Anti-icing performance of the superhydrophobic surface with micro-cubic array structures fabricated by plasma etching

Journal Pre-proof Anti-icing performance of the superhydrophobic surface with micro-cubic array structures fabricated by plasma etching Wenqing Hou, Yizhou Shen, Jie Tao, Yangjiangshan Xu, Jiawei Jiang, Haifeng Chen, Zhenfeng Jia

PII:

S0927-7757(19)31173-2

DOI:

https://doi.org/10.1016/j.colsurfa.2019.124180

Reference:

COLSUA 124180

To appear in:

Colloids and Surfaces A: Physicochemical and Engineering Aspects

Received Date:

9 July 2019

Revised Date:

15 September 2019

Accepted Date:

31 October 2019

Please cite this article as: Hou W, Shen Y, Tao J, Xu Y, Jiang J, Chen H, Jia Z, Anti-icing performance of the superhydrophobic surface with micro-cubic array structures fabricated by plasma etching, Colloids and Surfaces A: Physicochemical and Engineering Aspects (2019), doi: https://doi.org/10.1016/j.colsurfa.2019.124180

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Anti-icing performance of the superhydrophobic surface with microcubic array structures fabricated by plasma etching

Wenqing Hou,a Yizhou Shen,a,d Jie Tao,a,c,* Yangjiangshan Xu,a Jiawei Jiang,a Haifeng Chen,b Zhenfeng Jia,a

College of Materials Science and Technology, Nanjing University of Aeronautics and

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a

Astronautics, Nanjing 210016, P.R. China b

Department of Materials Chemistry, Qiuzhen School, Huzhou University, 759, East

Jiangsu Collaborative Innovation Center for Advanced Inorganic Function

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c

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2nd Road, Huzhou 313000, P. R. China

Composites, Nanjing Tech University, Nanjing 210016, P. R. China School of Materials Science and Engineering, Nanyang Technological University,

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Nanyang Avenue 50, Singapore 639798

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Wenqing Hou and Yizhou Shen contribute equally to this work.

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* Corresponding author: Prof. Jie Tao, E-mail: [email protected]; Fax/Tel: +86 25 5211 2911.

Graphical abstract

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Abstract: We designed and constructed a series of micro-cubic arrays on silicon surface by means of a selective plasma etching technology to explore the size effect of surface microstructure on anti-icing/icephobic performance in terms of ice adhesion strength and icing delay time in this work. It was confirmed that the micro-cubic array with the center-center spacing distance of 70μm could greatly delay the icing process to 1295s (~two orders of magnitude comparing with that on the substrate surface). This type of

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micro-structures could entrap more air pockets underneath the water droplets to form the stable Cassie-Baxter wetting state, leading to lower actual solid/liquid contact areal

fraction ~8.15% and larger heat transfer barrier. Meanwhile, the special interface

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configuration is beneficial to the reduction in ice adhesion strength. As the temperature

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decreases, the wetting state with varied has shifted. The ice adhesion strength of the surface was as low as 16kPa with the center-center spacing distance of 30μm for the

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micro-cubic arrays. In this case, the entrapped air pockets act as the micro-cracks under

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the shear force, which leads to lower fracture critical stress. The understanding of the size effect of microstructures on the icing delay ability and ice adhesion strength will

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be beneficial to the design of ideal anti-icing/icephobic materials.

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Keywords: ice adhesion strength; icing delay time; micro-spacing; wetting state

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1. Introduction Anti-icing on solid surfaces is of great importance in aircraft, railway, power transmission line, wind turbine, etc [1,2]. Up to now, many efforts have been made to develop the anti/de-icing strategies with higher efficiency and lower energy consumption [3]. Currently, there are two main strategies to prevent ice accumulation and remove ice from the surfaces. The first strategy is the conventional active method,

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including electrothermal and mechanical approaches [4], and the second one is passive icephobic materials with only a little external energy [5,6]. Since the conventional

deicing methods not only increase the cost of aircraft design and manufacture, but also

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reduce the service life of aircraft materials caused by cold-hot alternation and

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continuous vibration [7,8]. Therefore, the passive anti-icing technology, inspired by natural plants, has been getting more and more attentions due to its great superiority in

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low cost and high efficiency [7-9]. Under the inspiration of Lotus Leaf,

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superhydrophobic surface is proposed and widely developed to resist the infiltration of supercooled droplets [10-12]. Although it has been reported that some

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superhydrophobic surfaces show lower icephobicity [13], the mechanical interlocking caused by microstructure under subcooling environments is the main contribution to

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ice adhesion. However, the special interface configuration can well hold the ice on the surface without any interpenetration, and results in an ultralow ice adhesion strength [14,15]. Therefore, it is essential to explore the influence factors and mechanisms of ice adhesion on the superhydrophobic surface for the entire evaluation of anti-icing performance. Obviously, lower ice adhesion strength is beneficial to the reduction in 4

energy consumption using the traditional de-icing methods [16]. Also, the ice adhesion is highly depended on the surface roughness [17,18], ambient temperature and vapor pressure [7,19]. However, even with the same roughness, different surface configuration arrangement undoubtedly has a distinct effect on ice adhesion. Nevertheless, such studies are rarely reported. The surface morphology plays a critical role in wetting state and ice performance

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of superhydrophobic anti-icing surfaces [20,21]. Oberli et al. fabricated the coatings

with microstructures of micro-pillars, and investigated condensation and icing delay

performance [22]. However, the comparison between smaller and larger pillar

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substrates without controlling variables has little guidance to design ideal icephobic

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materials. In the perspective of fracture mechanics, He and Xiao et al. revealed a novel integrated macro-crack initiator mechanism and proposed a new approach to design surfaces

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introducing

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low-ice-adhesion

sub-structures

into

smooth

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polydimethylsiloxane coatings [23]. Although the ice adhesion of this new-designed material surface has reached as low as 5.7 kPa, it is not clear that how the sub-structures

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influence ice adhesion. Nguyen et al. investigated the contribution of actual solid-ice contact area and nanopillar height to anti-icing performance in terms of adhesion force

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and freezing time [24]. Although it has been reported that there is a sort of qualitative relationship between surface morphology and anti-icing performance, the selection of parameters is still in doubts. In this literature, the contact area is assumed instead of the actual contact area. Bengaluru Subramanyam et al. further classified the relationship between the ice adhesion and surface structures [25], and considered that the ice 5

adhesion strength was mainly determined by the surface nanostructures. However, the nanostructures are irregular, and it is hard to discuss the size effect of nanostructures on the ice adhesion strength. Furthermore, it is widely recognized that microscale structures produce a dominant role in the ice adhesion on the hierarchical superhydrophobic surface due to its larger porosity with ice embedded much more. In this work, we designed and constructed a series of micro-cubic arrays on silicon

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surfaces by means of plasma etching and obtained the hydrophobicity or superhydrophobicity after the fluorination modification. On this basis, the icing process was observed with the aim of revealing the roles of geometrical parameters of the

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designed microstructures on icing delay performance. Subsequently, the ice adhesion

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characteristics were analyzed in more details according to the experimental and simulated results, which greatly promoted the comprehensive insight into the

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2. Experimental

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icephobicity of superhydrophobic materials.

2.1. Materials and sample preparation

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Silicon wafers were selected as the substrate materials for the construction of micro-cubic array structures. The substrates were proceed into the size of 20mm×20mm.

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Regarding the related materials used in the experiments, the ethanol applied in this experiment was analytical grade and provided by Sinopharm chemical reagent Co., Ltd., China. Ultrapure deionized water from an Ulupure-II-20T water system (Chengdu, China) was used throughout the experiments. SU-8 photoresist was purchased from Gersteltec Sarl Co., Ltd., Switzerland. The photoresist developer was purchased from 6

Electron Machine Corporation (EMC), America. The mask used in photoetching process was customized from Rigorous Technology Co., Ltd, China. Additionally, as a modification agent, the commercial grade Heptadecafluoro-1,1,2,2-tetradecyl (FAS-17, purchased from Tokyo chemical industry Co., Ltd., Japan) was utilized to modify the micro-cubic array structures on the silicon substrate. According to previous researches on wetting state, it was demonstrated that the

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Cassie-Baxter wetting state for a certain volume of droplet could be transformed into

the Wenzel wetting state as the micro-spacing distance of structure increases [3,26]. Therefore, we designed various micro-spacing distances Sm between the both micro-

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pillars from 30μm to 130μm on silicon surfaces. The micro-cubic edge length was

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designed with the same value of height as 20μm, as shown in Figure 1(a). To obtain the designed micro-cubic structures, silicon substrates were firstly

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cleaned using ultra-sonication alternately with ethanol and deionized water for 10min

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and then dried in cold air. Subsequently, the substrate was covered by a layer of SU-8 photoresist with ~5μm, and a mask template with the designed patterns was placed on

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the surface of photoresist layer. On this basis, the formed setup was exposed in a UV environment for 5-10s using a standard UV mask aligner. As a consequence, the

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patterns can be successfully transformed to the substrate surface. The samples were treated using plasma etching device to selectively etch the substrate surface and finally generate the micro-cubic array structures, as shown in Figure 1(b). Lastly, the samples with the micro-cubic structures were modified in 1wt% FAS-17 ethanol solution for 24h and then dried in an 120°C oven for 2h for the hydrophobicity or 7

superhydrophobicity. 2.2. Characterization and non-wettability Sample morphologies were characterized by a field emission scanning electron microscopy (FE-SEM; Hitachi S4800, Japan). The chemical component of sample surfaces was analyzed by using an X-ray photoelectron spectrometer (XPS; AXIS UltraDLD, Kratos, Japan). The water contact angles (WCA) on as-fabricated samples

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with 6μL deionized water droplets were directly measured by a contact angle analyser

(Kruss DSA100, Germany). All samples were measured with five times at independent

2.3. Icing delay time and adhesion strength

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positions, and then all values were averaged statistically.

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The ice formation process of 4μL distilled water droplet was observed by a CCD camera. The test chamber was controlled with an absolutely dry environment (Relative

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humidity <5%), and the reference water droplet was deposited on the sample surface,

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which was placed on a cooling stage at -15°C. The icing delay time is defined as the duration from the moment when the water droplet contacts with the sample surface to

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the one of the whole droplet freezing into ice. Regarding the ice adhesion strength, a cuvette (with cross section of 10mm×10mm)

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fully filled with distilled water was firstly prepared, and then a sample was placed on the rabbet of the cuvette, where the treated sample surface was kept with the distilled water to make sure the same thickness of accreted ice [27]. Afterwards, this setup was placed in a refrigerator at -20°C for 24 h to form a steady ice cuboid sticking to the sample surface. The ice adhesion strength was measured using a custom-built apparatus, 8

as shown in Figure 2. The coarse adjustment slider can move forward along with the horizontal direction to remove the ice cuboid from the sample surface. Meanwhile, the ice adhesion strength can be detected by the dynamometer and transmitted to the computer at the time of ice separation. The ice removing process, especially the dynamic broken process, was accurately recorded by a microphotographic camera. In

2.4. Finite element simulation of ice removing process

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this test, each sample was measured for at least ten times.

The finite element analysis was carried out by using a commercial software,

Abaqus 6.12, to simulate the process of ice removing on the sample surface. Ice was

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modeled as an elastic three-dimensional solid. The sample model with varied surface

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morphology was also set as the elastic three-dimensional solid, recognizing ice fracture as linear elastic fracture process, as shown in Figure S1. Material properties are

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summarized in Table1. The models were meshed using 8-node linear brick,

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incompatible modes and were run using Simulia-Abaqus 6.12. 3. Results and discussion

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3.1. Surface morphology and chemical composition The desired microstructures were successfully fabricated to analyze the surface

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morphologies. It should be firstly noted that the surface morphologies of the asprepared micro-cubic array structures are displayed at the same magnification, i.e., Figure 3(a-g). Also, the micro-cubic structures evenly distribute on the sample surface without any defects, and the center-center spacing distance Sm continuously increases from 30μm to 130μm. These samples were labelled as Sample 1-7 according to the 9

center-center spacing distance. Furthermore, the side length of the micro-cubic structure was 20μm, as shown in Figure 3(h). The surface roughness Ra also exhibits the corresponding change trend from 8.89μm to 6.21μm [28], and there is a peak value of 10.00μm when the center-center spacing distance is 40μm (see Figure 3(j)). It is easy to understand that the surface of silicon sample tends to be smooth, no matter how large or small of center-center spacing distance. Therefore, Ra shows the trend of first

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increasing and then decreasing as the micro-spacing distance increases.

As well known, the chemical composition is another important factor to induce the

non-wettability except the surface microscopic structure, which was analyzed to verify

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the modification of the low-energy materials. During the modification process, the low-

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energy groups from FAS-17 firstly take place the hydrolytic reaction, connecting with -OH bonds on the substrate surface, and then occur the dehydration reaction with each

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other to form the continuous molecule membrane, as shown in Figure 4(a). According

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to the XPS measured results shown in Figure 4(b), the F1s, C1s and O1 speaks are obviously observed at 685.7eV, 285.0eV and 531.8eV after the low-energy

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modification [29-31]. In the high-resolution spectra of F1s peak, there are two peaks appearing at the positions of 686.5eV and 688.9eV, which are respectively assigned to

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-CF3 and -CF2, as shown in Figure 4(c). Similarly, there are many small peaks being found in the high-resolution of C1s, as shown in Figure 4(d), and the corresponding positions are located at 283.9eV, 284.7eV, 286.1eV, 286.8 eV, and 287.6eV, respectively, which can be accordingly assigned to C-H, C-C, C-O, CF2, and C=O. From the Figure 4(e), the hidden peaks into the main peak of O1s mainly reflect the presence of O-Si, 10

O-C, and O=C groups. Overall, these XPS analyses can well demonstrate that the lowenergy groups from FAS-17 have been grafted onto the surface of as-fabricated microcubic array structures. 3.2. Non-wettability Under the synergetic action of surface microstructures and chemical compositions, these sample surfaces display a certain extent of hydrophobicity or superhydrophobicity,

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and the measured results are shown in Table 2. As the center-center spacing distance Sm

increases, WCA firstly goes up slowly from 147.22° to 154.22° and then gradually reduces to 148.33°, when the center-center spacing distance reaches 100μm (i.e.,

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Sample 6), as shown in Figure 5(a). Meantime, the rolling-off angle firstly goes down

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from 8.5° to 3.5° and then increases to 8.0° gradually. Since the intrinsic chemical properties of all these samples are same with FAS-17, the macroscopic non-wettability

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is mainly determined by the geometrical conditions of the surface microstructures, i.e.,

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the center-center spacing distance of micro-cubic array structures in this work. The firstly raised stage of WCA from 147.22° to 154.22° results from the increase of center-

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center spacing distance, causing the stable Cassie-Baxter non-wetting model, where the sparse micro-cubic array structures are helpful to entrap more air pockets underneath

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water droplet [32,33]. As a consequence, the sample surface exhibits greater superhydrophobicity. Afterward, the further increased center-center spacing distance can cause the unstable Cassie-Baxter wetting state. Therefore, WCA gradually decreases from the 154.22° to 148.33° due to the embedded droplet into the vacancies of the 11

microstructures with larger center-center spacing. Then WCA on Sample 7 suddenly reduces to 118.14°, leading to stable Wenzel wetting state with the increased Sm. The calculated areal fraction on sample surfaces, defined as actual interface contact area based on wetting state over apparent contact area, as shown in Figure 5(b), verifies the correct analyses of wetting state on these surfaces above. 3.3. Icing delay time

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The solid-liquid wetting state determines the icing delay characteristics, which is the first defense line of anti-icing performance. The freezing processes of water droplet

with 4μL on these sample surfaces were researched to investigate the role of center-

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center spacing of the designed microstructures on icing delay performance, as shown

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in Figure 6. The icing delay time of droplet on Sample 5 is up to 1295s, much longer than those on other samples, which gives the credit to its higher capacity to entrap more

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air pockets with longer Sm [34-36]. The more air pockets acting as heat blocks have

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lower transfer efficiency [37,38]. In terms of ice nucleation rate, the heterogenous nucleation rate is dependent linearly on real contact area Ar, which is given by [39,40] (1)

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𝐽∝𝐴𝑟 𝑓 ′′ [𝑓 2 𝐵𝑒𝑥𝑝[−𝜖𝑓 ′ /𝑇(∆𝑇)2 ]

where 𝜖 = 16𝜋𝛾𝑐𝑓 3 𝛺 2 /3𝑘𝐵 𝑇𝑆 2 ; kB is Boltzmann’s constant; S is the entropy of

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melting per molecule; T and ∆T is the temperature and subcooled temperature, respectively; 𝛾𝑐𝑓 is the solid/liquid interfacial free energy; 𝛺 is the difference in free energy per unit volume between liquid and solid phases; f is interfacial correlation factor [41-43]. Among the first five samples (i.e., Sample 1-5) all at Cassie-Baxter wetting state, Sample 5 with smallest Ar has lowest nucleation rate based on Equation 12

(1), leading to more time for ice nucleation. Admittedly, the test results under the cooling conditions may be affected by the condensate droplets on the sample surfaces. The wetting state caused by microstructure configuration, however, has led to distinct nucleation preparation time accordingly [44-46]. Regarding the last two samples (i.e., Sample 6-7), the icing delay time exhibits the corresponding trend with that of nonwettability, where Sample 7 has icing delay time as low as 36s with larger three-phase

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line at Wenzel wetting state.

During the experiment as shown in Figure 6, the droplet suddenly becomes turbid

at some moment and then starts growth marked by the line. The growth speed is so fast

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that the time caused by ice growth process has less contribution during the whole icing

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delay time [47,48]. Therefore, the icing delay time highly depends on the wetting state

3.4. Ice adhesion

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and heterogenous nucleation related to the real contact area Ar.

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Under researches on non-wettability and icing delay performance, the ice adhesion characteristics were investigated to explore the anti-icing potential further. As shown in

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Figure 7(a), as the center-center spacing Sm of the designed microstructures increases, the ice adhesion shear strength τ firstly increases and then decreases, where there is a

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peak value of 86.8kPa on Sample 4. Among the first three samples (i.e., Sample 1-3), there is an approximately positive linear relationship between τ and Sm, where the ice adhesion strength on Sample 1 is as low as 16kPa. This trend is partly ascribed to the shift wetting state with lower WCA at low temperature, as shown in Figure 7(b). Therefore, it is confirmed that Sample 2 and Sample 3 are in the semi Cassie-Wenzel 13

transition [49]. Since the Sm of microstructures on Sample 3 is larger than that on Sample 2, the ice embedded deeper into the asperities of Sample 3 surface has stronger mechanical interlocking effect than that of Sample 2. Furthermore, the adhesion process is a complicated physical and chemical process with the interface interaction of Van Der Waals Forces, chemical bond cooperation and microscopic mechanical connection [50]. Under the synergistic effect of special

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microstructure configuration and adhesion work Wa, the adhesion strength can be deduced according to Griffith theory of elastic fracture mechanics. Since fracture

occurs mainly in accordance with the opening crack scenario according to the ice

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cocking phenomenon (see supplementary materials, as shown in Figure S2 and Figure

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S3), the critical strength is given by [51] 𝐸𝐺

𝜏𝑦𝑦 = √𝜋𝑏

(2)

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Where E and b are Young’s modulus and crack length, respectively. G is the surface

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energy, which is regarded as the adhesion work Wa. Since Wa is proportional to the solid-ice interface contact area Ar based on the definition, the critical stress can be

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written as [52]:

𝐸𝐺

𝐸𝑊

𝐸(𝛾𝑖𝑐𝑒 +𝛾𝑠𝑖𝑙𝑖𝑐𝑜𝑛 −𝛾𝑖𝑐𝑒−𝑠𝑖𝑙𝑖𝑐𝑜𝑛 )

𝜏𝑦𝑦 = √𝜋𝑏 = √ 𝜋𝑏𝑎 = √

𝜋𝑏

𝐴

∝k√ 𝑏𝑟

(3)

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Meanwhile, according to the microstructure configuration and wetting state, Ar is derived based on geometric configuration of solid-ice interface, as shown in Figure 7(c), therefore the critical stress can be written as: 𝑎+𝑚ℎ

𝜏𝑦𝑦 ∝√

𝑆 ( 𝑚 −1)

(4)

𝑎

Where a and Sm is the length and center-center spacing of the micro-cubic arrays, 14

respectively. Additionally, m and h are determined by solid-ice wetting state, where h is the depth of ice embedded in the grooves of the microstructures. The value of m ranges from 4 to 5. Among the first three samples, although the crack length increases as Sm increases, the Wa also increases, where the wetting state plays a pre-dominant role in ice adhesion strength. Whereas, regarding the last four samples (i.e., Sample 4-7), there is an

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approximately inversely relationship between τ and Sm. It is confirmed that the wetting state of the last four samples is Wenzel state according to Figure 7(c). On the basis of Equation (4), the value of a+mh is constant under same wetting state, therefore ice 𝑆

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adhesion strength is inversely proportional to √ a𝑚 − 1 . As the Sm increases, the

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theoretical ice adhesion strength decreases, which is in accordance with the test results. The test results could also be explained by weaker mechanical interlocking structure

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with the reduced three-phase line of contact caused by widening micro-spacing distance

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[53,54].

The Mises stress nephogram and shear stress nephogram of finite element

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simulation results are shown in Figure 8, where they all have consistent trends [55,56]. The shear stress distribution on Sample 1 is much lower than any others, verifying the

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correctness of the analyzed wetting state. Meanwhile, the surrounding columnar area of micro-cubic arrays on Sample 4 has much higher stress distribution, verifying the correctness of its Wenzel wetting state. The whole stress trend of finite element simulation is accordance again with the test results and analyses above, as the centercenter spacing of microstructures increases. 15

4. Conclusions In conclusion, a series of micro-cubic arrays on substrates were designed and fabricated successfully by means of a selective plasma etching method for the exploration of scale effect of microstructures on icephobic performance, including icing delay and ice adhesion performance. The micro-cubic arrays with micro-spacing distance of 70μm could greatly delay the icing process up to 1295s (~two orders of

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magnitude comparing to that on other surfaces). This type of micro-structures could

entrap more air pockets underneath the water droplets to form the stable Cassie-Baxter wetting state, leading to lower actual solid/liquid contact areal fraction ~8.15% and

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larger heat transfer barrier. Additionally, since the temperature decreases, the wetting

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state shifts accordingly. It was confirmed that the ice adhesion can be reduced to only 16kPa, when the micro-spacing distance is 30μm with more amount of air pockets at

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the apparent solid-ice interface. The special configuration with micro-cracks

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contributes to the lower ice breaking strength. In overall consideration of icing delay time, ice adhesion, service environment and duration, a comprehensive scheme for

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designing anti-icing materials should be established to provide the direct design

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foundation of ideal anti-icing/icephobic materials.

○s Supporting Information Figure S1 of the finite element simulation model of ice removing; Figure S2 of the ice removing process and the simulation results of shear stress and normal stress on the silicon surfaces during ice stripping; Figure S3 of the ice residue on the edge of the 16

sample surfaces and the simulation results of the normal stress distribution on the silicon sample surfaces after ice removing. (PDF)

Notes The authors declare no competing financial interest.

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Acknowledgements

J.T. and Y.S. acknowledge financial support from the National Natural Science

Foundation of China (No. 51671105, 51705244). Y.S., J.J. and W. H. thank the support

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of the Natural Science Foundation of Jiangsu Province (No. BK20170790), and H.C.

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acknowledges the General Project of Zhejiang provincial department of education (Y201737320). W.H., Z.J. and Y.X. thank the Project Funded by the Priority Academic

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Program Development of Jiangsu Higher Education Institutions and the NUAA

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Innovation Program for Graduate Education (kfjj20180609).

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Figure captions list: Figure 1. (a) Sketch image of the designed micro-cubic array structures; (b) Plasma

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etching process of silicon micro-cubic structures.

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Figure 2. (a) Simple diagram of the custom-built apparatus for ice removing process;

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(b-c) Pictures of the custom-built apparatus during ice removing experiments.

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Figure 3. SEM images of micro-cubic array surfaces with magnification of 100x,

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whose center-center spacing distance vary from 30μm to 130μm: (a) 30μm; (b) 40μm;

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(c) 50μm; (d) 60μm; (e) 70μm; (f) 100μm; (g) 130μm; (h) SEM images of micro-cubic array silicon surfaces with magnification of 500x; (i) Schematic diagram of micro-

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structure sample surface; (j) Surface roughness as a function of center-center spacing

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distance Sm of the as-fabricated micro-cubic structures.

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Figure 4. (a) Chemical reaction process to graft the low-energy groups onto the surface of the as-fabricated micro-cubic array structures; (b) XPS survey spectrum of the sample surface before and after the low-energy modification; (c-e) High-resolution

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spectrum of the F1s, C1s, and O1s after the modified sample surface.

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Figure 5. (a) WCA on the modified sample surfaces; (b) Calculated areal fraction on the fabricated surfaces.

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Figure 6. Icing delay time process on sample surfaces at -15°C, whose center-center spacing distance vary from 30μm to 130μm: (a) 30μm; (b) 40μm; (c) 50μm; (d) 60μm;

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(e) 70μm; (f) 100μm; (g) 130μm.

Figure 7. (a) Ice adhesion strength on surfaces in terms of experiments and finite element simulation; (b) WCA on the fabricated sample surfaces in terms of temperature; (c) Sketch diagram of geometric configuration on solid-ice interface. 28

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Figure 8. (a) Mises stress nephogram of finite element simulation results; (b) Shear

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stress nephogram S13 of finite element simulation results.

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Table caption list: Table 1. Material properties of silicon samples and ice Silicon

Ice

E [GPa]

190

10760

θ

0.27

0.325

ρ [kg/m3]

2320

919

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Properties

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Table 2. Water contact angle (WCA) and rolling-off angle on the fabricated sample surfaces Water contact angle (WCA)

Rolling-off angle

Sample 1

147.27°

8.5°

Sample 2

149.09°

4.0°

Sample 3

153.47°

3.5°

Sample 4

154.22°

4.0°

Sample 5

149.61°

Sample 6

148.33°

Sample 7

118.14°

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Sample

8.0°

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―

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