Summary
Calculations based on a (distance)−ε intermolecular potential (ε>3) enable study of the effects on adsorption of the geometry of the solid. This paper gives the closed form solution for the adsorptive potential about a homogeneous solid rectangular corner; and, through systematic superposition, closed form solutions for the following configurations also: the rectangular corner of a cavity; laminae and rectangular cracks occupying a quarter plane; semi-infinite rectangular prisms and prismatic cavities; rectangular parallelepipeds and brick-shaped cavities. These various results are developed in detail for the cases ε=6 and ε=4. The paradox that potentials for ε>3 seem to be obtainable more readily than Newtonian potentials (ε=1) is explained by the existence only for ε>3 of simple fundamental solutions for infinite homogeneous solid configurations.
Zusammenfassung
Berechnungen, denen ein intermolekulares Potential der Form (Abstand)−ε (ε>3) zugrunde gelegt ist, ermöglichen eine Untersuchung von Effekten der Adsorption auf die Geometrie des Festkörpers. Die vorliegende Arbeit gibt die Lösung in geschlossener Form für das Adsorptionspotential um eine feste, homogene, rechtwinklige Ecke an. Ausserdem werden durch systematische Superposition Lösungen in geschlossener Form für die folgenden Konfigurationen angegeben: die rechtwinklige Innenecke einer Mulde; viertelunendliche, ebene Platten und rechteckige Spalten; halbunendliche, reckteckige Prismen und prismatische Mulden; Quader und quaderförmige Höhlen. Diese Ergebnisse sind ausführlich dargestellt für die Fälle ε=4. Das Paradoxon. dass Potentiale mit ε>3 scheinbar leichter zugänglich sind als das Gravitationspotential (ε=1), wird dadurch erklärt, dass nur für ε>3 einfache Grundlösungen für unendliche, homogene Festköperkonfigurationen existieren.
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Philip, J.R. Inverse power law potentials in rectangular configurations. Journal of Applied Mathematics and Physics (ZAMP) 29, 631–643 (1978). https://doi.org/10.1007/BF01601489
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DOI: https://doi.org/10.1007/BF01601489