Adsorption entropies, measurement

Thus the entropy of localized adsorption can range widely, depending on whether the site is viewed as equivalent to a strong adsorption bond of negligible entropy or as a potential box plus a weak bond (see Ref. 12). In addition, estimates of AS ds should include possible surface vibrational contributions in the case of mobile adsorption, and all calculations are faced with possible contributions from a loss in rotational entropy on adsorption as well as from change in the adsorbent structure following adsorption (see Section XVI-4B). These uncertainties make it virtually impossible to affirm what the state of an adsorbed film is from entropy measurements alone for this, additional independent information about surface mobility and vibrational surface states is needed. (However, see Ref. 15 for a somewhat more optimistic conclusion.)... 

Measurements of deviation of the standard adsorption entropy at graphitized carbon black have been carried out for thietane and other heterocyclic molecules. The theoretical standard entropy for the thietane molecule shows a greater deviation from the experimental value in comparison to others, which seems to indicate that for thietane a simple model of an adsorbed molecule with 2° of freedom is not accurate <1997ZP1333>. 

For further discussion of the measurement of adsorption entropies, see F. Rouquerol. J. Rouquerol, G. Della Gatta and C. Letoquart, Thermochim. Acta 39 (1980) 151. 

The isotherm fields measured could be described with sufficient accuracy by using a modified Langmuir isotherm model, considering the dependence of adsorption enthalpy and adsorption entropy on ACC loading [4]. 

The adsorption enthalpie and entropie of single component can be extracted from adsorption data obtained under isothermal conditions by using two different methods. The first one is based on the van t Hoff equation and the second one on the Clausius-Clapeyron equation. These methods only need a set of adsorption isotherms measured at various temperatures. 

Fig. 7.11 Grapliic determination of adsorption enthalpy and entropy from isothermal adsorption data measured at various temperatures, a Van t Hoff method applied to the adsorption equilibrium constant deduced from the parameter of a thermodynamic model like Henry or Langmuir fitting well the adsorption isotherms, h Clausius-Clapeyron or isosteric method the isosters he below a limit Une, which corresponds to the liquefaction equihbrium of the adsorptive...

Before taking up the results of measurements of heats and entropies of adsorption, it is perhaps worthwhile to review briefly the various alternative procedures for obtaining these quantities. 

The prefactor at 500 K is Sjj = 1.49 x 10 , illustrating the reduction in entropy when a molecule from the gas phase becomes restricted in motion on an adsorption site on the surface. The activation energy has been measured to be slightly negative in this case, i.e. AErneasured = —0.034 eV which should be compared with... 

The Xj is a relative population of adsorption site of type i in the sample and cmax is the Cu+ ions concentration in the sample of the catalyst related to its volume V. F is the rate of flow of the carrier gas, e is a porosity of the layer of the catalyst bed. p is the rate of temperature change. The populations of the Cu+ site types and both desorption energies and desorption entropies for all Cu+ site types were optimized to obtain the best fit with the experimental data. All three experimental Cu-K-FER TPD curves were fitted at once together with all Cu-Na-FER previously measured TPD curves constraining the parameters AHads i and ASads,i to be the same for all samples. 

Gorman-Lewis D, Fein JB, Jensen MP (2006) Enthalpies and entropies of proton and cadmium adsorption onto Bacillus subtilis bacterial cells from calorimetric measurements. Geochim Cosmochim Acta 70 4862-4873... 

Hysteresis is observed not only in the sorption isotherms but also in calorimetric measurements of heat of wetting at different moisture contents, and it is thus a combined entropy and enthalpy phenomenon. A reliable explanation for this effect is not currently available, but there is speculation that it is due to the stresses which are induced as the cellulose swells. Since the swelling of cellulose is not completely reversible, mechanical recovery is incomplete and hysteresis will therefore be present both in the internal stress-strain curve of the sample, and also in the water adsorption isotherm. 

On the contrary, a more advanced methodology makes use of nonlinear chromatography experiments If the adsorption isotherms are measured under variable temperatures, the corresponding thermodynamic parameters for each site can be obtained in view of the van t Hoff dependency (site-selective thermodynamics measurements) [51,54]. Thus, the adsorption equilibrium constants of the distinct sites bi a = ns, s) are related to the enthalpy (A// ) and entropy (A5j) according to the following equation [54] ... 

For various alkanes over TON, MFI, MOR and FAU framework types the entropy of adsorption was calculated based on the measured values for the adsorption equilibrium constant and for the heat of adsorption. Figure 13.13 indicates that each time a linear relation is found between the entropy and the heat of adsorp-... 

B.E.T. equation for multimolecular adsorption depend on the ability of a diatomic molecule to rotate on the surface. Kemball (8, 9) measured entropies of substances physically adsorbed on mercury and found a range of freedem from complete mobility for acetone to complete immobility with water. 

The very low water adsorption by Graphon precludes reliable calculations of thermodynamic quantities from isotherms at two temperatures. By combining one adsorption isotherm with measurements of the heats of immersion, however, it is possible to calculate both the isosteric heat and entropy change on adsorption with Equations (9) and (10). If the surface is assumed to be unperturbed by the adsorption, the absolute entropy of the water in the adsorbed state can be calculated. The isosteric heat values are much less than the heat of liquefaction with a minimum of 6 kcal./mole near the B.E.T. the entropy values are much greater than for liquid water. The formation of a two-dimensional gaseous film could account for the high entropy and low heat values, but the total evidence 22) indicates that water molecules adsorb on isolated sites (1 in 1,500), so that patch-wise adsorption takes place. 

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