A Simple Statistical Mechanical Approach to the free Energy of the Electric Double Layer
Including the Excluded Volume Effect

Kralj‐Iglič, Veronika; Iglič, Aleš

doi:10.1051/jp2:1996193

Cited by 157 publications

(174 citation statements)

References 4 publications

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“…(23) assumes that at the distance r 1/2 from the charged cylindrical surface, the density of the number of the counterions (calculated relative to its value far from the charged cylindrical surface) drops to half of its value at the closest approach to the charged cylindrical surface. Fig.…”

Section: A Case Of the Univalent Electrolytementioning

confidence: 99%

“…In this work we used the PB theory that was upgraded by considering the effect of finite size of ions [23] for the description of the cylindrical electric double layer. We improved the derivation of the consistently related expressions for the equilibrium free energy of the system, the ion and solvent distribution functions and the differential equation for the electric potential [23] by using the method of undetermined multipliers within the canonical statistics.…”

Section: Introductionmentioning

confidence: 99%

“…We improved the derivation of the consistently related expressions for the equilibrium free energy of the system, the ion and solvent distribution functions and the differential equation for the electric potential [23] by using the method of undetermined multipliers within the canonical statistics. The effective thickness of the electric double layer in the cylindrical geometry is introduced.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Charged cylindrical surfaces: effect of finite ion size

Bohinc

Iglič

Slivnik

et al. 2002

Bioelectrochemistry

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“…These were qualitatively in agreement with the accepted electrochemical wisdom which states that the ion distribution in the immediate vicinity of an electrode consists of a Debye layer (where charge neutrality is not satisfied but the ion species are still relatively dilute) and a Stern layer, lying on the surface of the electrode, (where there is a massive preponderance of one of the ion species over the other species and water molecules). In this context we note that the equilibrium theories of Kralj-Iglic et al [19] and Borukhov et al [20] (which are based on statistical-mechanical approaches) yield exact solutions which predict similar behaviour in the double layer. It is worth emphasising, however, that both only consider the special case in which all the ions and the water molecules are of exactly the same size and do not address time-dependent issues.…”

Section: Resultsmentioning

confidence: 66%

“…In summary, the leading-order outer problem (19)(20)(21) satisfies the boundary conditions (39-40) on y = 0 and the unknown functions A(t), B(t) and V(t), which appear in the inner solution, are determined via (28).…”

Section: Matching the First-order Inner Solution To The Leading-ordermentioning

confidence: 99%

Time-dependent modelling and asymptotic analysis of electrochemical cells

Richardson

King

2006

J Eng Math

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A (time-dependent) model for an electrochemical cell, comprising a dilute binary electrolytic solution between two flat electrodes, is formulated. The method of matched asymptotic expansions (taking the ratio of the Debye length to the cell width as the small asymptotic parameter) is used to derive simplified models of the cell in two distinguished limits and to systematically derive the Butler-Volmer boundary conditions. The first limit corresponds to a diffusion-limited reaction and the second to a capacitance-limited reaction. Additionally, for sufficiently small current flow/large diffusion, a simplified (lumped-parameter) model is derived which describes the long-time behaviour of the cell as the electrolyte is depleted. The limitations of the dilute model are identified, namely that for sufficiently large half-electrode potentials it predicts unfeasibly large concentrations of the ion species in the immediate vicinity of the electrodes. This motivates the formulation of a second model, for a concentrated electrolyte. Matched asymptotic analyses of this new model are conducted, in distinguished limits corresponding to a diffusion-limited reaction and a capacitance-limited reaction. These lead to simplified models in both of which a system of PDEs, in the outer region (the bulk of the electrolyte), matches to systems of ODEs, in inner regions about the electrodes. Example (steady-state) numerical solutions of the inner equations are presented.

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Overcharging in Colloids: Beyond the Poisson–Boltzmann Approach

et al. 2003

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A broad range of manufactured products and biological fluids are colliods. The ability to understand and control the processes (of scientific, technological and industrial interest) in which such colloids are involved relies upon a precise knowledge of the electrical double layer. The traditional approach to describing this ion cloud around colloidal particles has been the Gouy-Chapman model developed on the basis of the Poisson-Boltzmann equation. Since the early 1980s, however, more sophisticated theoretical treatments have revealed both quantitative and qualitative deficiencies in the Poisson-Boltzmann theory, particularly at high ionic strengths and/or high surface charge densities. This review deals with these novel approaches, which are mostly computer simulations and approximate integral equation theories based on the so-called primitive model. Special attention is paid to phenomena that cannot be accounted for by the classic theory as a result of neglecting ion size correlations, such as overcharging, namely, the counterion concentration in the immediate neighborhood of the surface is so large that the particle surface is overcompensated. Other illustrative examples are the nonmonotonic behavior of the electrostatic potential and attractive interactions between equally charged surfaces. These predictions are certainly remarkable and, on paper, they can have an effect on experimentally measurable quantities (for instance, electrophoretic mobility). Even so, these new approaches have scarcely been applied in practice. Thus a critical survey on the relevance of ion size correlation in real systems is also included. Overcharging of macroions can also be brought about by adsorption of oppositely charged polyelectrolytes. Noteworthy examples and theoretical approaches for them are also briefly reviewed.

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A Simple Statistical Mechanical Approach to the free Energy of the Electric Double Layer Including the Excluded Volume Effect

Cited by 157 publications

References 4 publications

Charged cylindrical surfaces: effect of finite ion size

Charged cylindrical surfaces: effect of finite ion size

Time-dependent modelling and asymptotic analysis of electrochemical cells

Overcharging in Colloids: Beyond the Poisson–Boltzmann Approach

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