Mean-field theory of concentrated polyelectrolyte solutions: Statics and dynamics

Vilgis, Thomas A.; Borsali, Rédouane

doi:10.1103/physreva.43.6857

Cited by 76 publications

(72 citation statements)

References 46 publications

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“…We note that this result is the same as the one obtained by Borue and Erukhimovich 22) and by Vilgis and Borsali 7) , and was used by Donley et al 23) to study chain structure. The Debye-Hückel theory has also been applied to polyelectrolyte adsorption on surfaces by Ch atellier and Joanny 24) .…”

Section: A2supporting

confidence: 65%

“…In order to simplify the expressions, we use a smeared charge distribution on the polymers. It is noticed that many of the results obtained below have been derived by Vilgis and Borsali 7) using a different approach. For many cases, it is useful to expand the free energy functional of the inhomogeneous system around the homogeneous phase.…”

Section: A2mentioning

confidence: 87%

“…The continuum theory starts with a free energy functional for the polyelectrolyte systems. A theory of weakly charged polyelectrolyte solutions based on collective density variables has been studied by Vilgis and Borsali 7) using the random phase approximation. Using a Landau-type free energy functional, microphase separation in polyelectrolyte systems has been studied by Khokhlov and coworkers 8,9) .…”

Section: Introductionmentioning

confidence: 99%

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Theory of inhomogeneous weakly charged polyelectrolytes

Shi

Noolandi

1999

Macromol. Theory Simul.

116

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SUMMARY: A theory of inhomogeneous multicomponent systems containing weakly charged polyelectrolytes is developed. The theory treats the polymer conformation and the electrostatics simultaneously using a functional integral representation of the partition function. A mean-field approximation to the theory leads to two sets of coupled mean-field equations: a Poisson-Boltzmann type equation describing the electrostatic potential, and a set of self-consistent field equations describing the equilibrium densities. Asymptotic forms of the theory at weak and strong segregation limits are derived. The theory can be used to study the interfacial properties, microphase structures, and adsorptions of a variety of weakly charged polyelectrolyte systems. As a simple example, the interface between the polymer-rich and polymer-poor phases of a polyelectrolyte solution is studied.

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Section: A2supporting

confidence: 65%

Section: A2mentioning

confidence: 87%

Section: Introductionmentioning

confidence: 99%

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Theory of inhomogeneous weakly charged polyelectrolytes

Shi

Noolandi

1999

Macromol. Theory Simul.

116

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“…One explanation may be the lower charge parameter of PACs star as compared to that of PANa star (see Table 1). Indeed the peak position is very sensitive to the charge parameter as it has been predicted [35] and shown in other experiments. [2] The PACs star is not fully charged (see Table 1) because of the size of the Cs counterion, which Figure 5.…”

Section: Concentration Dependence and Molar Mass Effects In ''Salt-frmentioning

confidence: 54%

SAXS from Four‐Arm Polyelectrolyte Stars in Semi‐Dilute Solutions

Moinard

Taton

Gnanou

et al. 2003

Macro Chemistry & Physics

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We have performed small‐angle X‐ray scattering experiments on semi‐dilute solutions of highly charged star polyelectrolytes. Poly(sodium acrylate) (PANa) and poly(cesium acrylate) (PACs) stars with four arms were successfully synthesized by a combination of atom transfer radical polymerization and chemical modifications. Over a wide range of polyelectrolyte concentration Cp, these two systems as well as their equivalent linear polyelectrolytes were investigated at different ionic strengths. Scattering experiments show the existence of a scattering peak denoted as qmax, which disappears with the addition of a simple electrolyte, evidencing the electrostatic character of the interactions. We have also studied the effect of the charge parameter and the nature of the counterion (Na and Cs) on the scattering properties of these star polyelectrolytes. In the case of PACs, qmax scales with the polyelectrolyte concentration as Cp1/2 over the whole range of studied concentrations, whereas it scales as Cp1/2 (for Cp < 45 mg · ml−1) and Cp1/4 (for Cp > 45 mg · ml−1) in the case of PANa. Variation of qmax as a function of polyelectrolyte concentration Cp for PA1Cs (○) and PA2Cs (•) stars (error bars are indicated).magnified imageVariation of qmax as a function of polyelectrolyte concentration Cp for PA1Cs (○) and PA2Cs (•) stars (error bars are indicated).

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“…k is the scattering wave vector. Using the standard theory of polymer dynamics (25)(26)(27)(28)(29)(30)(31), the time evolution of ρ k ðtÞ is given by…”

Section: Significancementioning

confidence: 99%

Ordinary–extraordinary transition in dynamics of solutions of charged macromolecules

Muthukumar

2016

Proc. Natl. Acad. Sci. U.S.A.

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The occurrence of the ubiquitous and intriguing "ordinary-extraordinary" behavior of dynamics in solutions of charged macromolecules is addressed theoretically by explicitly considering counterions around the macromolecules. The collective and coupled dynamics of macromolecules and their counterion clouds in salt-free conditions are shown to lead to the "ordinary" behavior (also called the "fast" mode) where diffusion coefficients are independent of molar mass and polymer concentration and are comparable to those of isolated metallic ions in aqueous media, in agreement with experimental facts observed repeatedly over the past four decades. The dipoles arising from adsorbed counterions on polymer backbones can form many pairwise physical cross-links, leading to microgel-like aggregates. Balancing the swelling from excluded volume effects and counterion pressure with elasticity of the microgel, we show that there is a threshold value of a combination of polymer concentration and electrolyte concentration for the occurrence of the "extraordinary" phase (also called the "slow" mode) and the predicted properties of diffusion coefficient for this phase are in qualitative agreement with well-known experimental data.ordinary-extraordinary transition | slow mode | fast mode | polyelectrolyte dynamics | polyelectrolyte aggregation T he "ordinary-extraordinary" transition has been known over the past four decades from dynamic light-scattering (DLS) experiments on aqueous solutions of charged macromolecules such as DNA, polylysine, polystyrene sulfonate, polyvinyl pyridine, etc. (1-22). In the so-called "ordinary" behavior, the diffusion coefficient D determined from DLS increases, from the value D SE expected from the Stokes-Einstein law for dilute polyelectrolyte solutions at high enough monovalent salt concentrations c s sufficient to screen electrostatic interactions, to even higher values upon a decrease in c s . This observation is already intriguing, because the chain swells due to stronger intrachain electrostatic repulsion at lower values of c s and hence D is expected to decrease according to the Stoke-Einstein law. However, D actually increases! Even more strangely, upon further decrease in c s , an additional diffusion coefficient with very small values emerges, suggesting the presence of large aggregates. It is surprising that similarly charged, and hence electrostatically repulsive, polymers would aggregate at all and that they would break apart when electrostatic repulsion is screened by added electrolyte. In view of this mysterious nature, this behavior is called "extraordinary." In addition to these tantalizing facts, the occurrence of the ordinaryextraordinary behavior for solutions of charged macromolecules completely undermines the utility of the Stokes-Einstein law, which is the routine methodology for characterizing uncharged macromolecules in solutions.The diffusional modes corresponding to the ordinary and extraordinary behaviors are also called "fast" and "slow" modes, with their respective diffusio...

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Mean-field theory of concentrated polyelectrolyte solutions: Statics and dynamics

Cited by 76 publications

References 46 publications

Theory of inhomogeneous weakly charged polyelectrolytes

Theory of inhomogeneous weakly charged polyelectrolytes

SAXS from Four‐Arm Polyelectrolyte Stars in Semi‐Dilute Solutions

Ordinary–extraordinary transition in dynamics of solutions of charged macromolecules

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