DLVO counterion distribution

Theories of colloid stability based on electrostatics go way back beyond the DLVO theory, to the Gouy-Chapman theory of the electrical double layer proposed in the early 1910s and the Stem theory of counterion condensation proposed in 1924. There was much weighty speculation about the counterion distribution around colloidal particles throughout the 20th century, but nobody succeeded in measuring it until our work in 1997. This work is described in detail in Chapter 8. 

The effect of electrolyte concentration on the transition from common to Newton black films and the stability of both types of films are explained using a model in which the interaction energy for films with planar interfaces is obtained by adding to the classical DLVO forces the hydration force. The theory takes into account the reassociation of the charges of the interface with the counterions as the electrolyte concentration increases and their replacements by ion pairs. This affects both the double layer repulsion, because the charge on the interface is decreased, and the hydration repulsion, because the ion pair density is increased by increasing the ionic strength. The theory also accounts for the thermal fluctuations of the two interfaces. Each of the two interfaces is considered as formed of small planar surfaces with a Boltzmannian distribution of the interdistances across the liquid film. The area of the small planar surfaces is calculated on the basis of a harmonic approximation of the interaction potential. It is shown that the fluctuations decrease the stability of both kinds of black films. 

In the DLVO theory, the distribution of counterions in the immediate vicinity of the charged colloidal particle is assumed to obey the Poisson-Boltzmann distribution. 

---