Pressure effects, hysteresis

The pressure effects are reversible on repeated pressure changes without hysteresis. 

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. 

It frequently happens that the micropore effect, the enhancement of interaction potential and the resultant adsorption, ceases to appear when the value of w (and the corresponding relative pressure) is still below the beginning of the hysteresis loop. Within recent years, the micropore range... 

In formulating an explanation of this enhanced adsorption, there are several features to be accounted for the increase in adsorption occurs without hysteresis the amount of adsorbate involved is relatively small the Kelvin r -values are also small (e.g. for nitrogen, less than 17 A) and the effect is found in a region of relative pressures where, according to the simple tensile strength hypothesis, capillary condensate should be incapable of existence. 

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. 

When studying heterogeneous equilibria involving clathrates, one is faced with peculiar difficulties owing to the hysteresis effects mentioned in the introduction the solute in a clathrate crystal of hydroquinone, for instance, will not come to thermodynamic equilibrium with the vapor in which it is placed. Consequently it is impossible, or at least very difficult, to measure the equilibrium vapor pressure of the solute in a clathrate by placing some crystals in a tensometer (cf. the experiments of Wynne-Jones and Anderson,58 and those of Leech and Richards reported by Powell33). 

The isotherms represented in Fig. 1 give a general idea of the equilibria in the Pd-H system under different p-T conditions. Most experimental evidence shows, however, that the equilibrium pressure over a + /3 coexisting phases depends on the direction of the phase transformation process p a-p > pp-a (T, H/Pd constant). This hysteresis effect at 100°... 

Here the phenomenon of capillary pore condensation comes into play. The adsorption on an infinitely extended, microporous material is described by the Type I isotherm of Fig. 5.20. Here the plateau measures the internal volume of the micropores. For mesoporous materials, one will first observe the filling of a monolayer at relatively low pressures, as in a Type II isotherm, followed by build up of multilayers until capillary condensation sets in and puts a limit to the amount of gas that can be accommodated in the material. Removal of the gas from the pores will show a hysteresis effect the gas leaves the pores at lower equilibrium pressures than at which it entered, because capillary forces have to be overcome. This Type IV isotherm. 

The experimental arrangement chosen in these studies allows the diffusion processes in the region of the adsorption hysteresis to be followed. Adsorption hysteresis is the phenomenon of history-dependent adsorption and describes the effect that, in addition to the pressure, the concentration also depends on whether the given pressure has been attained from lower values (i.e., on the adsorption branch ) or from higher values (the desorption branch ) [54]. Irrespective of its... 

The desorption isotherm approach is the second generally accepted method for determining the distribution of pore sizes. In principle either a desorption or adsorption isotherm would suffice but, in practice, the desorption isotherm is much more widely used when hysteresis effects are observed. The basis of this approach is the fact that capillary condensation occurs in narrow pores at pressures less than the saturation vapor pressure of the adsorbate. The smaller the radius of the capillary, the greater is the lowering of the vapor pressure. Hence, in very small pores, vapor will condense to liquid at pressures considerably below the normal vapor pressure. Mathematical details of the analysis have been presented by Cranston and Inkley (16) and need not concern us here. 

Somewhat unusual pressure dependence of the nature of the spin transition curve has been found for chain-like SCO systems containing substituted bridging triazole ligands [163, 164]. Although the transition is displaced to higher temperatures with increase in pressure, the shape of the transition curve, unusually, is effectively constant, i.e. there is no significant change in the hysteresis width and the transition remains virtually complete. This has been taken to indicate that the cooperativity associated with the transitions in these and related systems is confined within the iron(II) triazole chains. 

The influence of pressure has also been used to tune the ST properties of these ID chain compounds. Application of hydrostatic pressure ( 6 kbar) on [Fe(hyptrz)3] (4-chlorophenylsulfonate)2 H20 (hyptrz=4-(3 -hydroxypro-pyl)-l,2,4-triazole) provokes a parallel shift of the ST curves upwards to room temperature (Fig. 5) [41]. The steepness of the ST curves along with the hysteresis width remain practically constant. This lends support to the assertion that cooperative interactions are confined within the Fe(II) triazole chain. Thus a change in external pressure has an effect on the SCO behaviour comparable to a change in internal electrostatic pressure due to anion-cation interactions (e.g. changing the counter-anion). Both lead to considerable shifts in transition temperatures without significant influence on the hysteresis width. Several theoretical models have been developed to predict such SCO behaviour of ID chain compounds under pressure [50-52]. Figure 5 (bottom) also shows the pressure dependence of the LS fraction, yLS, of... 

Before detailed enzyme reaction studies are carried out under pressure, a check on irreversible denaturation should be made. If the enzymatic activity is observed at saturating conditions, hysteresis effects should appear in raising and lowering of pressure if denaturation occurs. 

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