Distribution site energy

Heats op Adsorption from Heat op Immehsional Wetting Data 

It has already been pointed out that differential or integral heats of adsorption can be calculated from heat-of-immersion values without recourse to two or more isotherms where the amoimts preadsorbed on the sample before immersion are measured gravimetrically. This technique is particularly useful where chemisorption occurs at very low and difficult to measure equilibrium pressures. 

In comparison, too, direct calorimetric determination of heats of adsorption can be less accurate, although less tedious, than heat-of-immersion determinations. Lack of accuracy can occur with poorly conducting, non-metallic adsorbents, where long equilibrium times are required for vapor phase adsorption or where surface sites do not fill in strict accordance with the site energy distribution of the solid surface. Atoms or molecules can be expected to stick to the first part of the surface they strike when strong chemisorption occurs and then molecules are likely not to move freely over 

The heat curves, themselves, are informative. The kaolin-based pellet catalyst has a few more active sites then attapulgite, but its site activity decreases rapidly and to values only about 3 kcal./mole above the heat of liquefaction of the liquid at maximum coverage. Obviously, a distinction cannot be made between physical adsorption and chemisorption for some of the amine adsorbed at full coverage on the cracking catalyst. On the other hand, attapulgite has a much narrower distribution of adsorption energies, and the lowest heats are about double the heat of liquefaction of butyl amine. Therefore, it appears safe to conclude that the amount remaining after evacuation at 25° is chemisorbed. 

The surface coverage d is the ratio of the amine remaining adsorbed after evacuation at temperature T to the total adsorbed after saturation and evacuation at 25° to an ultimate vacuum between 10 and 10 mm. Hg. The maximum adsorption at 25° on attapulgite and the catalyst sample is large and covers about one-half of the total available area of the solids if 20.8 A, is used as the cross-sectional area of adsorbed butyl amine. 

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We have considered briefly the important macroscopic description of a solid adsorbent, namely, its speciflc surface area, its possible fractal nature, and if porous, its pore size distribution. In addition, it is important to know as much as possible about the microscopic structure of the surface, and contemporary surface spectroscopic and diffraction techniques, discussed in Chapter VIII, provide a good deal of such information (see also Refs. 55 and 56 for short general reviews, and the monograph by Somoijai [57]). Scanning tunneling microscopy (STM) and atomic force microscopy (AFT) are now widely used to obtain the structure of surfaces and of adsorbed layers on a molecular scale (see Chapter VIII, Section XVIII-2B, and Ref. 58). On a less informative and more statistical basis are site energy distributions (Section XVII-14) there is also the somewhat laige-scale type of structure due to surface imperfections and dislocations (Section VII-4D and Fig. XVIII-14). 

Fig. XVn-24. Site energy distribution for nitrogen adsorbed on Silica SB. (From Ref. 160.) (Reprinted with permission from J. Phys. Chem. Copyright by the American Chemical Society.)...

C. Point versus Patch Site Energy Distributions... 

The preceding material has been couched in terms of site energy distributions—the implication being that an adsorbent may have chemically different kinds of sites. This is not necessarily the case—if micropores are present (see Section XVII-16) adsorption in such may show an increased Q because the adsorbate experiences interaction with surrounding walls of adsorbent. To a lesser extent this can also be true for a nonporous but very rough surface. 

It is not surprising, in view of the material of the preceding section, that the heat of chemisorption often varies from the degree of surface coverage. It is convenient to consider two types of explanation (actual systems involving some combination of the two). First, the surface may be heterogeneous, so that a site energy distribution is involved (Section XVII-14). As an example, the variation of the calorimetric differential heat of adsorption of H2 on ZnO is shown in Fig. 

It would seem better to transform chemisorption isotherms into corresponding site energy distributions in the manner reviewed in Section XVII-14 than to make choices of analytical convenience regarding the f(Q) function. The second procedure tends to give equations whose fit to data is empirical and deductions from which can be spurious. 

FIGURE 13.5 Calorimetric and volumetric data obtained from adsorption calorimetry measurements Raw pressure and heat flow data obtained for each dose of probe molecule and Thermokinetic parameter (a), Volumetric isotherms (b), Calorimetric isotherms (c), Integral heats (d), Differential heats (e), Site Energy Distribution Spectrum (f). (From Damjanovic, Lj. and Auroux, A., Handbook of Thermal Analysis and Calorimetry, Further Advances, Techniques and Applications, Elsevier, Amsterdam, 387-438, 2007. With permission.)... 

To measure the site energy distribution or other surface properties of powders by measuring heats of immersion as a function of the amount of preadsorbed wetting liquid. Heats of immersion of the partly covered surfaces reveal the site energy distributions. For acid sites on cracking catalysts, for example, adsorbates of different basicity can be used to develop a topographical map of the surface activity. 

Single fibre pull-out test 179 Site energy distribution 47 Skin 124... 

The problem of obtaining site energy distributions from adsorption isotherms may be defined as follows ... 

The more desirable approach is to determine f(Q) from an assumed 0(P,T,Q) and the experimental adsorption isotherm. Sips (16) showed that Equation 1 could be treated by a Stieltjes transform, so that in principle an explicit function could be written for f(Q), provided the experimental isotherm function, 0, could be expressed in analytical form. Subsequently, Honig and coworkers (10, 11, 12) investigated this approach further. The difficulty is that only for certain types of assumed functions 0 and 0 is the approach practical. As a consequence the procedure has been first to restrict the choice of 0 to the Langmuir equation, and second to assume certain simple functions for 0 such as the Freundlich and Temkin isotherm equations. The system is thus forced into an arbitrary mold and again it is not certain how much reliance should be placed on the site energy distributions obtained. 

No method has so far been advanced for taking the experimental isotherm itself, irrespective of the complexity of its analytical representation, and from it, obtaining the site energy distribution consistent with any arbitrarily chosen local isotherm function, 0, no matter how complex. 

The procedure is first illustrated in terms of its application to the analysis of an isotherm calculated from an arbitrary assumed site energy distribution, f(Q). For reasons discussed in more detail later, the Langmuir equation—i.e., localized adsorption with no lateral interaction—appears very satisfactory as the form to use for 0(P,T,Q) ... 

Figure 1. Test of site energy distribution method...

Figure 2. Outline of procedure for obtaining site energy distributions...

The procedure so far is not new. Roginski, who proposed it, did not, however, suggest how to refine the approximate site energy distribution so obtained... 

The second approximation to the F vs. b plot is shown in Figure 2,a as well as F3 vs. 6, obtained by repeating the above procedure. In the present example F i vs. b was taken to be in the terminal approximation (also shown in Figure 1,6) and, by means of Equation 4, the integral site energy distribution F(Q) was obtained. The corresponding differential site energy distribution is shown in... 

However, had some more radically curved extensions of the experimental isotherm been assumed in Figure 3,a, a less uniform calculated site energy distribution would have resulted. In other words, the fit to the Temkin equation is in this case over too small a pressure range for the uniform site energy distribution implied by the equation to be considered more than a guess. 

The data for 376° and 449° C. give the same site energy distribution (Figure 3,h)—i.e., the calculated distribution is not temperature-dependent. This observation confirms the general consistency of the procedure and assumptions. 

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