Subscriber access provided by Imperial College London | Library New Concepts at the Interface: Novel Viewpoints and Interpretations, Theory and Computations Bi-Gaussian Stratified Wetting Model on Rough Surfaces Songtao Hu, Tom Reddyhoff, Debashis Puhan, Sorin-Cristian Vladescu, Weifeng Huang, Xi Shi, Daniele Dini, and Zhike Peng Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.9b00107 • Publication Date (Web): 04 Apr 2019 Downloaded from http://pubs.acs.org on April 9, 2019
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.
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 25 Langmuir
1 2 3 4 Bi-Gaussian Stratified Wetting Model on Rough Surfaces 5 6 7 Songtao Hu,† Tom Reddyhoff,‡ Debashis Puhan,‡ Sorin-Cristian Vladescu,‡ Weifeng Huang,§ Xi Shi,*,† 8 Daniele Dini,‡ Zhike Peng† 9 10 11 †State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai 12 200240, China 13 ‡ 14 Department of Mechanical Engineering, Imperial College London, London SW7 2AZ, UK 15 §State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, China 16 17 18 ABSTRACT: Wetting mechanisms on rough surfaces were understood from either a monolayer or a 19 multiscale perspective. However, it has recently been shown that the bi-Gaussian stratified nature of real 20 surfaces should be accounted for when modelling mechanisms of lubrication, sealing, contact, friction, 21 acoustic emission, and manufacture. In this work, a model combining Wenzel and Cassie theories was 22 23 put forward to predict the static contact angle of a droplet on a bi-Gaussian stratified surface. The model 24 was initially applied to numerically simulated surfaces, and subsequently demonstrated on hydrophilic 25 steel and hydrophobic self-assembled monolayer specimens with preset bi-Gaussian stratified 26 27 topographies. In the Wenzel state, both the upper and the lower surface components are fully wetted. In 28 the Cassie state, the upper component is still completely wetted while the lower component serves as gas 29 traps and reservoirs. By this model, wetting evolution was assessed, and the existence of different wetting 30 31 states and potential state transitions was predicted. 32 33 ■ INTRODUCTION 34 Wetting behavior occurs when a solid-gas interface transfers into a solid-liquid interface on a solid, and 35 36 it indicates the ability of the solid surface to accommodate and maintain permanent contact with the 37 liquid. Controlling the wettability of a solid is a research area of intense focus, which has resulted in a 38 significant number of applications including self-cleaning1,2, anti-icing3,4, antifogging5,6, antireflection7,8, 39 40 friction reduction9,10, etc. It is therefore of utmost importance to understand the intrinsic wetting 41 mechanism that occurs. Since Young introduced the theoretical modelling of static contact angle (CA, 42 serving as a key wetting index) on an ideal smooth surface, it has become well known that the roughness 43 44 of a surface can induce a significant effect on its wettability. Two famous hypotheses have been proposed 45 to explain the wetting mechanism of a rough surface. In the Wenzel11 case (see Figure S3a), the liquid 46 completely fills the valleys of a rough surface. The roughness extends the solid area in comparison to the 47 projected one, enhancing the intrinsic wettability of the solid (a hydrophilic surface turns into a more 48 49 hydrophilic one, while a hydrophobic surface becomes more hydrophobic). In the Cassie12 case (see 50 Figure S3b), gas is trapped into the valleys underneath the liquid, transforming the surface from a 51 continuous solid-liquid interface into a composite one consisting of solid-liquid and gas-liquid interfaces. 52 53 To date, these two theoretical models have been widely used to capture CAs on rough surfaces, however 54 these studies have been limited to scenarios of either a monolayer13−18 or a multiscale (fractal, 55 hierarchical)1925 topography. 56 57 In fact, most researchers have focused exclusively on either a Gaussian or a non-Gaussian 58 distribution of topographical heights from the view of monolayer point, overlooking the real-life case of 59 a bi-Gaussian stratified property (see Figure 1a) long-termly covered by the non-Gaussian one. As 60
ACS Paragon Plus Environment Langmuir Page 2 of 25
1 2 3 schematically illustrated in Figure 1b, a bi-Gaussian stratified surface consists of a large roughness-scale 4 5 Gaussian surface (lower component) and another Gaussian surface at a small roughness scale (upper 6 component), where the lower height is maintained on each node when combining the two components. 7 In contrast with a multiscale property emphasizing the properties (e.g., self-similarity, self-affinity) 8 exhibited by a rough surface at different scales, the bi-Gaussian one displays its two components in a 9 10 stratified (following a selective superposition rather than a direct superposition as depicted in Figure 1b) 11 formation at the same scale. 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 Figure 1. Topography of a bi-Gaussian stratified surface (a) and its schematic in a profile formation (b). 33 34 The bi-Gaussian stratified property of a rough surface was initially observed on automotive cylinder 35 36 liners through a two-stage manufacturing process (plateau honing),26 and was then extended to model 37 surfaces modified by a material wear.27 Notably, the bi-Gaussian stratified property should be 38 differentiated from the mother non-Gaussian property in three ways: (1) The bi-Gaussian stratified 39 40 surface can arise from a multi-stage subtractive manufacturing process,28 indicating its widespread 41 applicability. Moreover, an active service usually induces a material wear as similar to the multi-stage 42 subtractive manufacturing process,29 thus extending the applicability. (2) The mechanism of forming the 43 44 two components is clearly associated with specific actions. Namely, the lower component is produced 45 by the early manufacturing process or is the original unused surface, while the upper component is 46 generated by the following manufacturing stage or the material wear. (3) The functional performance of 47 the two components is clearly defined in comparison to a conventional monolayer surface. For instance, 48 49 in the tribological field, the upper component plays a predominant role in load bearing and wear 50 resistance, and the lower component acts as lubricant reservoirs and debris traps. 51 By reviewing the most relevant studies in the area of surface roughness, it becomes evident that the 52 53 bi-Gaussian stratified perspective has exhibited an excellent capability in revealing the mechanisms in 54 terms of lubrication, sealing, asperity contact, friction, acoustic emission, and manufacture.28−30 However, 55 to our knowledge, it has not yet been employed to analyze the wetting mechanism of rough surfaces. In 56 57 this paper, a model combining Wenzel and Cassie theories was established to predict the static CA of a 58 droplet on a bi-Gaussian stratified surface (see section “Theoretical Model”). In particular, the model 59 contains two special cases, i.e., Wenzel and Cassie states. In section “Model Demonstration”, the model 60
ACS Paragon Plus Environment Page 3 of 25 Langmuir
1 2 3 was initially investigated on numerically simulated bi-Gaussian stratified surfaces, and subsequently 4 5 demonstrated on hydrophilic steel specimens and hydrophobic self-assembled monolayer (SAM) coated 6 specimens with prescribed bi-Gaussian stratified topographies. Furthermore, the model was used to 7 explain and predict the existence of different wetting states and potential state transitions from a bi- 8 Gaussian stratified viewpoint (see section “Discussion”). 9 10 11 ■ MODEL 12 In the Wenzel model, the CA can be described as11 13 14 15 cos * r cos , (1a) 16 17 * 18 where is the apparent CA of a droplet on a rough surface, and is the intrinsic CA on an ideal smooth 19 surface modelled by the well-known Young equation. Herein, r is the ratio of the real area to the projected 20 one, acting as the roughness factor used to assess the area extension. As the value of r is always greater 21 than 1, the intrinsic wettability of a solid will be enhanced according to the Wenzel model. When the 22 23 liquid droplet is located on a heterogeneous solid surface, the reduced Cassie model can be applied12 24 25 * cos f cos f 1 , (1b) 26 27 28 where f is the fraction of the solid-liquid interface. For a rough heterogeneous solid, the Wenzel and the 29 Cassie models can be combined into a general formula as 30 31 32 cos * r f cos f 1. (1c) 33 34 The outstanding issue is how to accurately determine the values of r and f for a real rough surface 35 36 including, but not necessarily limited to, a bi-Gaussian stratified property. Kubiak et al.’s work14 on 2- 37 dimensional real rough surface profiles provides a feasible solution. In their study, the developed 38 roughness profile length ratio (R ) was used to evaluate the value of r. Hence, for a 3-dimensional 39 Lo 40 topography, the value of r can be calculated by using Sdr as below 41 42 r 1 Sdr , (2a) 43 MR f MR . 44 (2b) 45 46 Note that Sdr has been defined as the developed interfacial area ratio in ISO 25178, and the value of Sdr 47 has been normalized to be calculated over the whole surface. However, in eq 2a, the subscript, MR 48 49 (material ratio, see Figure S1a) indicates that the value of Sdr should be calculated in this case within the 50 nodes above an intersecting plane that is defined by a certain material ratio. In addition, eq 2a also 51 indicates that f in eq 1c is right the mentioned MR, thus yielding eq 2b. 52 53 Consequently, a general CA model combining Wenzel and Cassie theories can be established as 54 55 cos * (1 Sdr ) MR cos MR 1 . (3a) 56 MR 57 58 Notably, a special case (see Figure 2a) should be highlighted as below 59 60
ACS Paragon Plus Environment Langmuir Page 4 of 25
1 2 3 cos * (1 Sdr )cos . (3b) 4 100% 5 6 Herein, MR is equal to 100 %, indicating a fully wetting state (overall Wenzel state) where both the 7 upper and the lower components are in the Wenzel state. As the value of MR increases, the overall 8 wetting state of a bi-Gaussian stratified surface enters into the Cassie state. When MR reaches the 9 10 probability of the transition between the upper and the lower components Smq (see Figure S1b), the 11 general model becomes the second special case (see Figure 2b) rendered as 12 13 14 cos * (1 Sdr ) Smq cos Smq 1 . (3c) 15 Smq 16 17 18 In such case, an arbitrary assumption is employed: in the Cassie state, the boundary between the wetted 19 and unwetted parts of a bi-Gaussian stratified surface is right the transition between the two components. 20 In other words: in the Cassie state, the upper component is in the Wenzel state while the lower component 21 serves as gas traps and reservoirs; the case, whose MR equals to a value within the interval of (Smq, 100 22 23 %), corresponds to a mixed wetting state between the Wenzel and Cassie states. 24 25 26 27 28 29 30 31 32 33 34 35 36 37 Figure 2. Bi-Gaussian wettability in (a) Wenzel (MR = 100 %) and (b) Cassie (MR = Smq) states, where 38 the former case indicates that the upper and the lower components are in the Wenzel state, while the 39 40 latter case indicates that the lower component serves as gas traps and reservoirs and only the upper 41 component is in the Wenzel state. 42 43 44 ■ RESULTS AND DISCUSSION 45 Simulation results. Before detailing the experimental demonstration, the bi-Gaussian stratified 46 wetting model will be analyzed in this section employing various simulated surfaces. A simulation 47 approach (see section “Simulation of Bi-Gaussian Stratified Surface” in Supporting Information) was 48 49 adopted to numerically generate a series of bi-Gaussian stratified surfaces as wetting targets. Their inputs 50 are listed in Table S1. Simulation 0 acts as the fundamental case with Smq at 50 %, Spq (root mean square 51 of the upper component, see Figure S1b) at 0.1 m, and Svq (root mean square of the lower component, 52 53 see Figure S1b) at 1 m. In Simulations 1 and 2, Smq was changed to 30 % and 70 %; in Simulations 3 54 and 4, Spq was set to 0.2 m and 0.4 m; in Simulations 5 and 6, Svq was altered to 0.25 m and 0.5 55 m. Since the value of Smq cannot be directly set, the distance between the mean planes of the two 56 31 57 components was adopted to indirectly achieve the expected Smq. In Figure S2a, a stratified property 58 can be clearly observed on each simulated surface. When Smq increases, the proportion of the plateaus 59 (upper component) increases. In Figure S2b, the stratified property weakens as Spq increases because the 60
ACS Paragon Plus Environment Page 5 of 25 Langmuir
1 2 3 root mean square of the plateaus approaches that of the valleys. In Figure S2c, the stratified property 4 5 intensifies with a subsequent rise in Svq generated by an increased deviation of root mean squares 6 between the plateaus and the valleys. 7 According to eq 3a, the relation between the apparent CA and the intrinsic CA on the simulated 8 surfaces can be predicted for an assumed MR value. In Figure 3a, Simulation 0 is taken as a 9 10 demonstration with MR set to 10 %, 30 %, 70 % and 90 %. Referring to eqs 3b and 3c, MR is set to Smq 11 (equaling to 50 %) and 100 % to discuss the two special cases (Wenzel and Cassie cases), as depicted in 12 Figures 3b, 3c and 3d in terms of Smq, Spq and Svq. In the defined hydrophilic and hydrophobic regions, 13 14 a great Smq introduces a weak enhancing effect to the intrinsic wettability of the surface in the Wenzel 15 case, and weakens the hydrophobicity in the Cassie case; a great Spq, however, induces a strong 16 enhancing effect on the intrinsic wettability in the Wenzel case, and intensifies the hydrophobicity in the 17 18 Cassie case; a greater Svq, in addition, leads to a strong enhancing effect on the intrinsic wettability in 19 the Wenzel case, but plays a negligible role in affecting the hydrophobicity in the Cassie case because 20 both the upper component and the transition are kept unchanged resulting in constant fractions for solid- 21 liquid and liquid-gas interfaces. 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 Figure 3. Theoretical relation between apparent CAs and intrinsic CAs on simulated surfaces. (a) 54 Simulation 0 where MR is set to different probabilities: 10 %, 30 %, Smq, 70 %, 90 % and 100 %. (b) 55 Simulations with different Smqs (Simulation 1 with 30 %; Simulation 0 with 50 %; Simulation 2 with 70 56 57 %) where MR is set to 100 % and Smq. (c) Simulations with different Spqs (Simulation 0 with 0.1 m; 58 Simulation 3 with 0.2 m; Simulation 4 with 0.4 m) where MR is set to 100 % and Smq. (d) Simulations 59 with different Svqs (Simulation 5 with 0.25 m; Simulation 6 with 0.5 m; Simulation 0 with 1 m) 60
ACS Paragon Plus Environment Langmuir Page 6 of 25
1 2 3 where MR is set to 100 % and Smq. 4 5 6 Experimental results. In this section, the new bi-Gaussian stratified wetting model and the 7 conclusions drawn from the simulation analysis will be demonstrated. Five steel discs (termed as Steel 8 0, Steel 1, Steel 2, Steel 3 and Steel 4) made of AISI 52100 were provided by PCS Instruments as 9 10 hydrophilic specimens. Each disc had a mirror finishing to reach a 15-nm root mean square. A two-stage 11 abrasive manufacturing process, supported by the AutoMet™ 250 grinding and polishing machine, was 12 employed to process designed bi-Gaussian stratified topographies on the last four discs. Steel 1 13 14 successively underwent a 3-min rough grinding and a 1-min fine grinding; Steel 2 was subject to a 3-min 15 rough grinding and a 3-min fine grinding; Steel 3 successively survived a 3-min rough grinding and a 1- 16 min polishing; Steel 4 was fine ground for 3 min and polished for an additional 1 min. The applied load, 17 18 the head speed, and the plate speed were set to 100 N, 60 r/min, and 10 r/min. The untreated disc Steel 0 19 was regarded as the ideal smooth reference. It is highly important to note that the two-stage abrasive 20 manufacturing process has been adopted because it is a typical manner to generate bi-Gaussian stratified 21 topographies. The mode with two reverse circling motions on the grinding and polishing machine was 22 23 selected to ensure a randomness. 24 For hydrophobic materials (e.g., PTFE, PDMS), it is difficult to achieve bi-Gaussian stratified 25 topographies via a two-stage abrasive manufacturing process because these materials are extremely soft. 26 27 A feasible alternative is to form a hydrophobic coating on the steel disc surface with a preexisting bi- 28 Gaussian stratified topography. The SAM technology is recommended as an ideal solution because the 29 deposited layer is thin enough to preserve the original topography and is uniformly distributed to avoid 30 31 a chemical differentiation. Hence, another five steel discs (termed as SAM 0, SAM 1, SAM 2, SAM 3 32 and SAM 4) were employed. The last four discs had the same two-stage abrasive manufacturing process 33 as the hydrophilic group. Then, all the five discs were ultrasonically cleaned in acetone and isopropanol 34 each for 30 min, and had a natural drying in air. A 30-min oxygen plasma (oxygen : argon = 1 : 1) was 35 36 conducted to generate hydroxyl groups32. The resulting superhydrophilic discs were put into an oven to 37 encounter a chemical vapor deposition of 1H,1H,2H,2H-perfluorooctyltrichlorosilane at 120 C for 2 h33. 38 Following a natural cooling in the oven, the SAMs were formed on the discs. 39 40 A specified area (sampling interval is 3.57 m, node number is 640480) was measured by the 41 Wyko NT9100 white light interferometer on each specimen. To precisely position the specified area, 42 marks were made to determine the circumferential position, and the mean value of the inner and the outer 43 29 44 radii was employed to determine the radial position . The topographical results are displayed in Figure 45 4. In the hydrophilic (hydrophobic) group, Steel 0 (SAM 0) is regarded as the ideal smooth reference. 46 The other four exhibit a stratified property due to the two-stage abrasive manufacturing process. Steel 1 47 and Steel 2 (SAM 1 and SAM 2) both have deep valleys due to the first rough grinding stage, and have 48 49 similar plateaus due to the second fine grinding stage. However, the number of deep valleys on Steel 2 50 (SAM 2) is lower than that on Steel 1 (SAM 1) because Steel 2 (SAM 2) is subjected to a longer fine 51 grinding to reduce the mean plane of the upper component. Steel 3 (SAM 3) also has similar deep valleys 52 53 in comparison to Steel 1 and Steel 2 (SAM 1 and SAM 2), but presents much smoother plateaus. This is 54 attributed to the combination of a first rough grinding stage and a second polishing stage. In comparison 55 to Steel 3 (SAM 3), Steel 4 (SAM 4) has an initial fine grinding stage, resulting in shallower valleys. 56 57 58 59 60
ACS Paragon Plus Environment Page 7 of 25 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 Figure 4. Shaded relief maps of steel (a) and SAM (b) specimens together with static CAs. 47 48 49 The above conclusions can be also obtained by a visual probability material ratio curve (PMRC, 50 see Figure S1b) analysis, as displayed in Figure 5. In comparison to Steel 1 (SAM 1), Steel 2 (SAM 2) 51 has an overlapped lower part, an upper part with a similar slope, and a changed transition point. In 52 53 comparison to Steel 1 (SAM 1), Steel 3 (SAM 3) has an overlapped lower part but an upper part with a 54 smaller slope. In contrast with Steel 3 (SAM 3), Steel 4 (SAM 4) has an overlapped upper part but a 55 lower part with a smaller slope. Note that the surface-height coordinate was a relative result because of 56 29 57 a PMRC transfer listed as below: (1) the height of Steel 2 (SAM 2) was updated by transferring its 58 minimum height to the minimum height of Steel 1 (SAM 1); (2) the height of Steel 3 (SAM 3) was 59 updated by transferring its minimum height to the minimum height of Steel 1 (SAM 1); (3) the height of 60
ACS Paragon Plus Environment Langmuir Page 8 of 25
1 2 3 Steel 4 (SAM 4) was updated by transferring its maximum height to the maximum height of Steel 3 4 5 (SAM 3). To evaluate the degree of uniformity of the SAMs at the specified locations on the SAM 6 specimens, an EDS analysis was employed on the S-3400N SEM. According to the elemental 7 composition of 1H,1H,2H,2H-perfluorooctyltrichlorosilane, the weight ratios and the distributions of 8 fluorine and silicon were calculated. As depicted in Figure 6a, the weight ratios of fluorine and silicon 9 10 are kept unchanged around 3 % and 0.5 %, respectively. Moreover, the distributions of fluorine and 11 silicon are independent on the topographies, where SAM 1 is rendered in Figures 6b and 6c as an example. 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 Figure 5. PMRCs of steel (a) and SAM (b) specimens. 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 Figure 6. Weight ratios of fluorine and silicon on SAM specimens by a SEM-EDS analysis (a), and the 47 distributions of fluorine (b) and silicon (c) on SAM 1 as an example. 48 49 50 The measured static CAs of a 4-μL deionized water droplet on the topographies of steel and SAM 51 specimens are depicted in Figure 4. A sessile drop method was conducted three times on the same 52 53 specified area accounting for a good repeatability by supported by the Rame-Hart instrument under 54 controlled temperature (20 C) and relative humidity (45 %). The CAs were measured after 30 sec to 55 guarantee equilibrium. The experimental demonstration of the new bi-Gaussian stratified wetting model 56 57 can be conducted in two areas: (1) assessment of whether the relationship between the apparent CA and 58 the intrinsic CA can be exactly predicted by eqs 3b and 3c, in particular the latter one based on an 59 arbitrary assumption; (2) whether the trends relating to the effect of Smq, Spq and Svq on the wettability 60
ACS Paragon Plus Environment Page 9 of 25 Langmuir
1 2 3 (see Figure 3) drawn from eqs 3b and 3c are true. 4 5 As depicted in Figure 7a, the experimental CAs on hydrophilic steel specimens are in great 6 agreement with the theoretical ones predicted by eq 3b, indicating a MR value of 100% in the Wenzel 7 state. Moreover, as depicted in Figures 4a and 7a, Steel 2 induces a greater CA than Steel 1, Steel 3 8 produces a greater CA than Steel 1, and Steel 4 renders a greater CA than Steel 3, which are in perfect 9 10 agreement with the trends drawn from Figure 3. However, for the hydrophobic SAM specimens in Figure 11 7b, the CAs exhibit an inconsistent wetting behavior, i.e., only SAM 4 is predicted by eq 3c while SAM 12 1, SAM 2, and SAM 3 are predicted by eq 3b. Moreover, as depicted in Figures 4b and 7b, SAM 2 13 14 induces a greater CA than SAM 1, SAM 3 produces a greater CA than SAM 1, and SAM 4 renders a 15 greater CA than SAM 3, which violate the trends drawn from Figure 3. All these behaviors indicate that 16 SAM 1, SAM 2 and SAM 3 are in the Wenzel state, but SAM 4 is in the Cassie state. 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 Figure 7. Theoretical and experimental relations between apparent CAs and intrinsic CAs on steel (a) 34 and SAM (b) specimens. 35 36 37 The above inconsistent wetting behavior on SAM specimens can be explained by analyzing the 38 autocorrelation function of a surface. As depicted in Figure 8a, the autocorrelation length of SAM 4 is 39 40 much smaller than others. To vividly illustrate the effect of the autocorrelation length, Figure 8b 41 introduces Simulation 0 in the above section. Another simulated surface, whose autocorrelation length is 42 set to 10 times greater than that of Simulation 0, is newly generated. For Simulation 0, the nodes on the 43 44 upper component are interpenetrated by those on the lower component, serving as the plateaus to suspend 45 the droplet.34,35 However, for the case with a large autocorrelation length, the nodes on each component 46 are gathered together. These interconnected nodes on the lower component form a wide valley (see red 47 dash circle) to trap and reserve the droplet. 48 49 50 51 52 53 54 55 56 57 58 59 60
ACS Paragon Plus Environment Langmuir Page 10 of 25
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 Figure 8. (a) Autocorrelation lengths of SAM specimens. (b) Effect of autocorrelation lengths on 26 27 topographies. 28 29 The bi-Gaussian stratified wetting model has a capability to assess CA evolution. Hence, a 30 31 recording procedure for CA values was conducted after 1~2 sec when the water droplet contacted the 32 surface in order to avoid the error arising from the syringe evacuation. This is because that the evacuation 33 of the syringe was manually controlled, affecting the shape of a droplet. It can be observed that the 34 wetting state was established instantaneously when the droplet contacted the surface (see Movie S1). 35 36 Then, the CA continued to slightly decrease due to the water immersion, which can be assessed by the 37 value of MR in eq 3. In Figure 9 as exemplarily shown for SAM 4, the tiny CA decrease can be 38 quantitatively assessed by setting MR to Smq, Smq − 2 %, and Smq − 4 %. 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 Figure 9. Theoretical and experimental evolutions of CAs on SAM 4 for three repetitions. 56 57 58 Discussion about state transitions. As depicted in Figure 10, c is the threshold value equaling the 59 well-known Wenzel and the Cassie models36. From the bi-Gaussian stratified viewpoint, the Wenzel state 60
ACS Paragon Plus Environment Page 11 of 25 Langmuir
1 2 3 is the case whose MR is 100 %, and the Cassie state is the case whose MR is Smq. Hence, some disclosed 4 5 mixed state can be the case whose MR is a certain probability located in the interval of (Smq, 100 %). 6 Furthermore, a superhydrophobic state can be expected when MR is much smaller than Smq. In such 7 state, not only the lower component but also part of the upper component act as gas traps and reservoirs 8 (the upper component is in the Cassie state by itself). In addition, if the above mixed and superior Cassie 9 10 states are to occur, in addition to the already discovered state transition (see arrow 1) which can be 11 induced by external stimuli such as mechanical process37, evaporation38 and condensation39, another two 12 new state transitions (see arrows 2 and 3) can be looked forward. 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 Figure 10. Wetting states and state transitions. 37 38 ■ CONCLUSIONS 39 40 Researchers have tried to understand the wetting mechanism of a rough surface from a single-stratum or 41 a multiscale (fractal, hierarchical) perspective. However, the bi-Gaussian stratified property of many real 42 surfaces, long neglected due to the complexity of a non-Gaussian property, has been recently discovered 43 44 and employed to reveal the mechanisms of lubrication, sealing, asperity contact, friction, acoustic 45 emission and manufacture. In this study, a model combining Wenzel and Cassie theories has been 46 established to predict the static contact angle of a droplet on a bi-Gaussian stratified surface. The model 47 was initially investigated on numerically simulated bi-Gaussian stratified surfaces, and subsequently 48 49 demonstrated on hydrophilic steel specimens and hydrophobic self-assembled monolayer specimens 50 with prescribed bi-Gaussian stratified topographies. In the Wenzel state, both the upper and the lower 51 components are fully wetted. However, in the Cassie state, the upper component is still completely wetted 52 53 while the lower component serves as gas traps and reservoirs. The new model can also assess the wetting 54 evolution. Furthermore, by the new model, a further discussion was presented to explain and predict the 55 existence of different wetting states and potential state transitions from a bi-Gaussian stratified viewpoint. 56 57 58 ■ ASSOCIATED CONTENT 59 The Supporting Information is available free of charge on the ACS Publications website at DOI: 60
ACS Paragon Plus Environment Langmuir Page 12 of 25
1 2 3 xxxxxxxxxx. 4 5 Some more details about bi-Gaussian stratified surface theories and Wenzel and Cassie wetting 6 theories (PDF) 7 Static contact angle measurement (Movie S1) 8 9 10 ■ AUTHOR INFORMATION 11 Corresponding Authors 12 *E-mail: [email protected] (X.S.). 13 14 Notes 15 The authors declare no competing financial interest. 16 17 18 ■ ACKNOWLEDGEMENTS 19 This work was supported by China Postdoctoral Science Foundation (2017M621458), and National 20 Natural Science Foundation of China (11572192, 11632011). Also, the two-stage abrasive manufacturing 21 process, white light interferometer analysis, SEM-EDS analysis and contact angle measurement were 22 23 supported by Department of Mechanical Engineering in Imperial College London. 24 25 ■ REFERENCES 26 27 (1) Furstner, R.; Barthlott, W.; Neinhuis, C.; Walzel, P. Wetting and Self-Cleaning Properties of 28 Artificial Superhydrophobic Surfaces. Langmuir 2005, 21, 956−961. 29 (2) Nishimoto, S.; Bhushan, B. Bioinspired Self-Cleaning Surfaces with Superhydrophobicity, 30 31 Superoleophobicity, and Superhydrophilicity. RSC Adv. 2013, 3, 671−690. 32 (3) Farhadi, S.; Farzaneh, M.; Kulinich, S. A. Anti-Icing Performance of Superhydrophobic Surfaces. 33 Appl. Surf. Sci. 2011, 257, 6264−6269. 34 (4) Gam-Derouich, S.; Pinson, J.; Lamouri, A.; Decorse, P.; Bellynck, S.; Herbaut, R.; Royon, L.; 35 36 Mangeney, C. Micro-Patterned Anti-Icing Coatings with Dual Hydrophobic/Hydrophilic Properties. J. 37 Mater. Chem. A 2018, 6, 19353−19357. 38 (5) Liu, X.; Du, X.; He, J. Hierarchically Structured Porous Films of Silica Hollow Spheres via Layer- 39 40 By-Layer Assembly and Their Superhydrophilic and Antifogging Properties. ChemPhysChem 2008, 9, 41 305−309. 42 (6) Han, Z.; Feng, X.; Guo, Z.; Niu, S.; Ren, L. Flourishing Bioinspired Antifogging Materials with 43 44 Superwettability: Progresses and Challenges. Adv. Mater. 2018, 30, 1704652. 45 (7) MiN, W.; Jiang, B.; Jiang, P. Bioinspired Self-Cleaning Antireflection Coatings. Adv. Mater. 2008, 46 20, 3914−3918. 47 (8) Fan, P.; Bai, B.; Jin, G.; Zhang, H.; Zhong, M. Patternable Fabrication of Hyper-Hierarchical Metal 48 49 Surface Structures for Ultrabroadband Antireflection and Self-Cleaning. Appl. Surf. Sci. 2018, 457, 50 991−999. 51 (9) Choi, C.; Ulmanella, U.; Kim, J.; Ho, C.; Kim, C. Effective Slip and Friction Reduction in Nanograted 52 53 Superhydrophobic Microchannels. Phys. Fluids 2006, 18, 087105. 54 (10) Walker, G. M.; Albadarin, A. B.; McGlue, A.; Brennan, S.; Bell, S. E. J. Analysis of Friction Factor 55 Reduction in Turbulent Water Flow Using a Superhydrophobic Coating. Prog. Org. Coat. 2016, 90, 56 57 472−476. 58 (11) Wenzel, R. N. Resistance of Solid Surfaces to Wetting by Water. Ind. Eng. Chem. 1936, 28, 988−994. 59 (12) Cassie, A. B. D.; Baxter, S. Wettability of Porous Surfaces. Trans. Faraday Soc. 1944, 40, 546−551. 60
ACS Paragon Plus Environment Page 13 of 25 Langmuir
1 2 3 (13) Prabhu, K. N.; Fernades, P.; Kumar, G. Effect of Substrate Surface Roughness on Wetting 4 5 Behaviour of Vegetable Oils. Mater. Design 2009, 30, 297−305. 6 (14) Kubiak, K. J.; Wilson, M. C. T.; Mathia, T. G.; Carval, Ph. Wettability versus Roughness of 7 Engineering Surfaces. Wear 2011, 271, 523−528. 8 (15) Raillard, B.; Gouton, L.; Ramos-Moore, E.; Grandthyll, S.; Muller, F.; Mucklich, F. Ablation Effects 9 10 of Femtosecond Laser Functionalization on Steel Surfaces. Surf. Coat. Tech. 2012, 207, 102−109. 11 (16) Furuta, T.; Isobe, T.; Sakai, M.; Matsushita, S.; Nakajima, A. Wetting Mode Transition of Nanoliter 12 Scale Water Droplets During Evaporation on Superhydrophobic Surfaces with Random Roughness 13 14 Structure. Appl. Surf. Sci. 2012, 258, 2378−2383. 15 (17) Liang, Y.; Shu, L.; Natsu, W.; He, F. Anisotropic Wetting Characteristics versus Roughness on 16 Machined Surfaces of Hydrophilic and Hydrophobic Materials. Appl. Surf. Sci. 2015, 331, 41−49. 17 18 (18) Yuan, W.; Zhang, L. Lattice Boltzmann Simulation of Droplets Impacting on Superhydrophobic 19 Surfaces with Randomly Distributed Rough Structures. Langmuir 2017, 33, 820−829. 20 (19) Jagdheesh, R.; Pathiraj, B.; Karatay, E.; Romer, G. R. B. E.; Huis in't Veld, A. J. Laser-Induced 21 Nanoscale Superhydrophobic Structures on Metal Surfaces. Langmuir 2011, 27, 8464−8469. 22 23 (20) David, R.; Neumann, A. W. Computation of the Wetting Properties of Randomly Structured 24 Superhydrophobic Surfaces. J. Phys. Chem. C 2012, 116, 16601−16608. 25 (21) Bottiglione, F.; Carbone, G. Role of Statistical Properties of Randomly Rough Surfaces in 26 27 Controlling Superhydrophobicity. Langmuir 2013, 29, 599−609. 28 (22) Yong, J.; Yang, Q.; Chen, F.; Zhang, D.; Farooq, U.; Du, G.; Hou, X. A Simple Way to Achieve 29 Superhydrophobicity, Controllable Water Adhesion, Anisotropic Sliding, and Anisotropic Wetting 30 31 Based on Femtosecond-Laser-Induced Line-Patterned Surfaces. J. Mater. Chem. A 2014, 2, 5499−5507. 32 (23) Long, J.; Fan, P.; Gong, D.; Jiang, D.; Zhang, H.; Li, L.; Zhong, M. Superhydrophobic Surfaces 33 Fabricated by Femtosecond Laser with Tunable Water Adhesion: from Lotus Leaf to Rose Petal. ACS 34 Appl. Mater. 2015, 7, 9858−9865. 35 36 (24) Yang, Y.; Li, X.; Zheng, X.; Chen, Z.; Zhou, Q.; Chen, Y. 3D-Printed Biomimetic Super- 37 Hydrophobic Structure for Microdroplet Manipulation and Oil/Water Separation. Adv. Mater. 2018, 30, 38 1704912. 39 40 (25) Raut, H. K.; Ranganath, A. S.; Baji, A.; Wood, K. L. Bio-Inspired Hierarchical Topography for 41 Texture Driven Fog Harvesting. Appl. Surf. Sci. 2019, 465, 362−368. 42 (26) Corral, I. B.; Calvet, J. V.; Salcedo, M. C. Use of Roughness Probability Parameters to Quantify the 43 44 Material Removed in Plateau-Honing. Int. J. Mach. Tools Manufact. 2010, 50, 621−629. 45 (27) Pawlus, P.; Michalski, J. Simulation of Cylinder ‘Zero-Wear’ Process. Wear 2009, 266, 208−213. 46 (28) Hu, S.; Huang, W.; Shi, X.; Peng, Z.; Liu, X. Multi-Gaussian Stratified Modeling and 47 Characterization of Multi-Process Surfaces. Tribol. Lett. 2018, 66, 117. 48 49 (29) Hu, S.; Brunetiere, N.; Huang, W.; Liu, X.; Wang, Y. The Bi-Gaussian Theory to Understand Sliding 50 Wear and Friction. Tribol. Int. 2017, 114, 186−191. 51 (30) Hu, S.; Brunetiere, N.; Huang, W.; Liu, X.; Wang, Y. Stratified Revised Asperity Contact Model 52 53 for Worn Surfaces. J. Tribol. 2017, 139, 021403. 54 (31) Hu, S.; Brunetiere, N.; Huang, W.; Liu, X.; Wang, Y. Continuous Separating Method for 55 Characterizing and Reconstructing Bi-Gaussian Stratified Surfaces. Tribol. Int. 2016, 102, 454−462. 56 57 (32) Li, L.; Li, B.; Dong, J.; Zhang, J. Roles of Silanes and Silicones in Forming Superhydrophobic and 58 Superoleophobic Materials. J. Mater. Chem. A 2016, 4, 13677−13725. 59 (33) Li, Y.; Li, L.; Sun, J. Bioinspired Self-Healing Superhydrophobic Coatings. Angew. Chem. Int. Edit. 60
ACS Paragon Plus Environment Langmuir Page 14 of 25
1 2 3 2010, 49, 6129−6133. 4 5 (34) Liu, T. Y.; Kim, C. J. Turning a Surface Superrepellent even to Completely Wetting Liquids. Science 6 2014, 346, 1096−1100. 7 (35) Liu, X.; Gu, H.; Wang, M.; Du, X.; Gao, B.; Elbaz, A.; Sun, L.; Liao, J.; Xiao, P.; Gu, Z. 3D Printing 8 of Bioinspired Liquid Superrepellent Structures. Adv. Mater. 2018, 30, 1800103. 9 10 (36) Lafuma, A.; Quere, D. Superhydrophobic States. Nat. Mater. 2003, 2, 457−460. 11 (37) Hensel, R.; Helbig, R.; Aland, S.; Voigt, A.; Neinhuis, C.; Werner, C. Tunable Nano-Replication to 12 Explore the Omniphobic Characteristics of Springtail Skin. NPG Asia Mater. 2013, 5, e37. 13 14 (38) Nosonovsky, M.; Bhushan, B. Biomimetic Superhydrophobic Surfaces: Multiscale Approach. Nano 15 Lett. 2007, 7, 2633−2637. 16 (39) Furuta, T.; Sakai, M.; Isobe, T.; Nakajima, A. Effect of Dew Condensation on the Wettability of 17 18 Rough Hydrophobic Surfaces Coated with Two Different Silanes. Langmuir 2010, 26, 13305−13309. 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
ACS Paragon Plus Environment Page 15 of 25 Langmuir
1 2 3 ■ TOC GRAPHIC 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
ACS Paragon Plus Environment Langmuir Page 16 of 25
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 Figure 1 44 45 143x162mm (144 x 144 DPI) 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 ACS Paragon Plus Environment Page 17 of 25 Langmuir
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Figure 2 18 19 310x98mm (144 x 144 DPI) 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 ACS Paragon Plus Environment Langmuir Page 18 of 25
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 Figure 3 35 36 205x177mm (144 x 144 DPI) 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 ACS Paragon Plus Environment Page 19 of 25 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 Figure 4 46 47 160x298mm (144 x 144 DPI) 48 49 50 51 52 53 54 55 56 57 58 59 60 ACS Paragon Plus Environment Langmuir Page 20 of 25
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Figure 5 22 207x87mm (144 x 144 DPI) 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 ACS Paragon Plus Environment Page 21 of 25 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 Figure 6 29 30 146x98mm (144 x 144 DPI) 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 ACS Paragon Plus Environment Langmuir Page 22 of 25
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Figure 7 22 206x88mm (144 x 144 DPI) 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 ACS Paragon Plus Environment Page 23 of 25 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 Figure 8 35 36 161x139mm (144 x 144 DPI) 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 ACS Paragon Plus Environment Langmuir Page 24 of 25
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Figure 9 25 165x86mm (150 x 150 DPI) 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 ACS Paragon Plus Environment Page 25 of 25 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 Figure 10. 37 38 207x191mm (144 x 144 DPI) 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 ACS Paragon Plus Environment