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Spontaneous Pattern Formation by Dip Coating of Colloidal Suspensions on Homogeneous Surfaces Moniraj Ghosh, Fengqiu Fan,† and Kathleen J. Stebe* Department of Chemical & Biomolecular Engineering, Johns Hopkins UniVersity, 3400 North Charles Street, Baltimore, Maryland 21218 ReceiVed July 21, 2006. In Final Form: NoVember 2, 2006 We study the slow withdrawal of a partially wet vertical plate at velocity U from a suspension of well-wet particles. Periodic horizontal striped assemblies form spontaneously at the three-phase contact line on energetically uniform surfaces. Stripe width and spacing depend on the withdrawal velocity U relative to a transition velocity Ut. Thick stripes separated by large spaces form for U < Ut. For U > Ut, thin stripes separated by small spaces form. The stripe spacing is reduced by an order of magnitude and varies weakly with U until a maximum velocity is reached at which the stripes fail to form. A partially wet surface can entrain a meniscus. For U < Ut, the meniscus forms a finite contact angle wedge with a pinned contact line. As the plate moves upward, it stretches the meniscus until it becomes too heavy to be retained by the wet, porous network provided by the particles at the contact line. The contact line then jumps backward to find a new equilibrium location, and the process begins anew. For U > Ut, we infer that a film of thickness h is entrained above the meniscus. When h is smaller than the particle diameter D, particles aggregate where the entrained film thickens to match up to the wetting meniscus. When an entrained particle becomes exposed to air by evaporation, it becomes the new pinning site from which the next film is entrained. The film thickness h increases with U; at some velocity, h becomes comparable to D. Particles flow into the film and deposit there in a disordered manner. A diagram summarizing particle deposition is developed as a function of D, U, and h.
Ordered aggregates of particles have a wide range of potential applications including novel optical,1 sensing and data recording platforms,2 and templates for nonlithographic patterning and the creation of ordered microporous materials.3,4 One means of creating the assemblies is evaporative deposition,5,6 in which either partially wet solid surfaces are withdrawn from particle suspensions in a dip-coating configuration or drops of suspension are allowed to evaporate on solid surfaces. If the solid surfaces are smooth and energetically homogeneous, convection of the particles by the prevailing flow field to the three-phase contact line assembles the particles, and contraction of capillary bridges between them can draw the particles into ordered crystalline structures.5,6 If the rates of solvent evaporation and substrate withdrawal are carefully controlled, uniform crystalline structures can be created over areas of large extent.7 If the solid surfaces have patterned functionality or surface energy, solventsubstrate8-12 or particle-substrate interactions (e.g., Coulombic
attraction)4,13 can be used to guide particles to desired locations. If the solid substrates have patterned topology, particles can be swept into grooves or cavities by the three-phase contact line as the suspension recedes.14 However, patterned deposition of particles can occur even on energetically homogeneous substrates. In the work of Nguyen and Stebe,15 particles were deposited into polygonal structures driven by Marangoni-Benard convection. In the work of Abkarian et al.,16 periodic striped rings composed of particles formed spontaneously along a cylinder traversing the air-aqueous interface of a colloidal suspension. In this work, we further study spontaneous stripe formation on surfaces in dip-coating configurations. Here, we study the withdrawal of a vertical, partially wet plate at velocity U from a suspension of well-wet particles. Periodic horizontal striped aggregates of particles form spontaneously. The stripe width, stripe spacing, and degree of order in the particle aggregates depend on the value of U relative to a transition velocity Ut.
* To whom correspondence should be addressed: e-mail
[email protected]. † Present address: Saoirse Corp., 300 Technology Square, Cambridge, MA 02139.
Experimental Section
Introduction
(1) (a) Joannopoulos, J. D.; Villeneuve, P. R.; Fan, S. H. Nature 1997, 386, 143. (b) Yamasaki, T.; Tsutsui, T. Appl. Phys. Lett. 1998, 72, 1957. (2) (a) Holtz, J. H.; Asher, S. A. Nature 1997, 389, 829. (b) Velev, O. D.; Kaler, E. W. Langmuir 1999, 15, 1329. (3) (a) Velev, O. D.; Jede, T. A.; Lobo, R. F.; Lenhoff, A. M. Nature 1997, 389, 447. (b) Holland, B. T.; Blanford, C. F.; Stein, A. Science 1998, 281, 538. (c) Braun, P. V.; Wiltzius, P. Nature 1999, 402, 603. (d) Johnson, S. A.; Ollivier, P. J.; Mallouk, T. E. Science 1999, 283, 963. (4) Zheng, H.; Lee, I. L.; Rubner, M.; Hammond, P. AdV. Mater. 2002, 14 (8), 569 and references therein. (5) (a) Deegan, R. D.; Bakajin, O.; Dupont, T. F.; Huber, G.; Nagel, S. R.; Witten, T. A. Nature 1997, 389, 827. (b) Deegan, R. D. Phys. ReV. E 2000, 61, 475. (6) (a) Denkov, N. D.; Velev, O. D.; Kralchevsky, P. A.; Ivanov, I. B.; Yoshimura, H. Nature 1993, 361, 26. (b) Denkov, N. D.; Velev, O. D.; Kralchevsky, P. A.; Ivanov, I. B.; Yoshimura, H. Langmuir 1992, 8, 3183. (c) Dushkin, C. D.; Yoshimura, H.; Nagayama, K. Chem. Phys. Let. 1993, 204, 455. (d) Dimitrov, A. S.; Nagayama, K. Langmuir 1996, 12, 1303. (7) (a) Jiang, P.; Bertone, J. F.; Hwang, K. S.; Colvin, V. L. Langmuir 1999, 11, 2132. (b) Dushkin, C. D.; Lazarov, G. S.; Kotsev, S. N.; Yoshimura, H.; Nagayama, K. Colloid Polym. Sci. 1999, 277, 914. (c) Gu, Z.; Fujishima, A.; Sato, O. Chem. Mater. 2002, 14, 760. (d) Tilley, R. D.; Saito, S. Langmuir 2003, 19, 5115.
Materials and Methods. All glassware was soaked in H2SO4Nochromix solution (technical grade, Fisher Scientific) overnight and rinsed with filtered and deionized water with a resistivity of 18.0MΩ‚cm (Millipore Milli-Q 50). This water was also used to (8) (a) Fan, F.; Stebe, K. J. Langmuir 2004, 20, 3062. (b) Heule, M.; Scho¨nholzer, U. P.; Gauckler, L. J. J. Eur. Ceram. Soc. 2004, 24, 2733. (9) Fan, F.; Stebe, K. J. Langmuir 2005, 21 (4), 1149. (10) Fustin, C.; Glasser, G.; Spiess, H. W.; Jonas, U. Langmuir 2004, 20, 9114. (11) Kruger, C.; Jonas, U. J. Colloid Interface Sci. 2002, 252, 331. (12) Jonas, U.; Campo, A.; Kruger, C.; Glasser, G.; Boos, D. Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 8. (13) (a) Aizenberg, J.; Braun, P. V.; Wilzius, P. Phys. ReV. Lett. 2000, 84, 2997. (b) Guo, Q.; Arnoux, C.; Palmer, R. E. Langmuir 2001, 17, 7150. (14) (a) Cui, Y.; Bjork, M. T.; Liddle, J. A.; Sonnichsen, C.; Boussert, B.; Alivisatos, A. P. Nano Lett. 2004, 4 (6), 1093. (b) Yin, Y.; Lu, L.; Gates, B.; Xia, Y. J. Am. Chem. Soc. 2001, 123, 8718. (c) Li, J.; Xing, R.; Huang, W.; Han, Y. Colloids Surf., A 2005, 269, 22. (d) Juillerat, F.; Solak, H. H.; Bowen, P.; Hofmann, H. Nanotechnology 2005, 16, 1311. (15) Nguyen, V. X.; Stebe, K. J. Phys. ReV. Lett. 2002, 88, 164501. (16) Abkarian, M.; Nunes, J.; Stone, H. A. J. Am. Chem. Soc. 2004, 126, 5978.
10.1021/la062150e CCC: $37.00 © 2007 American Chemical Society Published on Web 01/06/2007
Patterns in Dip Coating of Colloidal Suspensions clean all substrates, wash all particles, and prepare all suspensions. The particles used in this study were made of surfactant-free polystyrene amidine-functionalized spheres (Molecular Probes Inc.) with diameters of 0.21 µm with cv 7.9%, 0.81 µm with cv 2.7%, and 2.1 µm with cv 3.2%, where cv is the reported coefficient of variation from the mean. All particles were washed three times by sequential centrifugation, decantation of the supernatant liquid, and resuspension in water by sonication. The suspensions were diluted with Millipore water to the desired volume fraction. A volume fraction of 0.1% was used for the 0.81 and 2.1 µm particles; a volume fraction of 0.01% was used for the 0.21 µm particles. Substrates were prepared from silicon (111) wafers (Montco Silicon Technologies Inc.) coated with 250 Å of Cr as the adhesion layer and 100-200 nm of Au. Substrate sizes were typically 10 mm × 20 mm. The wafers were sonicated in ethanol and then plasma-cleaned with argon. Cleaned substrates were used immediately. Particle Deposition. The solid substrate was dip-coated vertically from the colloidal suspension. Initially, the substrate was completely immersed in a 15 mL polypropylene beaker filled with the suspension of interest. It was then withdrawn vertically at a constant velocity U by action of a stepper motor. The withdrawal rate was varied from 10 µm/min to several centimeters per minute. The dip-coating device was made by reconfiguring a syringe pump. For the lower withdrawal velocities, a KDS 100 syringe pump (KDScientific) with a displacement of 0.529 µm per half-step was used. For the higher withdrawal velocities, a NE-1000 syringe pump (New Era Pump Systems Inc.), with a displacement of 0.85 µm per step was used. The entire setup was enclosed in a plexiglass box to minimize air convection. The temperature and humidity inside the chamber were monitored with a Fisher Scientific digital hygrometer. The relative humidity varied between 20% and 40%. Temperature was constant at 25 ( 3 °C. Characterization. After the substrate was withdrawn from solution, the residual patterns formed by the particles were imaged after the liquid had evaporated. Images were taken by use of an optical microscope (Nikon Eclipse ME 600L) equipped with a chargecoupled device (CCD) camera (Nikon DXM1200). Scanning electron micrographs allowed details of the particle arrangement in the stripes and intervening spaces to be resolved. The scanning electron microscope (SEM) images were obtained with a JEOL JSM-6700F field emission SEM in LEI/SEI mode. For improved sample conductivity, 100 Å Pt film was sputtered onto the particles. Contact angles were measured with a goniometer (Rame´-Hart, Inc.) for a 5 µL drop of the suspension on at least three different areas of the substrate; average values are reported. The readings were taken within 2 min of drop formation.
Results and Discussion The results for suspensions of 0.81 µm diameter particles are discussed first. Figure 1 shows the images of the stripe patterns formed by these particles on a gold-coated silicon wafer (θ ∼ 65°) as a function of withdrawal velocity U. Figure 2 shows stripe width (2) and spacing (O) also as a function of U. The spacing changes abruptly for U above the transition velocity Ut ) 150 ( 10 µm/min. (All experiments for this diameter particle were performed at least in triplicate. Error bars reported in Figure 2 indicate the standard error of the mean for the data.) For U < Ut, wide stripes form, composed of particles in crystalline order, with large spaces between them. The width of the spaces between the stripes remains nearly fixed in this regime; these regions contain disordered particles in a sparse monolayer. SEM images of the stripes and the space between them are reported in Supporting Information. Similar stripes were reported previously by Abkarian et al.16 When the partially wet substrate is immersed, a meniscus climbs the solid to satisfy the advancing contact angle. As the plate is withdrawn, the combined action of the plate velocity and rapid evaporation near the three-phase contact line convect particles toward the contact line, where they accumulate. (The evaporation rate from the planar surface
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Figure 1. Optical micrographs of the stripe patterns that form spontaneously on uniformly energetic gold-coated silicon wafers at different withdrawal velocities for 0.81 µm particles: (A) 10, (B) 80, (C) 160, and (D) 200 µm/min. The wafers are withdrawn vertically from the suspension. The stripes form perpendicular to the withdrawal direction. The scale bar indicates 100 µm. The stripes appear dark, and the intervening spaces, sparsely covered with disordered particles, appear lighter.
Figure 2. Stripe width and spacing as a function of the withdrawal velocity U for 0.81 µm particles on gold-coated silicon wafers (θ ) 65°). The transition velocity Ut for this system is ∼150 µm/min. (O) Stripe spacing; (2) stripe width.
estimated under laboratory conditions was typically ∼5 µm/ min.) The porous network of well-wet particles pins the contact line. Withdrawal of the plate and evaporation from the vessel raises the height of the meniscus relative to the bulk surface. Eventually, the meniscus becomes too heavy. It tears off and slides to a new position determined by the receding contact angle of the suspension on the substrate. This gravitationally driven jump mechanism repeats periodically, thus explaining the periodic stripe formation. The meniscus lifetime, that is, the time required for a meniscus to form, stretch, and jump, can be inferred from the ratio of the stripe spacing over the plate withdrawal velocity; for example, the stripe spacing is roughly 250 µm for U ) 100 µm/min, yielding a meniscus lifetime of 150 s. (Note, however, a quantitative predictive discussion requires information that is not available a priori. The maximum weight of a meniscus that can be retained by the porous band formed by the crystalline aggregate is not known. The meniscus recedes until it satisfies a receding contact angle for the suspension on the solid substrate, which typically has a sparse layer of particles between the stripes. This changes the wetting condition of the suspension on the surface, so the effective receding contact angle on the surface is also not known.)
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Ghosh et al.
In this gravity-dominated jump regime, the stripe width decreases as U increases. Consider the meniscus in a reference frame that moves with the three-phase contact line as the meniscus stretches. The flux of particles to the contact line is determined by the flow field owing to evaporation only. Since the evaporative flux does not become more rapid as U increases, fewer particles are driven to the contact line between depinning events. Hence stripes become narrower as U increases. For U > 50 µm/min, the stripe width becomes independent of U, and the degree of order in the stripes decreases (as shown in SEM images in Supporting Information). The withdrawal velocity in this regime is far greater than the evaporation flux, so few particles convect to the three-phase contact line between depinning events. For U > Ut, the stripe spacing changes abruptly to a tenth of that in the gravitationally driven jumping regime. Stripe width also changes abruptly at this velocity. Over a range of velocities, the spacing and width remain fixed and independent of U. We propose the following mechanism for this transition. Initially, the first stripe of particles forms at a pinned contact line as described above. However, for U > Ut, the dynamic contact angle is reduced to a sufficiently low value that a thin film is entrained on the plate. Contact angles are well-known to decrease in a dip-coating configuration.17 Particle accumulation at contact lines is also known to decrease effective contact angles.5 Here, the two mechanisms work together to reduce the contact angle to a critical value at which a thin film is drawn out of the meniscus. The entrained film moves with the plate, while the meniscus remains fixed. The entrained film thickness h can be estimated by use of the expression originally derived by Landau and Levich18 for uniform wetting layers that are infinite in extent formed by dip-coating from a Newtonian fluid with viscosity µ at constant velocity U:
h ) 0.946(γ/Fg)1/2Ca2/3
(1)
is the capillary length for a fluid of density F, where γ is the surface tension, and Ca is the capillary number, Ca ) µU/γ. For an aqueous system with U ) 150 µm/min, Ca ∼ 10-8. Since in our application the films are finite in extent, the use of this expression is approximate. The behavior of the particles for U > Ut depends on the value of h compared to the particle diameter D. For h < D, particles are driven by the flow toward the edge of the film but cannot enter because of their size. They wedge into the region where the liquid layer thickens to match to the wetting meniscus and accumulate there. When the liquid covering an entrained particle evaporates sufficiently, either the particle becomes the new pinning site for the contact line or a thin film is entrained on the plate itself. The stripe of particles moves upward with a thin film entrained beneath it. The time required for this to occur can be estimated a priori by considering the particle diameter divided by the evaporation rate. For the 0.81 µm particle in a liquid with a bulk evaporating rate of 5 µm/min, the time required to completely expose an entrained particle is 9.6 s. From experiment, the time available for a stripe to form can be inferred from the ratio of the stripe width to the withdrawal rate to be ∼2 s. This is fairly good agreement, since the evaporation rate near the contact line is large compared to the bulk value.19 Note also that the time available for stripe formation is small compared to the gravitationally dominated case, so narrow-width stripes form at higher frequency. SEM images of the particle aggregates and the regions between the stripes are reported in Supporting Information. (γ/Fg)1/2
(17) (a) Diaz, M. E.; Cerro, R. L. Thin Solid Films 2004, 460, 274. (b) Cerro, R. L. J. Colloid Interface Sci. 2003, 257, 276 and references therein. (18) Landau, L.; Levich, B. Acta Physicochim. URSS 1942, 17, 42. (19) Hu, H.; Larson, R. G. J. Phys. Chem. B 2002, 106, 1334.
Figure 3. Schematic representation of particle accumulation and the flow pattern when a flat plate is removed from a suspension. (A) Gravity-driven contact line jumping regime: U < Ut. Particles are convected by evaporative flux to the contact line. They pin the contact line at a finite contact angle. The meniscus is stretched by the plate motion. When it is too heavy, it tears off and jumps backward. (B) Film entrainment regime: U > Ut, h < D. A film of thickness h is entrained on the plate. Particles are too large to enter the film and accumulate to form a stripe roughly one particle high. The stripe eventually dries; a new three-phase contact line forms. (C) Transition to disorder: U . Ut, h ∼ D. Particles convect freely into the film and deposit without order.
For high enough U, the film thickness h becomes comparable to the particle diameter D. Particles are convected freely into the film by the streamlines adjacent to the substrate and deposit in a sparse disordered layer. No stripes form. These three cases are summarized schematically in Figure 3 with qualitative flow fields.17 To further test this hypothesized mechanism for narrow stripe formation, two additional series of experiments were performed with suspensions of particles with D of 0.21 and 2.1 µm. For the 0.21 µm particles at 0.01% volume fraction, the three regimes of particle deposition were again observed. The transition velocity Ut was approximately 80 ( 10 µm/min. For U < Ut, the 0.21 µm particles formed wide stripes in the gravitationally dominated regime; SEM images of this regime are reported in Supporting Information. For U > Ut, thin stripes form, with some deposition of particles between stripes. For U . Ut, there was nonuniform particle deposition. For the 2.1 µm particles at 0.1% volume fraction, four behaviors were observed. For low enough velocities (U ∼ 10 µm/min), gravitational settling of the particles was faster than convection to the three-phase contact line. Particles did not form stripes, and they deposited only sparsely and without order on the surface (data not shown). For U ) 0.1 cm/min, lines only a few particles wide form (see SEM images in Supporting Information). The spacing between the stripes compares well with the spacing in the study of the 0.81 µm diameter particles in the gravitationally dominated regime. The withdrawal velocity was increased in steps of 0.1 cm/min. At U ) 0.5 cm/min, the particles formed finely spaced (ill defined) thin stripes. The pinning ability of these particles is very poor because of their large size and lower number concentration. (Pinning is enhanced by the capillary bridges that form between particles that are in contact or nearly in contact. The curvature of these bridges scales inversely with the particle radius.) For U > 1 cm/min, only disordered layers form. These data are summarized in Figure 4, in which we report stripe width, stripe spacing, and entrained film thickness h, predicted as a function of the particle diameter D and the velocity of withdrawal U. Corresponding estimates for the entrained film thickness h (from eq 1) are also reported in the figure caption. In Table 1, these regimes are further characterized in terms of stripe width, height, separation, and order.
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Figure 4. Diagram summarizing particle deposition mode as a function of particle diameter D, withdrawal velocity U, and entrained film thickness h. All images are SEM images except for panels B and D. (A) U ) 10 µm/min; (B) U ) 100 µm/min, h ) 21 nm; (C) U ) 1 cm/min, h ) 400 nm; (D) U ) 10 µm/min; (E) U ) 160 µm/min, h ) 30 nm; (F) U ) 2 cm/min, h ) 750 nm; (G) U ) 0.1 cm/min; (H) U ) 0.5 cm/min, h ) 290 nm; (I) U ) 5 cm/min, h ) 1.5 µm. The scale bar in optical micrographs reported in panels B and D indicates 100 µm. The scale bars for the SEM images are indicated below each image. Table 1. Characterization of Stripes Formed in Gravitationally and Film Entrainment Driven Regimes D ) 0.21 µm
D ) 0.81 µm
D ) 2.1 µm
U stripe width (µm) stripe height stripe separation (µm)
U < Ut 10 µm/min 80.6 ( 5.7 ∼2 particles 125 ( 7 a
80 µm/min 36.2 ( 2.5 ∼4 particles 261.7 ( 6.4 ordered
0.1 cm/min ∼2 particles ∼1 particle 275 ( 13.9 ordered
U stripe width (µm) stripe height stripe separation (µm)
U > Ut 100 µm/min 13 ( 1.4 1 particle 148.3 ( 8.6 sparse
160 µm/min 4.7 ( 0.4 1 particle 6.8 ( 0.4 sparse
0.5 cm/min 32.8 ( 2.09a 1 particle 60.7 ( 5.42a sparse
a
Refer to images in Supporting Information.
In the film-entrainment regime, the transition velocities decrease with particle diameter. This suggests that aggregates of small particles are more effective in reducing the dynamic contact angle to its transition value, perhaps because smaller particles form denser porous structures between them. The value of U at which particles deposit in a disordered manner increases with particle diameter D consistent with the criterion that the entrained film thickness h must be comparable to D to sequester particles in the film. Recently, Huang et al.20 report results that are complementary to our own. In their experiments, a plate was withdrawn at a steady velocity from an aqueous subphase. The aqueous-air interface was covered with a monolayer of partially wet particles (20) (a) Huang, J.; Kim, F.; Tao, A. R.; Connor, S.; Yang, P. Nat. Mater. 2005, 4, 896. (b) Huang, J.; Tao, A. R.; Connor, S.; He, R.; Yang, P. Nano Lett. 2006, 6 (3), 524.
that remained at the interface under an applied surface pressure. By controlled withdrawal of the plate, thin, single-particle-wide stripes of particles were formed. These authors demonstrate the versatility of using three-phase contact lines with partially wet particles to effectively “print” particles on surfaces in desired locations. However, the withdrawal velocity was not varied systematically.
Conclusion We have demonstrated that periodic horizontal striped assemblies form spontaneously on energetically uniform surfaces in a dip coating configuration. The stripe width and spacing depend on the withdrawal velocity U relative to a transition velocity Ut. For U < Ut, wide stripes separated by large spaces form by a gravity-dominated mechanism. For U > Ut, narrow stripes separated by small spaces form. We infer that at Ut, a thin film of liquid is entrained above the meniscus. Particles too large to enter the film accumulate in the transition region between the thin film and the meniscus until the liquid evaporates there. Thereafter, the film is entrained again. For U . Ut, the film is thick enough for particles to be convected directly into the film, where they deposit in a disordered fashion. Acknowledgment. We acknowledge the contributions of Sarah Singson and the JHU-MRSEC for the use of the SEM. This work was supported by NSF CTS 0244592. Supporting Information Available: SEM images of the stripes and intervening spaces, resolving the particle arrangement and the height of the aggregates for various withdrawal velocities. This material is available free of charge via the Internet at http://pubs.acs.org. LA062150E
