PROPERTIES OF A DOUBLE-LAYER WITH ASYMMETRIC ELECTROLYTES - CYLINDRICAL AND SPHERICAL-PARTICLES WITH AN ION-PENETRABLE MEMBRANE

We consider a particle coated with a membrane immersed in an arbitrary a:b electrolyte solution. The membrane bears homogeneously distributed fixed charges and is penetrable to electrolytes, In particular, cylindrical and spherical particles are examined. The approximate analytical expressions for the thermodynamic properties of the system under consideration, including Helmholtz free energy, entropy, and the amount of co-ion adsorption, are derived, We show that if the radius of a particle is large enough, the present semianalytical treatment yields satisfactory results. Under typical conditions, the deviation from the exact value is on the order of 5%. If the curvature approaches zero, the present result reduces to the approximate solution for a planar geometry, and, if the thickness of the membrane approaches zero, it reduces to the approximate solution for a rigid charged surface and becomes the exact solution for the case of symmetric electrolytes. (C) 1995 Academic Press, Inc.