Comparison of density functional and modified Poisson-Boltzmann structural properties for a spherical double layer

Bhuiyan,; Outhwaite, C.W.

doi:10.5488/cmp.8.2.287

Cited by 35 publications

(28 citation statements)

References 27 publications

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“…(4) with a distance of closest approach, by PB + L. The special case of ξ(r) = 1 for r > R + a/2, which is a simple Stern correction to the PB theory, will be denoted simply by PB for consistency with literature (see for example Refs. [26,27]). The boundary conditions for ψ(r) are ψ(r) → 0 as r → ∞ and at the surface of the macroion either dψ/dr = −σ /ε 0 ε r or ψ(R) is specified.…”

Section: Theorymentioning

confidence: 97%

“…Recently López-Garcia et al [15] have studied the spherical double layer (SDL) around an isolated macroion, corresponding to a macroion at infinite dilution The radius of the macroion was chosen to be 100 nm, and at such a large radius, many properties of the SDL are similar to those of the PDL. We consider here comparisons with the MPB theory exclusion volume corrections to the PB equation for the PDL and SDL [23,[25][26][27]. In order to compare the MPB theories with the Langmuir-type theories it is necessary to incorporate a distance of closest approach of the ions to the surface into the Langmuir model.…”

Section: Introductionmentioning

confidence: 99%

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Comparison of exclusion volume corrections to the Poisson–Boltzmann equation for inhomogeneous electrolytes

Bhuiyan

Outhwaite

2009

Journal of Colloid and Interface Science

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Section: Theorymentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Comparison of exclusion volume corrections to the Poisson–Boltzmann equation for inhomogeneous electrolytes

Bhuiyan

Outhwaite

2009

Journal of Colloid and Interface Science

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“…Several theoretical approaches based on the modified Poisson-Boltzmann equations, 35 density functional theory, 36,37 and integral equations 26,38 have been used to describe the electrical double layer of coulombic systems in spherical geometry. In this work the hypernetted-chain/ mean spherical approximation (HNC/MSA) is employed, since in the past it has produced reliable numerical results, in good concordance with molecular simulations.…”

Section: Model Theory and Simulationsmentioning

confidence: 99%

Entropic effects in the electric double layer of model colloids with size-asymmetric monovalent ions

Guerrero-García¹,

González‐Tovar²,

Cruz³

2011

The Journal of Chemical Physics

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Articles you may be interested inElectric double layer for a size-asymmetric electrolyte around a spherical colloidThe structure of the electric double layer of charged nanoparticles and colloids in monovalent salts is crucial to determine their thermodynamics, solubility, and polyion adsorption. In this work, we explore the double layer structure and the possibility of charge reversal in relation to the size of both counterions and coions. We examine systems with various size-ratios between counterions and coions (ion size asymmetries) as well as different total ion volume fractions. Using Monte Carlo simulations and integral equations of a primitive-model electric double layer, we determine the highest charge neutralization and electrostatic screening near the electrified surface. Specifically, for two binary monovalent electrolytes with the same counterion properties but differing only in the coion's size surrounding a charged nanoparticle, the one with largest coion size is found to have the largest charge neutralization and screening. That is, in size-asymmetric double layers with a given counterion's size the excluded volume of the coions dictates the adsorption of the ionic charge close to the colloidal surface for monovalent salts. Furthermore, we demonstrate that charge reversal can occur at low surface charge densities, given a large enough total ion concentration, for systems of monovalent salts in a wide range of ion size asymmetries. In addition, we find a non-monotonic behavior for the corresponding maximum charge reversal, as a function of the colloidal bare charge. We also find that the reversal effect disappears for binary salts with large-size counterions and small-size coions at high surface charge densities. Lastly, we observe a good agreement between results from both Monte Carlo simulations and the integral equation theory across different colloidal charge densities and 1:1-electrolytes with different ion sizes.

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“…To date, the MPB approach remains one of the more successful statistical mechanical theories of the double layer in planar1,20, spherical21, and cylindrical22 geometries. The MPB theory utilized in this work is at the MPB5 level, which is presently the most accurate formulation of the theory.…”

Section: Model and Methodsmentioning

confidence: 99%

A modified Poisson–Boltzmann study of the singlet ion distribution at contact with the electrode for a planar electric double layer

Silvestre-Alcantara

Bhuiyan

Outhwaite

et al. 2010

Collect. Czech. Chem. Commun.

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The properties of the singlet ion distributions at and around contact in a restricted primitive model double layer are characterized in the modified Poisson-Boltzmann theory. Comparisons are made with the corresponding exact Monte Carlo simulation data, the results from the Gouy-ChapmanStern theory coupled to an exclusion volume term, and the mean spherical approximation. Particular emphasis is given to the behaviour of the theoretical predictions in relation to the contact value theorem involving the charge profile. The simultaneous behaviour of the coion and counterion contact values is also examined. The performance of the modified Poisson-Boltzmann theory in regard to the contact value theorems is very reasonable with the contact characteristics showing semi-quantitative or better agreement overall with the simulation results. The exclusionvolume-treated Gouy-Chapman-Stern theory reveals a fortuitous cancellation of errors, while the mean spherical approximation is poor. KeywordsElectric double layer; Contact value theorems; Density profile; Charge profile; Monte Carlo Alongside exact numerical simulations, exact analytical conditions are invaluable in statistical mechanics of Coulomb fluids in comparative assessment of different theories and/ or further theoretical development. These exact conditions can also help provide additional, useful checks on the consistency of simulations. One such condition in the electric double layer phenomenon is our principal concern in this paper. An electric double layer is formed when a charged electrode is brought in contact with a charged fluid and an ionic atmosphere develops in the vicinity of the electrode. The phenomenon has practical significance for a spectrum of systems in biology and industrial chemical processes. Here ρ s , d s and g s are, respectively, the average number density, the diameter and the electrode-ion distribution function of ionic species s, p is the bulk osmotic pressure and σ is the uniform surface charge density on the electrode with ε 0 and ε r , respectively, being the vacuum permittivity and relative permittivity of the solvent. Also, k B is the Boltzmann constant and T the absolute temperature. The relation was derived from force balance considerations at the electrode-electrolyte interface. It is local, easy to implement and, as a consequence, has been useful in checking theoretical descriptions of the electric double layer over the past three decades 1 .The other, relatively recent condition concerns the contact value of the charge profile in the planar double layer. This was derived by Holovko, Badiali and di Caprio4,5 (HBC), and Holovko and di Caprio6 starting from the Bogoliubov-Born-Green-Yvon (BBGY) hierarchy of equations7. For a double layer containing a restricted primitive model (RPM) electrolyte (the ions of the PM are now restricted to having a common diameter), and for symmetric valency salts -our interest in this paper, their relation is particularly simple, viz.,where g sum (x) = (1/2)(g ctr (x) + g co (x)), g diff (x...

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Comparison of density functional and modified Poisson-Boltzmann structural properties for a spherical double layer

Cited by 35 publications

References 27 publications

Comparison of exclusion volume corrections to the Poisson–Boltzmann equation for inhomogeneous electrolytes

Comparison of exclusion volume corrections to the Poisson–Boltzmann equation for inhomogeneous electrolytes

Entropic effects in the electric double layer of model colloids with size-asymmetric monovalent ions

A modified Poisson–Boltzmann study of the singlet ion distribution at contact with the electrode for a planar electric double layer

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