In Situ Observation of Meniscus Shape Deformation with Colloidal

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In Situ Observation of Meniscus Shape Deformation with Colloidal Stripe Pattern Formation in Convective Self-Assembly Yasushi Mino, Satoshi Watanabe, and Minoru T. Miyahara* Department of Chemical Engineering, Kyoto University, Katsura, Nishikyo, Kyoto 615-8510, Japan S Supporting Information *

ABSTRACT: Vertical convective self-assembly is capable of fabricating stripe-patterned structures of colloidal particles with well-ordered periodicity. To unveil the mechanism of the stripe pattern formation, in the present study, we focus on the meniscus shape and conduct in situ observations of shape deformation associated with particulate line evolution. The results reveal that the meniscus is elongated downward in a concave fashion toward the substrate in accordance with solvent evaporation, while the concave deformation is accelerated by solvent flow, resulting in the rupture of the liquid film at the thinnest point of the meniscus. The meniscus rupture triggers the meniscus to slide off from the particulate line, followed by the propagation of the sliding motion of the three-phase contact line, resulting in the formation of stripe spacing.

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INTRODUCTION Convective self-assembly of colloidal particles is an everyday observable phenomenon caused by the evaporation of a colloidal suspension,1,2 a typical example of which is a “coffee ring”.3 When the air−solvent−substrate contact line at a drying front is pinned, the solvent evaporating from near the contact line is replenished by convective flow from the interior, which carries dispersed particles into the drying front at the edge. The particles then form a close-packed deposit along the contact line due to the lateral capillary forces acting between them. This spontaneous process is gaining importance as a versatile template-free technique to arrange colloidal particles (e.g., metal and polymer particles,4−8 nanowires,9,10 biomolecules,11−13 carbon nanotubes,14,15 and graphene16,17) into not only uniform films but also patterned structures. In particular, striped colloidal patterns have attracted considerable attention because they are available for a wide field of possible applications.14,18−20 In our previous study,21 we demonstrated that, under specific conditions, a vertical convective self-assembly technique in which a hydrophilic substrate is vertically immersed in a colloidal suspension can produce horizontal stripe patterns, which exhibit well-ordered periodicity in their particulate line width and spacing on the order of micrometers. A characteristic feature of the stripe pattern is that the line spacing is © 2015 American Chemical Society

predominantly determined by the thickness of particulate lines, whose dependence cannot be explained by the widely accepted concept involving the depinning of a contact line from a particulate line during particulate film formation. We therefore proposed a possible mechanism for the stripe pattern formation, in which meniscus deformation into a concave shape toward a substrate plays a crucial role in creating the spacing. Our proposed model is demonstrated to reasonably account for the dependence on the particulate line thickness observed in the experimental results, although the actual shape deformation of a meniscus during the convective self-assembly process has been unclear. To further unveil the mechanism of stripe pattern formation in the convective self-assembly process, a possible approach is in situ observation of meniscus shape deformation associated with particulate line evolution in the self-assembly process. In situ observation approaches have achieved many breakthroughs in the investigation of colloidal assembly processes, such as the coffee ring effect,22−25 colloidal crystal growth,26−28 and the cracking of particulate films.29−32 The pattern formation process has also been explored by using in situ Received: February 5, 2015 Revised: March 18, 2015 Published: April 1, 2015 4121

DOI: 10.1021/acs.langmuir.5b00467 Langmuir 2015, 31, 4121−4128

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Langmuir observation techniques.33,34 Most of these studies, however, have focused on the convective self-assembly process in a drying droplet on a horizontal substrate to capture particle motion, most likely because such horizontal systems are relatively easy to observe with a simple experimental setup. As for a vertical assembly system, Bodiguel et al., who set up a confined space between two glass plates,35,36 and GonzãlezViñasn et al., who designed a custom-tailored vertical cell,37,38 monitored the trajectory of contact line motion and successfully observed the stick−slip motion of the contact line in situ. However, very few studies have investigated meniscus shape evolution in the particle assembly process because it is more difficult to trace a submicrometer-order change in a liquid film thickness. Although Maheshwari et al.34 and Wang et al.10 noted the possibility that a concave-shaped liquid surface causes the slip motion of a contact line from a growing particulate line in a drying droplet, satisfactory experimental demonstration is still lacking. Here, we observe in situ the deformation of a meniscus shape associated with stripe pattern evolution in a vertical convective self-assembly process. We illuminate the meniscus with a monochromatic light and analyze the interference fringes produced in the vicinity of the meniscus edge to quantitatively characterize the meniscus shape. Interference analysis reveals that the meniscus is elongated downward in a concave direction toward a substrate and ruptures at the thinnest point, ceasing the growth of a particulate line and resulting in the formation of spacing below the particulate line.

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Figure 1. Schematic illustration of the setup for in situ observation experiments, in which the meniscus edge is illuminated by a monochromatic light with a wavelength of λ = 475 ± 15 nm.

compared the experimentally determined shape with a theoretical model. Figure 2a shows the interference fringe

EXPERIMENTAL SECTION

Materials. The experiments employed aqueous suspensions of spherical silica particles (Spherica Slurry, Catalysts & Chemicals Ind. Co., Ltd., Japan) with a diameter of 270 nm, as reported by the manufacturer. These suspensions were diluted to a desired particle concentration ϕ [m3-particles/m3-suspension] with ultrapure water obtained from a Direct Q3 UV Water Purification System (EMD Millipore, Billerica, MA). Silicon wafer substrates (SUMCO Corp., Japan) were cut into 20 mm × 20 mm pieces; as a preliminary cleaning procedure, the pieces were then washed with acetone (99.5%, Kishida Chemical Ind., Ltd., Japan), ethanol (99.5%, Kishida Chemical Ind., Ltd., Japan), and ultrapure water in an ultrasonic bath. Then, immediately before use, wafer pieces were cleaned with a plasma cleaner (Harrick Plasma Inc., Ithaca, NY) to increase their hydrophilicity. In Situ Observation and Meniscus Shape Analysis. We immersed a silicon wafer substrate vertically in a colloidal suspension within a cubic glass vessel placed on a vibration isolation table (ADZA0806, Meiritz Seiki Co., Ltd., Japan) and directly observed the stripe formation process at the meniscus edge with a high-speed microscope (VW-9000, Keyence) set to face the substrate surface (Figure 1). Suspension temperature was controlled by a tape heater surrounding the cubic vessel. As a light source, we used a monochromatic light with a wavelength of λ = 475 ± 15 nm by filtering a white light produced by a mercury lamp. The lights reflected from the substrate and the meniscus surface interfered with each other, producing a fringe pattern at the meniscus edge. We analyzed the fringe pattern to characterize the meniscus shape, the details of which are described in the next section.

Figure 2. (a) Optical micrograph of the interference fringe pattern observed near the meniscus edge. (b) Schematic illustration of the interference of light reflected by the meniscus surface and the substrate. (c) Luminance profile along the vertical white line shown in micrograph (a). (d) Comparison between the meniscus shape obtained from the fringe pattern and that calculated by the Young− Laplace equation (eqs 3−5).

pattern that appeared near the meniscus edge. This is caused by the interference of light reflected by the meniscus surface and the substrate (Figure 2b). Consequently, the liquid film thickness hw can be calculated at locally brightest points as 2hw = m

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RESULTS AND DISCUSSION Analysis of Meniscus Shape. To confirm the validity of our in situ observation technique, we observed and characterized the shape of the meniscus that was formed on a hydrophilic substrate immersed vertically in water at ambient temperature, i.e., a meniscus shape without particles, and

λ nw

(1)

and at locally darkest points as

⎛ 1⎞ λ 2hw = ⎜m + ⎟ ⎝ 2 ⎠ nw

(2)

Here, λ is the wavelength of the incident light (475 nm), nw is the refractive index of the liquid (water) film, and m = 0, 1, 2, .... 4122

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the next position, which was followed by the formation of a new particulate line (t = 28 s). The meniscus shape obtained by analysis of the fringe patterns located along the white line at t = 0 (Figure 4) was monitored over time, and the resulting temporal variation of this shape is shown in Figure 5. The meniscus is stretched

We measured the reflected light intensity along the white line shown in Figure 2a (results shown in Figure 2c) and applied the above equations to the locally brightest and darkest points, respectively, identifying the meniscus shape (Figure 2d). The plotted shape is consistent with the shape that is theoretically obtained by using the Young−Laplace equation (eq 3, which is explained below), demonstrating the validity of our approach to characterize the meniscus shape through the fringe patterns. In Situ Observation of Stripe Pattern Formation. Vertical convective self-assembly produces stripe patterns of colloidal particles under fairly low particle concentration conditions, typically ϕ = 10−6−10−4.21 Figure 3 shows a typical

Figure 5. Temporal deformation of the meniscus shape defined by analyzing the resulting fringe patterns along the white line in the snapshot at t = 0 (Figure 4). Theoretically calculated meniscus shapes are also plotted as solid lines.

Figure 3. (a) Bright-field optical micrograph of the stripe pattern obtained using a 270 nm silica particle suspension with ϕ = 1.0 × 10−5 at T = 60 °C. (b) SEM image of the particulate line.

downward gradually until the meniscus slides off from the particulate line at t = 27.1 s. Meniscus elongation proceeds because the growth rate of a particulate film is slower than the evaporation rate, which drops the liquid level when using a relatively low concentration such as that employed in the present study, and thus the distance between the contact line and liquid level increases with solvent evaporation. Eventually, the meniscus breaks and slides off from the particulate film, and the contact line drops to the next position. The contact angle was measured to be 4.9° when the sliding motion of the contact line stopped at t = 28 s; this angle is in accordance with the static contact angle of the silicon wafer substrate we used. The meniscus shape after sliding is thus determined by hydrostatics rather than dynamics. It should be noted that the meniscus shape at t = 28 s is identical to that at t = 0 s. This selfregulating periodic motion of the meniscus results in welldefined stripe patterns. To compare the experimental and theoretical deformations in meniscus shape, we calculated the theoretical deformation of the meniscus shape based on the Young−Laplace equation, as follows. The theoretical meniscus shape is described by the Young−Laplace equation as

example of colloidal stripe patterns, obtained from a 270 nm silica particle suspension with ϕ = 10−5 at T = 60 °C. The stripe pattern exhibited uniform line width and spacing over an entire substrate with a dimension of a few centimeters (Figure 3a), and the particulate lines are composed of particles with a closepacked structure (Figure 3b). Figure 4 shows snapshots capturing the formation process of a monolayer particulate line at T = 60 °C from a 270 nm silica suspension with ϕ = 1.0 × 10−5 at a frame rate of 30 fps; the original video is available in the Supporting Information (Video S1). The time shown for each snapshot corresponds to the elapsed time in the original video, and the moment when the descending motion of a contact line stopped was set to t = 0. At t = 0, a particulate line was not observable at the meniscus tip, and the contact line had not been fixed to the substrate but was mobile. After a few moments, a new particulate line formed, which pinned the contact line. As evaporation progressed, the interference fringes gradually broadened along with the particulate line growth (t = 10−27 s), indicating the elongation of the meniscus shape. At t = 27.1 s, the meniscus tip slid off from the particulate line, and the contact line dropped down to

Figure 4. Snapshots capturing the process of monolayer particulate line formation at T = 60 °C from a 270 nm silica suspension with ϕ = 1.0 × 10−5 at a frame rate of 30 fps. The original video is available in the Supporting Information (Video S1). 4123

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Figure 6. (a) Snapshots capturing meniscus rupture in the process of bilayer stripe formation at T = 60 °C from a 270 nm silica suspension of ϕ = 2.0 × 10−5 at a frame rate of 250 fps. The original video is available in the Supporting Information (Video S2). (b) Meniscus shapes obtained from the analysis of fringe patterns (t = 0, 200, 248, 260, and 268 ms) and the theoretical meniscus shape at t = 0 calculated from the Young−Laplace equation (solid line).

x = − 2a 2 − z 2 + −

a cosh−1 2

2a a cosh−1 +h 2 H

2a + z

which agrees fairly well with the experimental results. This demonstrates that the meniscus is stretched downward by solvent evaporation and that its shape obeys the Young− Laplace equation. In the case of multilayer stripe formation, we also confirmed that the meniscus shapes deformed while obeying the Young−Laplace equation and that the contact angle was ∼5° when the sliding motion of the contact line stopped, which agrees with the static contact angle of the substrate. To further explore meniscus sliding behavior, we observed the meniscus shape deformation at the moment of meniscus breaking with a higher frame rate of 250 fps. Figure 6a shows snapshots capturing the process of bilayer stripe formation from a 270 nm silica suspension with ϕ = 2.0 × 10−5 at T = 60 °C; the original video is available in the Supporting Information (Video S2). The first snapshot (t = 0), in which the meniscus was already stretched downward, corresponds to ∼27 s in Figure 4. The meniscus then rapidly deformed concavely in the vicinity of the contact line (t = 200−260 ms), followed by the appearance of a hole in the liquid film (t = 264 ms), resulting in meniscus rupture and subsequent propagation in the horizontal direction (t = 268 ms). The meniscus shapes obtained by the analysis of the fringe patterns (t = 0, 200, 248, 260, and 268 ms) are shown in Figure 6b, as is the theoretical meniscus shape at t = 0 calculated from the Young−Laplace equation. The measured meniscus shape agrees well with the theoretical shape at t = 0 but starts to deviate from the calculated shape by deforming concavely toward the substrate. The meniscus quickly becomes more concave, on the order of milliseconds, and eventually ruptures at the concave face of the meniscus, which has the thinnest liquid film (t = 264 ms). The newly formed contact line then drops down to the next position. Figure 7 shows the meniscus shapes at the moment of meniscus rupture for various layer numbers, n = 1−5, of particulate lines. The meniscus is stretched longer when it attaches to a particulate line with a larger layer number. Because the position where the drop motion of the contact line stops is determined by eq 5 and the contact angle of the substrate (∼5° in the present work) is independent of the particulate line thickness, a thicker particulate line, which can stretch the meniscus longer, as shown in Figure 7, results in wider line

2a 2 − H2

(3)

with 2γ (ρs − ρair )g

(4)

H = a 1 − sin θ

(5)

a2 =

where ρs and ρair are the density of the suspension and the air, respectively; g is gravitational acceleration; γ is the surface tension; h is the thickness of the particulate line; θ is the angle between the vertical axis and the tangent of the meniscus at the point of contact with the particulate line (apparent contact angle); and H is the distance between the contact line and the liquid level (meniscus height). When either the apparent contact angle θ or the meniscus height H is known, these equations uniquely determine the meniscus shape. At t = 0, because the contact angle of the substrate is θ0 = 4.9°, the meniscus height H0 is calculated by eq 5, and the meniscus shape is calculated by eq 3. During a period of time t during particle assembly, the particulate line width increases by vct and the liquid level drops by vet, where vc is the growth rate of the particulate line and ve is the evaporation rate of the solvent. Because vc is slower than ve, the meniscus height at t = t becomes H0 + (ve − vc)t. Assuming that the growth rate is constant during the formation process, we can estimate vc from the resultant particulate line width and the time taken to form the line by analyzing the stripe formation process recorded in a video. Furthermore, analysis of the same video allows the calculation of ve from the width of a particulate line and adjacent space and the time taken to form them. Consequently, we calculated the meniscus shape at an arbitrary time t by using eq 3 with the meniscus height H0 + (ve − vc)t. After the meniscus break, the liquid level has lowered from the initial level by vet, so we can calculate the shape using eq 5 with the contact angle θ0 = 4.9° again. The theoretically calculated meniscus shapes are also plotted as solid lines in Figure 5, 4124

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Figure 7. Meniscus shapes at the moment of meniscus rupture for varied layer numbers of particulate lines, n = 1−5.

spacing. This reasonably accounts for the characteristic dependence of the line spacing on the thickness, which was reported in our previous work.21 The observed meniscus “rupturing” phenomenon that initiates sliding is consistent with our previously reported model,21 in which a stripe pattern forms through the rupture of the meniscus that concavely deformed into the substrate. In the present study, we discovered that meniscus rupture is triggered by the deviation of dynamic shape deformation from the Young−Laplace equation for tens of milliseconds before the rupture, although we assumed in the model that the meniscus break process is quasi-static for the prediction of resultant structures. A possible factor inducing the dynamic motion of the meniscus is convective flow near the meniscus tip. Because solvent evaporation from the meniscus edge is faster than that from the bulk surface with the help of the heat conduction from the substrate, and because the meniscus thickness near the contact line is almost as thin as the particulate line thickness, the linear flow velocity can be fast enough to deform the meniscus shape by applying hydrodynamic stress on the fluid. To examine the effect of the flow rate at the meniscus tip on the meniscus rupture phenomenon, we observed the rupture process under a lower temperature condition, T = 20 °C. We roughly estimated the flow rates at the edge of the meniscus to be ∼15 μm/s at 20 °C and ∼120 μm/s at 60 °C by calculating the evaporation rate at a particulate line based on the heat transfer from the substrate and atmosphere and the evaporative latent heat39 and by dividing the calculated evaporation rate by the meniscus thickness (≈ particulate line thickness). Because the rate of convective flow at T = 20 °C is too slow to transport dispersed particles into the contact line and produce a particulate line, we constructed a similar situation to the stripe formation process at T = 20 °C as follows. We preliminarily fabricated particulate monolayer lines on a substrate at T = 60 °C before the direct observation experiment. We subsequently immersed the substrate with particulate lines in water at T = 20 °C and continuously pumped the water out to drop the liquid level.40 Here, for a fair comparison, the rate of liquid level drop was set to be the same as the evaporation rate at T = 60 °C so that the slower convective flow rate near the meniscus tip was the only parameter that varied from the conditions at T = 60 °C. Images capturing the moments of meniscus rupture at T = 60 °C (Video S3) and 20 °C (Video S4) are shown in Figures 8a and 8b, and the analyzed meniscus shapes are shown in Figure 8c. Despite applying the same rate of the liquid level drop, the meniscus shape at T = 60 °C is less stretched and has

Figure 8. Snapshots capturing the moments of meniscus rupture at (a) T = 60 °C (Video S3) and (b) 20 °C (Video S4). (c) Meniscus shapes obtained from the analysis of the fringe patterns.

a larger curvature than that at T = 20 °C (Figure 8c), clearly demonstrating that convective flow toward the meniscus tip induces the dynamic shape deformation of the meniscus. Because the meniscus is held by the bottom edge of the particulate line, the faster convective flow of solvent at T = 60 °C applies larger stress, which dents the meniscus. Once the meniscus begins to deform concavely into the substrate, the decrease in the width of the flow channel increases the linear flow rate, thereby accelerating the dynamic deformation of the meniscus shape. On the other hand, when the solvent flow is slow, the stress available to dent the meniscus is weak, and the meniscus is therefore statically stretched longer while obeying the Young−Laplace equation. Stripe Pattern Formation Mechanism. On the basis of our results, we propose a mechanism of particulate stripe pattern formation in the vertical convective self-assembly process, which is schematically shown in Figure 9. When solvent evaporates from a meniscus, particles are carried into the meniscus edge by convective flow and form a particulate line, which holds the contact line of the meniscus. As solvent evaporation proceeds, the particulate line grows steadily while the liquid level gradually drops (Figure 9(a1)). Under relatively low particle concentration conditions, typically ϕ = 10−6 10−4, only a small number of particles are transferred to the contact line by convective flow, and hence the growth rate of the particulate line is slower than the rate of liquid level drop, resulting in elongation of the meniscus. At this stage, the shape deformation is static and follows the Young−Laplace equation (Figure 9(a2)) because the growth and evaporation rates are both slow. As the meniscus is stretched gradually, the liquid film starts to deform into a concave shape toward the substrate, as defined by the Young−Laplace equation. This deformation increases the linear flow rate toward the meniscus tip because of the narrowing in the flow channel as it is squeezed by the 4125

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Figure 9. (a) Proposed mechanism of particulate stripe pattern formation in the vertical convective self-assembly process. (b) Meniscus rupture triggering the sliding-off motion of the meniscus tip.

meniscus shape and determined that meniscus rupture triggers the sliding-off motion of the meniscus tip, followed by its propagation in the horizontal direction, thus creating stripe spacing. The stripe formation mechanism we have proposed based on our observation results is as follows. Because of the difference between the rate of liquid level drop and particulate line formation, the meniscus is stretched downward as the solvent evaporates. Although the meniscus keeps its static shape as described by the Young−Laplace equation at the early stage of line formation, its shape deforms quickly, deviating from static conditions, due to the hydrodynamic stress applied by the solvent flow around the meniscus tip. Eventually, the meniscus deforms concavely until its thickness reaches a critical value, resulting in meniscus rupture. This deformation of the meniscus is faster and larger when the linear velocity of the convective flow is faster. Because a thick particulate line decreases the solvent flow rate, the meniscus is stretched gently and longer, resulting in a wide line spacing. In this manner, our model successfully explains the dependence of particulate line spacing on its thickness.

concave face of the meniscus and the substrate. The increase in flow rate leads in turn to negative feedback, thus accelerating the concave deformation into a dynamic shape (Figure 9(a3,4)) because solvent flow applies stress on the meniscus surface. This event proceeds on the order of milliseconds, and eventually, when the meniscus thickness reaches a critical value that can maintain the liquid film, the meniscus ruptures (Figures 9(a4) and 9(b1,2)), followed by propagation in the horizontal direction (Figure 9(b3)). The newly created contact line slides down to the next position determined by the contact angle of the substrate (eq 5), and then the next particulate line starts to form (Figure 9(a5)). At a meniscus rupture event, several holes can appear simultaneously at a same height position because the meniscus shape is identical along the horizontal direction. These consecutive events repeat to spontaneously produce a highly periodic stripe pattern. As the particulate line thickness increases, an increase in the meniscus thickness slows the dynamic meniscus deformation and elongates the meniscus in a static fashion, which prolongs the period that elapses before reaching the critical thickness for inducing meniscus rupture. Consequently, the meniscus can be elongated downward for a greater distance, resulting in the formation of wider particulate lines. This model can reasonably explain the dependence of particulate line spacing on line thickness, which we previously reported.21

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ASSOCIATED CONTENT

S Supporting Information *

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Original video of snapshots capturing the process of monolayer particulate line formation at a frame rate of 30 fps (Figure 4); original video of snapshots capturing meniscus break in the process of bilayer stripe formation at a frame rate of 250 fps (Figure 6); original videos of snapshots capturing the moments of meniscus rupture at T = 60 °C (Figure 8a) and 20 °C (Figure 8b). This material is available free of charge via the Internet at http://pubs.acs.org.

CONCLUSION We observed the deformation of a meniscus shape during the particulate line evolution process in situ to unveil the mechanism of stripe pattern formation in convective selfassembly. By illuminating the meniscus with monochromatic light and analyzing the interference fringes appearing near the meniscus edge, we clarified the temporal deformation of the 4126

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected] (M.T.M.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported in part by JSPS Grants-in-Aid for Young Scientists (A) (Grant No. 23686109) and for JSPS Fellows (Grant No. 12J06026).

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DOI: 10.1021/acs.langmuir.5b00467 Langmuir 2015, 31, 4121−4128

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DOI: 10.1021/acs.langmuir.5b00467 Langmuir 2015, 31, 4121−4128