| Summary: | 碩士 === 國立臺灣大學 === 化學工程學研究所 === 94 === Approximate analytical expressions for the electrical potential of planar, cylindrical, and spherical surfaces are derived for the case when the dispersion medium contains counterions only. Based on the results for single surfaces, those for two identical surfaces can be derived. The curvature effect of a surface on the electrical potential distribution can be neglected when the order of its radius exceeds about 102 of the thickness of the corresponding double layer. If this effect needs be considered, it can be taken into account by multiplying a correction function to the electrical potential of a planar surface. The electrical potential at the center between two surfaces derived is readily applicable to the evaluation of the electrostatic force per unit area between two surfaces, or the osmotic pressure. For the same set of parameters, the magnitude of the osmotic pressure for various types of surfaces follows the order planar surface>cylindrical surfaces>spherical surfaces.
Furthermore, the planar 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 mid-plane 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.
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