Slit-shaped pore

The pore systems of solids are of many different kinds. The individual pores may vary greatly both in size and in shape within a given solid, and between one solid and another. A feature of especial interest for many purposes is the width w of the pores, e.g. the diameter of a cylindrical pore, or the distance between the sides of a slit-shaped pore. A convenient classification of pores according to their average width originally proposed by Dubinin and now officially adopted by the International Union of Pure and Applied Chemistry is summarized in Table 1.4. 

The slit-shaped model has come into prominence in recent years, as electron microscopy has revealed the prevalence of solids composed of platelike particles the technique, indeed, has now developed to the point where it is possible to identify the presence of slit-shaped pores, and even to measure their width. In the ideal case where the sides of the slit are truly planar and parallel, the hysteresis takes an extreme form since the mean radius of curva-... 

Fig. 3.16 A slit-shaped pore of width d, showing adsorbed film of thickness i and core of width d. ...

Calculations of the interaction energy in very fine pores are based on one or other of the standard expressions for the pair-wise interaction between atoms, already dealt with in Chapter 1. Anderson and Horlock, for example, used the Kirkwood-Miiller formulation in their calculations for argon adsorbed in slit-shaped pores of active magnesium oxide. They found that maximum enhancement of potential occurred in a pore of width 4-4 A, where its numerical value was 3-2kcalmol , as compared with 1-12, 1-0 and 1-07 kcal mol for positions over a cation, an anion and the centre of a lattice ceil, respectively, on a freely exposed (100) surface of magnesium oxide. 

A more detailed treatment has been given by Gurfein and his associates who chose as their pore model a cylinder with walls only one molecule thick. A few years later, Everett and Fowl extended the range of models to include not only a slit-shaped pore with walls one molecule thick, but also a cylinder tunnelled from an infinite slab of solid and a slit formed from parallel slabs of solid. 

Fig. 4.9 Enhancement of interaction potential in (i) a slit-shaped pore between parallel slabs of solid, (ii) a cylindrical pore in a block of solid. 0/0 is plotted against d/r (see text). (Reduced from a diagram of Everett...

Fig. 4.33 Model of cooperative adsorption in a slit-shaped pore.

The limits of pore size corresponding to each process will, of course, depend both on the pore geometry and the size of the adsorbate molecule. For slit-shaped pores the primary process will be expected to be limited to widths below la, and the secondary to widths between 2a and 5ff. For more complicated shapes such as interstices between small spheres, the equivalent diameter will be somewhat higher, because of the more effective overlap of adsorption fields from neighbouring parts of the pore walls. The tertiary process—the reversible capillary condensation—will not be able to occur at all in slits if the walls are exactly parallel in other pores, this condensation will take place in the region between 5hysteresis loop and in a pore system containing a variety of pore shapes, reversible capillary condensation occurs in such pores as have a suitable shape alongside the irreversible condensation in the main body of pores. 

The first stage in the interpretation of a physisorption isotherm is to identify the isotherm type and hence the nature of the adsorption process(es) monolayer-multilayer adsorption, capillary condensation or micropore filling. If the isotherm exhibits low-pressure hysteresis (i.e. at p/p° < 0 4, with nitrogen at 77 K) the technique should be checked to establish the degree of accuracy and reproducibility of the measurements. In certain cases it is possible to relate the hysteresis loop to the morphology of the adsorbent (e.g. a Type B loop can be associated with slit-shaped pores or platey particles). 

As pointed out earlier (Section 3.5), certain shapes of hysteresis loops are associated with specific pore structures. Thus, type HI loops are often obtained with agglomerates or compacts of spheroidal particles of fairly uniform size and array. Some corpuscular systems (e.g. certain silica gels) tend to give H2 loops, but in these cases the distribution of pore size and shape is not well defined. Types H3 and H4 have been obtained with adsorbents having slit-shaped pores or plate-like particles (in the case of H3). The Type I isotherm character associated with H4 is, of course, indicative of microporosity. 

The models of Matranga, Myers and Glandt [22] and Tan and Gubbins [23] for supercritical methane adsorption on carbon using a slit shaped pore have shown the importance of pore width on adsorbate density. An estimate of the pore width distribution has been recognized as a valuable tool in evaluating adsorbents. Several methods have been reported for obtaining pore size distributions, (PSDs), some of which are discussed below. 

Mcntasty el al. [35] and others [13, 36] have measured methane uptakes on zeolites. These materials, such as the 4A, 5A and 13X zeolites, have methane uptakes which are lower than would be predicted using the above relationship. This suggests that either the zeolite cavity is more attractive to 77 K nitrogen than a carbon pore, or methane at 298 K, 3.4 MPa, is attracted more to a carbon pore than a zeolite. The latter proposition is supported by the modeling of Cracknel et al. [37, 38], who show that methane densities in silica cavities will be lower than for the equivalent size parallel slit shaped pore of their model carbon. Results reported by Ventura [39] for silica xerogels lead to a similar conclusion. Thus, porous silica adsorbents with equivalent nitrogen derived micropore volumes to carbons adsorb and deliver less methane. For delivery of 150 V./V a silica based adsorbent would requne a micropore volume in excess of 0.70 ml per ml of packed vessel volume. 

As surface area and pore structure are properties of key importance for any catalyst or support material, we will first describe how these properties can be measured. First, it is useful to draw a clear borderline between roughness and porosity. If most features on a surface are deeper than they are wide, then we call the surface porous (Fig. 5.16). Although it is convenient to think about pores in terms of hollow cylinders, one should realize that pores may have all kinds of shapes. The pore system of zeolites consists of microporous channels and cages, whereas the pores of a silica gel support are formed by the interstices between spheres. Alumina and carbon black, on the other hand, have platelet structures, resulting in slit-shaped pores. All support materials may contain micro, meso and macropores (see text box for definitions). 

Figure 7. Schematic model based on the TEM image analysis and on in situ 7Li-NMR during galvanostatic reduction/oxidation of the carbon composite. During insertion, ionic lithium penetrates at first in the smallest interlayer spacings, then it diffuses in the slit-shaped pores where quasi-metallic clusters are formed.

By size of pore one can mean the diameter of an equivalent cylindrical or the distance between the sides of a slit-shaped pore (i.e., in general a diameter of the largest circle that can be inscribed in a flat cross section of a pore of arbitrary form). The basis of this classification is that each of the size ranges corresponds to characteristic adsorption effect that is manifested in the isotherm of adsorption [53,115], In micropores, the interaction potential is significantly higher than in wider pores, owing to the proximity of the walls. This explains that such pores become totally full with adsorbate at low relative pressures. In mesopores, one will observe formation of mono- and then multilayer molecular film forming over the walls. After formation of a multilayer molecular film,... 

All pore sizes are according to a slit-shaped pore model Bimodal distribution of Ce02 particles... 

The sample used by Naono et al. (1982) was a non-porous one (based on a t-plot) (Fig. 14.8) with a BET surface area of 22 m g . It developed a maximum surface area of 178 m g at 200 °C due to the formation of a system of slit-shaped pores ca. one nm wide (see Fig. 14.2 c). During this process, a contraction of ca. 30% occurred along [100] and [010], but not along [001], i.e. not along the tunnels. With increasing temperature, the pores widened to mesopores and irregular macropores. The surface area of the hematite that finally formed at 500 °C was only 23 m g . ... 

A soil is a condensed colloid system because the negatively charged, plateshaped crystals are assembled in parallel or near-parallel alignment, to form stable operational entities, described as clay domains. The crystals within a day domain can be represented by a three-plate crystal model in which one crystal separates the other two crystals to produce a slit-shaped pore, where the crystals overlap. This situation is illustrated in Figure 3.4. 

The surface separation in the slit-shaped pore is determined by the crystal thickness. For an illite [a fine-grained mica with a surface area of 1.6 X 10 m per kg], the slit-shaped pores have a median size of about 5nm and in the overlap pores the surface separation is about Inm. The stability of day domains within a soil is a crucial feature for agricultural production because the permeability of a soil to aqueous electrolyte solutions depends on this stability. Swelling of these domains reduces permeability. 

The interaction of clay crystals within a domain depends upon the DLVO repulsive pressure in the slit-shaped pores and the balance between repulsive pressure [Pr] from counterion hydration and the attractive pressure [Pa] generated by van der Waals forces and the recently discovered ion-ion correlation attraction between the counterions in the confined space of the overlap pores [see Kjellander et al., 1988a, b]. When Ca Is the counterion, the attractive pressure dominates and the overlap pores are stabilized In a primary potential minimum. However, when the crystal... 

The type B hysteresis curve is associated with slit-shaped pores or the space between parallel plates. Type C hysteresis is produced by a mixture of tapered or wedge-shaped pores with open ends. Type D curves are also produced by tapered or wedge-shaped pores but with narrow necks at one or both open ends. Type E hysteresis results from McBain s bottleneck pores. In pores of this shape, emptying of the wide portion will be delayed during desorption until the narrow neck can evaporate. Therefore, the desorption curve exhibits a small slope at high relative pressures and a large slope where the wide part of the pore empties. 

Fig. 14. Coion partition coefficients SN for uni-univalent electrolyte, CF/w = 21.7 mmol/dm3, Kpn = w, calculated by the EVM (line A) or the ESM for slit-shaped pores (lines B-F) (i) Single pores of radius r = 6 (line B) or 40 (line F) nm. (ii) Assemblies of two pores of equal surface charge density of mean radius 6 nm and individual radii (in nm) 5.306,40 (line C) 5.454,80 (line D) 4.583,40 (line E) where 98 % (C), 99 / (D), or 96 % (E) of the total pore wall surface area is in narrow pores 121). Note that the power law of Eq. (46) is obeyed over a considerable range in cases C and E...

Type H3 hysteresis loop, which does not level off near the saturation vapor pressure, is characteristic of the mesoporous materials being comprised of agglomerates of plate-like particles with slit-shaped pores.79,86 Type H4 loop, which features parallel and almost horizontal branches, is attributable to the adsorption/ desorption in narrow slit-like pores. However, Type H4 loop was recently reported for MCM-41 being comprised of particles with internal voids of irregular shape and broad PSD,90 and also... 

Here, AG is Gibbs free energy. For carbon materials being comprised of slit-shaped pores, the Dubinin-Radushkevich (D-R) equation is given as... 

In order to determine the PSD of the micropores, Horvath-Kawazoe (H-K) method has been generally used. In 1983, Horvath and Kawazoe" developed a model for calculating the effective PSD of slit-shaped pores in molecular-sieve carbon from the adsorption isotherms. It is assumed that the micropores are either full or empty according to whether the adsorption pressure of the gas is greater or less than the characteristic value for particular micropore size. In H-K model, it is also assumed that the adsorbed phase thermodynamically behaves as a two-dimensional ideal gas. 

X Average half-width of the slit-shaped pores... 

Everett and Powl51 (1976) have developed a pore size distribution model for the slit shaped pores of ultramicroporous carbons. This model has been further elaborated by Horvath and Kawazoe.52... 

Figure 2.7 Slit-shape pore model (Horvath and Kawazoe).

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