泛函数迭代法求解反胶束内双电层电势

A Functional Theoretical Approach to the Electrical Double Layer of a Spherical Reverse Colloid Particle

用泛函数分析理论中的迭代法求解了反胶束内关于双电层电势的Poisson Boltzmann (PB)方程 ,导出了泛电位下的第一、二次迭代的解析表达式 .与Debye H櫣ｃｋｅｌ (DH)线性近似及计算机的数值解进行对比表明 ,迭代解不仅在低电位条件下能与两者相符合 。

With the help of the iterative technique in functional analysis, the nonlinear Poisson-Boltzmann (PB) equation of the electrostatic double layer for inside of a spherical reverse colloid particle has been solved analytically under general potential condition and the corresponding expressions for the first as well as the second iterative solutions also have been deduced. Compared with the Debye-Huchel (DH) approximation and the numerical method, both the iterative solutions are identical with the results of the DH approximation and the numerical method under low potential condition. Moreover, they fit much better than the DH approximation to the precise numerical results for high potential.