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Colloid and Polymer Science
Erschienen in: Colloid and Polymer Science 4/2013

01.04.2013 | Original Contribution

Highly accurate and simple analytical approach to nonlinear Poisson–Boltzmann equation

verfasst von: S. Zhou, G. Zhang

Erschienen in: Colloid and Polymer Science | Ausgabe 4/2013

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Abstract

A novel method is suggested to analytically solve a nonlinear Poisson–Boltzmann (NLPB) equation. The method consists chiefly of reducing the NLPB equation to linear PB equation in several segments by approximating a free term of the NLPB equation by piecewise linear functions, and then, solving analytically the linear PB equation in each segment. Superiority of the method is illustrated by applying the method to solve the NLPB equation describing a colloid sphere immersed in an arbitrary valence and mixed electrolyte solution; extensive test indicates that the resulting analytical expressions for both the electrical potential distribution Ψ (r) and surface charge density/surface potential relationship (σ/Ψ 0) are characterized with two properties that mathematical structures are much simpler than those previously reported and application scope can be arbitrarily wide by adjusting the linear interpolation range. Finally, it is noted that the method is “universal” in that its applications are not limited to the NLPB equation.
Vorheriger Artikel Self-assembly behavior of fluorocarbon-end-capped poly(glycerol methacrylate) in aqueous solution
Nächster Artikel A simple way of preparing large compound vesicles loaded with and without silver nanoparticles based on polystyrene-block-polyacrylonitrile

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Metadaten
Titel
Highly accurate and simple analytical approach to nonlinear Poisson–Boltzmann equation
verfasst von
S. Zhou
G. Zhang
Publikationsdatum
01.04.2013
Verlag
Springer-Verlag
Erschienen in
Colloid and Polymer Science / Ausgabe 4/2013
Print ISSN: 0303-402X
Elektronische ISSN: 1435-1536
DOI
https://doi.org/10.1007/s00396-012-2805-9

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