2100
Langmuir 1996, 12, 2100-2110
Using Vibrational Noise To Probe Energy Barriers Producing Contact Angle Hysteresis E. L. Decker and S. Garoff* Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 Received November 9, 1995. In Final Form: January 23, 1996X We measure the macroscopic capillary rise height of water on a chemically heterogeneous solid surface in the presence of vibrational noise. The amount of relaxation of the macroscopic contact angle depends on the mechanical characteristics as well as the energy of the vibrations. The macroscopic recede and advance contact angles are functions of the vibration level. Large enough vibration levels mitigate hysteresis. Microscopic contact line configurations depend strongly on microscopic wettability variation on the solid surface. Our study has implications for contact angle measurements in normal vibration environments and for the retention of drops on inclined surfaces.
1. Introduction Measurement of contact angles on physically rough and/ or chemically heterogeneous solid surfaces is generally a procedure fraught with uncertainty.1-3 On such surfaces, the contact line (CL)sthe line where the solid, liquid, and vapor phases meetsis rough, and the local microscopic contact angle varies across the surface. If a spatially averaged contact angle is measured (e.g., averaged over several capillary lengths4 of a CL), then a range of average macroscopic contact angles between minimum (recede) and maximum (advance) angles occur on these surfaces. If the liquid advances across the surface and stops, the measured average macroscopic contact angle is larger than if the liquid recedes before the measurement. This dependence of the macroscopic contact angle on the history of the relative motion of the solid and liquid is a manifestation of contact angle hysteresis. The macroscopic angle can stably exhibit any value within the range from the recede angle to the advance angle. Our study probes the effect of vibrational noise on contact angles and on the amount of contact angle hysteresis. From our data, we extract information about the energy functionals governing CL’s on hysteretic surfaces. The effect of vibrations on contact angles impacts precise contact angle measurements. Since contact angle hysteresis prevents drops from rolling from inclined surfaces,5-7 the mitigation of hysteresis or the control of the amount of hysteresis on heterogeneous surfaces is important for engineering surfaces which shed or retain fluid drops. Interaction of vibrations with such systems determines the size of drops that are retained by the surface. Although the idea that contact angle measurements are affected by vibrations has long been predicted,1 few experimental studies have examined the effect in detail. Two studies used harmonic oscillations to study the effect of these vibrations on macroscopic contact angles.2,8 Vibrational noise may be better characterized as a string * Author to whom correspondence should be sent: phone, 412268-6877; fax, 412-681-0648; e-mail,
[email protected]. X Abstract published in Advance ACS Abstracts, April 1, 1996. (1) Johnson, R. E., Jr.; Dettre, R. H. In Surface and Colloid Science, Matejivic, E., Ed.; Wiley: New York, 1969; Vol. 2, pp 85-153. (2) Smith, T.; Lindberg, G. J. Colloid Interface Sci. 1978, 66, 363. (3) Zisman, W. In Contact Angle, Wettability and Adhesion; Advances in Chemistry Series 43; Fowkes, F., Ed.; American Chemical Society: Washington, DC, 1964; Chapter 1. (4) The capillary length ) (γLV/(∆Fg))1/2, where γLV is the liquidvapor surface tension, ∆F is the difference in density between the liquid and the vapor, and g is the acceleration due to gravity. (5) Dussan V., E. B.; Chow, R. T. P. J. Fluid Mech. 1983, 137, 1. (6) Dussan V., E. B. J. Fluid Mech. 1985, 151, 1. (7) Dussan V., E. B. J. Fluid Mech. 1987, 174, 381.
0743-7463/96/2412-2100$12.00/0
of spikes of varying amplitude. Hence, in our study we use pulsed movements to mimic vibrational noise. Using a slow pulse rate, we characterize both the effect of each individual noise spike as well as the accumulated effect of many spikes. Some theoretical studies have investigated the structure of the mechanical energy functional of ideal three-phase systems on surfaces with ordered patterns of wettability.1,9-12 Energy barriers in that functional arise from the heterogeneity of the surface and trap the CL in metastable positions. This gives rise to contact angle hysteresis. In the geometry of capillary rise (a vertical plate partially immersed in a fluid bath), the energy barriers hold the CL some distance above or below the equilibrium capillary rise height, where the height is the distance between the CL and the bulk fluid level. The equilibrium rise height occurs at the global energy minimum for the system. The presence of microscopic domains of a system captured in metastable energy wells is thought to be germane to many types of hysteresis.13-15 Thus we will discuss many of our experimental results in the context of local energy barriers for microscopic sections of the CL for which individual energy functionals can be envisioned. In our capillary rise experiments on a solid surface, we measured the macroscopically averaged capillary rise height. We also analyzed the microscopic CL configuration and the CL roughness as vibrations relaxed the CL toward its equilibrium rise height. Our main results are (1) larger vibration levels produced more relaxation, (2) large enough vibrations mitigated hysteresis, (3) the amount of relaxation depended also on the mechanical characteristics of the vibrations, (4) microscopic CL roughness varied during relaxation, but mainly at long length scales, and (5) microscopic CL configurations depended more strongly on the local wettability variations of the solid than on the macroscopic rise height within the range dictated by the hysteresis. In section 2, we describe the experimental procedure for microscopically imaging the CL and measuring the (8) Andrieu, C.; Sykes, C.; Brochard, F. Langmuir 1994, 10, 2077. (9) Neumann, A. W.; Good, R. J. J. Colloid Interface Sci. 1972, 38, 341. (10) Schwartz, L. W.; Garoff, S. J. Colloid Interface Sci. 1985, 106, 422. (11) Schwartz, L. W.; Garoff, S. Langmuir 1985, 1, 219. (12) Marmur, A. J. Colloid Interface Sci. 1994, 168, 40. (13) Everett, D. H.; Whitton, W. I. Trans. Faraday Soc. 1952, 48, 749. (14) Everett, D. H.; Smith, F. W. Trans. Faraday Soc. 1954, 50, 187. (15) Everett, D. H. Trans. Faraday Soc. 1954, 50, 1077.
© 1996 American Chemical Society
Contact Angle Hysteresis
Langmuir, Vol. 12, No. 8, 1996 2101
Figure 2. Doubly-integrated accelerometer data: (s) 250 µm upward pulse; (‚‚‚) 500 µm downward pulse.
Figure 1. Experimental apparatus: A, water; B, Aquapel coated glass plate; C, silicon wafer; D, contact line; E, needle close to water bulk level; F, Teflon beaker; G, mechanical driver.
macroscopically averaged rise height while delivering vibrational pulses to the system. In section 3, we first describe the macroscopic features of the noise dependence of contact angles and contact angle hysteresis. Then we describe the microscopic characteristics of the CL interacting with vibrational noise. In section 4, we discuss a microscopic energy functional model that we use to explain the results. We present two models to describe the interaction of the vibrations with these microscopic energy functionals. Where possible, we discuss the results from section 3 in terms of these models. In section 4.8, we describe the implications of our results to contact angles and contact angle hysteresis in normal vibration environments. 2. Experimental Section The experiments were performed on a vibration-isolated optics table (Newport, Model RS-48-12/XL-B). A glass plate (5 cm × 8 cm) was held vertically and partially immersed in a Teflon beaker overfilled with water (Figure 1). The water was purified and deionized by a Barnstead ROpure LP with a NANOpure II filtration system and had a surface tension of about 68 ( 1 dyn/cm. Although this low surface tension indicates minor contamination of the water, this contamination will not qualitatively change our results. The hysteretic surface was an Aquapel coating (a perfluorinated surfactant) on a glass plate purposely degraded by ultraviolet light in a high humidity atmosphere. It displayed contact angles of θr ≈ 43° (recede) and θa ≈ 73° (advance). The surface remained robust, showing highly reproducible and temporally stable wetting characteristics, even after multiple cleanings and experiments.16 An undegraded Aquapel coating provides a hydrophobic surface with θa as high as 110° and hysteresis below 10°. X-ray reflectivity and optical ellipsometry measured the glass substrate root mean square (rms) roughness to be e4 Å and showed the coating to be on the order of a molecular monolayer. The coating is completely removed by extreme UV and humidity exposure. The surface resulting from this extreme treatment is completely wet by water. Less exposure (as for our experimental surface) does not remove the coating and only (16) Nadkarni, G. D.; Garoff, S. Langmuir 1994, 10, 1618.
changes the chemistry of the outer portion of the monolayer. This is shown by a less than 1 Å change in the rms roughness from the incomplete degradation process as measured by X-ray reflectivity. Therefore, our surface exhibits random heterogeneity in surface energy. This makes it an ideal surface on which to study contact angle hysteresis. The random heterogeneity of our surface differentiates it from other experimental surfaces with patterned heterogeneity or randomly placed patches of one wettability on a surface with a different background wettability. The glass plate was connected to a Pasco mechanical driver, Model SF-9324, as shown in Figure 1. The CL was prepared in the recede/advance condition by raising/ lowering the plate at 7 µm/s until the macroscopically averaged CL began to slowly slide across the surface while microscopic portions of the CL exhibited frequent jumping. After the CL was prepared in the recede or advance condition, the motion of the plate was stopped and the CL was allowed to relax by ambient vibrations for 2-3 min until relaxation had mostly stopped. (On the optics table, we measured ambient rms accelerations on the order of 10-1 cm/s2.) Following the relaxation by ambient vibrations, the pulsing mechanism was turned on. Rectangular pulses of 7 ms width and 5 s period were fed to the mechanical driver. We measured the acceleration of the plate during the pulses with a quartz accelerometer, Model 303A03 from PCB Piezotronics. Values of the maximum acceleration for different pulse amplitudes varied between 7 × 102 and 3 × 103 cm/s2. Unless otherwise noted, the mechanical driver first pulled the plate upward and then pushed it back downward during a pulse. The mechanical driver brought the plate back to its initial position after each pulse to within a few micrometers, but we measured a small downward drift of the plate of 0.02-0.05 µm per pulse. To obtain the displacement of the plate versus time during a pulse, the measured acceleration was doubly integrated. The displacement shows that after rising during the first part of a pulse, the plate overshot on the way back down with a small amount of ringing afterward (Figure 2). Maximum displacement amplitudes were varied from 250 to 1000 µm. We imaged the CL using reflection video microscopy. The optical path is shown in Figure 3. The view of the CL (Figure 4) was videotaped, and the video frames were later grabbed and digitized by computer. The digitized CL configurations were obtained from the grabbed video images using a 5 × 5 moment-based operator17,18 and by (17) Lyvers, E. P.; Mitchell, O. R. IEEE Trans. Pattern Anal. Mach. Intell. 1988, 10, 927. (18) Lyvers, E. P.; Mitchell, O. R.; Akey, M. L.; Reeves, A. P. IEEE Trans. Pattern Anal. Mach. Intell. 1989, 11, 1293.
2102 Langmuir, Vol. 12, No. 8, 1996
Decker and Garoff
Figure 3. Imaging the CL: A, water meniscus; B, Aquapel coated glass plate; C, silicon wafer; D, half-silvered mirror; E, microscope; F, CCD camera; G, light source.
Figure 4. View of the CL: light region, dry surface; dark region, water meniscus.
Figure 6. Relaxation of macroscopic capillary rise heights and macroscopic contact angles: (O) 250 µm upward pulses; (0) 500 µm upward pulses; (4) 1000 µm upward pulses. (a) (s) Three relaxation runs from recede condition and (‚‚‚) 3 relaxation runs from advance condition. Time interval A is about 3 min of ambient relaxation before pulsing. (b) Expanded view of the first 34 pulses in recede. Ambient relaxation is not shown.
Figure 5. View of needle tip (above) and its reflection (below).
finding the position of maximum gradient in gray level (to subpixel resolution) in each pixel column of the image. Hence, the digitized CL’s have single pixel resolution in the horizontal direction and subpixel resolution in the vertical direction. The capillary rise height was obtained from the averaged CL height relative to the bulk water level. The bulk level was measured by viewing the tip of a needle which was lowered close to the water surface. A typical image is shown in Figure 5. The bulk level was the position halfway between the needle tip and the reflection from the surface of the water. Images of the needle tip and its reflection were videotaped with a second camera, and changes in the bulk level were tracked during the experiment. The macroscopic contact angle (θ) was calculated from the macroscopically averaged rise height (h) by19
[
θ ) sin-1 1 -
1h 2a
2
( )]
(1)
where a is the capillary length. 3. Results 3.1. Contact Angle Relaxation and Mitigation of Hysteresis. In Figure 6a, we show the results of carefully (19) Adamson, A. W. Physical Chemistry of Surfaces; Wiley: New York, 1990; p 390.
preparing the system three times in the advance condition and three times in the recede condition with the CL at the same place on the plate. Each time, we allow ambient vibrations to partially relax the system. We then deliver pulsed vibrations. For each of the runs in advance or recede, a constant pulse displacement amplitude of about 250, 500, or 1000 µm was used. These amplitudes refer to the maximum upward displacement of the plate during each pulse. To determine the macroscopic rise heights, the digitized CL configurations were averaged over a horizontal distance of 1.1 cm of the CL. The CL configurations were digitized at a resolution of about 22 µm horizontally and about 2.2 µm vertically. The results in Figure 6a show that for larger pulse amplitude, the CL relaxes further. Many pulses are required to reach a final state at each amplitude. In each of the six runs, only 22 data points are plotted; but in each run, the plate was pulsed about 360 times after the 3 min of ambient relaxation. For each amplitude, the amount of relaxation achieved with each successive pulse decreases. The decreasing relaxation is not consistently fit for all runs by an exponential functional form. Significant reduction of hysteresis requires pulse sizes that are a large fraction of the rise height. The plate had to move by about 1000 µm to allow the CL to reach an equilibrium rise height of about 1360 µm, where the recede and advance rise heights were about 2100 and 760 µm, respectively. Continued drift in relaxation seen at long times is probably a result of error in the bulk water level measurement or of the plate drift (see section 2). For large enough pulses, contact angle hysteresis is completely mitigated. For 1000 µm pulses, the same macroscopic rise height is achieved for CL’s prepared in both the advance and recede conditions. The value of the macroscopic equilibrium rise height reached by relaxation from both the advance and recede conditions satisfies the
Contact Angle Hysteresis
Langmuir, Vol. 12, No. 8, 1996 2103
Table 1. Relaxation for CL Prepared in Recede Conditiona Au
Ad
hr
hr′
hf
he
250(5) 510(5) 1010(5)
100(15) 160(15) 320(15)
2100(50) 2100(50) 2050(50)
2010(50) 2000(50) 1950(50)
1710(50) 1470(50) 1350(50)
1360(50)
a
All numbers are in micrometers with uncertainties in parentheses. Au ) upward pulse component. Ad ) downward pulse component. hr ) zero-vibration recede rise height. hr′ ) ambientrelaxed recede rise height. hf ) final relaxed recede rise height. he ) average equilibrium rise height. Table 2. Relaxation for CL Prepared in Advance Conditiona Au
Ad
ha
ha′
hf
he
250(5) 500(5) 1000(5)
100(15) 160(15) 320(15)
750(50) 750(50) 770(50)
840(50) 880(50) 880(50)
1160(50) 1370(50) 1370(50)
1360(50)
a
All numbers are in micrometers with uncertainties in parentheses. Au ) upward pulse component. Ad ) downward pulse component. ha ) zero-vibration advance rise height. ha′ ) ambientrelaxed advance rise height. hf ) final relaxed advance rise height. he ) average equilibrium rise height.
Figure 7. Control of macroscopic capillary rise heights and macroscopic contact angles by vibration levels: (O) run 1, (0) run 2; ambient relaxation not shown; (A) pulse level changed from 250 to 350 µm pulses, (B) (run 1) pulsing stopped, bulk level lowered at 100 µm/min, and then pulsing resumed with 250 µm pulses, (run 2) lowered bulk level at 13 µm/min while pulsing at 250 µm level, (C) contact angle matches that at A to within about 1°.
following relation to within our experimental uncertainty (see data in Tables 1 and 2)
1 he ) (hr + ha) 2
(2)
where he, hr, and ha are the macroscopic equilibrium, zerovibration20 recede, and zero-vibration advance rise heights, respectively. Applying the small slope approximation to the liquid-vapor interface, we get11
h ) a cos θ
(3)
1 cos θe ) (cos θr + cos θa) 2
(4)
and eq 2 becomes
Experimental results described by eq 4 have been reported earlier.8 In Figure 6b, we show the relaxation in rise height for the first 34 pulses of the three pulse amplitudes used in the runs displayed in Figure 6a. We only show the case for the CL prepared in recede, and we do not show the ambient relaxation before the pulses. The fall after the first pulse is larger for larger pulses. In addition, the total amount of relaxation after a given number of pulses is larger for larger pulses. Within our experimental uncertainty, total relaxation did not take the CL past the equilibrium capillary rise height. Therefore, if the equilibrium condition was attained by a given pulse level, then a larger pulse level just caused the CL to reach this condition in fewer pulses (e.g., the 500 and 1000 µm pulses in the advance condition). 3.2. Macroscopic Contact Angles Are Functions of Vibration Level. In Figure 7, we show the results of two runs for a CL prepared in the recede condition and relaxed with two pulse amplitudes (250 and 350 µm) sequentially during each run. Again, we took extreme care to prepare the CL in the same conditions and at the same place on the plate for the two runs. In both runs, the system relaxed for 3 min by ambient vibrations after we prepared it in the recede condition. We then caused (20) The rise height before ambient relaxation represents a limit where even the residual vibrational spikes on the optical table cannot relax the CL compared to its constant movement due to the forced, slow (7 µm/s) plate motion used to prepare the CL in the advance or recede conditions. Thus, this rise height approaches a “zero-vibration” limit.
Figure 8. Effects of direction of plate movement on relaxation of macroscopic capillary rise heights and macroscopic contact angles: A, ambient relaxation; (O) 500 µm downward pulses; (0) 250 µm upward pulses. Displacement of the plate from the upward and downward pulses is shown in Figure 2.
further relaxation with about 120 pulses of 250 µm amplitude (up to point A in Figure 7). We followed this with about 120 pulses of 350 µm amplitude, further relaxing the CL. After this point in the two runs (point B in Figure 7), we continued with two different procedures. In run 1, the pulsing was stopped and the bulk level was lowered at 100 µm/min, causing the rise height to increase and the contact angle to decrease. Then, we stopped lowering the bulk level and resumed the 250 µm pulses, relaxing the CL downward again and causing the contact angle to increase. In run 2, the 250 µm pulses were resumed directly after the 350 µm pulses. Here, the bulk level was lowered at 13 µm/min at the same time the 250 µm pulses were applied. This simultaneous lowering of the bulk level and pulsing caused the rise height to slowly increase until the 250 µm pulses could again have effect. The pulses then kept the rise height from increasing further even though the bulk level was lowering. The curves are very different in these two runs after point B where their histories begin to diverge. However, in both cases, the system approaches the same contact angle after the 250 µm pulses rerelaxed the CL. Note that the final contact angle (at point C) for the two runs is close (to within 1°) to the angle approached at the end of the initial train of 250 µm pulses (at point A). Thus, contact angles are functions of the pulse amplitude. 3.3. Effects of Mechanical Characteristics of Vibrations. In Figure 8, we show the effect of the initial direction of the pulse for two relaxation runs for CL’s prepared in the recede condition. In both runs, the CL
2104 Langmuir, Vol. 12, No. 8, 1996
Decker and Garoff
Figure 10. CL configurations before and during 358th 1000 µm pulse from recede: (s) before pulse at time t ) 0 s, and after pulse and backwaves at t ) 1.0 s. (Within resolution of the plot, there is almost no difference between these two configurations.) (- - -) t ) 0.33 s; (‚‚‚) t ) 0.40 s.
Figure 9. Relaxation of CL for times near a vibrational pulse: (O) macroscopically averaged CL position. (‚‚‚) plate position from doubly-integrated accelerometer data. All positions measured relative to CL position before pulse. (a) First 1000 µm pulse after ambient relaxation from recede. (b) First 1000 µm pulse after ambient relaxation from advance.
relaxed for 3 min by ambient vibrations before we started the pulses. For one run, the pulses were upward 250 µm pulses, meaning the plate was first pulled up by about 250 µm and then pushed back down with some overshoot and ringing (Figure 2). For the other run, the pulses were downward 500 µm pulses, meaning that the plate was first pushed down by about 500 µm and then pulled back up again with overshoot and ringing. Figure 8 shows very similar relaxation for the two runs, in contrast to the results shown in Figure 6a, where 250 and 500 µm upward pulses cause very different relaxation. Figure 2 shows the doubly-integrated accelerometer data for the two kinds of pulses used in the two runs. Note that the upward overshoot for the downward 500 µm pulses is about equal to the upward 250 µm pulse amplitude. The similarity of the relaxations with these two pulses shows that the upward component of the pulse is the relevant factor determining the amount of relaxation for CL’s prepared in the recede condition. In Figure 9a, we show the average CL position as a function of time immediately before and after the first 1000 µm pulse following 3 min of ambient relaxation in recede. The CL position is shown relative to its position before the pulse. In Figure 9b, we show the corresponding plot for the CL having first been prepared in advance. We have similar observations for other pulse amplitudes. Significant motion of the plate due to a pulse with accompanying ringing of the plate motion occurs over approximately 0.1 s, as seen in the displacement data in Figures 2 and 9. However, the relaxation of the CL due to one pulse continues over about 1 s as seen in Figure 9. The initial rise of the plate drags the CL up at least a significant fraction of the total plate displacement. We did not have sufficiently fast video rates to track exactly how the CL followed the motion of the plate, but we did catch the CL in two or three video frames during the
motion. Thus, the maximum height measured in these frames is a lower bound on the CL motion. For the first 1000 µm pulse (Figure 9a) the CL is pulled up at least 570 µm. For a 250 µm pulse, it is pulled up by at least 190 µm. In both cases the plate carries the CL above the zerovibration recede rise height. During the initial up and down motion of the plate (times
