Types of hysteresis loop

At relative pressures above 0.3, de Boer has identified five types of hysteresis loops which he correlated with various pore shapes. Figure 8.3 shows idealizations of the five types of hysteresis. 

In practice, several types of hysteresis loops are found their shapes are indicatives of the types of pores we are dealing with. For a full explanation we refer to refs. 1 and 16, which also describe the calculation of complete pore volume distributions. 

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. 

In the following discussion we will consider the application of percolation theory to describing desorption of condensate from porous solids. In Sections III,A-III,C we briefly recall types of adsorption isotherms, types of hysteresis loops, and the Kelvin equation. The matter presented in these sections is treated in more detail in any textbook on adsorption [see, e.g., the excellent monographs written by Gregg and Sing (6) and by Lowell and Shields (49) Sections III,D-III,H are directly connected with percolation theory. In particular, general equations interpreting the hysteresis loop are... 

According to modern classification, recommended by lUPAC [43], four general types of hysteresis loops designated by the symbols HI, H2, H3, and H4 are distinguished. Their shapes below are shown schematically in Fig. 6.1. 

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 temperature dependence of the Faraday and Kerr rotation in a number of amorphous Gd1 xFex alloys was studied by Hartmann (1982). Results obtained for the latter alloys are reproduced in fig. 53. These results have to be compared with the temperature dependence of the magnetization shown for Gd0 2Fe0 8 in fig. 52. It follows from the results of Hartmann that all the Gdt xFex alloys shown in fig. 53 have a compensation temperature, which decreases with increasing Fe concentration. However, no such features are seen in the magneto-optical effect in the sample is merely due to one of the two sublattice magnetizations. In accordance with this feature is the observation by means of hysteresis loops at temperatures above Tcomp but inverted types of hysteresis loops at temperatures... 

Fig. 54. Schematic representation of the temperature dependence of the total magnetization M and the type of hysteresis loops observed by means of magneto-optical effects in the temperature ranges above and below the compensation temperature Tcamp. The orientations and relative magnitudes of the Gd and 3d sublattice are indicated for each case by arrows.

Fig. 55. Concentration dependence of the saturation magnetization Ms and the longitudinal Kerr rotation 0.79 is indicated as an inset. (After Imamura and Mimura 1976.)...

Fig. 2 (a) Types of physisorption isotherms, (b) Types of hysteresis loops. 

The same type of hysteresis loop which was noted in the absorption of hydrogen in palladium, where a- and yS-phases co-exist, is observed also in the absorption of hydrogen by iron (31), where now the two phases are produced by allotropy in the metal. The permeability-temperature curve shows a break at this point (Fig. 63) (5i). Indeed, wherever a phase change occurs one may look for a variation in the permeability, so that the property of permeability may be used to determine transition points. The change in permeability of nickel towards hydrogen has similarly been used to characterise the Curie point in nickel (62). 

Figure 4.61. Types of hysteresis loop (irreversible adsorption-desorption processes) observed during adsorption into mesoporosity. Mesoporous carbons generally belong to the Type-Hl hysteresis loop (Sing et ai, 1985).

Fifteen shape groups of capillaries were analyzed by de Boer [2] from a consideration of five types of hysteresis loop which he designated Type A to Type E (Rgure 3.2). 

The shape of a hysteresis loop is influenced by many factors, porous structure being the dominant one of them and for this reason it appears as the basic property of our classification. Moreover, instead of looking for types of hysteresis loops, we prefer to define types of porous structures. What we propose is the following ... 

The presence of adsorption hysteresis is the special feature of all adsorbents with a mesopore structure. The adsorption and desorption isotherms differ appreciably from one another and form a closed hysteresis loop. According to the lUPAC classification four main types of hysteresis loops can be distinguished HI, H2, H3 and H4 (ref. l). Experimental adsorption and desorption isotherms in the hysteresis region provide information for calculating the structural characteristics of porous materials-porosity, surface area and pore size distribution. Traditional methods for such calculations are based on the assumption of an unrelated system of pores of simple form, as a rule, cylindrical capillaries. The calculations are based on either the adsorption or the desorption isotherm, ignoring the existence of hysteresis in the adsorption process. This leads to two different pore size distributions. The question of which of these is to be preferred has been the subject of unending discussion. In this report a statistical theory of capillary hysteresis phenomena in porous media has been developed. The analysis is based on percolation theory and pore space networks models, which are widely used for the modeling of such processes by many authors (refs. 2-10). The new percolation methods for porous structure parameters computation are also proposed. 

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