Pressure Hysteresis

It has been widely demonstrated that injection of water into both PTFE-treated and untreated GDMs requires positive capillary pressure while water withdrawal requires negative capillary pressures, where capillary pressure is defined as Pc = Pl — Pg- Various explanations for this behavior have been put forward, including contact angle hysteresis,59 the converging-diverging nature of void space 

particularly when contact angles are in the range of intermediate wettability. Consequently, each mechanism should be expected to play a role in GDM capillary behavior. For instance, the attribution of capillary pressure hysteresis entirely to hysteresis of the contact angle in the sense of Eq. (3)59 can be correct only if GDMs are composed of bundles of tubes of cylindrical cross section.60 

---

Type I isotherms are characterized by a plateau which is nearly or quite horizontal, and which may cut the p/p° = 1 axis sharply or may show a tail as saturation pressure is approached (Fig. 4.1). The incidence of hysteresis varies many Type I isotherms exhibit no hysteresis at all (Fig. 4.1), others display a definite loop, and in others there is hysteresis which may or may not persist to the lowest pressures ( low-pressure hysteresis ) (Fig. 4.2). Type 1 isotherms are quite common, and are no longer restricted, as seemed at one time to be the case, to charcoals. Many solids, if suitably prepared, will yield Type 1 isotherms the xerogcls of silica, titania, alumina... 

Fig. 4.25 Adsorption isotherms showing low-pressure hysteresis, (a) Carbon tetrachloride at 20°C on unactivated polyacrylonitrile carbon Curves A and B are the desorption branches of the isotherms of the sample after heat treatment at 900°C and 2700°C respectively Curve C is the common adsorption branch (b) water at 22°C on stannic oxide gel heated to SOO C (c) krypton at 77-4 K on exfoliated graphite (d) ethyl chloride at 6°C on porous glass. (Redrawn from the diagrams in the original papers, with omission of experimental points.)...

Low-pressure hysteresis is not confined to Type I isotherms, however, and is frequently superimposed on the conventional hysteresis loop of the Type IV isotherm. In the region below the shoulder of the hysteresis loop the desorption branch runs parallel to the adsorption curve, as in Fig. 4.26, and in Fig. 4.2S(fi) and (d). It is usually found that the low-pressure hysteresis does not appear unless the desorption run commences from a relative pressure which is above some threshold value. In the study of butane adsorbed on powdered graphite referred to in Fig. 3.23, for example, the isotherm was reversible so long as the relative pressure was confined to the branch below the shoulder F. 

The explanation of low-pressure hysteresis proposed by Amell and McDermott some thirty years ago was formulated in terms of the swelling of the particles which accompanies adsorption. The swelling distorts the structure, for example by prising apart weak junctions between primary... 

Fig. 4.26 Low-pressure hysteresis in the adsorption isotherm of water at 298 K on a partially dehydroxy la ted silica gel. O, first adsorption run (outgassing at 200°C) . first desorption A, second adsorption run (outgassing at 200°C) A. second desorption (after reaching p/p = 0-31) X, third adsorption run (outgassing at 25 C).

Fig. 4.27 Swelling and low-pressure hysteresis in the adsorption of n-butane on compacts of coal at 273 K. The following are plotted against the relative pressure (a) the amount adsorbed (b) the percentage increase on length (c) the decrease —Ajc in electrical conductivity. The curves for ethyl chloride were very similar to the above curves.

Extensive intercalation of polar molecules takes place in this substance in an irreversible manner, and marked hysteresis results (Fig. 4.28). The driving force is thought to be the interaction between the polar molecules and the exchange cations present in the montmorillonitic sheets, since non-polar molecules give rise to a simple Type B hysteresis loop with no low-pressure hysteresis. 

Rehydroxylation as a cause of low-pressure hysteresis is exemplified in the isotherm of Fig. 4.26, where the adsorbent was a partially dehydroxylated... 

Fig. 4.29 Adsorption isotherms of water vapour on caldte, after being balt-milted for different periods (A, B, C) and on precipitated calcium carbonate (D). Period of milling (A) 1000h (B) ISOh (C) 22h outgassing temperature 2S°C. Isotherms A, B and C (but not D) all showed extensive low-pressure hysteresis, but for clarity the desorption branch is omitted. The amount adsorbed is referred to 1 m of BET-nitrogen area. ...

Type V isotherms of water on carbon display a considerable variety of detail, as may be gathered from the representative examples collected in Fig. 5.14. Hysteresis is invariably present, but in some cases there are well defined loops (Fig. 5.14(b). (t ), (capillary-condensed water. Extreme low-pressure hysteresis, as in Fig. 5.14(c) is very probably due to penetration effects of the kind discussed in Chapter 4. 

The adsorption of water on a fully hydroxylated silica involves hydrogen bonding but is essentially physical in nature and is completely reversible in the low pressure range the isotherm is of Type II on a nonporous sample (Fig. 5.17(a)), and of Type IV, with no low-pressure hysteresis, on a porous sample (Fig. 5.18). 

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). 

Figure 1 shows a sharp decrease of low-pressure hysteresis loop when introducing copper in S-l, pointing to the formation of (CuO)n nanoclusters into the S-l intracrystalline channels and supermicropores. The adsorption data analysis (see Table 1) shows a decrease of both the total (BET) surface area and micropore volume of the CuS-1 sample with respect to the S-l matrix. 

The plateau region on the PCX cnrves in Fig. 2.43a is very flat, showing only a minimal slope (Sect. 1.4.1). However, each absorption-desorption pair of the PCX curves clearly exhibits a pressure hysteresis. This means that the pressure needed for absorption (hydride formation), is always greater than that of hydride decomposition, p. The cause of pressure hysteresis in metal hydride systems is not fnlly nnderstood. A number of models that attempted to explain this phenomenon... 

The model of Rabkin and Skripnyuk [75] seems to be quite attractive in its explanation of pressure hysteresis observed in Fig. 2.43a. Our results always show a log-normal frequency distribution of powder particles (Fig. 2.34), which points towards the possibility of the existence of large and small fractions of particle sizes. This, in turn, is compatible with the model which states that fully transformed and nontransformed particles can coexist depending on their sizes. 

For the sake of clarity, it must be mentioned that Huot et al. [24, 35] reported that at 350°C the absorption/desorption PCT plateau pressure hysteresis of the unmilled MgH was quite substantial, while the hysteresis of the same material milled for 20 h was very small. They argued that the plateau pressure difference observed for the uiimilled material was due to a very slow desorption kinetics which did not allow reaching equilibrium. In turn, ball milling increased desorption kinetics, which allowed reaching equilibrium and eliminated hysteresis. However, it must be noticed that the situation reported by Huot et al. is completely opposite to what is observed in Fig. 2.43, in which MgH synthesized by reactive mechanical milling shows a pressure hysteresis. 

E. Rabkin, V.M. Skripnyuk, On pressure hysteresis during hydrogenation of metalhc powders, Scripta Mater. 49 (2003) 477-483. 

Isotherms for an actual system are shown in Figure 2, The alloy has the chemical composition LaNili,. 3 is manufactured and marketed by Ergenics as HY-STOR Alloy 20T. Compared to the ideal curve (Figure l), the plateau is slightly sloped, the plateau limits are not as clearly defined and there is a measurable pressure hysteresis between absorption and desorption. 

Further comparison with benzene sorption on this sample yields striking results if the two isotherms are plotted on the same axis, as shown in Figure 1. The fact that these two isotherms may be completely superimposed suggests that the mechanism of tert-butyl alcohol sorption is similar to that observed in benzene sorption. This indicates that the sorption mechanism of tert-butyl alcohol on this material is more influenced by organic interactions with the surface phenyl groups than by polar interaction with surface hydroxyls. (It should be noted, however, that a small amount of rehydroxylation is indicated by the low pressure hysteresis.)... 

Numerous investigations have noted the instability of the physicochemical characteristics of Al(OR)3—the first members of the homologous series, which can display varied physical states, m.p., density, vapor pressure (hysteresis on measurement), viscosity, refraction coefficient, solubility in alcohols, and so... 

When the mercury pressure is reduced, hysteresis is usually observed. This will reflect some of the mercury being permanently trapped in ink-bottle pores and, as such, the ink-bottle pore volume is given by the residual mercury entrapped when the mercury pressure is reduced to atmospheric pressure. Hysteresis, however, can also result from structural damage sustained due to the very high mercury pressures involved. 

The peak height ratio between the antisymmetric and symmetric CHj stretching modes H-2880/H-2850 is plotted as a function of pressure in Figure 7. This parameter has been shown to reflect the magnitude of interchain interactions in systems that contain polymethylene chains [20]. An abrupt increase in this ratio, and thus an increase in the interchain interactions, is observed at the pressure-induced transition from the micellar to the coagel phase. Furthermore, it is also evident from Figure 7 that the transition has a considerable pressure hysteresis. Interestingly, pressure [76] and temperature [79] have different effects on the H-2880/H-2850 ratio in the micellar phase of... 

Figure 13.6 Piezoelectric coefficient d and tan<5p of a single phase Bi4Ti30i2 ferroelectric ceramic with highly anisotropic grains, at room temperature. On the right are shown charge-pressure hysteresis loops at selected frequencies, with a clockwise hysteresis at 0.07 Hz and counter-clockwise hysteresis at 70 Hz. See [17] for details.

---