Analytical solutions to the linearized poisson—boltzmann equation in cylindrical coordinates for different ionic—strength distributions

Rice, R. E.; Horne, Frederick H.

doi:10.1016/0021-9797(85)90359-5

Cited by 13 publications

(9 citation statements)

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“…The P-B equation for cylindrical pores gives an approximate analytical solution, which is valid only for very low surface potential (<25 mV), and should be solved numerically in most cases. 29,35,[72][73][74] Thus, though models shown here are already rather complex, physical ambiguities are not completely removed. This is a basic problem.…”

Section: Resultsmentioning

confidence: 90%

“…The G-C and G-C-Stern theory have been successfully utilized not only to electrochemical phenomena but also to electrophoretic behaviors of colloids 11 , membrane separation of ions 29 , and behaviors of ions at surface of metal oxides 14,30 , at ion-exchange resin surface [31][32][33][34][35] , or on the surface membrane. 13,15 However, the applications of these theories to chromatography have been very few.…”

Section: ·1 Electrostatic Potential In Separationmentioning

confidence: 99%

“…In some cases, modifications for starting P-B equation are necessary according to the geometry of the surface. 29,35,36 However, the P-B equations cannot be solved analytically, or give analytical solutions only with DebyeHückel approximation, which is valid only for very low electrostatic potential, in many cases.…”

Section: ·1 Electrostatic Potential In Separationmentioning

confidence: 99%

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Interpretation of Chromatographic Retention Based on Electrostatic Theories

Okada

1998

ANAL. SCI.

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Electrostatic potential is responsible for various phenomena, particularly for the behaviors of ionic species in solution and at various interfaces. In some modes of chromatography, electrostatic interaction often governs overall retention selectivity; ion-exchange chromatography is a typical example. Thus, though the understanding of electrostatic interaction is essential to interpret and predict chromatographic retention in some cases, sufficient attention has not been paid to its roles. There are some possible reasons for this situation: (1) direct estimation of the potential is usually difficult; (2) simple models not involving the contribution from electrostatic potential have given rather good explanations to experimental data. Some research groups have recently attempted to take electrostatic potential effects into consideration in various ways, and have successfully developed chromatographic models. These approaches are expected to facilitate understanding of chromatographic phenomena dominantly controlled by electrostatic interaction and to provide a view of more physical significance. In this review, the author mentions advantages of chromatographic models based on electrostatic theory over usual separated-phase models, and shows problems to be solved.

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Section: Resultsmentioning

confidence: 90%

Section: ·1 Electrostatic Potential In Separationmentioning

confidence: 99%

Section: ·1 Electrostatic Potential In Separationmentioning

confidence: 99%

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Interpretation of Chromatographic Retention Based on Electrostatic Theories

Okada

1998

ANAL. SCI.

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“…These are fitted to the theoretical curve obtained by solving the Poisson-Boltzmann equation in cylindrical coordinates. The solution of the linearized Poisson-Boltzmann equation in cylindrical coordinates is (18) , nAFI0(Kr) ~KtoDIM) (4) THEORY The basis for the electrostatic theory for ion pair chromatography is given in ref 2, so only a summary will be given here. The basic hypothesis of the electrostatic theory is that the equilibrium distribution of an analyte ion, B, is primarily determined by a chemical free-energy term, AG°B, and an electrostatic energy term, ß -The electrostatic energy term corresponds to the electrostatic work that is done on B when it is transported from the bulk of the mobile phase to a charged surface.…”

Section: Discussionmentioning

confidence: 99%

Adsorption isotherm of tetrabutylammonium ion and its relation to the mechanism of ion pair chromatography

Staahlberg¹,

Haegglund²

1988

Anal. Chem.

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To understand the mechanism of Ion pair chromatography, a correct description of the adsorption isotherm of the amphiphilic modifier Is Important. The adsorption Isotherm of tetrabutylammonlum Ion onto a RP-18 stationary phase Is determined with different electrolytic counterions (H2P04', CL, Br") and for two different Ionic strengths. The electrostatic surface potential created by the adsorbed tetrabutylammonlum Ions Is determined by applying the concepts of the electrostatic theory for Ion pair chromatography. The different experimentally determined adsorption Isotherms are found to coincide with the same surface-potential-modified Langmuir isotherm. The results are therefore In accordance with the electrostatic theory for Ion pair chromatography. ACKNOWLEDGMENTWe are most grateful to M. Almgren and B. Jonsson for valuable discussions during the preparation of this work and to A. Furángen for valuable discussions of the manuscript. The computer program for a numerical solution of the Poisson-Boltzmann equation was obtained from the

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“…The problem of modeling electrostatics of membranes with cylindrical pores was successfully solved by Rice and Horne (1985) and 30rdan (1982).…”

Section: G Miscellaneous Aspectsmentioning

confidence: 99%

Cell surface electrostatics and electrokinetics

Voigt¹,

Donath

1990

Springer Series in Biophysics

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SUMMARYTheoretical aspects of fixed charge distributions at cell surfaces are considered from the viewpoint of their discrete or continuous ("smeared") nature in surface layers of finite thickness. The method of Green functions provides an elegant means for a very compact presentation of the electric potential profile results under low potential conditions. The relationship between transmembrane and surface potentials is explained. Energetical aspects of and stress development in single and interacting charged layers are studied as well as a minimum electrostatic free energy model of the fixed charge distribution. In the second part the development of the electrokinetics of structured surfaces is outlined. The advantage of the application of irreversible thermodynamics is demonstrated with respect to generalization and compactness of the electrokinetic fundamental relationships. Analytical solutions for the minimum electrostatic free energy model are obtained. Results of particle electrophoresis in concentrated aqueous polymer solutions are discussed on the basis of depletion layer effects or related phenomena.

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Analytical solutions to the linearized poisson—boltzmann equation in cylindrical coordinates for different ionic—strength distributions

Cited by 13 publications

References 14 publications

Interpretation of Chromatographic Retention Based on Electrostatic Theories

Interpretation of Chromatographic Retention Based on Electrostatic Theories

Adsorption isotherm of tetrabutylammonium ion and its relation to the mechanism of ion pair chromatography

Cell surface electrostatics and electrokinetics

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