Department of Chemical Engineering, National Taiwan University, Taipei, Taiwan.
J Colloid Interface Sci. 2011 Apr 15;356(2):550-6. doi: 10.1016/j.jcis.2011.01.037. Epub 2011 Jan 15.
The electrical potentials of two identical planar, cylindrical, and spherical particles immersed in a salt-free dispersion are solved analytically by a perturbation approach for the case of constant surface charge density. The system under consideration simulates, for example, micelles, where the ionic species in the liquid phase come mainly from the dissociation of the functional groups on the droplet surface. We show that for planar particles, the present zero-order perturbation solution is exact, and for cylindrical and spherical particles, the first-order perturbation solution provides sufficiently accurate results, with an averaged percentage deviation on the order of 1% under typical conditions. In general, the higher the surface charge density, the higher the valence of counterions, the smaller the separation distance between two particles, and the smaller the curvature of particle surface, the better the performance of the perturbation solution.
通过微扰法，针对常表面电荷密度的情况，我们对两个相同的平面、圆柱和球形颗粒在无盐分散体中的电势进行了解析求解。所考虑的系统例如模拟胶束，其中液相中的离子物种主要来自于液滴表面官能团的解离。我们表明，对于平面颗粒，本零阶微扰解是精确的，而对于圆柱和球形颗粒，一阶微扰解提供了足够精确的结果，在典型条件下平均偏差百分比约为 1%。一般来说，表面电荷密度越高、抗衡离子的价态越高、两个颗粒之间的距离越小、颗粒表面的曲率越小，微扰解的性能越好。
