Ink-bottle pores

Fig. 3.12 Ink bottle pores with (o) cylindrical body and (/>). (c). tapering body the neck is cylindrical in each case.

Fig. 3J3 Calculation of pore size distribution in ink-bottle" pores, from mercury intrusion-extrusion experiment." (After Reverberi. )...

De Bruyne [41] has applied the same principles to other idealised shapes for pores. As would be expected, penetration into a re-entrant ink bottle pore is much less than for cylinders (Fig. 6). The critical importance of contact angle in determining the extent of penetration should be noted. 

With hysteresis loops of Type HI, the two branches are almost vertical and nearly parallel. Such loops are often associated with porous materials which are known to have very narrow pore size distributions or agglomerates of approximately uniform spheres in fairly regular array. More common are loops of Type H2, where the pore size distribution and shape are not well defined. This is attributed to the difference in adsorption and desorption mechanisms occurring in ink-bottle pores, and network effects. The Type H3 hysteresis loop does not show any limiting adsorption at high relative pressures and is observed in aggregates and macroporous materials. Loops of Type H4 are often associated with narrow... 

The extrusion curve shown in Fig. 1.16A cannot retrace the intrusion curve exactly because mercury is not expelled completely because it is entrapped in so-called ink-bottle pores [79, 96] (Fig. 1.17). 

The shape of the hysteresis loop in the adsorption/desorption isotherms provides information about the nature of the pores. The loops have been classified according to shape as A, B and E (De Boer, 1958) or as HI - H4 by lUPAC (Sing et al, 1985). Ideally, the different loop shapes correspond to cylindrical, slit shaped and ink-bottle pores the loops in the isotherm IV and V of Figure 5.3 correspond to cylindrical pores. Wide loops indicate a broad pore size distribution (for an example see Fig. 14.9). The absence of such a loop may mean that the sample is either nonporous or microporous. These generalizations provide some initial assistance in assessing the porosity of a sample. In fact the adsorption/desorption isotherms are often more complicated than those shown in Figure 5.3 owing to a mixture of pore types and/or to a wide pore size distribution. 

Due to aggregation of particles, ferrihydrite is microporous, i. e. the porosity is interparticular. Ferrihydrite precipitated at pH 8 from Fe " solution displayed a type IV isotherm with type E hysteresis (Crosby et al., 1983). The freshly precipitated material contained ink bottle pores 2-5 nm in diameter. Larger pores (ca. 20 nm) developed over an 11 day period. Between 83 and 95% of the total pore volume of a 2-line ferrihydrite was found to be due to micropores (Weidler, 1995). 

The total area of all pores to 15.1 A radius (Column 14) is 212.1 m g This area is usually less than the BET area since it does not include the surface contributed by micropores. An area larger than the BET area would be exhibited by ink-bottle pores in which a larger volume of gas is condensed in pores having a relatively small area. This is the case shown in the example in Table 8.1. 

Porosimetry curves exhibit various shapes. If hysteresis were caused by ink-bottle pores only one shape hysteresis curve should be observed. 

Regardless of the maximum pressure attained, depressurization always results in hysteresis. This would imply that ink-bottle pores are distributed over the entire range of pore sizes. Therefore, pores with very wide entrances would have to possess even wider inner cavities. 

Mann has proposed a stochastic theory based on a two-dimensional network of interconnecting pores with varying radii to explain hysteresis and entrapment in porosimetry. By assuming that filling of some of the larger radii pores is delayed until surrounding smaller pores are filled, a mechanism similar to the filling of ink-bottle pores, Mann s calculated porosimetry curves often approximate those from actual samples. 

The method is limited to pore radii larger than m 2 nm due to the maximal applicable pressure. An assumption made in the analysis is that a pore is accessible only by capillaries with larger radius. Pores with a narrow entrance and a wide body (called ink bottle pores ) lead to a hysteresis in the volume-pressure curve. 

In the second mechanism the topology of the pore network plays a role [394], During the desorption process, vaporization can occur only from pores that have access to the vapor phase, and not from pores that are surrounded by other liquid-filled pores. There is a pore blocking effect in which a metastable liquid phase is preserved below the condensation pressure until vaporization occurs in a neighboring pore. Therefore, the relative pressure at which vaporization occurs depends on the size of the pore, the connectivity of the network, and the state of neighboring pores. For a single ink bottle pore this is illustrated in Fig. 9.15. The adsorption process is dominated by the radius of the large inner cavity while the desorption process is limited by the smaller neck. 

Figure 9.15 Filling and emptying of a solid ink bottle pore with liquid from its vapor and the corresponding adsorption/desorption isotherms.

Another theory of adsorption hysteresis considers that there are two types of pores present, each having a size distribution. The first type are V-shaped, and these fill and empty reversibly. The second type have a narrow neck and a relatively wide interior. These ink-bottle pores are supposed to fill completely when a plp0 value corresponding to the relatively wide pore interior is reached, but once filled they retain their contents until plp0 is reduced to a value corresponding to the relatively small width of the pore neck. 

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. 

Figure 4.14 Pores may vary in size, shape, and connectivity a channel/cage structures b polygonal capillaries c ink bottle pores d laminae e slit pores.

This difference between H O and N adsorption data has been attributed to either the accessibility of water to interlayer spaces in the tobermorite gel or to the presence of ink bottle pores with narrow necks and wide bodies. The considerable increase (4-5 times) in pore surface and pore volume available to nitrogen in pastes containing calcium chloride suggests that the crumpled pore type of morphology is more open than the spicular type [20],... 

Many porous adsorbents give Type H2 hysteresis loop, but in such systems PSD or pore shape is not well-defined. Indeed, the H2 loop is especially difficult to interpret. In the past it was considered to be a result of the presence of the pores with narrow necks and wide bodies (ink-bottle pores), but it is now recognized that this provides an over-simplified picture and the pore connectivity effects must be taken into account.79... 

In Figure 6.15, the adsorption isotherm of N2 at 77 K on the silica 68bslE [42], where the capillary condensation effect is obvious, is shown. Capillary condensation is normally characterized by a step in the adsorption isotherm. In materials with a uniform PSD, the capillary condensation step is remarkably sharp [20], However, in practice, the hysteresis loop is seen in materials consisting of slit-like pores, cylindrical-like pores, and spherical pores, that is, ink-bottle pores [2,41], The... 

Kelvin equations describing capillary evaporation from slit-shaped pores or the filling and emptying of ink bottle pores can be calculated quite easily by using the appropriate expressions for cLA/dJV (see ref. 16). 

Fig. 12. Ink-bottle pores with cylindrical and tapering bodies.

A severe limitation of the bundle of capillaries model is that it can give erroneous readings for materials with "ink-bottle" pores. In this case, the pores are emptied at the capillary pressure of the neck followed by the discharge of the large cavity, resulting in a large reading of the desorbed volume at the capillary pressure of the "ink-bottle" neck. 

Morishige, K. and Tateishi, N. (2003). Adsorption hysteresis in ink-bottle pore. 

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. 

Ink Bottle Pore A description of one kind of shape of pore in a porous medium, in which a narrow throat is connected to a larger pore body. See also Porous Medium. 

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