Pore-Shape Effects in Determination of Pore Size of Ordered

J. Phys. Chem. C 2008, 112, 12921–12927

12921

Pore-Shape Effects in Determination of Pore Size of Ordered Mesoporous Silicas by Mercury Intrusion Anne Galarneau,† Benoıˆt Lefe`vre,† He´le`ne Cambon,† Benoıˆt Coasne,† Sabine Valange,‡ Zelimir Gabelica,§ Jean-Pierre Bellat,| and Francesco Di Renzo*,† Institut Charles Gerhardt Montpellier, UMR 5253 CNRS-UM2-ENSCM-UM1, ENSCM, 8 rue Ecole Normale, 34296 Montpellier Cedex 5, France, Laboratoire de Catalyse en Chimie Organique, UMR CNRS 6503, ESIP, UniVersite´ de Poitiers, Poitiers, France, LPI-GSEC, ENSCMu, UniVersite´ de Haute Alsace, 68093 Mulhouse Cedex, France, Institut Carnot de Bourgogne, UniVersite´ de Bourgogne, Dijon, France ReceiVed: July 24, 2007; ReVised Manuscript ReceiVed: May 19, 2008

MCM-41 and SBA-15 micelle-templated silicas are ideal reference materials to study the effect of surface roughness on pore size measurement by mercury intrusion, as the inner surface of the mesoporous channels is much rougher in the case of SBA-15 than MCM-41. In the case of MCM-41, the pressure of mercury intrusion is related to the pore size by the classical Washburn-Laplace law, while in the case of SBA-15, the pressure of intrusion is much higher than expected and classical models underevaluate the size of the channels. Defects on the pore surface of SBA-15 affect the mercury intrusion in a similar way as the deviation from cylindrical geometry does for the pores of spongelike silica glasses. The results vindicate the models of Wenzel and Kloubek on the effect of surface defects on the mercury contact angle, which is significantly larger for a rough surface than for a plane surface. The surface defects of SBA-15 does not affect the evaluation of the mesopore size by nitrogen adsorption, as they are filled at an early stage of the adsorption and do not interfere with capillary condensation. 1. Introduction Nitrogen adsorption and mercury intrusion porosimetry are the most widely used techniques to characterize the pore size and surface area of adsorbents and catalysts. In the case of cylindrical pores, nitrogen adsorption can be easily applied to the assessment of pores with diameter up to 50 nm, at the upper limit of mesoporosity.1 The smallest cylindrical pores in which mercury can be intruded at the 400 MPa pressure attained in most commercial instruments present a diameter of about 3 nm.2,3 Mesopores in MCM-41 and SBA-15 currently occur in the 3-10 nm diameter range,4,5 a size range appropriate to be studied by both techniques. These two materials therefore represent an ideal testbed to compare the performance of both techniques. The poor mechanical stability of MCM-41 has insofar prevented a successful characterization of their structural porosity by mercury intrusion.6 In the case of SBA-15, mercury intrusion studies have been performed on samples with 10 nm diameter and the results have been compared with the pore size measured by nitrogen adsorption.7,8 However, the specific properties of the pore system of SBA-15 have not yet been taken into account in the interpretation of porosimetry data. Indeed, the pore system of SBA-15 is more complex and can substantially vary with the conditions of synthesis.9,10 The main channels of SBA-15 prepared at low temperature are surrounded by a microporous corona, which introduces an important roughness at the surface of the main channels.11,12 For higher temperatures of preparation, the microporosity shrinks, the * Corresponding author: tel +33 607508148; fax +33 467163470; e-mail [email protected]. † Institut Charles Gerhardt Montpellier. ‡ Universite ´ de Poitiers. § Universite ´ de Haute Alsace. | Universite ´ de Bourgogne.

Figure 1. Schematic sections of channels and walls of (a) MCM-41, (b) SBA-15 synthesized at low temperature, and (c) SBA-15 synthesized at high temperature. The channel axes run horizontal in the plane of the page.

surface of the channels becomes flatter, mesoporous holes are formed in the walls, and connections can appear between the main channels.13 By comparison, the pore system of MCM-41 is much simpler and consists of mesoporous channels of constant section with a surface roughness not exceeding the roughness of the amorphous silica14–16 currently used as benchmark for the methods of mercury intrusion.17 A schematic representation of the pore systems of these phases is given in Figure 1. The purpose of this paper is to examine in which way the textural properties of differently ordered mesoporous silicas affect mercury porosimetry. The characterization of a series of SBA-15 samples with pore size from 5 to 10 nm and of a mechanically stable MCM-41, taken as typical examples, can provide information on the influence of both pore size and surface roughness on nitrogen adsorption and mercury intrusion. 2. Experimental Section 2.1. Preparation of Samples. The reagents used were P123 (ethylene oxide)20-(propylene oxide)70-(ethylene oxide)20 triblock copolymer and tetraethyl orthosilicate (TEOS, 98%) from Aldrich, hexadecyltrimethylammonium bromide (CTMABr, 99%), tetramethyl orthosilicate (TMOS, 99%), and methylamine (40% aqueous) from Sigma-Fluka, HCl (37% aqueous, Nor-

10.1021/jp075815+ CCC: $40.75  2008 American Chemical Society Published on Web 07/30/2008

12922 J. Phys. Chem. C, Vol. 112, No. 33, 2008 mapur) from Prolabo, and deionized water. All chemicals were used as received without further purification. SBA-15 samples of different pore size have been prepared by varying the temperature of the second step of the synthesis.9,10 The SBA-15 samples are named SBA-15-T, where T is the temperature (in kelvins) of the final step of the synthesis. The molar composition of the synthesis batch was 0.0168 P123/1 TEOS/5.87 HCl/97 H2O. Another sample prepared at 403 K with one-third water and HCl was named SBA-15-403-B. All the reagents except TEOS were mixed and stirred for 4 h at 313 K. After addition of TEOS, the system was further stirred for 20 h at 313 K and left unstirred in a Teflon-lined autoclave for 24 h at temperature T. The SBA-15 samples were calcined at 823 K in air flow. The MCM-41 mesoporous silica was prepared via an alkalimetal-free synthesis method by introducing in the reaction mixture a pH-controlling mineralizing agent from the shortchain alkylamine family.18 As extensively reported by Gabelica and Valange19 for the synthesis of framework metal-substituted MFI zeolites, short-chain alkylamines behave both as efficient mobilizing (toward silica) and/or complexing (toward metallic ions) agents and buffering agents through stabilizing the synthesis pH range to basic values (10-12). In this work, methylamine (MA) was used as an efficient and inexpensive mobilizing/buffering agent along with TMOS and CTMABr. The gel molar composition was 1 SiO2/0.215 CTMABr/0.6 MA/ 125 H2O. The heavy precipitate was heated at 383 K in a Tefloncoated stainless steel autoclave for 24 h. The product was recovered by filtration, washed with cold water, and dried at 353 K before being calcined under air flow in successive steps. It was first heated to 473 K (rate of 1 K min-1) and kept for 2 h at that temperature prior to further heating to 873 K (rate of 1 K min-1) and finally held at that temperature for another 4 h. Such mild heating conditions are recommended in order to prevent an extensive local heating and possible partial collapse of the material (generation of hot spots upon oxidative decomposition of the surfactant molecule). 2.2. Characterization of Samples. Nitrogen adsorptiondesorption isotherms at 77 K have been measured on a Micromeritics ASAP 2010 instrument. Before the measurement, samples have been outgassed at 523 K until a 4 × 10-3 hPa stable static vacuum was reached. Mesopore diameters have been evaluated by the Broekhoff-de Boer (BdB) method20,21 and by the non-local density functional theory (NLDFT) method according to the protocols of Ravikovitch and Neimark.22 The BdB method has been shown to be well adapted to the evaluation of pore size of MCM-41 with pore diameter larger than 4 nm23 and to provide results in reasonable agreement with the more general NLDFT method.24 Total pore volume and micropore volume have been determined by the R-S method,25 albeit this method has been shown not to provide a fully quantitative evaluation of shallow micropores present in SBA15.9 The mesopore volume was calculated as the difference between the pore volume and the micropore volume. Mercury intrusion-retraction curves have been measured at room temperature on a Micromeritics AutoPore III porosimeter. Before the measurement, samples were evacuated at 6 × 10-2 hPa. An equilibration time of 60 s was allowed for each experimental point. Comparison experiments with equilibration time of 300 s were performed. Pore diameters have been measured by the Washburn-Laplace equation by assuming a mercury surface tension of 0.485 N m-1 and a contact angle of 130°.

Galarneau et al.

Figure 2. Adsorption isotherms of N2 at 77 K on MCM-41 (9) and on SBA-15 synthesized at 333 (O) and 403 K (4).

3. Results 3.1. Nitrogen Volumetry. The isotherms of N2 adsorption on MCM-41 and on SBA-15 synthesized at relatively low and high temperature are reported in Figure 2. The pore diameter calculated by the Broekhoff-de Boer method20,21 and the NLDFT method, as well the micropore and total pore volumes for all samples, are reported in Table 1. The results of N2 volumetry correspond to the typical features characterizing the two phases. MCM-41 presents a sharp capillary condensation step in which lack of hysteresis is due to the condensation pressure being lower than the threshold of reversibility of pore filling.14,26 In the case of SBA-15, the mesopore size increases and the micropore volume decreases as the synthesis temperature increases. It can be observed that the pore diameter evaluated from the desorption branch of the isotherm is never significantly lower than the diameter from the adsorption branch. This indicates that N2 volumetry is unable to detect the restrictions of the channels of SBA-15 that have been evidenced by transmission electron microscopy.27 3.2. Mercury Intrusion in SBA-15. The plot of intrusion and retraction of mercury in a SBA-15 sample synthesized at high temperature (sample SBA-15-403-B) is shown in Figure 3. In the low-pressure part of the plot, the volume changes as the grains of SBA-15 are drawn together and the sample is densified by the advancing mercury.28 At a pressure around 0.33 MPa, mercury penetrates into the intergranular porosity of the sample. The size of the intergranular porosity can be evaluated from the intrusion pressure according to the Washburn-Laplace equation:

P ) -2γ cos θ/R

(1)

where P is the pressure at which the meniscus of a fluid with surface tension γ presents a contact angle θ with the internal surface of a cylindrical pore of radius R.29 The diameters of the intergranular pores calculated in this way are reported in Table 1 for all samples. For samples formed by closely packed particles, the size of the intergranular porosity is strictly related to the size of the particles. In the case of closely packed spheres, the size of the particles is assumed to be about three times the size of the openings among them. When the pressure increases further, some compaction of the sample takes place until, at a pressure around 250 MPa, mercury penetrates the structural porosity of SBA-15. The pore size corresponding to the intrusion pressure is reported in Table 1 for all samples and will be discussed below. When pressure decreases, the structural porosity is emptied at a pressure of about 100 MPa. The pore diameters calculated from the retraction data by use of the Washburn-Laplace equation are reported in Table 1.

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TABLE 1: Textural Data from N2 Volumetry and Mercury Porosimetrya N2 volumetry D(BdB), nm

Hg porosimetry

D(NLDFT), nm

intrusion

retraction

sample

desorp

adsorp

desorp

adsorp

VM(N2), cm3 g-1

Vµ, cm3 g-1

D(I), µm

D, nm

D, nm

VM(Hg), cm3 g-1

MCM-41 SBA-15-333 SBA-15-343 SBA-15-353 SBA-15-373 SBA-15-403 SBA-15-403-B

3.8 4.9 7.4 7.4 7.6 10.5 9.6

5.2 6.7 6.8 7.5 10.0 9.0

4.2 5.1 7.3 7.3 7.8 10.3 9.6

3.5 5.4 7.0 7.1 7.6 9.9 9.1

0.82 0.50 0.67 0.67 0.82 1.18 1.18

0.12 0.11 0.15 0.06 0.00 0.00

1.1 2.4 3.6 2.3 2.1 0.7 3.8

4.1 3.4 4.3 3.9 4.4 6.4 5.2

6.4 9.3 8.3 8.4 16.9 11.8

0.32 0.15 0.30 0.25 0.43 1.08 0.53

a D, pore diameter; VM, mesopore volume; Vµ, micropore volume; D(I), intergranular pore diameter. Pore sizes are from Broekhoff and de Boer20,21 or NLDFT (N2) or Washburn-Laplace (mercury) methods.

Figure 3. Intrusion-retraction cycles of mercury in SBA-15 synthesized at 403 K (sample SBA-15-403-B). (]) First cycle; ([) second cycle. Inset: intrusion-retraction cycles in the structural porosity in linear pressure scale.

A second cycle of mercury penetration in the same sample presents less compaction phenomena. In the second cycle, the pressures of intrusion and retraction of mercury in the structural porosity are the same as in the first cycle, indicating that the pore size has not been affected by the intrusion. However, the volume of mercury penetrating the structural porosity is significantly lower in the second cycle than in the first one. This effect is quite common and has to be attributed to the entrapment of a fraction of mercury inside the pores during the first intrusion step.30–32 Indeed, cavitation in the retraction step of the first cycle can isolate patches of mercury, which remain inside the pores and decrease the volume available for intrusion during the second cycle. The excellent reproducibility of the intrusionretraction pressures between the cycles indicates that the size of the pores has not been affected by mercury intrusion. 3.3. Kinetic Effects and Mechanical Stability upon Mercury Intrusion. The mesopore volume VM(Hg) reported in Table 1 for all samples corresponds to the volume of mercury penetrated in the structural porosity. This volume is usually much lower than the VM(N2) value measured from N2 volumetry, with the exception of sample SBA-15-403. This sample presents nearly the same mesopore volume when measured by mercury porosimetry and N2 volumetry and is characterized by the largest mesopore size and the smallest particle size [see D(BdB) and D(I) in Table 1]. Samples SBA-15-403 and SBA-15-403-B present nearly the same mesopore diameter and the same mesopore volume as measured by N2 volumetry, although sample SBA-15-403-B presents a much larger particle size and a much smaller mesopore volume penetrated by mercury. In the case of larger particles, mercury has to penetrate deeper channels and nonequilibrium problems can more likely affect the analysis.

Figure 4. Cycles of intrusion-retraction of mercury on sample SBA15-403-B with equilibration times of 60 s (]) and 300 s (2). Inset: intrusion-retraction cycles in the structural porosity in linear pressure scale.

To verify whether a kinetic effect is involved in the limited penetration of mercury in the mesopores, cycles of intrusionretraction of mercury in sample SBA-15-403-B have been measured in two independent experiments with different equilibration times for each experimental point, namely, 60 and 300 s. The corresponding plots are reported in Figure 4. The intrusion-retraction patterns for the two experiments were virtually identical, with the exception of the volume of structural mesopores penetrated by mercury, nearly one-half larger for the experiment with longer equilibration time. It seems likely that a too-fast increase of pressure causes heterogeneity in the penetration of mercury inside the pore system. Differential pressure between pores can lead to local damage that prevents further penetration of mercury. It is remarkable that intrusion and retraction pressures were not affected by the time of equilibration. Limitations to the intrusion of mercury are more important for samples with smaller mesopores, such as SBA-15s synthesized at lower temperature or MCM-41s. The intrusion-retraction pattern for the SBA-15-343 sample is shown in Figure 5 and differs from the pattern of SBA-15-403B by the values of intrusion-retraction pressure and the intruded volumes. Intrusion in the structural mesopores occurs at 290 MPa and retraction at 145 MPa, both in the first and in the second cycle. In the case of the SBA-15 with the smallest mesopores, the structural volume penetrated by mercury is less than onethird of the mesopore volume as measured by N2 volumetry (Table 1). Small-pore SBA-15s are expected to be mechanically more stable than the large-pore ones, due to the higher ratio beteen

12924 J. Phys. Chem. C, Vol. 112, No. 33, 2008

Galarneau et al.

Figure 5. Intrusion-retraction cycles of mercury in SBA-15 synthesized at 343 K (sample SBA-15-343). (]) First cycle; ([) second cycle. Inset: intrusion-retraction cycles in the structural porosity in linear pressure scale.

Figure 7. Pore size from Hg porosimetry data, calculated by (a) the Washburn-Laplace equation or (b) the Kloubek-Rigby-Edler equations, vs the pore size from N2 volumetry. (4, 2) MCM-41; (0, 9) SBA-15 samples; (O, b) porous glasses;49 (], [) silica gel.48 Open symbols, intrusion; solid symbols, retraction. The solid lines correspond to equal diameters from Hg porosimetry and N2 volumetry.

Figure 6. Intrusion-retraction cycles of mercury in MCM-41. (]) First cycle; ([) second cycle. Inset: intrusion-retraction cycles in the structural porosity in linear pressure scale.

pillar section and span.7,33–35 As a consequence, it is unlikely that the smaller fraction of volume penetrated by mercury is due to a structural collapse of the whole material. However, it has been observed that the mechanical failure of MCM-41 under uniaxial compression does not imply a progressive change of pore size but rather occurs by complete collapse of individual rows of pores.33,34,36 In this case, the reproducible pression of intrusion of mercury in two successive intrusion-retraction cycles allows us to attribute this pressure value to the intrusion of mercury in the uncollapsed pores. 3.4. Mercury Intrusion in MCM-41. The plot of intrusion and retraction of mercury in the sample of MCM-41 is shown in Figure 6. Intrusion in the structural porosity suddenly occurs at 320 MPa. The intruded volume is less than half the mesopore volume as measured by N2 volumetry. The retraction process differs from the pattern observed for the SBA-15 samples. No sharp retraction at a given pressure was observed but the structural porosity is slowly emptied when the pressure decreases from 200 to 10 MPa. During the second cycle, the intrusion in the structural porosity started at 140 MPa, a pressure lower than in the first cycle, and continued up to 300 MPa. According to the Washburn-Laplace law, the initial intrusion pressure in the second cycle corresponds to pores with diameter 8.5 nm, nearly twice the diameter of the original structural pores. Despite the different intrusion pressure, the intruded volume in the second cycle was very similar to the volume intruded in the first cycle. The retraction during the second cycle closely followed the retraction pattern of the first cycle.

A possible explanation of these observations is that the first intrusion of mercury modifies the pore structure of the solid, through the collapse of a fraction of the silica walls. The intrusion of mercury in a fraction of the pores can induce an anisotropic stress between empty pores and parallel pores occupied by mercury. The collapse of the pore walls under this differential pressure probably results in the merging of groups of pores, with a densification and strengthening of the remaining pore walls. The observed modification of the intrusion pattern could be accounted for by the collapse of alternated rows of pore walls under pressure from the inside of the pore system, with a corresponding increase of the average pore size and the preservation of the intruded volume. The random distribution of the collapsed silica walls could account for the widened pore size distribution. It can be observed that, in order to generate a differential pressure between parallel pores, mercury has necessarily penetrated the pore system and the pressure step at 320 MPa can be accepted as a proper value for the mercury intrusion pressure in the unmodified structural pores. 4. Discussion The comparison between the mesopore size evaluated by N2 volumetry and by Hg porosimetry through the WashburnLaplace equation is given in Figure 7a. The results of the two techniques are virtually identical in the case of MCM-41 but markedly differ in the case of the SBA-15 samples. The diameters of structural mesopores evaluated from the intrusion data are much smaller than the values evaluated by N2 volumetry. In contrast, the Washburn-Laplace equation applied to the retraction curve largely overestimates the pore diameters. This last phenomenon is quite normal, as a hysteresis loop in the intrusion-retraction cycles is nearly always observed and largely reduces the retraction pressure. The classical interpretation attributes the hysteresis to a difference between advancing and receding contact angles, a lower receding angle corresponding to emptying of the pore at a pressure lower than the intrusion pressure.37,38 The width of the hysteresis loop has been shown

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J. Phys. Chem. C, Vol. 112, No. 33, 2008 12925

to depend on the nature of the surface.39–41 Moreover, in the case of the retraction of a different nonwetting fluid, namely, water penetrating in pores of hydrocarbon-lined silica, the width of the hysteresis has been shown to critically depend on the geometry of the pore system. In the case of the connected pores of porous glass, the retraction seems to follow the WashburnLaplace equation with a receding angle smaller than the advancing angle.42 In the case of the independent unidirectional pores of MCM-41, the retraction pressure has been shown to depend on cavitation phenomena, related to the nucleation of the vapor phase in filled pores.43–45 In such a case, the retraction pressure cannot be related to the pore size by the WashburnLaplace equation. The Washburn-Laplace law is not the only method used to evaluate the size of pores from the pressure of intrusion of mercury. On the basis of the comparison between the intrusion-retraction pressure of mercury in porous glasses and the pore size observed by electron microscopy,17 Kloubek46 has elaborated two empirical equations, further developed by Rigby and Edler,47 to correlate the intrusion and retraction pressures of mercury with the pore size. The Kloubek-Rigby-Edler (KRE) equations for advancing and receding mercury are reported as eqs 2 and 3, respectively:

r)

302.533 + √91526.216 + 1.478p p

(2)

68.366 + √4673.91 + 471.122p p

(3)

r)

The pore sizes of our samples evaluated by the KRE equations are reported in Figure 7b. As far as the intrusion data are concerned, the results of the KRE equation do not significantly differ from the Washburn-Laplace equation with a contact angle of 131°, as admitted by Kloubek.46 The results are different when the retraction data on our samples are concerned, as the KRE equation for retraction provides diameters that are significantly lower than the pore size determined from N2 volumetry and only slightly exceed the diameters obtained from the intrusion data (Figure 7b). This suggests that the KRE equation correctly accounts for the width of the hysteresis loop in the SBA-15 samples, as it does for the porous glasses for which it has been originally established. Some recent literature data on porous glasses and silica gel monoliths are also reported in Figure 7 and seem to follow the same trend as our data on SBA-15 samples.48,49 In the case of mercury intrusion-retraction cycles measured on a silica gel monolith, a reversible intrusion proportional to pressure was observed before the intrusion in the structural porosity.48 The phenomenon, accounting for the loss of nearly 20% of the pore volume, has been attributed to the elastic strain of the material. In an isotropic material, the decrease of pore diameter corresponding to such a decrease of pore volume can be calculated from the equation D/D° ) (V/V°)0.33 and is found to correspond to a 7% decrease. This could account for nearly a third of the observed difference between pore size measured by mercury intrusion and pore size measured by nitrogen volumetry (Figure 7). It is worth remarking that this silica monolith seems to present astounding elastic properties. It has been shown that the correlations between geometry and crushing strength of ceramic foams can be successfully applied to MCM41 materials.33,34 The Young’s modulus of an isotropic open foam can be calculated as a function of the density as E*/ES ) 0.33F*/FS, where the asterisk indicates the properties of the cellular material and the subscript s indicates the properties of

Figure 8. Washburn-Laplace graph of the intrusion-retraction pressure of mercury in mesoporous silicas versus the pore size as determined from N2 desorption. (4, 2) MCM-41; (0, 9) SBA-15. Open symbols, intrusion; solid symbols, retraction. Contact angles: ( · · · ) 110°, (---) 130°, and (s) 180°.

the solid walls of the material (ES ) 94 GPa and FS ) 2.2 g cm-3 for vitreous silica).35 If the density F* of the cellular materials is calculated from the pore volume VP as F* ) 1/(VP + FS-1), the Young’s modulus of the silica monolith of ref 48 can be calculated as E* ) 1.6 GPa, a value more typical of polymers than of ceramic foams. In a more recent study, Porcheron et al.49 have studied the intrusion of mercury in silica glasses. In this case, if the reversible intrusion of mercury preceding the intrusion in the structural porosity is attributed to an elastic strain, the Young’s moduli can be calculated at 21 GPa for a CPG sample and 29 GPa for a Vycor sample, values in the usual range for ceramic foams. As samples with elasticities as different as those characterizing the samples of refs 48 and 49 present the same kind of deviation from the Washburn-Laplace equation (Figure 7), it seems likely that the elastic strain alone cannot account for the underevaluation of pore size by mercury intrusion. The relevance of the discrepancy between pore size from N2 volumetry and mercury intrusion can be better apprehended by considering its implications on the Washburn-Laplace equation. When the Washburn-Laplace equation (eq 1) is reported in a bilogarithmic graph, the pressure of intrusion P and the pore diameter D ) 2R are aligned on straight lines of slope -1 corresponding to a given contact angle θ. These WashburnLaplace lines for the dependence of intrusion pressure on pore size for several contact angles are drawn in Figure 8, in which the experimental intrusion and retraction pressures for SBA-15 and MCM-41 are also reported as a function of the pore diameter measured by N2 volumetry. In the case of MCM-41, N2 volumetry indicates a pore diameter of 3.8 nm. For such a diameter and the experimental intrusion pressure of 320 MPa, the Washburn-Laplace law is abided by a contact angle of 127°, very similar to the 130° angle considered as the normal value for intrusion in oxide pores.50 This indicates that the Washburn-Laplace law can be successfully applied to a sample of ordered mesoporous silica with pores of constant section and smooth inner surface, as is the case for MCM-41. As the Washburn-Laplace law implies a fixed value of the surface tension of mercury, it can be inferred that the surface tension of mercury, or at least the product of the surface tension by the contact angle, is significantly the same for macroscopical drops and for a meniscus with radius of 1.9 nm. In the case of SBA-15, the retraction pressures correspond to contact angles from 125° to 113°. These values are at the

12926 J. Phys. Chem. C, Vol. 112, No. 33, 2008

Figure 9. Evolution of contact angle and radius of the meniscus when mercury advances in a cylindrical pore with increasing diameter (modified from Kloubek).46

upper limit of the range of literature data on the receding angle of mercury on a glass surface.46 The best-fitting linear correlation of the retraction data on SBA-15 in the bilogarithmic graph has a slope of -1.25. In this kind of graph, the KRE equation for retraction corresponds to a slope of -1.5, and a slope of -1 has been observed in other instances of retraction from porous glasses.42 It seems that the retraction of mercury from SBA-15 follows a path similar to the one characterizing retraction from porous glasses. This is not the case for intrusion pressures on SBA-15 samples, which correspond to very high advancing angles, in most cases higher than 180° (Figure 8). Contact angles higher than 130° have been reported for several materials.51,52 However, contact angles higher than 180° seem to correspond to a physical impossibility as, in the case of a surface with infinite curvature radius, they should correspond to the separation of the meniscus from the surface. However, it has to be taken into account that SBA-15 has pores with connections and surface defects. These deviations from cylindrical geometry can account for an increase of the advancing contact angle and can explain why mercury intrusion in SBA-15 shares a common pattern with the intrusion in other noncylindrical pore systems, like porous glasses and gels. A model for the intrusion of mercury in pores with variable section has been proposed by Kloubek.46 In Figure 9, a schematic representation is given of the advancement of a meniscus of mercury inside a pore. Until the pore has a constant section, the meniscus advances at a pressure corresponding to the contact angle θ1 and the radius r1 of the meniscus (Figure 9a). When the meniscus reaches the rim of an enlargement of the pore, with slope of the tapering wall Φ, the contact angle with the tapering surface is θ2 ) θ1 - Φ, too small for further advancement of the meniscus (Figure 9b). When the pressure increases, the contact angle increases and the radius r2 of the meniscus decreases. When the radius of the meniscus r2 equals the radius of the pore R, the contact angle with the cylindrical portion of the wall is θ3 ) 180°. The contact line between mercury and surface does not advance until the contact angle with the tapering surface has reached the value θ4 ) θ2 + Φ ) θ1 (Figure 9c). At that moment, the meniscus advances again and the wider part of the pore is immediately filled. The mechanism proposed by Kloubek accounts for the need for higher pressure and a higher apparent contact angle for mercury to penetrate cylindrical pores with variable diameter. The variations of pore diameter and the connections between channels, which characterize SBA-15 and are not present in MCM-41, could explain the higher pressure needed for mercury to penetrate the SBA-15 samples (Figure 8). The presence of edges at which the slope of the pore wall changes can account for the higher-than-expected contact angles observed. It can be observed that SBA-15 samples synthesized at several temperatures also present abnormally high contact angles (Figure 8). It has been shown by the characterization of replicas of the pore system that SBA-15 samples synthesized at low temperature do not present connections between channels.10 Their pores, however, are lined by a corona of micropores,11,12 which

Galarneau et al. have been represented as cavities with nearly 1 nm depth and 1 nm diameter.13 In the case of wetting fluids, the presence of nanometric roughness has been shown to significantly increase the advancing contact angle.53 It is remarkable that the presence of microporous pits on the pore surface13 affects the advancement of the meniscus in the same way as the expansions of the channels observed in SBA-15 samples synthesized at higher temperature.27 This is in qualitative agreement with very early observations on the effect of surface roughness on the contact angle.54,55 Wenzel54 observed that, independently of the depth of the roughness, the contact angle θ with a rough surface was correlated with the contact angle θ0 with the corresponding plane surface by the equation

cos θ ) R* cos θ0

(4)

where R* is the expansion of the surface due to its roughness, namely, the ratio between the length of the actual path of the contact line to its projection in the average direction of the displacement of the meniscus. According to the Wenzel equation, the shift from 130° to 180° of the advancing contact angle would require a 55% expansion of the pore surface. Such a value is not very far from available textural data: for SBA-15 synthesized at temperature not higher than 373 K, the micropore surface represents from 40% to 50% of the total surface.9 It is worth considering that all comparisons between the results of mercury porosimetry and N2 volumetry are meaningful only if the pore diameters from N2 adsorption are correctly evaluated. It has been shown that the Broekhoff-de Boer method20,21 allows a correct evaluation of the pore size of MCM41.23 Does the difference in pore geometry between MCM-41 and SBA-15 affect the condensation pressure of N2 in the mesopores? Recently, argon adsorption in isolated and connected cylindrical mesopores has been modeled to verify whether lateral openings affect the adsorption behavior in mesoporous channels.56 The results have clearly shown that lateral pockets are filled at a pressure much lower than the condensation pressure in the main channels. As a consequence, any surface roughness has disappeared before the capillary condensation, and the pressure at which the mesopores are filled is not affected by surface defects. 5. Conclusions It is an often forgotten truism that the models used to calculate pore size from the pressure of condensation-evaporation of gas or from the pressure of mercury intrusion are valid only for a given geometry of the pores. Micellar-templated silicas are an especially convenient benchmark to verify the effects of geometry on the evaluation of the pore size, as their ordered structure has allowed them to be studied in higher detail than any other mesoporous material. The classical models to evaluate the pore size have been elaborated for simple geometries such as cylindrical pores with constant diameter. For solids that present the model geometry, like MCM-41, the evaluations of pore size by N2 volumetry (Broekhoff and de Boer method)20,21 and mercury porosimetry (Washburn-Laplace law) are in excellent agreement for pores having a diameter as small as 4 nm. The geometry of SBA-15 is more complex, with microporous pits on the pore surface and connections smaller than the pore size. These geometrical defects do not alter the evaluation of the pore size by N2 volumetry, as the smallest cavities are already filled when capillary condensation takes place. In contrast, the defects of the pore surface are not penetrated by liquid mercury, unable

Pore Shape and Mercury Intrusion to fill cavities smaller than 3-4 nm under the usual experimental conditions.32,57 The rims of the surface defects significantly alter the evaluation of the pore size by mercury porosimetry and markedly hinder the advancement of the mercury meniscus. The energy needed to overcome the surface defects significantly increases the apparent contact angle and leads to a severe underevaluation of pore size if this effect is not taken into account. This effect explain that a fair agreement has been found between the results of nitrogen adsorption by the BJH method and the results of mercury intrusion by the Washburn model7,8,32,49 because, in the case of samples with interconnected pores, the Washburn model underestimates pore size nearly as much as the BJH method does.23,58–61 The scale and shape of the defects are undoubtedly important, as ascertained by findings like the good agreement between the intrusion pressure evaluated by the Washburn-Laplace law and the microscopic measurements for pore systems with interconnections 8 nm large17 or the severe underevaluation of pore diameter by mercury intrusion in spongelike mesoporous silicas.62 The study of the influence of size and distribution of defects on the advancement of a meniscus is a blossoming field,55,63 and results at the nanoscale are badly needed to understand which complementary characterizations are needed to refine the size evaluation of small mesopores by mercury porosimetry. Acknowledgment. We are grateful to the reviewers of the Journal of Physical Chemistry for useful suggestions. References and Notes (1) Rouquerol, F.; Rouquerol, J.; Sing, K. S. W. Adsorption by powders and porous solids; Academic Press: San Diego, CA, 1999; 468 pp. (2) Giesche, H. In Handbook of Porous Solids, Vol. 1; Schu¨th, F., Sing, K. S. W., Weitkamp, J., Eds.; Wiley-VCH: Weinheim, Germany, 2002; p 309. (3) Lowell, S.; Shields, J. E. Powder Surface Area and Porosity; Chapman & Hall: London, 1991; 234 pp. (4) Beck, J. S.; Vartuli, J. C.; Roth, W. J.; Leonowicz, M. E.; Kresge, C. T.; Schmitt, K. D.; Chu, C.T.-W.; Olson, D. H.; Sheppard, E. W.; McCullen, S. B.; Higgins, J. B.; Schlenker, J. L. J. Am. Chem. Soc. 1992, 114, 10834. (5) Zhao, D.; Huo, Q.; Feng, J.; Chmelka, B. F.; Stucky, G. D. J. Am. Chem. Soc. 1998, 120, 6024. (6) Lind, A.; du Fresne Von Hoenesche, C.; Smått, J. H.; Linde´n, M.; Unger, K. Microporous Mesoporous Mater. 2003, 66, 219. (7) Hartmann, M.; Vinu, A. Langmuir 2002, 18, 8010. (8) Vinu, A.; Murugesan, V.; Bo¨hlmann, W.; Hartmann, M. J. Phys. Chem. B 2004, 108, 11496. (9) Galarneau, A.; Cambon, H.; Di Renzo, F.; Fajula, F. Langmuir 2001, 17, 8328. (10) Galarneau, A.; Cambon, H.; Di Renzo, F.; Ryoo, R.; Choi, M.; Fajula, F. New J. Chem. 2003, 27, 73. (11) Impe´ror-Clerc, M.; Davidson, P.; Davidson, A. J. Am. Chem. Soc. 2000, 122, 11925. (12) Ravikovitch, P. I.; Neimark, A. V. J. Phys. Chem. B 2001, 105, 6817. (13) Nossov, A.; Haddad, E.; Guenneau, F.; Galarneau, A.; Di Renzo, F.; Fajula, F.; Ge´de´on, A. J. Phys. Chem. B 2003, 107, 12456. (14) Branton, P. J.; Hall, P. G.; Sing, K. S. W.; Reichert, H.; Schu¨th, F.; Unger, K. K. J. Chem. Soc., Faraday Trans. 1991, 90, 2965. (15) Berenguer-Murcia, A.; Garcia-Martı´nez, J.; Cazorla-Amoro´s, D.; Martı´nez-Alonso, A.; Tasco´n, J. M. D.; Linares-Solano, A. Stud. Surf. Sci. Catal. 2002, 144, 83. (16) Coasne, B.; Hung, F. R.; Pellenq, R. J. M.; Siperstein, F. R.; Gubbins, K. E. Langmuir 2006, 22, 194. (17) Liabastre, A. A.; Orr, C. J. Colloid Interface Sci. 1978, 64, 1. (18) Valange, S.; Gabelica, Z.; Broyer, M.; Bellat, J. P. Unpublished results. (19) Gabelica, Z.; Valange, S. Microporous Mesoporous Mater. 1999, 30, 57.

J. Phys. Chem. C, Vol. 112, No. 33, 2008 12927 (20) Broekhoff, J. C. P.; de Boer, J. H. J. Catal. 1967, 9, 8. (21) Broekhoff, J. C. P.; de Boer, J. H. J. Catal. 1968, 10, 377. (22) Ravikovitch, P. I.; Neimark, A. V. G. Colloids. Surf., A 2001, 187, 11. (23) Galarneau, A.; Desplantier, D.; Dutartre, R.; Di Renzo, F. Microporous Mesoporous Mater. 1999, 27, 297. (24) Neimark, A. V.G.; Ravikovitch, P. I. Microporous Mesoporous Mater. 2001, 44, 697. (25) Sing, K. S. W. Chem. Ind. (London) 1968, 1520. (26) Trens, P.; Tanchoux, N.; Galarneau, A.; Brunel, D.; Fubini, B.; Garrone, E.; Fajula, F.; Di Renzo, F. Langmuir 2005, 21, 8560. (27) Liu, Z.; Terasaki, O.; Ohsuna, K.; Hiraga, K.; Shin, H. J.; Ryoo, R. ChemPhysChem 2001, 229. (28) Pirard, R.; Alie´, C.; Pirard, J. P. Powder Technol. 2002, 128, 242. (29) Washburn, R. W. Proc. Natl. Acad. Sci. U.S.A. 1921, 7, 115. (30) Makrı`, P. K.; Stefanopoulos, K. L.; Mitropoulos, A. C.; Kanellopoulos, N. K.; Treimer, W. Physica B (Amsterdam, Neth.) 2000, 276, 479. (31) Rigby, S. P.; Fletcher, R. S.; Riley, S. N. Appl. Catal., A 2003, 247, 27. (32) Porcheron, F.; Monson, P. A.; Thommes, M. Langmuir 2004, 20, 6482. (33) Galarneau, A.; Desplantier-Giscard, D.; Di Renzo, F.; Fajula, F. Catal. Today 2001, 68, 191. (34) Desplantier-Giscard, D.; Galarneau, A.; Di Renzo, F.; Fajula, F. Mater. Sci. Eng., C 2003, 23, 727. (35) Gibson, L. J.; Ashby, M. F. Cellular Solids. Structure and Properties, 2nd ed.;Cambridge University Press: Cambridge, U.K., 1997; 510 pp. (36) Broyer, M.; Valange, S.; Bellat, J. P.; Bertrand, O.; Weber, G.; Gabelica, Z. Langmuir 2002, 18, 5083. (37) Lowell, S. Powder Technol. 1980, 25, 37. (38) Lowell, S.; Shields, J. E. J. Colloid Interface Sci. 1982, 80, 192. (39) Baudry, J.; Charlaix, E.; Tonck, A.; Mazuyer, D. Langmuir 2001, 17, 5232. (40) Lam, C. N. C.; Wu, R.; Li, D.; Hair, M. L.; Neumann, A. W. AdV. Colloid Interface Sci. 2002, 96, 169. (41) Iapichella, J.; Meneses, J. M.; Beurroies, I.; Denoyel, R.; BayramHahn, Z.; Unger, K.; Galarneau, A. Microporous Mesoporous Mater. 2007, 102, 111. (42) Fadeev, A. Y.; Eroshenko, V. A. MendeleeV Chem. J. 1997, 39 (6), 109. (43) Giesche, H. Mater. Res. Soc. Symp. Proc. 1982, 80, 192. (44) Lefe`vre, B.; Saugey, A.; Barrat, J. L.; Bocquet, L.; Charlaix, E.; Gobin, P. F. Vigier. J. Chem. Phys. 2004, 120, 4927. (45) Lefe`vre, B.; Saugey, A.; Barrat, J. L.; Bocquet, L.; Charlaix, E.; Gobin, P. F.; Vigier, J. Colloids Surf., A 2004, 241, 265. (46) Kloubek, J. Powder Technol. 1981, 29, 63. (47) Rigby, S. P.; Edler, K. J. J. Colloid Interface Sci. 2002, 250, 175. (48) Thomas, M. A.; Coleman, N. J. Colloids Surf., A 2001, 187, 123. (49) Porcheron, F.; Thommes, M.; Ahmed, R.; Monson, P. A. Langmuir 2007, 23, 3372. (50) Joyner, L. G.; Barrett, E. P.; Skold, R. J. Am. Chem. Soc. 1951, 73, 3156. (51) Drake, L. C.; Ritter, H. L. Ind. Eng. Chem., Anal. Ed. 1945, 17, 787. (52) Groen, J. C.; Peffer, L. A. A.; Pe´rez-Ramírez, J. Stud. Surf. Sci. Catal. 2002, 144, 91. (53) Ramos, S. M. M.; Charlaix, E.; Benyagoub, A.; Toulemonde, M. I. Phys. ReV. E 2003, 67, 031604. (54) Wenzel, R. N. J. Phys. Colloid Chem. 1949, 53, 1466. (55) Ramos, S. M. M.; Charlaix, E.; Benyagoub, A. Surf. Sci. 2003, 540, 355. (56) Coasne, B.; Di Renzo, F.; Galarneau, A.; Pellenq, R. J. M. Langmuir 2006, 22, 11097. (57) Shields, J. E.; Lowell, S. Powder Technol. 1983, 36, 1. (58) Rathousky, J.; Zukal, A.; Franke, O.; Schulz-Ekloff, G. J. Chem. Soc., Faraday Trans. 1994, 90, 2821. (59) Ravikovitch, P. I.; Neimark, A. V. J. Phys. Chem. B 1997, 101, 3671. (60) Ravikovitch, P. I.; Neimark, A. V. AdV. Colloid Interface Sci. 2005, 109, 203. (61) Ustinov, E. A.; Do, D. D.; Jaroniec, M. J. Phys. Chem. B. 2005, 109, 1947. (62) Smått, J. H.; Schunk, S.; Linde´n, M. Chem. Mater. 2003, 15, 2354. (63) Starov, V. M.; Churaev, N. V. Colloids Surf., A 1999, 156, 243.

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