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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 model explains seemingly inconsistent observations of gas adsorption thermodynamics and kinetics in catalytic systems where surfaces can exist in a range of coordination structures, and it has been successfully applied to bimetallic catalytic systems where synergistic activity is observed.
[9] [10] More complex models include the Fruendlich isotherm and other modifications to the Langmuir model. This model explains the kinetics between reversible adsorption and desorption, assuming the adsorbate behaves as an ideal gas at isothermal conditions.
The Langmuir model of adsorption [2] assumes . The maximum coverage is one adsorbate molecule per substrate site. Independent and equivalent adsorption sites. This model is the simplest useful approximation that still retains the dependence of the adsorption rate on the coverage, and in the simplest case, precursor states are not considered.
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 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:
The result is equivalent to the Michaelis–Menten kinetics of reactions catalyzed at a site on an enzyme. The rate equation is complex, and the reaction order is not clear. In experimental work, usually two extreme cases are looked for in order to prove the mechanism. In them, the rate-determining step can be: Limiting step: adsorption/desorption
Polanyi's model of adsorption was met with much criticism for several decades after publication years. His simplistic model for determining adsorption was formed during the time of the discovery of Peter Debye's fixed dipoles, Niels Bohr's atomic model, and well as the developing theory of intermolecular forces and electrostatic forces by key figures in the chemistry world including W.H. Bragg ...