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Optical Intensity Gradient by Colloidal Photonic Crystals with a Graded Thickness Distribution Jian Li and Yanchun Han* State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Graduate School of the Chinese Academy of Sciences, 5625 Renmin Street, Changchun 130022, P. R. China ReceiVed October 5, 2005. In Final Form: December 15, 2005 Gradient colloidal crystals with a thickness gradient were prepared by the vertical deposition technique with vertically graded concentration suspensions. The thickness of the gradient colloidal crystal gradually changes at different positions along the specific gradient direction of the crystal. The thickness gradient was determined by the concentration gradient, depending on the initial colloidal concentration and the settling time. The optical transmission intensity at the dip wavelength can be tuned by changing the thickness of the colloidal crystals. The gradient colloidal crystals lead to a gradient of optical intensity at the dip in transmission light. The gradient of optical intensity at the dip increases as the thickness gradient of the colloidal crystal increases.
1. Introduction Two- or three-dimensional (2D/3D) colloidal structures assembled from monodisperse microspheres or nanospheres possess periodically dielectric structures and exhibit visible photonic crystal properties.1-5 These colloidal arrays are promising in the application to novel advanced materials and devices, including photonic band gap crystals,3-5 optical switches and filters,6,7 chemical and biochemical sensors,8-10 optoelectronic devices,11 templates for ordered microporous materials,12-16 and so forth. A primary requirement for the success of these applications is the ability to direct particle assembly to form ordered arrays over large domains on the flat or patterned substrates. Various strategies of colloidal assembly have been developed to obtain these colloidal structures, including gravity sedimentation,17,18 the use of capillary force,19-22 the fluidic cell * Corresponding author. Tel.: +86-431-5262175. Fax: +86-4315262126. E-mail:
[email protected]. (1) Halliwell, B. Nature, 2003, 426, 786. (2) Darragh, P. J.; Gaskin, A. J.; Terrell, B. C.; Sanders, J. V. Nature, 1966, 209, 13. (3) Debord, J. D.; Eustis, S.; Debord, S. B.; Lofye, M. T.; Lyon, L. A. AdV. Mater. 2002, 14, 658. (4) Xu, X.; Friedman, G.; Humfeld, K. D.; Majetich, S. A.; Asher, S. A. AdV. Mater. 2001, 13, 1681. (5) Mı´guez, H.; Meseguer, F.; Lo´pez, C.; Blanco, A Ä .; Moya, J. S.; Requena, J.; Mifsud, A.; Forne´s, V. AdV. Mater. 1998, 10, 480. (6) Lee, Y.-J.; Braun, P. V. AdV. Mater. 2003, 15, 563. (7) Lee, Y.-J.; Pruzinsky, S. A.; Braun, P. V. Langmuir 2004, 20, 3096. (8) Sharma, A. C.; Jana, T.; Kesavamoorthy, R.; Shi, L.; Virji, M. A.; Finegold, D. N.; Asher, S. A. J. Am. Chem. Soc. 2004, 126, 2971. (9) Xu, X.; Friedman, G.; Humfeld, K. D.; Majetich, S. A.; Asher, S. A. AdV. Mater. 2001, 13, 1681. (10) Burmeister, F.; Scha¨fle, C.; Matthes, T.; Bo¨hmisch, M.; Boneberg, J.; Leiderer, P. Langmuir 1997, 13, 2983. (11) Ha, N. Y.; Woo, Y. K.; Park, B.; Takezoe, H.; Wu, J. W. AdV. Mater. 2004, 16, 1725. (12) Imhof, A.; Pine, D. J. Nature 1997, 389, 948. (13) Velev, O. D.; Jede, T. A.; Lobo, R. E.; Lenhoff, A. M. Nature 1997, 389, 447. (14) Holland, B. T.; Blanford, C. F.; Stein, A. Science 1998, 281, 538. (15) Jiang, P.; Hwang, K. S.; Mittleman, D. M.; Bertone, J. F.; Colvin, V. L. J. Am. Chem. Soc. 1999, 121, 11630. (16) Deutsh, M.; Vlasov, Y. A.; Norris, D. J. AdV. Mater. 2000, 12, 1176. (17) Burmeister, F.; Scha¨fle, C.; Keilhofer, B.; Bechinger, C.; Boneberg, J.; Leiderer, P. AdV. Mater. 1998, 10, 495. (18) Lee, W.; Chan, A.; Bevan, M. A.; Lewis, J. A.; Braun, P. V. Langmuir 2004, 20, 5262. (19) Kim, E.; Xia, Y.; Whitesides, G. M. AdV. Mater. 1996, 8, 245. (20) Kim, E.; Xia, Y.; Whitesides, G. M. J. Am. Chem. Soc. 1996, 118, 5722.
method,23-25 dewetting,3,26-29 electrostatic interaction,30,31 electric field,32,33 microcontact printing,34 vertical deposition,35-39 and other novel methods.40-44 Recently, gradient colloidal crystals have also attracted much attention due to their potential application in photonic crystals, sensing materials, coatings, biomaterials, and microfluidic devices for sensing and catalysis.45-48 For example, Kim and John’s group prepared gradient colloidal photonic crystals by using colloidal crystals with gradients in the refractive-index distribution or in the lattice constant.45,46 These gradient colloidal structures can serve as a new type of band-gap-tunable photonic crystal based on positional variations without the need to apply any (21) Yi, D. K.; Kim, M. J.; Kim, D.-Y. Langmuir 2002, 18, 2019. (22) Yi, D. K.; Seo, E.-M.; Kim, D.-Y. Lamgmuir 2002, 18, 5321. (23) Yin, Y.; Lu, Y.; Xia, Y. J. Am. Chem. Soc. 2001, 123, 771. (24) Yin, Y.; Lu, Y.; Gates, B.; Xia, Y. J. Am. Chem. Soc. 2001, 123, 8718. (25) Xia, Y.; Yin, Y.; Lu, Y.; McLellan, J. AdV. Funct. Mater. 2003, 13, 907. (26) Guo, Q.; Arnoux, C.; Palmer, R. E. Langmuir 2001, 17, 7150. (27) Masuda, Y.; Tomimoto, K.; Koumoto, K. Langmuir 2003, 19, 5179. (28) Masuda, Y.; Itoh, T.; Itoh, M.; Koumoto, K. Langmuir 2004, 20, 5588. (29) Fustin, C.-A.; Glasser, G.; Spiess, H. W.; Jonas, U. Langmuir 2004, 20, 9114. (30) Masuda, Y.; Itoh, M.; Yonezawa, T.; Koumoto, K. Langmuir 2002, 18, 4155. (31) Zheng, H.; Lee, I.; Rubner, M. F.; Hammond, P. T. AdV. Mater. 2002, 14, 569. (32) Kumacheva, E.; Golding, R. K.; Allard, M.; Sargent, E. H. AdV. Mater. 2002, 14, 221. (33) Golding, R. K.; Lewis, P. C.; Kumacheva, E. Langmuir 2004, 20, 1414. (34) Yan, X.; Yao, J.; Lu, G.; Chen, X.; Zhang, K.; Yang, B. J. Am. Chem. Soc. 2004, 126, 10510. (35) Jiang, P.; Bertone, J. F.; Hwang, K. S.; Colvin, V. L. Chem. Mater. 1999, 11, 2132. (36) Meng, Q.-B.; Gu, Z.-Z.; Sato, O.; Fujishima, A. Appl. Phys. Lett. 2000, 77, 4313. (37) Wong, S.; Kitaev, V.; Ozin, G. A. J. Am. Chem. Soc. 2003, 125, 15589. (38) Masuda, Y.; Itoh, T.; Itoh, M.; Koumoto, K. Langmuir 2004, 20, 5588. (39) Cong, H.; Cao, W. Langmuir 2003, 19, 8177. (40) Zheng, H.; Rubner, M. F.; Hammond, P. T. Langmuir 2002, 18, 4505. (41) Ozin, G. A.; Yang, S. M. AdV. Funct. Mater. 2001, 11, 95. (42) Wu, H.; Thalladi, V. R.; Whitesides, S.; Whitesides, G. M. J. Am. Chem. Soc. 2002, 124, 14495. (43) Chen, X.; Sun, Z.; Zheng, L.; Chen, Z.; Wang, Y.; Fu, N.; Zhang, K.; Yan, X.; Liu, H.; Jiang, L.; Yang, B. AdV. Mater. 2004, 16, 1632. (44) Yang, S. M.; Mı´guez, H.; Ozin, G. A. AdV. Funct. Mater. 2002, 12, 425. (45) Park, J.-H.; Choi, W. S.; Koo, H. Y,; Kim, D. Y. AdV. Mater. 2005, 17, 879. (46) von Freymann, G.; John, S. K.; Kitaev, V.; Ozin, G. A. AdV. Mater. 2005, 17, 1273. (47) Zhang, J.-L.; Xue, L.-J.; Han, Y.-C. Langmuir 2005, 21, 5667. (48) Abkarian, M.; Nunes, J.; Stone, H. A. J. Am. Chem. Soc. 2004, 126, 5978.
10.1021/la052699y CCC: $33.50 © 2006 American Chemical Society Published on Web 01/13/2006
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external fields. In this work, we prepared gradient silica colloidal crystals with a thickness gradient that were self-assembled in an aqueous colloidal suspension with a vertically graded concentration distribution. The thickness of the gradient crystals gradually changes at different positions along the specific gradient direction of the crystal. The optical transmittance at the dip wavelength can be tuned at different positions on the gradient colloidal crystal. The gradient of optical intensity at the dip in transmission light is obtained along the specific gradient direction of the gradient colloidal crystal. 2. Experimental Section Monodispersed silica microspheres with a diameter of 232 nm were synthesized by means of the Sto¨ber-Fink-Bohn method.49 The silica microspheres were then dispersed in deionized water to the required volume fractions. A precleaned glass slide was vertically dipped into a 0.4 vol % (suspension A), 0.5 vol % (suspension B) or 0.75 vol % (suspension C) uniform aqueous suspension of the silica beads in a clean glass scintillation vial with a height of 4 cm and a volume of 6 mL. Then the uniform colloidal suspension was kept stationary in the saturated water vapor at room temperature for about 6 days. The microspheres in the suspension would subside in the gravitational field until the concentration of the top suspension approached zero. After a suspension with a graded concentration distribution formed, the vial containing the gradient suspension was laid into a glass box with a small outlet, as schematically shown in Figure 1a. In the box, the temperature was 60 °C and the relative humidity was about 50-60%. Then the silica microspheres began to self-assemble into the colloidal arrays in the evaporation process of the suspension (Figure 1a). The resulting gradient silica colloidal crystals were obtained after 3-5 days (Figure 1b). Gradient colloidal crystals A, B, and C were prepared with colloidal suspensions A, B, and C, respectively. The length of gradient colloidal crystals A, B, and C was about 15, 15, and 7 mm along the gradient direction, respectively. For comparison, uniform colloidal crystals were selfassembled at 60 °C by the vertical deposition technique. Scanning electron microscopy (SEM) micrographs were taken using a Philips XL-30-ESEM-FEG instrument operating at 20 kV. The samples for SEM were coated with a 20-30 Å layer of Au to make them conductive. The time-dependent change of the concentration gradient was obtained by directly measuring the absorption spectra of the colloidal suspensions with a vertically graded concentration in the vial on a HITACHI U-4100 spectrophotometer. Optical transmission spectra of these photonic samples were also measured on the spectrophotometer.
3. Results and Discussion Colloidal crystals can be self-assembled by a vertical deposition technique.35-39,50 Nagayama’s group prepared monolayer or multilayer colloidal films by carefully withdrawing a vertical substrate with the already-formed particle arrays from the colloidal suspension at a constant rate.50 Colvin’s group observed the growth process of successive multilayers when a wettable substrate dipped in a colloidal suspension was kept stationary.35 It is possible to vary the thickness of the colloidal crystal films from a few layers to hundreds of layers by controlling the parameters such as colloidal concentration. The average thickness of the silica colloidal crystals depends on the deposition parameters, including the volume fraction of the suspensions in the vertical deposition process:35,50
k)
βLjeφ 0.605dV(k) c (1 - φ)
(1)
(49) Stober, W.; Fink, A.; Bohn, E. J. Colloid Interface Sci. 1968, 26, 68. (50) Dimitrov, A. S.; Nagayama, K. Langmuir 1996, 12, 1303.
Figure 1. (a) Illustration of the vertical deposition technique for fabricating the gradient colloidal crystals in a graded-concentration colloidal suspension. (b) Scheme of the gradient optical intensity at the diffracted dip in the transmission light on the gradient colloidal crystals.
where k is the number of layers, L is the meniscus height, β is the ratio between the velocity of a particle in solution and the fluid velocity, φ is the particle volume fraction in solution, d is the particle diameter, je is the water evaporation rate, and V(k) c is the growth rate of the k-layer array. The value of the coefficient of proportionality, β, depends on the particle-particle and particle-substrate interactions and should vary from 0 to 1. The stronger the interactions are, the smaller the value of β is. For nonadsorbing particles and dilute suspensions, β is taken to be 1.50 For practical treatment, the meniscus height L depends on the temperature and humidity of the surrounding atmosphere, which can be experimentally determined.50 Jiang et al. experimentally verified that the final array thickness was not dependent on the solvent evaporation rate under different evaporation conditions (i.e., the evaporation rate je can be assumed to be 35 equal to the array growth rate V(k) c ). This is because, while faster solvent evaporation leads to faster array formation, it also leads to an increased solution influx into the array growth region. This increased influx of silica colloids balances the faster growth rate, leading to a film thickness independent of evaporation rate. As a result, the number of layers k actually depends on the particle volume fraction φ and the experimentally determined constant L.
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Figure 2. The number of layers versus the volume fraction of the silica microspheres.
Figure 3. Time-dependent change of the concentration and timedependent change of the concentration gradient of colloidal suspension A (0.4 vol %) in the vial.
Colloidal crystal films with a uniform thickness can be prepared by using a colloidal suspension with a uniform concentration. For the vertical deposition of 232 nm silica microspheres, the only parameter allowing control of the film thickness (or number of colloidal layers) is the particle concentration. According to eq 1, the number of layers is linearly dependent on the volume fraction of the particles when the volume fraction is very small (φ , 1). Figure 2 shows the linear relation of the number of layers versus the volume fraction of the silica microspheres. With the increase of the particle concentration, the number of layers will increase. Therefore, it is possible that gradient colloidal crystals can be prepared with colloidal suspensions with a vertical concentration gradient. The local thickness of the gradient colloidal crystals should be dependent on the local colloidal concentration. To obtain the colloidal suspensions with a vertically graded concentration, the uniform colloidal suspension was kept stationary in a glass vial for a long time at room temperature. The silica particles are heavier than the water they are dispersed in. Therefore, they will tend to settle toward the bottom of the container in the gravitational field until the concentration of the top suspension approaches zero and the concentration of the particles becomes higher near the bottom. But because of Brownian motion or diffusion, they diffuse upward and do not simply rest on the bottom, and eventually distribute themselves to form a graded concentration distribution. This is called sedimentation equilibrium. From mass transfer theory we have the migration of particles downward in the gravitational field and diffusion upward caused by the higher concentration near the bottom. At the steady state of sedimentation equilibrium, the two rates must be equal and opposite so that there is no net flux of particles in either direction:
of the particles instead of the concentration of the particles:
m φ(x) ) φ0 exp - Wx D
(
)
(5)
(4)
Equations 3 and 4 indicate that the concentration distribution of the particles with the height can be described by the Boltzmann distribution function.51,52 At the same time, eq 3 shows that the concentration gradient is linearly dependent on the initial concentration of the particles. Figure 3 shows the time-dependent concentration gradient of suspension A. The concentration gradient of the suspension increased as the settling time increased. The concentration of the top suspension approached zero after the colloidal suspension was kept stationary for 144 h. After the vertically graded concentration distribution formed, the silica microspheres began to self-assemble into gradient colloidal crystals at 60 °C, as schematically shown in Figure 1. First, a meniscus region was formed on the substrate due to wetting by the solution; evaporation of the solvent out of this thin meniscus led to a constant solution influx, which drew microspheres into the area of film formation (Figure 1a). During the solvent evaporation, these microspheres experienced interparticle capillary forces, which organized them into close-packed arrays. The resulting thickness is then entirely dependent on the flux of the microspheres into the meniscus. According to eq 1, the suspension with a concentration gradient leads to the gradient colloidal crystal because the local thickness of the gradient colloidal crystals is dependent on the local colloidal concentration. Gradient colloidal crystal B in Figure 4 was fabricated by using colloidal suspension B with a concentration gradient. The length of gradient crystal B is about 15 mm along the gradient direction. It is a challenge to use SEM for proof of sample gradient over centimeter distances. The SEM images in Figure 4 just exhibit the different microregions of gradient colloidal crystal B. We can see that there is only one layer at the top of the substrate (Figure 4a), and then the number of layers increases gradually from one layer to more than 70 layers on the wafer (Figure 4b-f). Some transitional stages with different thicknesses were captured. For example, the transitional stage between one layer and two layers is shown in Figure 4b. The SEM images in Figure 4 display a regular arrangement from the top surface to the bottom surface, which indicates that the samples have a high crystalline quality and that the colloidal crystals have a face-centered cubic (fcc) lattice. The cross-sections in Figure 4c,d, and the inset of f show the crystal structure of the inner (100), inner (111), and outer (111) crystal faces of the crystal. The inner (100) and inner (111) crystal faces of the fcc lattice are also directed by the arrows in Figure 4e.
Equation 4 can also be described with the volume fraction (φ)
(51) Davis, K. E.; Russel, W. B.; Glantschnig, W. J. Science 1989, 245, 507. (52) Xia, Y.; Gates, B.; Yin, Y.; Lu, Y. AdV. Mater. 2000, 12, 693.
dc flux ) mWc - D ) 0 dx
(2)
where W is the net weight of a particle, c is the concentration of particles within a sol layer with a thickness dx, m ) 1/(3πηd) is the mobility, η is the viscosity of fluid, d is the particle diameter, and D is the diffusion constant of the colloidal suspension. From eq 2, we also obtain the differential equation for c:
mW dc )c dx D
(3)
If we integrate over the height from 0 to x for eq 3, we can obtain
m c(x) ) c0 exp - Wx D
(
)
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Figure 5. (a) Positional transmission spectra of gradient colloidal crystal B shown in Figure 4. (b) Positional transmittance at the diffracted dip of 484 nm vs the position of gradient colloidal crystals A, B, and C, respectively. The inset shows the relationship between the positional fwhm and the position of gradient colloidal crystal B. (c) The transmittance at 484 nm and the fwhm of the transmission dips as a function of the number of layers for homogeneous colloidal crystal films.
Figure 4. SEM section profiles of gradient colloidal crystal B: (a) 1 layer, (b) 1-2 layers, (c) 7 layers, (d) 8 layers, (e) 21-22 layers, and (f) 66-73 layers. The inset shows the (111) face, which is oriented parallel to the surface of the substrate. Panels c and d also show the crystal structure of the inner (100) and inner (111) crystal faces of the fcc lattice. The inner (100) and inner (111) crystal faces of the fcc lattice are also directed by the arrows in panel e.
According to eq 3, the concentration gradient is linearly dependent on the initial uniform concentration of the particles. The larger the initial uniform concentration is, the larger the concentration gradient is. Gradient colloidal crystals A, B, and C were prepared with colloidal suspensions A, B, and C, respectively. We can deduce that the concentration gradient is A < B < C. As a result, the gradient of the gradient colloidal crystal is A < B < C (the micron-sized morphologies of gradient
crystals A and C were not shown here). It suggests that the gradient of the gradient colloidal crystal increases as the colloidal concentration gradient increases. Colloidal crystals have an ordered periodic modulation of dielectric constant between the silica microspheres and the air and can give rise to photonic crystal properties. The diffractive optical properties of these gradient colloidal crystal films have been characterized using the transmission spectra in normal incidence. Figure 5a exhibits the optical properties with respect to the position of gradient colloidal crystal B. All transmission measurements were carried out at each point with 1 mm spacing of the gradient colloidal crystal. The results clearly show that the transmittance at the stop bands could be successfully tuned depending on the position of the gradient colloidal crystals due to the local thickness variation. The transmittance at the band gap wavelength 484 nm gradually changes from 90% to 1% at the positions from the thin end to the thick end. Hence, the gradient colloidal crystal contributes the gradient optical intensity at the transmission dip along the gradient direction of the crystal, as shown in Figures 1b and 5b. The change of the optical intensity gradient crucially depends on the topology of the crystal structure. For example, the gradient of the dip optical intensity of crystal C is larger than that of crystal B because the thickness gradient of crystal C is larger than that of crystal B (Figure 5b). Therefore, the steeper gradient of the crystal leads to a steeper gradient of the transmittance at the diffracted dip. The optical intensity
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gradient on the gradient colloidal crystals was mainly caused by the thickness dependence of the optical properties of the colloidal crystals.53 Figure 5c shows the relationship between the transmittance at the diffracted dip and the number of layers for homogeneous colloidal crystal films. The optical transmission intensity at the diffracted dip exponentially decreases as the number of layers increases. Therefore, the gradient colloidal crystal integrates the optical properties of homogeneous colloidal crystals with different thicknesses and may be used for tunable optical filters that can modulate the optical intensity. The optical properties of the thick colloidal films are dominated by a strong diffraction effect. When the incident light is normal with respect to the (111) surface of the silica opals, the dip wavelength of the stop band can be described in the transmission spectra by Bragg’s law:
λ ) 2njd
(6)
Where d is the spacing between the crystalline planes in the (111) direction. In the case of the silica opal, this spacing is related to the silica spheric diameter D by d ) x2/3 D for the fcc structure. And nj, the effective refractive index, can be approximated by the equation
nj ) xfpnp2 + fvoidsnair2
(7)
where fp and fvoids are the filling ratio for the silica microspheres (fp ) 0.74) and the air voids (fvoids ) 0.26), respectively. Here, the refractive index of 232 nm silica microspheres is approximately np) 1.36, and that of air is nair ) 1.0. According to eq 7, the effective refractive index of the opals is 1.276. The dip wavelength of the stop band can be calculated to be 483 nm in the transmission spectra, which agrees with the experimental data. However, at the thinner end of the gradient colloidal crystal, the stop band also shifts toward long wavelengths, as shown in Figure 5. For thin colloidal films, the lights reflected from the top and bottom surface of the film will undergo thin-film interference because the refractive index of the colloidal film is less than that of the glass substrate.54,55 For this thin-film interference, the peak wavelength of an interference maximum (λ) is
mλ ) 2hknjk m ) 1, 2, 3, ... k ) 1, 2, 3, ...
(8)
where m is the resonance order, k denotes the number of layers in the colloidal multilayer, hk is the thickness of a multilayer built up from k particle layers (for model calculation of hk, see below), and njk is an effective refractive index of the multilayer treated as a continuous medium, which can be approximated by the equation
njk ) npfp,k + (1 - fp,k) k ) 1, 2, 3, ...
(9)
where np and fp,k are the refractive index and the volume fraction of the particles in the multilayers, respectively. The volume fraction fp,k depends on the structure of the multilayer. For the (53) Bertone, J. F.; Jiang, P.; Hwang, K. S.; Mittleman, D. M.; Colvin, V. L. Phys. ReV. Lett. 1999, 83, 300. (54) Dushkin, C. D.; Magayama, K.; Miwa, T.; Kralchevsky, P. A. Langmuir 1993, 9, 3695. (55) Cong, H.-L.; Cao, W.-X. Langmuir 2004, 20, 8049.
multilayers having 3D fcc lattices, simple geometrical considerations yield
fp,k )
3[3
1/2
πk + (k - 1)21/2]
k ) 1, 2, 3, ...
(10)
The thickness of the multilayer built up from k particle layers can be represented in the form
hk ) D + (k - 1)D(2/3)1/2 k ) 1, 2, 3, ...
(11)
For one-, two-, and three-layer films, the volume fraction of the particles can be calculated to be 60, 66, and 69%, respectively; the effective refractive indices can be calculated to be 1.23, 1.25 and 1.26, respectively; and the thicknesses are 232, 421, and 610 nm, respectively. For one-, two-, and three-layer films, according to eq 8, the wavelength (λ) of the reflected light, which will be eliminated from the white light by the thin-film interference, can be calculated to be 570 nm (m ) 1), 527 nm (m ) 2), and 512 nm (m ) 3), respectively. If other values of m are used, the calculated λ will be over the region of visible light that does not influence the film’s color. Therefore, the dip wavelength of the stop band shifts to short wavelength as the number of the colloidal layers increases. With the increase in the number of the layers, the experimental full width at half-maximum (fwhm) of the Bragg peak presents a monotonically exponential decay (Figure 5c). But the narrowing of the fwhm ceased and reached 28 nm above a certain critical thickness, which was calculated to be 13 layers for silica spheres according to the scalar wave approximation.53,56 In our study, the experimental data in Figure 5c agree with the calculated data. The narrowing of the fwhm from the increase of the thickness is a fundamental property of fcc colloidal arrays.53,56 From the thin end to the thick end of gradient crystal B, however, the fwhm decreased from 73 to 28 nm, then broadened from 28 to 41 nm (the inset in Figure 5b). At the thick end of gradient crystal B, the broadening of its fwhm resulted from the increase in the disorder of the colloidal arrays at the thick end.56,57 The disorder of the colloidal array increases as its thickness increases.35 In the presence of grain boundaries, point defects, and dislocations, the propagation of light inside a photonic crystal becomes diffuse, while, for frequencies outside the stop band, light propagation becomes diffuse in a cone around the zero order beam. For frequencies contained in the stop band, a combination of the interplay between coherent Bragg scattering and incoherent diffuse scattering, and the effect of energy bands leads to an enhancement of the diffuse intensity for those frequencies near the edges of the stop band.56-58 As a result, the increase of the disorder at the thick end of gradient crystal B broadened the attenuation dip that appears in transmission spectra and created an asymmetric shape of the spectral curve (Figure 5a).56-58 The primary maximum observed in each spectrum corresponds to the lowest energy stop band that opens at the L-point of the first Brillouin zone, while the lower intensity secondary oscillations (indicated by the arrows in Figure 5a), detected on both sides of the main peak, stem from the finite size of the crystal.56-60 (56) Galisteo-Lo´pez, J. F.; Palacios-Lido´n, E.; Castillo-Martı´nez, E.; Lo´pez, C. Phys. ReV. B 2003, 68, 115109. (57) Kaliteevski, M. A.; Martinez, J. M.; Cassagne, D.; Albert, J. P. Phys. ReV. B 2002, 66, 113101. (58) Astratov, V. N.; Adawi, A. M.; Fricker, S.; Skolnick, M. S.; Whittaker, D. M.; Pusey, P. N. Phys. ReV. B 2002, 66, 165215.
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These oscillations can be understood as Fabry-Perot fringes that occur because of the interference of the light reflected by the opposite surfaces of the opal domains. The fringes become smaller and more closely spaced in the thicker end. Remarkably, the Fabry-Perot oscillations appear different from both sides of the Bragg resonance, showing a rapid decrease in the oscillation magnitude on the high-energy side. In the case of thin colloidal films, the fringes indicate the high quality of the gradient crystals obtained by the vertical deposition technique.59,60
4. Conclusions In conclusion, we obtained gradient colloidal photonic crystals with a graded thickness distribution, which were prepared with colloidal suspensions including a graded-concentration distribution by the vertical deposition technique. The thickness gradient was determined by the concentration gradient linearly dependent on the initial colloidal concentration. The transmittance at the peak wavelength can be tuned by changing the thickness of the (59) Mı´guez, H.; Yang, S. M.; Ozin, G. A. Langmuir 2003, 19, 3479. (60) Maka, T.; Chigrin, D. N.; Romanov, S. G.; Sotomayor Torres, C. M. Prog. Electromagn. Res. 2003, 41, 307.
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colloidal crystals with sufficient uniformity. Positional thickness variation in the gradient colloidal crystals led to positionaltransmittance tunability. The gradient of optical intensity at the transmission dip was obtained on the gradient colloidal crystal, which increases as the gradient of the colloidal crystal increases. The gradient colloidal crystals may be useful for engineered photonic systems such as optical filters and optical diffraction gratings. Acknowledgment. This work is subsidized by the National Natural Science Foundation of China (50125311, 20334010, 20274050, 50390090, 50373041, 20490220, 20474065, 50403007, 50573077), the Ministry of Science and Technology of China (2003CB615601), the Chinese Academy of Sciences (Distinguished Talents Program, KJCX2-SW-H07), and the Jilin Distinguished Young Scholars Program (20010101). Supporting Information Available: Optical photographs at low magnification and other SEM section profiles of gradient colloidal crystal B, and transmission spectra of homogeneous colloidal films with different thicknesses. This material is available free of charge via the Internet at http://pubs.acs.org. LA052699Y
