Femtosecond laser fabrication of highly hydrophobic stainless steel surface with hierarchical structures fabricated by combining ordered microstructures and LIPSS

Femtosecond laser fabrication of highly hydrophobic stainless steel surface with hierarchical structures fabricated by combining ordered microstructures and LIPSS

Accepted Manuscript Title: Femtosecond laser fabrication of highly hydrophobic stainless steel surface with hierarchical structures fabricated by comb...

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Accepted Manuscript Title: Femtosecond laser fabrication of highly hydrophobic stainless steel surface with hierarchical structures fabricated by combining ordered microstructures and LIPSS Author: M. Mart´ınez-Calderon A. Rodr´ıguez A. Dias M.C. Morant-Mi˜nana M. G´omez-Aranzadi S.M. Olaizola PII: DOI: Reference:

S0169-4332(15)02392-2 http://dx.doi.org/doi:10.1016/j.apsusc.2015.09.261 APSUSC 31475

To appear in:

APSUSC

Received date: Revised date: Accepted date:

20-6-2015 25-9-2015 30-9-2015

Please cite this article as: M. Mart´inez-Calderon, A. Rodr´iguez, A. Dias, M.C. Morant-Mi˜nana, M. G´omez-Aranzadi, S.M. Olaizola, Femtosecond laser fabrication of highly hydrophobic stainless steel surface with hierarchical structures fabricated by combining ordered microstructures and LIPSS, Applied Surface Science (2015), http://dx.doi.org/10.1016/j.apsusc.2015.09.261 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Femtosecond laser fabrication of highly hydrophobic stainless steel surface with hierarchical structures fabricated by combining ordered microstructures and LIPSS M. Martínez-Calderona,b, A. Rodrígueza,b, A. Diasa,b,

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M.C. Morant-Miñanaa,b, M. Gómez-Aranzadia,b, S.M. Olaizolaa,b a

CEIT-IK4 & Tecnun (University of Navarra), Paseo Manuel Lardizábal 15, 20018 San Sebastián, Spain

Abstract

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CIC microGUNE, Goiru Kalea 9 Polo Innovación Garaia, 20500 Arrasate-Mondragón, Spain

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In this work we have developed hierarchical structures that consist of micro-patterned surfaces covered by nanostructures with a femtosecond laser. The first part of this work is a study to determine the microscale modifications produced on a stainless steel alloy (AISI304) surface at high pulse energy, different velocities, and number of overscans in order to obtain microstructures with a selected depth of around 10 μm and line widths of 20 μm. The second part of the work is focused on finding the optimal irradiation parameters to obtain the nanostructure pattern. Nanostructures have been defined by means of Laser Induced Periodical Surface Structures (LIPSS) around 250 nm high and a period of 580 nm, which constitute the nanostructure pattern. Finally, dual scale gratings of 50 mm2 were fabricated with different geometries and their effect on the measured contact angle. Combining the micro-pattern with the LIPSS nano-pattern, highly hydrophobic surfaces have been developed with measured static contact angles higher than 150º on a stainless steel alloy.

1. Introduction

Wettability control of material surfaces and super-hydrophobic behavior have attracted a lot of interest in recent years because of their importance and applicability in fundamental research and practical applications. It has been widely reported that the leaves of many plants such as lotus leaves, rose petals or animals like certain types of sharks show particular wetting characteristics like superhydrophobicity and selfcleaning ability [1], super-wicking effect [2] and drag reduction in water with antibiofouling properties [3]. It has been demonstrated that these surface wetting features are a direct consequence of their surface morphology because of the hierarchical structures that form their surfaces on the micro and nanometre scale, but also a matter of their surface chemistry [4]. The wettability of a surface can be characterized by the CA (contact angle). A hydrophilic surface has a CA below 90°. A surface with a CA higher than 90° is known as a hydrophobic surface. In order to declare a surface superhydrophobic two conditions must be fulfilled: a CA higher than 150º and a rolling angle smaller than 5º. The states of water droplets on a solid surface and the corresponding apparent contact angles

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(APCA) are generally classified into two categories, namely the Wenzel state and the Cassie–Baxter state [5], [6]. The Wenzel state is characterized by a homogeneous interface where the liquid is completely wetting the solid surface. The Cassie-Baxter state is characterized by a heterogeneous interface where air bubbles are trapped in the valleys between the nano and micropatterns, so that the liquid rests on a composite surface of solid and air. The corresponding APCA for the Cassie–Baxter state are much higher than for the Wenzel state. Current literature suggests also the existence of a heterogeneous wetting regime with partial liquid penetration, named metastable Cassie states [7].

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The design of self-cleaning surfaces [8], surfaces with improved corrosion resistance [9], enhanced or decreased cell adhesion in biomaterials and biocompatible coatings in order to increase the biomaterial compatibility in the human body [10], [11] or antibiofouling ability which is critical in marine industry [12] are examples of the potential interest that the wettability control allows to explode. There are a few different techniques that can be used to modify the morphology and the chemistry of a surface, like photolithography [13], laser interference lithography [14], chemical etching [15] or layer by layer assembly [16] among others. The problem is that normally these techniques involve several steps, additional materials, or delicate and time-consuming processes, which usually require high budgets and working inside a clean room.

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The challenge is to create a robust fabrication method which can be scaled up for industry and highly reproducible, with simpler and faster processes. In order to solve these problems, femtosecond laser micro-nano machining has emerged as an effective technique to create dual scaled surfaces with nano- and micro-structures [17], [18], [19]. Chloroalkylsilane and fluoroalkylsilane coatings are frequently used to greatly decrease the surface energies of the laser machined surfaces and to obtain the highest contact angles [20]. However, these organic compound coatings may have problems with mechanical and thermal stability and could be easily peeled off from the substrates. Moreover, toxic residues may be left on the surface and this prevents their effective use for certain applications due to their low compatibility with environment and living being. It has been demonstrated that only with the femtosecond laser texturing process, superhydrophobic surfaces can be obtained in different types of metals [21], [22]. In this work the main relevance is that we are generating nanopatterns formed by LIPSS (Laser Induced Periodical Surface Structures) in a controlled way, covering the previously micro-machined surface structures with different geometries, which is a novel fabrication process that tries to imitate the hierarchical structures found in nature with only the femtosecond laser irradiation technique and avoiding the use of additional chemical treatments of the surface. It has been also demonstrated that the hydrophobic behavior presented in the femtosecond-treated surfaces does not only depend on the introduced surface micro/nano roughness but also on chemical reactions and carbon compounds accumulated on the surface [23], [24]. The objective is to obtain highly hydrophobic surfaces starting from an initial hydrophilic stainless steel AISI 304 surface. To reach this purpose the fabrication process consists in the combination of ordered micro-machined structures with LIPSS,

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which have been demonstrated to be a very effective technique in order to generate controlled nanopatterns on the surface of bulk materials [25], polymers [26] or thin films [27], into hierarchical structures. The effect on the measured static APCA of these dual scale structures will be analyzed for different surface geometries.

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2. Experimental Section 2.1 Materials

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Austenitic stainless steel (AISI304) plates with a thickness of 0.5 mm were used. The material has been treated as it was received from the suppliers without any further pretreatment in order to ensure repeatability and to avoid any additional steps in the fabrication process. The initial average surface roughness (Ra) of the samples was 220 nm. Before and after being treated by the laser the samples were cleaned in a 10 min ultrasonic acetone bath, followed by a 10 min ethanol bath. After the laser treatment the samples were kept in a box exposed to open air atmosphere.

2.2 Micro-nano machining setup

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Samples were machined in open air atmosphere with a Ti: Sapphire laser system consisting of a mode-locked oscillator and a regenerative amplifier which was used to generate 130 fs pulses at a central wavelength of 800 nm, with a 1 kHz repetition rate. The pulse energy was adjusted with a two-step setup: a variable attenuator formed by a half-wave plate and a low dispersion polarizer. The 12 mm diameter laser beam was focused on the samples using a 10x microscope objective with a NA of 0.3. This objective together with a CCD camera was used for online monitoring the structuring process. A three dimensional translational stage moved the sample under the beam with different scan speeds allowing a variable overlap of pulses per spot (Figure 1a). The laser fluence was also controlled by varying the distance between the objective and the sample (increasing or decreasing the spot diameter). The layout of the experimental setup is shown in Figure 1b.

Figure 1: (a) Beam overlap dependence on the scanning velocity. (b) Schematic layout of the femtosecond laser machining setup.

2.3 Proposed hierarchical structure models

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For the fabrication of the hierarchical structures, a two-step femtosecond laser irradiation process is proposed. The first step consists in the fabrication of ordered microstructures. These patterns were performed in two different models: one dimensional trench patterns or two dimensional matrix patterns (Figure 2a) that consist of ablated lines or squares separated a certain distance (represented by the pitch value). The second step consist in the definition of the nanostructures. The objective is to perform a homogeneous LIPSS nanopattern covering all the previously fabricated micropatterned structures as depicted in Figure 2b.

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Figure 2: (a) Proposed trench and matrix micropattern models. (b) Proposed homogeneous LIPSS nanopattern covering the micropatterned surface.

2.4 Characterization

A JPK NanoWizard atomic force microscope in the intermittent contact mode using a silicon tip (r < 10 nm; aspect ratio < 6 : 1) with a force constant of 40 N m-1 and a resonant frequency of approximately 300 kHz was employed to study the topography of the fabricated stainless steel structures. The width and depth parameters were measured with a KLA Tencor profilometer. In addition to this, a 3D field-emission scanning electron microscope (FE-SEM) system supplied by FEI was used to study the topography. Free and open source software (Gwyddion) was used to perform two dimensional Fast Fourier Transforms (2D-FFT) of the FE-SEM micrographs which provide an effective way to analyze the LIPSS periods. Static APCA measurements were obtained by gently dispensing a 3.5 µl droplet of distilled water with a microsyringe on each sample surface. The whole process was recorded with a digital camera. In order to measure the static APCA, the recorded videos were analyzed and the APCA measured using the sessile drop method with the Low-Bond Axisymmetric Drop Shape Analysis (LBADSA) plugin for ImageJ [28]. Successive measurements were

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reproducible with an average error of ±2.5º. All contact angles measurements were carried out at room temperature.

3. Results and discussion

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3.1 Micro-patterns fabrication 3.1.1 Selection of the irradiation parameters

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In order to fabricate the micropatterned surfaces, a study of the ablation depth and line width as function of the laser pulse energy, scanning speed and number of overscans was performed. Based on theoretical calculations using the Cassie-Baxter equations and derivations [29], [30] the selected line width was 20 μm (see supporting information section). A depth of the microstructures of 10 μm was selected based on literature reports [4], [8], [31].

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To obtain these parameters, firstly the line width was studied as function of the pulse energy (Figure 3a) in order to determine the adequate energy to obtain the desired line width for the microstructures. From this study it was concluded that for values higher than 35.7 µJ the line width exceeds the 20 µm. After that, the ablation depth was studied for different values of the pulse energy and scanning velocities (or number of pulses), for one overscan (Figure 3b). The depth and width values were measured using a mechanical profilometer. The values were calculated from three different scans performed at different positions. From this study, it was concluded that in order to reach 10 µm of ablated depth, with these values of the pulse energy, more overscans were needed because with these energies the ablated depth did not reach the desired value of 10 µm. Therefore, the ablation depth was analyzed as function of the number of overscans for a scanning velocity of 1 mm/s (Figure 3c). After these studies the irradiation parameters selected were a pulse energy of 35.7 µJ, which corresponds to a fluence of 25.2 J/cm2, 3 overscans and a scanning velocity of 1 mm/s with a 1 kHz repetition rate. With these parameters an ablation depth of 10.4±0.5 µm and a line width of 19±0.3 µm were obtained.

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Figure 3: Study of the irradiation parameters to fabricate the micro-pattern with the desired geometry. The lines are plotted only for visualization purposes. (a) Line width as function of the pulse energy. (b) Ablation depth as function of N (number of pulses per spot) and different values of the pulse energy. (c) Ablation depth as function of the number of overscans for a scanning speed of 1 mm/s and different values of the pulse energy.

3.1.2 Fabricated micropatterned surfaces After the selection of the parameters, different microstructures were generated on the surface of the stainless steel. After vertical scanning micrometer lines were formed at the laser scanned paths (Figure 4a). When the laser scanning is performed in the horizontal direction, squared shaped microprotusions are formed (Figure 4b). At the intersection of two laser scanned some holes are observed because these areas experienced more laser shots. In the areas where no micro-machining has been performed the material is in its original state. On the contrary, some small nanostructures are generated inside the micro-machined lines [32], [33]. Pitch distances of 30, 50 and 90 μm were tested. The typical fabricated micropatterns for 50 μm can be observed in the scanning electron microscopy images in Figure 4.

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Figure 4: FE-SEM images of the fabricated micropatterned structures: (a) trench micropattern with a pitch distance of 50 µm; (b) matrix micropattern with a pitch distance of 50 μm. Detailed area scanned on: (c) trench micropattern; (d) matrix micropattern;

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3.2 Nano-patterns fabrication

3.2.1 Irradiation parameters effect on the generated LIPSS morphologies The aim of this study was to obtain a homogeneous LIPSS nanopattern to cover all the previously fabricated microstructures. The most common type of LIPSS generated in metallic surfaces are the LSFL (Low Spatial Frequency LIPSS), also called ripples. This periodical nanopatterns are a consequence of a spatial energy distribution. According to the generally accepted theories [34], [35], LSFL are generated by the interference of the incident laser beam with a surface electromagnetic wave generated at the rough surface which might include the excitation of surface plasmon polaritons (SPPs) [36], [37], [38]. This LSFL are perpendicular to the laser polarization and usually have a period close to the laser wavelength. There is another common type of LIPSS which are the HSFL (High Spatial Frequency LIPSS) with a period smaller than half of the laser wavelength. The generation mechanism of HSFL cannot be predicted with the classical theories and is not clarified nowadays, even though different theories have been proposed [39], [40]. The orientation can be either parallel or perpendicular to the laser polarization.

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The different LIPSS morphologies generated on the stainless steel surface for a range of different values of the number of pulses and the fluence were studied. As it can be observed in Figure 5, four different types of structures were obtained. Each type of structure is classified according to the total accumulated fluence (Fluence x Number of pulses). In Table 1 it can be appreciated, that for each surface morphology the values of this parameter have their own specific range. The first type of structure obtained at low number of pulses and low values of fluence (acc. fluence < 5 J/cm2), consists of nanoparticles with a diameter smaller than 100 nm (Figure 5a). For values of the accumulated fluence from 10.32 to 265.26 J/cm2 a pure ripple nanopattern was obtained (Figure 5b). According to the findings of other authors [17], [41] the measured average period was 580 nm with an orientation perpendicular to the laser polarization. For higher values of the accumulated fluence from 287.51 to 420.41 J/cm2 another type of LIPSS was observed, consisting of HSFL (High Spatial Frequency LIPSS) with a measured average period of 300 nm with an orientation perpendicular to the laser polarization (Figure 5c). The supported theory to explain the generation of this type of LIPSS is the one proposed in [40], HSFL are generated because when the ripple nanopattern reaches a certain depth a redistribution of the energy occurs concentrated in the valleys of the previously generated ripple nanopattern, splitting the period in nearly half of the previous one, for certain irradiation conditions. For higher values of the accumulated fluence (>400 J/cm2) simple trench patterns with a significant ablation depth are obtained (Figure 5d). Therefore it can be concluded that the surface morphology of the nanostructures can be controlled applying specific parameter values.

Figure 5: Different structures generated on the stainless steel surface depending on the irradiation parameters. (a) Nanoparticles generated for values of the accumulated fluence lower than 5 J/cm2. (b) LSFL generated for values of the accumulated fluence from 10.32 to 265.26 J/cm2. (c) HSFL generated for values of the accumulated fluence from 287.51 to 420.41 J/cm2. (d) Trench structure for accumulated fluence values higher than 400 J/cm2.

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Table 1: Accumulated fluence thresholds for the different observed structures Acc. Fluence (J/cm2)

a

Acc. Fluence (J/cm2)

a

Acc. Fluence (J/cm2)

a

Acc. Fluence (J/cm2)

Stucture type

Nanoparticles

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Lower threshold

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10.32

287.51

396.12

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265.26

420.41

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(a) Acc. Fluence = Fluence x Number of Pulses

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The results are plotted in Figure 6a, following the model proposed by Kietzig et al [42] as function of the irradiation parameters. Examples of the 2D-FFT scattering graphs used to calculate and analyze the LIPSS periods of each of the obtained FE-SEM images, are shown in Figures 6b and 6c. The LSFL nanopattern was selected for the fabrication of the proposed hierarchical structures being the easiest one to obtain in a homogeneous way and also the fastest one because requires lower number of pulses.

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Figure 6: (a) LIPSS morphologies generated on the stainless steel surface depending on the Fluence and the number of pulses. (b) 2D-FFT and its cross-sectional profile of the FE-SEM image 5b used to analyse the LSFL period (~580nm). (c) 2D-FFT and its cross-sectional profile of the FE-SEM image 5c used to analyse the HSFL period (~300nm).

In order to completely characterize the morphology of this type of LIPSS generated with an accumulated fluence of 40 J/cm2 an AFM analysis was performed (Figure 7). The LSFL were homogeneously distributed in large areas and were well aligned and self-organized. From the cross-section profiles the height and the width of the LIPSS can be measured. An average value of 250 nm high was obtained. The detailed image revealed the presence of small nanobubbles that are formed along the LIPSS, it can be explained for the low energies applied from the edge of the laser beam.

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Figure 7: AFM micrographs and cross-sectional profiles of samples irradiated with an accumulated fluence per spot of 40 J/cm2.

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3.2.2 Fabricated hierarchical micro-nano patterned structures

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Hierarchical structures with a dual scale roughness were successfully fabricated for a range of pitch distances for both micropattern models (trench and matrix) and also covered by the previously characterized LIPSS nanopattern. FE-SEM images of the final structures are shown in Figure 8. As it can be observed in Figures 8c and 8d, the LSFL nanopattern was generated all over the micropatterned surface and in the nonablated areas in a very homogeneous way, showing a representative micro/nanoscale binary structure.

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Figure 8: FE-SEM images of the fabricated hierarchical structures: (a) trench micropattern with a pitch distance of 30 µm covered by LIPSS; (b) matrix micropattern with a pitch distance of 50 μm covered by LIPSS. Detailed area scanned on: (c) trench micropattern; (d) matrix micropattern;

3.3 Wettability behavior

3.3.1 Temporal evolution of the APCA To show how the wetting property is affected by the surface, the contact angles of the laser irradiated and non-irradiated surfaces were measured. The initial contact angle of the non-treated stainless steel surface was measured to be 75º (Figure 9a). Right after the irradiation process the surface became very hydrophilic with contact angles smaller than 30º. The samples were stored in a closed box exposed to open air atmosphere, and after 120 hours the treated surfaces became highly hydrophobic depending on the selected irradiation process. Once the change happened the contact angle reached a constant steady state value which was maintained in time. Contact angle measurements were repeated on a daily basis and the value of the contact angle remained constant for 50 days after the femtosecond laser treatment. This change in the wettability behavior with the exposure to air has not any relation with the surface roughness introduced; otherwise the hydrophobic behavior would have appeared just after the femtosecond laser treatment. From these observations it is concluded that the hydrophobic behavior is a matter of the introduced surface roughness but also of the intrinsic change in the surface chemistry with the exposure to air after the laser irradiation. Some authors have

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3.3.2 Effect of nano-, micro- and hierarchical structures on APCA

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discussed this effect and attributed it to the chemical interaction with the ambient CO2. They proposed a decomposition reaction of ambient CO2 into carbon over oxygen deficient metal oxides, present due to the laser irradiation, resulting in an accumulation of carbon compounds on the femtosecond laser treated rough surface and increasing the surface intrinsic contact angle [22], [23].

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At this particular point the contact angle of the prepared surfaces can be compared. The resulting images of the most representative measurements of the APCA are presented in Figure 10. It can be observed that the contact angle for a surface with only the selected type of LSFL (Figure 9d) has an average value of 120º, which is higher than for a nontreated surface (Figure 9a) but not as high as when both, micro and nanopatterns are introduced (Figures 9e and 9f). This result proves that not only the LIPSS nanopattern is the responsible for the high hydrophobicity confirming that only the combination of the dual scale patterns, results in the highest measured APCAs. For micropatterned surfaces high values of APCA (Figures 9b and 9c) were measured when the values are compared with bare surfaces but in any case not as high as when dual scale structures are performed.

Figure 9: Droplet of 3.5 µl gently dispensed on some of the fabricated structures: (a) Nontreated surface. (b) Trench micropattern with 30 µm pitch distance. (c) Matrix micropattern with 30 µm pitch distance. (d) LSFL nanopattern without any micropattern. (e) Trench micropattern with 30 µm pitch distance covered by a LSFL nanopattern. (f) Matrix micropattern with 30 µm pitch distance covered by a LSFL nanopattern.

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The results of the measured APCA for the trench and the matrix model are presented in Figure 10 for the different values of pitch distance tested. The effect of the LIPSS nanopattern can be clearly observed. The structures covered by LSFL present significantly higher values of the static APCA. In the trench model, for a pitch distance of 90 μm a significant reduction in the measured APCA is observed. The highest APCA results are obtained for the smallest pitch distance tested in which the contact angle requirements for superhydrophobicity are fulfilled. As it was expected, when the Cassie-Baxter state is reached, the structure in which the pitch distance is lower and therefore the contact between the droplet and the surface decreases, the measured APCA is the higher one.

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The results of the measured APCA for the matrix model are similar to the trench model, again a clear increase in the APCA value is observed in all cases when the LIPSS are covering the micropatterns. In this case the values of the APCA are similar for pitch distances of 30 and 50 µm and again a significant decrease is observed for a 90 µm pitch distance. This result is obtained because with the matrix model, there is a significantly higher ablated amount of material and therefore less contact area between the droplet and the surface than in the trench model. Therefore, higher contact angles are easily obtained for larger pitch distances.

Figure 10: Average steady state APCA measured as function of the pitch distance of the fabricated structures. Results for the trench and matrix models, with and without the LIPSS nanopattern performed covering the surface.

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4. Conclusions

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Hierarchical structures were fabricated by a single one-step femtosecond laser fabrication process for different geometries in a highly controllable way. Adjusting the pitch distance value, highly hydrophobic structures can be obtained from an initially hydrophilic surface without any additional surface treatment. For pitch distances higher than 50 µm the measured apparent contact angles are significantly lower, showing that there is a limit in the pitch distance value in order to obtain highly hydrophobic behavior with the structures that have been fabricated. It has been also demonstrated that only when the LIPSS nanopattern is performed covering the micropatterned surface, the measured apparent contact angles values could be higher than 150º. These results prove that the LIPSS nanopattern helps to reach the Cassie-Baxter state and that dual scale structures are the best option in order to reach the highest possible contact angles.

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Highlights Femtosecond laser treatment to achieve highly hydrophobic behavior on stainless steel Combination of micro-machined patterns with LIPSS into hierarchical structures

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Contact angles as high as 156º with only the femtosecond laser irradiation

Table 1: Accumulated fluence thresholds for the different observed structures Acc. Fluence (J/cm2)

Stucture type

Nanoparticles

LSFL

Lower threshold

2.23

10.32

Upper threshold

4.46

265.26

Acc. Fluence (J/cm2)

a

Acc. Fluence (J/cm2)

HSFL

Trench

287.51

396.12

420.41

1188.35

a

M

(b) Acc. Fluence = Fluence x Number of Pulses

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Acc. Fluence (J/cm2)

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Femtosecond laser fabrication of highly hydrophobic stainless steel surface with hierarchical structures fabricated by combining ordered microstructures and LIPSS

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M. Martínez-Calderona,b, A. Rodrígueza,b, A. Diasa,b, M.C. Morant-Miñanaa,b, M. Gómez-Aranzadia,b, S.M. Olaizolaa,b

a

CEIT-IK4 & Tecnun (University of Navarra), Paseo Manuel Lardizábal 15, 20018 San Sebastián, Spain b

CIC microGUNE, Goiru Kalea 9 Polo Innovación Garaia, 20500 Arrasate-Mondragón, Spain

Supporting information

Figure 1: Proposed geometrical models of the micro-machined surface called trench (left) and matrix (right).

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Table 1: Wenzel and Cassie-Baxter equations applied to the proposed geometrical models showed in the Figure 1.

Wenzel

Cassie Baxter

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Trench Model

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Matrix Model

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For the Wenzel model it is clear that only if the material is inherently hydrophobic the surface could become more hydrophobic by modifying the roughness. Considering the contact angle of the non-treated surface and introducing different values of the geometrical parameters in the two proposed geometrical models (trench and matrix), the following graphs have been obtained for the Cassie-Baxter state (Figure 2a and 2b):

Figure 2: Theoretical approximation of the static contact angle using the Cassie-Baxter equations applied to: (a) Trench model and (b) Matrix model. As it is appreciated in the graphs, theoretically highly hydrophobic behaviour could be presented with 20 um line width starting from an initially hydrophilic surface (θ0 75 ºC).

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