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, ${\displaystyle k_{\text{B}}T}$. For two spheres of radius ${\displaystyle a}$ each having a charge ${\displaystyle Z}$ (expressed in units of the elementary charge) separated by a center-to-center distance ${\displaystyle r}$ in a fluid of dielectric constant ${\displaystyle \epsilon _{r}}$ containing a concentration ${\displaystyle n}$ of monovalent ions, the electrostatic potential takes the form of a screened-Coulomb or Yukawa potential,

$${\displaystyle \beta U(r)=Z^{2}\lambda _{\text{B}}\,\left({\frac {e^{\kappa a}}{1+\kappa a}}\right)^{2}\,{\frac {e^{-\kappa r}}{r}},}$$

where

• ${\displaystyle \lambda _{\text{B}}}$ is the Bjerrum length,
• ${\displaystyle U}$ is the potential energy,
• ${\displaystyle e}$ ≈ 2.71828 is Euler's number,
• ${\displaystyle \kappa }$ is the inverse of the Debye–Hückel screening length (${\displaystyle \lambda _{\text{D}}}$); ${\displaystyle \kappa }$ is given by ${\displaystyle \kappa ^{2}=4\pi \lambda _{\text{B}}n}$, and
• ${\displaystyle \beta ^{-1}=k_{\text{B}}T}$ is the thermal energy scale at absolute temperature ${\displaystyle T}$

The DLVO theory is named after Boris Derjaguin and Lev Landau, Evert Verwey and Theodoor Overbeek who developed it between 1941 and 1948.