Morphological Analysis of Physically Reconstructed Silica Monoliths

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Morphological Analysis of Physically Reconstructed Silica Monoliths with Submicrometer Macropores: Effect of Decreasing Domain Size on Structural Homogeneity Daniela Stoeckel,†,‡ Christian Kübel,§ Marc O. Loeh,‡ 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: Silica monoliths are increasingly used as fixedbed supports in separation and catalysis because their bimodal pore space architecture combines excellent mass transport properties with a large surface area. To optimize their performance, a quantitative relationship between morphology and transport characteristics has to be established, and synthesis conditions that lead to a desired morphology optimized for a targeted application must be identified. However, the effects of specific synthesis parameters on the structural properties of silica monoliths are still poorly understood. An important question is how far the macropore and domain size can be reduced without compromising the structural homogeneity. We address this question with quantitative morphological data derived for a set of eight macroporous− mesoporous silica monoliths with an average macropore size (dmacro) of between 3.7 and 0.1 μm, prepared following an established route involving the sol−gel transition and phase separation. The macropore space of the silica monolith samples is reconstructed using focused ion beam scanning electron microscopy followed by a quantitative assessment of geometrical and topological properties based on chord length distributions (CLDs) and branch-node analysis of the pore network, respectively. We observe a significant increase in structural heterogeneity, indicated by a decrease in the parameter k derived from fitting a kgamma function to the CLDs, when dmacro reaches the submicrometer range. The compromised structural homogeneity of silica monoliths with submicrometer macropores could possibly originate from early structural freezing during the competitive processes of sol−gel transition and phase separation. It is therefore questionable if the common approach of reducing the morphological features of silica monoliths into the submicrometer regime by changing the point of sol−gel transition can be successful. Alternative strategies and a better understanding of the involved competitive processes should be the focus of future research.

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INTRODUCTION

The hierarchical structure of silica monoliths investigated in this work results from a complex formation process involving spinodal decomposition.7 During the competition between the sol−gel transition and simultaneous polymer-induced phase separation (into a hydrogel and a solvent phase), the structure is at some point frozen due to the advancing polycondensation of silica oligomers, resulting in a macroporous−microporous monolith. Through treatment with alkaline solution, mesopores (if desired instead of micropores) are introduced into the silica skeleton via Ostwald ripening in a second step, leading to a macroporous−mesoporous monolith structure. The prospect of adjusting structural parameters of the interskeleton macropore space and the intraskeleton mesopore space independently

Porous silica (SiO2) in monolithic column format is widely used today in separation science1−3 and heterogeneous catalysis,4−6 mainly as an attractive alternative to traditional particulate packings (monolithic vs particulate beds). Silica monoliths are prominent representatives of materials with hierarchical pore space architecture,7−10 and their distinctly bimodal pore size distribution is essential to their performance as a chromatographic or catalytic support. Typically micrometer-sized macropores form a continuous, highly permeable network of flow-through channels dedicated to advectiondominated transport by fluid flow through the support and toward the micropores (or mesopores) inside the silica matrix, in which diffusion-limited transport prevails and whose tailored surface chemistry and surface area are critical to the specific analyte−surface interactions in chromatography and catalysis.1 © XXXX American Chemical Society

Received: November 25, 2014 Revised: February 3, 2015

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found many applications in materials science, with focused ion beam (FIB)-SEM as a prominent representative of the portfolio of available methods.26,27 Because of its access, robustness, and versatility with regard to the investigated material, FIB-SEM has rapidly evolved into an eligible microscopy technique over the last few years, filling a gap in the field of tomographic methods.28 Compared to other three-dimensional (3D) imaging methods, FIB-SEM and serial block face (SBF)-SEM tomography are currently the only available methods that combine a resolution of a few nanometers with relatively large sample volumes, which are necessary to capture the micrometer-sized heterogeneities in a sample material. FIB-SEM and SBF-SEM nanotomography thereby offer new possibilities to analyze pore structures with dimensions and heterogeneities from the micrometer to the submicrometer scale.29−35 For an investigation by SBF-SEM, the simple combination of in situ ultramicrotomy and SEM, the sample material is sliced with a diamond knife, which works with soft polymeric materials30,33 but not with hard silica monoliths. A comprehensive 3D reconstruction of the macropore space of silica monoliths can be obtained by the FIB-SEM slice-and-view procedure.36 Here, we apply the FIB-SEM slice-and-view procedure to a set of silica monolith samples prepared with average macropore sizes from the micrometer down to the submicrometer range. We are specifically interested in detecting any change in the morphological features that accompanies the reduction of the average macropore size into the submicrometer range. The set of silica monoliths comprises five research samples prepared inhouse with average macropore sizes of dmacro = 0.1−3.7 μm (as determined by MIP) and three samples provided by Merck Millipore (Darmstadt, Germany) with average macropore sizes of d macro = 0.22−0.39 μm. Complementary MIP, N 2 physisorption, and SEM data are used to qualitatively assess the macropore and mesopore space. The FIB-SEM-based reconstructions are subjected to a model-independent morphological analysis of the macropore space, comprising the size distribution of void space and silica skeleton thickness as well as pore connectivity and tortuosity. The reconstructed models will also be useful in the future for simulations of fluid flow and mass transport aimed at a fundamental understanding of the transport properties of silica monoliths.37,38 Our immediate goal is to identify how the varied parameters of the applied synthesis protocol affect the morphology of the prepared silica monoliths, specifically if reducing the average macropore size of silica monoliths compromises their structural homogeneity.

provides a unique opportunity to design monolithic supports whose hydrodynamic properties (macropores), diffusion regimes, mass-transfer resistances, and surface areas (micropores vs mesopores) are tailored to the demands of specific applications. Therefore, a major goal is to understand the influence of the many synthesis parameters, e.g., temperature, polymer concentration, type of silica precursor, and pH value, on the resulting porous silica structure. Previous studies have addressed the influence of morphological features on the performance of monolithic silica columns applied in high-performance liquid chromatography (HPLC). Several groups have identified a large domain size (sum of average macropore size and average skeleton thickness) together with a systematic radial heterogeneity of the macropore space as the main drawbacks of silica monoliths.1,11,12 Both structural characteristics influence the extent of hydrodynamic dispersion occurring in fluid flow through the macropore space of the monoliths, and substantial effort has been devoted to reducing the domain size while preserving a high degree of structural homogeneity.13−16 These investigations are still in progress and have received increasing amounts of attention as the domain size reaches the submicrometer range.17 Commonly, a decrease in domain size is achieved by changing the concentration or kind of polymer (the phase-separation inducer) in the starting mixture,14,15,18,19 to manipulate the dynamics of the competitive processes of sol−gel transition and phase separation. However, a satisfactory analysis of resulting morphological features can be performed only on the basis of experimental techniques capturing the complete microscopic structure. Consequently, empirical studies of the relationship between synthesis conditions and performance parameters are helpful but incomplete as long as the “true” morphology of the monolithic samples remains unknown. Linking morphological parameters reliably to functional properties requires a thorough characterization of both pore domains (interskeleton macropores and intraskeleton mesopores), which includes an accurate characterization of the pore size distribution (PSD) as well as the distribution of topological properties, such as the pore connectivity, throughout the material. Until now, the pore spaces of silica monoliths have mainly been probed by bulk methods such as mercury intrusion porosimetry (MIP), N2 physisorption, inverse size-exclusion chromatography, and thermoporosimetry.20,21 To convert the data obtained from these methods into a PSD, one must make assumptions about the basic pore geometry; however, such assumptions are difficult to verify, particularly for disordered pore spaces such as those of silica monoliths. Furthermore, bulk methods cannot resolve local topological properties and their distribution in a material. Alternatively, two-dimensional (2D) scanning electron microscopy (SEM) and transmission electron microscopy (TEM) combined with subsequent image analysis provide model-free insight into the pore structure at nanometer resolution. In particular, SEM, which is easily accessible, is often applied to estimate the domain size. However, 2D SEM and TEM images offer no reliable depth information and thus lack the required morphological details. Confocal laser scanning microscopy (CLSM), which provides the necessary depth information, has been used for reconstructing the macropore space of silica monoliths,12,17,22−25 but CLSM cannot resolve structural features in the submicrometer range. Nanoscale tomography was introduced to overcome the limitations of methods providing only 2D information and has

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EXPERIMENTAL SECTION

Chemicals and Materials. Tetramethoxysilane (TMOS), poly(ethylene glycol) (PEG, Mn = 104), and urea were obtained from Merck Millipore (Darmstadt, Germany). Methanol (HPLC grade) and NaOH (99% p.a.) were supplied by Carl Roth (Karlsruhe, Germany). Azobis(isobutyronitrile) (98%), divinylbenzene, n-pentane (98%), acetic acid (99%), and basic aluminum oxide were purchased from Sigma−Aldrich (Steinheim and Taufkirchen, Germany). A Milli-Q gradient water-purification system (Millipore, Bedford, MA) delivered HPLC-grade water. Three research samples (Merck 0.22, 0.34, and 0.39) were provided by Merck Millipore as bare silica rods with dimensions of 100 mm length and 4.6 mm diameter. Silica Monolith Synthesis. The synthesis of the in-houseprepared silica monolith samples was performed following a known route.39 TMOS (5.6 mL) was added to a solution of PEG (1.20 g) and urea (0.90 g) in 0.01 M acetic acid (10 mL) at 0 °C and stirred for 20 min. Seven milliliters of the homogeneous solution was then B

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Langmuir transferred into a polypropylene (PP) plastic vial and allowed to react at 25 °C in a water bath for 20 h. Then, a hydrothermal treatment was performed at 80 °C. The monolithic rod was transferred to a glass vial and covered with a 9% (w/w) urea solution. The temperature was raised over 10 h from room temperature to 80 °C and maintained for another 10 h. Afterward, the monolith was slowly cooled to room temperature, transferred into a PP plastic vial, and washed with methanol for 7 days, during which the methanol was changed daily. Finally, the monolithic rod was dried at 70 °C for 1 h and then, after raising the temperature from room temperature to 330 °C over 15 h, calcinated at 330 °C for 10 h. During calcination, the organic moieties in the material were decomposed. One monolith sample (“standard”) was prepared by strictly following this standard protocol; eight more silica monolith samples with different average macropore sizes were prepared by varying the PEG amount in the starting sol, as listed in Table 1 (samples P − 0.30 to P + 0.30). For example, the monolith

region of interest (ROI). Using the Slice&View package of the instrument software, we applied a 30 kV Ga+ ion beam with a current of 0.90−19.9 nA (see Table S1 for the exact preparation parameters of each studied sample) to successively remove material with defined thickness from the sample surface while imaging each newly generated surface by SEM. The milling axis defined the z direction in the stack. Image Processing. The Slice&View image stack was aligned in IMOD V4.740 by cross-correlation of a nonsectioned area next to the ROI. Afterward, the y position of each slice was corrected for the inclined viewing angle of the SEM. Finally, images were cropped into a stack of 8-bit grayscale images. The resulting 3D data set dimensions and voxel sizes are also listed in Table S1. Images were segmented in AMIRA (FEI Company, Hillsboro, OR). Voxels were assigned as belonging to the solid phase (mesoporous silica skeleton) or a void space (macropores) by a thresholding algorithm and by using the brush tool. The segmented image stack was subjected to Gaussian smoothing using a kernel with a standard deviation of 3 pixels. Threedimensional rendering of the binarized data set was realized in AMIRA. Geometrical Analysis of Void Space and Solid Phase. After segmentation, images were analyzed on the basis of chord length distributions (CLDs) as shown by Courtois et al.41 using software written in-house with Visual Studio C# 2008 (Microsoft Corporation, Redmond, WA). To calculate the CLD for the void space, random points were generated in the void area of the image stack; from each point, 32 vectors were projected in angularly equispaced directions, as described previously.25,33,34 These vectors either hit the skeleton or project out of the image. Chords that projected out of the image were discarded. Resulting chords are the sum of the absolute lengths of an opposing pair of vectors, describing a straight distance between two macropore−silica interfaces. Points of origin were generated until a total of 106 chords was collected for each image stack. Chords were binned and displayed in a histogram. From chords generated in the solid skeleton phase, a CLD of the silica phase (which contains the unresolved mesopore network) was obtained in a similar way. Resulting histograms (CLDs) were fitted to a k-gamma function using the Levenberg−Marquardt algorithm. Topological Analysis of the Macropore Space. The reconstructed volumes of the macropore space were skeletonized and subsequently analyzed on the basis of algorithms available as ImageJ plugins (Skeletonize3D and AnalyzeSkeleton, respectively).42 The skeletonization procedure reduces the pore space to a branch− node network while both topological and geometrical information are preserved. The resulting topological skeleton can be used to characterize pore lengths, connectivities, and tortuosities.34,43 We determined the total number of junctions (nj), which were further distinguished by the number of branches they connect; that is, nt is the number of triple-point junctions (connecting three branches), nq is the number of quadruple-point junctions (connecting four branches), and nx is the number of higher-node junctions (connecting five or more branches). The average pore coordination number Zav was calculated as the average number of pores (branches) attached to a junction (node) according to

Table 1. Preparation Conditions for the Silica Monoliths and Summary of the MIP Analysis preparation conditionsa PEG [g]

MIP analysis dmacro (median) [μm]

macropore volume [cm3 g−1]

standard (P)

1.20

1.0

2.110

P − 0.30 P − 0.20 P − 0.15 P − 0.10 P − 0.05 P + 0.10 P + 0.20 P + 0.30 Merck 0.22 Merck 0.34 Merck 0.39

0.90 1.00 1.05 1.10 1.15 1.30 1.40 1.50 not available not available not available

19.0 8.6 5.9 3.7 2.0 0.3 0.1 0.1 0.22b 0.34b 0.39b

1.780 1.950 1.930 2.100 1.960 2.120 1.900 2.020

a

The amounts of TMOS (1.20 g), urea (0.90 g), and acetic acid (10.0 mL) in the reaction mixture were identical for all in-house-prepared silica monolith samples. bData provided by Merck Millipore (Darmstadt, Germany). sample referred to as P − 0.15 was prepared with 1.20 − 0.15 g = 1.05 g of PEG in the starting sol. The research samples received from Merck Millipore were prepared by a procedure similar to that for our in-house monolith samples.18 Assessment of Macro- and Mesoporosity. The interskeleton macroporosity and intraskeleton mesoporosity of the prepared macroporous−mesoporous silica monoliths were checked by standard MIP and N2 physisorption measurements (Table 1; Figures S1 and S2 in the Supporting Information). FIB-SEM Tomography. The macropore space of five in-houseprepared and three Merck Millipore silica monolith samples was reconstructed by FIB 3D slice-and-view analysis.36 The procedure encompassed sample preparation, image acquisition, image alignment, and image processing analogous to those in our previous publication.34 From each sample rod, an ∼0.5-cm-thick slice was cut and embedded in poly(divinylbenzene) to avoid charging effects, enhance image contrast, and prevent depth-of-focus effects within the pores. A description of the embedding procedure is provided in the Supporting Information. FIB slice-and-view tomography was performed on a dual-beam-FIB system (Strata 400S, FEI, Hillsboro, OR) at the Karlsruhe Nano Micro Facility, Institute of Nanotechnology, Karlsruhe Institute of Technology, Germany. The SEM unit was operated at an acceleration voltage of 5 kV. A focused beam of Ga+ ions was used first to induce the deposition of a protective Pt layer (∼1 μm thick) on the sample to reduce curtaining effects and then to create a clean surface of the

Zav = 3

nq nt n +4 +5 x nj nj nj

(1)

Furthermore, the pore-level tortuosity of the macropore space was estimated by analyzing the individual branches of the derived skeleton. The pore tortuosity is defined as the geodesic distance of a pore (di) divided by the Euclidean distance between the pore entrance and exit (deucl,i). From this information, the average macropore tortuosity τav is calculated from

τav = C

1 j

j

∑ i=1

di deucl,i

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Figure 1. Scanning electron micrographs of the in-house-prepared silica monolith samples (standard and P + 0.30 to P − 0.30). Details of the preparation conditions and MIP analysis results are given in Table 1. The SEM images of the samples were arranged in accordance with the deviation from the standard PEG concentration in the starting sol.

Figure 2. Illustration of the analytical work flow. The obtained image stack was segmented (white, solid phase; black, void space) and computed into a 3D reconstruction. The reconstructed volume was evaluated using the CLD approach; resulting CLDs were fitted with a k-gamma function, providing information about the average pore/skeleton size and the statistical dispersion of the pore/skeleton size distribution. In addition, the pore space was subjected to a skeletonization process to obtain pore tortuosities and pore coordination numbers.

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PEG/1.20 g TMOS) down to 0.1 μm for the sample prepared with the highest PEG concentration (1.50 g PEG/1.20 g TMOS) in our series. N2 physisorption experiments using the nonlocal density functional theory (NLDFT)-based evaluation (desorption branch, cylinder pore model)44 yield very similar mesopore size distributions with a range of 5−10 nm and a maximum at 7−9 nm for all silica monolith samples (Figure S2). A BET surface area of 550−700 m2/g and a mesopore volume of ∼1 cm3/g are typical for silica monoliths with mesopores in this size range.39 The data obtained from MIP and N2 physisorption measurements confirm that we prepared

RESULTS AND DISCUSSION

The macroporosity−mesoporosity of the nine silica monolith samples prepared in-house was ascertained first by standard characterization methods MIP and N2 physisorption (Table 1, Figures S1 and S2). The data in Table 1 show that the average macropore size was reduced by increasing the PEG concentration (at constant TMOS concentration) in the starting sol. The average macropore size dmacro as determined from the median of the MIP-derived macropore size distribution ranged from 19.0 μm for the silica monolith sample prepared with the lowest PEG concentration (0.90 g D

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Figure 3. Three-dimensional reconstruction of the macropore space of silica monolith samples with decreasing average macropore size (MIP-derived median values dmacro). (Top row) Merck Millipore research samples. (Middle and bottom rows) In-house-prepared samples. (Bottom left) Picture of an exemplary monolith sample after calcination.

pore space was scanned with chords of variable lengths. Measured chords are collected, and the resulting distribution of chords represents the relative frequency with which a certain length appears in the sampled volume (Figure 2, top row). The CLD is an accurate method for describing the phase distribution in a two-phase system, e.g., a porous medium, because it captures the complete geometry and does not rely on a predefined model of the pore geometry. Also, its evaluation principle is not subject to size restrictions, which makes it especially valuable in describing disordered systems with varying domain sizes. A mathematical description of the CLD is achieved by fitting the histogram with a k-gamma function, as shown previously.12,17,25,33,34,38 The k-gamma function has been delineated as a descriptor of the void space distribution in disordered materials based on a statistical mechanics approach.45 It is defined by the mean and the standard deviation of the CLD

macroporous−mesoporous silica monoliths with a systematically varied average macropore size at a preserved average mesopore size. For a first impression of the structural changes induced by the variation of the PEG concentration in the starting sol, the silica monolith samples were investigated by conventional 2D SEM. By visual inspection of the scanning electron micrographs (Figure 1), morphological differences between the silica monolith samples can be detected. The structure of the silica skeleton changes noticeably from a friable to a smooth texture with decreasing PEG concentration in the starting sol (samples P + 0.30 to P − 0.10), and for very large negative deviations from the standard PEG concentration (P − 0.15 to P − 0.30), the skeleton shows globular buildups. For a quantitative evaluation of the morphological changes accompanying a reduced average macropore size, we selected from the set of in-house-prepared silica monoliths the sample obtained with the standard protocol as well as two samples each with smaller (P + 0.1 and P + 0.2) and larger (P − 0.1 and P − 0.05) dmacro values than for the standard sample. Additionally, we included three Merck Millipore research samples with dmacro in the submicrometer range (Table 1). The macropore space of the selected silica monolith samples was reconstructed by the FIB-SEM slice-and-view procedure.36 After image segmentation, where individual voxels were assigned to either a void (macropore) space or the solid (silica) phase, the binarized data set was computed into a 3D volume representation. Figure 2 provides a detailed schematic of the adapted work flow including the morphological, i.e., geometrical and topological, analysis. The reconstructed volumes displayed in Figure 3 seem to suggest that the macropore space becomes more heterogeneous with decreasing dmacro. To quantitatively assess the change in macropore space heterogeneity, we used CLD analysis. For this approach the solid−void border of the reconstructed macro-

f (lc) =

k−1 ⎛ l ⎞ kk lc ⎜⎜ −k c ⎟⎟ exp Γ(k) μc k ⎝ μc ⎠

(3)

where lc denotes the chord length, μc is the mean chord length as a first-moment parameter, and k is a second-moment parameter defined by the mean and the standard deviation σ as k = (μc2/σ2). μc (or, alternatively, the mode of the CLD) is a measure of the size of the flow-through macropores (not to be confused with the macropore diameter as obtained from the interpretation of MIP data that is based on an assumed pore geometry). Parameter k relates the width and tail of the CLD to the mean chord length. This parameter is an indicator of structural organization (or homogeneity),45 with larger k values representing higher homogeneity, i.e., a narrower CLD with respect to μc. The separation efficiency of silica monoliths as HPLC columns has been shown to improve with decreasing μc and increasing k values,12,17,25 as μc and k can be directly related to the individual contributions to hydrodynamic dispersion E

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Langmuir occurring in fluid flow through the macropore space of the monoliths.38 A smaller value of μc is expressed as a lower extent of transchannel dispersion, which results from the flow velocity bias over the largest lateral distance across an individual macropore; larger k values represent a higher homogeneity on the scale of one to two macropores, reducing the velocity bias between neighboring flow channels and thus the extent of short-range interchannel dispersion. The k values for the macropore space of commercial silica monoliths were found to be as large as 2.6−2.9 (void space) and 3.4−4.0 (solid phase).12,17 For our five in-house samples (cf. middle and bottom rows in Figure 3), μc of the void space was found to decrease from 7.20 μm for sample P − 0.1 to 0.43 μm for sample P + 0.2 (Table 2), that is, with dmacro decreasing

Figure 4. Correlation of parameters k and μc derived from the CLD analysis. (○) In-house-prepared monolith samples. (□) Monolith samples from Merck Millipore. (Dashed lines serve as a guide to the eye.)

Table 2. Results of the CLD Analysis Using Equation 3 μc [μm]

k [−]

mode [μm]

sample

void

solid

void

solid

void

solid

Merck 0.22 Merck 0.34 Merck 0.39 P + 0.2 P + 0.1 standard P − 0.05 P − 0.1

1.87 2.06 2.16 2.00 1.98 2.70 2.75 2.70

2.19 2.35 2.38 2.55 2.42 2.64 3.10 3.16

0.65 0.92 0.95 0.43 0.85 2.48 4.14 7.20

0.40 0.62 0.80 0.20 0.54 1.59 3.14 5.21

0.30 0.47 0.51 0.21 0.41 1.57 2.63 4.55

0.22 0.35 0.46 0.12 0.32 0.99 2.14 3.55

concentration, provided other synthesis conditions remain constant. Following the classical description of the initial stage of spinodal decomposition, the co-continuous structure is reproduced by the superposition of a number of sinusoidal compositional waves.46,49 As the synthesis progresses, the concentration difference between the conjugated phase domains increases and the interfacial energy piles up. In order to reduce the interfacial energy, the system reorganizes the domain structures toward a smaller interfacial surface area. This is achieved by coarsening of the structure while the preformed connectivity is maintained (so-called self-similar growth). Eventually, the structure will fragment to minimize interfaces with energetically unfavorable curvature. Earlier phase separation (relative to freezing) results in coarser structures, whereas a larger PEG concentration in the starting sol slows down the phase-separation process, resulting in smaller domain sizes. Possibly, the structure of the monoliths with submicrometer macropores was frozen at too early a stage in the progressing phase separation before the bicontinuous structure was fully developed and homogenized. This early structural freezing could explain why the monolith samples with small macropore size (dmacro < 1 μm) feature a marked structural heterogeneity (lower k values). On the other hand, because of the strong hydrogen bonds between silanol groups and PEG chains, the PEG−silica oligomer complex contains a considerable number of silanol groups that are temporarily hindered from free condensation with other silanol groups. Hence, inter- and intramolecular condensation is slowed down as well. The separating domains remain viscous but deformable before they are firmly cross-linked by progressing condensation.23 A relatively mobile silica phase could facilitate an unfavorable deformation of the phase-separated domains until the sol−gel transition occurs. Hara et al.15 have shown that lower preparation temperatures can yield silica monoliths with a more homogeneous macropore space (as evaluated from 2D SEM images), and their finding was supported by a better chromatographic performance of such silica monoliths. The heterogeneity resulting from a disturbed coarsening process of the phase-separating domains could be reduced by increasing the viscosity of the reaction mixture. This might be a potential approach toward improved structural homogeneity of monoliths with submicrometer macropores; other possible approaches are a change in the phase-separation inducer or the silica precursor. Also, simply changing the molecular weight of the PEG has been found to affect the phase-separation process

from 3.7 to 0.1 μm. Concomitantly, μc of the solid phase also decreased from 5.21 to 0.20 μm. Samples with larger dmacro (>1 μm) gave k values of ∼2.70 and ∼3.15 for the void space and solid phase, respectively; samples with smaller dmacro ( 1 μm seems to plateau at around 3.15, as shown in Figure 7. Interestingly, the average pore tortuosity τavthe pore tortuosity τ is defined as the absolute branch length of a pore divided by the Euclidean distance between the pore entrance and exitlikewise increases (Figure 7). This could just be an inherent feature of increasing pore connectivity, i.e., the pore space curvature increases due to additional interconnected flow paths in the pore space. However, Figure 1 has shown that at decreasing macropore size the surface structure of the monoliths also undergoes a noticeable change. Hence, the smaller average tortuosity value τav determined for silica monolith samples with larger dmacro could also stem from a smoothing of the pore walls (and an accompanying straightening of the pathway inside the flow-through pore) during the prolonged coarsening process. According to the theory of self-similar growth,7,23 after a certain stage in the phase-separation process is reached, the structure only increases in size while keeping its connectivity. Because connectivity is known to be a very sensitive measure of the occurrence of a morphological transition,62 this correlation between pore size and connectivity would support the

Figure 5. CLD analysis of the macropore space of the eight silica monolith samples. The solid lines connecting the symbols represent the shape of the histograms after normalization by the respective mode (lc,mode) of a distribution. G

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Figure 6. Relative connectivity ratios ni/nj for junctions in the skeletonized void space, with nj, the total number of junctions; nt, the number of triplepoint junctions (connecting three branches); nq, the number of quadruple-point junctions (connecting four branches); and nx, the number of highernode junctions (connecting five or more branches).

experimental finding in which further reductions of the domain size failed to improve the separation efficiency of silica monoliths in HPLC practice has been based on speculation. It was presumed that below a certain domain size the structural self-similarity of the monoliths breaks down, i.e., the morphological homogeneity deteriorates. But whether this is a fundamental property of silica monoliths or a problem that could be overcome by appropriate preparation methods still has to be answered. Possibly, an alternative route to smaller macropores than by reducing the PEG concentration in the starting sol needs to be established in order to obtain silica monoliths with submicrometer macropores and high structural homogeneity. By changing specific parameters in the synthesis and comparing the resulting monoliths, the analytical approach presented here will enable material scientists to systematically improve the macropore space morphology and to identify morphological features causing mass-transfer limitations. In general, 3D reconstruction of the actual pore structure is superior to statistical modeling of a porous medium in approaching a quantitative understanding of the relationship among morphology, transport, and thermodynamic processes, as well as the response of the materials to mechanical stress. Eventually, this strategy will enable us to overcome current efficiency limitations due to structural features and also to synthesize materials tailored to specific applications. However, to achieve this objective, more thorough studies on the structural evolution mechanism of silica monoliths are required. The in situ visualization of the phase-separation and polymerization process with techniques providing a sufficient spatiotemporal resolution and the systematic modification and optimization of the process are thus the next challenges. Our results demonstrate that topological data acquired from physically reconstructed samples are indispensable to refining pore network models because they provide precise local and average pore coordination numbers. Such data will help to improve the predictive power of pore network simulations regarding the implementation of coupled diffusion−reaction schemes in catalysis or the transport and dispersion of solutes. Furthermore, the presented approach is expected to advance the MIP analysis of microscopically disordered, macroporous materials by advancing the morphological description of these pore networks and putting restraints on some of the freely adjustable model parameters used in fitting procedures applied to the acquired experimental data.

Figure 7. Average pore connectivity Zav (eq 1) and average pore tortuosity τav (eq 2) vs the mean chord length μc for the macropore space of the eight silica monolith samples (cf. Table S2).

hypothesis that the structure of the monolith samples with submicrometer macropores was frozen too early to reach its final pore coordination and structurally equilibrated state. Associated with the increase in pore connectivity (Figure 7), the interpretation of the CLDs for the void space in terms of the extracted k value needs to be reconsidered. Because the k value (cf. Figure 4) is dominated by longer chords that reach into adjacent pores and make up the tail of a CLD, the lower k values (wider CLDs) obtained for the samples with smaller dmacro may be a consequence of higher pore connectivity and not increased macropore space heterogeneity. A closer look at the actual data, however, reveals that the largest decrease in pore connectivity occurs between samples P + 0.2 and P + 0.1 (Table S2), and the k value for sample P + 0.2 is even slightly larger than for sample P + 0.1 (Table 2). Also, the absolute change in the average pore coordination number from Zav = 3.13 to 3.47 in Figure 7 is not very pronounced. For that reason, a slightly lower k value for more highly connected pores appears possible, but the overall effect is probably of little significance.

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CONCLUSIONS Nanoscale tomography was applied to a series of macroporous−mesoporous silica monolith samples (prepared with systematically decreased average macropore size) to physically reconstruct and analyze the morphology of their disordered macropore space. In this work, we have shown for the first time with quantitative morphological data that the homogeneity of silica monoliths indeed suffers when the average macropore size decreases to below ∼1 μm. So far, the debate about the H

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ASSOCIATED CONTENT

S Supporting Information *

Details of the assessment of the monoliths’ macro- and mesoporosity by MIP and N2 physisorption, respectively. Description of the embedding procedure for the monoliths, FIB-SEM tomography conditions, and results of the geometrical and topological analyses of the reconstructed samples. 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 their help with the FIB-SEM measurements. The three silica monolith samples (Merck 0.22, 0.34, and 0.39) and associated MIP data were kindly provided by Dr. Karin Cabrera from Merck Millipore (Darmstadt, Germany).

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REFERENCES

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