Effect of Roughness Geometry on Wetting and Dewetting of Rough

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Effect of Roughness Geometry on Wetting and Dewetting of Rough PDMS Surfaces Mandakini Kanungo, Srinivas Mettu, and Kock-Yee Law* Xerox Corporation Xerox Research Center, Webster 800 Phillips Rd, 147-59B, Webster, New York 14580, United States

Susan Daniel School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14853, United States S Supporting Information *

ABSTRACT: Rough PDMS surfaces comprising 3 μm hemispherical bumps and cavities with pitches ranging from 4.5 to 96 μm have been fabricated by photolithographic and molding techniques. Their wetting and dewetting behavior with water was studied as model for print surfaces used in additive manufacturing and printed electronics. A smooth PDMS surface was studied as control. For a given pitch, both bumpy and cavity surfaces exhibit similar static contact angles, which increase as the roughness ratio increases. Notably, the observed water contact angles are shown to be consistently larger than the calculated Wenzel angles, attributable to the pinning of the water droplets into the metastable wetting states. Optical microscopy reveals that the contact lines on both the bumpy and cavity surfaces are distorted by the microtextures, pinning at the lead edges of the bumps and cavities. Vibration of the sessile droplets on the smooth, bumpy, and cavity PDMS surfaces results in the same contact angle, from 110°−124° to ∼91°. The results suggest that all three surfaces have the same stable wetting states after vibration and that water droplets pin in the smooth area of the rough PDMS surfaces. This conclusion is supported by visual inspection of the contact lines before and after vibration. The importance of pinning location rather than surface energy on the contact angle is discussed. The dewetting of the water droplet was studied by examining the receding motion of the contact line by evaporating the sessile droplets of a very dilute rhodamine dye solution on these surfaces. The results reveal that the contact line is dragged by the bumps as it recedes, whereas dragging is not visible on the smooth and the cavity surfaces. The drag created by the bumps toward the wetting and dewetting process is also visible in the velocity-dependent advancing and receding contact angle experiments.

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INTRODUCTION Wetting and spreading of liquid on a solid surface not only is an important topic in surface science but also intimately impacts our daily lives, such as washing, cleaning, lawn care, writing, painting, etc. A fundamental understanding of this subject is also crucial for many industrial applications, such as liquid transportation in fuel lines and microfluidic devices and coating and printing of flexible electronic devices and solar cells, just to name a few.1−7 Even as simple as ink writing with a fountain pen, Kim and co-workers8 found that the line width of the ink image on paper depends on the speed of the pen as well as the physicochemical properties of both ink and paper. While the volume of printed books and magazines has been on decline for over a decade,9 printing has evolved and has become a manufacturing technology for flexible electronic devices, displays, solar cells, textiles, ceramics, microfluidic devices, etc.4−7,10−19 Similar to writing with a fountain pen, understanding and controlling interactions between ink and substrate are keys to a successful implementation of ink printing in manufacturing. Arias et al.4 showed that balance between © XXXX American Chemical Society

pinning and overspreading of printed liquid ink on the solid surface is crucial in defining the position, resolution, and size in the fabrication of thin-film-transistor (TFT) array. Berson et al.,7 Fukuda et al.,12 Schuppert and co-workers13 as well as Wu14 all found that controlling ink−substrate interactions is essential to the functional performance of the printed silver electrodes. Jetted ink drop is also known to form the so-called coffee ring stain due to unoptimized spreading and drying, which is detrimental to the quality of the printed image.20 Both plastic and coated paper substrates have been used for printed/ flexible electronic applications.21−26 Figure 1 depicts representative optical profiles of two typical commercial printing substrates. These substrates are not atomic smooth, and their roughness ranges from the nano- to micrometer scale and the roughness is random.21−25,27 Surface with random roughness structure has shown to exhibit nonuniform wettability in the Received: November 12, 2013 Revised: June 2, 2014

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Water was used as a model liquid. Results show that the microtextures on the PDMS surfaces have profound effects on the wetting and dewetting performance. Comparing to the contact line of the controlled smooth PDMS surface, those of the model rough surfaces were found to be distorted by the microtextures with water pinning at the lead edge of both the bumps and the cavities on the rough surfaces. The effects of roughness geometry on wetting and dewetting under both static and dynamic conditions are highlighted. The implication of the results in printed electronic manufacturing is discussed.

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EXPERIMENTAL SECTION Materials and Fabrication of Various Rough PDMS Surfaces. Silicon Molds. The silicon molds used in this work were fabricated on 4 in. test grade silicon wafers (Montco Silicon Technologies, Inc.) by the conventional photolithographic technique at the Cornell Nanofabrication Facility (CNF) in Ithaca, NY. The silicon wafer was first cleaned with acetone followed by the application of an adhesion promoter P20. Then photoresist SPR700-1.2 (Shipley) was spin-coated onto the silicon wafer at 4000 rpm for 30 s. The photoresist was prebaked at 95oC for 60 s before light exposure. The lithographic mask was constructed by Photronics Inc. The texture for the hemispherical cavity silicon mold was defined via 5:1 (15 to 3 μm) reduction feature photolithography on Autostep 200, followed by transferring the patterns from the mask to the photoresist. This was followed by an image reversal process using ammonia baking for 90 min in the YES 58-SM image reversal oven. The silicon wafer was then flood exposed using a contact aligner, and the photoresist was developed by a tetramethylammonium hydroxide solution. The hemispherical cavity silicon mold (3 μm in diameter and 1.5 μm in depth) was created by isotropic etching the sample with SF6 (1 min), followed by stripping the resist with N-methyl-2-pyrrolidone. The surface of the resulting silicon mold was then modified by a fluorinated self-assembled monolayer (FOTS) synthesized from tridecafluoro-1,1,2,2-tetrahydrooctyltrichlorosilane using a MVD100 reactor from Applied Microstructures, Inc. This FOTS layer was heat cured in an oven at ∼150 °C for ∼30 min and was used as a release layer for the subsequent molding process. PDMS Surfaces with Bumps and Cavities. Sylgard 184 (Dow Corning Inc.) was thoroughly mixed with the merchant supplied curing agent in 10:1 weight ratio and degassed in vacuum for about an hour to remove any trapped air bubbles. This uncured mixture was poured onto the FOTS-coated hemispherical cavity silicon mold and cured overnight at 70 °C. The cured sample was cooled in a freezer for an hour, and the cured PDMS layer was peeled off gently from the silicon mold, resulting in a PDMS layer having arrays of hemispherical bumps on the surface. This bumpy PDMS layer could be surface modified with FOTS and served as a mold to fabricate PDMS layer with the cavity array surface. Essentially, uncured PDMS (Sylgard 184 with the curing agent in 10:1 ratio) was poured onto the FOTS-modified PDMS layer with the bumpy array on the surface. After curing, a PDMS layer having arrays of hemispherical cavities on its surface was obtained. Measurements and Characterization. Contact Angles. Contact angle measurements were carried out on an OCA20 goniometer from Dataphysics, which consists of a computercontrolled automatic liquid deposition system and a computerbased image processing system. DI Water (18 MΩ·cm, purified

Figure 1. Optical profiles of representative substrates for printed electronics (a) flexo coated biaxially oriented poly(propylene) and (b) digital-top-coat coated semigloss elite paper.

microscopic scale.28 For high quality, high resolution device manufacturing, variation of ink−substrate interaction in the micrometer scale can create nonuniformity in the printed device, which may eventually either affect the resolution or cause variation in device performance. Interactions between surface and liquid are known to have direct effects on the quality and performance of the printed device. While wetting and spreading are obviously important in the quality of the printed line and its resolution, dewetting has been shown to be a main cause of the well-known coffee stain effect. Indeed, Kim and co-workers29 reported that microstructures, which can lead to Cassie−Baxter or Wenzel state on the print surface can directly affect the spreading and pinning behavior as well as the quality of the printed ink lines. While pillar array surfaces have frequently been used to model the wetting and dewetting behavior of rough surfaces,30−33 they are not good models for printing substrates such as those shown in Figure 1. As pointed out in the Supporting Information, pillars are basically high aspect ratio protrusions on a flat surface (Figure S1). Recent studies showed that nanoprotrusions are capable of pinning and immobilizing the contact line during spreading27 and dewetting.34 We suggest that hemispherical bumps and cavities are better models since they do not have any apparent pinning sites like pillars that may complicate the understanding of the ink−surface interactions. In this work, PDMS surfaces with varying pitches of hemispherical bumps and cavities were fabricated to investigate the effect of roughness geometry (e.g., frequency, peaks, or valleys) on the wetting and dewetting behaviors of liquid on print surfaces. B

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geometry has an effect on the dynamic wetting and dewetting process. The velocity-dependent advancing and receding angles for the smooth PDMS surface were measured as control.

by a reverse osmosis process) was used as the test liquid. In a typical static contact angle measurement, ∼4 μL of the test liquid was gently deposited on the testing surface using a microsyringe; the static contact angle was determined by the computer software (SCA20), and each reported data is an average of more than five independent measurements. Typical measurement error is less than 2°. For dynamic measurements, the advancing contact angle was determined using the drop expansion method, by slowly adding a small volume (∼0.15 μL/s) of the probing liquid to a 1−2 μL sessile droplet on the test surface. The receding contact angle was measured by slowly removing (0.15 μL/s) the probing liquid from the expanded sessile drop. All reported data were an average of five measurements, using a pristine area of the substrate for each measurement. Drop Vibration Experiments. Typically, the test surface was firmly attached to the stem of a mechanical oscillator (Pasco Scientific, Model No. SF-9324), and a 10 μL water droplet was gently placed on the surface using a micropipet. The initial contact angle was found to be equivalent to the static contact angle determined from the goniometer. White noise generated by an Agilent signal generator (Model 33120A) amplified by a Sherwood power amplifier (Model RX-4105) was supplied to the drop through the oscillator using the procedure as described by Mettu and Chaudhury.35,36 The contact angle of the water droplet was determined after the vibration. Microscopy. Scanning electron micrographs (SEM) of various samples were taken on a S-4800 FESEM microscope from Hitachi. Optical microscopy was performed on the Zeiss Axiophot and Zeiss Axiomat microscopes (Germany). Experimentally, a 5 μL water droplet was first placed on the test surface, and the image of the advancing contact lines was recorded in the inverted mode. In the inverted mode, the image of the three-phase contact line was captured directly. The receding contact line was visualized by first evaporating a droplet of a very dilute Rhodamine B dye (Sigma-Aldrich) solution (∼5 × 10−6 g/mL) on the test surface, followed by capturing the contours of the evaporated drop by optical microscopy. Controlled experiments indicated that the contact angles of the dyes solution were identical to those of pure water. Dynamic Wetting and Dewetting Experiments. Velocitydependent advancing and receding contact angle measurements were carried out using a high-sensitivity micromechanical balance on a tensiometer (Dataphysics DCAT 21 from Germany). PDMS samples for these experiments consist of either bumps or cavities on both sides. They were prepared by casting and curing the PDMS material between two identical molds (hemispherical cavity mold for the bumpy surface and hemispherical bumpy mold for the cavity surface). The test sample was first firmly attached to the arm of the microbalance in the tensiometer and was then brought in contact with the test liquid in a beaker. Schematics showing the measurement of the velocity dependent advancing/receding contact angles are given in Figure S9 of the Supporting Information. When the sample was pushed into the test liquid (water) at a fixed velocity, the advancing contact angle at a given velocity was measured. The velocity studied ranges from 0.002 to 2 mm/s, and the maximum immersion depth of the sample was ∼8 mm. The velocity-dependent receding contact angle was determined by withdrawing the sample from the test liquid after maximum immersion. Model rough PDMS surfaces comprising arrays of bumps and cavities were studied to examine if roughness

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RESULTS AND DISCUSSION Fabrication of Model Rough PDMS Surfaces. The model rough PDMS surfaces were fabricated by first creating a silicon mold consisting of 3 μm hemispherical cavity arrays on a silicon wafer using the conventional photolithographic and etching procedures. After modifying the silicon mold surface with a fluorosilane release layer FOTS, synthesized from tridecafluoro-1,1,2,2-tetrahydrooctyltrichlorosilane, Sylgard 184 was poured onto the mold and cured. This results in a PDMS layer with arrays of bumps on the surface. PDMS layer with arrays of cavities on the surface was fabricated by using the above bumpy PDMS surface as a mold. This is done by first modifying the bumpy PDMS surface with FOTS followed by pouring Sylgard 184 onto the bumpy surface. After curing, a PDMS layer with array of cavities on the surface is obtained. Figure 2 summarizes the key steps in the fabrication process

Figure 2. (a) Schematic for the fabrication of the silicon mold and the model PDMS surfaces with array of bumps and cavities. (b) SEM micrograph of the 3 μm diameter hemispherical silicon mold. (c) SEM micrograph of the hemispherical bump on the PDMS surface created from the mold in (b). (d) SEM micrograph of the hemispherical cavity PDMS surface molded from the bumpy surface in (c).

along with the SEM micrographs of the representative silicon mold, a 3 μm hemispherical bump on the PDMS surface, and a 3 μm hemispherical cavity on the PDMS surface. Using the same procedure, PDMS surfaces with arrays of bumps and cavities of varying pitches have been fabricated by simply changing the pitches in the photomasks. The SEM micrographs of the representative bumpy array and cavity array surfaces are given in Figure S2 of the Supporting Information. Surface Properties of the Model Rough PDMS Surfaces. Wetting States. The surface properties of all model rough surfaces were studied by static and dynamic contact angle measurements with water as the test liquid, and the data are summarized in Table 1. The contact angle data for the smooth PDMS surface are included as reference. Wetting of liquid on a rough surface can be described by two classic wetting models. When the rough surface is fully wetted by the liquid, the apparent static contact angle is the Wenzel angle (θW) and is given by the Wenzel equation:37 C

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Table 1. Contact Angle (deg) Measurement Data for Model Rough PDMS Surfaces with Arrays of Bumps and Cavities array of bumps

array of cavities

pitcha

rb

θ Wc

θCBd

θe

θAf

θRg

CAHh

θe

θAf

θRg

CAHh

reff i

θWmod j

96 μm 48 μm 24 μm 12 μm 6 μm 4.5 μm smooth surface

1.00 1.01 1.02 1.1 1.4 1.7 1.00

110 110 111 112 118 126

110 110 110 112 118 125

116 115 117 122 129 138 110

117 119 120 125 131 144 112

69 71 68 61 68 83 72

48 48 52 64 63 61 40

117 117 118 124 128 136

120 120 119 129 132 140

76 77 79 81 83 88

44 43 40 48 49 52

1.05 1.11 1.22 1.44 1.87 2.16

111 112 115 119 130 138

a Center-to-center spacing between bumps or cavities. bThe classic Wenzel roughness ratio, actual surface area divided by projected area. cCalculated Wenzel angle from eq 1. dCalculated Cassie−Baxter angle (θCB) for cavity surface from eq 2. eStatic contact angle. fAdvancing contact angle. g Receding contact angle. hContact angle hysteresis, defined as (θA − θR). iEffective roughness factor calculated by correcting for the increase of contact line density at the three-phase contact line (ref 30). jModified Wenzel angle calculated according to method of Forsberg and co-workers (ref 30). [See Supporting Information for geometrical parameters and contact angle calculations for (b), (c), (d), (i), and (j)].

cos θ W = r cos θ

(1)

where r is the roughness ratio and is defined as the actual surface area of the rough surface divided by the projected surface area. θ is the static contact angle of the flat surface. The Wenzel roughness ratios (r) for the model rough PDMS surfaces of this work can be calculated from the radii and geometry of the bumps and cavities. The r values are the same for the bumpy and cavity surfaces of the same pitch. Details of the calculation are provided in the Supporting Information. From the r values, the Wenzel angles (θW) are calculated and are given in Table 1, column 3. For rough, porous surface where pockets of air can be created during wetting, a composite solid−liquid interface is formed. The apparent contact angle is the Cassie-Baxter angle (θCB) and is given by the Cassie−Baxter equation:38 cos θCB = r f f cos θ + f − 1

(2) Figure 3. Generalized, hypothetical schematics for the wetting of (a) the bumpy PDMS surface and (b) the cavity PDMS surface. On the bumpy PDMS surface, hL is the height needed to create the air pocket. On the cavity surface, hL is the sagging height.

where rf is the roughness of the solid−liquid interface and f is the solid area fraction of the projected wet area. Again, both rf and f for the bumpy and cavity surfaces can be calculated from the geometrical parameters, and the details are in the Supporting Information. Figure 3 shows the generalized, hypothetical wetting states for (a) the bumpy PDMS surface and (b) the cavity PDMS surface. On the bumpy PDMS surface, hL is the height needed to create the air pocket. On the cavity surface, hL is the sagging height. Since optical photographs (Figure 5) show that the contact lines for both bumpy and cavity surfaces are distorted and pinned at the lead edge of the rough structures, the results thus indicate that hL is 0 for both the bumpy and cavity surfaces. It is thus geometrically impossible to trap air on the bumpy surface when hL = 0 during wetting. In other words, bumpy PDMS surfaces are always in the Wenzel wetting state. However, a Cassie−Baxter-like state is still a possibility for the cavity surface when hL = 0. From the rf and f values, the Cassie−Baxter angles (θCB) for the cavity surfaces are also calculated (Table 1, column 4). The overall results in Table 1 show that the observed θ for the model rough PDMS surfaces (Table 1, columns 5 and 9) are not in agreement with neither the θW values nor the θCB values. The disagreement is not surprising as recent theoretical and experimental results have shown that the contact angles of rough surfaces tend to correlate more to the locality of the three phase contact line than the classic Wenzel and Cassie− Baxter angles due to pinning of the contact lines on rough

surfaces.30,39−43 Using the methodology of Forsberg and coworkers,30 a 1-dimensional modified Wenzel equation can be derived based on the geometry of the contact line observed in Figure 5, where θmod W is the modified Wenzel angle. ⎛ R⎞ R cos θ Wmod = ⎜1 − ⎟ cos θ + cos(θ + π /2) ⎝ D⎠ D

(3)

After rearranging eq 3 to the classical Wenzel format, the effective roughness ratio (reff) is obtained and is given by R r eff = 1 − (1 + tan θ ) (4) D eff mod Details for the derivations of r and θW and discussion of the wetting states are provided in the Supporting Information. The calculated reff and θmod W values are listed in Table 1, columns 13 and 14, respectively. Without exception, reasonably good agreements between θmod W and θ are observed for both bumpy and cavity surfaces, suggesting that both type of surfaces are in the fully wetted Wenzel states. This conclusion is supported by recent wetting studies of PDMS pillar array surfaces both theoretically and experimentally. Jopp et al.44 showed by free energy calculation that water will fill all the grooves between pillar arrays of PDMS, which is hydrophobic. Papadopoulos D

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and co-workers32 reported the visualization of the fully wetted liquid−solid interface between water and PDMS three dimensionally by laser scanning confocal microscopy. Additional evidence in support of this conclusion can also be found in the drop vibration experiments, which will be presented later in this paper. Effect of Pitch Length. Results in Table 1 show that the static contact angles (θ) increases as pitch length decreases for both types of rough surfaces (bumps and cavities) due to the increase in roughness on the PDMS surface. It is worthy pointing out that for the same pitch, where the roughness ratio is the same, the static contact angles for the bumpy and cavity surface are actually very similar. Interesting results are observed for the dynamic contact angle data. The advancing contact angles (θA) for the bumpy surface and the cavity surface are comparable for the same pitch, and they increase, from ∼116° to ∼138°, as reff increases from 1.05 to 2.16. Although a similar trend is also observed for the receding contact angles (θR) (increase as reff increases), the receding angles for the bumpy surfaces are consistently smaller than those of the cavity surfaces. In other words, for the same pitch, the hysteresis for the bumpy PDMS surface (column 8) is always larger than that of the cavity surface (column 12). Similar asymmetric hysteresis has been observed for pillar and porous array surfaces by Priest et al.31 In this work, we have visual evidence to show that bumps are exerting strong resistance and drag the receding contact line (Figure 8b), whereas minimal dragging is seen by the cavities (Figure 8c). Further evidence for the strong interaction between the bumps and the contact line can be seen in dynamic advancing/ receding angle experiments presented later in this work (Figure 9b and Figure S11a in the Supporting Information). We thus attribute the asymmetric hysteresis observed in this work to the dragging of the contact line by the bumps as the liquid recedes. Contact Line Location and Pinning. To better understand the wettability data, we choose the 12 μm pitch bumpy and cavity array PDMS surfaces for more detailed study. Figure 4a depicts the photographs of the ∼5 μL sessile water droplets

Figure 5. Expectedly, the contact line for the smooth PDMS surface is smooth and round (Figure 5a), whereas those on the

Figure 5. Optical photographs of the three-phase contact lines as imaged from the bottom of the water sessile droplets on (a) smooth, (b) 12 μm pitch bumpy, and (c) 12 μm pitch cavity PDMS surfaces.

bumpy and cavity surfaces are distorted by the microstructures (Figures 5b,c). This is consistent with the contact lines observed in other microtextured surfaces, where the threephase contact lines are all shown to follow the edge of the rough microstructures.31,32,39−43 A closer examination reveals that the three-phase contact lines in this work actually follow the lead edges of the bumps on the bumpy surface and the cavities on the cavity surface. As discussed later, the location for the water droplet to stop advancing is when all its kinetic energy is dissipated. The most likely location is after the advancing water climbs over the “last” bump on the bumpy surface or the wall from the bottom of the “last” cavity on the cavity surface (Figure S5 in Supporting Information). A schematic showing the top view and side view of the threephase contact lines on these surfaces is given in Figure 6. Both contact lines are shown pinning at the lead edges of the rough structures.

Figure 4. Images of the water sessile droplets on smooth and rough PDMS surfaces (a) before and (b) after 15 s vibration.

on the smooth PDMS surface, the 12 μm pitch bumpy PDMS surface, and the 12 μm pitch cavity PDMS surface. Their static contact angles are at 110°, 122°, and 124°, respectively. The location and the geometry of the contact lines on these surfaces were examined directly from the bottom of the water droplets, and the optical micrographs of the contact lines are given in

Figure 6. Schematics for the top view and side view of the three-phase contact lines for water droplets on the bumpy and cavity PDMS surfaces. E

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Wetting and spreading of a sessile drop on a horizontal solid surface is actually a very complex process. Shuttleworth and Bailey45 first reported that the final position of the advancing liquid depends not only on the surface energies of the liquid, the solid, and the solid−liquid interface but also the roughness of the surface and the manner in which the liquid is placed on the solid. To test the wetting states of the water droplets in this work, we subject all three water droplets in Figure 4a to a 15 s vibration according to the procedure described by Cwikel and co-workers,46 and the results are given in Figure 4b. All three sessile drops give the same static contact angles at ∼91° after the 15 s vibration. The results indicate that all three sessile droplets were in the metastable wetting states before the vibration. While the static contact angle for the smooth PDMS surface changes from 110° to 92° after vibration and the observation is consistent with that reported by Cwikel and coworkers,46 the results for the bumpy and cavity surfaces are very unusual as their contact angles after vibration suggest that water droplets on these rough surfaces also pin on the smooth areas of the rough PDMS surfaces! Indeed, recent optical microscopy results show that the contact lines on both bumpy and cavity PDMS surfaces also become much smoother after vibration and that they appear to be on the smooth area of the PDMS surfaces rather than distorted by the rough structures (Figures S6 and S7 in Supporting Information). In addition, we have recently completed a set of similar drop-vibration experiments with both bumpy and cavity surfaces of pitches ranging from 4.5 to 24 μm. Details of the results are summarized in Supporting Information. The results from the 6, 12, and 24 μm pitch surfaces indicate that the contact angles of all the rough surfaces are converging to ∼91° without exception (Figure S8). This suggests that water droplets are always in the metastable wetting states on the bumpy and cavity surfaces due to pinning effect. Vibration, which leads to depinning and relocation of the contact lines, results in the population of the most stable wetting states on these surfaces. The similar final θ values, to the smooth surface and among themselves, after vibration suggest that the most stable wetting states on the bumpy and cavity surfaces of pitch length varying from 6 to 24 μm also involve pinning the water droplets on the smooth area of the rough PDMS surfaces. Qualitatively, we observed that it would take more vibrational energy to depin and relocate the drop as the pitch decreases from 24 to 6 μm. For the 4.5 μm pitch bumpy and cavity surfaces, we were unable to obtain any stable water droplets after vibration. We suggest that, due to the increase in the density of the bumps or cavities on the 4.5 μm pitch surfaces, relocating the contact lines to the smooth area just becomes increasingly difficult. The drops just simply break up during vibration. This observation is actually an antidotal evidence for the occurrence of contact line pinning on the bumpy and cavity PDMS surfaces. Studies of liquid wettability on a rough surface can be traced back to 1936 when Wenzel37 reported that roughness in surface enhances liquid wettability when the contact angle of the flat surface is 90°. Shuttleworth and Bailey,45 Johnson and Dettre,47 Neumann and Good,48 and more recently by Long and coworkers49 all suggested that the process of wetting can be viewed as involving a series of metastable wetting states as the sessile drop is advancing toward its static state position. A schematic showing the relationship between the Gibbs free energy of the wetting states and the contact angle of the rough surface is given in Figure 7 (blue line). The potential energy

Figure 7. Schematic plot of the Gibbs free energy curves for wetting of a smooth PDMS surface (red line) and a rough (for both bumps and cavities) PDMS surface (blue line) by water as a function of the apparent contact angle. θS is the most stable contact angle.

curve for the smooth PDMS surface is shown in red based on the contact angle data in Table 1. According to Shuttleworth and Bailey45 and the molecular kinetic theory as well as molecular simulations,50−56 wetting a solid surface involves transfer of the kinetic energy of the sessile droplet (gained from gravity acceleration) to the kinetic energy for wetting after the liquid droplet contacts the surface. The liquid droplet will reach its static state once all of its kinetic energy is dissipated. If the friction on the advancing solid surface is high, all the kinetic energy in the sessile drop may dissipate prematurely before reaching the thermodynamically stable state. This will result in pinning of the sessile drops into the metastable wetting states with larger than expected apparent static contact angles. The generally large θ values observed in Table 1 for the bumpy and cavity PDMS surfaces relative to the calculated Wenzel angles (θW) can thus be attributed to this pinning effect.30,32,42 In the case of a fully wetted water droplet on a rough surface, Meiron and co-workers57 showed that vibration can convert a metastable wetting state to the most stable Wenzel state. The contact angle for the stable Wenzel state was found to be in agreement with the calculated Wenzel angle (θW). In this work, in contrast to that reported by Meiron and co-workers, the most stable contact angles for the bumpy and cavity surfaces are a lot smaller than the calculated θW (110°−126° versus ∼91°). The similar contact angles for all three surfaces after the 15 s vibration suggest that the contact lines on the rough surfaces relocate to the smooth area of the PDMS surfaces after depinning by vibration. This is supported by recent optical microscopy results (Figures S6 and S7) and implies that the stable Wenzel states for the bumpy and cavity surfaces are not as thermodynamically favorable as that of the smooth surface. We suggest that during vibrational excitation the contact lines depin, and the droplets on the bumpy and cavity surfaces are able to crossover (from blue to red) to the energy curve of the smooth PDMS surface (Figure 7). Since the surface energetics between the smooth and the rough PDMS surfaces are expected to be different, the similar contact angles for all three sessile drops in Figure 4b confirm F

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Figure 8. Optical photographs of the receding contact lines as imaged by evaporating a very dilute Rhodamine dye solution (∼5 × 10−6 g/mL) on (a) smooth, (b) 12 μm pitch bumpy, and (c) 12 μm pitch cavity PDMS surfaces. The arrows show the receding directions.

dewetting processes between water and the PDMS surfaces. However, in many industrial applications such as printing, both liquid and solid surface are constantly in motion. In the other words, both wetting and dewetting processes are not static. To gain insights about the dynamic liquid−solid interactions, we study the velocity-dependent advancing and receding contact angles with the 12 μm pitch bumpy and cavity PDMS surfaces on the tensiometer. A schematic of the experiment and the details of the velocity-dependent advancing and receding contact angle measurements are given in Figures S9 and S10 of the Supporting Information. Figures 9a−c show the dynamic advancing and receding contact angles for water on smooth PDMS surface, the 12 μm pitch bumpy PDMS surface, and the 12 μm pitch cavity PDMS surface, respectively. On the smooth PDMS surface, the dynamic advancing contact angle increases and the dynamic receding contact angle decreases as soon as substrate speed increases and they reach the steady dynamic θA and θR at ∼120° and ∼70°, respectively (Figure 9a). While the dynamic θA is larger than that determined by the static method, the dynamic and static θR are very comparable. The general velocity-dependent curve is comparable to other smooth surfaces reported in the literature.62,63 Very different result is obtained with the bumpy PDMS surface (Figure 9b). In the low-speed regime (