Colloids

 An exact solution of Poisson-Baltzmann equation for symmetric electrolytes for which

(19)

and

(20)

was found by Gouy-Chapman for double layer near a place. In this case, equation (11) reduces to

(21)

The solution to (21) is

(22)

where

(23)

The surface charge density, , i.e.

(24)

for  given by (22) and

(25)

for  apart.

For spherical particles, the surface charge density is

(26)

and the total surface charge of the sphere becomes