Editing DLVO theory (section)

{{short description|Theoretical model for aggregation and stability of aqueous dispersions}}

[[File:DLVO-Theorie.png|thumb|alt=LVO-Theorie|LVO-Theorie]]
In [[physical chemistry]], the '''Derjaguin–Landau–Verwey–Overbeek''' ('''DLVO''') '''theory''' explains the [[Particle aggregation|aggregation]] and [[kinetic stability]] of [[dispersion (chemistry)|aqueous dispersions]] quantitatively and describes the force between charged surfaces interacting through a liquid medium.
It combines the effects of the [[Van der Waals force|van der Waals]] attraction and the electrostatic repulsion due to the so-called [[double layer (interfacial)|double layer]] of [[counterion]]s.
The electrostatic part of the DLVO interaction is computed in the [[mean field approximation]] in the limit of low [[surface potential]]s - that is when the [[potential energy]] of an [[elementary charge]] on the surface is much smaller than the thermal energy scale, <math> k_\text{B} T</math>. For two spheres of radius <math>a</math> each having a charge <math>Z</math> (expressed in units of the elementary charge) separated by a center-to-center distance <math>r</math> in a fluid of [[dielectric constant]] <math>\epsilon_r</math> containing a concentration <math>n</math> of monovalent ions, the electrostatic potential takes the form of a screened-Coulomb or [[Yukawa potential]],

<math display="block">\beta U(r) = Z^2 \lambda_\text{B} \, \left(\frac{e^{\kappa a}}{1 + \kappa a}\right)^2 \, \frac{e^{-\kappa r}}{r},
</math>

where 
*<math>\lambda_\text{B}</math> is the [[Bjerrum length]],
*<math>U</math> is the [[potential energy]],
*<math>e</math> ≈ 2.71828 is [[Euler's number]],
*<math>\kappa</math> is the inverse of the [[Debye_length|Debye–Hückel screening length]] (<math>\lambda_\text{D}</math>); <math>\kappa</math> is given by <math>\kappa^2 = 4 \pi \lambda_\text{B} n</math>, and
*<math>\beta^{-1} = k_\text{B} T</math> is the thermal energy scale at absolute temperature <math>T</math>

The DLVO theory is named after [[Boris Derjaguin|Boris <u>D</u>erjaguin]] and [[Lev Landau|Lev <u>L</u>andau]], [[Evert Verwey|Evert <u>V</u>erwey]] and [[Theodoor Overbeek|Theodoor <u>O</u>verbeek]] who developed it between 1941 and 1948.