Determination of the cause of mercury entrapment during porosimetry experiments on sol–gel silica catalyst supports

Applied Catalysis A: General 247 (2003) 27–39

Determination of the cause of mercury entrapment during porosimetry experiments on sol–gel silica catalyst supports Sean P. Rigby a,∗ , Robin S. Fletcher b , Sandra N. Riley b a

Department of Chemical Engineering, University of Bath, Claverton Down, Bath, BA2 7AY, UK b Synetix, P.O. Box 1, Belasis Avenue, Billingham, Cleveland, TS23 1LB, UK Received 7 October 2002; received in revised form 9 January 2003; accepted 9 January 2003

Abstract In previous work, a modelling methodology was developed to determine statistical information, similar to that which can be obtained from 1 H MRI, on the spatial distribution of different pore sizes within porous media using mercury porosimetry. The new methodology has the advantage over MRI that it is suitable for application to chemically heterogeneous materials of interest in catalysis, such as coked catalysts and supported metals, that are not amenable to quantitative studies using conventional 1 H MRI. However, the new methodology relied upon the theory that the entrapment of mercury within many porous solids, such as sol–gel silicas, occurs because the spatial distribution of pore sizes within the material is not random, but is, in fact, highly correlated. Mercury entrapment is thought to occur in isolated, macroscopic (>10 ␮m in size) domains, containing similarly sized larger pores, that are completely surrounded by continuous networks of smaller pores. In this work mercury porosimetry experiments on silicas, consisting of a primary intrusion and retraction cycle, followed by re-injection of mercury and secondary retraction, have shown that the entrapment of mercury does not arise due to the alternative possibility of irreversible pore structural collapse. Light microscopy studies of transparent samples following mercury porosimetry experiments have confirmed that the spatial distribution of entrapped mercury is highly heterogeneous and occurs in particular macroscopic regions within the sample. These findings support the underlying theory of mercury entrapment used in previous simulations of the mercury porosimetry experiment. © 2003 Elsevier Science B.V. All rights reserved. Keywords: Porosimetry experiments; Sol–gel; Catalyst

1. Introduction Porous solids are generally characterised by parameters such as the overall average voidage fraction (porosity), pore size distribution (probability density function), specific surface area and pore connectivity (mean pore co-ordination number). However, all of these descriptors are one-dimensional. Experimental studies employing both magnetic resonance imaging ∗ Corresponding author. Tel.: +44-1225 384978. E-mail address: [email protected] (S.P. Rigby).

(MRI) [1,2] and micro-focus X-ray (MFX) imaging [3] techniques have shown that various different types of catalyst supports and adsorbents possess heterogeneities in the spatial distribution of local average porosity and pore size over macroscopic (>10 ␮m) length scales. These macroscopic heterogeneities have been shown to significantly influence both transient and steady-state diffusion [1,4] and (qualitatively) the deactivation of catalysts by coke deposition [5]. However, conventional 1 H MRI, using NMR relaxation time contrast, is unsuitable for obtaining quantitative information on structural heterogeneities in materials

0926-860X/03/$ – see front matter © 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0926-860X(03)00059-0

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that are relatively chemically heterogeneous. This is because the NMR relaxation times of a liquid imbibed within a porous material may vary from region to region of the sample due to chemical differences as well as changes in pore surface area-to-volume ratio. This limitation prevents the quantitative use of MRI techniques in the study of most materials of interest in catalysis, such as coked catalyst pellets. However, recently [6,7], it has been suggested that mercury porosimetry may also be used to obtain quantitative information on the same types of macroscopic structural heterogeneities that may be studied using MRI. Mercury porosimetry has several advantages over other potential techniques for pore structure characterisation. Due to the self-diffusion of the probe fluid, the most detailed level of spatial information that can be obtained from MRI is limited to the distribution of the local mean pore surface area-to-volume ratio that has been averaged over all of the pore sizes present within a volume defined by the rms displacement (∼10 ␮m) of the liquid molecules during the course of an experiment. However, recent work [8] has shown that the new methodology [6,7], based on mercury porosimetry, can also be used to determine the specific pattern of the spatial distribution of pore sizes particular to just one modal peak in a bidisperse material. With mercury porosimetry, this particular information may be obtained even when the typical spatial segregation between pores from each of the two modal peaks is only over very short length-scales that are several orders of magnitude below 10 ␮m. This information would not be possible to obtain using conventional 1 H MRI using relaxation time contrast. Three-dimensional TEM techniques [9] may be used to obtain a detailed three-dimensional reconstruction of the pore scale geometry of most mesoporous materials. However, the tiny size (∼500 nm) of the samples required to achieve the necessary resolution to directly study mesoporous materials severely limits the statistical reliability of the characterisation obtained from small samples of macroscopic objects, such as catalyst pellets. In contrast, mercury porosimetry is able to obtain a more statistically representative characterisation of a mesoporous medium. In order to extract information about the macroscopic structure of a mesoporous medium from mercury porosimetry data it is necessary to possess a detailed understand-

ing of the physical mechanisms involved in mercury intrusion and retraction processes in porous media. The basic mercury porosimetry experiment consists of increasing an imposed pressure in small increments and measuring the volume of mercury entering the sample during each pressure increment. The imposed pressure is generally related to a pore size via the Washburn [10] equation: p=−

2γ cos θ r

(1)

where p is the imposed pressure, γ the surface tension, θ the contact angle and r the radius of the pore. When using this equation to interpret raw mercury porosimetry data it is generally assumed that the parameters γ and θ are constants. In addition, it is also common practice to assume arbitrary values of θ. As a consequence of this type of assumption, a comparison of the pore-size distributions for different samples would then only be on a relative basis. A large amount of work described in the literature has demonstrated that the values of the surface tension and contact angle may vary with pore size [11], the nature of the surface [12], or whether the mercury is advancing or retreating [11–14]. However, a previous worker [11] has obtained calibrated, empirical expressions for the variation of the product γ cos θ with pore size for both mercury intrusion and retraction. This was done by correlating the pressure at which mercury intruded into, or retracted from, a model porous medium, which possessed regular pores of a uniform size, with the actual size of the pores obtained by electron microscopy [15]. The model porous media were controlled pore glasses. From these expressions for γ cos θ it is possible to obtain semi-empirical versions of Eq. (1) which take into account the variation of the surface tension and contact angle with pore size, and whether the mercury front is advancing into or retreating from a sample. The use of the alternative expressions to the Washburn equation allows the deconvolution of contact angle hysteresis effects from structural hysteresis effects. The semi-empirical versions of Eq. (1) have been used [7] to analyse the raw mercury porosimetry data for several different types of solely mesoporous, sol–gel silica to obtain absolute, rather than relative, pore sizes. The results from previous experimental work [7] have suggested that mercury entrapment is

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predominantly a macroscopic phenomenon, rather than being solely the microscopic process that is often assumed in many computer simulations of mercury porosimetry [16–18]. The different types of sol–gel silica considered in previous work [7] were studied both as whole pellets (size ∼3 mm) and as powder fragments (size ∼30–40 ␮m). It was found [7] that it was possible to use the semi-empirical, alternative expressions to the Washburn equation to obtain a complete and a priori superposition of the whole intrusion and extrusion curves for powdered samples over the complete range of applicability in pore size for the new expressions. The modal pore size for a pair of these curves was also found to be in close agreement with the corresponding value obtained completely independently by SAXS [7]. This particular finding confirmed that the semi-empirical, alternative expressions to the Washburn equation give rise to absolute values for pore sizes for other types of samples, in addition to the particular controlled pore glasses originally used to obtain them. As a result of analysing the porosimetry data for silica gel powders using the new expressions, no apparent hysteresis or mercury entrapment was observed. In contrast, when the raw data for whole pellet samples were analysed using the new equations, the superposition of the intrusion and extrusion curves only occurred at smaller mesopore sizes, and hysteresis and mercury entrapment were observed at larger mesopore sizes. These results suggested that, for the particular silica samples studied, the level of mercury entrapment is determined by the nature of the macroscopic (>40 ␮m) structure of the porous medium and not the pore scale properties, as is commonly assumed [16–18]. The silicas studied in previous work [7] were considered model materials since they were also amenable to the quantitative application of MRI techniques. This enabled a validation of the findings from mercury porosimetry to be obtained using MRI. MRI studies [2,19] of the sol–gel silica spheres showed that they possessed long-range (∼800 ␮m) correlations in the spatial distribution of local average pore size. The cause of the mercury entrapment in the whole pellets was thus attributed [7] to the presence of extended macroscopic domains, within which the pore sizes were relatively similar, being shielded by other surrounding heterogeneity domains with more disparate, and smaller, pore sizes. This suggestion was proposed in

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the light of the results of mercury porosimetry experiments conducted on glass micromodels by Wardlaw and McKellar [20]. The mercury porosimetry experiments, conducted by Wardlaw and McKellar [20], on micromodels consisting of pore networks etched in glass have suggested that non-random structural heterogeneity causes mercury entrapment. These workers found that for experiments on micromodels consisting of grids of pore elements of uniform size no mercury entrapment occurred. It was also found that no mercury entrapment occurred in glass micromodels where the sizes of individual, neighbouring pore grid elements were different, but relatively similar, and were distributed at random. However, Wardlaw and McKellar [20] also constructed two different types of non-random model systems. First, these workers constructed glass micromodels consisting of clusters of smaller pores occurring in isolated domains amidst a continuous network of larger pores. Second, Wardlaw and McKellar [20] constructed a different type of non-random model where isolated clusters of larger pores were located within a continuous network of smaller pores. In separate mercury porosimetry experiments on these two different types of non-random model it was found that mercury entrapment only occurred with the second type of model. Hence, it was shown that certain types of non-random structural heterogeneity will cause mercury entrapment. MRI studies [2] have shown that the sol–gel silica spheres studied in previous work [7] contain non-random spatial distributions of local average pore size. Further, the glass micromodel experiments [20] also explain why, when a real material is broken up into fragments that are smaller in size than the heterogeneity domains of similar pore size, no mercury entrapment occurs. This is because the particular pore shielding giving rise to the entrapment has then been removed. Based on additional experiments conducted by Wardlaw and McKellar [20] on networks consisting of narrow pore necks interspersed between larger pore bodies, subsequent workers [21] have concluded that once the relative sizes of neighbouring pore elements differ substantially (by a factor of ∼6) then mercury entrapment will also occur by “snap-off” of the mercury meniscus in the narrower pore necks. In recent work by Pirard et al [22] and Pirard and coworkers [23], it has been observed that even

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the relatively lowest pressures that are employed in mercury porosimetry can result in the irreversible crushing of pores within silica xerogels. 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. When a 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. This proposal was confirmed by carrying out the same mercury porosimetry experiments on samples sheathed in a membrane that was impermeable to mercury. The porosimetry data for this sample was found to have a form that would normally be interpreted as meaning that the intrusion and substantial entrapment of mercury was occurring, despite the impossibility of any real mercury penetration of the sample. However, the shapes of the apparent mercury intrusion and retraction curves were, in fact, due to pore collapse. Hence, these studies show that apparent mercury entrapment in porosimetry data may actually indicate that pore collapse is occurring instead. It is the first aim of the work presented here to obtain more direct evidence for the mercury entrapment mechanism proposed above by conducting mercury porosimetry experiments on a sol–gel silica sample which is transparent to visible light and the subsequent visual examination of the sample by light microscopy. The results of this study will also be compared with MRI studies of the same material. Second, a combination of special mercury porosimetry experiments, involving mercury re-injection and secondary retraction curves, and the subsequent visual inspection of the samples will be used to demonstrate that pore collapse is not occurring in the sol–gel silica materials studied here and previously [6,7].

2. Theory Liabastre and Orr [15] made a study of the morphology of controlled pore glasses using electron microscopy and mercury porosimetry. These workers obtained values for the diameters of the pores in the glasses by direct observation from microscopy. They compared these values with the corresponding values obtained from mercury intrusion and extrusion porosimetry via Eq. (1), assuming fixed values of contact angle and surface tension. Kloubek [11] used this data to determine the relationships for the variation of the product γ cos θ as a function of pore radius, for both advancing and retreating mercury menisci. Kloubek [11] obtained the expression: γ cos θA = −302.533 +

−0.739 r

(2)

for the variation of the product γ cos θ for an advancing (denoted by the subscript A) meniscus, which was valid for pore radii in the range 6–99.75 nm, and the expression: γ cos θR = −68.366 +

−235.561 r

(3)

for a retreating meniscus, which was valid for pore radii in the range 4–68.5 nm. By inserting Eqs. (2), or (3), into Eq. (1), and solving for r, it is possible to derive a relationship between the externally imposed pressure and the pore radius for mercury intrusion and retraction, respectively. For mercury intrusion the pore radius is given by: √ 302.533 + 91526.216 + 1.478p r= (4) p while for mercury retraction the pore radius is given by: √ 68.366 + 4673.91 + 471.122p r= (5) p Since Eqs. (2) and (3) are empirical in origin, then their use leads to an experimental error in the pore sizes obtained using Eqs. (4) and (5), which is estimated [11] to be ∼4–5%. These expressions are more complicated than the Washburn equation commonly used for this purpose, but have the advantage that they, additionally, take into account the variations that occur

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in the contact angle and surface tension as the radius of curvature of the liquid at the meniscus is decreased. Mercury porosimetry is an indirect method of characterising porous media and therefore requires a model porous structure in order to interpret the raw data. A detailed survey of the various different types of structural models that have been used to interpret mercury porosimetry data has been given elsewhere [24]. In previous work in the literature [21,25] the void spaces of various different types of porous media, such as rocks, have been represented by models consisting of networks of relatively wide pore bodies joined together by much narrower pore necks, rather than the typical cylindrical pore bond networks used elsewhere [16–18]. It has been suggested that, for these types of models, the pressure at which intrusion of mercury into a particular pore body occurs is controlled by the immediately adjacent pore neck sizes, whereas the pressure for the retraction of mercury from the pore bodies is predominantly controlled by the pore body size itself. In addition, so long as the ratio of the pore body size to the immediately adjacent pore neck size does not exceed a value of ∼6 [21] the mercury ganglion remains continuous and the mercury may leave the pore body through the pore neck in question. However, where this ratio exceeds a value of ∼6 the mercury meniscus will break, in a phenomenon known as “snap-off”, and the mercury within the pore body becomes entrapped. 3. Experimental 3.1. Mercury porosimetry Mercury porosimetry experiments were performed using a Micromeritics Autopore II 9220. The sample was first evacuated to a pressure of 6.7 Pa in order to remove physisorbed water from the interior of the sample. The standard equilibration time used in the experiments was 15 s. However, separate experiments were conducted using different equilibration times in the range between 15–3600 s. Since it is difficult to thoroughly clean entrapped mercury from a given sample after an experiment for re-use in a further mercury porosimetry experiment, each particular experiment was, instead, repeated on several samples of the same batch.

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3.2. Nitrogen sorption Samples for nitrogen sorption experiments consisted of either a small number of catalyst pellets, or a quantity of powder fragments. Nitrogen sorption experiments were carried out at 77 K using a Micromeritics ASAP 2000 apparatus. The sample tube and its contents were loaded into the degassing port of the apparatus and initially degassed at room temperature until a vacuum of 1.3 Pa was recorded. A heating mantle was then applied to the sample tube and the contents heated under vacuum, to 100 ◦ C for 1 h. This procedure was repeated in 100 ◦ C steps (or a 50 ◦ C step where appropriate) until a particular final temperature was reached. Final temperatures in the range 200–400 ◦ C were considered. The sample was then left under vacuum for a period of time (typically in the range 4–18 h) at a pressure of 8 × 10−4 Pa. The purpose of the thermal pre-treatment for each particular sample was to drive off any physisorbed water on the sample but to leave the morphology of the sample itself unchanged. A range of different thermal pre-treatment procedures were considered in order to determine whether the experimental results were sensitive to the temperature or time period used. For all samples, at this point the heating mantle was removed and the sample allowed to cool down to room temperature. The sample tube and its contents were then re-weighed to obtain the dry weight of the sample before being transferred to the analysis port for the automated analysis procedure. The sample was then immersed in liquid nitrogen at 77 K before the sorption measurements were taken. The adsorption and desorption isotherms obtained were analysed using the well-known Barrett–Joyner–Halenda (BJH) [26] method to obtain the pore size distributions. The film thickness for multilayer adsorption was taken into account using the well-known Harkins and Jura equation. In the Kelvin equation the adsorbate property factor was taken as 9.53 × 10−10 m and it was assumed that the fraction of pores open at both ends was 0.0 for both adsorption and desorption. It was therefore assumed that capillary condensation commenced at the closed end of a pore to form a hemispherical meniscus and the process of evaporation also commenced at a hemispherical meniscus.

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3.3. MRI Samples were prepared by impregnation with de-ionised water under ambient conditions for 24 h. This procedure has been shown [1] to give rise to complete pore filling, equivalent to that performed under vacuum conditions. 1 H NMR imaging experiments were performed using a Bruker DMX 200 NMR spectrometer with a static field strength of 4.7 T yielding a proton resonance frequency of 199.859 MHz. Spin density (which probe porosity) and spin-lattice relaxation time (T1 ) (which probe pore size) images were obtained together using a spin-echo pulse sequence employing 90◦ selective and 180◦ non-selective pulses. The imaging sequence was pre-conditioned using a saturation recovery pulse sequence and an echo time of 2.6 ms was used. All images acquired were of dimension 128 pixel × 128 pixel. The in-plane pixel resolution was 40 ␮m and the slice thickness was 1 mm. More detail concerning the image acquisition procedure is given elsewhere [1,2].

Fig. 1. Pore size distributions obtained using a BJH [26] analysis of the nitrogen adsorption (䊏) and desorption (䊉) isotherms obtained previously [6].

porosimetry data for powdered samples in Fig. 2 using Eqs. (4) and (5) leads to a complete superposition (within the errors present in Eqs. (2) and (3)) of the intrusion and extrusion curves over the range of validity of the equations. It can be seen that no intra-particle mercury entrapment occurs during a porosimetry

4. Results The material studied in this work, denoted G1, consists of transparent sol–gel silica spheres with a nominal diameter of ∼3 mm. The material was studied both as whole pellets and as powder fragments. The median particle size of the fragmented sample was ∼30 ␮m according to laser diffraction measurements. 4.1. Nitrogen sorption and mercury porosimetry The nitrogen sorption isotherms for whole pellets from batch G1 have been obtained previously [6]. Fig. 1 shows the pore size distributions obtained from the nitrogen adsorption and desorption isotherms using the standard BJH [26] analysis described in the Experimental section. Fig. 2 shows the raw mercury intrusion and extrusion curves for mercury porosimetry experiments conducted on typical samples of both whole and fragmented pellets. Fig. 3 shows the results of the analysis of the data in Fig. 2 using the semi-empirical alternatives to the Washburn equation (Eqs. (4) and (5)) described in the Theory section. It can be seen from Fig. 3 that the analysis of the raw

Fig. 2. Raw mercury intrusion (䊉) and retraction (䊏) data for whole (a) and fragmented (b) samples of pellets from batch G1. The lines shown are to guide the eye. The median particle size of the fragmented sample was ∼30 ␮m (by laser diffraction).

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Fig. 3. The resultant mercury intrusion (䊉) and retraction (䊏) curves obtained when the raw data shown in Fig. 2 were analysed using Eqs. (4) and (5), respectively, for whole (a) and fragmented (b) samples of pellets from batch G1. The lines shown are to guide the eye. The median particle size of the fragmented sample was ∼30 ␮m (by laser diffraction).

experiment on a powdered sample. However, in contrast, it can be seen that entrapment does occur during a porosimetry experiment on a sample of whole pellets from batch G1. The specific pore volume for pellets from batch G1 determined using a gravimetric method [27] is 1.06 ± 0.15 cc g−1 . From Figs. 1 and 3, it can be seen that the total specific pore volumes obtained from the pore size distributions for whole pellets from both mercury porosimetry and nitrogen adsorption are both identical, within intra-batch variability (given by the error quoted above), to the corresponding value obtained by a gravimetric method. The gravimetric method used the imbibition of the pore space with water. The water should be able to enter all of the mesoand macro-porosity present that is accessible from the surface. Due to machine limitations on achieving precise relative pressures close to a value of unity, it is not possible to cause the capillary condensation

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of liquid nitrogen in pores of sizes greater than ∼35 nm. Therefore nitrogen sorption only probes mesoporosity. The close similarity between the specific pore volumes obtained by all three different methods, namely gravimetric analysis, nitrogen sorption and mercury porosimetry, suggests that there is no shielded macroporosity present in pellets from batch G1 and that mercury enters all of the pore space directly accessible from the edge of the pellet. During the course of a mercury porosimetry experiment, the pressure is either increased or decreased in small steps, and a small volume of mercury then, either enters, or leaves, the sample, respectively. After each pressure change the volume of mercury within the sample is then allowed to come to equilibrium over a period of time. In order to determine whether the length of this equilibration time had any effect on the shapes of the intrusion and/or extrusion curves, and the level of mercury entrapment, separate mercury porosimetry experiments were conducted on different samples from batch G1 with different equilibration times, but always using the same pressure table. The pressure table is the set of absolute pressures corresponding to the data points that are used in the experiments. Due to intra-batch variability each particular experiment was repeated on multiple samples from the same batch. It was found that, within slight intra-batch variability, the length of the equilibration time, over the range of values between 15 and 3600 s, made no significant difference to the shape of the mercury intrusion or extrusion curves obtained. Where minor discrepancies between samples arose in the incremental volumes entering or leaving different samples at a particular pressure step, these were typically compensated at the next pressure step, such that the total volumes entering, or leaving, two different samples over the course of the whole experiment were identical, within the small intra-batch variability. In order to determine whether the high pressures used in mercury porosimetry cause structural damage and collapse in material G1, mercury re-injection and secondary retraction experiments were conducted. Samples from batch G1 were subjected to an initial primary intrusion up to the maximum pressure possible (∼412 MPa) with the apparatus used, and then the pressure was reduced back down to 0.131 MPa in the primary retraction curve. The sample was then re-intruded back up to the maximum pressure (forming

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Fig. 4. Raw mercury porosimetry data for both primary and secondary intrusion and retraction cycles. The data shown are the primary intrusion curve (䊊), the primary retraction curve (×), the re-injection curve (䊐), and the secondary retraction curve (+).

a re-injection curve) and finally the pressure was reduced back down to ambient conditions. The raw data from such an experiment on a sample from batch G1 are shown in Fig. 4. The curves resulting from an analysis of the raw data shown in Fig. 4 using the semi-empirical alternatives to the Washburn equation (Eqs. (4) and (5)) are shown in Fig. 5. In Fig. 5, it can be seen that, within the errors present in Eqs. (2) and (3), the primary intrusion, primary retraction, re-injection and secondary retraction curves all overlay each other at low pore sizes. From Fig. 5, it can also be seen that mercury leaves the sample in both

Fig. 5. Results of the analysis, using Eqs. (4) and (5), of the raw mercury porosimetry data shown in Fig. 4 for both primary and secondary intrusion and retraction cycles. The data shown are the primary intrusion curve (䊊), the primary retraction curve (×), the re-injection curve (䊐), and the secondary retraction curve (+).

the primary and secondary retraction curves over the pressure range corresponding to pores of sizes 60–100 nm. However, both the primary intrusion and re-injection curves are relatively flat over this interval. At the largest pore sizes the primary retraction and re-injection curves are coincident. Mercury begins to re-enter the sample in the re-injection curve over a pore size range of 10–30 nm and by a pore size of ∼10 nm the re-injection curve coincides again with the primary and secondary retraction curves. As can be seen from a comparison of Figs. 3 and 5, the flattening in the primary retraction curve between pore sizes of 10–60 nm followed by a further retraction of mercury between pore sizes of 60–100 nm is not common to all samples from batch G1. It is proposed that this relatively small effect is due to some slight intra-batch variability in pore structure between samples. However, this effect, present for some samples, is highlighted here because it is particularly relevant to the consideration of the possibility of pressure-induced pore collapse in batch G1. As mentioned in the Theory section, it has been proposed that, for pore structures consisting of narrow pore necks guarding access to wider pore bodies, the pressure at which mercury intrudes into the pores is controlled by the pore neck size, whereas the pressure at which it retracts is controlled by the pore body size. The data shown in Fig. 5 will thus be interpreted as follows. In the sample used to obtain the data in Fig. 5, there is, within a limited region of the sample, a small volume of void space consisting of pore bodies with sizes in the range 60–100 nm that are guarded by pore necks with sizes in the range 10–30 nm. In the primary retraction curve no entrapment occurs in this region of the pore space. This conclusion was drawn because the primary retraction and re-injection curves overlay each other for pore sizes larger than 100 and smaller than 10 nm. If larger pore necks guard larger pore bodies then it is unlikely that the “snap-off” ratio mentioned above would be exceeded and the mercury contained in the pore bodies is able to retract through the neighbouring pore necks without becoming entrapped. However, it is also noted that there may be a slight increase in the level of mercury entrapment during the retraction from the pore bodies in the size range 60–100 nm in the secondary retraction curve. In summary, these mercury porosimetry results indicate that there are some large pore bodies, with sizes in

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Fig. 6. (a) Light micrograph image of a sample from batch G1 following a full primary mercury intrusion and retraction cycle. The overall pellet diameter is 3 mm; (b) close-up view of a region of Fig. 6(a) containing an apparently isolated, entrapped mercury ganglion.

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the range 60–100 nm, present within the sample from batch G1, and these large pores are still present even following two separate increases of pressure up to ∼412 MPa. A comparison of the data shown in Figs. 4 and 5 shows that the close association between the (10–30 nm) pore necks in the re-injection curve and the (60–100 nm) pore bodies in the primary retraction curve is only revealed when the raw data is analysed using the semi-empirical alternatives to the Washburn equation and would not have been evident from an analysis of the data in Fig. 4 using the traditional approach with the Washburn equation. 4.2. Studies of entrapped mercury using light microscopy Light microscopy studies of fresh samples taken from batch G1 have shown that, while their surfaces may have some small cracks and blemishes, the

spheres are generally very clear. After some samples from batch G1 had been subjected to a full primary mercury intrusion and retraction experiment they were examined under a light microscope. An example of a typical pellet examined after mercury porosimetry is given in Fig. 6(a). The dark zones within the sphere in Fig. 6(a) correspond to regions containing large quantities of entrapped mercury, whereas the more transparent and paler regions correspond to areas with no, or much less, entrapped mercury. It can be seen from Fig. 6(a) that the spatial distribution of entrapped mercury is very heterogeneous, over macroscopic length scales. It can be seen that, towards the right hand limb of the sphere in Fig. 6(a), an apparently isolated domain of entrapped mercury is clearly visible surrounded by neighbouring clear zones containing little or no mercury. Fig. 6(b) shows a close-up view of this region. The close up view of the sphere in Fig. 6(b) clearly shows that the distribution

Fig. 7. Spin density image for a 3 mm nominal diameter sol–gel silica sphere from batch G1. (128 × 128 image, 1.0 mm slice, pixel = (40 ␮m)2 , echo time = 2.6 ms, repetition time = 2.0 s, number of scans = 40). Dark regions correspond to high porosity and light regions correspond to low porosity.

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of mercury entrapment is very heterogeneous and is concentrated into particular domains within the sample. The images in Fig. 6(a) and (b) show that the overall order of the length scales of the domains containing entrapped mercury is ∼100–1000 ␮m. It is noted that the pore size distributions obtained for pellets from batch G1, given in Figs. 1 and 3, suggest that the sizes of the pores present in G1 are in the range∼10–50 nm. The pores themselves are thus well below the resolution possible with light microscopy. Hence the domains of entrapped mercury appear as blobs trapped within the clear silica, as in Fig. 6(a). The typical size of the domains of entrapped mercury observed in Fig. 6(a) and (b) are larger than the size of the particles in the powdered sample used to obtain the porosimetry data given in Fig. 2(b). The presence of ganglia of entrapped mercury possessing distinctive morphologies, such as the one present in Fig. 6(b), enables the long term stability of the locations of entrapped mercury to be monitored. By studying the mercury ganglion evident in Fig. 6(b) on repeated occasions over several days, it was possible to determine that the entrapped mercury did not move once entrapped because the morphology and location of the ganglion remained constant.

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4.3. Comparison of the results of light microscopy and MRI studies NMR spin density images were obtained of thin slices through the centres of pellets from batch G1. An example of a spin density map is shown in Fig. 7. Spin density images provide a map of the spatial distribution of porosity across the pellet. From Fig. 7, it can be seen that the porosity is significantly higher in the more central region of the sphere than it is at the periphery. However, it can be seen that the spatial distribution of porosity in Fig. 7 is more homogeneous than the spatial distribution of regions of high mercury entrapment in the light micrograph in Fig. 6(a). This finding suggests that the lighter regions in Fig. 6(a) are not simply regions of the pellet with no, or completely inaccessible, porosity. Fig. 8 shows a light micrograph of a sample from batch G1 following a mercury porosimetry experiment. The dark regions in Fig. 8 correspond to large quantities of entrapped mercury, whereas the lighter regions contain little or no mercury. Whilst it is noted that the light micrograph images are 2D projections of the 3D spheres, it can be seen from Fig. 8 that the entrapped mercury is also generally concentrated towards the

Fig. 8. Light micrograph image of a second sample from batch G1 following a full primary mercury intrusion and retraction cycle. The overall pellet diameter is 3 mm.

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centre of the sphere and a band containing a smaller amount of entrapped mercury is located towards the periphery of the sphere. Therefore, for some samples, there is apparently a clear correlation between the total level of porosity present in a particular region of the sphere and the final level of mercury entrapment at the end of a porosimetry experiment.

5. Discussion Previous mercury porosimetry studies of silica xerogels by Pirard and co-workers [22,23] have suggested that the collapse of larger pores under the high imposed pressures during porosimetry is associated with the appearance of intrusion and seeming, almost complete, entrapment of mercury in the raw pressure-volume data. However, the complete absence of real entrapped mercury was revealed by light microscopy studies of the samples following the porosimetry experiments. The results described above indicate that the collapse of larger pores is unlikely to be occurring in samples from batch G1. The primary retraction and secondary retraction curves from porosimetry experiments have revealed the presence of relatively large pores of sizes 60–100 nm in a sample from batch G1. These large pores have been found to remain intact following repeated application of pressures up to ∼412 MPa. In addition, the light microscopy studies of whole pellets from G1 following porosimetry experiments have shown, first, that the spheres retain their overall structural integrity (and have not splintered into powder), and, second, clear indication of the presence of truly entrapped mercury within the interior of the spheres. These results suggest that the pore collapse observed for silica xerogels does not occur for spheres from batch G1. In addition, during a porosimetry experiment, the very highest pressures are required to force mercury into the, previously unfilled, smallest pores present in a sample. Hence, the highest pressures (∼412 MPa) may also potentially give rise to the collapse of the smallest unoccupied pores. However, the close similarity of the primary intrusion, primary retraction, re-injection and secondary retraction porosimetry curves in Fig. 5 at low pore sizes clearly indicates that the highest pressures are also not causing the collapse of the smallest pores in the sample. In summary, the results

suggest that no pore collapse is occurring at all during porosimetry experiments on pellets from batch G1. It has clearly been seen, from the light microscopy studies described above, that the overall sizes of the spatially extended domains of entrapped mercury observed in G1 are consistent with the theory for the cause of the mercury entrapment, during mercury porosimetry experiments on the whole pellet sample, described in the Introduction to this paper. The regions containing entrapped mercury in Fig. 6(a) are thus probably heterogeneity domains, consisting of local networks of pores with similar large sizes, that are completely surrounded by other domains containing relatively smaller pores. Once the whole sphere is broken up into particles with sizes less than those of the heterogeneity domains then the pore-shielding effect is completely removed and no mercury entrapment occurs. The macroscopic sizes (∼100–1000 ␮m) of the regions of entrapped mercury, evident in the light microscopy images, are also consistent with the correlation lengths (∼800 ␮m) for the heterogeneities in the spatial distribution of local average pore size obtained from 2D NMR spin-lattice relaxation time images of slices through silica pellets. As suggested previously [3], micro-focus X-ray imaging techniques would allow the quantitative determination of the 3D spatial distribution of entrapped mercury within a sample. This information could then be used to validate the model for the spatial distribution of pore size domains within a sample obtained using simulations of the mercury porosimetry experiment [6,7].

6. Conclusion Mercury porosimetry experiments, consisting of a primary intrusion and retraction cycle, followed by re-injection and secondary retraction, have shown that pore structural collapse does not occur during mercury porosimetry experiments on a particular type of sol–gel silica sphere. An examination of individual samples of the gel spheres, using light microscopy, following mercury porosimetry experiments has shown that mercury entrapment occurs in heterogeneously distributed, macroscopic domains within the sample. Once entrapped within a region of the sample, the mercury was found to remain stationary within the pore space for a long period of time. These findings

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are consistent with the theory that the mercury entrapment within the material studied arises due to the presence, in the pore network, of extended, macroscopic domains containing similar pore sizes surrounded by other domains of more disparate and smaller pore sizes. Hence, mercury porosimetry experiments may be used to determine the spatial distribution of the pore size domains.

Acknowledgements SPR would like to thank Professor L.F. Gladden and Dr. M.D. Mantle of the University of Cambridge for their assistance with the previous work [2] in which the NMR images, also utilised in this work, were obtained. The authors would also like to thank Ms. E.M. Holt and Mr. P. Trippett of Synetix for their assistance with obtaining the laser diffraction data used in this work. References [1] M.P. Hollewand, L.F. Gladden, J. Catal. 144 (1993) 254. [2] S.P. Rigby, L.F. Gladden, Chem. Eng. Sci. 51 (1996) 2263. [3] S.P. Rigby, R.S. Fletcher, J.H. Raistrick, S.N. Riley, Phys. Chem. Chem. Phys. 4 (2002) 3467. [4] S.P. Rigby, K.-Y. Cheah, L.F. Gladden, Appl. Catal. A 144 (1996) 377. [5] K.-Y. Cheah, N. Chiaranussati, M.P. Hollewand, L.F. Gladden, Appl. Catal. 115 (1994) 147. [6] S.P. Rigby, J. Colloid Interface Sci. 224 (2000) 382.

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[7] S.P. Rigby, K.J. Edler, J. Colloid Interface Sci. 250 (2002) 175. [8] S.P. Rigby, Stud. Surf. Sci. Catal. 144 (2002) 185. [9] A.J. Koster, U. Ziese, A.J. Verklejj, A.H. Janssen, J. de Graaf, J.W. Geus, K.P. De Jong, Stud. Surf. Sci. Catal. 130 (2000) 329. [10] E.W. Washburn, Phys. Rev. 17 (1921) 273. [11] J. Kloubek, Powder Technol. 29 (1981) 63. [12] L. Moscou, S. Lub, Powder Technol. 29 (1981) 45. [13] J. Van Brakel, S. Modry, M. Svata, Powder Technol. 29 (1981) 1. [14] S. Lowell, J.E. Shields, J. Colloid Interface Sci. 80 (1981) 192. [15] A.A. Liabastre, C. Orr, J. Colloid Interface Sci. 64 (1978) 1. [16] G.P. Androutsopoulos, R. Mann, Chem. Eng. Sci. 34 (1979) 1203. [17] R.L. Portsmouth, L.F. Gladden, Chem. Eng. Sci. 46 (1991) 3023. [18] V.G. Mata, J.C.B. Lopes, M.M. Dias, Ind. Eng. Chem. Res. 40 (2001) 4836. [19] S.P. Rigby, S. Daut, Adv. Colloid Interface Sci. 98 (2002) 87. [20] N.C. Wardlaw, M. McKellar, Powder Technol. 29 (1981) 127. [21] G.P. Matthews, C.J. Ridgway, M.C. Spearing, J. Colloid Interface Sci. 171 (1995) 8. [22] R. Pirard, B. Heinrichs, J.P. Pirard, in: B. McEnaney, T.J. Mays, J. Rouquerol, F. Rodriguez-Reinoso, K.S.W. Sing, K.K. Unger (Eds.), Characterisation of Porous Solids IV, Royal Society of Chemistry, Cambridge, 1997. [23] C. Alie, R. Pirard, J.P. Pirard, J. Non-Cryst. Solids 292 (2001) 138. [24] S.P. Rigby, in: A. Hubbard (Ed.), Encyclopedia of Surface and Colloid Science, Marcel Dekker, New York, 2002, p. 4825. [25] C.D. Tsakiroglou, A.C. Payatakes, J. Colloid Interface Sci. 146 (1991) 479. [26] E.P. Barrett, L.G. Joyner, P.H. Halenda, J. Am. Chem. Soc. 73 (1951) 373. [27] S.P. Rigby, L.F. Gladden, Chem. Eng. Sci. 54 (1999) 3503.