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Varying the Optical Stop Band of a Three-Dimensional Photonic Crystal by Refractive Index Control Zhong-Ze Gu,† Shoichi Kubo,‡ Weiping Qian,† Yasuaki Einaga,‡ Donald A. Tryk,‡ Akira Fujishima,‡ and Osamu Sato*,† Kanagawa Academy of Science and Technology, KSP Building East 412, 3-2-1 Sakado, Takatsu-ku, Kawasaki-shi, Kanagawa 213-0012, Japan, and Department of Applied Chemistry, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8565, Japan Received July 5, 2001. In Final Form: September 10, 2001 A method was developed to continuously adjust the position of the stop band of inverse opal by controlling the refractive index. The inverse opal films were fabricated using a coassembly of monodispersed polystyrene spheres and nanoparticles of silica and titania from aqueous suspensions followed by a calcination treatment. Varying the ratio of silica and titania in the suspensions gave the ability to finely adjust the refractive indices, which as a result changed the stop band.
Photonic crystals have recently been studied extensively because they offer unique ways of tailoring the propagation of light.1-9 A number of methods have been developed for their fabrication, among which the colloidal method provides a simple and efficient route to the fabrication of three-dimensional photonic crystals.9-14 Photonic crystals fabricated by the colloidal method form a cubic closepacked (ccp) structure. The ordered structure diffracts light, and as a result, it exhibits a stop band in its transmission spectrum. The position of the stop band at the L-point, λ, is estimated by13
λ ) 1.633dnaverage
(1)
where d is the center-to-center distance between two neighboring spheres and naverage is the average refractive index. For the application of opal and inverse opal as photonic crystals, it is critical to precisely control the position of the stop band. The usual method of adjusting the stop band is to change the center-to-center distance. A number of groups have shown that by changing the diameter of the monodispersed spheres, the stop band can be varied from ultraviolet to infrared.14,15 Recently, † ‡
Kanagawa Academy of Science and Technology. The University of Tokyo.
(1) Yablonovitch, E. Phys. Rev. Lett. 1987, 58, 2059-2062. (2) John, S. Phys. Rev. Lett. 1987, 58, 2486. (3) Photonic band gap materials; Soukoulis, C. M., Ed.; Kluwer Academic Publishers: Dordrecht, 1996; Vol. 315. (4) Joannopoulos, J. D.; Villeneuve, P. R.; Fan, S. H. Nature 1997, 386, 143-149. (5) van-Blaaderen, A. Science 1998, 282, 887-888. (6) Pendry, J. Science 1999, 285, 1687-1688. (7) Weissman, J. M.; Sunkara, H. B.; Tse, A. S.; Asher, S. A. Science 1996, 274, 959-960. (8) Wijnhoven, J. E. G. J.; Zevenhuizen, S. J. M.; Hendriks, M. A.; Vanmaekelbergh, D.; Kelly, J. J.; Vos, W. L. Adv. Mater. 2000, 12, 888-890. (9) Blanco, A.; Chomski, E.; Grabtchak, S.; Ibisate, M.; John, S.; Leonard, S. W.; Lopez, C.; Meseguer, F.; Miguez, H.; Mondia, J. P.; Ozin, G. A.; Toader, O.; van-Driel, H. M. Nature 2000, 405, 437-440. (10) See Adv. Mater. special issue: photonic crystals 2001, 13. (11) Velev, O. D.; Jede, T. A.; Lobo, R. F.; Lenhoff, A. M. Nature 1997, 289, 447-448. (12) Wijnhoven, J.; Vos, W. L. Science 1998, 281, 802-804. (13) Park, S. H.; Xia, Y. Langmuir 1999, 15, 266-273. (14) Jiang, P.; Bertone, J. F.; Hwang, K. S.; Colvin, V. L. Chem. Mater. 1999, 11, 2132-2140. (15) Mayoral, R.; Requena, J.; Moya, J. S.; Lopez, C.; Cintas, A.; Miguez, H.; Meseguer, F.; Vazquez, L.; Holgado, M.; Blanco, A. Adv. Mater. 1997, 9, 257-260.
it was also demonstrated that the stop band could be adjusted via a control of the center-to-center distance by the annealing method.15-17 The basic mechanism of the annealing method is the shrinkage of the material at elevated temperatures, which results in a decrease of the center-to-center distance. However, such shrinkage is not desirable for both opal and inverse opal because it can result in an increase in the number of cracks. Additionally, annealing at high temperatures can deform the ordered structure. Both of these defects decrease the optical qualities of the materials and limit their applications. As an alternative method, control of the average refractive index of the photonic crystal is derived to adjust the stop band. Such control has been realized by changing the volume fraction of the dielectric medium, by filling liquid with different refractive indices or by infiltrating materials with tunable refractive indices.18-26 In this paper, we will show a new approach to adjust the stop band using a nanocomposite with controllable refractive indices. The refractive index is an intrinsic property of a bulk material. Hence, at first glance, it seems to be difficult to engineer a particular refractive index. However, the situation is different for a nanocomposite composed of particles, with a size ranging up to several tens of nanometers. As the sizes of the particles are 1 or 2 orders of magnitude smaller than the wavelength of the light, a nanocomposite looks to the light like a continuous medium. Effective medium theory works for such a material; that is, the refractive index of the multicomponent nanocom(16) Miguez, H.; Meseguer, F.; Lopez, C.; Blanco, A.; Moya, J. S.; Requena, J.; Mifsud, A.; Fornes, V. Adv. Mater. 1998, 10, 480-483. (17) Gates, B.; Park, S. H.; Xia, Y. Adv. Mater. 2000, 12, 653-656. (18) Blanford, C. F.; Schroden, R. C.; AlDaous, M.; Stein, A. Adv. Mater. 2001, 13, 26+. (19) Rengarajan, R.; Jiang, P.; Colvin, V.; Mittleman, D. Appl. Phys. Lett. 2000, 77, 3517-3519. (20) Gu, Z.-Z.; Iyoda, T.; Fujishima, A.; Sato, O. Adv. Mater. 2001, 13, 1295-1298. (21) Gu, Z.-Z.; Hayami, S.; Meng, Q.-B.; Iyoda, T.; Fujishima, A.; Sato, O. J. Am. Chem. Soc. 2000, 122, 10730-10731. (22) Yoshino, K.; Satoh, S.; Shimoda, Y.; Kawagishi, Y.; Nakayama, K.; Ozaki, M. Jpn. J. Appl. Phys. 1999, 38, L961-L963. (23) Yoshino, K.; Nambu, H.; Oue, T.; Shimoda, Y.; Kawagishi, Y.; Nakayama, K.; Yablonskii, S.; Uto, S.; Ozaki, M. Mol. Cryst. Liq. Cryst. 2000. (24) Busch, K.; John, S. Phys. Rev. Lett. 1999, 83, 967-970. (25) John, S.; Busch, K. J. Lightwave Technol. 1999, 17, 1931-1943. (26) Kang, D.; Maclennan, J. E.; Clark, N. A.; Zakhidov, A. A.; Baughman, R. H. Phys. Rev. Lett. 2001, 86, 4052-4055.
10.1021/la0110186 CCC: $20.00 © 2001 American Chemical Society Published on Web 10/05/2001
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Langmuir, Vol. 17, No. 22, 2001
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Figure 2. A low-magnification SEM image of the inverse opal containing 28% titania. The image was taken at the position where the boundaries between domains can be observed. The domains with flat surfaces can extend over several hundred thousand square micrometers. The angles between boundaries, which are indicated by two white lines in the image, are 60° and 120°. The inset is a high-magnification image exhibiting the ordering of the air spheres in one of the domains. Such an image can be observed at any position.
Figure 1. (a) Scheme for the fabrication of inverse opals with variable refractive indices. First, a slide glass was vertically dipped into a glass vial containing a suspension of nanoparticles and monodisperse polystyrene spheres. Then, the vial was putted into a thermostat to evaporate the solution. After the film formed, the slide glass was put into a muffle furnace for calcination. (b) Relationship of the weight fractions of titania in solution and film. The marks indicate the experimental data, and the solid line is for visual guidance.
posite, ncomposite, takes the average value of the refractive indices of the components, which can be approximately calculated by27,28 2 ncomposite )
∑i ni2Vi
(2)
where ni and Vi are the refractive indices and volume fractions of the individual components. Apparently, varying the volume fraction of the nanoparticles can result in a change in the refractive index of the nanocomposite. This means that fine adjustment of the stop band can be achieved by changing the mixture ratio of the nanoparticles. The colloidal crystals with controllable refractive indices that we studied are the inverse opals, fabricated by the coassembly method, which have recently been developed by our group (Figure 1a).29 Silica nanoparticles with an average diameter of 6 nm, titanium nanoparticles with a diameter of 15 nm (Catalysts & Chemicals Ind. Co., Japan), and polystyrene spheres with a diameter of 420 nm (Duke Scientific Corporation, USA) were used for the fabrication. First, an aqueous suspension of titania nanoparticles was (27) Yamasaki, T.; Tsutsui, T. Appl. Phys. Lett. 1998, 72, 19571959. (28) Miguez, H.; Blanco, A.; Meseguer, F.; Lopez, C.; Yates, H. M.; Pemble, M. E.; Fornes, V.; Mifsud, A. Phys. Rev. B 1999, 59, 15631566. (29) Meng, Q.-B.; Gu, Z.-Z.; Sato, O.; Fujishima, A. Appl. Phys. Lett. 2000, 77, 4313-4315.
added to a suspension containing silica nanoparticles. The ratio between the silica and the titania in the mixture was controlled by varying the mixing ratio. The mixture of suspensions was then mixed ultrasonically with a monodispersed polystyrene suspension to obtain a homogeneous suspension. Following evaporation of the water (temperature, 50 °C; moisture, 30%), the solvent deposits a film composed of polystyrene and nanoparticles onto a glass substrate dipped vertically into the solvent. The growing speed of the film is about 2 mm/day. Finally, the composite films were calcined at 450 °C to remove the polystyrene spheres and to compact the nanoparticles to give the inverse opal films. Figure 1b shows the relationship between the weight fractions of titania in the film and in the solution. The fraction of titania in the films increased with that in the solutions, indicating that the composition of the inverse opal can be easily controlled by the mixing ratio in the solution. From the figure, it can also be derived that the fraction of titania in the inverse opal is always less than that in solution. This is because of the fact that the silica particles are smaller than the titania particles, which makes it easier for the silica particles to infiltrate the voids between the polystyrene spheres than it is for the titania particles. The microstructures of inverse opals containing different fractions of TiO2 were observed by scanning electron microscopy (SEM). Figure 2 shows the low magnification image of the inverse opal with 28% titania. Single domains with flat surfaces extend over several hundred thousand square micrometers. One domain is one single crystal with a ccp structure. The angles between the boundaries are 60° or 120°. The shape of the domains is the same as that of the (111) surface observed in atomic crystals with the ccp structure. A high-resolution image of one of the single domains is exhibited as an inset in Figure 2. A regularly ordered hexagonal arrangement can be observed everywhere. From the image, the second layer can also be clearly observed, which has the same order to its structure as that of the top layer. More details on the bulk structure were derived from cross-sectional observations, which showed that the ordered arrangement extended from the top surface to the substrate. The center-to-center distance
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Figure 3. Relationship between the stop band and the volume fraction of titania to the total volume occupied by silica and titania. The marks are the experimental data. The solid line is the fitting curve of the Bragg formula. The inset is the transmission spectra of the inverse opals with different volume fractions of titania.
is measured as 395 nm. The shrinkage is about 6%. This value is 1 order of magnitude smaller than the shrinkage found in the sol-gel method.30 The large single domains are the result of the low shrinkage. The morphologies are the same for all of the samples, regardless of the fraction of titania in the film. All of the samples exhibit flat surfaces and opalescent colors. Detailed studies of the optical properties of the stop bands were performed using normal transmission (30) Gu, Z.-Z.; Hayami, S.; Meng, Q.-B.; Fujishima, A.; Sato, O. Stud. Surf. Sci. Catal. 2001, 132, 297-300.
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measurements. The spot size of the light used for the detection was 10 mm × 5 mm. Strong extinction peaks were observed in all of the samples (Figure 3), indicating that high optical quality inverse opal of millimeter size can be derived by this method, regardless of the fraction of titania present. The extinction peak of the inverse opal composed of pure silica appears at 708 nm. This peak shifts to a longer wavelength with increasing fractions of titania, indicating that the stop band is varied by the components of the film. Because the center-to-center distance is the same, the shift of the stop band must be attributable to the refractive index, due to the change in composition. Since the refractive index of silica is about 1.5 while that of titania is about 2.5, the addition of titania increases the average refractive indices of the films according to eq 2, and as a result, the stop band shifts to a longer wavelength. The experimental data were fitted to eqs 1 and 2 and are plotted as a solid line in Figure 3. Apparently, the experimental data can be fitted extremely well. In conclusion, we demonstrated a new method of adjusting the stop band of inverse opal by taking advantage of the nanocomposite structure. The position of the stop band can easily be designed in a precise way by controlling the ratio between the components with different refractive indices. Since control of the refractive index was used to adjust the stop band, high-quality materials were derived. Acknowledgment. This work was supported in part by the Japan Society for the Promotion of Science and the Kanagawa Prefecture Joint-Research Project for Regional Intensive, Japan Science and Technology Corporation. LA0110186
