DLVO theory
In physical chemistry, the Derjaguin–Landau–Verwey–Overbeek (DLVO) theory explains the aggregation and kinetic stability of aqueous dispersions quantitatively and describes the force between charged surfaces interacting through a liquid medium.
It combines the effects of the van der Waals attraction and the electrostatic repulsion due to the so-called double layer of counterions.
The electrostatic part of the DLVO interaction is computed in the mean field approximation in the limit of low surface potentials - that is when the potential energy of an elementary charge on the surface is much smaller than the thermal energy scale,
where The DLVO theory is named after Boris Derjaguin and Lev Landau, Evert Verwey and Theodoor Overbeek who developed it between 1941 and 1948.
DLVO theory is a theory of colloidal dispersion stability in which zeta potential is used to explain that as two particles approach one another their ionic atmospheres begin to overlap and a repulsion force is developed.
At each distance, the net potential energy of the smaller value is subtracted from the larger value.
[2] At very close distances, the combination of these forces results in a deep attractive well, which is referred to as the primary minimum.
Particles rebound after interparticle contact, and remain dispersed throughout the medium.
[2] If the barrier is cleared, then the net interaction is all attractive, and as a result the particles aggregate.
[2] For a colloidal system, the thermodynamic equilibrium state may be reached when the particles are in deep primary minimum.
[6] In 1923, Peter Debye and Erich Hückel reported the first successful theory for the distribution of charges in ionic solutions.
[7] The framework of linearized Debye–Hückel theory subsequently was applied to colloidal dispersions by S. Levine and G. P. Dube[8][9] who found that charged colloidal particles should experience a strong medium-range repulsion and a weaker long-range attraction.
This theory did not explain the observed instability of colloidal dispersions against irreversible aggregation in solutions of high ionic strength.
In 1941, Boris Derjaguin and Lev Landau introduced a theory for the stability of colloidal dispersions that invoked a fundamental instability driven by strong but short-ranged van der Waals attractions countered by the stabilizing influence of electrostatic repulsions.
[12] DLVO theory is the combined effect of van der Waals and double layer force.
[13] But some useful assumptions can effectively simplify the process, which are suitable for ordinary conditions.
Assume that the pair potential between two atoms or small molecules is purely attractive and of the form w = −C/rn, where C is a constant for interaction energy, decided by the molecule's property and n = 6 for van der Waals attraction.
where Then the interaction energy of a large sphere of radius R and a flat surface can be calculated as
With a similar method and according to Derjaguin approximation,[16] the van der Waals interaction energy between particles with different shapes can be calculated, such as energy between A surface in a liquid may be charged by dissociation of surface groups (e.g. silanol groups for glass or silica surfaces[17]) or by adsorption of charged molecules such as polyelectrolyte from the surrounding solution.
This results in the development of a wall surface potential which will attract counterions from the surrounding solution and repel co-ions.
The region near the surface of enhanced counterion concentration is called the electrical double layer (EDL).
The total electrical double layer due to the formation of the counterion layers results in electrostatic screening of the wall charge and minimizes the Gibbs free energy of EDL formation.
The thickness of the diffuse electric double layer is known as the Debye screening length
At a distance of two Debye screening lengths the electrical potential energy is reduced to 2 percent of the value at the surface wall.
Alessio Zaccone and collaborators investigated the effects of shear-flow on particle aggregation[19] which can play an important role in applications e.g. microfluidics, chemical reactors, atmospheric and environmental flows.
Their work showed a characteristic lag-time in the shear-induced aggregation of the particles, which decreases exponentially with the shear rate.
[20] Since the 1940s, the DLVO theory has been used to explain phenomena found in colloidal science, adsorption and many other fields.
For example, DLVO theory has been widely applied to assess the degree of particle-particle interactions at controlled chemical conditions.
[23] Additional forces beyond the DLVO construct have been reported to also play a major role in determining colloid stability.
[24][25] DLVO theory is not effective in describing ordering processes such as the evolution of colloidal crystals in dilute dispersions with low salt concentrations.
