Pore Structure and Fluid Sorption in Ordered Mesoporous Silica. I

J. Phys. Chem. C 2009, 113, 15201–15210

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Pore Structure and Fluid Sorption in Ordered Mesoporous Silica. I. Experimental Study by in situ Small-Angle X-ray Scattering Susanne Ja¨hnert,† Dirk Mu¨ter,‡ Johannes Prass,‡ Gerald A. Zickler,‡,§ Oskar Paris,*,‡,| and Gerhard H. Findenegg*,† Institute of Chemistry, Stranski Laboratory, Technical UniVersity Berlin, D-10623 Berlin, Germany, Department of Biomaterials, Max Planck Institute of Colloids and Interfaces, D-14424 Potsdam, Germany, and Institute of Physics, UniVersity of Leoben, A-8700 Leoben, Austria ReceiVed: NoVember 14, 2008; ReVised Manuscript ReceiVed: April 25, 2009

Ordered and disordered pores in SBA-15 silica and the gradual filling of these pores by an adsorbed fluid (dibromomethane, CH2Br2) are investigated by in situ small-angle X-ray scattering. Adsorption into the microporous corona and film formation at the corrugated surface of the ordered cylindrical pores is described by two different geometrical models. The analytical form factor resulting from these models is used to fit the integrated intensities of up to 10 Bragg diffraction peaks from the mesopore lattice. Model fits for the evacuated sample yield the porosity caused by the ordered pores. From these results and the total porosity obtained by nitrogen sorption, we determine the contribution of the disordered porosity, which is nearly 20% for the present sample. The model fits also provide new insight into the adsorbate structure in the ordered pores at different stages of pore filling, while the analysis of diffuse scattering provides information about fluid adsorption in the disordered pores in the walls. It is shown that the filling of the wall porosity affects the evaluation of the adsorbed amount in the ordered pores and leads to a distinction between relative and absolute adsorbed amounts. Using absolute adsorbed amounts, the filling isotherm of the ordered pores and the overall pore filling isotherm can be derived and compared with direct adsorption measurements. On the basis of the results of the present study, a quantitative modeling of the pore morphology and fluid sorption in the ordered and disordered pore regions of SBA-15 is presented in a subsequent paper (part II, DOI 10.1021/jp810040k). 1. Introduction Ordered mesoporous materials with open-ended cylindrical pores of a few nanometers in diameter, such as MCM-411 or SBA-15,2 are promising candidates for a wide range of applications, including heterogeneous catalysis,3 gas storage,4 or size-selective separation processes.5 They also represent ideal model systems for studying the phase behavior of fluids and solids in confinement.6-8 Much information about the pore morphology of these nanoporous materials can be derived from gas adsorption isotherms.9,10 In mesopores (pores larger than about 2 nm in diameter), this process usually proceeds via the formation of an adsorbed film on the pore walls, which grows in thickness with increasing vapor pressure until a sharp increase of the adsorbed amount occurs due to capillary condensation of the vapor. Due to the confinement, condensation takes place at considerably lower pressure than in the bulk, as described by the Kelvin equation, which forms the basis of the pore size determination by physisorption measurements.10 The film formation at low pressures is often preceded or accompanied by a filling of smaller pores in the walls of the mesopores. While adsorption studies have been used successfully for a characterization of ordered mesoporous materials, the structural information obtained in this way is indirect and often incomplete. More direct information on structural aspects can be * Corresponding authors. E-mail: [email protected] (O.P.); [email protected] (G.H.F.). † Technical University Berlin. ‡ Max Planck Institute of Colloids and Interfaces. § Present address: Department of Physical Metallurgy and Materials Testing, University of Leoben, A-8700 Leoben, Austria. | University of Leoben.

derived from transmission electron microscopy,11 spectroscopic methods such as Raman12 and NMR,13-15 and in particular from X-ray16-21 and neutron scattering.22,23 In situ scattering experiments can provide structural information about the pore structure as well as the adsorbate for a series of points along a sorption isotherm.18-24 Structural information about the porous matrix and adsorbed fluids in ordered mesoporous materials can be extracted from scattering experiments by data fitting and modeling methods, either by adopting simple geometrical models for the density distribution which can be analytically Fourier transformed16,19,20 or by numerical Fourier transformation of more sophisticated density distributions.17,25 So far, these attempts were restricted to a modeling of the single-pore form factor, i.e., fitting of the integrated intensity of Bragg diffraction peaks arising from the ordered arrangement of mesopores on a crystal lattice. Diffuse scattering arising from structural disorder (e.g., disordered pores in the mesopore walls) has commonly been treated as a background and was not included in the modeling. On the other hand, the existence of disordered pores in the pore walls of SBA15 (e.g., transversal channels between the main pores) is generally accepted,16,26 but no reliable estimates of the extent of this wall porosity exist. As we demonstrate in this work, the contribution of the wall porosity can be estimated by comparing the overall porosity as derived from nitrogen adsorption with the pore volume obtained by modeling the integrated intensities of the Bragg diffraction peaks of the evacuated sample. Further information about the disordered porosity can be derived from the diffuse scattering and its dependence on pore filling. In this paper, we present X-ray scattering results from in situ adsorption of dibromomethane (DBM, CH2Br2) in SBA-15 at

10.1021/jp8100392 CCC: $40.75  2009 American Chemical Society Published on Web 07/31/2009

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TABLE 1: Characterization of the SBA-15 Sample by Nitrogen Adsorption and ex situ XRDa as, m2 g-1

Vp, cm3 g-1

φtot

DKJS, nm

DDFT, nm

a0, nm

730

1.01

0.690

8.90

8.14

11.52

Specific surface area as, specific pore volume Vp, total porosity φtot (based on a matrix density F˜ s of 2.16 g cm-3), pore diameter according to the improved KJS method (DKJS) and density functional theory (DDFT), and lattice parameter a0 of the mesopore lattice. a

room temperature. DBM was chosen because it has almost the same electron density in the bulk liquid state as silica, which facilitates the analysis of the scattering data. The pore structure and pore filling of the ordered cylindrical pores is determined by analyzing the integrated intensities of up to 10 Bragg peaks on the basis of analytical form factor models in which the corrugated pore wall and microporous corona as well as the adsorbate layer are taken into account in a simple but physically meaningful way. In addition, randomly distributed, uncorrelated pores in the walls of the ordered mesopore lattice are considered as the source of diffuse scattering. By combining nitrogen sorption and scattering data, we derive the specific pore volumes of ordered and disordered pores separately. While information about the adsorbate layer in the ordered pores can be extracted from the form factor models, such an approach is not possible for the disordered pores, as the geometry of these pores varies widely. In a subsequent paper (part II, DOI 10.1021/jp810040k), the results of the present study are used as input for a detailed quantitative modeling of the Bragg diffraction and the diffuse scattering by using a simple lattice model. It will be shown that the complex pore structure of SBA-15 and information about the adsorbate in the pores can be captured by this model. 2. Experimental Section 2.1. Characterization of SBA-15. The SBA-15 sample used in this work was taken from the same batch as in the earlier work.20 The properties of the sample were checked by nitrogen adsorption and ex situ small-angle X-ray diffraction (XRD) before and after the experiments. Results of the characterization are summarized in Table 1. The nitrogen adsorption isotherm is shown in Figure 1a, represented by the filling fraction f ) Vads/Vp as a function of the relative pressure p/p0. The specific surface area as was determined by the BET method (p/p0 range 0.05-0.3), and the specific pore volume Vp (pore volume per unit mass of silica) was taken from the amount adsorbed at p/p0 ) 0.98 using the mass density of liquid nitrogen at 77 K (0.8089 cm3 g-1). The values of as and νp obtained before and after the in situ small-angle X-ray scattering (SAXS) study agreed within 3%. The pore size of the cylindrical pores was derived from the nitrogen adsorption isotherms by two methods: (i) from a correlation between pore condensation pressure (p/p0 ) 0.757) and pore size based on a modeling of X-ray diffraction data (improved KJS method);27 (ii) from the desorption isotherm on the basis of the nonlocal density function theory (DFT).28 The mean mass density (skeletal density) of the silica matrix was determined by helium displacement measurements for a series of SBA-15 materials prepared in a similar way as the present sample and was found to be 2.16 ( 0.03 g cm-3.29 This value was adopted to calculate the total porosity φtot from the measured specific pore volume. 2.2. Adsorption of DBM in SBA-15. Dibromomethane (Merck, g99%) was used as received. The liquid had a mass density of 2.497 g cm-3 and a surface tension of 39.0 mN m-1 at 20 °C, in agreement with literature data;30 its saturated vapor

Figure 1. Adsorption isotherms in SBA-15 silica: (a) nitrogen at 77 K; (b) dibromomethane (DBM) at 293 K. f is the filling fraction, and p/p0 is the relative vapor pressure.

pressure at 25 °C was p0 ) 59 mbar. The adsorption of DBM in SBA-15 was measured with a home-built semiautomatic gas adsorption apparatus based on a symmetric two-pan vacuum ultramicrobalance (Sartorius Instruments, model S3D) described elsewhere.31 The adsorption isotherm of DBM in the present SBA-15 sample is shown in Figure 1b, where the filling fraction f is given by the adsorbed mass mads normalized to mmax, the maximum adsorbed mass at p/p0 ) 0.98. A value of mmax ) 2.60 ( 0.05 g of DBM/g of silica was obtained in repeated measurements. On the basis of the bulk density of liquid DBM, this adsorbed mass corresponds to a volume of 1.04 ( 0.02 cm3 g-1, in reasonable agreement with the pore volume determined by nitrogen adsorption. This indicates that the entire pore volume accessible to nitrogen is also accessible to DBM, although the volume of DBM molecules (0.116 nm3) is twice the volume of nitrogen molecules in the liquid state. The wettability of silica by DBM was assessed by contact angle measurements of sessile drops of DBM on silicon wafers having a native oxide layer. Measurements were made using an optical contact-angle measuring instrument (OCA 15, Data Physics, Filderstadt, Germany). An initial contact angle of 20 ( 5° was found which quickly increased to a steady value of 32 ( 2°. 2.3. In situ Synchrotron SAXS Experiment. The sample cell and gas dosing system used for in situ small-angle synchrotron X-ray scattering measurements on the physisorption of gases in ordered mesoporous solids was described previously.20,32 SBA15 powder was pressed into a pellet (0.3 mm thickness, 3 mm diameter) which was placed in the temperature-controlled specimen chamber with Kapton windows. Before the measurements, the sample pellet was outgassed in situ at 353 K at a pressure of p < 10-5 mbar. During the adsorption experiments, the sample was kept at 290 ( 0.1 K, while the gas dosing and inlet system was at ambient temperature (294 ( 1 K). Pressure measurements were made by a Baratron capacitance manometer. The small-angle synchrotron X-ray scattering measurements were performed at the microfocus (µ-Spot) beamline at BESSY (HZB Berlin, Germany).33,34 The X-ray beam from the 7T wavelength shifter source was focused by a toroidal mirror and

In situ SAXS Study of SBA-15 Silica

Figure 2. In situ synchrotron X-ray scattering profiles for SBA-15 as a function of relative vapor pressure p/p0 of DBM. Bragg diffraction peaks are indicated by the respective Miller indices of the 2D hexagonal lattice. The broad hump at q ≈ 4 nm-1 is from the Kapton outlet window of the sorption cell. The inset shows Porod plots35 of two selected profiles, demonstrating the validity of Porod’s law, I ) P/q4 + const (thick lines are linear fits in the indicated region).

monochromatized by a Si 111 double crystal monochromator to an energy of 15 keV (wavelength λ ) 0.0827 nm). Scattering patterns were collected with a CCD-based area detector (MarMosaic-225, MarUSA, Evanston) at a sample-detector distance of 800 mm using a He-filled flight tube. We used continuous gas dosing with a measurement time of 60 s for a single scattering pattern. Different dosing rates were employed so that the time for a full sorption cycle (adsorption and desorption) varied from a few hours to about 12 h. The data presented in Figure 2 were collected over a time of 2 h for the adsorption cycle. The 2D data were corrected for background scattering measured by removing the sorption cell from the beam. Data normalization with respect to the primary beam intensity and sample transmission was performed by using the scattering from the Kapton (polyimid) outlet window of the sorption cell. The Kapton foil produces a broad peak well outside the region of the diffraction peaks from SBA-15, and serves therefore as an internal standard for the intensity of the incident X-ray beam multiplied by the sample transmission (which changes upon DBM loading). The 2D scattering patterns were then azimuthally averaged using the software Fit2D. The resulting scattering profiles covered a range of 0.3 nm-1 < q < 4.5 nm-1, with q ) 4π sin (θ)/λ being the length of the scattering vector (2θ is the scattering angle). 3. Data Analysis 3.1. X-ray Scattering Profiles and Integrated Intensities. Small-angle X-ray scattering profiles of SBA-15 at closely spaced relative pressures p/p0 of DBM along an adsorption isotherm are presented in Figure 2. The pressure range extends from the evacuated sample up to p/p0 ) 0.82, which is well above the pore condensation pressure (see Figure 1). For the evacuated sample, six peaks corresponding to the (10), (11), (20), (21), (30), and (40) Bragg diffraction peaks of the 2Dhexagonal pore lattice are clearly visible, and four higher-order peaks, (22), (31), (32), and (41), become visible while (40) disappears as the sample is loaded with DBM. The intensities of the diffraction peaks in Figure 2 change in a nonmonotonous way as a function of the vapor pressure, and these changes represent the primary information of the experiment. The broad peak at q ) 3.9 nm-1 is caused by the Kapton exit window of

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Figure 3. Density-gradient model of ordered cylindrical mesopores in SBA-15: (a) Sketch of a section normal to the pore axes showing the 2D hexagonal arrangement of mesopores and the matrix with disordered pores indicated by different gray levels. (b) Single mesopore in a unit cell, to illustrate the definition of the density-gradient model. The radius R0 separates the silica matrix of mean density F0 from the microporous corona of gradually decreasing density and a corrugated inner pore surface. R1 and R2 represent the largest and smallest radii of the corrugated pore wall. (c) Radial density profiles obtained from part b assuming linear changes of the density within the different regions. Values with an asterisk correspond to empty pores. Adsorption of a fluid of equal electron density as the matrix is causing changes of the profile, as indicated in part d. From the changes in the parameters F1, R1, and R2, the volume of fluid adsorbed in the cylindrical pore fluid can be calculated.

the sorption cell and was used for data normalization (see the Experimental Section). The data analysis is based on a structural model of SBA-15 sketched in Figure 3. We infer that the individual silica grains constitute a 2D hexagonal lattice of cylindrical pores having a corrugated pore wall and a microporous corona. The matrix outside the corona is assumed to accommodate disordered pores of different sizes, shapes, and lengths, which may or may not connect the cylindrical pores. (In Figure 3, this wall porosity is indicated by different gray levels.) Accordingly, we assume that the total scattered intensity can be separated into two parts: Bragg diffraction from the mesopore lattice (IBragg) and diffuse small-angle scattering arising from disordered pores and other inhomogeneities of the matrix (Idiff). Bragg scattering is proportional to the product of the structure factor S(q) and the square of the scattering amplitude from a single mesopore (form factor) |F(q)|2 (K is an instrumental constant):

I(q) ) IBragg(q) + Idiff(q) ) KS(q)|F(q)| 2 + Idiff(q)

(1) S(q) is represented by a sum of δ-functions at reciprocal lattice points (positions of the Bragg diffraction peaks). The changes in the intensity of the Bragg peaks as a function of the vapor pressure can be attributed to changes of the form factor as a consequence of fluid adsorption. Similar to our previous work,20 we model the form factor by an analytical function and fit this model function to the integral intensities of the experimental Bragg diffraction peaks. The integral intensities of the individual Bragg diffraction peaks (hk) were determined by

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I˜Bragg(qhk) )

∫ IBragg(qhk)q2 dq

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(2)

where the diffuse scattering contribution was estimated from a double tangent at the base of the respective diffraction peak and subtracted separately for each peak. The total integrated intensity

I˜ )

∫0∞ I(q)q2 dq

(3)

was determined by numerical integration of the scattering profiles within the range 0.3 nm-1 < q < 3.0 nm-1 and extrapolated toward zero and infinity. Extrapolation of the integral toward infinity was possible by using Porod’s law,35 since all scattering curves at large q (q > 2.8 nm-1) were consistent with a q-4 behavior (see inset of Figure 2). It should be mentioned here that the roughness of the pore surface pertains to a different length scale than the scale that would affect Porod’s law. A constant intensity was assumed for q < 0.3 nm-1. According to eq 1, the total integrated intensity is given by the sum of the Bragg and diffuse scattering contributions

I˜ )

∑ I˜Bragg(qhk) + I˜diff ) 2π2φtot(1 - φtot)Fs2 + I˜inc hk

(4) φtot is the total porosity (volume fraction of ordered and disordered pores) of the sample, and I˜inc represents incoherent scattering contributions. The second equality in this relation holds because the present system conforms essentially to a twophase system35 as the condensed fluid and the silica matrix have nearly the same electron density. 3.2. Analysis of Bragg Scattering. In accordance with earlier work on SBA-15,16,19,20 we assume a 2D hexagonal lattice of cylindrical mesopores surrounded by a corona (see Figure 3a). Two geometrical models of the form factor |F(q)|2 are adopted in which the corona and the adsorbed fluid layer are modeled in different ways: the step-density model developed by Zickler et al.20 in which the corona and the liquid-like adsorbed layer are assumed to have uniform densities and a new densitygradient model which assumes layers of linearly varying density. By comparing the results obtained with the two models, we can assess the reliability of the pore volume of ordered pores and of the adsorbed amount in the ordered pores that are extracted by such an approach. Step-Density Model. This model20 assumes a corona of uniform (but variable) density Fˆ 1 and a liquid-like adsorbed film of variable thickness but constant density Fˆ 2. Mathematically, this model is defined by four density levels as follows (symbols Rˆ and Fˆ are used to distinguish the parameters of this model from those of the density-gradient model):

{

0 Fˆ 2 F(r) ) Fˆ 1 F0

0 e r < Rˆ2 Rˆ2 e r < Rˆ1 Rˆ1 e r < Rˆ0 Rˆ0 e r < a0 /2

(5)

Here, the first region represents the empty core in the center of the pore, the second region represents the adsorbed film of uniform liquid-like density Fˆ 2, the third region represents the porous corona of uniform mean density Fˆ 1, and the fourth region

represents the matrix of uniform density F0. When applying this model, only the two reduced densities R ) Fˆ 1/F0 and β ) Fˆ 2/F0 are of relevance. The parameters Rˆ0 and Rˆ1 (outer and inner radius of the corona) and R* (density of the empty corona) are determined by fitting the Bragg reflections of the evacuated sample. These three parameters determine the value of the j , defined as the radius of a cylinder equiValent pore radius R having the same volume per unit length as the model pore with porous corona. For the step-density model specified by eq 5

jˆ 2 ) Rˆ 2 + (1 - R*)(Rˆ 2 - Rˆ 2) R 1 0 1

(6)

Having fixed the values of Rˆ0 and Rˆ1, the Bragg reflection data for the sample containing increasing adsorbed amounts are analyzed by determining best-fit values of the reduced corona density R and the parameter Rˆ2, assuming a liquid-like density of the adsorbed fluid film (β ) 1). An appealing property of the step-density model is that it separates matrix and adsorbed film in a straightforward way so that the adsorbed amount can be calculated from the parameters for fluids of any electron density. Explicit expressions for the scattering amplitude F(q) for this model in the different stages of pore filling are given in j and the an earlier paper.20 From the equivalent pore radius R lattice parameter a0, one can calculate the specific pore volume connected with the ordered pores, Vord, and the amount of fluid adsorbed in the ordered pores, as outlined in Appendix A2. Density-Gradient Model. This new form factor model infers that the corona of the cylindrical pores consists of two regions: an outer region which is microporous and an inner region representing the corrugated pore wall of the mesopores. Figure 3b shows a sketch of such a mesopore for which we expect a gradual decrease of microporosity from the pore surface toward the matrix, as suggested by earlier studies.16,19 Figure 3c shows the corresponding radial electron density profile F(r) resulting from the azimuthal average with respect to the pore center. We assume that the density profile can be approximated by a linear behavior within each region:

{

0 e r < R2 0 F1 - k1(R1 - r) R2 e r < R1 F(r) ) F0 - k0(R0 - r) R1 e r < R0 F0 R0 e r < a0 /2

(7)

with k0 and k1 given by

k0 )

F0 - F1 R0 - R1

and

k1 )

F1 R1 - R2

The explicit analytical expression for the form factor |F(q)|2 of this density-gradient model is given in Appendix A1 (eq A2). In eq 7, again the first region represents the empty core in the center of the mesopore. In the absence of adsorbed fluid, the second region represents the corrugated (rough) pore walls and the third region the microporous corona. This model contains only one relevant density parameter γ ) F1/F0, which in the case of empty pores (γ*) represents the reduced mean electron density at the borderline from the porous corona to the j is corrugated pore wall. For this model, the equivalent radius R given by



j 2 ) 1 - γ* (R02 + R0R1 + R12) + R 3 γ* 2 (R + R1R2 + R22) (8) 3 1 Adsorption of a matching fluid (i.e., a fluid having the same electron density F0 as the silica matrix in the adsorbed state) will cause changes of the parameters R1, R2, and F1, which can be attributed to distinct adsorption processes: An increase of F1 indicates adsorption into the microporous corona, a decrease of R1 implies adsorption into indentations of the corrugated pore wall (and thus a smoothening of the wall; see Figure 3d), and a decrease of R2 is the signature of a film formed at the pore wall. Changes in the filling fraction of the ordered pore system caused by the adsorption of a matching fluid can be calculated from the changes in the model parameters, as explained in Appendix A2. 4. Results and Discussion 4.1. Results from Bragg Scattering. In order to apply the analytical models of section 3.2 to the experimental SAXS data, the integrated peak intensities of the individual Bragg peaks (eq 2) were calculated from the experimental scattering curves after subtracting the diffuse background from each peak. The analytical model functions of the step-density model20 and of the density-gradient model (Appendix A1, eq A2) were then used to fit intensities via a least-squares procedure using the MATHEMATICA NMINIMIZE function, as explained in detail earlier.20 Below, we describe the application of the new densitygradient model. It was applied at first to the evacuated sample and a limited number of data sets for gas pressures up to the pore condensation, to find the optimum value of R0 which was then kept constant. As the next step, best-fit values of the parameters R1, R2, and F1 for the evacuated sample were determined, which are denoted as R*1 , R*2 , and F*1 . In the same way, best-fit values of R1, R2, and F1 (at constant R0 and F0) were then obtained for increasing gas pressures from the respective sets of Bragg intensities I˜Bragg(qhk). It was found that the parameters R1 and F1 are strongly correlated when fitting without constraints. However, when introducing the (physically meaningful) constraint that F1 must not decrease with increasing pressure, quite stable results were obtained. The fits gave excellent agreement between the measured and calculated integrated peak intensities, as shown by the variance of the leastsquares fit (Figure 4d). For comparison, all data were also fitted with the step-density model. Empty Pores. Values of the radii Rˆ0 and Rˆ1, the reduced j for the stepdensity R* ) Fˆ 1/F0, and the equivalent radius R density model, and the respective parameters R0, R*1 , R*2 , γ* ) j for the density-gradient model are collected in Table F*1 /F0, and R 2. The density-gradient model gives a width of the microporous corona, R0 - R*1 = 0.7 nm, a reduced density at the outer end of the corona, F*1 /F0 ≈ 0.75, and a roughness of the pore wall, R*1 - R*2 = 1.3 nm. The parameters for the step model are consistent with those found in the previous study.20 Specifically, the pore radius Rˆ1 is in close agreement with the experimental pore radius derived on the basis of the density functional theory,28 i.e., Rˆ1 = RDFT ) 4.07 nm. Equally important in the present context is the finding that the two models yield very j and this value is in similar values of the equivalent radius R close agreement with the experimental pore radius based on j = RKJS ) 4.45 nm. This implies the KJS prescription,27 i.e., R that the pore volume contained in the ordered pores, Vord, can j by the method outlined be estimated in a reliable way from R

Figure 4. Fit parameters of the density-gradient model as a function of relative pressure p/p0 for the adsorption of DBM in SBA-15: (a) characteristic radii R1 and R2; (b) film thickness t ) R*2 - R2; (c) reduced density γ ) F1/F0; (d) fit variance χ2. The pore condensation region is indicated by vertical dashed lines.

TABLE 2: Structural Parameters for the Empty SBA-15 Material Obtained from Fitting the Step-Density Model (eq 5) and the Density-Gradient Model (eq 7) to the Integrated Bragg Intensitiesa Step-Density Model Rˆ0, nm

Rˆ1, nm

R*

jˆ *, nm R

5.14

4.06

0.61

4.51

Density-Gradient Model R0, nm

R *1 , nm

R *2 , nm

γ*

j *, nm R

5.60

4.86

3.52

0.747

4.49

j of the cylindrical pores was calculated The equivalent radius R from eqs 6 and 8, respectively. a

TABLE 3: Structural Properties of SBA-15 Derived from the Bragg Diffraction Data on the Basis of the Form Factor Models in Combination with the Total Pore Volume Wtot from Nitrogen Adsorptiona total (from N2 sorption)

ordered (from SAXS)

disordered (difference)

volume fraction φ 0.686 specific pore volume V 1.01 ( 0.02 (cm3 g-1)

0.554 ( 0.003 0.815

0.132 0.195

a

Measured values in bold type.

in Appendix A2. For the calculation of Vord, we adopt the value j ) 4.5 nm. Results are summarized in Table 3. R Table 3 indicates that for the present SBA-15 material which has a total porosity of φtot ) 0.686, about 80% of the total pore volume is contained in the ordered cylindrical pores and about 20% in the disordered pores in the walls. The uncertainty in φtot, which depends on the specific pore volume Vp and the matrix density F˜ s, is estimated to (3%. The uncertainty in φord, which j ; see is determined from X-ray data (parameters a0 and R Appendix 2, eq A4), is estimated to (1%. The uncertainty in φdis ) φtot - φord is (20% for the present sample, as it represents the difference of two quantities of similar magnitude. Pore Filling. Figure 4 shows the parameters R1 and R2, the average film thickness t ) R*2 - R2, and the reduced density γ ) F1/F0 for the density-gradient model plotted as a function of

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the relative pressure p/p0 of DBM, starting from the evacuated sample and extending up to the completely filled pores. Because DBM has nearly the same electron density as the silica matrix (FDBM/Fs ) 1.04), the changes in the parameters are directly related to the adsorption of the fluid in the pores. The graphs in Figure 4 suggest that different processes dominate as the pressure is gradually increased. At p/p0 < 0.2, the density F1/F0 increases strongly, indicating that adsorption into the corona is dominating in this pressure range, but F1/F0 continues to increase up to the onset of pore condensation where it reaches a value close to 1, as expected for complete filling of the corona. Adsorption into the corrugated wall starts at p/p0 ≈ 0.1, as indicated by a decrease of the radius R1 above this pressure, but the radius R2 also starts to decrease at p/p0 ≈ 0.1, suggesting that adsorption into wall corrugations and film formation are two closely related processes. The growth of the physisorbed film is the dominating process at p/p0 > 0.2, where the film thickness increases nearly linearly with the gas pressure up to the onset of pore condensation at p/p0 ≈ 0.67. The data for the pore condensation regime (0.67 < p/p0 < 0.78) are less reliable than those for lower pressures because the adsorption equilibrium was not fully attained under the experimental conditions and because the quality of the fit (variance χ2) becomes systematically worse (Figure 4d). An increase in χ2 is expected from the fact that, in the pore condensation region of a contrast-matching fluid like DBM, Bragg scattering is caused only by those pore domains in which pore condensation has not yet occurred, i.e., in which there is still an adsorbed film. Since the fraction of nonfilled pores decreases as the filling fraction increases, information about the structure of the adsorbed film results from a decreasing amount of nonfilled pore domains. For the domains in which the adsorbed film persists, the reduced corona density γ ) F*1 /F0 stays close to 1 (with increasing scatter) as p/p0 increases above 0.67 (Figure 4c), but the parameters R1 and R2 show opposite trends; viz., R1 continues to decrease but R2 increases with increasing pressure (Figure 4a). A decrease of the film thickness t after the onset of pore condensation (Figure 4b) can be rationalized on the basis of the Saam-Cole theory36 by the metastability of the film along the ascending branch of the adsorption isotherm. Hence, the film thickness is expected to attain its (smaller) equilibrium value as the liquid phase is nucleated in a nearby section of the pore. However, as mentioned above, these results must be taken with caution and further work is needed to confirm this observation. In the present density-gradient model, the radius R1 was introduced to distinguish between the processes of adsorption into the microporous corona and the smoothing of the rough pore walls by the adsorbed fluid. The graphs in Figure 4a show, however, that R1 decreases less steeply than R2 with increasing pressure, which implies that the roughness of the pore wall is not lowered but increased by the adsorption of a liquid-like film. Tentatively, we explain this behavior by incomplete wetting of the pore wall by the adsorbate, as suggested by the finite contact angle of DBM on a SiO2 surface (see section 2.2). In this case, adsorption will not lead to a uniform film but to patches of adsorbate. Accordingly, the adsorption of DBM may not cause a smoothing but an effective roughening of the pore walls, as seen by X-rays. Such a broadening of the density profile of a fluid in the pores was already observed in the in situ SAXS study of krypton in SBA-15 by Hofmann et al.19 The results on pore filling reported here were obtained on the basis of the density-gradient model. Qualitatively, similar results are obtained when the data are analyzed on the basis of

Ja¨hnert et al.

Figure 5. DBM adsorption in SBA-15: (a) Total integrated scattering intensity I˜, integrated intensity of the Bragg diffraction peaks I˜Bragg, and integrated diffuse scattering intensity I˜diff as a function of relative vapor pressure. The pore condensation region is indicated by vertical dashed lines. (b) Wall porosity φw as a function of relative pressure. The quantity 1 - φw(p) shown in the inset is proportional to the electron density of the wall F0(p). Data for the pore condensation region, where I˜diff is influenced by small-angle scattering from pore domains, are omitted in part b.

the step-density model. For the present system, the densitygradient model was preferred, as the fit variance (χ2) for this model is lower by a factor of 5-10 than that for the step-density model. Tentatively, this is attributed to nonideality effects of the SBA-15 grains which will cause a smearing of the average density profile at the pore walls. A density profile with sharp steps appears to be less suitable than a density-gradient model to account for these effects. In addition, the step profile can lead to unphysical situations (e.g., a partially filled corona having a lower density than the liquid-like adsorbed film). Such unphysical situations are avoided in the density-gradient model. Although the profile function (eq 7) considers no separate liquidfilm region, it is nevertheless possible to calculate the volume and density profile of the adsorbed fluid by subtracting the respective profile for the empty material. However, this is no longer possible for fluids having a different electron density than the matrix. In such cases, the step-density model (or some modification of it) should be used in order to extract direct information about the volume adsorbed and the density profile of the adsorbed fluid. 4.2. Diffuse Small-Angle Scattering. To highlight the effects arising from disordered pores in the walls, the diffuse smallangle scattering was analyzed. The integral intensity from diffuse scattering (I˜diff) was determined along eqs 2-4 by subtracting the integrated intensity from Bragg scattering, I˜Bragg ) ∑hk I˜Bragg(qhk), from the total integrated intensity I˜. Figure 5 shows the dependence of ˜I, ˜IBragg, and ˜Idiff on the relative pressure of the fluid. It is immediately seen that the diffuse scattering decreases considerably as the fluid pressure increases, which confirms that disordered pore regions contribute to the adsorption process. The total integral intensity I˜ decreases by about



20% from its initial value to the onset of pore condensation (p/p0 ) 0.67), and falls off sharply in the pore condensation region. The decrease of I˜ below pore condensation is due to a decrease of the diffuse scattering, ˜Idiff, while the Bragg scattering contribution I˜Bragg is slightly increasing up to this point. This antagonistic trend in the pressure dependence of I˜diff and I˜Bragg is most pronounced at low relative pressures (p/p0 < 0.10), where diffuse scattering becomes larger than the Bragg contribution. From the observed dependence of I˜diff on the fluid pressure, the filling of the disordered pores was estimated by the relation

˜Idiff - ˜Iinc ) ˜Iw ) Cφw(1 - φw)

(9)

Here, I˜inc is a pressure-independent incoherent scattering background which was chosen such that the net wall porosity term I˜w becomes zero at the highest fluid pressure. The second equality of eq 9, which relates I˜w to the wall porosity φw(p), applies because the present system conforms to a two-phase system. The wall porosity φw(p) is related to the volume fraction of disordered pores in the unit cell volume by φw(p) ) φdis(p)/ (φdis(0) + φs). To apply eq 9, the constant C was determined from the parameters for the evacuated sample (Table 3), using φw(0) ) 0.296. The resulting dependence of the wall porosity on the fluid pressure is shown in Figure 5b. The graph indicates that about half of the wall porosity is filled at relative pressures below 0.2, as expected for pore sizes below 2 nm. However, filling of the wall porosity continues well into the pore condensation region, indicating that significantly larger pores also exist in the walls. Note, however, that this conclusion relies on the chosen value of the background scattering intensity I˜inc of eq 9, which cannot be determined accurately due to additional contributions to ˜Idiff in the pore condensation region, as discussed below. In the pore condensation region, the diffuse scattering intensity I˜diff exhibits a pronounced local maximum (see Figure 5a) which is due to strong small-angle scattering at very low q (q < 0.5 nm-1). This maximum can be attributed to a new kind of disorder which is introduced by the condensation of the liquid in individual mesopores or sections of the mesopores. Since spatially separated regions of filled and unfilled mesopores modify the order of the pore lattice, this leads to additional diffuse scattering. In the simplest case of a spatially random filling of mesopores, the diffuse scattering can be described quantitatively by the so-called Laue scattering, which predicts a dependence on pore filling as I˜diff ∝ η(1 - η), where η ) η(p) is the mesopore filling fraction.22,37 Qualitatively, this leads to a maximum in the diffuse scattering at η ) 0.5, i.e., in the middle of the pore condensation region in agreement with the experimental observation in Figure 5. 4.3. Adsorption Isotherm from X-ray Data. From the results presented in sections 4.1 and 4.2, we can determine the adsorption isotherm of the fluid in the ordered and disordered pores. The method for calculating the adsorption in the ordered pores from the parameters of the form factor model is summarized in Appendix A3. For the present case of a contrastmatching fluid, the volume fraction of liquid adsorbed in the ordered pores, φF,ord(p), is derived by eq A8 from the decrease in the volume fraction of empty pore space φord(p) with increasing fluid pressure p. An analogous relation applies to the specific volume of adsorbed fluid, VF,ord(p). However, the existence of disordered pores in the walls causes a complication in the data analysis because the electron density of the matrix, F0, will not remain constant (as is implicitly assumed in the

Figure 6. DBM adsorption in SBA-15: (a) absolute and relative values abs of the volume fraction of adsorbed fluid in the ordered pores, φF,ord rel and φF,ord , as a function of the relative pressure p/p0; (b) comparison of the filling fraction derived from the in situ X-ray study (ftot total filling fraction, ford absolute value of filling fraction of ordered pores) with the filling fraction obtained by the gravimetric measurements (fgrav).

application of the form factor models) when the wall porosity is gradually filled with the fluid. The consequences of this hidden dependence on the evaluation of the adsorbed amount are outlined in Appendix A3. When adsorption-induced changes in the matrix density F0 are not taken into account, this implies that adsorption in the ordered pores is defined relative to the fluid density in the wall. Similar to the situation of high-pressure adsorption of fluids at solid surfaces,38 this relatiVe adsorption may be zero or even negative, although fluid has entered into the ordered pores. This is seen most easily at low pressures, when the fluid is enriched only in the corona and corrugated pore walls of the cylindrical pores as well as in the disordered pores (see density profile in Figure 3c). If the density F1 increases in the same proportion as (or to a lesser extent than) rel will be zero the wall density F0, the relative adsorption φF,ord (or negative), although the absolute adsorption in the ordered abs pores φabs F,ord is positive. The absolute adsorption φF,ord is obtained by introducing an adjusted relative density γ′ (defined by eq A10 in the Appendix) which takes into account adsorptioninduced changes in the matrix density F0. The resulting isotherms abs of φrel F,ord(p) and φF,ord(p) for DBM in the present SBA-15 sample at pressures below the onset of pore condensation are shown in Figure 6a. It can be seen that the absolute adsorption exceeds the relative adsorption by a factor of about 2. For a comparison with the gravimetric adsorption isotherm, we calculate the filling fraction of the ordered pores ford(p) and the total filling fraction ftot(p) (ordered plus disordered pores) by eqs A12 and A13 of Appendix A3. A comparison of these quantities with the filling fraction obtained by gravimetric adsorption measurements (cf. Figure 1b) is shown in Figure 6b. For the pressure range below pore condensation to which this analysis applies, ftot(p) exceeds the gravimetric adsorption isotherm by 15-20%. This deviation is still within the combined limits of experimental uncertainty, which is estimated as 12-15% for ftot from the X-ray analysis and 3-5% for f from the gravimetric measurements. The comparison of X-ray and gravimetric filling fraction isotherms in Figure 6b suggests that we have overestimated the disordered porosity φdis of the present SBA-15 by ca. 15%. A reduction of

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φdis to this extent affects the calculated adsorption in a dual way, namely, directly by lowering the adsorbed volume φF,dis and indirectly via the difference between relative and absolute adsorption in the ordered pores, which depends on the gradual filling of the wall porosity as the fluid pressure is increased (Figure 5b).

Ja¨hnert et al.

F(q b) )

Appendix A1. Form Factor in the Density-Gradient Model. The scattering amplitude is defined as the Fourier transform of the electron density distribution F(r b)

(A1)

This integral can be analytically solved for the radial density distribution F(r) of eq 7 and is given by a superposition of Bessel functions J1(qR) and hypergeometric functions 3/2Ψ(1;5/2) 2

5. Conclusions The present in situ synchrotron small-angle scattering study provides novel structural information about the pore morphology of template-based periodic mesoporous silica and the adsorption of fluids in the pores. Specifically, the following points emerge from the comprehensive investigation of adsorption of dibromomethane in SBA-15: Evacuated sample: • The analysis of the Bragg reflections from the ordered pore lattice in terms of two different geometrical models of the form factor |F(q)|2 yield closely similar values of the j which agree perfectly with the experiequivalent radius R mental pore radius RKJS determined from the N2 adsorption isotherm. • From the lattice parameter a0 and the equivalent pore radius j , the volume fraction of the ordered pores φord can be R calculated. From this value and the total porosity of the sample, one also obtains the volume fraction of disorderd pores φdis. For the present SBA-15 material, we find φord ) 0.55 and φdis ) 0.13, which implies that about 20% of the total pore volume is contained in disordered pores. Pore filling of ordered pores: • The analysis of the Bragg diffraction peaks in terms of the form factor models can be extended to the regime of pore filling. In the present case of a contrast-matching fluid, this formalism allows one to calculate the adsorption isotherm and the density profile of the fluid in the ordered pores. • At low pressures (p/p0 < 0.10), only adsorption into the corona takes place, but this process continues at higher pressures up to pore condensation. Film formation at the pore walls commences at pressures of p/p0 > 0.10. An observed decrease of the film thickness in the pore condensation region is attributed to the metastability of the film in the hysteresis region. • The adsorbed film does not cause a smoothing but in fact a roughening of the corrugated pore walls. This observation is explained tentatively by incomplete wetting of the pore walls by the present fluid. Information from diffuse scattering: • From the diffuse scattering of the evacuated sample and the gradual decrease of the scattering intensity with increasing fluid pressure, the adsorption into the disordered pores can be estimated on the basis of the two-phase model of small-angle scattering. • On the basis of the filling isotherm for the wall porosity, absolute values for the adsorption into the ordered pores can be derived. Reasonably good agreement of the adsorption isotherm derived from the in situ X-ray study with the respective adsorption isotherm obtained by gravimetric measurements is found.

r iqbbr d3r ∫ F(b)e

F(q) )

∑ ai i)0

bi J1(qRi)Ri2 + Ri33/2Ψ(1;5/2)(-q2Ri2 /4) qRi 3 2

∑

ai

i)0

Ri2 Ri3 + bi 2 3

(A2) where ai and bi denote the prefactors

() (

) () ( )

a0 F1 - k0R1 - F0 a1 ) k0R1 - F1 - k1R2 ; k1R2 a2

b0 k0 b1 ) k1 - k0 b2 k1

(A3)

A2. Volume of Ordered and Disordered Pores. According to Figure 3, we assume that the total pore volume of the silica sample is made up of the ordered arrays of cylindrical mesopores and of disordered pores in the mesopore walls. The volume fraction of the ordered cylindrical pores, φord, is obtained from the volume per unit length of the 2D unit cell, V ) (a02/2)3, and the corresponding volume occupied by the cylindrical j 2π, where R j is the equivalent pore radius mesopore, Vord ) R (eqs 6 and 8). Hence, the volume fraction of ordered pore space is

φord )

()

Vord j 2π R ) V √3 a0

2

(A4)

The volume fraction of disordered pore space φdis can be calculated from φord and the total volume fraction of pores (total porosity) φtot by

φtot ) VpF˜ s /(1 + VpF˜ s) ) φord + φdis

(A5)

where Vp represents the specific pore volume as obtained from the nitrogen adsorption isotherm and F˜ s is the mass density of the silica matrix as derived by helium displacement measurements (to be distinguished from the electron density Fs of silica used in the text). The volumes of ordered and disordered pore space per unit mass of silica ms ) VsF˜ s, where Vs is the matrix volume per unit length of the 2D hexagonal unit cell, Vs ) Vφs, are then given by

Vord )

Vord 1 φord ) , VsF˜ s F˜ s φs

Vdis )

Vdis 1 φdis ) VsF˜ s F˜ s φs

(A6) where φs ) 1 - φtot(p ) 0) is the volume fraction of silica. A3. Adsorption in the Ordered Pores. When part of the pore space is occupied by an adsorbed fluid (F), eq A5 is replaced by



φord(p) + φdis(p) + φF(p) ) φtot(p ) 0) ) 1 - φs

(A7) where p is the equilibrium pressure along the adsorption isotherm. If the fluid has the same electron density as the matrix, the sample still conforms to a two-phase system. Accordingly, eq A4 can be used to determine the volume fraction of empty space in the ordered pores φord(p), and eq A6 yields the respective specific volume of empty pore space Vord(p). Again, j (eqs 5 and 7) but now using the one starts by calculating R model parameters for the chosen relative pressure p/p0 (Figure 4). The volume of adsorbed liquid in the ordered pores, expressed as volume fraction in a unit cell (φF,ord) or as volume per unit mass of the matrix (specific adsorbed volume VF,ord), is then given by

φF,ord(p) ) φord(0) - φord(p) VF,ord(p) ) Vord(0) - Vord(p)

(A8)

where φord(0) ) φord and Vord(0) ) Vord are the respective values in the empty sample. The physical meaning of the quantities φF,ord(p) and VF,ord(p) needs further consideration for the following reason: In the analysis of the Bragg scattering data, the density profiles (eqs 5 and 7) are expressed in terms of the reduced density γ ) F1/F0 (density-gradient model) or R ) Fˆ 1/ F0 (step model). For materials with nonporous walls, adsorptioninduced changes of γ (or R) can be attributed solely to changes in F1 (or Fˆ 1), as the wall density F0 is constant. For SBA-15 silica, however, the analysis in section 4.2 indicates the existence of some wall porosity, φw(p) ) φdis(p)/(φdis(0) + φs). Filling of these disordered pores with a contrast-matching fluid causes an increase of the wall density from F*0 (evacuated sample) to Fs (skeleton density of silica), which is reached when the filling of the wall porosity has come to completion. In this case, there are two possible ways to relate changes in relative density to the adsorbed amount in the ordered pores at a given pressure (see Figure 7):

(a) relatiVe adsorption:

F1 F1 1 ) F0 Fs 1 - φw

γ≡

(A9)

(b) absolute adsorption:

F1 1 - φw γ′ ≡ )γ F*0 1 - φ*w

rel φF,ord

)

j *2 - R j abs2(p) R j *2 - R j rel2(p) R

j abs(p) are calculated j rel(p) and R where the equivalent pore radii R with reduced densities, as given by conventions a and b, respectively. The filling fraction of the ordered mesopores can abs (p) and φord(0) by be determined from φord

ford(p) ) 1 -

abs φord (p) φord(0)

(A12)

and the overall filling fraction f(p) is obtained from ford(p) and the wall porosity φw(p) by

f(p) ) 1 -

φabs ord(p) + φdis(p) φtot(0)

(A13)

where φdis(p) ) (φdis(0) + φs)φw(p). Acknowledgment. We are indebted to C. Li and S. Siegel for their help with the synchrotron radiation experiments at the BESSY µ-Spot beamline, to E. P. Resewitz and C. Ko¨nig for their contributions to the construction and improvement of the in situ sorption cell, and to S. Dodoo for contact angle measurements. We also acknowledge fruitful discussions with L. Solovyov and the critical comments of one of the reviewers. Financial support from the Deutsche Forschungsgesellschaft (DFG) within the Collaborative Research Center Sfb 448, Projects B1 and B14, is also gratefully acknowledged. References and Notes

(A10)

where we have used F*0 ) Fs(1 - φ*) w with φ*, w the wall porosity of the evacuated sample. Convention (a) expresses densities in the ordered pores relative to the fluid density in the wall and rel rel or VF,ord . These values thus gives a “relative adsorption” φF,ord are obtained when the reduced densities γ(p) are taken directly from Figure 4c. Convention (b) is based on the adjusted reduced density γ′(p) which attributes changes in this parameter solely to density changes in the ordered pores. This convention yields abs the “absolute adsorption” φabs F,ord or VF,ord which is obtained when the reduced densities γ′(p) of eq A10 are used instead of γ(p). From eqs A4 and A8-A10, one finds the following relation between the two quantities abs φF,ord

Figure 7. Sketch of the variation of the electron densities F1 and F0 with the relative pressure p/p0. Values in the empty material are indicated by an asterisk. Fs is the skeleton density of the matrix.

(A11)

(1) Kresge, C. T.; Leonowicz, M. E.; Roth, W. J.; Vartuli, J. C.; Beck, J. S. Nature 1992, 359, 710. (2) Zhao, D. Y.; Feng, J. L.; Huo, Q. S.; Melosh, N.; Fredrickson, G. H.; Chmelka, B. F.; Stucky, G. D. Science 1998, 279, 548. (3) (a) Taguchi, A.; Schu¨th, F. Microporous Mesoporous Mater. 2005, 77, 1. (b) Chen, H.-T.; Huh, S.; Wiench, J. W.; Pruski, M.; Lin, V.S.-Y. J. Am. Chem. Soc. 2005, 127, 13305. (c) Hess, C.; Wild, U.; Schlo¨gl, R. Microporous Mesoporous Mater. 2006, 95, 339. (4) Zelenˇa´k, V.; Badanicˇova´, M.; Halamova´, D.; Cˇejka, J.; Zukal, A.; Murafa, N.; Goerigk, G. Chem. Eng. J. 2008, 144, 336. (5) Katiyar, A.; Pinto, N. G. Small 2006, 2, 644. (6) Evans, R. J. Phys.: Condens.Matter 1990, 2, 8989. (7) Gelb, L. D.; Gubbins, K. E.; Radhakrishnan, R.; SliwinskaBartkowiak, M. Rep. Prog. Phys. 1999, 62, 1573. (8) Alba-Simionesco, C.; Coasne, B.; Dosseh, G.; Dudziak, G.; Gubbins, K. E.; Radhakrishnan, R.; Sliwinska-Bartkowiak, M. J. Phys.: Condens. Matter 2006, 18, R15. (9) (a) Kruk, M.; Jaroniec, M. Chem. Mater. 2001, 13, 3169. (b) Ravikovitch, P. I.; Neimark, A. V. J. Phys. Chem. B 2001, 105, 6817. (c) Ravikovitch, P. I.; Vishnyakov, A.; Neimark, A. V. Langmuir 2006, 22, 513. (d) Thommes, M.; Smarsly, B.; Groenevolt, M.; Ravikovitch, P. I.; Neimark, A. V. Langmuir 2006, 22, 756. (10) Thommes, M. Stud. Surf. Sci. Catal. 2007, 168, 495. (11) Tu¨ysu¨z, H.; Lehmann, C. W.; Bongard, H.; Tesche, B.; Schmidt, R.; Schu¨th, F. J. Am. Chem. Soc. 2008, 130, 11510.

15210


(12) Chytil, S.; Haugland, L.; Blekkan, E. A. Microporous Mesoporous Mater. 2008, 111, 134. (13) (a) Shenderovich, I. G.; Buntkowsky, G.; Schreiber, A.; Gedat, E.; Sharif, S.; Albrecht, J.; Golubev, N. S.; Findenegg, G. H.; Limbach, H.-H. J. Phys. Chem. B 2003, 107, 11924. (b) Shenderovich, I. G.; Mauder, D.; Akcakayiran, D.; Buntkowsky, G.; Limbach, H. H.; Findenegg, G. H. J. Phys. Chem. B 2007, 111, 12088. (14) Epping, J. D.; Chmelka, B. F. Curr. Opin. Colloid Interface Sci. 2006, 11, 81. (15) Valiullin, R.; Naumov, S.; Galvosas, P.; Karger, J.; Woo, H. J.; Porcheron, F.; Monson, P. A. Nature 2006, 443, 965. (16) Impe´ror-Clerc, M.; Davidson, P.; Davidson, A. J. Am. Chem. Soc. 2000, 122, 11925. (17) Solovyov, L. A.; Kirik, S. D.; Shmakov, A. N.; Romannikov, V. N. Microporous Mesoporous Mater. 2001, 44, 17. (18) Albouy, P. A.; Ayral, A. Chem. Mater. 2002, 14, 3391. (19) Hofmann, T.; Wallacher, D.; Huber, P.; Birringer, R.; Knorr, K.; Schreiber, A.; Findenegg, G. H. Phys. ReV. B 2005, 72, 064122. (20) Zickler, G. A.; Ja¨hnert, S.; Wagermaier, W.; Funari, S. S.; Findenegg, G. H.; Paris, O. Phys. ReV. B 2006, 73, 184109. (21) Muroyama, N.; Yoshimura, A.; Kubota, Y.; Miyasaka, K.; Ohsuna, T.; Ryoo, R.; Ravikovitch, P. I.; Neimark, A. V.; Takata, M.; Terasaki, O. J. Phys. Chem. C 2008, 112, 10803. (22) Smarsly, B.; Goltner, C.; Antonietti, M.; Ruland, W.; Hoinkis, E. J. Phys. Chem. B 2001, 105, 831. (23) Sel, O.; Brandt, A.; Wallacher, D.; Thommes, M.; Smarsly, B. Langmuir 2007, 23, 4724. (24) Guenther, G.; Prass, J.; Paris, O.; Schoen, M. Phys. ReV. Lett. 2008, 101, 086104. (25) Solovyov, L. A.; Belousov, O. V.; Dinnebier, R. E.; Shmakov, A. N.; Kirik, S. D. J. Phys. Chem. B 2005, 109, 3233.

Ja¨hnert et al. (26) (a) Ryoo, R.; Ko, C. H.; Kruk, M.; Antochshuk, V.; Jaroniec, M. J. Phys. Chem. B 2000, 104, 11465. (b) Liu, Z.; Terasaki, O.; Ohsuna, T.; Hiraga, K.; Shin, H. J.; Ryoo, R. ChemPhysChem 2001, 2, 229. (c) Galarneau, A.; Cambon, H.; Di Renzo, F.; Fajula, F. Langmuir 2001, 17, 8328. (d) Galarneau, A.; Cambon, H.; Di Renzo, F.; Ryoo, R.; Choi, M.; Fajula, F. New J. Chem. 2003, 27, 73. (27) Jaroniec, M.; Solovyov, L. A. Langmuir 2006, 22, 6757. (28) Ravikovitch, P. I.; Neimark, A. V. Stud. Surf. Sci. Catal. 2007, 160, 9. (29) Schreiber, A. Ph.D. Thesis, Technical University Berlin, Germany, 2002. (30) Ko¨ro¨si, G.; Kovats, E. J. Chem. Eng. Data 1981, 26, 323. (31) Groβ, S.; Findenegg, G. H. Ber. Bunsen-Ges. Phys. Chem. 1997, 101, 1726. (32) Zickler, G. A.; Ja¨hnert, S.; Funari, S.; Findenegg, G. H.; Paris, O. J. Appl. Crystallogr. 2007, 40, s522. (33) Paris, O.; Li, C.; Siegel, S.; Weseloh, G.; Emmerling, F.; Riesemeier, H.; Erko, A.; Fratzl, P. J. Appl. Crystallogr. 2007, 40, s466. (34) Paris, O. Biointerphases 2008, 3, FB16. (35) Glatter, O.; Kratky, O. Small-angle X-ray scattering; Academic Press: New York, 1983. (36) Saam, W.; Cole, M. W. Phys. ReV. B 1975, 11, 1086. (37) Kostorz, G. X-ray and neutron scattering. In Physical Metallurgy, 4th ed.; Cahn, R. W., Haasen, P., Eds.; North Holland: Amsterdam, The Netherlands, 1996; p 1115. (38) Findenegg, G. H.; Thommes, M. High-pressure adsorption of gases on planar surfaces and in porous materials. In Physical Adsorption: Experiment, Theory and Applications; Fraissard, J., Conner, C. W., Eds.; NATO ASI Series C; Kluwer: Dordrecht, The Netherlands, 1997; Vol. 491, pp 151.

JP8100392

Pore Structure and Fluid Sorption in Ordered Mesoporous Silica. I

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