Contact Line Structure and Dynamics on Surfaces with Contact Angle

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Contact Line Structure and Dynamics on Surfaces with Contact Angle Hysteresis E. L. Decker and S. Garoff* Department of Physics and Colloids, Polymers, and Surfaces Program, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 Received May 21, 1997. In Final Form: September 8, 1997X We examine the wetting properties of surfaces coated by organic monolayers having varying degrees of chemical damage. Macroscopic contact angles and contact angle hysteresis energy serve as one characterization of the surfaces. Measurement of contact line structure to micron resolution over centimeter lengths serves as another characterization. We also examine the dynamics of jumps along the contact line in the different regions around a contact angle hysteresis loop. We investigate the scaling of pinning and elastic energies and the influence of gravity in dictating contact line roughness at various length scales. We measure an approximate power-law for contact line roughness versus length scale. Contrary to many models for weak heterogeneity and dilute pinning, we see no correlation between contact line roughness and contact angle hysteresis. However, the contact line roughness does correlate with the contact angle. These observations reconfirm the dense, strong pinning nature of our surfaces. Qualitative energy functionals provide a useful language for examining and describing the results.

1. Introduction Wetting of solids by liquids is ubiquitous in industrial processes and nature. The sensitive dependence of wetting behavior on the details of the chemical nature and physical roughness of a surface has been long established.1,2 For physically and chemically homogeneous solid surfaces, wetting characteristics are well defined.1,3,4 Surfaces sufficiently homogeneous to exhibit such well-defined properties are almost impossible to attain. The wetting characteristics of the heterogeneous surfaces which pervade laboratory, industrial, and natural settings are still a matter of investigation. Such research is necessary to explain, predict, and control the wetting of ambient surfaces. The movement of a liquid over a heterogeneous solid surface is a specific example of the more general problem of an elastic interface moving through a medium with a randomly varying potential energy. The interface becomes pinned at sites within the disordered medium. The elasticity of the interface attempts to smooth over the deformations caused by the pinning sites. For wetting of a solid by a liquid, the liquid-vapor interfacial tension provides the elastic forces. At long length scales, gravity also smoothes the interface. The pinning forces can be produced by boundaries separating regions of different surface chemistry or by physical roughness. For a homogeneous surface there are no pinning forces. Figure 1 shows wetting of a solid plate, held vertically in a liquid, and defines quantities that characterize such a wetting system. The locus of points where the three phases (solid, liquid, and vapor) meet is called the contact line. The angle, θ, within the liquid between the solid-liquid and liquid-vapor interfaces at the contact line is called the contact angle. For this special case of a homogenous solid surface, the contact line is flat and everywhere perpendicular to the force of gravity. The contact angle * Author to whom correspondence should be sent. X Abstract published in Advance ACS Abstracts, November 1, 1997. (1) Zisman, W. A. In Contact Angle, Wettability and Adhesion; Fowkes, F., Ed.; Advances in Chemistry Series, Vol. 43; American Chemical Society: Washington, DC, 1964; Chapter 1. (2) Johnson, R. E., Jr.; Dettre, R. H. In Surface and Colloid Science; Matijevic´, E., Ed.; Wiley: New York, 1969; Vol. 2, pp 85-153. (3) Neumann, A. W. Adv. Colloid Interface Sci. 1974, 4, 105. (4) Joshi, Y. P. Eur. J. Phys. 1990, 11, 125.

S0743-7463(97)00528-3 CCC: $14.00

Figure 1. Wilhelmy plate geometry of a partially-immersed, vertical plate. h ) rise height. θ ) contact angle. CL ) contact line.

is well defined in terms of the interfacial energies for the solid-liquid, solid-vapor, and liquid-vapor interfaces.3,4 Historically, the simple characterization of the energetics of surfaces by contact angles has been fraught with irreproducibility and the fact that if a liquid advanced over a surface, the measured static contact angle was larger than if the liquid receded from the surface before the measurement.2 This behavior, called contact angle hysteresis, was shown to be the result of physical surface roughness and chemical heterogeneity.2 Various models have attempted to explain and predict the affect of such surface heterogeneity on contact angle hysteresis and contact line structure and dynamics.5-22 Theoretical (5) Neumann, A. W.; Good, R. J. J. Colloid Interface Sci. 1972, 38, 341. (6) Eick, J. D.; Good, R. J.; Neumann, A. W. J. Colloid Interface Sci. 1975, 53, 235. (7) Joanny, J. F.; de Gennes, P. G. J. Chem. Phys. 1984, 81, 552. (8) Pomeau, Y.; Vannimenus, J. J. Colloid Interface Sci. 1985, 104, 477. (9) Schwartz, L. W.; Garoff, S. J. Colloid Interface Sci. 1985, 106, 422. (10) Schwartz, L. W.; Garoff, S. Langmuir 1985, 1, 219. (11) Robbins, M. O.; Joanny, J. F. Europhys. Lett. 1987, 3, 729. (12) Li, D.; Neumann, A. W. Colloid Polym. Sci. 1992, 270, 498. (13) di Meglio, J.-M.; Europhys. Lett. 1992, 17, 607. (14) Nadkarni, G. D. The Complex Microscopic Contact Line Motion on Ambient Surfaces. Ph.D. Thesis, Carnegie Mellon University, Pittsburgh, PA, 1993. (15) Raphael, E.; Joanny, J. F. Europhys. Lett. 1993, 21, 483. (16) Andrieu, C.; Sykes, C.; Brochard, F. Langmuir 1994, 10, 2077. (17) Collet, P.; De Coninck, J.; Dunlop, F. J. Stat. Phys. 1994, 75, 37.

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models have focused on dilute, randomly positioned defects; patterned defects; and weakly pinning, continuous heterogeneity.5-12,15,17-20 In recent years, experimental models of heterogeneous surfaces have focused on patterned heterogeneity and dilute, strong pinning defects.13,14,16,21,22 Laboratory model surfaces with continuous heterogeneity mimic the complex contact line behavior of most heterogeneous surfaces.23,24 This complex behavior is not exhibited by patterned or dilute, strong defect models.25 We will show that new experimental and theoretical models are needed for a quantitative understanding of wetting on dense, strongly pinning, heterogeneous surfacessthe surfaces in common technological and everyday experience. In our studies of wetting behavior on heterogeneous surfaces, we have examined whether models of weak pinning or dilute, strong pinning are applicable for such surfaces. For instance, do contact line jumps and contact line roughness correlate with contact angle hysteresis, as suggested by the models? Do the elastic and pinning forces controlling contact line roughness scale with length? Does gravity participate as expected in wetting behavior? Can energy barriers, as discussed in models of the energy functional describing wetting, describe the microscopic structure and dynamics of contact lines and macroscopic contact angle hysteresis? Examination of both macroscopic and microscopic features of contact line structure and dynamics is necessary for a full understanding of wetting. Thus, there is a need to move beyond force measurements on large samples,26 which hide the nature of the individual jumps, and force measurements on small samples,27 which hide the essential coupling of events. In this paper, we first give background information for the description and analysis of contact angles and contact line structure and dynamics. We describe our experimental materials (the liquids and the heterogeneous surfaces). We then describe our experimental procedures for measuring contact angles, imaging contact lines to high resolution over macroscopic lengths, and tracking contact line dynamics for the slow motion of the solid surface relative to the bulk liquid. In the discussion of our results, we make frequent connections to energy barriers and the competition of elastic and pinning forces. 2. Background 2.1. Contact Angles. On heterogeneous solid surfaces, the local contact angle varies spatially across the surface. This is observed in the deformations of the contact line from the ideal, smooth shape that the contact line would have on a perfectly homogeneous surface with one value of contact angle at all points on the surface. The local contact angle is the boundary condition for the differential equation governing the shape of the liquid-vapor interface. Deformations of the contact line due to surface heterogeneity (and thus spatially varying values of the local contact angle) lead to deformations of the curved liquid-vapor interface which extend out from the contact line to distances comparable to the length of the contact (18) Crassous, J.; Charlaix, E. Europhys. Lett. 1994, 28, 415. (19) Mahale, A. D.; Wesson, S. P. Colloids Surf. A 1994, 89, 117. (20) Marmur, A. J. Colloid Interface Sci. 1994, 168, 40. (21) De Jonghe, V.; Chatain, D. Acta Metall. Mater. 1995, 43, 1505. (22) Drelich, J.; Wilbur, J. L.; Miller, J. D.; Whitesides, G. M. Langmuir 1996, 12, 1913. (23) Nadkarni, G. D.; Garoff, S. Langmuir 1994, 10, 1618. (24) Decker, E. L.; Garoff, S. Langmuir 1996, 12, 2100. (25) Decker, E. L.; Garoff, S. J. Adhes. 1997, 63, 159. (26) Johnson, R. E., Jr.; Dettre, R. H. In Wettability; Berg, J. C., Ed.; Surfactant Science Series, Vol. 49, Marcel Dekker: New York, 1993; Chapter 1. (27) Sauer, B. B.; Carney, T. E. Langmuir 1990, 6, 1002.

Decker and Garoff

line deformation.7 A macroscopically-averaged contact angle is obtained by averaging local contact angles over a macroscopic length along the contact line. This averaged angle gives the boundary condition predicting the macroscopic interface shape of the fluid body at distances further from the contact line than the deformations of the liquid-vapor interface extend. Thus, the use of the contact angle dictates whether local or macroscopically-averaged angles should be considered.25 On typical heterogeneous surfaces, macroscopic contact angles can take on any value within fairly reproducible extremes. The value of the contact angle depends on the history of the motion of the bulk liquid relative to the solid surface. On heterogeneous surfaces, the motion of the solid surface or bulk liquid can move the liquid-vapor interface with no motion of the pinned contact line relative to the solid. This can increase or decrease the contact angle. If such motion increases the contact angle, then the maximum angle attained just before the contact line unpins and advances further across the solid, displacing solid-vapor interface by new solid-liquid interface, is called the advancing contact angle. The minimum value, the receding contact angle, occurs for the opposite motion. 2.2. Contact Angle Hysteresis. Hysteresis in general is characterized by metastable states for the individual microscopic domains of a system.28-30 The averaged behavior of all the microscopic domains produces the value of a dependent macroscopic variable. Often, characterization of hysteresis involves measuring the change in this macroscopic dependent variable for variation of an independent variable. For a hysteretic system, the dependent variable attains different values depending on the history of variation of the independent variable. Irreversible energy loss occurs when variation of the independent variable causes energy barriers to decrease and microscopic domains, individually trapped in metastable states, to jump quickly to lower energy states. This motion is controlled by the system and is independent of the rate of change of the independent variable. Since the variation of the independent variable can be made quasistatic, the net energy lost in the microscopic jumps should relate to the macroscopic energy lost in traversing the hysteresis loop of the dependent variable versus the independent variable. For examination of contact angle hysteresis in terms of dependent and independent variables, it is useful to consider the Wilhelmy plate geometry. This geometry, used in our experiments, consists of a solid plate held vertically and partially immersed in a liquid (Figure 1). Far from the plate, the bulk liquid has a flat liquid-vapor interface, perpendicular to the force of gravity. Approaching the solid along the liquid-vapor interface, the meniscus either rises upward or is depressed downward to meet the solid, depending on the macroscopic contact angle. For a contact angle hysteresis cycle, the independent variable is the position of the solid surface in the laboratory reference frame. The plate can be moved up or down. For simple analysis, the dependent variable could be the macroscopic rise height, h, or contact angle, θ. For a measure of macroscopic energy per unit length of contact line, the dependent variable should be the cosine of the macroscopic contact angle multiplied by the liquid-vapor interfacial energy. We will trace through a contact angle hysteresis cycle and will discuss the contact line structure and dynamics (28) Everett, D. H.; Whitton, W. I. Faraday Soc. Trans. 1952, 48, 749. (29) Everett, D. H.; Smith, F. W. Faraday Soc. Trans. 1954, 50, 187. (30) Everett, D. H. Faraday Soc. Trans. 1954, 50, 1077.

Surfaces with Contact Angle Hysteresis

as well as the energy of the system. First we briefly review the energy per unit length of contact line in the Wilhelmy plate geometry.5,9,10,12,24 With the approximation of small slope of the liquid-vapor interface10 and ignoring the energy of contact line deformation, the total energy per unit contact line length depends quadratically on the rise height.9,10 (See Figure 2 in ref 9.) The minimum energy occurs at the rise height given by the “Cassie” average.31 A curve with increasing slope away from its global equilibrium should hold even if the small slope approximation for the liquid-vapor interface is not met and an exact parabolic shape is not maintained. This curved “spine” energy functional accounts for the gravitational potential energy, the elastic energy of the stretched liquidvapor meniscus (with the rough contact line replaced by a flat one), and the wetting energy for the areal average of the local differences between the solid-liquid and solidvapor interfacial energies. The spine is fixed relative to the bulk fluid level and does not change as the solid surface is moved up or down in the Wilhelmy plate geometry. Each local section of the true, broken contact line will have the same spine energy (due to the average contact line position); but additional functionality must account for the extra gravitational, elastic, and wetting energy caused by the local deformation of the contact line from its average position. This defect energy depends on the wettability of a local vicinity of the surface and is fixed relative to the plate. Variational changes in the local configuration of the contact line in the vicinity of the point being considered determine the dependence of the defect energy on the local rise height. Adding this defect energy to the spine evaluated at the rise height of the local section of the contact line produces a confining energy barrier that pins that section of the contact line. The size of this barrier will depend on both the defect energy and the spine energy functionals. In determining the total energy for a local section of the contact line, movement of the plate relative to the bulk liquid level does not change the defect energy, since it is fixed on the plate. However, motion of the plate causes the defect energy to be added at varying positions along the spine. Addition at the base of the spine, where the spine slope is small, produces the largest energy barriers. Addition where the spine is steep produces smaller barriers. The total energy for variational changes in the rise height of a local section of the contact line has an energy barrier to moving to a lower energy, and the size of the barrier can be changed by moving the solid surface relative to the bulk level. Having described the energy barriers proposed to be responsible for contact angle hysteresis, we now qualitatively examine the contact angle hysteresis cycle which arises from this picture (Figure 2). Beginning with the macroscopically-averaged rise height (or contact angle) at its advance value (point 1), all of the energy barriers are small (at a steep part of the spine). If the solid is raised, the macroscopic rise height increases (moving toward point 2), and the energy barriers increase (at less steep slopes along the spine). The energy barriers are the largest as the macroscopic rise height moves through the global equilibrium of the spine energy functional. Further motion of the solid out of the bulk liquid (somewhere between points 1 and 2) causes the energy barriers to begin to decrease, as they shift to positions on the other side of the spine where the spine slope is again increasing. From points 1 to 2 in Figure 2, the contact line, trapped by energy barriers, is pinned across its entire length. As the macroscopic rise height approaches its recede value, (31) Cassie, A. B. D. Discuss. Faraday Soc. 1948, 3, 11.

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Figure 2. Contact angle hysteresis loop for the Wilhelmy plate geometry. Rise height averaged over a 330 µm field of view versus plate position in the laboratory frame. The plot is compressed (jagged lines on vertical axes) to show the detail of experimental data (O) for water on sample AA1. The horizontal extent of the loop is arbitrary, depending on the length of plate travel within the flicker regime. The numbers are referenced in text.

some energy barriers are lowered far enough that microscopic sections of the contact line break loose from their pinned conditions and jump to new positions. These first jumps occur near the corner (point 3). The jumps occur either because the energy barriers are decreased to zero or because vibrational energy can cause local sections of the contact line to overcome the decreased barriers.2,10,12,24 When the system reaches the recede condition, the contact line “flickers” with continuous jumping and rearrangement (point 4). If the direction of motion of the solid is now reversed, the energy barriers increase, the contact line becomes repinned across its entire length, and the macroscopic rise height begins to decrease. The energy barriers increase until the system again passes through the global equilibrium, over to the other side of the spine energy functional (between points 5 and 6). As the solid continues to move and the macroscopic rise height approaches its advance value, the energy barriers decrease until microscopic sections of the contact line depin and again cause jumping events. These jumps begin near the corner, at point 7 in Figure 2. The flicker regime in the advance condition is marked at point 8. The area of the hysteresis loop is related to the irreversible energy loss from the microscopic jumping events. In the absence of vibrations, the loop should remain open even in the limit as the plate speed goes to zero. The existence of the energy barriers which pin the contact line and result in the dissipative jumps must account for macroscopic contact angle hysteresis. Thus, the vertical openness of the loop and the amount of hysteresis must be controlled by characteristics of the heterogeneous surface wettability which lead to the energy barriers. Examination of contact lines on approach to advance and recede should provide insight to the jumping events associated with contact angle hysteresis. 2.3. Competing Forces and Contact Line Structure. We study the rough structure of contact lines by analysis of the root mean square (rms) width of contact line configurations calculated over different length scales. Theories of wetting on random, heterogeneous surfaces suggest a power-law dependence of the rms width measured over different length scales arising from simple scaling mechanisms for the forces smoothing and roughening the contact line.11,32 Surface tension forces, arising from the elastic energy discussed in section 2.2, and gravitational forces tend to smooth the contact line, as

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dictated by the Laplace equation.5 Surface tension opposes the distortions of the liquid-vapor interface, including high curvatures along the contact line. Gravity (with an appropriate volume constraint on the system) opposes height variations of the liquid-vapor interface (including those at the contact line). Examining contact line roughness on various length scales provides information about how the relative strengths of the competing forces change with length. Consider the deformation of the contact line due to pinning forces in the absence of gravity. Both the elastic energy of the deformation and the pinning energy of the local wettability are greater for larger distortions (vertical amplitude and horizontal extent along the contact line). For random, weakly pinning surface heterogeneity, the elastic energy and pinning energy should increase with increasing length scale in a power-law fashion, with prefactors that depend on the solid-liquid, solid-vapor, and liquid-vapor interfacial energies.11 However, the exponent for the elastic energy power-law may be different from that for the pinning energy power-law. The relative scaling of the elastic and pinning energies should govern the scaling of contact line roughness with length scale. With assumptions of weak, random heterogeneity and ignoring gravitational potential energy, the rms width, w, (to be defined in section 3.4) of a contact line is predicted to scale with length, L, as11

w(L) ∝ LR

(1)

where R ) 1/2 for L < Ld and R ) 1/3 for L > Ld. The characteristic length, Ld, arises from considering the most energetically favorable distortions of the contact line. Ld is the minimum length of contact line over which the contact line distorts from its average position by a distance equal to the defect correlation length.11 Even if the assumptions of weak, random heterogeneity are not met (as for surfaces we examine), the contact line roughness may exhibit a roughness exponent, R, which is indicative of the relative scaling of the elastic and pinning energies. Gravity introduces extra smoothing at long length scales. The capillary length is the length scale where gravitational forces are of the same order of magnitude as surface tension. It is defined as

a)

( ) γlv ∆Fg

1/2

(2)

where γlv is the liquid-vapor surface tension, ∆F is the density difference between the liquid and the vapor, and g is the acceleration of gravity. For length scales much less than the capillary length, gravitational forces are negligible compared to surface tension, and so the contact line structure will be governed by the competition of the pinning forces with surface tension. As the length scale grows and approaches the capillary length, the contribution from gravity increases. Thus, we would expect a transition in w(L) near the capillary length. For length scales much greater than the capillary length, gravitational forces are much larger than surface tension, and so pinning forces will compete mainly with gravity. At large enough length scales, w(L) will saturate due to gravity. Nonstationarity in the wetting characteristics on length scales larger than the capillary length may cause the transition in w(L) near the capillary length to be less pronounced. For instance, a gradual wettability gradient extending over long distances might cause w(L) to increase (32) Ertas¸ , D.; Kardar, M. Phys. Rev. E 1994, 49, R2532.

for length scales well above the capillary length. Because of the extreme sensitivity of the contact angle to surface chemistry, even subtle, large scale variations in the wettability can produce large scale deformations of the contact line. At no length scale can vertical contact line deformation amplitudes be larger than the maximum possible rise or depression heights (corresponding to contact angles of 0° and 180°). Thus, on long enough length scales, gravity always dominates and contact lines must be flat, even for nonstationary surfaces. 2.4. Contact Line Structure and Hysteresis. Since both contact angle hysteresis and contact line roughness are attributed to the heterogeneity of the solid surface, one might expect a correlation between these phenomena. Models of dilute, random strong pinning centers, twodimensional arrays of heterogeneities, and weak, continuous heterogeneity suggest that contact line roughness should increase with increased contact angle hysteresis.7,10,11 However, for weak enough heterogeneity, some models predict contact line roughness without hysteresis.7,10 Also, some rather extreme examples with strong heterogeneity can produce significant contact line roughness with no contact angle hysteresis. For example, a surface with vertically-striped chemical heterogeneity has no hysteresis; however, the contact line will show large undulations with the periodicity of the striped pattern.5,9 Our results do not show correlation of contact line roughness with contact angle hysteresis on our experimental surfaces. 2.5. Chemically Heterogeneous Surfaces. Physical surface roughness and/or spatial variations in the surface chemistry of a solid surface produce hysteresis. Modeling of local wettability variations due to surface roughness is similar to that for chemical heterogeneity.7 Since the alteration of the experimental heterogeneous surfaces used in this paper is due to subtle changes in surface chemistry (section 3.1), we will discuss surface heterogeneity in terms of chemical heterogeneity. A chemically heterogeneous surface may exhibit variations on molecular and supermolecular scales. There will be some spatial correlation of the heterogeneity, at least over short distances (minimally at molecular sizes). We know wetting is very sensitive to surface heterogeneity; but the strength and spatial extent of the surface chemistry variation, which affect contact angles, are not known. In addition, thermal fluctuations and vibrational noise will cause the local contact line to sample some small region of the surface. Thus, at some small length scale, surface defects are “averaged” and are unable to pin the contact line. At longer length scales, the heterogeneity for truly random surfaces exhibits stationarity; and the macroscopically-averaged contact angle on one portion of the surface is the same as that on another portion. If only molecular and supermolecular scale variations occur in the surface chemistry, one might expect contact angles to show variation only over very short distances. However, the collective behavior of short-scale, weak heterogeneity is predicted to produce contact angle variation over larger scales.8,11,18 In addition, truly random surfaces may be extremely difficult to attain. Large scale correlations in heterogeneity may well be common on most natural surfaces. 3. Experimental Section 3.1. Samples and Materials. We examine the wetting characteristics of various surfaces. Each heterogeneous surface begins as a relatively uniform monolayer surfactant coating. The fresh surfaces are of two types: (1) a monolayer of Aquapel (a perfluorinated surfactant) on

Surfaces with Contact Angle Hysteresis

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Table 1. Contact Angles and Hysteresis Energies of Experimental Systemsg system A0a A1a A2a AA1wb AA1hb AA2c D0d D1d D2d D3d

θre

θae

γlv cos θr

γlv cos θa

hysteresisf

89.5 (2.0) 46.8 (2.2) 24.3 (2.7) 32.0 (1.6) 22.8 (2.6) 44.1 (1.5) 99.9 (1.4) 66.7 (3.4) 56.0 (2.7) 34.2 (2.7)

123.0 (1.6) 84.3 (2.7) 61.0 (3.7) 58.8 (1.7) 37.9 (2.2) 73.7 (1.1) 113.0 (1.4) 100.0 (5.0) 90.0 (5.0) 79.7 (2.4)

0.61 (2.5) 48.2 (2.0) 64.2 (1.5) 59.7 (1.2) 24.9 (1.0) 50.6 (1.5) -12.1 (1.7) 27.8 (3.8) 39.4 (2.8) 58.2 (1.9)

-38.9 (1.7) 6.99 (3.3) 34.1 (4.0) 36.5 (1.8) 21.3 (1.0) 19.8 (1.4) -27.8 (1.6) -12.2 (6.1) 0.0 (6.1) 12.6 (2.9)

39.5 (3.0) 41.2 (3.9) 30.0 (4.2) 23.2 (2.2) 3.59 (1.5) 30.8 (2.1) 15.7 (2.3) 40.1 (7.2) 39.4 (6.7) 45.6 (3.5)

a Aquapel sample degraded for time, t, with UV/ozone treatment and examined with water {(0) t ) 0 (fresh sample); (1) t ) 80 min; (2) t ) 100 min}. b Altered Aquapel, degraded by UV/ozone treatment {(w) examined with water; (h) examined with hexadecane}. c Altered Aquapel, degraded by UV/ozone treatment and examined with water. d Dodecanethiolate sample degraded for time, t, with UV/ozone treatment and examined with water {(0) t ) 0 (fresh sample); (1) t ) 4 min; (2) t ) 8 min; (3) t ) 16 min}. e θr and θa are, respectively, recede and advance contact angles in degrees. f Hysteresis ) γlv cos θr - γlv cos θa in erg/cm2. g Error bars in parentheses. (Used γlv ) 70.4 erg/cm2 for water and γlv ) 27 erg/cm2 for hexadecane.)

smooth glass plates and (2) a self-assembled monolayer of dodecanethiolate chemisorbed from ethanol solution onto a 100 Å thick gold film on smooth glass plates. For the Aquapel samples, the glass substrate rms roughness is e4 Å, as measured by X-ray reflectivity. The coating is on the order of a molecular monolayer, measured with X-ray reflectivity and optical ellipsometry. To produce more heterogeneous surfaces, the fresh monolayer surfaces are altered using UV/ozone cleaning techniques.23,24,33,34 We use a mercury grid lamp (BHK Inc., 88-9102-20), held 10 cm from the samples, which are slowly rotated to enhance uniformity of the UV exposure. For long time exposure, the entire monolayer is removed, as shown by its hydrophilic wetting. For shorter exposures (as for our experimental surfaces), the surface chemistry in the monolayer is partially altered. The rms surface roughness changes by ∼1 Å for the shorter exposures. Atomic force microscopy measurements suggest that the heterogeneity caused by the UV/ozone treatment is probably of molecular or supermolecular (but submicroscopic) lateral scale (perhaps ∼100 Å). All of the surfaces are carefully cleaned before each experiment. The Aquapel samples are first doused with a liquid detergent solution and then thoroughly rinsed in pure water. Then they are rinsed sequentially with ethanol, pure water, 2-propanol, and a final, thorough rinse of pure water. The thiolate surfaces are rinsed with ethanol and then with pure water. Before beginning experiments where the wetting liquid is not water, the plate is blown completely dry with purified nitrogen. The Aquapel coatings show excellent stability against water, even after long exposure to liquids and after multiple cleanings and experiments. In fact, contact line configurations are microscopically reproducible to high accuracy on these surfaces.23,24 The thiolate surfaces show slight changes in their wetting properties after several (∼10) hours of exposure to water. However, these slight changes will have little effect over the time scales of the measurement processes (∼1 h). We used water and hexadecane as the wetting liquids. The measured surface tension of our purified water is 70.4 ( 1 dyn/cm. This value reveals slight contamination but will not alter our conclusions. The hexadecane (Aldrich, H670-3) has a nominal surface tension of 27 dyn/ (33) Vig, J. R. J. Vac. Sci. Technol. A 1985, 3, 1027. (34) Vig, J. R. In Treatise on Clean Surface Technology; Mittal, K. L., Ed.; Plenum: New York, 1987; Vol. 1, Chapter 1. (35) Shafrin, E. G.; Zisman, W. A. In Contact Angle, Wettability and Adhesion; Fowkes, F., Ed.; Advances in Chemistry Series, Vol. 43, American Chemical Society: Washington, DC, 1964; Chapter 9.

Table 2. Comparison of Wetting Energy for Various Surface Chemistriesa surface

θw

γlv cos θw

θh

γlv cos θh

SiO2 CH2 CH3 CF2 CF3

0 94 111 108 120

73 -5 -26 -23 -37

0 0 46 46 78

27 27 19 19 6

a θw and θh are contact angle (advance ≈ recede) in degrees for water and hexadecane, respectively. Values for all surfaces except SiO2 are found in refs 1 and 35. γlv cos θ is the wetting energy in erg/cm2. (Used γlv ) 73 erg/cm2 for water and γlv ) 27 erg/cm2 for hexadecane.)

cm. Table 1 shows macroscopic contact angles and wetting energies of water and hexadecane on our surfaces. Since hexadecane has a lower surface tension than water, comparing the results of surface wetting by hexadecane and water shows the effects of lowering the elastic energy of the system. The two fluids will have different local pinning energies on the heterogeneous surfaces. We infer this from the differences in the wetting energy of various homogeneous surfaces by water and by hexadecane (Table 2). We see that the range of wetting energies of hexadecane on various surface chemistries is less than that of water. Since pinning energies on our surfaces arise from the differences of wetting energies on portions of the surface with different chemistries, the local pinning energies of hexadecane are likely lower than those of water on our heterogeneous surfaces. Two experimental conditions were examined with these systems. (1) One fluid (water) moved over the same region of an Aquapel or a thiolate surface for successively altered molecular arrangement of that surface by UV/ozone treatment. Here, we examine the effects of changing the surface heterogeneity and, potentially, the pinning energies, with no change in the elastic energy. (2) Two fluids (water and hexadecane) moved over the same region of an Aquapel surface. Here, we examine the effects of changing the elastic energy of the system and the pinning energies (by changing the density and interfacial energies of the liquids), but with both liquids on the identical heterogeneous surface. 3.2. Apparatus. For our contact line and contact angle measurements, we employ the Wilhelmy plate geometry for a sample (either 5 cm × 8 cm or 2.5 cm × 7.5 cm glass plate) held vertically in a container of the liquid. The container holding the liquid is either a 600 mL Teflon beaker (for contact lines in capillary rise) or a 10 cm × 10 cm × 10 cm optical glass cell (Helma, 704.006, for contact lines in capillary depression). The plate is raised or lowered by means of a vertically mounted translation stage

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connected to a linear actuator (Newport 860 Motorizor with Newport 860SC Speed Controller). The vertical position of the plate is tracked to within 25 µm over 10 cm of travel using a dial indicator (Starrett, 25-4041). We use two CCD cameras (Pulnix TM-740 and Sony XC-75) in our contact line imaging and rise height measurements. The camera viewing the contact line can be translated horizontally using a computer-controlled linear actuator (Newport 850F with a Newport Motion Master 2000 controller). Both cameras are connected to long-working-distance microscopes (Bausch & Lomb Monozoom 7) and to S-VHS VCRs (Panasonic AG-1960 and AG-1970). The time is tracked to 0.01 s and is recorded on all video images using time data generators (Panasonic WJ-810). From videotape, the camera images are transferred to computer by means of a frame grabber (Perceptics PixelGrabber or Data Translation QuickCapture). We use a reflection geometry to image the contact line.23,24 In this geometry, incident light propagates along the optical axis of the camera toward the sample. A reflective backing behind the plate reflects light directly back into the camera. Light is reflected off axis by the liquid meniscus. Thus, the contact line is the boundary between the light region of the image (the reflective backing) and the dark region (the liquid meniscus). We extract contact lines from the grabbed video images by finding the position of the maximum gradient in the gray level (to subpixel resolution) along each pixel column in the image.24 3.3. Measurements. For most of our contact line roughness measurements, video images are obtained of static contact lines. We obtain contact line images at different magnifications (and fields of view) for the different measurements. We use various magnification scales from 0.5 µm/pixel (high magnification) with a 330 µm field of view to 22 µm/pixel (low magnification) with a 14 mm field of view. For larger fields of view (up to 4 cm) at high magnifications (0.5-2.5 µm/pixel), we translate the camera horizontally along the averaged direction of the contact line while videotaping the image. We translate the camera in steps, so that the field of view from each translation step overlaps with the preceding and the following fields of view. Individual images of segments of the contact line are then pieced together. For the longest scans, we cannot employ our highest magnification because large vertical deviations of the contact line leave the vertical field of view as we translate the camera. To assure that we measure contact lines on the same regions of a surface in different runs, we track the vertical movement of the plate using a small fiducial mark scribed on the surface. We determine contact angles by measuring the rise (or depression) height of the meniscus of a liquid against the solid surface. The rise height is measured with the contact line in the recede or advance condition and the plate moving at 2-5 µm/s to keep the contact line in the flicker regime for the measurement. (This gives recede angles 1-2° less and advance angles 1-2° greater than static angles obtained after relaxation due to remaining vibrations on the optics table.24) We must image both the contact line and the bulk liquid level. If the meniscus rises upward on the plate (contact angles 90°), then the liquid is contained in the optical glass cell and the contact line and bulk liquid level are viewed through the cell.

Decker and Garoff

For contact angle measurements, one camera images the contact line in the reflection geometry and a second camera provides a clear view of the bulk liquid surface where the liquid-vapor interface is flat.24 A needle is held close to the bulk liquid surface and is illuminated from behind. The second camera images the silhouette of the needle and its reflection. In the resulting image, the position half way between the needle and its reflection is taken as the position of the bulk liquid surface.24 The rise height (local or macroscopically-averaged) is obtained from the contact line position from one camera and the bulk liquid level from the other camera. The contact angle, θ, is calculated from the rise height by36 θ)

π h - 2 sin-1 2 2a

( )

(3)

where h is the rise height and a is the capillary length for the liquid-vapor pair. For an average measure of the wetting of our surfaces, the rise height measurements are typically performed at a low magnification of 22 µm/pixel and a horizontal field of view of 14 mm. Thus, we measure macroscopic contact angles averaged over contact line lengths of nearly 5 capillary lengths for water (a ) 2.7 mm for water). The rise height was measured at 5-10 vertical regions on each surface, with each vertical region separated by 3-5 mm. The horizontally-averaged rise heights from the vertical regions of a surface were averaged to obtain the rise height for the surface. Several factors contribute to uncertainties in our rise height measurements. Uncertainties in the contact line and needle position from noise in the images are negligible compared to other factors. Variations in the rise height at various positions on the surface contribute 40-170 µm uncertainties and are included in the error bars in all reported results. During measurement of the rise height, one of the cameras must be moved horizontally after the height difference between the two cameras has been calibrated. Due to the long working distance of the microscope, even small imperfections in the stability of the optical mounts can cause vertical motions as large ∼0.5 mm during this motion. This leads to uncertainties as large as ∼10° in our contact angles but does not alter any of our conclusions. To examine jumps along the contact line, we use our highest magnification scale of 0.5 µm/pixel to image contact line segments of a field of view of 330 µm. The macroscopic contact angle is first brought to the advance or recede condition by raising or lowering the plate until the contact line begins to flicker with jumps. Then the plate motion is halted and the contact line relaxes away from the advance or recede condition by ∼500 µm due to mechanical vibrations. After relaxation, the plate motion is resumed at a slow speed of 2-5 µm/s. (We use as slow a speed as we can to minimize dynamic distortion of the contact line due to the plate motion. Further, since we want to understand quasistatic contact line dynamics, we use a plate speed much slower than the characteristic jump speed.23) The contact line is then videotaped as it moves from a completely pinned configuration into the advance or recede condition when many jumping events occur across the field of view. To precisely measure the contact line motion relative to the plate, both the contact line and small defects on the plate are simultaneously tracked, with both visible in each of a temporal sequence of images. The video images of the contact line approaching the advance or recede condition are digitized with a frame (36) Dussan, V. E. B.; Rame´, E.; Garoff, S. J. Fluid Mech. 1991, 230, 97.

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Figure 3. Contact line data, y(x). The contact line roughness calculation averages over segments of size L, centered at x0, and varies the position of x0 over a contact line of length D. The contact line is centered at x ) 0.

grabber at 3 frames/s and, for limited data, at our fastest rate of 30 frames/s. Contact lines are extracted from the digitized images. We obtain the average contact line positions relative to the laboratory frame and the surface. By subtracting temporally consecutive contact line configurations and plotting these differences versus position along the contact line as a function of time, we produce spatial-temporal maps of contact line jumping events. 3.4. Contact Line Roughness Analysis. Since analysis of interface roughness is subject to numerous complexities, we give some details of our analysis and its limitations. The discussion in this section is applicable to general interface roughness. We analyze contact line roughness by measuring the rms contact line width, w, as a function of averaging length, L, for contact line data, y(x), with a total horizontal extent D. (See Figure 3 and eqs 4-6.) First we find the width squared, σL2, of all sections of the contact line of length L < D/2 (eqs 4 and 5). We average these σL2 values and then take the square root to obtain the value of w for a given L (eq 6). We repeat the process for many values of L. yjL(x0) ) σL2(x0) ) w(L) )

1 L

∫

∫

1 L

x0+(L/2)

y(x) dx

(4)

[y(x) - yjL(x0)]2 dx

(5)

x0-(L/2)

x0+(L/2)

x0-(L/2)

[D -1 L∫

(D-L)/2 σ 2(x0) -(D-L)/2 L

]

dx0

1/2

(6)

When obtaining an ensemble-averaged w(L) from several contact line configurations, we actually obtain the average w2(L) for the several configurations and then take the square root. With this method, the ensemble averaging process is consistent with the averaging that takes place in eq 6 when obtaining w(L) for a single contact line configuration. This is equivalent to using the w2(L) values for individual contact line configurations as if they were σL2 values obtained from different sections of one long contact line. In practice, it is experimentally not easy to obtain an accurate measure of w(L) for contact lines on a given solid surface.37 We have identified three major sources of error in obtaining accurate measures of w(L): (1) insufficiently small discretization when imaging, (2) image noise causing edge detection errors when analyzing images, and (3) long wavelength features such as artificial tilts or real long wavelength features that bias the measurement of w(L). While insufficiently small discretization size causes measured roughness to be too smallsmainly at small length scalessimage noise causes the measured roughness to be too large at these same scales. Noise in the measured (37) Schmittbuhl, J.; Vilotte, J.-P.; Roux, S. Phys. Rev. E 1995, 51, 131.

contact line configurations occurs from edge finding errors due to pixel noise in the CCD camera. It is accentuated by poor image contrast between the liquid meniscus and the nonwetted region of the solid surface. Image contrast decreases at higher magnifications. With proper lighting conditions, we were not contrast limited at our highest magnification. We have found that our techniques for obtaining w(L) are reliable for L larger than 5-10 times the discretization size. Contact line features having wavelengths longer than the field of view can bias measurements of w(L) on all length scales. As shown below, when long wavelength features exist in a single contact line configuration, w(L) for that configuration depends on the length, D, of the contact line. If the contact line is written as a Fourier sum nmax

y(x) )

∑

cneinkx,

k ) (2π/λmax)

(7)

n)-nmax

where λmax is the maximum wavelength in the contact line, then eq 6 becomes nmax

w(L) ) {

∑

|cn|2(1 - sinc2(nkL/2)) -

n)-nmax nmax

{

∑

nmax

∑

cn*cm sinc((m - n)k(D - L)/2)[sinc((m -

n)-nmax m*n)-nmax

n)kL/2) - sinc(nkL/2) sinc(mkL/2)]}}1/2 (8)

where sinc(x) ) sin(x)/x. If k(D - L) . 1, then, to zeroth order, w(L) just becomes the first sum on the right side of eq 8. In this case, w(L) is independent of D. However, if k(D - L) j 1, then the measured w(L) will have an oscillatory dependence on D for different phases of the long wavelength component relative to the field of view. Therefore, if k(D - L) j 1, measuring a statistically representative w(L) requires a large enough ensemble of contact lines to average over the D dependence. We observe long wavelength features in our long contact line scans. Sometimes, a similar large scale feature will persist for contact lines at different vertical positions on a surface. These large scale contact line features might be a result of macroscopic inhomogeneity in the deposition of the fresh monolayers (which might also affect the subsequent alteration of the surfaces) and/or inhomogeneous alteration of the surfaces due to a residual gradient in the amount of UV exposure across the surface. When the longest wavelength features persist in our sampling, they bias w(L) for each contact line configuration as well as for ensemble-averaged w(L). Since this effect can exist across an entire surface, it cannot be removed by a larger ensemble of contact line scans. To remove the long wavelength features and obtain proper analysis of contact line roughness at smaller length scales, we subtract best-fit, second-order polynomials from all our long contact line scans. In addition to subtracting a loworder polynomial, we insure sufficient statistics in the averaging processes to obtain w(L) for a single contact line configuration by choosing the maximum value of L to be about half of D. For each surface examined with long contact line scans, we obtain a total of 3-10 scans at a high magnification. Between scans, the plate is raised or lowered so that the contact line samples vertical regions of the surface separated by 3-5 mm. The total region of plate examined by a typical set of long contact line scans is 4 cm horizontally and 2-3 cm vertically. These procedures

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Figure 4. Average contact line position versus plate position in the laboratory frame while approaching the recede condition on the degraded Aquapel sample AA1 with (a) water and (b) hexadecane. The line with slope 1 is drawn in as a guide indicating complete pinning of the contact line to the plate.

make our ensembles of long contact line scans sufficiently large to represent the roughness at the smaller length scales. 4. Results 4.1. Contact Line Dynamics. We observe the predicted qualitative behavior as we move our plates through a hysteresis cycle (Figure 2). The contact line does not pin at isolated sites and stretch around these sites with slipping of the nonpinned sections of contact line past other, less-hysteretic regions between the pinning sites, as it does on some microfabricated surfaces.38,39 Rather, the entire contact line remains pinned at all points (down to our resolution of ∼1 µm) until small jumps begin near the corners of the hysteresis loop (points 3 and 7 in Figure 2). The onset of discernible jumps at the corners can be seen in Figure 4a as a slight movement of the average contact line position relative to the plate. In addition, the spatial-temporal maps of jumps (Figure 5) show that jumping events begin very small, both in amplitude and in lateral scale. The amplitude and lateral extent of the jumps increase as the advance or recede condition is closely approached. The transition to the flicker regime in the advance or recede condition can be fairly abrupt with the range of rise height from onset of the initial jumps to the flicker regime being on the order of a few percent of the total vertical extent of the hysteresis loop (Figure 2). Figure 4 shows the differing behavior for the same solid surface moving through different liquids near the corners of contact angle hysteresis loops. The transition to the flicker regime is much more abrupt with hexadecane than with water, with more small jumps occurring before the transition to the flicker regime with water. (Similar to this behavior for hexadecane, water on the fresh surface (38) Nadkarni, G. D.; Garoff, S. Europhys. Lett. 1992, 20, 523. (39) Marsh, J. A.; Cazabat, A. M. Phys. Rev. Lett. 1993, 71, 2433.

Decker and Garoff

also shows fewer uncorrelated jumps before the flicker regime than for water on the altered surfaces.) In addition, the contact line dynamics for hexadecane are not the same at the corners near advance as for recede at the same position on the surface. For water, the behavior at the corner approaching advance is similar to that approaching recede. Within the flicker regime, the average contact line position relative to the laboratory frame varies up and down for water in advance and recede conditions on a degraded Aquapel sample and for hexadecane in the recede condition on this same sample. Sections of the contact line temporarily pin and then depin on time scales short enough that jumping motions continually occur across the contact line (without a well-defined begin or end for individual jumps) but long enough that the average contact line position fluctuates up and down (Figure 4). In contrast, for hexadecane in the advance condition on this same surface, the contact line is completely pinned until the contact line depins in a wavelike fashion, with the event propagating from one side of the contact line to the other. Then the contact line repins and moves with the plate over distances of ∼100 µm until the next large jump occurs. A contrasting extreme to this large scale correlated pinning and depinning is observed for water in the advance condition on the fresh Aquapel surface. Here, the dominant contact line motion shows slipping past the plate with smaller scale flickering and less up and down variation in the macroscopically-averaged rise height. 4.2. Contact Line Structure. Representative contact line configurations are shown in Figures 6, 7, and 8a. Representative ensemble-averaged w(L) plots are shown in Figures 8b, 9, and 10. These w(L) plots show that, at small length scales (micron scale to lengths on the order of the capillary length), contact line roughness increases with an approximate power-law behavior. At larger lengths (greater than the capillary length), the contact line roughness tends to saturate. Within the approximate power-law region, we measure a range for the contact line roughness exponent, R (eq 1), for an ensemble of contact lines for a given system. The range for the exponent reflects the deviations of the contact line roughness measurements from a true power-law behavior. This range of exponents arises from fits to subsets of the w(L) data truncated at a maximum L, as the maximum L is varied but remains below the capillary length. Except for the case of the fresh Aquapel surface (perhaps due to pixel noise), the lower end of the exponent range we use comes from a power-law fit for L ∼ 5-100 µm, while the upper end comes from a power-law fit for L ∼ 5-500 µm. For all cases, even though the power-law behavior is only approximate, we can use the range of the exponent to characterize w(L) for the different wetting systems. One might expect mechanisms that relax macroscopic contact angles to smooth contact line roughness. However, we have found that contact line roughness is not influenced by such relaxation. One way we relax the macroscopic contact angle is by moving the plate slowly toward the global equilibrium from the recede condition. For the example shown in Figure 6, as the plate (and the rise height) are lowered by ∼500 µm (40% of the total change in the rise height between the advance and recede conditions) during the relaxation, the contact line remains fixed to the plate. Figure 6 shows typical long contact line scans before and after such a quasistatic relaxation. Slight differences between these contact lines are most probably due to relaxation by ambient vibrations, causing tiny sections of the contact line to fall and reconfigure

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Figure 5. Contact line jumps for water approaching the recede condition on the degraded Aquapel sample AA1. The gray level is proportional to the difference between consecutive vertical positions of each point along the contact line during plate motion. Darker gray represents larger differences. (The gray scale is different for parts a and b.) Uniform light gray corresponds to complete pinning of the contact line, i.e., no difference in consecutive contact line configurations relative to the plate. Background noise is suppressed. (a) From the same data (taken at 3 frames/s) as Figure 4a. (b) Data taken at 30 frames/s showing detail at onset of jumps.

Figure 6. Slowly relaxing the contact line from the recede condition. Contact line configuration (A) before and (B) after lowering the plate by ∼500 µm. The vertical shift between contact lines in the figure is arbitrary.

during the process of lowering the plate and rescanning the contact line. However, these reconfigurations do not produce a smoother contact line. The contact line roughness does not change significantly on any length scale due to the quasistatic changing of the macroscopic contact angle anywhere along the sides of the hysteresis loop. Even at the extreme values for contact angles, with contact lines prepared in the advance or recede condition, the ensemble-averaged w(L) values are nearly identical (Figure 9). Vibrational relaxation from the advance and recede conditions and relaxation by jumps in the flicker regime

Figure 7. Contact line configurations for water on (A) the fresh Aquapel surface A0 and (B) the same sample degraded for 100 min with UV/ozone treatment (surface A2).

also do not smooth contact lines. We have previously reported that the roughness of a contact line configuration can increase or decrease due to large vibrational relaxation of the macroscopic contact angle toward the global equilibrium for the system.24 Large vibrations can cause the contact line to relax toward equilibrium and to sample new regions of the surface. The contact line configuration changes as it relaxes. The resulting contact line roughness varies up or down as the contact line moves to these new regions. In all cases of contact line relaxation, quasistatic motion between advance and recede conditions, during vibrational relaxation, and relaxation by jumps in the flicker regime, w(L) does not depend on the state of the

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Decker and Garoff

Figure 10. Ensemble-averaged rms contact line roughness versus length scale for water on the successively degraded Aquapel sample: (0) Fresh monolayer, A0.; (O) After 80 min of UV/ozone treatment, A1; (4) After 100 min of UV/ozone treatment, A2.

Figure 8. Different liquids on the same region of the same degraded Aquapel sample AA1. (a) Section of contact line configurations for (A) water and (B) hexadecane. (b) Ensembleaveraged rms contact line roughness versus length scale for (0) water and (O) hexadecane.

Figure 9. Ensemble-averaged rms contact line roughness versus length scale for water on the degraded Aquapel sample AA1: (O) contact lines prepared in the advance condition; (0) contact lines prepared in the recede condition.

macroscopic contact angle within its range between advance and recede. For the wetting of a sequentially-altered Aquapel surface by one liquid, only the pinning energies are changing from one alteration to the next. For these surfaces, the magnitude of contact line roughness increases at all length scales after each alteration. This is seen both in the contact line configurations (Figure 7) and in w(L) (Figure 10). For the Aquapel surface examined with hexadecane and water, both the elastic and pinning energies are smaller

for hexadecane than for water. The contact lines for the two liquids on the same region of the surface display similar features but with smaller amplitude large scale features with hexadecane (Figure 8a). The ensembleaveraged w(L) for the two cases shows that the magnitude of contact line roughness is nearly the same at small length scales (Figure 8b). However, the contact line roughness at longer length scales is greater for water than for hexadecane. In the approximate power-law regimes of w(L), we measure various exponent ranges for our different systems. For water on a fresh Aquapel sample (system A0 of Table 1), the exponent exhibits a range of 0.66-0.72. For water on all of our altered Aquapel samples (systems A1, A2, and AA1), the exponent range lies within 0.820.91 independent of the degradation time. Water and hexadecane (with their different densities and elastic energies), sampling the same regions of the same altered surface show very similar exponents: 0.82-0.87 for water and 0.77-0.86 for hexadecane. The slightly broader range for hexadecane (capillary length of 1.9 mm) may be due to gravitational smoothing having a greater effect at lengths on the order of 500 µm than with water (capillary length of 2.7 mm). None of our measured roughness exponents are compatible with theoretical values of 1/3 and 1/2.11 One reference has described the difficulty of obtaining accurate values of roughness exponents from experimental selfaffine interfaces using typical analysis techniques.37 This reference predicts absolute error bars of 0.1-0.2 due to the analysis technique alone. Even with such a large error bar we do not see agreement of our measured exponents with the theoretical value of 1/3 and only a small probability of agreement with 1/2 for water on the fresh Aquapel sample. Our experimental systems may simply not lie within the regime of weakly pinned contact lines treated by theory. Models of heterogeneous surfaces all suggest that contact line roughness should correlate with the amount of contact angle hysteresis.7,10,11 Figure 11 shows that the contact line roughness measured over a length scale of L ∼ 100 µm does not correlate with the macroscopic contact angle hysteresis for our surfaces. Our fresh monolayer surfaces even exhibit significant contact angle hysteresis (Table 1) and yet have very flat contact lines relative to those on the altered surfaces (Figure 7). Figure 12 shows that the contact line roughness does correlate with the wetting energy for the advancing contact angle.

Surfaces with Contact Angle Hysteresis

Figure 11. Hysteresis energy ) γlv(cos θr - cos θa) versus rms contact line roughness, w, for L ) 100 µm.

Figure 12. Wetting energy (advance) ) γlv cos θa versus rms contact line roughness, w, for L ) 100 µm.

Similar correlations occur for the recede and average wetting energies and for roughness at length scales of L ∼ 10-1000 µm. Evidently, the regimes considered in the models are not the conditions of our experimental study. 5. Discussion and Conclusions 5.1. Contact Line Structure and Competing Forces. Wetting on the surfaces considered here, probably representative of a large class of imperfectly-coated or chemically-degraded surfaces, exhibits strong, dense pinning of the contact line. As shown by our results, the local wettability of the surface contorts the contact line on all length scales at least down to our resolution limit of ∼1 µm. As we move our surfaces quasistatically, all points on the contact line are either pinned to the surface or moving rapidly across it in a jump. We do not observe points on the contact line pinned, with points in between sliding across the surface (i.e. at a fixed position relative to the bulk liquid), as predicted for surfaces with strong pinning defects separated by regions of the surface with little or no hysteresis. Thus, theoretical or experimental modeling as either dilute or dense distributions of isolated defects will not mimic the behavior on ambient surfaces such as ours. The experiments reported here and past observations on similar surfaces23,24 show that spatial variations of the local wettability control contact line configurations; the spine energy (as dictated by the position between advance and recede) has negligible effect. First, we observe that, during quasistatic motion between the advance and recede conditions, the contact line configurations remain fixed

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even though the contribution of the spine to the energy of the system has changed significantly. Second, contact line configurations at the same point on the surface are reproducible down to the micron scale even after nonquasistatic cycling of the surface through macroscopic motions.23 Third, relaxations from vibrations and jumps in the flicker regime cause contact lines to reconfigure and repin at new positions on the surface with either increased or decreased contact line roughness. Even though the jumps lower the spine energy, the local wettability dominates and its detailed spatial structure dictates that the contact line roughness can increase or decrease. The power-law-like behavior we observe for the contact line roughness on length scales less than the capillary length arises from the competition of surface tension and pinning forces. For all systems we examine, the scaling of these forces appears constant for length scales of ∼500 µm (a large fraction of the capillary length) down to at least ∼5 µm. We observe a difference in the power-law behavior for water on fresh surfaces compared to that on degraded surfaces. Since the elastic forces are the same for these systems, we can speculate that the heterogeneity structure on the fresh sample is different in some way from that on the degraded surfaces. Our results for hexadecane and water on the same regions of a surface show similar roughness scaling at small length scales. Thus, the elastic and pinning forces scale similarly for the two systems with only different fluids. However, the slope and magnitude of w(L) decreases above L ∼ 500 µm for hexadecane compared to water. This indicates that the influence due to gravity is more apparent at smaller L for hexadecane than for water. This is consistent with the smaller capillary length for hexadecane compared to water. The role of gravity smoothing contact lines on all surfaces is seen in the turnover in w(L) near the capillary length. We observe nonstationarity in the wettability of some surfaces at long lengths, which can limit the turnover and produce large scale features that compete with gravity to lengths well above the capillary length. Since wetting by hexadecane is less sensitive to chemical differences in the surface, the nonstationarity of the wettability results in smaller long length scale features than appear for water on the same surface. 5.2. Contact Line Dynamics and Energy Functionals. A microscopic section of the contact line jumps when the local energy barrier associated with that section has been lowered to zero (or near zero with vibrations present). Barriers may be driven to zero either by increases in the slope of the spine energy (due to motion of the plate relative to the bulk fluid level) or by changes in the local elastic energy as neighboring portions of the contact line rearrange. Since only small vertical translations of the surface are needed to move from the regime where the contact line is completely pinned to where it is continuously jumping (points 2-4 and 6-8 in Figure 2), the distribution of the energy barriers for various segments of the contact line must be narrow. For water on the degraded surfaces, the initial jumps are isolated and small both laterally and vertically. Here, in the initial approach to the advance or recede condition, contact line rearrangements of one portion of the contact line do not remove the energy barriers of neighboring sections of the contact line. Jumps remain isolated. As the system moves closer to the advance or recede condition, we observe that the jumps of neighboring sections of the contact line become coupled. Now the slope of the spine energy must have increased so much that all local barriers are very small

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and rearrangement of a portion of the contact line removes barriers for neighboring portions. Jumps become highly coupled. We note that the onset of coupled jumps is much more rapid for water on the fresh surface and hexadecane on the degraded surface than for water on the degraded surface. 5.3. Summary. We have observed the extreme complexity of wetting on surfaces with chemical heterogeneity. These surfaces are representative of a large class of surfaces which have been derivatized with organic coatings. As is common experience, even surfaces with advancing angles approaching the ideal for that surface chemistry can have high hysteresis energy. Damage to the surface chemistry of such surfaces changes the advance and recede contact angles but not necessarily the contact angle hysteresis energy. Contact line configurations are controlled by the spatial variations of the wettability

Decker and Garoff

energy of the surface and exhibit characteristics of strong, dense pinning. Qualitative features of proposed energy functionals are supported by our experiments. These features include the scaling of pinning and surface tension forces over a range of length scales and the general behavior of energy barriers trapping local portions of the contact line. However, the more quantitative features of the models, including roughness exponents and the correlation of roughness and hysteresis, do not describe wetting on surfaces such as ours. Successful models will have to account for strong, dense pinning of the contact line. Acknowledgment. We are grateful for support from the National Science Foundation (Grant DMR-9411900). LA970528Q