Volumetric isotherms

The analogy with thermal expansion coefficients is evident when one compares equations 1.98 and 1.99 with equations 1.90 and 1.91, respectively. For compressibility, as for thermal expansion, a mean coefficient that defines the volumetric variation (V2 — ft) for a finite pressure range (T2— I)) may be introduced. This coefficient, the mean volumetric isothermal compressibility, is given by... 

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.)... 

Figure 6. Adsorption of diethyl ether on silica at 24°C (A) volumetric isotherm on silica containing free OH groups (- -SiOSi) (B) volumetric isotherm on dehy-droxylated silica (D) spectroscopic isotherm on free OH groups (19)...

The volumetric isotherms are reported in Figure 5a. In the whole interval of CO pressure examined, the adsorbed amounts per unit surface area are definitely larger on the ceria-doped specimens than on pure alumina, and the difference between doped and non-doped systems increases with increasing CO pressure. (For instance, at pCO = 60 Torr, the uptake is 0.13 CO molecules per nm (0.21 qmol/m2) on pure alumina, whereas it is 0.31 and 0.40 CO molecules per nm2 (0.51 and 0.66 lamol/m ) in the case of ACE3 and ACE20 respectively). 

Low-coverage volumetric isotherm data [41, 42] were used to extract the isosteric heat of adsorption extrapolated to zero coverage, the gas-solid virial coefficient, and the two-dimensional second virial coefficient. It is found that fitting the two-dimensional virial coefficient obtained from the measurements in the vicinity of the surface in terms of Lennard-Jones inter-molecular potentials reduces the well depth obtained from the bulk by about 20%. In addition, the effective quadmpole moment of CO needs to be significantly reduced [42] by as much as about 50%. These fitted parameters are believed to account for various substrate mediation effects in some effective way (see Refs. 41 and 42 for more details concerning these param-eterizations). It is also concluded [41] that the asymmetric empirical parameterization of Ref. 238 should be replaced by models in which the similarity between the isoelectronic CO and N2 molecules is exploited for the non-electrostatic contributions as in Ref. 17. 

Fig. 1.5 Adsorption of CO at F = 303 K on Na-MFI (square) and K-MFI (circle) zeolites out-gassed at F = 673 K. a Volumetric isotherms (adsorbed amounts vs. equilibrium pressure), b Calorimetric isotherms (evolved heats vs. equilibrium pressure). Solid symbols first run, open symbols second run of adsorption. Experimental points interpolated by the Langmuir equation (vide infra)...

As an example of the influence of the adsorption temperature, the equilibrium data for water (H2O) adsorbed at T = 303, 353 and 423 K on a H-BEA zeolite specimen (outgassed at T = 873 K) are illustrated in Fig. 1.6. In Fig. 1.6a the three volumetric isotherms are reported (for experimental and samples details vide infra Sect. 1.4) as far as the equilibrium pressure Phio increases, the adsorbed amounts also increase more or less steeply according to the adsorption temperature. In Fig. 1.6b the amounts adsorbed at a constant equilibrium pressure (pnio = 6 Torr) are plotted against the adsorption temperature giving rise to an adsorption isobar (nods vs. Tads)- Note that... 

This is a purely empirical formula, where the term Vads represents the adsorbed amount, p the adsorptive pressure, whereas k and n are suitable empirical constants for a given adsorbent-adsorbate pair at temperature T. The adsorbed amount are normalized either to the mass of the adsorbent or to the exposed surface area. As an example see. Fig. 1.6a, where the adsorption volumetric isotherms of H2O on H—BEA zeolite are reported the experimental points were interpolated by the Freundlich isotherm equation. The Freundlich isotherm assumes that the adsorption enthalpy AaH (per site) varies exponentially with increasing equilibrium pressure. In fact, the experimental points in the correspondent heat of adsorption versus coverage plot were properly interpolated by an exponential fitting, as illustrated in Fig. 1.15 (vide infra Sect. 1.4.2.3). 

Fig. 1.9 Adsorption of H20vap adsorbed at T = 303 K on proton-exchanged (H-BEA, square) and all-silica (BEA, up triangle) zeolites pre-outgassed at T = 873 and 673 K, respectively, a Volumetric isotherms, b Calorimetric isotherms. Solid symbols ads. I open symbols ads. II. Adapted from Ref. [25] Fig.4...

Fig. 1.10 CO adsorbed at T = 303 K on zeolites Cu(I)-MFI diamond) and Na-MFI (square) volumetric (a) and calorimetric (b) isotherms. Both samples were pre-outgassed atT = GTi K. Solid symbol ads. 1 open symbols ads. II. Volumetric isotherms adapted from Ref. [23] Fig. 3a...

Cu(I)— and Ag(I)—MFI ads. II isotherms (both volumetric and calorimetric) lie below the ads. I correspondent isotherms, indicating the presence of irreversible phenomena. The irreversible adsorption component was quantified by taking the (ads. I - ads. n) difference in the volumetric isotherms at pco = 90 Torr. It was 30 % of total uptake (ads. I) for copper- and % for silver-exchanged zeolites. 

In Fig. 1.21a, the differential heats of adsorption of CO on H—BEA zeolite and on MFI-Silicalite are reported as a function of the adsorbed amounts. Volumetric isotherms are illustrated in the figure inset. In both cases the adsorption was fully reversible upon evacuation of the CO pressure, as typical of both physical and weak, associative chemical adsorption. For H-BEA a constant heat plateau at 60kJ mol was measured. This value is typical of a specific interaction of CO with coordinative unsaturated Al(III) atoms, as it was confirmed by combining adsorption microcalorimetry and molecular modeling [73, 74, 78, 89] Note that the heat value was close to the heat of adsorption of CO at cus Al(III) sites on transition catalytic alumina, a typical Lewis acidic oxide [55, 73], Once saturated the Al(III) defects, the heat of adsorption started decreasing down to values typical of the H-bonding interaction of CO with the Br0nsted acidic sites (- 30 kJ mol , as reported by Savitz et al. [93]) and with polar defects, either confined in the zeolite nanopores or at the external surface. 

Fig. 1.24 Adsorption (at T = 303 K) of CH3OH vapor on Ca-modified silica outgassed at F = 423 K. a Volumetric isotherms, b versus riads plots. Ads. lA diamond, solid symbols, ads. IIA diamond, open symbols. Ads. IB (run after evacuating overnight the sample previously kept 3 days in contact with < 80 Torr of CH3OH) triangle, solid symbols, ads. IIB triangle, open symbols. Adapted from Ref. [26] Fig. 12...

Fig. 15.7 a volumetric isotherms, b differential heats of adsorption versus coverage plots of H20ya adsorbed at T = 303 K on H-BEA (square) and on Si02-Al203 (diamond), H-BEA was pre-outgassed at T = 873 K, Si02-Al203 at T = 673 K. Solid symbols first run open symbols second run of adsorption. Adapted from ref. [7] Fig. 8... 

In Fig. 15.7, volumetric isotherms (Sect, a) and differential heats (Sect, b) of water vapor (H20vap) adsorption for the two investigated specimens are reported. The two samples, were pre-outgassed for 2h at either T = 873 K (H-BEA) ox T = 673K (Si02-Al203), at a residual pressure p < 0 Torr in order to ensure a maximum density of Lewis and Brpnsted acidic sites. 

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