DLVO theory

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The DLVO theory is named after Derjaguin, Landau, Verwey and Overbeek who developed it in the 1940s.

The theory 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 elemetary charge on the surface is much smaller than the thermal energy scale, $k B T$ . For two spheres of radius $a$ with constant surface charge $Z$ separated by a center-to-center distance $r$ in a fluid of dielectric constant $ε$ containing a concentration $n$ of monovalent ions, the electrostatic potential takes the form of a screened-Coulomb or Yukawa repulsion,

$\beta U(r) = Z^2 \lambda_B \, \left(\frac{\exp(\kappa a)}{1 + \kappa a}\right)^2 \, \frac{\exp(-\kappa r)}{r},$

where $λ B$ is the Bjerrum length, $κ - 1$ is the Debye-Hückel screening length, which is given by $κ 2 = 4πλ B n$ , and $β - 1 = k B T$ is the thermal energy scale at absolute temperature $T$ .