End effects of polyelectrolytes by the Mayer cluster integral approach

Woodbury, Charles P.; Ramanathan, G. V.

doi:10.1021/ma00229a016

Cited by 27 publications

(24 citation statements)

References 18 publications

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“…This situation is, of course, not tractable in numerical simulations; hence to achieve proper equilibration within a reasonable time, charged cylinders are customarily considered in a confining box (in lateral directions) of practically large size. As well known [4,10,11,12,24,26], lateral finite-size effects are quite small for sufficiently large Manning parameter (ξ > ξ c ). But at small Manning parameters (ξ ∼ ξ c ), these effects become significant and suppress the decondensation of counterions.…”

Section: A the Centrifugal Sampling Methodsmentioning

confidence: 73%

“…The threshold of CCT within the mean-field PB theory was considered by several workers [9,10,11,12,13,50,51]. It may be obtained from the asymptotic behavior of the density profile (∆ → ∞) as reviewed below.…”

Section: E Beyond the Onsager Instability: Many-body Effects And Elementioning

confidence: 99%

“…This enables us to investigate the critical limit of infinite system size (that is when the outer boundaries confining counterions tend to infinity) within tractable equilibration times in the simulations. The importance of taking very large system sizes becomes evident by noting that lateral finite-size effects, which mask the critical unbinding behavior of counterions, depend on the logarithm of system size in the cylindrical geometry [1,4,9,10,11,12,13,24,31,32,36,38,43,50,51], causing a quite weak convergence to the critical infinite-size limit.…”

Section: Introductionmentioning

confidence: 99%

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Scaling and universality in the counterion-condensation transition at charged cylinders

2006

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Counterions at charged rod-like polymers exhibit a condensation transition at a critical temperature (or equivalently, at a critical linear charge density for polymers), which dramatically influences various static and dynamic properties of charged polymers. We address the critical and universal aspects of this transition for counterions at a single charged cylinder in both two and three spatial dimensions using numerical and analytical methods. By introducing a novel Monte-Carlo sampling method in logarithmic radial scale, we are able to numerically simulate the critical limit of infinite system size (corresponding to infinite-dilution limit) within tractable equilibration times. The critical exponents are determined for the inverse moments of the counterionic density profile (which play the role of the order parameters and represent the inverse localization length of counterions) both within mean-field theory and within Monte-Carlo simulations. In three dimensions, we demonstrate that correlation effects (neglected within mean-field theory) lead to an excessive accumulation of counterions near the charged cylinder below the critical temperature (condensation phase), while surprisingly, the critical region exhibits universal critical exponents in accord with the mean-field theory. Also in contrast with the typical trend in bulk critical phenomena, where fluctuations are strongly enhanced in lower dimensions, we demonstrate, using both numerical and analytical approaches, that the mean-field theory becomes exact for the 2D counterion-cylinder system at all temperatures (Manning parameters), when number of counterions tends to infinity. For finite particle number, however, the 2D problem displays a series of peculiar singular points (with diverging heat capacity), which reflect successive de-localization events of individual counterions from the central cylinder. In both 2D and 3D, the heat capacity shows a universal jump at the critical point, and the energy develops a pronounced peak. The asymptotic behavior of the energy peak location is used to locate the critical point, which is also found to be universal and in accordance with the mean-field prediction.

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Section: A the Centrifugal Sampling Methodsmentioning

confidence: 73%

Section: E Beyond the Onsager Instability: Many-body Effects And Elementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Scaling and universality in the counterion-condensation transition at charged cylinders

2006

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“…However, as an approximate theory in its mathematical treatment, it has received several criticisms (24-34) based on discrepancies with experimental observations. These have resulted in the development of extended treatments of the polyelectrolyte theory, by application of the Poisson-Boltzmann (24)(25)(26)(27)(28)(29)(30) or Gouy-Chapman (3 1) equations. An extension of Manning's theory without an explicit reference to the condensed phase has been considered as we11 (32).…”

Section: An Assessment Of Nmr Measurements Of Binding Interactionsmentioning

confidence: 99%

Binding of magnesium and lanthanum ions to heparin in the presence of sodium ions. A relationship between ¹³C chemical shift displacements and counterion condensation theory

Dais¹,

Peng²,

Perlin³

1987

Can. J. Chem.

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. Interactions between beef lung heparin and M~" and La3+ counterions, in the presence of sodium ions, have been investigated by I3C-nmr spectroscopy. The chemical shift displacements observed for the carbons of the main disaccharide unit of heparin, when analysed on the basis of counterion condensation theory, indicate that the association between the heparin polyanion and Mg2+ is a delocalized process. This is analogous to the Ca2+/Na+/heparin system, despite the fact that the binding affinity of heparin for Ca2+ is stronger than that for Mg2+. By contrast, the interaction with La3+ is in excess of the theoretical predicted, which suggests that there is at least a partial site-binding of this counterion. In ca2+/~+/heparin systems in which M' = Na+ or K+, the selective binding preference of heparin for the univalent cations may be related to the order of their crystallographic ionic radii. A critical assessment is offered of the validity of this nmr spectroscopic approach to the study of counterion binding to heparin.PHOTIS DAIS, QIN-JI PENG et ARTHUR S. PERLIN. Can. J. Chem. 65, 1739 (1987). Faisant appel a la rmn du "C, on a ttudit les interactions entre 1'hCparine de poumon de bceuf et des ions Mg2+ et La3+, en prtsence d'ions sodium. Une analyse des dtplacements chimiques observts pour les carbones de l'unitt dissacharidique principale de l'htparine en faisant appel ? i la thtorie de condensation des contre-ions indique que l'association entre le polyanion de l'htparine et le Mg" est un processus dtlocalist. Ceci est analogue au systkme Ca2+/~a+/htparine, meme si l'affinitt de 1'hCparine pour le Ca2+ est plus forte que pour le Mg2+. Par ailleurs, l'interaction avec le La3+ est plus importante que celle prtvue sur une base thCorique; ceci suggere qu'il existe au moins un site de liaison partiel pour ce contre-ion. Dans les systkmes Ca2+/M+/hCparine, dans lesquels M+ = Na+ ou K+, on peut ttablir une correlation entre la liaison selective prtftrentielle pour les cations univalents et l'ordre de leurs rayons ioniques cristallographiques. On offre une Cvaluation critique de la validitt de cette approche par spectroscopie rmn pour ttudier la liaison de contre-ions avec l'htparine.[Traduit par la revue] Introduction In a previous study (l), the binding of calcium ions (Ca2+) by heparin in the presence of sodium ions was examined by monitoring 13C chemical shift displacements as a function of the calcium ion concentration and total ionic strength. The results (1) are consistent with the counterion condensation model (2-4), thereby indicating that the association between the heparin polyanion and calcium ions is a delocalized process, rather than one involving specific binding.We now report the results obtained for the interaction of beef lung heparin with magnesium (Mg2+) or lanthanum (La3+) ion, in the presence of sodium (and chloride) ions. Studies (5-8) on the binding of Mg2+ to heparin have shown that this cation interacts less strongly than Ca2+ and, in accord with the counterion condensation model, binds in ...

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“…Skolnick and Grimmelmann (38) show that in the infinite length approximation may be valid for finite chain length only if λ^π) is small relative to the length of the line. Using the Mayer cluster integrals Woodbury and Ramanathan (39) conclude that counterions do not condense onto finite length line charges . If the dielectric constant of the polyion differs from that of the bulk solvent then projection of the actual charge distribution onto a line may lead to difficulties in the application of the OosawaManning condensation theories.…”

Section: Macro-ion Characterizationmentioning

confidence: 99%

An Overview of Polyelectrolytes

Schmitz

1993

ACS Symposium Series

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Interests in solutions and suspension of macroions has been renewed in the past few years, as evidenced by the mini symposium upon which this present volume is based. Presented in this introductory chapter is a brief presentation of a selection of six topics that I believe deserves further consideration regarding these complex systems: 1) the definition of the screening parameter; 2) the mathematical form of the pairwise electrostatic energy between macroions; 3) the phenomenon of counterion condensation and its application to specific molecular geometry; 4) the use of the Gibbs versus the Helmholtz free energy in describing the thermodynamics of these charged systems; 5) the calculation of the electrostatic component to the persistence length of flexible polyions; and 6) the splitting of relaxation modes as detected by dynamic light scattering measurements.Studying polyelectrolytes is like taking a roller coaster ride. In the beginning one knows nothing about the field and therefore faces a steep upward learning curve. At some point one reaches a degree of understanding of the field and begins to publish the new results. Further investigations into the field have their ups and downs, sometimes even being thrown for a loop when unexpected results are obtained. Eventually, however, the excursion through the field of polyelectrolytes returns one to the starting point. To illustrate the above metaphor one only has to follow the history of a simple basic question: "Is the interaction between the charged macroions attractive or repulsive?"In 1938 Langmuir treated a solution of micelles in a manner similar to that of a simple salt crystal. He thus considered the counterions between the micelles as part of the interaction energy, which led to a major result (7):The interaction of these charges, just as in the sodium chloride crystal, gives an excess of attractive force and in order to have equilibrium it will be necessary not to have an additional attractive force, such as the van der Waals force postulated by Hamaker, but some new kind of repulsive force.In contrast to the conclusion of Langmuir, the currently accepted paradigm for the majority of the practitioners in the colloid field is the DLVO (Derjaguin-Landau-0097-6156/94/0548-0001$06.50/0

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End effects of polyelectrolytes by the Mayer cluster integral approach

Cited by 27 publications

References 18 publications

Scaling and universality in the counterion-condensation transition at charged cylinders

Scaling and universality in the counterion-condensation transition at charged cylinders

Binding of magnesium and lanthanum ions to heparin in the presence of sodium ions. A relationship between ¹³C chemical shift displacements and counterion condensation theory

An Overview of Polyelectrolytes

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End effects of polyelectrolytes by the Mayer cluster integral approach

Cited by 27 publications

References 18 publications

Scaling and universality in the counterion-condensation transition at charged cylinders

Scaling and universality in the counterion-condensation transition at charged cylinders

Binding of magnesium and lanthanum ions to heparin in the presence of sodium ions. A relationship between 13C chemical shift displacements and counterion condensation theory

An Overview of Polyelectrolytes

Contact Info

Product

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Binding of magnesium and lanthanum ions to heparin in the presence of sodium ions. A relationship between ¹³C chemical shift displacements and counterion condensation theory