Abstract
The electrical potential distribution around a charged colloidal particle in a solution of general electrolytes is governed by the nonlinear Poisson Boltzmann equation, which is a differential equation and difficult to solve analytically. In this paper we numerically calculate the electrical potential using nonlinear Qian Poisson Bolazmann integral equation (PBIE). First, we introduce the PBIE derived from the physical principles for electrostatic fields and thermodynamic systems. Then the PBIE is numerically solved by means of iteration, in which the discrete potential is solely used. Finally, the accuracy of the numerical solutions proposed here is discussed. The potentials for the colloidal particles with scaled radius κa of 0.1 2 and 0.22 are obtained in the case that scaled surface potential eζ/kT is equal to 1,2,4, and 6, respectively. The surface charge densities are also calculated to be compared with the accurate numerical solutions in 3-1 electrolyte given by Loeb et al (1961) and Oshima (1995). Excellent agreement is achieved. The relative errors of surface charge densities between the compared solutions are less than 1.0%.
Publication Date
1997-08-28
Online Available Date
1997-08-28
Revised Date
1997-08-28
Received Date
1997-08-28
Recommended Citation
Yongxian Qian.
Electrical Potential Distribution around a Charged Colloidal Particle: Nonlinear Integral Equation[J]. Journal of Electrochemistry,
1997
,
3(3): Article 1.
DOI: 10.61558/2993-074X.2655
Available at:
https://jelectrochem.xmu.edu.cn/journal/vol3/iss3/1
References
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