Letter pubs.acs.org/Langmuir
Morphological Analysis of Disordered Macroporous−Mesoporous Solids Based on Physical Reconstruction by Nanoscale Tomography Daniela Stoeckel,†,‡ Christian Kübel,§ Kristof Hormann,† Alexandra Höltzel,† Bernd M. Smarsly,‡ and Ulrich Tallarek*,† †
Department of Chemistry, Philipps-Universität Marburg, Hans-Meerwein-Strasse, 35032 Marburg, Germany Institute of Physical Chemistry, Justus-Liebig-Universität Gießen, Heinrich-Buff-Ring 58, 35392 Gießen, Germany § Institute of Nanotechnology and Karlsruhe Nano Micro Facility, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany ‡
S Supporting Information *
ABSTRACT: Solids with a hierarchically structured, disordered pore space, such as macroporous−mesoporous silica monoliths, are used as fixed beds in separation and catalysis. Targeted optimization of their functional properties requires a knowledge of the relation among their synthesis, morphology, and mass transport properties. However, an accurate and comprehensive morphological description has not been available for macroporous−mesoporous silica monoliths. Here we offer a solution to this problem based on the physical reconstruction of the hierarchically structured pore space by nanoscale tomography. Relying exclusively on image analysis, we deliver a concise, accurate, and model-free description of the void volume distribution and pore coordination inside the silica monolith. Structural features are connected to key transport properties (effective diffusion, hydrodynamic dispersion) of macropore and mesopore space. The presented approach is applicable to other fixed-bed formats of disordered macroporous−mesoporous solids, such as packings of mesoporous particles and organic-polymer monoliths.
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INTRODUCTION Solids with a hierarchically structured, disordered pore space, such as silica and organic-polymer monoliths as well as packings of mesoporous particles, are used as fixed beds in chemical separations and heterogeneous catalysis.1,2 The efficiency of a fixed bed in a separation or catalytic process depends on the mass transport properties of the constituting porous solid, which are in turn determined by the pore space morphology.3−6 Targeted optimization of the fixed-bed efficiency would require a knowledge of how preparation, morphology, and mass transport characteristics of a porous solid are related. At present, we are still far from establishing these relationships. The optimization of monolithic and particulate beds proceeds largely from empirical knowledge because accurate and comprehensive methods for their morphological characterization are lacking. The standard methods of gaining morphological information are mercury intrusion porosimetry (MIP) for the macropores (>50 nm)7 and gas physisorption for the mesopores (2−50 nm).8 To infer a pore size distribution from the experimental data one needs a morphological model. The investigated pore space is thus assumed to consist of welldefined, regular-geometry pores (slit, sphere, and cylinder) whose size can be described by one parameter, the pore diameter. The validity of these idealized models and thus the degree to which pore size distributions inferred from MIP and physisorption data approximate the true geometry of the pore © 2014 American Chemical Society
space cannot be judged when the latter has never been accurately determined. Whereas quantitative morphological data of the macropore space of silica and organic-polymer monoliths have become available through physical reconstructions by confocal laser scanning microscopy (CLSM) and serial block-face scanning electron microscopy, respectively,9−11 comparable data for the mesopore space of monoliths, whose smaller dimensions are more difficult to access, have not been released so far. Over the past decade, electron tomography has emerged as an excellent probe for mesoporous solids in heterogeneous catalysis.12 It has been used to determine the location, size, distribution, and loading of metal nanoparticles inside mesoporous materials and also to investigate the mesoporous support structures themselves.13,14 However, studies that present quantitative morphological data of disordered mesopore networks are still scarce.15−17 In this Letter, we propose a direct, concise, and accurate route to the morphology of macroporous−mesoporous solids, as exemplified by an in-house-prepared silica monolith. First, the monolith’s hierarchically structured, disordered pore space is physically reconstructed by nanoscale tomography.18 For the Received: June 20, 2014 Revised: July 3, 2014 Published: July 18, 2014 9022
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Figure 1. Physical reconstruction of the disordered pore space of a macroporous−mesoporous silica monolith by nanoscale tomography. The macropore space was reconstructed by FIB−SEM tomography and the mesopore space by STEM tomography. Shown are quadrilateral sections of the reconstructed volumes. to the surface region of the investigated area by ion-induced deposition. A 30 kV Ga+ beam with a current of 44 nA was used for milling. The SEM unit was operated at an acceleration voltage of 5 kV. The milling axis defined the z direction in the image stack. The final stack of aligned and y-position-corrected images had dimensions of 14.0 × 13.6 × 6.3 μm3 with voxels of 10.41 × 13.21 × 20 nm3 (x × y × z). For STEM tomography, a small piece cut from the monolith was ground in a mortar, and the crumbs were dusted over a holey Cu grid (Quantifoil Micro Tools, Jena, Germany) on which Au fiducial markers (6.5 nm diameter) were deposited from an aqueous suspension (CMC, University Medical Center, Utrecht, The Netherlands). Electron tomography was performed using an image-corrected Titan 80-300 TEM (FEI) operated at an acceleration voltage of 300 kV in STEM mode with a nominal beam diameter of 0.3 nm. STEM images (101) were collected with a high-angle annular dark-field detector over the range of −78 to 75°. The final stack of aligned, reconstructed, and denoised images had dimensions of 320 × 410 × 245 nm3 with voxels of 0.47 × 0.47 × 0.47 nm3 (x × y × z). The irregularly shaped, mesoporous silica crumb occupied a volume of ca. 255 × 430 (longest dimension) × 240 nm3 in the final image stack (Figure S4). Image Processing. FIB−SEM images were segmented by a thresholding algorithm, smoothed using a Gaussian kernel with a
macropore space, we choose focused ion beam−scanning electron microscopy (FIB−SEM), which is superior to CLSM at resolving macropores in the submicrometer range. For the mesopore space we use scanning transmission electron microscopy (STEM). The reconstructed volumes of macropore and mesopore space are then statistically evaluated to determine their geometrical and topological properties.
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EXPERIMENTAL SECTION
Monolith Synthesis and Characterization of Macroporosity−Mesoporosity. The investigated silica monolith was prepared following a known synthesis route.19 The macroporous skeleton was formed from a mixture of tetramethoxysilane, poly(ethylene glycol), and urea (Merck, Darmstadt, Germany); mesoporosity was introduced through hydrothermal treatment with urea (Figure S1). Macroporosity and mesoporosity were checked by standard MIP and N 2 physisorption measurements (Figure S2).20 Nanoscale Tomography. For FIB−SEM tomography, a 0.5-cmthick slice cut from the monolith was embedded in poly(divinylbenzene) to enhance the image contrast and prevent depthof-focus effects within the macropores (Figure S3). FIB slice-and-view tomography was performed using a Strata 400S dual-beam FIB system (FEI, Hillsboro, OR). A protective Pt layer (∼1 μm thick) was applied 9023
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Figure 2. Analysis of the void volume distribution in the macroporous−mesoporous silica monolith by CLDs. Chords scanning the solid−void border are projected from randomly chosen points Pi in the void space (scheme). The CLD gives the frequency with which a certain solid−solid distance appears in the reconstructed macropore and mesopore spaces, panels a and b, respectively. Solid lines indicate the fit of eq 1 to the data, from which the values for μ, k, and the mode were received. (c) Superposition of macropore and mesopore CLDs after normalization by the respective modes (0.71 μm and 7.33 nm).
(resolution ∼10 nm/pixel) was processed to yield a 14.0 × 13.6 × 6.3 μm3 volume of the macropore space. The sample for STEM tomography (voxel length ∼0.5 nm) was a crumb received from grinding a small piece of the silica monolith in a mortar. The sample was tilted in small angular increments over a wide angular range while a series of STEM images were acquired. The resulting image stack was aligned and processed to yield a 255 × 430 × 240 nm3 volume of the mesopore space. From a visual inspection of the reconstructed volumes shown in Figure 1, the mesopore space appears to be more heterogeneous than the macropore space. But assessing the relative heterogeneity of the void volume distribution requires a quantitative approach. For this task, namely, evaluating the geometrical properties of the reconstructed pore space, we used CLD analysis21 (Figure 2), where the solid−void (silica−pore) border is scanned with chords of variable length. The resulting distribution of chord lengths indicates the relative frequency with which a certain silica−silica distance occurs in the investigated pore space. The CLD is an abstract but accurate way to describe the void volume distribution, eliminating the need to define limits for individual pores or their geometric form. As such, CLD analysis is especially valuable for describing the pore space inside a continuous solid, such as that of a silica monolith, where, contrary to a particulate bed, defining individual pore limits would be difficult and possibly arbitrary. A k-Γ function, which describes the void volume distribution in disordered pore spaces,22 was fitted to the CLDs for macropore and mesopore spaces:
standard deviation of 3 pixels, restored to eliminate artifacts, and rendered in AMIRA (Visage Imaging, Berlin, Germany). STEM images were segmented manually, restored, and rendered in AMIRA. Because the investigated silica crumb did not fill the whole volume of the image stack and was irregularly shaped, the images as serial sections contained seemingly isolated patches of mesoporous silica and void space from the crumb’s surroundings. A variance filter (using a kernel with a 20 pixel radius) and a fill-holes algorithm were applied to the STEM images to envelope all image areas representing mesoporous silica. The subsequent morphological analysis was carried out only within the enveloped areas of mesoporous silica. Morphological Analysis. The processed image stacks were subjected to chord length distribution (CLD) analysis (Supporting Information). Collected chord lengths (106) were binned using bin sizes of 0.1 μm and 2 nm for macropore and mesopore space, respectively. The processed image stacks were skeletonized by the application of an iterative thinning algorithm (Figure S5). The received topological skeletons were evaluated to determine the total number of junctions (nj) and the number of triple-point (nt), quadruple-point (nq), and higher junctions (nx). The average pore coordination number was calculated from Zav = 3(nt/nj) + 4(nq/nj) + 5(nx/nj).
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RESULTS AND DISCUSSION
Figure 1 shows the hierarchically structured pore space that perforates the continuous body of a silica monolith and how its macropore and mesopore spaces were reconstructed. A slice cut from the in-house-prepared monolithic rod served as a sample in FIB−SEM tomography, where a focused beam of Ga+ removed layer-for-layer material from a region of interest on the sample surface, scanning each freshly generated surface with an electron beam. The resulting stack of SEM images 9024
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Figure 3. Slice through the reconstructed macropore and mesopore spaces of a silica monolith (white is silica, black is the void space). The topological skeleton is shown in blue.
f (lc) =
k−1 ⎛ l ⎞ kk lc exp⎜ −k c ⎟ k Γ(k) μ ⎝ μ⎠
so the long chord lengths observed in the mesopore CLD are not necessarily indicative of wide mesopores. Long chords could arise from a long-drawn pore or from two pores connected in a straight line. Nevertheless, large void volumes in the mesopore space are undesirable with respect to the separation efficiency and mechanical stability of a silica monolith employed in chromatography.1,3 The long tail of the mesopore CLD is responsible for its low homogeneity (kmeso = 1.82). A direct comparison of macropore and mesopore CLDs (Figure 2c), possible after the normalization of each CLD by its respective mode (0.71 μm and 7.33 nm), shows the heterogeneity of the mesopore space compared to that of the macropore space. This finding agrees with the heterogeneous nature of mesopore space formation through Ostwald ripening. Given that the mesopore space of a silica monolith has not been visualized before, it is unsurprising that morphological implications of the formation process have rarely been considered.24 Slices through the reconstructed volumes (Figure 3) provide a qualitative view of how the void volume is distributed in macropore and mesopore spaces. Contrary to the rather homogeneous macropore space, the mesopore space is a network of large pores connected by smaller necks (Figure 3b). This structural feature, known as ink-bottle pores, is a longstanding issue in the interpretation of physisorption data.8 A realistic morphological model of the mesopore space needs to take this structural feature into account. Figure 3 also shows 2D representations of the topological skeleton that could be traced in the reconstructed macropore and mesopore spaces. From the corresponding 3D analysis we determined the pore coordination numbers (Table 1).15,25 Besides the pore size
(1)
In eq 1, lc is the chord length, Γ is the Gamma function, μ is the first statistical moment of the distribution, and k = μ2/σ2 the ratio between the first and second (σ) statistical moments. Interpreted in morphological terms, μ is a measure of the average pore size (different from and not to be confused with the average pore diameter as obtained from the interpretation of MIP or physisorption measurements) and k is a measure of the homogeneity of the void volume distribution in a disordered pore space. Importantly, μ and k can be related to the individual contributions to hydrodynamic dispersion in flow through the monolith’s macropore space.9 Dispersion resulting from flow heterogeneity is generally an important transport characteristic of a material, which can limit its efficiency and use as a fixed bed in separation and catalysis. Here, a smaller value of μ means a shorter lateral distance that an analyte needs to cover in the mobile phase between two encounters with the monolith skeleton; this lowers the transchannel dispersion, which results from the flow velocity bias over the largest lateral distance across an individual macropore. Larger k values represent a narrower distribution relative to μ, that is, greater homogeneity on the length scale of one to two macropores; a more homogeneous macropore space reduces the velocity bias between neighboring flow channels and thus short-range interchannel dispersion. The separation efficiency of silica monoliths in chromatography has been shown to improve with increasing value of k and decreasing value of μ.23 Although silica monoliths that combine a small average macropore size with a rather homogeneous macropore space have occasionally been reported, no synthesis route guarantees this outcome yet.1,3 CLSM-based reconstructions of silica monoliths prepared under conditions similar to the investigated one have yielded values of μmacro = 2.53−4.85 μm and kmacro = 2.6−2.9.23 Compared to these values the investigated silica monolith has a favorably small average macropore size (μmacro = 1.21 μm) and a macropore space homogeneity (kmacro = 2.61) at the lower limit of the established range (Figure 2a). Because comparable morphological data for the mesopore space are not yet available, we relate our analysis of the mesopore space (Figure 2b) to the macropore space. The mesopore CLD features a long tail of chords (lc > 30 nm) that are much longer than the average value (μmeso = 16.23 nm) and occasionally reach macropore dimensions. Chord lengths cannot be translated into pore volumes without assuming a geometric pore model,
Table 1. Pore Coordination in the Macroporous− Mesoporous Silica Monolith macropore space mesopore space
Z=3
Z=4
Z≥5
Zav
87.2% 82.4%
10.9% 13.8%
1.9% 3.8%
3.15 3.21
distribution (cf. Figure 2), the pore coordination numbers in a pore network are important characteristics of its mass transport properties, e.g., the effective diffusion coefficient, and are used accordingly in transport simulations.26,27 But topological data of disordered mesoporous solids available in the literature are typically estimated by fitting within a model framework rather than explicitly determined. The physical reconstruction shows that pore coordination numbers in the silica monolith are far 9025
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from large values. More than 80% of pores in the reconstructed macropore and mesopore space have a coordination number of Z = 3, so the overall topology is well reflected by the average pore coordination number of Zav ≈ 3.2 (Table 1). The pore coordination for the macropore and mesopore spaces of the monolith is much lower than the popular cubic network models suggest,28 which may lead to unrealistic predictions of masstransport properties when connectivity is used as an adjustable parameter. Explicit topological data derived from physical reconstruction could refine pore network models and improve their predictive power.29
OUTLOOK The morphological analysis of a physically reconstructed silica monolith has shown that its macropore and mesopore spaces share highly similar topology but differ in their geometric properties. The mesopore space is characterized by a heterogeneous void volume distribution and the occurrence of ink-bottle pores. Improving the homogeneity of the mesopore space would be a worthwhile synthesis goal, as a narrower void volume distribution also decreases the likelihood of ink-bottle pores. Apart from the specific results obtained for our silica monolith sample, this work holds implications for disordered macroporous−mesoporous solids in general. For example, physical reconstruction could help to develop a practical methodology for calculating pore network connectivity and pore size distributions from scanning isotherms.30 To go beyond the morphological analysis and identify morphological descriptors for various mass-transport processes through numerical simulations, realistic models of disordered macroporous−mesoporous solids must be developed.10,29,31 Such models should be informed by and in accord with the morphological data received from physical reconstruction. The presented approach is applicable also to packings of mesoporous particles and organic-polymer monoliths and thus recommends itself for investigating the disordered macroporous−mesoporous solids employed as fixed beds in separation and catalysis. ASSOCIATED CONTENT
S Supporting Information *
Details of the synthesis of the silica monolith and assessment of macroporosity−mesoporosity by MIP and N2 physisorption. In-depth descriptions of FIB−SEM and STEM tomography, image processing, and analysis. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*Phone: +49-6421-2825727. Fax: +49-6421-2827065. E-mail: tallarek@staff.uni-marburg.de. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the Deutsche Forschungsgemeinschaft DFG (Bonn, Germany) under grant TA 268/6-1. We thank R. Prang and T. Scherer (Karlsruhe Institute of Technology, Karlsruhe, Germany) for help with FIB−SEM measurements. 9026
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(21) Gille, W.; Enke, D.; Janowski, F. Pore Size Distribution and Chord Length Distribution of Porous VYCOR Glass (PVG). J. Porous Mater. 2002, 9, 221−230. (22) Aste, T.; Di Matteo, T. Emergence of Gamma Distributions in Granular Materials and Packing Models. Phys. Rev. E 2008, 77, 021309. (23) Hormann, K.; Tallarek, U. Analytical Silica Monoliths with Submicron Macropores: Current Limitations to a Direct Morphology−Column Efficiency Scaling. J. Chromatogr., A 2013, 1312, 26−36. (24) Nakanishi, K.; Takahashi, R.; Nagakane, T.; Kitayama, K.; Koheiya, N.; Shikata, H.; Soga, N. Formation of Hierarchical Pore Structure in Silica Gel. J. Sol-Gel Sci. Technol. 2000, 17, 191−210. (25) Liang, Z.; Ioannidis, M. A.; Chatzis, I. Geometric and Topological Analysis of Three-Dimensional Porous Media: Pore Space Partitioning Based on Morphological Skeletonization. J. Colloid Interface Sci. 2000, 221, 13−24. (26) Armatas, G. S. Determination of the Effects of the Pore Size Distribution and Pore Connectivity Distribution on the Pore Tortuosity and Diffusive Transport in Model Porous Networks. Chem. Eng. Sci. 2006, 61, 4662−4675. (27) Gao, X.; Diniz da Costa, J. C.; Bhatia, S. K. Understanding the Diffusional Tortuosity of Porous Materials: An Effective Medium Theory Perspective. Chem. Eng. Sci. 2014, 110, 55−71. (28) Keil, F. J. Diffusion and Reaction in Porous Networks. Catal. Today 1999, 53, 245−258. (29) Langford, J. F.; Schure, M. R.; Yao, Y.; Maloney, S. F.; Lenhoff, A. M. Effects of Pore Structure and Molecular Size on Diffusion in Chromatographic Adsorbents. J. Chromatogr., A 2006, 1126, 95−106. (30) Cimino, R.; Cychosz, K. A.; Thommes, M.; Neimark, A. V. Experimental and Theoretical Studies of Scanning Adsorption− Desorption Isotherms. Colloids Surf., A 2013, 437, 76−89. (31) Hlushkou, D.; Hormann, K.; Höltzel, A.; Khirevich, S.; SeidelMorgenstern, A.; Tallarek, U. Comparison of First and Second Generation Analytical Silica Monoliths by Pore-Scale Simulations of Eddy Dispersion in the Bulk Region. J. Chromatogr., A 2013, 1303, 28−38.
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