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Encyclopedia of Geochemistry pp 1–2Cite as

Poisson-Boltzmann Equation

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Part of the book series: Encyclopedia of Earth Sciences Series ((EESS))

Definition

The Poisson-Boltzmann equation relates the electrostatic potential to the charge density as a function of spatial position in a system of charges. It has broad applicability and is particularly important for understanding the distribution of ions in geochemical systems.

Essential Concepts

The Poisson-Boltzmann equation forms the basis for a continuum understanding of strong electrolyte solutions, electrical double layers at charged surfaces, clay swelling , and colloidal stability, all of which are important topics in geochemistry. Practically it links the charge density and the electrostatic potential (and electric field through the derivative of the electrostatic potential) in a system of charged particles and may include solid surfaces. It is based on the well-known work by Gouy and Chapman, is further developed by Debye and Hückel, and is the electrostatic component of the DLVO (Debye,...

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References

  • Israelachvili, J. N., 2011. Intermolecular and Surface Forces, 3rd edn. Burlington: Academic.

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  • Israelachvili, J. N., and Adams, G. E., 1978. Measurement of forces between two mica surfaces in aqueous electrolyte solutions in the range 0–100 nm. Journal of Chemical Society Faraday Transaction 1, 74, 975–1001.

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  • Verwey, E. J. W., and Overbeek, J. T. H. G., 1948. Theory of the Stability of Lyophobic Colloids. New York: Elsevier.

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Author information

Authors and Affiliations

  1. Department of Soil, Water and Environmental Science, University of Arizona, Tucson, AZ, USA

    Joan E. Curry

Authors
  1. Joan E. Curry
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Corresponding author

Correspondence to Joan E. Curry .

Editor information

Editors and Affiliations

  1. Department of Earth, Cornell University Department of Earth, Ithaca, New York, USA

    William M. White

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Curry, J.E. (2016). Poisson-Boltzmann Equation. In: White, W. (eds) Encyclopedia of Geochemistry. Encyclopedia of Earth Sciences Series. Springer, Cham. https://doi.org/10.1007/978-3-319-39193-9_15-1

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  • DOI: https://doi.org/10.1007/978-3-319-39193-9_15-1

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  • Publisher Name: Springer, Cham

  • Online ISBN: 978-3-319-39193-9

  • eBook Packages: Springer Reference Earth and Environm. ScienceReference Module Physical and Materials ScienceReference Module Earth and Environmental Sciences

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