Multilayer adsorption surface area

Adsorption may in principle occur at all surfaces its magnitude is particularly noticeable when porous solids, which have a high surface area, such as silica gel or charcoal are contacted with gases or liquids. Adsorption processes may involve either simple uni-molecular adsorbate layers or multilayers the forces which bind the adsorbate to the surface may be physical or chemical in nature. 

Brunauer (see Refs. 136-138) defended these defects as deliberate approximations needed to obtain a practical two-constant equation. The assumption of a constant heat of adsorption in the first layer represents a balance between the effects of surface heterogeneity and of lateral interaction, and the assumption of a constant instead of a decreasing heat of adsorption for the succeeding layers balances the overestimate of the entropy of adsorption. These comments do help to explain why the model works as well as it does. However, since these approximations are inherent in the treatment, one can see why the BET model does not lend itself readily to any detailed insight into the real physical nature of multilayers. In summary, the BET equation will undoubtedly maintain its usefulness in surface area determinations, and it does provide some physical information about the nature of the adsorbed film, but only at the level of approximation inherent in the model. Mainly, the c value provides an estimate of the first layer heat of adsorption, averaged over the region of fit. 

Surface areas are deterrnined routinely and exactiy from measurements of the amount of physically adsorbed, physisorbed, nitrogen. Physical adsorption is a process akin to condensation the adsorbed molecules interact weakly with the surface and multilayers form. The standard interpretation of nitrogen adsorption data is based on the BET model (45), which accounts for multilayer adsorption. From a measured adsorption isotherm and the known area of an adsorbed N2 molecule, taken to be 0.162 nm, the surface area of the soHd is calculated (see Adsorption). 

The principle underlying surface area measurements is simple physisorb an inert gas such as argon or nitrogen and determine how many molecules are needed to form a complete monolayer. As, for example, the N2 molecule occupies 0.162 nm at 77 K, the total surface area follows directly. Although this sounds straightforward, in practice molecules may adsorb beyond the monolayer to form multilayers. In addition, the molecules may condense in small pores. In fact, the narrower the pores, the easier N2 will condense in them. This phenomenon of capillary pore condensation, as described by the Kelvin equation, can be used to determine the types of pores and their size distribution inside a system. But first we need to know more about adsorption isotherms of physisorbed species. Thus, we will derive the isotherm of Brunauer Emmett and Teller, usually called BET isotherm. 

Figure 5.19 shows an idealized form of the adsorption isotherm for physisorption on a nonporous or macroporous solid. At low pressures the surface is only partially occupied by the gas, until at higher pressures (point B on the curve) the monolayer is filled and the isotherm reaches a plateau. This part of the isotherm, from zero pressures to the point B, is equivalent to the Langmuir isotherm. At higher pressures a second layer starts to form, followed by unrestricted multilayer formation, which is in fact equivalent to condensation, i.e. formation of a liquid layer. In the jargon of physisorption (approved by lUPAC) this is a Type II adsorption isotherm. If a system contains predominantly micropores, i.e. a zeolite or an ultrahigh surface area carbon (>1000 m g ), multilayer formation is limited by the size of the pores. 

The amount of species of the adsorbed substance j (adsorbate) per unit area of the trae surface area of the electrode or of any other adsorbent will be labeled Aj and will be called real adsorption (in contrast to the notion of Gibbs adsorption T see Section 10.4.1). In the limiting case, all adsorbed particles are packed right again the adsorbent s surface. This limiting case is called monolayer adsorption. In other cases, several layers of the adsorbate can form on the adsorbent s surface multilayer adsorption). 

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). 

For microporous materials the 5bet values obtained are usually much higher than the real surface area, because in the region where the BET equation is applied (this equation assumes multilayer adsorption but not condensation) conden.sation already takes place. 

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 full interpretation of the relationships between direct or vat dye structure and substantivity for cellulose must take into account the contribution of multilayer adsorption of dye molecules within the pore structure of the fibre [71]. The great difference in substantivity between Cl Direct Red 28 (3.66) and the monoazo acid dye (3.67) that is the half-size analogue of this symmetrical disazo dye may be interpreted in terms of their relative tendencies to form multilayers within the fibre pores as a result of dye-dye aggregation. Saturation adsorption values of these two dyes on viscose fibres at pH 9 and 50 °C corresponded to monolayer coverage areas of approximately 90 and 11 m2/g of internal surface respectively [72]. In view of the smaller molecular area and greater mobility of the half-size acid dye, higher uptake than the direct dye would be anticipated if there were only a limited area of internal surface available for true monolayer adsorption. 

The determination of the specific surface area of a zeolite is not trivial. Providers of zeolites typically give surface areas for their products, which were calculated from gas adsorption measurements applying the Brunauer-Emmet-Teller (BET) method. The BET method is based on a model assuming the successive formation of several layers of gas molecules on a given surface (multilayer adsorption). The specific surface area is then calculated from the amount of adsorbed molecules in the first layer. The space occupied by one adsorbed molecule is multiplied by the number of molecules, thus resulting in an area, which is assumed to be the best estimate for the surface area of the solid. The BET method provides a tool to calculate the number of molecules in the first layer. Unfortunately, it is based on a model assuming multilayer formation. Yet, the formation of multilayers is impossible in the narrow pores of zeolites. Specific surface areas of zeolites calculated by the BET method (often termed BET surface area) are therefore erroneous and should not be mistaken as the real surface areas of a material. Such numbers are more related to the pore volume of a zeolite rather than to their surface areas. 

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... 

The simplest measure of surface area is that obtained by the so-called point B method. Many isotherms of Type II or IV show a straight section at intermediate relative pressures. The more pronounced the section, the more complete is the adsorbed monolayer before multilayer adsorption begins. As may be seen from Figure 17.9, the lower limit of the straight section is the point B which was identified by Emmett 24 and Yang 3 as corresponding to a complete monolayer. This interpretation is accepted as a convenient empiricism. 

Although there are several methods for analysis of nitrogen physisorption data, the most commonly used is BET surface area. Because for microporous materials the boundary conditions for multilayer adsorption are not fulfilled, the calculated BET surface area has no physical meaning. Such data should be considered proportional to the total micropore volume rather than the specific surface area. The Tplot method can be used to calculate the micropore volume and the mesopore... 

The majority of physisorption isotherms (Fig. 1.14 Type I-VI) and hysteresis loops (Fig. 1.14 H1-H4) are classified by lUPAC [21]. Reversible Type 1 isotherms are given by microporous (see below) solids having relatively small external surface areas (e.g. activated carbon or zeolites). The sharp and steep initial rise is associated with capillary condensation in micropores which follow a different mechanism compared with mesopores. Reversible Type II isotherms are typical for non-porous or macroporous (see below) materials and represent unrestricted monolayer-multilayer adsorption. Point B indicates the stage at which multilayer adsorption starts and lies at the beginning of the almost linear middle section. Reversible Type III isotherms are not very common. They have an indistinct point B, since the adsorbent-adsorbate interactions are weak. An example for such a system is nitrogen on polyethylene. Type IV isotherms are very common and show characteristic hysteresis loops which arise from different adsorption and desorption mechanisms in mesopores (see below). Type V and Type VI isotherms are uncommon, and their interpretation is difficult. A Type VI isotherm can arise with stepwise multilayer adsorption on a uniform nonporous surface. 

Nitrogen sorptiometry, also referred to as BET method (named after their inventors Brunauer [202], Brunauer and Emmet [203], and Teller and coworkers [204]), is an approach for the determination of the specific surface area of a (porous) support material based on the multilayer adsorption of nitrogen at the temperature of liquid nitrogen (77 K) according to following procedure ... 

Lippens and deBoer have shown that a plot of the volume adsorbed versus t calculated from equation (8.24) will yield a straight line of slope S X 10 from which the surface area can be calculated. Plots of this nature are termed V-t curves and generally give surface areas comparable to BET values provided that multilayer adsorption and not condensation into the pores takes place. 

In the Langmuir derivation the adsorbed molecules are allowed to interact with the adsorbent but not with each other The adsorbed layer is assumed to be ideal. This necessarily limits adsorption to a monolayer. Once the surface is covered with adsorbed molecules, it has no further influence on the system. The assumption that adsorption is limited to monolayer formation was explicitly made in writing Equations (72) and (73) for the saturation value of the ordinate. Ii is an experimental fact, however, that adsorption frequently proceeds to an extent that exceeds the monolayer capacity of the surface for any plausible molecular orientation at the surface. That is, if monolayer coverage is postulated, the apparent area per molecule is only a small fraction of any likely projected area of the actual molecules. In this case the assumption that adsorption is limited to the monolayer fails to apply. A model based on multilayer adsorption is indicated in this situation. This is easier to handle in the case of gas adsorption, so we defer until Chapter 9 a discussion of multilayer adsorption. 

If the specific area of the solid is the information sought, it is the amount of adsorption at monolayer coverage that must be measured. This is readily available in Type I adsorption, but requires considerable interpretation when multilayer adsorption takes place. Once determined, however, the number of molecules required to saturate a surface times the area occupied per molecule gives the surface area of a sample. This divided by the mass of the sample gives Asp. In addition, once the adsorption at monolayer coverage is identified, all other extents of adsorption can be expressed as fractions or multiples of the monolayer. 

With monolayer adsorption, we saw how the saturation limit could be related to the specific surface area of the adsorbent. The BET equation permits us to extract from multilayer adsorption data (by means of Equation (77)) the volume of adsorbed gas that would saturate the surface if the adsorption were limited to a monolayer. Therefore Vm may be interpreted in the same manner that the limiting value of the ordinate is handled in the case of monolayer adsorption. Since it is traditional to express both V and Vm in cubic centimeters at STP per gram, we write (see Equation (7.72))... 

Kuge and Yoshikawa (3) related a change in the gas chromatographic peak shape to the beginning of multilayer adsorption on the surface of the solid. For small adsorbate volumes, the peak shape is symmetrical. As the adsorbate volume is increased, a sharp front, diffuse tail, and a defect at the front of the peak top is observed (Figure 11.2). It then acquires a diffuse front and sharp tail. This point corresponds to the B point of the BET Type II adsorption isotherm at which the relative surface area may be calculated. 

The fact that all the fibers adsorb water in excess of the expected monolayer amounts suggests that the water adsorption is multilayer in nature, or that there is pore space which is accessible to water molecules—but not accessible to the Kr used to measure the specific surface area. The XPS analyses showed that the silane overlayers increased in thickness in the 4% and 6% B,03 fibers. But the increase in water adsorptivity with % B,03 is not in direct proportion to the increase in silane overlayer thickness it is considerably larger. This suggests that B,0, has influenced the chemical and physical structure of the adsorbed silane overlayer. It is likely that there is microporosity, free volume, and/or reactive sites within the silane overlayer, in general. 

Step isotherms (type H) are observed with porous materials and characterized by a second inhibition. At low pressure a single layer of molecules adsorbs to the surface as for Langmuir adsorption. At intermediate pressures, multilayers start to form and the pores are filled. The saturation at high pressures is caused by the reduction of effective surface area once the pores have been filled. 

The foregoing represent the classic models for physical adsorption, that of Langmuir (monomolecular adsorption and constant AH is, independent of the extent of surface coverage) and BET (multilayer adsorption and several AHacjs components). Many other models are available as well [13,15,30], These models require a knowledge of the area which each molecule occupies on the surface. 

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