DLVO theory

The DLVO theory (named after Derjagin, Landau, Verwey, Overbeek ) is a theoretical description that deals with the stability of colloidal systems on the basis of attractive and repulsive, steric, for example, electrostatic or van der Waals interactions between the dispersed particles employed.

The surfaces of the colloidal particles to be understood as capacitor plates to their surfaces to form electrochemical double layer in an electrolyte solution. Approaching the particles, so overlap the bilayers. The resulting repulsive forces have a greater range than the attractive van der Waals forces. Unprotected dispersions are electrostatically stabilized.

For two spheres with radius and a constant surface charge at a focus distance in a fluid with a dielektischen constant and a concentration of monovalent ions, the electrostatic potential as the Coulomb or Yukawa repulsion results

With as the Bjerrum length than the Debye- Hückel distance which is defined as and the thermal energy in the absolute temperature.

History

1923 Peter Debye and Erich Hückel presented for the first time their theory to describe the distribution of ionic charges in an ionic solution. The basic idea of applying the linearized Debye- Hückel theory to colloidal dispersion, came from Levine and Dube, who found that charged colloidal particles experience a strong repulsion at short distance and a weak attraction by far distance. However, this theory could not explain why colloidal dispersions in solutions with high ionic concentration aggregate. Derjaguin and Landau in 1941 presented a new theory of the stability of colloidal dispersions, in which the strong attractive van der Waals forces acting are superimposed at a short distance from the electrostatic forces which are stronger at large distance. Seven years later, Verwey and Overbeek independently prepared a solution, as the instabilities with so-called DLVO theory can be described.

Derivation of the DLVO theory

The DLVO theory combines the forces resulting from the van der Waals interactions and electrochemical double layer. To derive different conditions and different equations must be considered. However, the derivation is much simpler when considering some fairly conventional assumptions and are simply created through the combination of two separately derived theories.

Van der Waals attraction

Van -der- Waals forces is the umbrella term for all dipole -dipole interactions. Assuming that the potential between two atoms or small molecules only attractive and of the form w = -C/rn, with C as a constant for the interaction energy, and n = 6 for the van der Waals forces. And continue with the assumption that the interaction energy between one molecule and a planar surface resulting from the sum of the interaction energies of all the molecules from the interface with the molecule, the total interaction energy can be used for a molecule as a function of the distance D from the surface as follows be specified

In which

• W ( r) is the energy of interaction between the molecule and the surface,
• The density of the surface,
• Z is the distance perpendicular to the surface. z = 0 and z = D the molecule is the surface.
• X is parallel to the surface, where x = 0 represents the point of intersection.

Thus the interaction energy for large spheres of radius R to a planar surface may be calculated as follows

With

• W ( D ) is the interaction energy between the sphere and the planar surface.
• Is the density of the ball

Simplifies the Hamaker constant A is defined as

Which results in the following equation

Using a similar method and using the approximation Derjaguin the Van der Waals interactions between the particles, and different geometries may be calculated as follows

Electrochemical double layer

There are two ways to reduce the thickness of the electrochemical double layer. Firstly, the screening of the surface charge enhanced by addition of an electrolyte, and the layer can be compressed thereby. On the other hand, the surface potential can be reduced by specific ion adsorption.

If the particle spacing reduced, so that the attractive interactions are dominant over the repulsive forces, enters a coagulation of the particles.