The BET Analysis

Here V indicates the volume of gas adsorbed at STP, the volume of gas that is required for a monolayer, the vapor pressure of the bulk liquid at the same temperature, P the adsorptive pressure and C a constant. For analysis, the equation is rearranges into the transformed form  

The general approach to using transformed equations and the BET in particular is as follows  

Rework the data according to the transform required. In the case of the BET analysis, this means that the dependent variable (computer y) will be 

Plot the x-y data and determine the slope and intercept over the region which appears as a straight line. (For repeated experiments, be sure to use the same region for consistency.) Many spread sheets have linear regression analysis built-in, but be sure to properly specify the range. 

Equate the determined values of the slope, S ed intercept, with the expression for the slope and intercept in the transformed equation. Thus for the BET analysis, 

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If one restricts the number of layers of adsorbate that may be stacked up, as would be the case in the very narrow capillaries of a porous catalyst, the BET analysis must be modified to allow for this. If n is the number of permissible layers, it can be shown that the adsorption isotherm becomes ... 

EXAMPLE 9.5 Calculating the Adsorption Energy from the Brunauer-Emmett-Teller Isotherm. The BET analysis uses p/p0 rather than p as a variable just as we used this pressure ratio to compare Langmuir adsorption at different temperatures in Example 9.3. What corrections, if any, are needed in the apparent adsorption energy of about 14 kJ mole-1 as calculated in Example 9.3 ... 

Samples of rutile Ti02 were outgassed at elevated temperatures in some instances this was followed by subsequent exposure to 02 at 150°C. The following results were obtained by the BET analysis of N2 adsorption after various preliminary treatments ... 

If the standard BET procedure is to be used, it should be established that monolayer-multilayer formation is operative and is not accompanied by micropore filling (Section 11.2.1.8.C), which is usually associated with an increase in the value of C (>200, say). It should be appreciated that the BET analysis does not take into account the possibility of micropore filling or penetration into cavities of molecular size. These effects can thus falsify the BET surface areas and in case of doubt their absence should be checked by means of an empirical method of isotherm analysis or by using surface area reference samples (see Section 11.2.1.6.B). 

Bonding density is calculated using the value of carbon content (from CHN analysis) in carbon %w/w and the specific surface area, obtained from the BET analysis of base silica. Calculation is performed using the equation originally introduced by Berendsen and de Galan [68] ... 

The BET analysis of the adsorption isotherm systematically leads an overestimated value of the specific surface when compared to the intrinsic geometrical value. Gelb and Gubbins have also tested the BET equation for a model of silica glasses and obtained similar results [16]. 

To confirm that the spherical silica gel comprises of primaty nanogels, the pore structure was analyzed by the BET analysis. Contnuy to the expectations, the precursor and aged silica gels have relatively very low specific surface area. In Table I, the specific surface area of the precursor and aged silica gels was presented. As the addition amount of NH3 increased, the specific surface area increased. 

To investigate the detailed size distribution of the micropores, the BET analysis was minutely conducted at the very low pressure of N2. Fig. 4 represents the detailed incremental pore volume curves as a function of average pore diameter. It was clearly shown that the pore diameter of the micropores was about IS A, irresjiective of the aging conditions. 

The BET analysis on dolomite and charred dolomite is shown in Table 1. There is a rise in surface area on charring of the dolomite due to the calcining process which effectively creates a porous structure. 

In materials containing micropores (and mesopores), such as molecular sieves and activated carbons, the boundary conditions (multilayer adsorption) are not fulfilled and the BET analysis is not applicable here. When (traditionally) reported in the literature, the BET surface area should be understood as a niunber proportional to the pore volume rather than the specific surface area. Note also that conceptually the term specific surface area is inapplicable once the solid material surroimds sorbed molecules. 

Another approach treats the cell wall water as a solution phenomenon, with the water of hydration accounting for the first 4-6% of moisture adsorbed or the last moisture lost during desorption (essentially the same 4-6% that accounts for the monolayer in the BET analysis). All further adsorbed cell wall water is the water of solution. In a similar vein Harley and Avramidis (1993) calculate that where moisture contents exceed 20-25% the water of solution forms clusters of 10 or more water molecules that corresponds to a hydraulic spheroid about 0.6 nm in diameter. 

Gelb, L.D. and Gubbins, K.E. (1998). Characterization of porous glasses simulation models, adsorption isotherms, and the BET analysis method. Langmuir, 14, 2097-111. 

Based on their respective monolayer volumes as determined by the BET analysis of water sorption (see column 6 in Table I), the... 

This statement is also underlined by Figure 5.6a, which demonstrates that the measured volume of the IL in micro- and mesopores (2-lOOnm, which is the experimental range of the BET analysis) equals the calculated values for a filling degree of less than 15%. For the calculation of the volume occupied by the IL in the micro- and mesopores, Eq. (5.3) can be used, which is based on the simpHfying assumption that the volume covered by the IL is given by the product of the initial surface area and the (constant) layer thickness of the IL ... 

Wall thickness = (dioo 2/V3)-0.95 Dmcm-4i and Dmcm-4i= 4.20 Vmcm-4i/Smcm-4i = 3.292 nm. The resulting wall thickness =1.13 nm. From the BET analysis an idea about the pore size distribution can be obtained. The plot of the pore volume (cc/g) versus pore diameter (Angstrom) clearly shows that the measured average size of the pores is 2.53 nm. The calculated size of the pores is dioo-calculated pore thickness = (3.692-1.13) nm = 2.56 nm. So a good similarity between the measured and the calculated value is obtained. 

The specific surface area of the activated catalyst was found to increase with alumina content up to about 20 m /g at around 2% AI2O3 and then to remain constant (10), demonstrating the role of this additive as structural promoter that (together with other nonreducible phases such as hercynite and calcium ferrite) prevents sintering of the metallic iron particles into low surface area material. These values are compatible with the mean particle sizes of around 30 nm, as determined by mercury porosimetry and seen directly in the scanning electron microscope (Fig. 2) (11). This agreement further shows that the texture of the catalyst permits the N2 molecules of the BET analysis to reach essentially the whole internal surface. 

The BET analysis on the activated Ni clearly shows the high surface area of these materials. The bulk analysis data indicate the very complex nature of these materials. All samples contained considerable carbon and hydrogen. It is not clear at this point whether this is due to trapped solvent molecules or degradation products from the solvent. Klabunde has demonstrated that... 

All of these arguments would not have been necessary if surface areas had been correctly obtained in the first place. The assumption has to be abandoned that the BET analysis... 

Fix n and C at the values obtained finm the BET analysis (the latter was always obtained even when left fiee to change), set bounds on the monolayo covoage to be rou y 20% around that obtained from the BET analysis, and ftien fit the model to the experimental isothram several times to obtain an average for the range of fractality, r. ... 

Opinions differ on the applicability of the BET analysis to Type IB isotherms. Indications are that the method can be used to assess the... 

Fig. 6.26 Variation in N2 gas absorption with relative gas pressure, P/Pq maintained in the BET analysis...

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