Calculation of various universal properties for dilute polymer solutions undergoing shear flow

Zylka, Waldemar; Oettinger, Hans Christian

doi:10.1021/ma00002a023

Cited by 34 publications

(18 citation statements)

References 15 publications

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“…In both table 1 and figure 1, the results of renormalisation group calculations (RG) are also presented [ 25,47]. As mentioned earlier, the renormalisation group theory approach is an alternative procedure for obtaining universal results.…”

Section: Universal Properties In Theta Solventsmentioning

confidence: 97%

The kinetic theory of dilute solutions of flexible polymers: Hydrodynamic interaction

Prakash¹

1999

Rheology Series

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Section: Universal Properties In Theta Solventsmentioning

confidence: 97%

The kinetic theory of dilute solutions of flexible polymers: Hydrodynamic interaction

Prakash¹

1999

Rheology Series

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“…In this section, using arguments similar to those in the papers byÖttinger and co-workers, [16][17][18] we derive a perturbation expansion of τ p in the strength of excluded volume interaction, which is valid for arbitrary shear rates. A significant benefit of the perturbation expansion will be a better understanding of the nature of the Gaussian approximation.…”

Section: First Order Perturbation Expansionmentioning

confidence: 99%

Rouse Chains with Excluded Volume Interactions: Linear Viscoelasticity

Prakash

2001

Macromolecules

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Linear viscoelastic properties for a dilute polymer solution are predicted by modeling the solution as a suspension of non-interacting bead-spring chains. The present model, unlike the Rouse model, can describe the solution's rheological behavior even when the solvent quality is good, since excluded volume effects are explicitly taken into account through a narrow Gaussian repulsive potential between pairs of beads in a bead-spring chain. The use of the narrow Gaussian potential, which tends to the more commonly used δ-function repulsive potential in the limit of a width parameter d going to zero, enables the performance of Brownian dynamics simulations. The simulations results, which describe the exact behavior of the model, indicate that for chains of arbitrary but finite length, a δ-function potential leads to equilibrium and zero shear rate properties which are identical to the predictions of the Rouse model. On the other hand, a non-zero value of d gives rise to a prediction of swelling at equilibrium, and an increase in zero shear rate properties relative to their Rouse model values. The use of a δ-function potential appears to be justified in the limit of infinite chain length. The exact simulation results are compared with those obtained with an approximate solution which is based on the assumption that the non-equilibrium configurational distribution function is Gaussian. The Gaussian approximation is shown to be exact to first order in the strength of excluded volume interaction, and is found to be accurate above a threshold value of d, for given values of chain length and strength of excluded volume interaction.

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“…. Unlike in the case of an FENE dumbbell, it has not been possible to obtain the particular solution to equation (23). As a result, attention is confined here to obtaining the zero shear rate predictions of the narrow Gaussian potential,…”

Section: Zero Shear Rate Propertiesmentioning

confidence: 99%

Viscometric Functions for a Dilute Solution of Polymers in a Good Solvent

Prakash

Öttinger

1999

Macromolecules

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A dilute polymer solution is modeled as a suspension of non-interacting Hookean dumbbells and the effect of excluded volume is taken into account by incorporating a narrow Gaussian repulsive potential between the beads of each dumbbell. The narrow Gaussian potential is a means of regularising a deltafunction potential-it tends to the delta-function potential in the limit of the width parameter µ going to zero. Exact predictions of viscometric functions in simple shear flow are obtained with the help of a retarded motion expansion and by Brownian dynamics simulations. It is shown that for relatively small non-zero values of µ, the presence of excluded volume causes a swelling of the dumbbell at equilibrium, and shear thinning in simple shear flow. On the other hand, a delta function excluded volume potential does not lead to either swelling or to shear thinning. Approximate viscometric functions, obtained by assuming that the bead-connector vector is described by a Gaussian nonequilibrium distribution function, are found to be accurate above a threshold value of µ, for a given value of the strength of excluded volume interaction, z. A first order perturbation expansion reveals that the Gaussian approximation is exact to first order in z. The predictions of an alternative quadratic excluded volume potential suggested earlier by Fixman (J. Chem. Phys., 1966, 45, 785; 793) are also compared with those of the narrow Gaussian potential.

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Calculation of various universal properties for dilute polymer solutions undergoing shear flow

Cited by 34 publications

References 15 publications

The kinetic theory of dilute solutions of flexible polymers: Hydrodynamic interaction

The kinetic theory of dilute solutions of flexible polymers: Hydrodynamic interaction

Rouse Chains with Excluded Volume Interactions: Linear Viscoelasticity

Viscometric Functions for a Dilute Solution of Polymers in a Good Solvent

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