J. Phys. Chem. B 2001, 105, 831-840
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SANS Investigation of Nitrogen Sorption in Porous Silica Bernd Smarsly,*,† Christine Go1 ltner,† Markus Antonietti,† Wilhelm Ruland,‡ and Ernst Hoinkis§ Max-Planck-Institute of Colloids and Interfaces, Research Campus Golm, D-14424 Potsdam, Germany, UniVersity of Marburg, Fachbereich Chemie, Hans-Meerwein-Str., D-35032 Marburg, Germany, and Hahn-Meitner-Institut, Glienicker Str. 100, D-14091 Berlin, Germany ReceiVed: August 28, 2000
The mechanism of nitrogen sorption in porous silica was investigated by small-angle neutron scattering (SANS). Two samples of porous silica were studied containing mesopores (pore sizes 5.5 and 9.5 nm, respectively) and additional micropores of irregular shape and statistical distribution. SANS curves were recorded at a temperature of 78 K at various relative pressures p/p0 during adsorption. The experiment is based on contrast matching between silica and condensed nitrogen with regard to neutron scattering. The sorption process was characterized by the evaluation of the chord-length distributions extracted from SANS data for each p/p0. In addition, a general approach was developed to relate the SANS pattern during capillary condensation to the size distribution and the morphology of ordered mesopores. On the basis of these evaluation methods, various uptake mechanisms could be described, which are micropore filling, the formation of nitrogen layers, and capillary condensation. The analysis of the SANS data shows that the mean size of the remaining empty mesopores formally increases, and their size distribution becomes narrower during capillary condensation, which is in agreement with the predictions of the Kelvin equation. Furthermore, our study indicates a significant degree of additional microporosity, the origin of which is discussed. For comparison, the experiment and the data evaluation were also applied to a disordered porous silica with a broad pore size distribution. The combination of SANS and nitrogen sorption turned out to be a powerful technique to investigate both the mechanisms of sorption and the structure of porous silicas in one experiment.
1. Introduction The design and application of inorganic ceramics with ordered or disordered nanostructured pore systems is a major topic of current materials science. Several strategies have been developed to control pore morphology and alignment in two- or threedimensional superstructures, which is crucial for possible applications in catalysis, separation processes, and so forth.1-8 However, only a few techniques are available for an accurate and quantitative characterization of the structure. Nitrogen sorption and small-angle scattering techniques are especially widely used for the determination of the specific surface area, pore size and wall architecture of mesoporous and microporous materials. Although the analysis of nitrogen sorption data is applied as a standard characterization technique, the underlying mechanisms of adsorption and desorption are not yet understood on the level of the structures to be characterized. According to wellestablished theories of sorption, different mechanisms of sorption can occur in porous materials as a function of the pore size and the pressure of nitrogen. At the lowest relative pressure values p/p0, adsorption in micropores takes place, which is supposed to be a process of volume filling rather than capillary condensation.9,10 p0 is the saturation pressure at the given temperature. With increasing p/p0, a liquid-like film with the statistical thickness t(p/p0) is formed on the mesopore walls. Condensation * To whom correspondence should be addressed. † Max-Planck-Institute of Colloids and Interfaces, Research Campus Golm. ‡ University of Marburg, Fachbereich Chemie. § Hahn-Meitner-Institut.
of nitrogen within a pore occurs when the relative pressure p/p0 satisfies the Kelvin equation.9 Taking into account that capillary condensation in mesopores is preceded by the formation of liquid nitrogen films on the pore wall, the original Kelvin equation has to be corrected for the statistical film thickness t(p/p0).
rk(p/p0) )
2γVL RTln(p0/p)
+ t(p/p0)
(1)
where γ and VL are the surface tension and molar volume of the liquid condensate, respectively, and rk is the pore radius. Although the validity of this general picture of sorption in microand mesoporous materials is generally accepted, the details are still subject of theoretical discussion due to the lack of additional experimental techniques. The Kelvin equation is routinely used for the calculation of the mesopore size distribution. In the frequently used procedure of Barrett, Joyner, and Halenda, the porous solid is modeled by a group of independent cylindrical pores of different diameter existing in a thermodynamic equilibrium with the vapor.11 Because no additional determination of t(p/p0) has been available, empirical and theoretical approaches are used to estimate the film thickness from sorption measurements with nonporous solids or by simulation of adsorption on a planar system.12-15 Although the Kelvin equation is widely used for the interpretation of sorption data of various types of mesoporous materials, there are, however, uncertainities in the validity of this approach. It is an inherent drawback of this conventional description of sorption that the interpretation assumes a specific pore geometry (cylinders).
10.1021/jp003105x CCC: $20.00 © 2001 American Chemical Society Published on Web 01/04/2001
832 J. Phys. Chem. B, Vol. 105, No. 4, 2001 Consequently, independent experimental techniques would help to obtain deeper insights into the mechanisms of adsorption and desorption in porous materials. We apply an experimental technique (SANSADSO, recently developed at the Hahn-Meitner-Institut) for the investigation of nitrogen sorption by combining a standard sorption experiment with small-angle neutron scattering (SANS). Structural characteristics of a pore system, such as pore size, porosity, surface area, and other structural properties can be determined from SANS data. The SANS intensity I(q) of porous materials arises from the scattering contrast (F1 - F2)2 between the bulk material and the pores, where F1 and F2 are the coherent scattering length densities of these two phases. Adsorption of nitrogen in conjunction with SANS is based on the fortunate situation that the scattering length densities of amorphous silica and liquid nitrogen at T ) 78 K are nearly identical (F(SiO2) ) 3.43 × 1010 cm-2 and F(N2,liquid) ) 3.22 × 1010 cm-2). Hence, the scattering contrast between them is close to zero. As a consequence, filled pores become “invisible”, and only the remaining empty pores produce a measurable scattering intensity. By recording SANS curves at various p/p0 during adsorption and desorption, a direct correlation can be established between SANS data and the process of nitrogen sorption. Consequently, the combination of nitrogen sorption with SANS represents a promising technique for the elucidation of both the structural characteristics and the sorption mechanism. In most of the previous studies, the conjunction of smallangle X-ray scattering (SAXS) or SANS with sorption was applied to inorganic porous materials possessing broad pore size distributions without a defined pore morphology. In most of these studies, the samples were exposed to the adsorbate (H2O/ D2O, in most cases) prior to the SAXS/SANS measurements, thus involving a limited accuracy for controlling p/p0.16-24 In contrast, the SANSADSO experiment at the Hahn-MeitnerInstitut (Berlin) offers the opportunity to record SANS curves at any p/p0 which can be accurately controlled. SANSADSO has been used to study the condensation of C6D6 in porous oxides and carbon materials.25-29 Recently, Ramsay et al. applied the SANSADSO experiment to study the sorption of benzene in SBA-15 silica, a mesporous silica possessing a welldefined hexagonal pore structure and a narrow pore size distribution.30 However, only few attempts were made in these studies to interpret the scattering data quantitatively in terms of the different sorption processes. Indeed, neither the determination of t(p/p0) nor a suitable quantitative verification of the Kelvin equation have been carried out so far, which require distinguishable mesopores of a certain morphology. Nevertheless, a sufficiently broad pore size distribution is necessary to study the dependence of capillary condensation on the pore size. The mesoporous silicas used in this study were previously introduced by Go¨ltner et al.31-33 Their preparation involves the templating of lyotropic amphiphilic block copolymer phases of poly(styrene-b-ethylene oxide) (SE) in a sol-gel process. The sol-gel procedure is extensively used to produce mesoporous silicas by utilizing the self-assembly of amphiphilic molecules into ordered superstructures. By this procedure, porous silica is obtained with mesopores, the size of which can be controlled through variation of the length of the hydrophobic polystyrene block. Two mesoporous silicas, denoted here as “SE1010 silica” and “SE3030 silica” with pore diameters of 5.5 and 9.5 nm, respectively (Figure 1), are subjected to the investigation presented here. Although transmission electron microscopy (TEM) and SAXS analysis do not show an ideal hexagonal or cubic arrangement of the mesopores, but mesopores with a
Smarsly et al.
Figure 1. TEM micrographs of SE3030 silica (a) SE1010 silica (b). The mean size of the mesopores can be estimated to 5 nm for SE1010 silica and 9-10 nm in the case of SE3030 silica.
distorted spherical (“ink bottle”-like) shape and a certain polydispersity of pore sizes are evident from TEM. Hence, the morphology of the mesopores is characterized by translational and substitutional disorder, as will be shown below; it was a major aim of this study to achieve a reasonable characterization of the porosity. Besides, this type of mesoporous silica was chosen for several reasons. First, it possesses a pronounced mesopore structure, thus ensuring capillary condensation as one adsorption progresses. Second, nitrogen sorption measurements and SAXS studies indicated additional microporosity in these materials, the origin of which is still a matter of discussion (see Figure 2c).34 Consequently, these silicas have a distinct bimodal pore size distribution of mesopores and micropores. This offers the opportunity to study the different subsequent stages of sorption (micropore filling, formation of nitrogen layers on mesopore walls, and capillary condensation in mesopores) in a single sample. In particular, our study addresses the nature of the microporosity observed in the silicas studied here. Apart from the SE1010 and SE3030 silicas, a silica sample with totally nonordered porous network was examined, which was prepared by an analogous sol-gel procedure using poly(ethylene oxide) (PEO) as a “molecular” template (“PEO silica”). This sample shows a broad pore size distribution between micro- and mesopores up to ca. 5 nm in diameter. The investigation of this material was focused on the sorption in a pore system with a broad size distribution located between micro- and mesopores. At first, the experimental results are presented for the three samples of silica, proving the potential and applicability of this experiment. In the second part, we describe the different mechanisms occurring during nitrogen sorption. Suitable evaluation methods for SANS were developed and applied to relate the nitrogen sorption to the corresponding SANS patterns. In particular, methods are presented by which the processes of micropore filling, formation of nitrogen films and capillary condensation can be characterized quantitatively by means of SANS data.
Nitrogen Sorption in Porous Silica
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TABLE 1: Properties of the Three Samples of Silicas Used in This Study silica sample (m2/g)
SBET SSANS (m2/g) pore volume (cm3/g) micropore volume (cm3/g) mesopore size (nm) (BJH) pore size (nm) (TEM) pore size (nm) (SANS)
SE1010
SE3030
PEO
750 n.a. 0.78 0.11 4.8 5.5 5.4a
600 550 0.69 0.08 8.6 9.5 9.5a
900 830 0.49 0.4 3.2 1-4 1.3b
a Pore sizes according to eq 13. b The pore size D was estimated from lp and the porosity φ by usage of D ) lp/(1 - φ).45
2. Materials and Methods The synthesis of the porous silica samples involves the polycondensation of a silica precursor (tetramethyl orthosilicate, TMOS) within the aqueous domains of a lyotropic mesophase of poly(styrene-b-ethylene oxide) (SE). Amphiphilic block copolymers of the SE type were kindly provided by Th. Goldschmidt AG, Essen, Germany. Poly(ethylene oxide) (Mw ) 2 kg/mol) (Fluka) and TMOS (Aldrich) were used as received. The syntheses of the porous silicas is carried out by dissolving the porogen, poly(styrene-b-ethylene oxide) or poly(ethylene oxide), in TMOS under moderate heating. Hydrochloric acid (pH 2) is added at room temerature, which causes exothermal hydrolysis of TMOS. To remove the methanol, the mixture is evacuated on a rotary evaporator at 40 °C for 10 min. This hybrid material is left in a drying oven at 60 °C for 24 h. The organic material is removed by calcination at 500 °C in an oxygen atmosphere. Pore sizes can be controlled by varying of the block lengths of the block copolymers. For example, SE1010 silica contains a polystyrene and a poly(ethylene oxide) block with a molecular weight of Mw ) 1 kg/mol each, accordingly, the blocks of SE3030 have a molecular weight of Mw ) 3 kg/ mol. It was shown that the morphology of the pore system is directly related to the structure of the liquid crystalline phase of the amphiphilic block copolymers.31-33 The structural features of the samples are summarized in Table 1. Nitrogen sorption experiments were conducted using a Micromeritics Tristar instrument and a Quantachrome Autosorb-1 providing relative pressures as low as p/p0 g 10-5. The samples were degassed at 150 °C in vacuo for 24 h prior to investigation. TEM micrographs were obtained with a Zeiss EM 912 OMEGA operating at an acceleration voltage of 120 kV. Samples were ground and suspended in acetone. One drop of the suspension was applied to a carbon-coated 400 mesh copper grid and left to dry. SAXS measurements were carried out using a Nonius rotating anode (P ) 4 kW, λ ) 0.154 nm) with pinhole collimation and image plates as detectors. With the image plates placed at a distance of 40 cm from the sample, a scattering vector range from q ) 0.4-9.7 nm-1 (q ) 4π/λ sin θ) was available. The experimental setup of SANSADSO is installed within the evacuated sample chamber of the V4-SANS instrument at the Berlin Neutron Scattering Center BENSC. The apparatus is described in detail in ref 18 and was used previously to study the adsorption of nitrogen in a controlled-pore glass and silica glass monolith.35,36 The pressure was determined by use of a Baratron capacitance manometer (Type 398 HD-1000 made by MKS Instruments, Burlington, MA). The real time and the corresponding pressure, p, and temperature, T, of the sample were permanently recorded during the measurements. To reduce the scattering from silanol (Si-OH) groups, deuterium oxide was added to the samples to deuterate surface silanol, and
afterward the samples were dried in vacuo at 60 °C. This procedure was repeated for several times to achieve complete H/D-exchange. Finally, the silica powders were filled into a Suprasil 300 quartz cell with a path length of 1 mm and dried for 5 h at 250 °C in air. The cell was fixed to an aluminum frame and quickly inserted into the sample tube and evacuated at 100 °C at approximately 10-4 Torr for 1 h. The temperature of the aluminum frame was measured using two Pt-100 resistors and could be controlled to within ( 0.1 K. The neutron wavelength λ was 0.607 nm, the diameter of the incident beam was 5 mm. The SANS data were obtained by using sample/ detector distances of 16, 4, and 2 m, which correspond to an accessible q range of 0.05-2.8 nm-1. For the evacuated specimen transmission, coefficients g 0.93 were measured. The data reduction was carried out by using standard programs for the normalization of the efficiency of the two-dimensional detector, masking the detector cells near the beam stop and subtracting the scattering recorded from the empty cell and the electronic background.37 Absolute values for the scattering cross section dΣ(q)/dΩ in units of inverse centimeters were calculated by using scattering data from H2O. Here, dΣ(q)/dΩ is denoted as “intensity” I(q) for convenience. The influence of the wavelength dispersity on the evaluation of I(q) was checked by assuming a Gaussian distribution for the wavelengths centered at λ ) 0.607 nm and a width of σ ) 0.06 nm (fwhm). However, the influence of this effect on the interpretation turned out to be negligible and was not considered in the following calculations. The incoherent background due to nitrogen was subtracted for the evaluation. 3. Results and Discussion 3.1. Experimental Data. For both SE1010 silica and SE3030 silica, SANS curves were obtained at T ) 78 K in the range of q ) 0.05-2.7 nm-1, at different p/p0 corresponding to the different stages of the sorption and desorption processes. Figure 2, parts (a) and (b) show the nitrogen isotherms of SE1010 and SE3030 silicas indicating the pressures at which SANS curves were obtained. The shape of the isotherms is typical of mesoporous materials (type IV isotherm according to IUPAC classification)9 and shows a marked hysteresis loop, with a sharp step in the desorption branch that can be attributed to a percolation effect (“bottleneck effect”) during emptying of the mesopores.38 As a consequence of this percolation phenomenon, the equilibration time was too long to obtain usable SANS curves during the emptying of the mesopores within the time scale of the experiment. The specific surface areas of SE1010 and SE3030 silicas are 750 and 600 m2/g (according to BET), respectively. This large specific surface area is partly due to the presence of micropores, as can be concluded from t-plot and Rs-plot analysis of sorption data (Figure 2c) and a thorough evaluation of SAXS data.34,39 The intercept obtained from Rsplot is significantly different from zero indicating a substantial degree of microporosity, the values are shown in Table 1. Taking into account the uncertainties in the determination of microporosity in the presence of mesopores, our study aimed at a second method of independently quantifying the microporosity by the SANSADSO experiment. Because the changes of the SANS patterns during nitrogen adsorption are quite similar for SE1010 silica and SE3030 silica, we only describe the SANS features of SE1010. The SANS curves for SE1010 silica (Figure 3) show a marked interference peak with a maximum at q ) 0.8 nm-1 and a shoulder of lower intensity, which result from the ordering of the mesopores in the silica matrix. Starting from p/p0 ) 0, the SANS curves show
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Figure 3. SANS curves of SE1010 silica recorded at different relative pressures p/p0 during sorption of nitrogen. The data points are connected by lines for better visualization.
Figure 4. SANS curves of SE3030 silica recorded at different relative pressures p/p0 during sorption of nitrogen. The data points are connected by lines for better visualization.
Figure 2. Nitrogen isotherm of SE1010 silica (a) and SE3030 silica (b) with the relative pressures p/p0, at which SANS curves were obtained. (c) Rs-plot for SE1010 silica using the data given in ref 14 as comparative reference data. From the intercept, the micropore volume was estimated to be 0.11 mL/g. (d) Nitrogen isotherm of PEO silica.
several significantly different scattering features during the sorption process. At the final stage of nitrogen uptake, a marked decrease of the overall SANS intensity was observed at p/p0 ) 0.95, after condensation within the mesopores. This drop of I(q)
by a factor of 200 clearly proves that the scattering contrast between silica and nitrogen in the condensed state is negligible and that contrast matching is achieved. The remaining intensity is partially caused by incoherent scattering from condensed nitrogen. Several unexpected scattering patterns are observed during sorption between p/p0 ) 0 and the end of capillary condensation. Compared to the evacuated sample, I(q) increased significantly at small p/p0 by a factor of 2 at scattering vectors below q ≈ 1.3 nm-1. However, the intensity slightly decreased at larger scattering vectors. Because this effect is already apparent at the smallest p/p0 accessible in our experiment, it is attributed to the filling of micropores, as described below. A similar increase of I(q) was observed by Ramsay et al. for hexagonal mesoporous SBA-15 silica.30 With further increasing relative pressure, I(q) markedly dropped at q g 0.6 nm-1 due to condensation of nitrogen within the mesopores, but showed an unexpectedly large increase at q < 0.5 nm-1 at p/p0 ) 0.44. The corresponding SANS curves of SE3030 silica showed a similar, but less pronounced increase of I(q) at small q during capillary condensation. A distinct extended Porod regime was observed at high scattering vectors for SE3030 silica (Figure 4) but not for SE1010 silica. It should also be mentioned that the SANS curves of both SE1010 and SE3030 silicas did not show any positional shift
Nitrogen Sorption in Porous Silica
Figure 5. SANS curves of PEO silica measured at different relative pressures p/p0 during sorption of nitrogen. The data points are connected by lines for better visualization.
of the maxima of the strong interference peaks during the sorption process. However, the position of the broader interferences (at q ≈ 0.6 nm-1 for SE3030 silica) is significantly shifted to larger values of q, indicating that they not do correspond to a “structural factor”, but have to be interpreted as a variation of the mespore form factor in the course of nitrogen sorption on the pore walls. In both samples, the steep increase of I(q) at small q < 0.08 nm-1 follows a Porod behavior and must be attributed to the scattering from large grain boundaries. A comparable set of SANS patterns during the adsorption of nitrogen was obtained for the disordered porous PEO silica. The sorption isotherm of this material shows a small hysteresis loop, the BET specific surface area is 800 m2/g (Figure 2d). This silica has a broad pore size distribution with a mean pore size between micropores and mesopores. Consequently, the SANS curves did not show an interference maximum, which is indicative of a more less random microstructure (Figure 5). In agreement with the two ordered mesoporous silicas, I(q) for PEO silica was significantly increased in the low q region at medium p/p0, and, accordingly, I(q) dropped markedly at larger q due to micropore filling. In the case of PEO silica, usable SANS data were also obtained during the desorption cycle. 3.2. Evaluation of the SANS Data. In the following, the specific changes of the SANS patterns during nitrogen sorption are subjected to detailed interpretation with regard to a description of the underlying sorption mechanisms. In particular, the analysis addresses different aspects of the sorption process, which also requires different methods for the evaluation of SANS data. First, the influence of microporosity on the SANS patterns during sorption is discussed. Second, the SANS patterns are analysed with respect to a description of all the subsequent stages of nitrogen sorption in materials with a distinct pore size distribution. The analysis is also focused on a suitable characterization of the pore structure by SANS. As mentioned before, the SANS patterns of both SE1010 and SE3030 cannot be satisfactorily described by an ideal hexagonal or cubic morphology. Hence, different evaluation methods are needed to describe nitrogen sorption in a pore system characterized by a lower degree of order. For this purpose, the analysis is first performed on the basis of the so-called “chord-length distribution”, which allows the evaluation of SANS data without assuming a specific model for the pore morphology. Finally, the interpretation of SANS data is focused on the parameters that determine the capillary condensation in mesopores. A general approach was developed to relate the size distribution of an arrangement of polydisperse mesopores with translational disorder to the SANS
J. Phys. Chem. B, Vol. 105, No. 4, 2001 835 patterns occurring during capillary condensation, which is finally compared to the predictions of the Kelvin equation. Microporosity. The TEM micrographs show pore walls separating the mesopores of SE1010 and SE3030 with a thickness of ca. 2 and 4 nm, respectively. Our experiments indicate that the silica skeleton contains a significant number of micropores. As mentioned before, a significant increase of I(q) at small p/p0 and q < 1.3 nm-1 was observed for both SE1010 and SE3030 silica. Filling of micropores and smoothing surface roughness by nitrogen sorption results in an increase of the difference of the scattering-length densities between the still empty mesopores and the wall material, which is filled with nitrogen. Consequently, the larger scattering contrast between the bulk matter and the empty mesopores leads to an increase of I(q). Because the scattering intensity at higher q is dominated by smaller pores, I(q) is simultaneously decreased in the high q regime. Similar effects were also observed for the disordered PEO silica. The change of the scattering contrast and the corresponding volume fraction of microporosity were estimated for SE1010 silica and SE3030 silica by a comparison of the intensities of the main interference peaks for the evacuated state and the scattering curve at p/p0 ) 0.1. In this estimation, it is assumed that the increase of I(q) at small p/p0 is exclusively caused by filling of micropores. The volume fraction of micropores was thereby estimated to approximately 0.11 and 0.08 for SE1010 silica and SE3030 silica, respectively, which is in reasonable agreement with the nitrogen sorption data; we do not observe a shoulder of I(q) at high q or a significant deviation from Porod’s law with SE3030, and therefore, we can estimate the upper limit of the micropore volume fraction as 0.1. The presence of micropores is also supported by the Rsplot analysis of nitrogen sorption data (Figure 2c), from which volume fractions of 0.11 and 0.07 were estimated for SE1010 and SE3030 silica, respectively. The origin of this additional microporosity in mesoporous silicas is still a matter of discussion and subject of a systematic study on the porosity of SE silicas.34 Recent studies by Kruk et al. have also shown a substantial degree of microporosity in mesoporous SBA-15 silicas using the block copolymer SBA-15 as a template that is composed of PEO and PPO chains.40 Hence, the additional microporosity seems to be a general feature of mesoporous silicas obtained from the templating of lyotropic phases of block copolymers containing PEO chains as the hydrophilic block. The pronounced microporosity may be attributed to the PEO chains being embedded molecularly in the silica matrix, which would result in cavities of similar size in the pore walls after calcination. This interpretation is supported by recent NMR studies of de Paul et al. on the mobility of PEO chains of the amphiphilic block copolymer poly(isoprene-b-ethylene oxide) embedded in an inorganic matrix which was obtained via a sol-gel process.41 As a result, it was shown that the inorganic phase and PEO are intimately mixed on a molecular level. Consequently, the microporosity is probably due to the PEO chains and may be a general feature of mesoporous silicas prepared with amphiphilic block copolymers containing PEO as the hydrophilic block. Chord-Length Distribution g(r) as a Function of p/p0. To obtain a quantitative description of the nitrogen sorption without assuming specific models for the morphology of micropores and mesopores, the concept of the “chord-length distribution” (CLD) g(r) was used to evaluate the SANS data. The CLD was established previously to characterize the structure of two-phase systems, in particular porous materials, by the help of smallangle scattering data.42-47 Chord-length distributions play an important role in the quantitative evaluation of the SAXS of
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two-phase systems. The relationship between the CLD g(r) and the autocorrelation function γ(r) is given by
g(r) ) lpγ′′(r)
(2)
where lp is the average chord length (Porod length) of the system. lp is the first moment of g(r). The CLD represents a quantitative statistical description for the distances connecting phase boundaries in a two-phase system with sharp phase boundaries. Because the small-angle scattering pattern of a twophase system results from the distribution of the phase boundaries, the CLD is directly accessible from small-angle scattering data. The determination of the CLD is highly desirable, as it provides relevant material information, such as the average pore size, prevalent length scales and the specific surface area, which is especially useful for the characterization of disordered and weakly ordered materials. The specific surface area per volume S/V is directly related to the Porod length lp45
V S
lp ) 4φ(1 - φ)
(3)
where φ is the volume fraction of one of the two phases. In the limit of high q, the SANS intensity I(q) is related to lp and the surface area S is given by Porod’s law45
I(q)qf∞ )
2π(F1 - F2)2 S Vq4
)
8πQ lp4
(4)
where
Q ) Vφ(1 - φ)(F1 - F2)2 )
1 2π2
∫0∞q2I(q)dq
(5)
is the so-called “Porod invariant”. To validate the assumption of a two-phase system with sharp boundaries between silica and the voids, additional SAXS investigations were carried out with the evacuated samples up to q ) 9.6 nm-1. Although our SAXS setup covered a wide range of the scattering vector q, log(I) - log(q) plots did not show any indications of fractal structures on the nanometer scale in the silica samples. Moreover, the assumption of a two-phase system in terms of domains of identical scattering lengths densities is even reasonable for all stages of the sorption because the scattering length densities of silica and condensed nitrogen match closely, bulk silica and condensed nitrogen can be considered to be a continuous phase with respect to the scattering contrast relative to the remaining empty pores. The SANS intensity arises only from the interface between condensed nitrogen and the pores, and the inner surface area calculated by eq 3 corresponds to the nitrogen/pore interface area at a certain p/p0. Consequently, the evaluation CLDs for each SANS curve during nitrogen sorption provides a suitable description of the changes of the size of empty pores and the remaining free interface surface. I(q) of SE3030 silica and PEO silica showed a distinct Porod behavior, thus allowing a reliable determination of the CLDs. In both cases, at higher p/p0 a constant small incoherent background scattering from condensed nitrogen was observed, which was subtracted from the SANS data. Because the SANS curves of SE1010 do not show a Porod asymptote within the accessible q range, an evaluation of the CLD does not seem to be reliable in this case. The CLDs were determined for each SANS curve applying an evaluation technique, which involves fitting the whole range of the SANS curve with orthogonal basic functions, which are then analytically Fourier transformed.48
Figure 6. Chord length distributions g(r) obtained from SANS curves of SE3030 silica for each relative pressure p/p0 during nitrogen sorption. The changes of the shape of g(r) at small chords have to be related to the filling of micropores and smoothing of angular structures. The shift of the first maximum at r ≈ 5 nm (Max 1) to larger r can to be attributed to the formation of nitrogen layers on the mesopore walls, while the broad shoulder at r ≈ 10 nm (Max 2) corresponds to the pore size.
Compared with conventional algorithms,42-45 this approach is numerically more reliable. In this study, lp was calculated as the first moment of g(r) and Q was determined by eq 5. The analysis of the CLDs of SE3030 silica as a function of p/p0 illustrates the different processes occurring during sorption (Figure 6). Obviously, small structural elements rapidly disappear already at small p/p0. The behavior of the CLD g(r) at small r is determined by the general structure of the interface (edges, vertices, and curvature) and the occurrence of small structural units, in particular micropores.49-53 A value g(0) * 0 is due to the presence of angular interfaces in the pore system (“angularity”). Consequently, the behavior of the CLDs of SE3030 at small r reflects the filling of micropores and smoothing of angularity by nitrogen. From Figure 6, the size of the micropores could be estimated to be < 1.5 nm. A striking change of the shape of g(r) at larger r occurred upon sorption. As is evident from Figure 6, the position of the maximum at r ) 5 nm is succedingly shifted to ca. r ) 7.3 nm with increasing p/p0. Moreover, a second weak shoulder at r ≈ 10 nm is shifted to slightly lower r. On the basis of the theoretical concept of the CLD, these two maxima can be interpreted as the superposition of the size distributions of the empty “pores” and “walls” (i.e., the space between the pores). In principle, it is not possible to determine pore size distributions and the wall thickness directly from the CLD without further assumptions. However, in this case, a thorough analysis of TEM micrographs of SE3030 silica clearly shows that the first maximum has to be related to the average wall thickness and the second to the mean pore size (ca. 9.5 nm). Hence, the shift of the first maximum corresponds to the increase of the average wall thickness, which is the sum of the thickness of the silica walls and the thickness of the nitrogen layer adsorbed on the wall. Moreover, the shape of g(r) is in agreement with a model of polydispersed spherical mesopores showing transitional disorder with regard to the arrangement of the mesopores in the silica matrix. On the basis of this interpretation, the dependence of the nitrogen layer thickness on p/p0 could be estimated from the shift of the position of the first maximum (Figure 7). Despite the limited number of data points the t(p/p0) dependence is in a reasonable qualitative agreement with the Harkins-Jura equation established for porous silica and empirical data,13,14 thus proving the feasibility of this procedure. The experimentally determined
Nitrogen Sorption in Porous Silica
Figure 7. The thickness of nitrogen layers on mesopore walls as a function of the p/p0 for SE3030 silica. The data (filled squares) were obtained from the position of the first maximum in Figure 6. The solid line corresponds to a modified Harkins-Jura equation obtained for porous silica.13 The dashed lines corresponds to empirical data according to ref 14.
Figure 8. Dependence of the free interface area on the relative pressure p/p0 during nitrogen sorption for SE3030.
layer thickness exceeds the theoretical one at larger values of p/p0, which can be attributed to the onset of capillary condensation in the mesopores. Furthermore, the evaluation of the CLDs allowed a description of the nitrogen adsorption in terms of the remaining freeinterface area. A similar procedure was applied by Steriotis et al. to describe the adsorption of a H2O/D2O mixture in porous alumina.17 The remaining free-interface area for each p/p0 was calculated from lp and Q as described above. Figure 8 shows the decrease of the fraction of free interface area as a function of p/p0 in relation to the evacuated sample. The shape of the graph clearly illustrates the different stages of the adsorption process. Already at small p/p0 the free-interface area is drastically reduced due to the filling of micropores. From Figure 8, the microporosity can be estimated to be approximately 5060% of the overall inner surface area, which is consistent with nitrogen sorption measurements. The slight decrease of the free interface area between p/p0 ) 0.2 and p/p0 ) 0.6 obviously results from the successive formation of nitrogen layers on the mesopore walls and the decrease of the pore diameter. The substantial decrease of the free-interface area at p/p0 ) 0.7 corresponds to capillary condensation in the mesopores. A similar evaluation was carried out for the adsorption of nitrogen in PEO silica (Figures 9 and 10) characterized by a disordered pore system. In this case, CLDs were also calculated for the desorption branch. In agreement with SE3030 silica the CLDs show the filling of small pores and removal of angular
J. Phys. Chem. B, Vol. 105, No. 4, 2001 837
Figure 9. Chord length distributions calculated from SANS data at different p/p0 during adsorption and desorption for PEO silica. The graphs show the filling of micropores and smoothing out of angular structures during the sorption of nitrogen. Moreover, the shift of the maximum indicates an increase of the average size of free remaining pores.
Figure 10. Dependence of the interface area as a function of p/p0 during nitrogen sorption for PEO silica.
structures at small r and low p/p0 (Figure 9). A maximum is observed in all of the CLDs, which corresponds to the superposition of the chord distributions of walls and pores. In this case, the interpretation of the CLDs in terms of the pore filling processes is more complex due to the large polydispersity of the pores involved. However, the shift of the maximum of the CLDs to higher r indicates the formation of larger structural units during nitrogen sorption; as sorption progresses, the average size of the remaining empty pores as well as the average nitrogen/silica wall thickness increases. Both effects result in an increase of the mean chord length which is reflected by a shift of the CLD maximum toward larger values of r. The CLD corresponding to the desorption illustrates the emptying of the filled porous network; the mean size of empty pores decreases as nitrogen is partially removed from smaller pores. A further description of the sorption process is provided by the decrease of the free interface area during sorption (Figure 10). In this case of a disordered porous silica, the free interface area decreases continuously reflecting the broad size distribution of micropores and mesopores. Capillary Condensation in Mesopores. As pointed out, typical geometrically perfect pore morphologies (hexagonal, cubic) are not suitable to describe the arrangement of the mespores in SE3030 and SE1010 silica. However, both the TEM analysis and the g(r) evaluation show that the morphology of the mesopores is sufficiently well-defined to assume a specific structure model for the spatial distribution and morphology of
838 J. Phys. Chem. B, Vol. 105, No. 4, 2001
Smarsly et al.
the mesopores. Hence, a different approach was developed to investigate the final stage of capillary condensation in the mesopores. In particular, the analysis of SANS curves measured between p/p0 ≈ 0.3 and p/p0 ≈ 0.9 allows us to study the dependence of the layer formation and capillary condensation on the pore size distribution using a suitable structure model for the packing of the mesopores. On the basis of the TEM investigations, in this approach, the system of the mesopores is represented by a spatial distribution of polydisperse spheres (mesopores) in a solid matrix (silica), and it is assumed that the size and position of the mesopores are uncorrelated. In this model, the formation of nitrogen layers on the mesopore walls corresponds to a decrease of the sphere diameter, whereas the capillary condensation of nitrogen leads to the removal of statistically distributed spheres according to their size. Assuming that particle sizes and orientation are uncorrelated with the positions of the particles, a well-known general equation to evaluate the small-angle scattering of a system of colloidal polydisperse objects of uniform shape is given by
h˜ (R, p/p0) is of the same Gaussian type as the original distribution h(R). This assumption is reasonable in order to obtain a semiquantitative description of the mesopore condensation with respect to the validity of the Kelvin equation. The limited number of scattering curves did not allow an unambigious determination of additional quantitative parameters for the asymmetry of the distribution h˜ (R, p/p0). h˜ (R, p/p0) is ˜ 〉 and σ˜ 2R ) 〈R ˜ 2〉 - 〈R ˜ 〉2 determined by the parameters Rmin, 〈R which are related to h(R) by
I(q) ) k(〈|F(q)|2〉 + |〈F(q)〉|2 (S(q) - 1))
where 〈|F ˜ (q)|2〉 and |〈F ˜ (q)〉| are now functions of 〈R ˜ 〉 and 〈R ˜ 2〉. It has to be emphasized again that the validity of eq 13 is limited to the case of pure positional disorder with regard to the distribution of the polydispersed objects in the matrix. On the basis of the analysis of TEM micrographs and the SANS patterns, the interpore structure factor S(q) for the packing of mesopores was calculated by using the Percus-Yevick (PY) approach, which is based on a hard-sphere potential with the two parameters RPY and volume fraction ηPY.57-59 The application of the PY approach in this case is justified by several aspects; the PY approach has proven to be a suitable means of characterizing packings of spherical objects without crystalline order, which is a reasonable representation of our porous silicas. Because the pores are sufficiently separated from each other, the preconditions for the PY model are fulfilled. Also, from a practical point of view, the PY structure factor is advantageous compared to cubic or hexagonal packings, as it is determined by only two parameters. Because the position of the mesopores is fixed during capillary condensation, S(q) was assumed to remain constant for all p/p0. Hence, eq 13 relates the SANS patterns during condensation to the size of the mesopores being filled at a certain p/p0. Because the contribution of microporosity on SANS patterns is negligible at higher p/p0 due to micropore filling, the SANS curve for p/p0 ) 0.1 was used as the reference curve (c ) 1) for calculating the original distribution h(R), the scaling factor k and the structure factor S(q). SANS curves of SE1010 silica at p/p0 ) 0.1, p/p0 ) 0.33, p/p0 ) 0.44 and p/p0 ) 0.69 were fitted by eq 13 with the parameter Rmin. A corresponding evaluation with similar results was carried out for SE3030 silica, but is not shown here. Hence, in our model, the nitrogen sorption in the mesopores is represented as follows: At first, the formation of nitrogen layers on the walls leads to a decrease of the average pore size 〈R ˜ 〉. During capillary condensation, the filling of polydispersed mesopores occurs as a function of their size, but independently of their position, and is simulated by a formal decrease of the frequency c of unfilled mesopores. Figure 11 shows that a reasonable agreement between the model and the SANS data was obtained. In particular, the significant increase of I(q) at small q during capillary condensation is a consequence of the polydispersity and the statistical filling of the mesopores; smaller pores are preferentially filled at a certain p/p0, whereas it is assumed that no correlation exists between the size and the position of the mesopores. From our model, average pore radii of 2.7 and 4.8 nm and polydispersities
(6)
F(q) denotes the particle (mesopore) form factor, S(q) is the interparticle (“intermesopore”) structure factor, k is a scaling factor, and the 〈 〉 brackets represent the number-average of the spheres. This approach was previously used by Siemann and Ruland to interpret the SAXS data of block copolymers.54 Kotlarchyk and Chen55 and Pedersen56 applied this approach to various colloidal systems like microemulsions. Hence, eq 6 can be assumed valid for the arrangement of the unfilled mesopores. A similar procedure was used by Li et al. to describe the sorption of H2O in porous Vycor glass.21 In our case, the polydispersity of the mesopores was described using a Gaussian distribution for the number distribution of radii
h(R) )
[
(R - 〈R〉) 1 exp 2σ2R σRx2π
2
]
(7)
with the average radius 〈R〉 and variance σR as parameters
σ2R ) 〈R2〉 - 〈R〉2
(8)
The form factor of a sphere of radius R is given by
F(R,q) )
( 2πR q )
3/2
J3/2(Rq)
(9)
where J3/2(Rq) is a Bessel-function of the first kind of the order The distribution h(R) was chosen, as analytical expressions can be obtained for the averaged expressions for the form factors 〈|F(q)|2〉 and |〈F(q)〉| of polydisperse spheres.54 During capillary condensation, the number fraction c of unfilled mesopores decreases from 1 to 0 depending on the mesopore size and p/p0. Assuming that at, a certain p/p0, all mesopores with R < Rmin are filled, the fraction of unfilled mesopores is 3/ . 2
c)
∫R∞ h(R)dR ) 21 min
[ ( 1 + erf
)]
〈R〉 - Rmin σRx2
(10)
where h(R) is the original number distribution of unfilled mesopores. During capillary condensation the original distribution h(R) changes to distributions h˜ (R, p/p0), as the small mesopores are filled as a function of their sizes. Although the distribution h˜ (R, p/p0) should be asymmetric, it is assumed that
∫R∞ Rh(R)dR
(11)
∫R∞ R2h(R)dR
(12)
〈R ˜〉 )
1 c
〈R ˜ 2〉 )
1 c
min
min
Consequently, the dependence of SANS curves on the fraction of unfilled mesopores is described by a modification of eq 6
I(q,c) ) k(c〈|F ˜ (q)|2〉 + c2|〈F ˜ (q)〉|2 (S(q) - 1))
(13)
Nitrogen Sorption in Porous Silica
J. Phys. Chem. B, Vol. 105, No. 4, 2001 839 It should be mentioned that the procedure can easily be extended to pore systems with different morphologies, such as the hexagonal packing of cylindrical pores. As the only differences to the evaluation presented here, the form factor 〈|F(q)|2〉 and |〈F(q)〉| of cylinders and an appropriate structure factor S(q) have to be chosen, which is straightforward in the case of a highly ordered system. By contrast, for cylindrical pores showing a significant deviation from hexagonal geometry, the structure factor of Rosenfeld for 2D “hard disks” may be applied as an appropriate estimation.60,61 4. Conclusions and Outlook
Figure 11. Interpretation of the SANS data of SE1010 silica using a model in which the system of mesopores is represented by an ensemble of polydisperse hard spheres. k*(c〈|F(q)|2〉 - c2|〈F(q)〉|2) is shown for p/p0 ) 0.44 illustrating that the behavior of I(q) at low q is determined by the polydispersity of the mesopores.
Figure 12. Normalized number size distributions h(R) for unfilled mesopores obtained from the SANS curves in Figure 11. The arrows indicate the mean radius rk at which condensation occurs according to the Kelvin equation corrected for the film thickness t(p/p0) from ref 13 at the corresponding p/p0.
of σR/R ) 0.09 and 0.08 were calculated for SE1010 silica and SE3030 silica, respectively. The dependencies of the mesopore size distributions h˜ (R,p/p0) on p/p0 reflect the different stages of nitrogen adsorption (Figure 12). Compared with p/p0 ) 0.1, the shape of the mesopore size distribution curve for p/p0 ) 0.33 is quite similar because no condensation is observed. Moreover, the position of the maximum of h˜ (R,p/p0) shows a tendency to slightly smaller radii, which can be attributed to the formation of nitrogen layers on the mesopore wall. At higher p/p0, the mean pore size increases and the distribution becomes significantly narrower due to the condensation in smaller mesopores, in accordance with the predicitions of the Kelvin equation. The size distributions of the remaining empty mesopores were compared with the predictions of the Kelvin equation corrected by the film thickness t(p/p0) (see eq 1).13 Pores with radii smaller than rk should be filled at the corresponding pressure. As can be seen in Figure 12, a reasonable semiquantitative agreement exists between the distributions of the unfilled pores of SE1010 silica and the predictions of the Kelvin equation for rk. Hence, the evaluation presented here supports the assumption that, in contrast to desorption, capillary condensation is governed by the structural properties of the single pores and is less affected by the network morphology.38
In the present study, the combination of SANS and nitrogen sorption was used to elucidate the mechanism of nitrogen sorption in different meso- and microporous silicas with regular as well as disordered pore structures. Several significant SANS features were observed, which were fully consistent with the sorption process proposed and the structure of the materials, as revealed by TEM and other techniques. Different approaches were applied to relate the SANS patterns to the sorption process. In particular, the concept of the chord-length distribution represents a suitable approach to describe the subsequent stages of nitrogen sorption (i.e., micropore filling, formation of nitrogen layers on mesopore walls, and capillary condensation in mesopores) in ordered and disorded silicas. Moreover, the combination of nitrogen sorption with in-situ SANS proves to be a useful technique to study capillary condensation in mesopores. A general approach was developed to relate the SANS patterns during condensation to the size distribution and statistical filling of regularly distributed mesopores. This evaluation was in reasonable agreement with the predictions of the Kelvin equation. Hence, the technique presented here represents an experimental method to verify theories for sorption in mesoporous media. To bench-test current theories for sorption mechanisms in detail, it is intended to apply the technique also to more ordered mesoporous silicas with different morphologies. Besides, further evidence for the presence of microporosity in the SE silicas was obtained, the origin of this microporosity may have also implications of other mesoporous oxides prepared by using PEO-containing amphiphiles. The combination of the experiment with suitable evaluation algorithms offers the unique possibility to study topics which are hardly accessible by other analytical techniques, in particular layer formation and capillary condensation. Moreover, further insights into the mechanism of desorption from a porous network, in particular percolation effects, will be obtained from SANS curves recorded during desorption cycles. Acknowledgment. The authors would like to thank Th. Goldschmidt AG, Essen (Germany) for the generous supply of SE block copolymers, the Max-Planck society for financial support and Hahn-Meitner Institute for the facilities granted for the pursuit of this work. We also thank Dr. C. Burger for stimulating discussions and his help with respect to mathematics. Further thanks go to Nicolas Keller (Fritz-Haber-Institut, Berlin) for his help with the sorption measurements and especially to staff of the HMI informatics department (in particular K.H. Degenhardt and O. Sauer) for setting up the data acquisition for SANSADSO. References and Notes (1) Kresge, C. T.; Leonowicz, M. E.; Roth, W. J.; Vartuli, J. C.; Beck, J. S. Nature 1992, 359, 710. (2) Zhao, D.; Feng, J.; Huo, Q.; Melosh, N.; Fredrickson, G. H.; Chmelka, B. F.; Stucky, G. D. Science 1998, 279, 548.
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