DLVO theory

In <a href="/facts/Physical_chemistry/WqwnJjRM">physical chemistry</a>, the Derjaguin–Landau–Verwey–Overbeek (DLVO) theory explains the <a href="/facts/Particle_aggregation/GvDNtDVo">aggregation</a> and <a href="/facts/Kinetic_stability/H72SMWof">kinetic stability</a> of <a href="/facts/Dispersion_(chemistry)/HFq2QUys">aqueous dispersions</a> quantitatively and describes the force between charged surfaces interacting through a liquid medium.
It combines the effects of the <a href="/facts/Van_der_Waals_force/jyGU8Vh9">van der Waals</a> attraction and the electrostatic repulsion due to the so-called <a href="/facts/Double_layer_(interfacial)/QhTTkyVs">double layer</a> of <a href="/facts/Counterion/RNwGeM3l">counterions</a>.
The electrostatic part of the DLVO interaction is computed in the <a href="/facts/Mean_field_approximation/tJrwSURE">mean field approximation</a> in the limit of low <a href="/facts/Surface_potential/p067lYHS">surface potentials</a> - that is when the <a href="/facts/Potential_energy/I03KLbmn">potential energy</a> of an <a href="/facts/Elementary_charge/lPcj6CoQ">elementary charge</a> on the surface is much smaller than the thermal energy scale, 
 
 
 
 
 k
 
 B
 
 
 T
 
 
 {\displaystyle k_{\text{B}}T}
 
. For two spheres of radius 
 
 
 
 a
 
 
 {\displaystyle a}
 
 each having a charge 
 
 
 
 Z
 
 
 {\displaystyle Z}
 
 (expressed in units of the elementary charge) separated by a center-to-center distance 
 
 
 
 r
 
 
 {\displaystyle r}
 
 in a fluid of <a href="/facts/Dielectric_constant/vnKbPTn1">dielectric constant</a> 
 
 
 
 
 ϵ
 
 r
 
 
 
 
 {\displaystyle \epsilon _{r}}
 
 containing a concentration 
 
 
 
 n
 
 
 {\displaystyle n}
 
 of monovalent ions, the electrostatic potential takes the form of a screened-Coulomb or <a href="/facts/Yukawa_potential/TmPzXYpx">Yukawa potential</a>,

 
 
 
 β
 U
 (
 r
 )
 =
 
 Z
 
 2
 
 
 
 λ
 
 B
 
 
 
 
 
 (
 
 
 
 e
 
 κ
 a
 
 
 
 1
 +
 κ
 a
 
 
 
 )
 
 
 2
 
 
 
 
 
 
 e
 
 −
 κ
 r
 
 
 r
 
 
 ,
 
 
 {\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 

<ul><li>
 
 
 
 
 λ
 
 B
 
 
 
 
 {\displaystyle \lambda _{\text{B}}}
 
 is the <a href="/facts/Bjerrum_length/41aVddHH">Bjerrum length</a>,</li>
<li>
 
 
 
 U
 
 
 {\displaystyle U}
 
 is the <a href="/facts/Potential_energy/I03KLbmn">potential energy</a>,</li>
<li>
 
 
 
 e
 
 
 {\displaystyle e}
 
 ≈ 2.71828 is <a href="/facts/Euler%2527s_number/coEtSBk8">Euler's number</a>,</li>
<li>
 
 
 
 κ
 
 
 {\displaystyle \kappa }
 
 is the inverse of the <a href="/facts/Debye_length/WaCHqvlY">Debye–Hückel screening length</a> (
 
 
 
 
 λ
 
 D
 
 
 
 
 {\displaystyle \lambda _{\text{D}}}
 
); 
 
 
 
 κ
 
 
 {\displaystyle \kappa }
 
 is given by 
 
 
 
 
 κ
 
 2
 
 
 =
 4
 π
 
 λ
 
 B
 
 
 n
 
 
 {\displaystyle \kappa ^{2}=4\pi \lambda _{\text{B}}n}
 
, and</li>
<li>
 
 
 
 
 β
 
 −
 1
 
 
 =
 
 k
 
 B
 
 
 T
 
 
 {\displaystyle \beta ^{-1}=k_{\text{B}}T}
 
 is the thermal energy scale at absolute temperature 
 
 
 
 T
 
 
 {\displaystyle T}
 
</li></ul>
The DLVO theory is named after <a href="/facts/Boris_Derjaguin/XEw9Ec4J">Boris Derjaguin</a> and <a href="/facts/Lev_Landau/lNXQTC49">Lev Landau</a>, <a href="/facts/Evert_Verwey/ygV3bJ8f">Evert Verwey</a> and <a href="/facts/Theodoor_Overbeek/BydEmtIr">Theodoor Overbeek</a> who developed it between 1941 and 1948.

DLVO theory open-in-new

DLVO theory