Hysteresis loops, classification

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. 

The hysteresis loops to be found in the literature are of various shapes. The classification originally put forward by de Boer S in 1958 has proved useful, but subsequent experience has shown that his Types C and D hardly ever occur in practice. Moreover in Type B the closure of the loop is never characterized by the vertical branch at saturation pressure, shown in the de Boer diagrams. In the revised classification presented in Fig. 3.5, therefore. Types C and D have been omitted and Type B redrawn at the high-pressure end. The designation E is so well established in the literature that it is retained here, despite the interruption in the sequence of lettering. 

A new classification of hysteresis loops, as recommended in the lUPAC manual, consists of the four types shown in the Figure below. To avoid confusion with the original de Boer classification (p. 117), the characteristic types are now designated HI, H2, H3 and H4 but it is evident that the first three types correspond to types A, E and B, respectively, in the original classification. It will be noted that HI and H4 represent extreme types in the former the adsorption and desorption branches are almost vertical and nearly parallel over an appreciable range of gas uptake, whereas in the latter they are nearly horizontal and parallel over a wide range of relative pressure. Types H2 and H3 may be regarded as intermediate between the two extremes. 

Table 16-4 shows the IUPAC classification of pores by size. Micropores are small enough that a molecule is attracted to both of the opposing walls forming the pore. The potential energy functions for these walls superimpose to create a deep well, and strong adsorption results. Hysteresis is generally not observed. (However, water vapor adsorbed in the micropores of activated carbon shows a large hysteresis loop, and the desorption branch is sometimes used with the Kelvin equation to determine the pore size distribution.) Capillary condensation occurs in mesopores and a hysteresis loop is typically found. Macropores form important paths for molecules to diffuse into a par-... 

Fig. 1.14 Types of physisorption isotherms (I-VI) and hysteresis loops (H1-H4) according to the lUPAC classifications.

Figure 3. Classification of adsorption/desorption hysteresis loops.

Figure 73. The IUPAC classification of hysteresis loops (Sing et al., 1985).

The properties of a well-characterized sample of sodium montmorillonite were investigated in some detail by Cases et al. (1992). As expected, the nitrogen isotherm at 77 K had a well-defined H3 hysteresis loop and was therefore a good example of a Type lib isotherm in the new classification. The measurements were taken to a high... 

In the original IUPAC classification, the hysteresis loop was said to be a characteristic feature of a Type IV isotherm. It is now evident that this statement must be revised. Moreover, we can distinguish between two characteristic types of hysteresis loops. In the first case (a Type HI loop), the loop is relatively narrow, the adsorption and desorption branches being almost vertical and nearly parallel in the second case (a Type H2 loop), the loop is broad, the desorption branch being much steeper than the adsorption branch. These isotherms are illustrated in Figure 13.1 as Type IVa and Type IVb, respectively. Generally, the location of the adsorption branch of a Type IVa isotherm is governed by delayed condensation, whereas the steep desorption branch of a Type IVb isotherm is dependent on network-percolation effects. 

In fig. 1.31 the lUPAC-recommended classification is given for the most common types of hysteresis loops they are refinements of the general type IV in fig. 1.13. In practice, a wide variety of shapes may be encountered of which types HI and H4 are the extremes. In the former, the two branches are almost vertical and parallel over an appreciable range of V, whereas in the latter they remain more or less horizontal over a wide range of p/p(sat). Types H2 and H3 are intermediates. Many hysteresis loops have in common that the steep range of the desorption branch leads to a closure point that is almost independent of the nature of the porous sorbent and only depends on the temperature and the nature of the adsorptive. For example, it is at p/p(sat) = 0.42 for nitrogen at its boiling point (77 K) and at p/p(sat) = 0.28 for benzene at 25°C. 

The second set of data (Fig. 1, b) concerns a family of pillared clays Ali-xFe/)yVi ih systematically varied Al and Fe contents [16], The sorption data of the pillared clays samples exhibit at low pressure a high adsorption step and at higher relative pressure an H4-type (lUPAC classification) hysteresis loop that is transformed into an H2-type loop as the Fe content is being increased. Details of the preparation procedure and the results from the application of other characterization tests are provided in [16]. 

Figure la shows the nitrogen adsorption-desorption isotherms of the two pure materials as well as mixture X(50). According to BDDT classification, the adsorption-desorption isotherm obtained on the pure alumina sample, X(0), is of type IV with a type E hysteresis loop. This kind of isotherm is typical of a mesoporous material with cylindrical pores closed at one end. In contrast, the adsorption-desorption isotherm obtained on the pure Si-Ti co-gel, X(IOO), is of type I without hysteresis loop, which corresponds to an exclusively microporous material [ ] ... 

For the five mixtures, the cumulative mesoporous volume, Feds, and mesoporous surface area, S edB, and are both linear decreasing functions of the micropore content y (Figure 2b). The cumulative specific surface area SedB is definitely a better estimator of the mesoporous surface than the specific surface S xt computed Ifom the t-plot. The lUPAC classification states that mesopores are pores whose width is larger that 2 nm. In the case of the cylindrical pore model retained for the pore size distribution, this is equivalent to radii larger than 1 nm. It should however be stressed that the calculation of the cumulative surface and volume of the mesopores must not be continued at lower pressures than the closing of the hysteresis loop (gray zones of Figures 3a and 3b). If a black box analysis tool is used and if the calculation is systematically continued down to 1 nm, severe overestimation of the mesopores surface and volume may occur. 

The complete nitrogen isotherms of dealuminated Y zeolites are reported in Fig. 1. The curve of the parent H-Y zeolite corresponded to type I in the Brunauer classification, which was typical for the crystalline microporous materials [17]. As expected, the starting material showed no evidence of mesopores. Fig. 1 shows that the AHFS-treated samples with dealumination levels equal or lower than 50% were characterised by a very flat adsorption-desorption isotherm with nearly no hysteresis loop [18]. 

The first classification of hysteresis loops was proposed by de Boer (53), who has identified five types (A-E) of loops that may be correlated with various pore shapes. Subsequent experience has, however, shown that types C and D hardly ever occur in practice (6). A new classification of hysteresis loops recommended by lUPAC (6) consists of four types, i.e., HI, H2, H3, and H4 (Fig. 10). The first three types correspond to types A, E, and B, respectively, in the original de Boer classification. 

Fig. 10. lUPAC classification of hysteresis loops U is in arbitrary units. 

The forms of the isotherms and hysteresis loops have been subject to a classification initially proposed by Brunauer and taken up by the lUPAC. This classification shows the relationship between the form of the isotherms, the average radius of the pores and the intensity of the adsorbate-adsorbant interactions. Four types of isotherms out of the six proposed by the lUPAC are commonly encountered (Fig. 1.1). Similarly, the hysteresis loops correspond-... 

For adsorbents with sufficiently laig e porosities (often referred to as mesoporous systems) isotherms can exhibit hysteresis between the adsorption and desorption branches as illustrated schematically in figure 1. A classification of the kinds of hysteresis loops has also been made. It is generally accepted that such behavior is related to the occurrence of capillary condensation - a phenomenon whereby the low density adsorbate condenses to a liquid like phase at a chemical potential (or bulk pressure) lower than that corresponding to bulk saturation. However, the exact relationship between the hysteresis loops and the capillary phase transition is not fully understood - especially for materials where adsorption cannot be described in terms of single pore behavior. 

Figure 1. An adsorption/desorption isotherm of density vs. relative pressure showing a hysteresis loop of type H2 in the lUPAC classification (Sing et al., 1985).

A characteristic feature associated with pore condensation is the occurrence of sorption hysteresis, i.e pore evaporation occurs usually at a lower p/po compared to the condensation process. The details of this hysteresis loop depend on the thermodynamic state of the pore fluid and on the texture of adsorbents, i.e. the presence of a pore network. An empirical classification of common types of sorption hysteresis, which reflects a widely accepted correlation between the shape of the hysteresis loop and the geometry and texture of the mesoporous adsorbent was published by lUPAC [10]. However, detailed effects of these various factors on the hysteresis loop are not fully understood. In the literature mainly two models are discussed, which both contribute to the understanding of sorption hysteresis [8] (i) single pore model. hysteresis is considered as an intrinsic property of the phase transition in a single pore, reflecting the existence of metastable gas-states, (ii) neiM ork model hysteresis is explained as a consequence of the interconnectivity of a real porous network with a wide distribution of pore sizes. 

The adsorption isotherm of nitrogen (77 K) for the porous silica is shown in Figure 2. This has a type IV character in the lUPAC classification [17], exhibiting a hysteresis loop with a shape corresponding to a capillary condensation process in cylindrical pores [18]. The... 

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