The electrostatic Gibbs energy of finite-size ions near a planar boundary between two dielectric media

Kharkats, Yurij I.; Ulstrup, Jens

doi:10.1016/0022-0728(91)85055-t

Cited by 40 publications

(76 citation statements)

References 34 publications

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“…Indeed, as clearly shown by Stewart et at.133 in the case of cyclic voltammetry, the diffusion of the two reactants and the two products of the heterogeneous electron transfer reactions can lead to "funny" voltammograms, or steady-state curves which do not exhibit the familiar criteria of reversibility for a classical electrochemical reaction coupled with linear diffusion. In the case of cyclic voltammetry, the current for a reversible electron transfer reaction is calculated as the root of the quadratic equation: (41) where the coefficients This condition should also be fulfilled for the half wave, or more precisely the midpeak potential, to be equal to the standard transfer potential (as defined by Eq. (38), assuming further the equality of the diffusion coefficients of the reactants and products.…”

Section: + N 1 N2f Ln (/Do!-i)n 2 (/Dr2-i T! (40)mentioning

confidence: 99%

Charge Transfer across Liquid—Liquid Interfaces

Girault¹

1993

Modern Aspects of Electrochemistry

108

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Section: + N 1 N2f Ln (/Do!-i)n 2 (/Dr2-i T! (40)mentioning

confidence: 99%

Charge Transfer across Liquid—Liquid Interfaces

Girault¹

1993

Modern Aspects of Electrochemistry

108

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“…The four-layer model is in accordance with the effect discussed by Ulstrup and Kharkats that explains segregation of the ions with different radii into two layers at the sol's surface. [12][13] …”

Section: Introductionmentioning

confidence: 99%

Compact Layer of Alkali Ions at the Surface of Colloidal Silica

Tikhonov

2006

J. Phys. Chem. C

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The forces of electrical imaging strongly polarize the surface of colloidal silica. I used X-ray scattering to study the adsorbed 2-nm-thick compact layer of alkali ions at the surface of concentrated solutions of 5-nm, 7-nm, and 22-nm particles, stabilized by either NaOH or a mixture of NaOH and CsOH, with the total bulk concentration of alkali ions ranging from 0.1 to 0.7 mol/L. The observed structure of the compact layer is almost independent of the size of the particles and the concentration of alkali base in the sol; it can be described by a two-layer model, that is, a ∼6-8-Å-thick layer of directly adsorbed hydrated alkali ions with a surface concentration of ∼3 × 10 18 m -2, and a ∼13-Å-thick layer with a surface concentration of sodium ions of ∼8 × 10 18 m -2. In cesium-enriched sols, Cs + ions preferentially adsorb in the first layer replacing Na + ; their density in the second layer does not depend on the presence of cesium in the sol. The difference in the adsorption of Cs + and Na + ions can be explained by the ion-size-dependent term in the electrostatic Gibbs energy equation derived earlier by others. I also discuss the surface charge density and the value of surface tension at both the air/sol and the hexane/sol interfaces.

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“…Kharkats and Ulstrup resolved this problem by assuming that the ion has a finite size. 10 According to them, in continuous media approximation, the following is the free energy, F(z), of a spherical charge, q, with radius, a , at the boundary between two dielectric media imbedded within a spherical cavity: 1 2 16 2 1 ln 2 2 1 2 1 1 2 4 2 2 (1) and,…”

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confidence: 99%

“…[1][2][3] Many previous authors discussed the ionic distributions, surface tension, image forces, and single-ion free energy at the surface of an electrolyte solution. [4][5][6][7][8][9][10][11][12][13][14][15] Also, for decades molecular-dynamics simulations were extensively used to explore molecular structure and ion-specific effects at liquid surfaces. [16][17][18] However, here synchrotron…”

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confidence: 99%