Absolute Adsorption

1 TYPES OF ISOTHERMS FOR ADSORPTION FROM SOLUTION PHASE 

Two types of adsorption can be recognized when considering adsorption from binary solutions on solid surfaces the preferential or selective adsorption and the true 

This used to be called apparent adsorption and represents the surface excess, which is defined as the excess of solute in moles present in unit area of the solid-liquid interface over that present in a region of the bulk liquid containing the same number of moles of the solution. In other words, it represents the extent by which the bulk liquid is impoverished with respect to one component, because the surface layer is correspondingly enriched. 

Absolute adsorption (or simply adsorption) is equivalent to the actual quantity of that component present in the adsorbed phase, as opposed to its surface excess relative to the bulk liquid. Simply, it is the surface concentration. 

It may be mentioned that preferential adsorption is directly related to the experimentally measured quantity and can be expressed directly and unambiguously. Thus, isotherms based on preferential adsorption can normally be used in practical applications. The determination of absolute adsorption, however, have led to a much better understanding of the adsorption process and especially of the meaning of preferential adsorption. 

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Adsorption rates were not significantly affected by molecular weight, but flocculation was about 25% faster for the high molecular weight polymer. Two shear rate levels were tested 1800 s-1 and 8000 s-. The absolute adsorption and flocculation rates increased with shear rate as expected. The "pseudo" OFC appeared to be shifted to a higher value for the higher shear rate. Collision efficiencies were affected by both molecular weight and shear rate, as discussed below. 

The second concept that has to be considered is that of absolute adsorption or adsorption of an individual component. This can be considered as the true adsorption isotherm for a given component that refers to the actual quantity of that component present in the adsorbed phase as opposed to its relative excess relative to the bulk liquid. It is a surface concentration. From a practical point of view, the main interest lies in resolving the composite isotherm into individual isotherms. To do this, the introduction of the concept of a Gibbs dividing surface is necessary. Figure 10.6 shows the concept of the surface phase model. 

The values obtained for the parameter a = A (298 K) are not reported in Table 4.9, since absolute adsorption magnitudes are not directly measured by the FTIR methodology [97],... 

The adsorptive energy, U, defined by Equation 2, is temperature-dependent, because of the variation of aEvib with T. An absolute adsorptive potential that refers to the zero point energy of the adsorbed molecule, for which aEvib = V2Nhv, has the advantage of being temperature-independent. We define this quantity as... 

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. 

The absolute adsorption is predicted from theoretical calculations and is the amount of hydrogen which is adsorbed in the porous material, not considering the gas phase. The relation between the excess adsorption (N and the absolute adsorption (N ds) can be esily derived considering a typical adsorption experiment [21] The amount of gas adsorbed on a sample (Nads) is expressed as the total amount of gas introduced in the sample cell (N ) minus the free molecules in the gas phase. (2.4) ... 

Therefore the relation between experimentally measured excess adsorption and the absolute adsorption can be expressed as in (2.6) ... 

Especially under conditions for which the density ofthe gas phase is comparable to or higher than the density of the adsorbed phase (Qg/Qa 1), that is, low temperatures and high pressures, the excess adsorption differs from the absolute adsorption. 

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.

Experimental measurements yield excess adsorption molecular simulations calculate absolute adsorption. The relationship between the two variables is given by ... 

Vj, is the specific pore volume of the material typical values are 200-400 cm /kg for zeolites and up to 1000 cm /kg for activated carbon, n is the actual number of molecules contained in the micropores the excess adsorption subtracts from n the number of molecules which would have been present in the micropores at the bulk density in the absence of adsorption. The (oversimplified) case when absolute adsorption is described by the Langmuir equation and the gas obeys the perfect gas law p - PjRT) has been worked out in detail for the isotherms and thermodynmnic functions (enthalpy, entropy, etc.) [2j. 

The key step in this development is the recognition that a Type I adsorption equation like Eq. (1) applies to absolute adsorption n. Absolute adsorption refers to the actual number of molecules present in the micropores and increases monotonically with pressure to an asymptote called the saturation capacity m. Ebcperimental excess aulsorption isotherms pass through a maximum and then decrease with pressure. 

The principles of solution thermodynamics can be applied to absolute adsorption variables without any of these complications. For absolute variables, which arise naturally in molecular simulation, the pressure is a single-valued function of n, the differential functions exhibit no singularities, and the selectivity approaches a finite value as P —> oo. Absolute adsorption may be determined experimentally by measuring excess adsorption in the usual way (volumetric or gravimetric method) at sub-atmospheric pressure where the difference between absolute and excess adsorption is negligible. 

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. 

Abstract Paradoxes, problems and ideologies in the study of supercritical adsorption were discussed. A macroscopic interpretation of supercritical adsorption was presented basing on a general model that derived at fiom the Gibbs definition and a straightforward method of determining absolute adsorption. The model does not include any assumption, but relies on experimental data and keeps the formal continuity of adsorption theory. It was shown to apply for wide ranges of temperature and pressure, and bore an impact to the characterization of adsorbents. 

The experimentally measured amount adsorbed, n, is an excess quantity concentrated in the so-called adsorption space over the bulk gas phase, and the so-called absolute adsorption, nt, corresponds to the total quantity of adsorbate in the mentioned space. According to Gibbs, there is a thermocfynamically distinct inter ce between the bulk gas and the equilibrium adsorbed phase, the density of which p is remarkably higher than that of the bulk gas phase V, is the volume of the adsorbed phase, and the product... 

All isotherm equations were derived at for absolute adsorption. Therefore, there are more choices for the expression of rit. However, the initial part of supercritical isotherms looks like IVpe-I, and a simple model proposed for this kind of adsorption on heterogeneous sur ce [IS] was applied ... 

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. 

A proof for die existence of the border can be found in a parameter of the above-mentioned model of supercritical adsorption isotherms. Parameter n" in Eq.(2) indicates a saturated amount of absolute adsorption, which is the maximum adsorbate... 

Siperstein F., Talu O. and Myers A. L. Gas storage absolute adsorption versus excess adsorption. Proceedings FOA 7 (2001) pp.311-318. 

Experimentally, there are some difficulties in using methane or carbon dioxide as a probe at ambient temperatures. One is the need to adsorb at high pressures (in reference 6 pressures of up to 40 atmospheres were used). A second problem is that the correction needed to convert from siu ce excess to absolute adsorption, implying an assumption about the accessible pore volume, cannot be ignored, and may become dominant at h pressure. 

Molecular simulations yield absolute adsorption or the actual number of molecules in the nanopores. Experiments measure excess adsorption, which is the number of molecules in the nanopores in excess of the amount that would be present in the pore volume at the equilibrium density of the bulk gas. The difference between absolute and excess adsorption is negligible at the sub-atmospheric pressures of greatest interest. For supercritical gases adsorbed at high pressure (e.g. 100 bar), the difference between absolute and excess adsorption is too large to ignore. ... 

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.

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