Adsorptivity as a function

Thus from an adsorption isotherm and its temperature variation, one can calculate either the differential or the integral entropy of adsorption as a function of surface coverage. The former probably has the greater direct physical meaning, but the latter is the quantity usually first obtained in a statistical thermodynamic adsorption model. 

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. 28 Surfactant adsorption as a function of blend composition. Initial [surfactant] = 900 ppm. Adsorption on montmorillonite from 5% NaCl. (From Ref. 87.)... 

Figure 7.1. Uptake curves for first and second order adsorption as a function of gas dose given in Pascal seconds. In this example, the sticking coefficient is strongly activated, with an activation energy of 60 kj moTb...

Figure 7.13 Variation of the CO stripping charge formed from formic acid dissociative adsorption as a function of adatom coverage for a Pt(lll) electrode modified with Bi and Se, as indicated, in 0.5 M H2SO4 solution.

Critical Flocculation Electrolyte Concentration The critical flocculation electrolyte (Na2S0.) concentration was determined by following the average particle size of the dilute dispersion (where the particles were coated with PVA corresponding to the plateau adsorption) as a function of Na2S0 concentration, using a Coulters Nanosizer (Coulters Electronics Ltd) as described before (20). 

Fig. 9. Effect of the chain length of hydrocarbons on the adsorption enthalpy and rates of desorption. (A) Hydrocarbon in interaction with zeolite framework. Methyl groups interact with the framework oxygen protons exhibit an additional attractive force. (B) Heat of adsorption as a function of carbon number for zeolites MFI and FAU in the acidic and non-acidic form. (C) Relative desorption rates of a C12, Ci6, and C20 alkane compared to octane at 348 K. Values calculated from the linear extrapolation of the heat of adsorption values shown in (B).

No carrier is completely specific for a given trace metal metals of similar ionic radii and coordination geometry are also susceptible to being adsorbed at the same site. The binding of a competing metal to an uptake site will inhibit adsorption as a function of the respective concentrations and equilibrium constants (or kinetic rate constants, see below) of the metals. Indeed, this is one of the possible mechanisms by which toxic trace metals may enter cells using transport systems meant for nutrient metals. The reduced flux of a nutrient metal or the displacement of a nutrient metal from a metabolic site can often explain biological effects [92]. 

Figure 1.10 Differential heats of adsorption as a function of coverage for ammonia on H-ZSM-5 (o) and H-mordenite ( ) zeolites [70], In both cases, the heats decrease with the extent of NH3 uptake, indicating that the strengths of the individual acidic sites on each catalyst are not uniform. On the other hand, the H-ZSM-5 sample has a smaller total number of acidic sites. Also, the H-mordenite sample has a few very strong sites, as manifested by the high initial adsorption heat at low ammonia coverage. These data point to a significant difference in acidity between the two zeolites. That may account for their different catalytic performance. (Reproduced with permission from Elsevier.)...

Figure 2. Shift in system equivalence points (pH of 50% fractional metal adsorption) as a function of site concentration and macroscopic proton coefficient. Initial equivalence point of pH 8 and SOH. = 10 M are arbitrary reference conditions.

As a second example, consider the partitioning of Cd(II) between two adsorbents—a-TiC and (am)Fe20j.H20. Figure 11 shows Cd(II) fractional adsorption as a function of pH for binary mixtures of these adsorbents under experimental conditions such that Cddl) and SOUp are constant only the surface site mole fraction varies from one end-member to the next. As the site mole fraction shifts between the end-members, the fractional adsorption edges for the binary adsorbent mixtures varies between the limits defined by end-members. In the absence of particle-particle interactions, the adsorbents should act as independent ligands competing for complexa-tion of Cd(II). If this is the case, then the distribution of Cd(II) in such binary mixtures can be described by a composite mass-action expression (13) which includes a separate term for the interaction of Cd(II) with each adsorbent. 

Figure 11. Cd(Il) fractional adsorption as a function of pH in binary mixtures of a-Ti02 and (am)Fe203 -H20 at constant SOftj,.

Figure 1. Mn(II) adsorption as a function of pH. The solid lines are calculated using the constant capacitance model.

Figure 14. Changes of log) for acelone adsorption, as a function of the charge density on the Hgelectrode,fromAc+NM andAc + MeOH...

The studies relating the effect of temperature on adsorption was carried out at eight different temperatures (natural illite clay, 110°C, 200°C, 350°C, 450°C, 550°C, 750°C, 900°C) with a oil-grease concentration of 1,000 mg L and 5 g of illite clay sample, keeping the other parameters constants. Figure 20.2 shows oil-grease adsorption as a function of temperature. 

Fio. 2. Length changes of porous glass produced by water adsorption as a function of free-energy lowering ( ) (67),... 

The decrease of heat of adsorption as a function of surface coverage can be explained satisfactorily by interaction of the adsorbed atoms with each other. 

Fig. 6.94. Comparison of adsorption properties of different electrode surfaces. Bisulfate adsorption as a function of electrode potential on different platinum planes (110), (111), (100) and on polycrystalline platinum. Data obtained by the radiotracer technique. (Re-printed from Y.-E. Sung, A. Thomas, M. Gamboa-Aldeco, K. Franaszczuk and A. Wieckowski, J. Electroanal. Chem. 378 131, copyright 1994, Figs. 14 and 15, with permission from Elsevier Science.)...

Figure 9.3 is a sketch of an apparatus that can be used to determine the equilibrium extent of gas adsorption as a function of pressure. We outline how such an experiment is conducted at ambient temperature, even though adsorption studies are frequently conducted at low temperatures, particularly when determination of Asp is the objective of the experiment. A known mass of adsorbent is introduced into the sample tube and degassed as described above. Then the following set of pressure-volume readings are made, described here in terms of Figure 9.3. 

FIG. 9.10 Calorimetric heats of adsorption as a function of coverage for argon on carbon bis at 78K. The dashed line represents untreated black the solid line is after graphitization at 2000° The horizontal line is the heat of vaporization of argon. (Redrawn with permission from R. Beebe and D. M. Young, J. Phys. Chem., 58, 93 (1954).)... 

The energetics data are presented in terms of heat of adsorption as a function of average zeolite pore diameter. Average pore diameter is applicable to those zeolites with elliptical pore openings, and the pore dimensions employed are those usually used to characterize the zeolite. The heat of adsorption as a function of pore diameter was predicted to exhibit a maximum around 5 A for all the alkanes studied, as shown on Fig. 11. The optimum heat of adsorption of straight-chain alkanes appears to be achieved by a pore with dimensions close to that of the 10-ring channel in ferrierite. 

Fra. 11. Heat of adsorption as a function of pore diameter for alkanes ranging from butane to decane as found by CB-MC calculations. Reprinted with permission from Ref. 172. Copyright 1996 American Chemical Society. 

The decrease in the heat of adsorption as the pore size is increased beyond this size is not surprising dispersive interactions with the zeolite pore decrease. The behavior at lower pore dimensions is explained by considering the location of the sorbed molecules. In the cases of zeolites rho and A, the alkanes were found to adopt highly coiled conformations in the centers of the a-cages that form these structures. The alkanes thus are located in pores with a larger diameter than that usually used to characterize the zeolite (namely, the diameter of the windows that connect the cages). If the heat of adsorption as a function of pore diameter is replotted to reflect the locations of the sorbed molecules, a more straightforward inverse relationship is obtained. 

With the exception of the high initial heat of adsorption of CO on NiO(200), the differential heats of adsorption as a function of the amount of CO adsorbed are similar for both catalysts. Metallic nickel which exists in the sample prepared at 250°C. may chemisorb carbon monoxide (15). However, the metal content is small and cannot account for the heat released in these experiments on NiO(250), since the heat of chemisorption of CO on metallic nickel is still higher (42 kcal. per mole) than the heat registered during adsorption of the first dose (29 kcal. per mole). 

Non-ideality due to lateral interactions can be treated in two ways, by introducing surface activity coefficients in the adsorption isotherms or expressing the free energy of adsorption as a function of coverage, on the basis that the free energy of adsorption varies with coverage [94]. 

For cluster A, where each metal atom is supposed to contain one electron, the heat of adsorption as a function of ji is given in Fig. 18. The values calculated are found to be less than 1.33/3, which is the heat of formation of the MeH molecule. The largest decrease is found for the lowest values of /i. The large... 

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