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A Comparison between the Optical Properties of Amorphous and Crystalline Monolayers of Silica Particles† Antony S. Dimitrov,*,‡ Tetsuya Miwa,§ and Kuniaki Nagayama| L’ORE Ä AL Tsukuba Center, 5-5 Tokodai, Tsukuba, 300-2635 Japan, Frontier Research Program for Deep-sea Extremophiles (DEEP-STAR), Japan Marine Science and Technology Center (JAMSTEC), 2-15 Natsushima-cho, Yokosuka, 237-0061 Japan, and National Institute for Physiological Sciences, Myodai-cho, Okazaki, 444-8585 Japan Received February 25, 1999. In Final Form: May 6, 1999 We compared optical properties of amorphous and crystalline monolayers formed from silica particles on glass substrates. The crystalline monolayers were grown from water suspensions by forming suspension wetting film on the glass surface and controlling the rate of the receding glass-suspension-air threephase contact line. To form the amorphous monolayers, the particle powder was pressed toward the substrate and smeared by using a silicon rubber piece specially prepared with flat and smooth surface. The field emission scanning electron microscopy observations showed particles of slightly varying diameters randomly distributed within the amorphous monolayer. The crystalline layers were built of differently sized domains of hexagonally packed particles. Illuminated by daylight and observed by using a low power optical microscope or the naked eye, the amorphous monolayers of particles between 200 and 500 nm in diameter looked softly colored and matted. The crystalline monolayers of 500 and 1000 nm in diameter exhibited enhanced sharpness of color and brilliancy at some observation angles. The amorphous and crystalline 100 nm particle monolayers exhibited similar antireflective properties. The difference in color appearance between amorphous and crystalline monolayers was experimentally legitimated by the corresponding reflectivity spectra.
Introduction Monolayer films of submicrometer-sized particles are attractive by their characteristic optical properties. Metal colloids can impart color to glasses and cause them to absorb ultraviolet irradiation.1 By using small noble metal particles (Au, Ag) and UV-visual spectroscopy, Bar et al.2 showed that the microstructure of monolayer colloid coats is an important factor determining the optical properties of dendrimer-modified silicon oxide surfaces. Amorphous monolayers of small silica particles can significantly reduce the reflectivity of glasses without sacrificing other optical qualities.3,4 Small silica particles (from 150 to 400 nm in diameter) ordered in threedimensional array form the natural opal skeleton.5 Artificially produced opals find applications to study photonic band gap phenomena6 and to satisfy the human aesthetic needs.7-9 † Part of the experimental data was taken during the Nagayama Protein Array Project, ERATO, JRDC. ‡ L’ORE Ä AL Tsukuba Center. § Japan Marine Science and Technology Center. | National Institute for Physiological Sciences.
(1) Araujo, R. Physics of Non-Crystalline Solids; Pye, L. D., La Course, W. C., Stevens, H. J., Eds.; Taylor & Francis: London, U.K., 1992; pp 591-596. (2) Bar, G.; Rubin, S.; Cutts, R. W.; Taylor, T. N.; Zawodzinski, T. A., Jr. Langmuir 1996, 12, 1172-1179. (3) Endo, Y.; Ono, M.; Yamada, T.; Kawamura, H.; Kobara, K. Nyu Seramikkusu 1995, 8, 31-36. (4) Endo, Y.; Ono, M.; Yamada, T.; Kawamura, H.; Kobara, K.; Kawamura, T. Funtai Kogaku Kaishi 1995, 32, 170-175. (5) Sanders, J. V. Nature 1964, 204, 1151-1153. (6) Bogomolov, V. N.; Gaponenko, S. V.; Germanenko, I. N.; Kapitonov, A. M.; Petrov, E. P.; Gaponenko, N. V.; Prokofiev, A. V.; Ponyavina, A. N.; Silvanovich, N. I.; Samoilovich, S. M. Phys. Rev. E: Stat. Phys. 1997, 55, 7619-7625. (7) Hachisu, S.; Ysohimura, S. Nippon Kessho Gakkaishi 1981, 23, 217-226. (8) Horiuchi, N. Hoseki Gakkaishi 1978, 5, 61-65. (9) Kose, A. Hoseki Gakkaishi 1978, 5, 66-74.
An approach to form amorphous monolayers of monodisperse silica particles on black glass had been already reported by Iler.10 He prepared powders of silica particles with diameters from 15 to 200 nm by drying silica sols. Using the fingertip, he rubbed these powders on clean glass surfaces, thus producing monolayers. The first optical studies with monodisperse latex suspension were reported by Alfrey et al.11 Krieger and O’Neill12 classified the color phenomena observed in assemblages of small particles as follows: (1) colors observed in highly diluted latex suspensions attributed to Mie scattering by individual particles;13 (2) iridescent colors observed in relatively concentrated suspensions of 150-500 nm in diameter particles explained with Bragg diffraction from three-dimensional arrays formed inside the suspension; (3) iridescent colors observed when white light illuminates an ordered monolayer of particles with diameter greater than 400 nm. Recently, Dushkin et al.14 carried out interferometric studies on ordered multilayers of particles with diameters of 40 and 140 nm. According to their theory each particle layer is regarded as a homogeneous plane parallel layer with a thickness equal to the diameter of the particles and an optical density derived from the particle volume fraction in the monolayer. The developed model is not based on a requirement for the order arrangement inside the particle layers or on the material the particles are made from. In the present, we formed dense amorphous monolayers of silica particles on glass substrates and compared their (10) Iler, R. K. J. Colloid Interface Sci. 1972, 38, 496-501. (11) Alfrey, T., Jr.; Bradford, E. B.; Vanderhoff, J. W. J. Opt. Soc. Am. 1954, 44, 603-609. (12) Krieger, I. M.; O’Neill, F. M. J. Am. Chem. Soc. 1968, 90, 31143120. (13) Mie, G. Ann. Phys. 1908, 25, 377 (14) Dushkin, C. D.; Nagayama, K.; Miwa, T.; Kralchevsky, P. A. Langmuir 1993, 9, 3695-3701.
10.1021/la990225r CCC: $18.00 © 1999 American Chemical Society Published on Web 06/23/1999
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interference properties with the properties of the respective crystalline monolayers. Experimental Section Materials. The glass substrate plates were Microslide glasses 76 × 26 × 1 mm produced by Matsunami Glass Inc., Ltd, Japan. The silica (SiO2) particles with diameters of 100, 200, 300, 400, 500, and 1000 nm were supplied in powder state by Nippon Shokubai Co., Ltd., Japan. The water for suspending the particles as well as for washing the cell and substrate plates was filtered through an MILLI-Q SP.TOC. reagent water system. To create a stable wetting suspension film on the glass plates, the particle suspension needs additives in small quantities but strongly enhancing the wettability of the substrates. Experimentally, we prepared a solution to be added in small amounts into the particle suspension. It contained 1 mL of 0.1 M sodium dodecyl sulfate (SDS, Wako Pure Chemical Industries, Ltd), 10 µL of n-octanol (C8H15OH, Wako), 1 mL of 1 mg/mL milk casein (Chameleon Reagent) in 0.1 M sodium hydroxide (NaOH, Wako), and 4 mL of water. The total concentration of nonvolatile substances in this solution was 7.3 mg/mL. The silicon rubber used to produce the dense amorphous particle layers, was a room-temperature vulcanizing (RTV) rubber and was prepared just before the experiment. The silicon together with the polymerizing catalyst (trade number S-9) was purchased from Nisshiri, Japan. We mixed both counterparts according to the producer instructions (10 parts of silicon/1 part of catalyst) in a small 25-mL beaker. Silicon polymerized at room temperature (about 22 °C) for 2 days. Then, we broke the beaker and the soft silicon rubber unit, which had a smooth glasslike surface, was ready for use. Preparation of the Particle Suspensions. To form amorphous particle layers, we used the particle powders as provided by the supplier. To form crystalline particle layers, we first increased the particle monodispersity in the suspensions by using a two-step sedimentation. We suspended 20 g of silica particles in water and filled it up to 50 mL after homogenizing. Then, the water suspension settled until becoming transparent below the top surface. The process lasted from about 2 h in the case of 1000-nm particles to 2 days in the case of 100-nm particles. Later on, by using a micropipet we withdrew 1 mL from the middle of each suspension column and diluted it with water up to 10 mL in a test tube. This diluted suspension was homogenized and allowed to sediment again. After the top suspension part became transparent, we withdrew 2.5 mL from the middle of the suspension column, diluted it with water up to 8 mL, added 0.40.6 mL to wetting enhancing solution, and filled it with water up to 10 mL. Thus, the prepared suspension contained about 1 vol % particles. Before being used, the suspension was homogenized by successive, rapid up-down turnings for a couple of minutes. Experimental Setups and Procedures. The continuous growth of large-scale uniform crystalline layers (or 2D particle arrays) was performed in a laboratory setup, following procedures previously reported.15,16 In these experiments, we have slightly modified the working cell for the formation of silica particle monolayers (see Figure 1). When the microslides were coated with 300-nm diameter or smaller particles, we used the method of the controlled plate withdrawing described in ref 16. The microslide plate was vertically dipped into the suspension (see Figure 1A). The rate of substrate withdrawing was controlled to form monolayer particle arrays. Using a glass plate at an adjustable distance from the substrate allowed controlling the disjoining pressure, Π, in the film and, hence, the film thickness and meniscus slope at the forming array’s leading edge. The disjoining pressure, Π, is roughly proportional to the capillary rise height, H, which can be regulated by changing the distance h. Silica particles with diameters of 400 nm and more were settling rather quickly, thus exhausting the vicinity of the suspension film from particles and breaking the layer growth. For example, 1000-nm silica particles were quick to sediment and by using the above standard procedure a regular growth was possible for no (15) Dimitrov, A. S.; Nagayama, K. Chem. Phys. Lett. 1995, 243, 462-8. (16) Dimitrov, A. S.; Nagayama, K. Langmuir 1996, 12, 1303-1311.
Figure 1. Schematics of the experimental cells used to produce the crystalline monolayers of particles with diameters of 300 nm and smaller (A) and with diameters of 400 nm and larger (B). longer than 5 min (roughly corresponding to less than 0.5-mmwide stripe of 2D array). To coat the substrates with such heavy particles, we redesigned the cell geometry and orientation (Figure 1B). The substrate was horizontally placed on a translational stage. The translation rate was controlled in the same way as for the withdrawing substrate. The suspension was placed between two microcover glasses at about 0.5 mm distant to each other. The double-glass cell with the suspension was placed close to the microslide substrate at a distance of 0.1-0.2 mm as shown in Figure 1B, and then, the capillary connection between the substrate surface and suspension was made using the tip of a clean micropipet. Our cell, whose schematic is shown in Figure 1B, was also used by Matsushita et al.17 to study the distribution of components in composite two-dimensional arrays of latex particles. In both setup variants, the substrate can be withdrawn from the suspension (Figure 1A) or can slide horizontally (Figure 1B) with velocities between 0.1 and 30 µm/s. The array growth was monitored and recorded using a long-working-distance color video microscope with resolution power of about 100 µm. The single particles were not visible, but the formation of a monolayer or bilayer was clearly observed by the color appearance. We have prepared amorphous monolayers by smearing a few cubic millimeters of silica powder onto the substrate surface, using a method similar to that reported by Iler.10 Instead of fingertips, however, we used a freshly prepared silicon rubber piece. We also formed particle color coats on various surfaces other than glasssplastic, paint coat, leather, etc. The particles were slightly pressed with the previously prepared smooth silicon (17) Matsushita, S.; Miwa, T.; Fujishima, A. Langmuir 1997, 13, 2582-2584.
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Table 1. Particle Volume Fraction, φ (%), for Monolayers of 100, 300, 500, and 1000 nm in Diameter Particles 100 nm
300 nm
500 nm
1000 nm
58.1-56.5
Crystalline Monolayers 60.9-57.7 60.6-58.9
60.1-59.0
53.4-50.3
Amorphous Monolayers 54.3-52.1 45.1-41.9
53.7-52.0
rubber surface. While being pressed, the silicon piece was circulated along the substrate until a particle monolayer was formed. The status of the silicon surface was of extreme importance for the formation of a regular monolayer. A surface having high oil excess, as well as a dry surface, was not suitable to form visibly homogeneous monolayers. To form such, the silicon surface needed to be slightly oily. The monolayer homogeneity was determined visually by its color appearance. The monolayer structure was further detailed by using optical and scanning electron microscopy. Microscopes. We used Olympus BH and LEICA DMRB microscopes to observe the silica particles monolayers in reflected light at different magnifications. The microscope light source was a halogen lamp with enhanced intensity in the yellow spectral region. While taking the microphotographs shown in Figures 2-5, we used the LEICA microscope with a built-in daylight filter. In addition, we adapted this microscope with a Photonic multichanel analyzer, PMA-11, from Hamamatsu Photonics, Japan. Thus, we were also able to take the spectra of the light reflected from the samples. The working spectrum range was from 390 to 800 nm with a resolution of 2 nm. Having as a reference the light spectrum reflected by a bare substrate, our spectral analyzer allowed calculating the reflectivity of the sample as a function of the wavelength. We also determined that the minimum sample area, where the spectrum was integrally recorded had a diameter of about 20 µm when a dry 20× objective was used. We used a field emission scanning electron microscope (FESEM, S5000H, JEOL) to visualize the particle order in the crystalline and amorphous monolayers as well. The particle volume fraction in the monolayer, φ, was determined from electron microscope photographs. By using commercial software, we estimated the surface coverage with particles accepting that upright cylinders with radius r and height 2r cover the substrate, where r is the particle radius. The volume of spheres inscribing these cylinders equals 2/3 of the cylinders’ volume. Thus, we calculated φ by multiplying the planar surface coverage by 2/3. The particle boundaries were rather diffuse on the photographs, which created deviations in the estimated surface coverage. We estimated the minimum and maximum surface coverage by applying reasonable limit values for the particle and substrate point intensitiesssee the data for φ in Table 1.
Results We prepared amorphous and crystalline monolayers of silica particles with diameters of 100, 200, 300, 400, 500, and 1000 nm. The temperature of 22 °C and relative humidity of 50-60% appeared to be the most appropriate for formation of the 300-nm particle crystalline monolayers. With these particles we succeeded in forming quite large areas of crystalline monolayer in comparison to that formed by using smaller or bigger particles. Concerning the amorphous monolayer formation, we found that those from the smaller sized particles were easier to be formed while those from the larger sized particles strongly depended on the force applied normally to the silicon rubber piece. Below we characterize the microscopic patterns of crystalline and amorphous silica particle monolayers. Figures 2, 3, 4, and 5 show reflected-light optical microscope and SEM images of the monolayers formed of 100-, 300-, 500-, and 1000-nm particles, respectively. Using SEM images, we also calculated the particle volume fraction in these monolayersssee Table 1.
Figure 2. Images of amorphous (A) and crystalline (B) monolayers of 100 nm diameter silica particles taken in reflected light through an optical microscope. The SEM images in the respective insets show the close particle order. The light blue areas next right to the voids in (B) represent crystalline particle bilayers. (C) Relative reflectivity plotted as function of wavelength.
Figure 2 reproduces the similarities between amorphous (Figure 2A) and crystalline (Figure 2B) monolayers of 100 nm diameter particles. The optical microscope images demonstrate that the light reflected from the monolayers, amorphous and crystalline, has intensity lower than that of the light reflected from the glass surface. In other words, the 100-nm particle monolayers exhibited underlined antireflection properties within the whole visual spectrum. Reflectivity measurements showed an average intensity of about 55-60% from that of the reference bare substratessee Figure 2C. A comparison between Figure 2A and Figure 2B shows that the crystalline monolayer had slightly better antireflection properties than the amorphous one although the monolayer particle density did not significantly differ for both monolayers (see the SEM images in the Figure insets). The upper SEM image
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in Figure 2B reveals the crystalline monolayer domain structure, with an average domain size between 1 and 3 µm in diameter, i.e., about 500-1000 particles per domain. The bilayer islands seen in Figure 2B appear almost as bright as the substrate. Their brightness is similar to that observed with the monolayers of 200-nm particles. Seen under optical microscope in reflected light, the 200-nm particle crystalline monolayer was bright and slightly bluish. The respective amorphous monolayer was also bright and bluish. A maximum in the reflection spectrum was found at 465 nm wavelengths for the amorphous and at 490 nm for the crystalline monolayers. Seen by the naked eye, amorphous monolayers had a light blue coloration. This blue coloration was better seen when 200-nm silica powder was spread to form a monolayer onto a black substrate: glass, plastic, or leather. Under optical microscope, in reflected light, the 200nm particle crystalline bilayer looked blue with a slightly green shadow. The respective triple layer had a blue to violet coloration with two reflection maximums at 430 and 660 nm and a minimum at 530 nm. The 100- and 200-nm particles formed amorphous monolayers that slightly differed from the respective crystalline monolayers by their reflectivity under optical microscope. Parts A and B of Figure 3 show that the 300nm particle amorphous monolayers also looked similar to the crystalline ones. They could, however, be distinguished by the naked eye due to the brilliant light pink opalescence exhibited by the crystalline monolayers. This opalescence was better seen at oblique illumination and observation angles. A dark base screen behind the microslide substrate enhanced the opalescence contrast. SEM images in the insets (Figure 3A,B) show that the packing of the amorphous monolayers was not as tight as that of the crystalline monolayers even though the same interference coloring was observed under microscope in reflected light. The reflectivity spectra in Figure 3C show minimums at about 450 nm and maximums at about 630 nm. The reflectivity extremums for the crystalline monolayer are shifted by about 20-25 nm toward red in comparison with the reflectivity extremums for the amorphous monolayer. Similarly to the 200-nm particle monolayers the interference maximum light reflection from the 300-nm crystalline monolayers was 15-20% stronger than that from the respective amorphous monolayers. Observed in reflected light under a microscope, the 400nm particle crystalline and amorphous monolayers were both lightly green. We found a clear maximum in the green band for each reflection spectrum: for the crystalline monolayer, with top value at 505 nm and relative intensity around 80%; for the amorphous monolayer with top value at 515 nm and relative intensity around 60%. Under the microscope one could also see the dislocations between the different domains in the 400-nm particle crystalline monolayer. The bilayer domains of 400-nm particles were colored in red. Observed by the naked eye, the crystalline particle monolayer had enhanced brilliancy with nuances from bluish green to yellowish green depending on the illumination and observation angles. The respective amorphous monolayers were slightly bluish to light green white, but there was no brilliant color intermixing. Photographs and SEM images of amorphous and crystalline 500-nm particle monolayers are shown in Figure 4. They both looked brownish to red under the microscope. The 500-nm particle amorphous monolayer looked slightly darker with intermixed bright scattering parts. Observed by a naked eye the amorphous monolayers were colored similarly to those in Figure 4A when the illumination and observation angles were close to zero.
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Figure 3. Images of amorphous (A) and crystalline (B) monolayers of 300 nm diameter silica particles taken in reflected light through an optical microscope. The SEM images in the respective insets show the difference in the monolayer density and the close particle order. Interestingly (A) and (B) look similar in reflected light under the microscope. (C) Relative reflectivity plotted as function of wavelength.
When these angles were extended up to 60°, the monolayer coloration became slightly greenish. At the same illumination and observation angles, of about 60°, the 500nm particle crystalline monolayers were brilliant with intermixing colors of the whole visual spectrum. By using an optical microscope, we could observe individual particles within the 1000-nm particle monolayers. Figure 5A shows an amorphous 1000-nm particle monolayer. The bright spots randomly distributed over the entire image represent single or aggregated particles from the second layer. These are recognized in the inset SEM images. Figure 5B shows an optical microscope image of a crystalline 1000-nm particle monolayer. One can see single particles and even the particle alignment within the monolayer. The relatively good alignment of particles
Optical Properties of Silica Particles
Figure 4. Images of amorphous (A) and crystalline (B) monolayers of 500 nm diameter silica particles taken in reflected light through an optical microscope. The SEM images in the respective insets show the difference in the monolayer density and the close particle order. One can see that the amorphous 500 nm particle monolayer is less homogeneous than the respective 100 and 300 nm particle monolayers. (C) Relative reflectivity plotted as function of wavelength.
is demonstrated by the SEM images in Figure 5B. We estimated from Figure 5B that the average domain diameter varied between 20 and 50 µm, i.e., there were of about 500-2000 particles per each domainssimilar to the number of particles per domain within the 100-nm particle monolayers. Even though the crystalline and amorphous 1000-nm particle monolayers had similar light reflecting spectra under microscope (see Figure 5C), they looked completely different from each other when observed by the naked eye at natural daylight illumination. The amorphous particle layer looked rather white as silica powder itself, while the crystalline one exhibited brilliant coloring similar to that of polystyrene particle arrays.16 The silica particle mono-
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Figure 5. Images of amorphous (A) and crystalline (B) monolayers of 1000 nm diameter silica particles taken in reflected light through an optical microscope. Single particles and particle aggregates can be seen at the second layer in (A). One can distinguish the single particles and their order in (B). The SEM images in the inset detail the monolayer structure at different magnifications. (C) Relative reflectivity plotted as function of wavelength.
layer brilliancy, however, was slightly less intensive and less saturated in comparison with the polystyrene particle arrays. Discussion The mechanism of the crystalline monolayer formation has been already discussed in previous articles.15,16,18,19 Generally, the same mechanism applies to the formation of the crystalline monolayers from silica particles in this work. There are two necessary main conditions to obtain well-ordered particle monolayers in wetting films: (1) the (18) Dushkin, C. D.; Yoshimura, H.; Nagayama, K. Chem. Phys. Lett. 1993, 204, 455-460. (19) Nagayama, K. Colloids Surf. 1996, 109, 363-374.
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film thickness must be handled approximately equal to the particle diameter and (2) the particles must be pressed to each other by external forces coming, e.g., from a carefully maintained balance between the hydrodynamic influx and capillary forces. The necessity of these two conditions to be fulfilled was also indirectly confirmed by the mobile dynamic thin lamellar flow method,20,21 where small particles were gathered within a thin liquid film formed on a rotating cylinder surface. Amorphous Monolayer Formation. Let us now consider the formation of an amorphous particle monolayer. The dense packing of particles is clearly due to the applied external force pressing them to each other and simultaneously toward the substrate during the spreading process. Iler10 has suggested that the silica particles adhere onto the glass surface by forming hydrogen bonds between the silanol hydroxyl groups on the particle and substrate surfaces. He also proposed that more bonds were involved in the particle-substrate interaction than in the particleparticle interactions. Even though this hypothesis can provide an explanation, the question of why mainly monolayers were formed on the substrate surface while bilayers and multilayers were rarely obtained is still open for discussion. It also remained to be explained why only monolayers are formed onto other than glass surfacess plastic, leather, ceramics, etc. Generally, the fact only monolayers are formed means the formation free energy of a monolayer differs from the formation free energy of next layers. In addition to Iler’s hypothesis, we can see at least two more alternative and complementary reasons determining the formation of monolayers only. First, sub-microscopic thin liquid films are formed between the substrate and each particle. The liquid phase needed to form the films can be gathered from oil traces released by the freshly polymerized silicon. Another possibility for the liquid phase is water released from hydrated gel on the particle surfaces under the applied pressure. This gel is likely to be present on a freshly prepared silica particle surface. In our case due to the monolayer dependence on the silicon piece oiliness, we assume that the liquid phase was oil consisting of silicon oligomers. Films can be formed between the substrate and a particle and among the particles as well (Figure 6A). During the spreading process almost all of the particles can touch the silicon piece and be wetted with oil. The surface capillary forces predetermine the amount of liquid each particle can bare. We assumed that capillary bridges of extremely thin (e.g., monomolecular) wetting films connected the films formed between the substrate and each particle and among the particles as wellssee Figure 6A. Thus, for an ideal amorphous monolayer system we assumed that the capillary pressure jump, Pc ) Pl Pg, was constant for all films formed between the substrate and particles and among the particles. Here, Pl is the pressure of liquid phase in the film, Pg is the pressure of gas surrounding the monolayerssee Figure 6B. For such systems the Appendix shows that the capillary attraction force between a particle and the substrate is stronger than the force between two particles. Logically, the difference between these two forces should decrease as the particle radius increases due to flattening of the particle surface. This finding coincides with the experimentally observed tendency for the bigger particles to jump easier on the second layerscompare Figures 2A and 5A. (20) Picard, G.; Nevernov, I.; Alliata, D.; Pazdernik, L. Langmuir 1997, 13, 264-276. (21) Picard, G. Langmuir 1998, 14, 3710-3715.
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Figure 6. (A) Schematics representing possible particlesubstrate and interparticle capillary connections in our amorphous particle layers. (B) Sketch of the particle-substrate liquid film (in the right side) and the upper half of the particle-particle liquid film (in the left side). The lower part is a mirror image against the plane z ) 0 and is not shown. Here, θp is the running slope angle of the vector normal to the particle surface and describing it in cylindrical coordinate system z ) Z(r,θ,φ). The angle θ is the respective running slope angle for the liquid menisci. Particle surface meets liquid menisci in a circumference that projects into the points (zc, rc), where we accepted θ ) θp ) θc.
The second reason for the formation of a monolayer mainly can be due to electrostatic forces. The substrate material differs from that of the particles. It is well-known that rubbing of a glass rod on ebonite charges them oppositely. Thus, rubbing particles on the substrate surface during the spreading process may lead to opposite charging and consecutive attraction. The same particle surface charge is not suitable for the formation of a second layer. This electrostatic hypothesis could work only if the particles are not in direct contact with the substrate, i.e., there is an isolating dielectric film between them, e.g., an oil film. Coloring of the Silica Particle Monolayers. In principle, the coloring of particle layers when illuminated with white light is due to the layer structure, in which particles scatter the light. The light beams scattered by neighboring particles interfere with each other. Depending on interference conditions, we see the color of light that satisfies the condition for constructive interference or the color of light complementary to that satisfying the condition for destructive interference. Monolayer coloring strongly depends on the particle size. When observed by the naked eye and illuminated with white light, e.g., daylight, crystalline monolayers of 300-nm diameter and smaller particles exhibit continuous uniform coloring similar to respective amorphous monolayers. However, crystalline monolayers of 400-nm di-
Optical Properties of Silica Particles
ameter and bigger particles exhibit brilliant intermixing of colors depending on the illumination and observation angles. Thus, crystalline silica monolayers do not significantly differ from the respective polystyrene particle monolayers.16,22 In contrast to crystalline monolayers, the respective amorphous monolayers resemble the particle powder white color as the particle diameter increases. The difference in color properties of amorphous and crystalline monolayers mostly relates to the particle alignment, which is clearly observed with the biggest particles used here. A visual comparison between 1000nm particle monolayers shows a tremendous differences crystalline ones are brilliantly colored with color intermixing, while amorphous ones are white as the particle powder itself. The monolayers made of small 100-nm particles show general agreement with the interference theory developed by Dushkin et al.14 The monolayers of middle range sized particles (300-500 nm) show two types of coloring. The first one is in coincidence with the interference theory regarding the particle film as a continuous plate. The second type of coloring relates to the brilliant color intermixing, which is due to light scattering from the differently oriented domains in the monolayer. It depends on the illumination and observation angles. This type of coloring, however, does not immerge from amorphous monolayers, where domains do not exist. The coloring of an amorphous monolayer is due to the interference from a thin continuous film or to the interference within a particle. The light reflectance from a monolayer particle film is not strong enough, and thus the coloring of amorphous monolayers can be better observed when placed onto a dark surface, which reflects much less than the glass surface. The first-order constructive interference determines the color of monolayers from 200 to 300-nm diameter particles. While amorphous 200-nm particle monolayers were looking blue and those from 300 nm particles were pink to red, our expectations are that the whole variation of colors can be obtained by using particles with diameters from 200 to 300 nm. The greenish and brownish coloration of 400-nm and 500-nm particle monolayers is due to a second-order interference, whose intensity is in principle lower than those of first-order interference. A practical quantification of the color of a monolayer of silica particles with diameters from 200 to 300 nm can read
λ ) 2d(1 + 0.26φ) where λ is the wavelength at the interference maximum, which determines the color, d is the particle diameter, and φ is the particle volume fraction in the monolayer. We obtained the above equation by using eqs 2 and 5 in ref 14 and assuming the silica particle refractive index equal to 1.26 as reported by Bogomolov et al.6 The equation is valid only for the first-order constructive interference maximum. With the values for φ from Table 1 applied to 300-nm particle monolayers, the above equation gives λ ≈ 692 nm for the crystalline monolayer and λ ≈ 682 nm for the amorphous monolayer, which is close to the measured λ of 650 and 630 nm. Conclusions In this report we described methods to produce crystalline and amorphous silica particle monolayers. A capillarybased hypothesis explained the formation of amorphous (22) Nagayama, K.; Dimitrov, A. S. Polym. Mater. Sci. Eng. 1995, 73, 238-239.
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monolayers, which are generally free from multilayers. The color properties of crystalline and amorphous monolayers were compared to each other. The amorphous monolayers of particles with diameters between 200 and 300 nm can be used to create warm matted colors in the visual wavelength band. The crystalline monolayers of particles with diameters above 400 nm exhibit brilliant color intermixing depending on the illumination and observation angles. The 100-nm particle monolayers can be successfully used as antireflection coatings, where the crystalline monolayer has slightly better antireflection properties, but the amorphous monolayer is practically easier and faster to obtain. Acknowledgment. The authors thank Dr. C. Bouillon for critical reading the manuscript and his constructive comments. Appendix Below, we show a way to calculate the capillary attraction forces between a particle and the substrate, Fps, and between two identical particles, Fpp, for model systems such as that shown in Figure 6A. Then we calculate example forces for the case of 300-nm particles assuming that the diameter of particle-substrate films is about 60 nm, i.e., about five times smaller than the particle diameter. Figure 6B represents schematics of a particle-substrate film in the right side and the upper half of a particleparticle film in the left side. The lower part of the film represents a mirror image of the upper one and is not shown. Also, we omitted the thickness of wetting film capillary bridges for simplicity but accepted complete wetting of the solid surfaces, with a zero wetting contact angle. The solid particle surface is described by the equation of a sphere and the substrate surface is described by the equation of a plane. We chose a cylindrical coordinate system with origin at the point of contact and Z-axis piercing the particle through the center along the diameter. In such a coordinate system the surface description does not depend on the rotational angle φ. Then, we can write for the substrate plane:
z(r) ) 0
(1)
We describe the coordinates, (z, r) of particle surface points by using the particle radius, Rp, and the running slope angle, θp, defined between the positive Z-axis direction and the particle radius vector pointing at
r ) Rp sin θp z ) Rp(1 + cos θp)
(2)
The liquid surface is described by the Laplace equation of capillarity, Pc ) σ((1/R1) + (1/R2)), where R1 and R2 are the two principal radii of curvature at a point (z, r) from the liquid surface, Pc ) Pl - Pg is the capillary pressure jump across the surface, where Pl is the pressure in the film and Pg is the pressure in the air, and σ is the surface tension. Being exactly correct, the description of the menisci of submicrometer films by using the Laplace equation is a rather crude approximation because of the system’s small size. However, this approach gives an idea for the difference in magnitude of the attraction forces between two particles and between a particle and the substrate. From geometrical considerations 1/R1 ) sin θ/r and 1/R2 ) d sin θ/dr, where θ is the running slope angle as defined in Figure 6B. Then, the Laplace equation can
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be written as
d sin θ sin θ Pc + ) dr r σ
(3)
To complete the equations set one can add the slope of tangent in (z, r)
dz/dr ) -tan θ
(4)
We have neglected the gravity effect in eq 3, which can change Pc with no more than 0.01 Pa. The capillary pressure, Pc, across the menisci in our monolayers is greater than 105 Pa, which will not be influenced by the gravity correction of 0.01 Pa. We transformed eqs 3 and 4 set into the following system of two differential equations:
F ) 2πrcσ sin θc - πr2c Pc
-sin θ dz ) dθ Pc sin θ σ r dr -cos θ ) dθ Pc sin θ σ r
(5)
For the particle-substrate system, which is schematically shown in the right side of Figure 6B, and for the particleparticle system (see the left side of Figure 6B) one can write common boundary conditions, where a numerical integration starts
θ ) θc ;
r ) rc;
z ) zc
(6)
The complementary boundary conditions, where to stop the integration, differed for the systems in both sides of Figure 6B. We stopped the integration at
θ ) π/2;
r ) r0;
z)0
(7)
for the particle-particle system shown in the left side of Figure 6B and at
θ ) 0;
r ) r∞;
for the particle-substrate system shown in the right side of Figure 6B. To find the profiles satisfying the respective set of boundary conditions eqs 6 and 7 or eqs 6 and 8, we used a kind of variation procedure. Initially, we assumed a reasonable value for the angle θc and then calculated zc and rc according to eqs 2 at θp ) θc. By using the NDSolve function of Mathematica 3.0 software, we integrated eqs 5 from θ ) θc to θ ) π/2 for the particle-particle case or to θ ) 0 for the particle-substrate case. The integration in both cases gave a value for z. To satisfy the boundary conditions for eqs 7 or 8, we varied the value of θc and repeatedly integrated eqs 5 until obtaining z ) 0. Thus, we obtained the values for θc and rc needed to calculate the attraction force from the following equation:
z)0
(8)
(9)
The first term in the right side of this equation accounts for the surface force acting along the three-phase particleliquid-air contact line. The second term accounts for the pressure force integrated on the whole particle surface and projected along the Z-axis. We should note that the capillary pressure, Pc, is negative here by definition. Let us now calculate the attractive capillary forces for particle-substrate and particle-particle interactions. For model calculations with 300-nm particles, we have assumed that the liquid surface tension is 20 mN/m, i.e., σ ) 0.02 N/m. To have the film radii about five times smaller than the particle radii, the capillary pressure has to be about 100 atm. From the values σ ) 0.02 N/m, particle diameter 300 nm, and film diameter 60 nm, we evaluated Pc ) -1.33 × 107 Pa. Using the above-described procedure for the case of particle-substrate capillary attraction, we calculated: θc ) 168.8°, rc ) 2.91 × 10-8 m, and Fps ≈ 3.6 × 10-8 N. The respective parameters and capillary force for the case of particle-particle capillary attraction were θc ) 172.2°, rc ) 2.04 × 10-8 m, and Fpp ≈ 1.8 × 10-8 N. Thus, we have shown that capillary attraction between two particles is weaker than the respective particlesubstrate attraction. The difference increases as Pc increases, i.e., liquid quantity decreases. LA990225R
