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The pore-size distribution is a key descriptor of the void space of mesoporous materials, such as heterogeneous catalyst pellets, is used in explaining their properties. In general, the measured pore-size distribution curves are frequently inclined towards small pore sizes as illustrated in Figure 3.14 (Allen, 1999). For the same reasons stated above, mercury porosimetry can not be used to analyse closed pores. Thus, the technique can only provide a valid estimate of pore structure, when the sample has pores directly accessible to mercury or that are easily reached by mercury through larger pores (Moro and Bohni, 2002). In addition, the Washburn equation (Equation 3.31) assumes contact angle value of mercury and the cylindrical pore shape. However, various observations made by electron microscopy have shown that many traditional porous materials such as the silicas and aluminas appear to be random collections of packed spherical and hemispherical particles, as well as cylinder (Drewry and Seaton, 1995).

In addition, similar observations were made in cement-based materials where the pore size is randomly distributed and most pores are connected to the surface of the sample through a chain of pores with varying sizes and shapes. Therefore, with such a pore structure, mercury can not intrude into larger pores until the applied pressure is sufficient to force mercury to go through smaller throats. As a result, the standard mercury porosimetry results in an underestimate of large pores because of its intrinsic limitation due to ink- bottle type pores. These are pores that are connected to the surface by smaller neck entrances only, and thus, larger pores that are only accessible by smaller neck entrances will be underestimated in size and lead to hysteresis effects. The volume of these larger pores (ink-bottle pores) that is counted as the volume of smaller throats (pores) is referred to as the accessibility effect (Diamond, 2000). Therefore, the Washburn Equation (3.31) constitutes a special model that fails to take into account that real the real nature of pores media consist of a network of interconnected circular pores. Such a model may not represent the pores in actual materials but it’s generally accepted as the practical means of dealing with complex pore structures.

(a) (b)

Figure 3.16

Schematic illustration of two imaginary pore systems with a large pore and a small pore (Zhou et al., 2010)

The accessibility effect is illustrated in Figure 3.16 with two imaginary pore systems each with a large pore (with a diameter of d and a volume of ₁ v ) and a small pore (with a ₁

diameter of d and a volume of ₂ v ). In the left pore system shown in Figure 3.16, the ₂

large pore is directly connected to mercury, and thus, during mercury porosimetry measurement, the large pore is filled with mercury when the applied pressure is increased

to P and the small pore is filled with mercury when the applied pressure is increased to ₁

2

P . Therefore, for pore system in Figure 3.16 (a), the mercury porosimetry technique can

reveal the real pore size distribution. In contrast, in Figure 3.16 (b), the large pore is connected to mercury through the small pore. An applied pressure of P is not big enough ₁

to force mercury to intrude into the large pore, and thus, it is only when the applied pressure is increased to P that mercury intrudes into both the large and small pores. ₂

Therefore in this case, the mercury porosimetry result shows that the volume of the large pore is zero, and the volume of the small pore becomes the sum equals to v and ₁ v . As a ₂

result, the mercury porosimetry technique underestimates the volume of the large pore and overestimates the volume of the small pore.

Several researchers have spent effort on improving mercury porosimetry to eliminate the impact of the accessibility effect. One early unsuccessful attempt was made to correct for those poresthat could fill at a given pressure but failed, because they were connected to the mercury source onlyby smaller pores (Meyer, 1953). This researcher tried to determine the actual distribution of thepore sizes in a porous rock from the cumulative distributionof mercury injected into the rock with increasing pressure againstcapillary forces but in the process altered the distribution of the large pores. In a different approach, Liu and Winslow (1995) worked with cement-based materials where mercury was intruded progressively up to the maximum pressure, then reduced the pressure progressively to the minimum pressure, and re-intruded to the maximum pressure. The minimum intruding pressure was 0.5 psia, and the maximum was 60,000 psia for the initial intrusion step, however, due to instrumental limitations, the extrusion and the re-intrusion steps had applied pressures of the range of 29 to 60,000 psia. It was found that the processes of mercury extrusion and re- intrusion were fully reversible when appropriate advancing and receding contact angles were used. In addition, these researchers suggested that the pore system of cement paste can be divided into two parts (reversibly and irreversibly intruded pores). It was concluded that the reversibly intruded pores were more accessible to mercury and more closely correlated with the transport properties of cement-based materials.

addition, wood’s metal has low melting point, and thus can intrude at elevated temperatures and solidify in place by cooling at room temperature (Darot and Reuschle, 2003). Kaufmann (2010) used the Washburn Equation (3.31) to describe the relation between the applied pressure and the radius of the pores filled with Wood’s metal. The liquid metal (at elevated temperature), was intruded into the samples by applying different pressure regimes and then re-solidified in place. Subsequent scanning electron microscopy, even at the highest pressure, showed no crack formation was caused by this impregnation. The partial impregnation with this metal allowed the analysis of non-ink-bottle type pore space in a subsequent nitrogen sorption experiment and its comparison with an empty pore system. It was found that the relative pore size distribution was similar to that of an empty pore system, and thus, not influenced by the metal impregnation of ink-bottle type or large pores. Previously, Kaufmann and Leemann (2009) showed that the size of the ink-bottle pores can be excluded from analysis in such multi-cycle mercury porosimetry analysis; thus, the sizes of their neck entrances can be estimated. In addition, Kaufmann and Leemann (2009) found that the pore size distribution obtained by nitrogen sorption agreed well with that obtained by second mercury intrusion (i.e. when mercury intrusion– extrusion cycle was repeated twice). Therefore, the accessibility effect was considered to be reduced in the second mercury intrusion, since the ink-bottle pores were already filled in the first intrusion–extrusion cycle. Although the work Meyer (1953). Liu and Winslow (1995), Kaufmann and Leemann (2009), and subsequent report by Kaufmann (2010) made a big progress in the characterization of pore structure in porous materials, especially in cement-based materials by using Mercury porosimetry, these researchers could not provide a valid estimate of pore size distribution.

Subsequent work by Zhou et al. (2010) developed a new mercury porosimetry method that can overcome the accessibility effect and provide a more accurate estimate of the pore size distribution in porous materials especially in cement-based materials. The new technique as conducted following a unique mercury intrusion procedure in which the applied pressure was increased from the minimum to the maximum by repeating pressurization– depressurization cycles instead of a continuous pressurization followed by a continuous depressurization. In every pressurization–depressurization cycle, the intrusion and extrusion pressure values were calculated using the Washburn Equation (3.31) with the different advancing and receding contact angles calculated with the pressures at which

mercury intrudes into and extrudes out of an artificial straight cylindrical pore with known diameter. Therefore, by repeating the pressurization–depressurization cycles, the volumes of throat pores and ink-bottle pores can be measured at each throat pore diameter. These values were used to calculate the pore size distribution. The new method offered a better estimation of pore size distribution that compared well to the standard mercury porosimetry result. In addition, the pore size distribution measured by this technique had a better agreement with that obtained from nitrogen sorption, scanning electron image analysis, and the numerical simulations.

The work of Kaufmann (2010) and Zhou et al. (2010) provided a way of addressing the accessibility effect and a measure of pore size distribution in cement based materials that was proven tricky with other porous materials such as catalyst support pellets. Mercury porosimetry is often affected by pore shielding effects. Pirard et al. (1997) studied role of pore shielding in mercury porosimetry analysis. It was found that in experiments up to relatively low pressures of mercury, the mercury intrusion and retraction curves seemed to show that substantial mercury entrapment was occurring within the material. However, a close inspection of the sample following porosimetry, using light microscopy, revealed that, in fact, no mercury had become entrapped at all and the overall sample size had decreased. As higher mercury pressure was used, it was shown that mercury was then actually intruded into the structure because the subsequent microscopy studies revealed many mercury droplets entrapped within the pore structure. These findings were explained by the proposal that the initial rise in mercury pressure caused the collapse of the larger pores in the material which was then followed by the actual intrusion of smaller pores. Therefore, the apparent mercury entrapment in porosimetry data may actually indicate that pore collapse is occurring instead of entrapment. As a result, the multiple pressurization– depressurization cycles in Zhou et al. (2010) method can alter the physical structures of other porous materials such as the catalyst support pellets.

In a different approach, Rigby and co-workers (2004; 2005) interfaced gas adsorption and mercury porosimetry to measure pore size distribution in catalyst supports pellets. The two independent techniques, namely nitrogen sorption and mercury porosimetry, were utilised

geometry and topology of the internal pore network of mesoporous materials. The initial nitrogen sorption experiment was carried out at 77 K, and then the sample was allowed to reach room temperature (298.9 K) before transferring to the mercury porosimeter. Following mercury porosimetry, the sample was transferred back to the nitrogen sorption apparatus. The sample was then cooled to 77 K to freeze the mercury in place and the final nitrogen sorption experiment was commenced. The linear expansion coefficient for solid metals is typically ~ 10−5 K−1, and thus, the variation in the volume occupied by solid mercury between 234 and 77 K was expected to be miniscule. However, these kinds of approach carry a serious risk of contamination of the nitrogen porosimeter with mercury. Another drawback associated with this approach is the inability of the workers to tell if the mercury entrapped following mercury porosimetry has shifted to other parts of the sample. Nevertheless, it provides structural characterisations that are more statistically representative of a sample as a whole.