Influence of Surfactant Concentration and Background Salt on Forced

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Influence of Surfactant Concentration and Background Salt on Forced Dynamic Wetting and Dewetting Daniela Fell,†,‡ G€unter Auernhammer,*,† Elmar Bonaccurso,‡ Chuanjun Liu,†,§ Rudi Sokuler,†,‡ and Hans-J€urgen Butt† † ‡

Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany Center for Smart Interfaces, Technical University of Darmstadt, Petersenstrasse 32, 64287 Darmstadt, Germany ABSTRACT: Forced wetting and dewetting of polymer surfaces in aqueous solutions containing cationic surfactant cetyltrimethylammonium bromide (CTAB) has been studied with a rotating cylinder half immersed in the solution. The receding contact angle decreases with faster withdrawing speeds. This decrease is enhanced when adding CTAB. The addition of salt to the CTAB solution further enhances the effect but does not have a significant effect alone. We interpret this change in the dynamic contact angle with a surfactant-induced Marangoni effect.

1. INTRODUCTION The wetting of a solid surface by a liquid is a basic element of many natural phenomena and technical applications. Examples include the spreading of liquid drops in coatings on metals, glass, plastics, or paper and the effective distribution of pesticides on leaf surfaces. The wetting of single-component liquids has been studied extensively. (See reviews in refs 1 and 2.) The wetting of surfactant solutions is more complex and much less understood. It is more complex because the adsorption and orientation of a surfactant at or with respect to an interface depend on time. Close to a moving three-phase contact line (TPCL), gradients in surface tension are created that influence the wetting process. Added surfactants, in particular, when added to aqueous solutions, can drastically affect wetting and spreading. Therefore, surfactants are used to control the extent or the speed of wetting. Surfactants reduce the liquid-solid contact angle and allow an aqueous solution to spread on nonpolar surfaces.1-5 Most studies on the wetting of surfactant solutions are concerned with spontaneous spreading6-12 (i.e., that driven only by differences in surface tension, not by external forces). Forced wetting and dewetting of surfactant solutions is less understood, although it is important in technical applications such as printing, coating, and oil recovery. Most of the studies concentrate on the thickness of the coating films (ref 13 and references therein). Chaudhuri and Paria14 used a Wilhelmy plate made of Teflon and measured dynamic contact angles in aqueous solutions of Triton X-100, sodium dodecylbenzene sulfonate, and CTAB. At wetting velocities of 0.2 and 1 mm/s, they observed a decrease in the hysteresis between the advancing and receding contact angle when adding surfactant even at concentrations lower than one tenth of the critical micelle concentration (cmc). The addition of salt enhanced the effect of the surfactant on the contact angle. Here, we analyze the forced wetting and dewetting of two nonpolar surfaces in aqueous surfactant solutions using a rotating r 2011 American Chemical Society

cylinder. With a rotating cylinder,15-19 higher wetting velocities can be achieved than with the Wilhelmy plate technique. The horizontal cylinder is half immersed in the solution. On the side where the surface of the cylinder leaves the liquid bath, the liquid is forced to dewet its surface. On the opposite side, it enters the liquid and the wetting of the surface is enforced.

2. EXPERIMENTAL SECTION The cylinders were made of polished stainless steel. The surface was slightly convex in order to allow better imaging of low contact angles from the axial direction (Figure 1). The diameter of the cylinders was 12.5 cm, and the width was either 4 or 6 cm. The bath is about 10 cm in width, 17 cm in depth, and 15 cm in height. Two nonpolar coatings were used: A polymer-based sealant usually used to protect metal parts on cars (NanoTec Felgenversiegelung, NIGRIN, containing nanoparticles) and polystyrene. The sealant was applied evenly to the cylinder. After drying, it was polished with a soft lint-free cloth. To coat a cylinder with polystyrene, the cylinder rotated at a speed of 8 cm/s in a 0.4 wt % solution of polystyrene (Mw = 300 kg/mol) in tetrahydrofuran. Because of the evaporation of the solvent, a polystyrene film remained on the cylinder. The film was dried in air for 2 h before being immersed in water. The horizontally oriented cylinder rotated in the liquid bath, being immersed to half its height. The contact angle and the meniscus height were imaged with a camera (Photron, Fastcam SA-1, 12
magnification, working distance of about 30 cm) in side view at 1000 frames/s. To record the shape of the TPCL, the same camera was mounted in front of the setup at 2
magnification operated at 250 frames/s. The liquids tested were Milli-Q water, solutions of cationic surfactant CTAB (CH3(CH2)15Nþ(CH3)3Br-, cmc = 0.9 mM in water), and aqueous salt solutions. All experiments were carried out with a closed cell so that the atmosphere was saturated with water vapor. Received: November 24, 2010 Revised: January 31, 2011 Published: February 14, 2011 2112

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Figure 1. Schematic of the experimental setup.

Figure 3. Contact angle vs the rotation speed for different CTAB concentrations on the polymer sealant (A) and on polystyrene (B). The CTAB concentration is given by the cmc (cmc = 0.9 mM). Negative velocities indicate the speed with which the cylinder enters the liquid (advancing contact angle). Positive velocities refer to the cylinder surface being rotated out of the liquid (receding contact angle). The parameters for the fit (continuous line) with eq 1 were K0 = 3
105 Hz, λ = 0.65 nm, γ = 0.072 N/m, and Θ0 = 78
for the polymer sealant and K0 = 1.5
105 Hz, λ = 0.7 nm, γ = 0.072 N/m, and Θ0 = 77
for polystyrene. The insets show the respective low-speed regimes in more detail. Figure 2. Images taken from the three-phase contact line looking horizontally normal to the cylinder surface. Images were recorded at velocities of 2, 4, 6, and 8 cm/s in pure water on a polystyrene-coated cylinder. The arrow indicates the position of the three-phase contact line at low speed. The scale bar corresponds to 3 mm. To determine if there is some CTAB residue after the cylinder and the bath were cleaned, they were rinsed several times with Milli-Q water. The measurement after intense rinsing resulted in results that were similar to those for pure water at the beginning of the measurement cycle.

3. RESULTS AND DISCUSSION Influence of Speed on Contact Angles. Pure water had a static contact angle of 78
on the polymer sealant and 77
on polystyrene. When the cylinder surface was moved out of the liquid (positive speed, dewetting) at low speed (v < 2 cm/s), a straight horizontal TPCL was observed (Figure 2A). Dewetting was complete and the solid was dry above the TPCL. The receding contact angle was uniquely defined. At intermediate velocities of typically 4 cm/s, at some positions a liquid film was temporarily drawn upward for 1 to 2 mm (Figure 2B). Four centimeters per second corresponds to a capillary number of Ca = ηv/γ ≈ 6
10-4. Here, η is the viscosity of the liquid, v is the

speed of the surface of the rotating cylinder, and γ is the surface tension of the liquid. Further increasing the speed led to the formation of a triangular liquid film spanning the whole width of the cylinder (Figure 2C).20 This change in the shape of the TPCL interfered with the measurement of the contact angle, and measurements had to be stopped at this point. At very high speed (v > 8 cm/s), a trail of drops formed at the upper corner of the triangle and remained on the surface of the cylinder (Figure 2D). Such “pearling drops” were also observed by Podgorski et al.21 for drops sliding down a tilted plane. At even higher speeds, we observe the transition from a defined TPCL to the entrainment of a liquid film, known as the Landau-LevichDerjaguin (LLD) transition.22-25 The receding contact angle observed when moving the solid surface out of the liquid decreased with increasing speed (Figure 3). When reversing the rotation direction, the advancing contact angle is observed. It increased with increasing speed. The change was strong for speeds up to ∼1 cm/s, and then it leveled off. Advancing contact angles could be observed only up to roughly the same speed as receding contact angles. Otherwise, the liquid film being transported around half the cylinder arrived at the plunging side of the cylinder and changed the results. Influence of Surfactant on the Dynamic Contact Angles. When CTAB was added, the static and dynamic contact angles 2113

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Figure 5. Schematic microscopic picture of the region around the threephase contact line. The thin, straight arrows indicate the movement of the cylinder surface and the flow of the liquid.

Figure 4. Advancing and receding contact angle vs CTAB concentration at different velocities measured on the polymer sealant (left) and on a polystyrene coating (right).

decreased (Figure 3). The effect is more dramatic at a positive speed (receding contact angle). In other words, at a CTAB concentration approaching the cmc, only slow rotation velocities of the cylinder are required to pull the liquid up and form a film that is stable enough to survive half a rotation. The effect increases with increasing CTAB concentration. For concentrations above 0.7 cmc, the liquid was pulled upward even at a speed as low as 0.1 cm/s. The changing shape of the receding TPCL observed for water at speeds between 2 and 8 cm/s (Figure 2) could also be observed in the presence of CTAB. The critical velocities were, however, slower than in pure water. For a concentration of about 0.2 cmc, the triangular structures start to form at velocities of ∼|0.5| cm/s. At negative speed, the advancing contact angle decreased with increasing CTAB concentration. The effect was, however, much less pronounced than for the receding contact angles (Figure 4). We observed a slightly different and more drastic effect than described by Chaudhuri and Paria.14 On a Teflon surface, they observed an increase in the receding contact angle when adding 0.01 mM CTAB from 46 to 67
. Then the receding contact angle remained relatively constant ((3
) up to 1.5 mM. At a speed of 0.1 cm/s (the maximal speed in ref 14), we observed a continuous decrease in the receding contact angle from 63 to 30
at 0.5 mM. The advancing contact angle decreased from 115 to 95
at 0.03 mM. For higher concentrations, the contact angle remained between 84 and 100
. When comparing our findings to the formation of LLD films on fibers that are pulled out of a surfactant solution,13 we find a stronger effect. Similar to the work by the Quere group, the effect is pronounced at concentrations well below the cmc. Whereas the film thickness changes only by about a factor of 2 with the surfactant concentration, we observe that the receding speed for a specific contact angle decreases by up to 1 order of magnitude with increasing surfactant solution. The presence of surfactant at the onset of the LLD transition is much stronger than for the thickness of the LLD film. Comparison with Theory. Advancing and receding contact angles could be fitted with the molecular-kinetic theory of Blake and Haynes.26 The molecular-kinetic theory focuses on the dissipation occurring in the immediate vicinity of the moving

contact line because of the process of attachment/detachment of liquid molecules to/from the solid surface. The movement depends on the net frequencies of forward and backward molecular displacements within the TPCL zone. With the displacement frequency K0 and the mean distance between the interaction sites λ, the dynamic contact angle and the speed are related by " # γλ2 ðcos Θ0 - cos Θd Þ v ¼ 2K0 λ 3 sinh ð1Þ 2kB T Here, kB is Boltzmann’s constant and T is the temperature. Contact angles recorded on the polymer sealant could best be fitted with mean values of K0 = 3
105 Hz, λ = 0.63 nm, and Θ0 = 78
using γ = 0.072 N/m; the fitting parameters were K0, λ, and Θ0. On polystyrene, the corresponding mean values were K0 = 1.5
105 Hz, λ = 0.71 nm, and Θ0 = 77
. When fitting only the advancing contact angles, we obtained K0 = 8
105 Hz, λ = 0.7 nm, and Θ0 = 90
for the sealant and K0 = 106 Hz, λ = 0.82 nm, and Θ0 = 97
for polystyrene. Receding contact angles could be best fitted with K0 = 2.3
106 Hz, λ = 0.6 nm, and Θ0 = 65
(sealant) and K0 = 1.2
106 Hz, λ = 0.66 nm, and Θ0 = 66
(polystyrene). These values agree with the results in the literature for water on polymer surfaces.26-28 Whether the successful fit reflects the real microscopic process of the binding and unbinding of water molecules or if it has to be taken only as phenomenological agreement cannot be decided on the basis of our results. We also mention that advancing contact angles measured with pure water or salt solutions could not be fitted with the hydrodynamic theory of Voinov29 or Cox.30 Such a conclusion was also reached earlier.31 Thus, the hydrodynamic drag is not the limiting factor in the wetting or dewetting of polymer surfaces. Interpretation of Dynamic Contact Angles Measured with Surfactant. When adding surfactant, the receding contact angles decreased much more steeply with speed than without surfactant. The effect scales with the “relative concentration”, defined here as the actual concentration divided by the cmc. At least three effects might contribute to the decreasing contact angle (Figure 5). Marangoni Effect. When the liquid recedes, water has to flow out of the region close to the TPCL. The flow of water depends on the hydrodynamic boundary conditions. At the solid-liquid interface, we can assume a no-slip boundary condition. In contrast, a pure water-air interface is mobile and cannot withstand shear stress tangential to the air-water interface. In the presence of surfactants, the situation changes because gradients in the surface excess of surfactants can cause an effective no-slip 2114

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Langmuir boundary condition. Such a Marangoni effect32 also delays the rise of bubbles in surfactant solutions,33-36 stabilizes foam films, or enhances the repulsive hydrodynamic force between fluid interfaces.37-39 In our case, the Marangoni effect would delay the outflow of liquid and cause the dynamic contact angle to decrease. A gradient is created because on the receding side of the TPCL the dissolved surfactant has not had time to equilibrate with the bulk. On the receding side, a new air-water interface is continuously created by the rotating cylinder. Establishing equilibrium between the surfactant in the bulk and in the interface takes time and is limited by the diffusion of surfactant toward the interface. The situation is even more complex because the diffusion constant depends on the amount of surfactant bound in micelles and that dissolved as individual molecules.40 Surfactant micelles diffuse slowly, but single molecules diffuse quickly. Thus, equilibrium between the bulk and interface may be established faster at low concentration, where most of the surfactant is not aggregated to micelles. The higher the concentration, the more surfactant molecules are inside the micelles (i.e., the slower the mean diffusion coefficient). Surfactants may also change the hydrodynamic boundary condition at the solid-liquid interface. An influence on the experiments of forced wetting is, however, not likely. All experiments indicate that if there is any influence, surfactants should increase rather than decrease slip.41,42 Disjoining Pressure. At the TPCL, the solid-liquid and the air-liquid interfaces merge. In close proximity, where the distance between the solid-liquid and the liquid-vapor interface is still below ∼100 nm, the surface force acts between the two interfaces. Merging would be delayed if a long-range repulsive surface force acts between the interfaces. For example, the positively charged headgroups of the surfactants adsorbed at both interfaces lead to electrostatic double-layer repulsion. This long-range repulsion would keep the interfaces apart and delay dewetting on the receding side. Evaporation/Condensation. Wayner et al. pointed out that the movement of the TPCL can be influenced by condensation from ambient vapor or the evaporation of liquid into the vapor phase. Shanahan quantified the effect of condensation due to the curvature of the liquid at the TPCL and surface forces on spreading for low wetting speeds.43 In our case, evaporation and condensation can greatly influence the wetting/dewetting process. A quantitative evaluation is, however, difficult because the wetting/dewetting speeds are relatively high and evaporation/condensation might be influenced by changes in the local surfactant or salt concentration. An increased/decreased concentration of salt or surfactants would also change the local vapor pressure of water. In addition, surfactants can change the rate of transfer of a solvent from the liquid to the vapor phase. Typically, this change is low, if detectable at all.44 Effect of Salt. To estimate the contribution of these effects, we added additional background salt. Added salt should reduce the repulsive electrostatic double-layer force, and the effect of a disjoining pressure should decrease. At the same time, salt decreases the cmc of CTAB.45 Thus, with increasing salt concentration the effect of surface elasticity should increase because the mean diffusion constant increases. Experiments showed that salt enhances the effect of surfactant and leads to an even stronger decrease of the contact angle with speed. As one example, the effect of added NaCl to 0.027 mM

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Figure 6. Contact angle vs speed of the rotating cylinder for CTAB solutions (0.027 mM) with different concentrations of added NaCl. The cylinder was coated with a layer of polystyrene.

CTAB on polystyrene is plotted in Figure 6. In 0.027 mM CTAB, the critical speed for the LLD transition is 4 cm/s. When adding 5, 25, or 50 mM NaCl, the transition speed is decreased to 2, 1, and 0.3 cm/s. Without CTAB, the addition of salt led to no significant change in the dynamic contact angle. These results indicate that the electrostatic double layer repulsion is not the reason for the enhanced decrease in the dynamic receding contact angle. The effect of salt is more likely that of reducing the cmc and increasing the size of the micelles (refs 46-48 and references therein). This would enhance the effect of surfactant at lower concentrations. In addition, the presence of salt facilitates the adsorption of surfactant to hydrophobic surfaces,49 which would also lead to a decreasing contact angle. Estimation of Critical Speed. A calculation of the gradient of surface tension at the liquid-vapor interface is difficult because different processes occur on comparable length and time scales. One would need to take the diffusion of individual surfactant molecules and micelles, hydrodynamic flow, and the kinetics of adsorption into account. To at least estimate the length scale, we apply a simple diffusion model, neglecting hydrodynamic flow effects. On the receding part, where the liquid dewets the solid surface, a fresh liquid surface is created. For simplicity, we assume that initially a liquid wedge with a low contact angle Θ is created at the TPCL (Figure 7, schematic). The coordinate parallel to the solid surface starting at the TPLC is x. The surfactant at concentration c0 is initially homogeneously distributed in the liquid. At the TPCL, a fresh liquid surface is continuously created that is supposed to be free of surfactant. Then the surfactant diffuses to the surface until equilibrium is established between the interface and the bulk phase. We consider a slice at a certain x where the film has a thickness of h = x tan Θ. In the first step, we allow only diffusion in the vertical direction. Diffusion in one direction over a distance h takes a characteristic time of τh = h2/(2D), where D is the diffusion coefficient. Because h = x tan Θ, the diffusion time between the TPCL and the slice under consideration is always a factor of 1/tan2 Θ larger. For angles smaller than approximately 20
, there is at least 1 order of magnitude difference between the time scales of the diffusion along and across the liquid wedge. 2115

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this is at 20.3 μm. With a diffusion coefficient of CTAB molecules of40 D = 5.5
10-10 m2/s, the time required for a horizontal CTAB gradient to equilibrate is roughly τx = R2/(2Dtan2 Θ) = 0.38 s. If we divide the horizontal distance R/tan Θ by this relaxation time, then we obtain a critical speed of vc = 2Dtan Θ/R = 0.05 mm/s. For speeds above vc, we expect the Marangoni effect to hinder dewetting. For speeds much below vc, Marangoni effects should be negligible. Considering that hydrodynamic flow will accelerate equilibration, this rough estimate leads to the right order of magnitude of the critical speed.

Figure 7. Surface tension calculated with eq 4 with γ0 = 72 mN/m, h = x tan Θ, Θ = 20
, R = 7.4 μm, and initial concentrations of 0.1, 0.2, and 0.3 cmc. The schematic shows the parameters used.

For this reason, a decoupling of both diffusion processes seems to be justified. To take adsorption into account, a linear adsorption isotherm was assumed: Γ = Rc for c e cmc and Γ = Γ0 for c > cmc. Here, Γ is the surface excess of surfactant at the liquid-vapor interface in mol/m2. Using the Gibb’s adsorption isotherm for CTAB, we can write c dγ ð2Þ Γ¼ 2RT dc Inserting Rc for Γ and integrating, we obtain the film pressure γ0 - γ ¼ 2RcRT ð3Þ Here, γ0 is the surface tension of pure water, γ is the actual surface tension at a given surfactant concentration, R is the gas constant, and T is the temperature. The factor of 2 was added to take the ions into account, which dissociate from CTAB. For high concentrations (c > cmc), γ0 - γ¥= 0.033 N/m. With cmc = 0.9 mM, we obtain R = 7.4 μm. Once equilibrium has been established, in the vertical slice the initial concentration ci (mol/m3) and the new concentration c are related by cih = ch þ Γ for ci e cmc. This leads to ci h hðγ0 - γi Þ and γ0 - γ ¼ ð4Þ c¼ hþR hþR Here, γ0 - γi = 2RciRT. Equation 4 shows the physical significance of R: for a film thickness of h = R, the bulk concentration drops by a factor of 2 because of adsorption. It is also a characteristic thickness of the film that is necessary for the film pressure to increase by half of its maximal value. For thicker films, the film pressure is higher, and for thinner films, the film pressure is less than half the final value. Figure 7 shows the surface tension of an aqueous solution of CTAB with a contact angle of 20
once the CTAB was allowed to diffuse in a vertical direction and establish equilibrium with the surface. For concentrations below the cmc, the shape of the curves is independent of the actual concentration. A gradient in the surface tension in the horizontal direction extends to a distance of several tens of micrometers. In the second step, we estimate how long it would take to equilibrate this horizontal gradient in surface tension. The film has reached a thickness of h = R at x = R/tan Θ. In our example,

4. CONCLUSIONS For hydrophobic surfaces, the receding contact angle of water decreases with increasing retraction speed. This decrease in the contact angle is strongly enhanced by the addition of a cationic surfactant. At a speed of 0.5 cm/s and a surfactant concentration of only 0.2 cmc, a Landau-Levich-Derjaguin film is already formed. The addition of salt further enhances this decrease. We attribute this to a Marangoni effect: At the TPCL, a new liquid surface is created, which still has a high surface tension as compared to the interfaces farther away from the TPCL whose surfactant concentration is already equilibrated with the bulk. The resulting gradient in surface tension slows the drainage of the liquid film. ’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. Fax: þ49-6131-379100. Phone: þ49-6131-379 113. Present Addresses §

Key Laboratory of Biomedical Polymers, College of Chemistry and Molecular Science, Wuhan University, 430072 Wuhan, PR China.

’ ACKNOWLEDGMENT We thank Stefan Geiter for technical support. C.L. acknowledges financial support from the Humboldt Foundation. ’ REFERENCES (1) Starov, V. M.; Velarde, M. G.; Radke, C. J. Wetting and Spreading Dynamics; CRC Press: London, 2007. (2) Bonn, D.; Eggers, J.; Indekeu, J.; Meunier, J.; Rolley, E. Rev. Mod. Phys. 2009, 81, 739. (3) Hill, R. M. Curr. Opin. Colloid Interface Sci. 1998, 3, 247. (4) Nikolov, A. D.; Wasan, D. T.; Chengara, A.; Koczo, K.; Policello, G. A.; Kolossvary, I. Adv. Colloid Interface Sci. 2002, 96, 325. (5) Varanasi, K. S.; Garoff, S. Langmuir 2005, 21, 9932. (6) Hyypia, J. Anal. Chem. 1948, 20, 1039. (7) Marmur, A.; Lelah, M. D. Chem. Eng. Commun. 1981, 13, 133. (8) Troian, S. M.; Wu, X. L.; Safran, S. A. Phys. Rev. Lett. 1989, 62, 1496. (9) Birch, W. R.; Knewtson, M. A.; Garoff, S.; Suter, R. M.; Satiia, S. Colloids Surf., A 1994, 89, 145. (10) Frank, B.; Garoff, S. Colloids Surf., A 1996, 116, 31. (11) Stoebe, T.; Hill, R. M.; Ward, M. D.; Davis, H. T. Langmuir 1997, 13, 7276. (12) Dutschk, V.; Sabbatovskiy, K. G.; Stolz, M.; Grundke, K.; Rudoy, V. M. J. Colloid Interface Sci. 2003, 267, 456. (13) Quere, D. Annu. Rev. Fluid Mech. 1999, 31, 347. (14) Chaudhuri, R. G.; Paria, S. J. Colloid Interface Sci. 2009, 337, 555. 2116

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