Dynamic charge regulation model for the electrostatic forces between ionizable materials

P.M. Biesheuvel

Research output: Contribution to journalArticleAcademicpeer-review

8 Citations (Scopus)


The electrostatic repulsion between similar surfaces with ionizable surface groups interacting across aqueous solutions is calculated for plane parallel and curved surfaces for the case in which the solution phase is at thermodynamic equilibrium, but the charged surface is not in equilibrium with the solution. Simulations are made for approaching and retracting oxidic surfaces for which the (equilibrium) surface chemistry is described by a standard 2-pK model. Population balances describe the concentration of each surface species as a function of the rates of the different reactions with the ions in solution. Approaching surfaces experience a higher repulsion than predicted by thermodynamic equilibrium, with the upper limit being the repulsion at a constant surface charge (at very high approach velocities). For retracting surfaces the electrostatic repulsion is lower than that for equilibrium and may decrease to zero when the surfaces are sufficiently discharged at contact and pulled apart fast enough. In that case, and with the attractive van der Waals force still operating, a net attractive force is predicted, which might explain the pull-off force (adhesion force) often measured in the atomic force microscope and the surface force apparatus.
Original languageEnglish
Pages (from-to)5566-5571
Publication statusPublished - 2002


  • colloid particle interaction
  • double-layer relaxation
  • electrolyte-solutions
  • hydrophilic surfaces
  • 2 spheres
  • water
  • adhesion
  • silica
  • coagulation
  • microscopy

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