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Biophys J. Sep 1984; 46(3): 387–407.
PMCID: PMC1434960

The Smoluchowski-Poisson-Boltzmann description of ion diffusion at charged interfaces.


A theoretical description of ion diffusion in the electric field set up by the double layer in the neighborhood of a charged interface is presented. Such a description is needed for the understanding of diffusion-controlled chemical kinetics and transport of ionic species in a variety of systems of interest in biophysics, electrochemistry, and colloid science. The ion dynamics are taken to be governed by the Smoluchowski diffusion equation and the average electrostatic field is obtained from the nonlinear Poisson-Boltzmann equation. Diffusion in finite regions with partially absorbing boundaries of planar, cylindrical, or spherical geometry is considered. The complete analytical solution of the Smoluchowski-Poisson-Boltzmann equation for counterions between two planar charged interfaces is given. Simple expressions are derived for certain useful integral quantities, viz., mean absorption times and absorption probabilities, in all geometries considered. Finally, lateral counterion diffusion and its consequences for surface re-encounter-enhanced chemoreception is considered.

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Selected References

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  • Richter PH, Eigen M. Diffusion controlled reaction rates in spheroidal geometry. Application to repressor--operator association and membrane bound enzymes. Biophys Chem. 1974 Oct;2(3):255–263. [PubMed]
  • Berg HC, Purcell EM. Physics of chemoreception. Biophys J. 1977 Nov;20(2):193–219. [PMC free article] [PubMed]
  • Fuoss RM, Katchalsky A, Lifson S. The Potential of an Infinite Rod-Like Molecule and the Distribution of the Counter Ions. Proc Natl Acad Sci U S A. 1951 Sep;37(9):579–589. [PMC free article] [PubMed]
  • Shoup D, Szabo A. Role of diffusion in ligand binding to macromolecules and cell-bound receptors. Biophys J. 1982 Oct;40(1):33–39. [PMC free article] [PubMed]

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