Kinetic derivation of common isotherm equations for surface and micropore adsorption

Abstract

t The Langmuir equation is one of the most successful adsorption isotherm equations, being widely used tofit Type I adsorption isotherms. In this article we show thatthe kinetic approach originally used by Langmuir for 2Dmonolayer surface adsorption can also be used to derive a1D analogue of the equation, applicable in ultramicroporeswith single-file diffusion. It is hoped that such a demonstration helps dispel the idea that the Langmuir isothermequation cannot apply to some micropores as more than amathematical correlation. We furthermore seek to extendthe insight provided by the simple kinetic derivation of theLangmuir equation to other isotherm equations capable ofmodelling Type I isotherms. The same kinetic approach isthus also used to derive the Volmer, Fowler-Guggenheimand Hill-de Boer equations, both for surface (2D adsorbedphase) and micropore adsorption (1D and 3D adsorbedphases). It is hoped that this will help make more intuitively clear that these equations can be used as phenomenological models in some instances of adsorption inmicropores