New Approach to Evaluate Pore Size Distributions and Surface Areas

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10670

J. Phys. Chem. B 1999, 103, 10670-10678

New Approach to Evaluate Pore Size Distributions and Surface Areas for Hydrophobic Mesoporous Solids Michal Kruk, Valentyn Antochshuk, and Mietek Jaroniec* Department of Chemistry, Kent State UniVersity, Kent, Ohio 44240

Abdelhamid Sayari Department of Chemical Engineering and CERPIC, UniVersite´ LaVal, Ste-Foy, Que´ bec, Canada G1K 7P4 ReceiVed: July 1, 1999

A new approach to pore size and surface area analysis for hydrophobic mesoporous solids is proposed. Welldefined materials with strongly hydrophobic surfaces were prepared via chemical bonding of octyldimethylsilyl (ODMS) ligands to the surface of large-pore MCM-41 samples. Nitrogen statistical film thickness curves (t-curves) were determined for hydrophobic pores. These t-curves were fitted with the nitrogen adsorption isotherm for a macroporous silica modified with ODMS groups in order to derive the reference t-curve valid in the entire range of relative pressures. An empirical expression for the reference t-curve was found. The reference t-curve and the previously derived corrected form of the Kelvin equation were used to calculate pore size distributions for hydrophobic mesoporous materials, allowing to correctly reproduce the total pore volume, average pore size, and surface area determined using independent calculation procedures. The reference nitrogen adsorption isotherm on hydrophobic materials is reported in a tabular form. Moreover, the accuracy of the BET specific surface area was discussed. Thus, this study allowed us to develop the methodology for accurate and consistent characterization of hydrophobic mesoporous materials using nitrogen adsorption.

1. Introduction Porous solids with hydrophobic surfaces, for instance organosilane-modified silicas, constitute an important group of adsorbents used in chromatography and solid-phase extraction.1,2 Development of proper characterization techniques is vital to the successful synthesis and application of these materials. One of the commonly used characterization tools is nitrogen adsorption, which allows one to determine the specific surface area and pore size distribution, and to probe surface properties of porous materials.3,4 Strongly hydrophobic porous solids, such as modified silicas with high surface coverage of long-chain alkylsilanes,1,2 exhibit nitrogen adsorption properties markedly different from those of porous oxides, which manifests itself in very weak interactions with nitrogen molecules.5,6 This in turn creates serious problems in determination of structural properties on the basis of adsorption data, for instance making it difficult to compare specific surface areas of samples before and after the chemical modification.5 Because of the recent advances in the field of hydrophobic porous solids, including the synthesis of ordered mesoporous solids with tailorable pore sizes, structures and surface properties,7-11 development, and refinement of methods for their characterization is strongly needed. The aim of the current study was to elaborate proper methodology for characterization of hydrophobic porous solids using nitrogen adsorption data. Octyldimethylsilyl-modified large-pore MCM-41 silicas were used as model adsorbents to calibrate the pore size analysis and to test the evaluation of the specific surface area. Empirical equations were found, which can be used for an accurate, self-consistent, and yet simple * Corresponding author: tel. (330) 672 3790; fax (330) 672 3816; e-mail [email protected]

determination of the pore size distributions for materials with hydrophobic surfaces. Moreover, the standard reduced adsorption isotherm on octyldimethylsilyl-modified macroporous silica is reported to facilitate the pore size evaluation for hydrophobic materials and comparative adsorption analysis of their surface properties. 2. Materials and Methods 2.1. Materials. Macroporous silicas LiChrospher Si-1000 and Si-4000 were acquired from EM Separations, Gibbstown, NJ and modified via the chemical attachment of octyldimethylsilyl (ODMS) groups as described elsewhere.10 The ODMS-modified LiChrospher Si-1000 and LiChrospher Si-4000 silicas will be referred to as RO1 and RO2, respectively. Large-pore MCM41 silicas with average pore sizes of 5.53 and 6.24 nm were prepared via the postsynthesis hydrothermal restructuring,12,13 and their structural properties were reported earlier.13,14 These two samples were chemically bonded with ODMS ligands using a procedure described elsewhere.9 The ODMS-modified MCM41 will be referred to as the MO samples and the modified 5.53 and 6.24 nm MCM-41 silicas are denoted as MO1 and MO2, respectively. 2.2. Measurements. Carbon content in the modified samples was determined using a LECO CHNS-932 elemental analyzer (St. Joseph, MI). Nitrogen adsorption isotherms were acquired at 77 K using a Micromeritics ASAP 2010 volumetric adsorption analyzer (Norcross, GA). Before the adsorption measurements, the modified samples were degassed for 2 h at 413 K. 2.3. Calculation Methods. Standard Characterization Methods. The BET specific surface area, SBET,3,4 was determined using nitrogen adsorption data in the relative pressure range from 0.04 to 0.2. The cross-sectional area, ω, of nitrogen

10.1021/jp992264h CCC: $18.00 © 1999 American Chemical Society Published on Web 11/06/1999

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molecule was assumed to be equal to 0.162 nm2.3 The total pore volume, Vt,3 was evaluated on the basis of the amount adsorbed at the relative pressure of about 0.99. The primary mesopore volume, Vp, and the external surface area, Sex, were evaluated using the Rs plot method3,13 with ODMS LiChrospher Si-1000 (RO1) as a reference adsorbent. The standard reduced adsorption, Rs, range from 1.5 to 2.0 was used. The standard reduced adsorption is defined as the amount adsorbed at a given pressure divided by the amount adsorbed at a relative pressure of 0.4.3 The total surface area, St, of the ODMS MCM-41 samples was also estimated on the basis of low-pressure adsorption data using the Rs plot method (Rs range from 0.0 to 0.5). The surface coverage of bonded ODMS ligands was from the carbon content for the modified sample and the BET specific surface area for the unmodified sample as described elsewhere.15 Pore Size Calculations. The pore diameter of the unmodified MCM-41 samples was determined in our previous work13,14 using the following geometrical formula:16

wd ) cd

(

)

FVp 1 + FVp

1/2

(

)

Vp

1/2

Vp,MCM-41[1 - xc(M - 1.008)/(12.001 nc)]

(2)

where wd and Vp,MCM-41 are the pore diameter calculated using eq 1 and the primary mesopore volume, respectively, for the unmodified MCM-41; Vp is the primary mesopore volume of the modified MCM-41; xc is the mass fraction of carbon in the modified material; M is the molecular mass of the bonded ligand (that is -Si(CH3)2C8H17); and nc is the number of carbon atoms in this bonded group (that is 10). Both circular and hexagonal pore shape can be adapted in calculations. However, if one assumes that the pore shape changes as a result of the modification, for instance from hexagonal to circular, the pore diameter for the hexagonal pore should be defined as the diameter of a circle, which has the same area as the hexagonal cross section. Determination of the Statistical Film Thickness. The statistical film thickness, t(p/p0), of nitrogen adsorbate in pores of the modified MCM-41 (as a function of the relative pressure, p/p0) was calculated using the following equation:14

[ (

Vp(p/p0) ) V(p/p0) -

)]

Vp,max - Vp(p/p0) wmod 1t(p/p0) ) 2 Vp,max

Sex SBET,ref

Vref(p/p0)

(4)

where V(p/p0) and Vref(p/p0) are adsorption isotherms for the modified MCM-41 sample and the reference modified silica, respectively. Sex is the external surface area of the modified MCM-41 and SBET,ref is the BET specific surface area of the reference modified silica. The adsorption capacity of primary mesopores of the modified MCM-41 was assumed to be equal to the amount adsorbed at a relative pressure of 0.85: Vp,max ) Vp(0.85). The derivation and application of eqs 3 and 4 were discussed in more detail elsewhere.14 Determination of the Specific Surface Area. For comparative purposes, the specific surface area of primary mesopores of the modified MCM-41 materials, Sp, was evaluated using relations between the surface area, pore diameter, and pore volume for circular pores (see ref 16 and references therein)

(1)

where d is the (100) interplanar spacing determined from X-ray diffraction, F is the pore wall density (assumed to be 2.2 g cm-3), and c is a constant characteristic of the pore geometry. The constant c is equal to 1.213 for circular pore geometry, and also for hexagonal pore geometry if one defines the pore diameter as the diameter of a circle of the same area as the hexagonal pore cross section. In some cases, it is more convenient to define the diameter of the hexagonal pore as a distance between the centers of the sides of the hexagonal cross section, and under this definition c is equal to 1.155. The pore diameter, wmod, of the ODMS-modified MCM-41 was determined using the following formula:9

wmod ) wd

determined as follows:14

Sp )

4Vp wmod

(5)

To evaluate the geometrical surface area of pores of the modified MCM-41 materials using the standard BET data, suitable corrections were made in order to account for geometrical constraints on the monolayer formation in cylindrical or hexagonal pores

S′BET ) SBET

wmod wmod Vm,BET ω NA ) wmod - σ V0 wmod - σ

(6)

where σ is the diameter of the nitrogen molecule (assumed to be equal to 0.354 nm), NA is the Avogadro number (6.022 × 1023 mol-1), V0 is the molar volume of gas at STP (22410 cm3 mol-1), and Vm, BET is the BET monolayer capacity. The correction wmod/(wmod - σ) was introduced to account for the fact that the molecules forming the monolayer on the surface of the cylindrical (or hexagonal) pore of the size wmod have their centers located on the circle (or hexagon) of the diameter wmod - σ.14 It should be noted that in the case of the hexagonal pores, their diameter is defined in eq 6 as the distance between midpoints of the sides of the hexagonal cross section. The monolayer capacity can also be evaluated on the basis of the t-curve data. Namely, the amount adsorbed, Vm,tc, at the relative pressure corresponding to the statistical film thickness equal to σ ) 0.354 nm can be regarded as an accurate estimation of the monolayer capacity, which can be used to evaluate the specific surface area, Stc. After introduction of the correction for the shape of pores of MCM-41, the following equation for the specific area, S′tc, is obtained:

S′tc ) Stc

Vm,tc wmod wmod ) ω NA wmod - σ V0 wmod - σ

(7)

3. Results and Discussion

1/2

(3)

where p is the equilibrium vapor pressure, p0 is the saturation vapor pressure, Vp,max is the maximum amount adsorbed in primary mesopores, and Vp(p/p0) is the amount adsorbed in the primary mesopores of the ODMS-modified material as a function of the relative pressure. The latter quantity was

3.1. Reference Adsorption Isotherm for Highly Hydrophobic Porous Solids. The ODMS-modified silica, RO1, had a carbon content of 0.94% and the surface coverage of ODMS groups equal to 3.08 µmol m-2. A nitrogen adsorption isotherm for this sample is shown in Figure 1 and the isotherm data are provided in Table 1. The BET specific surface area was equal to 22.6 m2 g-1. As expected from previous studies of the unmodified LiChrospher Si-1000 silica, the modified material

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TABLE 1: Standard Adsorption Isotherm for RO1 (ODMS LiChrospher Si-1000)a p/p0

Rs

p/p0

Rs

p/p0

Rs

p/p0

Rs

4.66 × 10-6 1.33 × 10-5 2.71 × 10-5 4.38 × 10-5 6.23 × 10-5 1.20 × 10-4 1.84 × 10-4 2.51 × 10-4 3.18 × 10-4 3.89 × 10-4 4.62 × 10-4 5.35 × 10-4 6.09 × 10-4 7.83 × 10-4 9.54 × 10-4 1.13 × 10-3 1.32 × 10-3 1.51 × 10-3 1.71 × 10-3 2.15 × 10-3 2.61 × 10-3 3.10 × 10-3 3.61 × 10-3 4.13 × 10-3 4.67 × 10-3

0.0014 0.0024 0.0035 0.0045 0.0054 0.0081 0.0105 0.0129 0.0151 0.0173 0.0194 0.0214 0.0233 0.0276 0.0315 0.0354 0.0392 0.0430 0.0467 0.0546 0.0623 0.0699 0.0774 0.0847 0.0919

5.23 × 10-3 5.80 × 10-3 6.38 × 10-3 7.15 × 10-3 7.72 × 10-3 8.35 × 10-3 8.97 × 10-3 9.59 × 10-3 0.0102 0.0114 0.0126 0.0150 0.0176 0.0201 0.0251 0.0301 0.0401 0.0501 0.0577 0.0700 0.0800 0.0900 0.100 0.120 0.140

0.990 0.106 0.113 0.122 0.128 0.135 0.141 0.147 0.154 0.164 0.175 0.194 0.213 0.230 0.262 0.289 0.336 0.376 0.403 0.441 0.469 0.495 0.519 0.563 0.602

0.160 0.180 0.200 0.220 0.240 0.260 0.281 0.301 0.321 0.341 0.360 0.381 0.400 0.420 0.440 0.460 0.480 0.500 0.520 0.540 0.560 0.580 0.600 0.620 0.640

0.639 0.673 0.707 0.739 0.769 0.800 0.829 0.858 0.887 0.916 0.944 0.972 1.001 1.029 1.057 1.086 1.116 1.147 1.179 1.211 1.243 1.277 1.312 1.348 1.386

0.660 0.680 0.700 0.720 0.740 0.761 0.781 0.801 0.821 0.841 0.861 0.881 0.900 0.910 0.920 0.930 0.940 0.950 0.960 0.968 0.979b 0.988b 0.992b

1.425 1.466 1.509 1.554 1.603 1.655 1.711 1.772 1.840 1.913 1.995 2.090 2.191 2.254 2.323 2.394 2.483 2.583 2.703 2.886 (3.21)b (3.67)b (4.32)b

a p/p , relative pressure; R , standard reduced adsorption. The amount adsorbed for ODMS LiChrospher Si-1000 can be calculated by multiplying 0 s the Rs values listed above by 7.76 cm3 STP g-1. The statistical film thickness can be calculated by multiplying the Rs values listed above by 0.617 nm. b Data for ODMS-modified LiChrospher Si-4000; the amount adsorbed the latter can be calculated by multiplying the Rs values listed above by 2.89 cm3 STP g-1.

Figure 1. Nitrogen adsorption isotherm for the LiChrospher Si-1000 macroporous silica with chemically bonded octyldimethylsilyl groups (RO1). Low-pressure adsorption data are denoted by filled symbols and are drawn using a logarithmic scale.

was essentially macroporous, which manifested itself in a gradual increase in the amount adsorbed as the relative pressure was increased up to about 0.97. This gradual increase is characteristic of multilayer adsorption on the surface of porous oxides and modified porous oxides. At higher relative pressures, an abrupt increase in the amount adsorbed was observed, which can be attributed to capillary condensation in pores of the size above about 50 nm, that is in macropores. A rather narrow, but noticeable hysteresis loop was observed at relative pressures above 0.95, which confirmed that the rapid increase in adsorption close to saturation was due to capillary condensation rather

than multilayer adsorption. A low-pressure hysteresis loop typical for silicas modified with long-chain alkyldimethylsilyl ligands 9,10 was also observed. RO1 exhibited a very low adsorption at relative pressures below 0.001, which was reported to be characteristic of chemically modified silicas with high coverage of long-chain alkyldimethylsilyl ligands and is markedly different from the adsorption behavior of unmodified silicas.6,9,10 This behavior was attributed to very weak interactions of nitrogen molecules with alkyl chains that screen the silica surface.6,9,10 Because of its macroporous character, RO1 can be considered as a suitable reference adsorbent for the Rs plot analysis. To additionally eliminate the possible influence of capillary condensation on the standard adsorption data, a macroporous silica of lower specific surface area (that is LiChrospher Si-4000) was also chemically modified with ODMS groups and the resulting sample (RO2) was studied using nitrogen adsorption. RO2 had a BET specific surface area of 8.5 m2 g-1 and exhibited nitrogen adsorption properties very similar to those of RO1. However, the adsorption isotherm for the former exhibited almost reversible adsorption behavior at pressures close to saturation, which indicated that the adsorption process proceeded essentially via multilayer adsorption in the whole pressure range studied. Thus, the reference adsorption data for RO1 were extended to higher relative pressures using the data for RO2 (see Table 1). It should be noted that the reference adsorption isotherm reported herein was based primarily on the data for the modified silica with the higher surface area (that is RO1) to reduce errors involved in volumetric nitrogen adsorption measurements for materials of very low specific surface areas. 3.2. Adsorption Properties of ODMS-Modified MCM-41. Carbon contents and surface coverages of ODMS ligands for the MO1 and MO2 samples are provided in Table 2. It can be seen that the surface coverages were lower for the modified MCM-41 samples than for RO1. It should be noted that when the procedure used to prepare RO1 was applied to modify a

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TABLE 2: Selected Parameters for the Modified MCM-41 Samplesa sample

xc

MO1 0.189 MO2 0.151 a

SC Sex Vp Vt wmod wBJH (µmol m-2) (m2 g-1) (cm3 g-1) (cm3 g-1) (nm) (nm) 2.41 2.25

10 20

0.38 0.36

0.39 0.40

4.04 4.08 4.58 4.65

Symbols used are described in the Notation section.

Figure 2. Nitrogen adsorption isotherms for two large-pore MCM-41 silicas with chemically bonded ODMS groups. The nitrogen adsorption isotherm for MO1 is compared with the adsorption isotherm for an unmodified MCM-41 silica of similar pore size distribution. To allow for a better comparison, the adsorbed amounts for the latter were multiplied by 0.428.

large-pore MCM-41, even lower surface coverages than those reported here for MO1 and MO2 were obtained. Therefore, the differences in the surface coverages for RO1 and the MO samples may be related to (i) different surface concentrations of silanols, (ii) different accessibility of silanols, and/or (iii) differences in curvature of the pore surface. As reported previously,13,14 the unmodified MCM-41 samples used in the current study exhibited pronounced hysteresis loops with adsorption and desorption branches close to parallel. The capillary condensation steps were centered at relative pressures of about 0.57 and 0.61 for the MCM-41 samples used to prepare MO1 and MO2, respectively. As a result of modification, the capillary condensation steps shifted to much lower relative pressures (see Figure 2) and the shape of the hysteresis loops changed to triangular with the desorption branches much steeper than the adsorption branches. It should be noted here that desorption data are often used3 or even recommended17 to calculate pore size distributions. If one adopts this idea, the narrowing of the capillary evaporation step can be considered as a proof of the narrowing of the pore size distribution (PSD) after the surface modification. However, this is highly unlikely, since PSD of the modified phase is determined primarily by the PSD of the support used for modification (see for instance refs 9 and 18, where results of modifications for two MCM-41 materials with markedly different widths of PSDs were reported). Moreover, nonuniformity of the surface coverage and/ or conformation of bonded ligands may account for an additional broadening of PSD after surface modification. Thus, the narrowing of PSD as a result of the surface modification considered here is highly unlikely, which in turn strongly

indicates that the application of desorption data in the pore size analysis may lead to grossly misleading results. As convincingly demonstrated elsewhere,14 nitrogen desorption data are not suitable for the mesopore size analysis, especially for materials with pores in the range from about 4 to 10 nm, because of two primary reasons. First, it is well known3,14 that in the case of nitrogen adsorption isotherms, the desorption branch usually follows the adsorption branch at relative pressures below about 0.4 even in the case of capillary condensation in mesopores, but at higher relative pressures, capillary condensation is accompanied with adsorption-desorption hysteresis. It was shown recently that in the region of transition from the reversible to irreversible nitrogen adsorption behavior (that is in the relative pressure range from about 0.4 to 0.5), the capillary condensation pressure gradually and smoothly increases as the pore size increases, as it does at pressures preceding and following the transition region (that is below 0.4 p/p0 and above 0.5 p/p0, respectively).14 In contrast, as the pore size is increased, the capillary evaporation pressure increases much more slowly in the transition region than in the preceding and following pressure ranges, making the relation between the capillary evaporation pressure and the pore size quite complicated and rather inconvenient for application in the pore size analysis.14,19 Second, for a particular pore size, the position of the desorption branch is dependent on the sample structure, which is likely to be related to pore blocking effects, either within porous networks3 or within single pores with constrictions.14 The pore blocking effects lead to a delayed capillary evaporation (see ref 14 and references therein) and render the relation between the capillary evaporation pressure and the pore size ambiguous. It can be concluded that the adsorption behavior of the ODMSmodified MCM-41 samples confirms that desorption data should not be used to calculate pore size distributions, especially for ordered mesoporous materials, where the accuracy of results is particularly important. As was shown previously14,19 and will be confirmed below, the application of adsorption data allows for an easy and essentially artifact-free calculation of the mesopore size distributions for unmodified and modified MCM41, provided the statistical film thickness curve used adequately describes adsorption on the pore walls of the material under study. It was already demonstrated that the introduction of organosilyl ligands on the silica surface changes surface properties of the adsorbent with respect to nitrogen molecules, the effect being particularly pronounced in the case of long-chain alkyldimethylsilyl groups.9,10 These changes manifest themselves in a different shape of Rs plots calculated using a macroporous silica reference adsorbent.9,20,21 As illustrated in Figure 3 for MO1, such Rs plot curves exhibited pronounced downward deviations at low relative pressures (which correspond to low Rs values). In contrast, the Rs plot calculated for MO1 using the ODMSmodified silica (RO1) as the reference adsorbent was approximately linear in the low-pressure range, which is reminiscent of the comparative plots for the MCM-41 silicas obtained using nitrogen adsorption data for reference macroporous silicas. Slight upward deviations of the considered Rs plot (see Figure 3) were probably due to the fact that the MO samples had slightly smaller surface coverages of ODMS ligands than that of RO1. Thus, the siliceous surface of the former might not be as effectively screened by the aliphatic ligands as the surface of the latter. Anyway, it is clear that the surface properties (with respect to nitrogen) of the MO samples are highly similar to those of the ODMS-modified reference adsorbent, which has a relatively high surface coverage of bonded ligands. It has been

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Figure 3. The Rs plots for MO1 calculated using reference adsorption isotherms for the unmodified LiChrospher Si-1000 macroporous silica and ODMS-modified LiChrospher Si-1000 macroporous silica (denoted as RO1).

TABLE 3: Comparison of Specific Surface Areas Evaluated Using Different Methods for the Modified MCM-41 Samplesa SBET S′BET Sp Sp+ Sex SBJH Stc S′tc sample (m2 g-1) (m2 g-1) (m2 g-1) (m2 g-1) (m2 g-1) (m2 g-1) (m2 g-1) MO1 MO2

390 340

430 370

380 310

390 340

390 340

350 310

380 340

a Symbols used are described in the Notation section. Surface areas were rounded to the nearest 10 m2 g-1.

reported that for alkyldimethylsilyl-modified silicas (alkyl ) octyl, butyl), the surface properties are almost independent of the surface coverage6 and the chain length of bonded ligands,9 provided the surface coverage is sufficiently high. This suggests that high-energy adsorption sites, such as unreacted silanols, are effectively screened by the bonded ligands.6,9 This also implies that the surface coverage of alkyldimethylsilyl groups is relatively uniform and essentially there are no domains of unmodified silica. Despite the aforementioned slight differences in the surface properties between the ODMS-modified MCM-41 samples and the ODMS-modified reference macroporous silica, it is possible to use the Rs plot data to estimate the total surface area, St, of the modified MCM-41 materials on the basis of low-pressure adsorption data. Using the Rs range from 0.0 to 0.5 (that is the relative pressure range from about 10-6 to 0.09), St was determined to be 420 and 370 m2 g-1 for MO1 and MO2, respectively. These estimates are reasonably close to the BET specific surface areas for these samples (see Table 3) estimated on the basis of data at much higher relative pressure of 0.040.2. This opens an opportunity to improve the estimation of the specific surface area of modified samples, which exhibit capillary condensation in the pressure range used for the BET analysis. It should be noted that in the case of MO1 and MO2, St is formally equivalent to SBET, since SBET for the reference adsorbent was used in calculations and both of these samples are nonmicroporous. Thus, the observed differences between St and SBET were mostly due to slight differences in the surface properties between the reference adsorbent and the samples under study.

It is well known that differences in the surface properties of adsorbents usually do not have any dramatic effects on adsorption in the multilayer formation region. So, the reference data for the unmodified silica21 can be used for estimation of the external surface area, Sex, and primary mesopore volume, Vp, for the modified materials using the Rs plot method. However, the accuracy of these estimations can be improved using a proper modified reference adsorbent. Thus, RO1 was applied as a reference adsorbent for determination of Sex and Vp of the MO samples, and the results are provided in Table 2. 3.3. Determination of the Statistical Film Thickness for ODMS-Modified Silicas. Differences in the statistical film thickness of adsorbate on the pore walls of the modified and unmodified MCM-41 silicas are evident from the comparison of adsorption isotherms for these materials. Shown in Figure 2 are nitrogen adsorption isotherms for MO1 and an MCM-41 sample with an average pore size of 4.62 nm (determined using eq 1).14 These two samples exhibited a similar capillary condensation pressure range and thus are expected to have a similar pore size (this will be confirmed later). The modified material exhibited much lower adsorption at relative pressures preceding the capillary condensation. The lower the pressure, the larger the difference was observed. Therefore, one can expect that an accurate pore analysis for the modified materials requires an application of a proper statistical film thickness curve. The statistical film thickness curve (t-curve) can be obtained on the basis of the adsorption isotherm for a suitable reference adsorbent, so the data for RO1 are suitable for this purpose. The statistical film thickness at a given pressure is proportional to the amount adsorbed (for a flat surface): tref(p/p0) ) constant × Vref(p/p0), but the value of the proportionality constant is rather difficult to determine with a reasonable accuracy, as already pointed out by Sing and co-workers.22 To overcome this difficulty, an approach developed recently by Kruk, Jaroniec, and Sayari (KJS)14 was employed. The KJS approach is based on the application of well-defined porous materials of known pore size and geometry, such as MCM-41, to derive relations between the capillary condensation/evaporation pressure and the pore size, and to establish absolute values of the statistical film thickness on the pore walls. The t-curve data for the well-defined materials are later used to determine the proportionality constant mentioned above. The relations developed on the basis of the KJS approach can easily be implemented in standard methods of the mesopore size analysis, for instance in the BarrettJoyner-Halenda (BJH) method.23 MCM-41 silicas are currently the best model mesoporous materials available because of their simple pore geometry and tailored pore size.14 The pore size of organosilane-bonded MCM-41 can readily be calculated from the pore volume changes after modification.9 Since the pore size of MCM-41 significantly decreases as a result of introduction of large organosilane ligands, it is necessary to use samples with as large pore sizes as possible. Therefore, the calibration of the t-curve for mesoporous materials with hydrophobic surfaces was based in the current study on the adsorption data for ODMS-modified large-pore MCM-41. The pore sizes of the modified materials were determined using eq 2 and found to be 4.04 and 4.58 nm for MO1 and MO2, respectively. These values were subsequently used in eq 3 to determine the statistical film thickness curves shown in Figure 4. The circular pore geometry was assumed. It can be seen that the t-curves for the MO samples were in good agreement with one another at relative pressures below 0.2-0.3, that is below the onset of capillary condensation.

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Figure 4. Nitrogen statistical film thickness curves for ODMS-modified MCM-41 samples and their fit by the adsorption isotherm for the ODMS-modified LiChrospher Si-1000 macroporous silica.

An agreement in the low-pressure range (relative pressure below about 0.01) was also very good. On the basis of the t-curves for the MO samples, it is possible to determine the relative pressure at which the monolayer capacity is reached. Following the work of de Boer and coworkers,3,24 it is assumed here that the monolayer statistical film thickness for nitrogen is equal to 0.354 nm. This assumption is somewhat arbitrary and other values of the monolayer statistical film thickness can be adapted as needed, but the value provided above will be used to facilitate the discussion. It was found that for the MO samples, the statistical film thickness of 0.354 nm was reached at the relative pressure of about 0.125 (under assumption of the circular pore geometry). As demonstrated above, a macroporous sample RO1 was shown to exhibit similar nitrogen adsorption properties to those of the MO samples. Thus, it was assumed that for RO1, the statistical film thickness of 0.354 nm was also reached at the relative pressure of 0.125. Under this assumption, the t-curve for RO1 (later referred to as the reference t-curve) was determined. The values of the statistical film thickness can be evaluated on the basis of the data provided in Table 1 using an appropriate conversion factor provided therein. The obtained reference t-curve is in a good agreement with the t-curves for the MO samples (see Figure 4), but the former exhibited somewhat lower statistical film thickness values at low relative pressures, which may be related to the higher coverage of ODMS ligands on the surface of this sample. As expected, the t-curves for the MO samples exhibited increasing deviations from the reference t-curve when the capillary condensation pressure was approached.14,19 To facilitate the application of the reference t-curve (Table 1) in the pore size analysis, its empirical representation, tref,a, (in the form of the Harkins-Jura adsorption isotherm4) was derived by fitting the t-curve data in the relative pressure range from 0.1 to 0.95:

(

tref,a(p/p0)[nm] ) 0.1

)

8.873 0.08004 - log(p/p0)

0.6147

(8)

It needs to be noted that the surface of ODMS-modified samples may exhibit some roughness. However, similarity in low-pressure nitrogen adsorption isotherms for various ODMS-

modified silicas6,9 suggests that if it is actually the case, different samples exhibit similar surface roughness. So, the t-curve reported herein provides an effective statistical film thickness calculated under the assumption of the smooth surface, and thus may actually incorporate the effects of the surface roughness. The obtained t-curve is expected to be especially accurate for a variety of alkyldimethylsilyl-modified silicas (for instance with octyl, butyl, or decyl groups),6,9,10 provided the coverages of bonded ligands are sufficiently high. For samples with lower coverages of the aforementioned ligands or with bonded ligands of less hydrophobic character, the t-curve reported herein will be somewhat less accurate and a proper calibration similar to that described in this work may provide better t-curve data, and consequently, may facilitate comparative analysis and calculation of pore size distributions. 3.4. Calculation of Pore Size Distributions for Hydrophobic Mesoporous Materials. Calculations of mesopore size distributions are often based on the model, which assumes that adsorption on the mesopore wall proceeds via multilayer formation until the capillary condensation is reached and mesopores of a given size are completely filled with the condensed adsorbate.3 The pressure at which the capillary condensation takes place is determined by the radius of the pore space confined by the adsorbate film on the pore walls (this space will be referred to as a “core”). Thus, the relation between the pore radius and the capillary condensation pressure is composed of two terms: (i) an expression for the core radius as a function of the capillary condensation pressure, and (ii) an expression for the statistical film thickness as a function of the relative pressure. It was recently demonstrated that the relation between the core radius, rc, and the capillary condensation pressure of nitrogen in cylindrical pores is described by a simple empirical equation14 similar in the form to the well-known Kelvin equation3

rc(p/p0)[nm] )

2γVL RT ln(p0/p)

+ 0.3

(9)

where γ and VL are the surface tension and the molar volume of liquid nitrogen at 77 K, R is the universal gas constant, and T is the absolute temperature (γ ) 8.88 × 10-3 N m-1, VL ) 34.68 cm3 mol-1, and R ) 8.314 J mol-1 K-1). The empirical correction equal to 0.3 nm was determined on the basis of an extensive study of a series of MCM-41 silicas,14 and its validity was further confirmed in subsequent study of another series of high-quality MCM-41 silicas obtained using different synthesis procedures.19 It is thus expected that the relation between the capillary condensation pressure and the pore radius, rp, for the hydrophobic materials should assume the following form:

rp(p/p0)[nm] )

2γVL RT ln(p0/p)

+ tref(p/p0) + 0.3

(10)

where tref(p/p0) is described by the data provided in Table 1 or by an approximate eq 8. On the basis of eq 10, pore size distributions (PSDs) were calculated for the MO samples by employing the BJH method.23 As discussed above, adsorption rather than desorption branches of the nitrogen isotherms were used in calculations. The resulting PSDs were compared with those calculated using eq 10 with the reference t-curve for unmodified silicas.14,21 As can be seen in Figure 5, the PSDs calculated using the proper t-curve (that is, the t-curve for the modified samples) are almost free from artificial tails extending

10676 J. Phys. Chem. B, Vol. 103, No. 48, 1999

Figure 5. Pore size distributions for the ODMS-modified MCM-41 silicas calculated using the standard t-curves for unmodified and ODMSmodified silicas.

toward the micropore range, which were obtained in the case of application of the t-curve for silica-based materials. What is even more remarkable, the calculation procedure correctly reproduced the total pore volume of the modified materials, which was overestimated by about 25%, when the t-curve for silica-based materials was used. The consistency of the calibration approach used was also strongly supported by the fact that the resulting pore size distributions were centered at pore diameter values almost identical to those evaluated independently using eq 2 (see Table 2). These results indicate that the correction term in eqs 9 and 10 (that is 0.3 nm) is essentially independent of the surface properties of mesoporous solids. Thus, eq 10 with an appropriate t-curve can be applied in characterization of unmodified and modified mesoporous silicas with various surface properties as well as in studies of nonsilica-based mesoporous materials with cylindrical pores, for instance carbon nanotubes.25 3.5. Evaluation of the Specific Surface Area. Because of the well-defined structure of MCM-41, one can use these materials to calibrate not only the pore size analysis but also the surface area determination.14 In the case of modified MCM41 materials, their pore geometry is not likely to deviate significantly from that of the unmodified samples. This allows one to obtain an estimation of the specific surface area of primary mesopores on the basis of the primary mesopore volume and primary mesopore diameter using eq 5. The resulting primary mesopore surface areas for the MO samples are listed in Table 3 along with the total surface areas evaluated as sums of the primary mesopore surface areas (eq 5) and the external surface areas. The specific surface areas for the MO samples were also obtained using the BJH procedure (see Table 3). In calculations, the surface area corresponding to small tails on PSDs in the micropore range (see Figure 5) was neglected, since the appearance of these tails can be attributed to slight differences in the surface properties between the MO samples and the reference adsorbent RO1. The agreement between the total surface areas obtained using eq 5 and the BJH method calibrated for hydrophobic surfaces appears to be obvious due to the fact that both of these approaches assume the same pore geometry. However, this agreement is by no means trivial and it actually results from a proper calibration of the t-curve used in the BJH

Kruk et al. procedure. For instance, the BJH calculations for the ODMSmodified materials performed using the t-curve for unmodified silicas gave surface areas as high as 510 and 440 m2 g-1 for MO1 and MO2, respectively, despite the fact that the pore sizes were quite accurately reproduced (see Figure 5). Thus, the proper choice of the t-curve is crucial in obtaining reasonable estimates of the specific surface area using the BJH method. Evaluation of the specific surface area of the modified MCM41 materials can also be achieved by determining the amount adsorbed corresponding to the monolayer statistical film thickness. This amount adsorbed can obviously be regarded as the monolayer capacity. Assuming the circular pore geometry, monolayer capacities of 80.6 and 71.2 cm3 STP g-1 were determined for MO1 and MO2. Using 0.162 nm2 as the crosssectional area of nitrogen molecule, the surface areas, Stc, were obtained (see eq 7) and the resulting values are listed in Table 3. After introduction of the correction for the circular pore shape (eq 7), somewhat higher values of the total surface area, S′tc, were obtained. The S′tc values were essentially the same as the ones obtained using eq 5 as well as the calibrated BJH procedure. Since the estimation of the specific surface area on the basis of the monolayer capacity and the cross-sectional area provided results in excellent agreement with those from other evaluation methods used, it can be concluded that the crosssectional area of 0.162 nm2 is valid for highly hydrophobic alkyldimethylsilyl-modified silicas. It should be noted that when the hexagonal rather than cylindrical pore geometry is assumed in the surface area considerations for the modified MCM-41 materials, all of the aforementioned surface area estimations (that is Sp, SBJH, Stc, and S′tc) are about 5% higher. In the case of calculations based on the primary mesopore volume and primary mesopore diameter, the constant in eq 5 would be equal to 4.2 instead of 4 (see ref 16 and references therein). In the case of calculations based on the BJH method, it is possible to assume that the hexagonal pore geometry (the t-curve would have to be determined for the hexagonal pore geometry, as will be discussed below) and the resulting pore size distributions would be essentially identical, but the obtained surface areas would be 5% higher. This is because of the fact that for the same pore volume and pore cross-sectional area, the surface area of the hexagonal pore is 5% larger than that of the circular pore. Finally, in the case of the monolayer capacity estimation on the basis of the statistical film thickness, the definition of the pore diameter as a distance between the centers of the sides of the hexagonal cross section would have to be adopted. As a result, the estimated statistical film thickness would be about 5% lower than that for the cylindrical pore geometry, and thus the monolayer statistical film thickness would be achieved at higher pressures and the corresponding monolayer capacity would be about 5% higher. So, in all three cases, the assumption of the hexagonal pore geometry would lead to surface area estimations, which would be 5% higher than those for the cylindrical pore geometry. It is interesting to compare the results of the three independent but yet consistent methods of the surface area estimation (those providing Sp + Sex, SBJH, and S′tc) with the results of the standard BET method (see Table 3). It can be seen that the BET surface area values evaluated in the relative pressure range from 0.04 to 0.2 are essentially the same as those obtained on the basis of the three other methods. However, this agreement is likely to be coincidental, since the BET surface area should be corrected for an effect of the pore wall curvature using eq 6. After this correction is introduced, the corrected BET surface areas are

Pore Size and Surface Area Analysis higher than the results obtained using the other methods. This is an obvious consequence of the fact that the actual monolayer capacities determined on the basis of the statistical film thickness constitute only 89% and 91% of the BET monolayer capacities for MO1 and MO2, respectively. If one assumes the hexagonal rather than circular pore geometry, the agreement would somewhat improve to 93% and 96%. One is tempted to conclude that the lack of agreement indicates an inaccuracy of the BET method. However, it needs to be kept in mind that the estimation of the BET specific surface area is strongly dependent on the range of data points used. For instance, it was shown that the estimates of SBET differ by more than 30% for silicas, when different relative pressure intervals within the range from 0.001 to 0.25 were chosen.21 The same problem arises for the ODMSmodified materials. The estimates of the BET specific surface area vary widely depending on the pressure interval used. Thus, one can conclude that the BET specific surface area for these materials is somewhat ill-defined. Another interesting and useful conclusion is that since the estimations of the BET surface area for different pressure ranges cover a broad range of values, it is possible to find a pressure range suitable to reproduce the monolayer capacity and the actual surface area determined using some independent methods. For instance, if one assumes that the ODMS-modified MCM-41 materials have circular pores, the proper range of relative pressures for the BET calculations would be, for instance, 0.0007-0.2 or 0.01-0.12 on the basis of the data for the MO samples. As can be seen from the discussion presented above, it is possible to arrive at consistent estimations of the specific surface area for the modified MCM-41 materials. From the practical point of view, it would be also interesting to be able to determine the specific surface area for samples with less well-defined porous structures than those of the model solids. As was suggested above, one can use the standard BET calculations, provided a proper range of data points is used. Actually, the errors involved in the BET analysis using the nitrogen crosssectional area of 0.162 nm2 and the pressure range of 0.04-0.2 were not particularly large (up to about 10%). These errors may actually be 5% smaller if the pores of the modified MCM-41 samples are hexagonal rather than circular. Moreover, as will be discussed below, the accuracy of the monolayer capacity evaluation in the pressure range mentioned above is much less satisfactory for unmodified silicas than for the octyldimethylsilyl-modified samples. This suggests that the agreement between the actual monolayer capacity and the BET monolayer capacity may improve as the surface becomes more hydrophobic and, for instance, would be better for RO1 than for MO samples with the lower surface coverage. So, the standard BET analysis for alkylsilyl-modified porous materials is likely to provide quite reasonable results, as already demonstrated by Jelinek and Kovats.5 It is important to note here that these authors used the monolayer capacity evaluated on the basis of the standard BET method, since independent and more reliable estimations of the monolayer capacity were not available. So, their estimation of the nitrogen cross-sectional area based on the monolayer capacity values depends on the accuracy of the latter. As discussed above, in the case of alkyldimethylsilyl-modified silicas, the BET monolayer capacity is quite close to other more reliable estimations. So, it is not surprising that Jelinek and Kovats’ estimation of the cross-sectional area of nitrogen molecule on the surface of alkyldimethylsilyl-modified silica provided results close to the commonly used value of 0.162 nm2, whose validity was confirmed by the current study. However, in the case of unmodified silicas, which were also

J. Phys. Chem. B, Vol. 103, No. 48, 1999 10677 studied by these authors, the actual monolayer capacity is much smaller than the BET monolayer capacity estimated in the commonly used relative pressure range such as 0.04-0.2 (used in the current study) or 0.05-0.23 (used by Jelinek and Kovats). For instance, in the case of unmodified large-pore MCM-41 used in the current study, the monolayer capacity determined on the basis of the statistical film thickness constituted only about 77% of the BET monolayer capacity (or 81% if the pores of these materials are hexagonal rather than circular). This indicates that the cross-sectional area of 0.135 nm2 for nitrogen on the silica surface, which was reported by Jelinek and Kovats assuming the accuracy of the monolayer capacity, was underestimated by about 20% due to the overestimation of the BET monolayer capacity. On the basis of these considerations, one can conclude that the actual cross-sectional area of nitrogen on silica surface is close to the commonly accepted value of 0.162 nm2, and there is no reason to believe that the cross-sectional area of nitrogen is significantly different for organosilanemodified silicas and bare silicas. However, the inaccuracy in evaluation of the monolayer capacity for porous silicas using the standard BET method needs to be accounted for when one compares specific surface area changes resulting from the surface modifications. Further studies of evaluation of the specific surface area for silica-based materials are underway. 4. Conclusions The current study demonstrated that modified MCM-41 materials can be used to calibrate methods for evaluation of pore size distributions and surface areas using the KrukJaroniec-Sayari (KJS) procedure. The KJS approach is generally applicable for unmodified and modified ordered mesoporous materials of different surface properties and can be used to calibrate reference data suitable for accurate and consistent analysis of various ordered and disordered, unmodified and modified materials with different surface properties. Acknowledgment. The donors of the Petroleum Research Fund administered by the American Chemical Society are gratefully acknowledged for support of this research. Notation c ) constant in eq 1 d ) X-ray diffraction (100) interplanar spacing [nm] M ) molecular weight of the organosilane ligand [g mol-1] NA ) Avogadro number [mol-1] nc ) number of carbon atoms in the organosilane ligand p ) equilibrium vapor pressure [Pa] p0 ) saturation vapor pressure [Pa] p/p0 ) relative pressure R ) universal gas constant [J mol-1 K-1] rp ) pore radius [nm] rc ) core radius [nm] SBET ) BET specific surface area [m2 g-1] S′BET ) BET specific surface area corrected for an effect of the pore wall curvature (eq 6) [m2 g-1] SBET, ref ) BET specific surface area of a reference adsorbent [m2 g-1] SBJH ) specific surface area evaluated using the BJH method [m2 g-1] Sex ) external surface area [m2 g-1] Sp ) primary mesopore surface area evaluated for the circular pore geometry using eq 5 [m2 g-1]

10678 J. Phys. Chem. B, Vol. 103, No. 48, 1999 Stc ) specific surface area evaluated from the monolayer capacity determined on the basis of the t-curves calculated using eq 3 [m2 g-1] S′tc ) specific surface area evaluated from the monolayer capacity determined on the basis of the t-curves, and corrected for an effect of the pore wall curvature (eq 7) [m2 g-1] SC ) surface coverage of organosilane ligands [µmol m-2] t ) statistical film thickness for ODMS-modified MCM-41 calculated using eq 3 [nm] tref ) statistical film thickness for the reference adsorbent [nm] (data provided in Table 1) tref, a ) statistical film thickness for the reference adsorbent approximated by an empirical eq 8 [nm] Vp ) primary mesopore volume [cm3 g-1] Vt ) total pore volume [cm3 g-1] VL ) molar volume of a liquid [cm3 mol-1] Vm,BET ) BET monolayer capacity [cm3 STP g-1] Vm, tc ) the monolayer capacity determined from the t-curves calculated using eq 3 [cm3 STP g-1] Vp ) amount adsorbed in primary mesopores as a function of relative pressure [cm3 STP g-1] Vp,max ) maximum amount adsorbed in primary mesopores [cm3 STP g-1] Vref ) adsorption isotherm for the reference adsorbent [cm3 STP g-1] V0 ) molar volume of ideal gas at standard temperature and pressure (STP) [cm3 mol-1] wBJH ) pore diameter evaluated using the BJH method with eq 10 [nm] wd ) pore diameter of MCM-41 evaluated using eq 1 [nm] wmod ) pore diameter of organosilane-modified MCM-41 evaluated using eq 2 [nm] xc ) mass fraction of carbon in the organosilane-modified samples Rs ) standard reduced adsorption - amount adsorbed divided by the amount adsorbed at a relative pressure of 0.4 γ ) surface tension [N m-1]

Kruk et al. F ) MCM-41 pore wall density [g cm-3] σ ) statistical monolayer thickness [nm] ω ) cross-sectional area of an adsorbed molecule [nm2] References and Notes (1) Packings and Stationary Phases in Chromatographic Techniques; Unger, K. K., Ed.; Marcel Dekker: New York, 1990. (2) Vansant, E. F.; Van der Voort, P.; Vrancken, K. C. Characterization and Modification of the Silica Surface; Elsevier: Amsterdam, 1995. (3) Gregg, S. J.; Sing, K. S. W. Adsorption, Surface Area and Porosity; Academic Press: London, 1982. (4) Jaroniec, M.; Madey, R. Physical Adsorption on Heterogeneous Solids; Elsevier: Amsterdam, 1988. (5) Jelinek, L.; sz. Kovats, E. Langmuir 1994, 10, 4225. (6) Bereznitski, Y.; Jaroniec, M.; Kruk, M.; Buszewski, B. J. Liq. Chromatogr. 1996, 19, 2767. (7) Feng, X.; Fryxell, G. E.; Wang, L.-Q.; Kim, A. Y.; Liu J.; Kemner, K. M. Science 1997, 276, 923. (8) Mercier, L.; Pinnavaia, T. J. AdV. Mater. 1997, 9, 500. (9) Jaroniec, C. P.; Kruk, M.; Jaroniec, M.; Sayari, A. J. Phys. Chem. B 1998, 102, 5503. (10) Antochshuk, V.; Jaroniec, M. J. Phys. Chem. B 1999, 103, 6252. (11) Brunel, D. Microporous Mesoporous Mater. 1999, 27, 329. (12) Khushalani, D.; Kuperman, A.; Ozin, G. A.; Tanaka, K.; Garces, J.; Olken, M. M.; Coombs, N. AdV. Mater. 1995, 7, 842. (13) Sayari, A.; Liu, P.; Kruk, M.; Jaroniec, M. Chem. Mater. 1997, 9, 2499. (14) Kruk, M.; Jaroniec, M.; Sayari A. Langmuir 1997, 13, 6267. (15) Buszewski, B.; Jaroniec, M.; Gilpin, R. K. J. Chromatogr. A 1994, 673, 11. (16) Kruk, M.; Jaroniec, M.; Sayari, A. Chem. Mater. 1999, 11, 492. (17) Ravikovitch, P. I.; Haller, G. L.; Neimark, A. V. AdV. Colloid Interface Sci. 1998, 76-77, 203. (18) Jaroniec, M.; Jaroniec, C. P.; Kruk, M.; Ryoo, R. Adsorption 1999, 5, 315. (19) Kruk, M.; Jaroniec, M.; Kim, J. M.; Ryoo, R. Langmuir 1999, 15, 5279. (20) Kruk, M.; Jaroniec, M. In Surfaces of Nanoparticles and Porous Materials; Schwarz, J. A., Contescu, C., Eds.; Marcel Dekker: New York, 1999; p 443. (21) Jaroniec, M.; Kruk, M.; Olivier, J. P. Langmuir 1999, 15, 5410. (22) Bhambhani, M. R.; Cutting, P. A.; Sing, K. S. W.; Turk, D. H. J. Colloid Interface Sci. 1972, 38, 109. (23) Barrett, E. P.; Joyner, L. G.; Halenda, P. P. J. Am. Chem. Soc. 1951, 73, 373. (24) Lippens, B. C.; Linsen, B. G.; de Boer, J. H. J. Catal. 1964, 3, 32. (25) Iijima, S. Nature 1991, 354, 56.