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Chemical Research in Chinese Universities ›› 2005, Vol. 21 ›› Issue (5): 592-596.

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Solution of the Poisson-Boltzmann Equation for a Cylindrical Particle with a Limited Length: Functional Theoretical Approach

WANG Zheng-wu1, GU Ming-yan1, ZHANG Ge-xin1, YI Xi-zhang2   

  1. 1. School of Chemical and Material Engineering, Southern Yangtze University, Wuxi 214036, P. R. China;
    2. Institute of Theoretical Chemistry, Shandong University, Jinan 250100, P. R. China
  • Received:2004-11-18 Online:1905-03-14 Published:2011-08-06
  • Supported by:

    Supported by the National Natural Science Foundation of China(No.20473034) and the Taihu Scholar Foundation of Southern Yangtze University(2003).

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Abstract: With the help of the method of separation of variables and the Debye-Hüchel approximation, the Poisson-Boltzmann equation that describes the distribution of the potential in the electrical double layer of a cylindrical particle with a limited length has been firstly solved under a very low potential condition. Then with the help of the functional analysis theory this equation has been further analytically solved under general potential conditions and consequently, the corresponding surface charge densities have been obtained. Both the potential and the surface charge densities coincide with those results obtained from the Debye-Hüchel approximation when the very low potential of zeΨ?kT is introduced.

Key words: Cylindrical particle, Electrical double layer, Poisson-Boltzmann equation, Surface charge density, Functional analysis theory