Dewetting Behavior of Aqueous Cationic Surfactant Solutions on

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Dewetting Behavior of Aqueous Cationic Surfactant Solutions on Liquid Films Abia B. Afsar-Siddiqui, Paul F. Luckham, and Omar K. Matar* Department of Chemical Engineering & Chemical Technology, Imperial College London, SW7 2AZ, U.K. Received March 10, 2004. In Final Form: June 14, 2004 Previous experimental work has shown that the spreading of a drop of aqueous anionic surfactant solution on a liquid film supported by a negatively charged solid substrate may give rise to a fingering instability (Afsar-Siddiqui, A. B.; Luckham P, F.; Matar, O. K. Langmuir 2003, 19, 703-708). However, upon deposition of a cationic surfactant on a similarly charged support, the surfactant will adsorb onto the solid-liquid interface rendering it hydrophobic. Water is then expelled from the hydrophobic regions, causing film rupture and dewetting. In this paper, experimental results are presented showing how the surfactant concentration and film thickness affect the dewetting behavior of aqueous dodecyltrimethylammonium bromide solutions. At low surfactant concentrations and large film thicknesses, the film ruptures at a point from which dewetting proceeds. At higher concentrations and smaller film thicknesses, the ruptured region is annular in shape and fluid moves away from this region. At still higher concentrations and smaller film thicknesses, the deposited surfactant forms a cap at the point of deposition that neither spreads nor retracts. This variation in dewetting mode is explained by considering the relative Marangoni and bulk diffusion time scales as well as the mode of assembly of the surfactant adsorbed on the solid surface.

1. Introduction The presence of surface tension gradients across a thin liquid film of uniform height induces shear stresses at the air-liquid interface. These stresses distribute the liquid from areas of low surface tension to areas of high surface tension and, in doing so, also deform the interface resulting in height variations. This so-called Marangoni flow can be generated by the presence of nonuniformly distributed surface active material on a liquid film or by temperature gradients along it.1 The disturbances in film height that result from Marangoni stresses may, in some cases, be so severe as to lead to film rupture and subsequent dewetting. This is undesirable in, for example, gravure printing and photofinishing applications where a uniform finish is often required.2 Marangoni drying, however, relies on Marangoni stresses, created by alcohol vapor across the surface of a wet substrate to dewet the area of contact.3,4 This is an effective means of drying integrated circuits and liquid crystal displays. Thus it is important to understand the conditions that give rise to rupture and dewetting. Rupture of a thin film is driven by the presence of van der Waals forces, a component of intermolecular forces that becomes significant for film thicknesses of order 1000 Å5,6 or less. Intermolecular forces can be characterized by an interaction potential of the film, Φ(H), where H denotes the local film thickness. This represents the long-range (van der Waals) and short-range (Born repulsion) inter* To whom correspondence may be addressed. E-mail: o.Matar@ imperial.ac.uk. (1) Edwards, D. A.; Brenner, H.; Wasan, D. T. Interfacial Transport Processes and Rheology; Butterworth-Heinemann: New York, 1991. (2) Schwartz, L. W.; R. R. V.; Eley R. R.; Petrash, S. J. Colloid Interface Sci. 2001, 234, 363. (3) Leenars, A. F. M.; Wuethorst, J. A. M.; van Oekel, J. J. Langmuir 1990, 6, 1701 (4) O’Brien, S. B. G. M. J. Fluid Mech. 1993, 254, 649. (5) Ruckenstein, E.; Jain, R. K. J. Chem Soc., Faraday Trans. 1974, 70, 132. (6) Israelachvili, J. N. Intermolecular and Surface Forces; Academic: London, 1985

actions between the air-liquid and solid-liquid interfaces and is defined as the free energy required in bringing these two interfaces together from infinity to a distance H. If Φ(H) is positive for all values of H, then the film is said to be stable. If the second derivative of Φ(H), Φ′′(H), is negative, then the film is unstable and will spontaneously thin. This mechanism is termed spinodal dewetting, due to its similarity to spinodal decomposition of mixtures, which occurs when the second derivative of the free energy with respect to composition becomes negative.7-10 A film that is unstable for small film thicknesses but stable at larger thicknesses is termed metastable. Spinodally stable films can dewet only through the nucleation of a hole in the film. This may be as a result of heterogeneities on the solid-liquid interface, such as defects11,12 or chemical patterning,13,14 or at the air-liquid interface, such as dust particles15 or surface active agents.16,17 Such disturbances cause local changes in the chemical potential giving rise to flows away from regions of high chemical potential. The resulting thinning of the film may be so severe that long-range intermolecular forces become significant. These further thin the film to a microscopically thin equilibrium thickness that is governed by the long-range attractive forces and the short-range repulsive interactions between the air-liquid and solid-liquid interfaces, thus setting (7) Cahn, J. W.; Hillard, J. E. J. Chem. Phys. 1957, 28, 258. (8) Brochard-Wyart, F.; Daillant, J. Can. J. Phys. 1990, 68, 1084. (9) Mitlin, V. S. J. Colloid Interface Sci. 1993, 156, 491. (10) De Gennes, P. G.; Brochard-Wyart, F.; Quere D. Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves; Springer-Verlag, New York, 2003; Chapters 7 and 10. (11) Jacobs, K.; Herminghaus, S.; Mecke, K. R. Langmuir 1998, 14, 965. (12) Strange, T. D.; Evans, D. E.; Hendrickson, W. A. Langmuir 1997, 13, 4459. (13) Kargupta, K.; Konnur, R.; Sharma, A. Langmuir 2001, 17, 1294. (14) Konnur, R.; Kargupta, K.; Sharma, A. Phys. Rev. Lett. 2000, 84, 931. (15) Kheshgi, H. S.; Scriven, L. Chem. Eng. Sci. 1983, 38, 525. (16) Kheshgi, H. S.; Scriven, L. Chem. Eng. Sci. 1991, 46, 519. (17) Warner, M. R. E.; Craster, R. V.; Matar, O. K. Phys. Fluids 2002, 14, 11.

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Figure 1. A schematic side view of a ruptured film resting on a solid substrate. Downstream of the dewetted region, the fluid forms an elevated rim. lD denotes the width of the elevated rim and RD denotes the radius of the dewetting hole.

up the conditions that give rise to rupture and the formation of a dry patch or hole. This hole precedes the dewetting process and occurs through the transport of material away from the hole. Kheshgi and Scriven16 demonstrated the dewetting of a spinodally stable film by placing a 5 µL drop of methanol on a 0.4 mm glycerine/water film on a horizontal glass plate. Fluid is drawn away from the deposited region by Marangoni stresses and forms an elevated rim further downstream; 4 s later rupture occurs. Rupture creates a dry patch which grows as liquid moves away from it and accumulates into a rim, the width and height of which increase with time as shown schematically in Figure 1. The native film ahead of the rim is motionless as verified by the use of talc particles.18 The width of the rim, lD, is predicted to grow with time as t1/2.19 The radius of the dewetting hole, RD, is predicted to grow linearly with time over long times. However, thin film experiments show that the dewetting exponent can range from 0.7 to 0.9 for the duration of hole growth.20 Dewetting through the retraction of the film edge is termed “autophobing”. In a spreading situation, the contact angle will generally decrease as spreading progresses until a final contact angle is achieved. However, in the case of autophobing, the contact angle first decreases and then increases as the solution first spreads and then retracts. A surfactant solution may autophobe when the surfactant headgroup and surface are mutually attractive. The attraction between the surfactant headgroup and the surface causes the headgroup to adsorb onto the substrate leaving the hydrophobic tails exposed. This lowers the surface energy so that the solution can no longer wet the now hydrophobic surface and thus retracts.21 This was demonstrated by Frank and Garoff 22-24 using the cationic surfactant cetyltrimethylammonium bromide [CTAB]. Drops of 0.1cmc aqueous CTAB solution, at concentrations below 0.45 times the critical micelle concentration (cmc), exhibit autophobing behavior on uncoated horizontal silicon oxide substrates. There is an increase in the contact angle of 5-10° over a period of 30 s with the final contact angle being 25°. Above a concentration of 0.45cmc, drops do not spread or retract but maintain their initial contact angle, as previously observed by Marmur and Lelah25 using a range of cationic surfactants on glass slides. Woodward and Schwartz26 found a systematic dependence of the dewetting mechanism of a surfactant solution on the solution concentration and free energy of the surface. Monolayers of octadecylphosphonic acid (OPA) (18) Redon, C.; Brochard-Wyart, F.; Rondelez, F. Phys. Rev. Lett. 1991, 66, 715. (19) Brochard-Wyart, F.; Martin, P.; Redon, C. Langmuir 1993, 9, 3682. (20) Ghatak, A.; Khanna, R.; Sharma, A. J. Colloid Interface Sci. 1999, 212, 483. (21) Birch, W. R.; Knewtson, M. A.; Garoff, S.; Suter, R. M.; Satija, S. Langmuir 1995, 11, 48. (22) Frank, B.; Garoff, S. Langmuir 1995, 11, 87. (23) Frank, B.; Garoff, S. Langmuir 1995, 11, 4333. (24) Frank, B.; Garoff, S. Colloids Surf., A 1996, 116, 31. (25) Marmur, A.; Lelah, M. D. Chem. Eng. Commun. 1981, 13, 133. (26) Woodward, J. T.; Schwartz, D. K. Langmuir 1997, 13, 6873.

Afsar-Siddiqui et al.

were deposited on a freshly cleaved mica surface at various solution concentrations and for varying immersion times. On removal of the mica disks from solution, three distinct behaviors were noted: the surface emerged wet and remained wet; the surface emerged wet and then ruptured to form a dry patch which continued to grow (dewetting); or the sample emerged dry (autophobing). It was found that the behavior tends from wetting through dewetting to autophobing as the solution concentration increases and as the hydrophobicity of the surface increases. The aim of this experimental study is to systematically explore the dependence of the dewetting mode on surfactant concentration and film thickness. Drops of aqueous dodecyltrimethylammonium bromide (DTAB) solution, over a range of concentrations above and below the cmc, have been deposited on water films up to 200 µm in thickness. It has been found that across the studied parameter range there are three types of dewetting behavior. These tend from hole formation, through to autophobing, and finally cap formation, in which the deposited surfactant forms a cap that neither spreads nor retracts, with increasing surfactant concentration and decreasing film thickness, but simply remains throughout the experiment. This behavior may be explained by considering the relative Marangoni and bulk diffusion time scales as well as the mode of assembly of the surfactant adsorbed on the solid surface. 2. Experimental Details 2.1. Materials. The liquid substrate was ultrapure water obtained from a Barnstead NANOpure II filter system with a resistively of less than 18 MΩ cm and a surface tension of 72.2 ( 0.5 mN/m at 25 °C. This was also used to clean the glassware and syringe as well as to make up the surfactant solutions. The surfactant was DTAB (dodecyltrimethylammonium bromide, MW 308.3, 99+%, Aldrich) which is a soluble cationic surfactant with a cmc of 1.4 × 10-2 M.27 The surfactant was made up to the desired concentration using ultrapure water. The surface tension of the surfactant solutions was determined using a platinum Wilhelmy plate suspended from a Kruss microbalance, at a constant temperature of 25 °C. 2.2. Visualization Technique. The experiments were performed in a circular glass Petri dish 15 cm in diameter with an optically flat bottom. This was positioned in a four-point adjustable level stage. The setup was illuminated from above using a fiber optic lamp and the image projected onto a tracing paper screen placed beneath the glass dish. A Pulnix CCD progressive scan camera (model TM6710) was used to record the images at a rate of 120 frames/s via a mirror (camera position 1). This entire system rested on an antivibration table to isolate the system from vibrations greater than 1 Hz. A schematic diagram of the setup is shown in Figure 2. On occasions, the CCD camera was positioned above the Petri dish to observe, at a glancing angle, the spreading of the liquid drop (camera position 2). 2.3. Experimental Procedure. To ensure complete wettability, the Petri dishes were soaked for at least 12 h in a 2% RBS 50 surfactant solution (Chemical Concentrates Ltd.) before being thoroughly rinsed with ultrapure water. They were then left in an ultrasonic bath for at least 1 h to ensure that all traces of detergent were removed from the glass surface. The outside of the Petri dish was then dried, as were the inside walls, leaving a continuous water film over the base only. The exact height of this liquid film was calculated from the weight of the water layer. The error in the film thickness was estimated to be no more than 4%, based on film evaporation between weighing and the start of experimentation and the curvature of the Petri dish where the side walls are fused to the base. The glassware used to make up the surfactant solutions was also cleaned in the same way as the Petri dishes. Solutions were used within 24 h to avoid any decrease in surface activity.28 (27) Mukerjee, P.; Mysels, K. J. National Bureau of Standards, US Department of Commerce, Washington, DC, 1970.

Dewetting Behavior of Surfactant Solutions

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Figure 2. Schematic diagram of the experimental setup. Table 1. Variation of the Spreading Behavior of Aqueous DTAB Solutions with Initial Surfactant Concentration and Initial Film Thickness initial surfactant concn (mM) 0.56 (0.04cmc) 5.6 (0.4cmc) 11.2 (0.8cmc) 16.8 (1.2cmc) 22.4 (1.6cmc) 56 (4cmc)

25 µm

initial film thickness 50 µm 100 µm

200 µm

hole formation no spreading autophobing cap formation autophobing cap formation autophobing cap formation autophobing cap formation

A 20 µL precision Hamilton syringe was used for drop delivery. This was flushed several times with the surfactant solution to be used before the desired amount was drawn, in this case a volume of 9 µL. The Petri dish with the desired film thickness was placed on the adjustable stage. A drop of surfactant was first released from the syringe such that it hung from the tip of the needle. The apex of the drop was then contacted with the water film and was drawn across the water surface by Marangoni stresses. This method proved to be the least disturbing to the water surface. The spreading was followed for about 20 s after deposition, and the images were analyzed using commercially available software. Each spreading run was repeated at least three times to ensure good reproducibility with complete cleaning of all the equipment prior to each run.

3. Results The deposition of DTAB over a range of concentrations on different film thicknesses gives rise to three distinct types of behavior. At very low concentrations, there is stable spreading for several seconds, after which a hole forms and dewetting ensues (hole formation). At intermediate concentrations and on thick films, the spread surfactant solution retracts to a cap at the point of deposition (autophobing). At high concentrations and on thinner films, the spread surfactant does not retract but remains as a flattened cap in the center (cap formation). Table 1 summarizes the behavior of DTAB solutions over a range of surfactant concentrations and film thickness. (a) Hole Formation. This type of behavior is observed at very low surfactant concentrations (0.04cmc) on film thicknesses ranging from 25 to 100 µm. Figure 3 shows the typical formation and growth of a dewetting hole for aqueous DTAB solutions at low concentration. Upon surfactant deposition, the surfactant spreads in a stable and circular manner for approximately 8 s at all film thicknesses (Figure 3A). The spreading exponent associated with the leading edge for this time is about (28) Burcik, E. J.; Vaughn, C. R. J. Colloid Interface Sci. 1951, 6, 522.

0.26. This is close to the theoretically predicted value of 0.25 for surfactant spreading under the influence of Marangoni forces, thus suggesting that this part of the spreading is Marangoni-driven.29 From a random point within the spreading front (Figure 3B), a rupture site is formed and liquid is pushed outward leaving an apparently dry region in its path (Figure 3C). No thinning of the film is apparent prior to the formation of the rupture site; however, the asymmetric nature of the hole reflects the height variations in the film. On the 25 µm water film, the dewetting continues for several seconds while on the thicker 50 and 100 µm water films, dewetting is complete within 1 s and the expelled liquid is pushed out toward the leading edge. Both the surfactant leading edge and the dewetting front continue to advance but now with an exponent of about 0.5 (Figure 3D). The spreading rate of the surfactant leading edge is about 1 mm/s throughout for all film thicknesses. On a thicker 200 µm film there is little appreciable spreading (Figure 4A), before the drop retracts (Figure 4B) and subsequently sinks into the water film within a few seconds. The Bond number, Bo, is defined as Bo ) (FgHo2)/S, where F is the liquid film density, g is the gravitational acceleration, Ho is the initial film thickness, and S is the spreading pressure, and it gives an indication of the strength of gravitational forces relative to Marangoni stresses. The Bond number at the leading edge of a 200 µm Marangoni-driven film at this low concentration is close to 1. It appears, therefore, that gravitational effects at this film thickness and surfactant concentration are sufficiently significant to overwhelm Marangoni forces and cause flow reversal.29 (b) Autophobing. At higher surfactant concentrations, but still below the cmc, the spreading surfactant drop advances some distance under the influence of Marangoni forces before it retracts (autophobes). The extent of the spreading and retraction are functions of the surfactant concentration and the film thickness. The autophobing surfactant solution may retract completely either to a rounded cap close to the point of surfactant deposition or to a more flattened cap with a smaller contact angle, again close to the point of initial deposition. Figure 5 shows the autophobing behavior typically seen on a thin film at intermediate surfactant concentrations, where the surfactant droplet retracts to a rounded cap soon after surfactant deposition. Upon deposition, a spreading front is visible ahead of a cap of surfactant that has formed at the point of surfactant deposition (Figure 5A). The white ring immediately downstream of the spreading front is indicative of film thinning just ahead of the leading edge. This most likely occurs when the advancing elevated edge encounters the undisturbed film and experiences a sudden decrease in velocity, thus causing a thinning further ahead. The faint front ahead of the spreading front visible throughout the spreading is thought to be a shock wave arising from the deposition of the surfactant on the surface in this particular experiment. Almost immediately after deposition (0.3 s), the cap has retracted (Figure 5B), leaving a dewetted region between the cap and the surfactant front. The front continues to advance radially with time (Figure 5C) and develops crenulations at later times (Figure 5D). The region between the shock wave and the spreading front is not dewetted. A similar sequence of events occurs with 0.8cmc (11.2 mM) on a 50 µm water film (not shown) on a similar time scale. (29) Gaver, D. P.; Grotberg, J. B. J. Fluid Mech. 1990, 213, 127; 1992, 235, 399.

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Figure 3. A 9 µL drop of 0.04cmc (0.56 mM) DTAB solution spreading on a 50 µm thick water film: (A) 1 s after deposition when spreading is stable; (B) 8 s after deposition, a rupture site has formed and liquid is moving away from this region; (C) 8.5 s after deposition, dewetting continues; (D) 12 s after deposition, the dewetting front begins to merge with the advancing front at the surfactant leading edge. Schematic inferred height profiles (through the vertical dashed lines in parts b and c) are given below each image. Table 2. Variation in Approximate Onset Time (seconds) for Autophobing with Surfactant Concentration and Water Film Thickness for Aqueous DTAB Solutions initial surfactant concn (mM) 5.6 (0.4cmc) 11.2 (0.8cmc) 16.8 (1.2cmc) 22.4 (1.6cmc)

25 µm 0.125

initial film thickness 50 µm 100 µm 0.16 0.12

0.3 0.2 0.12 0.04

200 µm 0.42 0.24 0.16 0.08

On thicker 50 and 100 µm films, the surfactant advances further before retracting as illustrated in Figures 6 and 7. In Figures 6 and 7, upon surfactant deposition, the surfactant leading edge is seen as a dark ring with a shock wave ahead. Just behind the leading edge is a faint lighter front that is thought to correspond to the region of the film thinned by Marangoni forces (Figure 6A). The thinned film then ruptures isolating the flattened cap of spreading surfactant from the elevated front ahead (Figures 6B and 7A). There is an additional light ring further upstream visible in Figure 7A, but it is unclear what this corresponds to. The cap quickly retracts leaving behind a dewetted region between itself and the front (Figure 6C). The region between the shock wave and the dewetting front is not dewet. After several seconds, distortions appear in the dewetting front (Figures 6D and 7B). Similar behavior is also observed on deposition of 0.4 and 0.8cmc solutions on 100 and 200 µm water films. At these high film thicknesses, the shock wave is seen to travel much faster. At concentrations just above the cmc (1.2 and 1.6cmc) on 100 and 200 µm films, the film thins and ruptures but the subsequent retraction is not to a rounded cap at the point of deposition but to a flattened cap with a smaller contact angle (Figure 8). Tables 2 and 3 show the time and radius, respectively, at which the dewetting becomes apparent for each of the autophobing cases. These tables show that the time and radius at which the dewetting becomes apparent increases with increasing film thickness and decreasing surfactant concentration. (c) Cap Formation. Over certain parameter ranges, the majority of the deposited surfactant remains as a flattened cap at the point of deposition, a behavior that we have termed “cap formation”. The cap neither spreads nor retracts for the duration of the spreading, remaining

Figure 4. A 9 µL drop of 0.04cmc (0.56 mM) DTAB solution spreading on a 200 µm thick water film: (A) ∼1 s and (B) ∼2 s after deposition. Table 3. Variation in Approximate Onset Radius (millimeters) for Autophobing with Surfactant Concentration and Water Film Thickness for DTAB Solutions initial surfactant concn (mM) 5.6 (0.4cmc) 11.2 (0.8cmc) 16.8 (1.2cmc) 22.4 (1.6cmc)

25 µm 7

initial film thickness 50 µm 100 µm 8 6

15 12 11 10

200 µm 18 16 15 14

at a constant radius typically around 10 mm for all the studied experimental conditions. Further downstream, the elevated front continues to advance slowly downstream for the duration of the spreading; its speed appears to depend on the surfactant concentration. Figure 9 illustrates typical cap formation behavior observed on thin (25 µm) films at a surfactant concentration of 0.8cmc, the lowest surfactant concentration at which such behavior is seen. In the autophobing case, Marangoni-driven spreading was observed for some fractions of a second before the thinned region of the film ruptured. In the case of cap formation, a dewetted region forms between the cap and the front almost immediately (Figure 9A). The cap remains at a radius of approximately 10 mm throughout the duration of the spreading and appears to be distorted at the edges, while the dewetting front advances slowly downstream (Figure 9B). A shock wave is visible just ahead of the dewetting front even at late times. Similar spreading behavior is seen when depositing 1.2cmc surfactant solution on a 25 µm thick film.


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Figure 5. A 9 µL drop of 0.4cmc (5.6 mM) DTAB solution spreading on a 25 µm thick water film: (A) at 0.08 s, a spreading front and a cap can be seen; (B) at 0.3 s, the cap has retracted; (C) at 5 s, the dewetting front continues to grow; (D) at 17 s, crenulations are evident in the dewetting front. The outermost faint front visible throughout the spreading is thought to be a shock wave. Schematic inferred side views are also given.

Figure 6. A 9 µL drop of 0.4cmc (5.6 mM) DTAB solution spreading on a 50 µm thick water film: (A) at 0.08 s, the spreading front of the surfactant is seen as a dark ring and a lighter front is just visible inside this; (B) at 0.2 s, the thin region of the film has ruptured isolating the spreading surfactant drop from the front ahead; (C) at 0.5 s, the surfactant drop has retracted into a cap; (D) at 16 s, crenulations are evident in the dewetting front. The faint wave visible ahead of the leading edge is thought to be a shock wave. Inferred side views are shown below each image.

Figure 10 shows the behavior of a 1.6cmc solution on a 25 µm water film. As the concentration is increased on a given film thickness, the rate of advance of the dewetting front decreases. Figure 10 shows that even after several seconds the dewetting front has not moved appreciably and the cap has remained at a radius of about 5 mm throughout the spreading. A shock wave is visible just ahead of the dewetting front even at late times. Similar spreading behavior is seen when depositing 4cmc surfactant solution on a 25 µm thick film. Figures 11 and 12 show the typical dewetting behavior of DTAB solutions above the cmc on thicker (50 and 100 µm) films. Behavior similar to that shown in Figures 11 and 12 is also observed when spreading 1.6 and 4cmc solutions on 50, 100, and 200 µm films. On the thickest films, the shock wave travels much faster and is, therefore, not visible. There appear to be slight crenulations in the dewetting front and also at the edge of the cap. 4. Discussion Since there is a surface tension gradient across the liquid film upon surfactant deposition, the initial stages of

spreading are likely to be Marangoni driven. This is accompanied by surfactant diffusion through the bulk and adsorption onto the solid-liquid interface because of the attractive interaction between the surfactant headgroup and the substrate. Ionic surfactant adsorption to a charged surface typically follows three regimes, with increasing surfactant concentration:30,31 (i) The surfactant monomers adsorb with their polar moiety in contact with the surface in response to Coulombic attraction. The counterions in the diffuse double layer just outside the surface are exchanged for surfactant ions with the same charge. The hydrophobic tails can either lie flat on the surface or align perpendicular to the surface. For alkyl chains with greater than nine carbon atoms (as in this case), the tails are more likely to align horizontally.32 (30) Koopal, L. K.; Goloub, T. In Surfactant Adsorption and Surface Solubilization; Sharma, R., Ed.; American Chemical Society: Washington, DC, 1995. (31) Jo¨nsson, B.; Lindman, B.; Holmberg, K.; Kronberg, B. Surfactants and Polymers in Solution; John Wiley and Sons: Chichester, 1999.

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Figure 7. A 9 µL drop of 0.4cmc (5.6 mM) DTAB solution spreading on a 100 µm thick water film: (A) after 0.4 s, the leading edge of the surfactant is seen as a dark ring and a lighter front is just visible inside this; (B) after 16 s, the surfactant has retracted to a rounded cap in the center and crenulations are evident in the growing outer dewetting front. Inferred side views are shown below the images.

Figure 8. A 9 µL drop of 1.6cmc (22.4 mM) DTAB solution spreading on a 200 µm thick water film: (A) 0.5 s after deposition, the thinned region and elevated leading edge can be seen; (B) 20 s after deposition, the spreading surfactant cap has retracted and the dewetting front has developed crenulations at late times. Inferred height profiles are given beneath each image.

(ii) The ion exchange leads to a higher surfactant concentration close to the solid surface as compared to the bulk. This induces a surface micellization process at the solid-liquid interface at bulk concentrations below the bulk cmc. The analogous surface concentration is known as the critical surface aggregation concentration (csac) and is typically of the order of one-tenth the value of the cmc of the surfactant.33 These surface aggregates have been termed hemimicelles.34 The tail groups start to align perpendicularly to the surface, while the headgroups are still in contact with the surface. (iii) As the tail groups align perpendicularly to the solidliquid interface, a hydrophobic surface is created and the hydrophobic chains of the surfactant adsorb onto this. The exact mode of assembly of the surfactant molecules is dependent on both the interaction of the surfactant with the surface and also the interaction between the hydrophobic moieties of the surfactant that gives rise to the so-called hydrophobic effect.31 In the case of DTAB (32) Zajac, J.; Partyka, S. In Adsorption on New and Modified Inorganic Sorbents Studies in Surface Science and Catalysis; Dabrowski, A., Tertykh, Y. A., Eds.; Elsevier Science: Amsterdam, 1996. (33) Atkin, R.; Craig, V. S. J.; Biggs, S. Langmuir 2000, 16, 9374. (34) Gao, Y. Y.; Du, J. H.; Gu, T. R. J. Chem. Soc., Faraday Trans 1 1987, 83, 2671


adsorption on a glass surface, the surface-surfactant interaction is stronger than the interaction between the hydrophobic chains and so a bilayer structure is formed. This occurs at bulk concentrations of around the cmc. Surfactant adsorption giving rise to a hydrophobic surface is followed by film rupture and formation of a dewetted region from which liquid moves away. A typical dewetting event is illustrated in Figure 13. Upon surfactant deposition on a liquid support, Marangoni forces will give rise to surface deformations. Surfactant will diffuse more rapidly through the Marangoni thinned region to adsorb at the solid-liquid interface (Figure 13a). The assembly of the molecules is dependent on the surfactant concentration. This region of the solid surface then becomes hydrophobic and water is repelled from this area, thus causing further thinning of the film to the extent that long-range intermolecular forces become significant (Figure 13b). Since the disjoining pressure is negative, van der Waals forces act to further thin the film, while short range repulsive forces (Born repulsion) resist thinning. A dry patch or hole results with a microscopically thin equilibrium dewetting thickness, te. Water moves away from the hole via a dewetting front (Figure 13c). The results show that there is a dependence of the dewetting behavior on both surfactant concentration and film thickness. With increasing surfactant concentration, the hydrophobicity of the solid surface increases up to the cmc and decreases thereafter as the surfactant headgroups are exposed. In addition, the significance of Marangoni forces changes relative to bulk diffusion as the surfactant concentration increases and there are two competing effects. The Marangoni time scale can be defined as tm ) (µR2/SHo), where µ is the film viscosity, R is the radial extent of spreading, S is the spreading pressure, and Ho is the initial film thickness. The bulk diffusion time scale can be defined as tDb ) (Ho2/Db), where Db is the bulk diffusivity. As the surfactant concentration increases, the Marangoni time scale is reduced in relation to the time taken for the surfactant to diffuse through the bulk and adsorb onto the solid surface. However, an increased concentration provides a greater source of surfactant that can potentially adsorb at the solid-liquid interface and the rate of surfactant adsorption is dependent on the surfactant concentration. The higher the concentration of the surfactant, the greater the rate of adsorption. Pagac et al.35 have shown that for CTAB adsorbing onto a silica surface at 0.55cmc, it takes 900 min to reach equilibrium adsorption, at 0.89cmc, it takes 45 min, while at 11cmc, it takes only 2 min. It is assumed that DTAB adsorption will follow a similar trend. Hence increasing the surfactant concentration will also progressively reduce the time scale for adsorption onto the solid surface. Table 2 shows that the dewetting becomes apparent sooner at higher surfactant concentrations, indicating that the latter effect is dominant. Variations in the film thickness can also give rise to changes in the significance of surfactant diffusion in relation to Marangoni forces. As the film thickness increases, there is reduced viscous dissipation which allows more rapid spreading. This reduces the Marangoni time scale in relation to the diffusion and adsorption time; a similar effect to increasing the surfactant concentration. However, more rapid flow will promote more severe film thinning at the base of the drop, which will reduce the diffusion time of the surfactant through the bulk. Table 2 reveals that, since dewetting becomes apparent more quickly on thinner films, the former effect dominates. (35) Pagac, E. S.; Prieve, D. C.; Tilton, R. D. Langmuir 1998, 14, 2333.


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Figure 9. A 9 µL drop of 0.8cmc (11.2 mM) DTAB solution spreading on a 25 µm thick water film: (A) after 0.05 s, there is a front and a flattened cap; (B) after 0.5 s; (C) after 19 s, the cap has remained at a constant radius throughout the spreading while the outer front has continued to grow. The outermost front is thought to be a shock wave. Inferred height profiles are given beneath each image.

Figure 10. A 9 µL drop of 1.6cmc (22.4 mM) DTAB solution spreading on a 25 µm thick water film: (A) after 0.05 s, a cap of radius 5 mm has formed, ahead of which is the dewetting front and a shock wave; (b) after 0.5 s, a cap of radius 5 mm has formed, ahead of which is the dewetting front and a shock wave; (C) after 8 s, the dewetting front has advanced only slightly. Inferred height profiles are also shown.

Figure 11. A 9 µL drop of 1.2cmc (16.8 mM) DTAB solution spreading on a 50 µm thick water film: (A) after 0.5 s, there is a cap ahead of which is a dewetting front and a shock wave; (B) after 16 s, the cap has remained at a constant radius throughout the spreading while the dewetting front has continued to grow. The outermost front is thought to be a shock wave.

The results can now be explained in the light of these considerations. Upon deposition of a 0.04cmc drop of surfactant, a surface tension gradient causes Marangoni

Figure 12. A 9 µL drop of 4cmc (56 mM) DTAB solution spreading on a 100 µm thick water film: (A) after 0.3 s, there is a front and a flattened cap; (b) after 19 s, the cap has remained at a constant radius throughout the spreading while the outer front has continued to grow.

forces to spread the surfactant downstream. The spreading exponent of 0.26 confirms that the flow at this stage is Marangoni driven. Because of the low bulk surfactant concentration, the adsorption rate is low and it is likely that, since the csac has not yet been reached, the surfactant

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Figure 13. Schematic representation of the events that lead to the formation of a dewetting hole: (a) Film thinning and surfactant adsorption onto the solid surface preferentially from the Marangoni-thinned region as shown by the arrow. (b) Repulsion of water from the hydrophobic solid surface causing further film thinning. The arrows show the direction of water flow. (c) Formation of a dry patch or hole following still further thinning by intermolecular forces. Water then moves away from the hole as shown by the arrows.

monomers adsorb onto the solid surface with their tail group lying horizontally on the surface. After several seconds, there is sufficient adsorption at the solid-liquid interface from the thinned region of the film to create a hole. The time taken for the hole to form is dependent on the time taken for surfactant to diffuse through the bulk liquid film and adsorb onto the solid-liquid interface. It is expected that this would occur sooner on an initially thin film. However, the results show that hole formation occurs at 8 s on all film thicknesses, the reasons for which are not yet understood. At higher surfactant concentrations, autophobing is seen. This case is similar to hole formation, but film thinning results in the formation of a dry “ring” rather than a hole. This causes the fluid upstream of the dry region to retract, while the downstream fluid moves away from the dry patch via a dewetting front. The time of formation of the dry ring depends on the surfactant concentration and film thickness. From Tables 2 and 3, it appears that the factors that promote film thinning (initially thin films and high surfactant concentrations) cause dewetting to become apparent sooner. At a concentration of 0.4cmc on a 25 µm film and 0.8cmc on a 50 µm film, the cap is seen to retract almost immediately upon surfactant deposition (Figure 5). This suggests that


the time scale for diffusion and adsorption is of the same order of magnitude as the Marangoni time scale, since the surfactant was not able to spread appreciably. At the same concentrations on thicker films, the surfactant is seen to spread under the influence of Marangoni forces before dewetting becomes apparent (Figures 6 and 7). This is because the ratio of the Marangoni time to the diffusive time scale is reduced (i.e., it takes longer for surfactant to diffuse across a thick film). The relatively high contact angle, around 90°, of the retracted cap suggests that the dewetted region is highly hydrophobic and the surfactant is oriented with the hydrocarbon chains exposed. The crenulations in the dewetting front are thought to arise as the front becomes unstable to small height and concentration disturbances ahead. At concentrations above the cmc, the fluid retracts to a cap of smaller contact angle. At these concentrations, it is expected that the adsorbed surfactant will form a bilayer at the solid-liquid interface, which presents a less hydrophobic surface to the surfactant solution. Over certain parameter ranges, the surfactant droplet does not appear to spread before retracting, but a flattened cap forms upon surfactant deposition that neither spreads nor retracts (cap formation). This indicates that the time scale for adsorption onto the solid surface is less than or of the same order of magnitude as the time scale for Marangoni flow. At this concentration, either a surfactant bilayer, or, more likely, adsorbed cylindrical micelles given the recent AFM images of Ducker et al.36 for DTAB adsorbed to silica, will be present ahead of the cap of surfactant. This presents a less hydrophobic surface to the surfactant than the hemimicelle formation at lower surfactant concentrations and so the contact angle of the cap is smaller and the cap is more flattened (Figures 9-12). At 1.6cmc and 4cmc on a 25 µm thick film, the dewetting front does not appear to advance downstream. This may be due to the surfaces rapidly becoming hydrophilic on these relatively thin water films. One would expect the surface to be covered with adsorbed surfactant micelles which would be hydrophilic in nature, preventing further dewetting. 5. Conclusions When the surfactant headgroup and substrate exhibit a mutual attraction, then dewetting is seen to occur. The dewetting patterns vary with surfactant concentration and water film thickness. At low concentrations, dewetting proceeds through hole formation in the thinned region of the film. At higher concentrations, the thinned region of the film ruptures leaving a dewetted ring. Fluid upstream of this retracts into a cap of surfactant at the point of initial deposition (autophobing). Downstream of the dry ring liquid moves away from the hydrophobic region via a dewetting front. At still higher concentrations, the deposited surfactant forms a cap at the point of deposition that neither spreads nor retracts (cap formation). This variation of dewetting behavior can been explained by considering the relative Marangoni and bulk diffusion time scales as well as the mode of assembly of the surfactant adsorbed on the solid surface. Acknowledgment. We are grateful to the EPSRC for funding of this project. LA040041Z (36) Ducker, W. A.; Wanless, E. J. Langmuir 1996, 12, 5915.

Dewetting Behavior of Aqueous Cationic Surfactant Solutions on

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