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On the Formation and Structure of Nanometric Polyhedral Foams: Toward the Dry Limit Robert W. Corkery* and Andrew Fogden‡ Physical Chemistry 1, Center for Chemistry and Chemical Engineering, Lund UniVersity, SE-221 00 Lund, Sweden ReceiVed August 13, 2007. ReVised Manuscript ReceiVed May 28, 2008 High surface area, high porosity, nanometric polygonal silica foams with hierarchically connected and uniformly sized pore systems are reported here. We observe a remarkable increase in foam cell sizes from mesoscopic to macroscopic dimensions upon swelling the self-assembled template with oil. The resultant structures resemble classical macroscopic soap foams and display, among other features, Plateau borders and volume fractions approaching the dry limit of 100%. In well-developed foams of this kind, dimensionally isometric polyhedral cells are connected by relatively short, flat cylindrical mesopores through polyhedral faces and micropores through the walls. For one sample, with approximately 75 nm diameter primary foam cells, we infer three separate sets of cell-connecting mesopores puncturing tetragonal, pentagonal, and hexagonal faces of the component polyhedra. A multiple step model of foam formation is discussed where an organic silica precursor progressively hydrolyzes and condenses as a growing flexible shell from the core-corona interface of oil-swollen triblock copolymer micelles or microemulsion droplets, inducing a clouding phenomena in the otherwise stabilizing poly(ethylene oxide) chains, leading to aggregation, deformation, and jamming to high volume fractions.
Introduction Macroscopic and microscopic surface-tension-based foams and foamlike networks are useful in many industrial contexts because of their utility in lightweight materials, insulation, packaging, fire-fighting, and so forth. Foams are also incredibly interesting structures in crystallography, mathematics, and physics because of their minimized surface energies and efficiency in partitioning of 3D space. Plateau established the overriding rules for their mechanical equilibrium, namely that foam cells are trivalent polyhedra, the polygonal faces of which are surfaces of constant mean curvature and meet at 120°, and with polyhedral edges meeting at the tetrahedral angle of cos-1 (-1/3) (approximately 109.47°). The most efficient partitioning of space (lowest S/V ratio) satisfying these rules is by an ordered foam known as the Weaire-Phelan structure,1 made up of two polyhedra packed into a cubic array in the Pm3jn space group. Lord Kelvin’s foam, made up of tetrakaidecahedra, remains the most efficient partitioning with a single polyhedral tile. Most foams are not symmetric tilings but random tilings of space, and thus their structures are complicated by their nonperiodicity. Matzke’s approach to construction of foams, by applying equal volume drops one at a time,2 was labor intensive. He subsequently analyzed these foams for various topological and geometric statistics including the number of unique polyhedra and occurrence frequencies of polygonal faces. Recently Kraynik et al.3,4 employed a computationally intensive approach to * To whom correspondence should be addressed. YKI, Institute for Surface Chemistry, Box 5607, SE-114 86 Stockholm, Sweden. Telephone: +46 850106071. Fax: +46 8208998. E-mail: Robert.Corkery@ surfchem.kth.se. ‡ Current address: Applied Mathematics Department, Australian National University, Acton ACT 0200, Australia. (1) Weaire, D.; Hutzler, S. The Physics of Foams, 1st ed.; Oxford University Press: New York, 1999. (2) Matzke, E. B. Am. J. Bot. 1946, 33, 58. (3) Kraynik, A. M.; Reinelt, D. A.; van Swol, F. Phys. ReV. E 2003, 67, 031403. (4) Kraynik, A. M.; Reinelt, D. A.; van Swol, F. Phys. ReV. Lett. 2004, 93, 208301.
simulate and analyze random foams, using a large number of polydisperse cells at the dry foam limit, that is, where the solid volume fraction is negligible. The structural analysis confirmed and extended many of Matzke’s and others’ findings, in particular suggesting the primary importance of the number of faces per polyhedral tile. Despite a significant body of publications devoted to the structure and dynamics of foams at various length scales, many aspects of foam structures remain understudied. Very little is known and has been published on the formation and structure of nanoscale random foams, mainly owing to the absence of real experimental examples near the dry limit. One approach involves concentrating spherical oil droplets beyond their jamming limit, which for random monodisperse sphere packings occurs at a volume fraction of approximately 64% (72% for highly polydisperse systems), and at which the coordination number is approximately 6, that is, a sphere contacts 6 neighbors.5 Beyond this jamming limit, the spheres begin to deform, with their coordination number rising to 13.7 for random foams at the dry limit. The process that allows this increase in coordination number in surfactant froths during drainage is a stick-slip-like shearing rearrangement in local parts of the foam. This probably also occurs during jamming of emulsion droplets. Mason et al.6 used osmotic pressure to jam silicone nanoemulsions to a volume fraction of 81%, during which they monitored I(q) using smallangle neutron scattering (SANS) to determine the structure factor for jammed emulsions. Surfactant-templated, ordered mesoporous silica materials have been known since the beginning of the 1990s7–10 when FSM-16 and MCM-41 materials were reported. In 1998, a second major (5) Gardiner, B. S.; Tordesillas, A. J. Rheol. 2005, 49, 819. (6) Mason, T. G.; Graves, S. M.; Wilking, J. N.; Lin, M. Y. J. Phys. Chem. B 2006, 110, 22097. (7) Yanagisawa, T.; Shimizu, T.; Kuroda, K.; Kato, C. Bull. Chem. Soc. Jpn. 1990, 63, 988. (8) Inagaki, S.; Fukushima, Y.; Kuroda, K. J. Chem. Soc., Chem. Commun. 1993, 680. (9) Beck, J. S.; Vartuli, J. C.; Roth, W. J.; Leonowicz, M. E.; Kresge, C. T.; Schmitt, K. D.; Chu, C. T.-W.; Olson, D. H.; Sheppard, E. W.; McCullen, S. B.; Higgins, J. B.; Schlenker, J. L. J. Am. Chem. Soc. 1992, 114, 10834.
10.1021/la801228x CCC: $40.75 2008 American Chemical Society Published on Web 08/19/2008
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Table 1. Summary of Sample Number, The Temperature and Oil Content of Its Synthesis, And the Following Properties of Its Calcined Silica Product: Primary Repeat Distance (USAXS and SAXS), Cell Size (TEM), Six Measurements of Pore Size, Volume and Specific Surface Area From N2 Sorption, and Type of Product (TEM and SEM)
# 25c 26c 27c 28c 29c 30c 31c 32c 33c 35c 37c 37cb 38c 40c 41c 42c 45c 46c 47c 48c
synth TMB/ USAXS SAXS TEM N2 pore N2 pore BdB-FHH BdB-FHH BET surface temp P123 d-space d-space cell size pore vol surface area size vol (°C) ratio (nm) (nm) (nm) (m2 · g-1) (nm) (cm3 · g-1) (cm3 · g-1) area (m2 · g-1) 35 55 75 35 55 75 35 55 75 35 75 75 55 35 55 75 75 75 75 75
1 1 1 2 2 2 0.5 0.5 0.5 0 5 5 0 0.167 0.167 0.167 0 7.5 15 22.5
27.7 33.5 22.4 28.9 48.3 25.8
23.5 30.5 24.1 27.1 9.8
54.6 11.0 22.7 27.6 11.8 52.3 75.7 73.9
27.0 35.9 67.5 28.6 34.4 55.0 29.4 27.9 67.2 11.3 73.5 11.8 11.3 23.6 29.1 10.4 73.8 99.5 131.6
BET surface area micropores (m2 · g-1)
28.9 41.5 57.0
2.38 2.86 2.66
2.38 2.77 2.13
1012 992 975
783 762 767
185 194 269
7.8 74.9 87.4
1.22 3.97 3.64
1.22 3.97
731 820
777 644 495
170 177 147
814
266
658
164
112.2
3.26
advance in this field was the report that block copolymer surfactants could be used to yield mesostructured materials11 (e.g., SBA-15) with unit cell size and wall thickness exceeding that previously achievable by the smaller alkyl-chain-based surfactant template systems. Further expansion in pore size was achieved by introducing a low molecular weight swelling agent into the more hydrophobic interior of the liquid crystalline template. Crystallographically ordered materials with 15 nm pores have been obtained by this route. Relatively high swelling agent content typically leads to pore systems with less crystallographic order and broader pore size distributions. These highly swollen systems have accordingly received less interest from material scientists; however, they can provide an ideal means to generate nanoscale foamlike material. Schmidt-Winkel et al.12,13 reported swelling of the p6mm hexagonal phase templated by the poly(ethylene oxide)poly(propylene oxide)-poly(ethylene oxide) triblock copolymer Pluronic P123 at 37-40 °C, using trimethylbenzene (TMB) to increase unit cell size from 6 to 12 nm, at a TMB/P123 weight ratio of 0.2-0.3. Beyond this ratio, they observed the transition to a spherical void-containing foam structure (so-called “mesocellular foams” or MCFs) with pore diameters from 22 nm to a maximum of 42 nm (at a TMB/P123 ratio of 2.5), having a maximum pore volume around 2.3-2.4 cm3 · g-1 from nitrogen sorption, corresponding to around 84% porosity. They describe the foam cells as uniform, slightly deformed spheres, with windows of 8-22 nm diameter connecting cells and tunable window size using varying amounts of ammonium fluoride.14 They postulated that the transition is driven by a need to decrease the micelle surface-to-volume ratio as more oil is added, though with little change in the mean curvature of the system. (10) Kresge, C. T.; Leonowicz, M. E.; Roth, W. J.; Vartuli, J. C. Nature 1992, 359, 710. (11) Zhao, D.; Feng, J.; Huo, Q.; Melosh, N.; Fredrickson, G. H.; Chmelka, B. F.; Stucky, G. D. Science 1998, 279, 548. (12) Schmidt-Winkel, P.; Lukens, W. W., Jr.; Zhao, D.; Yang, P.; Chmelka, B. F.; Stucky, G. D. J. Am. Chem. Soc. 1999, 121, 254. (13) Lettow, J. S.; Han, Y. J.; Schmidt-Winkel, P.; Yang, P.; Zhao, D.; Stucky, G. D.; Ying, J. Y. Langmuir 2000, 16, 8291. (14) Schmidt-Winkel, P.; Lukens, W. W., Jr.; Yang, P.; Margolese, D. I.; Lettow, J. S.; Ying, J. Y.; Stucky, G. D. Chem. Mater. 2000, 12, 686.
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875
phase foam foam asymm foam foam foam asymm foam wormy foam foam foam p6mm foam foam p6 mm p6 mm foam asymm foam? onion foam foam foam
Schmidt-Winkel et al.15 used SANS to examine the template droplets in the absence of a silica source and found that block copolymer micelle size increased with both TMB content and temperature. They obtained linear fits of hard-sphere micellar size versus cube root of the TMB content, as predicted for a linear swelling law. At 40 °C, they observed a leveling off of the swelling above a TMB/P123 ratio of 0.5 and a monodisperse diameter around 25 nm for the HCl-H2O-P123-TMB system. Addition of ethanol allowed swelling of the (silica-free) micelles to over 50 nm. Bhattacharya and Gubbins16 used a lattice Monte Carlo approach to modeling the formation of the foams. They found that silica was important in stabilizing the oil-rich templates during mesocellular foam formation, predicted pore sizes of 40-70 nm at oil/surfactant ratios of 1.5-2, observed a simulated transition via a lamellar phase (rather than an undulating cylinders transition structure13), and qualitatively simulated window pores between cells. They proposed that the stabilization effect of silica on the ternary system worked by enhancing the oil solubility of the amphiphiles. For the oil-water-surfactant system at high oil, they simulated a phase separation into surfactant-rich and oil-rich phases, whereas when silica was present, the phase separation was into surfactant-rich and water-rich phases. They offered no physical-chemical explanation for this. The work reported here examines the expansion of silica foam cell sizes as a function of swelling agent beyond those previously reported, in particular by extending the foregoing studies to elevated temperature. This yields polygonal foams with pores beyond 100 nm and porosities up to 90%. Foam structures obtained are systematically characterized using scanning electron microscopy (SEM), transmission electron microscopy (TEM), nitrogen sorption, and small- or ultrasmall-angle X-ray diffraction (SAXS or USAXS).
Materials and Methods The silica foams were produced by the following procedure. A total of 2 g of the triblock copolymer EO20PO70EO20 (Pluronic P123, BASF) was dissolved in 45 mL of H2O and 30 mL of 4 M HCl with (15) Schmidt-Winkel, P.; Glinka, C. J.; Stucky, G. D. Langmuir 2000, 16, 356. (16) Bhattacharya, S.; Gubbins, K. E. J. Chem. Phys. 2005, 123, 134907.
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Figure 1. USAXS I(q) versus q patterns with linear intensity scales from (a) foam 32c (inset: same data shown with log intensity scale) and (b) foam 37c.
stirring in a 125 mL Teflon bottle and heated to constant temperature (35-75 ( 5 °C) in a water bath. Oil (1,3,5-trimethylbenzene, TMB), if used, was added and mixed for 1 min at high stirring (ca. 1000 rpm), producing a milky dispersion. Next, 4.3 mL of tetraethylorthosilicate (TEOS, 98%) was added with high stirring maintained for 1 min and subsequently slowed to ∼250 rpm. A dispersed white precipitate formed after 5, 18, or 60 min (at 75, 55, or 35 °C, respectively). After a further 18-24 h at constant temperature ((5 °C), the stirring was stopped, and the dispersion was opaque and milky. The vessel was then heated at 80 °C without stirring for an additional 1-2 days, forming a floating loose floc. The height of the floc column was greater for higher temperature and/or higher oil content syntheses and was used to qualitatively assess the openness of the structure formed. Excess solvent was poured off, and the precipitate was filtered (with difficulty for low-temperature, high oil runs), washed with excess water, air-dried at room temperature or 50-70 °C to a solid powder, and then weighed. Dry samples were then calcined at 550 °C in air for 3-24 h. Selected samples were subjected to further calcinations at 700, 850, and 1000 °C for up to 24 h. TEM samples were prepared by evaporating sonicated ethanol dispersions of the product onto Cu grids. Imaging was carried out at 120 kV on a Philips CM120 BioTWIN Cryo microscope fitted with a Gatan biofilter (GIF100) and a Gatan MSC 791 chargecoupled device (CCD) camera, and at 200 kV on a JEOL 2000FX microscope. SEM images were collected on samples after platinum coating (ca. 4 nm thick) at 2-15 kV using a Hitachi 4500 field emission scanning electron microscope (FESEM). Nitrogen sorption analysis was carried out at 77 K on a Micromeritics ASAP 2400 instrument using sample sizes of around 0.08 g. Pore sizes were obtained from the adsorption and desorption branches of the isotherm using the BdB-FHH method.17 SAXS spectra were collected over 2 h using Cu KR radiation with a wavelength of 1.542 Å (generator settings: 50 kV and 40 mA; generator: Seifert ID 3000) and an evacuated Kratky compact camera configuration, and detected using a position sensitive wire (OED 50M, MBraun, Graz; 1024 channels, each 53.6 µm wide). USAXS spectra were collected using Cu KR radiation with a wavelength of 1.542 Å (generator settings: 50 kV and 280 mA) and a hybrid Bonse-Hart/Kratky camera.18 Data were collected for 3 min every step (2” of arc) in the USAXS region for sample 37c.
Results Products. Total yield weights for the experiments were assessed by comparing input masses to dry weights of SiO2. The yields were usually high, with a median of 83% (standard (17) Lukens, W. W., Jr.; Schmidt-Winkel, P.; Zhao, D.; Feng, J.; Stucky, G. D. Langmuir 1999, 15, 5403. (18) Konishi, T.; Yamahara, E.; Furuta, T.; Ise, N. J. Appl. Crystallogr. 1997, 30, 854.
deviation: approximately 15%) after all process steps. Losses were mainly incurred in transfers and filtering, but they could be made near quantitative. Median weight loss on calcination of dried samples was 82% of the expected weight loss (with 15% standard deviation). The amount of water retained and the amount of oil lost during drying was the uncertainty in these numbers. We found that experiments producing homogeneous foam products were readily reproducible. For all samples prepared with TMB/P123 ratios between 0.5 and 5, homogeneous foams comprised the vast majority (>95%) of the yield. Beyond a ratio of 5, small amounts of oil separated from the microemulsion droplets, giving a mixture of foams and curved silica sheets, probably templated by larger emulsion droplets. Below 0.5, foams occurred together with various other minor phases including 2D hexagonal (p6mm) SBA-15. Foam yields and homogeneity were assessed qualitatively using extensive TEM and SEM imaging and arguments based on product density, surface area, X-ray scattering, and nitrogen sorption isotherms. Table 1 summarizes the matrix of samples and their key measured parameters discussed below. Small- and Ultrasmall-Angle X-ray Scattering (SAXS and USAXS). SAXS and USAXS data are reported in Table 1 for 13 foams. The scattering curves I(q) exhibited sharp diffraction maxima for all foams having dimensionally isometric cells. All such samples showed at least two or three peaks in each curve, with some foams yielding four peaks. All products displayed the usual broad wide-angle X-ray diffraction maxima typical of amorphous silica walls (not shown), with no other peaks. The q-values of the first peaks for both USAXS and SAXS profiles for the foams are given as equivalent d-values (q ) 2π/d) in Table 1 and Figure 7. Foams synthesized with the P123/oil template system can be tuned to d-spacings ranging from 22 nm to at least 76 nm, and even beyond 100 nm. The data show that foam cell size increases proportionally to the cube root of the added TMB content and also increases with temperature. Figure 1a is the scattering profile for a homogeneous isometric foam formed at 0.5 TMB/P123 and 55 °C, clearly displaying three maxima and one shoulder. From extensive TEM imaging (including tilt series) of this foam 32c (and others; see below), it was evident that spatially periodic positional ordering of cells is not common, presumably owing to cell-size polydispersity. A very rare exception was stacks of random ABA- and ABC-type close packed cell layers apparently formed near the vessel walls. Nonetheless, fitting of the USAXS data to known cubic and hexagonal motifs was attempted. A hexagonally close packed (hcp) structure fit the data reasonably well (calculated q-values:
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Figure 2. Series of spherical to polyhedral foams with increasing swelling agent. Scale bar at bottom left is 100 nm and is the same for all images. Images are of samples (top row) 41c, 32c, and 26c; (middle row) 29c, 30c, and 37c; and (bottom row) 46c, 47c, and 48c.
0.024, 0.043, and 0.060 Å-1; observed: 0.024, 0.042, and 0.061 Å-1). A reasonable fit could also be found for a face centered cubic (fcc) lattice (calculated: 0.024, 0.044, and 0.059 Å-1). A body centered cubic structure gave calculated values slightly different from those observed, and a simple cubic structure did not fit well. This suggests that the foam structure may have an average structure related to hcp or fcc structures or that scattering is dominated by small areas of ordered mesocrystalline lattices that are buried within particles and are inaccessible to TEM imaging. Transmission Electron Microscopy. More than 560 TEM images were recorded to characterize the foam structures and assess the effect of oil swelling and temperature (see Figures 2 and 3). Silica wall thicknesses determined from TEM images were ∼3.8-4.5 nm for most foam samples (e.g., 4.5 nm for foam 37c), independent of cell size. The transition from distorted spherical cellular foams to distinctly polyhedral cellular foams (PCFs) occurred for TMB/P123 ratios between 2 and 5. However, even the distorted spherical cells had a polyhedral nature down to a TMB/P123 ratio of 0.167 at 55 °C. The critical radius of curvature on passing from spherical to polyhedral cells is likely a function of the stiffness of the silica walls during formation, though a full analysis was not undertaken. Scanning Electron Microscopy. Figure 4a clearly shows micropores roughly less than 2 nm in diameter set in the microtextured walls of every visible cell. The spherical nature of cells when uncoordinated, and some 120° junctions of three cell clusters, typical of classical soap foams, are also apparent. Figure 4b shows exterior foam cells and interior polygonal silica froth texture, with the latter probably exposed during a shear from the SEM sample preparation knife. The highly packed interior in this image suggests that the foam cells are very close to tiling 3D space without gaps, and is indicative of jamming efficiencies approaching 100%. Figure 4b also indicates the average cell size is maintained through volumes several orders of magnitude larger than individual cells. Foams 47c and 48c were also imaged using SEM (not shown), and they displayed similar textures, though debris-covered. The debris is thought to originate from the breakage of large shells templated on phase separated oil (as seen beyond TMB/P123 ratios of 5).
Figure 3. After calcining foam 37c at 550 °C, it was then further calcined at (a) 850 °C for 16 h and (b) 1000 °C for 24 h. Note in (a) that the cells with rounded constant curvature on the exterior of the foam cell aggregate. (c) Foam 48c synthesized with the highest oil content (TMB/P123 ratio of 22.5). Of 185 cells in this nearly close packed 2D monolayer, 95% are 5-, 6-, or 7-sided, with approximately 120° vertices. Average number of sides is 6.07, roughly as expected for a 3-connected 2D network.
Nitrogen Sorption Experiments. The sorption isotherms for selected calcined foams (and the p6mm SBA-15 material, sample 35c) are shown in Figure 5. In SBA-15 and all three foams, the progression of the relative pressure of condensation increases as expected for increasing pore sizes from 7.8 nm for SBA-15 to 74.9 nm for foam 37c. The polyhedral foams exhibit pronounced
Formation/Structure of Nanometric Polyhedral Foams
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Figure 4. SEM images of foam 37c: (a) microporous spherical cells on the exterior of a foam particle and (b) foam with both interior and exterior surfaces, with spherical cells on the exterior and space-filling polygonal cells in the interior. Scale bars 100 nm.
Figure 5. N2 isotherms for the calcined samples: (a) 35c SBA-15, (b) 28c foam, (c) 29c foam, and (d) 37c foam.
hysteresis that is qualitatively different from that displayed by the SBA-15 material of Figure 5a. In particular, for each foam, the adsorption branch during condensation is steeper than its desorption branch. Further analysis of the gas sorption and NMR cryoporometric freezing/melting behavior has been reported elsewhere.19 Pore size distributions for selected foams were calculated from their isotherms using the BdB-FHH method,17 and the distributions derived from the adsorption and desorption branches for (19) Vargas-Florencia, D.; Furo´, I.; Corkery, R. W. Langmuir 2008, 24, 4827.
foam 37c are given in Figure 6. In such well-formed foams with dimensionally isometric cells, the adsorption branch gives a clear and significant peak in the pore size distribution. This is interpreted as the size of the primary cellular pores. Ready and fast access to these pores is afforded by the large number of micropores and mesoporous windows through polygonal cell faces, providing a rapid transport of nitrogen throughout the sample during condensation, as reflected in the very steep branch of the adsorption isotherm. During desorption, the less steep isotherm is interpreted as an ink-bottle type effect where micropores remain blocked and mesoporous windows act as the conduits for gas
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Figure 6. Pore size distribution for foam 37c (5:1 TMB/P123) using the BdB-FHH method: (a) from the adsorption branch, with a peak near 75 nm and (b) from the desorption branch, with peaks near 8, 15, and 24 nm.
suggests that the TEM imaging is reasonably representative of these structures. In the case of foam 37c, the TEM pore diameter of 73.5 nm with a standard deviation of 12.7 nm was determined from 72 separate cell measurements. The polydispersity can be estimated as about 45% for this sample (mean/standard deviation for number averaged data). In comparison, the polydispersity for the surfactant-water micelles was 15-19% from neutron and light scattering.20
Discussion Figure 7. Foam cell and pore size increase with increasing trimethylbenzene content, corresponding to foams synthesized at 75 °C. SAXS and USAXS rescaled primary peak positions (triangles, filled and unfilled, respectively); TEM cell diameter (filled circles); SEM cell diameter (open squares); peak in N2 adsorption pore size distribution (open circles); Spherical cell diameters from a comparative study at 40 °C14 (open tilted squares). The dashed line is a calculated swelling trend (asymptotically linear with increasing oil) based on a constant number of micelles/cells during swelling and an initial size of 35 nm for a TMB/P123 ratio of 0.167. The total calculated cell volume increases 8-fold as the radius is doubled (a simple model to determine the relative increase in cell size for a monodisperse system with added oil).
evaporation. Since these are smaller than the primary cells, they remained filled with gas until much lower p/p0 than required for primary cell filling, hence the hysteresis. The pore-blocking effect during desorption amounts to a capillary resistance. In most of the well-formed foams examined here, a single desorption peak was observed, suggesting that the window pores controlling relative desorption pressure are of a uniform average size. In the case of the sample foam 37c having highest porosity (90%) and specific pore volume (almost 4 cm3 · g-1), and thus the closest to the dry foam limit, a series of three desorption peaks are observed (Figure 6b). We interpret these as a set of different sized windows through the polyhedral cell faces, as discussed below in some detail. Swelling of Foams: Combined SAXS, USAXS, TEM, SEM, and N2 Data. In Figure 7, the fit of various data to the predicted trend line suggests the main influence on the swelling beyond 50 nm is primarily due to the entrained oil. Other factors affecting micelle size are addressed later in the discussion section. Cell diameters are obtained by rescaling the d-spacing of the main peak in SAXS and USAXS by a factor (1.3) determined from a SANS study on jammed nanoemulsions6 (see below). The TEM cell sizes are based on averaging many measurements of wall to wall diameters for individual cells and then are averaged over many cells and many particles in different parts of the TEM grid. The good agreement with rescaled scattering predictions
Foam Cell Sizes from X-ray Scattering. In a previous SAXS study,12 the cell sizes of calcined mesocellular foams (with spherical cells reported up to 40 nm in diameter) were derived by fitting I(q) to a form factor, F(q)2, for spheres. However, I(q) contains information about the interactions between cells, and these dominate the intensity profile when the cells are packed together in a foam. The interaction terms are primarily due to positional ordering, and their contribution to scattered intensity is captured in an effective structure factor Seff(q) (only “effective” because the shape changes from spherical to polyhedral). Essentially Seff(q) ) I(q)/F(q). For micellar systems, the structure factor will dominate the scattering intensity at high volume fractions, and the form factor fitting is only valid at low volume fractions. The structure factor for random foams could be determined by Fourier transformation of real-space data sets of simulated foams such as those of Kraynik et al.3,4 However, we are not aware of any structure factor determinations for foams near the dry limit. Accordingly, we simplify the analysis by deriving a factor relating general foam cell diameter to a peak q-value close to the dry foam limit. Mason et al.6 report I(q) data as a function of volume fraction (up to 81%) for a series of dilute through highly jammed nanoemulsion droplets. Extrapolation of their plot of q(φ)a versus volume fraction φ to the dry foam limit then uniquely defines the cell diameter. This is more easily visualized by replotting Figure 5 of Mason et al.6 as our Figure 8 below. As the positional ordering dominates the intensity profile at high volume fractions, the q-value for I(q) maxima (from S(q) dominance) will not depend upon whether the diffracting element is, for example, a sphere or a shell. Therefore, we assume that the data of Mason et al.6 for spheres can be applied to our case of shells to determine cell size. A second assumption is that the general trends continue to the ultimate dry foam limit at 100%. (20) Lettow, J. S.; Lancaster, T. M.; Glinka, C. J.; Ying, J. Y. Langmuir 2005, 21, 5738.
Formation/Structure of Nanometric Polyhedral Foams
Figure 8. Plot of volume fraction versus the ratio of primary to secondary peak position (solid squares) and the ratio of known sphere diameter to primary peak position (solid circles). The fit lines are visual aids.
Given this, at pore volume fractions of 85-90% for foams in this study, from Figure 8, it seems quite reasonable as a first estimate to use a factor of 1.30 to rescale primary d-values for I(q) scattering maxima to effective foam cell sizes. As an example, the scattering maximum for foam 37c occurs at a d-spacing of 54.6 nm, thus corresponding to a foam cell size of 71.0 nm, in excellent agreement with the cell size determined from other methods (see Table 1 and Figure 7). The ratio of primary to secondary peak d-values in Figure 8 appears to converge to approximately 1.71 or 3, very close to the observed value in all USAXS scattering curves I(q) measured here (1.7-1.8) for large-celled foams and slightly lower than the SAXS-determined ratios (1.8-1.9) for the smaller-celled foams. As shown in Figure 7, cell diameter follows an approximately linear trend with the cube root of TMB content. The extent of the swelling behavior is reasonably well predicted using our simple equivalent volume sphere model for foam cell polyhedra with increasing volume of oil and an initial value set at the lowest observed cell spacing. By taking an initial value of the sphere diameter as equal to an observed SAXS cell diameter (specifically, 35 nm at a TMB/P123 ratio of 0.167), other factors such as the amount of water entrained in the EO part of the micelle or microemulsion droplet are implicitly included. Factors Influencing the Swelling of Triblock Copolymer Micelles. Many factors influence the formation, stability, structure, and swelling of block copolymer micelles, and these in turn must be considered in developing a reasonable understanding of the final foam structures obtained when templating micelles and microemulsion droplets. A short review of the structure of Pluronic micelles and the contextually relevant factors to be considered in developing a model for foams and their swelling as a function of oil and temperature is given in the Supporting Information. Formation of Polyhedral Foams. On integration of the structural information obtained from the polyhedral foams, using several lines of independent experimental evidence and previous studies on SBA-15 formation,21–23 a likely picture of polyhedral foam formation (beyond the critical oil required for polyhedral cells) emerges. A seven-stage model is given when the order of addition is H2O-HCl-P123-TMB-TEOS: 1. Formation of dispersed, swollen spherical micelles or microemulsion phase with TEOS partitioning to two pools: (21) Flodstro¨m, K.; Teixeira, C. V.; Amenitsch, H.; Alfredsson, V.; Linde´n, M. Langmuir 2004, 20, 4885. (22) Flodstro¨m, K.; Wennerstro¨m, H.; Alfredsson, V. Langmuir 2004, 20, 680. (23) Epping, J. D.; Chmelka, B. F. Curr. Opin. Colloid Interface Sci. 2006, 11, 81.
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the oil-rich cores and emulsified TEOS droplets in the aqueous phase. 2. Hydrolysis of TEOS near the core-corona interface and at the surface of emulsified TEOS droplets and subsequent partitioning of hydrolyzed species to the corona from both TEOS pool surfaces. (Note that if prehydrolysis of TEOS is employed, oligomeric silica species are expected to partition directly to the corona.) 3. Formation of a flexible silica/EO composite shell in the corona via partial condensation of hydrolyzed silica species starting near the core-corona interface and extending outward, dehydrating and contracting the corona and decreasing the effective length of EO groups that otherwise sterically stabilize microemulsion droplets in the water continuum. 4. Phase separation, precipitation, or clouding out of swollen micelles or microemulsion droplets into polydisperse random spherical packings driven by net attractive forces. 5. Jamming, deformation, and topological rearrangement of individual droplets, drainage of aggregates driven by Laplace pressure differentials between faces and Plateau borders, and increase in polyhedral coordination number as space filling becomes more efficient. 6. Irreversible “zippering” condensation of silanols on apposed droplets and further condensation of silicate species to higher polymers and degrees of cross-linking to further highly pack the polyhedral aggregates. 7. Formation of pores (holes) in the faces as the surface area of each original spherical cell increases at roughly constant volume during deformation and as a result of wall shrinkage due to increased silica condensation in and at the surface of the film. In addition, holes grow by hole-fusion/dilation during calcination. 1. Oil Swollen Micelle/Microemulsion Formation. Initially, the P123 molecules form spherical micelles in the aqueous, acidic medium, with almost complete partitioning of P123 from the aqueous phase, particularly in the presence of oil as discussed above, including increase in micelle size with added oil and effects of HCl, ethanol, and salts. Oil in the core also ensures the PO groups are likely dehydrated and EO groups are almost completely expelled to the corona, unlike the case of the oil-free systems. The EO groups in the corona are likely charged due to attractive hydrogen bond interactions with H3O+ ions in the acidic environment. These micelles remain dispersed through electrosteric repulsion of their charged EO coronas. 2. TEOS Hydrolysis. Hydrolysis of TEOS occurring at the interface of the hydrophobic pools of TEOS produces ethanol, and this will exert various complex effects on the self-assembly and kinetics of further hydrolysis. Of primary importance, it will reduce the surface tension between the hydrophobic pools and their media, thus inducing a nonlinear increase in the hydrolysis rate via increased interfacial areas at the core-corona boundaries and the TEOS-water interface. In acidic media, the metastable hydrolysis products are small linear chains and rings of low molecular weight oligomeric species, and these consequently enrich the corona with silica precursor species. With the addition of TEOS to oil-free P123-HCl-water template systems, spherical micelles are found prior to any precipitation (see below), and therefore, it is likely that the oil-swollen micelles here are also spherical until after the postprecipitation deformation. 3. Partial Condensation of Silica in Corona. In SBA-15 formation from oil-free templating, this stage is reported to be
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initiated at the core-corona interface,24 with a timing of approximately 5-25 min depending on reactants and conditions.21,22,24,25 This makes sense, as EO groups in the inner core and their closely associated hydronium ions and hydrolyzed TEOS products are in closer average proximity than the less dense outer corona, and thus, partial condensation could proceed faster due to a higher rate of silanol-silanol encounters. The presence of an oil interface coincident with the core-corona interface in oil-swollen systems could enhance this effect as the boundary will be a sharper one and diffusive crowding of the various inner corona hydrophilic species may be expected. The decreasing number of hydroxyls per Si vertex in the developing (and densifying), partially cross-linked silica network growing from this interface will allow some decoupling from the EO chains (due to less hydrogen bond interactions), but will eventually result in a volumetric contraction of the entire corona as the chains become trapped in the compacting silica network. This contraction of the corona during cross-linking has been observed in the SBA-15 system using in situ synchrotron SAXS.21 EO chains exposed at the exterior of micelle/microemulsion droplets become effectively shorter as their mobility is restricted by the underlying and increasingly condensed, though flexible, silica network through which they penetrate. 4. Micellar Aggregation, Phase Separation, and Precipitation. The increasing loss of EO chain conformational freedom, corona dehydration, decreasing coronal charge and steric stabilization, and increasing attractive van der Waals forces between oil cores (as the corona shrinks) all are probably factors in micellar aggregation and precipitation. The flexibility of the silica network during the early part of this stage is critical to the formation of polyhedral foams, as it is for SBA-15. It is known from electron paramagnetic resonance (EPR) measurements that this coat can be flexible for several hours after initiating synthesis of SBA15,24 and also from the observed deformation of aggregated spherical micelles to elongated micelles occurring after flocculation and precipitation.22 In the foam syntheses reported here, the precipitation time was independent of the oil content, so these observations can be applied to foams, that is, the precipitation occurs around the same time and for similar reasons as for SBA15 synthesis. For our foams, precipitation times are temperature dependent (59, 18, and 5 min at 35, 55, and 75 °C, respectively, for a TMB/P123 ratio of 0.167, as expected if precipitation occurs via increased silanol condensation reactions (in the lower EO corona) and the associated destabilization of the micellar dispersion. The timing of precipitation for the low-temperature syntheses here is coincident with the development of initial hexagonal order in SBA-15 synthesized at 35 °C by Flodstro¨m et al.21,22 Significantly, this is well before convergence to the final intensities for all four main reflection peaks in SBA-15 (92 min), and thus, by analogy, the foam walls here are incompletely polymerized at precipitation time, allowing their later contraction and deformation to polyhedral cells. Since higher temperature foams precipitated faster, this lends weight to the argument that flocculation of micelles is controlled by silica condensation rate and that, largely independent of temperature, a similar composition of polymer, TEOS, HCl, and TMB will precipitate as spherical micelles with flexible walls at roughly the same degree of total silica condensation, that is, partially complete. The micropores (up to 2 nm) through the silica cell walls of calcined foams obtained here (see Figure 3) indicate that, when micelle aggregates form, bundles of silica-
free EO chain loops protrude through apposed, condensing silica surfaces and come into contact during flocculation, either by clouding out (and perhaps driving aggregation) or as a consequence of other attractive mechanisms inducing flocculation. 5. Deformation, Jamming, and Topological Rearrangements. The final polyhedral geometry of individual foams cells (see Figures 2–4) must occur after hydrolysis and probably during and after precipitation, and prior to substantial intermicellar silica condensation. As the hydrolyzed silica species continue to condense and the corona of individual micelles continues to shrink, the loose aggregate will also shrink until the condensation front approaches the micelle surfaces. At this time, it is most likely that the loosely packed individual micelles undergo polyhedral deformation. The driving force for the deformation is probably similar to that for the phase separation, that is, due to net attractive hydrophobic interaction of EO groups. This reduces the surface area between intermicellar water and dehydrated, hydrophobic EO groups trapped at the micelle/ microemulsion droplet. The exit of water through developing drainage channels is spontaneous and analogous to water expulsion leading to net attractive forces between hydrophobic chains during classical surfactant micellization.26,27 Therefore, differential Laplace pressures within the draining aggregate tend to equilibrium via formation of foam features such as Plateau junctions and so forth. Mechanistically, this would resemble a zipper action (see Figure 9) for progressive micellar fusion that radiates away from points of closest micellar contact in the loosely bound aggregates. As the micelles jam to higher packing fractions, the same mechanism will drive the aggregates to undergo topological transformations that increase the average micellar coordination number from around 6 to approaching 13.7. This is conditional upon relatively low degrees of covalent intermicellar cross-linking. Intercoronal water produced from condensation reactions during deformation would be expected to drive some degree of microphase separation of clouded-out EO groups and silica, with silica moving toward hydrophilic Plateau borders and EO groups moving to the center of the growing, less-hydrophilic polyhedral faces, which can later result in intercellular mesopores. The effect of NaF on similar materials supports this idea.12 6. IrreVersible Silica Cross-Linking of Micelles within the Aggregates. During and after jamming to very high volume fractions, silica condensation will occur across micellar/microemulsion droplet interfaces and irreversibly arrest further topological rearrangements. A zipping style of silanol condensa-
(24) Ruthstein, S.; Frydman, V.; Goldfarb, D. J. Phys. Chem. B 2004, 108, 9016. (25) Impe´ror-Clerc, M.; Grillo, I.; Khodakov, A. Y.; Durand, D.; Zholobenko, V. L. Chem. Commun. 2007, 834.
(26) Claesson, P. M.; Kjellander, R.; Stenius, P.; Christenson, H. K. J. Chem. Soc., Faraday Trans. 1 1986, 82, 2735. (27) Fletcher, P. D. I.; Petsev, D. N. J. Chem. Soc., Faraday Trans. 1997, 93, 1383.
Figure 9. Jamming and consequent irreversible zippering action of surface tension driven foam formation in self-assembled silica foams. Eventually, the area increase per unit cellular volume during deformation/zippering and wall densification during silica condensation will lead to thinning and microphase separation of the siliceous component of the wall and consequent formation of short, flat cylindrical mesopores running perpendicularly through the center of fused flattened faces (between the arrow tails).
Formation/Structure of Nanometric Polyhedral Foams
tion across droplets could conceivably drive deformation; however, it is then difficult to see how topological transformations could occur during jamming to high volume fractions, since initial covalent linkages of skins on undeformed droplets will largely fix the coordination number of individual droplets, disallowing jamming of dimensionally isotropic cells to high volume fractions. In all electron microscopy images of wellformed foams, the vast majority of cells are dimensionally isotropic and convex. Exceptions occur in the larger cell foams that are more polydisperse, on the exterior of foams, and in 2D sheets. If we accept the EO-clouding mechanism as the main driver for deformation and jamming, then the final stages of precalcination condensation occur across the polygonal faces and around the Plateau borders of the highly jammed aggregates. If the EO groups and silica precursors microphase separate on a particular droplet to any extent up until this point, as suggested above, then the density of cross-linked silica species will be higher in the Plateau borders than in the face centers. 7. Formation of Punctures through Polyhedral Faces. During deformation to dimensionally isotropic polyhedral forms, the formerly spherical cells undergo an increase of approximately 10% in surface area at fixed volume. This requires that the EO/ siliceous coronas (cell walls) be flexible. Ongoing polymerization (condensation) of silica in the walls would result in a net shrinkage of the walls with some lateral shrinkage contributing to the formation of the punctures between cells. Calcination would likely ensure that poorly formed holes (with rough edges) in the faces between cells become more well-defined, tending toward smooth circular or polygonal shapes, via migration and fusion events driven by lowering the surface (line) tension at hole edges. Microphase separation of some EO groups to the center of flattened faces during deformation would be converted to wellformed mesopores in the faces during calcination. Resemblance of the Present Nanometric Polyhedral Foams to Macroscopic Foams near the Dry Limit. At the dry limit, foams contain isotropic polyhedra that fill space, with faces joined at 120° and Plateau borders joined tetrahedrally at 109.47°. The foams here display isotropic polyhedra delimited by Plateau borders consistent with those close to the dry limit. The degree of space filling in foams is set by the free space between the packed foam cells. In the foams here, this is set by the space between the adjacent silica/EO surfaces of the deformed micelle or microemulsion droplets. Upon drainage and calcination, this interfoam cell space approaches zero. Therefore, the porosity of the foams here is not a direct measure of the approach to the dry limit, since the (half) silica walls are intrinsic parts of each polyhedron, having grown on the exterior of individual micelles (micremulsion droplets). In a loose, random aggregate of individual spherical micelles, each micelle will be in contact with perhaps six other micelles. As the proposed fusing areas between cells become larger, roughly circular faces grow radially away from the contact points along with a moving front of molecular water from co-condensing silanols. These fronts eventually “crash” into other growing faces, developing drainage networks on skeletal polygonal boundaries. The increase in surface area of the micelle as it becomes more polyhedral (at constant volume) demands that the wall be flexible under the shear induced in polyhedral aggregates. Indeed, the whole system is subject to minimizing its surface free energy, and the surface-energy-lowering deformation and consequent covalent zippering is spatially homogenized by minimizing the local surface area per micelle, resulting in polyhedral aggregates with classical random polydisperse foam
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character. The relatively large free space previously trapped between undeformed spheres in a glassy packing (approximately 36%) becomes thin unidimensional drainage channels, joined tetrahedrally as in classical dry foam Plateau junctions. The “dry” faces meet at 120° edges, and the polyhedral packing efficiency closely approaches 100% (space filling or the dry limit). The edges have cross sections that resemble foam struts, and their radius of curvature in cross sections appears to be fixed at about 8-15 nm, independent of the foam cell size. Individual foam struts have lengths that are proportional to their cell size, also indicating the aggregate develops by minimizing its surface area. As a consequence, the best developed foam 37 exhibits 90% porosity (approaching 100% polyhedral space filling), mainly with 4-, 5-, and 6-sided polygonal faces observed using TEM imaging and inferred from analysis of nitrogen sorption data. This compares favorably with the findings of Kraynik4 for random polydisperse foams. These structures resemble jammed nanoemulsions, in particular comparable with the uranyl stained, jammed emulsions of Mason et al.28 Mason et al. noted their materials are valuable for understanding the deformability of emulsions upon jamming to very high volume fractions, yet our silica foams, while topologically similar, are orders of magnitude more stable under the conditions of most characterization techniques and thus offer an excellent vehicle for studying nanoscale oil droplet deformation during concentration and more generally the structure of nanoscale foam objects.
Conclusion We have observed that oil-swollen poly(ethylene oxide)poly(propylene oxide)-poly(ethylene oxide) block copolymers can be used as templates for the synthesis of siliceous cellular structures bearing remarkable resemblances to classical, random, polyhedral space-filling foams near the dry limit. In the “driest” of these foams here, unusually high porosities of up to 90% were found, with a specific surface area of 644 m2 · g-1 and exceptional thermal and mechanical stability. The polyhedra of these foams are very close to 100% volume fraction and thus represent the closest approach to well-characterized dry foams of any known material at the nanometric scale. Various aspects of foam formation and structure were directly assessed using TEM, SEM, USAXS, SAXS, and N2 porosimetry, with a high degree of success in correlating results. The likely formation pathway for the polyhedral foams is that oil-swollen micelles transition to oil-swollen microemulsion droplets when the polymer reaches a critical extension limit. The transition to macroporous polyhedral foams from the distorted spherical cells of mesocellular foams is likely to be a combination of the swelling effect of temperature, ethanol, HCl, and oil content. The stability of the microemulsion droplets beyond the mesoporous range is considered to be due to the partial polymerization of silica and its likely effect in reducing the clouding temperature of the Pluronic polymer to a greater extent as it becomes more polymerized, allowing its partitioning to the separated oil core. The polymerization of silica during the clouding of the polymer leads to a packed arrangement of the micelles to fill space with their surface areas to some extent minimized in a manner similar to that of macroscopic foams, with various features such as Plateau borders supporting this view. Micropores and mesopores in the silica walls and the dimensionally isometric polyhedral cells form a hierarchical pore structure, and the mesopores are likely centered in polyhedral faces, connecting neighboring cells, and formed from growth of holes in the center of faces during deformation-induced cell S/V
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ratio increase, silica densification during condensation, and during calcination. Remarkably, we have evidence that, in the most porous foam found here, pores form in 4-, 5-, and 6-sided polygonal faces shared by neighboring polyhedra. Ongoing work is aimed at a deeper understanding of the formation and structure of these foams using techniques such as in situ X-ray scattering and electron microscopy. Preliminary electron tomography performed on these foams appears to give unique additional structural information, and results will be reported elsewhere after a detailed analysis. Acknowledgment. We thank S. Stowe (Australian National University, Canberra), T. Konishi (Rengo Co. Ltd., Osaka), and
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B. Svensson (Lund University) for FESEM, USAXS, and nitrogen sorption analyses, respectively. R.W.C. was funded by the NFR, Sweden. We also thank Bengt Kronberg (YKI, Sweden) for helpful discussions on the mechanics of foam formation. Supporting Information Available: Short review of the structure of Pluronic micelles and the contextually relevant factors to be considered in developing a model for foams and their swelling as a function of oil and temperature. This material is available free of charge via the Internet at http://pubs.acs.org. LA801228X (28) Mason, T. G.; Wilking, J. N.; Meleson, K.; Chang, C. B.; Graves, S. M. J. Phys.: Condens. Matter 2006, 18, R635.
