Poisson–Boltzmann for oppositely charged bodies: an explicit derivation

Paillusson, Fabien, Barbi, Maria and Victor, Jean-Marc (2009) Poisson–Boltzmann for oppositely charged bodies: an explicit derivation. Molecular Physics, 107 (13). pp. 1379-1391. ISSN 0026-8976

Full content URL: http://dx.doi.org/10.1080/00268970902893156

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Item Type:Article
Item Status:Live Archive


The interaction between two parallel charged plates in ionic solution is a general starting point for studying colloidal complexes. An intuitive expression of the pressure exerted on the plates is usually proposed, which includes an electrostatic plus an osmotic contribution. We present here an explicit and self-consistent derivation of this formula in the only framework of the Poisson–Boltzmann (PB) theory. We also show that, depending on external constraints, the correct thermodynamic potential can differ from the usual PB free energy. For asymmetric, oppositely charged plates, the resulting expression predicts a non-trivial equilibrium position with the plates separated by a finite distance. The depth of this energy minimum is decisive for the stability of the complex. It is therefore crucial to obtain its explicit dependence on the charge densities of the plates and on the ion concentration. Analytic expressions for the position and depth of the energy minimum were derived in 1975 by Ohshima [Colloid Polym. Sci. 253, 150 (1975)] but, surprisingly, these important results seem to have been overlooked. We retrieve these expressions in a simpler formalism, more familiar to the physics community, and give a physical interpretation of the observed behavior.

Keywords:Colloids, Charged Systems, Electrolytes, Poisson–Boltzmann theory, parallel plates, oppositely charged, colloid complex, energy profile
Subjects:F Physical Sciences > F300 Physics
F Physical Sciences > F170 Physical Chemistry
Divisions:College of Science > School of Mathematics and Physics
ID Code:17972
Deposited On:24 Jul 2015 08:34

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