Continuous Convective Assembling of Fine Particles into Two

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Continuous Convective Assembling of Fine Particles into Two-Dimensional Arrays on Solid Surfaces Antony S. Dimitrov† and Kuniaki Nagayama* Nagayama Protein Array Project, ERATO, JRDC, Tsukuba Research Consortium, 5-9-1 Tokodai, Tsukuba, 300-26 Japan Received March 22, 1995. In Final Form: September 13, 1995X Forming regular textures of an arbitrary size on smooth solid surfaces is the challenge of future technology to produce new types of optical gratings, optical filters, antireflective surface coatings, selective solar absorbers, data storage, and microelectronics. Here we present a novel approach to form such sophisticated textures: controlling the growth of particle arrays on smooth and wettable solid surfaces. The obtained centimeter-size polycrystalline monolayer films consist of closely packed fine particles. Coloring of the monolayer which arises from the light diffraction, interference, and scattering exclusively inherent in textured films shows the size of the differently oriented crystal domains building the film. The results show that the higher the particle monodispersity, the lower the particle volume fraction, and the higher the environmental humidity, the larger the size of the forming domains.

Introduction Textured surfaces of controlled periodicity are of growing importance for several fields of science and technology. Surface roughness with a periodicity of 10-100 nm is responsible for the recently discovered silicon luminescence.1 Random and periodic roughness on a submicrometer scale is the basis of optical elements, such as gratings,2 interferometers,3 and anti-reflection coatings.4,5 Selective solar absorbers6 utilize surfaces textured on a micrometer-scale periodicity. Textured surfaces can play an important role in photovoltaics,7 and those with a perfect periodicity promise novel technologies for data storage, optics, and microelectronics.8 For example, the surfaces textured by a monolayer of two-dimensional (2D) arrays of 1-µm diameter particles can carry information greater than 100 Mbits/cm2. This information density increases with the inverse square of the particle diameter. The simplest but uncontrolled way to texture solid surfaces by particle arrays is to spread a thin layer of a particle suspension onto a substrate and leave the suspension to dry.9 Another approach to form thin particle layers is to apply the spin-coating technique, in which a suspension of fine particles rapidly spreads over a rotating substrate.10,11 Recently, experimental results revealed the microscopic mechanism of the formation of very thin * Author to whom correspondence should be addressed. Present address: Department of Life Sciences, Graduate School of Arts and Sciences, The University of Tokyo, Komeba, Meguro-ku, Tokyo 153, Japan; phone, 3-5454-6739; fax, 3-5454-4332; e-mail, [email protected]. † Present address: L’Oreal Tsukuba Center, Tokodai 5-5, Tsukuba, 300-26 Japan: Ph, +81(298)47-7984; fax, +81(298)477985; e-mail, [email protected]. X Abstract published in Advance ACS Abstracts, February 1, 1996. (1) Canham, L. T. Appl. Phys. Lett. 1990, 57, 1046-1048. (2) Kumar, A.; Whitesides, G. M. Science 1994, 263, 60-62. (3) Burch, J. M. Nature 1953, 171, 889-890. (4) Yoldas, B. E.; Partlow, D. P. Appl. Opt. 1984, 23, 1418-1424. (5) Hinz, P.; Dislich, H. J. Non-Cryst. Solids 1986, 82, 411-416. (6) Hahn, R. E.; Seraphin, B. O. In Physics of Thin Films; Academic: New York, 1978. (7) Yablonovich, E.; Cody, G. IEEE Trans. Electron Devices 1982, ED-29, 300-305. (8) Hayashi, S.; Kumamoto, Y.; Suzuki, T.; Hirai, T. J. Colloid Interface Sci. 1991, 144, 538-547. (9) Perrin, J. Ann. Chim. Phys. 1909, 18, 5-114. (10) Deckman, H. W.; Dunsmuir, J. H. Appl. Phys. Lett. 1982, 41, 377-379. (11) Deckman, H. W.; Dunsmuir, J. H. J. Vac. Sci. Technol. B 1983, 1, 1109-1112.

layered arrays from micrometer-sized latex particles in wetting films on glass substrates12 and from nanometersized latex particles on glass and mica substrates.13 Both papers pointed out the importance of water evaporation and particle volume fraction in the array formation. The experiments were done using cylindrical cells (i.e., in restricted areas), and a variety of structures were successively obtained from the center toward the wall of the cell in the progression of areas with no particles, hexagonal-packed monolayers, square-packed bilayers, hexagonal-packed bilayers, etc. Although the microscopic mechanism for the array growth was revealed, the parameters that govern the overall growth process were not completely quantified, and a procedure to obtain largesized particle arrays was not proposed. Until now, techniques for the fabrication of particle array films on solid substrates did not allow us to control the growth process, commonly resulting in a variety of defects, restricted size, and instabilities (e.g., sequences of uncontrollable voids and multilayers). The controlled and continuous growth of layered particle arrays on large surface areas remained to be developed. We started trying to control the nucleation and growth of layered particle arrays during our previous experiments on mercury.14 By varying the capillary pressure in this cell, we succeeded in forming a particle-free void surface, particle monolayers (or monolayer particle array film), and particle bilayers. Whereas the capillary pressure influences both the meniscus slope and the velocity of the contact line, the controlling mechanism was not yet well understood. Varying the meniscus slope12 was once suggested as a means of controlling the formation of layered arrays from a monolayer to multilayers, but this approach can be applied only to relatively small cells, up to a centimeter in diameter. Another drawback was that the homogeneous area of the obtained particle arrays never exceeded a millimeter in diameter. Here, we propose a novel approach to control the growth process and to obtain large-sized polycrystalline monolayers of particle arrays. Our approach is based on two breakthroughs: (1) linear, continuous growth of the arrays, where the substrate is slid in the opposite direction, (12) Denkov, N. D.; Velev, O. D.; Kralchevsky, P. A.; Ivanov, I. B.; Yoshimura, H.; Nagayama, K. Langmuir 1992, 8, 3183-3190. (13) Dushkin, C. D.; Yoshimura, H.; Nagayama, K. Chem. Phys. Lett. 1993, 204, 455-460. (14) Dimitrov, A. S.; Dushkin, C. D.; Yoshimura, H.; Nagayama, K. Langmuir 1994, 10, 432-440.

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but with the same rate, as that of the growing arrays and (2) quantitative analysis of the array growth rate to clarify the parameters that govern the overall growth process. Actually, our first idea of controlling the relative position of the array’s leading edge is the key in producing largesized, homogeneous particle arrays (assuming they can be produced on a small scale by any of the previous techniques). The second idea is the control of the acceleration or deceleration of the array production by changing the environmental conditions, such as humidity, temperature, and particle volume fraction. The simplest way to initiate and maintain a linear growth of thin particle arrays is to dip a clean, wettable solid plate into a suspension of particles. When the plate is kept stationary, we found that monolayers and successive multilayers of particle arrays spontaneously start to form on the plate surface from the plate-suspensionair contact line down to the bulk suspension. The homogeneous formation of a monolayer or multilayer was successfully maintained by carefully withdrawing the substrate (the solid plate) together with the already formed particle arrays from the suspension. In fact, when the withdraw rate equals the array formation rate, then these arrays can be continuously formed to any size. We developed and built a laboratory apparatus for fabricating monolayer particle array films on glass plates with our film formation technique. Using this apparatus, we produced polycrystalline monolayers from particles with diameters ranging from 79 to 2106 nm and dense amorphous monolayers from large-sized protein holoferittin molecules. We paid particular attention to the monolayer particle arrays formed from particles with diameters above 400 nm. The centimeter-sized monolayer particle arrays obtained from these particles illuminated in white light exhibited iridescent coloring, which allows distinguishing of the boundaries between differently oriented domains and the defects in the film at low magnification or even with the naked eye when the particles cannot be seen. At a glance, our technique looks like the well-known Langmuir-Blodgett (LB) technique. The main difference is that in our experiments the film on the substrate is being formed at once from the substances dissolved in the solution bulk, while using LB technique requires the film to be initially formed on the solution surface and then to be transferred onto the substrate. Theoretical Considerations Schematics and Regular Formation of Particle Array Films. The profile of growing monolayer particle arrays from a bulk suspension onto a flat substrate plate in the vicinity of the array’s leading edge is schematically shown in Figure 1. The width of the plate is large enough that the growth disturbances at the edges can be neglected, namely, in our model the array’s leading edge is a straight line parallel to the plane of the horizontal suspension surface. 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 surface15 and (2) interactions between the particles that lead to specific textures. The primary driving force for the convective transfer of particles is the water evaporation from the freshly formed particle arrays. In an atmosphere saturated with water vapor and after establishing mechanical equilibrium, the (15) Denkov, N. D.; Velev, O. D.; Kralchevsky, P. A.; Ivanov, I. B.; Yoshimura, H.; Nagayama, K. Nature 1993, 361, 26.

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Figure 1. Sketch of the particle and water fluxes in the vicinity of monolayer particle arrays growing on a substrate plate that is being withdrawn from a suspension. The inset shows the menisci shape between neighboring particles. 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.

pressure balance in an infinitely small bulk volume inside the wetting film is

Π + Pcp ) Pc + Ph,

where Ph ) ∆ρghc

(1)

where Π is the sum of van der Waals and electrostatic disjoining pressures for the suspension wetting films on the substrate plate, Pcp is the capillary pressure due to the curvature of the liquid surface between neighboring particles in the particle film (see the inset in Figure 1), Pc is a reference capillary pressure, Ph is the hydrostatic pressure in a vertical film, hc is the relative height, ∆F is the density difference between the suspension and the surrounding gas atmosphere, and g is the gravity acceleration. When the evaporation of water starts, the right-side terms in eq 1 stay almost constant for a given hc. If we assume that Pc is related to the horizontal suspension surface, i.e., Pc ) 0, then due to the decrease in the total suspension volume as the water evaporates, hc slowly increases. We minimized the change in hc by adding an amount of suspension to compensate the suspension volume decrease. The left-side terms in eq 1, however, increase due to the increase in the curvature of the menisci between the particles; namely, Pcp increases, and due to the thinning of the film Π also increases. (In some cases, ∂π/∂h > 0, where h is the film thickness; but these films are not stable and not suitable for our technique.) Therefore, in an atmosphere unsaturated with water vapor, a pressure gradient, ∆P, from the suspension toward the wetting film arises due to the water evaporation

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(the flux je in Figure 1). The pressure gradient

∆P ) (Π + Pcp) - (Pc + Ph)

(2)

produces a suspension influx from the bulk suspension toward the wetting suspension film. This influx consists of a water component, jw, and of a particle flux component, jp. The water flux jw compensates for the water evaporated from the film je, and the particle flux jp causes particles to accumulate in the film, thus forming dense structures. Naturally, the particle structures thus formed follow the film geometry.16,17 The thickness of vertical wetting films increases from the plate-suspension-air contact line downward toward the bulk suspension due to the hydrostatic pressure. Then, successive monolayers, bilayers, trilayers, etc. are expected to be formed as the continuous particle flux jp fills up the space between the substrate and the film surface. In fact, we observed the formation of successive multilayers when a wettable plate dipped in a suspension of fine particles was kept stationary. The detailed hydrodynamic description of the process of an array growth appears to be a complicated task and might be a subject of further studies. Here, we applied the approach of the material flux balance at the array’s leading edge13,18 and calculated the rate of the substrate withdrawal, which must actually be equal to the rate of the array growth. For a regular and continuous formation of 2D particle arrays onto a substrate plate, which is schematized in Figure 1, the total water evaporation flux from the 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, we introduce an evaporation length, l ) Jevap/je. Here, the evaporation flux from a pure water surface, je, depends on the temperature and humidity of the surrounding atmosphere. Both parameters can be experimentally determined. For the steady state process of an array growth the water evaporation, Jevap, is exactly compensated by the water flow from the bulk suspension into the arrays, Jw, that is, Jw ) Jevap and, hence

where φ ) NpVp is the particle volume fraction in the suspension and 1 - φ ) NwVw is the water volume fraction. The particle flux, jp, drives the growth of particle arrays because the particles attach to the array’s leading edge and remain there. 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, namely, the product of the array growth rate, vc, thickness of the arrays, h, and array density, 1 -  ( is the porosity of the arrays)

vch(1 - ) ) hf jp

(5)

By substituting jw from eq 3 into eq 4 and the resulting expression for jp into eq 5, the rate of the array growth is

vc )

βljeφ h(1 - )(1 - φ)

(6)

In the derivation of eq 6, the values of h and (1 - ) are not important. What is important is their product, which shows the total volume of particles per unit area. To connect h and (1 - ) with the real geometry of the particle arrays, we assume that h is the distance from the substrate to the tops of the particles; namely, for a particle monolayer, h ) d (d is the diameter of the particles). Then (1 - ) is geometrically calculated from the conditions for densely (hexagonally) packed spheres, namely, 1 -  ) 0.605. Taking into account that the dense particle multilayers are, in fact, monolayers displaced one over another, we can substitute h(1 - ) with 0.605kd for k-layer particle arrays. Then, for the formation of dense twodimensional particle arrays (monolayers and multilayers as well), we estimate the withdrawal rate of the substrate plate, vw, by rewriting eq 6

vw ) v(k)c )

je φ βl 0.605 kd(1 - φ)

(7)

(4)

Here, vc(k) is the growth rate of the k-layer array. Equation 7 shows that the growth rate of the dense arrays depends on the particle volume fraction, φ, water evaporation rate, je, diameter of the particles, d, number of layers, k, and an experimentally determined constant, the product βl. Forces Gathering the Particles into 2D Arrays. Recent works have suggested that the interactions between particles confined in thin films can be attributed to electrostatic19,20 and lateral capillary forces.21,22 As it was suggested12,13 and later proven by direct observations,14 the lateral capillary forces are able to gather particles into layered arrays. The phenomenon was observed in situ using polystyrene spheres in wetting films on mercury, where the thickness of the film was controlled by injecting suspension into or withdrawing it from the cell.14 It was observed that in an atmosphere relatively saturated with water vapors the assembling of the particles into array nuclei starts extremely slowly (the average particle velocity of 1.7-µm particles was less than 0.1 µm/s when they were at a distance of about 10-15 µm). However, when the atmosphere in the cell was not saturated with water vapors, the particles were assembling rather quickly. Hence, the rate of the assembling, which is caused by the water evaporation from the film, becomes much higher than those caused by the

(16) Pansu, B.; Pieranski, Pi.; Pieranski, Pa. J. Phys. (Paris) 1984, 45, 331-339. (17) van Winkle, D. H.; Murray, C. A. Phys. Rev. A 1983, 34, 562573. (18) Dimitrov, A. S.; Nagayama, K. Chem. Phys. Lett. 1995, 243, 462-468.

(19) Pieranski, P.; Strzelecki, L.; Pansu, B. Phys. Rev. Lett. 1983, 50, 900-903. (20) Murray, C. A.; van Winkle, D. H. Phys. Rev. Lett. 1987, 58, 12001203. (21) Kralchevsky, P. A.; Nagayama, K. Langmuir 1994, 10, 23-36. (22) Kralchevsky, P. A.; Paunov, V. N.; Ivanov, I. B.; Nagayama, K. J. Colloid Interface Sci. 1992, 151, 79-94.

hf jw ) lje

(3)

where Jw ) hf jw and Jevap ) lje. Here, hf is the thickness of the wetting film at the height of the array’s leading edge and is usually slightly smaller than the thickness of the particle arrays, h. The compensation water influx, jw, is defined as Jw ) NwVwvwt, where Nw is the number of water molecules per unit volume, Vw is the water molecule volume, and vwt is the macroscopic mean velocity of the water molecules. The macroscopic mean velocity of the suspended particles, vp, is proportional to vwt, namely, vp ) βνwt. The value of the coefficient of proportionality, β, depends on the particle-particle and particle-substrate interactions and should vary from 0 to 1. The stronger the interactions, the smaller the value of β. For nonadsorbing particles and dilute suspensions, β approaches 1. Then, the particle flux, jp, which is defined as jp ) NpVpvp (where Np and Vp are the number of particles per unit volume and the volume of a single particle, respectively), is proportional to jw,

jp )

βφ j 1-φ w

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lateral capillary forces. In the experiments reported here, which were carried out in an atmosphere that was not saturated with water vapor, the assembling process was mainly caused by the water evaporation from the wet stripped area that was being formed in the vicinity of the array’s leading edge. After carrying the particles from the suspension bulk toward the array’s leading, the water influx, which compensates for the evaporation, presses them toward the array while poring through the array cavities. The polystyrene particles and the glass plates that we used were negatively charged and repulsed each other when they were in close contact inside the suspension. The close interparticle electrostatic repulsion and the hydrodynamic influx pressure at the array’s leading edge determine the dense packing of the particles in our experiments. The dense hexagonal packing in this case is known as an Alder transition.23 In competition, the close neighboring particles are attracted to each other by the lateral capillary immersion forces, which also cause dense hexagonal packing. The relation between the packing force due to the hydrodynamic pressure of the water influx and the packing force due to the lateral capillary forces depends on the pressure gradient ∆P defined in eq 2 and, thus, on the thickness of the wetting film, hf. Our preliminary theoretical description shows that the lateral capillary part of the packing force increases with the square of the hydrodynamic part. Also, increasing the lateral capillary forces (i.e., decreasing hf and increasing ∆P in eq 2) leads to an increase in the friction force between the substrate and particles, which may suppress the rearrangement processes inside the array and may lead to a formation of smaller domains. Furthermore, we expect that depending on the balance between the hydrodynamic stream and lateral capillary forces, which can be regulated (for example, by changing ∆P, hc, or je), smaller or larger highly ordered domains can be formed onto the substrate plate. Origin of Particle Array Formation. We have already regarded the process of regular array growth and the forces acting on the particles during this process. Below, we consider the origin of the array growth process, i.e., how the particle arrays start to grow. When the wettable plate is dipped into the suspension, a wetting film arises upward along the plate. Due to the hydrostatic pressure in such vertical wetting films, the film thickness, hf, decreases as the relative height, hc, increases. Thus, the water-air interface may actually have a relatively high inclination toward the substrate (water-plate interface) and may cause a capillary force, which pushes the particles out of the film regions thinner than the diameter of the particles.14,21 Hence, the lateral capillary forces are not able to initiate the array growth process in our experiments. Furthermore, at this initial stage of the array formation process, because of the absence of particles in the wetting film, Pcp in eq 2 is equal to zero and cannot increase to produce the pressure difference ∆P, which can create suspension influx toward the film. However, the dependence of the film thickness, hf, on the disjoining pressure, Π, for wetting films can become very steep when hf is on the order of hundreds nanometers, i.e., the derivative ∂π/∂h can approach extremely large negative values for hf less than 1 µm. At such thicknesses the vertical films exhibit a slight dependence of hf on the height hc. Furthermore, when water evaporates from such a film the disjoining pressure, Π, increases, thus creating pressure difference ∆P despite that Pcp ) 0 (see eq 2). The created ∆P produces suspension influx, which carries (23) Alder, B. J.; Hoover, H. G.; Young, D. A. J. Chem. Phys. 1968, 49, 3688-3696.

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Figure 2. Onset of particle array formation in a wetting film. The particle diameter is slightly larger than the thickness h0. Then, water evaporation from the film causes suspension influx from the bulk toward the film. The monolayer particle arrays are initiated successfully, and their growth can continue.

particles and stores them into the film. We must note here that the wetting film can rupture at high evaporation rates due to the hydrodynamic friction in the compensation influx or at thicknesses less than some value h0, at which the derivative can change its sign and becomes positive. Usually, h0 is little less than the thicknesses of steep ∂π/ ∂h. Depending on the relationship between the diameter of the particles and the thickness h0, particle arrays or irregularly placed bumps of particles may start to be formed or no particles may remain on the substrate.24 The onset of a particle array is schematically illustrated in Figure 2 for the case when h0 is slightly smaller than the diameter of the particles, d. When d is less than h0, irregularly placed bumps of particles usually remain after drying the film, and when d is much greater than h0, no particles remain after the film drying; they are pushed toward the bulk by the inclined meniscus (see ref 24 for details). Requirements for the Array Formation Process. The phenomena described above are general for a wide range of substrates and suspensions. The requirements for producing regular particle monolayers on solid substrates can be summarized as follows. (1) The substrate must be well wettable by the suspension, and a wetting film with relatively parallel surfaces and thickness on the order of but less than the particle diameter must be formed. (2) For the formation of densely packed structures, the particles must be able to slide on the substrate before the film dries; e.g., in the case of adsorbing particles, an amorphous layer is expected to be formed. (3) The suspension must be stable, and in the case of larger particles (∼1 µm and above), the particle sinking must be prevented. (4) To prevent the aggregation of particles at the suspension surface, the evaporation must be restricted near the particle film; that is, the atmosphere at the suspension meniscus as well as at the suspension surface far from the film must be saturated with water vapor. (5) The water evaporation from the particle arrays must be slow enough. At high evaporation rates instabilities in the array growth may arise as, for example, rupturing or stripping of the array film.25 Experimental Section Materials. Microslides 76 × 26 × 1 mm (Matsunami Glass Ind., LTD, Japan) were used in our experiments as the solid substrate plates. The specifications of the polystyrene particles (Stadex, Japan Synthetic Rubber) that were used are given in Table 1. The volume fraction of particles was 1 vol %. The (24) Dimitrov, A. S. Ph.D. Thesis, The University of Tokyo, Tokyo, 1995. (25) Adachi, E.; Dimitrov, A. S.; Nagayama, K. Langmuir 1995, 11, 1057-1060.

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Figure 4. Experimental data for the growth rate of monolayer particle arrays plotted as a function of the inverse particle diameter.

Figure 3. Schematics of the setup for layered particle array formation. Table 1. Specifications of the Latex Particles Given by the Manufacture latex code

diameter (nm)

polydispersity (nm)

SS-021-P SC-171-S SC-108-S SC-953-S SC-081-S SC-051-S SC-048-S SC-032-S SC-015-S SC-008-S

2106 1696 1083 953 814 506 479 309 144 79

(17 (47 (10 (9 (23 (10 (5 (4 (2 (2

suspensions were filtered through cellulose acetate membrane filters, which had a pore size ranging from two to four times greater than the particle diameter. Thus, the particle aggregates were removed. To control the properties of the wetting suspension film on the glass plates, we added small amounts of sodium dodecyl sulfate (SDS), sodium chloride (NaCl), octanol (Wako Pure Chemical Industries, LTD), and a protein (milk casein, Chameleon Reagent, Japan, or ferritin, Boehringer Mannheim GmbH, Germany) to the suspensions. The total amount of the additives did not exceed 5 vol.% of the particle volume fraction in the suspension. We added no more than 0.001 mol/L SDS, 0.001 mol/L octanol, and 0.01 mg/mL ferritin to the suspension. The water for suspension dilution, as well as for washing the cell and substrate plates, was taken from a MILLI-Q SP.TOC.reagent water system. Laboratory Setup. Our idea for continuous growth of largescale uniform particle arrays has been tested in laboratory conditions. The schematic of the setup we used is presented in Figure 3. The working cell was made in-house from pieces of microslides connected to each other by a polymeric glue. It has a small gap at the top for withdrawing the substrate. A 1-mm gap was chosen to minimize solvent evaporation from the meniscus and confine evaporation to the particle array film. The substrate plate hangs on a nonelastic string, which is attached to the periphery of a 2-cm inner diameter wheel. A stepper motor driver rotates the wheel using a gearbox. Thus, the substrate can be withdrawn from the suspension at a rate from 0.1 to 30 µm/s. The array growth process is observed and recorded using a horizontally placed video-microscope having a resolution power of about 350 nm. Array Formation Procedure. When ferritin was not added to the suspension, the glass plates were kept in a chromic mixture at least overnight, and then they were rinsed with water and soaked for more than 1 h in 0.1 M SDS solution (when particles larger than 506 nm were used) or in pure ethanol (when particles smaller than 479 nm were used). The plates soaked in the SDS solution were rinsed again with water and placed under a beaker to dry. The plates soaked in ethanol were placed directly under a beaker. Because the laboratory setup and the cell were open to room atmosphere, the existence of organic traces in the air often led to dewetting of the substrate plates, causing the wetting film to destabilize and rupture. Adding proteins significantly

improved the wettability of the plates. When a protein was added to the suspension, the glass plates were used directly from the original packaging, without additional treatment. The experimental cell was sonicated for about 10 s in a Ney 300 Ultrasonic water bath before each experiment. Then, the cell was washed using a soap solution, rinsed with plenty of water, and dried. After the experimental cell was dried, the cell and a glass substrate were mounted in the apparatus. The stepper motor driver for withdrawing the substrate was set at a rate three to five times higher than that estimated for a monolayer formation. Then, we filled the cell with a suspension and started to withdraw the substrate plate. To obtain a uniform thickness at the leading edge of the growing particle arrays, we monitored the array growth and gradually decreased the substrate withdrawal rate accordingly. While the regular growth was established, we regulated the substrate withdrawal rate by switching on or off the power of the stepper motor. To initiate a bilayer formation, we reduced the withdrawal rate by half. When the bilayer started to grow, we readjusted the withdrawal rate to obtain uniform thickness at the leading edge of the growing arrays. Color Enhancement. The arrays from micrometer-sized particles exhibit brilliant coloring when illuminated by white light in their native state, after forming and drying. We enhanced this brilliance by coating the particles with silver or gold (up to 10 nm thick) using a vacuum-coating technique. An added benefit of this coating is the stabilization of the arrays on the substrate, which, in fact, are fragile before the metal coating. Structure Observation. The obtained centimeter-sized monolayer particle arrays show interesting color properties. We observed the monolayer particle arrays with the naked eye, light microscopy, and electron microscopy. The macroscopic view and scattering of white light were observed by the naked eye. The surface structure was determined using an optical microscope (Olympus, Japan) in reflected light with a dark-field option. Details in the structures were figured out using a field-emission scanning electron microscope (S-5000H, Hitachi, Japan).

Results Array Formation Process and the Diameter of the Particles. During these experiments we measured that the temperature was 23.7 ( 0.5 °C and the relative humidity was 50 ( 2%. The suspensions were used as supplied by the producer without further purification. Experimental data for the growth rate of monolayer particle arrays versus the inverse particle diameter are presented in Figure 4. The relative experimental error in a single measurement for the array growth rate was less than 10%. The plotted data show that the total water evaporation flux per unit length at the array’s leading edge, Jevap ) lje, does not depend on the particle diameter. In other words, the data lay on a straight line, and according to eq 7 the evaporation rate must be constant. From the slope of this straight line we obtained Jevap ) 8.6 × 10-7 cm2 s-1, assuming β ) 1 in eq 7. In an independent experiment, we measured the evaporation rate of pure water as je ) 4.3 × 10-6 cm s-1 by weighing a small vessel with water at the same experimental conditions. This allowed us to calculate the evaporation length, namely,

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Dimitrov and Nagayama

Figure 6. A dark-field microphotograph of a monolayer containing defects of multilayers and voids. The monolayer particle arrays are formed using a suspension of 479-nm particles contaminated with particle aggregates.

Figure 5. A part of the leading edge of a growing monolayer particle array. The upper-half of the photographs shows the formations of (A) differently oriented small domains of ordered 814-nm particles and (B) a single domain of ordered 953-nm particles. The lower-half shows particles dragged by the water flow toward the forming monolayer. Because of the high velocity on a microscale, vp ∼100 µm/s, the particles are seen as short fuzzy lines. The particles (one is indicated by an arrow in B) seen as bright spots have large diameter (compared with the average one) and are wedged into the wetting film.

l ) 0.20 cm. We also observed (using a low-magnification microscope) that the width of the wet particle arrays is around 0.50 cm, which is in agreement with the calculated l. Polydispersity of the particles influences the quality of the obtained monolayer particle array films. A low polydispersity is necessary, but not sufficient, to obtain large uniformly oriented domains of highly aligned particles. Figure 5A shows a growing monolayer of 814nm particles with polydispersity of 2.8%. In contrast, Figure 5B shows the formation of a single domain of 953nm particles with polydispersity of 1%. In these cases the larger particles initiated dislocations in the arrays, thus forming a monolayer of differently oriented domains. Much larger particles or impurities, which can be regarded as particles strongly deviated in size, tremendously disturbed the monolayer growth and, in most cases, caused multilayers to be formed. Figure 6 represents a low-magnification view of monolayer particle arrays with islands of multilayers (mainly bilayers and only a few trilayers) and some voids. This monolayer was formed using a suspension of 479-nm particles without filtering; in other words, the suspension contained aggregates of particles. The large-sized polycrystalline 2D array that was obtained using the suspension of 953-nm polystyrene particles is shown in Figure 7A. The single-colored regions in this photograph show a single domain of highly ordered

particles or, at least, neighboring domains that are unidirectionally aligned. The electron microphotographs of this monolayer array confirmed the hexagonal dense packing of the particles, which has been formed during the process of array growth and is seen in Figure 5. One sees in Figure 7A that the domain size is much larger along the central microslide region than along both peripheral regions, where the coloring shows even some disturbances in the array uniformity. Figure 7B shows a low-magnification microphotograph of small-sized domains formed along on the microslide peripheral regions, while Figure 7C shows large-sized domains formed along on the central microslide regions. Actually, we have controlled the array growth process observing only along on the central microslide regions, where the film thickness was regulated to be equal or slightly less than the diameter of the particles. A dependence of the color pattern on the size of the particles is shown in Figure 8. The microphotographs were taken from a direction normal to the arrays (i.e., observation angle of 0°) and illuminated by sunlight at an incidence angle of 58o. The particle diameters in the monolayer arrays were 309 (Figure 8A), 479 (8B), 953 (8C), 1083 (8D), and 2106 nm (8E). These microphotographs show that monolayer arrays from small particles, especially those with diameters less than the wavelength of visible light, exhibit uniform coloring due to interference of the light (for a relating interference theory see ref 26). In contrast, two-dimensional arrays from particles that have diameters larger than the wavelength of the visible light exhibit brilliant diffraction colors, which depend also on the size and orientation of the domains. Discussion The mechanism for an array formation on substrate plates dipped in water suspensions or solutions is the same as that behind scum formation on the walls of swimming pools, kitchen sinks, etc. Everywhere water contacts wettable surfaces and evaporates, the substances dissolved in the water accumulate in the wetting films in the vicinity of the three-phase contact line. The phenomenon is quite general and depends mainly on the wettability of the surfaces and on the properties of the wetting films, rather than on the precise chemical nature of the substances dissolved or dispersed in the water. The array formation procedure developed by us is general and should work without any pitfalls, if the (26) Dushkin, C. D.; Nagayama, K.; Miwa, T.; Kralchevsky, P. A. Langmuir 1993, 9, 3695-3701.

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Figure 7. Photographs of dried macroscopic monolayer array films of 953-nm polystyrene particles on glass substrates illuminated in reflected light. (A) Macroscopic view of the monolayer. (B) Microphotograph of the small domains formed in the peripheral areas of the plate, where the evaporation was higher; i.e., the film at the array’s leading edge was much thinner than the particle diameter. (C) Large domains formed along the central part of the plate, where the film thickness was on the order of the particle diameter.

following conditions are met: the suspension, the atmosphere around the cell, the substrate plate, and the cell itself are free from impurities; the substrate is completely wettable by the suspension; the particles have the same diameter and do not adsorb onto the substrate. Under the laboratory conditions, however, these conditions are not easily maintained.

For example, polydispersity of the particle suspensions usually creates instabilities in the array growth. Whereas slightly different particles create dislocations and cause a small size of the forming domain (Figure 5), the particle aggregates or other large impurities are able to cause multilayer formation (Figure 6). Due to the slower growth of the multilayers (note in eq 7 that the number of layers,

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Figure 8. Microphotographs of monolayer particle array films illuminated by sunlight at an incidence angle of 58° and an observation angle of 0° (i.e., normal to the array). The particle diameters are (A) 309, (B) 479, (C) 953, (D) 1083, and (E) 2106 nm.

k, is in the denominator), voids may also appear behind the large impurities. However, the developed techniques for coating the solid surfaces by 2D particle arrays showed that the process of array formation is inherently stable and such kinds of instabilities are damped with time. For example, Figure 6 shows a bilayer initiated by a particle aggregate and then a small area of a trilayer, and before restoring the monolayer growth, a void area appears. Further, the monolayer continues to grow if it does not meet another large particle. The dependence of the array growth rate on the diameter of the particles is plotted in Figure 4. Our aim in these experiments was to validate eq 7 for the rate of array growth, and we were not interested in the quality

and the size of these arrays. Because adding surfactant to the suspension changes the evaporation rate and, also, filtering the suspension from impurities changes the particle volume fraction, we used the suspensions as they are supplied by the producer, with a definite composition. Domain Size and the Wetting Film Thickness. The ability to form large-sized domains mainly depends on the quality of the suspension, thickness, and the stability of the wetting film on the substrate plate. With highquality suspensions, which means those free from impurities with uniform particles, we can form larger or smaller domains by controlling either the wetting film thickness at the array’s leading edge or the rate of evaporation (see Figure 7). In the laboratory-made experimental setup,

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the evaporation rate along the plate periphery was higher than that along the plate central area. Thus, the wetting film, which was being formed in the vicinity of the array’s leading edge, had smaller thickness on the plate peripheral areas than on the central areas. The particles driven into the thinner film regions by the suspension influx started to attract each other due to the lateral capillary immersion forces, thus forming small hexagonally packed aggregates. These 2D aggregates were pressed to the array’s leading edge in different orientations. The further alignment of the particles was hampered due to the pressing by the capillary menisci towards the substrate plate. The particles approaching the array’s leading edge through the wetting film with thickness on the order of the particle diameter (along the central plate regions) do not attract each other due to the immersion forces. They were pressed by the hydrodynamic flux one by one, thus finding free positions in the growing domains. The dislocations in this case are formed due to the slightly larger particles, which we could not remove from the suspension. Monolayer Particle Arrays as Diffraction Gratings. The theory of the diffraction grating has been already developed.27 However, the mechanical way for producing echelette or echelon gratings is very difficult and requires special equipment. The difficulties are greater when the groove density is higher. We hope that our technique for producing 2D arrays allows the production of good quality gratings for reflected and transmitted light in a relatively inexpensive way, as well. Actually, there is a difference between the regular diffraction gratings and particle arrays, which have 6-fold axial symmetry. These differences might be accounted for using also the theory of diffraction of a 2D arrangement of assembled particles.28 For the time being, however, we just note the light dispersion from monolayer particle arrays. Figure 8, for example, illustrates a decomposition of the white light in colors (see also eq 18 in ref. 27). For taking these pictures, the incidence angle was fixed at 58° and the observation one at 0°. Thus, the color (or the wavelength) depended on the grating period and the order of interference. Carefully observing the hexagonally packed particle monolayer (see, e.g., the upper part of Figure 5B), one can find that depending on the array orientation the grating period can have two major values: the interparticle distance (which in fact is equal to the diameter of the particles for densely packed monolayers) or the interparticle distance multiplied by x3/2. Thus, the monolayer array of 309-nm particles in Figure 8A are dark but slightly blue due to the interference as described in ref 26. Actually, using 309-nm particle monolayers, we were able to observe only the blue grating spectral color when both the incidence and the observation angles were above 60°. As the size of the particles becomes higher, the decomposition of the white light in colors becomes clearly dependent on the domain orientation, which might (27) Born, M.; Volf, E. Principles of Optics, 6th ed.; Pergamon Press: New York, 1993; pp 401-414. (28) Goodwin, J. W.; Ottewill, R. H.; Parentich, A. J. Phys. Chem. 1980, 84, 1580-1586.

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be explained by the absolute increase in the difference between the two major grating periods and by also taking into account that only the first- and second-order interference maximums have enough intensity to be seen. Our Technique for Formation of 2D Particle Arrays and the LB Technique. At first glance, our technique for producing particle monolayer arrays on solid substrates inspires similarities to the well-known LB technique, where the organic monolayers on a water surface are first formed and afterward transferred to solid surfaces. There is, however, a basic difference. For the LB technique the organic layer must be formed on the water surface, which means that the transferred material must be insoluble or attached to an insoluble substance. During the transfer process the structure can be broken due to the hydrodynamic flow in the formed wetting film or due to the surface roughness. In our technique, the layer and its structure are simultaneously formed directly on the solid surface. The particles or molecules are dispersed (dissolved) in the bulk suspension (solution), and a continuous formation of the layers can be established. Thus, the surfaces that are being coated can, in fact, be infinitely large. We must note here that when the LB technique is applied in an atmosphere that is unsaturated with water vapor, substances from the bulk are expected to be incorporated in the transferred structure due to water evaporation from the drying wetting film formed during the transfer procedure. Our development shows to the users of the LB technique that for better transfer of the obtained Langmuir layers, the surrounding atmosphere must be saturated with water vapor, even though the organic layer on the water surface suppresses the evaporation process. Conclusions We developed a coating procedure for continuous formation of 2D particle arrays, analyzed the parameters determining the array growth, developed an experimental apparatus, and produced centimeter-sized monolayer arrays from small polystyrene particles. When illuminated by white light, the obtained monolayer particle arrays exhibited brilliant iridescent coloring. The method for producing the particle arrays looks similar to the LB technique; however, the intimate mechanism is totally different. The driving force in our technique is water evaporation, the arrays are being formed from particles that are completely immersed in water, and they should not adsorb onto the water surface and the substrate as well. We hope this technique will be used in future for preparation of optical units or electronic ROM (read only memory) devices. Acknowledgment. We acknowledge the discussions with our colleagues Dr. S. Ebina, Dr. H. Yoshimura, Dr. T. Miwa, and Mr. E. Adachi, who helped to develop our technique and to prepare this article. LA9502251