Homogeneous, Core−Shell, and Hollow-Shell ZnS Colloid-Based

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Homogeneous, Core-Shell, and Hollow-Shell ZnS Colloid-Based Photonic Crystals Ian D. Hosein and Chekesha M. Liddell* Department of Materials Science and Engineering, Cornell UniVersity, Ithaca, New York 14853 ReceiVed September 4, 2006. In Final Form: NoVember 23, 2006 Ordered ZnS-based colloidal crystals from homogeneous, core-shell, and hollow building blocks were prepared via electrosteric colloid stabilization combined with a convective assembly technique. The polyelectrolyte stabilized colloids assembled into face-centered cubic arrays with the (111) face perpendicular to the substrate. Structureproperty correlations were made using scanning electron microscopy, scanning transmission electron microscopy, and UV/visible/near-IR spectroscopy. Multilayer film growth, with film thickness of several micrometers, was achieved. Optical spectra showed (111) stopgaps along with pronounced higher order peaks. The spectral position of the photonic stopgap can be predicted using a volume average refractive index and the Maxwell-Garnett formula for the homogeneous and core-shell particles, respectively. This work holds the promise of harnessing ZnS for optical property engineering and enhanced photonic band gap materials.

Introduction Photonic crystals (PCs) are periodic dielectric structures that tunably inhibit the propagation of light of specific frequency and direction.1,2 This optical phenomenon is expected to advance technologies in areas such as optical circuits, chemical and biological sensing, photovoltaics, and high reflectivity coatings. Colloid-based photonic crystals are particularly attractive due to the low cost of large area deposition, the diversity of colloid chemistries, and the ease of three-dimensional fabrication using self-assembly methods. Colloidal crystals have been prepared from both polymer and silica spheres, using several techniques including convective assembly, confinement-assisted assembly, and sedimentation.3 Crystals of these materials possessed incomplete photonic band gaps,4 but can be used as templates for the infiltration of higher refractive index materials to obtain complete band gaps (inverted opal structures).5 Modifying the distribution of dielectric materials by incorporating certain core-shell (i.e., high-index core, low-index shell) architectures into PCs more than doubles the photonic band gap width compared to the traditional inverted opal structure.6,7 Numerical calculations have also shown that in addition to the complete 8-9 band gap, finely tuned 2-3 pseudogap (stopband) features can be achieved, for example by infiltrating the interstitial pores between hollow ZnS shells of precisely adjusted thickness with a high refractive index medium such as InAs.8 ZnS colloids of both homogeneous and hollow-shell morphology have been utilized as building blocks for PCs in the present * Corresponding author. E-mail: [email protected]; address: 128 Bard Hall, Cornell University, Ithaca, NY 14853; phone: (607) 255-0159, fax: (607) 255-2365. (1) Yablonovitch, E. Phys. ReV. Lett. 1987, 58, 2059-2062. (2) John, S. Phys. ReV. Lett. 1987, 58, 2486-2489. (3) Lopez, C. AdV. Mater. 2003, 15, 1679-1704. (4) Moroz, A.; Sommers, C. J. Phys.: Condens. Matter 1999, 11, 997-1008. (5) Blanco, A.; Chomski, E.; Grabtchak, S.; Isbate, 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, 437-439. (6) Busch, K.; John, S. Phys. ReV. E 1998, 58, 3896-3908. (7) King, J. S.; Gaillot, D.; Yamashita, T.; Neff, C.; Graugnard, E.; Summers C. J. Mater. Res. Soc. Symp. Proc. 2005, 846. (8) Yi, G.; Yang, S. J. Opt. Soc. Am. B 2001, 18, 1156-1160. (9) Piper, W. W.; Marple, D. T. F.; Johnson, P. D. Phys. ReV. 1958, 110, 323-326. (10) Scholz, S. M.; Vacassy, R.; Dutta, J.; Hofmann, H.; Akinc, M. J. Appl. Phys. 1998, 83, 7860-7866.

work. The material possesses a high refractive index9 (cubic ZnS n589 ≈ 2.36) and low adsorption in the visible regime.10 ZnS can also be doped with manganese to induce photoluminescence for optically active photonic materials.11 Additionally, arrays and crystals of homogeneous ZnS colloids may be useful in nanofabrication for the submicron placement of materials such as carbon nanotubes, semiconductor nanowires, and nanobelts. The metal catalysts needed to grow the electronic materials are often sulfurphilic, and their attachment to self-assembled ZnS colloids could promote more uniform and controllable substrate coverage. However, fabricating colloidal crystals using the selfassembly of ZnS-based colloids is challenging. The high density of the particles causes rapid settling from suspensions. Also, the limited particle stability in aqueous suspensions12,13 leads to particle aggregation.14 Velikov et al. demonstrated that a stabilizing shell of silica can be deposited on ZnS colloids in an ethanol solution through the slow hydrolysis of TEOS with ammonia.15 Thin-film colloidal crystals of the stabilized particles on glass substrates were produced using a vertical deposition technique.16 Although silica core-ZnS shell particles were synthesized by the same group,15 assemblies of the particles into colloidal crystals were not reported. Polystyrene (PS)-core-ZnS-shell particles were also functionalized with mercaptoacetic acid and redispersed in a basic potassium hydroxide solution in order to increase the electrostatic charge on the ZnS shell surface.17 The stabilized particles were convectively assembled at room temperature between two glass slides, slowly withdrawn from the particle suspension at 23 µm/ s. This method produced monolayers with only very limited local order. Stabilization using small molecule adsorption may not have induced repulsive interactions strong enough for the (11) Bhargava, R. N.; Gallagher, D.; Hong, X.; Nurmirk, A. Phys. ReV. Lett. 1994, 72, 416-419. (12) Duran, J. D. G.; Ontiveros, A.; Chibowski, E.; Gonzalez-Callebero, E. J. Colloid Interface Sci. 1999, 214, 53-63. (13) Duran, J. D. G.; Guindo, M. C.; Delgado, A. V.; Gonzalez-Caballero, F. Langmuir 1995, 11, 3648-3655. (14) Hunter, R. J. Introduction to Modern Colloid Science; Oxford University Press: New York, 1993; Chapters 4-5. (15) Velikov, K. P.; van Blaaderen, A. Langmuir 2001, 17, 4779-4786. (16) Velikov, K. P.; Moroz, A.; van Blaaderen, A. Appl. Phys. Lett. 2002, 80, 49-51. (17) Breen, M. L.; Dinsmore, A. D.; Pink, R. H.; Qadri, S. B.; Ratna, B. R. Langmuir 2001, 17, 903-907.

10.1021/la062592q CCC: $37.00 © 2007 American Chemical Society Published on Web 02/03/2007

ZnS Colloid-Based Photonic Crystals

formation of long-range ordered crystals from the colloids. Solvent evaporation at room temperature may have also been insufficient for the transport of large particles to achieve the high local volume fraction at the drying front necessary for crystallization. In this report, we describe the fabrication of ZnS PC materials with homogeneous sphere, core-shell, and hollow-sphere bases via electrosteric stabilization with polyelectrolytes and heatassisted convective assembly. Polyelectrolyte adsorption has been shown to enhance colloid stability and abate particle settling.18,19 Furthermore, the increased assembly temperature induces convective flows within the aqueous medium, which continually mix and homogenize the particle suspension.20-22 The method also ensures sufficient particle transport to the drying front. After particle assembly, the polymer coatings can be more easily removed by heating or plasma etch than can a silica surface modification. Experimental Section Materials. Zinc nitrate hexahydrate (Zn(NO3)2‚6H2O) and sodium hydroxide pellets (NaOH) were purchased from Fisher Scientific. Nitric acid (ACS grade, 68.0-70.0%) was acquired from Mallinckrodt Laboratory Chemicals. Thioacetamide (TAA, ACS reagent grade, 99%), poly(vinylpyrrolidine) (PVP, molecular weight (MW) of 360 000 g/mol), and poly(sodium 4-styrenesulfonate) (PSS, MWs of 70 000 g/mol and 1 000 000 g/mol) were purchased from SigmaAldrich. Aqueous suspensions of PS spheres were obtained from Polysciences. Chemicals were used as received. Borosilicate glass vials (outer diameter × height ) 19 × 51 mm) were purchased from Fisher Scientific. Copper transmission electron microscopy (TEM) grids were obtained from Electron Microscopy Sciences. Ultrapure, 18.2 MΩ water was supplied by a combined reverse osmosis and UV Barnstead Nanopure Diamond water purification system (Barnstead International, models D12671 & D11911). ZnS Synthesis. In a volumetric flask, 3.7188 g of zinc nitrate was dissolved in 200 mL of water along with 159 µL of nitric acid (15.7M). The solution was heated to 80 °C in a constant-temperature bath. A 7.5130 g portion of TAA was added, and the contents were transferred to an Erlenmeyer flask. The Erlenmeyer flask was sealed with Parafilm and placed into the heated bath. The reaction was terminated by quenching in a -10 °C chilling circulator bath. The particles were centrifuged, separated from the supernatant, and redispersed in water three times. The ZnS colloids were collected by filtration on mixed cellulose ester membrane filters and were allowed to dry at room temperature. PS@ZnS Synthesis. A 1 mL portion of PS suspension (2.6 wt %) was dispersed in 50 mL of water in a volumetric flask. Two hundred milligrams of PVP was added, and the mixture was sonicated. A 3.7188 g portion of zinc nitrate and 10 µL of nitric acid (15.7 M) were added along with 200 mL of water. The suspension was preheated at 80 °C for 5 min in the heating bath. A 7.5130 g portion of TAA was added, and the suspension was quickly transferred to a 250 mL Erlenmeyer flask. The flask was sealed with Parafilm and was returned to the bath. The reaction was quenched at -10 °C in a cold bath of dynalene heat transfer fluid. The particles were washed three times in water. The suspension was filtered through nitrocellulose filter paper to collect the particles. Assembly. An ∼20 mg portion of ZnS (PS@ZnS) colloids in dry powder form was dispersed in 10 mL of 0.5 M NaCl salt solution containing 50 mg of dissolved PSS polyelectrolyte. The mixture was stirred for 2 h. The particles were washed by centrifugation and (18) Balastre, M.; Persello, J.; Foissy, A.; Argillier, J. F. J. Colloid Interface Sci. 1999, 219, 155-162. (19) Balastre, M.; Argillier, J. F.; Allain, C.; Foissy, A. Colloid Surf. A: Physiochem. Eng. Aspects 2002, 211, 145-156. (20) Vlasov, Y. A.; Bo, X. Z.; Sturm, J. C.; Norris, D. J. Nature 2001, 414, 289-293. (21) Ye, Y. H.; LeBlanc, F.; Hache, A.; Truong, V. Appl. Phys. Lett. 2001, 78, 52-54. (22) Wong, S.; Kitaev, V.; Ozin, G. A. J. Am. Chem. Soc. 2003, 125, 1558915598.

Langmuir, Vol. 23, No. 5, 2007 2893 Table 1. Structural Properties of ZnS-Based Colloids

colloid ZnS PS@ ZnS ZnS shell

core size (nm)

CV (%)

core-shell size (nm)

CV (%)

shell thickness (nm)

CV (%)

206 350 202 356 190 354

6 5 8 5 4 4

344 490 330 450

4 3 5 4

71 67 70 48

9 8 12 12

were redispersed in water three times to ensure removal of residual polymer and salt. The particles were retrieved by filtration using cellulose acetate filter paper. Two to eight milligrams of the PSSsurface-modified ZnS (PS@ZnS) powder was redispersed in 2 mL of water, and the suspension was adjusted to pH 10 with aliquots of NaOH solution. The suspension was transferred to a clean glass vial and was left in an oven at 65 °C overnight. ZnS Hollow-Shell Crystals. PS@ZnS colloidal crystals were calcined in a high-temperature furnace at 400 °C for 4 h (heating rate, 5 °C/min) to produce colloidal crystals with a hollow-shell basis. Characterization. Scanning electron microscopy (SEM) images were obtained with an LEO 1550 field-emission microscope at an accelerating voltage of 1 keV. Dark-field TEM images were taken with an ultrahigh vacuum scanning transmission electron microscope (STEM) at 100 keV accelerating voltage. Copper TEM grids were used as the sample support. Elemental analysis was conducted using a Princeton Gamma-Tech energy dispersive X-ray detector on the TEM with a beam voltage of 20 kV. Powder X-ray diffraction (XRD) was performed using a Scintag X-ray diffractometer with Cu KR radiation. Absorption spectra were collected on a UV/vis/near-IR Shimadzu spectrophotometer (model UV-3101PC) with a beam spot size of ∼5 mm. Fourier transform infrared (FTIR) spectra were obtained using a Mattson Infinite FTIR Gold spectrometer. Samples were examined on a polished NaCl disk substrate. Electrophoretic measurements were performed on a Malvern Zetasizer Nano-ZS at 25 °C using a disposable cell (∼760 µm sample volume, ∼0.01 wt % sample concentration in water).

Results and Discussion Table 1 displays the structural properties of the ZnS-based colloids used in this work. Figure 1a shows an SEM image of the ZnS particles produced by the homogeneous nucleation of ZnS23 from zinc nitrate and TAA precursors. Monodisperse spherical ZnS particles from 100 nm to several microns can be produced with minimal surface roughness and secondary particles.24 Figure 1b shows an SEM image of the PS-coreZnS-shell particles, herein referred to as PS@ZnS, synthesized using a modified chemical bath deposition method. The SEM images indicate the monodispersity of both the homogeneous and core-shell particles. The STEM image in Figure 1c also clearly shows the uniform shell thickness. The particle composition was tailored by selecting the initial core size and adjusting the growth time to obtain a desired ZnS shell thickness. The XRD spectrum shown in Figure 1d corresponds to the sphalerite cubic ZnS phase. Elemental analysis confirmed the presence of Zn and S in the particle shell (Figure 1e). PSS was selected as a stabilizer due to its high charge density and large degree of dissociation in water over a wide pH range.18 The polyelectrolyte was absorbed from 0.5 M NaCl solutions. Figure 2 shows the FTIR spectrum of PSS-coated ZnS colloids (black) and of a thin film of PSS (red) on a polished NaCl disk. The PSS-coated ZnS and PSS control film have corresponding (23) Celikkaya, A.; Akinc, M. J. Am. Ceram. Soc. 1990, 73, 2360-2365. (24) Wilhelmy, D. M.; Matijevic, E. J. Chem. Soc., Faraday Trans. 1984, 80, 563.

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Figure 1. Characterization of ZnS-based colloids: (a) homogeneous ZnS, 340 nm; (b) PS@ZnS, 356 nm core and 63 nm shell; (c) STEM dark-field image of the PS@ZnS particles in image b; (d) XRD spectrum of PS@ZnS; (e) EDS of PS@ZnS. The copper peak is from the TEM grid.

Figure 2. FTIR of PSS film (control, red) and PSS-coated ZnS colloids (black).

transmission dips at wavenumbers 2929 and 1620 cm-1, and several between 1200 and 900 cm-1, confirming that PSS was adsorbed to the ZnS surface. The amplitude of the dips for the PSS-coated ZnS sample was greatly reduced compared to the control, partially because of the low concentration of polyelectrolyte in the composite particles. Signal masking also occurred due to moisture trapped within the pores of particles,25 which persisted when the powder was dried under ambient conditions. The broad -OH signal ∼3438 cm-1 is indicative of the water in the particle. Polyelectrolyte adsorption onto the colloid surface and the resulting colloidal stability were apparent from electrophoretic measurements (Figure 3a,b). The increase in electrophoretic mobility from -1.79 to -3.70 µm‚cm/V‚s confirmed (25) Liddell, C. M.; Summers, C. J. J. Colloid Interface Sci. 2004, 274, 103106.

the charging of the colloid surface through polyelectrolyte absorption. A change in the zeta potential of the particles was observed from approximately -20 mV for a bare ZnS surface12,13 to -50 mV, as expected for PSS-stabilized particles.18 The enhanced stability extended the time required for particles to settle, from less than 1 h to several days. The stabilized colloids were assembled at a particle concentration of ∼0.5 wt % in water adjusted to pH 10. The suspension liquid was evaporated from a clean vial in an oven at 65 °C. A schematic of the heat-assisted convective particle transport to the meniscus and the subsequent assembly is provided in Figure 4a. The films formed on the vial walls displayed bright iridescence (Figure 4b), which was the first indication that ordered colloidal crystals were formed. Sections from the walls of the glass vials were cut using a dremel equipped with a diamond wheel and were examined by SEM. Figure 5a,b shows the top view and cross-sectional images of the homogeneous ZnS colloidal crystals. Ordered packing was observed with domain sizes of approximately 20 µm. The packing was characteristic of the (111)-textured face-centered cubic (fcc) lattice. The majority of the single-crystal domains were separated by a disordered grain boundary region, approximately 2-3 particles wide. The crystals also contained some vacancy and line defects. Ordered colloidal crystals with a similar texture and grain size were also obtained from PS@ZnS colloids (Figure 5c,d). Colloidal crystals of hollow ZnS shells were produced from the core-shell particle assemblies by calcination at 400 °C. The inset of Figure 5d displays several ruptured ZnS shells (202 nm PS particle templates) on a cleaved surface of the sample, showing the hollow ZnS shell basis. The quality of the assemblies depended on the MW of the polyelectrolyte used to stabilize the particles. Ordered assemblies were produced with a MW of 70 000 for 206 nm ZnS colloids and a MW of 1 000 000 for 340 nm ZnS colloids. When the larger MW (1 000 000) was used with the 206 nm colloids and the smaller MW (70 000) was used with the 340 nm colloids,

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Figure 3. Electrophoretic measurements on ZnS colloids: (a) zeta potential for bare (left) and coated (right) ZnS colloids; (b) electrophoretic mobility of bare (left) and coated (right) ZnS colloids.

Figure 5. Colloidal crystals from ZnS-based colloids: (a) top view and (b) cross-sectional images of crystals made from 340 nm homogeneous ZnS particles; (c) top view and (d) cross-sectional images for 356 nm PS@ZnS crystals. Inset in the panel d is a crosssection view of a hollow-sphere assembly (templated on 202 nm core PS colloids). Broken shells demonstrate the hollow-shell morphology.

Figure 4. Convective assembly method: (a) schematic of convective assembly on a glass vial wall; (b) iridescent film and color gradient on glass vial.

disordered films formed. The attachment and conformation of the polymer on the surface is determined by the length of the polymer chain relative to the colloid diameter.26 The lower MW polyelectrolyte can take on a “hairy” structure26 on the smaller colloid surface, where the polymer chain is attached at several regions along its length, and the remaining chain length extends out into the liquid medium. This conformation produces the electrosteric repulsion needed to stabilize the colloids. The critical polymer length to achieve the hairy conformation scales with colloid size. The lower MW polyelectrolyte on the larger 340 nm colloid may yield a conformal polymer coating on the surface, which provides less stability since little remaining chain length (26) Walker, H. W.; Grant, S. B. J. Colloid Interface Sci. 1996, 179, 552-560.

extends into the liquid. The steric contribution to the repulsion between the colloids is thus diminished. The larger MW on the 340 nm colloid provides the desired hairy conformation. Additionally, it is entropically unfavorable for the larger MW electrolyte to adsorb with multiple contacts onto the high curvature surface of the smaller 206 nm colloid,27 where chain length is much larger than the particle diameter. Additionally, films with eight layers or more became increasingly disordered as the number of layers increased. A fine grained polycrystalline structure with small domains (∼8 µm) of fcc packing mixed with local regions of square packing was also observed in these thick films. Such packing may be indicative of a non-close-packed body-centered cubic (bcc) phase. The softsphere colloidal phase diagram for highly charged particles indicates an enhanced region of stability for the bcc crystal structure compared to that of the uncharged hard-sphere system.28 Figure 6 shows the optical spectra obtained at normal incidence to the (111) crystallographic axis for colloidal crystals with homogeneous ZnS, PS@ZnS, and hollow ZnS shell colloidal building blocks. Both ZnS and PS@ZnS samples showed the presence of an L-stopband (circled) as well as defined high(27) Kunze, K. K.; Netz, R. R. Phys. ReV. Lett. 2000, 85, 4389-4392. (28) Murray, C. MRS Bull. 1998, 23, 33-38.

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Figure 6. Absorbance spectra for ZnS-based colloidal crystals: (a) ZnS homogeneous samples, diameters 206 nm (dotted) and 340 nm (solid); (b) PS core-ZnS shell samples, core sizes 202 nm (dotted) and 356 nm (solid); (c) ZnS hollow-shell colloidal crystals produced by calcination of the samples in panel b. Table 2. Bragg Peaks of ZnS Homogeneous, Core-Shell, and Hollow-Shell Colloidal Crystals colloid ZnS PS@ZnS ZnS-Shell

size (nm)

number of layers

λBragg calcd (nm)

λBragg exptl (nm)

206 350 344 490 330 450

4 3 4 4 4 4

583 968 907 1252 840 1008

575 960 920 1274 833 1017

neff ) (1 - f)nair + fnZnS

energyflat band29 peaks associated with the higher energy pseudogaps in the photonic band structure. The L-stopband peaks are relatively small due to the number of crystal layers in the sample and the presence of defects. The insets provide enlarged views of the Bragg peak positions associated with the L-stopbands. Peaks were confirmed to arise from Bragg scattering by matching the peak positions with those predicted by the Bragg equation for diffraction at normal incidence,30,31

λ ) 2dhklneff

(1)

where neff is the effective refractive index of the colloidal crystal, and dhkl is the interplanar spacing (d111 ) x2/3D, for particles of diameter D). In the calculations, the wavelength dependence is considered for both PS32 and ZnS:33

1.0087 × 104 λ2

(2)

1.208 × 107 λ2 - 0.732 × 107

(3)

nPS2 ) 1.5683 + nZnS2 ) 5.164 +

determine the refractive indices. The refractive index of the homogeneous ZnS colloid and ZnS shell are lower than the bulk value due to porosity (28% and 23%, respectively).10 The thin polyelectrolyte coating was not considered in the calculations. The effective refractive index of the assembly of homogeneous ZnS particles was approximated using a volume average34,35

where the wavelength λ is in nanometers and angstroms, respectively, and the experimental bragg peaks are used to (29) Miguez, H.; Kitaev, V.; Ozin, G. A. Appl. Phys. Lett. 2004, 84, 12391241. (30) Jethmalani, J. M.; Ford, W. T. Langmuir 1997, 13, 3338-3344. (31) Holtz, J. H.; Holtz, J. S. W.; Munro, C. H.; Asher, S. A. Anal. Chem. 1998, 70, 780-791.

(4)

where f is the volume fraction occupied by the spheres (0.74 for fcc), nair is the refractive index of air, and nZnS is the refractive index of ZnS. The effective refractive index of the core-shellbased colloidal crystals was calculated using the MaxwellGarnett expression for a dielectric material consisting of coated spheres in an air medium.4 The Maxwell-Garnett mixing formula36 gives the effective dielectric constant eff for spherical inclusions in a background medium from which the effective refractive index (neff ) xeff) can be determined:4

eff ≈ b(1 + 2fR)/(1 - fR)

(5)

where b is the background dielectric (air), R is the polarization factor of the spherical inclusion, and f is the volume fraction of the spherical inclusions (0.74 for fcc). The polarization factor, or polarizability, is the relative tendency of a charge distribution to be distorted by an external electric field. The computation begins with calculating the polarization factors for both the core and shell dielectric materials. For dielectric spheres or shells, this can be expressed in terms of the material dielectric constant (32) Goodwin, J. W.; Ottewill, R. H.; Parentich, A. J. Phys. Chem. 1980, 84, 1580. (33) Palik, E. D. Handbook of Optical Constants of Solids; Academic Press: New York, 1998; pp 597-619. (34) Sunkara, H. B.; Jethmalani, J. M.; Ford, W. T. Chem. Mater. 1994, 6, 362-364. (35) Lu, Y.; Yin, Y.; Li, Z. Y.; Xia, Y. Langmuir 2002, 18, 7722-7727. (36) Maxwell-Garnett, J. C. Philos. Trans. R. Soc. 1904, 203, 385.

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() and background medium dielectric constant (b):

R)

 - b  + 2b

(6)

Thus, for the shell dielectric material, the polarization factor is

Rshell )

shell - air shell + 2air

(7)

in the effective refractive index of the composite crystal as the filling fraction of the high-index material was lowered. The contraction (shrinkage) of the crystal structure as a result of calcination also reduced the lattice constant and contributed to the observed blue shifts. For example, polymer burn-out from the 202-nm-core PS@ZnS sample produced peak positions equivalent to those for a structure built from 190 nm template core particles (if no shrinkage occurred upon removal). Measurements on SEM images revealed an air sphere core of 190 nm diameter within the ZnS shell colloids.

In the case of the core, the shell acts as the background medium, and the polarization factor is

Rcore )

core - shell core + 2shell

(8)

Defining x ) rcore3/rcore-shell3, the polarization factor of the coreshell sphere is given as4

Rcore-shell )

R0 + xR1(b + 2)/( + 2) 1 + 2xR1R0

(9)

where Rc is the polarization factor of a coated sphere. Finally, this value can be substituted into eq 5 to compute the effective dielectric for a colloidal crystal of core-shell spheres. The calculated and measured wavelength positions of the (111) stopbands for the homogeneous and core-shell particle assemblies are summarized in Table 2. The Bragg peak positions were observed in the visible and near-infrared spectral regions. Shoulder-type features rather than true peaks mark the positions of the Bragg reflection in the case of the hollow-shell samples. Reasonable agreement between experiment and theory was found. As expected, a red shift in the peak position with increasing particle size occurred for all crystals, regardless of whether the building block morphology was homogeneous, core-shell, or hollow ZnS spheres. Removing the polymer core from crystals with PS@ZnS building blocks caused a decrease in the Bragg peak position, that is, from 920 to 833 nm for samples with a 202 nm PS core, and from 1274 to 1017 nm for samples with a 356 nm PS core size. The peak behavior arose from the decrease

Conclusion In summary, polyelectrolyte-stabilized ZnS-based colloids were self-assembled into ordered colloidal crystals using the convective assembly method. Hollow ZnS shell colloidal crystals were achieved by burning out the PS cores from PS@ZnS assemblies. The L-stopgap was probed at normal incidence to the (111) planes of the crystals, and higher energy flat bands were also apparent. A volume averaged refractive index was sufficient to model the Bragg peak positions for the ZnS homogeneous colloids, while the Maxwell-Garnett formula was appropriate in the case of the core-shell ZnS colloids. Stopband positions in the visible and near-infrared spectral regions depended on the composition and placement of the high refractive index ZnS material within the PC. Work is in progress to extend the number of layers in the ordered crystals and to tune the stopgap properties by controlling the particle shell thickness on the nanoscale. Acknowledgment. This work was supported in part by the NSF CAREER Award (DMR-0547976). Authors acknowledge the Cornell Center for Materials Research for the use of shared experimental facilities (NSF MRSEC program, DMR-0079992). We also thank Nelson Felix for aid in obtaining the FTIR spectra. Supporting Information Available: Preparation conditions for ZnS colloids of varying size; STEM images of homogeneous and hollowshell ZnS colloids; thick colloidal films from PS@ZnS core-shell colloids. This material is available free of charge via the Internet at http://pubs.acs.org. LA062592Q