Approximate Analytical Expression for Surface Potential as a Function of Surface Charge Density
Journal
Journal of Colloid And Interface Science
Journal Volume
170
Journal Issue
1
Pages
220-228
Date Issued
1995
Author(s)
Kuo Y.-C.
Abstract
The surface potential is derived as a function of surface charge density for a nonplanar solid surface immersed in an arbitrary a:b electrolyte solution. This relation is essential to the evaluation of the basic thermodynamic properties of an electrical double layer. The approximate analytical expression is based on a perturbation method characterized by the following ratio: radius of a surface/thickness of a double layer. An attempt is also made to take the inverse of the surface-charge density-surface potential relation for a spherical surface immersed in both 1:1 and 1:2 electrolyte solutions as reported by H. Ohshima, T. W. Healy, and L. R. White (J. Colloid Interface Sci.90, 17, 1982). For a 1:1 electrolyte solution, the maximum deviation from the exact value is on the order of 3% for a double layer of thickness smaller than one half the radius of a surface, and this is almost independent of the magnitude of surface charge density. For a 1:2 electrolyte solution, the maximal deviation appears to increase slightly with surface charge density. At a relatively low surface charge density, the deviation is on the order of 3% for a double layer having thickness less than one-half the radius of a sphere, and it is on the order of 5% at a relatively high surface charge density. ? 1995 by Academic Press, Inc.
Type
journal article