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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.
The Hertz–Knudsen equation describes the non-dissociative adsorption of a gas molecule on a surface by expressing the variation of the number of molecules impacting on the surfaces per unit of time as a function of the pressure of the gas and other parameters which characterise both the gas phase molecule and the surface: [1] [2]
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.
The langmuir (symbol: L) is a unit of exposure (or dosage) to a surface (e.g. of a crystal) and is used in ultra-high vacuum (UHV) surface physics to study the adsorption of gases. It is a practical unit, and is not dimensionally homogeneous, and so is used only in this field. It is named after American physicist Irving Langmuir.
The Langmuir adsorption equation is used to model monolayer adsorption where all surface adsorption sites have the same affinity for the adsorbing species and do not interact with each other. Gerhard Ertl in 1974 described for the first time the adsorption of hydrogen on a palladium surface using a novel technique called LEED. [4]
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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.
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: