Adsorbents capillaries

For porous adsorbents capillary condensation is a common phenomenon. It leads to hysteresis in the adsorption curve. 

In case of mesopores whose walls are formed by a great number of adsorbent atoms or molecules the boundary of interphases has a distinct physical meaning. That means that the adsorbent surface area has also a physical meaning. In micropores the action of adsorption forces does not occur throughout their volume but at a close distance from their walls. Therefore the mono- and multilayer adsorption takes place successively on the surface of mesopores and their final fill proceeds according to the mechanism of adsorbate capillary condensation [14]. The basic parameters characterizing mesopores are then specific surface area, pore volume and pore-size or pore-volume distribution. Mesopores, like macropores play also an essential role in the transport of adsorbate molecules inside the micropores volume. 

The mechanism of adsorption on the macropores surface does not differ from that on flat surfaces. The specific surface area of macroporous solids is very small, that is why adsorption on this surface is usually neglected [57]. For obvious reasons, the adsorbate capillary condensation does not occur in macropores. 

The capillary condensation phenomenon was discovered by Zsigismody [139], who investigated the uptake of water vapour by silica materials. Zsigismody proved that the condensation of physicosorbed vapours can occur in narrow pores below the standard saturated vapour pressure. The main condition for the capillary condensation existence is the presence of liquid meniscus in the adsorbent capillaries. As it is known, the decrease of saturated vapour pressure takes place over the concave meniscus. For cylindrical pores, with the pore width in the range 2-50 nm, i.e., for the mesopores, this phenomenon is relatively well described by the Kelvin equation [14]. This equation is still widely applied for the pore size analysis, but its main limitations remain unresolved. Capillary condensation is always preceded by mono- and/or multilayer adsorption on the pore walls. It means that this phenomenon plays an important, but secondary role in comparison with the physical adsorption of gases by porous solids. Consequently, the true pore width can be assessed if the adsorbed layer thickness is known. 

It should be noted that here, as with capillary rise, there is an adsorbed film of vapor (see Section X-6D) with which the meniscus merges smoothly. The meniscus is not hanging from the plate but rather fiom a liquidlike film [53]. The correction for the weight of such film should be negligible, however. 

While Eq. III-18 has been verified for small droplets, attempts to do so for liquids in capillaries (where Rm is negative and there should be a pressure reduction) have led to startling discrepancies. Potential problems include the presence of impurities leached from the capillary walls and allowance for the film of adsorbed vapor that should be present (see Chapter X). There is room for another real effect arising from structural peiturbations in the liquid induced by the vicinity of the solid capillary wall (see Chapter VI). Fisher and Israelachvili [19] review much of the literature on the verification of the Kelvin equation and report confirmatory measurements for liquid bridges between crossed mica cylinders. The situation is similar to that of the meniscus in a capillary since Rm is negative some of their results are shown in Fig. III-3. Studies in capillaries have been reviewed by Melrose [20] who concludes that the Kelvin equation is obeyed for radii at least down to 1 fim. 

Calculate the vapor pressure of water when present in a capillary of 0.1 m radius (assume zero contact angle). Express your result as percent change from the normal value at 25°C. Suppose now that the effective radius of the capillary is reduced because of the presence of an adsorbed film of water 100 A thick. Show what the percent reduction in vapor pressure should now be. 

Protein adsorption has been studied with a variety of techniques such as ellipsome-try [107,108], ESCA [109], surface forces measurements [102], total internal reflection fluorescence (TIRE) [103,110], electron microscopy [111], and electrokinetic measurement of latex particles [112,113] and capillaries [114], The TIRE technique has recently been adapted to observe surface diffusion [106] and orientation [IIS] in adsorbed layers. These experiments point toward the significant influence of the protein-surface interaction on the adsorption characteristics [105,108,110]. A very important interaction is due to the hydrophobic interaction between parts of the protein and polymeric surfaces [18], although often electrostatic interactions are also influential [ 116]. Protein desorption can be affected by altering the pH [117] or by the introduction of a complexing agent [118]. 

The Washburn equation has most recently been confirmed for water and cyclohexane in glass capillaries ranging from 0.3 to 400 fim in radii [46]. The contact angle formed by a moving meniscus may differ, however, from the static one [46, 47]. Good and Lin [48] found a difference in penetration rate between an outgassed capillary and one with a vapor adsorbed film, and they propose that the driving force be modified by a film pressure term. 

As a general rule, adsorbates above their critical temperatures do not give multilayer type isotherms. In such a situation, a porous absorbent behaves like any other, unless the pores are of molecular size, and at this point the distinction between adsorption and absorption dims. Below the critical temperature, multilayer formation is possible and capillary condensation can occur. These two aspects of the behavior of porous solids are discussed briefly in this section. Some lUPAC (International Union of Pure and Applied Chemistry) recommendations for the characterization of porous solids are given in Ref. 178. 

Below the critical temperature of the adsorbate, adsorption is generally multilayer in type, and the presence of pores may have the effect not only of limiting the possible number of layers of adsorbate (see Eq. XVII-65) but also of introducing capillary condensation phenomena. A wide range of porous adsorbents is now involved and usually having a broad distribution of pore sizes and shapes, unlike the zeolites. The most general characteristic of such adsorption systems is that of hysteresis as illustrated in Fig. XVII-27 and, more gener-... 

Adsorbents such as some silica gels and types of carbons and zeolites have pores of the order of molecular dimensions, that is, from several up to 10-15 A in diameter. Adsorption in such pores is not readily treated as a capillary condensation phenomenon—in fact, there is typically no hysteresis loop. What happens physically is that as multilayer adsorption develops, the pore becomes filled by a meeting of the adsorbed films from opposing walls. Pores showing this type of adsorption behavior have come to be called micropores—a conventional definition is that micropore diameters are of width not exceeding 20 A (larger pores are called mesopores), see Ref. 221a. 

This equation describes the additional amount of gas adsorbed into the pores due to capillary action. In this case, V is the molar volume of the gas, y its surface tension, R the gas constant, T absolute temperature and r the Kelvin radius. The distribution in the sizes of micropores may be detenninated using the Horvath-Kawazoe method [19]. If the sample has both micropores and mesopores, then the J-plot calculation may be used [20]. The J-plot is obtained by plotting the volume adsorbed against the statistical thickness of adsorbate. This thickness is derived from the surface area of a non-porous sample, and the volume of the liquified gas. 

The basis of the classification is that each of the size ranges corresponds to characteristic adsorption effects as manifested in the isotherm. In micropores, the interaction potential is significantly higher than in wider pores owing to the proximity of the walls, and the amount adsorbed (at a given relative pressure) is correspondingly enhanced. In mesopores, capillary condensation, with its characteristic hysteresis loop, takes place. In the macropore range the pores are so wide that it is virtually impossible to map out the isotherm in detail because the relative pressures are so close to unity. 

If the adsorbent contains mesopores, capillary condensation will occur in each pore when the relative pressure reaches a value which is related to the radius of the pore by the Kelvin equation, and a Type IV isotherm will... 

It must always be borne in mind that when capillary condensation takes place during the course of isotherm determination, the pore walls are already covered with an adsorbed him, having a thickness t determined by the value of the relative pressure (cf. Chapter 2). Thus capillary condensation occurs not directly in the pore itself but rather in the inner core (Fig. 3.7). Consequently the Kelvin equation leads in the first instance to values of the core size rather than the pore size. The conversion of an r value to a pore size involves recourse to a model of pore shape, and also a knowledge of the angle of contact 0 between the capillary condensate and the adsorbed film on the walls. The involvement of 0 may be appreciated by consideration... 

In general there are two factors capable of bringing about the reduction in chemical potential of the adsorbate, which is responsible for capillary condensation the proximity of the solid surface on the one hand (adsorption effect) and the curvature of the liquid meniscus on the other (Kelvin effect). From considerations advanced in Chapter 1 the adsorption effect should be limited to a distance of a few molecular diameters from the surface of the solid. Only at distances in excess of this would the film acquire the completely liquid-like properties which would enable its angle of contact with the bulk liquid to become zero thinner films would differ in structure from the bulk liquid and should therefore display a finite angle of contact with it. 

Fig. 3.15 (a) A pore in the form of an interstice between close-packed and equal-sized spherical particles. The adsorbed him which precedes capillary condensation is indicated, (b) Adsorption isotherm (idealized). 

When the relative pressure falls to pj/p", the second group of pores loses its capillary condensate, but in addition the film on the walls of the first group of pores yields up some adsorbate, owing to the decrease in its thickness from t, to t. Similarly, when the relative pressure is further reduced to pj/p°, the decrement (nj-Wj) in the uptake will include contributions from the walls of both groups 1 and 2 (as the film thins down from tj to fj), in addition to the amount of capillary condensate lost from the cores of group 3. It is this composite nature of the amount given up at each step which complicates the calculation of the pore size distribution. 

Consider stage i in the desorption process where the thickness of the adsorbed film is and the pores of radius r, have just lost their capillary condensate. The volume of multilayer lining the pores of any radius r, where r > ri, will then be (since the pores are cylindrical) ... 

In formulating an explanation of this enhanced adsorption, there are several features to be accounted for the increase in adsorption occurs without hysteresis the amount of adsorbate involved is relatively small the Kelvin r -values are also small (e.g. for nitrogen, less than 17 A) and the effect is found in a region of relative pressures where, according to the simple tensile strength hypothesis, capillary condensate should be incapable of existence. 

At the point where capillary condensation commences in the finest mesopores, the walls of the whole mesopore system are already coated with an adsorbed film of area A, say. The quantity A comprises the area of the core walls and is less than the specific surface A (unless the pores happen to be parallel-sided slits). When capillary condensation takes place within a pore, the film-gas interface in that pore is destroyed, and when the pore system is completely filled with capillary condensate (e.g. at F in Fig. 3.1) the whole of the film-gas interface will have disappeared. It should therefore be possible to determine the area by suitable treatment of the adsorption data for the region of the isotherm where capillary condensation is occurring. 

These various considerations led Pierce, Wiley and Smith in 1949, and independently, Dubinin, to postulate that in very fine pores the mechanism of adsorption is pore filling rather than surface coverage. Thus the plateau of the Type 1 isotherm represents the filling up of the pores with adsorbate by a process similar to but not identical with capillary condensation, rather than a layer-by-layer building up of a film on the pore walls. 

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