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

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.

Keywords:

• Cylindrical particle
• electrical double layer
• Poisson‐Boltzmann equation
• surface charge density
• functional analysis theory

Acknowledgments

The authors wish to express the deepest gratitude to the National Natural Science Foundation (to grant No. 20473034) and the Taihu Scholar Foundation (2003) of Southern Yangtze University for its financial support.