Mass Transport and Electrode Accessibility Through Periodic Self

Langmuir 2007, 23, 5689-5699

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Mass Transport and Electrode Accessibility Through Periodic Self-Assembled Nanoporous Silica Thin Films Ta-Chen Wei and Hugh W. Hillhouse* School of Chemical Engineering, Purdue UniVersity, West Lafayette, Indiana 47907 ReceiVed September 15, 2006. In Final Form: January 29, 2007 Ordered nanoporous silica films have attracted great interest for their potential use to template nanowires for photovoltaics and thermoelectrics. However, it is crucial to develop films such that an electrode under the nanoporous film is accessible to solution species via facile mass transport through well-defined pores. Here, we quantitatively measure the electrode accessibility and the effective species diffusivity for nearly all the known nanoporous silica film structures formed by evaporation-induced self-assembly upon dip-coating or spin-coating. Grazing-angle of incidence small-angle X-ray scattering was used to verify the nanoscale structure of the films and to ensure that all films were highly ordered and oriented. Electrochemical impedance spectroscopy (EIS) was then used to assess the transport properties. A model has been developed that separates the electrode/film kinetics and the film transport properties from the film/solution interface and bulk solution effects. Accounting for this, the accessible area of the nanoporous film coated FTO electrode (1 - θ) is obtained from the high-frequency data, while the effective diffusivity of the ferrocene dimethanol (DFDM) redox couple is obtained from intermediate frequencies. It was found that the degree of order and orientation in the film, in addition to the symmetry/topology, is a dominant factor that determines these two key parameters. The EIS data show that the (211) oriented double gyroid, (110) oriented distorted body center cubic, and (211) distorted primitive cubic silica films have significant accessibility (larger than 26% of geometric area). However, the double-gyroid films showed the highest diffusivity by over an order of magnitude. Both the (10) oriented 2D hexagonal and (111) oriented rhombohedral films were found to be highly blocking with only small accessibility due to microporosity. The impedance data were also collected to study the stability of the nanoporous silica films in aqueous solutions as a function of pH. The distorted primitive silica film showed much faster degradation in pH 7 solution when compared to a blocking film such as the 2D hexagonal. However, silica films maintained their structure at pH 2 for at least 12 h.

1. Introduction Ordered nanoporous inorganic materials formed via selfassembly of surfactants and metal oxide clusters1-4 are unique because they possess regular arrays of uniform channels which can be tuned in the range of 2-15 nm by the choice of the templating surfactant molecule. Self-assembled nanoporous materials were initially made in powder form but were later synthesized in a continuous thin film morphology by heterogeneous nucleation and solution growth.5,6 However, this method is time consuming and not readily extended to large substrates. Another method was developed7,8 to form homogeneous continuous films by spin-coating9,10 or dip-coating.7 After coating the substrate with a thin liquid film of precursors, self-assembly * To whom correspondence [email protected].

should

be

addressed.

E-mail:

(1) 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, 10834-10843. (2) Kresge, C. T.; Leonowicz, M. E.; Roth, W. J.; Vartuli, J. C.; Beck, J. S. Nature 1992, 359, 710-712. (3) Firouzi, A.; Kumar, D.; Bull, L. M.; Besier, T.; Sieger, P.; Huo, Q.; Walker, S. A.; Zasadzinski, J. A.; Glinka, C.; Nicol, J.; Margolese, D.; Stucky, G. D.; Chmelka, B. F. Science 1995, 267, 1138-1143. (4) Huo, Q. S.; Margolese, D. I.; Ciesla, U.; Feng, P. Y.; Gier, T. E.; Sieger, P.; Leon, R.; Petroff, P. M.; Schuth, F.; Stucky, G. D. Nature 1994, 368, 317321. (5) Aksay, I. A.; Trau, M.; Manne, S.; Honma, I.; Yao, N.; Zhou, L.; Fenter, P.; Eisenberger, P. M.; Gruner, S. M. Science 1996, 273, 892-898. (6) Yang, H.; Kuperman, A.; Coombs, N.; MamicheAfara, S.; Ozin, G. A. Nature 1996, 379, 703-705. (7) Lu, Y. F.; Ganguli, R.; Drewien, C. A.; Anderson, M. T.; Brinker, C. J.; Gong, W. L.; Guo, Y. X.; Soyez, H.; Dunn, B.; Huang, M. H.; Zink, J. I. Nature 1997, 389, 364-368. (8) Brinker, C. J.; Lu, Y. F.; Sellinger, A.; Fan, H. Y. AdV. Mater. 1999, 11, 579. (9) Ogawa, M. J. Am. Chem. Soc. 1994, 116, 7941-7942. (10) Ogawa, M. Chem. Commun. 1996, 1149-1150.

occurs upon evaporation of the solvent. As a result, this method has been coined evaporation-induced self-assembly8 (EISA) or evaporation-controlled self-assembly (ECSA).11 While first demonstrated with cationic surfactants, Zhao and co-workers12-16 extended the method to nonionic block copolymer surfactants such as those based on triblock poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) copolymers. These commercially available surfactants are inexpensive, benign, and available with a wide range of hydrophilic and hydrophobic block lengths, EOx-POy-EOx. Nanoporous materials that are self-assembled using these types of templates can possess mesoporosity (due to the hydrophobic PO blocks) and microporosity (due to the interpenetration of the hydrophilic EO segments with the inorganic species).17 As a result, here we use the term “nanoporous” to describe the resulting silica films. Continuous nanoporous silica films with a specific topology may be reproducibly synthesized by EISA by careful selection of the composition of the coating solution,18 control of the relative (11) Gibaud, A.; Grosso, D.; Smarsly, B.; Baptiste, A.; Bardeau, J. F.; Babonneau, F.; Doshi, D. A.; Chen, Z.; Brinker, C. J.; Sanchez, C. J. Phys. Chem. B 2003, 107, 6114-6118. (12) Zhao, D.; Yang, P.; Melosh, N.; Feng, J.; Chmelka, B. F.; Stucky, G. D. AdV. Mater. 1998, 10, 1380-1385. (13) Zhao, D. Y.; Feng, J. L.; Huo, Q. S.; Melosh, N.; Fredrickson, G. H.; Chmelka, B. F.; Stucky, G. D. Science 1998, 279, 548-552. (14) Zhao, D. Y.; Huo, Q. S.; Feng, J. L.; Chmelka, B. F.; Stucky, G. D. J. Am. Chem. Soc. 1998, 120, 6024-6036. (15) Zhao, D. Y.; Yang, P. D.; Margolese, D. I.; Chmelka, B. F.; Stucky, G. D. Chem. Commun. 1998, 2499-2500. (16) Yang, P. D.; Zhao, D. Y.; Chmelka, B. F.; Stucky, G. D. Chem. Mater. 1998, 10, 2033-2036. (17) Imperor-Clerc, M.; Davidson, P.; Davidson, A. J. Am. Chem. Soc. 2000, 122, 11925-11933. (18) Alberius, P. C. A.; Frindell, K. L.; Hayward, R. C.; Kramer, E. J.; Stucky, G. D.; Chmelka, B. F. Chem. Mater. 2002, 14, 3284-3294.

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humidity (RH) during coating,11,19-21 and control of the aging time.22 Nanoporous silica or other nanoporous metal oxide films have been reported that have nanoscale structure defined by the 2D hexagonal phase with hexagonal plane group p6mm,7,13,23 a 3D hexagonal phase with space group P63/mmc,15,24,25 a bodycentered cubic phase with space group Im3hm,12,26,27 a primitive cubic phase with space group Pm3hn,15,20,28 a face-centered cubic phase with space group Fm3hm,21,29 and a double-gyroid cubic phase with space group Ia3hd.22,30 Note that all the films undergo a uniaxial contraction toward the substrate during drying and calcination. For some cases, the symmetry of the distorted structure after the contraction has been solved. For instance, a (10) oriented planar hexagonal p6mm f (10) oriented planar rectangular c2mm,23 a (110) oriented body centered cubic Im3hm f (010) oriented orthorhombic Fmmm,27 and a (111) oriented face centered cubic Fm3hm f (111) oriented rhombohedral R3hm.29 Such nanoporous metal oxide films have potential applications as low dielectric constant films,31,32 low refractive index films,27,33,34 hydrogen sensors,35 photomodulated mass-transport layers,36 nanostructured magnetic materials,37 nanostructured solar cells,38 and nanostructured thermoelectrics.39 For the latter three applications, the nanoporous framework is filled and used as a nanoscale template to make either a well-defined nanostructured composite or the template removed to yield a nanowire array. However, if nanoporous frameworks are to be used as templates for electrodeposition of nanowires, it is necessary that the ionic species that serve as the reactants for the interfacial electrodeposition reaction are able to reach the substrate. Thus, the electrode must be accessible, despite being coated by the film. In addition, the transport through the film must be facile. For electrodeposition of wires of uniform length (effective pore filling), the elec(19) Cagnol, F.; Grosso, D.; Soler-Illia, G.; Crepaldi, E. L.; Babonneau, F.; Amenitsch, H.; Sanchez, C. J. Mater. Chem. 2003, 13, 61-66. (20) Grosso, D.; Cagnol, F.; Soler-Illia, G.; Crepaldi, E. L.; Amenitsch, H.; Brunet-Bruneau, A.; Bourgeois, A.; Sanchez, C. AdV. Funct. Mater. 2004, 14, 309-322. (21) Tate, M. P.; Eggiman, B. W.; Kowalski, J. D.; Hillhouse, H. W. Langmuir 2005, 21, 10112-10118. (22) Urade, V. N.; Wei, T. C.; Tate, M. P.; Hillhouse, H. W. Chem. Mater. 2007, 19, 768-777. (23) Klotz, M.; Albouy, P. A.; Ayral, A.; Menager, C.; Grosso, D.; Van der Lee, A.; Cabuil, V.; Babonneau, F.; Guizard, C. Chem. Mater. 2000, 12, 17211728. (24) Grosso, D.; Balkenende, A. R.; Albouy, P. A.; Lavergne, M.; Mazerolles, L.; Babonneau, F. J. Mater. Chem. 2000, 10, 2085-2089. (25) Besson, S.; Ricolleau, C.; Gacoin, T.; Jacquiod, C.; Boilot, J. P. J. Phys. Chem. B 2000, 104, 12095-12097. (26) Besson, S.; Ricolleau, C.; Gacoin, T.; Jacquiod, C.; Boilot, J. P. Microporous Mesoporous Mater. 2003, 60, 43-49. (27) Falcaro, P.; Grosso, D.; Amenitsch, H.; Innocenzi, P. J. Phys. Chem. B 2004, 108, 10942-10948. (28) Besson, S.; Gacoin, T.; Ricolleau, C.; Jacquiod, C.; Boilot, J. P. J. Mater. Chem. 2003, 13, 404-409. (29) Eggiman, B. W.; Tate, M. P.; Hillhouse, H. W. Chem. Mater. 2006, 18, 723-730. (30) Hayward, R. C.; Alberius, P. C. A.; Kramer, E. J.; Chmelka, B. F. Langmuir 2004, 20, 5998-6004. (31) Schuth, F.; Schmidt, W. AdV. Mater. 2002, 14, 629-638. (32) Fan, H. Y.; Bentley, H. R.; Kathan, K. R.; Clem, P.; Lu, Y. F.; Brinker, C. J. J. Non-Cryst. Solids 2001, 285, 79-83. (33) Schmidt, M.; Boettger, G.; Eich, M.; Morgenroth, W.; Huebner, U.; Boucher, R.; Meyer, H. G.; Konjhodzic, D.; Bretinger, H.; Marlow, F. Appl. Phys. Lett. 2004, 85, 16-18. (34) Konjhodzic, D.; Bretinger, H.; Wilczok, U.; Dreier, A.; Ladenburger, A.; Schmidt, M.; Eich, M.; Marlow, F. Appl. Phys. A: Mater. Sci. Process. 2005, 81, 425-432. (35) Urade, V. N.; Hillhouse, H. W. J. Phys. Chem. B 2005, 109, 1053810541. (36) 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, 551-554. (37) Luo, H. M.; Wang, D. H.; He, J. B.; Lu, Y. F. J. Phys. Chem. B 2005, 109, 1919-1922. (38) Hou, K.; Tian, B. Z.; Li, F. Y.; Bian, Z. Q.; Zhao, D. Y.; Huang, C. H. J. Mater. Chem. 2005, 15, 2414-2420. (39) Hillhouse, H. W.; Tuominen, M. T. Microporous Mesoporous Mater. 2001, 47, 39-50.

Wei and Hillhouse

trodeposition should be kinetically limited. Thus, the diffusion must be facile. Further, the pores themselves must be monodisperse, well-ordered, and well-oriented to yield a well-ordered and well-oriented nanowire array. As a result, the development of highly ordered and oriented nanoporous films with facile mass transport to an underlying accessible electrode surface is a key prerequisite for the development of templated nanofabrication at this length scale. Previously, many structures of nanoporous silica films have been synthesized on a variety of substrates. However, the accessibility of the substrate has never been examined in a quantitative or systematic manner, and there is no information about diffusion in the films. Nitrogen adsorption is usually used to quantitatively determine the accessible pore volume and surface area of the nanoporous silica powders.40,41 It can also be used to determine such parameters for films. However, due to the small quantity of material in the thin film, typically several dozen films are required for one measurement. In addition, this technique is inadequate to answer the question as to whether the probe molecule (in this case nitrogen) can reach the substrate from the gas phase above the film. Even if gas adsorption shows that certain probe molecules can enter the pore, pore orientation or a dense interfacial layer can prevent access to the substrate. Further, no information is gained about mass transport in the pore system. The ion diffusion rates within nanoporous silica powders have also been reported42,43 from experiments where the concentration change of metal ions in solution were monitored from initially ion-loaded nanoporous silica particles. The diffusivity was evaluated by fitting the kinetics of the concentration change with mathematical models based on diffusion from a sphere. However, such calculations rest on an assumption of the distribution of the initial loading. Ideally, these issues can be addressed by electrochemical methods to analyze the nanoporous films. In these techniques, current (or voltage) is detected only from probe molecules that reach a reactive patch of the substrate. To date, there are only a few papers36,44-46 that report electrochemical measurements from self-assembled nanoporous film coated electrodes. However, all of these reports rely on either chronoamperometry or cyclic voltammetry, which include large contributions from diffusion outside of the film. In a typical cyclic voltammetry experiment, the length scale for diffusion is much larger than the features of interest in self-assembled nanoporous films (including the film thickness and pore size), and as a result, the method is poorly suited for quantitative measurements of electrode accessibility or transport in such films. In contrast, in electrochemical impedance spectroscopy (EIS) interfacial kinetics may be separated from transport processes, as well as other non-faradaic contributions. Previously, this technique has been used to characterize defects in self-assembled monolayers (SAMs) such as those created by the adsorption of alkane thiols on gold.47-49 However, the length scales involved here are quite different. In SAMs, defects are on the order of (40) Gregg, S. J.; Sing, K. S. W. Adsorption, Surface Area, and Porosity; Academic Press: New York, 1982. (41) Kruk, M.; Jaroniec, M.; Sayari, A. J. Phys. Chem. B 1997, 101, 583-589. (42) Bibby, A.; Mercier, L. Chem. Mater. 2002, 14, 1591-1597. (43) Walcarius, A.; Etienne, M.; Lebeau, B. Chem. Mater. 2003, 15, 21612173. (44) Song, C. J.; Villemure, G. Microporous Mesoporous Mater. 2001, 44, 679-689. (45) Rohlfing, D. F.; Rathousky, J.; Rohlfing, Y.; Bartels, O.; Wark, M. Langmuir 2005, 21, 11320-11329. (46) Etienne, M.; Walcarius, A. Electrochem. Commun. 2005, 7, 1449-1456. (47) Finklea, H. O.; Snider, D. A.; Fedyk, J.; Sabatani, E.; Gafni, Y.; Rubinstein, I. Langmuir 1993, 9, 3660-3667. (48) Sabatani, E.; Cohenboulakia, J.; Bruening, M.; Rubinstein, I. Langmuir 1993, 9, 2974-2981. (49) Janek, R. P.; Fawcett, W. R.; Ulman, A. Langmuir 1998, 14, 3011-3018.

Self-Assembled Nanoporous Silica Thin Films

micrometers in scale are separated by tens or hundreds of micrometers. In the nanoporous films reported here, ideally, the active patches of electrode should be less than 10 nm in diameter, with each patch separated from the next also by less than 10 nm. Here, we report the details of the use of electrochemical impedance spectroscopy to quantitatively determine the electrochemically accessible area of a conducting electrode that is coated by a self-assembled nanoporous silica film and the effective diffusion coefficient of the electroactive species through the pore system. To our knowledge, these are the first quantitative measurements of these parameters. Using this method, we examine the effects of nanopore topology, orientation and order of the film, and the nature of the surfactant used to template the film. We also employ this same method to quantitatively analyze the stability of the nanopore network in aqueous solution as a function of pH. A key feature of this study is the broad range of topologies and surfactant systems examined and the care taken to ensure that the films were of known structure, orientation, and perfection.

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Figure 1. Geometry used for GISAXS data collection.

2.1. Synthesis of Nanoporous Silica Films. All films were synthesized on fluorine-doped SnO2 (FTO) glass substrates obtained from Pilkington (TEC 15). Before coating, FTO substrates were cleaned by immersing in 1 wt % Alconox at 65 °C for 30 s followed by rinsing with copious quantities of RO water and air-dried. All films were prepared by evaporation induced self-assembly via dipcoating the FTO substrates in the coating solutions (listed below) at a withdrawal rate of 1 mm/s (unless otherwise stated) using a KSV Instruments LM. After substrate withdrawal from the solution, all films were left in the dip-coating chamber for at least 12 h. The RH was controlled and kept constant in the dip-coating chamber during coating and posttreatment by mixing saturated and dry air streams to yield the desired RH. The films were then calcined in air at 400 °C for 4 h with 1 °C/min ramps to remove the surfactant template. The nanoporous silica film coated FTO substrates were then examined by optical microscopy and verified to be crack free down to a length scale of less than 1 µm using an Olympus BX51 optical microscope. The calcined silica film on FTO was scanned cross ways along the width by using an Alphastep 200 Tencor profilometer to measure the film thickness. The coating solutions for EISA syntheses were prepared as follows (listed separately on the basis of the type of surfactant used for templating). All chemicals were used as received. EO20-PO70-EO20 Templated Films. The nonionic triblock copolymer surfactant EO20PO70EO20 was obtained from BASF (tradename Pluronic P123). Rhombohedral R3hm and planar rectangular c2mm silica films were synthesized by dip-coating as reported by Tate.21 Lamellar silica films were synthesized by dip-coating as reported by Alberius.18 EO106-PO70-EO106 Templated Films. The nonionic triblock copolymer surfactant EO106-PO70-EO106 was obtained from BASF (tradename Pluronic F127). For orthorhombic Fmmm silica films, a solution of prehydrolyzed silica precursors was prepared by mixing 8 g of TEOS, 5.34 g of ethanol, and 0.7 g of HCl solution (2.7 mM) for 1 h. A second solution containing 30.4 g of ethanol, 2.8 g of HCl (38 mM), and 2 g of Pluronic F127 were added the previous solution. The solution was aged for 2 days at room temperature in a closed vessel before deposition. The films were dip-coated at 40% RH. The synthesis of silica film by F127 is based on Gross’s work.50 EO17-PO12-C14 Templated Films. The nonionic triblock copolymer surfactant EO17-PO12-C14 was obtained from DOW. For double-gyroid silica films,22 6.35 g of a pH 1.76 solution of HCl in water was added to 12.86 g of ethanol in an HDPE bottle. TEOS (12.2 g) was then added quickly. The bottle was immediately sealed and stirred for exactly 20 min. Immediately after this prehydrolysis, 13.9 g of 37 wt % EO17-PO12-C14 in ethanol (equilibrated for 12

h) was added to form the coating solution. The coating solution was then aged for 10 days. The films were dip-coated at 40% RH. For planar rectangular (c2mm) films, 11.97 g of 27 wt % EO17-PO12C14 in ethanol was added to the prehydrolyzed TEOS solution. The coating solution was then stirred for 5 min at 5 °C. These films were dip-coated at 20% RH. For rhombohedral films (R3hm), 14.5 g of 10 wt % EO17-PO12-C14 in ethanol was added to the same prehydrolyzed TEOS solution. The coating solution was then stirred for 5 min at 5 °C. These films were dip-coated at 60% RH. EO20-C16 Templated Films. The nonionic surfactant EO20-C16 (manufactured by ICI Americas under the tradename Brij 58) was obtained from Sigma. Orthorhombic Fmmm silica films were synthesized by spin-coating as reported by Luo.37 Brij 58 (0.4 g), 8.4 g of ethanol, 0.8 g of 1 M HCl, and 2 g of TEOS were mixed for 30 min at room temperature. The film was spin-coated at 3000 rpm for 2 min and then immediately moved to a chamber having 40% RH. C16(TMA)+Br- Templated Films. The cationic surfactant “CTAB” (C16H33N(CH3)3Br) was obtained from Aldrich. Distorted 3D hexagonal (P63/mmc), distorted primitive cubic (Pm3hn), and rectangular c2mm silica films were synthesized by dip-coating as reported by Grosso.20 However, here it was found that the wellorganized P63/mmc films formed at CTAB/TEOS ) 0.12 with 60% RH and the Pm3hn films were formed at CTAB/TEOS ) 0.16 with 40% RH. 2.2. Grazing Incidence Small-Angle X-ray Scattering (GISAXS) Characterization. 2D GISAXS data were collected from the assynthesized and calcined samples using a three-pinhole camera, microfocus X-ray source, an Osmic MaxFlux confocal X-ray optics, and a gas-filled 2D multiwire detector at a camera length of 1424 (chamber 1) or 484 mm (chamber 2). The detector was calibrated using an isotropic silver behenate powder standard enclosed in a capillary holder. For GISAXS measurements, the films were mounted on a two-axis goniometer such that at zero angle of incidence, the substrate normal was horizontal and perpendicular to the incident beam (see schematic in Figure 1). Due to the presence of an intense specular beam at grazing angles of incidence, a lead strip was used to attenuate the scattering along the specular plane. The 2D intensity data are shown on a log scale with a color map chosen to show both strong and weak features for each pattern. The 2D intensity data are plotted as a function of 2θf and Rf, the in-plane and out-of-plane exit angles for the scattered intensity, respectively. The location of diffraction spots were simulated and overlaid on experimental data using NANOCELL.51 This code uses the distorted wave Born approximation (DWBA) to simulate diffraction patterns from a nanostructured film with flat vacuum/film and film/substrate interfaces. The scattering at these interfaces is treated dynamically to account for refraction and reflection effects while the scattering from the nanostructure is treated kinematically (single scattering approximation). Given the space group, lattice constants, and angle

(50) Grosso, D.; Balkenende, A. R.; Albouy, P. A.; Ayral, A.; Amenitsch, H.; Babonneau, F. Chem. Mater. 2001, 13, 1848-1856.

(51) Tate, M. P.; Urade, V. N.; Kowalski, J. D.; Wei, T. C.; Hamilton, B. D.; Eggiman, B. W.; Hillhouse, H. W. J. Phys. Chem. B 2006, 110, 9882-9892.

2. Experimental and Theoretical Methods

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of incidence, the code simulates the Bragg spot positions (2θf and Rf for each peak) for GISAXS from nanostructured thin films. Similar to traditional crystallographic analysis, the absence of a predicted peak is neutral, while the presence of a peak that is not predicted rules out a match. By comparing all known self-assembled phases (and the lower symmetry phases that result from contraction) and all possible orientations with the experimental 2D pattern, the phase and orientation of the films can be determined unambiguously. Further, since the incident beam paints a streak across the entire substrate, this technique provides quantitative information about phase purity and homogeneity. 2.3. Electrochemical Measurements. A standard three-electrode cell connected to an EG&G PAR 283 potentiostat was used for all electrochemical experiments. Samples of calcined nanoporous films on FTO were used as the working electrode (1-3 cm2 geometric area submersed) with a platinum counter electrode (20 cm2) and an Ag/AgCl reference electrode. All potentials reported are with respect to the Ag/AgCl reference electrode reaction. The electrolyte was composed of 1 mM 1,1′-ferrocenedimethanol (FDM) redox couple with 1 M KCl and 0.01 M HCl supporting electrolyte such that pH ≈ 2. The experiments were all conducted at ambient laboratory temperature (21 °C). For EIS measurements the potentiostat was connected to a Solartron 1260 frequency response analyzer. The formal reduction potential for the FDM+/FDM redox couple, which ranged from 0.21 to 0.23 V, was first measured by applying a potential ramp between -0.1 and 0.6 V at a scan rate of 50 mV/s for each sample. A dc bias equal to the measured formal potential was first applied for at least 1 min to generate equimolar concentrations of the oxidized and reduced forms of the redox couple near the electrode interface. While maintaining this dc bias, a small amplitude sinusoidal ac bias (10 mV rms) of a given frequency (f) was then applied about this equilibrium potential. The impedance of the cell was then measured at each frequency over the range 0.1 Hz to 100 kHz. The equivalent circuit models developed are discussed below and are given in terms of the angular frequency ω ) 2πf. In the experiments of studying the stability of silica film in various pH values, electrolytes containing 5 mM ferricyanide redox couple with 1 M KCl were used. The pH values were then adjusted by adding various amount of HCl or KOH. 2.4. Data Analysis for EIS Spectra. The real and imaginary parts of the impedance were plotted parametrically with frequency (Argand diagrams) and individually versus frequency (Bode diagrams). These data were fit to equivalent circuit models by complex nonlinear least-squares (CNLS) implemented in Mathematica using the Levenberg-Marquardt algorithm to minimize the weighted sum of the absolute squares of the deviation between the measured complex impedance at each frequency and that calculated from the equivalent circuit model with the trial values of the fitted parameters:

s ) 2

1 Nω - N p

Nω

Z equivalent (ωn; Np Parameters) - Zωmeasured circuit n

n)1

Zωmeasured n

∑|

2

|

(1)

Np parameters were fitted based upon Nω values of the complex impedance. Typically, Np ranged from 4 to 6 while Nω was about 60. As formulated, the sum of squares for both the real and imaginary parts are weighted by the magnitude of the measured impedance, as opposed to weighting the deviation of the real (imaginary) part only by the measured real (imaginary) part. It has been noted previously by MacDonald52 that the variance obtained by this weighting scheme is superficially low. This is indeed true, and for the models used here, this weighting scheme does de-emphasizes deviations in the imaginary part at high frequencies. However, this weighting scheme was found more robust for convergence, and the variance of the fit defined in eq 1 was used only as a relative goodnessof-fit parameter to compare various models. In addition, Bode diagrams of the data and fitted model were examined to ensure a good fit. (52) Macdonald, J. R. Electrochim. Acta 1990, 35, 1483-1492.

3. Results and Discussion 3.1. Synthesis and Characterization of Nanoporous Film Coated Electrodes. In order to investigate the electrode accessibility and mass-transport properties of the films and discern the effects of pore topology and templating surfactant, 12 different structures of nanoporous silica films were synthesized. Eleven of the nanostructures (seven different topologies with three topologies synthesized from multiple surfactants) were prepared in a highly oriented, highly ordered continuous film morphology, as determined by GISAXS, Figure 2. The symmetry, highly ordered nature, and the orientation of the films were all determined by comparing/overlaying the experimental 2D GISAXS patterns with those predicted by DWBA calculations using NANOCELL.51 The results of the symmetry identification, phase orientation, and lattice constants are shown in Table 1. However, given this information, the pore connectivity is still not known exactly for many of these films. This feature is illustrated in Figure 3. Two structures are shown that both have identical symmetry and orientation (110 oriented Im3hm that contracts to a 010 oriented Fmmm upon drying). The particular electron density distributions shown in Figure 3 were generated using the level surface approximation53 to the I-WP triply periodic minimal surface.54,55 While nanoporous films have been shown to have this symmetry and have been shown by adsorption to have pores connecting the cages, there is no proof that the exact pore shape and topology conform to the I-WP surface, and we use the I-WP surface here for illustrative purposes only. 3.2. Electrochemical Impedance Spectroscopy from Nanoporous Silica Film Coated Electrodes. EIS is performed by applying a small amplitude ac bias on top of a dc bias that is set equal to the measured formal potential of the redox couple. Thus, on average, the electrode is in equilibrium with the solution and experiences only a small perturbation due to the ac signal. The complex impedance Z(ω) may then be calculated from the measured ac current for each frequency tested. The frequency dependence of the various faradaic and non-faradaic electrochemical processes are different and may be separated by fitting Z(ω) to an appropriate equivalent circuit model. The Randles equivalent circuit56,57 has been used extensively to describe simple electrode process having a single-step charge-transfer reaction. This equivalent circuit (Figure 4a) captures the basic effects of interfacial reaction kinetics, diffusion, electric double-layer capacitance, and solution resistance. Over the range of voltages probed, the FTO electrode approximates an ideal polarizable electrode for the supporting electrolyte and solvent. Thus, these species do not contribute to the faradaic current, but the electrolyte does yield a polarization current due to the formation of the electrical double layer at the interface. The electric double layer was modeled here by a constant phase element (CPE) given by

Zdl(ω) )

1 Tdl(iω)Pdl

(2)

When Pdl ) 1, this circuit element models a parallel plate capacitor with capacitance Tdl, which when connected in parallel with a resistance gives a single RC time constant. Values of Pdl < 1 (53) Wohlgemuth, M.; Yufa, N.; Hoffman, J.; Thomas, L. E. Macromolecules 2001, 34, 6083-6089. (54) Schoen, A. H. NASA Technical Note #D5541 1970, 16. (55) Anderson, D. M.; Davis, H. T.; Scriven, L. E.; Nitsche, J. AdV. Chem. Phys. 1990, 77, 337-396. (56) Bard, J.; Faulkner, L. R. Electrochem. Methods 2001. (57) Randles, J. E. B. Discuss. Faraday Soc. 1947, 1, 11-19.


Langmuir, Vol. 23, No. 10, 2007 5693

Figure 2. Experimental 2D GISAXS patterns for synthesized films and NANOCELL overlays of the predicted peaks positions based on the space group, orientation, and lattice constants reported in Table 1. (a) Lamellar, (b) 2D hexagonal, and (c) rhombohedral silica films by Pluronic P123; (d) double-gyroid, (e) 2D hexagonal, and (f) rhombohedral silica films by EO17-PO12-C14; (g) distorted body-centered cubic silica film by Brij 58 and (h) by F127; (i) 2D hexagonal, (j) 3D hexagonal, and (k, l) distorted primitive cubic by CTAB in a camera length of 424 and 1424 mm, respectively.

model the effects of a distribution of time constants.58 Such effects are commonly observed in electrochemical studies (even on well-prepared electrodes) and arise from surface heterogeneity. The faradaic response is modeled by a charge-transfer resistance (Rct) and a mass-transfer impedance (Zmt) connected in series. Since the amplitude of the applied ac voltage is small, the relation between the current and the overpotential is linear (when the response is kinetically controlled). This allows the resistance to charge transfer to be expressed as a function of the standard rate constant and the electrode area. Previously, Amatore59 showed that for partially blocked electrodes where the characteristic diffusion length is much larger than the active patches and the distance between the active patches (as is the case here), the electrode behaves like an unblocked electrode, but with an apparent rate constant (k0app) that depends on the coverage, θ, as

k0app ) k0(1 - θ)

(3)

Thus, the charge-transfer resistance can be expressed as follows

for an n electron reaction with transfer coefficient equal to 0.5 and equimolar concentrations of the oxidized and reduced species:

Rct )

RT n F AgCk0(1 - θ) 2 2

(4)

Ag is the geometric area of the electrode. k0 is the true standard rate constant and is measured by EIS on a bare electrode under identical conditions. (1 - θ) is the fraction of exposed area of the nanoporous film coated electrode. C is the concentration in bulk solution. A partition coefficient is intentionally not included in the denominator (and is thus assumed to be unity). We have taken two steps to eliminate partitioning due to interactions with the silica walls. First, the pH is maintained at the isoelectric point of the silica, and thus the -OH groups on the silica walls resemble the environment in solution. Second, the formal potential (58) Macdonald, J. R.; Barsoukov, E. Impedance spectroscopy: theory, experiment, and applications; Wiley: New York, 2005. (59) Amatore, C.; Saveant, J. M.; Tessier, D. J. Electroanal. Chem. 1983, 147, 39-51.

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Table 1. Structural Parameters Determined from GISAXS common name

templating surfactant

space group upon self-assembly

space group after contraction

orientation

double gyroid

D17

Ia3hd

211

primitive cubic

CTAB

Pm3hn

211

BCCa

Brij 58

Im3hm

Fmmm

110b (010c)

BCCa

F127

Im3hm

Fmmm

110b (010c)

3D hexagonal

CTAB

P63/mmc

P63/mmc

001

lamellar 2D hexagonal

P123 P123

1D ordering p6mm

1D ordering c2mm

100 10

2D hexagonal

D17

p6mm

c2mm

10

rhombohedral

D17

Fm3hm

R3hm

111

rhombohedral

P123

Fm3hm

R3hm

111

2D hexagonal

CTAB

p6mm

c2mm

10

lattice constants a, b, c (Å); R, β, γ (deg) 171, 176, 176; 91.1, 92.3, 92.3 83.9, 89.3, 89.3; 92.2, 94.8, 94.8 80, 86, 120 90, 90, 90 146, 180, 240; 90, 90, 90 55, 55, 57; 90, 90, 120 182 128, 132, 1; 90, 90, 90 145, 84, 1; 90, 90, 90 76, 76, 76; 86, 86, 86 106, 106, 106; 87, 87, 87 64, 46, 1; 90, 90, 90

a

BCC represents body-centered cubic. b The orientation of the film upon self-assembly. c The orientation of the film using the space group after contraction.

Figure 3. Illustrations of possible nanoporous film structures that are commensurate the symmetry and orientation determined for bodycentered cubic nanoporous silica films. The structures shown were generated using the I-WP level surface (body centered cubic symmetry, space group Im3hm) and are oriented with the (110) plane parallel to the substrate. (a) A contour level of -0.01 is shown to illustrate the case where the pores are not connected. (b) A contour level of -0.15 is shown to illustrate the case where the pores are connected. The placement of the unit cell for the Fmmm space group is also shown.

was measured for each film coated electrode prior to collecting EIS spectra, and the coated electrodes were potentiostated at that formal potential immediately before the ac bias was applied to generate equal concentrations of the oxidized and reduced species in the film. Thus, since all other quantities are known, the fraction of the electrode surface that is accessible through the pore structure (1 - θ) may be calculated from eq 4 once the charge-transfer resistance has been determined. While the charge-transfer resistance is determined by the highfrequency data, the mass-transfer impedance dominates at lower frequencies. In fact, since the length scale probed in EIS experiments is a function of the frequency, the technique may be used to probe the coating/solution as a function of distance from the electrode. The appropriate diffusion length scale for EIS is given by δEIS(ω) ) xD/ω. Thus, upon decreasing frequencies, regions farther from the electrode are probed. It is important to note that it is not simply the location at x ) δEIS(ω) that yields the impedance at ω. Z(ω) results from the net effects of the region 0 < x < δEIS(ω). As a result, at high enough frequencies, only the region in the nanoporous film is probed. The nanoporous films reported here are ca. 500 nm thick. Thus, if the diffusivity of FDM in the film is equal to that in bulk solution (measured by EIS on bare electrodes to be 2.1 × 10-6

Figure 4. Randles equivalent circuit is shown in (a). Note that the faradaic impedance is enclosed by the dashed line. The physical model corresponding to this circuit is shown in part (b).

cm2/s), then at frequencies of f >100 Hz, the mass-transport impedance comes primarily from diffusion within the film. If


Langmuir, Vol. 23, No. 10, 2007 5695

diffusion is less facile in the film, then this frequency drops precipitously. For diffusivity equal to 2.0 × 10-8 cm2/s, this limiting frequency is about 1 Hz. For a given film thickness and diffusivity in the film, we define this quantity as the film frequency, ωf ) Df/L2. In order to determine the diffusivity in the film, EIS spectra may (in principle) be analyzed at high frequencies using a Randles equivalent circuit with a mass-transfer impedance based on the solution of Fick’s Law for a 1D semi-infinite domain, yielding the standard infinite-length Warburg impedance that depends on the film diffusivity. However, in order to consider the film semiinfinite, δEIS(ω) should be several orders of magnitude large than L. At such high frequencies, the mass-transfer-impedance is difficult to separate from the charge transfer and double layer impedances. This problem is avoided by conducting the EIS experiments over a much broader frequency range and including the impedance of the nanoporous film/bulk solution interface and the 1D diffusion in the bulk solution in the model of the overall mass-transfer impedance. In particular, we make use of the Bisquert’s constant phase element restricted diffusion model.60 This model expresses the 1D solution of Fick’s Law in the Laplace domain for an arbitrary boundary condition at x ) L with a sinusoidal forcing function at x ) 0. The implications of this model have been discussed further by both Bisquert et al.61 and Diard et al.62 Here, we use this model to account for the impedance effects from the region from L e x < ∞. The mass-transfer impedance from a film coated electrode with an arbitrary boundary condition at L (given by the masstransfer function Zb) is expressed as

1+ Zmt(ω) ) Rw

Zb Rw

x x

jω coth xjω/ωf ωf

Zb jω + Rw ωf

(5)

jω coth xjω/ωf ωf

In this expression, Rw is the mass-transfer resistance in the film and is given by

Rw )

2RT L F2AgC Df

(6)

ωf is the film frequency and is equal to Df/L2. Since the film thickness L of the nanoporous inorganic films here is readily measured by profilometry, the only unknowns are the film the diffusivity in the film, Df, and the mass-transfer impedance in the region L e x < ∞ described by Zb. Ideally, Zb results from pure 1D semi-infinite diffusion and is expected to have a constant slope of 1 at low frequencies (in an Argand diagram). However, as is the case for many systems,58,60 the low-frequency slope is constant, but deviates slightly from 1. This constant phase element behavior is observed in measured data shown in Figure 5. It is precisely this scenario in which the formulation above has its greatest utility. One can account for the low-frequency behavior by setting Zb equal to a constant phase element, given by

Zb(ω) )

1 Tb(jω)pb

(7)

(60) Bisquert, J.; Garcia-Belmonte, G.; Bueno, P.; Longo, E.; Bulhoes, L. O. S. J. Electroanal. Chem. 1998, 452, 229-234. (61) Bisquert, J.; Garcia-Belmonte, G.; Fabregat-Santiago, F.; Bueno, P. R. J. Electroanal. Chem. 1999, 475, 152-163. (62) Diard, J. P.; Le Gorrec, B.; Montella, C. J. Electroanal. Chem. 1999, 471, 126-131.

Figure 5. Argand diagram of EIS data collected for a bare FTO electrode and a body-centered cubic nanoporous film coated FTO electrode. The constant phase element behavior (constant slope at low frequencies) is observed for both cases with the slope equal to 1 for the bare electrode and equal to 1.48 for the nanoporous film coated electrode.

By using this function, the low-frequency behavior is accurately removed from the intermediate and high-frequency data. This allows one to accurately determine the diffusion coefficient in the film. In summary, F and R are fundamental constants; Ag, C, and T are experimental parameters that are set and known; the film thickness L is measured by profilometry, and the standard rate constant k0 is measured on a bare electrode by EIS. This leaves only the accessible area (1 - θ) and the film diffusivity Df as fitting parameters along with the parameters for the double layer capacitance, Tdl and Pdl, and the impedance due to effect beyond the film, Tb and Pb. The behavior of this model with variations in the key parameters is shown in Figure 6. Complex nonlinear least-squares fitting resulted in models with good agreement to the experimental data. Model fits to the limiting cases of a completely blocked and completely accessible electrode are shown in Figure 7a. To test the limit of low accessibility, a dense silica film was prepared according to Brinker.63 Also, a trial was conducted with no redox couple. Both fits give a lower limit of the measurable accessibility. The values of (1 - θ) obtained were 0.0002 and 0.0009, respectively. In the other limit of a completely accessible electrode, a bare FTO electrode was tested and fitted to a Randles circuit. The fit yielded values of Rs ) 44.6 Ω, Rct ) 41.2 Ω, Cdl ) 21.1 µF, and D ) 2.1 × 10-6 cm2/s. Rs is the high-frequency limit of the impedance spectrum and was measured to be close to 44.6 Ω for all experiments. This resistance comes from the typical uncompensated solution resistance, as well as the sheet resistance of the large FTO substrates used for dip-coating of the films. The sheet resistance of the FTO glass used is 15 Ω per square. Given the width (1 cm) and length (2.7 cm) of the FTO substrate, the calculated resistance due to conduction through the substrate is 40.5 Ω. Thus, the measured high-frequency resistance arises mainly due to the resistance of the FTO substrate. At intermediate frequencies, the spectrum is determined mainly by the chargetransfer resistance (Rct) and the double-layer capacitance (Cdl). The fitted charge-transfer resistance of 41.2 Ω was used to calculate the standard rate constant for the FDM+/FDM couple on FTO using eq 4 and the known geometric area of the submersed region of the substrate. This yielded a value of 0.0045 cm/s. This was conducted for several different immersed areas and different (63) Brinker, C. J.; Keefer, K. D.; W., S. D.; Ashley, C. S. J. Non-Cryst. Solids 1982, 48, 47-64.

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Figure 6. Equivalent circuit model used to fit the nanoporous film coated electrode data. Characteristic curves are shown for the following cases: (a) Kinetically limited: Simulated traces are shown for several values of accessible area when the mass-transfer impedance goes to zero. (b) Diffusion limited: Simulated traces are shown for several film diffusivities when the interfacial chargetransfer resistance goes to zero. (c) Mixed control: Simulated traces are shown for various accessible areas with typical values for other components. (d) Mixed control: Simulated traces are shown for various film diffusivities with typical values for other components.

substrates, and yielded only a small variation in the rate constant. By the nature of this method, any intrinsic electrode surface roughness is lumped in with the standard rate constant. The double-layer capacitance was fitted to be 21.1 µF. This value is commensurate with the expected range for an electrochemical double layer. The low-frequency region of the EIS spectrum is dominated by transport to the electrochemical interface. The fitted value of the diffusivity (2.1 × 10-6 cm2/s) was calculated assuming DO ) DR and is in good agreement with the expected diffusivity in bulk solution. The EIS data and fitted spectra shown in Figure 7b are for a distorted body-centered cubic nanoporous silica film coated FTO electrode. A representation of the structure of the film is shown in Figure 3. Immediately, it can be seen from the EIS data that FDM can access the substrate, and thus Figure 3b is a more accurate representation than Figure 3a. The fitted value of (1 - θ) was 0.61, and the diffusivity in the film was 2.6 × 10-8 cm2/s. 3.3. Effect of Disorder. In order to gain the most meaningful results from EIS experiments discussed above, one must ensure that the nanostructure of the film is uniform through the thickness of the film and the films must be crack free. In order to see the effects of the former, we synthesized and compared the EIS response of two nanoporous silica films with c2mm symmetry. The typical “finger print” pattern showing channels that meander in the plane of the substrate are observed for both films (Figure 8c and d). Note that the 2D hexagonal packing of cylinders (plane group p6mm) distorts to a 2D rectangular packing of cylinder (plane group c2mm) upon the uniaxial contraction experienced during drying.7 However, this is not expected to affect the topology of the pore system. One film was synthesized such that the cylindrical pores are oriented parallel to the substrate throughout the thickness of the films.21 The GISAXS pattern from this film is shown in Figure 8b. The fact that the pattern is composed of spots indicates that the structure is oriented with

Figure 7. Argand diagram of EIS with FDM+/FDM on (a) bare FTO immersed in solution with pH 2 and (b) a body-centered cubic nanoporous silica film coated FTO electrode (the structure is similar to that shown in Figure 3b).

channels parallel to the surface (as seen in the FESEM) throughout the thickness of the film. Also note that the overlay of the predicted peak positions based on the c2mm plane group match the observed data. The second film was synthesized by using a smaller Si/EO (2.43) such that the cylinder orientation is not the same through the thickness of the film. While the cylinders are parallel to the surface but the FESEM images showed smaller domains in Figure 8c, below the surface of the film the channel orientation and order are disturbed. This was first observed in cross-sectional TEM images7 of EISA films but may be easily identified here by the semicircle seen in the GISAXS pattern (Figure 8a). The EIS data shown in Figure 8e shows a distinct difference in the accessibility of these films. The disordered c2mm film showed a much better accessibility than well-organized c2mm silica film. However, the disordered film cannot be used as templates for electrodeposition of uniformed and well-organized nanowires. Both of these films would have identical X-ray diffraction patterns when collected by a powder X-ray diffractometer. Thus, GISAXS data is a necessity to developing films where the transport through the film matters. In addition, cracking would cause similar effects in the EIS response. However, the films showed no cracks down to a length scale of 500 nm observed by optical microscopy at a magnification of 1000.


Langmuir, Vol. 23, No. 10, 2007 5697

Figure 9. Plot of exposed area as a function of time for (a) 2D hexagonal silica film (b) distorted primitive cubic silica film in solutions with various pH values.

Figure 8. GISAXS patterns of (a) disordered and (b) 2D hexagonal silica films by P123; FESEM images of (c) disordered and (d) 2D hexagonal silica films by P123; (e) Argand diagram of the silica films. In each GISAXS pattern, the circles represent diffraction from the refracted incident beam and the squares indicate the diffraction from the refracted and reflected incident beam.

3.4. Solution-Phase Stability of Nanoporous Films. Many applications will dictate the solution chemistry and pH in which nanoporous silica films are employed. Therefore, we have examined the effects of pH on the nanopore structure and the accessibility of the substrate. We collected EIS data continuously and observed the change in the charge-transfer resistance (and hence accessibility) as a function of time. Ferricyanide ion (Fe(CN)63-) is used as the redox couple for this experiment. The data (Figure 9) showed that the degradation of nanoporous silica film can be very severe in neutral or basic solutions. A 2D hexagonal silica film about 300 nm thick completely dissolved in 4 h in solution at pH 10. The film was stable in solution at pH 2, which is near the isoelectric point of silica for at least 12 h (Figure 9a). However, for primitive cubic silica film, the degradation in basic solutions is even more severe. The faster dissolution of nanoporous silica film can be due to the high accessibility of distorted Pm3hn film (see Table 2 below). In addition, we observed a smaller exposed area (∼10%) right after immersing in solution beyond pH 7. This is due to a smaller partition coefficient caused by the repulsive force between negatively charged silica wall and anionic redox couple. In order to study the effect of nanopore topology without damaging the

structure, the following EIS data were collected from each film in solution at pH 2. 3.5. Effect of Phase and Surfactants. As highlighted in the section above, in order to examine the effects of nanopore topology, one must first synthesize ordered and oriented thin films. We have undertaken a systematic synthesis effort and fabricated highly oriented films with lamellar, 2D rectangular c2mm (2D hexagonal p6mm), 3D hexagonal, orthorhombic Fmmm (body-centered cubic Im3hm), rhombohedral R3hm (face-centered cubic Fm3hm), distorted primitive cubic phase (Pm3hn), and distorted double-gyroid (distorted cubic Ia3hd) silica films. No single surfactant can generate all these topologies, but the same phase may be generated by several surfactants. The synthesis results showing the GISAXS patterns with overlays of the predicted peak positions are shown in Figure 2, while the corresponding EIS data from each film are shown in Figure 10. The fitted parameters from each film are shown in Table 2. Oriented nanoporous films based on the 2D hexagonal phase with channels parallel to the substrate were highly blocking, as expected. However, films synthesized by different surfactants showed different results. The films templated by the ionic surfactant CTAB were completely blocking and could not be distinguished from a dense silica film. On the basis of an analysis of the sensitivity of the fitting procedure, the EIS spectra could be fitted by either a film with (1 - θ) less than 0.001 or a diffusivity perpendicular to the substrate of less than 2 × 10-12 cm2/s. However, all the films synthesized by poly(ethylene oxide) head group surfactants showed slightly higher accessibilities (greater than 0.01) and diffusivities (greater than 5 × 10-10 cm2/ s). This increase in accessibility and transport is attributed to the presence of some microporosity in the wall generated by EO segments in the micellar corona that intermix with the silica and leave micropores upon calcination.17 In contrast, the rhombohedral films synthesized from EO head group surfactants were observed

5698 Langmuir, Vol. 23, No. 10, 2007

Wei and Hillhouse Table 2. Parameters Obtained from EIS Data ωf (rad/s)

common name (surfactant)

area (cm2)

Rs (Ω)

Tdl ×106

Pdl

Cdl (µF)

Tb ×106

Pb

active area (1 - θ)

diffusivity (cm2/s)

Dfilm/Ds

no film double gyroid (D17) primitive cubic (CTAB) BCC (Brij 58) BCC (F127) disordered 2D hexagonal (P123) 3D hexagonal (CTAB) lamellar (P123) 2D hexagonal (P123) 2D hexagonal (D17) 2D hexagonal (CTAB) rhombohedral (D17) rhombohedral (P123)

1.50 1.50

44.2 44.8

29 63

0.96 0.83

23.2 22.2

3200

0.53

1.00 0.33

2.1 × 10-6 9.1 × 10-7

1.0 0.44

3.0 × 10-5 1.9 × 10-4

364

1.05

30.8

35

0.98

33.6

440

0.58

0.26

6.4 × 10-8

0.03

9.0 × 10-5

25

2.10

64.5

15

0.98

14.4

920

0.52

0.55

6.3 × 10-8

0.03

1.6 × 10-4

25

2.00

72.5

20

0.98

17.0

580

0.51

0.61

2.6 × 10-8

0.013

2.1 × 10-4

10

3.00

26.1

100

0.85

33.6

760

0.50

0.27

2.7 × 10-8

0.013

1.0 × 10-4

11

1.38

37.9

50

0.87

23.8

310

0.54

0.05

9.0 × 10-9

0.004

1.3 × 10-4

4

0.45

34.2

0.94

6.8

20

0.50

0.12

3.2 × 10-9

0.002

2.6 × 10-4

1

3.00

25.5

40

0.87

26.3

130

0.60

0.09

8.6 × 10-10

0.0004

1.7 × 10-3

0.3

1.25

47.4

21

0.90

20.3

100

0.50

0.01

5.7 × 10-10

0.0003

2.6 × 10-4

0.2

1.50

44.2

36

0.94

N.A.

-

-

b

c

-

2.0 × 10-5

-

1.00

44.3

49

0.88

-

-

-

b

c

-

2.8 × 10-4

-

1.50

44.5

43

0.93

N.A.

-

-

b

c

-

7.0 × 10-5

-

8.8

s2

a The unit for Tdl and Tb is F cm-2 sp-1. b The value is smaller than 0.001 when the diffusion limitation is neglected. c The value is smaller than 2.0 × 10-12 when the kinetics limitation is neglected.

Figure 10. Argand diagram of (a) lamellar, 2D hexagonal, and rhombohedral silica films by Pluronic P123 (b) 2D hexagonal, 3D hexagonal, and distorted primitive cubic by CTAB (c) double-gyroid, 2D hexagonal, and rhombohedral silica films by EO17-PO12-C14 (d) contracted body-centered cubic silica film by Brij 58 and F127.

to be completely blocking (not distinguishable from dense silica coated electrode). This surprising result suggests that the intercage connectivity of the rhombohedral film is poor or that there may be a nonporous thin silica layer between the substrate and the

nanoporous film. However, stable carbon replicas64 can be made from the rhombohedral films, which indicates that there is some microporosity. As expected, lamellar films show blocking behavior before calcination. However, after calcination many


Langmuir, Vol. 23, No. 10, 2007 5699

Figure 11. Cross-section and the exposed electrode area for (a) 2D hexagonal silica film by CTAB (b) face-centered cubic silica film (c) body-centered cubic silica film (d) double-gyroid silica film.

cracks with a width of several micrometers were formed and can be observed by optical microscope. The crack area estimated by EIS is about 12% of the geometrical area. The orthorhombic and distorted primitive cubic phases showed a much better accessibility (greater than 0.26), but both films had diffusivities (∼10-8 cm2/s) which are significantly reduced from bulk solution values (2.1 × 10-6 cm2/s). This indicates that there is some intercage connectivity within the film where the diameter of the window is larger than the FDM and FDM+. The results are commensurate with articles reporting the formation of nanowire networks in films with the orthorhombic and primitive cubic structures.37,65,66 The double-gyroid films exhibited by far the best diffusivity of the nanoporous silica topologies measured. The diffusivity was measured to be 44% of the bulk solution value. In double-gyroid films, two continuous mesopore systems are present and separated by a silica wall. Each pore system is a three-connected network, with three-way junctions occurring about every 10 nm. Thus, species are expected to be able to move easily through the mesoporous channels. The structure is shown schematically in Figure 11. The electrode accessibility, facile species transport, and highly ordered pore system of this phase have recently been exploited to template a variety of nanowire structures22 that are stable upon removal of the silica wall. The resulting structures are significantly more ordered than nanowire structures templated with orthorhombic nanoporous films, owing to the fact the junctions are defined by self-assembly and the mesopores, not irregular cage interconnections or microporosity.

4. Conclusions Here we present the first quantitative and systematic measurements of diffusivities in highly ordered and well-characterized nanoporous silica thin films. It was found that the degree of order and orientation in the film can be a dominant factor that (64) Kim, T. W.; Ryoo, R.; Gierszal, K. P.; Jaroniec, M.; Solovyov, L. A.; Sakamoto, Y.; Terasaki, O. J. Mater. Chem. 2005, 15, 1560-1571. (65) Kumai, Y.; Tsukada, H.; Akimoto, Y.; Sugimoto, N.; Seno, Y.; Fukuoka, A. T.; Ichikawa, M.; Inagaki, S. AdV. Mater. 2006, 18, 760. (66) Shi, K. Y.; Peng, L. M.; Chen, Q.; Wang, R. H.; Zhou, W. Z. Microporous Mesoporous Mater. 2005, 83, 219-224.

determines the transport and the degree to which the electrode under the film is accessible. For highly ordered films, both 2D hexagonal and rhombohedral films were found to be highly blocking with only small effects observed due to microporosity. In fact, for EO head group surfactants, the rhombohedral phase turns out to be the most blocking. This property may make this phase attractive for low dielectric constant and low refractive index films, as the low accessibility may help prevent infiltration of the void regions during subsequent fabrication steps. The double-gyroid, orthorhombic, and primitive cubic phases all allow significant access to the substrate for the FDM redox couple used in the experiments. However, the effective diffusion coefficient perpendicular to the substrate was highest for the double-gyroid phase by over an order of magnitude. This indicates that the modulated pore structure (-cage-window-cagewindow-) provided by orthorhombic and primitive cubic structures inhibit transport through the film. So, while these phases do provide accessibility to the substrate, they do so in a qualitatively different manner than the double-gyroid phase. In principle, additives may be used to open up or connect the cages of the rhombohedral structures or expand the openings in orthorhombic or distorted primitive cubic phases. However, this has yet to be demonstrated in films. These results also beg further questions. For instance, why do BCC derived phases yield access to the substrate while FCC derived phases do not? Is there an underlying difference in the formation mechanism of these films? Additionally, the method discussed in the current paper may be applied with a variety of different probe molecule sizes and charges analyze size-exclusion effects and quantitatively determine the diffusion coefficients as the size of the molecule. Acknowledgment. The authors wish to acknowledge: financial support from the National Science Foundation under the CAREER Award (0134255-CTS), the use of the NSF-funded facility for in-situ X-ray Scattering from Nanomaterials and Catalysts (MRI Program Award No. 0321118-CTS), and Michael P. Tate for FESEM imaging. LA062699D

Mass Transport and Electrode Accessibility Through Periodic Self

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