Colloids

Electrical Double Layer Interactions for Colloidal Systems
Most colloidal particles carry electrostatic charges. Since the dispersion as a whole is neutral, there must be an excess of ions of opposite charge in the solution. These excess ions are found near the surface of suspended colloidal particles and form what is called a "diffused electrical double layer." The double layer has a profound effect on interactions of colloidal particles.

Ion Distribution Near a Colloidal Particle
Consider the diffusion of ions near a charged surface. The convective diffusion equation for the number concentration,  is given as

(1)

where  is the velocity due to the electric field. Force balance of a single ion gives

(2)

where E is the electric field strength given as

(3)

and  is the electric field potential.

Equation (2) leads to

(4)

where

(5)

is used. Using (3) and (4) in (1), we find

(6)

or

(7)

Integrating (7), one finds

(8)

the well-known Boltzmann distribution. Note that the potential .

Using Coulomb's law and equation (3), we find

(9)

where  is the charge density given as

(10)

Using (10) in (9), the Poisson-Baltzamann equation follows, i.e.

(11)

Solution of (11) gives . Equation (11) is restricted to low electrolyte concentrations, since ions are treated as point charges.