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Langmuir 2006, 22, 7936-7941
Three-Dimensional Centimeter-Sized Colloidal Silica Crystals Formed by Addition of Base Nao Wakabayashi,† Junpei Yamanaka,*,† Masako Murai,† Kensaku Ito,‡ Tsutomu Sawada,§ and Masakastu Yonese† Faculty of Pharmaceutical Sciences, Nagoya City UniVersity, 3-1 Tanabe, Mizuho, Nagoya, Aichi 467-8603, Faculty of Engineering, Toyama UniVersity, 3190 Gofuku, Toyama 930-8555, and National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan ReceiVed March 24, 2006. In Final Form: June 10, 2006 Three-dimensional (3D) centimeter-sized colloidal crystals can be spontaneously formed simply by dropping a NaOH solution (10 mM, ∼10 µL) into an aqueous dispersion of dilute charged colloidal silica (particle diameter 110 nm, particle volume fraction φ ) 0.023, 3-4 mL). The charge number of the silica particle increases with pH. Upon adding the NaOH solution, first, sub-millimeter-sized polycrystals are formed in the upper part of the sample due to charge-induced crystallization. The local φ value in the crystal region becomes nonuniform. The crystals with a high φ value accumulate at the bottom of the cell and then grow upward as columnar crystals. The crystal widths increase discontinuously with the growth, and in some cases, 3D centimeter-sized crystals are formed. The centimeter-sized crystals are also obtainable by the controlled diffusion of the base from its dilute reservoir. The present findings may prove valuable in the fabrication of large 3D single-crystalline photonic materials.
I. Introduction Sub-micrometer-sized colloidal particles dispersed in liquid media self-assemble to form ordered crystal structures under appropriate conditions.1 These “colloidal crystals,” whose Bragg diffraction wavelengths can lie in the visible light regime, have received considerable attention as novel photonic materials. Since the application of colloidal crystals is greatly restricted due to their size, various ingenious approaches2 have recently been devised to fabricate large single crystals. They include shear annealing,3 colloidal epitaxy,4 and directed growth,5 whereby well-oriented thin colloidal crystals with a large areassometimes >1 cm2sand thicknesses of ∼10 µm to 1 mm have been obtained. However, it is still difficult to construct large three-dimensional (3D) crystals. Although millimeter- to nearly-centimeter-sized 3D crystals have occasionally been obtained in charged colloids,6-8 specific crystallization conditions are required near the crystaldisordered phase boundaries, where the nucleation rates are extremely suppressed. Here, we report that a 3D centimeter* To whom correspondence should be addressed. E-mail: yamanaka@ phar.nagoya-cu.ac.jp. † Nagoya City University. ‡ Yoyama University. § National Institute for Materials Science. (1) (a) Russel, W. B.; Saville, D. A.; Schowalter, W. R. Colloidal Dispersions; Cambridge University Press: New York, 1989. (b) Arora, A. K., Tata, B. V. R., Eds. Ordering and Phase Transition in Charged Colloids; VCH: New York, 1996. (c) Ise, N.; Sogami, I. S. Structure Formation in Solution; Springer: Berlin, 2005. (2) Van Blaaderen, A. MRS Bull. 2004, 29, 85-90. (3) (a) Clark, N. A.; Hurd, A. J.; Ackerson, B. J. Nature 1979, 281, 57-60. (b) Stipp, A.; Biehl, R.; Preis, T.; Liu, J.; Fontecha, A. B.; Scho¨pe, H. J.; Palberg, T. J. Phys.: Condens. Matter. 2004, 16, S3885-S3902. (c) Kanai, T.; Sawada, T.; Toyotama, A.; Kitamura, K. AdV. Funct. Mater. 2005, 15, 25-29. (4) Van Blaaderen, A.; Wiltzius, P. Nature 1997, 385, 321-232. (5) Cheng, Z.; Russel, W. B.; Chaikin, P. M. Nature 1999, 401, 893-985. (6) (a) Okubo, T. Langmuir 1994, 10, 1695-1702. (b) Palberg, T.; Mo¨nch, W.; Schwarz, J.; Leiderer, P. J. Chem. Phys. 1995, 102, 5082-5087. (7) Konishi, T.; Ise, N.; Matsuoka, H.; Yamaoka, H.; Sogami, I. S.; Yoshiyama, T. Phys. ReV. B 1995, 51, 3914-3917. (8) (a) Yamanaka, J.; Koga, T.; Ise, N.; Hashimoto, T. Phys. ReV. E 1996, 53, R4314-R4317. (b) Yamanaka, J.; Yoshida, H.; Koga, T.; Ise, N.; Hashimoto, T. Phys. ReV. Lett. 1998, 80, 5806-5809. (c) Yoshida, H.; Yamanaka, J.; Koga, T.; Koga, T.; Ise, N.; Hashimoto, T. Langmuir 1999, 15, 2684-2702.
sized colloidal crystal can be formed simply by dropping a solution of sodium hydroxide into charged colloidal silica. The crystallization of charged colloids is driven by strong long-range electrostatic interactions between the particles. When the particle size is constant, the major parameters governing the interaction magnitude are the surface charge number of the particles (Z), ionic strength of the medium (I), and particle volume fraction (φ). The crystals are formed at a moderately high Z, large φ, and low I. We previously reported that dispersions of colloidal silica particles, whose Z value inherently increases with pH, undergo charge-induced crystallization upon the addition of sodium hydroxide (NaOH).8 Furthermore, we recently reported that the diffusion of a weak base, pyridine (Py), in a silica colloid from its dilute reservoir results in unidirectional crystal growth.9 In this previous study, the crystal growth was examined under acidic conditions, where the silica particles were charged (tSiOH + Py f tSiO- + PyH+) by the reaction-diffusion of undissociated Py molecules. By this method, we obtained columnar-shaped crystals with a length of several centimeters and a width of up to 1 mm. However, in the case of a strong base such as NaOH, directed growth was rarely observed under acidic conditions since the concentration of the diffusible species (in this case, excess NaOH in a medium) was negligibly small.9 In the present paper, we demonstrate that, under alkaline conditions, NaOH is diffusible in silica colloids, which results in crystal growth; this diffusion-reaction process causes remarkable spatiotemporal nonuniformity in φ. Furthermore, the width of the crystal obtained by diffusion of the base can be as large as 1 cm, and not submillimeter, as observed previously. These were observed when the NaOH solution (10 mM, ∼10 µL) was gently dropped onto a disordered (noncrystal) silica colloid (φ ) 0.023, 3-4 mL), as illustrated in Figure 1. Upon adding the NaOH solution at time t ) 0 (a), sub-millimeter-sized polycrystals were formed immediately, and they gradually increased in number (b). The local φ value in the crystal region (9) Yamanaka, J.; Murai, M.; Iwayama, Y.; Yonese, M.; Ito, K.; Sawada, T. J. Am. Chem. Soc. 2004, 126, 7156-7157.
10.1021/la0607959 CCC: $33.50 © 2006 American Chemical Society Published on Web 07/25/2006
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Figure 2. Experimental setup for controlled directed growth.
Figure 1. Crystallization process initiated by dropping NaOH solution onto colloidal silica starting from t ) 0.
(and hence the density of dispersion) became nonuniform, and the higher density part settled due to gravity (c). Crystals with a high density accumulated at the bottom of the cell in 1 h (d). Then, the small sedimentary crystals grew upward as columnar crystals (e). Their widths increased discontinuously, and sometimes 3D centimeter-sized crystals were formed in ∼100 h (f). The organization of this paper is as follows. The experimental details are given in section II. We then present the characteristics of our colloidal silica when the base concentration is homogeneous throughout the sample (section III.A). The settling of the crystals (Figure 1a-c) is described in section III.B. The upward growth process (Figure 1e,f) and optical characterizations of the crystals are reported in sections III.C and III.D, respectively. In section III.E, we describe a controlled and directed growth by the diffusion of the base from its reservoir, whereby the centimeter-sized crystals are obtained more sophisticatedly. The conclusions of this work are given in section IV. II. Experimental Section A. Materials. Colloidal silica was purchased from Nippon Shokubai Co., Ltd., (Osaka, Japan) as an aqueous dispersion stabilized under an alkaline condition. It was dialyzed in cellulose tubes (pore size 2.4 nm) against purified water for more than 30 days. The completeness of the dialysis was determined by conductivity measurements. Then, after the addition of a mixed bed of cationand anion-exchange resin beads (AG501-X8(D), Bio-Rad Laboratories, Hercules, CA), it was kept standing for at least one week for further deionization. The particle diameter, as estimated by a dynamic light-scattering method, was 110 nm (size polydispersity 8% in standard deviation). The φ value of the sample was determined by a drying-out method using the specific gravity of the silica particles (2.17), which was obtained by a pycnometer method. All the silica
samples were used in the experiments without the addition of extraneous salts. The water was purified using the Milli-Q Simpli-Lab system (Millipore, Massachusetts); this water had an electrical conductivity of 0.4-0.6 µS/cm. The concentration of ionic impurities in the water was estimated to be 2 µM. In the sample preparation process, polystyrene and Teflon apparatuses were used instead of glassware to avoid contamination by ionic impurities from the glass wall. B. Methods. 1. Crystallization by Dropping NaOH. Colloidal silica (φ ) 0.023) was introduced into a poly(methyl methacrylate) cell with a size of 1 × 1 × 4.5 cm. A 10 mM aqueous solution of NaOH was gently dropped onto the colloids by using a mechanical micropipet under an argon gas flow, and the cell was sealed with a plastic film. The crystallization was observed in a room thermostated at 24 °C. 2. Controlled Directional Crystallization. The experimental setup is illustrated in Figure 2. We used a poly(methyl methacrylate) cell (1 × 1 × 4.5 cm) having a semipermeable gel membrane with a thickness of 6 mm at its bottom. The cell was filled with silica colloids (φ ) 0.05) and kept in contact with the base reservoir (50 mL). The crystal growth was examined at room temperature. 3. ConductiVity, pH, and Viscosity Measurements. Electrical conductivity measurements were performed using a DS-12 conductivity meter (Horiba Co., Ltd., Kyoto, Japan) and a platinum electrode with a cell constant of 0.933 cm-1. The temperature was controlled at 25 ( 0.05 °C. The pH values were measured with an F-13 pH meter (Horiba) at room temperature, and were corrected to those at 25 °C. Viscosity measurements were carried out using an Ubbelohde capillary viscometer (shear rate of ∼890 s-1 for water) at 25 ( 0.02 °C under an argon atmosphere. The measurements were repeated at least three times, and the average values were used. 4. Spectrometry and Determination of Local φ. A fiber-optic spectrophotometer, MCPD-8300 (Photal Co., Ltd., Osaka, Japan), was employed for right-angle reflection and transmission spectrometry. The local φ values of the crystals were estimated from the observed Bragg wavelength λm by using the λm-φ relationship (approximately λm ∝ φ-1/3), which was independently determined for homogeneous crystals.
III. Results and Discussion A. Influence of Base Concentration on Equilibrium Characteristics. In the crystallization process shown in Figure 1, the concentration of NaOH (C) in the colloid varies spatiotemporally in a wide range. In this section, we describe the influence of C on several important characteristics of the colloidal silica when C is homogeneous throughout the sample. 1. Particle Charge Number and Excess Base Concentration. The silica particles have a slight negative charge in water due to the self-dissociation of silanol groups on their surfaces (t SiOH T tSiO- + H+). The present silica sample had Z ) 220 in the absence of a base, as determined from electrical conductivity
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Figure 3. Equilibrium characteristics of the silica colloid as a function of the base concentration C: (a) [OH-] and charge number Z (φ ) 0.02); (b) crystallization phase diagram φ; (c) relative viscosity ηr (φ ) 0.02). The red dashed line is the Einstein theoretical value for a dilute hard-sphere dispersion.
measurements performed using a method described elsewhere.10 Since silanols are weak acids, Z increases with C owing to the neutralization reaction of the silanols (tSiOH + NaOH f tSiO+ Na+).11 At a sufficiently small C, the added base is almost entirely used up for this charging-up reaction,10 while at very high values of C, it is present in excess in the medium (illustrated in the upper part of Figure 3). Hereafter, the concentration of the excess NaOH is referred to as Cex. The concentration of the Na+ ions that are present as counterions of the silanols (Cc) is equal to C - Cex. Z is given by Z ) (NACc)/(103n), where n is the particle number density (≡φ/(4πap3); ap is the particle radius) and NA is Avogadro’s constant. Figure 3a shows the molar concentration of the OH- ion in a medium, [OH-], which was determined by pH titration, plotted against C on a double-logarithmic scale (red circles). The φ value was 0.02, which was close to that for the drop crystallization experiments (φ ) 0.023). The Z values were estimated from the above-mentioned relation by assuming Cex ) [OH-]. At around a neutral condition, the dissociation of the water molecule also makes a significant contribution to [OH-]. However, since the [OH-] values themselves are considerably smaller than C (for example, C ≈ 100 µM at pH ) 7 and [OH-] ) 0.1 µM), they had little effect on the estimation of Z. The Z values thus obtained are shown by the blue circles in Figure 3a.12 (10) Yamanaka, J.; Hayashi, Y.; Ise, N.; Yamaguchi, T. Phys. ReV. E 1997, 55, 3028-3036. (11) Iler, R. K. The Chemistry of Silica; Wiley: New York, 1979. (12) We note that the “effective” charge number Ze is considerably smaller than Z due to the counterion condensation effect. The I value is approximately equal to Cex + (1/2)fCc, where f ≡ Ze/Z. An empirical relationship between Z and Ze for the silica particle for Cex ≈ 0 has been reported in ref 8c.
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2. Crystallization Phase Diagram. Figure 3b shows the phase diagram for the present silica colloid defined by C and φ. The samples were homogenized by shaking after the NaOH additions, and the crystal states were assigned after 10 min by detecting the Bragg diffractions. In the absence of NaOH, the colloids were disordered, whereas they underwent charge-induced crystallization at critical C values (C*) of ∼20 µM, almost independent of φ (the critical Z value is smaller for larger φ). With a further increase in C, they re-entered into disordered states at C ≡ C**, which is presumably due to a large Cex, as suggested by the viscosity behavior described below. (We note that suppressed crystallization at high Z values has been observed for colloidal silica8 even when Cex ≈ 0, and also for dispersions of highly charged polystyrene particles with strong acid groups13 (Z ) 14000) when Cex ) 0.) The visible-light reflection spectra of the crystal states were examined in a wide range of C (20, 50, 100, 200, and 500 µM) at φ ) 0.02 and 0.03. In all cases, they exhibited maximum diffraction at λ ) λm and higher order diffraction at λ ) λm/x2. For φ ) 0.02, the third-order diffraction was also observed at λ ) λm/x3 (∼400 nm), which is in the visible-light regime. This diffraction pattern is attributable to randomly oriented polycrystals that have body-centered-cubic (bcc) lattice symmetry; the Bragg peaks are ascribed to diffractions by the {110}, {200}, and {211} lattice planes. The bcc structure was also observed in previous scattering studies on dilute silica crystals.7,8 3. Viscosity BehaVior. The viscosity of the colloids strongly depends on the magnitude of the interparticle interaction. Figure 3c shows a plot of the relative viscosity ηr against C at φ ) 0.02 (ηr ) η/η0; η and η0 are the viscosities of the colloid and medium (water), respectively). ηr first increased with C and reached a maximum value at C ≈ 80 µM. With a further increase in C, ηr decreased remarkably and approached the Einstein theoretical value for a dilute hard-sphere dispersion (ηr ) 1 + (5/2)φ, red dashed line in Figure 3c). This suggests that, at sufficiently high C values, the interaction is substantially screened by the presence of excess base. B. Settling of Crystals Due to Dropping of NaOH. When the NaOH solution (volume V ) 2-20 µL) was dropped onto the silica colloid (volume V ) 3 or 4 mL), the resulting chargeinduced crystallization caused significant nonuniformity in φ, whereby higher density crystals settled. In this section, we describe a process for (V, V) ) (3 mL, 10 µL) in which all small crystals formed in the upper part of the sample accumulated at the bottom of the cell and then grew upward to form large crystals. The settling of the crystals and the subsequent upward growth were reproduced effectively in more than 30 independent experiments. For V g 15 µL, a part of the small crystals remained without sedimentation, resulting in a sub-millimeter-sized polycrystal structure throughout the sample; for V e 6 µL, all the small crystals accumulated at the bottom of the cell, but they did not grow into large crystals (see section III.C). When the NaOH solution was added from the middle of the cell along the vertical direction, a part of the resulting small crystals floated to the sample surface, while the others settled. The floating crystals partly settled over time and accumulated at the bottom of the cell. Figure 4 shows images of the evolution of crystallization with time t after the addition of NaOH. The crystal regions are iridescent due to the Bragg diffractions, while the disordered regions have a blue opaque appearance. After addition of the base, the submillimeter-sized crystals that were immediately formed in the (13) Toyotama, A.; Sawada, T.; Yamanaka, J.; Kitamura, K. Langmuir 2003, 19, 3236-3239.
Silica Crystals Formed by Addition of Base
Figure 4. Images of settling of crystals in colloidal silica (φ ) 0.023, 3 mL) generated by adding a solution of NaOH (C ) 10 mM, 10 µL).
Figure 5. (a) Overview of a settling sample (t ) 7 min). (b) Reflection spectra obtained at the various heights indicated in (a) (shifted vertically for clarity). The dashed line represents the Bragg wavelength for a homogeneous system, λm0 ()698 nm). The triangles with each spectrum indicate the {200} diffraction calculated for bcc symmetry. (c) Local φ values determined from the Bragg wavelengths. The dashed line shows the φ value for a homogeneous system, φ0 ()0.023).
upper part of the sample gradually increased in number. The crystals began to settle (a-c) and accumulated at the bottom of the cell within 1 h (d). The subsequent upward growth process for the same sample is shown in Figure 4e for reference. The local φ values in the crystal region were determined by in situ fiber-optic reflection spectrometry after the settling of the crystals. Figure 5a shows an overview of such a sample (t ) 7 min). Figure 5b shows the right-angle reflection spectrum of the sample at six heights at the center of the cell (shown by Figure 5a,b), measured in circular areas with diameters of ∼1 mm. The dashed line in Figure 5b represents λm for a homogeneous crystal, λm0 ) 698 nm. It is evident that λm is significantly smaller than λm0 at lower heights. Each spectrum showed a second diffraction peak at λ ≈ 500 nm, which is in close agreement with that expected for the bcc lattice order (λ ) λm/x2, shown by triangles for each spectrum). Thus, we were able to determine the local φ values from λm by using the λm-φ relationship obtained for the homogeneous bcc crystal. Figure 5c shows the variation in φ plotted against the heights of the measured points (y). The dashed line represents φ in a homogeneous colloid, φ0 ) 0.023. Clearly the addition of NaOH (only 10 µL) caused a remarkable nonuniformity in φ, whereby crystals with high φ values sank to the bottom. We observed that crystals with low φ values gradually dissipated into the disordered region. The maximum
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value of the associated local density difference in the colloid, which was estimated using the φ values and the specific gravity of the silica particle, was ∼0.01 g/cm3. A likely explanation for the above-mentioned process is as follows. The added NaOH solution (C ) 10 mM) yields a large excess base concentration Cex of ∼200 µM (Figure 3a).14 Although the colloid assumes a disordered state at this C value (Figure 3b), the region that satisfies the crystallization condition (C* e C e C**) should be enlarged due to the diffusion of the base. Throughout these processes, the C values are spatially nonuniform, which gives rise to inhomogeneity in Z and I. Then, to attain a local interparticle force balance, φ-which is another important governing parametersshould also become nonuniform, thereby causing the crystals to settle. The viscosity behavior (Figure 3c) suggested that the interaction magnitude significantly decreased with C for C > 80 µM and was close to the hard-sphere limit at C ≈ 10 mM. Thus, the local regions in the colloid with sufficiently high C should possess a larger φ than φ0. In other words, the sedimentary crystals should contain a large amount of excess base, which facilitates the subsequent upward growth. In addition to the above-mentioned mechanism, the electric fields generated by NaOH diffusion would lead to the uphill diffusion of the negatively charged silica particles.15 The electrophoretic mobility of the OH- ion in water is considerably larger than that of the Na+ ion, which generates electric fields having a direction opposite that of the diffusion. This also accounts for the larger φ at higher C. It has been reported that highly charged colloids exhibit gascrystal phase separation under salt-free or low-salt conditions.16 Then, the φ values of the crystal regions are greater than the average even in equilibrium. The presently observed settling of the crystals might partly be due to such nonuniformity, when C is not very high. C. Upward Crystal Growth. The sedimentary polycrystals grew upward when the V values were sufficiently large, as seen in Figure 4e. This is explainable in terms of the reaction-diffusion of the large amounts of excess base contained in them. The interface between the crystal and disordered regions became almost horizontal within a few hours, presumably due to gravity. Figure 6 shows the time evolution of the height of this interface (h) measured from the bottom of the sample (averaged values for at least four independent samples). The colored symbols connected by solid lines are those for V ) 3 mL at four V values. Substantial growths were observed for V g 8 µL, while at smaller V values, the crystals gradually melted over time. We note that V ) 6 µL gives C ) 20 µM at complete homogenization, which is close to C* (Figure 3b). Thus, it is reasonable that a marked crystal growth was observed for V > 6 µL. The gradual melting at V ) 6 µL is probably due to the presence of a trace amount of ionic impurities such as sodium carbonates, which are produced by a neutralization reaction of the base with airborne carbon dioxide; this would cause significant crystal melting near C*. In Figure 6, the black solid circles connected by a dashed line represent the growth for (V, V) ) (4 mL, 13.3 µL); this was chosen so that V/V is the same as that for (V, V) ) (3 mL, 10 µL). The crystal growth rate markedly decreased with t. This is expected due to a finite amount of the diffusible species as well as a rapid reduction in Cex with decreasing C. We note that a (14) Here, we assume that instantaneous equilibrium is locally attained for the neutralization of the silanols. If this is not the case, Cex should be larger, which favors the enlargement of the crystal region. (15) Prieve, D. C.; Anderson, J. L.; Ebel., J. P.; Lowell, M. E. J. Fluid Mech. 1984, 148, 247-269. (16) Mohanty, P. S.; Tata, B. V. R.; Toyotama, A.; Sawada, T. Langmuir 2005, 21, 11678-11683.
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Figure 6. Upward crystal growth curves. h is the height of the interface between the crystal and disordered regions. V and V are the volumes of the colloid and the added NaOH, respectively.
Figure 8. Reflection (a) and transmission (b) images of three samples (#1-#3) containing large crystals [(V, V) ) (4 mL, 13.3 µL), t ) 5 days].
Figure 7. (a) Overview of the sample showing the variation in the size and shape of the crystals with growth [(V, V) ) (4 mL, 13.3 µL), t ) 3 days, S/C ) sedimentary and columnar crystals, L ) large crystals, and D ) disordered region]. The 3D centimeter-sized crystal part is shown by an arrow. (b) Magnified image of (a).
trace amount of sodium carbonate, which may be present in the colloids as an impurity, would effectively promote crystal growth, particularly in the late stage of growth. We separately confirmed that the diffusion of sodium carbonate or sodium hydrogen carbonate results in directional crystallization,9 the details of which will be reported in a separate paper. The size and shape of the crystals significantly varied with growth. Under the growth conditions shown in Figure 6, millimeter-sized columnar-shaped crystals were first formed from the small sedimentary crystals. In all the cases where V g 8 µL, the width of the crystals increased discontinuously. Figure 7a shows an overview of the samples obtained for (V, V) ) (4 mL, 13.3 µL) at t ) 3 days. The images were taken under illumination with a halogen lamp. The S/C region in Figure 7a is that which contains the sedimentary and columnar crystals. Above the S/C region, large crystalsssub-centimeter- to centimeter-sizedswere formed (hereafter referred to as the L region). A magnified image
of the zone near the boundary between the S/C and L regions is shown in Figure 7b. As seen in Figure 7a, in some cases, the large crystals grew such that their cross section corresponded with that of the cell, 1 × 1 cm2; simultaneously, they grew vertically upward to a height of over 1 cm to form 3D centimetersized cubic crystals (shown by an arrow in Figure 7a). Above the L region, the sample is disordered (D). Figure 8 shows the images of three samples containing large crystals (denoted as #1-#3) that were formed under (V, V) ) (4 mL, 13.3 µL) at t ) 5 days. (The images were taken under illumination with white LEDs; a, reflection; b, transmission). The large crystals reflected incident light of a specific wavelength that met the Bragg condition (Figure 8a), simultaneously exhibiting good transparencies (Figure 8b). The L region appeared when h increased to ∼1.0 and 1.2 cm for (V, V) ) (3 mL, 10 µL) and (4 mL, 13.3 µL), respectively. As seen in Figure 6, the growth rate decreased to ∼0.1 mm/h around these h values. The decrease in the growth rate would explain the observed increase in the crystal width. In homogeneous colloids, large crystals were formed near the crystallization phase boundaries, as reported in previous studies;6-8 for the present silica colloids, we observed a maximum crystal size of ∼2 mm (φ ) 0.02 and C ≈ 20 µM; cf. Figure 2b). Although the formation of millimeter- to almost-centimetersized 3D crystals has been reported in homogeneous systems,6-8 the crystallization conditions are very severe (e.g., φ < 0.001), wherein the nucleation rate is extremely suppressed. To the best of our knowledge, the colloidal crystals obtained in this study by simply dropping the base are some of the largest crystals reported thus far. D. Optical Characteristics of the Crystals. We examined the reflection and transmission properties of the crystals by fiberoptic spectrometry. Figure 9a shows the transmission image of a sample containing a large 3D crystal, which was obtained for (V, V) ) (3 mL, 10 µL) at t ) 3 days. Parts b and c of Figure 9 show the reflection and transmission spectra of the sample,
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Figure 9. (a) Transmission image of a sample containing large crystals [(V, V) ) (3 mL, 10 µL), t ) 3 days]. (b, c) Reflection and transmission spectra for the sample shown in (a), obtained in a circular area with a diameter of ∼1 mm at various heights (indicated by the numbers in (a)) at the center of the cell.
Figure 11. Large crystals formed by unidirectional growth due to base diffusion (φ ) 0.05, t ) 3 days).
Figure 10. Local λm and φ values vs altitude y for the samples shown in Figure 8. Averaged values for samples #1 - #3. The error bars represent the standard deviations.
respectively, obtained at the cell center (1, small sedimentary polycrystals at the cell bottom, 2, large crystals, and 3, disordered region, as indicated in Figure 9a). Although both the crystals showed sharp reflection peaks, only the large crystal showed a distinct transmission dip, despite a thickness of 1 cm. The transmittance of this crystal at the dip edges was 20-30%; the transmittance for a 1 mm thick crystal was ∼80%, as estimated by the Lambert-Beer rule. This value is as high as that observed for a 1 mm thick crystal prepared separately in a homogeneous colloid (φ ) 0.02) using a thin cell. The lower λm value observed for the sedimentary crystals is reasonable due to their inherent higher density. Figure 10 shows λm for the samples in Figure 8 (averaged value for the three samples) as a function of y. The boundary between the S/C and L regions was placed at y ≈ 1.2 cm. The Bragg wavelength showed a monotonic red shift of ∼3 nm per 1 mm height throughout the crystalline part (h ≈ 3 cm). The φ values estimated from λm are also shown in Figure 10. The fabrication of large crystals with a more uniform lattice spacing will be addressed in future studies. E. Controlled Unidirectional Growth. In the abovementioned crystal growth process, the upward-directed growth is a vital step in the formation of the large crystals. This is facilitated by the controlled diffusion of the base from its dilute reservoir through a semipermeable membrane (Figure 2). We
used a similar experimental setup for the Py diffusion to obtain columnar crystals with a length of 3 cm, but submillimeter in width, in several tens of hours.9 Here we adopted a slower growth rates3 cm in ∼3 dayssto obtain larger crystals, as shown in Figure 11. We used a 100 µM NaOH solution as the base after exposure to air (pH 9.4). Without this exposure, a very low degree of crystallization, if any, was observed. Thus, airborne carbon dioxide effectively promotes the growth, as described above. The composition of the base solution, estimated from the acid-base equilibrium for NaOH + H2CO3 in an aqueous solution, was [NaOH]/[Na2CO3]/[NaHCO3] ) 24/7/62 µM. Here, we note that the entire sample comprised centimeter- or subcentimeter-sized crystals, at variance with that obtained by dropping NaOH. This is presumably because the base concentration was kept sufficiently low throughout the growth.
IV. Conclusions In the present paper, we showed that 3D centimeter-sized colloidal crystals can be formed simply by dropping a base solution onto dilute charged colloidal silica. The observed growth process was an interesting combination of the reaction-diffusion of the base, charge-induced crystallization, and settling of the crystals. In our opinion, the present findings present an intriguing example of coupled nonequilibrium phenomena in charged colloids. Additionally, they should prove valuable in the fabrication of large 3D single-crystalline photonic materials. Acknowledgment. This work was supported by a Grantin-Aid of the Ministry of Education, Science and Culture, Japan (to J.Y. and M.Y.). A part of this work was performed as the “Pilot Applied Research Project for the Industrial Use of Space” of the Japan Aerospace Exploration Agency (JAXA) and the Japan Space Utilization Promotion Center (JSUP). LA0607959
