Super liquid-repellent surfaces –
Interactions and gas capillaries
Mimmi Eriksson
Academic Dissertation which, with due permission of the KTH Royal Institute of Technology, is submitted for public defense for the Degree of Doctor of Philosophy on Friday 9 October 2020, at 10:00 a.m. in Kollegiesalen, Brinellvägen 8, Stockholm.
Doctoral Thesis in Chemistry KTH Royal Institute of Technology Stockholm, Sweden 2020
Abstract
Super liquid-repellent surfaces have attracted a lot of interest in recent years. In addition to the large scientific interest there are many potential technological applications ranging from self-cleaning materials to microfluidic devices. In this thesis, interactions between liquid-repellent surfaces in liquids were studied, with the aim to investigate the detailed mechanisms of super liquid-repellence, such as superhydrophobicity and superamphiphobicity. An atomic force microscope (AFM) was used to measure the interaction forces between super liquid-repellent surfaces and a microsphere in different liquids. Additionally, a setup combining AFM with laser scanning confocal microscopy (LSCM) was used, which enabled simultaneous imaging in order to capture the microscopic events between the sphere and the surface during a force measurement. The confocal images successfully visualized how the strongly attractive forces measured between liquid-repellent surfaces are due to the formation of a gaseous capillary bridge between the two surfaces. Similar long-ranged forces with capillary formation and growth were observed both in water and in lower surface tension liquids. Additionally, the confocal images enabled determination of the capillary shape and volume, and the data showed an increase of the capillary volume during the major part of the process of separating the surfaces. A gaseous layer underneath the liquid at super liquid-repellent surfaces was also visualized with LSCM, and it was concluded that this gaseous layer is responsible for the formation and growth of large gas capillaries. It was found that an increased amount of available gas in the gaseous layer influenced the interactions and allowed the capillary to grow larger during separation. Further, theoretical calculations based on the size and shape of the capillary suggested that a small under pressure in the capillary drives the gas to flow from the gaseous surface layer into the capillary, facilitating growth during separation.
Keywords: superhydrophobicity, superamphiphobicity, wetting, capillary forces, AFM, LSCM.
Sammanfattning
Extremt vätskeavvisande ytor har väckt stort intresse de senaste åren.
Förutom det stora vetenskapliga intresset finns det många potentiella tekniska tillämpningar, allt från självrengörande material till mikrofluidala system. I denna avhandling studerades hur vätskeavvisande ytor interagerar i vätskor, detta i syfte att undersöka de detaljerade mekanismerna bakom extrem vätskeavvisning. Ett atomkraftmikroskop (AFM) användes för att mäta interaktionskrafterna mellan vätskeavvisande ytor och en mikrosfär i olika vätskor. En uppställning som kombinerade AFM med laserkonfokalmikroskopi (LSCM) möjliggjorde samtidig avbildning för att fånga de mikroskopiska händelserna mellan partikeln och ytan under en kraftmätning. Konfokalbilderna visualiserade framgångsrikt hur de starkt attraktiva krafterna mellan vätskeavvisande ytor orsakas av bildandet av en gasformig kapillär mellan de två ytorna.
Liknande långväga krafter med kapillärbildning observerades både i vatten och i vätskor med lägre ytspänning. Dessutom möjliggjorde konfokalbilderna beräkning av kapillärens form och volym och detta visade en ökning av kapillärvolymen under huvuddelen av separationsprocessen. En gasformig film under vätskan vid extremt vätskeavvisande ytor visualiserades med LSCM och slutsatsen drogs att denna gasfilm är ansvarig för bildandet och tillväxten av stora gaskapillärer. Det visade sig att en ökad mängd gas i denna gasfilm påverkade interaktionerna och tillät kapillären att växa sig större under separationen. Vidare visade teoretiska beräkningar utifrån kapillärens storlek och form att ett litet undertryck i kapillären driver gasen att strömma från den gasformiga ytfilmen in i kapillären och detta bidrar till tillväxten under separationen.
Nyckelord: superhydrofobicitet, superamfifobicitet, vätning, kapillär- krafter, AFM, LSCM.
List of publications
This thesis is based on the following papers:
I Mimmi Eriksson, Mikko Tuominen, Mikael Järn, Per M. Claesson, Viveca Wallqvist, Hans-Jürgen Butt, Doris Vollmer, Michael Kappl, Patrick A.C. Gane, Joachim Schoelkopf, Hannu Teisala and Agne Swerin. Direct Observation of Gas Meniscus Formation on a Superhydrophobic Surface. ACS Nano, 2019, 13, 2246-2252.
II Mimmi Eriksson, Per M. Claesson, Mikael Järn, Mikko Tuominen, Viveca Wallqvist, Joachim Schoelkopf, Patrick A.C. Gane and Agne Swerin. Wetting Transition on Liquid-Repellent Surfaces Probed by Surface Force Measurements and Confocal Imaging. Langmuir, 2019, 35, 13275-13285.
III Mimmi Eriksson, Per M. Claesson, Mikael Järn, Viveca Wallqvist, Mikko Tuominen, Michael Kappl, Hannu Teisala, Doris Vollmer, Joachim Schoelkopf, Patrick A.C. Gane, Jyrki M. Mäkelä and Agne Swerin. Gas capillaries and capillary forces at superamphiphobic surfaces: Effects of liquid surface tension. Submitted, 2020.
IV Mimmi Eriksson, Per M. Claesson, Mikael Järn, Viveca Wallqvist, Mikko Tuominen, Michael Kappl, Hannu Teisala, Doris Vollmer, Joachim Schoelkopf, Patrick A.C. Gane, Jyrki M. Mäkelä and Agne Swerin. Superhydrophobic surfaces: Effects of gas layer thickness on capillary interactions. Manuscript.
The papers are referred to in the text by their Roman numerals and the full versions are appended at the end of the thesis.
Contributions to the included publications
Paper I All experimental work and data analysis. Major part of manuscript preparation.
Paper II All experimental work and data analysis. Major part of manuscript preparation.
Paper III Major part of experimental work (except LFS-coating, cross- sectional SEM and XPS) and data analysis. Major part of manuscript preparation.
Paper IV Major part of experimental work (except LFS-coating and cross-sectional SEM) and data analysis. Major part of manuscript preparation.
Related work not included in this thesis
V Mimmi Eriksson and Agne Swerin. Forces at Superhydrophobic and Superamphiphobic Surfaces. Current Opinion in Colloid &
Interface Science, 2020, 47, 46-57.
VI Haiyan Yin, Maziar Sedighi Moghaddam, Mikko Tuominen, Mimmi Eriksson, Mikael Järn, Andra Dédinaité, Magnus Wålinder and Agne Swerin. Superamphiphobic Plastrons on Wood and their Effects on Liquid Repellence. Materials & Design, 2020, 195, 108974.
Summary of included publications
Paper I
Laser scanning confocal microscopy was combined with colloidal probe atomic force microscopy to obtain microscopic images of gas capillaries during force measurements between a superhydrophobic surface and a hydrophobic microsphere in water. The confocal images provided visual proof that the long-range attractive interactions acting on separation are due to capillary formation and volume growth. The capillary shape and size were extracted from confocal images allowing direct calculations of the Young-Laplace capillary pressure. It was concluded that the pre-existing gaseous layer at the superhydrophobic surface facilitates the formation and growth of the capillary, and that an under pressure in the capillary drives the gas flow from this gaseous layer into the capillary allowing the volume to increase during separation.
Paper II
The relation between wettability and interaction forces of a nanostructured superhydrophobic and a smooth hydrophobic surface was studied by adding ethanol to water at different concentrations. Colloidal probe atomic force microscopy measurements between a hydrophobic microsphere and the superhydrophobic surface showed attractive interactions consistent with the formation of a large and growing gas capillary in water and when ethanol was introduced at 20 vol%. Laser scanning confocal microscopy confirmed the presence of a gaseous layer at the superhydrophobic surface consistent with a Cassie-Baxter type wetting state for both water and 20 vol% ethanol. For the ethanol concentration 40 vol% where no force curves related to a growing capillary were observed, confocal images indicated that the surface structure was wetted by the liquid with no or small amounts
of trapped gas. This indicates that a gaseous layer at the surface is needed for large gas capillaries to form and grow. Additionally, no force curves with attractions in the micrometer range were observed between the hydrophobic microsphere and a smooth hydrophobic surface. However, in this case, interactions consistent with the formation of a small gas capillary with constant volume during separation were observed in water and 20 vol% ethanol, where the macroscopic contact angles were larger than 90°.
Paper III
The setup combining colloidal probe atomic force microscopy and laser scanning confocal microscopy utilized in Paper I, was used to study interactions involving a superamphiphobic surface and to investigate whether and how surface interactions and gas capillary formation were affected by the surface tension of the liquid. Force measurements between a hydrophobic microsphere and a superamphiphobic were performed in three liquids with different surface tensions: water (73 mN m-1), ethylene glycol (48 mN m-1) and hexadecane (27 mN m-1). Attractive interactions due to bridging gas capillaries were observed in all three liquids, and the range and magnitude of the forces as well as the capillary size decreased with decreasing liquid surface tension. While the wetting properties were similar on the superamphiphobic surface for all three liquids, it was found that the wettability of the probe particle highly influenced the interactions.
When this contact angle was below 90°, a repulsion due to deformation of the liquid-gas interface at the superamphiphobic surface was observed prior to capillary formation. Calculations of the free energy due to capillary formation from the shape of the capillary meniscus and comparing with force measurements, suggested a small under pressure in the capillary during the dynamic measurements.
Paper IV
In this paper, it was investigated how the coating thickness and the thickness of the gaseous layer on superhydrophobic coatings influence the interactions and gas capillary size and shape. Superhydrophobic samples with different coating thicknesses were prepared by applying an increased number of liquid flame spray coating cycles. With laser scanning confocal microscopy, it was confirmed that the thickness of the gaseous layer increased with increasing coating thickness. During colloidal probe atomic force microscopy measurements between the superhydrophobic samples and a hydrophobic microsphere, attractive capillary forces with the formation of bridging gas capillaries were observed for all five coatings. It was found that the range of the attractive force and the capillary size increased with increasing coating thickness. The results indicated that the amount of available gas in the gaseous layer is influencing the capillary formation and growth.
Acknowledgements
I want to express my sincere gratitude to all people who in any way have helped and supported me during this thesis work.
First, I would like to thank my supervisors, Agne Swerin and Per Claesson, for giving me the opportunity to join this project and for your valuable support, engagement and scientific guidance. To my co-supervising-team, Mikael Järn, Mikko Tuominen and Viveca Wallqvist, thank you all for your encouragement and support as well as contributions to interesting discussions during our project meetings.
To all my co-authors on the papers, without you this thesis would be a completely different story. Thank you all for great collaborations.
Joachim Schoelkopf and Patrick Gane, thank you for always showing such great engagement and enthusiasm in the project. Hans-Jürgen Butt, Doris Vollmer, Michael Kappl and Hannu Teisala, thank you for inviting me to Mainz and for sharing your knowledge. Thanks to Jyrki Mäkelä for inviting us to Tampere and to Janne Haapanen and Paxton Juuti for preparing excellent coatings.
I would also like to thank everyone at the Max Planck Institute for Polymer Research for making me feel welcomed and for all help and technical support during my stays.
To all colleagues (past and present) at RISE, thanks for all help, support and stimulating discussions (both scientific and non-research-related) as well as contributing to a nice working atmosphere. Thanks to everyone at the Division of Surface and Corrosion Science at KTH for help, nice discussions and a friendly environment.
Thanks to all my friends and family for your love and support, and Lisa, thank you for being my greatest support during this work and in life.
Finally, I would like to acknowledge the Swedish Foundation for Strategic Research and Omya International AG for funding this project, as well as Knut and Alice Wallenbergs stiftelse for travel grants supporting my attendance at an international conference.
Abbreviations
2D Two dimensional
3D Three dimensional
ACA Advancing contact angle
AFM Atomic force microscopy
CA Contact angle
CAH Contact angle hysteresis
CB Cassie-Baxter
CVD Chemical vapor deposition
LFS Liquid flame spray
LSCM Laser scanning confocal microscopy LV-SEM Low vacuum scanning electron microscopy FOTES 1H,1H,2H,2H-perfluorooctyl-trietoxysilane FOTCS 1H,1H,2H,2H-perfluorooctyl-trichlorosilane
PMI N-(2,6-diisopropylphenyl)-3,4-perylene dicarboxylic acid mono imide
RA Roll-off angle
RCA Receding contact angle
SEM Scanning electron microscopy TEOS Tetraethyl orthosilicate TPCL Three-phase contact line TTIP Titanium tetraisopropoxide XPS X-ray photoelectron spectroscopy
Contents
Introduction 1
Theoretical background 3
Wetting ... 3 Surface forces ... 12
Experimental methods 23
Super liquid-repellent coatings ... 23 Force measurements ... 31 Imaging ... 37
Results and discussion 43
Superhydrophobic and superamphiphobic surfaces ... 43 Interactions involving superhydrophobic surfaces and observations of gas capillaries ... 48 Interactions involving superamphiphobic surfaces and the effect of liquid surface tension ... 57 Capillary growth and the effect of the amount of available gas ... 65 Calculations of capillary forces and comparison to measurements .... 69 Concluding remarks and future perspectives 79
References 83
Chapter 1 Introduction
Extremely non-wetting or liquid-repellent surfaces have been a known phenomenon for centuries [1, 2]. Although water-repellence has been a well-known property in nature [3, 4], the interest in liquid-repellent surfaces was rather limited before 1997 when the origin of the water- repellent and self-cleaning properties of the lotus (Nelumbo nucifera) leaf was explained [5]. Researchers and scientists have always found inspiration from nature, which through billions of years of evolution has found its way of developing smart and creative solutions. Just like many other technological advances have been developed by mimicking the brilliant solutions already found in nature, the design of artificial water- repellent surfaces was originally inspired by the many natural surfaces with special wettability [6]. In recent years, scientists have also succeeded to produce surfaces which can repel other liquids such as oils [7, 8]. To create super liquid-repellent surfaces, the detailed surface topography and chemistry are important. So far, the successful approach has been to combine a specific microstructure with a low surface energy material [9].
Since the late 1990s, the research interest in liquid-repellent surfaces has increased rapidly. In addition to a large scientific interest in extreme liquid- repellence there are many potential technological applications such as self- cleaning materials, corrosion protection and prevention of ice-formation or bacterial growth [10, 11]. However, there are still challenges that need to
be addressed in order to bring super liquid-repellent surfaces into real- world applications. First, the complex surface structures are highly susceptible to mechanical wear, and abrasion can lead to loss of the liquid- repellent properties [12]. A good mechanical durability is therefor of prime importance for any practical applications [13]. Second, fluorinated chemicals are commonly used to achieve the low surface energy [14], and many of these substances have been shown to have majors concerns for both the environment and human health [15]. To solve these challenges, there is a need for more research in the area of liquid-repellence in order to understand the underlying mechanisms. In particular, an extended fundamental understanding of the interplay between microscopic and macroscopic wetting properties and the interactions between surfaces and liquids is needed. With a complete fundamental understanding, the appropriate surface structure and chemistry can be combined in the optimization of future super liquid-repellent surfaces. Most importantly, with these insights, unwanted chemicals (such as perfluorinated compounds) can be avoided, and mechanical durable materials and coatings can be developed by safe and environmentally friendly processes.
Thus, the work in this thesis may contribute to the UN sustainable development goals and in particular to goal number 6, clean water and sanitation and goal number 12, responsible consumption and production.
This thesis work elucidated the detailed mechanisms of super liquid- repellence with the focus on how such surfaces interact in liquids. The outline of the thesis is structured as follows: The following chapter, Chapter 2, provides the reader with a theoretical background of the wettability of super liquid-repellent surfaces and the relevant surface forces needed to understand interactions between such surfaces. The most important instrumental techniques and procedures that were employed during the work are described in Chapter 3. In Chapter 4, the key results and findings are summarized and discussed. Finally, Chapter 5 presents the main conclusions and implications of the presented work together with suggestions for further studies.
Chapter 2
Theoretical background
Wetting
Wetting on smooth and rough surfaces
Wetting of ideal surfaces – the Young equation
The wettability of a solid surface is defined by the shape of a liquid droplet resting on the surface. The contact angle (CA) θ, where the liquid, solid and vapor meets in the three-phase contact line (TPCL), is most often used for characterization of wettability. On an ideal (perfectly smooth, inert and chemically heterogeneous) surface the thermodynamic equilibrium contact angle can be described by Young’s equation [16]:
𝛾LVcos 𝜃Y= 𝛾SV− 𝛾SL (1)
Here, θY is the Young contact angle and SV, SL and LV are the interfacial tensions of the solid-vapor, solid-liquid and liquid-vapor interfaces, respectively (illustrated in Figure 1). The maximum contact angle of a liquid drop on a smooth surface is obtained if the surface free energy of the liquid (LV) is as high as possible and the surface free energy of the solid (SV) is as low as possible. This can be achieved for a droplet of water (LV = 72 mN
m-1) on a surface of hexagonally packed -CF3 groups (SV = 6.7 mN m-1), resulting in a contact angle in the order of 120° [17]. This value can be seen as the chemical upper limit of contact angles for a liquid drop on a smooth surface.
Figure 1. A liquid droplet on an ideal surface.
Real surfaces are not ideal
It is important to know that Young’s equation (Eq. 1) is generally not applicable for real surfaces. First, the condition of thermodynamic equilibrium is generally not fulfilled in practice. For instance, evaporation of the droplet can take place even if the atmosphere is saturated [18].
Second, most real surfaces are not ideal and generally display both chemical heterogeneity and surface roughness. Even if a surface may appear macroscopically smooth, it typically exhibits micro-, nano- or even molecular scale roughness. It is well-known that surface roughness may enhance (or reduce) wettability, and contact angles on real surfaces can exceed the upper limit (120°) predicted by Young’s equation [19, 20]. When considering real surfaces, it is also important to distinguish between the macroscopic apparent contact angle and the microscopic contact angle. The apparent contact angle θapp, is obtained from the macroscopic shape of the drop and is typically the angle measured experimentally by goniometry and the sessile drop method. The measured angle typically describes an average of the contact angles along the three-phase contact line. On the microscale, the contact angle may deviate from the apparent contact angle, e.g. due to surface roughness or chemical heterogeneity. The microscopic contact angle is equal to the contact angle measured on a smooth and homogeneous flat surface of the same material. The microscopic contact angle can vary along
the contact line and cannot be easily measured. On an ideal surface the microscopic contact angle equals the Young contact angle.
Wetting of rough surfaces – the Wenzel and Cassie-Baxter models Wetting of rough surfaces is often described by the two opposing wetting models by Wenzel [19] and Cassie and Baxter [20]. When a liquid is described to be in the Wenzel wetting state, the liquid penetrates the surface depressions and fully wets the structure (Figure 2).
Figure 2. Liquid droplets in the Wenzel and Cassie-Baxter states.
The Wenzel equation relates the apparent contact angle of a droplet in the Wenzel state (𝜃appW ) to the Young contact angle:
cos 𝜃appW = 𝑟 cos 𝜃Y (2)
The roughness factor r is defined as the ratio between the real surface area and the projected surface area of a flat surface. According to the Wenzel equation, surface roughness will enhance the hydrophilicity or hydrophobicity. A hydrophilic material (θY < 90°) will be even more wetted when surface roughness is increased. Similarly, for a hydrophobic material (θY > 90°) the apparent contact angle will increase with increasing roughness.
In opposite to the Wenzel state, a liquid droplet can be suspended on top of the surface features with pockets of air (or vapor) trapped underneath
(Figure 2). A liquid taking this configuration is described to be in the Cassie- Baxter (CB) wetting state. In the CB state, the droplet rests on a composite interface (in this case consisting of patches of air and solid) and the apparent contact angle (𝜃appCB) relates to the Young contact angle according to the CB equation [20]:
cos 𝜃appCB = 𝑓scos 𝜃Y+ 𝑓s− 1 (3)
Here, fs is the liquid-solid area fraction, i.e. the ratio between the area where the liquid is in contact with the solid and the projected composite area. In contrast to the Wenzel equation, the CB equation predicts that high apparent contact angles (θapp >> 90°) can be achieved not only if θY > 90° but also if θY < 90°, provided that the liquid-solid area fraction is small enough.
Validity of the Wenzel and Cassie-Baxter equations
The Wenzel and CB equations (Eqs. 2 and 3) are often used in the literature to determine the present wetting state of textured surfaces, and good agreement between experimentally measured contact angles and theoretically calculated values using the Wenzel or CB equations are often reported. However, the validity of the equations is debated and it has been especially emphasized whether the apparent contact angle can actually be predicted by interactions within the contact area beneath the droplet or at the three-phase contact line [21]. The validity of the Wenzel and CB equations was early questioned [22-24] and later experiments designed to test the validity have disproved them [25, 26]. A debate on the topic was started after Gao and McCarthy published their paper with the provocative title
“How Wenzel and Cassie were wrong” in 2007, where they stated that contact angles is only determined by interactions at the TPCL and that the interfacial area within the contact perimeter is irrelevant [26]. In an extensive review by Erbil, both views of the TPCL and interfacial contact area were presented [21]. Several important points from published papers supporting the two sides were summarized, and it was concluded that most data found in the literature are inconsistent with the Wenzel and CB theories.
However, while the use of the Wenzel and CB equations is questioned and in general should be avoided, the Wenzel and CB wetting states (Figure 2) are well established concepts and can still be valid as visual descriptions of wetting states on textured surfaces.
Contact angle hysteresis
From the models described above it appears as wettability of a liquid on a solid surface can be described by one (equilibrium) contact angle.
Experimentally, this sole value of the contact angle is often referred to as the “static” or “equilibrium” contact angle of a drop “as placed”. In reality, however, the situation is more complicated and there is rarely a single
“static” contact angle. In fact, when a liquid droplet is placed on a solid surface the contact angle can take any value between an upper and a lower limit, depending on how the droplet was placed on the surface. The minimum value is given by the receding contact angle (RCA) θrec, measured when the liquid front is receding over the solid surface. Similarly, the maximum value is determined by the advancing contact angle (ACA) θadv
as measured when the liquid advances over the surface. The advancing contact angle is larger than the receding one, and the difference between ACA and RCA is called the contact angle hysteresis (CAH). Contact angle hysteresis arises from chemical and/or topographical heterogeneities in the surface and on an ideal surface the CAH is zero. The contact angle hysteresis may be a rough measure on the drop adhesion to the surface, as a larger CAH suggests that the drop adheres stronger to the surface.
Figure 3. Measuring advancing and receding contact angles.
The advancing and receding contact angles (and thus also the contact angle hysteresis) may be measured by either increasing (liquid advancing) and decreasing (liquid receding) the volume of a sessile drop or by tilting the surface so that the drop starts moving downhill (Figure 3). By tilting the surface, the roll-off (or sliding) angle (RA), that is the tilt angle at which the drop starts moving, can also be measured. The lower roll-off angle the lower liquid adhesion to the surface.
Super liquid-repellent surfaces
Definitions and terminology
Super liquid-repellence is still a relatively new research field and the terminology is not very well-defined. In the vast and increasing number of publications on super liquid-repellence over the last decades, many terms have been created and used to describe different surfaces of special wettability. Although there have been attempts to create a common and accurate terminology [27], the use of different definitions and terms are still found. A surface which exhibit extreme water-repellence is commonly called superhydrophobic. A water droplet on a superhydrophobic surface will take an almost spherical shape. In addition, the droplet will not adhere to the surface and easily rolls off, leaving a completely dry surface behind.
The commonly used definition of a superhydrophobic surface is a high apparent water contact angle of ≥ 150° with a low contact angle hysteresis and roll-off angle of ≤ 5-10° [13, 28-31]. This definition is, however, not entirely unambiguous. As mentioned, “static” contact angles depend on how the droplet is placed on the surface and can in principle take any value between the receding and advancing contact angles. The roll-off angle on the other hand depends on the droplet volume. Therefore, other definitions have been proposed and one suggestion is to use a single criteria of a high apparent receding contact angle (≥150°) [32]. The advantage with this definition is that the receding contact angle determines the roll-off angle and it does not, when accurately measured, depend on droplet size [33].
Superamphiphobic is commonly used to describe a surface which is super repellent to both water and oily liquids (or other polar or nonpolar lower surface tension liquids) [34, 35]. The commonly used definition for superamphiphobicity is generally the same as for superhydrophobicity, i.e.
a high apparent contact angle and a low roll-off angle, with the extension to include also liquids with lower surface tension in addition to water. Another frequently used term to describe such surfaces exhibiting both water- and oil-repellence is superomniphobic [9, 36] and other less frequently used terms includes superhygrophobic [37, 38] and superlyophobic [39, 40].
Surface design
When designing super liquid-repellent surfaces there are two key aspects to take into consideration: surface chemistry and surface structure. From the point of surface chemistry, the strategy has been to achieve a surface energy as low as possible in order to maximize the non-wettability. As mentioned, the lowest known surface energy is achieved by using fluorine chemistry and perfluorinated compounds are still typically used in the literature [14, 41, 42]. However, there have been recent attempts towards fabricating fluorine-free super liquid-repellent surfaces [43, 44]. For instance, Liu and Kim reported that using a specific surface morphology, any material can be made super-repellent even to the lowest known surface tension liquids (fluorinated alkanes) regardless of the surface chemistry [44]. For future sustainable and fluorine-free super liquid-repellence it is highly interesting to find surfaces of special wettability in nature, as nature cannot synthesize perfluorinated chains. Examples like the springtail (Collembola) skin [45]
proves that it is possible to obtain surfaces with oleophobic properties without using fluorinated materials. Another interesting observation from nature, indicating that the surface chemistry might not be the decisive parameter, is a study suggesting that the wax on the lotus leaf is actually moderately hydrophilic [46]. The water contact angle on a smooth carnauba wax (assumed to be similar to the wax on the lotus leaf) surface was found to be 74°.
As for surface structure, the goal is to minimize the contact between the liquid droplet and the solid substrate and to maintain a CB wetting state.
Once the liquid penetrates the surface depressions and a transition to the fully wetted Wenzel state occurs, the droplet is pinned, and the super liquid- repellent property is lost. This wetting transition is typically a reversible process [47]; thus, it is critical that the surface design can maintain a stable CB wetting state. For water it is considerably easier to design a structure which can maintain the CB state than for low surface tension liquids. For instance, a simple microstructure of cylindrical pillars can be sufficient for water. A liquid drop is placed on the structured surface, resting on top of the pillars with air trapped underneath, i.e. CB state (cross-section in Figure 4).
Figure 4. Wetting on model structures.
The liquid-air interface between the pillars will be curved and the curvature depends on the pressure difference across the interface, P. If the microscopic contact angle between the liquid and the pillar θm (Figure 4), is smaller than the advancing contact angle of the material θadv the TPCL is pinned and the CB state is maintained; this, of course, provided the pillars being high enough so that the curved interface does not touch the surface between the pillars. In this case the fully wetted Wenzel state will occur even if θm < θadv. In contrast, if θm > θadv, the TPCL will slide down the pillar walls as the liquid wets the material until the structure is fully wetted. Following the argument above, we see that for simple pillar structures the liquid can be maintained in the CB state if θadv > 90°. In the case where the liquid is water, this simple structure is sufficient if using a hydrophobic material. However, for oils this is not sufficient due to the fact that θadv < 90° for oils on all known materials. To repel liquids when θadv < 90° it is necessary to design the surface structure with a re-entrant or overhang morphology (Figure 4).
With this type of structure, it is possible to maintain the CB state for liquids with θadv ≈ 30° [44]. For a liquid which will completely wet the material (θadv
≈ 0°), a doubly re-entrant structure is needed in order to maintain the CB state (Figure 4). This type of microstructure has been shown to repel all liquids (even liquids with very low surface tension < 20 mN m-1) regardless of the surface energy of the material [44]. Again, we note that with the right surface design, the surface chemistry is not decisive for achieving super liquid-repellent properties. The model structures shown in Figure 4, have been proven to show super liquid-repellence both experimentally (e.g. [8, 44]) and using computer simulations (e.g. [48, 49]). These ordered and well- defined structures can be fabricated by using e.g. photolithographic techniques [8, 44, 50] or 3D printing technology [51-53].
In addition to using well-defined model structures, re-entrant morphology can also be realized by randomly ordered structures. One drawback of using random structures is that it is more challenging to achieve a surface design with doubly re-entrant structures. Hence, surface chemistry is important for achieving superamphiphobicity for random structures and fluorine chemistry is still most often used. A major advantage, on the other hand, is that random structures often form a hierarchical structure which is advantageous for designing robust superamphiphobic surfaces [54]. A hierarchical structure exhibits topography variation in two (or more) length scales. For hierarchical superamphiphobic surfaces, typically one is in the micrometer scale and one in sub-micrometer scale. Hierarchical structures are commonly found in nature to achieve robust and mechanical durable water-repellence. One example of a natural hierarchical structure is the well- known lotus leaf [5]. Its surface is covered by micron-sized protrusions of epidermal cells which are further covered by epicuticular wax tubules of 200 nm in diameters. Hierarchical surface designs can also enhance the mechanical robustness. Low mechanical robustness is still the main issue for liquid-repellent surfaces to be used in real applications [12, 13].
Microscale (and macroscale) structures are more mechanical robust and can protect the weaker submicron structures in between, with retained antiwetting properties [55-57].
Random structures are typically fabricated by bottom-up processes e.g.
deposition of nanoparticles [58-61] or nanofilaments [62, 63]. This is typically advantageous as these processes can be applied on a variety of substrates and materials and can be easy up scalable. It is also possible to utilize the underlying microstructure of the substrate in order to create overhanging re-entrant morphologies on e.g. wood [64], textile [65, 66] or paper [67, 68]. Another approach is to combine top-down fabricated microstructures with bottom-up randomly deposited nanostructures [69, 70].
Randomly ordered structures can also be realized using top-down processes such as laser texturing [71, 72] or different etching techniques [73-76].
Surface forces
In this section, the most relevant surface forces for this work will be presented: van der Waals interactions, interactions between hydrophobic surfaces and capillary forces.
van der Waals interactions
The van der Waals force is a result of interactions of electromagnetic nature between molecules and typically includes contributions from dipole-dipole (Keesom orientation interactions), dipole-induced dipole (Debye inductive interactions) and instantaneous dipoles due to fluctuations in the distribution of electronic charge (London dispersive interactions). The van der Waals force is always attractive between identical materials but can in some cases be repulsive for dissimilar materials. A simple expression for the van der Waals force (FvdW) between macroscopic bodies can be obtained by a pair- wise summation of the interactions between the molecules in the two bodies via integration. For interactions between a sphere (radius R) and a flat surface at a distance D the expression is given by [77]:
𝐹vdW= − 𝐴𝑅
6𝐷2 (4)
Here, A is called the Hamaker constant and depends on the materials and interacting media involved. The Hamaker constant can be calculated from the dielectric properties of the two surfaces and the intervening medium using the Lifshitz theory. An interesting feature of the Lifshitz theory is that it, unlike the earlier Hamaker approach, ignores the atomistic nature of the interacting bodies and the separating medium. Instead it just considers the fluctuating electromagnetic fields that extend from every surface and can be related to their frequency-dependent dielectric properties. For two identical materials “1” interacting across a medium “3”, the equation is given as [77]:
𝐴 = 3
4𝑘𝑇 (𝜀1−𝜀3
𝜀1+𝜀3)2+3ℎe
16√2
(𝑛12−𝑛32)2
(𝑛12+𝑛32)3 2⁄ (5)
where i is the dielectric constant, ni the refractive index for medium i, e
the electronic absorption frequency in the UV region (typically assumed to be the same in all media, 3 1015 s-1), T the absolute temperature, k the Boltzmann’s constant and h the Planck’s constant. In Eqs. 4 and 5 retardation effects due to the finite speed of light have been ignored, which does not introduce any significant error at small separations (below a few tens of nanometers).
Interactions between hydrophobic surfaces
Smooth hydrophobic surfaces
The first measurements of interactions between hydrophobic surfaces in aqueous solution was reported almost 40 years ago by Israelachvili and Pashley [78]. The measured interactions showed a long-range attractive force, much stronger than the expected van der Waals force and it decayed exponentially with separation distance. This first report was soon followed by many others observing similar long-range (in the tens to hundreds of nanometers range) interactions [79-89]. The mechanisms of this long-range
“hydrophobic force” puzzled scientists for many years and the suggestions explaining the origin of the attraction were several. Some suggested
explanations include water structural effects [79, 90, 91], hydrodynamic forces [92, 93] or contamination from hydrophobic species [94, 95].
However, the formation of bridging air or vapor capillaries has become the most widely accepted explanation [80, 96-100]. The theory of a bridging gas capillary (also called cavity, bridge, bubble or meniscus) is supported by e.g.
direct visual observations [80, 101], effects of de-gassing the water [102- 105] and by the similarity to liquid capillary bridges between hydrophilic surfaces in humid atmosphere [100]. The theory of capillary forces will be further explained in the following section.
Figure 5. Schematic of the typical shape of a force-distance curve measured between smooth hydrophobic surfaces and illustrations of the corresponding capillary formation and break-up.
Figure 5 shows a schematic of the typical shape of a force-distance curve measured between two smooth hydrophobic surfaces. The force-distance curve is obtained by measuring the interaction forces when two surfaces are brought together (approach, black line) and separated (retraction, red line).
On approach, the force is zero at large separation distances with no interaction between the surfaces. When the separation becomes sufficiently small, a sudden attraction (defined as a negative force) starts to appear (A).
This attraction is assigned to the formation of a bridging air/vapor capillary between the two surfaces (B). After the surfaces make contact at zero distance, the separation is again increased upon retraction and the attractive force is decreasing due to elongation of the capillary while keeping a (close to) constant capillary volume (C-D). At a certain separation, the capillary ruptures and the force returns to zero (E).
Rough hydrophobic and superhydrophobic surfaces
While interactions between smooth hydrophobic surfaces have been widely studied over the last decades, studies on interactions between superhydrophobic or topographically structured hydrophobic surfaces are few. Singh et al. reported the first measurements on interactions between superhydrophobic surfaces in 2006 [106]. They observed interactions extending into the micrometer range, i.e. much longer in range than previously observed on smooth surfaces. Optical imaging revealed a bridging capillary between the two surfaces giving rise to the strong attraction, and the authors argued the capillary formation being caused by capillary evaporation of confined water. Furthermore, the shape of the force curve was distinctly different from what was previously seen on smooth hydrophobic surfaces. The same kind of shape, which clearly did not follow the assumption of a constant capillary volume, was later observed on topographically structured hydrophobic surfaces [107]. It was suggested that the capillary would grow due to an inflow of air from the reservoir trapped in the rough surface during separation. The theory was supported by more detailed studies on superhydrophobic surfaces, which also showed that capillary growth type of force curve increased in frequency going from interactions between hydrophobic-hydrophobic to superhydrophobic- hydrophobic to superhydrophobic-superhydrophobic surfaces [108, 109].
Figure 6 shows a schematic of force-distance curves measured between two topographically structured (super)hydrophobic surfaces. As in the case for smooth hydrophobic surfaces, a sudden attraction is observed at a certain separation distance on approach (A) and assigned to the formation of a
bridging gas capillary (B). However, the striking difference in the shape as compared to the case of smooth hydrophobic surfaces is seen on retraction.
Rather than decreasing right after contact (C), the attractive force is increasing due to a growing capillary caused by an inflow of gas from the reservoir of trapped gas in the structures of the superhydrophobic surfaces (D). After the attraction reaches a maximum value the force starts to decrease before the capillary finally ruptures whereby the attraction disappears (E).
Figure 6. Schematic of the typical shape of a force-distance curve measured between two topographically structured (super)hydrophobic surfaces and illustrations of the corresponding capillary formation, growth and break-up.
Capillary forces
It is well-known that hydrophilic particles can adhere to each other due to an attractive force caused by a liquid capillary bridge. The capillary can form by capillary condensation or by accumulation of adsorbed liquid. However, a capillary bridge can also form as a liquid bridge in another immiscible liquid or, as mentioned in the previous section, as a gas/vapor bridge in a
non-wetting liquid. Most literature on capillary forces is focused on liquid capillary bridges [110-116], however the theory describes the shape of the capillary and is analog with the case of a gas capillary [117, 118]. In this thesis, if nothing else is specifically stated, the capillary is assumed to be a gas bridge surrounded by liquid.
Figure 7 shows the schematic of an axisymmetric capillary bridge between a sphere (radius R) and a plane separated by a distance D. The capillary position is described by the contact radius rs on the flat surface and the angle
on the sphere. The contact angles p and s are the contact angles of the capillary on the spherical particle and the flat surface, respectively, and by convention, the contact angles are on the liquid side of the interface.
Figure 7. Illustration of a bridging capillary between a spherical particle and a flat surface.
The capillary (sometimes called meniscus or pendular ring) causes an attractive force between the two surfaces, a capillary force. The capillary force in the normal (vertical) direction, includes two contributions. The first one (F) is due to the surface tension acting on the wetted perimeter:
𝐹𝛾 = 2π𝑟c 𝛾 sin 𝜃 (6)
The second contribution (FΔP) is caused by the capillary pressure P:
𝐹Δ𝑃 = π𝑟c2Δ𝑃 (7)
The total capillary force Fcap is calculated as:
𝐹cap= 𝐹Δ𝑃 − 𝐹𝛾 (8)
The capillary force can be evaluated on either the sphere or the flat surface, and the magnitude should be the same under equilibrium conditions. On the flat surface the contact radius rc is equal to rs and for the sphere the contact radius is given by rp = R sin (Figure 7). Similarly, the contact angle is the contact angle on the flat surface s or particle p, respectively. If the contact radius, contact angle and capillary pressure are known, the capillary force can be directly calculated using Eqs. 6-8. The capillary pressure can be calculated from the shape of the capillary liquid-gas interface using the Young-Laplace equation.
Young-Laplace capillary pressure
The Young-Laplace equation relates the curvature of a liquid interface to the pressure change across the interface, i.e. the difference in pressure P between the two phases. In the absence of gravitation, or when gravity is negligible, the Young-Laplace equation is given by:
Δ𝑃 = 𝛾 (1
𝑟1+ 1
𝑟2) (9)
Here, r1 and r2 are the principal radii of curvature of the interface. There are two principal curvatures at any given point on a 2D surface. The two principal radii of curvature are given by the radius of the curved surface in two perpendicular normal planes at that point. For instance, for a spherical drop (or bubble) of radius rd, the two radii are r1 = r2 = rd and the curvature is 2/rd. In the case of a capillary bridge, the two principal radii are given by the radius in the vertical plane (r1) and radius in the horizontal plane (r2), illustrated in Figure 7. In this case, r1 describes the concave curvature of the interface and is defined as negative, while r2 is positive since it describes the convex curvature. The form of the Young-Laplace equation as given in Eq.
9, uses an important approximation, called the circular (or toroidal)
approximation. Using the circular approximation, it is assumed that the shape of the interface in the vertical plane (the meridional profile) can be described by a circle of radius r1. In many cases, the exact shape of the gas- liquid interface is rather described by other classes of geometrical curves e.g. nodoids or unduloids [110, 119]. However, for small capillaries, the difference between numerical calculations of the exact shape and the circular approximation are generally small and can be neglected [113].
When the circular approximation is not applicable, the full Young-Laplace equation needs to be solved in order to obtain the exact shape of the gas- liquid interface. For an axisymmetric capillary bridge and when the gravity effect is negligible, the following form of the Young-Laplace equation is valid [110, 119, 120]:
2𝐻̃ = ℎ′′
(1+ℎ′2)3 2⁄
+ ℎ′
𝑟(1+ℎ′2)1 2⁄
(10)
where 𝐻̃ is the constant mean curvature of the liquid-gas interface and 2𝐻̃ ≡∆𝑃
𝛾 , ℎ′ ≡𝑑ℎ
𝑑𝑟 , ℎ′′≡𝑑2ℎ
𝑑𝑟2 (11)
Here, h is the height of the interface and r the distance from the central axis.
The full Eq. 10 is difficult to solve analytically, however it has been solved in the limit of 𝑟 ≪ 𝜅, where 𝜅 = √𝛾 𝜌𝑔⁄ is the capillary length; the liquid surface tension, the density of the liquid and g = 9.82 m s-2 the gravitational acceleration. In this limit several approximate analytical formulas to describe the meniscus shape have been derived [121-124]. An approximate formula to describe the shape of a liquid meniscus around a spherical microparticle have been proposed by Schellenberger et al. [125]:
ℎ(𝑟) = 𝑟psin 𝛼 [ln ( 4𝜅
𝑟+√𝑟2−𝑟02sin2𝛼
) − 0.577] + 𝑏 (12)
Here, rp = R sin is the contact radius on the particle, α = p – the angle of the gas-liquid interface with the horizontal and 0.577 the Euler-Mascheroni constant. The constant b has no physical meaning and is added as the equation otherwise diverges for large r. Eq. 12 is valid for 𝑟 ≪ 𝜅and Bond number Bo ≪ 1 (Bo ≡ 𝑅 𝜅⁄ ).
Constant capillary volume
An explicit expression for the capillary force of a bridging capillary of constant volume V between a sphere and a plane (as illustrated in Figure 7) has been derived by Butt and Kappl [113]:
𝐹cap= 4π𝛾𝑐𝑅 (1 − 𝐷
√𝑉
π𝑅+𝐷2
) (13)
where
𝑐 =cos(𝜃p+𝛽)+cos 𝜃2 s (14)
In the derivation of Eq. 13, it is assumed that the circular approximation is applicable and that r2 >> r1 (which is valid if R >> r1). Fitting of Eq. 13 have been shown to agree with measurements between smooth hydrophobic surfaces (force curve as illustrated in Figure 5) [107, 126, 127]. However, as Eq. 13 is only valid for constant capillary volume, force curves measured between rough (super)hydrophobic surfaces (force curve as illustrated in Figure 6) often cannot be fitted to Eq. 13 [107-109, 126].
Free energy approach
Another approach to determine capillary interactions is to calculate the free energy change due to capillary formation [96, 128]. The total free energy change Gcap includes contributions from the surface tension GA and the capillary pressure GPV:
