Langmuir 2002, 18, 1649-1654
1649
Surfactant Self-Assemblies Controlling Spontaneous Dewetting Dan Qu, Robert Suter, and Stephen Garoff* Department of Physics, Center for Complex Fluids Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 Received August 3, 2001. In Final Form: November 16, 2001 We have examined the structures of surfactant self-assemblies left on substrates as a contact line spontaneously retreats across the surface during an autophobing event. A continuous structural gradient is formed during the spontaneous retreat: from molecules lying down on the surface with low packing densities in a region never touched by the solution, to molecules standing up with higher packing densities in a region where the contact line has moved slowly. Despite significant free volumes within the selfassemblies, there is no evidence of clustering of molecules. We have observed a clear correlation between retreating contact line speeds and deposited surfactant structures. The dynamics during at least a later period of the autophobing event is dominated by the time evolution of Young’s force dictated by the selfassembly near the contact line.
1. Introduction The wetting behavior of surfactant solutions is critically controlled by the self-assembly of surfactant molecules at the interfaces near the contact line.1-6 Autophobing, the spontaneous retreat of the contact line of a surfactant solution immediately after spontaneous spreading, is a well-known example of the wetting behavior of surfactant solutions. It occurs when an attraction between the headgroup and the surface causes the headgroup of the surfactant to adsorb to the surface and the tail group to be exposed to solution. The surfactant solution no longer wets the adsorbed monolayer and the fluid spontaneously retracts.7 In a drop spreading geometry, the drop first begins to spread and then spontaneously retracts. If a substrate is continuously forced into a bulk surfactant solution, the advancing contact line is pinned to the substrate, jumps forward and then autophobes. This “stickjump” behavior is attributed to the adsorption of a surfactant barrier on the solid-vapor interface ahead of the advancing contact line.5,8,9 In both cases, the direction of contact line motion changes spontaneously. Only a change in the Young’s force at the contact line can induce such a change in the direction of contact line motion. Surfactant self-assemblies very near the contact line at the solid-liquid, liquid-vapor, and solid-vapor interfaces control this force. To examine spontaneous dewetting by surfactant solutions, this paper focuses on the autophobing of an aqueous solution of CTAB (cetyltrimethylammonium bromide), a cationic surfactant, on SiO2, an anionic substrate for pH∼7. Frank has shown that the area left behind the spontaneously retreating contact line of this solution is covered by * To whom corresponence should be addressed. (1) Troian, S. M.; Wu, X. L.; Safran, S. A. Phys. Rev. Lett. 1989, 62, 1496. (2) Bose, A. In Wettability, Surfactant Science Series; Marcel Dekker Inc.: New York, 1993; Vol. 49. (3) Hill, R. M. Curr. Opin. Colloid Interface Sci. 1998, 3, 247. (4) Frank, B.; Garoff, S. Langmuir 1995, 11, 87. (5) Frank, B.; Garoff, S. Langmuir 1995, 11, 4333. (6) Luokkala, B. B.; Garoff, S.; Tilton, R. D.; Suter, R. M. Langmuir 2001, 17, 5917. (7) Zisman, W. A. Adv. Chem. 1964, 43, 1. (8) Cohen Stuart, M. A.; Cazabat, A. M. Prog. Colloid Polym. Sci. 1987, 74, 64. (9) Princen, H. M.; Cazabat, A. M.; Choen Stuart, M. A.; Heslot, F.; Nicolet, S. J. Colloid Interface Sci. 1988, 126, 84.
Figure 1. Condensation figure of a typical sample after a spontaneous and then a forced retreat of the contact line.
regions of different surfactant self-assemblies and having different wettabilities.5 Figure 1 shows a condensation figure performed by blowing saturated water vapor onto the substrate after an autophobing event has occurred. The region marked D is a region of bare, hydrophilic substrate. Region A is beyond the farthest point exposed to the bulk solution yet its shade indicates the presence of surfactant molecules. B1 and B2 are both crossed by the contact line during the spontaneous retreat. Previously, these two regions had not been differentiated. Region C is the area crossed by a forced, steady retreat of the contact line after the autophobing event is over. Earlier ellipsometric data across the regions indicate a qualitative difference in the molecular packing in these regions.5 However, the detailed structure and the wettability in each region have not been resolved. Further, research to date has gained neither a full understanding of the mechanism that controls the spontaneous retreat nor the interaction between the contact line motion and the surfactant structures near the contact line during the retreat. Our work is motivated by the previous results of Frank.5 We further elucidate the surfactant structures in the regions shown in Figure 1, analyze the forces that control the spontaneous retreat during an autophobing event, and relate the surfactant structures to the contact line motion. We find a gradient across these regions in both surface wettability and surfactant structure. These gradients correlate to a variation of contact line retreating speed. The outer topography in all regions has similar
10.1021/la011237r CCC: $22.00 © 2002 American Chemical Society Published on Web 02/08/2002
1650
Langmuir, Vol. 18, No. 5, 2002
Qu et al.
2. Experimental Section 2.1 Sample Preparation. We used [100] oriented silicon wafers with their native oxide layer (Unisil Corporation) as our substrates. The substrates were carefully cleaned by a procedure which leaves the surfaces completely wettable by water.4,5 Purum grade CTAB was used as received from Fluka Chemical Corp. Our 0.25 × critical micellar concentration (cmc) and 0.4 cmc CTAB solutions had liquid-vapor interfacial tensions of 63.8 ( 1.2 dyn/cm and 57.1 ( 1.2 dyn/cm, respectively. We did not observe any substantial difference in the behavior for the two concentrations. We produced the self-assemblies by first advancing the substrate vertically into the bulk CTAB solution at a fixed speed (U ) 100 µm/s) controlled by a motion stage (Newport Motion Controller MM2000). The contact line on the substrate exhibits a stick-jump motion followed by a spontaneous retreat.5 We stopped the motor immediately after a jump, just as the spontaneous retreat began. We recorded the contact line position during the jump and the subsequent spontaneous retreat of the contact line with video microscopy.5 When the spontaneous retreat had ended, we pulled the sample out of the bulk solution at 100 µm/s. 2.2 Probing the Structures and Wettabilities on the Solid. We used condensation figures and AFM capillary force measurements to examine the surface wettability along the z direction in Figure 1. Condensation figures are a simple, rapid way to qualitatively differentiate regions of subtly differing wettabilities on a surface.10 They reveal subtle changes in molecular orientation and packing of the surfactants, but quantitative interpretation in terms of these variations is difficult. Since the images of the condensation figures depend critically on the ambient humidity, as well as vapor streaming temperature and strength,11 we do not attempt to use this technique to compare different surfaces. Rather, this technique provides the unique ability to sense spatial variations in surfactant structure across a single surface in very short times after dynamic wetting events. To obtain a more quantitative picture of the wettability, we measured the pull-off force12 between an AFM tip and the substrate as a function of z. This pull-off force is dominated by the force needed to break the capillary bridge formed between the tip and the surface. It is correlated monotonically, at fixed relative humidity, to the hydrophilicity of the surface.13 Therefore, by moving across a surface at fixed relative humidity (∼20% RH), we have a
semiquantitative measure of the variation of the local wettability across the sample. We used tapping mode AFM imaging to measure the detailed topography in each region. This method has been used to image adsorbed surfactant structures.14,15To prove that our measurement conditions did not alter the surfactant structures, we scanned each region at least twice and interpreted only image features that appeared in all images. Differences in processing and filtering methods of the images also had no effect on the results we will present. To determine the resolution we could attain under our experimental conditions, we also imaged a test sample that contained CTAB clusters formed by soaking substrates in a 0.02 cmc CTAB solution for 24 h and removing them from solution in the same manner as for our other samples. The method for forming these clusters was suggested by Hayes and Schwartz.16 On these test samples, we were able to resolve image features ∼300 Å in diameter and ∼6 Å in height without any damage to the islands from multiple scans at the same AFM settings used to image the autophobed samples. To probe the molecular packing of the self-assemblies left behind the retreating contact line, we used ex-situ scanning ellipsometry and in-situ X-ray reflectometry. In the ex-situ experiments, after an autophobing event, we withdrew the substrate from the solution at a controlled speed and mounted the sample on the experimental stage. In the in-situ experiment, we did not withdraw the substrate from the bulk solution and scanned in the z direction while the substrate remained in contact with the solution. In this case, the contact line at the bottom of the sample receded as the bulk solution evaporated, producing a contact line speed ∼0.1 µm/s. In the ex-situ ellipsometry experiment, we measured the optical impedance of CTAB structures along the z direction with a spot size ∼20 µm. We interpret this impedance as a measure of some combination of thickness and molecular packing density of the monolayer or submonolayer. We concentrate on the interpretation of only one of the two ellipsometric parameters, ∆, since ∆ is more sensitive to the properties of very thin films.4,17 While models for an effective film thickness in terms of ∆ can be made, these models depend on assumptions about the index of refraction of the monolayer for single wavelength ellipsometry. Since the densities and orientations of molecules are varying across the sample, an assumption of a constant index of refraction could be erroneous. Thus, we report relative ∆ as a function of z and interpret ∆ as some combination of thickness and packing density in the monolayer. To re-enforce the result from the ellipsometry experiment and obtain time evolution information of the structural transitions, we measured the X-ray reflectivity of the samples in-situ. Traditional experiments using X-ray reflectometry perform scans over a long range of the scattering angle θ or the scattering wavenumber Q(θ) ) (4π/λ)sinθ (where λ is the X-ray wavelength). Figure 2 shows examples of two such scans of CTAB layers formed by forced retreats (similar to that in the C region of autophobed samples) at different retreating speeds, as well as one scan of the bare substrate (similar to that in the D region). Qualitatively, when the surfactant layer is
(10) Beysens, D.; Knobler, C. M. Phys. Rev. Lett. 1986, 57, 1433. (11) Fritter, D.; Knobler, C. M.; Beysens, D. A. Phys. Rev. A 1991, 43, 2858. (12) Weisenhorn, A. L.; Hansma, P. K.; Albercht, T. R.; Quate, C. F. Appl. Phys. Lett. 1989, 55, 2491. (13) Van der Werf, K. O.; Putman, C. A. J.; de Grooth, B. G.; Greve, J. Appl. Phys. Lett. 1994, 65, 9.
(14) Sikes, H. D.; Woodward, J. T.; Schwartz, D. K. J. Phys. Chem. 1996, 100, 9093. (15) Woodward, J. T.; Schwartz, D. K. J. Am. Chem. Soc. 1996, 118, 7861. (16) Hayes, W. A.; Schwartz, D. K. Langmuir 1998, 14, 5913. (17) Tompkins, H. G. A User’s Guide to Ellipsometry; Academic Press: New York, 1993.
roughness and there is no evidence of molecular clustering even in the least dense region. The spontaneous retreat of the contact line can be divided into two different regimes, each controlled by a different time scale and governed by a different power law of velocity with time. At least in the later stage of the retreat, the contact line motion cannot be controlled by hydrodynamics of a pure fluid nor a Marangoni flow due to surface tension gradients on the liquid-vapor interface. Rather, the motion must be controlled by the time varying Young’s force determined by the evolving surfactant structures at the three interfaces near the contact line. This correlation of contact line retreating speed with surfactant structure is a two-way interplay and is critical in the spontaneous dewetting of surfactant solutions.
Surfactant Self-Assemblies
Langmuir, Vol. 18, No. 5, 2002 1651
Figure 2. Reflectivity curves of two different layers formed by forced retreats (similar to that in the C region) at different retreating speeds and one curve of a bare substrate. Circles: bare substrate. Crosses: C region produced at U ) 2 mm/s. Triangles: C region produced at U ) 10 µm/s.
thicker, the first reflectivity minimum occurs at smaller Q; and when the layer is more densely packed, the modulation depth of the first minimum is greater. However, the structure can only be unambiguously determined from scans even longer than those shown in Figure 2.18 Since we are interested in the structural transition through the regions in Figure 1, we should ideally perform one scan over θ at each position through all the regions with a beam spot that is smaller than the transition between regions. To obtain some resolution in the z direction, we reduce the X-ray spot size to ∼100 µm in the z direction. With such a spot size, scans with sufficient statistics to interpret structures in detail would take many tens of hours, while the CTAB structures evolve in hours. Instead, we place our detector at a fixed scattering angle and observe the reflectivity change as a function of z position. A scan along z can be completed in a relatively short time. For example, we can fix Q at 0.26 Å-1 in Figure 2 and scan the beam in the z direction across the regions from D to C within about 1.5 h after the formation of the sample. In this experimental mode, if the layer structure varies with z, the reflectivity will also vary. Since the most sensitive part of the reflectivity curve is around the first minimum, we placed our detector at the Q for the first minimum of the reflectivity curve of a forced retreating sample. The sample was prepared by a forced retreat in the same speed used to produce the C region in the ex-situ samples. Despite the disadvantage that this fixed-Q method does not produce complete information of the layer structure, our extensive knowledge of the X-ray reflectivity from CTAB structures18,19 enables us to interpret the reflectivity vs position as a transition of a rough combination of thickness with packing density. Complete structural determination at 100 µm-z resolution would be impossible with present, nonsynchrotron sources. 3. Results and Discussion 3.1 Transition in Surface Wettability of Surfactant Assemblies. As discussed earlier, the condensation figure on an autophobed sample indicates five regions of different wettabilities, three related to regions of surfactant deposition during the spontaneous retreat of the contact line. The boundary marked in Figure 1 between the A and B regions is determined independently of the condensation figure from the highest position of the contact line just (18) Luokkala, B. B.; Garoff, S.; Suter, R. M. Phys. Rev. E 2000, 62, 2405. (19) Birch, W. R.; Knewtson, M. A.; Garoff, S.; Suter, R. M.; Satija, S. Colloids Surf. 1994, 89, 145.
Figure 3. z-profiles of (a) AFM measurement of capillary force; (b) normalized ellipsometric parameter ∆; (c) normalized X-ray reflectivity 1.5 h after autophobing; (d) contact line retreating speed; (e) condensation figure and its gray scale; (f) schematic of suggested model of surfactant structures. Since not all measurements can be made on the same sample, the z-axes in (a), (b), and (c) are rescaled so the widths of regions B and A match those in (d) and (e).
after the jump as recorded by the video microscopy. Clearly, this highest point of contact of the surface with the solution corresponds to a change in wettability. Region D exhibits water condensation into thin films, indicating a hydrophilic surface. The A region shows surfactant deposition even though the bulk solution has not touched this region of the surface. Within the region uncovered by the spontaneous retreat of the contact line, the B region, B1 corresponds to an earlier stage with faster retreating speeds while B2 corresponds to a later stage with slower retreating speeds. This qualitative picture from the breath figure sets the stage for our more quantitative measurements of wettability and surfactant structures in these regions. Figure 3(a) shows the result of AFM measurements of the local capillary force along the z direction. We see that the hydrophilicity of these regions decreases in the order D > A > B > C, with a continuous grade of wettability transition through the B and A regions. 3.2 Surfactant Structures after the Spontaneous Retreat. Figure 3(b) shows the normalized ellipsometric parameter, ∆, vs the z-position measured over the interval of time from 1 h to 1.5 h after the spontaneous retreat. We see a smooth transition of layer thickness convolved
1652
Langmuir, Vol. 18, No. 5, 2002
Qu et al.
Figure 4. Normalized X-ray reflectivity vs z-position in an in-situ measurement at different times after a jump of the contact line. Crosses: after 1.5 h. Circles: after 2.5 h. Squares: after 4 h. Triangles: after 6 h. ×’s: after 7 h. The z ) 0 position is set at the boundary between A and B.
with packing density along the z direction, similar to that of the capillary force.20 The region of forced retreat (C) has the thickest layer and/or highest packing density and region A has the thinnest layer and/or lowest packing density. We note that while the forced retreating speed in C is 100 µm/s, the same speed as reached by the spontaneous retreat at about z ∼ 0.75 mm in B region (see Figure 3(d)), the structures are clearly different. This difference may either arise from the much shorter exposure time of the substrate to the solution as the B region is formed or to the unsteady flow during the spontaneous retreat in B as opposed to the steady flow in C. To observe the time evolution of the profile, we carried out the in-situ experiment with X-ray reflectometry. Figure 4 shows the normalized reflectivity vs the z-position. The reflectivity decreases in the order D < A < B < C, a trend compatible with a transition from a clean substrate to a loosely packed and/or thin layer to a more densely packed and/or thicker layer. We can determine the position of the contact line since the reflected beam hitting the bulk meniscus drives the reflectivity signal to zero. This point is about ∼100-200 µm below the lowest data point recorded in each of the curves in Figure 4. We see that as time increases, evaporation causes the bulk level to drop and consequently the C width to grow. The boundary between B and C remains sharp over time and the reflectivity in C is constant, indicating both a constant thickness and a constant packing density in the C region. The reflectivity profile also confirms that both the A and the B regions are smoothly graded in structure at times g 1.5 h after the autophobing event, as shown by the ex-situ ellipsometry data. Within the detectability of this experiment, the reflectivity profile from the B/C boundary to the end of the A region (the A/D boundary) is the same from 1.5 h to 7.5 h after the jump. This indicates that the structures have stabilized after 1.5 h (but likely stabilize in much shorter times) and no longer evolve with time even though the bottom of the sample is touching the bulk solution. From Figure 3(b) and 3(c), we note the similarity between the X-ray and ellipsometry profiles, indicating a similarity in how these two probes sense structure. In loosely packed surfactant self-assemblies, we should ask how the free volume is distributed throughout the monolayer. Is the molecular density uniform (as might be the case if the surfactant tails are highly conformationally (20) The fact that these two curves have somewhat differing shapes is the result of the differing responses of the two measurement techniques to the surfactant structure. AFM is sensitive to the hydrophilicity and thus the mixture of CH2 and CH3 groups exposed at the outer surface of the surfactant structure. Ellipsometry is sensitive to the integrated optical response across the full depth of the monolayer.
Figure 5. AFM topographical images (tapping mode, 1 µm × 1 µm) for (a) A region; (b) test sample. Examples of surfactant islands on test sample shown.
disordered) or is there molecular clustering (as might occur if the molecules are more ordered, but the tails cluster because of the head-tail size mismatch)?21 For very lowdensity assemblies, Langmuir suggested that surfactant molecules at a liquid/vapor interface will self-assemble into clusters on the order of 102 Å, minimizing the free energy through the van der Waals attractions among the tails of the surfactants.22 Data from long X-ray reflectometry scans in the C region and previous data on similarly produced CTAB monolayers19,23 suggest that C is not a densely packed monolayer. Both our ellipsometry and X-ray data indicate that the average packing densities in the A and the B1 regions are even lower. To search for any sign of clustering in our assemblies, we used tapping mode AFM to acquire topographical images of the regions A, B, C, and D (included as reference to the substrate topography). Figure 5(a) shows a topographical image in the A region where the clustering would be most likely to appear. Images from the other three regions are indistinguishable from that in the A region, with RMS roughness ∼0.4 Å and peak-to-valley distance of ∼4 Å. All images are 1µm × 1µm, scanned and processed in an identical manner. These images contrast with the image of our test sample that contains islands (Figure 5(b)) which shows sharply defined molecular clusters ∼300 Å in diameter and ∼6 Å in height. Such surfaces have RMS roughness of 0.8 Å and peak-to-valley distance of 12 Å. Thus, assuming the condition of the tips that we used in our test sample and (21) Safran, S. A.; Robbins, M. O.; Garoff, S. Phys. Rev. A 1986, 33, 2186. (22) Langmuir, I. J. Chem. Phys. 1933, 1, 756. (23) Birch, W. Ph.D. Thesis, Department of Physics, Carnegie Mellon University: Pittsburgh, PA, 1993.
Surfactant Self-Assemblies
autophobed sample are similar, we conclude that there is no evidence of molecular clustering on the 100 Å scale in any of the regions that contain surfactants on the autophobed sample. In addition to the absence of actual clusters in the less dense regions of our assemblies, we observe no topographical evidence of strong density fluctuations in any region. The upper topographies of the different regions are similar despite their differing heights and densities. 3.3 Suggested Model of Surfactant Structures. The results in section 3.1 and 3.2 provide a picture of the selfassembled structures near the contact line. The CTAB headgroup and the tail group are ∼6 Å and ∼5 Å in diameter, respectively, and the extended length of the tails is ∼28 Å, as measured from CPK atomic models.19 The A region has the lowest thickness and/or the largest area per molecule and is the most hydrophilic. The ellipsometry data is compatible with a monolayer thickness of ∼4 Å in the A region if the index of refraction is assumed to be that of bulk hydrocarbon (n ) 1.45). The AFM topographical images show that there is not any topographical feature thicker than ∼4 Å if their lateral size is greater than 100 Å. Therefore, a plausible structure in the A region is that molecules lying down cover the surface either fully or partially. If these molecules completely cover the substrate and lie flat, the area per molecule is ∼102 Å. The C region has the highest thickness and/or smallest area per molecule and is the most hydrophobic. Previous X-ray reflectometry data have shown that in the C region, the area per molecule is ∼50 Å2.23 while our ellipsometry data is compatible with a monolayer thickness of ∼16 Å. This represents loosely packed molecules standing up on the surface in the C region. Both our X-ray reflectivity and ellipsometry results strongly suggest that the packing density and thickness increase monotonically as we move from A through B to C. While the B/C boundary is sharp even up to 1.5 h after the autophobing, the A/B boundary is within the graded structure and is a smooth transition instead of a sharp step. This structure is shown schematically in Figure 3(f). 3.4 Interplay of Surfactant Self-Assembly and Contact Line Motion. By considering the molecular densities of each of the interfaces near the contact line, we see that molecules must undergo considerable rearrangement as they pass through the retreating contact line. The time scale of this rearrangement will affect the evolution of the unbalanced Young’s force driving the retreat. As discussed in the previous section, the B region has a packing density between that of the A region (∼102 Å2) and the C region (∼50 Å2). At the solid-liquid interface, equilibrium adsorption coverage is ∼500 Å2/molecule and ∼167 Å2/molecule, and the initial adsorption rates are ∼0.1 mg/(m2‚min) and ∼0.3 mg/(m2‚min) for 0.25 cmc and 0.4 cmc solutions, respectively.24 Since the contact line jumps to a clean portion of the surface during a typical jump motion,5 within the first 0.2 s of the autophobing (the time that the contact line sweeps across B1, see Figure 6(a)), the solid-liquid interface near the contact line must have a coverage > 2.4 × 105 Å2/molecule. Thus, there is virtually no contribution from the solid-liquid interface to the self-assembly on the solid-vapor interface in the B1 region. Even after the 100 s needed to sweep across the B2 region, the contribution to the deposited selfassembly from the solid-liquid interface remains low. Using the results from surface tension measurements and the Gibbs equation, we determine the equilibrium coverage (24) Velegol, S. B.; Fleming, B. D.; Biggs, S.; Wanless, E. J.; Tilton, R. D. Langmuir 2000, 16, 2548.
Langmuir, Vol. 18, No. 5, 2002 1653
Figure 6. (a) Contact line retreating speed vs time during an autophobing event. (b) Contact line retreating speed vs time of water on Aquapel sample. Solution concentration ) 0.25 cmc.
for the liquid-vapor interface to be 30 to 40 Å2/molecule. Since the liquid-vapor interface equilibrates within 0.1 s after each jump,5 the liquid-vapor interface may attain this density as it sweeps through the B region and does have sufficient molecular density to produce the selfassembly in the B region. However, we cannot rule out the possibility that molecules in the bulk solution deposit onto the solid-vapor interface through the contact line motion. Therefore, molecules in the B region on the solidvapor interface come from the liquid-vapor interface and/ or the solution during the spontaneous retreat. Regardless of the source, the molecules must undergo considerable rearrangement as they pass through the contact line. Since the details of the self-assembly will dictate the unbalanced Young’s force driving the contact line retreat, we must consider this self-assembly as a possible limiting step in the spontaneous retreat. Figure 7(a, b) shows the contact line position vs time, and velocity vs z-position during the autophobing. We see a difference in the contact line speed behavior in the B1 and the B2 regions as located independently by condensation figures. (The uncertainty in determining the B1/ B2 boundary comes from an uncertainty in determining the first frame of the retreat just after the jump when the contact line speed is ∼6 mm/s.) There is a clear indication that different contact line speed regimes are producing different self-assembled structures as indicated by the condensation figure. In Figure 3, we further demonstrate this correlation between self-assembly properties and contact line speed by comparing the velocity vs position profile with the condensation figure, AFM force measurement as well as ellipsometry and X-ray results. With the exception of the AFM wettability measurement in the B1 region, the correlation is easily seen. This result, that different speeds of a spontaneous retreat produce different self-assembled structures, agrees with results on selfassemblies produced by the forced retreat of contact lines of CTAB solutions as shown in Figure 2 and reference 25. However, as noted in section 3.2, self-assemblies produced
1654
Langmuir, Vol. 18, No. 5, 2002
Qu et al.
of pure liquid, if the contact line movement is unsteady, the duration of the unsteadiness will be of the inertial time scale τi ) FL2/µ, where F is the liquid density, L is the capillary length of the fluid, and µ is the viscosity. If the contact line movement is quasi-steady, the duration of the quasi-steadiness will be of the viscous time scale τv ) Lµ/σ, where σ is the liquid-vapor surface tension.28 In the immediate vicinity of the contact line, there will also be evaporative molecular transport causing an evaporation time scale τe ) τv F/Fv where Fv is the density of the vapor phase.29,30 For our system, τv ) 0.25 s, τv ) 10-5 s, and τe ) 1-10 s. We see that the inertial time scale is compatible with the time scales of regime I in the retreating of water and the B1 region in the retreating of the CTAB solutions. The evaporative mechanism may account for regime II in the retreating of water, but is unlikely to account for the relaxation in the B2 region of the CTAB solutions at t > 10 s. Thus, the retreat in the surfactant solution is very likely controlled by the time evolution of surfactant self-assembly formation. The rearranging and self-assembling of surfactant molecules at the interfaces in the microscopic vicinity of the contact line drive a temporally evolving Young’s force on the contact line. It is the characteristic time of the evolution of this force that controls the latter stages of the autophobing. Figure 7. (a) Contact line position vs time during an autophobing event. (b) Contact line speed vs position during an autophobing event. The two vertical bars indicate the uncertainty in determining the B1/B2 boundary.
by spontaneous retreat and forced retreat at the same speed do not produce the same self-assemblies. Figure 6(a) shows the spontaneous retreating speed of the contact line vs time. We see different power law dependences on time in the B1 and the B2 regions, with powers -0.53 ( 0.21 and -0.892 ( 0.002, respectively. We note that these power-law behaviors for spontaneously retreating contact lines of surfactant solutions are very different than those for the spontaneous advancing of the contact line of simple fluids.26-28 To better understand the effect of surfactant self-assembly at the contact line on the spontaneous retreat, we compare the results above with the spontaneous retreat of pure water across a hydrophobic surface where only the hydrodynamics of a pure liquid is operating. To cause the spontaneous retreat of water, we pinned the contact line of water on the edge of a surface coated with a highly hydrophobic, Aquapel monolayer. By lowering the surface slowly into the bulk water, we depressed the contact line well below its equilibrium level. At some point the contact line released from the edge and jumped across the surface, in a fashion similar to the stick-jump behavior of CTAB solutions. We stopped moving the surface immediately after the jump and observed the spontaneous retreat of the water contact line. Figure 6(b) shows the change of contact line retreating speed vs time. We once again find two regimes (I and II) of retreating speed. However, all the retreating is completed in a much shorter time than the autophobing of the surfactant solution, indicating some mechanism unique to the surfactant solutions must be driving the retreat at least in the later stage of B2 region. Several mechanisms, each with their characteristic time scales, could control the contact line motion. In a system (25) Eskilsson, K.; Yaminsky, V. V. Langmuir 1998, 14, 2444. (26) Tanner, L. H. J. Phys. D: Appl. Phys. 1979, 12, 1473. (27) De Ruijter, M. J.; De Coninck, J.; Oshanin, G. Langmuir 1999, 15, 2209. (28) Suo, Y.; Stoev, K.; Garoff, S.; Rame´, E. Langmuir 2001, 17, 6988.
4. Summary We have probed the surfactant structures left behind an autophobing, i.e., a spontaneously retreating, contact line of two low concentration CTAB solutions. We have discovered transitions in wettability and in layer thickness/packing density through different regions left behind the contact line. Region A, never touched by the solution during the autophobing process but still surfactant coated, has the lowest thickness and/or largest area per molecule and is the most hydrophilic. Region C, created by either forced retreat or bulk fluid evaporation at a steady speed, has the highest thickness and/or smallest area per molecule and is the most hydrophobic. Region B, which the contact line sweeps across during the autophobing event, is a smooth transition from A to C despite a distinct break in contact line velocity behavior as it sweeps across the region. We have probed the detailed topographical structures in these regions with AFM and found them to have similar roughness and no evidence of molecular clustering. Molecules forming these self-assemblies pass through the contact line from either the liquid-vapor interface, the bulk fluid, or both. As they pass through the contact line, considerable molecular rearrangement occurs. The different retreating speeds during the spontaneous retreat create different molecular structures. In turn, the instantaneous structures of the self-assembled surfactant molecules in the microscopic vicinity of the contact line determine the time varying Young’s force that drives the spontaneous retreat. The essence of autophobing of ionic surfactant solutions lies in the interplay of surfactant self-assembling at the contact line and the driving of fluid motion by that self-assembly. Acknowledgment. We thank Barry Luokkala and Robert Tilton for valuable discussions. This work was supported by the National Science Foundation under research grant DMR-98022. LA011237R (29) Pomeau, Y. C. R. Acad. Sci. (Paris) 2000, 238, serie Iib, 1-6. (30) Andrieu, C.; Beysens, D. A.; Nikolayev, V. S. J. Fluid Mech. 2001., in press.
