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The kinetic derivation applies to gas-phase adsorption. However, it has been mistakenly applied to solutions. The multiple-adsorbate case is covered in the competitive adsorption sub-section. The model assumes adsorption and desorption as being elementary processes, where the rate of adsorption r ad and the rate of desorption r d are given by
Brunauer, Emmett and Teller's model of multilayer adsorption is a random distribution of molecules on the material surface. Adsorption is the adhesion [1] of atoms, ions or molecules from a gas, liquid or dissolved solid to a surface. [2] This process creates a film of the adsorbate on the surface of the adsorbent.
The shape of the isotherms is sensitive to the order of kinetics of the adsorption and desorption processes, [2] and though the exact forms can be difficult to find, simulations have been used to find general functional forms for isotherms of dissociative adsorption for specific systems. [10]
This equation is known as Freundlich adsorption isotherm or Freundlich adsorption equation. As this relationship is entirely empirical, in the case where adsorption behavior can be properly fit by isotherms with a theoretical basis, it is usually appropriate to use such isotherms instead (see for example the Langmuir and BET adsorption theories ...
The Gibbs adsorption isotherm for multicomponent systems is an equation used to relate the changes in concentration of a component in contact with a surface with changes in the surface tension, which results in a corresponding change in surface energy. For a binary system, the Gibbs adsorption equation in terms of surface excess is
Classification of Sorption Isotherms by Brunauer Type I through V. He found that Type II and Type III isotherms require highly porous materials or desiccants, with first monolayer adsorption, followed by multilayer adsorption and finally leading to capillary condensation, explaining these materials high moisture capacity at high relative humidity.
The linear isotherm can be used to describe the initial part of many practical isotherms. It is typically taken as valid for low surface coverages, and the adsorption energy being independent of the coverage (lack of inhomogeneities on the surface). The Henry adsorption constant can be defined as: [2]
BET model of multilayer adsorption, that is, a random distribution of sites covered by one, two, three, etc., adsorbate molecules. The concept of the theory is an extension of the Langmuir theory, which is a theory for monolayer molecular adsorption, to multilayer adsorption with the following hypotheses: