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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
The adsorption rate is dependent on the temperature, the diffusion rate of the solute (related to mean free path for pure gas), and the energy barrier between the molecule and the surface. The diffusion and key elements of the adsorption rate can be calculated using Fick's laws of diffusion and Einstein relation (kinetic theory).
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 ...
Sten Yngve Dennis Lagergren (6 May 1876 – 4 April 1922) was a Swedish physical chemist known for his fundamental findings in adsorption kinetics.. Lagergrens's 1898 article "Zur Theorie der Sogenannten Adsorption Gelöster Stoffe" [1] (To the theory of the so-called adsorption of dissolved materials) brought him a lasting fame.
BET theory (Brunauer-Emmett-Teller) provides a calculation to describe the physical adsorption of gas molecules on a solid surface. Because of the complexity of the process, these calculations are only moderately successful; however, Stephen Brunauer was able to classify sorption isotherms into five generalized shapes as shown in Figure 2.
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
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: