Calorimetric isotherms

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.)... 

The computation of the integral molar entropy of adsorption at any coverage requires knowledge of the adsorption isotherm " = "(p) at a given temperature combined with the calorimetric isotherm Q = Q" (p). We must emphasize the fact that Q is measured by definition under reversible conditions. Therefore, when applying Eq. (48) to experimental data, the quasireversibility of the process must be verified. 

Murat, M. and Karmazsin, E.. "Influence de L origine du Gypse sur La Vitesse D hydration du Semihydrate. Etude par Calorimetric Isotherme, Proceedings of Ewfof(vpsum. Barcelona. Spain, 1977. 

Figure 2.27. Differential calorimetric isotherms of hydrogen and oxygen adsorption on Ir/Si02 (cited in D.Yu.Murzin, On surface heterogeneity and catalytic kinetics, lndusrrial and Engineering Chemistry Research. 44 (2005), 1688-1697)...

Tian-Calvet heat flow equipment (Setaram) was used for microcalorimetric measurements. Every sample was evacuated (10 Pa) overnight at 673 K before the successive introduction of small doses of the probe gas (ammonia or carbon dioxide). The equilibrium pressure relative to each adsorbed amount was measured by means of a differential pressure gauge (Datametrics). The run was stopped at a final equilibrium pressure of 133.3 Pa. The adsorption temperature was maintained at 353 K, in order to limit physisorption. After overnight outgassing at the same temperature, a second run was carried out up to 133.3 Pa. The adsorption and calorimetric isotherms were obtained from each adsorption/readsorption... 

It was established that the linear growth rate of the mesophase domains (the light bands) is constant during a rather long period of time and only at the terminal stages, a certain levelling-olf occurs (typical results are shown in Fig. 9). The calorimetric isotherms of the heat evolution resulting from the mesophase formation (Fig. 10) have an S-shape as in the case of crystallization of polymers. However, the heat of transition decreases considerably when temperature increases. 

The analysis of these calorimetric isotherms in terms of the Avrami equation (Fig, 11) shows that the kinetics of the mesophase formation is described by the Avrami parameter n = 1.75 0.05. Such a value of the morphological parameter was interpreted as two-dimensional growth of lamellar structures on heterogeneous nuclei. 

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)...

In the following, the very simple case of CO adsorbed at r = 303 K on dehydrated Na- and K-MFI will be discussed (vide supra in Fig. 1.5 the experimental volumetric and calorimetric isotherms). The number of CO molecules adsorbed per gram of zeolite at pco represents the number of occupied sites (Ns), whereas the number of charge-balancing cations exposed per gram of zeolite represents the total available sites (N). 

Adsorbed amounts and integral heat evolved will be suitably reported as a function of the increasing equilibrium pressure, i.e. as volumetric and calorimetric isotherms, respectively. Adsorbed amounts riads = X tsuads were obtained by adding the individual doses amounts, Anads, and will be reported either as mol per unit mass (mol g ) or per unit surface area (mol m ), or as molecules per square nanometer. In zeolites, in order to compare from a structural point of view the affinity of different zeolites towards the given adsorptive, the adsorbed amounts will be more suitably... 

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...

In Fig. 1.16 the differential heat of NH3 adsorption on one of the all-silica defective specimens discussed above (Sil-A) will be compared with the correspondent heat of adsorption on the Brpnsted acidic H-MFI zeolite. Note that Sil-A will be hereafter named MFI—def, in agreement with the nomenclature of the correspondent volumetric-calorimetric isotherms illustrated in Fig. 1.12. 

---