J. Phys. Chem. B 2007, 111, 1545-1551
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Effects of Liquid Bridge between Colloidal Spheres and Evaporation Temperature on Fabrication of Colloidal Multilayers Young Gun Ko*,† and Dong Hun Shin‡ Department of Biologic and Materials Sciences, UniVersity of Michigan, 1011 North UniVersity AVenue, Ann Arbor, Michigan 48109-1078, and Electronic Components R&D Center, LS Cable, 555, Hogye-dong, Dongan-gu, Anyang-si, Kyungki-do 431-080, Korea ReceiVed: NoVember 6, 2006; In Final Form: December 17, 2006
For the application of colloidal crystal films as “photonic band gap” materials, their domain size and thickness are significant. The substrate withdrawing speed, the colloidal suspension volume fraction, and the colloidal suspension temperature have been studied for the domain size and thickness controls of colloidal crystals in this study. Stable dispersions of monodispersed polystyrene spheres with a diameter of 245 nm were synthesized according to a general emulsion polymerization for colloidal crystal films. By experimental results and the theoretical relationship between the number of layers and other parameters, we could know that the water bridge between colloidal spheres (which is formed by capillary force) influences the number of colloidal crystal layers significantly.
1. Introduction Three-dimensional photonic crystals are materials with threedimensional periodic variation of the refractive indices. These crystals have potential use in various applications such as waveguides,1 optical filters,2 switches,3 high-density magnetic data storage devices,4 and chemical and biochemical sensors.5 Three-dimensional photonic crystals offer a significant advantage over two-dimensional photonic crystals: they allow the full control of light propagation in all three dimensions. Threedimensional photonic structures are, however, more difficult to prepare than two-dimensional photonic crystals, since they need a patterning in all three dimensions. Two-dimensional photonic crystals are usually made by processes known from silicon technology, which include either (i) lithography and deep etching or, alternatively,6 (ii) electrochemical processes.7 However, with these techniques, it becomes very difficult to control a periodic structure in the depth. Therefore, the preparation of 3D photonic crystals is dominated by techniques such as the self-assembly of preformed objects. And unlike lithography-based techniques that have shown mostly two-dimensional features, a colloidal self-assembly approach can produce complex and regular threedimensional structures including channellike,8 spherical,9 cylindrical,10 ellipsoidal,11 and rectangular shapes as well as more complex forms such as star-shaped assemblies.12 Colloidal selfassembly method is inexpensive, offers relative ease of processing, and requires short processing time, compared to the stepwise manner of microfabrication techniques. The most common methods are electrophoretic deposition,13 gravitational sedimentation of colloidal particles,14,15 vertical deposition by evaporation16,17,18 or by lifting the substrate,19 ice crystallization,20 deposition on a horizontal substrate,21 centrifugation,22 colloidal assembly at an air-water interface,23 fluidic cell method,24 and colloidal assembly on a liquid metal surface.25 * Corresponding author. Telephone: +734-647-4205. Fax: +734-6472110. E-mail:
[email protected]. † University of Michigan. ‡ LS Cable.
A great deal of effort has been expended in the study of the thick colloidal PBG crystals for use in optical band stop filters because reflectance is a function of the number of stacked layers in colloidal crystals. As such, it is very important to control the thickness of colloidal crystals. Generally, crystal thickness has been controlled by the concentration of colloidal suspensions; thicker colloidal crystals are obtained in higher concentrations of a suspension. Especially, in the vertical deposition method by lifting the substrate, lifting speed is also important. The vertical deposition method by lifting the substrate is essentially similar to Nagayama’s method,26 which was mainly developed and optimized for the purpose of producing twodimensional monolayer films. In this method, colloidal crystal films are fabricated by lifting the substrate out of the suspension at a constant speed instead of relying on the evaporation of the solvent. In that manner, thick colloidal multilayer films can be made. In his method, because the evaporation of the solvent was derived to control the solvent surface, the concentration of particles changes during evaporation, which may have an effect on the film thickness. Therefore, it is not easy to control the crystal film thickness. In the vertical deposition method by lifting the substrate, the thickness of the film can be controlled from just a single layer to multilayers by changing the lifting speed. And Nagayama’s theoretical relationship between the thickness and the withdrawal rate of the substrate plate is somewhat distinguished from experimental data. When the colloidal suspension evaporates or the substrate is lifted up, the liquid bridge between two colloidal particles on the substrate is formed by the capillary force27 which makes self-assembled colloidal particles.28 Nagayama’s theory is based on monolayers. Therefore, the liquid bridge between two colloidal particles dose not influence the relationship between the thickness and the withdrawal rate considerably. However, the liquid bridge between two colloidal particles is important in the multilayers because of the large shrinkage due to the water evaporation between colloidal particles. The aim of our study is the model development of the relationship between the self-assembled colloidal film thickness
10.1021/jp0672860 CCC: $37.00 © 2007 American Chemical Society Published on Web 01/26/2007
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Figure 1. Schematic of self-assembled colloids on the vertical substrate and normal transmittance spectra of the colloidal crystal film at different positions at 50° of light incidence (here for the polystyrene diameter of 245 nm). Glass substrate is withdrawn in the controlled speed with colloidal suspension heating. Self-assembled polystyrene colloid on the glass substrate shows orange color on the surface of the colloidal suspension. However, it shows blue color at higher position (i.e., in dry state).
and the colloidal volume fraction or the withdrawal rate of the substrate plate by modifying Nagayama’s equation considering the liquid bridge effect between colloidal particles. Moreover, the shapes of self-assembled colloidal domains were studied under various suspension temperatures. 2. Materials and Methods 2.1. Synthesis of Monodispersed Polystyrene Colloidal Particles and Substrate Treatment. Styrene (bp 145-146 °C, 99%, Aldrich Chemical Co.) was distilled at reduced vacuum to remove traces of the inhibitor 4-tert-butylcatechol (bp 285286 °C). Thermal self-initiation during transit and storage is prevented by the addition of a small quantity of inhibitor (1015 ppm) by the manufacturer. The risk of thermal self-initiation is minimized during the removal of the initiator by distilling at reduced pressure, and the use of a dark environment reduces the risk of light-initiated polymerization. Colloidal polystyrene (PS) spheres were synthesized by an emulsion polymerization using a free radical initiator (potassium persulfate, K2S2O8, 99%, Aldrich). 20 g of styrene (99%, Aldrich), 200 g of deionized water, 0.2 g of potassium persulfate (99%, Aldrich), and 0.14 g of sodium dodecyl sulfate (SDS, 99%, Aldrich) were added into the reaction flask, and then the polymerization was carried out in aqueous solution at 70 °C
for 7 h under a nitrogen atmosphere. The reaction mixture was agitated using a twin-paddled overhead stirrer at 350 rpm. The size distributions of synthesized polystyrene particles were obtained from dynamic light scattering (DLS, Malvern Zetasizer 3000) instrument. In this condition, monodisperse 245 nm diameter polystyrene colloidal particles were synthesized. The used deionized water (18.2 MΩ cm-1) was obtained from a Milli-Q water system. Glass slides (25 mm × 75 mm × 1 mm, Marienfeld Co.) used for the substrates were treated using a piranha solution containing 30% hydrogen peroxide and 70% sulfuric acid for 30 min at ambient temperature. Subsequently, they were rinsed several times with deionized water, sonicated in deionized water once (10 min), rinsed several times with spectroscopic grade ethanol, and sonicated in ethanol once (10 min). The remaining ethanol on the glass surface was removed using nitrogen gas. The glass substrates are hydrophilic after the treatment. The contact angles of water on the substrates were measured as ∼0°. Contact angles were measured by face contact angle meter (Kyowa Interface Science Co., Model CA-D). 2.2. Preparation of Colloidal Crystals Film on the Substrate. The colloidal crystals films were prepared by lifting the substrate after vertical deposition onto the colloidal suspension as shown in Figure 1. Experimental procedures are as follows;
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a suspension of the particles was diluted to a definite concentration (0.1-5.0 vol %) using deionized water. Then, a hydrophilic glass substrate was immersed vertically into the dispersion and lifted up with a constant speed (0.1-50 µm/s), which was precisely controlled by a motor. The temperature was set from 25 to 60 °C. A field-emission scanning electron microscope (FE SEM, HITACHIS S-4200) was used to observe the structures and morphologies of the self-assembled colloidal crystals. A thin layer of gold was sputtered onto the samples prior to imaging. To reveal an edge appropriate for cross-sectional analysis, samples were scraped using a sharp razor blade. Optical properties of the polystyrene colloidal crystal films were evaluated by measuring their transmission spectra at different angles of light incidence using an UV-vis spectrometer (Hanson Technology Co., Operon-3000). 3. Results and Discussion 3.1. Fabrication of Self-Assembled Colloidal Film and Control of Film Thickness. When the colloidal particles arrayed on the glass substrate by lifting the substrate after the vertical deposition onto the colloidal suspension, self-assembled polystyrene colloids showed orange color on the surface of the colloidal suspension. However, blue color was observed in the higher position by the naked eye, as depicted in Figure 1. Therefore, transmittance spectra of these two positions were measured at 50° of light incidence. After withdrawing the substrate, spectra were obtained quickly. The stop band position (λmin) of the fabricated colloidal film at higher position of the glass substrate is 535 nm, while that of the fabricated colloidal film on the surface of the colloidal suspension is 650 nm. The optical properties of colloidal particle arrays vary depending on the size of the nanocolloids.29 The spectral peak positions are related to sphere diameter because the diffraction property approximately obeys Bragg’s law:
mλ ) 2nd sin θ
(1)
where m is the order of diffraction, λ is the diffracted wavelength in a vacuum, n is the effective refractive index of the system (medium and colloidal particle), d is the spacing between the diffracting planes, and θ is the Bragg glancing angle between the incident light propagation direction and the diffracting planes. There are two different ways to tune this distance. One way is to change the diameter of the colloidal spheres,30 and the other way is to increase the separation between the colloidal spheres by solvents.31 In this experiment, the distance between the polystyrene particles, which are on the surface of the colloidal suspension, are separated by deionized water. Therefore, because the distance between the polystyrene particles in wet state is longer than that in the dry state,32 the color was observed orange on the surface of the colloidal suspension while the color of higher position was blue. FE SEM images of self-assembled polystyrene colloidal crystals and normal incidence transmittance spectra of colloidal crystal films at different angles of light incidence are shown in Figure 2. The spheres were organized as ordered close-packed face-centered cubic (fcc) structure with (111) planes as shown in FE SEM images. This colloidal crystal film was fabricated at 25 °C and 5.0 vol % with 0.1 µm/s of the withdrawing speed. The high optical quality of the film can be judged by the naked eye. In Figure 2b, the colors of the film change from yelloworange to blue with increasing incident angle. Detailed information on the optical properties of the opal films was derived by the measurement of UV-vis spectra. The spectra show the transmission of the colloidal crystal film composed of 245 nm
Figure 2. (a) FE SEM images of self-assembled polystyrene colloidal crystals and (b) normal incidence transmittance spectra of colloidal crystal films at different angles of light incidence (here for the polystyrene diameter of 245 nm). The angles are 0, 5, 10, 20, 40, and 50° in the direction of the arrow.
polystyrene spheres. The relationship stop bandwidth of ∆λ/λ0 is ca. 7%, where ∆λ is the width at half-maximum of the peak and the λ0 is the center wavelength of the peak. This value agrees approximately with the theoretical calculation result for a fcc crystal. The peak positions in the spectra depend on the angle between the normal vector of the substrate and the detecting light, and they shift to shorter wavelength with increasing detection angle. The relationship between the peak position and the detecting angle is fitted by the Bragg formula.33
λmax ) 1.633d((nsphere f + nvoid(1 - f))2 - sin2 θ)1/2 (2) where d is the diameter of the sphere (245 nm in this experimental). nsphere and nvoid are the refractive indices of the spheres and voids, respectively. The values of the refractive indices are 1.6 for polystyrene spheres and 1 for air voids. f is the volume fraction, and the value is 0.74 in the fcc structure. θ is the angle of light incidence. The experimental results matched well with the calculation in Figure 2b. Figure 3 shows the dependence of the film thickness on the suspension volume fraction and the withdrawing speed. The film thickness of the controlled crystal films can be controlled by
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Figure 4. Schematic presentation of the particle and water fluxes in the vicinity of multilayer particle arrays growing on a substrate plate that is being withdrawn from a suspension. Here Vw is the substrate withdrawal rate, Vc is the array growth rate, jw is the water influx, jp is the respective particle influx, je is the water evaporation flux, and h is the thickness of the array.
Figure 3. Dependence of the film thickness on the suspension volume fraction and withdrawing speed (here for the polystyrene diameter of 245 nm): (a) pseudolinear relationship between film thickness and volume fraction for different withdrawing speeds and (b) relationship between film thickness and withdrawing speed for different volume fractions. Plots of the thickness as functions of volume fractions and withdrawing speeds are performed using Nagayama’s equation.
changing either the suspension volume fraction or the withdrawing speed. The suspension volume fractions for the fabrication of self-assembled colloidal films were varied from 0.1 to 5.0 vol %. And various withdrawing speeds for each different colloidal suspension were used from 0.1 to 1.5 µm/s. Nagayama’s theoretical relationship between the thickness and the concentration is26
k)
βljeφ 0.605dV(1 - φ)
(3)
where k is the layer number, V is the growth rate of the film determined by the withdrawing speed, φ is the particle volume fraction, je is the solvent evaporation rate, d is the diameter of colloidal spheres, l is the meniscus height, and β is the ratio between the velocity of a particle in solution and fluid velocity. Figure 3a,b graphs were plotted by the above equation. The number of layers increases linearly with the suspension volume fraction for all withdrawing speeds in Figure 3a. However, these fitting lines are the function of φ/(1 - φ). When the experimental data of the number of layers were plotted on the withdrawing speeds according to eq 3, the fitted curves were well-matched with the data at low particle volume fractions.
However, big deviations were shown as particle volume fractions increased. Other research groups showed the same results.34 Sato et al.35 made a few remarks that such phenomena could be due to changes in solvent evaporation speed, because in the case where films are fabricated at high lifting speed, the spheres crystallize at a position farther from the solvent surface than for those fabricated at low speed. We think that multilayers contain a large amount of water in forms of liquid bridges between polystyrene spheres. This effect was not considered on Nagayama’s model because that model was based on the monolayer. Therefore, in the high suspension volume fractions, there should be big deviations in that model. In this study, Nagayama’s model was modified considering the referred effect. 3.2. Model Schematics Considering the Liquid Bridge between Colloidal Spheres and Its Fitting. The growing multilayers of self-assembled particles from a bulk suspension onto a flat glass substrate is schematically shown in Figure 4. A substrate is first immersed vertically into a suspension containing monodispersed spheres. And then, that is withdrawn. Colloid crystallization is initiated in a particle layer on a substrate by strong attractive capillary forces mediated by a bridging meniscus, which tends to minimize its free surface area due to the surface tension of the liquid.28 Such a liquid bridge is formed between spheres at the drying front when the liquid film reaches a thickness equal to the sphere diameter. Before the self-assembled colloidal film drying, the film shows different optical properties in comparison with the dried film as shown in Figure 1. van der Waals and electrostatic forces for the suspension wetting film on the substrate plate also influence the formation of self-assembled colloidal particles. These effects drive particle aggregation in the top layer and create a multilayer. The large surface area of a mesoporous multilayer facilitates solvent evaporation and induces as a secondary process a solvent flux from the suspension bulk through the growing crystal front to the drying particle layer. In this experiment, the withdrawing speed also influences the formation of colloidal film significantly except the evaporation rate. Particles from the suspension bulk
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Figure 5. Relationship between film thickness and withdrawing speed for different volume fractions. Plots of the thickness as a function of withdrawing speed are performed using the proposed equation in this study. In comparison with Figure 2b, the best fits of film thickness data on withdrawing speed are obtained by means of the developed model.
are dragged to the growing crystal front by this solvent flux and settle epitaxially there. According to Nagayama’s model, the formation of layered arrays can be conveniently split in two main stages: (1) convective transfer of particles from the bulk of the suspension to the thin wetting film due to water evaporation from the film surface36 and (2) interaction between the particles that lead to specific textures. In Figure 4, the total water evaporation flux from particle arrays per unit length of the array’s leading edge, Jevap, is the integral of water evaporation flux, je(z) along the axis Z, Jevap ) ∫∞0 je(z) dz. For practical treatment, Nagayama’s group introduced an evaporation length, l ) Jevap/je. By this method, they obtained
hf jw ) lje jp )
βφ j 1-φ w
(4) (5)
For deriving the above equations, equations of Jw ) Jevap, Jw ) hf jw, Jevap ) lje, Jw ) NwVwVwt, Vp ) βVwt, jp ) NpVpVp, φ ) NpVp (the particle volume fraction), and 1 - φ ) NwVw (the water volume fraction) are defined. The values of the evaporation flux from a pure water (je), the thickness of the wetting film at the height of the array’s leading edge (hf), the compensation water influx (jw), the number of water molecules per unit volume (Nw), the water molecule volume (Vw), the macroscopic mean velocity of the water molecules (Vwt), the macroscopic mean velocity of the suspended particles (Vp), the value of the coefficient of proportionality (β), the particle flux (jp), the number of particles per unit volume (Np), and the volume of a single particle (Vp) are used in these equations. The above flux equations are derived by Nagayama. However, in his model, the water between arrayed particles was not considered significantly for getting the equation of the relation ship for the stock of the particles at the array leading edge because his model was based on a monolayer like the wellknown Langmuir-Blodgett (LB) film.37 He just introduced an evaporation length (l), and that length can reduce the error between his model and experimental data in colloidal monolayer or thin multilayers. In thick multilayers, much of the amount
Figure 6. FE SEM images show larger colloidal crystal domain size at higher colloidal suspension temperatures. Suspension temperatures are (a) 25, (b) 40, and (c) 60 °C.
of water is between particles and this cannot be bypassed. Considering the liquid bridge, the next equation is obtained.
Vch(1 - ) + Γ ) hf jp
(6)
The stock of the particles at the array leading edge (hf jp) is equal to the increase in the total particle volume in the arrays and the water volume flux between particles (Γ). In eq 6, Vc is the product of the array growth rate, h is the thickness of the array, and 1 - ( is the porosity of the arrays) is the array density. We can substitute h(1 - ) with 0.605kd and Γ with kΓ′ for k-layer particle arrays for densely (hexagonally) packed spheres. d is the diameter of the particles, and Γ′ is the water volume flux between particles in vertical monolayer direction. Between two same-size particles, the mean curvature (kH)38 and the curvature length (lH) are used for the calculation of Γ′. However, for practical treatment, Γ′ is obtained by fitting experimental data using eq 7 in this study. After substituting jw from eq 4 into eq 5 and the resulting expression for jp into eq 6, by using the above parameters, the
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Figure 7. Schematic for a pinned contact line at different evaporation temperatures. Evaporating water at the contact line induces a flow of particles toward the edge of the upper crystal domain. However, some particles pinned to the substrate. Once the contact line slips, it keeps moving until it runs into a fixed particle, at which point it may become pinned again. In the higher evaporation temperature, water evaporation flux leads more colloidal particles toward the edge of the upper crystal domain. Therefore, larger colloidal crystal domains should be obtained.
relationship between the number of the self-assembled colloidal (k) and other parameters is
k)
j eφ βl 0.605dVw + Γ′ (1 - φ)
(7)
Here we assume that the withdrawal rate of the substrate plate, Vw, is equal with Vc. According to eq 7, the experimental data of the relationship between the number of the layer and the withdrawing speed is plotted as shown in Figure 5. For plotting, d ) 245 nm (0.245 µm) was used. In comparison with Figure 2b, the best fits of the film thickness data on the withdrawing speed are obtained by means of the developed model in this study. In 0.1 vol % of the particle volume fraction, Γ′ is 0 µm2/s. At this value, the developed eq 7 is the same as Nagayama’s eq 3. And in 5.0 vol % of the particle volume fraction, Γ′ is 0.0289 µm2/s. The
value of Γ′ increased with the increase of the particle volume fraction. By this result, we can know that eq 7 can be used in the high particle volume fraction (the highly multilayered film can be fabricated in the high particle volume fraction; therefore, the eq 7 can be used in the highly multilayered film), and Γ′ is important because it indicates the liquid bridge effect between particles in the highly multilayered film, although it is small in comparison with the withdrawal rate of substrate plate (Vw). 3.3. Fabricated Patterns of Colloidal Particles on a Glass Substrate with Increasing Temperatures. Figure 6 shows the FE SEM images of the colloidal domains fabricated by increasing growth temperature. The growth temperature influences the thin film formed in a number of ways. An increase of domain size with increasing temperature was observed by FE SEM. The FE SEM images not only demonstrate the increase of domain size as temperature increases but also suggest changes of the domain shape and the direction of the cracking. At 25 °C,
Fabrication of Colloidal Multilayers the size of the horizontal domains cracking is observed largely, and the small size of the vertical domains cracking is also observed. At 40 °C, the domains are larger than those in 25 °C, and the domains are in general larger than 60 µm in any direction. These increase with increasing temperature, and at 60 °C, domains of 100-350 µm length are obtained. At this temperature, the length of the horizontal direction is larger than that of the vertical direction. A schematic for colloidal crystal growth at different evaporation temperature is shown in Figure 7. When the glass substrate is withdrawn upward, a colloidal particle is first pinned on it. A similar idea is introduced by Stone et al.39 After the particle is pinned, other colloidal particles move to a pinned particle by the water influx from water evaporation.40-42 Then, they assemble three-dimensionally by capillary force. The region of the highest evaporation rate is in front of the pinned particle on the substrate.43 This region induces the direction of the water flow. It is well-established that there is a flow of water toward the edge because the evaporation rate from a pinned drop is greatest at the edge.44 Once colloidal particles are pinned, the contact line is also pinned. This view of contact line pinning and depinning is essentially stochastic and contrasts with a detailed physical model proposed by Adachi et al.45 If the water influx toward the pinned and assembled particles by osmotic pressure and water evaporation is less than the flow toward colloidal suspension by interfacial tension, the contact line moves and the next pinning site forms. Other colloidal particles move to a pinned particle by the water influx from water evaporation again. The contact line keeps moving until the interfacial tension becomes stable because the contact line is in an elongated state, and as such it is possible for the pinned contact line to provide the elastic forces.46 Then, they assemble three-dimensionally by capillary force. These phenomena occur periodically. By these results, domains form in the selfassembled colloidal film. In the higher evaporation rate, more particles flow toward the pinned and assembled particles. Therefore, in higher evaporation temperature, we believe that larger domains form in the self-assembled colloidal film, as shown in Figure 6. McComb et al.47 got a result that the cracking always occurs along the closed packed 〈110〉 directions, and we also got the same result. 4. Conclusions The fabrication of colloidal crystal films on vertical substrates with different withdrawing speeds, suspension concentrations of colloidal polystyrene spheres, and temperatures have been demonstrated in this study. The thickness of the colloidal films grown on the substrate could be controlled by either withdrawing speeds or suspension concentrations of colloidal spheres. By experimental results and the theoretical relationship between the number of layers and other parameters, we could know that the water (which is formed by capillary force) between colloidal spheres influences the number of colloidal crystal layers significantly. The large domain size of self-assembled colloidal films is important in manufacturing three-dimensional photonic crystals. Temperature was the most significant factor to fabricate the three-dimensional photonic crystal (3D PC) film having large domain size and low crack density. At high temperature, a large domain was obtained because of a high evaporation rate. The effect of the evaporation rate on manufacturing a large domain size has been well-discussed in this paper. We hope that the discussed mechanism of the crystal growth on the vertical substrate and experimental results help in the fabrication of the thick 3D PC film having large domain size and low crack density.
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