under shear, in several respects, specifically hydrodynamic interactions are taken into account by a preaveraged hydrodynamic tensor. I like to stress that the Harris-Hearst model does not correctly describe the equilibrium properties of a semiflexible polymer, 63,69 but an adequate description of flexible polymers can be expected.…”

Section: Introductionmentioning

confidence: 93%

“…The above eigenfunctions are different form those of the Harris-Hearst model. 28,68 The constants c n follow from the normalization condition and the wave numbers n and n Ј are determined by the boundary conditions ͑2͒ and ͑3͒. 56,66,67,71 The amplitudes n ͑t͒ obey the equations…”

Section: A Equations Of Motionmentioning

confidence: 99%

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Conformational and rheological properties of semiflexible polymers in shear flow

Winkler

2010

The Journal of Chemical Physics

136

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A theoretical description is provided for the nonequilibrium conformational and dynamical properties of a polymer in shear flow. Using a mean-field semiflexible chain model, which accounts for hydrodynamic interactions within the preaveraging approximation, analytical expressions are derived for the dependence of the deformation, orientation, and relaxation times on polymer persistence length and shear rate. Moreover, the rheological properties of a dilute polymer solution are discussed. The model yields shear thinning at large Weissenberg numbers. The analytical results are compared with fluorescence microscopy measurements of individual DNA molecules, which yield qualitative and partial quantitative agreement.

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“…Similar models have been used to describe fluorescence resonance energy transfer 16,17 ͑FRET͒ and DNA dynamics in laminar flows. 18 The following section recapitulates the GLE formalism. Section III discusses the semiflexible polymer model, which is defined in terms of a Hamiltonian H, in which a local bending energy is included.…”

Section: Introductionmentioning

confidence: 99%

Multiple time scale dynamics of distance fluctuations in a semiflexible polymer: A one-dimensional generalized Langevin equation treatment

Debnath

Min

Xie

et al. 2005

The Journal of Chemical Physics

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Time-dependent fluctuations in the distance x(t) between two segments along a polymer are one measure of its overall conformational dynamics. The dynamics of x(t), modeled as the coordinate of a particle moving in a one-dimensional potential well in thermal contact with a reservoir, is treated with a generalized Langevin equation whose memory kernel K(t) can be calculated from the time-correlation function of distance fluctuations C(t) identical with x(0)x(t). We compute C(t) for a semiflexible continuum model of the polymer and use it to determine K(t) via the GLE. The calculations demonstrate that C(t) is well approximated by a Mittag-Leffler function and K(t) by a power-law decay on time scales of several decades. Both functions depend on a number of parameters characterizing the polymer, including chain length, degree of stiffness, and the number of intervening residues between the two segments. The calculations are compared with the recent observation of a nonexponential C(t) and a power law K(t) in the conformational dynamics within single molecule proteins [Min et al., Phys. Rev. Lett. 94, 198302 (2005)].

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Effects of stiffness on the flow behavior of polymers

Abstract: A constitutive framework for the non-Newtonian pressure tensor of a simple fluid under planar flows

Cited by 16 publications

References 36 publications

Dynamics of a semiflexible polymer or polymer ring in shear flow

Dynamics of a semiflexible polymer or polymer ring in shear flow

Conformational and rheological properties of semiflexible polymers in shear flow

Multiple time scale dynamics of distance fluctuations in a semiflexible polymer: A one-dimensional generalized Langevin equation treatment

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