Langmuir physical adsorption

Adsorption isotherms are by no means all of the Langmuir type as to shape, and Brunauer [34] considered that there are five principal forms, as illustrated in Fig. XVII-7. TVpe I is the Langmuir type, roughly characterized by a monotonic approach to a limiting adsorption at presumably corresponds to a complete monolayer. Type II is very common in the case of physical adsorption... 

Because of their prevalence in physical adsorption studies on high-energy, powdered solids, type II isotherms are of considerable practical importance. Bmnauer, Emmett, and Teller (BET) [39] showed how to extent Langmuir s approach to multilayer adsorption, and their equation has come to be known as the BET equation. The derivation that follows is the traditional one, based on a detailed balancing of forward and reverse rates. 

The rate of physical adsorption may be determined by the gas kinetic surface collision frequency as modified by the variation of sticking probability with surface coverage—as in the kinetic derivation of the Langmuir equation (Section XVII-3A)—and should then be very large unless the gas pressure is small. Alternatively, the rate may be governed by boundary layer diffusion, a slower process in general. Such aspects are mentioned in Ref. 146. 

The analogy with physical adsorption is reflected in the use of a Langmuir ad-... 

Most solid sorbents rely on vapors being sorbed by a physical adsorption mechanism the substance enters the internal pores of the sorbent and is held there by attractive forces considerably weaker and less specific than those of chemical bonds. These weakly attractive forces facilitate desorption for subsequent analysis. The mechanisms for physical adsorption have been studied extensively and are described mathematically by equations such as the Langmuir isotherm. 

Transient deposition of hydrocarbons on zeolites during a cold start operation of the DOC can be modeled by the rate laws based on Langmuir or Temkin mechanism for physical adsorption/desorption (cf., e.g. Goralski et al., 2000 Koltsakis and Stamatelos, 2000 Kruglov and Aris, 1995 Kryl et al., 2005 Twigg, 2006). The rate laws for the adsorption and desorption of hydrocarbons are then... 

The Type I isotherm is reminiscent of Figure 7.16, the Langmuir isotherm. The plateau is interpreted as indicating monolayer coverage. We see that this type of behavior implies a sufficiently specific interaction between adsorbate and adsorbent to be more typical of chemisorption than physical adsorption. 

The regularities of reactions on the catalyst surfaces are of a very complicated nature and their description is only possible on the basis of schematic and simplified physical models. A model of this kind should, on the one hand, reflect the main features of the phenomenon and, on the other hand, result in comprehensible mathematical expressions. The model of an ideal adsorbed layer or, in terms of the author of the model, Langmuir, simple adsorption (20) is the simplest and historically the first of the models retaining their importance until now. 

Type I isotherms (e.g. ammonia on charcoal at 273 K) show a fairly rapid rise in the amount of adsorption with increasing pressure up to a limiting value. They are referred to as Langmuir-type isotherms and are obtained when adsorption is restricted to a monolayer. Chemisorption isotherms, therefore, approximate to this shape. Type I isotherms have also been found for physical adsorption on solids... 

Before 1916, adsorption theories postulated either a condensed liquid film or a compressed gaseous layer which decreases in density as the distance from the surface increases. Langmuir (1916) was of the opinion that, because of the rapidity with which intermolecular forces fall off with distance, adsorbed layers are not likely to be more than one molecular layer in thickness. This view is generally accepted for chemisorption and for physical adsorption at low pressures and moderately high temperatures. 

Solid surfaces are usually heterogeneous therefore, since adsorption at the more active sites is favoured, heats of both monolayer physical adsorption and chemisorption might, in this respect, be expected to become significantly less exothermic as the surface coverage increases, as, for example, shown at low pressures in Figures 5.12a and 5.12b. This, in turn would cause the initial slope of an adsorption isotherm to be steeper than that predicted according to the Langmuir equation or the BET equation. 

The classic models for physical adsorption are those of Langmuir and of Bru-nauer, Emmett and Teller. Langmuir proposed a model of gas adsorption involving monomolecular adsorption and constant AHads, independent of the extent of surface coverage ... 

Gnllet Y, Llewellyn PL.Tosi Pellenq N and Rouquerol J (1993) In Proc Fourth International Conference on Fundamentals of Adsorption (M Suzuki, ed), Kodansha, Tokyo, p 235 GubbinsKE (1997) In Physical Adsorption Experiment Theory and Applications I Fraissard and W C Connor, eds) Kluwer Dordrecht, p 65 GurvichLG (1915)/ Russ Phys C him, 4,1, 805 Haber J (1991) Pure Appl Chem, 63,1227 Kiselev A V (1965) Disc Faraday Soc, 40, 205 Kiselev A V (1967) Adv Chromatogr, 4,113 Langmuir I (1916)/ Am Chem Soc, 38,2221 Langmuir I (1917)/ Am Chem Soc, 39, 1848 Langmuirl (1918)/ Am Chem Soc, 40,1361... 

The Langmuir equation for the adsorption isotherm is not suitable for physical adsorption because it only applies to monolayer adsorption. In practical work the semi-empirical equation of Brunauer, Emmet and Teller (BET equation) is used ... 

E. L. Fuller Jr. and K.A. Thompson, Chemical and Geometric Factors in Physical Adsorption/ Desorption of Gases on Solids, Langmuir, 3 (1987) 171. 

The type I isotherm corresponds to the Langmuir case when adsorption is confined to a monolayer. The multilayer physical adsorption of gases by nonporous solids, in a vast majority of cases, gives rise to a type II isotherm, which can be described by the Brunauer, Emmet, and Teller (BET) equation (6,51). 

Adsorption of solutes onto solid surfaces from solution can occur by physical adsorption, involving weak van der Waals forces, or by a chemical process. Adsorption data can be analysed using the Langmuir equation or, if multilayer adsorption occurs, by the Freundlich equation. 

Except for the competitive Langmuir isotherm (Table 10.7), the simple isotherm models cannot consider competition between multiple sorbates for a single sorption site. They are most applicable to physical adsorption of molecular species where the sorbate is held by much weaker hydrogen bonds or residual bonds. Adsorption of ions and complexed species is generally best studied with models that can consider more independent variables. To accurately predict adsorption of ions that compete for adsorption sites and also form important complexes, may require a model that considers as many as a dozen or more variables. 

It is common in soil chemistry for adsorption of organics from solution to be of more interest than adsorption from vapor. This usually does not involve multilayer adsorption because of the tendency of water molecules to compete effectively for adsorption sites, at least if physical adsorption is the main process. In such cases, the Langmuir equation may be more accurate in describing adsorption results than the BET equation. The Langmuir equation is readily converted from the linear form used in gas... 

Dependence of Adsorption Parameter K on Salt Concentration The physical meaning of Equation 5.48 can be revealed by chemical-reaction considerations. For simplicity, let us consider Langmuir-type adsorption i.e., we treat the interface as a two-dimensional lattice. We will use the notation Bg for the fraction of the free sites in the lattice, 0, for the fraction of sites containing adsorbed surfactant ion S , and 02 for the fraction of sites containing the complex of an adsorbed surfactant ion + a bound counterion. Obviously, we can write 0q -1- 0i -1- 02 = F The adsorptions of surfactant ions and counterions can be expressed in the form ... 

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