Crystal Growth near Moving Contact Lines on Homogeneous and

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Crystal Growth near Moving Contact Lines on Homogeneous and Chemically Patterned Surfaces R. Z. Rogowski and A. A. Darhuber* Mesoscopic Transport Phenomena Group, Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands Received March 11, 2010. Revised Manuscript Received May 1, 2010 We have systematically investigated how solution crystallization in the proximity of moving contact lines can be modulated by the parameters of the coating flow as well as chemical patterning of the substrate surface. We have studied the monoclinic model substance nicotinamide in the solvent isopropanol, which tends to form needle-like crystals in bulk solution. Three crystallization regimes were identified dependent on the coating speed. At high speeds viscous entrainment dominates over solvent evaporation, and an essentially azimuthally isotropic, spherulithic morphology results. For intermediate speeds a branched morphology with preferential alignment parallel to the coating direction is observed. For low speeds, filament-like crystal patterns well aligned with the coating direction were obtained.

1. Introduction Hydrodynamic flows can have a strong influence on the conformations of single molecules and supramolecular assemblies. Talbott and Goddard studied flow-induced birefringence in polymer solutions.1 Atkins and Taylor2 and Perkins et al.3 investigated the stretching of DNA molecules in elongational flows. A number of groups have utilized the large local stresses involved with moving liquid-solid-gas contact lines to stretch and align DNA and carbon nanotubes along certain directions on a solid substrate.4-8 In the field of biomineralization, control over the shape of crystals growing from solution is sought by substrate templating or the use of additives such as polymers, lipids, peptides, and proteins.9-12 Qin et al. used a patterned self-assembled monolayer to restrict liquid entrainment to small hydrophilic patches on a substrate.13 Arrays of small droplets of CuSO4 and KNO3 solutions were deposited at well-defined locations by means of dip-coating. After solvent evaporation compact crystallites adhered to the substrate with dimensions as small as 50 nm, which are determined by the size of the hydrophilic patches and the solute concentration. Meyer and Braun investigated the crystallization behavior of poly(ethylene oxide) (PEO) solutions in chloroform on chemically patterned surfaces.14 Using an AFM tip, they induced heterogeneous nucleation after dip-coating and observed a branched *To whom correspondence should be addressed. (1) Talbott, W. H.; Goddard, J. D. Rheol. Acta 1979, 18, 505. (2) Atkins, E. D. T.; Taylor, M. A. Biopolymers 1992, 32, 911. (3) Perkins, T. T.; Smith, D. E.; Chu, S. Science 1997, 276, 2016. (4) Bensimon, D.; Simon, A. J.; Croquette, V.; Bensimon, A. Phys. Rev. Lett. 1995, 74, 4754. (5) Yokota, H.; Johnson, F.; Lu, H.; Robinson, R. M.; Belu, A. M.; Garrison, M. D.; Ratner, B. D.; Trask, B. J.; Miller, D. L. Nucleic Acids Res. 1997, 25, 1064. (6) Wang, W.; Lin, J.; Schwartz, D. C. Biophys. J. 1998, 75, 513. (7) Petit, C. A. P.; Carbeck, J. D. Nano Lett. 2003, 3, 1141. (8) Ko, H.; Peleshanko, S.; Tsukruk, V. V. J. Phys. Chem. B 2004, 108, 4385. (9) Mann, S. J. Chem. Soc., Dalton Trans. 1997, 3953. (10) Aizenberg, J.; Black, A. J.; Whitesides, G. M. Nature 1999, 398, 495. (11) Yu, S.-H.; C€olfen, H. J. Mater. Chem. 2004, 14, 2124. (12) Aizenberg, J. Adv. Mater. 2004, 16, 1295. (13) Qin, D.; Xia, Y.; Xu, B.; Yang, H.; Zhu, C.; Whitesides, G. M. Adv. Mater. 1999, 11, 1433. (14) Meyer, E.; Braun, H.-G. J. Phys.: Condens. Matter 2005, 17, S623.

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lamellar morphology which they ascribed to a diffusion-limited aggregation process. In this article we systematically explore to what extent the continuous deposition of a substance that tends to form needleshaped crystals can be influenced by a well-defined stationary hydrodynamic flow field as well as chemical substrate patterning. The crystals adhere strongly to hydrophilic glass surfaces, which leads us to the conclusion that capillary and viscous effects do not directly influence the crystal growth morphology. Rather, in concert with solvent evaporation they determine the shape of the liquid meniscus in contact with the substrate and thus solute supersaturation, which governs crystal growth. This mechanism therefore invites the development of microfluidic strategies for active manipulation of the shape of growing crystals. Moving liquid-solid-air contact lines of volatile liquids are simple to generate. However, according to first-order theoretical models, both the hydrodynamic stress and the evaporation rate diverge,15,16 the latent heat of evaporation usually induces temperature nonuniformities, and in case of solutions the concentration distribution exhibits very high gradients near contact lines. The combination of these factors pushes the system far from thermodynamic equilibrium, and highly complex phenomena can emerge. A detailed theoretical model of the influence of evaporation on material deposition at receding contact lines has been presented very recently by Berteloot et al.,17 who predicted the existence of two regimes depending on the coating speed U. At high speeds, the coating thickness h was found to scale according to the Landau-Levich-Derjaguin18,19 relation h ∼ U2/3, whereas at low speeds a scaling h ∼ U-2 was predicted for the so-called evaporation regime. Le Berre et al.20 recently investigated the diecoating of phospholipid solutions and confirmed experimentally the existence of two deposition regimes. Their exponents R obtained (15) Huh, C.; Scriven, L. E. J. Colloid Interface Sci. 1971, 35, 85. (16) Deegan, R. D.; Bakajin, O.; Dupont, T. F.; Huber, G.; Nagel, S. R.; Witten, T. A. Nature 1997, 389, 827. (17) Berteloot, G.; Pham, C.-T.; Daerr, A.; Lequeux, F.; Limat, L. Europhys. Lett. 2008, 83, 14003. (18) Landau, L.; Levich, B. G. Acta Physicochim. URSS 1942, 17, 42. (19) Deryaguin, B. C. R. Acad. Sci. URSS 1943, 39, 1. (20) Le Berre, M.; Chen, Y.; Baigl, D. Langmuir 2009, 25, 2554.

Published on Web 05/20/2010

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Rogowski and Darhuber Table 1. Concentration Dependence of Viscosity and Surface Tension of Nicotinamide Solutions in Isopropanola concentration (wt %)

Figure 1. (a) Schematic sketch of the dip-coating setup. (b, c) Entrainment height of a volatile liquid at (a) high and (b) low speeds.

from fitting the phospholipid film thickness with a powerlaw h ∼ UR were close to the values R = 2/3 for the LandauLevich regime and R = -1 for the evaporation regime, for which they provided theoretical support from a mass balance argument. In this article, we explore the potential of dip-coating as a means of controlling the crystallization behavior of nicotinamide, which tends to form needle-like crystals under suitable conditions. We systematically vary the speed of dip-coating, the solution concentration, and the chemical surface composition of the substrates and investigate their influence on the crystal morphology. After a brief introduction of dip-coating we describe the experimental setup and procedure. Two distinct dip-coating regimes, depending on the relative importance of viscous entrainment and evaporation, are described in section 4 along with their effect on crystal arrangement. At high speeds, relatively thick liquid films were entrained and spherulite formation occurred; at intermediate speeds, a branched morphology was observed; at very low speeds crystal ribbons or filaments formed, that were very well aligned with the coating direction. In sections 4.6 and 4.7 we discuss the formation of horizontal bands or striations as well as the influence of hydrodynamic instabilities, respectively.

2. Dip-Coating of Homogeneous and Chemically Patterned Surfaces Dip-coating is widely used in many technological applications ranging from fabrication of optical interference filters,21 photonic crystals and chemical sensors,22 selective material deposition on patterned surfaces,23 to high-performance organic field-effect transistors.24 It offers advantages such as low investment cost, high uniformity on large coating areas, ease of use, and allows for a large variety of coating materials. Films can be fabricated in an ambient atmosphere, and their thickness can be controlled by adjusting the viscosity or concentration of solutes.25 Dip-coating involves the immersion and subsequent withdrawal of a substrate at constant speed from a reservoir of liquid as sketched in Figure 1a. The thickness h¥ of an entrained nonvolatile liquid film on a flat, homogeneous, and completely wettable substrate has been derived theoretically by Landau and Levich18 and Deryaguin:19 h¥ ¼ 0:946lc Ca2=3

ð1Þ

(21) Arfsten, N. J.; Eberle, A.; Otto, J.; Reich, A. J. Sol-Gel Sci. Technol. 1997, 8, 1099. (22) Jiang, P.; Bertone, J. F.; Hwang, K. S.; Colvin, V. L. Chem. Mater. 1999, 11, 2132. (23) Fan, H. Y.; Lu, Y. F.; Stump, A.; Reed, S. T.; Baer, T.; Schunk, R.; Perez-Luna, V.; Lopez, G. P.; Brinker, C. J. Nature 2000, 88, 5119. (24) Wang, G.; Hirasa, T.; Moses, D.; Heeger, A. J. Synth. Met. 2004, 146, 127. (25) Kobayashi, H.; Takahashi, M.; Kotani, M. Chem. Phys. Lett. 2001, 349, 376.

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viscosity (mPa 3 s)

surface tension (mN/m)

0 2.12 23.17 1.37 2.18 23.22 3.71 2.24 23.35 5.66 2.48 23.55 6.62 2.54 23.70 a Surface tension has been measured with a Wilhelmy plate technique at a temperature of 22 C; viscosity using a Brookfield LVDV-IIþPRO viscometer at 22.5 C.

Here, lc =(σ/Fg)1/2 is the capillary length, Ca=μU/σ the capillary number, μ the Newtonian viscosity, σ the surface tension, and F the density. Equation 1 is valid provided that the capillary number Ca is much smaller than unity. In the case of hydrophilic stripes on partially wettable surfaces, Darhuber et al.26 predicted the maximum height h¥ of an entrained liquid film to scale proportional to U1/3 which they confirmed experimentally. Davis computed the numerical constant of proportionality, leading to h¥ ¼ 0:356wCa1=3

ð2Þ

where w is the width of a hydrophilic stripe, which constitutes the dominant length scale provided that w , lc .27

3. Experimental Section 3.1. Materials. The main material system investigated is nicotinamide (Fluka, product # 72340, purity 99.5%) dissolved in isopropanol (JTBaker, Finyte grade, purity 99.8%) at various concentrations. Isopropanol is a polar volatile liquid with a boiling point of 356 K, mass density 786 kg/m3, vapor density 2.1 kg/m3, viscosity μ=1.96 mPa 3 s, and surface tension σ=23.15 mN/m, which slightly increases with increasing solute concentration as shown in Table 1. Nicotinamide crystallizes from most common solvents in the monoclinic system with unit-cell parameters a1 = 9.435 A˚, a2 = 15.65 A˚, a3 = 3.974 A˚, and β = 9980 , which corresponds to the space group P21/a.28 Further experiments were conducted with phthalic acid (PA, Aldrich, purity >99.5%, product number 80010) dissolved in ethanol and isopropanol and tryglycine sulfate (TGS, custom synthesized) in water. Both PA and TGS belong to the same monoclinic crystal system as nicotinamide.29,30 Soda-lime glass slides and silicon wafers were used as substrates for the crystallization experiments. 3.2. Sample Preparation. The substrates were first cleaned with “piranha” solution (1:1 mixture of 98% sulfuric acid H2SO4 and 30% hydrogen peroxide H2O2) and then thoroughly rinsed with deionized water. The unpatterned, homogeneous glass substrates were stored in isopropanol before dip-coating. In the case of chemically patterned substrates, only small volumes of piranha solution were selectively applied onto the hydrophilic stripes during the cleaning procedure. Prior to dip-coating the patterned substrates, the cleaning procedure was repeated in order to eliminate possible contaminations. Chemically patterned substrates were manufactured from Si wafers and glass slides using photolithography.31 After cleaning, the substrates were spin-coated with a thin layer of Allresist AR-P3510 positive photoresist, using hexamethyldisilazane (26) Darhuber, A. A.; Troian, S. M.; Davis, J. M.; Miller, S. M.; Wagner, S. J. Appl. Phys. 2000, 88, 5119. (27) Davis, J. M. Phys. Fluid. 2005, 17, 038101. (28) Wright, W. B.; King, G. S. D. Acta Crystallogr. 1954, 7, 283. (29) Xie, J.; Wen, W.; Xuan, Y. Anal. Sci. 2008, 24, x95. (30) Malyarevich, A. M.; Posledovich, M. R. J. Appl. Spectrosc. 1996, 63, 49. (31) Darhuber, A. A.; Davis, J. M.; Troian, S. M.; Reisner, W. W. Phys Fluids 2003, 15, 1295.

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Figure 2. Nicotinamide crystal patterns on a homogeneous glass substrate obtained by dip-coating at (a) 22.5, (b) 12.5, (c) 7.5, and (d) 12.5 mm/s. Most spherulites exhibit a filamental morphology. (d) shows an example of a banded morphology. Image width (a-c) 11 mm and (d) 0.67 mm.

(HMDS) as an adhesion promoter. The photoresist layer was then exposed to UV light using a mask printed on a transparent polymer foil. Subsequently, the photoresist layer was developed with Allresist AR 300-35 developer. After drying, a monolayer of 1H,1H,2H,2H-perfluorooctyltrichlorosilane (PFOTS, Aldrich, product # 190690) was attached to the exposed regions by immersing it into a 0.1 wt % PFOTS-dodecane solution for 10 min. After rinsing in neat dodecane, the photoresist was stripped with acetone and the cleaning procedure mentioned above was applied.

3.3. Coating Procedure and Sample Characterization. Figure 1 shows a sketch of the dip-coating setup used in our experiments, which consists of a computer-controlled linear translation stage (Newport UTS150CC) powered by a dc motor. Substrates to be dip-coated were affixed to the stage with a plastic forceps. The setup was placed in an enclosure providing HEPAfiltered laminar air flow in order to minimize the influence of the ambient environment on the crystallization process. The substrates were first immersed and after a period of approximately 7-10 s withdrawn at a constant speed U from a reservoir filled with a solution of nicotinamide. The substrates were left to dry at room temperature in the same vertical orientation as during coating. After coating the total mass of the crystals deposited on the substrates was measured with a Kern ALT 220-5 DAM balance with a resolution of 10 μg. No special measures against water absorption by nicotinamide from ambient humidity have been taken. The crystal morphology was characterized optically with an Olympus BX51 polarizing microscope.

4. Experimental Results and Discussion 4.1. Dip-Coating Regimes. Two coating regimes can be distinguished by the competition between viscous entrainment and the rate of evaporation. At “fast” coating speeds U, a liquid film of considerable length L is first entrained and then slowly evaporates. In this regime, the entrainment time L/U is much smaller than the drying time h/(∂h/∂t), which has the consequence that the entrained film covers the entire length of the substrate L prior to evaporation as indicated in Figure 1b. For large values of U, the nicotinamide concentration in the entrained liquid film is essentially uniform during coating, as evaporation of isopropanol is given insufficient time to significantly increase the solute concentration. At dip-coating speeds below U = 1 mm/s for isopropanol, the entrained liquid film begins to dry before the sample is completely withdrawn from the liquid reservoir. For small values of U, the Langmuir 2010, 26(13), 11485–11493

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Figure 3. Total mass m of the crystal layer deposited on one side of a homogeneous hydrophilic glass substrate as a function of dipcoating speed U for different solute concentrations. The substrate dimensions were 25 mm  75 mm; the immersed area was 25 mm  50 mm. The straight lines correspond to eq 3.

vertical position of the contact line becomes comparable to the static height of capillary rise Δhs, as indicated in Figure 1c. For a zero contact angle Δhs = 21/2lc .32 This leads to a strong evaporation-driven concentration gradient from the bulk of the solution toward the contact line. Supersaturation is induced, and thus crystallization commences in the vicinity of the contact line already during sample withdrawal. Thus, the influence of evaporation and the dip-coating process on crystal alignment is expected to gain significance at lower speeds. 4.2. Crystallization on Homogeneous Surfaces after “Fast” Dip-Coating. Figure 2 presents microscope images of nicotinamide crystals deposited onto glass substrates (dimensions 25 mm 50 mm) at different withdrawal speeds. The patterns consist of many spherulitic crystal aggregates, the average size of which slightly increases with increasing U. No correlation between the coating direction and the aggregate morphology is observed. Similar spherulithic morphologies were observed for solutions of PA in isopropanol and ethanol as well as for drop-cast aqueous solutions of TGS. Nucleation commenced at the liquid contact lines, where the evaporative flux of the solvent is generally highest,16,33,34 such that supersaturation was achieved there earlier than in the interior of the entrained liquid layer. Data regarding the dependence of average spherulite dimensions on coating speed are available as Supporting Information. The complete lack of any directional alignment in the crystal morphology in the fast dip-coating regime is, therefore, a consequence of random nucleation both at the contact lines and sample edges as well as in the bulk of the solution layers. In Figure 3 the total deposited crystal mass m is plotted as a function of dip-coating speed U for different nicotinamide weight fractions C0 of 6.62 (close to saturation), 5.66, 3.71, and 1.37 wt %. The straight lines in Figure 3 represent power-law relations m = b1U2/3 obtained from eq 1 by multiplication with the immersed surface area S of the substrate, the solution density Fsol, and the solute weight fraction C0, leading to b1 ¼ 0:946lc ðμ=σÞ2=3 SC0 Fsol

ð3Þ

(32) Pozrikidis, C. Introduction to Theoretical and Computational Fluid Dynamics; Oxford University Press: New York, 1997. (33) Deegan, R. D.; Bakajin, O.; Dupont, T. F.; Huber, G.; Nagel, S. R.; Witten, T. A. Phys. Rev. E 2000, 62, 756. (34) Hu, H.; Larson, R. G. J. Phys. Chem. B 2002, 106, 1334.

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Figure 4. Total mass m of nicotinamide crystals deposited on a homogeneous glass substrate as a function of the solute concentration C0 for several values of the dip-coating speed U. Straight lines correspond to linear fits m = kC0 with fit parameters k in units of mg/wt % given in the legend.

Figure 6. (a-c) Planar nicotinamid spherulites growing in a thin film of an evaporating isopropanol solution. Image width 3.05 mm. (d) Spherulite radii increase linearly with time. Curves are shifted along the abscissa for clarity.

Figure 5. Microscope images illustrating branched crystal growth at dip-coating speeds of (a, b, d) 8 μm/s and (c) 30 μm/s and solute concentrations of (a-c) 5.66 wt % and (d) 1.37 wt %. The arrow depicts the direction of dip-coating. Image width: (a) 4.62 mm, (b, c, d) 400 μm.

Excellent agreement between the experimental data and the theoretical prediction can be seen in the high-speed region above several mm/s. Figure 4 presents experimental data for the total mass m of nicotinamide crystals deposited versus solute concentration for different values of U. The straight lines correspond to linear fit functions m=kC0 with fit parameter k, which are excellent approximations to the experimental data. As expected, there is thus no direct influence of the solute concentration on the deposition process in the high-speed regime. Below U ≈ 1 mm/s, the experimental data in Figure 3 deviate from power-law behavior, which is reflected in a gradual transition of the crystal morphology from predominantly spherulitic, i.e., statistically axisymmetric within individual spherulites,35 at higher speeds to branched (Figure 5b-d) at speeds below 0.1 mm/s. The latter morphology is aligned along the coating direction and exhibits translational invariance in a statistical sense, with the exception of the horizontal bands to be discussed in section 4.6. This transition is occasionally accompanied by the occurrence of asymmetric, comet-shaped spherulites as shown in Figure 5a. (35) Keith, H. D.; Padden, F. J. J. Appl. Phys. 1963, 34, 2409.

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Very similar patterns have been observed for polymer spherulites growing in a temperature gradient.36 In our case supersaturation takes over the role of the temperature gradient. 4.3. Spherulite Growth Kinetics. In order to investigate the spherulitic growth process in more detail, we performed dropcasting experiments. A drop of solution of typically 10 μL volume was deposited onto a hydrophilic glass slide under a miscroscope. The bulk of the droplet evaporated quickly leaving a thin layer behind, in which spherulites started to nucleate and grow (see Figure 6a-c). In all experiments the spherulite radius increased linearly with time (Figure 6d) at a rate Usp that slightly depends on concentration ranging from Usp =12 ( 1 μm/s at 0.6 wt % to 18 ( 2 μm/s at 5.46 wt %. The spherulitic growth speeds Usp constitute a velocity scale intrinsic to the crystal growth process. Such linear spherulite dynamics have been observed in a large number of systems, such as atomic and molecular crystals and polymers grown from melt or solution for one-, two-, or threedimensional aggregates,35,37-43 which indicates the possibility that a universal governing mechanism exists. Spherulites exhibit a branched crystal morphology as seen in Figures 2 and 6a-c, which is also observed for dip-coating at intermediate speeds in Figure 5. In contrast to dendritic morphologies frequently occurring in melt-crystallization, neighboring nicotinamide branches do not include well-defined crystallographic angles but apparently arbitrary angles typically below 30. An interesting question is what physical mechanism determines the size or spacing δ of the branches. Keith and Padden35,37 give a (36) Smith, P.; Pennings, A. J. Eur. Polym. J. 1976, 12, 781. (37) Goldenfeld, N. J. Cryst. Growth 1987, 84, 601. (38) Adamski, P.; Kazimierski, P. J. Cryst. Growth 1984, 66, 593. (39) Hamada, S. Bull. Chem. Soc. Jpn. 1971, 44, 104. (40) Heijna, M. C. R.; Theelen, M. J.; van Enckevort, W. J. P.; Vlieg, E. J. Phys. Chem. B 2007, 111, 1567. (41) G. E. W. Schulze, G. E. W.; Wilbert, H.-P. Colloid Polym. Sci. 1991, 269, 981. (42) Mori, T.; Kubota, N.; Abe, S.; Kishimoto, S.; Kumon, S.; Naruse, M. J. Cryst. Growth 1993, 133, 80. (43) Billon, N.; Haudin, J. M. Colloid Polym. Sci. 1993, 271, 343.

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Figure 8. Control volume near tip of growing crystal.

Figure 7. Mass of the deposited crystal m on a homogeneous glass substrate as a function of dip-coating speed U. Dashed lines are fitted functions m ∼ U R; solid lines correspond to eq 3.

criterion based on diffusive transport δ ∼ D/vi, where D is the diffusion coefficient and vi the growth speed of the crystal interface. Estimating the diffusion coefficient of nicontinamide as 3  10-10 m2/s and using vi = Usp ≈ 15 μm/s gives a length scale of 20 μm, which is compatible with the branch spacings observed experimentally in Figures 2d and 5b,d. 4.4. Crystallization on Homogeneous Surfaces during “Slow” Dip-Coating. In Figure 7 we present the total crystal mass m as a function of U for two concentrations of 5.66 and 1.37 wt %. Two deposition regimes can be clearly distinguished with a characteristic threshold speed Uth, below which the m(U) dependence qualitatively changes character; i.e., m begins to grow with decreasing withdrawal speed. The experimental data were fitted with power-law functions m ∼ UR, where the solid lines correspond to the “fast” dip-coating regime with R=2/3, whereas the dashed ones to the “slow” regime (R ≈ -1). Very similar results were obtained recently by Le Berre et al.,20 who investigated die-coating of noncrystalline phospholipid solutions. Their exponents R obtained from fitting the phospholipid film thickness with a power law h¥ ∼ UR are equal to R = -1.14 for the evaporation regime and R = 0.76 for the Landau-Levich (LL) regime, respectively. Berteloot et al.17 very recently presented a theoretical model detailing the influence of evaporation on material deposition at receding contact lines. Assuming a specific analytical form of the evaporative flux distribution, they predicted the existence of a stagnation zone a distance of ld ∼ U-2 from the contact line, where the net flux of solution vanishes. The authors argue that all the solute up to a distance ld from the contact line is deposited onto the substrate and implicitly assume that the solute concentration in their control volume is uniform and equal to the bulk concentration. This leads them to the prediction d ∼ U-2 and thus an exponent R=-2. The scaling m ∼ U-1 in the evaporation regime can be derived from mass balances for the solvent and solute. Following Le Berre et al.,20 we consider the control volume sketched in Figure 8, which is stationary in a laboratory reference frame. The substrate moves at constant speed U, whereas the free liquid surface remains stationary for an infinitely large reservoir. The right boundary (1) is sufficiently remote from the contact line for overall solute concentration gradients to be insignificant. In steady state, the solvent evaporating across boundary (2) is replenished by flow across boundary (1): Z Z Z JB 3 nB dS þ FuB 3 nB dS ¼ Qev þ FuB 3 nB dS ¼ 0 ð4Þ ð2Þ

ð1Þ

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ð1Þ

Here, nB is the outward unit normal vector of the control volume, uB is the velocity field, J is the evaporative flux, and Qev is the integrated evaporation rate in the contact line region. In the case of diffusionlimited evaporation, the evaporative flux exhibits a singularity near acute contact lines.16 This is, however, not physically realistic, as upper bounds to the rate of evaporation of liquids exist,44 as indicated by the solid line in Figure 7. For the solute mass balance we assume that the solute is nonvolatile and does not adsorb on any interface. From the interfacial balance condition45 it then follows that the diffusive flux Bj and convective solute flux cuB cancel at the liquid-air interface. For dilute solutions the diffusive flux can be written as Bj = -Dr Bc, where c is the solute concentration (in units of kg/m3), leading to - nB 3 Drc þ cuB 3 nB ¼ 0

ð5Þ

For simplicity, we assume that crystal growth only occurs at boundary (4), although that does not qualitatively alter our reasoning. Crystal growth usually proceeds at a rate R = f(css), which is a unique and monotonically increasing function of the local supersaturation css. In steady state, the growth rate must equal the dip-coating speed, R = U. Application of the mass conservation law for the solute in the control volume ZZ ð1 - 5Þ

ðjB þ cuBÞ 3 nB dS ¼ 0

ð6Þ

therefore, leads to Fcryst Udwsub ¼ Qev C0

ð7Þ

m ¼ Fcryst Sd ¼ Qev C0 S=ðwsub UÞ

ð8Þ

or equivalently

where wsub is the width of the sample and C0 is the bulk solute weight fraction. This indicates that the exponent R equals -1 in the evaporation regime and that the total deposited crystal mass is proportional to C0, which agrees well with the experimental results in Figures 4 and 7. The exact shape of the control volume h(x,y), i.e. the contact line region, only affects the overall mass of the crystal deposit through the integral evaporation rate Qev. It is, however, important for the conformation and arrangement of the crystal filaments. The surface profile h(x,y) is determined by the evaporative flux J(x,y), the dynamic contact angle corresponding to the withdrawal speed, which is modified in the presence (44) Penner, S. S. J. Phys. Chem. 1948, 52, 367. (45) Slattery, J. C.; Sagis, L.; Oh, E.-S. Interfacial Transport Phenomena; Springer: New York, 2007; p 700.

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of evaporation,46-49,17 the dependence of viscosity and surface tension on solute concentration and temperature, i.e., on the subtle interplay of a large number of phenomena, which makes an accurate local description of the crystallization dynamics highly challenging. Because of the different scaling exponents, the Landau-Levich and evaporation regime are separated by a well-defined threshold speed, which can be determined from eqs 1, 3, and 7 as Uth ¼ ½Qev =0:946wsub lc ðμ=σÞ2=3 Fsol 3=5

ð9Þ

The experimental values are Uth =0.18 mm/s for C0 =5.66 wt % and 0.16 mm/s for C0 = 1.37 wt %. We measured the evaporation rate of nicotinamide solutions on hydrophilic stripes using a precision balance. The solute concentration varied between 1.37 and 5.66 wt %. Small volumes of the solution were applied on a hydrophilic stripe of dimensions 0.75 mm  30 mm on a glass substrate and then left to evaporate freely at room temperature (T = 293 K). We measured the liquid mass m(t) before crystallization initiated and found that the evaporation rate slightly increases with nicotinamide concentration from 0.05  10-5 to 0.06  10-5 g/s for concentrations of 1.37 and 5.66 wt %, respectively. In order to get an estimate for Qev in the control volume sketched in Figure 8, which has only a single contact line, we divided the experimental values obtained with hydrophilic stripes by a factor of 2. Inserting Qev = 0.025  10-5 g/s into eq 9 and correcting for the sample width yields a value of Uth = 0.38 mm/s, which slightly overestimates the experimental values (see Figure 7). The discrepancy is not unexpected, however, as during the dip-coating process evaporation from the contact line is retarded by the presence of isopropanol vapor emerging from the liquid reservoir surface, which is absent for evaporation from stripes. This hypothesis is substantiated by repeating the dipcoating experiments with different reservoir fill levels. Since the vapor density of isopropanol is higher than air, it tends to accumulate between the solution surface and the rim of the reservoir container and to partially saturate the atmosphere there. For a fill level of 17 mm below the rim we measured a 10-fold decrease in deposited mass as compared to the standard fill level of 3-4 mm below the rim used for all experiments presented. The small difference (0.02 mm/s) in the threshold speeds for the two solution concentrations presented in Figure 7 can be explained by the dependence of Qev on C0. By using eq 9 with experimental values of evaporation rates for different concentrations, one expects a difference in the order of 0.05 mm/s, again comparable with the experimental values. Figure 9 illustrates typical crystal morphologies obtained at very low speeds of dip-coating U , Usp for two solute concentrations of 3.71 and 1.37 wt %. In Figure 9a,b crystal filaments with a pronounced alignment along the dip-coating direction can be seen. The crystal filaments overlap each other in case of higher solute concentration (Figure 9a), whereas they form well-separated bunches for the lower concentration used (Figure 9b). Images c and d show regions very close to the edge of the glass substrates, which left the solution reservoir last during the dip-coating process. The crystal filaments are thicker for higher concentration and arrange into aggregates with a very well-defined wavelength at the end of the substrates. Images c and d, which were taken with polarizer and analyzer crossed, indicate better alignment of the (46) (47) (48) (49)

Wayner, P. C., Jr. Langmuir 1993, 9, 294. Anderson, D. M.; Davis, S. H. Phys. Fluids 1995, 7, 248. Hocking, L. M. Phys. Fluids 1995, 7, 2950. Elbaum, M.; Lipson, S. G.; Wettlaufer, J. S. Europhys. Lett. 1995, 29, 457.

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Figure 9. Crystal patterns obtained at a very low speed of dipcoating U = 1.8 μm/s for two solute concentrations of (a, c) 3.71 wt %, and (b, d) 1.37 wt %. Images c and d were taken with crossed polarizers. The arrow indicates the dip-coating direction. Image width 150 μm.

crystal ribbons at their ends as compared with the interior of the sample. Such a formation of well-aligned filaments is not limited to nicotinamide. We observed the same phenomenon with phthalic acid dissolved in isopropanol during slow dip-coating, which also belongs to the monoclinic class of symmetry. Sele et al. recently investigated the controlled deposition of 6,13-bis(triisopropylsilylethynyl)pentacene (TIPS-PEN) dissolved in toluene by dipcoating and its effect of crystal morphology and orientation on transistor performance.50 They found that for withdrawal speeds, U > 1 mm/s, the entrained TIPS-PEN film consists of small, arbitrarily shaped and oriented crystal grains, which is similar to nicotinamide patterns deposited in the LL regime (Figure 2). When the dip-coating speed was decreased down to 150 μm/s, elongated needle-like crystals appeared, which apparently correspond to the transition between the LL and evaporation regime that we observed for nicotinamide. 4.5. Crystallization on Chemically Patterned Surfaces. Figure 10 shows a dependence of total crystal mass on the dipcoating speed on silicon and glass substrates containing hydrophilic stripes of 30 mm length and 1.5 mm or 0.75 mm width. The stripes were oriented parallel to the dip-coating direction. The solid lines correspond to fit functions m ∼ U R. The dashed lines correspond to relations m ∼ U1/3 obtained by multiplying eq 2 with the hydrophilic surface area S = Lw of the substrate covered with crystals, the solution density F, and the solute concentration C0: m¼

2 0:356w2 ðμU=σÞ1=3 FLC0 3

ð10Þ

Here w and L denote the width and length of the hydrophilic stripe, respectively. The factor 2/3 accounts for the approximately parabolic cross section of the liquid height profile. The dashed lines in Figure 10 lie below the experimental data and do not reproduce the power law exponent for the larger width w = 1.5 mm. We attribute this behavior to the fact that their widths are comparable to the capillary length lc = 1.72 mm of isopropanol. These experiments therefore fall within a transition (50) Sele, C.; Kjellander, C.; Niesen, B.; Thornton, M.; van der Putten, B.; Myny, K.; Wondergem, H.; Moser, A.; Resel, R.; van Breemen, A.; van Aerle, N.; Heremans, P.; Anthony, J.; Gelinck, G. Adv. Mater. 2009, 21, 4926.

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Figure 10. Total mass of nicotinamide crystal deposited on hydrophilic stripes versus dip-coating speed. Solid lines correspond to fit functions m ∼ UR and dashed ones to eq 10.

regime beyond the limits of validity of both eqs 1 and 2 as recently studied experimentally by Brasjen and Darhuber.51 Figure 11 presents crystal patterns of nicotinamide on a 0.75 mm wide hydrophilic stripe on a glass substrate for two solute concentrations of 1.37 and 5.66 wt %, dip-coated at U = 1.5 μm/s. The stripes were not completely immersed into the reservoir solution. The approximate position of the reservoir meniscus was 1-2 mm below the top end of the stripes and is indicated by the arrows in Figure 9a,b. The evaporative flux is highest at the contact lines and the stripe edges, corresponding to local maxima of the supersaturation. Nucleation therefore likely commenced at the contact lines, and nicotinamide branches emerge from these nucleation centers in essentially all directions. A transition from branched growth to directional alignment can be seen at larger distances from the top of the stripe. When branches intersect the stripe edges at an angle j g 30, they typically cease to grow. For small intersections angles j e 30 the crystal ribbons bend and become aligned with the stripe direction. If the entire hydrophilic stripe is initially completely immersed in the reservoir solution, such a transition from branched to aligned is absent and the aligned ribbon morphology persists along the entire length of the stripes. Since the evaporative flux and therefore supersaturation is highest at the stripe edges, locally more crystal is deposited as indicated by the darker grayscale values in Figure 11a-c. For the higher concentration, even three-dimensional growth out of the substrate plane is observed as indicated in Figure 11c. Equation 5 predicts local maxima in the concentration distribution near evaporating solution-air interfaces, which may favor crystallite growth away from the substrate plane. Figure 11c,d illustrates that the density of the individual crystal filaments increases with the solute concentration. At lower concentrations less dense layers of relatively well-aligned crystal ribbons without 3D growth at the stripe edges are obtained (Figure 11d). The image was taken with crossed polarizers and thus indicates relatively uniform orientation of crystal optic axes. Figure 11e shows an interesting effect occurring at the end of the hydrophilic stripe, where neighboring filaments bunch together as indicated by the arrows. The origin of this effect is currently not clear. It is reminiscent of elastocapillary aggregation (51) Brasjen, B. J.; Darhuber, A. A. Proceedings of the European Coating Symposium; Karlsruhe, 2009. (52) Bico, J.; Roman, B.; Moulin, L.; Boudaoud, A. Nature 2004, 432, 690.

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Figure 11. Transition from a branched morphology to directional alignment for concentrations of (a, c, e) 5.66 wt %, (b, d) 1.37 wt %, and (f) 3.71 wt % on a 0.75 mm wide hydrophilic stripe. (c) Nicotinamide ribbons at a distance of 15 mm from the top of the stripe. Image d was taken with crossed polarizer and analyzer. The black arrow corresponds to the dip-coating direction; the speed of withdrawal was (a-e) 1.5 μm/s and (f) 1.8 μm/s. (e) Ribbons form bunches at the end of a hydrophilic stripe for high but not for low concentrations. Image widths (a-d) 1.94 mm and (e) 150 μm.

of fibers during dip-coating.52 We speculate that once the crystals have grown beyond the hydrophilic stripe, their adhesion to the substrate is significantly weaker and therefore their susceptibility to capillary forces is enhanced, possibly leading to the observed phenomenon. A similar effect is observed in Figure 8c,d for growth on homogeneously hydrophilic glass slides, which somewhat discourages the hypothesis of elastocapillary bunching because the filament adhesion on hydrophilic surfaces is typically high. At the lower end of the glass slide in Figure 8c,d as well as at the lower end of the hydrophilic stripe, significantly more liquid is entrained locally due to breakup of the liquid meniscus to the reservoir. This causes a significant (though temporary) increase in liquid film thickness and consequently reduction in supersaturation and crystal growth speed. According to linear stability theory,37 the lateral length scale governing branch separation increases with decreasing growth velocity, which may qualitatively account for the effects shown in Figures 9c,d and 11e. Figure 11f shows the filament morphology on a hydrophilic stripe that was inclined by j=45 in an azimuthal direction with respect to the (vertical) dip-coating direction during withdrawal. The filament alignment exhibits a directional spread approximately from j=25 to 45, i.e., from an orientation parallel to the stripe to one closer to the direction of withdrawal. Three-dimensional growth features are visible at the stripe edge that was further away from the reservoir, where the evaporation rate was expected to be highest. It appears that the filaments originate at DOI: 10.1021/la101002x

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nucleation centers located at the upper stripe edge and end rather abruptly at the lower stripe edge, i.e., the one in closer proximity to the reservoir. The azimuthal spread in the filament alignment distribution is comparable for stripes coated vertically (Figure 11d) and under 45 (Figure 11f). Meyer and Braun have studied the crystallization behavior of 0.15 wt % PEO solutions in chloroform on chemically patterned surfaces.14 They used dip-coating at typical velocities of 2 mm/s and polymer molecular weights between 2000 and 10 000. They observed branched lamellar PEO crystal morphologies on the hydrophilic regions whereas the hydrophobic regions remained clear. The authors report that under suitable conditions the deposits were amorphous after dip-coating for extended periods of time, which allowed them to use an AFM tip to induce heterogeneous nucleation at predefined locations. In view of the relatively high withdrawal speed of 2 mm/s, their experiments likely fell into the LL regime, which may explain the low degree of correlation of the branch alignment with respect to the coating direction. 4.6. Horizontal Banding. In Figure 4a-c, light and dark bands can be distinguished that are aligned approximately horizontally and thus perpendicular to the dip-coating direction. The dark regions are bands of increased crystal accumulation. These bands span the entire width of the sample (25 mm), which indicates that a concerted, nonlocal phenomenon is responsible for their formation. They are reminiscent of striations observed in melt growth, where temperature fluctuations modulate the effective supercooling and hence the crystal growth rate.53,54 In our case, their origin may be due to pinning-depinning interactions of the contact line with crystal deposits on the glass substrate.55,56 Similar patterns have frequently been observed with DNA,57 polymer solutions,58 and colloidal suspensions.59-64 During the drop-casting experiments described in section 4.4, we observed that temporal fluctuations of the overall evaporation rate, for instance due to air currents, also gave rise to band formation. When the dip-coating experiments were repeated with a low reservoir fill level of 10-20 mm below the rim, the contact line region was shielded from exterior air currents. No striation patterns were observed. It therefore appears that in our case any pinning-depinning effects are a consequence of air flow fluctuations, but not the dominant mechanism in themselves. In the case of crystal growth mediated by solvent evaporation, air convection directly increases the supersaturation and hence the crystal growth rate by enhancing the evaporative flux as indicated by the dashed line in Figure 8. Because an increased evaporation rate causes more evaporative cooling, the effective supersaturation is further enhanced for solutes for which the saturation concentration decreases with (53) Hurle, D. T. J. J. Cryst. Growth 1972, 13/14, 39. (54) Scheel, H. J. J. Cryst. Growth 2006, 287, 214. (55) Vorl€ander, D.; Ernst, I. Z. Phys. Chem. (Muenchen, Ger.) 1918, 93, 521. (56) Flood, H.; Tronstad, L. Kolloid-Z. 1934, 68, 333. (57) Maheshwari, S.; Zhang, L.; Zhu, Y.; Chang, H.-Ch. Phys. Rev. Lett. 2008, 100, 044503. (58) Xu, J.; Xia, J.; Won Hong, S.; Lin, Z.; Qiu, F.; Yang, Y. Phys. Rev. Lett. 2006, 96, 066104. (59) Adachi, E.; Dimitrov, A. S.; Nagayama, K. Langmuir 1995, 11, 1057. (60) Abkarian, M.; Nunes, J.; Stone, H. A. J. Am. Chem. Soc. 2004, 126, 5978. (61) Ray, M. A.; Kim, H.; Jia, L. Langmuir 2005, 21, 4786. (62) Lee, J. A.; Reibel, K.; Snyder, M. A.; Scriven, L. E.; Tsapatsis, M. ChemPhysChem 2009, 10, 2116. (63) Ghosh, M.; Fan, F.; Stebe, K. J. Langmuir 2007, 23, 2180. (64) Lara-Cisneros, G.; Loredo-Osti, A.; Femat, R.; Perez, E. Phys. Rev. E 2008, 77, 036223.

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Figure 12. Influence of tears-of-wine-like instabilities on crystallization pattern. Image width (a) 4.32 mm and (b) 2.03 mm.

decreasing temperature, as is the case for nicotinamide in isopropanol. 4.7. Influence of Hydrodynamic Instabilities. Volatile liquid mixtures and solutions frequently exhibit instabilities near contact lines. Examples include the well-known tears-of-wine effect,65-68 festoon instability,69-71 and Langmuir-Blodgettand dewetting-related structure formation.72,73 Two examples of related instabilities in our system are shown in Figure 12a,b. Figure 12a shows a sample with spherulithic crystal morphology. Horizontal bands of periodic fingers of lateral wavelength λ ≈ 300 μm occur with a vertical separation of several millimeters. Only one of these bands is shown. Their origin is related to thin films that are driven upward more or less periodically from the meniscus region presumably due to surface tension gradients. These films spread in an unstable fashion, develop fingers, and may locally add additional nicotinamide to the already present crystal layer or partially redissolve it, which gives rise to the observed grayscale contrast. Figure 12b shows the region close to the initial contact line position up to which the sample was immersed into the liquid reservoir prior to its withdrawal. A series of fingers with lateral separation λ ≈ 500 μm are visible, presumably of similar origin as the ones in Figure 12a. Since the lateral length scale of this instability is on order several hundred micrometers, we conclude that it does not influence the dynamics and size selection of nicotinamide filament formation and branching, which occurs on length scales of several to few tens of micrometers.

5. Summary and Conclusions We have investigated how the crystal growth of nicotinamide dissolved in isopropanol is influenced by the solution deposition parameters during dip-coating as well as by chemical patterning of the substrate surface. On chemically homogeneous surfaces, three crystallization regimes were identified dependent on the coating speed. At high speeds, spherulithic morphologies were observed that showed no correlation with the coating direction. For intermediate speeds a branched morphology with preferential alignment parallel to the coating direction is found. For low speeds, filament-like crystal patterns well aligned with the coating direction were obtained.

(65) Vuilleumier, R.; Ego, V.; Neltner, L.; Cazabat, A. M. Langmuir 1995, 11, 4117. (66) De Ryck, A. J. Colloid Interface Sci. 1999, 209, 10. (67) Fanton, X.; Cazabat, A. M. Langmuir 1998, 14, 2554. (68) Hosoi, A. E.; Bush, J. W. M. J. Fluid Mech. 2001, 442, 217. (69) Redon, C.; Brochard-Wyart, F.; Rondelez, F. J. Phys. II 1992, 2, 1671. (70) Poulard, C.; Benichou, O.; Cazabat, A. M. Langmuir 2003, 19, 8828. (71) Tarasov, O. A.; Gorbacheva, N. A. Tech. Phys. Lett. 2007, 33, 157. (72) Huang, J.; Kim, F.; Tao, A. R.; Connor, S.; Yang, P. Nature Mater. 2005, 4, 896. (73) Karthaus, O.; Grasjo, L.; Maruyama, N.; Shimomura, M. Chaos 1999, 9, 308.

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On chemically patterned surfaces, only the hydrophilic regions allow for liquid entrainment and crystal growth. This provides a potential means of tailoring the density, size, and shape of crystallites. In the case of hydrophilic stripes, we found that the average filament growth direction globally follows the azimuthal orientation of the stripes. However, a significant spread of the filament direction distribution on order of 20 was observed. Generally, the filament crystal quality and alignment were better for lower solute concentrations, presumably because then the nucleation threshold was exceeded only in a small region very close to the moving contact line.

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Acknowledgment. The authors gratefully acknowledge funding from the Dutch Polymer Institute (DPI) through project #665. We thank Xiaoran Li, Charlotte Kjellander, and Gerwin Gelinck from the Holst Centre Eindhoven for inspiring discussions and David Sinz for his help with sample preparations. Supporting Information Available: Additional data about the average spherulite size as a function of dip-coating speed as well as a movie of the spherulite growth process depicted in Figure 6a-c. This material is available free of charge via the Internet at http://pubs.acs.org.

DOI: 10.1021/la101002x

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