BET, monolayer

As is seen from Fig. 2.L, the BET equation yields an isotherm which (so long as c exceeds 2) has a point of inflection this point is close to, but not necessarily coincident with, the point where the amount adsorbed is equal to the BET monolayer capacity. 

The ease of locating Point B depends on the shape of the knee of the isotherm.If the knee is sharp, corresponding to a high value of c. Point B can be located with accuracy even if the linear branch of the isotherm is short (see Fig. 2.10, curve (i)). When the knee is rounded, when c is small, Point B becomes difficult to locate, and the estimated value of rig may then differ widely from the BET monolayer capacity n . As will be seen shortly it is doubtful, indeed, how far isotherms in which Point B cannot be identified easily should be used for the estimation of monolayer capacity from either Point B or the BET plot. In practice, this reservation would include all isotherms having a value of c below 20. 

Fig. 2.20 Adsorption isotherms of carbon dioxide at — 78 5°C in TK 800 outgassed at 25 C and lOOO C (triangles). The BET monolayer is indicated as n on each isotherm.

When it is desired to evaluate the specific surfaces of a set of closely related samples of solid, however, only one of the samples needs to be calibrated against nitrogen (or argon), provided that all the isotherms of the alternative adsorptive can be shown to have indentical shape. A simple device for testing this identity, by use of the a,-plot, is described in Section 2.13 by means of the a,-plot it is also possible to proceed directly to calculation of the specific surface without having to assign a value to or to evaluate the BET monolayer capacity, of the alternative adsorptive. 

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 ... 

When the values of the BET monolayer capacity calculated from Type III isotherms are compared with independent estimates (e.g. from nitrogen adsorption) considerable discrepancies are frequently found. A number of typical examples are collected in Table 5.1. Comparison of the value of the monolayer capacity predicted by the BET equation with the corresponding value determined independently (columns (iv) and (v)) show that occasionally, as in line 6, the two agree reasonably well, but that in the majority... 

Even so, it is of interest to calculate the BET monolayer capacity from the composite isotherm of Fig. 5.12(b). Though the isotherm did not conform very closely to the BET equation, the isosteric net heat of adsorption was... 

As will be seen shortly, an analogous result is obtained with the silica-water system, where the BET monolayer capacity of water calculated from the water isotherm is roughly equal to the hydroxyl content of the silica surface. 

The relationship between the BET monolayer capacity of physically adsorbed water and the hydroxyl content of the surface of silica has been examined by Naono and his co-workers in a systematic study, following the earlier work by Morimoto. Samples of the starting material—a silica gel—were heated for 4 hours in vacuum at a succession of temperatures ranging from 25 to 1000°C, and the surface concentration of hydroxyl groups of each sample was obtained from the further loss on ignition at 1100°C combined with the BET-nitrogen area. Two complete water isotherms were determined at 20°C on each sample, and to ensure complete... 

In Table 5.3, is compared with the total hydroxyl concentration (Ni, + N ) of the corresponding fully hydroxylated, sample. The results clearly demonstrate that the physical adsorption is determined by the total hydroxyl content of the surface, showing the adsorption to be localized. It is useful to note that the BET monolayer capacity n JH2O) (= N ) of the water calculated from the water isotherm by the BET procedure corresponds to approximately 1 molecule of water per hydroxyl group, and so provides a convenient means of estimating the hydroxyl concentration on the surface. Since the adsorption is localized, n.(H20) does not, of course, denote a close-packed layer of water molecules. Indeed, the area occupied per molecule of water is determined by the structure of the silica, and is uJH2O) 20A ... 

The BET monolayer capacity N, calculated from the first water isotherm included both physisorbed and chemisorbed water, whereas that from the second isotherm iV, included only the physisorbed water. Thus the difference (iV, - N,) gave the amount of chemisorbed water taken up as hydroxyl groups during the isotherm determination. N, + iV ) was therefore the total concentration of hydroxyl groups on the surface when the second water isotherm was being measured. 

The adsorption isotherm of N, on FSM-16 at 77 K had an explicit hysteresis. As to the adsorption hysteresis of N-, on regular mesoporous silica, the dependencies of adsorption hysteresis on the pore width and adsorbate were observed the adsorption hysteresis can be observed for pores of w 4.0nm. The reason has been studied by several approaches [5-8]. The adsorption isotherm of acetonitrile on FSM-16 at 303K is shown in Fig. 1. The adsorption isotherm has a clear hysteresis the adsorption and desorption branches close at PIP, = 0.38. The presence of the adsorption hysteresis coincides with the anticipation of the classical capillary condensation theory for the cylindrical pores whose both ends are open. The value of the BET monolayer capacity, nm, for acetonitrile was 3.9 mmol g. By assuming the surface area from the nitrogen isotherm to be available for the adsorption of acetonitrile, the apparent molecular area, am, of adsorbed acetonitrile can be obtained from nm. The value of am for adsorbed acetonitrile (0.35 nnr) was quite different from the value (0.22 nm2) from the liquid density under the assumption of the close packing. Acetonitrile molecules on the mesopore surface are packed more loosely than the close packing. The later IR data will show that acetonitrile molecules are adsorbed on the surface hydroxyls in... 

Figure 1-10 BET Monolayer Plot. Source From T.P. Labuza, Sorption Phenomena in Foods, Food Technol., Vol. 22, pp. 263-272, 1968.

Figure 3.23. Gas adsorption gravimetry percentage enor in surface area as a result of neglecting totally the buoyancy effect on the adsorbent (assumptions nitrogen BET, monolayer at 100 mbar, bulk density of adsorbent from 1 to 8).

Broekhoff and van Dongen (1970) suggested that it is not appropriate to use the BET monolayer capacity to calculate 0. Instead, they proposed that appropriate values of the three adjustable parameters (0, kH and k2) should be selected to obtain the best fit. When applied in this manner, Equation (4.8) was claimed to be a useful... 

The specific surface area, a (BET), is obtained from the BET monolayer capacity, m, by the application of the simple relation ... 

From an experimental standpoint, the availability of liquid nitrogen and the range of commercial equipment now available make it relatively easy to determine full nitrogen adsorption-desorption isotherms at 77 K. This is an additional reason why nitrogen is now internationally accepted as the standard BET adsorptive (IUPAC Sing et al., 1985), with the convention that routine work, it is assumed that the nitrogen monolayer is in a close-packed liquid state at 77 K, irrespective of the actual structure of the BET monolayer. 

A low C value is more difficult to interpret. As we have seen, the BET monolayer cannot be determined with high accuracy and the same is true for the corresponding value of a. This may explain why some reported values of a appear to be much larger than expected. For example, a and C values of 0.7 nm2 and 10, respectively, have been reported for pentane on silica, in comparison with the values of 0.5 nm2 and 60 for pentane on graphitized carbon (Kiselev and Eltekov, 1957). 

Fractal plots of log nm versus log a for two porous silicas are shown in Figure 63 (here, nm is the BET monolayer capacity). Both plots are linear, giving Dx = 2.98 for the silica gel and Dx = 2.09 for the controlled pore glass. These values reflect the extremes of the fractal scale, the latter being close to the ideal value for a flat surface. 

The best value for the effective molecular cross-sectional area, o(Kr), of krypton in the BET monolayer at 77 K has been under discussion for many years. In their original work on krypton adsorption, Beebe et al. (1945) recommended the value 0.195 nm2 for o(Kr) and this empirical value is still used by many investigators. For the adsorption of krypton on graphitized carbon, Ismail (1990, 1992) gives preference to the value molecular area calculated from the liquid density and determined by X-ray scattering. This, of course, implies that Kr and N2 molecules undergo localized adsorption on the same sites. For ungraphitized carbons, Ismail (1992) recommends cr(Kr) = 0.214 nm2. 

The situation is more complicated when Point B is either non-existent (as with the alkanes) or ill-defined (as with argon and krypton) since the physical significance of the BET monolayer capacity, nm, is now questionable. However, some progress can be made if we proceed in the following way instead of using an assumed value of molecular area o, to obtain a(BET), we now derive the apparent value of a from a(S) and nm. The values of apparent molecular area, a(np), of adsorbed neopentane in Table 10.3 are calculated from its BET monolayer capacity, nm(np), and the surface... 

This work has again drawn attention to the difficulties involved in deriving the surface area from the BET-monolayer capacity. Grillet et al. (1985) have pointed out that the use of nitrogen may lead to an uncertainty of up to 30% in the area of rutile ... 

For. a number of reasons, nitrogen (at 77 K) is generally considered to be the most suitable adsorptive for standard surface area determination and for this purpose it is usually assumed that the BET monolayer is close-packed (with the molecular area taken as 0.162 nm2). One advantage of nitrogen is that the path of its multilayer isotherm is not very sensitive to differences in adsorbent structure. A useful check on the validity of nm is that the value of C(BET) should be neither too low nor too high if C(BET) < 50, Point B is not sufficiently sharp if C(BET) > 200, there is either a significant micropore filling contribution or localized adsorption on specific sites. 

Adsorption using different probe molecules is available for determination of the pore entrance structure. N2 molecules adsorbed near the pore entrance at 77 K often block further adsorption, indicating the presence of ultramicropores and pore-neck structures. The preadsorption technique is also effective for elucidation of the pore entrance structure. Fractal analysis using adsorption is helpful to understand the fine structure of nanopore walls. [10,11] However, the probe molecules must be carefully chosen and the monolayer capacity must be evaluated precisely, because the BET monolayer should not be used. 

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