Polyelectrolyte solutions containing mixed valency ions in the cell model: A simulation and modified Poisson–Boltzmann study

Das, T. P.; Bratko, D.; Bhuiyan, L. B.; Outhwaite, C.W.

doi:10.1063/1.475211

Cited by 75 publications

(92 citation statements)

References 49 publications

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“…The valency of counterions is v ct = À 1, while the valency of coions is v co = 1. The mean electrostatic potential is obtained by solving the differential equation that follows from expression (16) d 2 UðrÞ dr 2 þ 1 r dUðrÞ dr…”

Section: A Case Of the Univalent Electrolytementioning

confidence: 99%

Charged cylindrical surfaces: effect of finite ion size

Bohinc

Iglič

Slivnik

et al. 2002

Bioelectrochemistry

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A simple statistical mechanical approach is applied to calculate the profile of the density of the number of particles and the profile of the electrostatic potential of an electric double layer formed by a charged cylindrical surface in contact with electrolyte solution. The finite size of particles constituting the electrolyte solution is considered by including the excluded volume effect within the lattice statistics while the electrostatic interactions are considered by means of the mean electrostatic field. It is shown that the excluded volume effect decreases the density of the number of counterions and increases the electrostatic potential near the charged cylindrical surface. The effect is more pronounced for high area densities of charge of the charged surface and for larger counterions. Further, it is shown that the ratio between the density of the number of the counterions near the charged cylindrical surface and the density of the number of counterions far from the charged surface reaches a plateau at large linear charge densities for ions of finite size, while no plateau is reached for dimensionless ions. The effective thickness of the electric double layer in cylindrical geometry is introduced. It is shown that the effective thickness increases with increasing counterion size while its dependence on the area density of charge of the charged surface exhibits a minimum. The theoretical approach presented in this work can be used for description of the electrostatics of the thin cylindrical structures in biological systems such as DNA, protein macromolecules and charged micro and nano tubes. D

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Section: A Case Of the Univalent Electrolytementioning

confidence: 99%

Charged cylindrical surfaces: effect of finite ion size

Bohinc

Iglič

Slivnik

et al. 2002

Bioelectrochemistry

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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%

“…The simulations suggest that the PB equation is generally semiquantitative in describing equilibrium properties for monovalent systems but is less certain for higher and/or multivalent systems. Formal theories such as the MPB theory on the other hand, have been more successful, with the MPB being able to predict, for example, charge inversion 17 and give a rather good fit to experimental partial structure functions in DNA, PSS, 18 and polyamines. 19 An important structural feature of the charge cloud around a polyion is the ion-ion correlation.…”

Section: Introductionmentioning

confidence: 97%

“…4͒. Besides the classical Poisson-Boltzmann ͑PB͒ theory, 1,5,6 formal statistical mechanical approaches such as the hypernetted chain/mean spherical approximation ͑HNC/MSA͒, 13,14 the PB/MSA, 15 and the modified PB ͑MPB͒ theory [16][17][18][19] have been utilized in conjunction with the cylindrical cell model. The theoretical efforts have been supplemented by numerical computer simulations, viz., with parameters corresponding to DNA, [20][21][22][23][24][25][26][27][28][29][30] PSS, 31,32 ionenes, 33 and polyamines, 19 the focus being principally on polyionsimple ion correlation and the thermodynamics of the solution.…”

Section: Introductionmentioning

confidence: 99%

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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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“…The dynamics of the ions and their interaction should satisfy the charge continuity equation and the Poisson equation. This is expressed in a rigorous manner by the PNP equations [88][89][90][91][92][93]:…”

Section: A Poisson-nernst-planck Equationsmentioning

confidence: 99%

Self-Consistent Approach to Global Charge Neutrality in Electrokinetics: A Surface Potential Trap Model

Wan

Liao

et al. 2014

Phys. Rev. X

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In this work, we treat the Poisson-Nernst-Planck (PNP) equations as the basis for a consistent framework of the electrokinetic effects. The static limit of the PNP equations is shown to be the charge-conserving Poisson-Boltzmann (CCPB) equation, with guaranteed charge neutrality within the computational domain. We propose a surface potential trap model that attributes an energy cost to the interfacial charge dissociation. In conjunction with the CCPB, the surface potential trap can cause a surface-specific adsorbed charge layer σ. By defining a chemical potential μ that arises from the charge neutrality constraint, a reformulated CCPB can be reduced to the form of the Poisson-Boltzmann equation, whose prediction of the Debye screening layer profile is in excellent agreement with that of the Poisson-Boltzmann equation when the channel width is much larger than the Debye length. However, important differences emerge when the channel width is small, so the Debye screening layers from the opposite sides of the channel overlap with each other. In particular, the theory automatically yields a variation of σ that is generally known as the "charge regulation" behavior, attendant with predictions of force variation as a function of nanoscale separation between two charged surfaces that are in good agreement with the experiments, with no adjustable or additional parameters. We give a generalized definition of the ζ potential that reflects the strength of the electrokinetic effect; its variations with the concentration of surface-specific and surfacenonspecific salt ions are shown to be in good agreement with the experiments. To delineate the behavior of the electro-osmotic (EO) effect, the coupled PNP and Navier-Stokes equations are solved numerically under an applied electric field tangential to the fluid-solid interface. The EO effect is shown to exhibit an intrinsic time dependence that is noninertial in its origin. Under a step-function applied electric field, a pulse of fluid flow is followed by relaxation to a new ion distribution, owing to the diffusive counter current. We have numerically evaluated the Onsager coefficients associated with the EO effect, L 21 , and its reverse streaming potential effect, L 12 , and show that L 12 ¼ L 21 in accordance with the Onsager relation. We conclude by noting some of the challenges ahead.

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Polyelectrolyte solutions containing mixed valency ions in the cell model: A simulation and modified Poisson–Boltzmann study

Cited by 75 publications

References 49 publications

Charged cylindrical surfaces: effect of finite ion size

Charged cylindrical surfaces: effect of finite ion size

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

Self-Consistent Approach to Global Charge Neutrality in Electrokinetics: A Surface Potential Trap Model

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