Langmuir 2006, 22, 5533-5536
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Suspended Self-Assembled Opal Membranes Andrew K. Bohaty and Ilya Zharov* Department of Chemistry, UniVersity of Utah, Salt Lake City, Utah 84112 ReceiVed January 25, 2006. In Final Form: May 5, 2006 Suspended self-assembled opal membranes have been prepared from 440- or 170-nm-diameter silica spheres by evaporation of their colloidal solutions over vertically oriented 0.3-mm-thick silicon wafers containing frustum-shaped openings. Robust 0.5 × 0.5 mm2 membranes with a thickness of ca. 300 µm have been reproducibly prepared using 170 nm silica spheres. The membranes show regular fcc packing with an exposed (111) orientation and are formed in a process that involves drawing silica spheres into the opening with the solvent meniscus.
Introduction Nanopores are important in fundamental studies of molecular transport and molecule-surface interactions on the nanoscale level,1 in separations,2 and in sensing.3 Nanoporous membranes have been prepared by lithography/etching techniques,4 anodic oxidation of aluminum films,5 track etching of polymers,6 selfassembly of block copolymers,7 surfactant-directed self-assembly,8 and templating colloidal crystals.9 Suspended porous membranes have been prepared via Langmuir-Blodgett transfer using polymer-silica monolayers.10 Synthetic opals are promising candidates for nanoporous membranes. They form via self-assembly of submicrometersized silica spheres into a close-packed face-centered cubic (fcc) lattice11 and contain highly ordered arrays of three-dimensional interconnected pores, approximately 15-80 nm in size for opals assembled from 100- to 500-nm-diameter spheres. The diffusive flux of small molecules normal to the (111) plane of an infinitely thick opal is only ca. 10 times smaller relative to that of free solution, independent of the size of the spheres used to synthesize the opal.12 Recently, we described studies of ion transport through 1.2 µm thin nanoporous opal films assembled on a solid support (a Pt microelectrode shrouded in glass)13,14 and showed that ionic flux in amine-modified nanoporous opal films can be controlled by pH13,14 and ionic strength14 in both aqueous and nonaqueous * Corresponding author. E-mail:
[email protected]. (1) Tanev, P. T.; Butruille, J.-R.; Pinnavaia, T. J. In Chemistry of AdVanced Materials; Interrante, L. V., Hampden-Smith, M. J., Eds.; Wiley-VCH: New York, 1998; p 329. (2) Davis, M. E. Nature 2002, 417, 813. (3) Bayley, H.; Martin, C. R. Chem. ReV. 2000, 100, 2575. (4) Tong, H. D.; Jansen, H. V.; Gadgil, V. J.; Bostan, C. G.; Berenschot, C. G. E.; van Rijn, C. J. M.; Elwenspoek, M. Nano Lett. 2004, 4, 283. (5) Toh, C.-S.; Kayes, B. M.; Nemanick, E. J.; Lewis, N. S. Nano Lett. 2004, 5, 767. (6) Yoshida, M.; Asano, M.; Suwa, T.; Reber, N.; Spohr, R.; Katakai, R. AdV. Mater. 1997, 9, 757. (7) Thurn-Albrecht, T.; Schotter, J.; Kastle, C. A.; Emley, N.; Shibauchi, T.; Krusin-Elbaum, L.; Guarini, K.; Black, C. T.; Tuominen, M. T.; Russell, T. P. Science 2000, 290, 2126. (8) Liu, N. G.; Dunphy, D. R.; Atanassov, P.; Bunge, S. D.; Chen, Z.; Lopez, G. P.; Boyle, T. J.; Brinker, C. J. Nano Lett. 2004, 4, 551. (9) Xu, H.; Goedel, W. A. Angew. Chem., Int. Ed. 2003, 42, 4694. (10) Xu, H.; Goedel, W. A. Langmuir 2002, 18, 2363. (11) Wong, S.; Kitaev, V.; Ozin, G. A. J. Am. Chem. Soc. 2003, 125, 15589. (12) Newton, M. R.; Morey, K. A.; Zhang, Y.; Snow, R. J.; Diwekar, M.; Shi, J.; White, H. S. Nano Lett. 2004, 4, 875. (13) Newton, M. R.; Bohaty, A. K.; White, H. S.; Zharov, I. J. Am. Chem. Soc. 2005, 127, 7268. (14) Newton, M. R.; Bohaty, A. K.; White, H. S.; Zharov, I. Langmuir 2006, 22, 4429.
Figure 1. Scheme of the formation of a suspended opal membrane in a frustum-shaped opening in a 300-µm silicon wafer.
solutions. Although these films allow the control of ion transport to an electrode and will find applications in electrochemistry and sensing, opal films cannot be used in transport studies of nonredox-active molecules because they are brittle and cannot be separated from the solid support. Herein we describe the formation of suspended nanoporous opal membranes peripherally supported in a 0.3-mm-thick silicon substrate. Experimental Section A 0.3-mm-thick Si(100) wafer (1 × 1 cm2) was used as a substrate in which either an array of openings shaped as a truncated square pyramid (i.e., a square pyramidal frustum) with 50 × 50 µm2 smaller dimension (2a, Figure 1) or a single 40 × 40, 100 × 100, 250 × 250, or 500 × 500 µm2 opening was manufactured using standard lithography and etching methods. A wafer was suspended vertically in a 10 mL vial containing a 3.0 wt % solution of either 170 ( 14 or 440 ( 11 nm diameter silica spheres13-15 dispersed in absolute ethanol. The vial was placed under an elevated crystallization dish in a vibration-free environment. The solvent was evaporated at room temperature overnight. For wafers containing multiple 50 × 50 µm2 openings, opal membranes were reproducibly suspended over all openings dozens of times. The same result was obtained for single 100 × 100 µm2 openings. For openings larger than 100 × 100 µm2, the success rate for suspended opal membrane preparation was 80%. Diffusion measurements were conducted by placing a 0.3-mmthick silicon wafer supporting a single suspended opal membrane made with 170 or 440 nm silica spheres between two connected 1 cm Pyrex cuvettes, one containing a 2 mM solution of rhodamine (15) Stoeber, W.; Fink, A.; Bohn, E. J. Colloid Interface Sci. 1968, 26, 62.
10.1021/la0602463 CCC: $33.50 © 2006 American Chemical Society Published on Web 06/01/2006
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Letters Table 1. Diffusion Rates, RD, through Suspended Opal Membranes of Various Sizes and Thickness of Suspended Opal Membranes Calculated from SEM and RD Measurements
Figure 2. SEM images of a 0.3-mm-thick silicon wafer containing frustum-shaped openings with a 50 × 50 µm2 smaller dimension after opal film formation using 440 nm silica spheres. (A) Front side of the wafer with five filled and one unfilled (marked with white arrow) opening. (B) Front and (C) back of a filled opening.
Figure 3. SEM images of an opal membrane peripherally supported (A) in a 50 × 50 µm2 opening in a 0.3-mm-thick silicon wafer showing (B) a close-packed fcc lattice of the 440 nm silica spheres in the supported opal membrane and (C) an opal membrane in a 500 × 500 µm2 opening in a 0.3-mm-thick silicon wafer. B in water and another one containing pure water. The silicon wafer was placed between two EPDM gaskets to prevent leaking. The smaller opening of the opal-filled frustum was placed facing the rhodamine B solution. The dye diffusion rate was measured by recording the absorbance in the receiving cuvette at a wavelength of 555 nm for 18 h while stirring both solutions. Measurements were conducted using an Ocean Optics USB2000 spectrometer. Data points were recorded every 300 s with an initial delay of 10 ms.
Results and Discussion Figure 2 shows SEM images of the silicon wafer after the opal deposition. As clearly seen in the images, with the exception of one square opening (shown here for comparison) all are filled with an opal. A closer examination of the opal reveals a peripherally supported colloidal crystal (Figure 3A) with fcc packing of silica spheres and an exposed (111) crystal plane (Figure 3B). To optimize the preparation of the suspended opal membranes further, we studied their assembly from water, ethanol, and acetonitrile solutions over openings of different sizes using 170 and 440 nm silica spheres. The suspended membranes were formed in openings of all four sizes when using 170 nm silica
opening size 2a × 2a, µm
RD × 10-14, mol‚s-1
40 × 40 100 × 100 250 × 250 500 × 500
0.45 1.53 2.11 6.73
membrane thickness, µm SEM RD 39 73 300 300
44 77 314 345
spheres and in the openings of the two smaller sizes when using 440 nm silica spheres, regardless of the solvent used. The 440 nm silica spheres also formed membranes in a 250 × 250 µm2 opening when ethanol was used as the solvent. Thus, it appears that the solvent dielectric constants (80, 24, and 37) and surface tensions (70, 22, and 19 dyne‚cm-1) for water, ethanol, and acetonitrile, respectively, do not significantly influence the formation of the membranes. We were unable to prepare opal membranes using hexane or diethyl ether because the silica spheres settled to the bottom of the vial before the solvent could evaporate. Taken together, these observations suggest that membrane formation is controlled by the rate of sedimentation of the silica spheres, and as long as the spheres remain in solution for the duration of the evaporation process, suspended opal membranes will be formed. The largest opening in which we are able to suspend an opal membrane reproducibly is 0.5 × 0.5 mm2 (Figure 2C), but membranes as large as 1 × 1 mm2 have been prepared, albeit they were not as robust. The suspended opal membranes did not show visible cracks or holes by SEM (Figures 2 and 3) and could withstand immersion in water, ethanol, and acetonitrile. The pore density for the opal membranes formed from 170 and 440 nm silica spheres is 6 × 109 and 8 × 108 pores‚cm-2, respectively. Our attempts to measure the cross section of the opal membranes by removing them from the silicon support were unsuccessful because the membranes shattered into irregular pieces when being removed. However, the thickness of the suspended opal membranes (Figure SI1) can be determined by measuring the dimensions of the membrane inside the frustumshaped opening using SEM (e.g., Figures 2C and SI2) and applying straightforward geometrical considerations.16 Membrane thicknesses obtained this way are listed in Table 1. The membrane thickness increases from 39 µm for a 40 × 40 µm2 opening in a nearly logarithmic manner and reaches 300 µm for a 500 × 500 µm2 opening (Figure 4A). Diffusion measurements provide another way of measuring the thickness of the suspended opal membranes and testing them for the absence of cracks and pinholes. Diffusion through colloidal crystals has been the subject of numerous theoretical treatments17 and of a recent investigation by electrochemical methods.12 We measured diffusion rates of rhodamine B in water through the suspended opal membranes spectrophotometrically (Table 1) and found that the rate increases nearly linearly with increasing area of the membrane (Figure 4B) but much more slowly than expected for a membrane with constant thickness. Indeed, the diffusion rate through an opal membrane can be calculated as
RD ) JopalS
(1)
(16) See Supporting Information. (17) Mahan, G. D.; Sofo, J. O. Phys. ReV. B 2000, 62, 2780, and references therein.
Letters
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of the cuboid corresponding to the smaller frustum dimension (2a, Figure 1). We described S as
S ) So
Figure 4. (A) Suspended opal membrane thickness calculated using SEM (blue) and diffusion rate (red) measurements as a function of the frustum-shaped opening area. (B) Diffusion rate of rhodamine B through suspended opal membranes as a function of the frustumshaped opening area measured spectrophotometrically (blue) and calculated for a 40-µm-thick membrane: green, using eqs 1 and 2; and red, using eqs 1, 2, and 4.
where Jopal is the molecular flux across the opal membrane and S is its area.18 The molecular flux can be expressed as
Jopal )
∆C D L τ sol
(2)
where ∆C is the concentration gradient across the membrane, L is the thickness of the membrane, Dsol is the diffusion coefficient in solution (3.6 × 10-6 cm2‚s-1 for rhodamine B in water19), the void fraction () is 0.26, and the tortuosity (τ) is ca. 3.0.12 A plot generated using eqs 1 and 2 for the diffusion rate as a function of membrane area for a 40-µm-thick membrane (Figure 4B) shows a rapid linear increase in the diffusion rate with the opening size area, in striking contrast to the experimental observations (Figure 4B). Using eqs 1 and 2, the opal membrane thickness can be calculated as
L)
∆C D S RD τ sol
(3)
For cylindrical or cuboidal membranes, S corresponds to the membrane area. However, using the smaller frustum opening area 4a2 as S in eq 3 results in significantly underestimated membrane thicknesses. This is not unexpected given that the diffusion rate through a widening opening is anticipated to be much higher compared to that of a uniformly wide opening, as has been shown for conically shaped pores.20,21 Thus, we used a correction coefficient to calculate the effective membrane area using the frustum volume relative to the volume (18) Cussler, E. L. Diffusion: Mass Transfer in Fluid Systems, 2nd ed.; Cambridge University Press: New York, 1997. (19) Rani, S. A.; Pitts, B.; Stewart, P. S. Antimicrob. Agents Chemother. 2005, 49, 728. (20) Li, N.; Yu, S.; Harrell, C. C.;. Martin, C. R. Anal. Chem. 2004, 76, 2025. (21) Zhang, B.; Zhang, Y.; White, H. S. Anal. Chem. 2006, 78, 477.
[
V F - VC +1 VF
]
(4)
where So is the smaller opening area, 4a2, VF is the frustum volume, and VC is the cuboid volume.16 The correction coefficient is particularly large for the 40 × 40 µm2 opening (1.98) and becomes smaller for the larger openings (1.90 for 100 × 100, 1.70 for 250 × 250, and 1.49 for 500 × 500 µm2 openings). A plot generated using eqs 1, 2, and 4 for the diffusion rate as a function of membrane area for a 40-µm-thick membrane (Figure 4B) shows an even steeper linear increase in the diffusion rate with the opening size compared to that calculated using eqs 1 and 2. The opal membrane thicknesses calculated using eqs 3 and 4 are shown in Table 1 and Figure 4A. The thicknesses increase with increasing membrane area and are in excellent agreement with the thicknesses obtained from SEM measurements. The slow linear increase in diffusion rates measured for suspended opal membranes of increasing area and the good agreement between measured and calculated membrane thickness are confirmations (in addition to direct SEM imaging) that these membranes do not contain major defects. The diffusion rate of 2.0 × 10-14 mol‚s-1 measured for a 250 × 250 µm2 opal membrane prepared using 440 nm silica spheres, which is similar to that observed for the 250 × 250 µm2 membrane assembled from 170 nm silica spheres described above, also speaks to the latter effect. Despite these observations, the ultimate test for the lack of defects in the suspended opal membranes would be the degree of membrane permselectivity, which we are presently studying and which will be reported elsewhere. The thickness of the opal film prepared by the vertical deposition of 170 nm silica spheres onto a flat silicon substrate from a 3 wt % colloidal solution is only 20 µm. The much larger thickness of the opal membranes formed inside the frustumshaped openings suggests that the membranes do not assemble during a simple evaporation of the colloidal solution but form via a more complex process that involves drawing silica spheres into the opening with the solvent meniscus. A similar directed self-assembly of opals has been reported inside V-shaped channels in silicon wafers.22,23
Conclusions We demonstrated that self-assembled suspended opal membranes can be prepared from 170- or 440-nm-diameter silica spheres by evaporating their colloidal solutions over vertically oriented 0.3-mm-thick silicon wafers containing frustum-shaped openings. Robust 0.5 × 0.5 mm2 (for 170 nm silica spheres) and 0.25 × 0.25 mm2 (for 440 nm silica spheres) membranes with regular fcc packing of silica spheres have been reproducibly obtained. The suspended membrane thickness increases from 40 to 300 µm with increasing size of the frustum-shaped openings. We are presently studying in detail the process leading to membrane formation and methods of controlling the membrane thickness, as well as surface modification in order to introduce permselectivity into suspended opal membranes. Acknowledgment. I.Z. is grateful to the Camille and Henry Dreyfus Foundation for a New Faculty Award. We thank Mr. (22) Ozin, G. A.; Yang, S. M. AdV. Funct. Mater. 2001, 11, 95. (23) Yang, S. M.; Ozin, G. A. Chem. Commun. 2000, 2507.
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Brian Baker (University of Utah Microfabrication Lab) for the preparation of silicon substrates. Supporting Information Available: Determination of opal membrane thickness. SEM images of the back sides of opal membranes suspended in a frustrum-shaped opening. Geometrical parameters of
Letters suspended opal membranes. Derivation of eq 4. Correction coefficients and effective areas for suspended frustrum-shaped opal membranes. This material is available free of charge via the Internet at http:// pubs.acs.org. LA0602463
