Langmuir theory of adsorption

A gas in contact with a solid will establish an equilibrium between the molecules in the gas phase and the corresponding adsorbed species (molecules or atoms) which are bound to the surface of the solid. The position of equilibrium will depend on a number of factors such as the relative stabilities of the adsorbed and gas phase species involved, the temperature of the system, and the pressure of the gas above the surface. 

Langmuir considered the surface of a solid to be made up of elementary sites each of which could adsorb one gas molecule. He assumed that all the elementary sites are identical in their affinity for a gas molecule and that the presence of a gas molecule on one site does not affect the properties of neighboring sites. 

If 0 is the fraction of the surface occupied by gas molecules, the rate of evaporation from the surface is r x 0, where r is the rate of evaporation from the completely covered surface at a certain temperature. The rate of adsorption of molecules on the surface is proportional to the fraction of the area that is not covered (1 - 0) and to the pressure of the gas. Thus, the rate of condensation is expressed as P(1 - 0), where is a constant at a given temperature and includes a factor to allow for the fact that not every gas molecule that strikes an unoccupied space will stick. 

At equilibrium the rate of evaporation of the adsorbed gas is equal to the rate of condensation  

If we rearrange Equation 13.19, it can be seen that a linear relationship develops between 

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Although the Langmuir theory of adsorption is used frequently for technical process development it is a crude approximation, as surface reconstruction frequently occurs. Adsorbed molecules change the structure of the surface layer and the catalytic properties of surface sites are not equal in the ability to bind chemisorbed molecules. The rate is dependent on spatial arrangement and the heat of adsorption depends on coverage (Figures 2.27, 2.28). 

Catalysis involves an alternative mechanism in which the catalyst is involved. Catalysis is divided into three classes heterogeneous catalysis, homogeneous catalysis, and enzyme catalysis. Heterogeneous catalysis at the surfaces of solids involves adsorption of the reactants. We discussed the Langmuir theory of adsorption and applied it to heterogeneous catalysis. Homogeneous catalysis involves mechanisms with steps that occur in a single phase, and example reactions were analyzed. 

Langmuir s research on how oxygen gas deteriorated the tungsten filaments of light bulbs led to a theory of adsorption that relates the surface concentration of a gas to its pressure above the surface (1915). This, together with Taylor s concept of active sites on the surface of a catalyst, enabled Hinshelwood in around 1927 to formulate the Langmuir-Hinshelwood kinetics that we still use today to describe catalytic reactions. Indeed, research in catalysis was synonymous with kinetic analysis... 

Langmuir Quantitative theory of adsorption of gases on surfaces... 

It should be mentioned that the extension of the Langmuir theory to adsorption from binary adsorbate systems is thermodynamically consistent only in the special case where Q = Q2. However, that thermodynamic consistency is of secondary importance if Eq. (18) provides the correct analytical description of the adsorption phenomena. 

Many theories of adsorption, following Langmuir, have assumed that the rate of adsorption is proportional to (1 — 0), i.e., to the fraction of the surface which is bare or not yet covered. Langmuir first proved the (1 — 0) law by measuring experimentally how the thermionic work function

changed with time as thorium reached the surface of a tungsten filament at a constant rate (10). He then assumed that tp decreased linearly with 0 and thus deduced that dd/di was proportional to (1 — 0). But this assumption has been shown to be incorrect for such cases as Cs on W, Ba on W, SrO on W, and other systems. Hence it follows that the (1 — 0) law is not valid. The experiments described above for N2 on W not only show that dQ/dt is not proportional to (1 — 0), but they show by a direct experiment that dd/dt for a constant arrival rate is independent of 0 between 0 = 0 and 1.0. 

The oxidation of CO is the simplest reaction and has been the most intensively studied since Langmuir first presented a theory of adsorption and catalysis for this reaction [13]. Supported Au NPs such as Au/Ti02, Au/Fe203 and Au/Co304 are extraordinarily active in CO oxidation, even at 200 K, and are much more active than the other noble metals catalysts at temperatures below 400 K [14—16]. Gold clusters composed of several atoms can promote the reaction between CO and 02 to form C02 at as low as 40 K [17]. Most recently, Lahr and Ceyer [18] have extended the temperature range at which the activity for CO oxidation is observed to as low as 70 K by using an Au/Ni surface alloy. 

A fundamental advance in the theory of adsorption phenomena was made in 1916 when Langmuir suggested that adsorption was to be regarded as a chemical process occurring on an energetically uniform surface and that the adsorbed phase was a unimolecular layer of non-interactive molecules. However, it soon became impossible to describe some important phenomena of catalysis without denying the concept of a uniform surface. 

P.I. Ravikovitch and A.V. Neimark, Density Functional Theory of Adsorption in Spherical Cavities and Pore Size Characterization of Templated Nanoporous Silicas with Cubic and Three-dimensional Hexagonal Structures, Langmuir, 2002, 18, 1550-1560. 

Ravikovitch, P.I. and Neimark, A.V. (2002). Density functional theory of adsorption in spherical cavities. Langmuir, 18, 1550—60. 

In October, 1914, as Langmuir s notebook indicates, the problem of surfaces and forces remained unsolved. But by the time Langmuir arose to address the American Chemical Society on March 5, 1915, his uncertainties had been completely cleared up. In a masterful landmark paper entitled Chemical Reactions at Low Pressures, he surveyed his clean up experiments introduced his theory of adsorption, based on the adsorption isotherm and described the reaction between carbon monoxide and oxygen in contact with platinum as a catalytic reaction. The theory here outlined, he concluded, would seem to be generally applicable to all heterogenous reactions, even at atmospheric pressures. (2)... 

We start this book with a chapter (Chapter 2) on the fundamentals of pure component equilibria. Results of this chapter are mainly applicable to ideal solids or surfaces, and rarely applied to real solids. Langmuir equation is the most celebrated equation, and therefore is the cornerstone of all theories of adsorption and is dealt with first. To generalise the fundamental theory for ideal solids, the Gibbs approach is introduced, and from which many fundamental isotherm equations, such as Volmer, Fowler-Guggenheim, Hill-de Boer, Jura-Harkins can be derived. A recent equation introduced by Nitta and co-workers is presented to allow for the multi-site adsorption. We finally close this chapter by presenting the vacancy solution theory of Danner and co-workers. The results of Chapter 2 are used as a basis for the... 

Langmuir (1918) was the first to propose a coherent theory of adsorption onto a flat surface based on a kinetic viewpoint, that is there is a continual process of bombardment of molecules onto the surface and a corresponding evaporation (desorption) of molecules from the surface to maintain zero rate of accumulation at the surface at equilibrium. 

We note here that there are other theories of adsorption/desorption kinetics that offer expressions for the adsorption/desorption rate that are different from the ART expression but also lead to the Langmuir isotherm when d0/dt = 0. It is rather strange that adsorption systems with different kinetics of the adsorption/ desorption processes have the same form at equilibrium. 

The adsorption on a solid surface, the types of adsorption, the energetics of adsorption, the theories of adsorption, and the adsorption isotherm equations (e.g., the Langmuir equation, BET equation, Dubinin equation, Temkin equation, and the Freundlich equation) are the subject matter of Chapter 2. The validity of each adsorption isotherm equation to the adsorption data has been examined. The theory of capillary condensation, the adsorption-desorption hysteresis, and the Dubinin theory of volume fllhng of micropores (TVFM) for microporous activated carbons are also discussed in this chapter. 

Ravikovitch PI, Neimark AV Density functional theory of adsorption in spherical cavities and pore size characterization of templated nanoporous sihcas with cubic and three-dimensional hexagonal structures, Langmuir 18(5) 1550-1560, 2002. 

In the following, we consider the equilibrium and kinetics of adsorption of surfactants at the air-water interface on the basis of Langmuir s theory of adsorption of gases on solids. According to Langmuir s theory, it is assumed that the adsorption surface consists of sites, which can be occupied by adsorbed molecules. These sites correspond to the minimum of surface free energy. At achieving the balance between the adsorbed molecules and molecules of gas, only some parts of the potentially available adsorption sites are occupied by gas molecules. This part is equal to 0, and the total number of molecules Na adsorbed on the surface obeys the ratio... 

For reasons which will become clear in the following, the Langmuir isotherm has played (and continues to play) a special role in the theory of adsorption. The Langmuir isotherm, which describes submonolayer localized adsorption without lateral interaction, is given by... 

Derivation of the dependency of surface tension of solutions with the concentration if a specific theory of adsorption is assumed, e.g. it can be shown that the Langmuir theory (discussed in Chapter 7) yields the Szyszkowski equation. 

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