On the Uniqueness of the Receding Contact Angle: Effects of

Article pubs.acs.org/Langmuir

On the Uniqueness of the Receding Contact Angle: Effects of Substrate Roughness and Humidity on Evaporation of Water Drops Paola G. Pittoni, Chia-Hui Lin, Teng-Shiang Yu, and Shi-Yow Lin* Department of Chemical Engineering National Taiwan University of Science and Technology, 43 Keelung Road, Section 4, Taipei 106, Taiwan ABSTRACT: Could a unique receding contact angle be indicated for describing the wetting properties of a real gas− liquid−solid system? Could a receding contact angle be defined if the triple line of a sessile drop is not moving at all during the whole measurement process? To what extent is the receding contact angle influenced by the intrinsic properties of the system or the measurement procedures? In order to answer these questions, a systematic investigation was conducted in this study on the effects of substrate roughness and relative humidity on the behavior of pure water drops spreading and evaporating on polycarbonate (PC) surfaces characterized by different morphologies. Dynamic, advancing, and receding contact angles were found to be strongly affected by substrate roughness. Specifically, a receding contact angle could not be measured at all for drops evaporating on the more rugged PC surfaces, since the drops were observed strongly pinning to the substrate almost until their complete disappearance. Substrate roughness and system relative humidity were also found responsible for drastic changes in the depinning time (from ∼10 to ∼60 min). Thus, for measurement observations not sufficiently long, no movement of the triple line could be noted, with, again, the failure to find a receding contact angle. Therefore, to keep using concepts such as the receding contact angle as meaningful specifications of a given gas−liquid−solid system, the imperative to carefully investigate and report the inner characteristics of the system (substrate roughness, topography, impurities, defects, chemical properties, etc.) is pointed out in this study. The necessity of establishing methodological standards (drop size, measurement method, system history, observation interval, relative humidity, etc.) is also suggested.

1. INTRODUCTION In the study of wetting behaviors of sessile drops, great heedfulness is required in defining what is intended for contact angle. In the literature, terms such as equilibrium, apparent, asplaced, advancing, receding, maximum advancing, and minimum receding contact angles have been employed for describing either static or dynamic angles. Different terminologies have often been used for describing equal concepts, or contrariwise, the same terms have been indicated for illustrating diverse notions. Generally, the term equilibrium contact angle (θeq) has referred to the angle, defined by the well-known Young’s equation, formed at the interface between gas, liquid, and an ideal substrate (homogeneous, rigid, perfectly flat, and on which chemical reactions, diffusion, or molecular reorientation are not present).1−3 Theoretically, when all the ideal conditions defined by Young’s equation were respected, just the equilibrium contact angle would be measured.1−3 However, for drops sitting on real substrates, differences between the observed static or dynamic angles and θeq have always been noted.1−4 For measurements of static contact angles, although the experiments have been conducted once the equilibrium (or meta-equilibrium) state is reached, the recorded angles have been found to be dependent on system characteristics such as substrate roughness or drop size.1,2,5−11 Even if historically this © 2014 American Chemical Society

contact angle has been often erroneously reported as the equilibrium contact angle of the given system, the term apparent contact angle has been recently adopted.2,8,11−14 Referring to the contact angle measured after the initial drop spreading, the expression as-placed contact angle was introduced in the 2008 work by Tadmor and Yadav.15 The as-placed contact angle has been defined as the contact angle a drop adapts as a result of its (gentle) placement on a surface, and it has been proved15 to be dependent on drop size and material properties (surface tension and density). Other authors16−19 indicated this angle as advancing contact angle, and this definition was also used in this study. For dynamic contact angles, terms such as advancing (θa) and receding (θr) contact angles have been commonly employed, although some discrepancies in the terminology can be detected.1,2,20−22 Generally, the term advancing contact angle has been used to indicate the threshold value of the contact angle beyond which the three-phase contact line was observed actually advancing during a wetting process (Figure 1a). In the special case of the study of sessile drops sitting on tilting planes (Figure 1d), the term advancing contact angle has been employed to indicate the angle formed at the drop front at Received: November 29, 2013 Revised: July 1, 2014 Published: July 16, 2014 9346

dx.doi.org/10.1021/la501455d | Langmuir 2014, 30, 9346−9354

Langmuir

Article

contact angle has been determined through manual forced dewetting by removing the liquid from the drop by means of a syringe, quite different values have been reported in literature.24,39 Again with the work by Erbil et al.24 as an example, variations of 12−14% were noted in the θr values of water drops sitting on PMMA (θr = 42°−56°) and PET (θr = 52°−66°) substrates, when different rates of liquid withdrawal were applied. It has been pointed out, in fact, that unlike forced dewetting rates used during the experiments were the major cause of discrepancies in θr values for this method.24,39,45 In this respect, the evaporative process allows a minimum and kind of “standardized” rate of liquid withdrawal,18,19,24,39 and for this reason, in the past decade it has been one of the favorite methods for determining θr. However, the relative humidity in the experimental chamber has been proved to influence the rate of evaporation,39,47,48 that is, the rate of liquid withdrawal from the drop. Therefore, differences in the setting of relative humidity led to recording diverse evaporative behaviors.24,39,49,50 Despite this proven effect, the only two studies published on the influence of relative humidity on dynamic contact angle solely analyzed strong pinning cases.49,50 Thus, no conclusive investigations on the effects of relative humidity on the receding contact angle have been reported. Furthermore, even for measurements conducted on drops evaporating at the same relative humidity, dynamic contact angles are still affected by value discrepancies,2,39 and a quite large range of θr has been reported for apparently alike gas− liquid−solid systems.1,2,17−19,24,34,39,43 Specifically, the substrate roughness was indicated by Bourgès-Monnier and Shanahan18,19 as possible cause of the differences in θr values, since they observed unlike pinning behaviors for drops evaporating on two differently rough epoxy resins. Afterward, several works reported the influence of substrate topology on pinning and depinning of the triple line and/or on values of the receding contact angles.25,28,29,32−34,38,40,43 Zhang et al.,32 for example, measured values of θr between 48° and 76° for water droplets evaporating on polydimethylsiloxane (PDMS) substrates formed by spherical cap arrays with different cap heights. However, no previous work has been conducted to analyze methodically the behavior of drops evaporating on irregular rough surfaces prepared from the same substrate, and evaporative processes on customized microstructured surfaces have been more commonly investigated.28,29,32,33,38,43 Additionally, in several recent studies, a triple-line recoil stage has not been detected at all during almost the whole evaporative process. 1,2,17−19,32,34,36,49,50 In their works, Bourgès-Monnier and Shanahan18,19 noted that depinning of the three-phase contact line was totally absent for drops sitting on a rough epoxy resin, on which the drop evaporated by decreasing its contact angle until completely disappearing. Similar strong pinning configurations were reported for different liquids/rough surfaces by Orejon et al.,34 Zhang et al.,32 and Pittoni et al..17 In 2011, Bormashenko et al.36 reported similar behavior for drops evaporating on extremely smooth substrates that showed ionic, covalent, or metallic bonds on the surface on the order of 1 eV. For all these systems,1,2,17−19,32,34,36,49,50 in which the droplet did not show a receding movement, staying pinned to the solid surface almost until its complete disappearance, a constant minimum contact angle has not been observed. As discussed above, when complex real surfaces were involved, many open questions, consequences of a historically oversimplified theory of wettability, have been pointed out. A

Figure 1. Schematic illustration of advancing (θa) and receding (θr) contact angles for different measurement methods: (a) forced wetting, (b) forced dewetting, (c) evaporation, and (d) tilting plane.

the moment in which the drop started moving. Analogously, the term receding contact angle has generally referred to the threshold value of the contact angle beyond which the triple line was observed actually receding during a dewetting (Figure 1b) or evaporative (Figure 1c) process. Again, for drops sitting on tilting planes (Figure 1d), the term receding contact angle has been used to indicate the angle at the rear of the drop at the moment in which the drop started displacing. It is worth noting that some authors termed these angles as maximum advancing and minimum receding contact angles to emphasize their limit values (maximum and minimum, respectively), reached just before the three-phase contact line was observed moving. Despite the dissimilarities in the nomenclature, advancing and receding contact angles have been historically considered as unique and fundamental characteristics of a specific gas− liquid−solid system. However, especially in the past decade, many works reported a scatter in the θa/θr values for apparently similar gas−liquid−solid systems, in which actually unlike inner properties, such as substrate physical or chemical heterogeneities, roughness, random local defects, superficial molecular reorientations, or entrained air bubbles, were present.1−4,10,13,15,17−20,23−44 Even though the main causes of these value disparities have been ascribed to specific characteristics of the analyzed systems, frequently those intrinsic properties (substrate roughness, topography, impurities, flaws, chemical inhomogeneities, etc.) have not been clearly stated in the literature. Additionally, when diverse methods or different protocols within the same method have been used, discrepancies in the values of the receding contact angle of exactly alike gas−liquid−solid systems have been reported.1−4,15,19,20,24,26,27,31,39,41,42,45,46 For example, when the titling plane technique has been employed for experiments, disparities in θr values have been substantial. Erbil et al.,24 for example, noted differences of 14−15% in the θr values of water drops with unlike sizes placed on poly(methyl methacrylate) (PMMA; θr = 54°−78°) and poly(ethylene terephthalate) (PET; θr = 59°−75°) surfaces. In fact, receding contact angles obtained by the tilting plane method have been demonstrated to be greatly affected by the drop volume.3,24 Moreover, Krasovitski and Marmur26 showed that θr values were actually functions of the tilt angle itself and differed from those measured on horizontal surfaces. Even when the receding 9347


Langmuir

Article

standard definition of the receding contact angle, an investigation on its actual uniqueness, determination of possible influences on its value, and the eventual impossibility in measuring it are issues that must be put under focus and clarified. In order to answer these questions, the evaporation of pure water drops on polycarbonate (PC) substrates typified by five distinct irregular roughnesses was deeply investigated via the sessile drop method coupled with video-enhanced image digitization technology and a best-fitting algorithm. The evaporation dynamics were measured in terms of variation of drop contact angle, wetting diameter, drop volume, and drop shape. Influences of substrate roughness and relative humidity on contact angle measurements are delineated.

2. EXPERIMENTAL SECTION 2.1. Apparatus. A similar apparatus to the video-image-enhanced sessile drop tensiometer used in the present study has been detailed in Lin et al..16 The equipment was used to create silhouettes of the sessile drop, take video images of these silhouettes, and digitize the images. The apparatus consisted of an image forming and recording system, a drop forming system, an air thermostat, a humidity system, and a video-image profile digitizer. The image forming and recording system consisted of a light source (halogen lamp with constant light intensity; Oriel, QTH 63200), a lens system for producing a collimated beam, an objective lens (effective focal length 60 mm, f/no. 7.1), a video recorder, and a solid-state video camera [MS-4030 charge-coupled device (CCD), Sierra, Scientific Co.]. The lens system consisted of two plano-convex lens, a quartz neutral density (ND) filter, and a pinhole. The samples were installed on adjustable stages (with three translational degrees of freedom, rotation, and tilting) placed on a vibration-isolated workstation. The drop forming system consisted of a stainless-steel needle connected to the normally closed port of a three-way miniature solenoid valve (Lee Co.) via 1/16 in. i.d. Teflon tubing. The common port of the valve was connected to a gastight Hamilton syringe placed in a syringe pump. The valve was controlled by the output signal of a D/A card. The video-image system (Picolo, Euresys) digitized the pictures into 480 × 640 pixels, each of which was assigned a gray level value with an eight-bit resolution. The rate of image acquisition was 30 images/s. The air thermostat and humidity system was comoised of an air chamber, an air fan, a heater, a cooling coiled copper pipe, a thermistor probe, a humidifier, and a humidity detector. The humidifier and humidity detector were connected to the air chamber to increase and monitor the humidity of the air inside the chamber. The air chamber was made of 1 cm thick poly(methyl methacrylate) and the coiled copper pipe was connected to a refrigerated circulator outside the air chamber. A personal computer collected the temperature from the thermistor probe via a thermometer and controlled a power supplier [with a proportional-integral-derivative (PID) controller], which was connected with the heat generator. 2.2. Materials. The water used was purified by a Barnstead NANOpure water purification system with a specific conductance of less than 0.057 μS/cm. The polycarbonate, PC (CAS 24936-68-3), used in this work was purchased from Sun-Fung Co. Ltd., Taiwan. Some measurements were conducted on the original PC surface, used as-is. The other PC substrates underwent a grinding process for 15 min. The average grit sizes used (ISO 6344 grit designation) were 5, 8, 35, and 125 μm. Atomic force microscopy (AFM) analysis was conducted for investigating the unlike polymers’ topographies (Figure 2) and measuring surfaces roughnesses. Areas of 100 × 100 μm size were scanned in contact mode and the AFM images were analyzed for calculating the root-mean-square roughness, Rq, found to be 15 nm for the original PC substrate and 32, 114, 609, and 1159 nm for the other ground surfaces. From these roughness values, in this study the

Figure 2. AFM images of polymer (PC) surfaces analyzed in this study: (a) R15 (Rq = 15 nm), (b) R32 (Rq = 32 nm), (c) R114 (Rq = 114 nm), (d) R609 (Rq = 609 nm), and (e) R1159 (Rq = 1159 nm).

different substrates are named as R15, R32, R114, R609, and R1159, respectively. R15 substrates (Figure2a) exhibited smoother and more homogeneous surfaces; also random little irregularities, probably due to impurities and other contaminations, were detected by AFM examination. After the grinding processes, PC substrates presented an increasing number of defects and inhomogeneities: R32 and R114 (Figure2b,c) were characterized by striped-like topographies, while R609 and R1159 (Figure2d,e) showed more rugged surfaces. 2.3. Methods. The experimental protocol adopted during all the measurement runs was as follows. The polymer substrate was first rinsed with pure water and then carefully dried with a nitrogen gas flow. Afterward, the polymer substrate was placed on the stage in the air thermostat and leveled by adjusting the stage. The water sessile drop was then formed on the solid surface by the drop forming system. The moment in which the drop was gently deposited on the substrate was set as t = 0. Sequential digital images of the drop were then taken. The initial drop diameters were D0 = 2.3 ± 0.1 mm for all the measurement runs. The relative humidity, Hr, in the experimental chamber was increased by a humidifier and initially kept at ≥90%. At t = 60 s, the humidity was decreased to 42%, 55%, 65%, and 75% for different measurement runs. The relative humidity in the chamber decreased from 90% to the above-mentioned lower humidity values in about 3 min, and the Hr stability inside the chamber was ±1.5%. All experiments were undertaken at 25 ± 0.1 °C. The captured images were then processed to determine the drop edge coordinates. An edge detection routine was devised in the following way.16,51 To each pixel of the digital image was assigned a gray level, ranging from level 0, corresponding to the black region inside the drop, to level 255, corresponding to the bright region outside the drop. Close to the drop edge, the transition between levels 0 and 255 occurred in a few pixels and was continuous. The variation was symmetric in the immediate vicinity of level 127.5, and the change was almost linear. Therefore, the drop edge location was obtained by first interpolating a straight line between two symmetric points that bounded the gray level 127.5 and assuming the edge in the position of the interpolated line corresponded to an intensity of 127.5. The image system was calibrated by digitizing a stainless-steel ball with a known diameter of 1.577 ± 0.002 mm. The coordinates of the digitized sphere were processed to calibrate the average length between pixels along a row and along a column. The calibration procedure yielded values of 10.07 μm/pixel horizontally and 10.18 μm/pixel vertically. The uncertainty for the edge location was around 0.1 pixel.16,51 9348


Langmuir

Article

The theoretical shape of the sessile drop was then derived from the classical Laplace’s equation52−55 as fully described in Lin et al.16 The contact angle was set as the tangential angle of the intercept point between the theoretical sessile drop profile and air−solid interface. The error in the contact angle measurement was around 0.2°.

and up to t = 60 s, when the relative humidity in the experimental chamber was kept higher than 90% (stage I), all the drops exhibited similar behavior, freely spreading on the substrate, no matter upon which substrate they were sitting. The triple line was observed to slightly advance and then stop after ∼30 s. The dynamic contact angles were noted to be almost constant (Figure4a,c), presenting a small decrease at the end of this stage, probably since incomplete saturation of the atmosphere allowed a little evaporation of the drop.56,57

3. RESULTS Generally, four distinct stages18,19 could be identified in the course of spreading and evaporation of a sessile drop deposited on a solid surface. For typifying these stages, the spreading and evaporation of a drop placed on a R15 substrate (original PC) were used as an example as described below. During the initial spreading (stage I), when the atmosphere was maintained saturated in water vapor (Figure 3a, Hr curve),

Figure 4. Time dependence of contact angle θ for drops spreading and evaporating on PC substrates R15 (curve 1), R32 (curve 2), R114 (curve 3), R609 (curve 4), and R1159 (curve 5) for different humidity conditions: (a, b) humidity transition 90% → 42% and (c, d) humidity transition 90% → 55%.

The contact angles (advancing contact angles) measured during this phase showed a nearly constant value (θa values discrepancy = ±2°) among all the experimental runs for drops spreading on substrates characterized by the same superficial roughness (Table 1). However, quite diverse values of the

Figure 3. (a) Time dependence of contact angle θ, drop volume V, relative humidity Hr, and wetting diameter D for a drop spreading and evaporating on a R15 substrate (original PC). (b, c) Evolution of (b) drop silhouettes and (c) drop profiles. Numbers indicate the lifetime (seconds) of the sessile drop.

Table 1. Average Advancing and Receding Contact Angles for Different Surface Roughness/Relative Humidity Conditions during Evaporation

the value of the dynamic contact angle was observed to be almost constant (Figure 3a, θ curve, θa = 86.3°). Afterward, the atmosphere conditions inside the experimental chamber were altered, so that the relative humidity around the drop diminished (Figure 3a, Hr curve), greatly enhancing the evaporation (Figure 3a, V curve). This phase (stage II or constant contact radius mode, CCR) was characterized by a constant wetting diameter (Figure 3a, D curve), with the drop triple line pinned to the substrate (Figure 3b,c, t = 3 and 309 s). During the CCR mode, the contact angle was noted to decrease (Figure 3a, θ curve) until the drop started receding (depinning of the triple line). Stage III (or constant contact angle mode, CCA) was typified by a constant contact angle (Figure 3a, θ curve, θr = 73.8°) and a decreasing wetting diameter (Figure 3a, D curve). The triple line was recorded to freely move during this stage (Figure 3b,c, t = 610−1512 s). Finally, stage IV was characterized by a decrease of both wetting diameter and contact angle (Figure 3a, D and θ curves), leading to the final disappearance of the drop. These four stages were observed for most, but not all, of the drops spreading and evaporating on the ground substrates investigated in this study. Immediately after the drop deposition

humidity transition 90% → 42%



substrate

θa (deg)

θr (deg)

θa (deg)

θr (deg)

θa (deg)

θr (deg)

R15 R32 R114 R609 R1159

86.3 88.2 96 109.3 119.6

73.8 55.5 43.1 XXX XXX

86.6 85.7 96 109.3 117.5

72 54.5 41.3 XXX XXX

85.4 86 99 107.3 120.3

70.3 53.5 43.8 XXX XXX

advancing contact angle were noted, depending upon which substrate the drops were spreading, as shown in Figure4 and clearly reported in Table 1. Specifically, with increasing Rq, the advancing contact angles were observed to undergo a substantial increment (from ∼85° to ∼120°). After the first minute, when the relative humidity in the chamber was decreased (stage II or CCR mode), the wetting diameter exhibited an approximately constant value (Figure 5a,c). During this stage, in fact, all the drops clearly showed a pinned configuration of the three-phase contact line (Figure 6). 9349


Langmuir

Article

Figure 5. Time dependence of (a, c) wetting diameter D and (b, d) volume V for drops spreading and evaporating on PC substrates R15 (curve 1), R32 (curve 2), R114 (curve 3), R609 (curve 4), and R1159 (curve 5) for different humidity conditions: (a, b) humidity transition 90% → 42% and (c, d) humidity transition 90% → 55%.

This anchoring of the triple line was mainly due to superficial asperities and irregularities present on all the polymeric substrates, as shown by the AFM analysis illustrated in Figure 2. Since liquid withdrawal during drop evaporation (Figure 5b,d) could not be compensated by recoil of the triple line (Figure 6), a continuous diminution of the dynamic contact angles was recorded for all drops during stage II (Figure 4b,d). The decrease in contact angle exhibited a curved trend for all the evaporating drops (Figure 4b,d), and the curvature increasing with increased substrate roughness. Similar behavior of the dynamic contact angle has been reported by Zhang et al.32 for drops evaporating on structured PDMS substrates, characterized by microspherical caps with six different cap heights. After about 10−40 min (beginning of stage III, CCA mode), drops sitting on smoother surfaces (R15, R32, and R114) depinned. Suddenly the three-phase contact line appeared free to recede (Figure 6a,b) and the wetting diameter started to diminish almost linearly with time (Figure 5a,c, curves 1−3). For these evaporating drops exhibiting free movement of the triple line, the contact angles (receding contact angles) were observed to be almost constant during stage III (Figure 4b,d, curves 1−3). However, as previously noted for the advancing contact angles, a drastic difference in the values of the receding contact angle was observed with increasing substrate roughness (Figure 4b,d, curves 1−3; Table 1). Specifically, the average values of θr were noted to decrease from ∼74° to ∼42° with increasing Rq. Moreover, the depinning time (Figure 5a,c, curves 1−3) was recorded to greatly increase (from ∼10 to ∼40 min) with increased surface roughness. Interestingly, the receding contact angles showed a nearly constant value for drops evaporating at different relative humidities on substrates characterized by the same Rq (Figures 7a and 8, Table 1). However, Hr was observed to greatly

Figure 6. Evolution of drop profiles during the spreading and evaporation processes at 90% → 55% humidity transition for different substrates: (a) R32, (b) R114, (c) R609, and (d) R1159. Numbers indicate the lifetime (seconds) of the sessile drops.

influence the depinning time (Figure7b), and specifically, with increased relative humidity, the depinning time increased consistently (from ∼20 to ∼60 min). The relative humidity affected also liquid withdrawal and, consequently, drop lifetime (Figure 7c). Drops evaporating at Hr = 42% almost completely disappeared after ∼30 min, while after almost 1.5 h, drops evaporating at 75% relative humidity were still not totally vanished. For R609 and R1159, the rugged imperfections were so massive (Figure 2d,e) that the drop triple line was noted to be strongly anchored to the substrate surface essentially during the whole measurement process (Figure 6c,d). Therefore, depinning was not observed almost until the complete vanishing of the drop (Figure 5a,c, curves 4 and 5), and so, for drop evaporation on these rugged surface, no stage III (CCA mode) was recorded. As shown in Figure 4b,d for curves 4 and 5, the dynamic contact angle continuously decreased until drop disappearance. This observation was repeatedly noted for different humidity conditions in the experimental chamber (Hr = 75%, 65%, 55%, and 42%). Even for the largest liquid withdrawal (Hr = 42%), the triple line was not able to move from its pinning position. Without an actual movement of the three-phase contact line (that did not recede) and no CCA mode, it was impossible to determine a receding contact angle for drops evaporating on R609 and R1159, as reported in Table 1. 9350


Langmuir

Article

4. DISCUSSION Here the findings of this study, reported in section 3, are analyzed from a more general point of view to enhance how greatly the receding (or advancing) contact angle is actually affected by the intrinsic properties of the system and the measurement procedures. Regarding the influence of substrate roughness on the advancing contact angle, a massive increment of θa values with increasing Rq was noted in this study (Figure 9a). Similar

Figure 7. Time dependence of (a) drop contact angle θ, (b) drop wetting diameter D, and (c) drop volume V for drops spreading and evaporating on R114 substrates under different conditions: humidity transitions 90% → 42% (curve 1), 90% → 55% (curve 2), and 90% → 75% (curve 3).

Figure 9. Roughness dependence of average (a) advancing θa and (b) receding θr contact angles. Error bars indicate uncertainty for different measurements runs and relative humidities.

observations have been reported for static contact angles of several systems,1,2,5−11 and they will not be analyzed further in this discussion. However, it is worth noting that these static angle values have also been observed to depend not only on surface roughness but also on drop size2,3,15 and surface morphology.2,11 In section 1 we wondered if the receding contact angle could be considered as a unique specification for a gas−liquid−solid system. If by “gas−liquid−solid system” is intended the mere general system, as often reported in literature, we demonstrated that the receding contact angle is not unique. For example, in this study several different values of θr were found for the air− water−PC system. Specifically, the receding contact angles were recorded to strongly decrease with increasing substrate roughness (Figure9b). Real surfaces are generally not homogeneous, chemically inert, rigid, and perfectly flat. For this reason, the triple line is not always free to recoil, and the dewetting process can be viewed as a competition between capillary and friction forces.1,2,23,27,58,59 The capillary forces are proportional to the surface tension of the liquid and tend to make the triple line recede. Friction forces between the solid and liquid are instead due to local defects, chemical bonds, roughness, or molecular reorientation of the solid surface and tend to pin the threephase contact line.20,37 When the imbalance in the equilibrium

Figure 8. Humidity dependence of receding contact angle θr for drops evaporating on R15 (curve 1), R32 (curve 2), and R114 (curve 3) substrates.

Finally, at the beginning of stage IV, all the drops exhibited again some similar trends, no matter upon which substrate they were sitting: wetting diameter and contact angle both decreased until complete disappearance of the drop occurred (Figures 4b,d and 5a,c). 9351


Langmuir

Article

The actual indication of these common protocols for the measurement of receding (or advancing) contact angles is a very delicate matter and, thus, far beyond the purpose of this study. However, this discussion was intended as a “breaking through” initial point for a debate that must be faced and carried out by our academic community.

introduced by anchoring of the three-phase contact line cannot overcome the capillary forces due to volume reduction, the drop depins. As viewed in this study, different substrate roughnesses lead to diverse pinning configurations, and thus they result in different values of the measured receding contact angle. However, it is noteworthy that the discrepancies in θr values do not solely depend on the substrate roughness but, more properly, on the morphology of the solid surface. In fact, with increasing Rq, superhydrophobic surfaces, which present rough topographies but upon which the liquid sits on top of solid nano- and/or microstructures leaving air under the droplet (Fakir state), could show different trends for the receding contact angle.60 Furthermore, the influence of substrate roughness and relative humidity on depinning time (and so on transition time between CCR and CCA modes)38,43 is extremely relevant for measurement of the receding contact angle. In fact, for experiments conducted during too-short times (e.g., less than 10 min), depinning of the triple line might not be detected at all, with the consequent impossibility to determine θr. It is worth mentioning that observation time (as evidenced in this study), “aging” effects, and, in general, system history have been found to influence the values of contact angles measured by many different techniques.1,2,4,20,31,41,42 However, a simple increase in measurement time might not be enough to actually find a unique receding contact angle. In fact, when capillary forces due to the evaporation process do not overcome friction forces, the triple line does not depin almost until complete vanishing of the drop, and the dynamic contact angle continuously decreases until the drop disappears. This strong pinning case has been clearly observed in this study for drops evaporating from the most rugged polymer surfaces. Without an actual receding movement of the triple line or a constant contact angle value, we concluded that a receding contact angle cannot be found for strongly pinned drops. It could be argued that, by use of another technique (such as, for example, forced dewetting), a receding contact angle might be, actually, measured for these surfaces. Even if this argument could be correct, nevertheless, this directly implies that the measurement protocol indeed determines the failure/success in finding θr. From these remarks it appears evident how, if a meaningful receding contact angle has to be indicated for a given gas− liquid−solid system, its value must be reported for specific characteristics of the examined system (substrate roughness, topography, impurities, defects, chemical properties, etc.) and for specific methodological conditions (drop size, measurement method, system history, observation interval, relative humidity, etc.). Just in relation to these very precise properties of the system and method protocols, the receding contact angle could be viewed as unique. At this point we consider whether, for actually comparing different θr results reported in literature, that is, being able to confront the wettability of diverse materials, it would be worth identifying a common measurement standard or at least a set of standard protocols for different methods. Similar unified tests have been introduced for measuring a great number of different material properties, such as hardness (Vickers, Brinell, Rockwell, Knoop), toughness (Charpy, Izod), tensile stress and compressive strength (Universal testing machine), glass transition temperature (ISO 11357-2:2013), density in plastic materials (ISO 60:1977, ISO 61:1976), and many more.

5. CONCLUSIONS In this study, analysis of the behavior of sessile water drops spreading and evaporating on polycarbonate (PC) substrates typified by five distinct irregular roughnesses was systematically conducted. Relationships between measured dynamic and advancing/receding contact angles and the specific substrate roughness were investigated. Additionally, the influence of relative humidity on the drop evaporation behavior was analyzed. When the relative humidity in the experimental chamber was kept above 90% (stage I), although the spreading behavior was almost the same for all the measurement runs, the advancing contact angles exhibited a quite diverse range of values: with increased roughness of the substrate, the advancing contact angles were observed to increase. Afterward, when the relative humidity in the chamber was decreased (stage II), all the evaporating drops clearly showed a pinned configuration of the triple line, and the dynamic contact angle was observed to diminish. However, after about 10−40 min, drops sitting on smoother surfaces (R15, R32, and R114) depinned and the contact angles started to show almost constant values. Lower receding contact angles were recorded with increasing Rq. Contrariwise, the triple line depinning was not observed at all for sessile drops sitting on the rougher PC substrates, which kept the same constant wetting diameter almost until complete disappearance of the drop, while the contact angle was recorded to continuously decrease. Therefore, for drops exhibiting strong pinning of the triple line, a receding contact angle could not be measured. Differences in the relative humidity were noted to alter the system depinning time, so that Hr could actually influence measurement timing. However, generally, diverse conditions of relative humidity in the experimental chamber just slightly changed the receding contact angle value. Although similar analyses were previously reported in literature for sparse diverse cases,2,14,44 the fundamental repercussions of these findings were never explicitly collected and pointed out as in this study. The critical roles played by characteristics of the system and experimental protocols in measuring θr are indicated. Furthermore, the necessity of identifying common methodological standards is suggested in order to keep using the receding contact angle as a meaningful specification in evaluating the wettability of a given system.

■

AUTHOR INFORMATION

Corresponding Author

*Telephone +886-2-2737-6648; fax +886-2-2737-6644; e-mail [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We express great appreciation to NSC for the financial support (100-2221-E-011-101). 9352


Langmuir

■

Article

(26) Krasovitski, B.; Marmur, A. Drops down the Hill: Theoretical Study of Limiting Contact Angles and the Hysteresis Range on a Tilted Plate. Langmuir 2005, 21, 3881−3885. (27) Sefiane, K.; Tadrist, L. Experimental Investigation of the Depinning Phenomenon on Rough Surfaces of Volatile Drops. Int. Commun. Heat Mass Transfer 2006, 33, 482−490. (28) Anantharaju, N.; Panchagnula, M. V.; Vedantam, S.; Neti, S.; Tatic-Lucic, S. Effect of Three-Phase Contact Line Topology on Dynamic Contact Angles on Heterogeneous Surfaces. Langmuir 2007, 23, 11673−11676. (29) Anantharaju, N.; Panchagnula, M.; Neti, S. Evaporating Drops on Patterned Surfaces: Transition from Pinned to Moving Triple Line. J. Colloid Interface Sci. 2009, 337, 176−182. (30) Guilizzoni, M.; Sotgia, G. Experimental Analysis on the Shape and Evaporation of Water Drops on High Effusivity, Microfinned Surfaces. Exp. Therm. Fluid Sci. 2010, 34, 93−103. (31) Bormashenko, E.; Bormashenko, Y.; Oleg, G. On the Nature of the Friction between Nonstick Droplets and Solid Substrates. Langmuir 2010, 26, 12479−12482. (32) Zhang, C.; Zhu, X.; Zhou, L. Morphology Tunable Pinning Force and Evaporation Modes of Water Droplets on PDMS Spherical Cap Micron-Arrays. Chem. Phys. Lett. 2011, 508, 134−138. (33) Varnik, F.; Gross, M.; Moradi, N.; Zikos, G.; Uhlmann, P.; Müller-Buschbaum, P.; Magerl, D.; Raabe, D.; Steinbach, I.; Stamm, M. Stability and Dynamics of Droplets on Patterned Substrates: Insights from Experiments and Lattice Boltzmann Simulations. J. Phys.: Condens. Matter 2011, 23, No. 184112. (34) Orejon, D.; Sefiane, K.; Shanahan, M. E. R. Stick-Slip of Evaporating Droplets: Substrate Hydrophobicity and Nanoparticle Concentration. Langmuir 2011, 27, 12834−12843. (35) Tadmor, R. Approaches in Wetting Phenomena. Soft Matter 2011, 7, 1577−1580. (36) Bormashenko, E.; Musin, A.; Zinigrad, M. Evaporation of Droplets on Strongly and Weakly Pinning Surfaces and Dynamics of the Triple Line. Colloids Surf., A 2011, 385, 235−240. (37) Belman, N.; Jin, K.; Golan, Y.; Israelachvili, J. N.; Pesika, N. S. Origin of the Contact Angle Hysteresis of Water on Chemisorbed and Physisorbed Self-Assembled Monolayers. Langmuir 2012, 14609− 14617. (38) Chen, X.; Ma, R.; Li, J.; Hao, C.; Guo, W.; Luk, B. L.; Li, S. C.; Yao, S.; Wang, Z. Evaporation of Droplets on Superhydrophobic Surfaces: Surface Roughness and Small Droplet Size Effects. Phys. Rev. Lett. 2012, 109, No. 116101. (39) Erbil, H. Y. Evaporation of Pure Liquid Sessile and Spherical Suspended Drops: A Review. Adv. Colloid Interface Sci. 2012, 170, 67− 86. (40) Nguyen, T. A. H.; Nguyen, A. V.; Hampton, M. A.; Xu, Z. P.; Huang, L.; Rudolph, V. Theoretical and Experimental Analysis of Droplet Evaporation on Solid Surfaces. Chem. Eng. Sci. 2012, 69, 522− 529. (41) N’Guessan, H. E.; Leh, A.; Cox, P.; Bahadur, P.; Tadmor, R.; Patra, P.; Vajtai, R.; Ajayan, P. M.; Wasnik, P. Water Tribology on Graphene. Nat. Commun. 2012, 3, No. 1242. (42) Tadmor, R. Misconceptions in Wetting Phenomena. Langmuir 2013, 29, 15474−15475. (43) Xu, W.; Leeladhar, R.; Kang, Y. T.; Choi, C.-H. Evaporation Kinetics of Sessile Water Droplets on Micropillared Superhydrophobic Surfaces. Langmuir 2013, 29, 6032−6041. (44) Wang, L.; McCarthy, T. J. Shear Distortion and Failure of Capillary Bridges. Wetting Information beyond Contact Angle Analysis. Langmuir 2013, 29, 7776−7781. (45) Spelt, J. K.; Rotenberg, Y.; Absolom, D. R.; Neumann, A. W. Sessile-Drop Contact Angle Measurements Using Axisymmetric Drop Shape Analysis. Colloids Surf. 1987, 24, 127−137. (46) Bormashenko, E.; Bormashenko, Y.; Whyman, G.; Pogreb, R.; Musin, A.; Jager, R.; Barkay, Z. Contact Angle Hysteresis on Polymer Substrates Established with Various Experimental Techniques, Its Interpretation, and Quantitative Characterization. Langmuir 2008, 24, 4020−4025.

REFERENCES

(1) de Gennes, P. G.; Brochard-Wyart, F.; Quéré, D. Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves; Springer: New York, 2003. (2) Bormashenko, E. Wetting of Real Surfaces; de Gruyter GmbH: Berlin and Boston, 2013. (3) Mittal, K. L., Ed. Contact Angle, Wettability and Adhesion, Vol. 3; VSP International Science Publishers: Utrecht, The Netherlands, and Boston, MA, 2003. (4) Blake, T. D. Dynamic Contact Angle and Wetting Kinetics. In Wettability; Berg, J. C., Ed.; Marcel Dekker, New York, 1993; pp 251− 309. (5) Wenzel, R. N. Resistance of Solid Surfaces to Wetting by Water. Ind. Eng. Chem. 1936, 28, 988−994. (6) Cassie, A.; Baxter, S. Wettability of Porous Surfaces. Trans. Faraday Soc. 1944, 546−551. (7) Huh, C.; Mason, S. G. Effects of Surface Roughness on Wetting (theoretical). J. Colloid Interface Sci. 1977, 60, 11−38. (8) He, B.; Patankar, N. A.; Lee, J. Multiple Equilibrium Droplet Shapes and Design Criterion for Rough Hydrophobic Surfaces. Langmuir 2003, 19, 4999−5003. (9) Marmur, A. Wetting on Hydrophobic Rough Surfaces: To Be Heterogeneous or Not To Be? Langmuir 2003, 19, 8343−8348. (10) Cho, K. L.; Wu, A. H.-F.; Liaw, I. I.; Cookson, D.; Lamb, R. N. Wetting Transitions on Hierarchical Surfaces. J. Phys. Chem. C 2012, 116, 26810−26815. (11) Sarkar, A.; Kietzig, A.-M. General Equation of Wettability: A Tool to Calculate the Contact Angle for a Rough Surface. Chem. Phys. Lett. 2013, 574, 106−111. (12) Extrand, C. W. Model for Contact Angles and Hysteresis on Rough and Ultraphobic Surfaces. Langmuir 2002, 18, 7991−7999. (13) Long, J.; Chen, P. On the Role of Energy Barriers in Determining Contact Angle Hysteresis. Adv. Colloid Interface Sci. 2006, 127, 55−66. (14) Marmur, A. Soft Contact: Measurement and Interpretation of Contact Angles. Soft Matter 2006, 2, 12. (15) Tadmor, R.; Yadav, P. S. As-Placed Contact Angles for Sessile Drops. J. Colloid Interface Sci. 2008, 317, 241−246. (16) Lin, S.-Y.; Chang, H.-C.; Lin, L.-W.; Huang, P.-Y. Measurement of Dynamic/Advancing/Receding Contact Angle by Video-Enhanced Sessile Drop Tensiometry. Rev. Sci. Instrum. 1996, 67, 2852−2858. (17) Pittoni, P. G.; Chang, C.-C.; Yu, T.-S.; Lin, S.-Y. Evaporation of Water Drops on Polymer Surfaces: Pinning, Depinning and Dynamics of the Triple Line. Colloids Surf., A 2013, 432, 89−98. (18) Bourgès-Monnier, C.; Shanahan, M. E. R. Influence of Evaporation on Contact Angle. Langmuir 1995, 11, 2820−2829. (19) Shanahan, M. E. R.; Bourgès, C. Effects of Evaporation on Contact Angles on Polymer Surfaces. Int. J. Adhes. Adhes. 1994, 14, 201−205. (20) Liang Ling, W. Y.; Ng, T. W.; Neild, A.; Zheng, Q.; Ling, W. Y. L. Sliding Variability of Droplets on a Hydrophobic Incline due to Surface Entrained Air Bubbles. J. Colloid Interface Sci. 2011, 354, 832− 842. (21) Crick, C. R.; Parkin, I. P. Preparation and Characterisation of Super-Hydrophobic Surfaces. Chem.Eur. J. 2010, 16, 3568−3588. (22) Quéré, D.; Reyssat, M. Non-Adhesive Lotus and Other Hydrophobic Materials. Philos. Trans. R. Soc., A 2008, 366, 1539− 1556. (23) Joanny, J. F.; de Gennes, P. G. A Model for Contact Angle Hysteresis. J. Chem. Phys. 1984, 81, 552−562. (24) Erbil, H. Y.; McHale, G.; Rowan, S. M.; Newton, M. I. Determination of the Receding Contact Angle of Sessile Drops on Polymer Surfaces by Evaporation. Langmuir 1999, 15, 7378−7385. (25) Soolaman, D. M.; Yu, H.-Z. Water Microdroplets on Molecularly Tailored Surfaces: Correlation between Wetting Hysteresis and Evaporation Mode Switching. J. Phys. Chem. B 2005, 109, 17967−17973. 9353


Langmuir

Article

(47) Picknett, R. G.; Bexon, R. The Evaporation of Sessile or Pendant Drops in Still Air. J. Colloid Interface Sci. 1977, 61, 336−350. (48) Hu, H.; Larson, R. G. Evaporation of a Sessile Droplet on a Substrate. J. Phys. Chem. B 2002, 106, 1334−1344. (49) Chhasatia, V. H.; Joshi, A. S.; Sun, Y. Effect of Relative Humidity on Contact Angle and Particle Deposition Morphology of an Evaporating Colloidal Drop. Appl. Phys. Lett. 2010, 97, No. 231909. (50) Girard, F.; Antoni, M.; Faure, S.; Steinchen, A. Influence of Heating Temperature and Relative Humidity in the Evaporation of Pinned Droplets. Colloids Surf., A 2008, 323, 36−49. (51) Lin, S.-Y.; Mckeigue, K.; Maldarelli, C. Diffusion-Controlled Surfactant Adsorption Studied by Pendant Drop Digitization. AIChE J. 1990, 36, 1785−1795. (52) Bashforth, F.; Adams, J. C. An Attempt to Test the Theories of Capillary Action by Comparing the Theoretical and Measured Forms of Drops of Fluid; Cambridge University Press: Cambridge, U.K., 1883. (53) Padday, J. F. The Profiles of Axially Symmetric Menisci. Philos. Trans. R. Soc., A 1971, 269, 265−293. (54) Rotenberg, Y.; Boruvka, L.; Neumann, A. W. Determination of Surface Tension and Contact Angle from the Shapes of Axisymmetric Fluid Interfaces. J. Colloid Interface Sci. 1983, 93, 169−183. (55) Huh, C.; Reed, R. L. A Method for Estimating Interfacial Tensions and Contact Angles from Sessile and Pendant Drop Shapes. J. Colloid Interface Sci. 1983, 91, 472−484. (56) Butt, H.-J.; Golovko, D. S.; Bonaccurso, E. On the Derivation of Young’s Equation for Sessile Drops: Nonequilibrium Effects Due to Evaporation. J. Phys. Chem. B 2007, 111, 5277−5283. (57) Golovko, D. S.; Butt, H.-J.; Bonaccurso, E. Transition in the Evaporation Kinetics of Water Microdrops on Hydrophilic Surfaces. Langmuir 2009, 25, 75−78. (58) Shanahan, M. E. R. Simple Theory of “Stick-Slip” Wetting Hysteresis. Langmuir 1995, 1041−1043. (59) Reyssat, M.; Quéré, D. Contact Angle Hysteresis Generated by Strong Dilute Defects. J. Phys. Chem. B 2009, 113, 3906−3909. (60) Susarrey-Arce, A.; Marín, Á . G.; Nair, H.; Lefferts, L.; Gardeniers, J. G. E.; Lohse, D.; van Houselt, A. Absence of an Evaporation-Driven Wetting Transition on Omniphobic Surfaces. Soft Matter 2012, 8, 9765−9770.

9354


On the Uniqueness of the Receding Contact Angle: Effects of

Recommend Documents