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The Langmuir adsorption model deviates significantly in many cases, primarily because it fails to account for the surface roughness of the adsorbent. Rough inhomogeneous surfaces have multiple site types available for adsorption, with some parameters varying from site to site, such as the heat of adsorption.
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 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.
While the Langmuir model assumes that the energy of adsorption remains constant with surface occupancy, the Freundlich equation is derived with the assumption that the heat of adsorption continually decrease as the binding sites are occupied. [16] The choice of the model based on best fitting of the data is a common misconception. [15]
The sticking probability is the probability that molecules are trapped on surfaces and adsorb chemically. From Langmuir's adsorption isotherm, molecules cannot adsorb on surfaces when the adsorption sites are already occupied by other molecules, so the sticking probability can be expressed as follows:
The simplest mathematical model to explain the Vroman Effect is the Langmuir model using the Langmuir isotherm. [ 9 ] [ 10 ] More complex models include the Fruendlich isotherm and other modifications to the Langmuir model.
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where A is the reactant and S is an adsorption site on the surface and the respective rate constants for the adsorption, desorption and reaction are k 1, k −1 and k 2, then the global reaction rate is: = = where: r is the rate, mol·m −2 ·s −1