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2005•Journal of Dispersion Science and TechnologyRequires access

Solution of the Poisson‐Boltzmann Equation about a Cylindrical Particle: Functional Theoretical Approach

Zhengwu Wang, Minyan Gu, Ganzuo Li, Xizhang Yi

Open publisher page 2 citations

Abstract

By using the iterative method in functional analysis, the Poisson‐Boltzmann (PB) equation, which describes the distribution of the potential in the electrical double layer of a cylindrical particle, has been solved analytically under general potential conditions. Both the potential and the surface charge density coincide with those results obtained from the Debye‐Hüchel approximation when the very low potential of zeψ≪kT is introduced. The advantage of this method is that it has completely overcome the restriction that the BP equation can be solved analytically only under the Debye‐Hüchel approximation condition.

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What this paper is about

By using the iterative method in functional analysis, the Poisson‐Boltzmann (PB) equation, which describes the distribution of the potential in the electrical double layer of a cylindrical particle, has been solved analytically under general potential conditions. Both the potential and the surface charge density coincide with those results obtained from the Debye‐Hüchel approximation when the very low potential of zeψ≪kT is introduced. The advantage of this method is that it has completely overcome the restriction that the BP equation can be solved analytically only under the Debye‐Hüchel approximation condition.

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OpenAlex reports 2 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

By using the iterative method in functional analysis, the Poisson‐Boltzmann (PB) equation, which describes the distribution of the potential in the electrical double layer of a cylindrical particle, has been solved analytically under general potential conditions. Both the potential and the surface charge density coincide with those results obtained from the Debye‐Hüchel approximation when the very low potential of zeψ≪kT is introduced. The advantage of this method is that it has completely overcome the restriction that the BP equation can be solved analytically only under the Debye‐Hüchel approximation condition.

Key concepts: Poisson–Boltzmann equation, Poisson's equation, Charge density, Debye, Poisson distribution, Debye length, Physics, Debye–Hückel equation

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