Isotherm shape

As pointed out in Section XVII-8, agreement of a theoretical isotherm equation with data at one temperature is a necessary but quite insufficient test of the validity of the premises on which it was derived. Quite differently based models may yield equations that are experimentally indistinguishable and even algebraically identical. In the multilayer region, it turns out that in a number of cases the isotherm shape is relatively independent of the nature of the solid and that any equation fitting it can be used to obtain essentially the same relative surface areas for different solids, so that consistency of surface area determination does not provide a sensitive criterion either. 

Many models have been proposed for adsorption and ion exchange equilibria. The most important factor in selecting a model from an engineering standpoint is to have an accurate mathematical description over the entire range of process conditions. It is usually fairly easy to obtain correcl capacities at selected points, but isotherm shape over the entire range is often a critical concern for a regenerable process. 

The basic measurement of adsorption is the amount adsorbed v, which usually is given in units of cm of gas adsorbed per gram of adsorbent. Usually this quantity is measured at constant temperature as a function of pressure p (in mm Hg), and hence is termed an isotherm. Isobars and isosteres also can be measured, but have little practical utility. It has been found that isotherms of many types exist, but the five basic isotherm shapes are shown in Figure 1, where />ois the vapor pressure. 

There are several isotherm models for which the isotherm shapes and peak prohles are very similar to that for the anti-Langmuir case. One of these models was devised by Fowler and Guggenheim [2], and it assumes ideal adsorption on a set of localized active sites with weak interactions among the molecules adsorbed on the neighboring active sites. It also assumes that the energy of interactions between the two adsorbed molecules is so small that the principle of random distribution of the adsorbed molecules on the adsorbent surface is not significandy affected. For the liquid-solid equilibria, the Fowler-Guggenheim isotherm has been empirically extended, and it is written as ... 

The way in which a material adsorbs a gas is referred to as an adsorption isotherm. All adsorption isotherms can be described by five representative curves, given in Fig. 1. The isotherm shapes reflect specific conditions for adsorption, such as pore size and heats of adsorption [6]. The most common type of isotherm and the most useful for BET measurements is the Type II isotherm. The inflection point of this isotherm usually indicates monolayer coverage of the adsorbate [9]. 

This work prompted a flurry of activity in the mid- to late 1980s to find the type IM isotherm. A number of inventions can be found in which alumina, or silica gel are blended with zeolites type X or Y to mimic the shape of the isotherm that Collier defined. Mol Sieve type DDZ-70(g) is in fact one of only a few true type IM isotherms. This product and Engelhard s type ETS-10 both have the required isotherm shape for water and deliver the benefits expected, to wit excellent capacity for water, self-sharpening mass transfer zone and low energy investment required to regenerate. Mol Sieve type DDZ-70(g) is used commercially in rotors... 

The five isotherms shapes depicted in Fig. 3.1 each reflect some unique condition. Each of these five isotherms and the conditions leading to its occurrence are discussed below. 

Rarely, if ever, does the BET theory exactly match an experimental isotherm over its entire range of relative pressures. In a qualitative sense, however, it does provide a theoretical foundation for the various isotherm shapes. Of equal significance is the fact that in the region of relative pressures near completed monolayers (0.05 P/Pq 0.35) the BET theory and experimental isotherms do agree very well, leading to a powerful and extremely useful method of surface area determination. 

The sparsity of data regarding type III isotherms, with C values of 2 or less, leaves open the question of the usefulness of the BET method for determining surface areas when type III isotherms are encountered. Often in this case it is possible to change the adsorbate to one with a higher C value thereby changing the isotherm shape. Brunauer, Copeland and Kantro, however, point to considerable success in calculating the surface area from type III isotherms as well as predicting the temperature coefficient of the same isotherms. 

The gravimetric and volumetric methods involve dosing the sample with adsorbate the system subsequently comes to an equilibrium pressure which depends on the dosing volume, the isotherm shape, and the quantity of adsorbent. The continuous flow method produces data at the concentration of adsorbate in the flow stream. Therefore, the exact position of the data point can be chosen. 

Another case that is less frequently encountered involves the situation in which previously sorbed molecules lead to a modification of the sorbent which favors further sorption (Fig. 9.3e). Such effects have been seen in studies involving anionic or cationic surfactants as sorbates. In some of these cases, a sigmoidal isotherm shape (Fig. 9.3/) has been observed, indicating that the sorption-promoting effect starts only after a certain loading of the sorbent. 

There are differences in isotherm shape, and for DTAB the behavior is not amenable to a simple explanation. Of particular interest are plots of the amount adsorbed against the mean ionic activity of the surface active agent (including the counterion of the added electrolyte). In the case of DTAB all the data, including others at various salt concentrations up to 0.5M, lie on one line which, after an initial steep rise, is linear to the c.m.c. This indicates that for other than the initial strong adsorption at low concentrations (possibly because of specific interactions with the surface) the adsorption follows the law of mass action. For SDS a similar result is obtained except that positive deviations from the straight line occur below a — 4 X 10 3M for the cases (salt concentration < O.lAf) when there is a point of inflection in the isotherm. These deviations may reflect specific interactions of the DS" with the surface when the ions are adsorbed in parallel orientation. 

The influence of temperature can be seen on Figs. 8-9. The storage capability is increasing for lower temperatures. Figure 9 compares the behaviour of the adsorption isotherms at different temperature levels for two of the more promising samples steam activated Busofit-M8 and wood-based carbon WAC 3-00 . The shape of the isotherms in the two cases is dissimilar. The isotherms for the 77 and 153 K exhibit a classical type 1 isotherm shape indicating a microporous material. The isotherms at room temperature exhibit a much less pronounced curvature (more like type II isotherm). As is seen from plots (Fig. 9) experimental data fit the calculated adsorption values (Dubinin-Radushkevich equation) with an error sufficient for practical purposes. 

The preceding set of equation is valid only for Langmuir adsorption isotherms, and numerical simulation must be used to obtain the flow rates for other adsorption isotherm shapes or for multicomponent mixtures. 

The adsorption capacity of activated carbon for pyrene is very high (up to 0.6 g/g). The uptake decreases with increasing pressure but increases with temperature. This is in correspondence with results from literature found for the adsorption of DDT [10] or phenanthrene [11] on activated carbon. One important information is the shape of the adsorption isotherms. This kind of isotherm shape is generally favourable for adsorption. For that it is possible to regen-... 

The H2O adsorption isotherms for AIPO1.-5, -11, -17, and -20 are shown in Figure 17. For comparison, the hydrophilic NaX and the hydrophobic silicalite are included. The isotherm shape for A1P0 -11 and A1P0 -17, like that of NaX and silicalite, is Type I, typical of micropore filling. The isotherm shape of the AlPOi.-20... 

The validity of this simplifying assumption is evidently dependent on the isotherm shape the error is likely to be within a few percent provided that C 100. Experience confirms that the errors in the estimation of rtm by the single point method become appreciable when C < 80. 

In principle, a /-plot can be used to assess the micropore capacity provided that the standard multilayer thickness curve has been determined on a non-porous reference material with a similar surface structure to that of the microporous sample. In our view, it is not safe to select a standard isotherm with the same BET C value (i.e. the procedure recommended by Brunauer (1970) and Lecloux and Pirard (1979)) since this does not allow for the fact that the sub-monolayer isotherm shape is dependent on both the surface chemistry and the micropore structure. 

A systematic study of krypton adsorption on exfoliated graphite was subsequently undertaken by Thorny and co-workers (Thorny and Duval, 1969 Thorny et al., 1972). Their stepwise isotherm, determined at 77.3 K, is shown in Figure 4.1. The layer-by-layer nature of the physisorption process is clearly evident - at least up to four molecular layers. This isotherm shape is remarkably similar to that of the krypton isotherm on graphitized carbon black reported by Amberg et al., (1955). 

The as-plots for sample DC(1200)6 were found to be linear over the recorded ranges of both isotherms. This correspondence of isotherm shape is to be expected since the adsorbent structure has not been appreciably changed as a result of the 6-hour calcination at 1200°C. The multilayer sections of the other as-plots were for the most part linear, but the monolayer sections all exhibited significant deviation. The fact that the linear multilayer plots can be back-extrapolated to the origin was an indication that the multilayer development had not been affected to any great extent by the change in structure of the adsorbent. 

Representative nitrogen isotherms and the corresponding comparison plots are shown in Figure 10.27. The latter have been constructed by taking the undecomposed Mg(OH)2 as the reference material. Any change in isotherm shape is therefore manifested as a non-zero intercept and/or a deviation from linearity. 

Somewhat similar differences in isotherm shape have been reported by other investigators (Franke et al., 1993 Rathousky et al., 1994 Ravikovitch et al., 1995 Schmidt et al., 1995 Llewellyn et al., 1996). Very recently (Branton et al., 1997), a 3.4 nm siliceous form of MCM-41 has been found to give a reversible Type IV nitrogen isotherm with a sharp pore-filling step in the range p/p = 0.33-0.37. The values of the BET area and pore volume derived from the nitrogen isotherm are recorded in Table 12.5. Carbon tetrachloride isotherms were determined on the 3.4 nm siliceous MCM-41 at the temperatures of 273, 288, 303 and 323 K. These isotherms were essentially of Type V that at 325 K was completely reversible, while the others had narrow, almost vertical hysteresis loops of Type HI (see Figure 12.8). 

---