Counterion Condensation in Solutions of Rigid Polyelectrolytes

Nyquist, Rebecca M.; Ha, Bae‐Yeun; Liu, Andrea J.

doi:10.1021/ma9811021

Cited by 60 publications

(74 citation statements)

References 36 publications

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“…II B 2 and model the system of interacting PE chains by superposing two charge density profiles ̺ (1) (r) as given via Eq. (16). In other words, we assume them to maintain the same profiles as in the case of isolated chains and to completely interpenetrate, whereby both charge distributions are shifted with respect to each other by the vector D connecting the chains' centers of mass (see Fig.…”

Section: Comparison To MD Resultsmentioning

confidence: 99%

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Soft effective interactions between weakly charged polyelectrolyte chains

Konieczny

Likos

Löwen

2004

The Journal of Chemical Physics

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We apply extensive Molecular Dynamics simulations and analytical considerations in order to study the conformations and the effective interactions between weakly charged, flexible polyelectrolyte chains in salt-free conditions. We focus on charging fractions lying below 20%, for which case there is no Manning condensation of counterions and the latter can be thus partitioned in two states: those that are trapped within the region of the flexible chain and the ones that are free in the solution. We examine the partition of counterions in these two states, the chain sizes and the monomer distributions for various chain lengths, finding that the monomer density follows a Gaussian shape. We calculate the effective interaction between the centers of mass of two interacting chains, under the assumption that the chains can be modeled as two overlapping Gaussian charge profiles. The analytical calculations are compared with measurements from Molecular Dynamics simulations. Good quantitative agreement is found for charging fractions below 10%, where the chains assume coil-like configurations, whereas deviations develop for charge fraction of 20%, in which case a conformational transition of the chain towards a rodlike configuration starts to take place.

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Section: Comparison To MD Resultsmentioning

confidence: 99%

“…13,14 Another issue concerning isolated PE chains that has attracted considerable interest, is that of Manning condensation 15 along the stiff, rodlike backbone. The fraction of condensed counterions has been examined both in theory 16,17 and in experiments. 18,19 Counterion condensation and fluctuations have been…”

Section: Introductionmentioning

confidence: 99%

Soft effective interactions between weakly charged polyelectrolyte chains

Konieczny

Likos

Löwen

2004

The Journal of Chemical Physics

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“…4.4, correcting this point would lead to an increased osmotic coefficient, since finite rods show less condensation (indeed, none in the limit of zero density). Moreover, the theoretical treatment of finite rods by Nyquist et al 36 produces too large coefficients even at finite densities. Hence, finite size effects of the rods are unable to explain the additional reduction of the osmotic coefficient.…”

Section: Discussionmentioning

confidence: 99%

“…10,17 Possible reasons for this shortcoming may be related to the two state model or the random phase approximation employed in Ref.. 36 …”

Section: Finite Rodsmentioning

confidence: 99%

The osmotic coefficient of rod-like polyelectrolytes: Computer simulation, analytical theory, and experiment

Deserno

Holm

Blaul

et al. 2001

The European Physical Journal E

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The osmotic coefficient of solutions of rod-like polyelectrolytes is considered by comparing current theoretical treatments and simulations to recent experimental data. The discussion is restricted to the case of monovalent counterions and dilute, salt-free solutions. The classical PoissonBoltzmann solution of the cell model correctly predicts a strong decrease in the osmotic coefficient, but upon closer look systematically overestimates its value. The contribution of ion-ion-correlations are quantitatively studied by MD simulations and the recently proposed DHHC theory. However, our comparison with experimental data obtained on synthetic, stiff-chain polyelectrolytes shows that correlation effects can only partly explain the discrepancy. A quantitative understanding thus requires theoretical efforts beyond the restricted primitive model of electrolytes.

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“…Since its discovery, the CCT has been at the focus of numerical [23,24,25,26] and analytical [27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44] studies. Under particular dispute has been the connection between CCT and the celebrated Kosterlitz-Thouless transition of logarithmically interacting particles in two dimensions [31,45,46,47].…”

Section: Introductionmentioning

confidence: 99%

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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Counterion Condensation in Solutions of Rigid Polyelectrolytes

Cited by 60 publications

References 36 publications

Soft effective interactions between weakly charged polyelectrolyte chains

Soft effective interactions between weakly charged polyelectrolyte chains

The osmotic coefficient of rod-like polyelectrolytes: Computer simulation, analytical theory, and experiment

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

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