Langmuir monolayer adsorption model

Langmuir monolayer adsorption model can also be used to deal with chemisorption process due to its simplicity. However, in the Langmuir adsorption model, the hypothesis of the uniformity of solid surface is different from the actual surface. So it needs necessary amendments. In the chemisorption, it often occurs with the competitive and dissociative adsorption, and their adsorption isotherm equations can be obtained by Langmuir adsorption model, respectively. 

In the limit of monolayer adsorption model Eq. (16) reduces to the Langmuir-Freund-lich isotherm which, nowadays, seems to be the most widely used expression to correlate experimental adsorption isotherms in the submonolayer coverage region. 

Langmuir s monolayer adsorption model can only describe the first type of adsorption isotherms which happen frequently in micro-pore adsorbents (pore size... 

The number of gas molecules can be measured either directly with a balance (gravimetric method) or calculated from the pressure difference of the gas in a fixed volume upon adsorption (manometric method). The most frequently apphed method to derive the monolayer capacity is a method developed by Brunauer, Emmett, and Teller (BET) [1], Starting from the Langmuir equation (monolayer adsorption) they developed a multilayer adsorption model that allows the calculation of the specific surface area of a sohd. The BET equation is typically expressed in its linear form as... 

Langmuir (1918) laid down a systematic and theoretically grounded adsorption isotherm, the well-known Langmuir isotherm, which has served as a basis for a number of future isotherms, such as the BET isotherm, described in 1.4.1.3. The basic assumptions of the Langmuir adsorption model include monolayer coverage, localized adsorption (i.e., the specific adsorption sites exist and the interactions are between a specific molecule and the site), and homogeneous materials. In addition, the heat of adsorption is independent of coverage. He proposed that the rate of adsorption is proportional to the dimensionless pressure of the adsorbate, p/po (= p ), where po is the saturated vapor pressure, and the... 

The assumption of monolayer adsorption in the Langmuir isotherm model is unrealistic in most cases, and a modification to multilayer adsorption should be considered. In 1938, Brunauer, Emmett, and Teller modified the Langmuir approach of balancing the rates of adsorption and desorption for the various molecular layers [Brunauer et al., 1938], This approach is known as the BET method. The BET isotherm assumes that the adsorption of the first layer has a characteristic heat of adsorption A Ha and the adsorption and desorption on subsequent layers are controlled by the heat of condensation of the vapor, A Hc. The derivation of the BET equation is beyond the scope of this book however, a common form of the BET equation is given as... 

A frequently used adsorption model that allows for adsorption in multilayers has been introduced by Brunauer, Emmett and Teller [10] and is known as the BET equation. With the exception of the assumption that the adsorption process terminates at monolayer coverage, these authors have retained all the other assumptions made in deriving the Langmuir adsorption isotherm. Hence all objections to the application of the Langmuir equation apply here, too. 

The BET model appears to be unrealistic in a number of respects. For example, in addition to the Langmuir concept of an ideal localized monolayer adsorption, it is assumed that all the adsorption sites for multilayer adsorption are energetically identical and that all layers after the first have liquid-like properties. It is now generally recognized that the significance of the parameter C is oversimplified and that Equation (4.33) cannot provide a reliable evaluation of... 

The fact that many Type I isotherms appear to obey a simple form of Langmuir equation - Equation (4.13) - over a wide range of pressure was for many years accepted as confirmatory evidence for the Langmuir model. According to this view (Brunauer, 1945), the limiting plateau would be the result of monolayer adsorption on the pore walls. 

The Langmuir-adsorption model predicts an asymptotic approach to monolayer surface coverage as adsorbate partial pressure approaches saturation this is the Type-I isotherm of Figure 5.7. The Langmuir model, though proven for many ultraclean, well-ordered surfaces interacting with small-molecule adsorbates, is oversimplified for many real-world systems. Nonetheless, it is the foundation upon which much of adsorption theory is built and as such provides a useful con-... 

The Brunauer-Emmett-Teller (BET) adsorption model was developed to account for multilayer adsorption. The BET model can be thought of as the sum of two terms the Langmuir model is used to account for coverage from zero to the completion of the first monolayer, while the second and all subsequent layers (not treated by the Langmuir model) are assumed to have a heat of adsorption equal to the heat of vaporization of the bulk liquid phase of the adsorbing species. The heat of adsorption of the first monolayer usually exceeds the liquid s heat of vaporization. Although it might seem a erode oversimplification, the BET model works well for many systems that involve physisorption of simple molecules,... 

Adsorption of ions at surfaces has been one of the classical fields of interest in regard of catalysis and separation. Among various surfoces, Langmuir monolayers mimic the structure of cell membranes and hence these biomimetic surfaces are a model system that enables one to investigate surface phenomena analogous to the membrane surfoces [1,2]. 

Adsorptivity of various ions to Langmuir monolayers has been known to be quite different from that in the bulk phase after extensive studies done by theoretical models and empirical techniques involving XPS, neutron scattering, FTIR, etc [3, 4]. Most of the empirical studies were done ex-situ because there exists difficulties in dealing with the monolayers at the air/water interface in-situ. Recently, much progress has been reported especially on the in-situ FTIR spectroscopy for the air/water interfaces [S, 6]. 

Before examining the NMR, it is useful to consider some adsorption and desorption studies of this standard catalyst. Hydrogen chemisorption data have been modeled by a Langmuir isotherm for pressures between 1 and 80 Torr (Fig. 26a) (80) but also by a Temkin isotherm at pressures between 0.1 and 100 Torr (Fig. 26b) (48). The Langmuir isotherms in Fig. 26a give H/Pt ratios for monolayer adsorption of 1.17 (circles) and 1.06 (triangles). The break point in the Temkin isotherm of Fig. 26b corresponds to H/Pt = 0.82 (48). (The part of the isotherm below 0.1 Torr has not often... 

BET models. The Freundlich isotherm is an empirical relationship, while the Langmuir and BET isotherms are based on theoretical developments. The Langmuir isotherm is based on the concept of monolayer adsorption, while the BET isotherm assumes multilayer adsorption. 

Since different models can be used to represent local adsorption on sites of the same adsorption energy, i.e., energetically homogeneous sites, the current review starts with the very popular and simplistic model formulated by Langmuir in 1918 [96]. This model describes localized monolayer adsorption by neglecting lateral attractive interactions in the surface phase and leads to the following expression for 0 ... 

Many different equations have been used to interpret monolayer—multilayer isotherms [7, 11, 18, 21, 22] (e.g., the equations associated with the names Langmuir, Vohner, HiU-de Boer, Fowler-Guggenheim, Brunauer-Emmett-Teller, and Frenkel-Halsey-Hill). Although these relations were originally based on adsorption models, they are generally applied to the experimental data in an empirical manner and they all have Hmitations of one sort or another [7, 10, 11]. 

In monolayer adsorption, all the adsorbed molecules are in contact with the surface layer of the adsorbent [46]. The adsorbate molecules are thus adsorbed on a fixed number of localized sites, each of which can only hold one adsorbate molecule (the molecules of the adsorbate are not deposited on others already adsorbed, only on the free surface of the adsorbent). The most suitable models describing the monolayer theory are the Langmuir-type ones. They presume that all adsorption sites are energetically equivalent and that there is no interaction between the adsorbed molecules [47]. 

Several other theoretical models [47-49] have attempted to give a more realistic description than the Langmuir and BET models of the gas-surface interactions that lead to physical adsorption. The variable parameters in these models are the interaction potential, the structure of the adsorbed layer (mobile or localized monolayer of multilayer), and the structure of the surface (homogeneous or heterogeneous, number of nearest neighbors). 

The full range of adsorption isotherms under the lUPAC system is shown in Figure 7.46. Brunauer, Emmett and Teller were able to extend Langmuir s theory of monolayer adsorption to obtain an isotherm (the BET equation) which models Type II behaviour, for meso- and macroporous systems. Briefly, in the theory, molecules in one layer act as adsorption sites for molecules in the next layer, so that the adsorbed layer is not of uniform thickness, but rather is made up of a random stack of molecules. The theory has limitations, such as the assumption of liquid-like behaviour in all adsorbed layers but the first however, it has become a... 

Next, we will discuss one of the recent equations introduced by Nitta and his co-workers. This theory based on statistical thermodynamics has some features similar to the Langmuir theory, and it encompasses the Langmuir equation as a special case. Basically it assumes a localised monolayer adsorption with the allowance that one adsorbate molecule can occupy more than one adsorption site. Interaction among adsorbed molecules is also allowed for in their theory. As a special case, when the number of adsorption sites occupied by one adsorbate molecule is one, their theory is reduced to the Fowler-Guggenheim equation, and further if there is no adsorbate-adsorbate interaction this will reduce to the Langmuir equation. Another model of Nitta and co-workers allowing for the mobility of adsorbed molecules is also presented in this chapter. 

---