Chain Collapse and Counterion Condensation in Dilute Polyelectrolyte Solutions

Brilliantov, Nikolai V.; Кузнецов, Д. В.; Klein, R.

doi:10.1103/physrevlett.81.1433

Cited by 157 publications

(233 citation statements)

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“…Finally, the third theory, referred to as counterionfluctuation theory, argues that the collapse of a PE is due to negative pressure arising from fluctuations in the density of condensed counterions, which move freely within a PE globule [4]. Such a physical picture of the condensed counterion motion agrees with the recent results of molecular dynamics (MD) simulations [14].…”

supporting

confidence: 76%

“…With increasing charge density, the PE attains an extended conformation, regardless of the solvent quality and counterions begin to condense onto the PE, renormalizing its charge density [3,7,8]. Further increase of the PE charge density results in an effective attraction between similarly charged monomers of the PE and it collapses into a globule conformation, independent of the solvent quality [4][5][6][9][10][11][12][13][14]. …”

mentioning

confidence: 99%

“…In contrast, a flexible polyelectrolyte (PE)-charged polymer in the presence of counterions-undergoes an extended to collapsed transition in both good and bad solvents. Unlike neutral polymers, the conformations of a PE depend not only on the solvent quality, but also crucially on the interplay between electrostatic energy and translational entropy of counterions [4,5]. The strength of the electrostatic interactions depends on the charge density along the PE, which is quantified by the dimensionless Bjerrum length l B .…”

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confidence: 99%

“…To describe the counterintuitive phenomenon of PE collapse in a good solvent, several competing theories have been proposed [4,19,[23][24][25][26][27]. The first theory is based on modeling the collapsed conformation as an amorphous ionic solid [19].…”

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confidence: 99%

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Mechanism of Chain Collapse of Strongly Charged Polyelectrolytes

et al. 2016

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We perform extensive molecular dynamics simulations of a charged polymer in a good solvent in the regime where the chain is collapsed. We analyze the dependence of the gyration radius R g on the reduced Bjerrum length l B and find two different regimes. In the first one, called a weak electrostatic regime,, which is consistent only with the predictions of the counterion-fluctuation theory. In the second one, called a strong electrostatic regime, we find R g ∼ l −1=5 B. To explain the novel regime we modify the counterion-fluctuation theory. DOI: 10.1103/PhysRevLett.117.147801 Introduction.-The conformational states of a flexible neutral polymer in different solvents are well known. It is extended in a good solvent due to favorable excluded volume interactions with the solvent molecules and collapses into a compact globule in a bad solvent [1][2][3]. In contrast, a flexible polyelectrolyte (PE)-charged polymer in the presence of counterions-undergoes an extended to collapsed transition in both good and bad solvents. Unlike neutral polymers, the conformations of a PE depend not only on the solvent quality, but also crucially on the interplay between electrostatic energy and translational entropy of counterions [4,5]. The strength of the electrostatic interactions depends on the charge density along the PE, which is quantified by the dimensionless Bjerrum length l B . For small charge density, counterions are dispersed away from the PE, and the chain is in an extended necklace conformation when in a good or theta solvent [3], and is collapsed into a compact globule in a bad solvent [3,6]. With increasing charge density, the PE attains an extended conformation, regardless of the solvent quality and counterions begin to condense onto the PE, renormalizing its charge density [3,7,8]. Further increase of the PE charge density results in an effective attraction between similarly charged monomers of the PE and it collapses into a globule conformation, independent of the solvent quality [4][5][6][9][10][11][12][13][14].

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confidence: 76%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Mechanism of Chain Collapse of Strongly Charged Polyelectrolytes

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“…Our work suggests that these factors are also crucial in determining the collapse of flexible and semi-flexible polyelectrolytes recently studied in Refs. [8][9][10][11][12]. Experimental observations show that the size of the precipitating particles is indeed a relevant parameter in the problem [1,6].…”

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Attractive interactions between rodlike polyelectrolytes: Polarization, crystallization, and packing

1999

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We study the attractive interactions between rod-like charged polymers in solution that appear in the presence of multi-valence counterions. The counterions condensed to the rods exhibit both a strong transversal polarization and a longitudinal crystalline arrangement. At short distances between the rods, the fraction of condensed counterions increases, and the majority of these occupy the region between the rods, where they minimize their repulsive interactions by arranging themselves into packing structures. The attractive interaction is strongest for multivalent counterions. Our model takes into account the hard-core volume of the condensed counterions and their angular distribution around the rods. The hard core constraint strongly suppresses longitudinal charge fluctuations.PACS numbers: 61.20. Qg, 61.25.Hq, 87.15.Aa Strongly charged polymers precipitate from a dilute solution into compact structures when high-valence counterions (oppositely charged particles) are added to the solution [1][2][3][4][5][6]. The counterions experience strong electrostatic attractions to the backbone of the chains, and a finite fraction of them "condense", i.e., are found within short distance from the chains [7]. Counterions are more attracted to compact chains or aggregates of rod-like chains. This creates the possibility of a transition from single chains with a small number of condensed counterions to almost neutral aggregates of chains, or even mono-molecular collapse in the case of flexible polymers. These aggregates are stable only when the internal arrangement of the counterions within them, provides a strong enough cohesive energy.In this letter we study the attraction between two rodlike polyelectrolytes. We show that it is essential to include the size and angular degrees of freedom (around the rods) of the counterions as well as the discrete nature of the charge along the polyelectrolytes to find the origin and strength of the counterion mediated attraction. Our work suggests that these factors are also crucial in determining the collapse of flexible and semi-flexible polyelectrolytes recently studied in Refs. [8][9][10][11][12]. Experimental observations show that the size of the precipitating particles is indeed a relevant parameter in the problem [1,6].It has been argued that longitudinal charge fluctuations resulting from the thermal motion of point counterions induce attractions between rod-like polyelelctrolytes [13,14] and induces "buckling" of semiflexible polyelelctrolytes [11,12]. Here, we show that such charge fluctuation are suppressed when the hard core volume of monomers and counterions are taken into account. Instead, we find that the counterions arrangement around the rods create a non-zero transversal polarization as the distance between the chains decreases. At very short distances between the rods we find strong longitudinal correlations but only at very short wavelengths, implying a crystalline state along the rod, reinforcing, for the case of multivalent counterions, the attractive interactio...

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Polyelectrolytes in Solution and at Surfaces

Netz

Andelman

2003

Encyclopedia of Electrochemistry

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This chapter deals with charged polymers (polyelectrolytes) in solution and at surfaces. The behavior of polyelectrolytes is markedly different from that of neutral polymers. In bulk solutions, i.e. disregarding the surface effect, there are two unique features to charged polymers: first, due to the presence of long-ranged electrostatic repulsion between charged monomers, the polymer conformations are much more extended, giving rise to a very small overlap concentration and high solution viscosity. Second, the presence of a large number of counter-ions increases the osmotic pressure of polyelectrolyte solutions, making such polymers water soluble as is of great importance to many applications. At surfaces, the same interplay between monomer-monomer repulsion and counter-ion degrees of freedom leads to a number of special properties. In particular, the adsorption behavior depends on both the concentration of polymers and added salt in the bulk. We first describe the adsorption behavior of single polyelectrolyte molecules, and discuss the necessary conditions to obtain an adsorbed layer and characterize its width. Depending on the stiffness of the polyelectrolyte, the layer can be flat and compressed or coiled and extended. We then proceed and discuss the adsorption of polyelectrolytes from semi-dilute solutions. Mean-field theory profiles of polyelectrolyte adsorption are calculated as function of surface charge density (or surface potential), the amount of salt in the system and the charge fraction on the chains. The phenomenon of charge inversion is reviewed and its relevance to the formation of multilayers is explained. The review ends with a short overview of the behavior of grafted polyelectrolytes.

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Chain Collapse and Counterion Condensation in Dilute Polyelectrolyte Solutions

Abstract: A quantitative theory for polyelectrolytes in salt-free dilute solutions is developed. Depending on the electrostatic interaction strength, polyelectrolytes in solutions can undergo strong stretching (with polyelectrolyte dimension R g ϳ l

Cited by 157 publications

References 21 publications

Mechanism of Chain Collapse of Strongly Charged Polyelectrolytes

Mechanism of Chain Collapse of Strongly Charged Polyelectrolytes

Attractive interactions between rodlike polyelectrolytes: Polarization, crystallization, and packing

Polyelectrolytes in Solution and at Surfaces

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