BET isotherme

Fig. 2.8 The adsorption of nitrogen at 77 K on nonporous samples of silica and alumina, ranging from 2-6 to 11-5 m g for silica and from 58 to 153m g for alumina. n/n is plotted against pjp°. (A) O, silica , alumina. (B) BET isotherm (Equation 2.12) with c values of 100-2(X).

When the value of c exceeds unity, the value of n can be derived from the slope and intercept of the BET plot in the usual way but because of deviations at low relative pressures, it is sometimes more convenient to locate the BET monolayer point , the relative pressure (p/p°) at which n/n = 1. First, the value of c is found by matching the experimental isotherm against a set of ideal BET isotherms, calculated by insertion of a succession of values of c (1, 2, 3, etc., including nonintegral values if necessary) into the BET equation in the form ... 

The classical isotherm for multilayer adsorption on a homogeneous, flat surface is the BET isotherm [Brunauer, Emmett, and Teller, J. Am. Chem. Soc., 60, 309 (1938)]... 

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 5.17. To derive the BET isotherm the surface is divided into regions covered by / adsorbate layers each region is characterized by a fractional coverage Oj...

The BET method has its limitations and several improvements exist, but these are beyond the scope of our treatment. We note that the BET isotherm is valid under the following assumptions ... 

Figure 5.19. Schematic presentation of a Type II BET isotherm, observed with nonporous powders.

Figure S.20. Schematic presentation of a Type I BET isotherm, often observed with zeolites.

Figure 5.21. Schematic presentation of a Type IV BET isotherm, commonly observed for silica and alumina supports.

Give the essential assumptions made in deriving the BET isotherm. Ho v does the BET isotherm differ from the Langmuir isotherm ... 

S. D. Beyea, A. Caprihan, S. J. Glass, A. DiGiovanni 2003, (Non-destructive characterization of nanopore microstructure spatially resolved BET isotherms using nuclear magnetic resonance imaging),/. Appl. Phys. 94 (2), 935—41. 

Inasmuch as the Langmuir equation does not allow for nonuniform surfaces, interactions between neighboring adsorbed species, or multilayer adsorption, a variety of theoretical approaches that attempt to take one or more of these factors into account have been pursued by different investigators. The best-known alternative is the BET isotherm, which derives its name from the initials of the three individuals responsible for its formulation, Brunauer, Em-... 

Sensitivity of the C-constant of BET-isotherm to the content of micropore volume in mesoporous matrix... 

Influence of micropore volume on the value of C-constant of BET-isotherm was studied for series of different zeolites with mesoporous alumina. Results showed the great sensitivity of Cbet value on micropore content especially in the range up to about 7-12 % wt of zeolite, where it increases to extremely high, nonrealistic values (over 1000-2000). 

Keywords C-constant, BET-isotherm, microporous solids, mesoporous matrix, t-plot... 

Physical adsorption of nitrogen was carried out on an ASAP 2400 Micromeritics apparatus. Before measurements, samples were evacuated overnight at 350 °C at vacuum of 2 Pa. For all samples the same adsorption data table was used. Collected adsorption data were treated by BET-isotherm in the range 0.05 < P/micropore volume and mesopore + external surface, t-plot method, with master isotherm of nonporous alumina (Harkins-Jura) was used, t-plot was linearized in the range of 0.35 < t < 0.6 nm. 

Figure 3. Influence of NaY-zeolite content in y-Al203 on the C-constant value of BET-isotherm...

For a given value of n, a plot of straight line from the slope of which V may be calculated. The simpler, infinite, form of the BET isotherm is given by equation 17.15. The appropriate plot gives a straight line, from the slope and intercept of which V may be calculated. Equation 17.15 is most likely to apply at low relative pressures. 

The results of Na versus Pa are analyzed by an equation first derived by Brunauer, Emmet, and Teller, and the resultant isotherm is called the BET isotherm. Typically one measures the amount of N2 adsorbed for a particular pressure at 78 K (the boiling point of N2 at a pressure of 1 atm) as sketched in Figure 7-24. There are several regimes of an adsorption isotherm. At low densities the density increases linearly with pressure. When the density approaches one monolayer, the surface saturates. As the pressure approaches the saturation pressure of the gas, bulk condensation of liquid OCCUrs. This condensation can occur preferentially in pores of the solid due to capillary condensation, and the amount of gas and pressure where this occurs can be used to determine the pore volume of the catalyst. 

As we see in the course of the chapter, these two approaches frequently clash. The adsorption isotherm of Brunauer, Emmett, and Teller (BET), which is discussed in Section 9.5, is an excellent example of this. The model on which the BET isotherm is based has been criticized by many theoreticians. At the same time, the isotherm itself has become virtually... 

Until now, we have focused our attention on those adsorption isotherms that show a saturation limit, an effect usually associated with monolayer coverage. We have seen two ways of arriving at equations that describe such adsorption from the two-dimensional equation of state via the Gibbs equation or from the partition function via statistical thermodynamics. Before we turn our attention to multilayer adsorption, we introduce a third method for the derivation of isotherms, a kinetic approach, since this is the approach adopted in the derivation of the multilayer, BET adsorption isotherm discussed in Section 9.5. We introduce this approach using the Langmuir isotherm as this would be useful in appreciating the common features of (and the differences between) the Langmuir and BET isotherms. 

The BET isotherm has subsequently been derived by a variety of methods, but, as mentioned in the previous section, we follow the approach of the original derivation, namely, a... 

How is the BET isotherm used to determine the surface area of powders ... 

At low pressures, the coverage of adsorbed species increases linearly with. However, as the overpressure of A gets large, the amount of adsorbed A(s) begins to saturate. That is, the coverage begins to approach 6a = 1, which is a monolayer, and (in this model) further adsorption cannot take place. (The BET isotherm, discussed in Section 11.4.6, describes multilayer adsorption.)... 

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