Bottle-neck pores

McBain accounted for hysteresis by assuming that the pores contained a narrow opening and a wide body, the so-called bottle-neck shape. His model asserts that during adsorption the wide inner portion of the pore is filled at high relative pressures but cannot empty until the narrow neck of the pore first empties at lower relative pressures during desorption. Therefore, for bottle-neck pores the adsorption isotherm corresponds to the equilibrium condition. However, the model proposed by McBain ignores the question of how condensation into the wider inner portion of the pore can occur once the narrow neck has been filled at low relative pressures. 

On thermodynamic grounds pore-size distributions are measured using the desorption isotherm, (see equations 8.8 and 8.9). The exception to this are bottle-neck pores exhibiting type E hysteresis. In this case the equilibrium isotherm is that of adsorption because the unstable state is associated with the condition that the wide portion of the pore is unable to evaporate until the narrow neck empties. Regardless of which isotherm is used, however, the mathematical treatment remains the same. 

The method shown in Table 8.1 uses data from either the adsorption or desorption isotherm. However, as stated previously, the desorption curve is usually employed except in those cases where the adsorption curve corresponds to the thermodynamically more stable condition such as in the case of bottle-neck pores. In either case, for ease of presentation, the data is evaluated downward from high to low relative pressures. 

Gas separation is achieved by two alternative mechanisms kinetic separation and selective adsorption. Kinetic separation is based on the kinetically-controlled gas diffusion caused by the constrictions of the apertures of the pores. The diameters of the bottle-necked pores are in the same range as those of the adsorbed molecules. Thus, when a CMS is used in an air separation process, the oxygen molecules, which have a smaller diameter than the nitrogen molecules. 

The pores grow in size with exposure time Low tortuosity factors Low pore surface area per total paint volume Few bottle-neck structures... 

Intrusion-extrusion hysteresis has been attributed to ink-bottle shaped pores. In pores of this type intrusion cannot occur until sufficient pressure is attained to force mercury into the narrow neck, whereupon the entire pore will fill. However, on depressurization the wide-pore body cannot empty until a lower pressure is reached, leaving entrapped mercury in the wide inner portion. The ink-bottle model ignores several factors which may reduce it to an untenable concept. These include the following ... 

The nitrogen adsorption-desorption isotherms at 77 K showed that the pore structures of smectite-type materials are of a bottle-neck type [3]. The surface areas of Ni-481 and Ni-359 treated at 873 K were 381 and 184 m2 g 1, respectively (Figure 2). The synthetic smectites have large surface areas because many small fragments with the same smectite structure are intercalated in the interlayer region [4]. 

A severe limitation of the bundle of capillaries model is that it can give erroneous readings for materials with "ink-bottle" pores. In this case, the pores are emptied at the capillary pressure of the neck followed by the discharge of the large cavity, resulting in a large reading of the desorbed volume at the capillary pressure of the "ink-bottle" neck. 

The pore diameter will affect the bonded phase by controlling the coverage density of the alkyl-bonded phase and the migration of analytes in and out of (he pores during sorption. When the silica has pores less than -10 nm diameter (he possibility of bottle-necking occurs (Fig. 2.2). In this case, the pore cannot be easily accessed by the monochlorosilane reagent and so there are zones of the sorbent that remain underivatized. 

Figure 2.2. Example of bottle-necking of silica pores, which prevents bonding of the alkyl phase in the deeper pores of the silica gel. [Reproduced from the Journal of Chromatographic Science by permission of Preston Publications, A Division of Preston Industries, Inc. Also published with permission of the authors, Horvath and Melander (1977).]...

With respect to the absolute values of porosity parameters, the data from adsorption isotherms are much less reliable. When considering these data, one has to remember that they actually characterize an equivalent model system composed of an ensemble of open-ended, independent cylindrical capillaries of constant width. This model is far from the real structure of a polymeric adsorbent. Another serious drawback is the rather arbitrary choice between the adsorption and the desorption branches of the hysteresis loop for the calculations. If, indeed, open-ended channels are anticipated in the material, the desorption branch should give more representative results. On the other hand, if closed ink-bottle-type pores are present, the adsorption branch could be used. Filling of a bottle-type pore starts at a low p/p value corresponding to the diameter of the neck and ends at a higher relative pressure corresponding to the size of the bottle s interior, whereas evaporation proceeds at a single p/p value determined by the meniscus in the neck. Partially for this reason, the... 

The measured pore size distribution curves are frequently biased towards the small pore sizes due to the hysteresis effect caused by ink bottle shaped pores with narrow necks accessible to the mercury and wide bodies which are not. Meyer [24] attempted to correct for this using probability theory and this altered the distribution of the large pores considerably. Zgrablich et al. [25] studied the relationship between pores and throats (sites and bonds) based on the co-operative percolation effects of a porous network and developed a model to take account of this relationship. The model was tested for agglomerates of spheres, needles, rods and plates. Zhdanov and Fenelonov [26] described the penetration of mercury into pores in terms of percolation theory. 

The variant of the cylindrical model which has played a prominent part in the development of the subject is the ink-bottle , composed of a cylindrical pore closed one end and with a narrow neck at the other (Fig. 3.12(a)). The course of events is different according as the core radius r of the body is greater or less than twice the core radius r of the neck. Nucleation to give a hemispherical meniscus, can occur at the base B at the relative pressure p/p°)i = exp( —2K/r ) but a meniscus originating in the neck is necessarily cylindrical so that its formation would need the pressure (P/P°)n = exp(-K/r ). If now r /r, < 2, (p/p ), is lower than p/p°)n, so that condensation will commence at the base B and will All the whole pore, neck as well as body, at the relative pressure exp( —2K/r ). Evaporation from the full pore will commence from the hemispherical meniscus in the neck at the relative pressure p/p°) = cxp(-2K/r ) and will continue till the core of the body is also empty, since the pressure is already lower than the equilibrium value (p/p°)i) for evaporation from the body. Thus the adsorption branch of the loop leads to values of the core radius of the body, and the desorption branch to values of the core radius of the neck. 

Fig. 3.12 Ink bottle pores with (o) cylindrical body and (/>). (c). tapering body the neck is cylindrical in each case.

Perhaps the best known explanation of reproducible hysteresis in mercury porosimetry is based on the ink bottle model already discussed in connection with capillary condensation (p. 128). The pressure required to force mercury with a pore having a narrow (cylindrical) neck of radius r, will be... 

In a pore system composed of isolated pores of ink-bottle shape, the intrusion curve leads to the size distribution of the necks and the extrusion curve to the size distribution of the bodies of the pores. In the majority of solids, however, the pores are present as a network, and the interpretation of the mercury porosimetry results is complicated by pore blocking effects. 

Pores may be present as structural features (e. g. between domains) or as a result of aggregation of particles. They may also be the result of partial dehydroxylation (oxide hydroxides) or dissolution. Although the shapes of pores can be quite variable, there are some definite, basic forms. The commonest of these are 1) slit shaped, the walls of which may or may not be parallel 2) ink bottle which are closed upon all sides but one from which a narrow neck opens and 3) cylindrical. Upon partial dissolution, pores bounded by well-defined crystal planes (e. g. 102 in goethite) develop (Chap. 12). 

In those cases where pores are ink-bottle in shape, a method, proposed by Reverberi for calculating the sizes of the narrow and wide portions of the pore from intrusion-extrusion curves can be used. The method involves scanning the hysteresis loop by means of a series of pressurization and partial depressurization cycles in order to determine the volume of the wide inner portion of pores having neck radii in various radius intervals. 

In the second mechanism the topology of the pore network plays a role [394], During the desorption process, vaporization can occur only from pores that have access to the vapor phase, and not from pores that are surrounded by other liquid-filled pores. There is a pore blocking effect in which a metastable liquid phase is preserved below the condensation pressure until vaporization occurs in a neighboring pore. Therefore, the relative pressure at which vaporization occurs depends on the size of the pore, the connectivity of the network, and the state of neighboring pores. For a single ink bottle pore this is illustrated in Fig. 9.15. The adsorption process is dominated by the radius of the large inner cavity while the desorption process is limited by the smaller neck. 

Another theory of adsorption hysteresis considers that there are two types of pores present, each having a size distribution. The first type are V-shaped, and these fill and empty reversibly. The second type have a narrow neck and a relatively wide interior. These ink-bottle pores are supposed to fill completely when a plp0 value corresponding to the relatively wide pore interior is reached, but once filled they retain their contents until plp0 is reduced to a value corresponding to the relatively small width of the pore neck. 

This difference between H O and N adsorption data has been attributed to either the accessibility of water to interlayer spaces in the tobermorite gel or to the presence of ink bottle pores with narrow necks and wide bodies. The considerable increase (4-5 times) in pore surface and pore volume available to nitrogen in pastes containing calcium chloride suggests that the crumpled pore type of morphology is more open than the spicular type [20],... 

Many porous adsorbents give Type H2 hysteresis loop, but in such systems PSD or pore shape is not well-defined. Indeed, the H2 loop is especially difficult to interpret. In the past it was considered to be a result of the presence of the pores with narrow necks and wide bodies (ink-bottle pores), but it is now recognized that this provides an over-simplified picture and the pore connectivity effects must be taken into account.79... 

During desorption, as the relative vapor pressure is reduced, pore solids in which capillary condensation occurs often show a hysteresis loop. The simplest interpretation of this phenomenon is given by the ink-bottle model (6). In the framework of this model (Fig. 12) the adsorption and desorption processes are controlled, respectively, by the void and neck sizes. Thus, desorption from a given pore occurs at a lower pressure than adsorption. 

However, as Everett (60) pointed out, the analogy of a pore as a narrownecked bottle is overspecialized, and in practice a series of interconnected pore spaces rather than discrete bottles is more likely. In the latter case, a void with the radius r > rp is empty during the desorption process only if it is connected with the outer surface by a chain of voids and necks with r > Kp. Thus, the emptying of a given pore is not solely determined by its immediate characteristics. Hence, a correct analysis of the desorption branch of the isotherm should take into account the three-dimensional interconnection of various voids. This problem can be solved by using percolation theory, as has been done by W ll and Brown (14), Kheifets and Nei-mark (15-17), Mason (18-21), Fenelonov et al. (22-25), Palar and Yortsos (26,27), Mayagoitia et al. (28-32), Yanuka (33), and Seaton (34). 

Normally, the moisture sorption-desorption profile of the compound is investigated. This can reveal a range of phenomena associated with the solid. For example, on reducing the RH from a high level, hysteresis (separation of the sorption-desorption curves) may be observed. There are two types of hysteresis loops an open hyteresis loop, where the final moisture content is higher than the starting moisture content due to so-called ink-bottle pores, where condensed moisture is trapped in pores with a narrow neck, and the closed hysteresis loop may be closed due to compounds having capillary pore sizes. 

The analysis of the hysteresis loop using the adsorption branch or the desorption branch depend on the shape of the pore. For the ink-bottle shape, once the pore is full the desorption will occur from the narrow neck and this is replenished from the larger parts of the pore thus analysis of the desorption branch... 

Kraemer " and McBain explained hysteresis on the basis of pore geometry of the adsorbent These workers considered the pores of the adsorbent as ink-bottle shaped, so that the vapor pressure during adsorption is determined by condensation in larger diameters of the bottle, while the pressure at which desorption occurs corresponds to the narrow neck. Rao and Katz found this hypothesis to furnish a qualitative explanation for their observations on adsorption-desorption hysteresis with several gels and sorbates. However, this concept could not explain the complete elimination of the hystereus effect without a marked fall in the adsorption capacity. 

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