BET adsorbate

BET studies of both the commercial and laboratory scale particles discussed above indicate that there is little internal area accessible to BET adsorbate molecules. This holds for both amorphous and polycrystall ine particles. If the individual particles are composed of multiple crystalline substructures, internal defects capable of adsorption would be expected. However, the BET measurements. show that internal pore.s, if they are present, are not accessible to adsorbate gases. A possible explanation is that annealing by solid-state diffusion occuin sufftcienily rapidly al the temperatures of formation to block access of the external gas to dislocations and grain boundaries. However, the origins of the crystallites within the particles and the mechanisms of crystallization tire not understood al present. 

Figure 7.11. Energetic scheme of a BET adsorbate. Adsorption sites can take not only one but several molecules. Interactions between admolecules are not taken into account [7.1-7.5].

Fig. 13 Fe-Nx-C catalysts EESEM images of Fe-Nx-C SBA15 (a) and Fe-Nx-C meso (b) BET adsorbed volumes, included also the non-templated Fe—Nx-C catalyst (c), and XPS analysis of the Fe-Nx-C meso catalyst (d). Data from [71]...

Cassel [29,30] showed, using Gibbs adsorption isotherm, that the surface tension of the adsorbed film atP = Pq is negative, arising from the total disregard of the interaction forces. Since the BET model assumes the existence of localized adsoq>tion at all levels, the molecules being located on top of one another, and since the adsorption can take place in the nth layer before the (n-/>th layer is filled, the adsorbed phase is built up not as a series of continuous layers, but as a random system of vertic molecular columns. Halsey [31] pointed out that the combinational entropy term associated with these random molecular piles is responsible for the stability of the BET adsorbed layers at... 

The characteristic isotherm concept was elaborated by de Boer and coworkers [90]. By accepting a reference from a BET fit to a standard system and assuming a density for the adsorbed film, one may convert n/rim to film thickness t. The characteristic isotherm for a given adsorbate may then be plotted as t versus P/P. For any new system, one reads t from the standard r-curve and n from the new isotherm, for various P/P values. De Boer and co-work-ers t values are given in Table XVII-4. A plot of t versus n should be linear if the experimental isotherm has the same shape as the reference characteristic isotherm, and the slope gives E ... 

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. 

Another limitation of tire Langmuir model is that it does not account for multilayer adsorption. The Braunauer, Ennnett and Teller (BET) model is a refinement of Langmuir adsorption in which multiple layers of adsorbates are allowed [29, 31]. In the BET model, the particles in each layer act as the adsorption sites for the subsequent layers. There are many refinements to this approach, in which parameters such as sticking coefficient, activation energy, etc, are considered to be different for each layer. 

Flere is the volume of gas required to saturate the monolayer, V the total volume of gas adsorbed, P the sample pressure, P the saturation vapour pressure and C a constant related to the enthalpy of adsorption. The resulting shape of the isothemi is shown plotted in figure Bl.26.6 for C = 500. A plot of P/V(P - Pq) against P/Pq should give a straight line having a slope (C - )/y C and an intercept The BET surface area is... 

Two parameters must be measured to apply the BET equation, the pressure at the sample and the amount adsorbed at this pressure. There are tlnee conmron methods for measuring the amount of gas adsorbed, called the volumetric method, the gravimetric method and the dynamic method, of which the volumetric method is the connnonest [21],... 

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. 

From the earliest days, the BET model has been subject to a number of criticisms. The model assumes all the adsorption sites on the surface to be energetically identical, but as was indicated in Section 1.5 (p. 18) homogeneous surfaces of this kind are the exception and energetically heterogeneous surfaces are the rule. Experimental evidence—e.g. in curves of the heat of adsorption as a function of the amount adsorbed (cf. Fig. 2.14)—demonstrates that the degree of heterogeneity can be very considerable. Indeed, Brunauer, Emmett and Teller adduced this nonuniformity as the reason for the failure of their equation to reproduce experimental data in the low-pressure region. 

Fig. 2.7 The BET plot for nitrogen adsorbed at 78 K on sodium chloride. (p/p°)/e(l — pfp°) is plotted against p/p° v = amount adsorbed in cm (stp). (Courtesy Maciver and Emmett.)...

Similar discrepancies were found for other vapours by Harris and Emmett, who quoted their results as the ratio fi of the BET area calculated from the isotherm of the particular adsorbate to the BET nitrogen area (Table 2.7). The value of fi varied, again sometimes widely, for any one gas on different adsorbents, so that the divergences could not be removed by use of a single revised value of a for a given vapour. 

To obtain a reliable value of from the isotherm it is necessary that the monolayer shall be virtually complete before the build-up of higher layers commences this requirement is met if the BET parameter c is not too low, and will be reflected in a sharp knee of the isotherm and a well defined Point B. For conversion of into A, the ideal adsorptive would be one which is composed of spherically symmetrical molecules and always forms a non-localized film, and therefore gives the same value of on all adsorbents. Non-localization demands a low value of c as c increases the adsorbate molecules move more and more closely into registry with the lattice of the adsorbent, so that becomes increasingly dependent on the lattice dimensions of the adsorbent, and decreasingly dependent on the molecular size of the adsorbate. 

In the pioneer work of Foster the correction due to film thinning had to be neglected, but with the coming of the BET and related methods for the evaluation of specific surface, it became possible to estimate the thickness of the adsorbed film on the walls. A number of procedures have been devised for the calculation of pore size distribution, in which the adsorption contribution is allowed for. All of them are necessarily somewhat tedious and require close attention to detail, and at some stage or another involve the assumption of a pore model. The model-less method of Brunauer and his colleagues represents an attempt to postpone the introduction of a model to a late stage in the calculations. 

Striking confirmation of the conclusion that the BET area derived from a Type IV isotherm is indeed equal to the specific surface is afforded by a recent study of a mesoporous silica, Gasil I, undertaken by Havard and Wilson. This material, having been extensively characterized, had already been adopted as a standard adsorbent for surface area determination (cf. Section 2.12). The nitrogen isotherm was of Type IV with a well defined hysteresis loop, which closed at a point below saturation (cf. F, in Fig. 3.1). The BET area calculated from it was 290 5 0 9 m g , in excellent agreement with the value 291 m g obtained from the slope of the initial region of the plot (based on silica TK800 as reference cf. p. 93). 

Fig. 4.29 Adsorption isotherms of water vapour on caldte, after being balt-milted for different periods (A, B, C) and on precipitated calcium carbonate (D). Period of milling (A) 1000h (B) ISOh (C) 22h outgassing temperature 2S°C. Isotherms A, B and C (but not D) all showed extensive low-pressure hysteresis, but for clarity the desorption branch is omitted. The amount adsorbed is referred to 1 m of BET-nitrogen area. ...

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... 

BET. This model (33) estimates the coverage corresponding to one monolayer of adsorbate and is used to measure the surface areas of soHds ... 

The external surface area of the filler can be estimated from a psd by summing the area of all of the equivalent spheres. This method does not take into account the morphology of the surface. It usually yields low results which provide Htde information on the actual area of the filler that induences physical and chemical processes in compounded systems. In practice, surface area is usually determined (5) from the measured quantity of nitrogen gas that adsorbs in a monolayer at the particle surface according to the BET theory. From this monolayer capacity value the specific surface area can be determined (6), which is an area per unit mass, usually expressed in m /g. 

Surface Area. The most important features influencing the performance of carbon blacks are aggregate size and surface area. Surface area is measured by gas- and Hquid-phase adsorption techniques, and depends on the amount of adsorbate required to form a surface monolayer. If the area occupied by a single-adsorbate molecule is known, a simple calculation will yield the surface area. A low temperature nitrogen absorption method, based on the original method of Bmnauer, Emmett, and Teller (BET) (30), has been adopted by ASTM as standard method D3037-86 (2). 

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). 

Surface Area. Overall catalyst surface area can be determined by the BET method mentioned eadier, but mote specific techniques are requited to determine a catalyst s active surface area. X-ray diffraction techniques can give data from which the average particle si2e and hence the active surface area may be calculated. Or, it may be necessary to find an appropriate gas or Hquid that will adsorb only on the active surface and to measure the extent of adsorption under controUed conditions. In some cases, it maybe possible to measure the products of reaction between a reactive adsorbent and the active site. Radioactively tagged materials are frequentiy usehil in this appHcation. Once a correlation has been estabHshed between either total or active surface area and catalyst performance (particulady activity), it may be possible to use the less costiy method for quaHty assurance purposes. 

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