Hysteresis isotherms

Fig. 26 Hysteresis isotherms for the 1/5 palmitic acid/(A) racemic and (B) enantiomeric stearoylserine methyl ester (17% palmitic acid) monolayer system at 25°C. Arrows indicate direction of expansion and compression. Reprinted with permission from Arnett et al., 1989. Copyright 1989 American Chemical Society.

Figure 1. Hysteresis isotherm of polymer 3S on a water/air interface. The compression and decompression rate is 50 Mm/min.

The hysteresis isotherms presented in Fig. 14 illustrate very clearly for the Aerocat catalyst the differences between sintering in vacuum and... 

A comparison of virgin, steam-treated, and used Fluid Filtrol catalysts is presented in Fig. 19 and Table I. The hysteresis isotherm for the virgin material has been discussed in some detail by Oulton (42). Virgin Filtrol has an area of 339 sq. m./g., which is considerably smaller than... 

The hysteresis isotherm for titania, to which earlier reference has been made, is plotted in Fig. 31. Although there is some interest in titania as a catalyst it is included here principally because in adsorption research it may be considered the classical example of a nonporous finely... 

The reversible Type Ila isotherm is the normal form of nitrogen isotherm given by a non-porous or macroporous adsorbent and is indicative of unrestricted monolayer-multilayer adsorption. The adsorption branch of a Type Ilb isotherm appears to have the same characteristic Type II shape as a normal monolayer-multilayer isotherm, but the multilayer section of the desorption branch is quite different -giving rise to a form of adsorption hysteresis. Isotherms of this type are generally given by aggregates of platy particles or solids containing slit-shaped mesopores. 

The hydration shell is formed with the increasing of the water content of the sample and the NA transforms from the unordered to A- and then to B form, in the case of DNA and DNA-like polynucleotides and salt concentrations similar to in vivo conditions. The reverse process, dehydration of NA, results in the reverse conformational transitions but they take place at the values of relative humidity (r.h.) less than the forward direction [12]. Thus, there is a conformational hysteresis over the hydration-dehydration loop. The adsorption isotherms of the NAs, i.e. the plots of the number of the adsorbed water molecules versus the r.h. of the sample at constant temperature, also demonstrate the hysteresis phenomena [13]. The hysteresis is i( producible and its value does not decrease for at least a week. 

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. 

A characteristic feature of a Type IV isotherm is its hysteresis loop. The exact shape of the loop varies from one adsorption system to another, but, as indicated in Fig. 3.1, the amount adsorbed is always greater at any given relative pressure along the desorption branch FJD than along the adsorption branch DEF. The loop is reproducible provided that the desorption run is started from a point beyond F which marks the upper limit of the loop. 

The model proposed by Zsigmondy—which in broad terms is still accepted to-day—assumed that along the initial part of the isotherm (ABC of Fig. 3.1), adsorption is restricted to a thin layer on the walls, until at D (the inception of the hysteresis loop) capillary condensation commences in the finest pores. As the pressure is progressively increased, wider and wider pores are filled until at the saturation pressure the entire system is full of condensate. 

Examples are provided by the work of Carman and Raal with CF2CI2 on silica powder, of Zwietering" with nitrogen on silica spherules and of Kiselev" with hexane on carbon black and more recently of Gregg and Langford with nitrogen on alumina spherules compacted at a series of pressures. In all cases, a well defined Type II isotherm obtained with the loose powder became an equally well defined Type IV isotherm with the compact moreover both branches of the hysteresis loop were situated (drove the isotherm for the uncompacted powder, but the pre-hysteresis region was scarcely affected (cf. Fig. 3.4). The results of all these and similar... 

Closer examination reveals that the swing upwards in the Type IV isotherm not infrequently commences before the loop inception, showing that enhanced adsorption, not accompanied by hysteresis, can occur. The implications of this important fact are explored in Section 3.7. 

In calculations of pore size from the Type IV isotherm by use of the Kelvin equation, the region of the isotherm involved is the hysteresis loop, since it is here that capillary condensation is occurring. Consequently there are two values of relative pressure for a given uptake, and the question presents itself as to what is the significance of each of the two values of r which would result from insertion of the two different values of relative pressure into Equation (3.20). Any answer to this question calls for a discussion of the origin of hysteresis, and this must be based on actual models of pore shape, since a purely thermodynamic approach cannot account for two positions of apparent equilibrium. 

The procedures are based on an imaginary emptying of the pores by the step-wise lowering of relative pressure, from the point already referred to where the mesopore system is taken as being full up a relative pressure of 0-95po is frequently adopted as starting point with isotherms having a hysteresis loop of Type A or Type E. (With Type B, as will appear later, the validity of pore size calculations is doubtful.)... 

The evidence obtained in compaction experiments is of particular interest in the present context. Figure 3.22 shows the results obtained by Avery and Ramsay for the isotherms of nitrogen on compacts of silica powder. The hysteresis loop moved progressively to the left as the compacting pressure increased, but the lower closure point did not fall below a relative pressure of 0-40. Similar results were obtained in the compaction of zirconia powder both by Avery and Ramsay (cf. Fig. 4.5), and by Gregg and Langford, where the lower closure point moved down to 0-42-0-45p° but not below. With a mesoporous magnesia (prepared by thermal decomposition of the hydrated carbonate) the position of the closure point... 

It was noted earlier (p. 115) that the upward swing in the Type IV isotherm characteristic of capillary condensation not infrequently commences in the region prior to the lower closure point of the hysteresis loop. This feature can be detected by means of an a,-plot or a comparison plot (p. 100). Thus Fig. 3.25(a) shows the nitrogen isotherm and Fig. 3.25(h) the a,-plot for a particular silica gel the isotherm is clearly of Type IV and the closure point is situated around 0 4p° the a,-plot shows an upward swing commencing at a = 0-73, corresponding to relative pressures of 013 and therefore well below the closure point. 

Figure 3.26(a) and (h) gives results for nitrogen on a compact of silica. Curve (a) is a comparison plot in which the adsorption on the compact (ordinates) is plotted against that on the uncompacted powder (abscissae) there is a clear break followed by an increased slope, denoting enhanced adsorption on the compact, at p/p° = 0-15, far below the lower closure point ( 0-42) of the hysteresis loop in the isotherm (curve (b)). A second compact, prepared at 64 ton in" rather than 130 ton in", showed a break, not quite so sharp, at p/p° = 0-35. 

Striking confirmation of the conclusion that the BET area derived from a Type IV isotherm is indeed equal to the specific surface is afforded by a recent study of a mesoporous silica, Gasil I, undertaken by Havard and Wilson. This material, having been extensively characterized, had already been adopted as a standard adsorbent for surface area determination (cf. Section 2.12). The nitrogen isotherm was of Type IV with a well defined hysteresis loop, which closed at a point below saturation (cf. F, in Fig. 3.1). The BET area calculated from it was 290 5 0 9 m g , in excellent agreement with the value 291 m g obtained from the slope of the initial region of the plot (based on silica TK800 as reference cf. p. 93). 

Fig. 3.28 The Kiselev method for calculation of specific surface from the Type IV isotherm of a compact of alumina powder prepared at 64 ton in". (a) Plot of log, (p7p) against n (showing the upper (n,) and lower (n,) limits of the hysteresis loop) for (i) the desorption branch, and (ii) the adsorption branch of the loop. Values of. 4(des) and /4(ads) are obtained from the area under curves (i) or (ii) respectively, between the limits II, and n,. (6) The relevant part of the isotherm.

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... 

Experimental findings in the intervening years have tended to support and extend this concept. The results obtained by Ramsay and Avery in their studies of the effect of compaction on the nitrogen isotherms of two finely divided powders, one of zirconia and the other of silica, are especially instructive in the present context. As in earlier studies (cf. Chapter 3) the isotherm on the original powder was of Type II, but on compaction it first became Type IV with a well defined hysteresis loop, which moved... 

It has already been noted (p. 195) that some Type I isotherms exhibit a kind of hysteresis which persists to the lowest pressures (cf. Fig. 4.2) some adsorbate is retained even after prolonged outgassing ( lO Torr) at the temperature of the isotherm determination, and can only be removed if the pumping is carried out at an elevated temperature. Further examples are shown in Fig. 4.25, as well as in Fig. 4.23. 

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. 

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).

The swelling of the adsorbent can be directly demonstrated as in the experiments of Fig. 4.27 where the solid was a compact made from coal powder and the adsorbate was n-butane. (Closely similar results were obtained with ethyl chloride.) Simultaneous measurements of linear expansion, amount adsorbed and electrical conductivity were made, and as is seen the three resultant isotherms are very similar the hysteresis in adsorption in Fig. 4.27(a), is associated with a corresponding hysteresis in swelling in (h) and in electrical conductivity in (c). The decrease in conductivity in (c) clearly points to an irreversible opening-up of interparticulate junctions this would produce narrow gaps which would function as constrictions in micropores and would thus lead to adsorption hysteresis (cf. Section 4.S). 

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