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 distribute d fixed charges and is penetrable to electrolytes, In particular, cyli ndrical and spherical particles are examined. The approximate analytic al expressions for the thermodynamic properties of the system under co nsideration, including Helmholtz free energy, entropy, and the amount of co-ion adsorption, are derived, We show that if the radius of a par ticle is large enough, the present semianalytical treatment yields sat isfactory results. Under typical conditions, the deviation from the ex act value is on the order of 5%. If the curvature approaches zero, the present result reduces to the approximate solution for a planar geome try, and, if the thickness of the membrane approaches zero, it reduces to the approximate solution for a rigid charged surface and becomes t he exact solution for the case of symmetric electrolytes. (C) 1995 Aca demic Press, Inc.