DLVO theory

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Simplified representation of the contributions of different energies to the overall energy function of the DLVO theory (overall interaction).

The DLVO theory (named after Boris Derjaguin , Lew Dawidowitsch Landau , Evert Verwey , Theodoor Overbeek ) is a theoretical description that deals with the stability of colloidal systems on the basis of attractive and repulsive, for example steric, electrostatic or van-der- Waals interactions between the dispersed particles employed.

The surfaces of the colloidal particles are understood as capacitor plates, on the surfaces of which electrochemical double layers are formed in an electrolyte solution . When the particles approach, the double layers overlap. The resulting repulsive forces have a greater range than the attractive Van der Waals forces. In this way, unprotected dispersions are electrostatically stabilized.

For two spheres with the radius and a constant surface charge at a center of gravity in a fluid with a dielectric constant and a concentration of monovalent ions, the electrostatic potential results as the Coulomb force or Yukawa repulsion

with as the Bjerrum length , as the Debye-Hückel distance , which is defined as and with as thermal energy at the absolute temperature .

history

In 1923 Peter Debye and Erich Hückel presented their theory for the first time to describe the distribution of ion charges in an ionic solution. The basic idea of ​​applying the linearized Debye-Hückel theory to colloidal dispersion came from Levine and Dube, who found that charged colloidal particles experience strong repulsion at close distances and weak attraction at great distances. However, this theory failed to explain why colloidal dispersions aggregate in solutions with high ionic concentration. In 1941 Derjaguin and Landau presented a new theory about the stability of colloidal dispersions, in which the strongly attractive Van der Waals forces at a short distance are superimposed by the electrostatic forces that act more strongly at greater distances. Seven years later, Verwey and Overbeek independently presented a solution for describing the instabilities using the so-called DLVO theory.

Derivation of the DLVO theory

The DLVO theory combines the forces resulting from the van der Waals interactions and the electrochemical double layer . Different conditions and different equations have to be considered for the derivation. However, the derivation can be simplified significantly, taking into account some fairly common assumptions, and simply created by combining two separately derived theories.

Van der Waals attraction

Van der Waals forces is the umbrella term for all dipole-dipole interactions. Assuming that the potential between two atoms or small molecules is only attractive and of the shape , with as a constant for the interaction energy and for the Van-der-Waals forces. And further with the assumption that the interaction energy between a molecule and a planar surface results from the sum of the interaction energies of all molecules from the interface with the molecule, the total interaction energy for a molecule depending on the distance from the surface can be given as follows become

With

the interaction energy between the molecule and the surface ,
the number density of the surface ,
the distance perpendicular to the surface with
the molecule at and
the surface at as well
the distance parallel to the surface .

With this, the interaction energy for large spheres with the radius R to a planar surface can be calculated as follows

With

the interaction energy between the sphere and the planar surface and
the number density of the sphere .

Simplified, the Hamaker constant A is defined as

which results in the following equation

With a similar method and with the Derjaguin approximation , the Van der Waals interactions between particles and different geometries can be calculated as follows

Two balls:
Sphere area:
Two areas: per unit area

Electrochemical double layer

There are two ways to reduce the thickness of the electrochemical double layer . On the one hand, the shielding of the surface charge can be strengthened by adding electrolyte and the layer can be compressed as a result. On the other hand, the surface potential can be reduced by specific ion adsorption.

If the particle distance is reduced to such an extent that the attractive interactions become dominant over the repulsive forces, the particles coagulate .

literature

  1. Peter Debye, Erich Hückel: The theory of electrolytes. I. Lowering of freezing point and related phenomena . In: Physikalische Zeitschrift . tape 24 , 1923, pp. 185-206 .
  2. ^ S. Levine: Problems of stability in hydrophobic colloidal solutions I. On the interaction of two colloidal metallic particles. General discussion and applications . In: Proceedings of the Royal Society of London A . tape 170 , no. 941 , 1939, pp. 145-164 , JSTOR : 97213 .
  3. ^ S. Levine, Dube: Interaction between two hydrophobic colloidal particles, using the approximate Debye-Huckel theory. I. General properties . In: Transactions of the Faraday Society . tape 35 , 1940, p. 1125-1141 , doi : 10.1039 / TF9393501125 .
  4. B. Derjaguin, L. Landau: Theory of the stability of strongly charged lyophobic sols and of the adhesion of strongly charged particles in solutions of electrolytes . In: Acta Physico Chemica URSS . tape 14 , 1941, pp. 30-59 , doi : 10.1016 / 0079-6816 (93) 90013-L .
  5. EJW Verwey, J. Th. G. Overbeek: Theory of the stability of lyophobic colloids . Elsevier, New York 1948, OCLC 2313484 .
  6. ^ WB Russel, DA Saville, WR Schowalter: Colloidal Dispersions . Cambridge University Press, New York 1989, ISBN 978-0-521-34188-2 .
  7. M. Elimelech, J. Gregory, X. Jia, RA Williams: Particle Deposition and Aggregation Measurement. Modeling and simulation . Boston 1995, ISBN 978-0-7506-0743-8 .
  8. ^ F. London: The general theory of molecular forces . In: Transactions of the Faraday Society . tape 33 , 1937, ISSN  0014-7672 , pp. 8-26 , doi : 10.1039 / TF937330008B .
  9. B. Derjaguin: Studies on Friction and Adhesion, IV . In: Colloid Journal . tape 69 , no. 2 , 1934, ISSN  1435-1536 , pp. 155-164 , doi : 10.1007 / BF01433225 .