Tseng Shiojenn, Jiang Ji-Ming, Hsu Jyh-Ping
Department of Mathematics, Tamkang University, Tamsui, Taipei 25137, Taiwan, Republic of China.
J Colloid Interface Sci. 2004 May 1;273(1):218-23. doi: 10.1016/j.jcis.2003.09.029.
Employing an iterative method in functional theory, the electrical potential distribution for the case of a cylindrical surface is solved. Although the analytical result derived is of an iterative nature, the second-order solution is found to be sufficiently accurate under conditions of practical significance. For the case of constant surface potential, the radius and the surface potential of a cylindrical surface can be estimated based on the extreme of the electrical potential distribution. The effects of the key parameters, including the number and the valence of the ions on a surface, the length of a particle, the relative permittivity of the liquid phase, the temperature, and the concentration of electrolyte on the surface potential, are examined. The general behavior of these effects is similar to that for a spherical surface, except that the surface potential of a cylindrical surface is independent of the electrolyte concentration. The present approach is also applicable to the case where a cylindrical surface remains at a constant charge density.
采用泛函理论中的迭代方法，求解了圆柱面情形下的电势分布。尽管所推导的解析结果具有迭代性质，但发现二阶解在实际有意义的条件下足够精确。对于表面电势恒定的情形，可基于电势分布的极值来估计圆柱面的半径和表面电势。研究了包括表面离子的数量和价态、粒子长度、液相相对介电常数、温度以及表面电解质浓度等关键参数对表面电势的影响。这些影响的一般行为与球面情形类似，不同之处在于圆柱面的表面电势与电解质浓度无关。本方法也适用于圆柱面保持恒定电荷密度的情形。
