Brunauer-Emmett-Teller multilayer theory

Popper and Bariska (1972) studied the moisture sorption properties of wood chemically modified with acetic (or phthalic) anhydride and analysed the results using Brunauer-Emmett-Teller (BET) theory and the H-H model. Acetylation was found to reduce the number of sorption sites, whereas little effect was noted with phthaloylation. By dividing the sorption isotherm into a monolayer component and a multilayer component using the H-H model, it was shown that there was a large reduction in the... 

Because the Langmuir isotherm is not an adequate description of most systems, Equation (2.9) is not used much for area measurement. A number of other isotherm formulations utilize adsorption in surface area measurements, however (cf. Young Crowell, 1962, for example). The best known and most widely used is the BET (Brunauer, Emmett Teller, 1938) theory, a generalization of the Langmuir model to multilayer absorption. Assuming that for the second and succeeding molecular... 

The Brunauer-Emmett-Teller (45) theory of physical adsorption was the first and is still probably the best and most useful theory of multilayer adsorption covering the complete range in p. This is not to say, however, that it is a really satisfactory theory. As will be made clear below, the assumptions of the theory are extremely crude, but they are still sufficiently good to contain a number of the important qualitative features actually observed experimentally. The role of the BET theory in physical adsorption is in fact rather analogous to that of the van der Waals equation in the theory of liquids it was the first important theory in the field it has stimulated virtually all the work that followed it it is still extremely useful as a qualitative guide but it is not quantitatively correct. 

Direct methods of measuring adsorption are essentially restricted to the measurements of adsorption at the solid surface from a gas phase. At sufficiently high specific surface area, 5i (m /g), the adsorption can be determined directly as the increase in mass. High-surface-area materials include highly disperse adsorbents with fine pores, such as activated charcoal, zeolites, and various catalysts for which the surface area is on the order of tens and hundreds of square meters per gram. The adsorption on such surfaces from a gas phase can also be determined by measuring a decrease in the gas (vapor) pressure, p, in a closed vessel. The multilayer adsorption of noncorrosive gasses is a commonly used method to determine the surface area of adsorbents on the basis of the Brunauer-Emmett-Teller (BET) theory included in all classic texts on physical chemistry. 

The sigmoidal shape of the nitrogen isotherm of Figure 1 is quite amenable to analyses by the Brunauer-Emmett-Teller (BET) multilayer theory (8). The BET surface area calculated is 2.8 mVg. This value is quite consistent with the predominant l-to-10- xm size distribution observed on this sample with an optical microscope. Assuming cubic habits and density of about 2.3 g/cm, we find the range of specific surface area to be 0.26 to 2.6 m /g. Apparently the sorbed N2 does penetrate into the internal portion of the particles only to a limited extent. 

Brunauer-Emmett-Teller (BET) [20], Langmuir isotherm theory is applied when a monolayer of molecules is sorbed on a homogeneous surface where each site requires the same energy to adsorb molecules. The Freundlich isotherm also assumes a monolayer, but allows for an exponential distribution of adsorption energies. BET isotherms provide for multilayer adsorption. 

The adsorption isotherms provide information about the surface properties of the fibres or paper in the column. For example, the surface area in the column may be deduced from the shape of the isotherm according to the Brunauer-Emmett-Teller theory for multilayer adsorption (13, lJO. This theory gives the number of molecules, Nm, which forms a layer one molecule thick on the surface of the adsorbent. If the area, am, occupied by each vapour molecule adsorbed on the surface is known, then the total surface area, A, is simply given by... 

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). 

Conventional bulk measurements of adsorption are performed by determining the amount of gas adsorbed at equilibrium as a function of pressure, at a constant temperature [23-25], These bulk adsorption isotherms are commonly analyzed using a kinetic theory for multilayer adsorption developed in 1938 by Brunauer, Emmett and Teller (the BET Theory) [23]. BET adsorption isotherms are a common material science technique for surface area analysis of porous solids, and also permit calculation of adsorption energy and fractional surface coverage. While more advanced analysis methods, such as Density Functional Theory, have been developed in recent years, BET remains a mainstay of material science, and is the recommended method for the experimental measurement of pore surface area. This is largely due to the clear physical meaning of its principal assumptions, and its ability to handle the primary effects of adsorbate-adsorbate and adsorbate-substrate interactions. 

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... 

Brunauer, Emmett and Teller, in 1938, extended Langmuir s kinetic theory to multilayer adsorption. The BET theory assumes that the uppermost molecules in adsorbed stacks are in dynamic equilibrium with the vapor. This means that, where the surface is covered with only one layer of adsorbate, an equilibrium exists between that layer and the vapor, and where two layers are adsorbed, the upper layer is in equilibrium with the vapor, and so forth. Since the equilibrium is dynamic, the actual location of the surface sites covered by one, two or more layers may vary but the number of molecules in each layer will remain constant. 

As noted above, the range of pressures over which gas adsorption studies are conducted extends from zero to the normal vapor pressure of the adsorbed species p0. An adsorbed layer on a small particle may readily be seen as a potential nucleation center for phase separation at p0. Thus at the upper limit of the pressure range, adsorption and liquefaction appear to converge. At very low pressures it is plausible to restrict the adsorbed molecules to a mono-layer. At the upper limit, however, the imminence of liquefaction suggests that the adsorbed molecules may be more than one layer thick. There is a good deal of evidence supporting the idea that multilayer adsorption is a very common form of physical adsorption on nonporous solids. In this section we are primarily concerned with an adsorption isotherm derived by Brunauer, Emmett, and Teller in 1938 the theory and final equation are invariably known by the initials of the authors BET. 

In Langmuir model, the maximal adsorption is that of a monolayer. Langmuir adsorption isotherms all saturate at high vapor pressures. This is unrealistic for many cases. In order to consider the adsorption of multilayers, Brunauer, Emmett, and Teller extended the Langmuir theory and derived the so-called BET adsorption isotherm [378], The basic idea in the BET theory was to assume a Langmuir adsorption for each of the layers (Fig. 9.8). 

The BET theory, developed by Brunauer, Emmett, and Teller [26], is based on the kinetic model of adsorption proposed by Langmuir [24,25] and was extended to describe the multilayer adsorption by the introduction of some assumptions listed below ... 

The method as a rule used for the determination of the specific surface of a material is the Brunauer-Emmet-Teller (BET) method [2,4,5], The BET theory of multilayer adsorption for the calculation of specific surface area, S, was originally developed by Brunauer, Emmett, and Teller [2,4,5], The adsorption process, within the frame of the BET theory, is considered as a layer-by-layer process. In addition, an energetically homogeneous surface is assumed so that the adsorption field is the same in any site within the surface. Additionally, the adsorption process is considered to be immobile, that is, each molecule is adsorbed in a concrete adsorption site in the surface. Subsequently, the first layer of adsorbed molecules has an energy of interaction with the adsorption field, and a vertical interaction between molecules after the first layer,, is explicitly analogous to the liquefaction heat of the adsorbate. Besides, adsorbed molecules do not interact laterally. 

By introducing a number of simplifying assumptions, Brunauer, Emmett and Teller (1938) were able to extend the Langmuir mechanism to multilayer adsorption and obtain an isotherm equation (the BET equation), which has Type II character. The original BET treatment involved an extension of the Langmuir kinetic theory of monomolecular adsorption to the formation of an infinite number of adsorbed layers. 

BET surface area the surface area calculated from the Brunauer, Emmett, and Teller theory of multilayer adsorption of a gas on a solid surface. 

Brunauer, Emmett, and Teller were the first to propose a theory for multilayer adsorption (BET theory). Since the behavior of adsorbed molecules is even more difficult to describe in detail than that of molecules in the liquid state, the BET theory contains some rather drastic assumptions. In spite of this, it is still a generally useful theory of physical adsorption. The BET theory gives a correct semiquantitative description of the shape of the isotherm and provides a good means of evaluating (which is then used to estimate the surface area of the soM). 

Water vapor adsorption isotherms have been obtained on cotton from room temperature up to 150°C [303,304]. Theoretical models for explaining the water vapor sorption isotherms of cellulose have been reviewed [303]. Only adsorption theories will be discussed here at ambient temperatures. The shape of the isotherm indicates that multilayer adsorption occurs and thus the Brunauer, Emmett and Teller (BET) or the Guggenheim, Anderson and deBoer (GAB) theory can be applied. In fact, the BET equation can only be applied at relative vapor pressures (RVPs) below 0.5 and after modification up to a RVP of 0.8 [305]. The GAB equation, which was not discussed in the chapter in the book Cellulose Chemistry and Its Applications [303], can be applied up to RVPs above 0.9 [306]. Initially as the RVP... 

Gas-solid equilibria have been studied for over 200 years, since Fontana showed that activated charcoal adsorbs gases and vapors at room temperature [1]. A considerable amoxmt of theoretical and experimental literature is available. The Gibbs isotherm [2] and the multilayer adsorption theory of Brunauer, Emmett and Teller [3], provide serious theoretical guidelines and support in understanding the results of experimental studies. Although, gas-sohd isotherms are difficult to predict quantitatively [4], this branch of adsorption thermod3mamics is much easier than liquid-solid adsorption because of the relative simplicity of the gas-sohd interface as compared to the liquid-solid interface. The Gibbs equation relates the amoimt of a compoimd adsorbed per unit surface area of a hquid-gas or a hquid-hquid interface and the surface or interfacial tensions [2]. This relationship provides a useful theoretical framework. 

The total surface area is calculated from the amount of physical adsorption of nitrogen at 77 K. During the thirties Brunauer, Emmett, and Teller [1,2] presented a theory dealing with the multilayer adsorption of gases on solids. They assumed that the first layer of gas molecules is adsorbed more strongly than subsequent layers, and that the heat of adsorption of subsequent layers is constant. They also assumed the absence of lateral interaction between adsorbed molecules. On the basis of these much criticized assumptions they derived an adsorption isotherm, which describes the experimentally determined adsorption isotherms excellently. From the adsorption isotherm a value corresponding to the volume of the adsorbed monolayer is calculated. With physical adsorption the amount of gas adsorbed is usually plotted as a function of the relative pressure, that is the pressure... 

A solid particle exposed to a gas will adsorb gas molecules on to its exposed surfaces. The derivation of a multilayer adsorption theory for gases on solid surfaces by Brunauer, Emmett and Teller in 1938 led to the development of the so-called BET adsorption methods for measuring the specific surface area of particulate solids. Several techniques are available (BS 4359/1, 1982 Lowell and Shields, 1984 Allen, 1990). 

All the empirical equations dealt with in Section 3.2 are for adsorption with monolayer coverage, with the exception of the Freundlich isotherm, which does not have a finite saturation capacity and the DR equation, which is applicable for micropore volume filling. In the adsorption of sub-critical adsorbates, molecules first adsorb onto the solid surface as a layering process, and when the pressure is sufficiently high (about 0.1 of the relative pressure) multiple layers are formed. Brunauer, Emmett and Teller are the first to develop a theory to account for this multilayer adsorption, and the range of validity of this theory is approximately between 0.05 and 0.35 times the vapor pressure. In this section we will discuss this important theory and its various versions modified by a number of workers since the publication of the BET theory in 1938. Despite the many versions, the BET equation still remains the most important equation for the characterization of mesoporous solids, mainly due to its simplicity. 

Hence, we had to look for a completely different approach, and finally draw the conclusion, that the vapor pressure of an IL in the particles is governed by multilayer adsorption. This is an analog to the BET theory of Brunauer, Emmett, and Teller, which is well known from gas adsorption [58]. If the height of the sample (fixed bed) is small, the intraparticle vapor pressure is established throughout the small fixed bed, and hence also appears at the face surface of the sample. This Model V is schematically shown in Figure 6.11. 

The milestone towards development of the adsorption science was the multilayer isotherm equation proposed by Brunauer, Emmett and Teller in 1938 [120]. The multilayer adsorption theory was preceded by two significant works by Brunauer and Emmett which appeared in 1935 [121] and 1937 [122]. 

BET Isotherm The Langmuir isotherm does not consider adsorption beyond a monolayer. Multilayer adsorption was treated by Stephen Brunauer, Paul Emmett, and Edward Teller (Brunauer, Emmett and Teller, 1938, see box) and named after the initials of their surnames as the BET theory. The BET theory is an extension of the Langmuir theory to multilayer adsorption with the following hypotheses AadsHmon is the enthalpy of adsorption for the first monolayer, AadsWr is that for the second and higher layers, and the Langmuir theory can be applied to each layer. We then have ... 

Except for type I (Langmuir) isotherms, all the other types referred to in Section 3.2 imply that the extent of adsorption does not reach a limit corresponding to completion of a monolayer. The formation of multilayers, however, is implicit in the theory proposed by Brunauer, Emmett and Teller (1938) who, in agreement with Langmuir, argued that the rate of condensation (adsorption) onto the bare surface equals the rate of evaporation from the first layer of adsorbate. If 0 denotes the fraction of surface which is bare and Zm 01 the number of first layer sites occupied (in which Zm is the number of molecules necessary to complete a monolayer and 0i is the corresponding... 

Various boundary conditions limit each of the theories, hence a range of equations have been developed to cover the various phenomena equation developed by Brunauer, Emmett and Teller commonly known as the BET equation. This equation is for multilayer adsorption, but is based upon the Langmuir equation where adsorption is restricted to a monolayer. Both of these equations are developed below, although the application of the Langmuir equation to gas adsorption is restricted to adsorption in micropores where adsorption is limited to a monolayer due to pore geometry. Langmuir adsorption isotherms are common in adsoiption of solute from solution. 

The most important step in the study of adsorption came with a derivation by Brunauer, Emmett and Teller for the multilayer adsorption of gases on solid surfaces [22]. The multilayer adsorption theory, known generally as the BET equation, has occupied a central position in gas adsorption studies and surface area measurement ever since. 

BET equation An equation used in the theory of multilayer adsorption of atoms onto a surface. It is based on the assumption that the forces that produce condensation of moisture on a surface are also responsible for the binding energy of multilayer adsorption. It is named after Brunauer, Emmett, and Teller. 

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