The Brunauer, Emmett and Teller BET theory

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. 

Using the Langmuir theory and equation (4.5) as a starting point to describe the equilibrium between the vapor and the adsorbate in the first layer 

By analogy, for the fraction of surface covered by two layers one may write 

The BET theory assumes that the terms v, E and A remain constant for the second and higher layers. This assumption is justifiable only on the grounds that the second and higher layers are all equivalent to the liquid 

Replacing 6 in equation (4.27) with 6q from equation (4.18d) yields 

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The most definitive surface area measurements are probably those made by nitrogen adsorption using the BET theory. Neither the Brunauer, Emmett and Teller (BET) theory nor equation (11.5), used to calculate surface area from mercury intrusion data makes any assumptions regarding pore shape for surface area determinations. When these two methods are compared there is often surprisingly good agreement. When... 

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... 

Most subsequent sorption theories, including those discussed here, have followed this general approach and postulate two forms of sorbed water. These theories may be classified into at least two general types based on the sorption mechanism assumed. One type assumes sorption on internal surfaces and is represented by the Dent theory (52), which is a modification of the classic Brunauer, Emmett, and Teller (BET) theory (53). The second type assumes that the wood-water system forms a solution, exemplified by the Hailwood-Horrobin theory. There have been other theories, not discussed here, that have also been applied to explain water sorption by hygroscopic materials (JO, 54, 55). 

The mathematical models that have been applied to the physical adsorption from liquid solutions are generally extensions of the theories that have been developed to describe the sorption of gases on solid surfaces with modifications to account for the competition between the solute and solvent for the adsorption sites. Two of these models have been applied to the adsorption isotherms of nonelectrolytes from solution they are the Langmuir model and the Brunauer, Emmett, and Teller (BET) model in addition the Freundlich empirical equation has also been used. In the Langmuir model it is assumed that the adsorbed species forms a monolayer on the surface of the adsorbent, that the adsorbed molecules... 

The most well-known method for determining the specific surface area of powders is based on a theory of multimolecular adsorption of gases developed by Brunauer, Emmett, and Teller (BET) (1). The BET method involves the determination of the quantity of a gas which, when adsorbed on the surface of the solid, would completely cover the solid with a monolayer of the gas. 

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

The theory of physical adsorption of gas molecules on solid surfaces was derived by Brunauer, Emmett, and Teller (BET). The theory serves as the basis for the most widely used technique to assess specific surface area of powders and solids. It extends the Langmuir isotherm concept. 

To obtain the monolayer capacity from the isotherm, it is necessary to interpret the (Type II) isotherm in quantitative terms. A number of theories have been advanced for this purpose from time to time, none with complete success. The best known of them, and perhaps the most useful in relation to surface area determination, is that of Brunauer, Emmett and Teller. Though based on a model which is admittedly over-simplified and open to criticism on a number of grounds, the theory leads to an expression—the BET equation —which, when applied with discrimination, has proved remarkably successful in evaluating the specific surface from a Type II isotherm. 

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. 

Brunauer, Emmett, and Teller extended the Langmuir theory to multimolecular layer adsorption [8]. They related the condensation rate of gas molecules onto an adsorbed layer and the evaporation rate from that layer for an infinite number of layers. The linear form of the relationship is called the BET equation ... 

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... 

In 1938, Brunauer, Emmett and Teller(12) and Emmett and de Witt(13) developed what is now known as the BET theory. As in the case in Langmuir s isotherm, the theory is based on the concept of an adsorbed molecule which is not free to move over the surface, and which exerts no lateral forces on adjacent molecules of adsorbate. The BET theory does, however, allow different numbers of adsorbed layers to build up on different parts of the surface, although it assumes that the net amount of surface which is empty or which is associated with a monolayer, bilayer and so on is constant for any particular equilibrium condition. Monolayers are created by adsorption on to empty surface and by desorption from bilayers. Monolayers are lost both through desorption and through the adsorption of additional layers. The rate of adsorption is proportional to the frequency with which molecules strike the surface and the area of that surface. From the kinetic theory of gases, the frequency is proportional to the pressure of the molecules and hence ... 

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. 

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). 

Finally, one could say that if Brunauer, Emmett and Teller had used the linear transformations (6) or (7) to check their model, the BET theory would not have been published. Indeed, we would have been left without one of the most interesting theories and one of the simplest models for the determination of the surface area of many solids. 

We have continued to report BET sorption capacities (expressed as specific surface areas) in light of current practices. Such practice allows us to compare our results to those reported by others where no other measure of sorption capacity is given. This is really a tribute to the landmark work of Brunauer, Emmett, and Teller (8), for providing a comprehensive and useful tool for studying surface phenomena. The fault lies in the application of the theory beyond its realm of applicability. Even the concept of internal surface area derived in this manner is misleading. Actually, the BET sorption capacity is only a measure of the sorption capacity in the region of the knee and probably should be reported in concentration terms (mmol/g, mg/g, cm (STP)/g, etc.) to avoid providing an erroneous concept to the novice. 

One of the most widely used isotherms is based on the BET theory, named from the initials of Brunauer, Emmett, and Teller. The BET theory is an extension of the Langmuir isotherm to include the adsorption of two or more molecular layers assuming, in addition to assumptions 1-3 listed above, that... 

Gas adsorption is the preferred method of surface-area determination. An isotherm is generated of the amount of gas adsorbed against gas pressure, and the amount of gas required to form a monolayer is determined. The surface area can tTien be calculated using the cross-sectional area of the gas molecule. Outgassing of the powder before analysis should be conducted very carefully to ensure reproducibility. Commonly, nitrogen at liquid nitrogen vapor pressure is used but, for low surface-area powders, the adsorbed amounts of krypton or xenon are more accurately found. Many theories of gas adsorption have been advanced, but measurements are usually interpreted by using the BET theory [Brunauer, Emmett, and Teller, J. Am. Chem. Soc., 60,309 (1938)]. 

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). 

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... 

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. 

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 ... 

Figure 3.3.43 Shapes of adsorption isotherms according to the BET (Brunauer, Emmett, and Teller) theory for various values of Cbet (not considering capillary condensation and surface inhomogeneities) (a) Equation (3.3.47a) for an unlimited number of layers (b) n-layer BET equation for Cbet = 100, if the number cannot exceed Umax, that is, for adsorption in a limited space such as a capillary, Eq. (3.3.47b).

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. 

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... 

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