Adsorption, calorimetric measurements isotherms

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. 

Despite the importance of mixtures containing steam as a component there is a shortage of thermodynamic data for such systems. At low densities the solubility of water in compressed gases has been used (J, 2 to obtain cross term second virial coefficients Bj2- At high densities the phase boundaries of several water + hydrocarbon systems have been determined (3,4). Data which would be of greatest value, pVT measurements, do not exist. Adsorption on the walls of a pVT apparatus causes such large errors that it has been a difficult task to determine the equation of state of pure steam, particularly at low densities. Flow calorimetric measurements, which are free from adsorption errors, offer an alternative route to thermodynamic information. Flow calorimetric measurements of the isothermal enthalpy-pressure coefficient pressure yield the quantity 4>c = B - TdB/dT where B is the second virial coefficient. From values of obtain values of B without recourse to pVT measurements. 

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.)... 

As we have seen, an adsorption isotherm is one way of describing the thermodynamics of gas adsorption. However, it is by no means the only way. Calorimetric measurements can be made for the process of adsorption, and thermodynamic parameters may be evaluated from the results. To discuss all of these in detail would require another chapter. Rather than develop all the theoretical and experimental aspects of this subject, therefore, it seems preferable to continue focusing on adsorption isotherms, extracting as much thermodynamic insight from this topic as possible. Within this context, results from adsorption calorimetry may be cited for comparison without a full development of this latter topic. 

These observations suggest that the heterogeneous effect in the S02-modenite system represents an extreme case, so much so that chemisorp-tive bonds may be stipulated (probably between the S02 and the cations). These effects would, of course, involve energy emission and show up in the calorimetric measurements. However, the specificity of the adsorption would tend to show a relatively temperature-insensitive isotherm in the low-pressure region, thus rendering the isosteric techniques of obtaining heats of adsorption/chemisorption ineffective. 

Adsorption Data for Argon on Bone Mineral at —195°. In previous sections we have emphasized that the polarizability of the adsorbate on the polar bone mineral surface contributes to high heats of adsorption. For comparison we have made calorimetric measurements of the heat of adsorption of argon at —195° on the bare surface of bone mineral and on a methanol-covered surface. The data for differential heats of adsorption of argon at —195° are shown in Figure 3 and isotherms as measured on the pilot sample are recorded in Figure 4. 

Probably the most significant comparisons which can be made are of values of properties determined from calorimetric measurements with values calculated from adsorption isotherms. Two general methods are available for the comparison of values of enthalpies determined from experiments of the two types. One involves two differentiations The change in the partial molal enthalpy, AH2, of X2, for Process 4, is determined from the differentiation with respect to n2/n1 of the integral heat of adsorption measured in a series of calorimetric experiments of the type represented by Equation 1. The values of the differential heats of adsorption (heats corresponding to the differential Process 4) are compared with values determined from the temperature variation of AG2/T for a series of values of n2/n in Process 4. This type of comparison has been made successfully by several groups of authors (3, 5, 10). 

Microcalorimeters are well suited for the determination of differential enthalpies of adsorption, as will be commented on in Sections 3.2.2 and 3.3.3. Nevertheless, one should appreciate that there is a big step between the measurement of a heat of adsorption and the determination of a meaningful energy or enthalpy of adsorption. The measured heat depends on the experimental conditions (e.g. on the extent of reversibility of the process, the dead volume of the calorimetric cell and the isothermal or adiabatic operation of the calorimeter). It is therefore essential to devise the calorimetric experiment in such a way that it is the change of state which is assessed and not the mode of operation of the calorimeter. 

As noted above, many investigations have been made of the adsorption of water on non-porous silicas. Less attention has been given to the dehydroxylation of porous silicas. An early study by Dzhigit et al. (1962) of the adsorption water vapour on a mesoporous silica gel involved both isotherm and calorimetric measurements. It was found that at very low surface coverage the adsorption enthalpy was not significantly affected by dehydroxylation, but a large difference became apparent as the surface coverage increased. A slow uptake of water vapour, which occurred after dehydroxylation, was attributed to chemisorption. 

Finally, it should be noted that calorimetric measurements can also be used to monitor adsorption phenomena at the solid-liquid interface (in a solvent). This method has been used to measure the adsorption heats evolved upon injection of dilute solutions of pyridine in alkanes ( -hexane, cyclohexane) onto an acidic solid itself in a slurry with -hexane. The amount of free base in solution is measured separately with a UV-Vis spectrometer, leading to an adsorption isotherm that is measured over the range of base addition used in the calorimetric titrations. The combined data from the calorimetric titration and adsorption measurements are analyzed simultaneously to determine equihbrium constants, quantities of sites per gram and acid site strengths for different acid sites on the solid. 

Summarizing, an attempt has been made to provide a systematic account of the thermodynamic properties of the adsorbed phase. The Gibbs adsorption equation, as an extension of the Clausius-Clapeyron equation, has played a key role in linking experimental isotherm data to the determination of molar or differential entropies and enthalpies. Similarly, calorimetric measurements can be systematically applied to obtain the same type of information. 

The simplest information from physical adsorption is, of course, the specific surface area, which has already been considered. At lower surface coverage than used for surface area measurements, the small differences between adsorption energies at different sites become detectable, and either adsorption measurements as a function of temperature, calorimetric measurement of heats of adsorption, or analysis of the adsorption isotherms themselves can reveal the existence of different heats of adsorption for different portions of the surface, together with the fraction of the surface belonging to each portion. 

Pore size distributions are determined from the hysteresis loop in gas adsorption/desorption isotherms and from calorimetric measurements by the shift in the melting (or freezing) peak for a phase transition of water inside the pores. The determination of the fractional rejection properties is done by permeation experiments of a macromolecular solute with a broad molecular weight distribution (MWD). The MWD of permeate and feed are compared and translated into a fractional rejection curve. The comparison of results obtained from these three independent methods for some characteristic membranes gives an indication of the strength and weakness of each of the methods studied. 

Muris et al. [31] used adsorption isotherms and calorimetric measurements, to study CH4 (and Kr) adsorbed on as-received carbon nanotubes produced by arc discharge, also from Montpellier. This study provided the first complete monolayer isotherm for any gas adsorbed on nanotube bundles. They found that for both CH4 and Kr there were two substeps present in the first-layer data. These two substeps indicate that in the first layer adsorption occurs on two... 

Another example of physical interest arises in flash desorption. There the population and desorption energy of molecules held in different states of binding can be determined in detail. To compare these measurements with the results of calorimetric and isotherm studies, the desorption energy for each state must first be properly weighted by its population. This is illustrated for the adsorption of CO on tungsten in Fig. 31. There a diminution of the differential heat of adsorption... 

Flow calorimetric measurements of the isothermal Joule-Thomson coefficient of a vapour also provide information on gas non-ideality which is fiee from adsorption errors. Basically, all that is required is a fixed-throttle flow calorimeter, free of heat leaks, fitted with an electric heater as shown in Figure 9 so that isothermal measurements can be made [77-alb/wor]. 

Values of the enthalpy of adsorption, determined either from the variation of adsorption with temperature (isosteric enthalpy of adsorption) or by direct calorimetric measurements, provide a valuable insight into the mechanism of adsorption. When taken together wifri the data from adsorption isotherms, they provide information which could not be extracted from either set of data alone. Heats of adsorption and other thermodynamic parameters can be obtmned either by direct calorimetric determination, -AH =j n (where ria = adsorbed amount), or by using the Clausius-Clapeyron equation and the data from isosteric measurements. However, the faacX tiiat adsorption is often irreversible in the presence of micropores, fr equently makes estimates of adsorption heats obtained from isosteres very unreliable. 

Water adsorption isotherms and calorimetric measurements have revealed that the surface of freshly calcined FSM materials is hydrophobic because of the small number of silanol groups. The material becomes more hydrophilic once... 

Another method for estimating surface heterogeneity is based on the calorimetric measurements of effects of adsorption which are more sensitive to the nature of a particular adsorption system than adsorption isotherms [292,294-298], This method is promising for characterization of adsorbent heterogeneity, but it needs accurate calorimetric data for a given adsorption system [299]. 

Further information is obtained if the amount of liquid adsorbed on the surface of the particle is also determined, permitting the combination of the data on heat of immersion with those on the amount of adsorbed liquid. Thus, molar adsorption enthalpies can be given for the characterization of the stabilizing adsorption layer [12-16]. A further benefit of adsorption excess isotherms is that it is possible to calculate from them the free enthalpy of adsorption as a function of composition. When these data are combined with the results of calorimetric measurements, the entropy change associated with adsorption can also be calculated on the basis of the second law of thermodynamics. Thus, the combination of these two techniques makes possible the calculation of the thermodynamic potential functions describing adsorption [14,17-19]. 

Values of the enthalpy of adsorption, determined either from the variation of adsorption with temperature (isosteric enthalpy of adsorption) or by direct calorimetric measurements, provide a valuable insight into the mechanism of adsorption. When taken together with data of adsorption isotherms, they provide information which could not be extracted from either set of data alone. 

Calorimetric measurements at 303 K of the adsorption heats for polar molecules (water, methanol, ethanol) on VPl-5 and AIPO4-11 were performed byjanchen et al. [268], and the results were compared with the corresponding data on AIPO4-5, two silica molecular sieves, and Na-X. Prom the measured data, it followed that the adsorption heats on the investigated aluminophos-phates were smaller than on the hydrophilic Na-X and larger than on the hydrophobic Si02 molecular sieves. Electrically neutral aluminophosphates exhibited a medium hydrophihc character. The stepwise course of the heat curves and isotherms of the polar molecules on VPl-5 may be related to the structure of the as-synthesized VPl-5 as an aluminophosphate dihydrate phase, in accordance with MAS NMR results. 

Experimentally, q is very difficult to measure directly. Attempts to find the partial of ln(P/Pj) with respect to l/Tby measuring the isotherm at two or more temperatures have not been very accurate. This is due to the uncertainty in the shape of the isotherm compared to the precision that is acceptable. Direct calorimetric measurements have been more successful. Calorimetric measurements are more precise but they measure the integral heat of adsorption, Q, and the molar heat of adsorption, Q, as defined by Morrison et al. [17]. Another quantity, the integral energy of adsorption, Q, was defined by Hill [18,19] for constant volume conditions. These quantities can be obtained with more accuracy and precision than the isosteric heat. Nevertheless, the isosteric heat is often reported. 

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