Light-Diffracting Fringes of Cylindrical Colloidal Crystals

Figure 6.8 exhibit the OM images for CCC-460 and CCC-660. Their surface displayed sparkling appearance in various color strips, and the color strips were aligned to each other.

With a fixed light source, these color fringes were attributed to the light diffracting by the colloidal crystals from different angles.

(a) (b)

Previously, V. Rastogi et al. [52] provided a model to demonstrate the reflection of parallel light waves that underwent a constructive or destructive interference, as shown in Fig. 6.9.

The following equation derived from geometry in the figure illustrates the path difference of light waves;

𝒎𝝀 = 𝒅 × [𝒔𝒊𝒏(𝟗𝟎 − 𝜽) + 𝒔𝒊𝒏(𝝓 − 𝜽)] [eq. 6.4]

where m is the integrals for the number of sets of fringes, λ is the wavelength of individual color fringe, d is the lattice spacing of (111) plane, and θ and 𝝓 are two specific angles defined from horizontal plane to the position of incident beams.

Because of the small diameter of the as-prepared CCCs, only the fringes in first order (m = 1) were obtained on the surface. Hence, the wavelength for the diffracting lights could be calculated through the equation by measuring each set of angles. Meanwhile, these fringes were observed under optical microscope, which inferred the incident light was normal to the surface (φ ~ 90°). Therefore, the equation could be further simplified to:

𝝀 = 𝒅 × 𝟐𝒔𝒊𝒏 𝟗𝟎 − 𝜽 = 𝟐𝒅 𝐜𝐨𝐬 𝜽 = 𝟒𝒅𝒔/𝑫 [eq. 6.7]

where s is the distance from the middle line to the fringe, and D is the diameter of the CCCs.

From the modified equation, the wavelength of reflection can be easily calculated by the position of their fringes from OM images, as shown in Fig. 6.10. The inset bars exhibits the corresponding color of each wavelength via the RGB value translated from standard CIE 1931 chromaticity diagram [53]. The colors shown in Fig. 6.10 were partially matched with that obtained in OM observation. The deviation in color matching might be induced by a small tilt of the incident light.

Figure 6.9 A schematic for theoretical calculation of fringe formation.

Figure 6.10 Wavelength of fringes versus the s/D plot of the CCCs for m = 1. The inset bars show the corresponded color created with RGB values on CIE 1931 chromaticity diagram.

NIO-660 with different number of layers. The Ni film provided a large reflectance in Mid-IR region, and maintained its value at 80% before entering the near-IR range. The noises detected at 2.62 and 4.25 μm were generated by the H2O and CO2, respectively. With a semi-layer NIO, the sample displayed a curve similar to that of the Ni film but at a slightly reduced reflectance. It suggested that the concave semi-layer structure engendered additional light scattering. Moreover, the PBG behavior was recorded as the layer number was increased. The NIO-660 with seven layers inverse structure revealed a curve whose intensity exhibited pronounced decay below 4 μm. In addition, the photonic band edge, defined at 50% reflectance, was observed at the wavelength of 2.25 μm on the plot.

The reflectance spectra of NIO-460 with different layer numbers are provided in Fig. 6.12.

As expected, the PBG nature became evident as the thickness of NIO-460 was increased. As the layer number was increased to five, we could obtain characteristic photonic band edge, which was at the wavelength of 1.68 μm. Like the grid with smaller size, the reduction in the reflectance of NIO-460 occurred at a lower wavelength compared with that of NIO-660.

The position for the photonic band edge can be approached with the real εreal(λ) and imaginary εi(λ) dielectric constants of metals. The photonic band edge was predicted at a specific

Figure 6.11 Mid-IR reflection spectra recorded from NIO-660 and Ni film.

Figure 6.12 Mid-IR reflection spectra recorded from NIO-460 and Ni film.

Figure 6.13 provides the reflectance spectra of CIOs. In the measurement, the light source was illuminating at normal angle to the surface of CIOs. The reflectance from CIO revealed a characteristic oscillation in the region of long wavelength. It suggested that the CIO might serve as a cavity, rendering an optical resonance of standing EM waves. This evidence also inferred that the diameter of the CIOs was rather uniform so an optical resonance could be observed.

Figure 6.13 Mid-IR reflection spectra recorded from (a) CIO-660 and (b) CIO-460.

(a) (b)

Chapter 7

Conclusions

Planar and cylindrical colloidal crystals were fabricated by electrophoretic depositions using 460 and 660 nm PS microspheres. With a moderate EPD rate, the PS microspheres were self-assembled into close-packed structures on the ITO substrate. However, in preparing the CCCs, the ordered arrangement of PS microspheres was affected by the curved surface of CF. The size difference between the microspheres and CFs determined the quality of CCCs. Hence, the CCC-460 revealed a higher quality than the CCC-660 as a result of size difference. Because the increase in the size of substrate provided a relatively flatter surface, the arrangement of PS microspheres on the CFs became ordered with the EPD time.

In addition, the EPD rate on the CF was much larger than that on the ITO since the size of the CF was in micron scale.

Potentiostatic electrodeposition was carried out on the colloidal crystals to fabricate their nickel inverse opals. With a confined plating area, the growth of (220) plane was suppressed in NIOs. Moreover, the NIO-460 displayed only one preferred orientation of (111) plane.

The current density versus time plot was recorded to connect with the thickness for the NIOs during the NED process. By controlling the NED time, semi-layer and multi-layer NIOs were successfully fabricated. In cylindrical cases, the NED rate for the CCC-660 was higher than that of CCC-460. A higher NED rate in the CCC-660 was resulted from its defective EPD layer, which was easier for Ni ions replenishment. Besides, the CIOs provided

temperature of 50 ℃. In contrast, thermal oxidation at 250 ℃ could not only remove the PS entirely without structure distortion, but also improve the crystallinity of NIOs.

In electrical properties, the sheet resistance of NIO-460 was larger than that of NIO-660.

It suggested that the transport path for electrons was increased by the porous structure of NIOs. Furthermore, the CIOs revealed a lower resistivity than that of pure CF. In optical analyses, the as-prepared PCCs presented a high reflectance of 60 % at their photonic band gaps. On the other hand, the CCCs provided broader peaks because of the bending of the colloidal crystals. Moreover, the light-diffracting fringes were observed on the surface of the CCCs. By calculating the position of fringe, the observed color could be derived with CIE 1931 chromaticity diagram. Besides, the NIO displayed a photonic band edge in mid-IR range, and this character became obvious as the layer number of NIO was increased. For CIO, the reflectance with additional oscillation was observed as a result of optical resonance in a cavity structure.

References

[1] Yablonovitch E. Inhibited spontaneous emission in solid-state physics and electronics.

Physical Review Letters. 1987;58(20):2059-62.

[2] John S. Strong localization of photons in certain disordered dielectric superlattices.

Physical Review Letters. 1987;58(23):2486-9.

[3] Lee JH, Leung W, Ahn J, Lee T, Park IS, Constant K, et al. Layer-by-layer photonic crystal fabricated by low-temperature atomic layer deposition. Appl Phys Lett.

2007;90(15):3.

[4] Xia YN, Gates B, Yin YD, Lu Y. Monodispersed colloidal spheres: Old materials with new applications. Adv Mater. 2000;12(10):693-713.

[5] Noda S, Tomoda K, Yamamoto N, Chutinan A. Full three-dimensional photonic bandgap crystals at near-infrared wavelengths. Science. 2000;289(5479):604-6.

[6] Goncalves MC, Bras J, Almeida RM. Process optimization of sol-gel derived colloidal photonic crystals. Journal of Sol-Gel Science and Technology. 2007;42(2):135-43.

[7] Kim SH, Jeon SJ, Yi GR, Heo CJ, Choi JH, Yang SM. Optofluidic assembly of colloidal photonic crystals with controlled sizes, shapes, and structures. Adv Mater.

2008;20(9):1649-55.

[8] Dziomkina NV, Hempenius MA, Vancso GJ. Symmetry control of polymer colloidal monolayers and crystals by electrophoretic deposition onto patterned surfaces. Adv Mater.

2005;17(2):237-40.

hard sphere to soft and dipolar. Nature. 2003;421(6922):513-7.

[11] Besra L, Liu M. A review on fundamentals and applications of electrophoretic deposition (EPD). Progress in Materials Science. 2007;52(1):1-61.

[12] Yang PD, Deng T, Zhao DY, Feng PY, Pine D, Chmelka BF, et al. Hierarchically ordered oxides. Science. 1998;282(5397):2244-6.

[13] Li F, Badel X, Linnros J, Wiley JB. Fabrication of colloidal crystals with tubular-like packings. Journal of the American Chemical Society. 2005;127(10):3268-9.

[14] Lin YK, Herman PR, Xu W. In-fiber colloidal photonic crystals and the formed stop band in fiber longitudinal direction. Journal of Applied Physics. 2007;102(7).

[15] Moon JH, Kim S, Yi GR, Lee YH, Yang SM. Fabrication of ordered macroporous cylinders by colloidal templating in microcapillaries. Langmuir. 2004;20(5):2033-5.

[16] Li JZ, Herman PR, Valdivia CE, Kitaev V, Ozin GA. Colloidal photonic crystal cladded optical fibers: Towards a new type of photonic band gap fiber. Optics Express.

2005;13(17):6454-9.

[17] Yu XD, Lee YJ, Furstenberg R, White JO, Braun PV. Filling fraction dependent properties of inverse opal metallic photonic crystals. Adv Mater. 2007;19(13):1689-92.

[18] Yang YL, Hou FJ, Wu SC, Huang WH, Lai MC, Huang YT. Fabrication and characterization of three-dimensional all metallic photonic crystals for near infrared applications. Appl Phys Lett. 2009;94(4):3.

[19] Lin SY, Ye DX, Lu TM, Bur J, Kim YS, Ho KM. Achieving a photonic band edge near visible wavelengths by metallic coatings. Journal of Applied Physics. 2006;99(8).

[20] Waterhouse GIN, Waterland MR. Opal and inverse opal photonic crystals: Fabrication and characterization. Polyhedron. 2007;26(2):356-68.

[21] Blanco A, Chomski E, Grabtchak S, Ibisate M, John S, Leonard SW, et al. Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near

[22] Cong HL, Cao WX. Two-dimensionally ordered copper grid patterns prepared via electroless deposition using a colloidal-crystal film as the template. Advanced Functional Materials. 2005;15(11):1821-4.

[23] Hao Y, Zhu FQ, Chien CL, Searson PC. Fabrication and magnetic properties of ordered macroporous nickel structures. Journal of the Electrochemical Society.

2007;154(2):D65-D9.

[24] Yablonovitch E, Gmitter TJ. Photonic band-structure: the face-centered-cubic case.

Physical Review Letters. 1989;63(18):1950-3.

[25] Yablonovitch E, Gmitter TJ, Leung KM. Photonic band structure: the face-centered-cubic case employing nonospherical atoms. Physical Review Letters. 1991;67(17):2295-8.

[26] Ho KM, Chan CT, Soukoulis CM, Biswas R, Sigalas M. Photonic band gaps in 3-dimensions: new layer--by-layer peroidic structures. Solid State Communications.

1994;89(5):413-6.

[27] Busch K, John S. Photonic band gap formation in certain self-organizing systems.

Physical Review E. 1998;58(3):3896-908.

[28] Palik ED. Handbook of optical constants of solids. London: Academic press 1985. p.323.

[29] Wang Z, Chan CT, Zhang W, Ming N, Sheng P. Three-dimensional self-assembly of

[33] Cregan RF, Mangan BJ, Knight JC, Birks TA, Russell PS, Roberts PJ, et al. Single-mode photonic band gap guidance of light in air. Science. 1999;285(5433):1537-9.

[34] Garcia-Santamaria F, Lopez C, Meseguer F, Lopez-Tejeira F, Sanchez-Dehesa J, Miyazaki HT. Opal-like photonic crystal with diamond lattice. Appl Phys Lett.

2001;79(15):2309-11.

[35] Everett DH. Basic principles of colloid science. Royal Society of Chemistry. 1988.

[36] Solomentsev Y, Bohmer M, Anderson JL. Particle clustering and pattern formation during electrophoretic deposition: A hydrodynamic model. Langmuir. 1997;13(23):6058-68.

[37] Huang YJ, Lai CH, Wu PW. Fabrication of Large-Area Colloidal Crystals by Electrophoretic Deposition in Vertical Arrangement. Electrochemical and Solid-State Letters. 2008;11:P20.

[38] Miguez H, Yang SM, Tetreault N, Ozin GA. Oriented free-standing three-dimensional silicon inverted colloidal photonic crystal microfibers. Adv Mater. 2002;14(24):1805-8.

[39] Wang H, Li X, Nakamura H, Miyazaki M, Maeda H. Continuous particle self-arrangement in a long microcapillary. Adv Mater. 2002;14(22).

[40] Zheng YB, Juluri BK, Huang TJ. The self-assembly of monodisperse nanospheres within microtubes. Nanotechnology. 2007;18(27):275706.

[41] Moon JH, Yi GR, Yang SM. Fabrication of hollow colloidal crystal cylinders and their inverted polymeric replicas. Journal of Colloid and Interface Science. 2005;287(1):173-7.

[42] Paunovic M, Schlesinger M. Fundamentals of electrochemical deposition:

Wiley-Interscience 2006. p. 53-8.

[43] Kavan L, Zukalova M, Kalba M, Graetzel M. Lithium insertion into anatase inverse opal.

Journal of the Electrochemical Society. 2004;151:A1301.

[44] Bartlett PN, Baumberg JJ, Coyle S, Abdelsalam ME. Optical properties of nanostructured metal films. Faraday Discussions. 2004;125:117-32.

platinum, palladium and cobalt films using polystyrene latex sphere templates. Chemical Communications. 2000;2000(17):1671-2.

[46] Chung YW, Leu C, Lee JH, Yen JH, Hon MH. Fabrication of various nickel nanostructures by manipulating the one-step electrodeposition process. Journal of the Electrochemical Society. 2007;154:E77.

[47] Napolskii K, Sapoletova N, Eliseev A, Tsirlina G, Rubacheva A, Gan'shina E, et al.

Magnetophotonic properties of inverse magnetic metal opals. Journal of Magnetism and Magnetic Materials. 2009; 321:833-5.

[48] Napolskii KS, Sinitskii A, Grigoriev SV, Grigorieva NA, Eckerlebe H, Eliseev AA, et al.

Topology constrained magnetic structure of Ni photonic crystals. Physica B: Physics of Condensed Matter. 2007;397(1-2):23-6.

[49] Chung YW, Leu IC, Lee JH, Yen JH, Hon MH. Fabrication of egg-shell-roofed macroporous nickel films by a template-mediated electrodeposition process.

Electrochimica Acta. 2007;53(4):1703-7.

[50] Sumida T, Wada Y, Kitamura T, Yanagida S. Construction of stacked opaline films and electrochemical deposition of ordered macroporous nickel. Langmuir.

2002;18(10):3886-94.

[51] Biesheuvel PM, Verweij H. Theory of cast formation in electrophoretic deposition.

Journal of the American Ceramic Society. 1999;82(6):1451-5.

[52] Rastogi V, Melle S, Calderon OG, Garcia AA, Marquez M, Velev OD. Synthesis of Light-Diffracting Assemblies from Microspheres and Nanoparticles in Droplets on a Superhydrophobic Surface. Adv Mater. 2008;20(22):4263-8.