Hsu Jyh-Ping, Yu Hsiu-Yu, Tseng Shiojenn
Department of Chemical Engineering, National Taiwan University, Taipei, Taiwan 10617.
J Phys Chem B. 2006 Apr 13;110(14):7600-4. doi: 10.1021/jp060090f.
Both exact and approximate analytical solutions of the Poisson-Boltzmann equation for two planar, parallel surfaces are derived for the case when a dispersion medium contains counterions only, and the results obtained are used to evaluate the critical coagulation concentration of a spherical dispersion. A correction factor, which is a function of the valence of counterions, the surface potential of a particle, and the potential on the midplane between two particles at the onset of coagulation, is derived to modify the classic Schulze-Hardy rule for the dependence of the critical coagulation concentration on the valence of counterions. The correction factor is found to increase with the increase in the valence of counterions and/or with the increase in the surface potential. However, it approaches a constant value of 0.8390 if the surface potential is sufficiently high.
针对分散介质仅包含抗衡离子的情况，推导了两个平面平行表面的泊松 - 玻尔兹曼方程的精确解和近似解析解，并将所得结果用于评估球形分散体的临界聚沉浓度。推导了一个校正因子，它是抗衡离子价、颗粒表面电势以及聚沉开始时两个颗粒之间中平面上电势的函数，用于修正经典的舒尔茨 - 哈迪规则中关于临界聚沉浓度与抗衡离子价的依赖关系。发现校正因子随抗衡离子价的增加和/或表面电势的增加而增大。然而，如果表面电势足够高，它会趋近于0.8390的恒定值。
