Langmuir 2000, 16, 2957-2961
2957
Contact Angles on Surfaces with Mesoscopic Chemical Heterogeneity J. T. Woodward,† H. Gwin, and D. K. Schwartz* Department of Chemistry, Tulane University, New Orleans, Louisiana 70118 Received August 6, 1999. In Final Form: November 3, 1999 The contact angle of water was measured on surfaces composed of random hydrophilic and hydrophobic patches with typical length scales of 10-100 nm. By quenching self-assembled monolayers at various stages of growth, the fractional surface coverage of the hydrophobic patches was varied in the range 0.04-0.97 as determined by atomic force microscopy. The cosine of the contact angle of water cos θ was systematically lower than the prediction of the mean field Cassie equation cos θC. The deviation from this prediction cos θC - cos θ had an approximately linear dependence on the total contour length between hydrophobic and hydrophilic patches (a measure of the degree of heterogeneity). The contact angle was insensitive to droplet size, suggesting that line tension effects were minimal. Also, contact angles of hexadecane were in good agreement with the Cassie prediction. We propose two possible explanations for the observed behavior. Long-range (approximately 5 nm) hydrophobic interactions may result in a relatively hydrophobic boundary region around each hydrophobic patch which effectively increases the coverage of the hydrophobic phase altering the equilibrium contact angle. Alternatively, an increased density of “pinning” sites may prevent the contact angle from relaxing to the equilibrium value.
Introduction The wetting of solid surfaces by liquids has great practical importance because of its relevance to processes such as painting, coating, and lubrication.1 When the interfacial free energies satisfy the inequality γSV < γLV + γSL the liquid does not wet the solid at equilibrium and discrete droplets of liquid are observed. In this expression, γ is an interfacial free energy and the subscripts specify the particular interface (S ) solid, L ) liquid, and V ) vapor). For smooth and homogeneous surfaces, the “contact angle” at the three phase line is given by Young’s equation, cos θ ) (γSV - γSL)/γLV.2 For practical reasons, there is a good deal of interest in the effects of surface inhomogeneity and/or surface roughness on surface wetting and the subject has been studied for some time.3 A simple model for a heterogeneous surface is composed of “patches” of two types of surface phase. A mean field approach to this problem leads to an expression ascribed to Cassie4
cos θ ) χA cos θA+ χB cos θB where χA and χB ) 1 - χA are the fractional surface coverage of the A and B phases, respectively, and θA and θB are the contact angles on a surface composed purely of that phase. However, measured contact angles often differ significantly from this weighted average.5-8 Generally, the deviation is such that the measured value of cos θ is lower * To whom correspondence should be addressed. FAX: 504-8655596. Phone: 504-862-3562. E-mail:
[email protected]. † Current address: Biotechnology Division, National Institute of Standards and Technology, Gaithersburg, MD 20899. (1) deGennes, P. G. Rev. Mod. Phys. 1985, 57, 827. (2) Adamson, A. W.; Gast, A. P. Physical Chemistry of Surfaces, 6th ed.; John Wiley & Sons: New York, 1997. (3) Neumann, A. W. Adv. Colloid Interface Sci. 1974, 4, 105. (4) Cassie, A. B. D. Discuss. Faraday Soc. 1952, 75, 5041. (5) Woodward, J. T.; Ulman, A.; Schwartz, D. K. Langmuir 1996, 12, 3626. (6) Woodward, J. T.; Schwartz, D. K. Langmuir 1997, 13, 6873. (7) Bierbaum, K.; Grunze, M. Langmuir 1995, 11, 2143. (8) Drelich, J.; Wilbur, J. L.; Miller, J. D.; Whitesides, G. M. Langmuir 1996, 12, 1913.
than the Cassie prediction. The contact line on heterogeneous surfaces has been shown to be metastable, resulting in a range of possible values of cos θ, ranging between “advancing” or “receding” values. This contact angle hysteresis has traditionally been used to characterize surface heterogeneity3 and in recent years the subject has been addressed in several theoretical9-15 and experimental10,11,16-21 studies. In this paper we focus on surfaces that are flat but chemically heterogeneous on length scales in the range 10-100 nm (mesoscopic length scales). The surfaces are prepared by adsorption/self-assembly of amphiphilic molecules on flat mica surfaces and characterized by atomic force microscopy (AFM). The measured values of cos θ for water droplets are systematically lower than the Cassie equation prediction, and we show that the discrepancy can be quantitatively related to the degree of surface heterogeneity (as measured by the total contour length of the boundaries between phases per unit area). Previous contact angle measurements using hexadecane, however, were in good agreement with the Cassie equation.5 The insensitivity of the contact angle to droplet size suggests that line tension effects are minimal. Since hydrophobic interactions have been observed to extend a good distance into a water phase,22-26 this could mean that the lateral influence of hydrophobic islands may not (9) Joanny, J. F.; de Gennes, P. G. J. Chem. Phys. 1984, 81, 552. (10) Schwartz, L. W.; Garoff, S. J. Colloid Interface Sci. 1985, 106, 422. (11) Schwartz, L. W.; Garoff, S. Langmuir 1985, 1, 219. (12) Israelachvili, J. N.; Gee, M. G. Langmuir 1989, 5, 288. (13) Swain, P. S.; Lipowsky, R. Langmuir 1998, 14, 6772. (14) Wolansky, G.; Marmur, A. Langmuir 1998, 14, 5292. (15) Frink, L. J. D.; Salinger, A. G. J. Chem. Phys. 1999, 110, 5969. (16) di Meglio, J. M. Europhys. Lett. 1992, 17, 607. (17) Andrieu, C.; Sykes, C.; Brochard, F. Langmuir 1994, 10, 2077. (18) Decker, E. L.; Garoff, S. Langmuir 1996, 12, 2100. (19) Decker, E. L.; Garoff, S. Langmuir 1997, 13, 6321. (20) Joanny, J. F.; Robbins, M. O. J. Chem. Phys. 1990, 92, 3206. (21) Kumar, S.; Reich, D. H.; Robbins, M. O. Phys. Rev. E 1995, 52, R5776. (22) Israelachvili, J. N.; Pashley, R. M. Nature 1982, 300, 341. (23) Israelachvili, J. Intermolecular and Surface Forces; Academic Press: London, 1991. (24) Hato, M. J. Phys. Chem. 1996, 100, 18530.
10.1021/la991068z CCC: $19.00 © 2000 American Chemical Society Published on Web 01/08/2000
2958
Langmuir, Vol. 16, No. 6, 2000
Woodward et al.
Figure 1. AFM images (1 µm × 1 µm) of partial self-assembled monolayers of OPA on mica. The height of high features is approximately 2 nm. The annotation on each image indicates the immersion time in 0.2 mM solution.
end immediately at a surface boundary, but may continue into a boundary region with some finite width. Our results are explained if we use a width of about 5 nm, well within the range of hydrophobic interactions that have been measured experimentally.24 An alternative explanation is that the number of “pinning” points for the contact line may vary systematically with heterogeneity, affecting the degree of relaxation toward the equilibrium contact angle. Experimental Details Self-assembled monolayers (SAMs) of octadecylphosphonic acid (OPA) were deposited by immersing freshly cleaved mica disks into solutions with concentration in the range 0.01-2 mM (using tetrahydrofuran as a solvent) for various immersion times. The details of OPA synthesis were reported previously.5 The samples were imaged with a Nanoscope III atomic force microscope (Digital Instruments; Santa Barbara, CA). All images were taken in contact mode using silicon nitride tips in air under ambient conditions. AFM images and IR spectra showed that these incomplete SAMs were partially covered by densely packed submonolayer “islands” of OPA.5,6,27-30 Therefore, the fractional surface coverage of the monolayer could be quantitatively determined using image analysis. Surface coverage was calculated using two different methods: one involving the height histogram of a given image5,6 and another using edge detection to count pixels belonging to individual islands.29,30 The error bars indicated in the figures are a combination of statistical uncertainties obtained from analyzing AFM images from at least six widely separated locations on each sample and errors associated with discrepancies between the two measurement methods (there was no systematic trend in this discrepancy). For both methods, care was taken to compensate for the effects of convolution with the AFM tip. To perform an approximate deconvolution of the AFM tip size from individual island size we examined the apparent half-width at halfmaximum of cross sectional profiles of the smallest observable islands in both vertical and horizontal directions-for use as an upper limit. From these we established that convolution with this particular tip added approximately 7.0 nm to the radius at half max of an island. If one assumes a spherical tip and an island height of 2 nm, this implies a tip radius of 26 nm, which is within the typical range observed for these integral silicon nitride tips. This number was used to correct the size of islands as well as in the calculation of total coverage.29,30 Since the peak in the histogram corresponding to pixels that are part of islands was often asymmetric because of tip convolution effects at island edges (in particular, this peak has a prominent shoulder), we computed the surface coverage by doubling the integrated intensity of the “high” half of this peak.5,6,28 (25) Craig, V. S. J.; Ninham, B. W.; Pashley, R. M. Langmuir 1999, 15, 1562. (26) Ederth, T.; Claesson, P.; Liedberg, B. Langmuir 1998, 14, 4782. (27) Woodward, J. T.; Schwartz, D. K. J. Am. Chem. Soc. 1996, 118, 7861. (28) Woodward, J. T.; Doudevski, I.; Sikes, H. D.; Schwartz, D. K. J. Phys. Chem. B 1997, 101, 7535. (29) Doudevski, I.; Hayes, W. A.; Schwartz, D. K. Phys. Rev. Lett. 1998, 81, 4927. (30) Doudevski, I.; Schwartz, D. K. Phys. Rev. B 1999, 60, 14.
The boundary lengths were taken from the same AFM images that were used to determine surface coverage. The images were made binary using a thresholding procedure and the number of pixels at the boundary were determined. Uncertainties due to arbitrary choice of the threshold level were estimated by varying the threshold level within a reasonable range and comparing the resulting number of boundary pixels. The error bars shown in the figures are a combination of this experimental uncertainty and the statistical uncertainty from analyzing several images from macroscopically separated regions of each sample. Contact angle measurements were made using a custom-built contact angle goniometer. For measurements of the so-called “static” contact angle, we followed a procedure described by Bain et al.31,32 in which a 1 µL drop was formed at the end of a needle and brought into contact with the surface. The needle was removed and the contact angle measured. Contact angles were measured from both sides of 3-5 droplets on each sample, and the mean and standard deviation of these measurements are reported (the typical uncertainty is in the range (1-2°). To measure advancing or receding contact angles, the angle was measured as a microliter syringe was used to add liquid to or remove liquid from the drop. The contact angle measurements were improved over those in a previous publication5 in that they were performed under saturated vapor pressure conditions.
Results Typical AFM images of the partial self-assembled monolayers (SAMs) are shown in Figure 1. These images were from samples immersed in 0.2 mM solution for various times (annotated on images). However, samples used in this study were made with a wide range of solution concentration and immersion times. Systematic AFM, wettability, and infrared studies5,6,27-30 have lead us to the following understanding of the surface structure. Bright areas represent islands (1.9 ( 0.2 nm high) of closely packed well-ordered OPA molecules. These islands are terminated by methyl groups and are, therefore, quite hydrophobic. The dark regions between islands represent either bare mica or a very dilute layer of isolated adsorbed OPA molecules. These regions are relatively hydrophilic. As the images demonstrate, the typical length scales of surface heterogeneity are in the range 10-100 nm. Figure 2 shows the measured cos θ of water plotted against the measured fractional surface coverage of the monolayer islands. Each data point represents an individual sample. The dark circles and squares are intended to highlight two sets of four samples each that displayed a particularly large range of contact angle although the surface coverages were identical within experimental uncertainties. The solid line represents an estimate of the Cassie equation prediction. The high coverage endpoint corresponds to a contact angle of 95°, which was a typical measurement for “complete” films. The low coverage (31) Bain, C. D.; Troughton, E. B.; Tao, Y.-T.; Evall, J.; et al. J. Am. Chem. Soc. 1989, 111, 321. (32) Bain, C. D.; Whitesides, G. M. Angew. Chem. 1989, 101, 522.
Contact Angles on Surfaces
Figure 2. The cosine of the contact angle of water versus the fractional island coverage of the OPA monolayer as measured by AFM. Two groups of samples are indicated by special symbols (filled squares or circles) for comparison with the same samples in Figures 3 and 4. The line indicates the prediction of the Cassie equation as discussed in the text.
Langmuir, Vol. 16, No. 6, 2000 2959
Figure 4. The cosine of the contact angle of water corrected by a term proportional to the measured boundary length per unit area of that particular sample versus the island coverage of the same sample. The solid line is the Cassie equation prediction.
4.6 ( 0.2 nm. If we use the linear dependence as a correction to cos θ (Figure 4), we find that, except for a few outlying points, the data are all now in agreement with the Cassie equation. Discussion
Figure 3. The deviation of the measured cos θ from that predicted by the Cassie equation plotted against the total length per unit area of the boundary between high and low regions in the AFM images. The solid line is the best fit to the data going through the origin.
endpoint corresponds to a contact angle of about 20° and was determined by extrapolating the data to zero coverage. If the regions between islands were completely bare, one would expect the data to extrapolate to unity at zero coverage. However, since there is most likely a dilute coverage of adsorbed molecules in the “low” surface phase, it is reasonable to postulate a non-zero contact angle of this phase. The contact angle hysteresis measured on selected samples was quite large, typically greater than 20°, and an order or magnitude larger than the reproducibility of the static contact angle from drop to drop on the same surface. There is a clear and systematic deviation of the measured cos θ from the Cassie equation prediction. Moreover, the scatter of the data is significantly larger than the experimental uncertainties (in the cos θ coordinate). This led us to explore a possible connection between the contact angle and the actual morphology of the surface beyond the simple issue of fractional surface coverage. Given the lack of a theoretical prediction as to how the morphology might affect the static contact angle, we took a phenomenological approach. One morphological parameter that is straightforward to measure is the total contour length between surface phases per unit area (L h ). This parameter is related to the degree of heterogeneity of the surface. In fact, as shown in Figure 3, the deviation of cos θ from the Cassie prediction (∆ cos θ ) cos θC - cos θ) has an approximately linear dependence on L h for the samples we measured. The slope of the best linear fit to the data (constrained to pass through the origin) is w )
Although the correlation between ∆ cos θ and boundary length shown in Figure 3 is compelling, we must be careful to point out that it is possible that the apparent dependence is, in fact, “accidental”. For example, we do not have independent control over coverage and morphology and there is likely to be some correlation between coverage and boundary length. Certainly the samples with very small boundary lengths are all at very low or very high coverage. By preparing samples from different solution concentrations, however, we can bias the competition between island nucleation and island growth.29 These two processes lead to samples with relatively large and small boundary lengths, respectively. This is noticeable in the substantial intermediate coverage range where there is a fair amount of scatter. For example, if one considers the cluster of data at a coverage of 0.20 ( 0.02 (filled squares in Figures 2-4) or the cluster at a coverage of 0.31 ( 0.02 (filled circles in Figures 2-4), one finds a fairly large range of cos θ values in Figure 2. These samples are depicted by the same symbols in Figure 3 and it is clear that even for samples with the same coverage (within experimental error) there is good correlation between ∆ cos θ and boundary length (which varies by nearly a factor of 2). If we consider that L h -1 is an approximate measure of the average feature size, the effective range of feature size in our experiments is 20-100 nm. Previous systematic studies of wetting on heterogeneous surfaces, where the surface structure was directly characterized, used patterning techniques which resulted in patterns having oneor two-dimensional periodicity with lateral dimensions of 10 µm or larger.8,10,11,33,34 Since the contour length density of these surfaces is at least 2 orders of magnitude smaller than the smallest value we report, we would expect effects such as we observe to be minute on such samples. Also, close observations of contact angles on such “large” patterns often reveal that the droplet boundary is not uniform, particularly when the three-phase line crosses many boundaries, instead it is corrugated in relation to the underlying pattern. In these cases, the macroscopic (33) Wiegand, G.; Jaworek, T.; Wegner, G.; Sackmann, E. J. Colloid Interface Sci. 1997, 196, 299. (34) Neumann, A. W.; Godd, R. J. J. Colloid Interface Sci. 1972, 38, 341.
2960
Langmuir, Vol. 16, No. 6, 2000
contact angle can deviate from the Cassie prediction. Both the large scale of the pattern as well as the severe anisotropy created by stripes make the situation quite different from the one we consider with random, mesoscopic heterogeneity. Theory and calculations related to contact angles on heterogeneous surfaces fall into several categories. Some have been aimed at explaining wetting on the macroscopically patterned surfaces mentioned above.13,15,35 Others are appropriate for a dilute density of isolated defect sites9 and still another, developed to explain molecularscale heterogeneity12 predicts that measured contact angles will be smaller than predicted by the Cassie equation instead of larger as we observe. Since our experiments fall into a different regime of heterogeneity than are considered by these theories, the specific predictions may not be directly applicable. However, the general picture of contact line motion on heterogeneous surfaces as a progression from one metastable state to another10,11,16-21,36 is an important framework from which to view our results. One explanation for a deviation from the Cassie equation may be the existence of a line tension13,14,37 acting at the contact line. If this were the case, then ∆ cos θ should be inversely proportional to the droplet size. There have been reports of such measurements with values of the line tension on the order of 1 µJ/m.38,39 In other cases, however, the variation in the contact angle with droplet size was extremely small, nonexistent, or even negative.8 For our samples, the change in contact angle was generally within experimental uncertainty ((1°) when the droplet diameter was varied in the range 1.5-6 mm (these experiments were performed on six representative samples). When the contact angle did change with droplet size, no distinct trend was observed, the change was essentially random. Presumably this was due to pinning at isolated defect sites that became more likely with larger droplets. Therefore, we cannot ascribe the relatively large deviations from the Cassie equation shown in Figure 1 to a line tension. Although the Cassie equation provides a prediction of how the equilibrium contact angle depends on heterogeneity, it is not clear that our measured contact angles are good representations of the equilibrium values. In general, one expects that a droplet will have a contact angle somewhere in the range between the receding and advancing angles. In the sessile drop technique, the contact line advances as the drop is placed on the surface. After the spreading is finished, there is some amount of relaxation toward the equilibrium angle. It has been shown that the amount of relaxation is related to the type and amount of mechanical vibrations.17,18 Therefore, the measured static contact angle (and even the measured advancing and receding angles) are sensitive to the vibrations to which the interface is exposed. Clearly, removal of the needle results in significant vibrations applied to the droplet. Although the process is not controlled carefully, the results are surprisingly reproducible from droplet to droplet on the same surface. This suggests that, in fact, the vibrational history of each droplet is fairly similar.18 An important question is whether the trend of this reproducible value with the length scale of surface heterogeneity reflects an underlying (35) Lenz, P.; Lipowsky, R. Phys. Rev. Lett. 1998, 80, 1920. (36) Good, R. J. J. Am. Chem. Soc. 1952, 75, 5041. (37) Marmur, A. Colloids Surf. A 1998, 136, 81. (38) Li, D.; Neumann, A. W. Coll. Surf. 1990, 43, 195. (39) Duncan, D.; Li, D.; Gaydos, J.; Neumann, A. W. J. Colloid Interface Sci. 1995, 169, 256.
Woodward et al.
trend of the equilibrium contact angle. Another possibility is that the degree of relaxation may vary systematically with surface heterogeneity. We briefly describe scenarios which could explain each of these two possibilities. Hydrophobic interactions near boundaries on the surface could explain why the equilibrium contact angle would vary with the length scale of surface heterogeneity. Direct measurements of attraction between hydrophobic surfaces immersed in water have revealed interactions that extend tens of nanometers.22-26 Although some of the longer range interactions may be due to factors not strictly related to surface hydrophobicity, a recent estimate by Hato24 put the extent of true hydrophobic interactions in the range 5-20 nm. If the effect of a hydrophobic surface is felt at these distances in the direction normal to the surface it is reasonable to expect that the influence of a hydrophobic patch on the surface will extend laterally past its boundary as well. This would also explain why contact angle measurements on the same samples using hexadecane were in good agreement with the Cassie equation.5 A simple model can be based on three types of surface region, hydrophobic, hydrophilic, and boundary. The coverage of the boundary region is equal to the boundary length per unit area times a boundary width. An extended version of the Cassie equation incorporating three surface phases could then be used:
cos θ ) χM cos θM + χS cos θS + χB cos θB where the subscript M refers to monolayer, S to subh , where strate, and B to boundary. We can take χB ) wL w is the (unknown) boundary width, and as an lower limit we can approximate cos θB ) cos θM. The prediction then reduces to
cos θ ) (χM + wL h ) cos θM + (1 - χM - wL h ) cos θS and effectively amounts to the monolayer coverage being offset by an amount proportional to the boundary length. Reducing further gives ∆ cos θ ) wL h (cos θS - cos θM) ≈ wL h . The value of w that is consistent with the data is approximately the slope of Figure 3, i.e., w ) 4.6 ( 0.2 nm. This is a lower limit of the boundary width based on the approximations made; however, it is well within the range of the hydrophobic interaction measured in surface force apparatus experiments. On the other hand, the measured static contact angles may not truly reflect a trend in the equilibrium contact angle. It is possible that the equilibrium contact angle is, in all cases, in good agreement with the Cassie equation but that the degree of relaxation toward the equilibrium value is systematically smaller as the length scale of the surface heterogeneity gets smaller. This could be due to an increase in the number of strength of “pinning” sites for the contact line. In this context, the agreement of the measured hexadecane contact angles to the Cassie prediction may be because the hydrophilic/hydrophobic boundaries represent defects in the “weak pinning” limit while the same boundaries are “strong pinning” with respect to water. These two pictures, based on equilibrium and dynamic considerations respectively, are mutually exclusive and the current experimental results cannot convincingly distinguish between the two. Similar experiments on wellcharacterized surfaces where the vibrational level is carefully controlled and varied could provide more reliable measurements of the average equilibrium contact angle17,18 and help to resolve this question.
Contact Angles on Surfaces
Conclusions Systematic measurements of contact angles were made on chemically heterogeneous surfaces where the length scale of the heterogeneity was in the range 10-100 nm. These model surfaces were prepared by self-assembly and characterized by AFM. The cosine of the contact angle of water cos θ was systematically lower than the prediction of the mean field Cassie equation, cos θC. The deviation from this prediction cos θC - cos θ had an approximately linear dependence on the amount of boundary between hydrophobic and hydrophilic patches (a measure of the degree of heterogeneity). The contact angle was insensitive to droplet size, suggesting that line tension effects were minimal. Also, contact angles of hexadecane are in good
Langmuir, Vol. 16, No. 6, 2000 2961
agreement with the Cassie prediction. One explanation for these observations is that long-range (approximately 5 nm) hydrophobic interactions result in a relatively hydrophobic boundary region around each hydrophobic patch which effectively increases the coverage of the hydrophobic phase. Another possibility is that the dynamic relaxation of the contact angle toward the equilibrium value depends systematically on the length scale of surface heterogeneity. Acknowledgment. We thank Abraham Ulman for preparation of the OPA. This work was supported by the National Science Foundation (Grant CHE-9614200). LA991068Z
