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Diffuse double layer interaction between two parallel plates with constant surface charge density in an electrolyte solution III. Potential energy of double layer interaction

Summary

By using the non-linearPoisson-Boltzmann equation, the potential energy of the diffuse double layer interaction between two parallel plates with constant surface charge density in a symmetrical electrolyte solution is calculated from the free energy of the double layers. The two plates may have unequal surface charge densities, dielectric constants and thicknesses. For very small plate separations, where the influence of the electric field which is induced within the plates by the overlapping of the double layers becomes important, the free energy is calculated by considering a charging process in which all the surface charges are increased at the same rate. For separations where the influence of the field within the plates may be neglected, a discharging process is used in which all the charges in the system are decreased at the same rate, and the potential energy of the double layer interaction is expressed in terms of elliptic integrals.

Zusammenfassung

Durch Benutzung der nichtlinearenPoisson-Boltzmannschen Gleichung wird die potentielle Energie der Wechselwirkung der diffusen Doppelschichten zwischen zwei parallelen Platten mit der konstanten Dichte der Oberflächenladung in einer symmetrischen Elektrolytlösung berechnet aus der freien Energie der Doppelschichten Die zwei Platten können ungleiche Dichten der Oberflachenladung, dielektrische Konstanten und Dicken haben. Für sehr kleine Trennungen der Platten, wo der Einfluß des elektrischen Feldes, der innerhalb der Platten durch das Überlappen der Doppelschichten induziert wird, von Wichtigkeit wird, wird die freie Energie berechnet durch Betrachtung eines Ladungsprozesses, in dem alle Oberflächenladungen in demselben Maße vermehrt werden. Für Trennungen, wo der Einfluß des Feldes innerhalb der Platten vernachlässigt werden kann, wird ein Entladungsprozeß benutzt, in dem alle Ladungen in dem System in demselben Maße vermindert werden, and wird die potentielle Energie der Wechselwirkung der Doppelschichten ausgedrückt mittels elliptischer Integrale.

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Ohshima, H. Diffuse double layer interaction between two parallel plates with constant surface charge density in an electrolyte solution III. Potential energy of double layer interaction. Colloid & Polymer Sci 253, 150–157 (1975). https://doi.org/10.1007/BF01775681

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Keywords

  • Free Energy
  • Dielectric Constant
  • Potential Energy
  • Surface Charge
  • Double Layer