关键词: 电势分布, 胶体粒子, 双电层, Poisson－Boltamann方程, 积分方程, 数值解

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%.