Multilayer adsorption definition

A still different approach to multilayer adsorption considers that there is a potential field at the surface of a solid into which adsorbate molecules fall. The adsorbed layer thus resembles the atmosphere of a planet—it is most compressed at the surface of the solid and decreases in density outward. The general idea is quite old, but was first formalized by Polanyi in about 1914—see Brunauer [34]. As illustrated in Fig. XVII-12, one can draw surfaces of equipo-tential that appear as lines in a cross-sectional view of the surface region. The space between each set of equipotential surfaces corresponds to a definite volume, and there will thus be a relationship between potential U and volume 0. 

Adsorbents such as some silica gels and types of carbons and zeolites have pores of the order of molecular dimensions, that is, from several up to 10-15 A in diameter. Adsorption in such pores is not readily treated as a capillary condensation phenomenon—in fact, there is typically no hysteresis loop. What happens physically is that as multilayer adsorption develops, the pore becomes filled by a meeting of the adsorbed films from opposing walls. Pores showing this type of adsorption behavior have come to be called micropores—a conventional definition is that micropore diameters are of width not exceeding 20 A (larger pores are called mesopores), see Ref. 221a. 

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. 

Surface Coverage The ratio of the amount of adsorbed material to the monolayer capacity. The definition is the same for either of monolayer and multilayer adsorption. 

Free gel was added to definite concentrations of the MB solutions (2-20 mg/1) at room temperature and was noted for its adsorption. It is clear from Figure 13.3 that the dye adsorption increases sharply with an increase in the initial dye concentration. When Cq was reached at 5 ppm and 10 ppm, the was reached at 10.04 and 20.81 respectively, which were much higher than reported Qe values of other adsorbents (Table 13.3). Equilibrium adsorption isotherm is an important criterion to determine the mechanism of dye adsorption on hydrogel. The Langmuir and Freundlich models are widely used to examine the adsorption isotherms. Freundlich isotherm models are based on the assumption that the surface of the adsorbent is not homogeneous. The experimental data in Figure 13.3 was also analyzed with the Freundlich isotherm model, which describes a heterogeneous system with multilayer adsorption. The linear form of Freundlich isotherm equation... 

Zsigismody, as the first one, drew attention to adsorption on the capillary inner walls which is primary in relation to the capillary condensation [139]. This unusually correct observation corresponds to modern views about the processes of gases and vapours uptake by porous (i.e. industrial) adsorbents. Such a process usually includes mono- and multilayer adsorption followed by the capillary condensation in the final stage of uptake. A quantitative part of capillary condensation in the uptake of a definite vapour changes for different adsorbents depending on their porous structure. This process is dominant for the adsorbents where mesopores constitute a larger part [140]. 

Since with this choice q(N) behaves definitively as qo for large N, the C M theory can predict a phase transition at p = po. The final stages of multilayer adsorption are therefore characterized by a kind of local melting produced by filling molecular voids in the adsorbed slab. This process can also be viewed as a kind of reconstruction occurring in the final stages. 

The final group of equations focuses on the latter stages of adsorption, where the mesopores (ca. 2 nm to 50 nm in width according the lUPAC definition [9,10]) are filled. This is the region where capillary condensation occurs and the Kelvin equation is the simplest of these interpretations. There are numerous variations on the Kelvin equation that account for effects like multilayer adsorption prior to crqrillary condensation (i.e., BJH method [18]), disjoining pressure effects in die condensed liquid (i.e., DBdB method [19]), etc. 

Brunauer, Emmett, and Teller later derived equations for multilayer adsorption which reduce to Langmuir s equation in the case of a monolayer. The hyperbolic isotherm may be written v = VgbP/(l +bP), P = v/b(v —v), or P/v = l/bVg + P/Vg, where is the cc STP of adsorbate required to form a monolayer per gram of adsorbent, and b is a constant dependent on temperature and the nature of the adsorbate and adsorbent. The last form is particularly useful for the extension of data by interpolation since the plot of P/v versus P is linear. At low pressures, or perhaps more definitively low... 

It may also occur that the multilayer adsorption begins only at a definite relative pressure, P, as has been assumed in the modifications of the BET theory. In this case, the basic dynamic equilibrium equation of the cloud (C) model, Eq. (354), should be modified as... 

Perhaps the most important uses of gas adsorption are the estimation of the surface area of materials, the definition of the type of porosity, the computation of pore volumes, and the calculation of pore-size disfribution. For these purposes, an equation for multilayer adsorption will clearly be most usefirl. As is well known, the generalization of Langmuir s equation to the multilayer case is the so-called BET (Brunauer-Emmett-Teller) equation or BET model [164],... 

The definition of fCjr and %j Eq. (148) means that the upper limit of integration in Eq. (52) is equal to the saturation pressure, i.e.,/ uj =pQ or/ j.jjj = 1 if Eq. (52) is written in relative pressures. This upper limit of integration corresponds to the supposition that - according to the BET and other multilayer theories - the total mono-layer capacity ( ) is completed at pQ. The proposed name for Eq. (148) is the TM equation. Where m refers to the multilayer adsorption. 

This definition implies that 0 < 0 < 1, namely that adsorption is limited to a monolayer, which is valid if the bonding of the first layer of the adsorbate to the substrate is much stronger than that of subsequent layers to each other. Multilayer adsorption can occur under suitable conditions, but will not be discussed here. 

It is convenient to divide the extent of adsorption into three categories submonolayer, monolayer, and multilayer. We discuss them in this order. The thermodynamics of adsorption may be developed around experimental isotherms or around calorimetric data. We begin with the definition of adsorption isotherms and how they are determined experimentally (Section 9.2). 

For small inert molecules it can be difficult to assess directly the monolayer, as the heat of adsorption is so small that it approaches the heat of condensation. This leads to parallel adsorption in the first and subsequent layers and therefore does not allow definition of the monolayer capacity. A way to circumvent this difficulty is to determine the adsorption in the presence of multilayers and to relate the sorbed amount to the monolayer capacity. This approach was first... 

Discussing and comparing the basic adsorption theories presented so far, it is difficult to say which one is fundamentally right. The Polanyi thermodynamic theory neither determines a definite adsorption isotherm equation nor gives a detailed mechanism of the process. Development of this theory for description of adsorption on microporous substances leads to the analytical DR equation but its character is semiempirical. The Langmuir and BET theories introduce the concept of localized mono- and multilayer formed on the energetically homogeneous solid surface. 

In Eq. (354), k and k are kinetic constants of the rate of adsorption and desorption, respectively, is the average heat of adsorption taking place on the first (already adsorbed) layer, is the total (monolayer plus multilayer) adsorbed amount, and n is the amount of gas adsorbed onto the first layer only. From the definitions of n, rf and n it follows that... 

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