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Finite Size Effects in Ordered Macroporous Electrodes Fabricated by Electrodeposition into Colloidal Crystal Templates David Hung, Zhu Liu, Neepa Shah, Yaowu Hao,† and Peter C. Searson* Department of Materials Science and Engineering, Johns Hopkins UniVersity, Baltimore, Maryland 21218 ReceiVed: October 14, 2006; In Final Form: December 19, 2006
Ordered macroporous electrodes (OMEs) formed by template synthesis have physical properties that are determined by the template. For colloidal crystal templates, these structures are inverse replicas of the fcc crystal structure with pore dimensions determined by the particle diameter in the colloidal crystal. The dimensions of the solid phase are determined by the interstitial space between the particles in the crystal. Here we demonstrate finite size effects in ordered macroporous gold electrodes. The adsorption of octadecane thiol is used to demonstrate that for structures fabricated from colloidal crystals with particle sizes less than 500 nm the resistance is dominated by surface scattering.
Introduction Macroporous materials, defined as materials with pore dimensions greater than 50 nm,1 provide high surface-to-volume ratios and periodic architectures, making them attractive for a wide range of applications. Random macroporous structures can be formed by aggregation and sintering of particles or by etching one component from a binary alloy system. The fabrication of ordered macroporous structures can be achieved by deposition into an ordered colloidal crystal. Ordered metal oxide macroporous structures have been produced by the condensation of metal alkoxides2,3 and the precipitation of inorganic precursors.4 Infiltration of nanometer-sized colloidal particles has been used to produce both inorganic and metallic macroporous structures.5,6 These processes generally involve a subsequent high-temperature annealing or calcination step. Electrochemical deposition into colloidal crystal templates has been used to produce ordered macroporous structures from a range of transition and noble metals7-13 as well as other compounds.14,15 Although there is emerging literature on template synthesis of ordered macroporous materials using self-assembled colloidal crystals, there are relatively few reports on the properties of these structures. Ferromagnetic ordered macroporous structures have been shown to exhibit unusual magnetic properties,10,11 and ordered macroporous gold and platinum structures exhibit novel optical properties.16,17 Various metal oxide ordered mesoporous electrodes have been explored for battery applications.3,4,15 The physical properties of ordered macroporous structures formed by template synthesis are dependent on the colloidal crystal template. Theoretical calculations have shown that the face-centered cubic (fcc) lattice is the lowest energy state for self-assembly of particles, although there is a relatively small energy difference between the fcc and hcp lattices.18 Under ideal equilibrium conditions, the ordered macroporous structures are inverse replicas of the fcc lattice with a solid fraction of 0.26 * To whom correspondence should be addressed. E-mail: searson@ jhu.edu. † Present address: Materials Science and Engineering Program, University of Texas, 500 West First St., Woolf Hall, Rm 325, Box 19031, Arlington, TX 76019.
and a porosity of 0.74 independent of the particle size in the template. As we discuss later, for a given height the surface roughness of the replica is dependent on 1/r where r is the particle radius. The pore dimensions in these ordered macroporous materials are determined by the particle size in the colloidal crystal. Similarly, the dimensions of the solid phase are determined by the interstitial space between the particles in the crystal and hence are dependent on the particle diameter and the crystal structure of the template. Because the feature sizes in the solid phase decrease with decreasing particle diameter in the template, finite size effects are expected when the particle size in the template becomes comparable to a characteristic length scale of interest. The mean free path lm for most metals is on the order of a few tens of nanometers, and hence surface scattering is significant in films where the thickness is less than lm or in wires where the diameter is less than lm. This effect has been exploited in a number of applications. For example, resistance changes in ultrathin metal films have been used to monitor underpotential deposition and the adsorption of halide ions and alkanethiols.19-23 Here we report on finite size effects in ordered macroporous structures formed by electrodeposition of gold into colloidal crystals self-assembled from polystyrene particles. Finite size effects are demonstrated by measuring the resistance of the structures upon injection of octadecanethiol. We show that the solid ligaments in structures formed from templates with particle diameters of less than 500 nm are sufficiently small such that the electrical resistance is dominated by surface scattering. Experimental Section Fabrication of Ordered Mesoporous Au Electrodes. The ordered mesoporous electrodes were fabricated by electrodeposition into colloidal crystal templates. The fabrication process is shown schematically in Figure 1. The substrates were prepared by sputtering a 10 nm chromium adhesion layer followed by 300 nm gold onto Si wafers. The wafers were rinsed with acetone (Pharma, ACS grade), ethanol (Pharma, ACS grade), and MilliQ deionized water and dried with nitrogen before use. The colloidal crystal templates were self-assembled by gravitational sedimentation. Polystyrene latex particles with
10.1021/jp066760z CCC: $37.00 © 2007 American Chemical Society Published on Web 02/03/2007
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Figure 1. Schematic illustration of template synthesis of ordered macroporous electrodes (OMEs): (a) self-assembly of a colloidal crystal template on conducting substrate (e.g., tin oxide), (b) electrodeposition of electrode, and (c) removal of particles.
diameters of 114, 202, 535, 771, and 1053 nm in 2.6 vol % aqueous suspension were obtained from Polysciences Inc. For 114- and 202-nm-diameter particles, the suspensions were diluted to 0.29 vol % with MilliQ water; for 535-nm-diameter particles, the suspension was diluted to 0.29 vol % with 22 vol % ethanol; and the 771 and 1053 nm particles were diluted to 0.52 vol % with 20 vol % ethanol. Empirically we observed that for smaller diameter particles longer assembly times were required to achieve high-quality colloidal crystals. To increase the sedimentation time and decrease the evaporation rate, the particle concentration was decreased and the suspensions were diluted only with water. Assembly of high-quality crystals from larger diameter particles could be achieved at faster rates, and hence relatively high concentrations were used and the suspensions were diluted with ethanol. The colloidal crystal templates were formed by locating a Viton o-ring (1.23 cm diameter, 3.53 mm thick) on a gold substrate. A Teflon o-ring (internal diameter of 0.965 cm, outside diameter of 2.09 cm, and thickness of 1.52 mm) with a rectangular cross section was then placed on top of the Viton o-ring. A volume of 0.19 mL of the suspension of the polystyrene particles was then placed in the well on the gold substrate and maintained at about 90% relative humidity for a period of up to 7 days for the smaller particle diameters. Electrodeposition into the colloidal crystal template was performed in a three-electrode cell with a Pt mesh counter electrode and a Ag/AgCl (3 M NaCl) reference electrode (Ueq ) 0.200 V vs SHE). The gold substrate underneath the template served as the working electrode. The template was then carefully immersed into a gold plating solution of 0.02 M (5.0 g L-1) sodium gold sulfite (Na3Au(SO3)2, TG-25E-RTU, Technic Inc.). Deposition was performed at -0.5 V (Ag/AgCl). This potential was selected to give a deposition current density of about 50 µA cm-2. In all cases a total charge of 1 C cm-2 was deposited corresponding to a thickness of about 2 µm. After deposition, the solution was removed and the structure was washed with water and dried. The polystyrene particles were then removed by soaking in toluene for 24 h. Characterization. The surface area of the ordered macroporous electrodes was determined by analysis of cyclic voltammograms recorded in 1 M H2SO4 (EMD, ACS grade) in a three-electrode cell. For OMEs with 114 and 202 nm pore diameters, a drop of ethanol was first placed on the electrode to improve wetting prior to introducing the sulfuric acid. The cyclic voltammograms were obtained over the potential range from 0 to 1.6 V (Ag/ AgCl) at a scan rate of 50 mV s-1.
Scanning electron microscope images were obtained using a JEOL 6700F operating at 10 kV. Fabrication of Free-Standing OMEs. Free-standing OMEs were fabricated using a sacrificial release layer. Colloidal crystal templates were formed on 300-nm-thick silver films evaporated onto silicon wafers with a 10 nm chromium adhesion layer. Silver was deposited at -0.7 V (vs Pt) from 0.04 M (8.3 g L-1) silver succinimide (C4H5NO2Ag, Silver Cyless, Technic Inc.) in a two-electrode configuration with a Pt mesh counter electrode. The deposition current was approximately 90 µA cm-2. After deposition, the silver succinimide solution was slowly removed by pipet down to a level that the template remained submerged; then, MilliQ water was introduced slowly. This procedure was repeated several times. The gold deposition solution was then introduced, and gold was deposited using the same conditions as described in the previous section. After deposition and the subsequent removal of the colloidal crystal template, the OME films were placed in a petri dish and immersed in a small amount of dilute (50 vol %) HNO3 (EMD, ACS grade) to dissolve the silver. A cover slip was first placed on top of the film to prevent curling and deformation upon release from the silver-coated silicon support. After approximately 10 min, the silver was completely dissolved and the cover slip was removed. The nitric acid was removed using a pipet, and MilliQ water was introduced at the same time. Finally, the free-standing OME was immersed in ethanol. A microscope slide was immersed into the ethanol below the floating OME, and upon withdrawing the glass slide the OME film was transferred onto the glass. Ordered Macroporous Au Devices. The Au OMEs adhered well to the glass substrate. Gallium-indium eutectic was used to make contacts for four point probe resistance measurements. The contacts were sealed using a vinyl chloride/acetate copolymerbased glue (Starbrite liquid electrical tape). Resistance measurements were performed by scanning the current from -100 to 100 µA using a Keithley 235 current source and measuring the corresponding voltage change with a Keithley 2182 nanovoltmeter. The OME film was initially placed in ethanol (Pharma, ACS grade) to obtain a stable resistance; then 100 µL of 10 mM octadecanethiol (ODT, CH3(CH2)17SH, Sigma Aldrich) was injected into the ethanol. Results and Discussion The combination of gravitational sedimentation and slow evaporation ensures the assembly of well-ordered colloidal
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Figure 2. (a) Optical image of a colloidal crystal formed from 535nm-diameter polystyrene particles, (b) cross-section SEM image of a colloidal crystal formed from 535 nm polystyrene particles, (c) planview SEM image of an ordered macroporous gold electrode with 535nm-diameter pores after removal of the polystyrene particles, (d) crosssection SEM image of an Au OME with 1.053-µm-diameter pores, (e) cross-section SEM image of an Au OME with 535-nm-diameter pores, and (f) cross-section SEM image of an Au OME with 114-nm-diameter pores.
crystals. Figure 2a shows a plan-view optical image of a typical 4-µm-thick colloidal crystal. The opalescence clearly shows the 3-fold symmetry and illustrates the long-range order and the high quality of the crystal. The high relative humidity also serves to minimize cracks in the crystal associated with the drying process. Cracks and voids result in nonuniform deposition in the crystal and lead to the formation of defects with relatively large volume in the replica. Such defects provide low resistance paths in the structure. Figure 2b shows a cross-section SEM image of the crystal confirming the excellent ordering. Electrodeposition of gold was performed at relatively low overpotential in order to achieve uniform deposition in the colloidal crystals. The deposition charge was 1 C cm-2 corresponding to a thickness of about 2 µm. The thickness of the porous film is independent of the pore size because the volume fraction of pore space in the colloidal crystal is constant (0.26). Figure 2c shows a plan-view SEM image of an ordered macroporous gold electrode with 535 nm pores after removal of the polystyrene particles. Figure 2d-f shows cross-section SEM images of ordered macroporous gold electrodes formed from crystals with particle diameters of 114, 535, and 1053 nm, respectively. The surface area of the ordered macroporous electrodes was determined using cyclic voltammetry. Figure 3a shows a typical voltammogram for an ordered macroporous electrode formed from a colloidal crystal with 114-nm-diameter particles. At positive potentials the voltammogram shows the onset of oxygen adsorption at about 1.2 V followed by the onset of oxygen evolution at 1.5 V. On reversing the scan direction, a characteristic oxygen reduction peak is seen at about 0.9 V. Figure 3b shows the oxygen reduction peaks for ordered macroporous electrodes with different pore diameters. The increase in peak current with decreasing particle diameter in the colloidal crystal reflects the increase in surface area associated with the increasing number of particle layers in the films. Recall that the film thickness is 2 µm in all cases.
Hung et al.
Figure 3. (a) Cyclic voltammogram for a gold OME with a pore diameter of 114 nm in 1 M H2SO4 at a scan rate of 50 mV s-1. (b) Reduction waves for a gold film and ordered macroporous electrodes with different pore sizes in 1 M H2SO4 at a scan rate of 50 mV s-1. In all cases the thickness of the OMEs was 2 µm.
Figure 4. Surface roughness factor vs colloidal crystal particle diameter. The roughness factor was determined from the charge under the oxide reduction waves in voltammograms.
Figure 4 shows the roughness factor for the ordered macroporous electrodes determined from the charge associated with the oxygen reduction peak divided by the charge measured for oxygen reduction at a planar gold electrode. The charge associated with the planar gold film was 435 µC cm2, slightly smaller than the value of 480 µC cm2 reported in the literature.24 Also shown in Figure 4 is the theoretical roughness factor for 2-µm-thick ordered macroporous electrodes. We assume that the surface area of the ordered macroporous electrode is equal to the total area of the particles in a perfect fcc colloidal crystal. The projected area of a sphere in a close-packed monolayer is 2r2x3. Thus, the roughness factor for a single layer of closepacked spherical particles is 4πr2/2r2x3 ) 2π/x3 ()3.63) independent of particle size. In the (111) direction of an fcc crystal, the spacing between each layer of particles is (2x6/3)r ()1.63r). The theoretical roughness factor is calculated by multiplying the roughness factor for a single monolayer by the number of monolayers of particles in a 2-µm-thick electrode. From the above discussion, it can be seen that for constant electrode thickness the roughness factor increases with r-1. Figure 4 shows that the roughness factor determined from voltammetry is in excellent agreement with the theoretical value
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Figure 6. Schematic illustration of (a) tetrahedral and (b) octahedral sites in an fcc lattice.
Figure 5. Cross-section SEM image showing an ordered macroporous electrode with a lower silver release layer and an upper gold layer.
for the larger particle diameters. This result shows that the ordered macroporous structures can be reasonably modeled as replicas of well-ordered colloidal crystal templates with low defect density. The maximum experimentally determined roughness factor of 39.7 (for d ) 114 nm) corresponds to a specific surface area of 4.2 m2 g-1. The deviation seen for ordered macroporous electrodes fabricated from crystals with 114-nmdiameter particles is due to the loss of area at the contact points. Two processes may contribute to this effect. First, poor wetting of the deposition solution in these occluded regions may lead to enlarged contact points. Second, coarsening may also play a role in reducing the surface area at regions of high curvature, such as near the contact points. Surface diffusion of gold in many solutions is known to be relatively fast. We note that we did not attempt to optimize the deposition procedure to minimize this effect. In fabricating resistive devices to measure finite size effects, it is necessary to eliminate the shunting effect of the gold substrate used for electrodepositon. Free-standing ordered macroporous electrodes were obtained by first depositing a silver release layer into the colloidal crystal before deposition of the gold layer, as shown schematically in Figure 1e-f. Figure 5 shows a cross-section SEM image of an ordered macroporous electrode with a lower silver region and an upper gold region. By immersing the electrode in nitric acid, the silver layer is dissolved and the gold macroporous layer is released from the substrate and can be transferred to an insulating substrate. Finite Size Effects. Finite size effects can be observed in the electrical resistance of a conductor when the feature size (e.g., wire diameter) is less than the mean free path for electrons, lm.25 In conventional diffusive transport, the mean free path is less than the characteristic feature size and the resistance is dominated by lattice scattering in the bulk of the material. However, when the feature size is less than the mean free path the resistance becomes dominated by surface scattering. For an ideal surface, electrons are elastically scattered (specularly reflected) upon collision with the surface, with no change in momentum in the direction of the electric field. However, the presence of defects and adsorbates can lead to diffusive (inelastic) scattering that results in a change in resistance. Thus, if a significant fraction of the electrons at a real surface are elastically scattered then the presence of an adsorbate can lead to increased inelastic scattering and hence a measurable change in resistance. The mean free path for electrons in gold is about 50 nm,26 and hence we expect to observe finite size effects for feature
Figure 7. Diameter of the largest sphere that will fit into tetrahedral and octahedral interstitial sites vs the particle diameter in the colloidal crystal.
sizes less than about 50 nm. The ordered macroporous structure can be considered as a network of small gold particles connected by narrow ligaments. The structure is an inverse replica of the colloidal crystal template; thus, the “ligaments” arise from the narrow regions for gold deposition in between two adjacent polystyrene spheres, and the “particles” are replicas of the interstitial sites in the colloidal crystal lattice. The fcc lattice has both tetrahedral and octahedral interstitial sites, which correspond to the largest solid features in the ordered macroporous electrode. In the fcc unit cell, there are four octahedral interstitials and eight tetrahedral interstitials. The total void space is 0.26 of the unit cell and the unit cell volume is volume 32r3/x2, where r is the radius of the particles forming the crystal template. The two types of interstitial site are illustrated schematically in Figure 6. Tetrahedral interstitials are formed between four spheres where the sphere in the top layer occupies a 3-fold hollow site. Octahedral interstitials are formed between six spheres and correspond to the unoccupied 3-fold hollow sites in the lower layer. The diameter of the largest spheres that can fit into the interstitial sites are 0.225r and 0.414r for the tetrahedral and octahedral interstitials, respectively, where r is the radius of the particles forming the colloidal crystal template. Figure 7 shows the diameter of the largest spheres that can fit into the interstitial sites versus the particle diameter in the colloidal crystal template. For example, for a colloidal crystal template formed from 1-µm-diameter particles, the diameters are 225 and 413 nm for the tetrahedral and octahedral interstitials, respectively, much larger than the electron mean free path. For crystal templates formed from 100-nm-diameter particles, the diameters are 23 and 41 nm for the tetrahedral and octahedral interstitials, respectively, smaller than the mean free path. For crystal templates formed from 200-nm-diameter particles, the diameters are 45 and 83 nm for the tetrahedral and octahedral interstitials, respectively, comparable to the mean free path. Thus, we would expect to observe finite size effects for the ordered macroporous
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Hung et al. smaller feature sizes in the ordered macroporous electrodes formed from colloidal crystals with smaller particles sizes result in a larger fraction of surface-scattered electrons and hence a larger effect size. A similar inverse relationship between normalized resistance change and film thickness has been reported for the chemisorption of carbon monoxide and hydrogen on nickel.25 These results demonstrate that ordered macroporous electrodes formed by template synthesis in colloidal crystals exhibit finite size effects associated with diffusive scattering at the surface. These structures exhibit high surface-to-volume ratios and periodic architectures with physical properties that are dependent on the particle size in the colloidal crystal template and the deposited material. In addition to the novel magnetic and optical properties already established for metallic ordered macroporous structures, we have demonstrated finite size effects.
Figure 8. (a) Normalized resistance change vs time on injection of octadecanethiol into ordered macroporous electrodes formed from colloidal crystals with 202-nm-diameter particles and (b) maximum resistance change vs pore diameter.
electrodes formed from colloidal crystals with particle diameters up to about 200 nm. Figure 8a shows typical normalized resistance versus time curves for ordered macroporous electrodes in ethanol upon the injection of 10 mM ODT. The initial resistances of the ordered macroporous electrodes increased with decreasing pore diameter, as expected from the corresponding decrease in the feature size of the solid phase (see Figure 7). For the electrodes shown in Figure 8 fabricated from crystals with 114-, 202-, and 535-nmdiameter particles, the resistances were 0.21, 0.070, and 0.060 Ω , respectively. The relatively low resistance of the structures highlights the necessity for four point probe measurements. For the electrodes formed from colloidal crystals with 114-nmdiameter particles, on injecting ODT, the resistance increases over a period of about 10 min by about 2%. For the electrodes formed from colloidal crystals with 202-nm-diameter particles, the maximum increase in resistance is about 0.5%, and for the electrodes formed from colloidal crystals with 535-nm-diameter particles, the maximum increase in resistance is about 0.15%. No measurable resistance change was observed for electrodes formed from colloidal crystals with larger particle sizes. We note that the ODT concentration is sufficient to ensure complete coverage of the ordered macroporous electrodes. Taking the surface concentration of an ODT monolayer on gold as 7.7 × 10-10 mol cm-2, the concentration is at least 35 times larger than that required for monolayer coverage, depending on the surface roughness of the electrode. A resistance increase of 2% is comparable to values of about 3% reported for adsorption of long-chain alkanethiols on 50nm-thick gold films23 and nanoporous gold nanowires with about 20-nm-diameter feature sizes.27 The response time is slightly longer than that reported for ultrathin films and nanoporous nanowires and is likely due to the much longer diffusion length to the internal regions of the electrode. For the electrode formed from a colloidal crystal template with 114-nm-diameter particles, the electrode is about 20 particle layers thick. Figure 8b shows the resistance change plotted versus the particle size in the colloidal crystal template. As expected, the
Summary We have fabricated ordered macroporous electrodes by electrodeposition of gold into colloidal crystal templates formed by the self-assembly of polystyrene particles with diameters from 114 to 1053 nm. The surface area of these electrodes, at least for larger pore diameters, agrees very well with the expected value. Theoretical analysis of the dimensions of the solid ligaments in the solid phase suggests that surface scattering should be significant in ordered macroporous electrodes formed from colloidal crystals with smaller particle diameters. The resistance change associated with the adsorption of octadecane thiol was used to demonstrate finite size effects in ordered macroporous electrodes with pore diameters less than 500 nm. These results indicate that free-standing ordered macroporous electrodes could be used as resistive sensors for the detection of chemisorbed species in solution or the vapor phase. Acknowledgment. This work was supported by the JHU MRSEC (NSF grant no. DMR05-20491). References and Notes (1) McCusker, L. B.; Liebau, F.; Engelhardt, G. Pure Appl. Chem. 2001, 73, 381-394. (2) Holland, B. T.; Blanford, C. F.; Stein, A. Science 1998, 281, 538540. (3) Kavan, L.; Zukalova, M. T.; Kalbac, M.; Graetzel, M. J. Electrochem. Soc. 2004, 151, A1301-A1307. (4) Yan, H. W.; Sokolov, S.; Lytle, J. C.; Stein, A.; Zhang, F.; Smyrl, W. H. J. Electrochem. Soc. 2003, 150, A1102-A1107. (5) Velev, O. D.; Tessier, P. M.; Lenhoff, A. M.; Kaler, E. W. Nature 1999, 401, 548-548. (6) Jiang, P.; Bertone, J. F.; Colvin, V. L. Science 2001, 291, 453457. (7) Jiang, P.; Cizeron, J.; Bertone, J. F.; Colvin, V. L. J. Am. Chem. Soc. 1999, 121, 7957-7958. (8) Xu, L. B.; Zhou, W. L. L.; Frommen, C.; Baughman, R. H.; Zakhidov, A. A.; Malkinski, L.; Wang, J. Q.; Wiley, J. B. Chem. Commun. 2000, 997-998. (9) Bartlett, P. N.; Birkin, P. R.; Ghanem, M. A. Chem. Commun. 2000, 1671-1672. (10) Bartlett, P. N.; Ghanem, M. A.; El Hallag, I. S.; de Groot, P.; Zhukov, A. J. Mater. Chem. 2003, 13, 2596-2602. (11) Eagleton, T. S.; Searson, P. C. Chem. Mater. 2004, 16, 50275032. (12) Kulinowski, K. M.; Jiang, P.; Vaswani, H.; Colvin, V. L. AdV. Mater. 2000, 12, 833-838. (13) Wijnhoven, J. E. G. J.; Zevenhuizen, S. J. M.; Hendriks, M. A.; Vanmaekelbergh, D.; Kelly, J. J.; Vos, W. L. AdV. Mater. 2000, 12, 888890. (14) Braun, P. V.; Wiltzius, P. Nature 1999, 402, 603-604. (15) Bartlett, P. N.; Dunford, T.; Ghanem, M. A. J. Mater. Chem. 2002, 12, 3130-3135. (16) Bartlett, P. N.; Baumberg, J. J.; Birkin, P. R.; Ghanem, M. A.; Netti, M. C. Chem. Mater. 2002, 14, 2199-2208. (17) Baumberg, J. J.; Kelf, T. A.; Sugawara, Y.; Cintra, S.; Abdelsalam, M. E.; Bartlett, P. N.; Russell, A. E. Nano Lett. 2005, 5, 2262-2267.
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