Theory of the electric double layer using a modified poisson–boltzman equation

Outhwaite, C.W.; Bhuiyan, L. B.; Levine, S.

doi:10.1039/f29807601388

Cited by 143 publications

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“…Blum (4) (11,12) have used the modified Poisson-Boltzmann (MPB) approximation. In addition, Croxton and McQuarrie (13,14) have used the Born-Green-Yvon (BGY) approximation.…”

Section: Introductionmentioning

confidence: 99%

The application of the generalized mean spherical approximation to the theory of the diffuse double layer

Henderson¹,

Blum²

1981

Can. J. Chem.

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This paper is dedicated to Dr. Sam Levine on the occasion of his 70th birthday DOUGLAS HENDERSON and LESSER BLUM. Can. J. Chem. 59, 1906Chem. 59, (1981. A system of charged hard spheres near a uniformly charged hard wall is considered. An approximation is established by postulating a closure for the Ornstein-Zernike (OZ) equations for this system. In this paper these OZ equations are solved for a closure in which the direct correlation functions are equal to the wall-ion potentials plus a sum of exponential functions. As a specific application of this solution we use one exponential and adjust two parameters to satisfy an approximate contact value theorem and give the same diffuse layer potential as is obtained using the hypernetted chain (HNC) approximation. Once this fit is made, the density, charge, and potential profiles can be easily calculated. The agreement with the corresponding HNC results is good.Comparison with the simpler Poisson-Boltzmann theory of Gouy and Chapman (GC) shows the GC theory to be better than one would expect. However, appreciable differences between the present results and the GC results for the diffuse layer potential are found.DOUGLAS HENDERSON et LESSER BLUM. Can. J. Chem. 59, 1906 (1981). On a fait une etude d'un systeme de spheres dures chargees situees pres d'un mur solide charge d'une f a~o n uniforme. On a Ctabli une approximation en faisant I'hypothese que les equations de Omstein-Zernike (OZ) de ce systeme sont fermees. Dans le cadre de ce travail, nous avons resolu ces equations de correlation OZ par le biais d'une fermeture dans laquelle les fonctions de correlation directe sont egales aux potentiels mur-ions auxquels on ajoute une fonction exponentielle. Une application specifique de cette solution a etC faite; utilisant une exponentielle et ajustant deux parametres afin de trouver des valeurs satisfaisantes pour le theoreme de valeur de contact approximative, nous avons trouvk pour le potentiel de couche diffuse la m&me valeur que celle obtenue en faisant appel $ ]'equation d'hyperchaine (EHC). Lorsque cette correlation est etablie, on peut facilement calculer les profils de densite, de charge et de potentiel. I1 existe un bon accord avec les resultats correspondants obtenus par I'kquation (EHC). Une cornparaison avec la theorie plus simple de Poisson-Boltzmann developpke par Gouy et Chapman (GC) revele que cette theone de GC est meilleure que prevue. Cependant on trouve que les differences appeciables entre les rtsultats actuels et les resultats de GC sont dues au potentiel de couche diffuse.[Traduit par le journal] Introduction a serious loss since at high charge densities on the Henderson et a/. (1) have formulated the Ornstein-wall, and also at high electrolyte concentrations, Zernike equation in a form appropriate for the study these contributions dominate. Nonetheless, calof surfaces near a wall. Probably the most interesting culations based upon this primitive model are of applications of these equations is to the study of an interest for two reasons. Firstly, ...

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“…Blum (4) (11,12) have used the modified Poisson-Boltzmann (MPB) approximation. In addition, Croxton and McQuarrie (13,14) have used the Born-Green-Yvon (BGY) approximation.…”

Section: Introductionmentioning

confidence: 99%

The application of the generalized mean spherical approximation to the theory of the diffuse double layer

Henderson¹,

Blum²

1981

Can. J. Chem.

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“…The Poisson equation in Eq. 2 was solved numerically for the electric potential φ(z) using the quasi-linearization procedure 44,45 were obtained previously by fitting to X-ray reflectivity data from LiCl, RbCl and CsCl samples at one positive high potential. 26 When Eq.…”

Section: Resultsmentioning

confidence: 99%

Ion Distributions at Electrified Water-Organic Interfaces: PB-PMF Calculations and Impedance Spectroscopy Measurements

Hou

Luo

et al. 2015

J. Electrochem. Soc.

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The interface between two immiscible electrolyte solutions consisting of alkali chlorides in water and the organic electrolyte BTPPATPFB in 1,2-dichloroethane is characterized with X-ray reflectivity, interfacial tension and impedance spectroscopy measurements over a range of applied voltage between the bulk solutions. X-ray reflectivity probes the interfacial ion distribution on the sub-nanometer length scale, whereas interfacial tension and impedance spectroscopy characterize quantities such as interfacial excess charge and differential capacitance that represent integrations over the interfacial ion distribution. Predictions of interfacial ion distributions by the recently introduced PB-PMF method, which combines Poisson's equation with ion potentials of mean force, provide excellent agreement, within one to two experimental standard deviations, with both X-ray reflectivity and interfacial tension measurements. However, the agreement with the differential capacitance measured by impedance spectroscopy, and modeled by the Randles equivalent circuit, is not as good. Values of measured and calculated differential capacitance can deviate by as much as 20% for applied electric potential differences larger than approximately ±100 mV. These comparisons indicate that our understanding of the ion distributions that underlie these measurements is adequate, but that further understanding of the modeling of impedance spectroscopy data is required for quantitative agreement at larger applied electric potential differences. Ion distributions at interfaces underlie many electrochemical and biological processes, including electron and ion transfer across biomembranes and liquid interfaces, phase transfer catalysis and solvent extraction. The interface between two immiscible electrolyte solutions (ITIES) has been used as a model system to study ion and electron transfer across liquid-liquid interfaces by electrochemical techniques.1,2 These techniques characterize the interfacial ion distribution in terms of integrated properties such as interfacial excess charge or differential capacitance, which can be calculated by integrating the ion distribution over the spatial coordinate perpendicular to the interface.The differential capacitance of ITIES has been widely investigated.3-5 Impedance spectroscopy data for ITIES are often modeled by the Randles equivalent circuit to yield the interfacial differential capacitance. 6 Although this model is convenient in many circumstances, its limitations have been discussed in the literature. For example, Samec and co-authors reported limited agreement between the results from interfacial tension and impedance spectroscopy measurements of the interface between aqueous and 1,2-dichloroethane (DCE) electrolyte solutions and suggested that the Randles equivalent circuit might be at fault at high electric potential differences. 7,8 Impedance spectroscopy studies of ITIES have measured interfacial differential capacitance that depends on the nature of the ions. 4,[9][10][11][12][13][14] Interfac...

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“…Grahame generalized the Gouy-Chapman theory to multivalent ions [7]. Subsequently, more refined theories and numerical simulations were developed to incorporate short-range interactions, image charges, finite size ionic radius, and ion-ion correlations [8,9,10,11,12]. More recently, modifications of PB theory have been developed to incorporate hydration forces [13,14,15].…”

Section: Ion Distribution Near a Charged Surfacementioning

confidence: 99%

“…1.4 and the Boltzmann distribution, expressed as 9) providing the counterion (n + ) and co-ion (n − ) distributions shown in Fig. 1.1(B).…”

Section: Ion Distribution Near a Charged Surfacementioning

confidence: 99%

Ion distributions at charged aqueous surfaces: Synchrotron X-ray scattering studies

2009

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Theory of the electric double layer using a modified poisson–boltzman equation

Cited by 143 publications

References 0 publications

The application of the generalized mean spherical approximation to the theory of the diffuse double layer

The application of the generalized mean spherical approximation to the theory of the diffuse double layer

Ion Distributions at Electrified Water-Organic Interfaces: PB-PMF Calculations and Impedance Spectroscopy Measurements

Ion distributions at charged aqueous surfaces: Synchrotron X-ray scattering studies

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