Absolute adsorption isotherm

In the work of Isirikyan and Kiselev (1961), adsorption isotherms of nitrogen were determined at 77 K in considerable detail on four different graphitized thermal blacks (with BET areas in the range 6.5-29.1 m2g 1). The isotherms are plotted in Figure 9.3 in a normalized form, as the amount adsorbed per unit area (in pmol m-2) against the relative pressure, p/p°. Kiselev and his co-workers referred to such isotherm plots as absolute adsorption isotherms , but of course they are not stricdy absolute since they are dependent on the validity of the BET-nitrogen areas - with the usual assumption that o(N2) = 0.162 nm2. 

Figure 2.2 Typical shapes of the absolute adsorption isotherm and excess absorption isotherm. The inflection of the excess adsorption isotherm can occur at high pressures.

The absolute adsorption isotherm as a function of gas-phase fuga ity is obtained directly from molecular simulations based on the grand canonical Monte Carlo (GCMC) method. Since the difference between absolute and excess adsorption is negligible at sub-atmospheric pressure, the low-pressure portion of the absolute isotherm can adso be determined from experiment. Eq. (2) is suitable for extrapolating the absolute isotherm from low to high pressure and Eq. (3) provides the conversion to excess adsorption. Experiments are needed to test these predictions of adsorption at high pressure. 

Because n, is the total mass confmed in the adsorbed phase, it must vary with the experimental condition, therefore, should be determined as a function of temperature and pressure. A straightforward method was proposed by the author [18-19]. It is known from Eq.l that /i = /i, if Fg/Og can be neglected comparing to n. Therefore, we can use the experimental values of n that comply with the constraint to formulate the model of absolute adsorption. The experimental data experienced twice transformations to reach a linear plot as was usually done for the establishment of a model for a set of data. The experimental data were utilized to the utmost in the transformation processes, and the data that do not comply with the constraint were sifted out. A plot of ln[ln(<9n)] versus np (p in kPa) was thus constructed. Parameter S was used to adjust the magnitude of n in order to avoid evaluating the logarithm of negative numbers. Its value could be set at 1, 10 or 100. A model with two parameters were obtained from the linear plots for the absolute adsorption isotherms ... 

Perfect fit was observed at experimental isotherms of different adsorption systems in large ranges of temperature and pressure [20,21]. Shown in Fig.l and Fig.2 are only examples. The model for absolute adsorption isotherm was obtained basing on the data at relatively low pressure, but the model fits the data at high pressure as well. It is concluded that the adsorption mechanism of supercritical adsorption does not change as pressure increases although maximum or even negative (excess) adsorption was observed. 

Figure 7. Absolute adsorption isotherms of n-hexane on (1) silica gel, (2) carbosil prepared on the basis of this silica gel, and (3) the same carbosils undergone hydro-thermal treatment with water at 250°C.

Figure 8. Absolute adsorption isotherms of chloroform. Symbols are the same as in Fig. 7.

Figure 10. Absolute adsorption isotherms of water vapour on (1) aerosil modified hy-drothermally (HTT) with water at 250°C, and on the following carboaerosils (2) carboaerosil 5 % C, HTT, 250°C, H2O (3) carboaerosil 5 % C, HTT, 100°C, 5% H2O2 (4) carboaerosil 19.6 % C, HTT, 350°C, H2O.

Figure 13. Absolute adsorption isotherm of n-hexane for the adsorbents listed in Table 5.

Murata and Kaneko [29] proposed a new equation of the absolute adsorption isotherm [30] for a supercritical gas in order to describe the adsorption of methane on activated carbons. The environmental aspects of supercritical gases confined in nanospaces have been reviewed by Kaneko [31]. The model assumes that the adsorption in micropores is slightly enhanced compared with that on a flat surface. The authors supported this assumption on the basis of comparison plots of experimental data obtained on activated carbons and flat surfaces like nonporous carbon black. 

In the 1950s, A. Kiselev, Zhdanov, and co-workers (12, 84, 155-159) showed that when the adsorption isotherms of water are expressed as absolute isotherms (referred to as the unit surface of the SiC>2 sample), widely different forms of amorphous silica having a completely hydroxyl-ated state adsorb the same amount of water at the same relative pressure (p/po <0.3). Thus the plots of absolute adsorption isotherms for different samples showed that the surfaces of these samples are of a similar nature. The adsorption properties of nonporous silica and silica having large pores (i.e., an absence of micropores) depend above all on the presence of OH groups and on the degree of hydroxylation of the surface. 

The absolute adsorption isotherms for —30°C and 70 C were calculated from the 20°C isotherm using the integrated form of Eq. (1) and the differential enthalpy plotted on Fig. 2. The reasonable approximation was made that the differ itial enthalpy is independent of temperature. No other assumptions were needed to calculate the excess adsorption isotherms... 

Figure 6.5. Absolute adsorption isotherms for water on different wide-pore amorphous silicas at room temperature (after the silicas were treated at 200 °C). The line shows the average of data from the literature (Kiselev, 1986 Zhuravlev, 1993).

Isirikyan AA, Kiselev AV. The absolute adsorption isotherms of vapors of nitrogen, benzene and n-hexane, and heats of adsorption of benzene and n-hexane on graphitized carbon blacks. I. Graphitized thermal blacks. J Phys Chem 1961 65 601-607. 

Fig. 2 shows the simulated methane adsorption isotherms for a variety of IRMOF materials. In order to judge the performance of the materials, both the amount adsorbed per volume and per mass are shown. The materials with the best volumetric performances are the ones with the smallest linker molecules and therefore the smallest cavities (see Fig. 1 and Table 1). Within the group of the smaller IRMOFs, materials that consist of linker molecules with more carbon atoms (e.g. the dicarboxylate naphthalene linka- of lRMOF-7 compared to the dicarboxylate benzene linker of IRMOF-1) show a better performance, as the additional carbon atoms result not only in an increased surface area but also in strongs interactions between the methane molecules and the cavities. Fig. 2 a also illustrates that the interpenetrated IRMOFs, which have comparable (in the case of IRMOF-15) or even smaller cavities (IRMOF-9), show a similar performance. At higji pressures the differences between the absolute and the excess amount adsorbed become apparent. Whereas the absolute adsorption isotherms start to level off, the excess adsorption isotherms show a maximum, which is expected for any gas above its critical temperature when the increase of the bulk gas density is larger than the increase in the density of the adsorbate (see Eq. (1)). 

At very high pressure, when foe absolute adsorption isotherms level off (compare Fig. 2) and foe rapacity of foe cavities is reached, foe solute amount adsorbed (i.e. foe number of methane molecules present in the porra) is proportional to foe free volume or porosity of foe materials as illustrated by Fig. 5 a. Note, that this relationship only holds true for foe solute amount adsorbed and not foe excess amount adsorbed as foe excess adsorption isotherms show a maximum at hi pressure. The energy distribution (Fig. S b) foows tlmt energetically less fovourable sites within foe pores such as foe centre of foe cavities (deno by foe sharp peak around -1 kJ mol" in lRMOF-10) gain in importance as every available space within foe cavities is occipi by methane molecules. 

First we show the adsorption isotherm of a very small pore (6.5 A). This pore can only accommodate one layer. Figure 4a shows the simulated absolute adsorption isotherm as well as the mass excess density isotherm using the 5-site model. The solid line with black symbols is the absolute density based on the accessible pore width, while the dashed line is that based on the physical width. The solid line is the excess density. 

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