Subscriber access provided by - Access paid by the | UCSB Libraries
Article
Probing liquid-solid and vapor-liquid-solid interfaces of hierarchical surfaces using high-resolution microscopy Katherine T. Flynn Bolte, Rajesh Prabhu Balaraman, Kexin Jiao, Michael D. Tustison, Kiah S. Kirkwood, Chuanhong Zhou, and Punit Kohli Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b00298 • Publication Date (Web): 28 Feb 2018 Downloaded from http://pubs.acs.org on March 1, 2018
Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.
Langmuir is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.
Page 1 of 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Langmuir
Probing liquidliquid-solid and vaporvapor-liquidliquid-solid interfaces of hierarchical surfaces using highhighresolution microscopy Katherine T. Flynn Bolte,a Rajesh Prabhu Balaraman,a Kexin Jiao, Michael Tustison, Kiah S. Kirkwood, Chuanhong Zhou, and Punit Kohli1,2* 1Department of Chemistry and Biochemistry Southern Illinois University Carbondale, IL 62901 2Department of Materials Science and Engineering Northwestern University Evanston, IL 60201 aEqual contribution to this manuscript *
[email protected] *
[email protected] Abstract Liquid-solid (LS) and vapor-liquid-solid (VLS) interfaces are important to the fundamental understanding of how surface chemistry impacts industrial processes and applications. Superhydrophobic surfaces, from structural hierarchies, were fabricated by coating flat smooth surfaces with hollow glass microspheres. These surfaces are referred to as structural hierarchical modified microsphere surfaces (SHiMMs). Two phase LS and threephase VLS interfaces of water droplets on SHiMMs, with an apparent static contact angle (aSCA) of ~160° were probed at microscale using environmental scanning electron microscopy (ESEM) and high resolution optical microscopy (OM). Both ESEM and OM confirmed the presence of air pockets in 3 µm-150 µm range at the VLS triple phase of the droplet peripheral contact line. The wetting characteristics of the LS interface in the interior of the water droplet was probed using energy dispersive spectroscopy (EDS) which corroborated well with the VLS triple-phase observations, confirming the presence of both the microscale air pockets and fractional complete wetting of the SHiMMs. The superhydrophobic water droplets on the SHiMMs also exhibited relatively high adhesion to the SHiMMs – a tilt angle of 10°-40° was needed for detaching the droplets off the surfaces. Semi-quantitative three-phase contact line analysis and experimental data indicated high water aSCA and large adhesion on the microscale roughened SHiMMs is attributed to pinning of the probe liquid both at the triple VLS and interior LS interfaces. The control over microroughness and surface chemistry of the SHiMMs will allow tuning of both the static and dynamic liquid-surface interactions. Keywords Superhydrophobicity, Surface roughness, Surface energy, Micro-spheres; Keywords: words Modulated-adhesion; Nanoscale and microscale air-pockets Introduction The relationship between surface tension and wetting was first described in 1908 by Thomas Young.1 The evidence of surface repellency and hydrophobicity from structural hierarchy induced physical roughness came in the early twentieth century when Ollivier and coworkers observed high water repellency on glass surfaces coated with candle-soot.2 In this work the apparent static contact angle (aSCA) for water, approaching 180o, was 1
ACS Paragon Plus Environment
Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
observed by applying a layer of candle soot to surfaces.2-4 Wenzel introduced surface roughness as a physical factor contributing to water repellency on surfaces, but pointed out that rough “pores” should maintain specific dimensions in order to sustain the air pockets that support impinging water droplets.5 Cassie and Baxter expanded on Wenzel’s model of surface wetting and postulated that it was not just surface roughness, but a combination of nano- and micro-scaled surface rough features arranged in a hierarchy, that prevented the water drops from wetting the surface.6 Over a century later, the super-hydrophobic properties of candle-soot films were investigated again by Vollmer and coworkers.7 In this work, the authors confirmed that the micro-scale, fractal structure of the deposited hydrophobic candle soot was responsible for superhydrophobicity with a water aSCA~165°. These results pointed to surface superhydrophobicity with contributions from both the surface topography and surface chemistry. 8-12 There is a longstanding debate about applicability range and accuracy of Wenzel and Cassie-Baxter theories for the prediction and explanation of aSCA, liquid drop adhesion, and contact angle hystersis.13-15 McCarthy argued that the contact angle behavior is influenced through the three-phase contact line along the sitting droplet periphery, and that the interfacial area within the contact perimeter is irrelevant.15 This argument is recently countered by Choi et al. who demonstrated that the Cassie-Baxter wetting mechanism can predict equilibrium aSCA.16 The imaging of the LS and VLS can provide crucial information regarding interfacial wetting on superhydrophobic surfaces and may help in sorting out this debate.16-19 High resolution imaging of the VLS has provided an enhanced understanding of the wetting mechanism on roughened surfaces.18, 20-21 Although a variety of studies are performed to image the contact line of highly dynamic drops on ordered, mono-dispersed roughened surfaces,12, 17, 22 the experiments on the triple contact line of drops on highly heterogenous roughened surfaces are scarce.23 These studies are useful because many surfaces found in nature possess patterns that are hierarchal and fractal in nature.24-25 In nature, many surfaces, for example, the Lotus leaf (nelumbo mucifera)26-28 and “rose-petal-like”12, 29 surfaces show how the superhydrophobicity of these surfaces provides integral functions to plants. The biomimicry of such natural surfaces can provide simple but powerful tools for developing new smart materials for a wide range of applications including: anti-fog,30 highly repellant non-adhesive and resistant biofilms,31-36 and device fabrication.37-43 Whereas the lotus surfaces are known to possess high aSCA and low water adhesion to the leaf surface, the rose-petal exhibits high aSCA of water droplets in addition to high surface adhesion.12, 29, 4446 Therefore, nature allows for differential wetting and adhesive properties needed for plants to minimize negative effects and/or to utilize these tailored surface properties for enhancing their functionality.2, 47-49 Further, it is also instructive and important to study the LS interface at the interior of the drop which may aid in sorting and solving the debate on the roles of the contact line and interior interfacial area on contact angle, adhesion, and contact angle hysteresis. In this paper, we probe LS and VLS interfaces of the structural hierarchical surfaces composed with highly polydispersed microspheres possessing surface roughness at microscale using high spatial resolution microscopy.50-52 We fabricate and characterize SHiMMs by depositing hollow microspheres on planar glass surfaces that yielded microroughed“rose-petal-like” characteristics superhydrophobic surfaces (aSCAs of 2 ACS Paragon Plus Environment
Page 2 of 22
Page 3 of 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Langmuir
158+8° and 135+5° for water and oil respectively). SHiMMs exhibited relatively high water adhesion requiring a tilt angle of the substrate ranging between 10o and 40o to detach water droplets from the SHiMMs. ESEM and OM allowed us to probe the wetting mechanism at the VLS triple interface of the contact line at microscale resolution. The air pockets dimension (dair) at the VLS interface in 3 µm 10 >5 4±3 20 ± 15 0
Dynamics Characteristics Spreading Spreading Sliding Sliding Pinning Spreading
TEOS -
3M ImK30 3M ImK30 3M ImK30 3M ImK30 3M ImK30 3M ImK30
TEOS TEOS
None
PDMS OCTES OCTES
0 0 0 93 ± 1 150 ± 5 140 ± 2
0 0 0 31 ± 11 24 ± 21 19 ± 15
Spreading Spreading Spreading Pinning Pinning Pinning
3M ImK30
TEOS
OCTES
157 ± 8
20 ± 10
3M ImK30
None
FSilane
148 ± 4
8±7
Pinning/Sliding /Rolling Pinning/Sliding / Rolling
Table 1. 1 aSCA, hysteresis, and dynamic characteristics of surfaces with different microroughness and surface coatings. The interaction of water and other hydrophilic liquid droplets on a given surface is believed to stem from Wenzel, Cassie-Baxter or a combination of these states. Depending upon the interfacial interactions between the surface and droplets, the adhesion of the droplets is known to vary even though aSCA values are similar. For example, the lotus-leaf and rose petal show large water aSCAs, the adhesion of water droplets on lotus leaf and rose petal are low and high respectively.12, 26-29 For designing surfaces with desired surface properties, the LS and VLS interfacial understanding is crucial. Here, we report probing LS and VLS interfaces formed by water droplets on hierarchal SHiMMs using high-resolution optical and electron microscopy. In these studies, we found that interfacial liquid-surface interactions are important for controlling the adhesion of the water droplets on a surface. 6 ACS Paragon Plus Environment
Page 7 of 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Langmuir
Figure 2. Static contact angle analysis on SHiMMs. (A) SCA of water and oil droplets on OCTES and fluorosilane treated SHiMMs ~157±8° (A) and 135±5° (B) respectively. (C) A water droplet of 2.5 mm diameter on OCTES-treated SHiMMs (inclination of 36°) showing a hysteresis of 30° (θa and θr are 160o and 130o respectively). (D) A plot of aSCA versus liquid surface tension of probe liquids on a fluorosilane treated SHiMMs. Probe liquids include: water (72.8 mJ/m2), glycerol (64 mJ/m2), formaldehyde (58 mJ/m2), benzyl alcohol (39 mJ/m2), pyridine (38mJ/m2). The error bar in (D) is the standard deviation of aSCA (n=8). The scale bar in (B) is 0.26 cm.
Wetting characteristics of native glass and SHiMMs. With a surface energy of 72 mN/m, an
untreated clean glass surface readily spreads both water and oil droplets (Fig. S4 and Table 1). The high surface energy of glass and UV-treated cleaned glass surfaces makes water droplets spread on glass surfaces exhibiting low values of both the aSCA and ∆θh (150o.63-65 The wetting properties of glass can be tailored by imparting surface roughness at the nanoand micro-scale and by applying appropriate surface modification for controlling local and global surface energy.58-60 The creation of the micro-roughening on flat, smooth glass surfaces by deposition of the microspheres in our studies yielded superhydrophilic-like surfaces (aSCA≈0) where the water droplets quickly spread across the surface (Table 1). The superhydrophilicity is a result of large number of pores and cervices with high surface energy allowing capillary forces within cervices and pores to transport water from the surface into pores and cervices thereby yielding superhydrophilic surfaces. The deposition of OCTES-functionalized polydispersed ImK30 microspheres yielded water aSCA of 158±7° (n = 39) (Fig. 2). A typical surface profile of the top layer of the thermallyfused microspheres and surface roughness (~300 nm) plots are shown in Fig. 2SA and 2SB respectively. These surfaces, however, lacked long-term mechanical stability in ambient wet laboratory conditions due to loss of microspheres from the surface. The loss of microspheres was quantified through mass difference of the SHiMMs before and after sonication of the SHiMMs (Table 1S). The mass difference confirmed that nearly all of the microspheres were lost during a moderate sonication of SHiMMs in ethanol for 10 minutes (Table S1). The fact that the microspheres were physically adsorbed on the underlying glass surface led to the loss of microspheres over time exposing high energy surface (i.e.; the silanol groups on the glass surface) to the probing liquid. Further, there was also a decrease in the surface roughness after loss of microspheres. Overall, the formation of a high surface energy surface through silanol groups and a decrease in the surface roughness resulted in a decrease in the water aSCA on SHiMMs. Therefore, for stable interfacial properties of the SHiMMs, enhanced microsphere adhesion with the glass surface was explored through the application of the chemical binder. A molecular binder, tetraethoxysilane (TEOS) that covalently bound silanol groups of the microspheres with flat glass surface and interparticles was used for enhancing the mechanical stability of SHiMMs. A 5% TEOS solution was prepared by adding 2-3 drops of glacial acetic acid to stirring ethanol (5 mL) followed by the addition of TEOS (250 µL) to this mixture. The TEOS coating on SHiMMs was cured by placing them on a hot plate for a period of 3 hrs. The mechanical stability of the TEOS modified SHiMMs was tested by sonicating the TEOS-modified SHiMMs and comparing the weight loss with the SHiMMs without a TEOS treatment. TEOS treatment on SHiMMs significantly improved the mechanical stability of the microspheres. The weight loss for TEOS treated surfaces was reduced by ~80% compared to those of the untreated surfaces (Table S1). The OCTEStreated TEOS-SHiMMs showed water aSCA=157+8o without any significant decrease in aSCA value for more than 3 weeks. Fluoro-silane treatment of the SHiMMs also yielded high aSCAs both for water (158+7°) and oil (135+5o) droplets. The water aSCA-drop size dependence in 1.8 to 2.6 mm diameter range was also performed for the SHiMMs. The average water aSCA for the SHiMMs was 153±7o which falls within the statistical limit of aSCA=158±7° for all measurements suggested that statistically there is no dependence of the droplet dimension on the water aSCA within 1.8-2.6 mm diameter range. The addition of TEOS to the SHiMMs provided a sol-gel scaffold network that yielded significant enhancement in the mechanical stability of the immobilized microspheres on the surfaces.66-69 8
ACS Paragon Plus Environment
Page 8 of 22
Page 9 of 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Langmuir
Figure 3. 3 High spatial resolution imaging of vapor-liquid-solid triple interface. (A) An ESEM of a water droplet on SHiMMs exhibiting air-pockets in 3 mm-100 mm range at the vapor-liquid-solid interface. (B) A higher magnification ESEM image of (A) showing microscale air-pockets at the VLS interface. (C) An optical micrograph of a 3.1 mm water droplet on a SHiMMs. (D) A higher magnification optical micrograph of (C) showing both air pockets and wetting of the liquid-solid interface at the periphery contact line. False colors were obtained using Mountains map. Color codes are as follows: Blue: Water; green: microspheres; black: air; and orange: glass surface. The SHiMMs surfaces were found to be prone to droplet pinning and high hysteresis. A tilt angle usually in 10°-40° range was needed for detaching the water droplets from the SHiMMs (Fig. 3C). We estimated tilt (roll-off) angle using Extrand–Gent model (Eq. 1):16, 70 (cos θ*rec - cos θ*ad ) Eq. 1 sin w = 2γ LV DTLC (πρ gV ) π 3V DTCL = 2 cos(θav − ) Eq. 2 3 2 π (2 - 3cosθav + cos θav) where ω, γLV, θ*rec, θ*ad, V, and θav are tilt angle, liquid-vapor surface tension (72 mJ/m), apparent receding experimental angle (127o), apparent advancing experimental angle (157o), volume of the droplet (4.2×10-9 m3), and average of apparent advancing and 9 ACS Paragon Plus Environment
Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
receding angles (142o) respectively. DTCL=1.3 mm is the diameter of triple phase contact line estimated using Eq. 2. We estimate ω≈27o using Eq. 1 - in agreement with experimental data. An investigation into the aSCA hysteresis (∆θh =θA-θR) on the SHiMMs was also performed by measuring advancing (θA) and receding (θR) angles of water droplets placed on the SHiMMs. In our experiments, ∆θh=20±15° was observed for water droplets on the SHiMMs. Relatively large ∆θh was attributed to pinning of the water droplet contact line on the SHiMMs. Often, the pinning of droplets on the SHiMMs was overcome by increasing the kinetic energy of the impinging droplet. This was done by increasing the fall height of the droplets thereby overcoming the energetic barrier for droplet detachment. For example, in the movie, the kinetic energy (KE) ~6 x 10-7 J of a drop (diameter ~ 1 mm) falling from a height of 1.5 cm rolled off from the surface. These results indicate that whereas the water droplets with zero or small kinetic energy on the SHiMMs were prone to surface pinning, the water droplets with sufficient kinetic energy were able to overcome the energetic barrier for detaching the droplets from the SHiMMs (Fig. 4 supplementary movie M1).
Figure 4. 4 Video still-frames show a 6) Droplet falling and 7) flattening upon initial SHiMMs impact. The droplet forms a (10) spheroid shape before 11) bouncing off the SHiMMs. The high hysteresis of the drop bounce, land and second bounce are shown in frames 12, 13 and 14. Frames 15-16 shows the droplet in a rolling motion after the second bounce in frame 14 before the droplet finally rolls off the SHiMMs in frame 17 (see supplementary movie M1). 10 ACS Paragon Plus Environment
Page 10 of 22
Page 11 of 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Langmuir
In frames 7 and 10 of M1, we observed that upon impact with the SHiMMs the falling droplet flattened out, forming a pancake-like shaped droplet (Fig. 4). In some cases, the pinned water droplets were also dislodged by the impact of kinetically favored droplets. This is probably due to conversion of some kinetic energy of the droplet into the surface energy upon impact with the SHiMMs.71 The subsequent frames showed the droplet regaining its spherical shape (Frame 11) and partially pancaking again (Frame 12). The droplet flattening followed by regain of the sphericity indicated that there is likely an underlying interfacial pressure overcoming the surface interactions and gravity effects of the falling droplet. Partial conversion of the kinetic energy to droplet surface energy through its impact on the surface and vice-versa may contribute to shape-changes in the droplet and its jumping off the surface. This behavior continued until the surface tension of the drop can no longer overcome the gravity allowing rolling off of the droplets. Microscopic analysis of the vapor-liquid-solid interface for water droplets on the SHiMMs. High-resolution imaging of contact line (vapor-liquid-solid interface) using EM and OM are recently reported.16-20, 72 The microscopic studies on the LS in the interior of the droplets are scarce in literature.18 By utilizing high spatial resolution microscopic analysis, we intend to gain enhanced understanding on the droplet and aSCA by probing LS and VLS interfaces on microscale-roughened SHiMMs. These studies may aid in designing surfaces with appropriate properties for desired applications. We utilized high-resolution ESEM and the OM studies to probe VLS interface at the peripheral contact line of the water droplet on the SHiMMs. The ESM and OM experiments provided strong evidence of the presence of both the air-pockets and complete wetting at the VLS interface (Fig. 3). ESEM imaging of the water droplets on SHiMMs was performed with a chamber pressure ~900 Pa, relative humidity (RH) ~80-90%, and 3oC. Lower temperature and high humidity may reduce water evaporation for imaging the VLS interfaces without significantly altering the dimension and interfacial tension of the water droplet. Under these conditions, the evaporation rate of the water in the ESEM chamber is expected to be a few pL/s.20 The darker regions in the ESEM indicate a lack of strong secondary electron signal due to the presence of air pockets whereas the bright area (higher secondary electron signal) depicts the presence of water in the electron micrographs (Figs. 3A, 3B and 5S). The dimension of the air-pockets in EM and OM at the VLS interface were in ~3 µm and 150 µm range (Figs. 3 and S5). Due to high humidity and low vacuum conditions in the ESEM chamber, the VLS interfacial imaging at the nanoscale resolution was not feasible to accurately measure the spatial features at submicro- and nano-scale levels. We however cannot rule out the presence of nano and sub-micron scale air-pockets at the VLS interface. Interestingly, the microscale water aSCA at the VLS interface in the ESEM measurements were ~140-160o which is close to the macroscale water SCA of the parent water droplets - in agreement with Varanasi’s studies.20 The triple VLS interface at the peripheral contact line was also imaged using OM under ambient atmosphere conditions. A close examination of the triple VLS interface using OM revealed air-pockets at the VLS interface in 42 µm-150 µm range (Figs. 3C and 3D) in agreement with our EM measurements. Importantly, the imaging conditions employed for the OM and EM experiments are quite different. The OM experiments were performed in the ambient conditions whereas the EM experiments were conducted at low temperature 11 ACS Paragon Plus Environment
Langmuir 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
in vacuum, and high humidity conditions. Lower temperature in the EM experiments tends to increase the water surface tension. However, high humidity and vacuum condition tend to lower the water surface tension. For example, the surface tension of water at 5°C and 90% RH, similar to those of the EM experimental conditions employed here, has a surface tension value of ~76 mN/m.73 We therefore expect that the differences in the surface tension of water for the ESEM and OM experiments are likely minimum and that the effect of surface tension on the surface wetting is less likely to affect the results observed in our ESEM and OM results. Overall, the experimental results from the ESEM and OM confirmed that presence of both Cassie-Baxter (corresponding to air-pockets) and Wenzel (wetting of spherical microspheres) mechanisms at the peripheral triple VLS interface yielding superhydrophobic surfaces stable for >6 days in ambient laboratory conditions (Fig. S6). Further evidence of Cassie-Baxter wetting was observed by the presence of a grey/silver plastron layer at the interface of the SHiMMs and bulk water. The grey film at the waterSHiMMs interface is indicative of the existence of total internal reflection of air in between the bulk water and the SHiMMs.
Figure 5. A schematic of closely packed monodispersed spheres of radius r for contact line (black line) analysis. Blue circles represent monodispersed hollow glass microspheres. The black arc represents a water droplet segment at the VLS interface.
High water adhesion on superhydrophobic SHiMMs. Although SHiMMs exhibited large
water aSCA, the adhesion of the water droplets on SHiMMs was also strong. Large tilt angles (10°-40° range) were needed for detaching the water droplets from the surface (Table 1). Although the ESEM and OM imaging confirmed presence of the air pockets and complete wetting at both the LS and VLS interfaces of the SHiMMs, the strong water adhesion on SHiMMs is not immediately apparent from the microscopic imaging results but the imaging studies do provide important information regarding the adhesion of water droplets on the SHiMMs. We employed pinned contact line fraction analysis for evaluating the adhesion of probing water droplets on the SHiMMs using a formulation similar to that is proposed by Varanasi’s group.20 Fig. 5 shows a contact liquid line (dotted green line) projected on hexagonally packed microspheres representing SHiMMs (blue circles). Monodispersed microspheres were assumed for the SHiMMs which simplified the projected contact line analysis. This is because the close packing of polydispersed microspheres is beyond the scope of this manuscript.74 The polydispersity of the microspheres will not be 12
ACS Paragon Plus Environment
Page 12 of 22
Page 13 of 22 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Langmuir
further taken into account for the evaluation of the pinned fraction. The effective pinned fraction (φMS) is given by p’/τ, where p’ and τ are circumference of microsphere and average microsphere pitch respectively. φMS is an important parameter that provides useful information on (de)pinning and adhesion of droplets situated on a surface. On one extreme case, φMS → 0 is expected for an ideal Cassie-Baxter wetting mechanism for a probing liquid droplet on a surface. This ideal wetting is similar to a rain droplet in air with ߛ a radius (ro) 1 is also consistent with the observation that the water droplets on the SHiMMs are not adhered (10o