Counterion-counterion correlation in the double layer around cylindrical polyions: Counterion size and valency effects

Molecular dynamics simulations were employed in models of peripherally charged dendrimers in solutions of explicit solvent and monovalent counterions in order to explore aspects of the dynamic behavior of counterions. The present study explores the effects of varying strength of electrostatic interactions for models of two dendrimer generations, in explicit solvent solutions below the dendrimer overlap concentration. Counterion diffusional motion as well as residence lifetimes of pairs formed by charged dendrimer beads and condensed counterions is monitored in the different electrostatic regimes. Spatiotemporal characteristics of self- and collective counterion motion are explored by means of space-time Van Hove correlation functions. A characteristic scaling law is found to describe the counterion diffusion coefficient as a function of Bjerrum length in the strong electrostatic regime, independent of the size of the dendrimer molecules at the examined volume fractions. The change noted in the diffusional motion of counterions in the range of strong Coulombic interactions is also reflected to their relevant residence times. Development of dynamic heterogeneities in counterion self-motion is observed during the gradual increase in the strength of electrostatic interactions, characterized by the emergence of distinct counterion populations in terms of their mobility. The time scale for the development of such a mobility contrast in the self-motion of the counterions can be correlated with that describing their collective motion as well. The latter increases with Bjerrum length but remains shorter compared to the time scale at which free diffusional motion sets in. Findings from the present study provide further insight on the mechanisms pertinent to ion migration in macroion dispersions and may serve as a basis for the interpretation of ionic motion in a broader range of polyelectrolyte systems.

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“…22,26,56 Figure 7 shows the dependence of self-Van Hove spectra on dendrimer concentration at constant Bjerrum length but different time periods.…”

Section: A Self-motionmentioning

confidence: 99%

Dynamics of counterions in dendrimer polyelectrolyte solutions

Karatasos

Krystallis

2009

The Journal of Chemical Physics

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“…Note that in this work, the magnitude of the valencies is unity, viz., ͉z + ͉ = ͉z − ͉ = 1. The interaction potential u pi ͑r͒ between the polyion and an ion of species i as a function of the perpendicular distance r from the polyion long axis is given by 16,17,34,35 …”

Section: Modelmentioning

confidence: 99%

“…Because of the nature of the quantity, the doublet correlation g͑r 1 , r 2 ͒, which describes the correlation between two ions at r 1 and r 2 , respectively, is difficult to evaluate. In two previous papers, 34,35 henceforth to be denoted by I and II, respectively, we made some strides toward studying this correlation by calculating the canonical average ͗g͑r 1 , r 2 ͒͘ over the cylindrical cell volume in salt-free polyelectrolyte solutions. The results for both point and finite-sized counterions as functions of valency and polyion concentration were highly informative and very encouraging.…”

Section: Introductionmentioning

confidence: 99%

Ionic correlations in the inhomogeneous atmosphere surrounding cylindrical polyions: Catalytic effects of polyions

Piñero

Bhuiyan

Reščič

et al. 2008

The Journal of Chemical Physics

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The structural properties of linear polyelectrolyte solutions in the presence of a salt as evidenced through ionic correlations in the inhomogeneous atmosphere around a polyion and their consequence such as the catalytic potential are studied by using Monte Carlo simulation techniques. The simulations are performed on the cylindrical cell model where a uniformly charged hard cylinder mimics the linear polyion, which is caged in its own cylindrical cell containing counterions and salt. The cell (volume) average of the interionic correlations is presented as a function of the polyion and salt concentrations and ion radius. These results are utilized to study the catalytic effects of polyions as manifested through the changes in the collision frequency between ions in the double layer surrounding the polyion relative to that in the pure electrolyte solution. The reported results suggest a strong influence of the added salt/polyelectrolyte concentration ratio on the structural properties of the solution and hence on ion-ion collision frequency. The machine simulations are supplemented by nonlinear Poisson-Boltzmann results. Fair agreement between two different theoretical methods of calculating the collision frequency is obtained.

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“…18 Beyond the PB equation, the MPB theory takes the ion size and interionic correlations into account in a potential formulation. 19 In both HNC/MSA theory and DFT, the interionic correlations are considered by the Ornstein-Zernike integral equation with the MSA. 20 Although both the MPB and HNC/MSA theories are comparable to the partially perturbative DFT in describing the structure of electric double layer, the DFT possesses several advantages.…”

Section: Introductionmentioning

confidence: 99%

Ion distributions, exclusion coefficients, and separation factors of electrolytes in a charged cylindrical nanopore: A partially perturbative density functional theory study

Peng¹,

Yu²

2009

The Journal of Chemical Physics

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The structural and thermodynamic properties for charge symmetric and asymmetric electrolytes as well as mixed electrolyte system inside a charged cylindrical nanopore are investigated using a partially perturbative density functional theory. The electrolytes are treated in the restricted primitive model and the internal surface of the cylindrical nanopore is considered to have a uniform charge density. The proposed theory is directly applicable to the arbitrary mixed electrolyte solution containing ions with the equal diameter and different valences. Large amount of simulation data for ion density distributions, separation factors, and exclusion coefficients are used to determine the range of validity of the partially perturbative density functional theory for monovalent and multivalent counterion systems. The proposed theory is found to be in good agreement with the simulations for both mono- and multivalent counterion systems. In contrast, the classical Poisson-Boltzmann equation only provides reasonable descriptions of monovalent counterion system at low bulk density, and is qualitatively and quantitatively wrong in the prediction for the multivalent counterion systems due to its neglect of the strong interionic correlations in these systems. The proposed density functional theory has also been applied to an electrolyte absorbed into a pore that is a model of the filter of a physiological calcium channel.

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Counterion-counterion correlation in the double layer around cylindrical polyions: Counterion size and valency effects

Cited by 14 publications

References 42 publications

Dynamics of counterions in dendrimer polyelectrolyte solutions

Dynamics of counterions in dendrimer polyelectrolyte solutions

Ionic correlations in the inhomogeneous atmosphere surrounding cylindrical polyions: Catalytic effects of polyions

Ion distributions, exclusion coefficients, and separation factors of electrolytes in a charged cylindrical nanopore: A partially perturbative density functional theory study

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