Monolayer adsorption theory

The Monolayer Adsorption Theory of Polyatomic Lattice Gases from QFS... 

Langmuir investigated adsorption phenomena systematically in the early 20th century and proposed the famous monolayer adsorption theory in 1918. Langmuir s theory is the foundation of the kinetics of surface catalytic reaction. Other adsorp>-tion theories basically are the amendment or supplement to Langmuir s adsorption theory. 

BET method. The most commonly used method for determining the specific surface area is the so-called BET method, which obtained its name from three Nobel prize winners Brunauer, Emmett and Teller (1938). It is a modification of the Langmuir theory, which, besides monolayer adsorption, also considers multilayer adsorption. The equation allows easy calculation of the surface area, commonly referred to as the BET surface area ( bet). From the isotherms also pore-radii and pore-volumes can be calculated (from classical equation for condensation in the pores). 

A major advance in adsorption theory generalized the treatment of monolayer adsorption and incorporated the concept of multilayer adsorption. This is known as the BET theory after Brunauer, Emmett and Teller [32], The adsorption of a gas on a solid surface can be described by... 

The Gibbs adsorption theory (Birdi, 1989,1999, 2002, 2008 Defay et al., 1966 Chattoraj and Birdi, 1984) considers the surface of liquids to be monolayer. The surface tension of water decreases appreciably on the addition of very small quantities of soaps and detergents. The Gibbs adsorption theory relates the change in surface tension to the change in soap concentration. The experiments that analyze the spread monolayers are also based on one molecular layer. The latter data indeed conclusively verifies the Gibbs assumption (as described later). Detergents (soaps, etc.) and other similar kind of molecules are found to exhibit self-assembly characteristics. The subject related to self-assembly monolayer (SAM) structures will be treated extensively (Birdi, 1999). However, no procedure exists that can provide information by direct measurement. The composition of the surface of a solution with two components or more would require additional comments. 

Uniform accessibility and reactivity of the electrode interface are the main hypotheses for developing the EHD impedance theory. However, in many cases a real interface deviates from this ideal picture due for example either to incomplete monolayer adsorption leading to the concept of partial blocking (2D adsorption) or to the formation of layers of finite thickness (3 D phenomena). 

Some time ago Brunauer (1970) argued that monolayer adsorption of nitrogen and other small molecules does occur on the walls of micropores wider than about 0.7 nm. Although as we have seen, Brunauer s original theory is now questionable, some recent evidence does support his view that monolayer adsorption can take place on the walls of the wider micropores before secondary micropore Ailing occurs. These aspects are discussed in later chapters. 

Particle Surface Area Determination Methods From the standard definitions of particle surface area, it can be seen that various determination methods are used for surface area measurement, such as adsorption (including Langmuir s equation for monolayer adsorption and the BET equation for multilayer adsorption), particle size distribution, and permeability methods. The different methods are rarely in agreement because the value obtained depends upon the procedures used and also on the assumptions made in the theory relating the surface area to the phenomena measured. The most common methods used for measuring particle surface area are described below. 

Using the lattice-gas theory of monolayer adsorption in the mean field (or Bragg-Williams) approximation gives the C,T dependence of n, i.e. the vacancy isotherm, in the form [402,403]... 

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 Horvath-Kawazoe (HK) method is capable of generating model isotherms more efficiently than either molecular simulation (MS) or density functional theory (DFT) to characterize the pore size distribution (PSD) of microporous solids. A two-stage HK method is introduced that accounts for monolayer adsorption in mesopores prior to capillary condensation. PSD analysis results from the original and two-stage HK models are evaluated. 

The measurement of pore size distributions is well established. However, the use of BET surface area measurements for zeolitic materials has been called into question due to potential multiple adsorption and nonconformity of monolayer adsorption implicite in the BET theory. The type of gas used, the method of data analysis, and even the use of the term surface area for a zeolitic material has been seriously questioned lately. On the other hand, most commercial manufacturers supply a surface area determined often by a three point or even a one point procedure that some researchers feel tells something about the material. 

The main hypotheses for developing the EHD impedance theory are that the electrode interface is uniformly accessible and the electrode surface has uniform reactivity. However, in many cases, real interfaces deviate from this ideal picture due, for example, either to incomplete monolayer adsorption leading to the concept of partial blocking (2-D adsorption) or to the formation of layers of finite thickness (3-D phenomena). These effects do not involve the interfacial kinetics on bare portions of the metal, which, for simplification, will be assumed to be inherently fast. The changes will affect only the local mass transport toward the reaction sites. Before presenting an application of practical interest, the theoretical EHD impedance for partially blocked electrodes and for electrodes coated by a porous layer will be analyzed. 

Very interesting studies have been made of the pattern for UPD on single crystal metal substrates [49]. A commensurate pattern is usually observed for the formation of a partial monolayer. The theory of UPD and formation of the initial monolayer is an area of active research. Of course, the phenomenon of UPD is restricted to formation of a monolayer. Once this has formed, the deposition process reverts to one of metal ion M"+ on metal M. By comparing the UPD process with anion-specific adsorption, the role of partial charge transfer in these processes is clarified. 

Physisorption arises from the van der Waals forces, and these forces also condense gas molecules into their liquid state. Thus, in principle, there is no reason to stop upon completion of a monolayer during physisorption. Indeed, the formation of multi-layers, which are basically liquid in nature, is very common in physisorption experiments. Brunauer, Emmett and Teller developed a theory in 1938 to describe physisorption, where the adsorbate thickness exceeds a monolayer, and this isotherm equation is known by the initials of the authors (B.E.T.). The original derivation of the B.E.T. equation is an extension of Langmuir s treatment of monolayer adsorption from kinetic arguments. Later, in 1946, Hill derived this equation from statistical mechanics. In the B.E.T. isotherm, it is assumed that ... 

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]. 

The new capillary condensation theory, if essentially valid, claims that the shape of isotherms measured up to saturation, that is, x = PjP = 1, is determined by the pore size distribution of porous bodies, and so any theory to explain sorption isotherms by thermodynamic or kinetic mechanisms becomes meaningless except with respect to the formation of monolayer adsorption. Therefore an important problem in sorption is to investigate the pore structure of sorbent specimens, which are easily varied by varying the conditions of their preparation, and to elucidate the pore structure in relation to the material properties. 

In Secs. II and III we shall summarize the present state of the theory of physical adsorption, starting with the simplest case of essentially independent molecules on a surface (very low equilibrium gas pressure) and then considering monolayer adsorption with interactions, and finally multilayer adsorption. In Sec. IV, the thermodynamics of adsorption will be discussed. 

In this respect and regarding the discussion on the initial passivations, as pointed out by an increasing number of writers, the oxide-film and adsorption theories do not contradict but rather supplement one another. In looking at the primary act of passivation as the formation of a tightly held monolayer containing oxide or hydroxide anions and metal... 

The molecular adsorption isotherm on nonporous solids can be well described by the BET theory. The deviation from the linearity of the t plot gives information on the sort of pores, the average pore size, the surface area, and the pore volume. However, the t plot analysis has the limited applicability to the microporous system due to the absence of explicit monolayer adsorption. The construction of the alpha plot does not need the monolayer capacity, so that it is applicable to microporous sohds. 

Although particle size measurement methods mentioned in 3.2 earher provide information on surface area, those methods are based on the assumption that the particles are smooth sohd spheres without taking particle morphology into consideration. Unlike those methods, BET measurements are based on monolayer adsorption of gas molecules on the surface of sohd materials. These methods can also be used to reflect the surface morphology of particles (e.g., porosity). The BET theory was first pubhshed in 1938 by Brunauer et al. [67]. The BET theory is expressed in the equation in the succeeding text ... 

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. 

The theory of Nitta et al. (1984) assumes a localised monolayer adsorption on surface with an allowance for multi-site adsorption. This is an extension of the Langmuir isotherm for localised monolayer adsorption. Nitta et al. s theory is based on the statistical thermodynamics, and its derivation is given briefly below. 

The BET theory is an extension of Langmuir s theory of monolayer adsorption to multilayer adsorption with the following hypotheses (i) physical adsorption in layers infinitely, (ii) no interaction between the layers, (iii) Langmuir theory is... 

Whatever is the mechanism of OHad and Oad formation, the principal point of this adsorption theory is that Pt surface atoms are stable in their positions in the lattice and the integrity of the Pt lattice is retained after an adsorption-desorption cycle in the voltammetry studies. The formation of adsorbed layer is described quantitatively by adsorption isotherms at equilibrium, e.g., Temkin or Frumkin adsorption isotherms and corresponding kinetic equations such as the Elovich equation. Intrinsic to the adsorption theory is the concept of the maximum surface concentration corresponding to monolayer coverage by the ad-particles on all available adsorption sites. " ... 

The second type of isotherms are S-shape curves, which happen frequently in experimental measurements, corresponding to the adsorption on mesoporous (pore size >20 nm) solid materials. The first bend in the isotherm should correspond to the monolayer saturation, but no horizontally stable level appears which means that adsorption can be multilayer rather than monolayer. The section of the curve at high pressures goes up very fast due to the occurrence of capillary condensation in small pores. Other types of isotherms also predict the occurrence of multilayer adsorption. So, the assumption of monolayer absorption proposed by Langmuir has to be modified, and thereafter BET, Temkin s and Preudlich s adsorptive theory were developed. 

The first theoretical treatment of adsorption on sohd surfaces was the famous theory of Langmuir, which still occupies a central position in surface science [23]. His well-known equation describes localized, monolayer adsorption on homogeneous adsorbent when attractive interactions between adsorbed molecules are neglected ... 

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