Types of hysteresis

Rarely have hysteresis loops been found which have not closed, at the low end, usually by relative pressures of 0.3. According to the Kelvin equation, pore radii corresponding to relative pressures less than 0.3 would be smaller than 15 A. Since monolayer formation is usually complete when the relative pressure reaches 0.3, the radius available for condensation would be diminished by the thickness of the monolayer or by about two molecular diameters. The radius of this center core would then be approximately one or two molecular diameters. It would be difficult to establish the validity of the Kelvin equation for pores this small, and it is entirely possible that adsorption and desorption in micropores proceed by the same path, thereby precluding hysteresis. 

Placing the above value for dV/dS into equation (8.6) yields a modified form of the Kelvin equation, namely. 

During desorption the center core evaporates from a hemispherical meniscus therefore, the Kelvin equation is applicable. 

From equations (8.13) and (8.7), it is evident that condensation into and evaporation out of the inner core will occur when 

Therefore, for a real system of pores of approximately cylindrical 

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In other studies on MOS structures, the two types of hysteresis, normal and abnormal, are suggested to arise from the ion displacement in the insulator and to the trapping at the interface states. The presence of site-radiation-induced polymerization has been used to provide increased film stability and has been described as an application for high-resolution electron beam lithography for the fabrication of microcircuitry. 

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. 

Since advancing and receding contact angles are likely to be different in these experiments, mercury permeation curves are expected to be different, depending on whether the mercury is being pushed in or out of the plugs. This type of hysteresis is indeed observed. We encounter another type of hysteresis associated with pore filling in Chapter 9 (Section 9.7a). 

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... 

Hi) Failure of adsorption equilibration. Origins (i) and (ii) apply when the three tensions involved have their equilibrium values, i.e. when all adsorption processes are relaxed. However, Incomplete adsorption at any of the three interfaces also gives rise to differences between a(adv) and a(rec). This phenomenon is not a real type of hysteresis but rather the result of lack of patience if we wait long enough the Deborah number De = r(ads)/t(obs) becomes 1. Here T(ads) is the characteristic time for the establishment of adsorption equilibrium and t(obs) the measuring time. However, as these phenomena are often observed, we shall include them in the present discussion. A typical illustration, already referred to in connection with [3.2.1] is that of a benzene droplet placed on top of pure water. First it spreads, but later it retracts to form a droplet. The reason is that it takes some time to equilibrate benzene adsorption at the water-air interface. 

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).

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