Cross-over in polymer solutions

Farnoux, B.; Boué, François; Cotton, J. P.; Daoud, M.; Jannink, G.; Nierlich, Martine; Gennes, P. G. de

doi:10.1051/jphys:0197800390107700

Cited by 141 publications

(84 citation statements)

References 23 publications

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“…Scaling laws predicting the dependence of dynamic and static properties of polymer melts and solutions have been pioneered by de Gennes and coworkers (Daoud et al, 1975;deGennes, 1980;Farnoux et al, 1978). Macromolecular dimensions can be quantified through the characteristic ratio, C N , defined as C N = /R 2 \/(N-1)// 2 , where ÍR 2 \ is the mean square end-to-end distance, (N-1) is the number or bonds along the chain backbone and / the bond length (here equal to sphere diameter).…”

Section: Characteristic Scaling Regimesmentioning

confidence: 99%

Monte Carlo simulations of densely-packed athermal polymers in the bulk and under confinement

Foteinopoulou

Karayiannis

Laso

2015

Chemical Engineering Science

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HIGHLIGHTS• Identification of the maximally random jammed state for polymer packings.• Molecular simulation of the phase transition in hard-sphere chains.• Molecular modelling of the effect of confinement in densely-packed athermal polymers.• Numerical calculation of the topological constraints in polymeric systems.• First-principles calculation of the scaling regimes in flexible polymers. ABSTRACTWe review the main results from extensive Monte Carlo (MC) simulations on athermal polymer packings in the bulk and under confinement. By employing the simplest possible model of excluded volume, macromolecules are represented as freely-jointed chains of hard spheres of uniform size. Simulations are carried out in a wide concentration range: from very dilute up to very high volume fractions, reaching the maximally random jammed (MRJ) state. We study how factors like chain length, volume fraction and flexibility of bond lengths affect the structure, shape and size of polymers, their packing efficiency and their phase behaviour (disorder-order transition). In addition, we observe how these properties are affected by confinement realized by fiat, impenetrable walls in one dimension. Finally, by mapping the parent polymer chains to primitive paths through direct geometrical algorithms, we analyse the characteristics of the entanglement network as a function of packing density.

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Section: Characteristic Scaling Regimesmentioning

confidence: 99%

Monte Carlo simulations of densely-packed athermal polymers in the bulk and under confinement

Foteinopoulou

Karayiannis

Laso

2015

Chemical Engineering Science

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“…8 -10,24,25 To complete the model, we now describe our treatment of the nonbonded interactions. From neutron scattering data 26,27 for dilute solutions of linear polymer in a good solvent, one finds ideal chain behavior at small distances along the chain, and good solvent behavior at large distances. In this spirit, we consider the increase in energy due to the overlap of two submolecules ͑i.e., beads͒.…”

Section: Modelmentioning

confidence: 99%

Stochastic simulations of DNA in flow: Dynamics and the effects of hydrodynamic interactions

Jendrejack

Pablo

Graham

2002

The Journal of Chemical Physics

271

364

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We present a fully parametrized bead-spring chain model for stained -phage DNA. The model accounts for the finite extensibility of the molecule, excluded volume effects, and fluctuating hydrodynamic interactions ͑HI͒. Parameters are determined from equilibrium experimental data for 21 m stained -phage DNA, and are shown to quantitatively predict the non-equilibrium behavior of the molecule. The model is then used to predict the equilibrium and nonequilibrium behavior of DNA molecules up to 126 m. In particular, the HI model gives results that are in quantitative agreement with experimental diffusivity data over a wide range of molecular weights. When the bead friction coefficient is fit to the experimental relaxation time at a particular molecular weight, the stretch in shear and extensional flows is adequately predicted by either a free-draining or HI model at that molecular weight, although the fitted bead friction coefficients for the two models differ significantly. In shear flow, we find two regimes at high shear rate (␥ ) that follow different scaling behavior. In the first, the viscosity and first normal stress coefficient scale roughly as ␥ Ϫ6/11 and ␥ Ϫ14/11 , respectively. At higher shear rates, these become ␥ Ϫ2/3 and ␥ Ϫ4/3 . These regimes are found for both free-draining and HI models and can be understood based on scaling arguments for the diffusion of chain ends.

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“…This has been shown long time ago by Neutron Scattering experiments for "thermal" blobs in the semi-diluted solutions at rest [44], and recently by MC simulation for "tensile" blobs in the stretched chain problem [45]. In the latter case, the crossover is detected for q orthogonal to the external force and can be ascribed to the fact that scattering at small q's in these directions comes from pairs of monomers which are far apart in the elongation direction and therefore do not interact directly through the EV potential.…”

Section: Introductionmentioning

confidence: 97%

Excluded volume effects on the structure of a linear polymer under shear flow

Pierleoni

Ryckaert

2000

The Journal of Chemical Physics

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The effect of excluded volume interactions on the structure of a polymer in shear flow is investigated by Brownian Dynamics simulations for chains with size 30 ≤ N ≤ 300. The main results concern the structure factor S(q) of chains of N=300 Kuhn segments, observed at a reduced shear rate β =γτ = 3.2, whereγ is the bare shear rate and τ is the longest relaxation time of the chain. At low q, where anisotropic global deformation is probed, the chain form factor is shown to match the form factor of the continuous Rouse model under shear at the same reduced shear rate, computed here for the first time in a wide range of wave vectors. At high q, the chain structure factor evolves towards the isotropic equilibrium power law q −1/ν typical of self-avoiding walk statistics. The matching between excluded volume and ideal chains at small q, and the excluded volume power law behavior at large q are observed for q orthogonal to the main elongation axis but not yet for q along the elongation direction itself, as a result of interferences with finite extensibility effects. Our simulations support the existence of anisotropic shear blobs for polymers in good solvent under shear flow for β > 1 provided chains are sufficiently long.

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Cross-over in polymer solutions

Cited by 141 publications

References 23 publications

Monte Carlo simulations of densely-packed athermal polymers in the bulk and under confinement

Monte Carlo simulations of densely-packed athermal polymers in the bulk and under confinement

Stochastic simulations of DNA in flow: Dynamics and the effects of hydrodynamic interactions

Excluded volume effects on the structure of a linear polymer under shear flow

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