Influence of Fluid Flow on the Deposition of Soluble Surfactants

Soluble surfactants are often deposited from volatile solvents through moving contact lines. In this study, we demonstrate that altering the flow fiel...
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Langmuir 2008, 24, 6705-6711

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Influence of Fluid Flow on the Deposition of Soluble Surfactants Through Receding Contact Lines of Volatile Solvents Benjamin K. Beppler,†,‡ Kalyani S. Varanasi,†,‡ Stephen Garoff,*,†,‡ Guennadi Evmenenko,§ and Kristina Woods† Department of Physics, Carnegie Mellon UniVersity, Pittsburgh, PennsylVania 15213, Center for Complex Fluids Engineering, Carnegie Mellon UniVersity, Pittsburgh, PennsylVania 15213, and Department of Physics and Astronomy, Northwestern UniVersity, EVanston, Illinois 60208 ReceiVed February 14, 2008. ReVised Manuscript ReceiVed April 11, 2008 Soluble surfactants are often deposited from volatile solvents through moving contact lines. In this study, we demonstrate that altering the flow field near such a contact line fundamentally changes the deposited surfactant structure. At slow contact line speeds, the substrate emerges dry. A densely packed, tilted monolayer of surfactant is deposited along the solid-vapor interface from the rolling fluid motion at the contact line. At faster speeds, the substrate emerges with an evaporating thin film entrained on its surface. Surfactant is confined in the film in a constantly increasing concentration environment. Monodisperse crystalline islands nucleate and grow on the surface with sizes and shapes controlled by varying the deposition conditions. These results contrast with disordered deposits that result from evaporation at a pinned contact line. Our results suggest that dip-coating with control of dipping speed and evaporation rate may provide better control of deposition through contact lines of evaporating solvents.

1. Introduction Dynamic wetting processes control the deposition of solute molecules or suspended particles in many coatings technologies. Classically,insolublesurfactantsaredepositedviaLangmuir-Blodgett (LB) or Langmuir-Schaefer (LS) methods.1,2 In these methods, the substrate may emerge dry from the solution or wetted with a fluid film that is then expelled. Even when soluble surfactants are adsorbed to a solid-solution interface by self-assembly, the self-assemblies are often pulled through the solution contact line for study at the solid-vapor interface.2–5 Much research presently focuses on the deposition of nanoparticles and large polymer molecules through receding contact lines of volatile solvents including methods based on LB and LS deposition,6–8 drying drops,9–12 and dip-coating.13 In all these processes, the fluid flow near a moving or stationary contact line will impact the deposited structure. This paper investigates how several critical aspects of these effects can be controlled. We examine the deposition of a soluble surfactant on a substrate withdrawn from an aqueous solution both when the * To whom correspondence should be addressed. E-mail: sg2e@ andrew.cmu.edu. † Department of Physics, Carnegie Mellon University. ‡ Center for Complex Fluids Engineering, Carnegie Mellon University. § Northwestern University.

(1) Schwartz, D. K. Surf. Sci. Rep. 1997, 27, 245–334. (2) Swalen, J. D.; Allara, D. L.; Andrade, J. D.; Chandross, E. A.; Garoff, S.; Israelachvili, J.; Mccarthy, T. J.; Murray, R.; Pease, R. F.; Rabolt, J. F.; Wynne, K. J.; Yu, H. Langmuir 1987, 3, 932–950. (3) Perkin, S.; Kampf, N.; Klein, J. J. Phys. Chem. B 2005, 109, 3832–3837. (4) Mellott, J. M.; Schwartz, D. K. J. Am. Chem. Soc. 2004, 126, 9369–9373. (5) Mellott, J. M.; Hayes, W. A.; Schwartz, D. K. Langmuir 2004, 20, 2341– 2348. (6) Dabbousi, B. O.; Murray, C. B.; Rubner, M. F.; Bawendi, M. G. Chem. Mater. 1994, 6, 216–219. (7) Santhanam, V.; Liu, J.; Agarwal, R.; Andres, R. P. Langmuir 2003, 19, 7881–7887. (8) Fried, T.; Shemer, G.; Markovich, G. AdV. Mater. 2001, 13, 1158–1161. (9) Chopra, M.; Li, L.; Hu, H.; Burns, M. A.; Larson, R. G. J. Rheol. 2003, 47, 1111–1132. (10) Whetten, R. L. Nat. Mater. 2006, 5, 259–260. (11) Narayanan, S.; Wang, J.; Lin, X. M. Phys. ReV. Lett. 2004, 93, 135503. (12) Bigioni, T. P.; Lin, X. M.; Nguyen, T. T.; Corwin, E. I.; Witten, T. A.; Jaeger, H. M. Nat. Mater. 2006, 5, 265–270. (13) Dimitrov, A. S.; Nagayama, K. Langmuir 1996, 12, 1303–1311.

Figure 1. Normalized reflectivity of the X-ray beam versus the momentum change, q, on SiO2 surfaces. (O) Data, (s) fit. Substrate withdrawn at 5 µm/s from 0.8 cmc CTAB.

substrate emerges dry from the solution and when a film is entrained and then evaporates. We contrast these depositions to that from a drying drop with a pinned contact line, the classic “coffee stain.”14–16 At slow receding speeds (below the critical speed, Ucrit),17 our substrates emerge dry and surfactant must be deposited through a moving contact line. Surfactants self-assemble at the liquid-vapor and the solid-liquid interface and are also present in the bulk solution approaching the contact line. In this case, we find that evaporation of the solvent has little effect and a rearrangement of surfactant molecules occurs as they pass through the contact line and form a rather well ordered monolayer. The rolling fluid motion near the contact line18–20 (14) Truskett, V.; Stebe, K. J. Langmuir 2003, 19, 8271–8279. (15) Hu, H.; Larson, R. G. J. Phys. Chem. B 2002, 106, 1334–1344. (16) Deegan, R. D.; Bakajin, O.; Dupont, T. F.; Huber, G.; Nagel, S. R.; Witten, T. A. Nature 1997, 389, 827–829. (17) Sedev, R. V.; Petrov, J. G. Colloids Surf. 1991, 53, 147–156. (18) Huh, C.; Scriven, L. E. J. Colloid Interface Sci. 1971, 35, 85–101. (19) Dussan, E. B.; Davis, S. H. J. Fluid Mech. 1974, 65, 71–95. (20) Dussan, E. B. Annu. ReV. Fluid Mech. 1979, 11, 371–400.

10.1021/la8004882 CCC: $40.75  2008 American Chemical Society Published on Web 05/30/2008

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keeps the surfactant concentration from rising at least until a very small region in the immediate vicinity of the contact line. At higher receding speeds (>Ucrit), a film is entrained on our substrates. Surfactant is trapped in almost pluglike flow in the film and deposited as the solvent evaporates.21,22 We find that as the surfactant concentration grows and the surfactant progresses up the film, rather monodisperse crystallites of surfactant form and are deposited on the emerging solid-vapor interface. In contrast, surfactant deposited at a pinned, evaporating contact line (“coffee stain” deposition) forms a disordered deposition as surfactant is swept to the contact line by the varying evaporation rates across the meniscus.

2. Materials and Experimental Methods 2.1. Sample Preparation. We used oriented silicon wafers [100] (International Wafer Service, Inc.) with a native oxide layer (1-2 nm) as our high energy substrates. The substrates were acid-cleaned as described elsewhere.23,24 Low-energy surfaces were silicon wafers coated with a monolayer of octadecyltrichlorosilane (OTS).25 Cetyltrimethylammonium bromide (CH3(CH2)15N(CH3)3Br; CTAB) and sodium dodecyl sulfate (CH3(CH2)11SO4Na; SDS) were used as received from Fluka Chemical Corp. (Buchs, Switzerland). Both are assayed at >99% purity. We made aqueous solutions using RO pure water (from a Barnstead Nanopure II water system with post treatment to remove organic impurities) with resistivity >17.5 MΩ · cm. The concentrations used in this study were 0.3 and 0.8 times the critical micelle concentration (cmc) where the cmc is 1 mM for CTAB and 8 mM for SDS.26 Care was taken to use SDS solutions within 5 days of mixing to prevent contamination via hydrolysis. The substrates (∼1 cm × 10 cm for AFM, 1 in. × 3 in. for XRR) were suspended vertically in the center of a Teflon beaker (diameter ) 8 cm) overfilled with the solution. The substrates were retracted from the fluid bath at controlled speeds, U, by a motorized stage (Newport Motion Controller, Newport Klinger Corporation, CA). The speed of the motor was calibrated by tracking the motion of features on a plate moved by the stage. First, the substrates were advanced into the solution at speeds ranging from 500-2000 µm/s. They were left soaking in the solution for ∼1 h or more in order to bring the solid-liquid interface into equilibrium with the solution.27 They were then withdrawn at speeds, U, ranging from 2 to 2000 µm/s. The receding contact line was imaged using video reflectance and interference microscopy.22,28–30 The experiments were performed at ambient laboratory temperature which ranged between 20 and 25 °C. Experiments varied the residence time (film length ÷ pulling speed) of surfactants in the films above Ucrit from 20 to 900 s by controlling the humidity around the substrate from 10% to 90% at a constant pulling speed of U ) 200 µm/s. 2.2. Surface Structures at Solid-Vapor Interface. We use a variety of techniques to study the structure and quantify the surface excess at the solid-vapor interface, including optical ellipsometry, X-ray reflectometry (XRR) and atomic force microscopy (AFM). 2.2.1. Ellipsometry. We use a modified Gaertner Auto-Gain Ellipsometer L104B (Gaertner Scientific Corporation, Chicago IL) with a He-Ne laser (λ ) 6328 Å) and a beam size of 0.8 mm with a Labview 6.0 control panel. Our implementation of ellipsometry is given elsewhere.29 We measure the two ellipsometric parameters, ∆ and Ψ, of the reflected, polarized laser beam from the sample (21) Qu, D.; Rame, E.; Garoff, S. Phys. Fluids 2002, 14, 1154–1165. (22) Qu, D. Ph.D. Thesis, Carnegie-Mellon University, Pittsburgh, PA, 2001. (23) Kumar, N.; Varanasi, K.; Tilton, R. D.; Garoff, S. Langmuir 2003, 19, 5366–5373. (24) Frank, B.; Garoff, S. Colloids Surf., A 1996, 116, 31–42. (25) Varanasi, K. Ph.D. Thesis, Carnegie-Mellon University, Pittsburgh, PA, 2005. (26) Frank, B. Ph D. Thesis, Carnegie-Mellon University, Pittsburgh, PA, 1995. (27) Velegol, S. B.; Fleming, B. D.; Biggs, S.; Wanless, E. J.; Tilton, R. D. Langmuir 2000, 16, 2548–2556. (28) Nadkarni, G. D.; Garoff, S. Langmuir 1994, 10, 1618–1623. (29) Frank, B.; Garoff, S. Langmuir 1995, 11, 4333–4340. (30) Frank, B.; Garoff, S. Langmuir 1995, 11, 87–93.

Beppler et al. surface. Of the two, ∆ is more sensitive to the properties of the deposited surfactant structures.22 The change in ∆ from the bare substrate to a substrate with deposited surfactant (≡δ∆) is linearly related to the change in thickness:

(

δ∆ ) C 1 -

)

1 t n2

(1)

where t is the thickness of the adsorbed surfactant, n is the refractive index of the deposited layer, and C is a constant that depends on the optical properties of the substrate being investigated.31 To determine δ∆ for surfactants on SiO2 surfaces, we measure ∆ on both clean and coated surfaces at typically 10 points across the surface and determine δ∆ for those deposition conditions. While we do not have an absolute value of the thickness, we do assume that if δ∆ is the same for two different deposition conditions, the surface excess on those two surfaces is the same. 2.2.2. X-ray Reflectometry. We use XRR to determine the thickness and area per molecule of surfactant deposited at the solid-vapor interface. For samples withdrawn below Ucrit, reflectometry is performed using an in-house rotating anode source. Details of both the experimental and analysis methods used are reported elsewhere.32–34 This technique is robust in determining layer thickness and area/molecule when we have a structure that is laterally uniform on scales larger than the coherence length of the X-rays. Above Ucrit, when we have lateral inhomogeneities on the 1-10 µm scale in the deposited structure, reflectometry is performed using a synchrotron source. XRR studies were performed at beam line X23B of the National Synchrotron Light Source using a four-circle Huber diffractometer in the specular reflection mode (i.e., incident angle θ was equal to exit angle). The reflected intensity was measured as a function of the momentum transfer component qz ) (4π/λ) sin θ, perpendicular to the reflecting surface. X-rays of energy E ) 10.0 keV (λ ) 1.24 Å) were used for all measurements. The beam size was 0.4 mm vertically and 1.4 mm horizontally. The samples were kept under slight overpressure of helium during the measurements to reduce the background scattering from the ambient gas and radiation damage. All experiments were performed at room temperature. The background was measured at θ ( 0.1° off the specular direction and subtracted from the specular counts. Details of the data acquisition and analysis procedures are given elsewhere.35 2.2.3. Atomic Force Microscopy. To complement the XRR and ellipsometry data, we use AFM to characterize the surface topography of the surfactant deposited on the solid-vapor interface. We use a Multimode Nanoscope IIIa (Digital Instruments, Inc.) in contact mode with a 150 µm scanner (serial no. 6219) at 23 ( 3 °C. Pyramidal AFM probes of silicon nitride, featuring cantilevers with spring constants ranging from 0.03 to 0.5 N/m, were purchased from Thermomicroscopes, Sunnyvale, CA (model No. MSCT-AUHN). The cantilevers are UV-ozone cleaned for 20 min prior to the experiment. A new cantilever is used each time we scan a new sample. Multiple scans, at rates of 0.5-5 Hz with a deflection set point between 1-1.5 V, were made on a surface both in the friction and height mode. If a feature appears repeatedly in the same region in both modes, we assume it is real and not an artifact of the tip altering the sample. Changing the scan angle does not deform these features. We process the final images to remove noise that might prevent us from recognizing real features. We use analysis tools in the Nanoscope software (v5.30r2) such as bearing and section analysis to analyze the images. (31) Tompkins, H. G. A user’s guide to ellipsometry; Academic Press, Inc.: San Diego, 1993. (32) Luokkala, B. B.; Garoff, S.; Suter, R. M. Phys. ReV. E 2000, 62, 2405– 2415. (33) Birch, W. R.; Knewtson, M. A.; Garoff, S.; Suter, R. M.; Satija, S. Langmuir 1995, 11, 48–56. (34) Birch, W. R.; Knewtson, M. A.; Garoff, S.; Suter, R. M.; Satiia, S. Colloids Surf., A 1994, 89, 145–155. (35) Evmenenko, G.; van der Boom, M. E.; Kmetko, J.; Dugan, S. W.; Marks, T. J.; Dutta, P. J. Chem. Phys. 2001, 115, 6722–6727.

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Table 1. Thickness and Molecular Density of the Monolayer along the Solid-Vapor Interface at 0.8 and 0.3 cmc CTAB on SiO2 Obtained from the XRR fit for U < Ucrit concentration

thickness (Å)

area (Å2/molecule)

0.3cmc 0.8cmc

12.8 ( 0.75 16.3 ( 1.1

75 ( 19.3 23 ( 2.2

2.2.4. IR Microscopy. The samples were characterized by synchrotron Fourier transform infrared (FTIR) spectro-microscopy at the Advanced Light Source at Lawrence Berkeley National Laboratory at beamline 1.4.36,37 The spectra were collected in reflection mode with a ThermoNicolet Nexus 870 FTIR and a Continumm XL IR Microscope under ambient conditions in the 4000-650 cm-1 spectral region with a diffraction-limited IR beam with a diameter ranging from 3-10 µm. The sample collection stage was purged with dry nitrogen during data collection to decrease the presence of water vapor in the scans, and the sample spectra were collected with a liquid nitrogen cooled mid-infrared Midband MCT detector (MCT-B) operating in the 600-10 000 cm-1 spectral range. Each spectral map is composed of individual IR measurements consisting of 128 averaged scans with a spectral resolution of 4 cm-1.

Figure 2. δ∆ on bare SiO2 surface withdrawn from 0.3 (circles) 0.8 cmc (triangles) CTAB at fixed evaporation rate. Ucrit for 0.8 cmc is indicated by the dashed line. For 0.3 cmc, Ucrit > 2 cm/s.

3. Results and Discussion 3.1. Substrate Emerging Dry: U < Ucrit. Figure 1 shows the XRR data from surfactant deposited on the solid-vapor interface of SiO2 from 0.8 cmc CTAB, along with the fit to the data. A similar quality fit is found for data from deposition at 0.3 cmc. Table 1 lists the thickness and area per molecule of the deposited surfactant. The listed uncertainty in the fitting parameters includes modeling the surfactant as maintaining or losing the Brcounterion in the deposited layer. More detailed studies have shown that the CTAB is deposited with heads in contact with the surface and very little water retained in the film.34 Ellipsometry, as shown in Figure 2, indicates that the molecular density and thickness is constant for deposition speeds near but below Ucrit in agreement with the results of Eskilsson and Yaminsky.38 The relatively dense packing of the molecules suggests a welldefined chain direction with just a few gauche conformers.32 Since the all-trans length for CTAB is 27 Å, these parameters indicate that a densely packed, tilted monolayer of surfactant is deposited along the solid-vapor interface. AFM images of deposited films show defects in the complete monolayer near the initial contact line position. The depth of these defects for 0.8 cmc as measured with AFM (16 ( 2 Å) is consistent with the tilted monolayer thickness determined using XRR. 3.1.1. Flow Field and Deposition Mechanism. In a pure nonvolatile fluid receding from a solid, the fluid velocity along the liquid-vapor interface points away from the contact line.18,25,39,40 Evaporation in solvents with volatility similar to the surfactant solutions used here show no significant modification of the flow near moving contact lines.21 In contrast, by tracking the motion of particles along the liquid-vapor interface (surface particle image velocimetry),25 we examined that the direction of the fluid flow on the liquid-vapor interface of the CTAB solutions is toward the contact line on the SiO2 substrate. Further, detailed measurements of the shape of the liquid-vapor interface near the contact line show that the viscous bending near the contact line is small and follows the form seen for pure fluids. Since the no-slip boundary condition at the solid-liquid interface controls the fluid movement outside some microscopic inner re(36) Martin, M. C.; McKinney, W. R. Proc. Mater. Res. Soc. 1998, 524, 11. (37) Holman, H. Y. N.; Martin, M. C.; McKinney, W. R. Spectrosc.-Int. J. 2003, 17, 139–159. (38) Eskilsson, K.; Yaminsky, V. V. Langmuir 1998, 14, 2444–2450. (39) Cox, R. G. J. Fluid Mech. 1986, 168, 195–220. (40) Cox, R. G. J. Fluid Mech. 1986, 168, 169–194.

Figure 3. Schematic flow fields for three pulling speed regimes: dry recede with U < Ucrit (left); film entrainment with U > Ucrit (center); and coffee stain deposition with U ) 0 (right).

gion,19,20,39,40 and evaporation has little impact, conservation of solvent mass requires a dividing streamline emanating into the fluid from the contact line (Figure 3). This rolling flow coupled with a negligible effect from evaporation prevents any significant increase in surfactant concentration from occurring near the moving contact line. We may therefore assume that bulk solution and interface properties are maintained until very near the contact line. Measurements of the surface excess concentrations approaching the contact line indicate that the monolayer deposition on the emerging surface does not result from the layer at the liquid-vapor interface laying down on the preexisting solid-liquid structure as is typical for many LB depositions. At 0.8 cmc, the SiO2 surface carries surfactant toward the contact line at 50.4 ( 4.2 Å2/molecule arranged in a complex spherical admicellar structure,27 while the liquid-vapor interface carries 37.8 ( 4.7 Å2/ molecule toward the contact line at approximately the substrate withdrawal speed (as determined by surface particle image velocimetry). Thus, surfactant approaching the contact line must re-self-assemble in the vicinity of the contact line to form the densely packed, tilted monolayer (23 Å2/molecule) observed at the solid-vapor interface. In addition, excess surfactant is rejected by the solid-vapor interface and must be returned to the bulk through the dividing streamline of solvent near the contact line. Even if no other dynamic effect occurs, the surfactant rearrangement will begin when the solid-liquid and liquid-vapor interfaces are close enough to interact. Previous studies report

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Figure 5. Typical AFM image showing dewetted regions devoid of islands. The scale bar indicates 10 µm.

Figure 4. AFM image (top) and cross sectional height along the solid black line (bottom) of typical island structure. The scale bar indicates 10 µm.

the presence of a proximal desorption process41–43 once the solid-liquid and liquid-vapor interfaces reach a separation of three times the solution Debye length (∼30 nm for this system). Using a typical microscopic contact angle of 3° (measured in our images of the liquid/vapor interface) and 1 µm/s < U < 100 µm/s, the rearrangement process occurs within 0.006 and 0.6 s. This short time suggests surfactant rearrangement near the moving contact line must be a complex, driven process. Similar experiments with an OTS-coated surface produce surfactant deposition on the emerging surface below the detectability limit of our ellipsometer which is Ucrit. When the substrate is withdrawn sufficiently rapidly, a film is entrained on the surface. Figure 2 shows that as one crosses Ucrit, the amount of surfactant deposited on the solid-liquid interface jumps. In contrast to U < Ucrit, the amount deposited increases with U, and the smooth monolayer deposited below Ucrit is replaced by a heterogeneous structure on the micrometer scale along the solid-vapor interface, as shown in the typical AFM results in Figure 4. Clearly, two different deposition mechanisms operate above and below Ucrit. (41) Subramanian, V.; Ducker, W. J. Phys. Chem. B 2001, 105, 1389–1402. (42) Lokar, W. J.; Ducker, W. A. Langmuir 2002, 18, 3167–3175. (43) Atkin, R.; Craig, V. S. J.; Wanless, E. J.; Biggs, S. J. Phys. Chem. B 2003, 107, 2978–2985.

AFM images show islands of surfactant with lateral dimensions on the order of tens of micrometers and very monodisperse heights. This general structure is independent of pulling speed (for U > Ucrit), surfactant-substrate interaction (as shown by the fact that it exists for both CTAB and SDS on the anionic SiO2 surface), and film residence time. The island shapes are reminiscent of the islands that grow at the solid-liquid interface in bulk solution but over time scales >10× longer than our samples.5 On SiO2, island heights (the step height between the top of the island and the region between islands) are dominantly 60 ( 5 Å, independent of U and residence time. Typical height variations within a single sample are smaller than this uncertainty, usually varying by no more than 3-4 Å. Variation from sample to sample, however, approaches 10 Å. While 60 Å is the dominant height observed, higher islands, quantized in roughly 30 Å increments, are also often observed, up to a maximum of 270 Å. The higher the island, the less frequently it is observed, i.e., 90 Å is more common than 120 Å, which is more common than 150 Å, etc. Additionally, higher islands occur more frequently for moderate residence times (∼100-300 s) than for low (∼30 s) or high (∼300-900 s) residence times. Thirty angstrom islands are never observed. The percent of the substrate covered by islands increases with U from 27% ( 4% at 200 µm/s to 61% ( 8% at 1000 µm/s for the SiO2 substrate, independent of residence time. Higher islands (g90 Å) occupy 50% of the total island coverage at moderate residence times. AFM bearing analysis suggests that the total amount of surfactant deposited remains constant independent of residence time, as the samples which consist of a relatively large percentage of higher islands consistently show a proportional drop in the percentage of substrate covered by islands. At very high residence times (>700 s) on SiO2, areas with no islands appear as shown in Figure 5. These regions typically extend to tens of micrometers in diameter, but ranged from a few micrometers to hundreds of micrometers in diameter on a few samples. Island height and global coverage properties are unaffected by the presence of these regions, i.e., lateral island density between the open regions increases to account for the

Influence of Fluid Flow on the Deposition of Soluble Surfactants

Figure 6. Normalized X-ray reflectivity (top) and diffraction (bottom) of 0.8 cmc CTAB deposited at 200 µm/s (above Ucrit). Solid black arrows in the top panel indicate minima spacing consistent with a 16 Å layer, while dashed gray arrows indicate Kiessig fringes consistent with a full film thickness of 105-108 Å.

lack of islands within these regions such that the overall coverage is consistent with other samples at similar pulling speeds. The presence of these regions appears to be unaffected by pulling speed. Figure 6 shows the X-ray specular reflectivity and diffraction from a typical sample. The low-angle data are very complex due to the lateral heterogeneity of the surface layer, but some important structural details of the system can be obtained. XRR patterns exhibit clear minima, “Kiessig fringes,” that correspond to the destructive interference of the reflections from the top and bottom of the sample on the substrate. We can estimate the total thickness of the film around 105-108 Å (different samples) from 2π/∆qz, where ∆qz is the spacing between the minima. Patterson analysis shows a large primary maximum, and its position indicates an overall thickness of the film of ∼110 Å. There is also a pronounced secondary peak, indicating the presence of a 16 Å layer. Since the substrate surface is flat and the CTAB surface is relatively rough, this 16 Å layer is most likely located at the substrate.44 Combining these results with the AFM images, we infer that the 16 Å layer corresponds to a continuous layer covering the substrate where islands are not deposited, while the 108 Å layer corresponds (44) Yu, C. J.; Richter, A. G.; Kmetko, J.; Dugan, S. W.; Datta, A.; Dutta, P. Phys. ReV. E 2001, 6302, 021205.

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to the regions with crystalline islands on the substrate. The higher angle data show Bragg peaks corresponding to a lattice constant of 52 Å, equal to the c axis of the unit cell of crystalline CTAB.45 The presence of peaks indexed with odd values of the Miller index corresponding to the direction normal to the substrate show that the islands contain crystallites with half-integer unit cells in the c axis, as well as full unit cells. Rocking curves of the 0,0,10 peak show the crystallite c axis is within (0.3° of the normal to the substrate. Due to the complexity of the reflection data and the convolution of the scattering with the in-plane correlation of the exiting X-ray beam, it is difficult to obtain an average molecular area for either layer but we can roughly estimate that the 16 Å thick layer has ∼30 Å2/molecule (for details of data analysis methods, see Evmenenko et al.35). No in-plane diffraction peaks could be unambiguously measured on the sample (data are not shown). We use the frequency of the antisymmetric methylene stretching region (2918-2924 cm-1) to measure trans-gauche isomerization in the molecular chains on the sample.46,47 Our IR microscopy shows areas on the sample comparable to the lateral dimensions of the islands (∼10 µm) where two distinct peaks are seen, indicating that regions with some chain disorder (with the antisymmetric stretching modes at 2923 cm-1) coexist with regions of little or no chain disorder (with the antisymmetric stretching modes at 2917 cm-1). Other regions show single peaks with stretches at frequencies between these extremes. At present, we do not have the capability to correlate these areas with features on the samples. Our AFM, XRR, and IR data give us a clear picture of the layer of surfactant deposited about Ucrit. The continuous base layer of surfactant is remarkably similar to the layer deposited below Ucrit. It is 16 Å thick and is composed of tilted CTAB molecules with some chain disorder and a molecular area of ∼30 Å2. Beside this base layer are islands of crystalline CTAB (monoclinic with a ) 5.66 Å, b ) 7.26 Å, c ) 51.9 Å and β ) 94.0°).48 In the case of the samples analyzed by X-rays, these crystallites were 2 unit cells high along the c axis (four interdigitated layers). In more extensive AFM surveys of all our samples, we have observed islands three or greater layers high. We have never observed islands one or two layers high. Note that due to the interdigitated structure of the CTAB unit cell, no energetic preference exists for exposing even versus odd numbers of half-unit cells at the outside of the structures deposited at the solid-vapor interface. The c axes of the crystallites are very well aligned with the normal to the substrate. 3.2.1. Flow Field and Deposition Mechanism. For a surface withdrawn from a volatile solvent above Ucrit, viscous forces drive fluid into the film while evaporation removes solvent, thinning the film as one moves upward.21 A stagnation point exists along the liquid-vapor interface for a pure fluid at the meniscus level, near the entrance to the film.49 For films as thin as those treated here, gravitational drainage is negligible and the flow within the film is unidirectional and almost pluglike for a pure fluid with evaporation rates similar to those of the CTAB solutions discussed here.21 Using surface particle image velocimetry, we see no evidence of a stagnation point for CTAB solutions; the velocity along the liquid-vapor interface is always up into the film. Theory also suggests that (45) Iwamoto, K.; Ohnuki, Y.; Sawada, K.; Seno, M. Mol. Cryst. Liq. Cryst. 1981, 73, 95–103. (46) Porter, M. D.; Bright, T. B.; Allara, D. L.; Chidsey, C. E. D. J. Am. Chem. Soc. 1987, 109, 3559–3568. (47) Mendelsohn, R.; Moore, D. J. Chem. Phys. Lipids 1998, 96, 141–157. (48) Campanelli, A. R.; Scaramuzza, L. Acta Crystallogr. C 1986, 42, 1380– 1383. (49) Landau, L.; Levich, B. Acta Physicochim. URSS 1942, 17, 42–54.

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for surfactant solutions, the stagnation point can be pushed into the bulk fluid (see Figure 3).50,51 Surfactant is therefore fed into the film along the solid-liquid and liquid-vapor interfaces. An elementary mass balance calculation shows a significant amount of surfactant must also be fed into the film via a bulk channel, consistent with the stagnation point having moved off the liquid-vapor interface. Once in the film, the surfactant is trapped, and as it moves higher in the film, solvent evaporates, increasing the concentration of the nonvolatile surfactant. Eventually the solvent fully evaporates, leaving the surfactant to deposit along the solid-vapor interface. Depending on U and evaporation rate, interference microscopy of the drying film indicates that the film is roughly a wedge with a base leaving the meniscus on the order of 1-10 µm thick, a wedge angle of e1°, and a length 1-50 mm. For a 0.8 cmc solution, the fluid in the film crosses the cmc about one-third of the way up the film. Since the surfactant concentration in the film is increasing and the Krafft point (the point on the phase diagram where the solubility curve crosses the cmc) of CTAB is slightly below the experimental temperature, the Krafft boundary is crossed at a higher temperature and concentration than the Krafft point at some position in the film, and crystals begin to nucleate.52 Typically in our experiments, T ≈ 25 °C. At this temperature, the phase boundary is ∼10-100 cmc.53 Thus, the appearance of crystals indicates we have reached this concentration at some position in the film. This concentration is reached far enough from the tip of the film such that the film at this point can still easily be viewed as two noninteracting interfaces separated by bulk solution. It is unclear whether nucleation occurs preferentially in the film or along the solid interface, although micellar aggregates in the fluid and admicellar aggregates along the solid-liquid interface would serve as ideal heterogeneous nucleation sites. As surfactant is continuously confined moving toward the film tip, structural forces between surface and bulk aggregates, as well as freshly nucleated crystalline CTAB, must be driving the rearrangement of surfactant and the alignment of the island structures observed after complete evaporation. Previous studies examining structural forces between interfaces bounding micellar solutions54,55 suggest this interaction becomes important when the two interfaces are ∼100 nm apart, but the presence of crystallites in solution could also have a significant influence. Dewetted regions observed for high residence times result when the evaporating film remains thin for a long enough period of time that thermal fluctuations nucleate holes in the film sooner than evaporation alone would fully remove solvent. The moving contact line of the dewetting front sweeps the islands away, leaving only the base surfactant monolayer, perhaps in a manner similar to the action of the moving contact line below Ucrit. Changing the surfactant-substrate interaction can impact the deposited structure for U > Ucrit. Using 0.8 cmc SDS instead of CTAB does not appreciably change the deposited structure. Crystalline islands still form and cover a comparable amount of the substrate despite the fact that an electrostatic repulsion prevents any surfactant from entering the film along the solid-liquid interface. However, an OTS-coated substrate pulled from a 0.8 cmc CTAB solution forms islands with typical step heights of 120 Å and comparably less surface coverage. Here, the substrate (50) Stebe, K. J.; Barthe`s-Biesel, D. J. Fluid Mech. 1995, 286, 25–48. (51) Rame, E. Phys. Fluids 2007, 19, 078102. (52) Laughlin, R. G. The Aqueous Phase BehaVior of Surfactants; Academic Press, Inc.: San Diego, 1994. (53) Vautier-Giongo, C.; Bales, B. L. J. Phys. Chem. B 2003, 107, 5398–5403. (54) Nikolov, A. D.; Wasan, D. T. J. Colloid Interface Sci. 1989, 133, 1–12. (55) Nikolov, A. D.; Kralchevsky, P. A.; Ivanov, I. B.; Wasan, D. T. J. Colloid Interface Sci. 1989, 133, 13–22.

Beppler et al.

Figure 7. AFM image (top) and cross-sectional height along the solid black line (bottom) of typical CTAB coffee ring on SiO2. The scale bar indicates 10 µm.

surface chemistry has changed the island growth mechanism into preferentially growing upward rather than outward. Therefore, the ability of an evaporating thin film to nucleate crystalline islands is common to these systems with diverse surfactant-surface interactions, while the details of their growth can be controlled via pulling speed, residence time, and surfactant-substrate interaction. 3.3. Deposition at a Pinned Contact Line: the “Coffee Stain”. To further emphasize that deposited structure is fundamentally controlled by a flow field, we contrast the above two cases with the classic coffee stain deposition process.14–16 In this process, evaporation of a solvent near a pinned contact line (i.e., U ) 0) preferentially deposits surfactant along the contact line. For 0.8 cmc CTAB on SiO2, we have produced a deposited ring that is ∼1 mm wide and consists of rough, unoriented crystalline CTAB ∼200 nm high. A typical deposit is shown in Figure 7. The larger evaporative flux near the pinned contact line drives a flow field and therefore a net surfactant flux toward the contact line (see Figure 3). The contact line remains pinned for a finite amount of time due to some combination of contact angle hysteresis and pinning on the growing deposit. The elastic energy in the deforming liquid-vapor interface grows until the receding contact angle is reached or the pinning energy is overcome. The contact line then depins and recedes to a new location. This slip-stick motion can repeat several times, leaving lines of surfactant deposited at each pinning point. This flow field supports a concentration gradient which preferentially deposits surfactant at the pinned contact line. The concentration crosses the Krafft

Influence of Fluid Flow on the Deposition of Soluble Surfactants

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transition somewhere within the complex flow field, and unoriented, polydisperse crystals are deposited.

point which is inside the fluid meniscus, unlike in the case of a pure fluid. The increasing surfactant concentration drives the nucleation which, unlike the other cases, is not impacted greatly by the rather benign flow field in the film. The size and shape of the crystalline islands can be controlled by varying the deposition conditions. These two controlled depositions contrast to the disordered deposition formed at a pinned contact line. Preferential evaporation near the contact line demands a flow toward and increased surfactant concentration near the pinned contact line. Surfactant forms unorganized crystals at the pinned contact line. This contrast in structural order of the deposit suggests that dip-coating with control of dipping speed and evaporation rate may provide better control of deposition through contact lines of evaporating solvents.

4. Summary We have seen that flow fields near the contact line have a strong influence on the morphology of soluble surfactant deposited from a volatile solvent. When a high-energy substrate is withdrawn slowly from a bulk fluid bath (U < Ucrit), the substrate emerges dry. A densely packed, tilted monolayer of surfactant with some gauche isomerization is deposited along the solid-vapor interface. Surfactant is supplied to the contact line along both the solid-liquid and liquid-vapor interfaces and excess surfactant is rejected back into the bulk solution by the rolling fluid motion near the contact line. The surfactant causes a dividing streamline to emanate from the contact line in contrast to the pure fluid case. Surfactant molecules undergo large, forced rearrangement as they pass through the contact line, yet the energetics of the system trying to form a low energy surface causes a well-ordered monolayer to emerge. At faster speeds (U > Ucrit), the substrate emerges with an evaporating thin film which confines surfactant into a constantly increasing concentration environment. Crystalline islands, with monodisperse heights, nucleate and grow with a tilted surfactant monolayer in between. Surfactant moves into the film along both interfaces, as well as from the bulk fluid, moving past a stagnation

Acknowledgment. The authors thank Enrique Rame, James Schneider, and Robert Tilton for helpful discussions in preparation of this work and Dimitar Draganov for making the X-ray measurements below Ucrit. G.E. was supported by the U.S. NSF Grant No. DMR-0705137. XRR measurements were performed at Beam Line X23B of the National Synchrotron Light Source, supported by the U.S. DOE. B.B., K.V., and S.G. also acknowledge the support of NASA Grants No. NAG3-2449 and NNC04GA34G. LA8004882