Charge fluctuations and counterion condensation

Lau, Andy T. Y.; Lukatsky, D. B.; Pincus, P.; Safran, S. A.

doi:10.1103/physreve.65.051502

Cited by 67 publications

(95 citation statements)

References 33 publications

(22 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In agreement with the preceding results, the counterionic density in the immediate vicinity of the charged cylinder increases for increasing Ξ exhibiting large deviations from the mean-field prediction (see Ref. [74] for a similar trend at charged plates). For a given surface charge density σ s , the observed trend is predicted, e.g., for increasing counterion valency, q, since the coupling parameter scales as Ξ ∼ q 3 (Eq.…”

Section: Electrostatic Correlations At Surface and For Large ξsupporting

confidence: 89%

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

2006

View full text Add to dashboard Cite

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.

show abstract

Section: Electrostatic Correlations At Surface and For Large ξsupporting

confidence: 89%

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

2006

View full text Add to dashboard Cite

show abstract

“…Here we employ the two state model (figure 1) in which counterions are divided into two classes, namely, condensed and non-condensed (free) ions [12]: some of counterions can bind to an oppositely charged surface, in spite of entropic penalty, due to the electrostatic attraction being greater than the thermal energy. On the other hand, counterions tend to remain in the bulk to gain entropy.…”

mentioning

confidence: 99%

Charge inversion on membranes induced by multivalent-counterion fluctuations

Kim¹,

Sung²

2005

J. Phys.: Condens. Matter

View full text Add to dashboard Cite

Based on the two state model, we study the condensation of counterions on oppositely charged membranes in the presence of monovalent salts. Using the Gaussian approximation, we evaluate the contribution of two-dimensional charge fluctuation to the free energy, from which the number of condensed counterions is determined self-consistently. It is shown that charge inversion can occur upon the addition of divalent ions of millimolar range, or of trivalent ions of micromolar range. The driving force for the overcharging mechanism is the charge correlation induced by thermal fluctuation, in which the multivalency of the counterions plays a crucial role.(Some figures in this article are in colour only in the electronic version)Counterions in watery solution dominantly distribute near an oppositely charged surface of macroions, forming a diffuse electric double layer. The structure of a double layer of counterions, which has been usually described by the mean-field Poisson-Boltzmann theory, is of great importance in interaction and phase behaviours of macroions [1,2]. When the macroions are subject to an external electric field, they instantaneously reach a stationary velocity due to the viscous friction from the ambient solution. This is called electrophoresis, and it provides an efficient way to probe the double layer structure and thus to measure the surface potential of charged colloidal systems [3,4]. The counterions strongly bound to the macroion play an important role in this transport property by renormalizing the electrokinetic charges of the surface [5]. According to the Poisson-Boltzmann theory, the macroion charge is only partially compensated (neutralized) by the counterions so that the sign of the net charge is retained even in the presence of the strongly associated counterions.It has been however observed that the counterions can further condense on the surface beyond compensation of the macroion charge, leading to reversal of the drift direction in electrophoretic experiments [6]. This phenomenon is called charge inversion, and has been

show abstract

“…[3][4][5][6][7][8][9][10] For example, one surprising phenomenon beyond MF theory is the so-called fluctuation-driven counterion condensation in a simple system with single charged surface and its oppositely charged counterions. [11][12][13][14] Another interesting phenomenon is the attraction between two highly likely-charged surface immersed in electrolytes or polar solution, [14][15][16][17][18] as observed in experiments and in computer simulations. These phenomena cannot be captured within PB theories [19][20][21] as PB theory only predicts pure repulsion between likely-charged surfaces.…”

Section: Introductionmentioning

confidence: 93%

Electrostatic correlations near charged planar surfaces

Deng

Karniadakis

2014

The Journal of Chemical Physics

View full text Add to dashboard Cite

Electrostatic correlation effects near charged planar surfaces immersed in a symmetric electrolytes solution are systematically studied by numerically solving the nonlinear six-dimensional electrostatic self-consistent equations. We compare our numerical results with widely accepted mean-field (MF) theory results, and find that the MF theory remains quantitatively accurate only in weakly charged regimes, whereas in strongly charged regimes, the MF predictions deviate drastically due to the electrostatic correlation effects. We also observe a first-order like phase-transition corresponding to the counterion condensation phenomenon in strongly charged regimes, and compute the phase diagram numerically within a wide parameter range. Finally, we investigate the interactions between two likely-charged planar surfaces, which repulse each other as MF theory predicts in weakly charged regimes. However, our results show that they attract each other above a certain distance in strongly charged regimes due to significant electrostatic correlations. © 2014 AIP Publishing LLC.

show abstract

Charge fluctuations and counterion condensation

Cited by 67 publications

References 33 publications

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

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

Charge inversion on membranes induced by multivalent-counterion fluctuations

Electrostatic correlations near charged planar surfaces

Contact Info

Product

Resources

About