Isotherm plots multilayer adsorption

Thus a plot of Ply versus F is a straight line with slope = jym and intercept = alym. This is called the Langmuir adsorption isotherm. For multilayer adsorption, the more complicated treatment developed by Brunauer, Emmet, and Teller (BET) allows for the determinatiOTi of surface areas (Fig. C.8). 

Sing (see Ref. 207 and earlier papers) developed a modification of the de Boer r-plot idea. The latter rests on the observation of a characteristic isotherm (Section XVII-9), that is, on the conclusion that the adsorption isotherm is independent of the adsorbent in the multilayer region. Sing recognized that there were differences for different adsorbents, and used an appropriate standard isotherm for each system, the standard isotherm being for a nonporous adsorbent of composition similar to that of the porous one being studied. He then defined a quantity = n/nx)s where nx is the amount adsorbed by the nonporous reference material at the selected P/P. The values are used to correct pore radii for multilayer adsorption in much the same manner as with de Boer. Lecloux and Pirard [208] have discussed further the use of standard isotherms. 

Adsorption of dispersants at the soHd—Hquid interface from solution is normally measured by changes in the concentration of the dispersant after adsorption has occurred, and plotted as an adsorption isotherm. A classification system of adsorption isotherms has been developed to identify the mechanisms that may be operating, such as monolayer vs multilayer adsorption, and chemisorption vs physical adsorption (8). For moderate to high mol wt polymeric dispersants, the low energy (equiUbrium) configurations of the adsorbed layer are typically about 3—30 nm thick. Normally, the adsorption is monolayer, since the thickness of the first layer significantly reduces attraction for a second layer, unless the polymer is very low mol wt or adsorbs by being nearly immiscible with the solvent. 

Figure 5.13 Isotherm and BET plot for the multilayer adsorption of nitrogen on a non-porous sample of silica gel at 77 K...

In principle, the as-method is not restricted to nitrogen adsorption and can be applied to any gas-solid physisorption system irrespective of the shape of its isotherm it can be used to check the validity of the BET area and also to identify the individual mechanisms (monolayer-multilayer adsorption, micropore filling or capillary condensation). Numerous examples of different as-plots are to be found in subsequent chapters. Here, we are concerned with the general principles of the as-method of isotherm analysis with particular reference to the evaluation of surface area. The distinctive features of various hypothetical as-plots are revealed in Figure... 

The most straightforward form of as-plot is Type 11(a) in Figure 6.1, which is for a typical Type II isotherm with a moderate value of C ( 100). The extensive range of linearity and the zero intercept are the result of unrestricted monolayer-multilayer adsorption on a non-porous solid of very similar surface structure to that of the reference material. In this case the shapes of the experimental and standard isotherms are virtually identical and therefore the slope of the as-plot is directly proportional to the ratio of the surface areas, a(S)/aref. Thus, if the value of aKl is already known, it is a simple matter to calculate atest, which we denote a(S) to indicate it is calculated by the as-method. 

In this case, it is the initial part of the isotherm which corresponds to monolayer-multilayer adsorption on the mesopore walls. If the corresponding section of the as-plot is linear and back-extrapolates to the origin, the slope provides a measure of a(S) which is now the total surface area. We may also conclude that there are no... 

The as-plots for nitrogen on VN3 in Figure 10.5 have been constructed from the desorption isotherms. In each case, the hack-extrapolated linear portion gives a positive intercept on the n axis and an upward deviation can be seen at p/p° 0.7. This behaviour is typical of adsorption at low pjp° occurring both on the external surface and within narrow micropores. At higher pip0, the upward deviation indicates that the multilayer adsorption on the external surface is accompanied by interparticle capillary condensation, which is partly responsible for the narrow hysteresis loop. 

The nitrogen isotherm data on non-porous hydroxylated silica in Table 10.1 (Bharabhani et al, 1972) have been used to construct the as-plot in Figure 12.6. Since the initial linear section can be back-extrapolated to the origin, we are reasonably sure that monolayer—multilayer adsorption has occurred on the mesopore walls before the onset of pore filling at / //>° = 0.41 and therefore that there was no detectable primary micropore filling at low / // - Similar results have been obtained by Kruk et al (1997b) and Sayari et al. (1997). 

The BET model is strictly incompatible with the energetic heterogeneity exhibited by most solid surfaces. The range of linearity of the BET plot is always restricted to a limited part of a Type II isotherm, which rarely extends above p/p° 0.35 and in some cases no higher than pjp° 0.1. In fact, a more useful empirical relation for multilayer adsorption is the FHH equation, which is generally applicable over a wide range of pjp°. 

Multilayer adsorption isotherms are usually analyzed in terms of the Brunauer, Emmett, Teller equation C/Cm = cx/(l —x)(l —x-f cx), wherex s P/Pq. where Pq is the saturation vapor pressure of the liquid c is a parameter, and the other symbols have been defined earlier. Find the equation for the spreading pressure for X < 1. Sketch plots of C/Cm and of fvs. x. 

A plot of log(A /m) against log c should be linear, with an intercept of log a and slope of Xjn-, it is generally assumed that, for systems that obey this equation, adsorption results in the formation of multilayers rather than a single monolayer. Figure 6.17 shows Freundlich isotherms for the adsorption of local anaesthetics on activated carbon the method of calculating the constants a and jn from these plots is given in Example 6.5. 

An important modification of the de Boer f-plot has been proposed by Sing and his co-workers [20], who introduced the concept of "standard isotherm" for each adsorbent system. The standard isotherm is defined for a non-porous adsorbent with a similar composition to that of the porous one being investigated. He further introduced a quantity, Ug = n/riy) where nx is the amount adsorbed on the non-porous reference material, to be used for the correction of pore radii for multilayer adsorption. 

Equation (3.27) can be applied to both adsorption and desorption branches of the isotherm. For the model of a bundle of capillary tubes, it is more appropriate to use the desorption branch of the isotherm for the determination of the pore size distribution. The basic idea is that the effective meniscus radius is the difference between the capillary radius and the thickness of the multilayer adsorption at p/p°, which can be obtained from de Boer s t-plot. In practice, at each desorption pressure, P, the capillary radius can be calculated from Eq. (3.27). The actual pore radius is then the sum of the calculated capillary radius and the estimated thickness of the multilayer. The exposed pore volume and surface area can be obtained from the volume desorbed at that specific desorption pressure. This step can be repeated at different desorption pressures. Except for the first desorption step, the desorbed volume should be corrected for the multilayer thinning on the sum of the area of the previously exposed pores. The pore size distribution can then be determined from the slope of the cumulative volume versus r curve. 

The total surface area is calculated from the amount of physical adsorption of nitrogen at 77 K. During the thirties Brunauer, Emmett, and Teller [1,2] presented a theory dealing with the multilayer adsorption of gases on solids. They assumed that the first layer of gas molecules is adsorbed more strongly than subsequent layers, and that the heat of adsorption of subsequent layers is constant. They also assumed the absence of lateral interaction between adsorbed molecules. On the basis of these much criticized assumptions they derived an adsorption isotherm, which describes the experimentally determined adsorption isotherms excellently. From the adsorption isotherm a value corresponding to the volume of the adsorbed monolayer is calculated. With physical adsorption the amount of gas adsorbed is usually plotted as a function of the relative pressure, that is the pressure... 

The second method of obtaining the pore size distribution is based on interpretation of the adsorption isotherms for N2 or other gases. The calculations allow for multilayer adsorption and eventually pore filling by capillary condensation [1]. Sometimes the adsorption and desorption plots show... 

Figure 4.2 shows typical plots of a type 11 isotherm as a function of both the pressure and its logarithm. It is quite different from type I, in that the amount adsorbed does not reach saturation but diverges as the pressure approaches a saturation value, usually the adsorbate vapor pressure Py. At this point, condensation is likely taking place. Figure 4.2c is a pictorial representation of the physical situation, showing the onset of multilayer adsorption the interaction energy of an... 

FIGURE 4.3 Schematic plot of a type III isotherm from lUPAC classification (Sing 1985)as a function of pressure (a) and the logarithm of pressure (b). The dashed line shows the point of monolayer saturation, and the dotted line marks the point of the adsorbate vapor pressure. Note the similitude with type II (Figure 4.2). In (c), a schematic drawing of the (ideal) situation is shown multilayer adsorption takes place, and here the adsorhate-surface interaction is similar or weaker than the adsorbate-adsorbate interaction, thus multilayer growth takes place as soon as the first layer forms. 

From the comparison plots obtained distinctive characteristics of adsorption on MCM-41 materials can be derived. The initial direct proportionality between a and a can be ascribed to the monolayer-multilayer adsorption on the pore walls. The small pores of AIMS-63 are filled completely by this process, which manifests itself by a knee in the comparison plot (Fig.2 0- With larger pore samples, such as TiMS-6 and AIMS-20, capillary condensation occurs, which causes a steep upward swing passing gradually into a plateau. Depending on the pore size this upward swing may occur in the reversible (Fig.2b) or irreversible (Fig.2c) parts of isotherm. 

Brunauer, Emmett, and Teller later derived equations for multilayer adsorption which reduce to Langmuir s equation in the case of a monolayer. The hyperbolic isotherm may be written v = VgbP/(l +bP), P = v/b(v —v), or P/v = l/bVg + P/Vg, where is the cc STP of adsorbate required to form a monolayer per gram of adsorbent, and b is a constant dependent on temperature and the nature of the adsorbate and adsorbent. The last form is particularly useful for the extension of data by interpolation since the plot of P/v versus P is linear. At low pressures, or perhaps more definitively low... 

The micropore volume is obtained from the backward extrapolation of the linear branch of the as plot to Os = 0 the intercept on the j -axis gives the effective origin for the monolayer-multilayer adsorption on the external surface. The Ug method has been used for the adsorption of various gases on a range of solids [67]. It has also been used for potential pore size reference materials and the results compared with mercury rosimetry [68]., For nitrogen, a normalizing factor of 2.87 was calculated from the silica TK 600 isotherm [69]. 

Another example of alcohol adsorption will be given from the data obtained for adsorption of benzyl alcohol on to alumina and well-crystallized kaolin (KGa-1) from carbon tetrachloride solutions. A SEM image of the alumina can be seen in Fig. 7. The mineral is a high-area form of aluminum oxide. Elemental analysis by X-ray fluorescence spectroscopy shows that the alumina surface contains more than 99.9% aluminum oxide. X-ray diffraction measurement indicates an amorphous surface structure. The adsorption isotherms for benzyl alcohol on to the alumina and the kaolin can be seen in Fig. 8. The isotherms are plotted on a log-log form in order to elucidate the region at low alcohol concentration. One can see that the shape of the isotherms represents typical multilayer adsorption with well-defined monolayer plateau sections. The plateaus represent the adsorption capacity of the minerals for monolayer adsorption. The data for the adsorption density at the plateaus correspond to an available area for each alcohol molecule of 0.54 nm. At higher alcohol concentrations, the increase in the adsorption densities represents a multilayered stacking of alcohol. 

Regarding the application of the Langmuir equation to physical gas adsorption on homogeneous surfaces, good examples are difficult to find. Those systems that do obey the Langmuir equation appear to be microporous. Of course, the Initial parts of multilayer isotherms fulfil the Langmuir equation, and these will be dealt with in the appropriate section. The various ways of plotting and the Information obtainable from such plots have been discussed in sec. 1.4. 

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