Robust omniphobic surfaces by mimicking the springtail skin morphology

DISSERTATION

zur Erlangung des akademischen Grades Doctor rerum naturalium (Dr. rer. nat.)

vorgelegt

der Fakultät Mathematik und Naturwissenschaften der Technischen Universität Dresden

von

Dipl.-Ing. René Hensel

geboren am 11. März 1981 in Sebnitz

Eingereicht am 15. November 2013 Disputation am 14. Juli 2014

Die Dissertation wurde in der Zeit von Juni 2009 bis November 2013 am Leibniz- Institut für Polymerforschung Dresden e.V. und Max-Bergmann-Zentrum für Biomaterialien Dresden angefertigt.

Gutachter: Prof. Dr. Carsten Werner Max Bergmann Center for Biomaterials Dresden Leibniz-Institut für Polymerforschung Dresden Technische Universität Dresden

Prof. Dr. Thomas Speck Albert-Ludwigs-Universität Freiburg Botanischer Garten Freiburg

Abstract

Human beings have long been inspired by the unique materials, processes, and objects found in nature that have been developed through evolution over Gyr. Today, one of the famous examples of nature-inspired concepts is the water-repellent cuticle of the lotus flower, Nelumbo nucifera, which exhibits the so called self-cleaning effect. Such repellent and self-cleaning or easy-to-clean surfaces can be useful in a myriad of technological processes and products, in particular, by reducing expensive cleaning procedures or cleaning intervals. The repellence of the lotus leaf arises from the fact that a water droplet contacts only the tips of the rough plant surface and, thus, the contact area as well as the adhesion of liquids to the surface is drastically reduced and the droplet can easily roll off. Although water-repellent and self-cleaning surfaces are currently available , their application area and longevity are strongly restricted due to the following common limitations: (i) Despite an excellent water-repellence, such surfaces do often not repel liquids with lower surface tensions such as oils or water that contains surfactants. (ii) The energetic barrier against complete wetting, which is the loss of repellence, is often even less than the kinetic energy of falling rain droplets. Thus, such structures are neither applicable for outdoor coatings nor suitable for large immersion depths. (iii) The most lotus-inspired surface exhibits an insufficient mechanical resistance and a short long-term durability.

In the present thesis, a novel surface modification strategy is evolved that has been inspired by the cuticle integuments of springtails (Collembola). Springtails are soil- dwelling arthropods. Their skin exhibits water and oil repellence, i.e. an omniphobic wetting characteristic, and are mechanically more stable than the cuticular surfaces of plant. Springtails exhibit both features as an evolutionary adaptation to maintain their cutaneous respiration in temporary rain-flooded soil habitats. Thus, mimicking their robust and effectively repellent surface characteristics may overcome the common limitations of lotus-inspired surface coatings and may offer exciting opportunities for emerging applications.

The aim of the thesis is to find out the physicochemical origin of the unique wetting characteristic, in particular, the omniphobicity and the high pressure resistance of the collembolan cuticle. Furthermore, as a proof of principle, the obtained findings shall be

I

translated into a synthetic surface coating. Thus, the structure of this thesis includes the whole biomimetic path – An obtained natural phenomenon is translated into technology via understanding of biology.

Within this thesis, the characteristic skin morphology of Tetrodontophora bielanensis, Orthonychiurus stachianus, and Folsomia candida are intensively investigated. The impact of the individual surface features on the wetting characteristics is investigated by an adaptive replication approach, in which the polymer replicas are tuneable with respect to their surface morphology as well as their surface chemistry. Microscopic studies, contact angle goniometry, and plastron collapse tests at elevated pressures are utilized to characterize the replicas in reference to the natural templates. It has been found that the wetting barrier of the collembolan cuticle, even for liquids with low surface tension is solely based on a structural control by nanoscopic so called primary granules, which exhibit overhanging (mushroom-shaped) cross-sectional profiles.

The high-pressure resistance of springtail skin, which has experimentally been obtained in the plastron collapse tests, are further substantiated by analytical and numerical analyses. Therefore, a pressure-based model is developed and the transition phenomena, canthotaxis and the Laplace breakthrough, are introduced. A clear depiction of the physicochemical origin of the wetting resistance has been further given in detail by abstract models, which are evolved base on the mushroom-shaped profiles of the nanoscopic primary granules. For example, it has been found that the Laplace breakthrough is irrespective to the intrinsic contact angle and, thus, independent to the surface chemistry of the surface features.

Finally, a manufacturing process to generate free-standing polymer membranes is developed. The design of the membranes is based on the obtained results of the set of experimental, analytical and numerical analyses. Wetting experiments and abrasion tests successfully prove a novel and promising strategy for the fabrication of omniphobic coatings. In particular, the mechanical durability and the enforced wetting resistance and long-term stability upon complete immersion, which are most striking features of the springtail skin, are effectively transferred by the biomimetic approach.

II

Zusammenfassung

Die Menschheit inspiriert sich seit jeher von natürlichen, meist einzigartigen Materialien, Prozessen und Strukturen, die sich im Laufe der Evolution seit mehr als 3,8 Milliarden Jahren entwickelt haben. Heutzutage ist die wasserabweisende und sich selbstreinigende Blattoberfläche der Lotuspflanze, Nelumbo nucifera, eines der bekanntesten Beispiele für jenen naturinspirierten Ansatz. Solche wasserabweisenden und sich selbstreinigende Oberflächen wecken ein großes industrielles Interesse hinsichtlich verschiedenster technologischer Prozesse und Produkte des täglichen Lebens, vor allem aufgrund ihres Potentials Reinigungsintervalle zu reduzieren beziehungsweise Reinigungsprozeduren gänzlich einzusparen. Der wasserabweisende Effekt bei der Lotuspflanze wird hauptsächlich durch deren raue Oberflächenstruktur hervorgerufen. Wassertropfen berühren nur die Spitzen der Strukturen, wodurch die Kontaktfläche als auch die Adhäsion zwischen Flüssigkeit und Blattoberfläche reduziert wird. Obwohl wasserabweisende und selbstreinigende Oberflächen heutzutage kommerziell erhältlich sind, ist deren Anwendungsbereich und Langlebigkeit meist durch die folgenden Einschränkungen begrenzt: (i) Trotz exzellenter wasserabweisender Eigenschaften versagen solche Oberflächen meist im Kontakt mit öligen Substanzen. (ii) Die energetische Barriere, welche eine komplette Benetzung der Oberfläche verhindert, ist meist kleiner als die kinetische Energie von fallenden Regentropfen, wodurch solche Oberflächen weder für Außenanwendungen noch für große Eintauchtiefen geeignet sind. (iii) Die Langlebigkeit ist aufgrund einer unzureichenden mechanischen Stabilität der Oberflächenstrukturen oft nur sehr gering.

In dieser Arbeit wird eine neue Strategie zur Oberflächenmodifizierung vorgestellt, die von den Hautstrukturen der Springschwänze (Collembola) inspiriert wurde. Springschwänze sind im Boden lebende Arthropoden. Ihre Haut weist wasser- und ölabweisende Eigenschaften auf und ist zudem beständiger gegenüber Abrasion als Blattoberflächen. Beide Eigenschaften spiegeln eine evolutionäre Anpassung hinsichtlich der Gewährleistung ihrer Atmung, welche diffusionsgetrieben über ihre gesamte Hautoberfläche erfolgt, in einem zeitweise regenüberfluteten Bodenhabitat wieder. Die Nachahmung dieser robusten und flüssigkeitsabweisenden Hautoberfläche eröffnet somit die Möglichkeit die herkömmlichen Einschränkungen von Lotusblatt-inspirierten Oberflächen zu überwinden und bietet potentiell Möglichkeiten hinsichtlich neuer Anwendungen und Anwendungsbereiche.

III

Das Ziel dieser Arbeit ist herauszufinden, welchen physikalisch chemischen Ursprung diese bisher in der Natur einzigartige Benetzungseigenschaft der Springschwanzhaut hat. Anhand dieser Ergebnisse wird anschließend eine synthetische Oberflächenstrukturierung erzeugt, die dieses Phänomen in die Technik überführt. Die Arbeit umfasst somit den gesamten biomimetischen Pfad – Ausgehend vom Beobachten eines natürlichen Phänomens über das Ermitteln der zugrunde liegende Theorie und einer Abstraktion in ein geeignetes Modell bis hin zum Transfer in die Technologie.

In dieser Arbeit werden die Morphologie der Haut von Tetrodontophora bielanensis, Orthonychiurus stachianus und Folsomia candida intensiv untersucht. Zunächst werden die unterschiedlichen Oberflächenstrukturtypen hinsichtlich ihres Einflusses auf das Benetzungsverhaltens untersucht. Hierfür wird ein adaptiver Prozess zur Abformung der Hautstrukturen entwickelt, der in Bezug auf die Morphologie und Chemie der Replikatoberfläche präzise variiert werden kann. Mikroskopische Untersuchungen, Kontaktwinkelmessungen und Benetzungstests unter erhöhten hydrostatischen Druck werden zur Charakterisierung der Polymerreplikate in Bezug auf die natürliche Hautoberfläche durchgeführt. Die Benetzungsbarriere bei Springschwänzen, auch gegen Flüssigkeiten mit geringerer Oberflächenspannung, wird auf die nanoskopischen primären Granülen und deren pilzförmigen Querschnitt zurückgeführt.

Die experimentell ermittelte hydrostatische Druckresistenz wird analytisch und numerisch weiter untersucht. Hierfür wird ein physikalisches Modell entwickelt, woraus sich zusätzlich die Übergangsphänomene Canthotaxie und Laplace-Durchbruch ableiten lassen. Mithilfe abstrahierter geometrischer Modelle auf Basis des pilzförmigen Querschnitts der nanoskopischen primären Granülen wird der physikalisch-chemische Ursprung der Benetzungsresistenz dargelegt. Beispielsweise ist der Laplace-Durchbruch komplett unabhängig vom intrinsischen Kontaktwinkel des Materials und demzufolge unabhängig von der Oberflächenchemie der Oberflächenstrukturen.

Im letzten Schritt dieser Arbeit wird ein Herstellungsprozess für freistehende Polymermembranen entwickelt. Die Ergebnisse der experimentellen, analytischen sowie numerischen Untersuchungen bilden die Grundlage für das Design dieser Membranen. Benetzungsuntersuchen und Abrasionstests zeigen erfolgreich die Umsetzung robuster, omniphober Oberflächen nach dem Vorbild des Springschwanzes. Vor allem die mechanische Beständigkeit und der Widerstand gegen eine erzwungene Benetzung, welches die herausragenden Eigenschaften der Springschwanzhaut sind, konnten somit effektiv durch den biomimetischen Ansatz umgesetzt werden.

IV

Acknowledgements

I would like to express my sincere thanks to my family and all supervisors, co-workers, and friends who contributed to the completion and supported me throughout this work.

First, I would like to thank Prof. Dr. Carsten Werner who combined Ralf Helbig’s previous work on springtails together with my background on microfabrication techniques to start up the Collembola research group in a critical situation of my thesis. He has always been interested in my work, provided me valuable advices and scientific expertise, and gave me the scope for novel developments.

I would like to thank Prof. Dr. Thomas Speck, Professor for Functional Morphology and Biomimetics and Director of the Botanic Garden of the University Freiburg, for reviewing this thesis as a second referee.

Particularly, I am grateful to PD Dr. Hans-Georg Braun for being a motivated member of my thesis advisory committee and his unconditional help, always stimulating suggestions and numerous discussions throughout the time of research at the Leibniz Institute of Polymer Research Dresden.

I would like to thank Prof. Dr. Michael Mertig, Director of the Kurt-Schwabe Institute Meinsberg, for his guidance and assistance as a former supervisor and his great commitment as an external member of my thesis advisory committee.

I am very grateful to Prof. Dr. Gerlach, Director of the Solid-State Electronics Laboratory at the TU Dresden, who gave me the opportunity to join the interdisciplinary Training Research Group “Nano- and Biotechniques for Electronic Device Packaging” (DFG 1401/2). I would to thank all fellows for the friendly and scientific atmosphere within the TRG and a great time at the seminars and the excellent and stimulating workshops. In particular, I am grateful to Andreas Finn who spent a lot of time in providing me quite nice master structure, the basis step for my own research. In our regular Mensa meetings, he always came up with new ideas and suggestions to improve the production processes from back-end to front-end and to enhance the performance of the final structures.

I am very grateful to my colleagues Julia Nickerl and Dr. Ralf Helbig within the Collembola group for the wonderful discussions in our seminars, critical reviews of all my manuscripts including this thesis, the shared idea of making the short movie about

V

our research, and the great time also after work. In my opinion, this was the best interdisciplinary team I know.

Furthermore, I would like to thank all colleagues of the Institute of Biofunctional Polymer Materials for the pleasant atmosphere and their encouragement, collaborations and assistance throughout this work. In particular, I would like to thank Heather Weber for proofreading of parts of this thesis. I am very grateful to Jannik Bäumer for his active participation and perseverance in making polymer replicates.

I am also very grateful to all external collaborators as Prof. Dr. Neinhuis (Institute of Botany, TU Dresden), Dr. Sebastian Aland and Prof. Dr. Axel Voigt (Institute of Scientific Computing, TU Dresden), Dr. Robert Kirchner (PSI, Villingen, Switzerland), Dr. Teja Roch (Fraunhofer IWS, Dresden), Lydia Bahrig (Physical Chemistry, TU Dresden), Anne Jantschke (Bioanalytical Chemistry, TU Dresden), Dr. Ihsan Amin (Macromolecular Chemistry, TU Dresden) for their support and contributions.

I owe a debt of gratitude to my friends for always supporting me in tackling the scientific and non-scientific problems in my daily life.

Finally, I am very grateful to my family members and my daughter, whom I dearly love and appreciate.

VI

Table of contents Abstract ...... I Zusammenfassung ...... III Acknowledgements ...... V List of figures...... IX Table of symbols...... XI List of abbreviations ...... XIII 1 Introduction ...... 1 2 Fundamentals ...... 7 2.1 Biomimetics ...... 7 2.1.1 Biomimetic surfaces ...... 9 2.1.1.1 Structure-property relationships of arthropod cuticle ornamentation...... 10 2.1.1.2 Springtails and their cuticle ornamentation ...... 12 2.2 Wetting phenomena on solid surfaces ...... 14 2.2.1 Surface tension ...... 15 2.2.1.1 Capillary length and Bond number ...... 16 2.2.1.2 Laplace’s law ...... 17 2.2.2 Wetting on solids...... 17 2.2.2.1 Young’s law ...... 18 2.2.2.2 Pinning effects ...... 19 2.2.2.3 Wetting on real surfaces ...... 20 2.2.2.4 Homogeneous and heterogeneous wetting ...... 21 2.2.2.5 Omniphobic surfaces ...... 24 2.2.2.6 Stability of the heterogeneous wetting state – The wetting resistance ...... 25 2.3 Imprint lithography – Patterning by molds ...... 26 2.3.1 Particle replication in non-wetting templates ...... 28 2.3.2 3D replication techniques...... 28 2.3.3 Reverse imprint lithography ...... 31 2.3.4 Imprint lithography in biomimetics ...... 31 3 Materials and methods ...... 33 3.1 Animals ...... 33 3.2 Replication of the springtail skin ...... 34 3.2.1 Mold preparation ...... 34

VII

3.2.2 Fabrication of faithful PEGda replicas – Route A ...... 34 3.2.3 Fabrication of PEGda replicas without PGs – Route B ...... 34 3.2.4 Surface treatment ...... 35 3.3 Membrane manufacturing...... 37 3.3.1 Silicon master fabrication ...... 37 3.3.2 Polymer feature replication ...... 37 3.4 Contact angle goniometry ...... 38 3.5 Immersion tests ...... 38 3.6 Rheology ...... 38 3.7 Wear testing ...... 39 3.8 Electron microscopy imaging and focused ion beam preparation...... 39 3.9 Numerical FEM-simulations ...... 40 3.9.1 Sharp solid-fluid interface ...... 41 3.9.2 Diffuse solid-fluid interface ...... 41 4 Results and discussion ...... 45 4.1 Replication of springtail skin ...... 45 4.2 Analytical studies of the wetting resistance ...... 51 4.2.1 Analytical Theory ...... 52 4.2.2 Springtail skin ...... 55 4.2.3 Abstracted profiles ...... 60 4.3 FEM-simulation of the enforced wetting dynamics ...... 65 4.3.1 Single cavities ...... 65 4.3.2 Hierarchically patterned surfaces ...... 69 4.4 Bio-inspired omniphobic polymer membranes ...... 73 5 Conclusions ...... 81 References...... 87

VIII

List of figures

Figure 1.1 Schematic and wetting of four different surfaces...... 2 Figure 1.2 Shear load stability of a microscopic pillar structures with (a) smooth and (b) grooved side walls...... 3 Figure 2.1 A patch of arthropod cuticle that represents the characteristic layer structure...... 10 Figure 2.2 Cuticle ornamentation of springtails...... 12 Figure 2.3 Citations of key papers in biomimicry studies related to interfacial materials with special wettability from 2002 to 2012...... 15 Figure 2.4 Illustration showing the interfacial energies at the three-phase contact line of a droplet on a solid surface...... 18 Figure 2.5 Illustration of the thermodynamic equilibrium conditions at the three-phase contact line...... 18 Figure 2.6 Illustrations that show the pinning of an advancing contact line...... 20 Figure 2.7 Illustration of the equilibrium conditions of the three-phase contact line at a rough surface...... 21 Figure 2.8 Illustration showing the homogeneous wetting on a rough surface by Wenzel model...... 22 Figure 2.9 Illustration showing the heterogeneous wetting state on a rough surface by Cassie-Baxter model...... 22

Figure 2.10 Relationship between the intrinsic contact angle and the apparent contact angle regarding the two models of wetting on textured surfaces...... 23 Figure 2.11 Droplets of water in heterogeneous wetting state and hexadecane in homogeneous wetting state...... 24 Figure 2.12 Springtail colony of O. stachianus...... 25 Figure 2.13 Transition from heterogeneous to homogeneous wetting state...... 26 Figure 2.14 Scheme of the imprint process flow...... 27 Figure 2.15 Scheme of the PRINT process flow...... 29 Figure 2.16 Scanning electron micrograph of the mesh structure featured by cross-shaped particles, which were modified by incorporation of silica colloids...... 30 Figure 2.17 Schematic illustration of the two-step fabrication process ...... 30 Figure 2.18 Scheme of the reverse imprint process flow...... 32 Figure 3.1 Representative SEM images of each step in the replication process...... 36

IX

Figure 3.2 Schematic illustration of the experimental setup for immersion tests...... 39 Figure 3.3 A dynamic contact line in a diffuse-interface framework...... 40 Figure 4.1 Skin pattern of T. bielanensis (European giant springtail)...... 46 Figure 4.2 Replication process flow and the contact angle measurements...... 47 Figure 4.3 SEM images regarding the disappearance of the hairy structures...... 48 Figure 4.4 Pressure resistance of the heterogeneous wetting state...... 50 Figure 4.5 Illustration of two distinctive pressure-induced wetting transition phenomena...... 53 Figure 4.6 Skin surface topography of the springtail O. stachianus...... 56 Figure 4.7 Analytical calculations of the Laplace pressure across the liquid-air interface for certain positions of the three-phase contact point...... 59 Figure 4.8 Geometrical models based on nanoscopic surfaces structures of O. stachianus...... 61

Figure 4.9 Contour plot of calculated breakthrough pressures, , displaying the resistance against wetting transition for three distinctive types of model structures...... 62 Figure 4.10 Analytical calculations of the Laplace pressure across liquid-air

interface for a serif T-shaped profile with ⁄ ratio of ...... 63 Figure 4.11 The ratio of serif width to cavity radius that determines at which serif edge the breakthrough for different intrinsic contact angles occurs...... 64 Figure 4.12 Numerical simulations displaying the pressure-induced wetting transition dynamics inside cavities with different cross-sectional profiles and an intrinsic contact angle of ...... 66 Figure 4.13 Maximally determined interface curvature (normalized) by numerical simulations (scatters) and analytical calculations (lines) for different cross-sectional profiles...... 67 Figure 4.14 Advancement of diffuse interface around sharp edge...... 68 Figure 4.15 Numerical FEM simulations to explore the dynamics of the Cassie- Wenzel transition...... 70 Figure 4.16 Recovery effect in Cassie-Wenzel transition...... 71 Figure 4.17 Springtail skin morphology and process scheme for manufacturing polymer membranes with similar structural features...... 74 Figure 4.18 Contact angle goniometry...... 75 Figure 4.19 Immersion experiments...... 77 Figure 4.20 Wear tests of polymer membranes in comparison to pillar arrays...... 79 Figure 5.1 Summary of the biomimetic approach, which is presented within this thesis...... 82

X

Table of symbols

Symbol Description Unit

cavity diameter [m]

area [m2]

double well potential

Bond number

concentration field variable

Cahn-Hilliard mobility constant

thickness [m]

area fraction of solid surface

force [N]

constant of gravitation [m s-2]

Gibbs energy [J]

height [m]

curvature [m-1]

molecular weight [g mol-1]

number average molecular weight [g mol-1]

surface normal

pressure [Pa]

hydrostatic pressure [Pa]

Laplace pressure [Pa]

breaktrough pressure [Pa]

roughness ratio

roughness ratio of wet solid area

radius [m]

spreading coefficient [N m-1]

velocity [m s-1]

work [J]

surface tension [N m-1]

XI

Symbol Description Unit

surface energy [J m-2]

surface free energy [J m-2]

interfacial energy of solid-liquid interface [J m-2]

interface thickness

advancing contact angle [°]

apparent contact angle [°]

Cassie-Baxter contact angle [°]

receding contact angle [°]

Wenzel contact angle [°]

intrinsic contact angle, Young contact angle [°]

capillary length [m]

chemical potential [J mol-1]

viscosity [Pas]

density [kg m-3]

scaled surface tension

phase field variable

geometrical edge angle [°]

XII

List of abbreviations

3D three-dimensional

EDX energy dispersive X-ray spectrometry

FEM finite element method

FIB focused ion beam

ITRS international technology roadmap for semiconductors

PDMS polydimethylsiloxane

PEGda poly(ethylene glycol) diacrylate

PEGdma poly(ethylene glycol) dimethacrylate

PFPEdma perfluoropolyether dimethacrylate

PG primary granule

PRINT particle replication in non-wetting templates

SEM scanning electron microscopy

SG secondary granule

Teflon AF amorphous fluoropolymer Teflon

TEM transmission electron microscopy

UV ultraviolet

XIII

Chapter 1

Introduction

Recent trends and developments in materials science relate to ultra-performance, multifunctional, smart, and responsive materials.[1] In nature, a high diversity of such types of (bio)materials can be found everywhere.[2] Typically, biomaterials have simultaneously to comply with many (environmental) conditions and, therefore, they are often complexly and hierarchically assembled.[3-5] Human beings have long been inspired by those natural materials and utilized them as models for the development of novel materials, devices, and processes. Today, mimicry of nature is an established interdisciplinary field of research that is referred to as biomimetics; It combines biology, physics, chemistry, material sciences, robotics, and engineering and benefits from several advances of the respective fields.[6] By convention, the major goal of biomimetics is to decipher how natural systems work, whereas the way of (bio)prospecting is usually triggered by technological needs.[7,8] In a further step, the obtained knowledge can then be utilized as a source of guiding principles and ideas along with imagination for novel developments.[9]

Mimicking natural surfaces and their complex interplay of morphology and chemical and physical properties, is the field of biomimetics, known as biomimetic surfaces.[10] Studying natural surfaces is of great interest due to their link between organisms and their environment where physical, chemical, and biological reactions and processes take place and a broad range of distinct phenomena can be observed.[11] As an example, one can consider an aqueous droplet originating from rain or fog: Upon contact the droplet may spread out over the entire surface or may completely be repelled. Furthermore, the aqueous phase may slide along a certain direction across the surface or may stick to a certain region of the surface. This variety of different interactions comply with certain functions, which are usually specific adaptions of organisms to survive in their environmental conditions.[1,12] For example, many natural surfaces, which instantly repel aqueous droplets, often also have the ability to remain clean from dust particles.

1 Chapter 1

Figure 1.1. Schematic and wetting of four different surfaces. The contact area between the droplet (blue) and the surface is reduced by surface roughness (nano- and microstructure as well as the hierarchical structure) in comparison to the flat surface. All displayed rough surfaces are principally able to repel aqueous droplets. Adapted from ref. [13], Copyright 2011, with permission from Elsevier.

This purity is provided by the surface roughness that reduces the contact area as well as the adhesion of dust particles and water droplets. A rolling water droplet is than easily able to capture dust particles lying on the surface due to their higher adhesion to the liquid than to the solid, as demonstrated for the lotus leaf 15 years ago.[14,15] The self- cleaning phenomenon relates to a defence mechanism of plant against potentially dangerous pathogens such as bacteria and fungi.[16] Furthermore, a dry surface of aquatic plants is necessary for sufficient photosynthesis due to the higher diffusion of

CO2 in air than in water.[17] In addition, water-repelling surfaces facilitate walking on water by trapping of air inside a bunch of micro-setae that covers the legs as known from semi-aquatic arthropods such as water strider.[18,19] The air-retaining capability of such repellent surfaces further allows several semi-aquatic arthropods to respire under water upon immersion, as known from the fisher spider Dolomedes triton or the backswimmer Notonecta or supports the construction of a diving bell as known from the aquatic fisher spider Argyroneta aquatica.[20,21] However, before translating of such a phenomenon into engineered surfaces, the fundamental physical and chemical principles have to be understood. For instance, the surface morphology and chemistry of the lotus leaf was intensively studied over the last two decades and inspired engineers to manufacture water-repellent surfaces within a broad range of feasible applications. It was found that the hierarchical morphology of the waxy cuticle plays an important role in water repellence.[22] Nevertheless, an abstraction into simplified, non-hierarchical structures such as needle-like nanostructures or microscopic bulb or pillar structures also addresses a water-repellent characteristic in a preliminary manner as depicted in Figure 1.1.[10,13] Such non-hierarchical structures are easier to fabricate by several common

2 Introduction

Figure 1.2. Stability against shear loads, , of a microscopic pillar structures with (a) smooth and (b) grooved side walls: (a) The highest bending stress occurs at the bottom of the pillar (Scale bar: ); (b) The highest bending stress occurs at the tapered, overhanging part of the pillar (Scale bars: ). micromanufacturing processes such as lithography, etching, deposition or replication techniques.[13] However, such an abstraction into needle or pillar structures entails a serious list of drawbacks:

- The repellence is often restricted to aqueous media and fails for liquids with lower surface tensions such as oils or water containing surfactants.[23] - The energetic barrier against complete wetting, i.e. the loss of repellence, of the surface is often even less than the kinetic energy of falling rain droplets and, thus, the structures are neither applicable for outdoor coatings nor suitable for large immersion depths.[24,25] - The inherent fragility of the tiny surface features limits the resistance to shear- loads, e.g. by scratching.[26,27]

So far, these limitations significantly impede a broad range of applications, thus, the concept of liquid-repellent surfaces has to be revised to overcome these drawbacks.

In recent studies, surface morphologies were evolved that can also repel low-surface- tension liquids by structure elements with mushroom-shaped cross sections.[28-30] However, such a profile possesses a mechanically weak point at the tapered, overhanging part of the pillar with respect to shear loads due to the implemented predetermined breaking point, which further reduces the longevity (Figure 1.2).

3 Chapter 1

In nature, even more interesting surface features, which combine both water and oil repellence (=omniphobicity) and mechanical resistance, was recently found: the cuticle integuments of springtails (Collembola).[31-33] Differing from insects, most springtails respire by cutaneous respiration.[34] Consequently, the entire cuticle has to be dry and clean to prevent suffocation due to a blocked gas exchange. Hence, the springtail skin repels several liquids even aqueous media containing surface-active substances originating from decaying organic matter.[32] Springtails are soil-dwelling arthropods and the cuticle surface has to resist against abrasion during locomotion in soil and litter.[32] A recent study has suggested that the skin pattern of springtails may have the potential to revise the concept of liquid-repellent surfaces by overcoming the common and above mentioned limitations concerning longevity, repellence against low-surface- tension liquids and resistance against enforced wetting.[32,33] Recapitulating the robust and effectively repellent surface characteristics of springtail skin in engineered materials may offer exciting opportunities for demanding applications. However, the identification and mechanistic understanding of the omniphobic and mechanically stable surface patterns evolved by springtails has yet not been clarified and still defines a challenge.

The aim of the present work is to explore a detailed mechanistic understanding of the underlying design principles of the springtail skin with respect to:

- Omniphobicity, - High hydrostatic pressure resistance, - Mechanical robustness.

The findings should further provide the basis for translation into an engineered surface coating that combines the listed properties and provides the potential to overcome the restrictions of previously discussed superhydrophobic surfaces, which are usually inspired by the surface morphology of the lotus leaf.

Previous microscopic studies revealed that the collembolan cuticle is hierarchically assembled.[35-39] The entire body of these animals is typically covered with nanoscopic primary granules and interconnecting ridges; together forming gas permeable nanocavities that are arranged in a comb-like pattern, which is a unique characteristic for springtails. Transmission electron micrographs revealed that the primary granules protrude above the ridges, thus, the nanocavities exhibit overhangs. At the microscopic scale, springtails can possess papillose secondary granules and bristles in a high diversity of size and shape that depends on ecological and taxonomic aspects.[31]

4 Introduction

To dissect the contributions of surface morphology and surface chemistry with respect to the omniphobic performance of the springtail skin, a tuneable polymer replication process has been developed. Using this approach, the skin pattern of T. bielanensis (European giant springtail) are translated into polymer replicas with defined variations in nanoscopic surface morphology and surface chemistry. Static contact angle measurements and in situ plastron collapse tests at elevated pressures are performed to characterize the set of obtained polymer replicas in reference to the natural skin surface.

In addition to the experimental data, analytical calculations are done to explore the origin of the obtained high wetting resistance, i.e. the resistance against complete wetting of the collembolan cuticle. Therefore, cross-sections of the skin are analysed by transmission electron microscopy. To get access to an analytical approach, the overhanging part of the cross-sectional profiles of the nanoscopic primary granules is fitted by polynomials. A model is developed that a priori affords an evidence of the wetting resistance by determination of the breakthrough pressure. Furthermore, the breakthrough phenomena canthotaxis and the Laplace breakthrough are defined. The obtained results are set into a general context by abstracted model profiles. To consolidate the analytical results and to gain further insights into the actual dynamics of the wetting transition process, numerical simulations are performed. Furthermore, this approach allows for studying the impact of the hierarchical assembled springtail skin, in particular, the interplay between the primary and the secondary granules. It also supports the experimental findings that the wetting transition occurs in a two-step process, whereas the first step is reversible before the second irreversible transition step occurs.

As a proof of concept, free-standing polymer membranes are developed, which are inspired by the cuticle ornamentation of springtails. The manufacturing process is based on a reverse imprint lithography approach that allows for an accurate design due to the top-down strategy. The omniphobic performance of the polymer membranes is demonstrated by in situ plastron collapse and long-term immersion tests. The mechanical durability of the membranes is shown by wear tests in comparison to a pillar surface using a nanotribometer setup.

5 Chapter 1

6

Chapter 2

Fundamentals

2.1 Biomimetics

Human beings have been inspired by nature’s designs and mechanisms since a long time.[40,41] In particular, the genius Leonardo da Vinci already adapted the gliding flight performance of birds for the construction of air vehicles and proposed basic flight mechanisms about 500 years ago.[40,41] However, the term ‘biomimetic’ was first coined by American biophysicist Otto Schmitt in 1957 as he reported on artificial electrical stimuli for mimicking the natural nerve impulse of squids.[41,42] In 1960, Jack E. Steele coined the term ‘bionics’ (synonymous with biomimetic) at the first bionics symposium in Dayton, Ohio, USA.[6] The motivation of the symposium was to bring together engineers and biologist in order to get them out of their comfort zone: “The manner in which bionics will mark its greatest contribution to technology is not through the solution of specific problems or the design of particular devices. Rather it is through the revolutionary impact of a whole new set of concepts, a fresh point of view”.[43] In the 1970s, the term bionics was popularized by the television series “The Six Million Dollar Man” and “The Bionic Woman”. The stories were based on the novel Cyborg by Martin Caidin. Since then, in the United States the word bionics is more or less appropriated for superhuman made of humans featuring electromechanical implants. However, the German equivalent of biomimetics is Bionik.[6,44]

Today, biomimetics is a still growing, vibrant and diverse research field stimulated by multidisciplinary research that benefit from new discoveries and methods in the fields of biology, physics, chemistry, robotics, and engineering. The number of publications rapidly increases, i.e. doubling every 2-3 years with about papers in 2011.[45] Currently, the term and its synonym ‘biomimicry’ are used for a broader range of research so that the definition of biomimetics vary between researchers from different disciplines.[44,46] From recent discussions, it turns out that biomimetics should conceptionally include two essentials: Natural phenomena are investigated to find basic

7 Chapter 2 principles existing in nature and to get a deeper understanding of biology, which can be adapted in an abstracted way by engineers via applied research. The following definition by the Association of German Engineers (VDI) provides a good summary of this conceptional approach:[8] “Biomimetics combines the disciplines of biology and technology with the goal of solving technical problems through the abstraction, transfer, and application of knowledge gained from biological models.” Consequently, mere one to one copies are not regarded to biomimetics. Moreover, a biomimetic approach consists of a process flow:[7]

Understanding of biology → Abstraction → Translation in technology.

In practice, the depicted way and, of course, the starting point of biomimetics are not really straightforward. On the one hand, initial questions that could be asked are: “For which technical application a certain natural phenomenon can be good for?” or the other way around “Which findings in biology can be helpful for certain applications?”.[7]

The list of examples, which consider a typical pathway starting from a certain natural phenomena to potential applications via abstraction, is long. The following brief examples should give an impression of the broad spectrum of biomimetics based on recently explored findings:

(I) Silk fibers produced by spiders or silkworms already inspired the Chinese for making clothes or woven textiles for writing some 3000 years ago. Silk fibers have a tensile strength greater than steel, although the fiber formation process takes place in ambient conditions without any access to high temperatures and elevated pressures. Furthermore, the fibers and the web of a spider are insoluble, biocompatible, antibacterial, and can resist to rain, wind and sunlight. Therefore, spider silk has great potential for technical or medical applications. However, the native molecular structure of silk, and their hierarchical multiscale organization into fibers were only deciphered over the last decades and allowed in a next step for the recombinant silk production of genetically engineered analogues in sufficient yield and purity (for review see ref. [47]). These findings, along with novel developed strategies concerning the assembly of the recombinant proteins, paved the way for the fabrication of tailored micro and macroscopic silk morphologies such as capsules, foams, nonwoven fabrics, hydrogels, films, or colloids that do not exist in nature, but could be useful for application as high performance biomaterials.[48]

8 Fundamentals

However, biomimetics is not restricted to inspiration from the molecular or microscopic scale level. The next example shows how the paradise flower inspired architects to build up macroscopic hingeless façade shading systems.

(II) Structures occurring in nature inspire architects since a long period of time. In modern architecture, one of the arising questions is how to reduce the complexity of moving structures.[49] According to this question, one answer has been found on the Strelitzia’s (paradise) flower, which possesses a peculiar protruding perch that bend down when a bird sits on it. The bending actuates a lateral unfolding mechanism that opens the sheath, so that the bird can sip the nectar from the inside of the flower. This natural concept was explored, abstracted and finally transferred to a registered product called Flectofin, which is made of fiber-reinforced polymers and consists of a backbone and a fin.[50] When the backbone is bent it causes a torsional buckling (flapping) of the fin without any hinge. The development of the first prototypes was done in a straight forward way, starting from understanding of biology, followed by abstraction, and finally the translation into technology, as explained above. Interestingly, the system was subsequently optimized to reduce stress peaks in the flapping mechanism in reverse kind of biomimetics. Therefore, a screening for biological solutions has been carried out and was finally found in the contour geometry of Eucalyptus leaves. The efficiency of the developed façade shading system was presented at the Thematic Pavilion at EXPO 2012 in Yeosu, Korea where 108 individually controllable fins with a height between 3 and were installed.

2.1.1 Biomimetic surfaces

Natural surfaces (from both the plant and the animal kingdom) often possess amazing shapes and structures that exhibit several remarkable properties. Some of these functions found in nature, which arouse commercial interests, are superhydrophobicity, self- cleaning, drag reduction in flow, anti-icing, energy conversion and conservation, high adhesion, reversible adhesion, non-fouling, aerodynamic lift, anti-reflection, anti- fogging, structural coloration, thermal insulation, self-healing, sensory-aid mechanisms, and so on.[1,12,51] Since almost all biological surfaces are multifunctional, it makes them even more interesting from the point of view of biomimetics.[52] The major challenge is to find out characteristic (structural and/or chemical) principles of natural surfaces, which is again a prerequisite before abstracting and transferring a phenomenon

9 Chapter 2

Figure 2.1. A patch of arthropod cuticle that represent the characteristic layer structure: epidermal cells, the endocuticle, the exocuticle and the epicuticle. (a-d) show some integumental outgrowths: (a) hairs, (b) papillae, (c) ridges or gratings, and (d) scales. Adapted from ref. [53], Copyright 2010, with permission from Elsevier. observed in nature into engineered applications. Hence, getting knowledge of structure- property relationships is the key to success.

2.1.1.1 Structure-property relationships of arthropod cuticle ornamentation Over the last decades, modern electron microscopy techniques enabled access to study of natural surfaces and helped to reveal their nano or microscaled exquisite details. This section will focus on arthropod cuticle ornamentations and their functions as an impressive example of a broad diversity of evolutionary evolved surface morphologies. In general, the cuticle of arthropods represents a non-living, and depending on the taxa, more or less sclerotized, exoskeleton that maintains the shape to the organism and affords mechanical stability to their body. The cuticle ornamentation, which is located at the interface between living organisms and the environment, can serve a variety of functions: (i) barrier against dry, wet, cold, or hot environments; (ii) being part of respiratory system; (iii) being part of mechano- and chemoreceptors; or (iv) causes coloration, air retention, or body cleaning.[52,54] A typical layer structure of an arthropod cuticle and several integumental outgrowths such as hairs, papillae, ridges, gratings, bristles, and scales decorating the epicuticle (the outermost skin layer) is depicted in Figure 2.1.[53]

10 Fundamentals

The following paragraphs shall give an overview of integumental outgrowths of arthropods cuticles and present their tailored functions adapted to environmental conditions and provide inspiration for innovations.

(I) Hairs are typically short (a few microns long) and slender (less than a micron in diameter) and can fulfil several tasks. For instance, hairy structures can act as a wetting barrier and afford the formation of an air layer (also referred to as plastron or physical gill) immediately upon immersion into aqueous media that prevent drowning of many wetland insects or spiders.[55,56] It was found that the life-time of such plastrons depends on the hair density and can be further supported by an hierarchical arrangement of short and long hairs as found on backswimmer insects (Notonecta).[57] Furthermore, a non-wetting hairy structure decorating the legs of aquatic or semiaquatic arthropods such as water strider or fisher spider is a common strategy for locomotion and living on water.[19] Here again, tiny air bubbles are trapped within the hairy structure, which allow such animals to float. Furthermore, several hexapods utilize hairs as attachment devices, enabling contact to smooth and/or rough substrates.[58] Other functions of hairs include protection against abrasion or filtering of food.[53]

(II) Papillae or bumps are conical protrusions from the nanoscale up to the microscale. Microscopic bumps with a water attracting top and a water repelling side-wall allow harvesting of water from humid air. Such bumps cover the entire forewings of Namibian beetles (Stenocara gracilipes), which live in the Namib Desert on the southwest coast of Africa.[59,60] Water from the ocean fog condensates at the water-attracting tips and form droplets, which, when large enough, slide downward into its awaiting mouth. A further function of microscopic papillose structures can be mechanical protection to ensure the integrity of a certain nanostructure, covering the papillae side walls, and can extend the long-term durability of those smaller structures.[31,32] Hexagonal arranged nanoscaled papillae cover the surface of compound eyes of some insects, e.g. the moth-eye. These patterns effectively provide a gradual change of the refractive index from that of air to that of the cuticle. Consequently, there is no sharp interface between both media, so that light can passes through without any reflection or refraction and, therefore, without any loss.[53]

(III) Bristles and scales are larger and more ornate than hairs. Bristles are cylindrical while scales are flattened plates. In contrast to bristles, scales are restricted to several insect orders such as butterflies or beetles.[53] Both integumental outgrowths exhibit a

11 Chapter 2

Figure 2.2. Cuticle ornamentation of springtails. The rhombic or hexagonal comb pattern is formed by small primary granules connected by ridges. Additionally, some - but not all - species possess papillose secondary granules (SG), which can significantly differ in shape, depending on the specific habitat and body size of the respective species. Reprinted from ref. [32], Copyright 2011, with permission from the Creative Commons License. sub-ornamentation that forms complex patterns consisting of ridges running parallel to the longer axis of the scale, cross ribs joining them, or larger pores.[53] Such patterns are often photonic structures due to their structural dimensions and periodical arrangements in the range of the wavelength of the visible light that leads to interference effects. Thus, these patterns are responsible for a structural coloration without pigments and dyes that is mainly related to visual communication: namely, to communicate with conspecifics and to avoid predation.[61-64] Beside communicative functions, scales and bristles can serve for thermoregulation, friction-reduction, or water-repellence, which again represents examples of perfect adaption to the environment by evolutionary evolved multifunctional properties.[54,65]

2.1.1.2 Springtails and their cuticle ornamentation Springtails (Collembola) are the first hexapods to appear in the fossil record, during the early Devonian about 400 million years ago.[66] Today, they are probably the most widespread and abundant terrestrial arthropods on Earth[34] and an integral component of the soil community and ecology[67] with more than 8000 species, which were identified so far.[68] External (and internal) systematics are still in discussion, but some

12 Fundamentals phylogenetic analyses indicated that springtails most probably represent a separate taxon within the hexapod clade and form a sister group of insects.[69]

In the 1960s and 1970s, optical and electron microscopy revealed the hierarchically arranged and highly textured springtail cuticle of several selected species.[35-39] The unique ornamentation typically consists of nanoscaled primary granules (minor tubercles) and interconnecting ridges; together forming nanocavities that are arranged in a rhombic or hexagonal comb-like pattern, which covers the entire body (Figure 2.2).[32] At the microscopic scale, some species possess papillose secondary granules (major tubercles) that are completely decorated by primary granules excluding the smooth domes at the top of these papillae. Furthermore, thin bristles or scales represent the tertiary structure. Recently, 40 species from 4 orders were examined to get a more general view of the springtail cuticle morphology.[31] It was found that the observed patterns correlates concerning their vertical distribution of preferred habitats, varying between deep in soil and on the surface. Interestingly, the size and spacing of the nanostructure (primary granules) was rather similar for all analysed species and could be concluded as a unique surface feature of springtails; while, in turn, the secondary and tertiary structures showed a significant diversity of occurrence, size, shape, and spacing by a clear ecological and taxonomic dependency.[31]

Differing from insects, most springtails lack any trachea, but respire directly through their cuticle. In particular at the bottom of the nanocavities, which are formed by primary granules and ridges, the cuticle has to be highly gas permeable.[70] The gas exchange occurs over the entire body area, so that the survival is greatly affected by the humidity of the surrounding environment. For instance, under arid conditions (high saturation deficit) the animals loose considerable amounts of water by transpiration.[70,71] In turn, the springtail cuticle has to possess a barrier against complete wetting to prevent suffocating due to a blocked gas exchange in wet conditions. The consequent repellence of aqueous media evolved by the springtail cuticle has been known for more than a half century.[39,70,72] However, the remarkable wetting resistance of the skin surfaces against wetting by low-surface-tension liquids such as alkanes or ethyl alcohol were only recently found using immersion tests.[32]

Being soil-dwelling arthropods, springtails are permanently exposed to granular matter that requires an adequate level of protection against abrasion damage. In particular, its lack of resistance against shear loads by scratching may dramatically reduce the long- term durability of the nano- and microscopic cuticle ornamentations. In first sand

13 Chapter 2 abrasion tests, it was found that the pronounced comb-like formation of primary granules and ridges acts as a mechanically self-supporting network, where the interconnecting ridges inhibits bending of the primary granules. Thus, allowed for a higher shear load dissipation as a prerequisite for a sufficient mechanical stability in contrast to the fragile wax crystals of superhydrophobic plants.[32]

In sum, the collembolan cuticle is entirely covered by an almost perfect, hierarchically assembled pattern of nano and microscopic granules, ridges, and bristles. The cuticle exhibits interesting characteristics such as non-wetting, non-fouling, and is stable against abrasion, which probably represents an evolutionary adaptation to maintain cutaneous respiration in temporary rain-flooded habitats consisting of soil, litter, and decaying wood and leaves.[73,74]

However, the reasons for these characteristics are still not completely identified and need further quantitative analyses. In terms of biomimetics, it would be further interesting to mimic these characteristics; in particular, a combination of them may have higher potential for real applications and may possibly overcome common limitations in the field of superhydrophobic and non-fouling surfaces.

2.2 Wetting phenomena on solid surfaces

The wetting of solid surfaces is an important characteristic that needs to be understood and controlled, in particular, in technological processes and many areas of fundamental research.[75,76] The aim of this section is to provide the fundamentals of wetting on solid surfaces that are necessary to understand certain specific phenomena. In the last decades, it turns out that the wettability of solids can be tuned with respect to particular demands. Examples of special wettability of natural and synthetic (often inspired by nature) surfaces can range from complete spreading to complete repelling of (various) liquids,[77] allow for directional or switchable liquid manipulation,[78] restore after physical damage,[79] or prevent or enforce phase changes such as condensation[80] or icing.[81] To obtain such characteristics, the surfaces represent unique nano- and microscaled textures that were often explored by biomimetic studies, i.e. reflected by a multitude of key papers in the last decade as depicted in Figure 2.3.[76]

14 Fundamentals

Figure 2.3. Citations of key papers in biomimicry studies related to interfacial materials with special wettability from 2002 to 2012. Reprinted from ref. [76], Copyright 2013, with permission from Materials Research Society.

2.2.1 Surface tension

Inside the bulk of a liquid droplet the molecules are in equilibrium state due to similar interactions with neighbour molecules in all directions. Consequently, the attractive cohesive forces result in a net zero force. The situation changes at the surface of the liquid, where the attraction to the neighbouring medium (e.g. vacuum or air) is usually not equal to the intermolecular interactions. For instance, water molecules at the water- air interface of a droplet are pulled inward due to a much lower attraction to the neighboured air molecules compared to cohesive forces inside the droplet. The resulting net force on the surface creates an increased internal pressure in comparison to the neighbouring medium. Thus, the liquid-air interface contract to a minimal area. This contractive tendency is responsible for the shape of droplets and is referred to as surface tension, , and its dimension is a tensile force by length unit ( ).

The surface tension can be also explained in terms of energy, which is than referred to as surface free energy, . At the surface the molecules of the liquid exhibit unsaturated bonds, which is less favourable, in comparison to the completely saturated molecules inside the bulk. To saturate the free bonds the number of surface molecules must be minimized that result again in a minimal surface area. The dimension of the surface free energy is energy by surface unit ( ).

15 Chapter 2

Since any curvature of the liquid phase results in an enhanced surface area, the total free energy of the system is enhanced. Consequently, it is pushed back by a restoring force that is referred to as capillary force, . The capillary force is proportional to the surface free energy (or surface tension):

. (2.1)

Furthermore, one can calculate the work that is needed to increase the surface of the system by:[82]

. (2.2)

From this expression one can deduces that surface tension ( ) and surface free energy ( ) are indeed equivalent.

2.2.1.1 Capillary length and Bond number In this section a characteristic length scale is introduced in order to estimate whether capillary or gravitational forces are dominating in a certain system. In the macroscopic world, the capillary force is negligibly weak: If a liquid is not contained, it spreads out. However, in the microscopic range, one can observe that liquids are shaped as spherical droplets, i.e. driven by the capillary force, which restores the minimal surface area as explained above. The reason for this transition is that the capillary force and the gravitational force scale different with respect to the characteristic length of the system. As an example one can consider a hanging droplet, which is first attached to the tip of a needle and continuously growing and finally dripping off. The capillary force is proportional to the radius of droplet: . In contrast, the gravitational force increases with the third power of the radius: . The critical radius, , before the droplet drips off is obtained by balancing both forces and is called the capillary length, :[82]

√ ⁄ . (2.3)

Thus, the capillary length can be utilized to estimate the transition from a system that is dominated by capillary forces ( ) to a system that is dominated by gravity ( ). As an example, the capillary lengths of water and hexadecane are about and , respectively.

For a static system, the ratio of the capillary to the gravitational effects can be calculated, which is referred to the dimensionless Bond number:[82]

16 Fundamentals

, (2.4)

in which is more generally the characteristic length of the system (e.g. radius of the droplet or radius of a capillary tube), the density of the liquid, and the acceleration due to gravity. implies that capillary and gravitational effects are equal, whereas indicates that capillary effects dominate and indicates that gravity dominates.

2.2.1.2 Laplace’s law As described in section 2.2.1, the inward directed net force increases the internal pressure inside the droplet in comparison to the surrounding gaseous phase. The pressure difference between inside and outside is referred to as the Laplace pressure, , given by the Young-Laplace equation:[82]

( ), (2.5)

in which is the surface tension and the mean curvature, and and are the principle radii of curvature of the interface. For a spherical droplet the Laplace pressure is given by:

, (2.6)

in which is the radius of the droplet.

2.2.2 Wetting on solids

In section 2.2.1 it was shown that the interface of a liquid, which is completely surrounded by a gaseous phase can be characterized by the interfacial energy (i.e. equal to the surface tension or the surface free energy). The total free energy of such a fluid two-phase system forces the liquid to contract to a spherical droplet as the minimal surface area. This former considered two-phase system changes to a three-phase system when the droplet comes into contact with a solid phase. The behaviour of the droplet at the solid surface is referred to as wetting and can be characterized by the spreading coefficient, , given by the Young-Dupré equation:[82]

( ), (2.7) where and are the interfacial energies between the solid-gas, and the solid-liquid

17 Chapter 2

Figure 2.4. Illustration showing the interfacial energies at the three-phase contact line of a droplet on a solid surface. phase boundary, respectively. When , the liquid wets the entire surface, i.e., complete wetting due to the fact that the energy of the solid-gas interface is higher than the sum of the solid-liquid and the liquid-gas interfacial energies. In contrast, when , the liquid only partially wets the surface and the three interfaces join one another at a three-phase contact line (also referred to as triple line).

2.2.2.1 Young’s law The angle (Figure 2.4) between the tangents of the liquid-gas and the liquid-solid interface that intersect in the three-phase contact line of a partially wetted ideal (i.e.,

Figure 2.5. Illustration of the thermodynamic equilibrium conditions at the three-phase contact line. (a) Relation between contact angle and surface free energy. (b) The Gibbs energy versus the contact angle for a droplet on an ideal solid surface, showing the single minimum at the Young contact angle, . Adapted from ref. [83], Copyright 2009, with permission from Annual Reviews.

18 Fundamentals

smooth, rigid, and chemically homogeneous) solid surface is referred to as the Young or intrinsic contact angle and can be calculated by the Young’s law, which he derived in 1805:[84]

, (2.8)

This equation represents the force balance acting at the three-phase contact line. By convention, there exist a transition at from an intrinsically hygrophilic (

) to an intrinsically hygrophobic ( ) surface that can dramatically change the macroscopic behaviour of a liquid in a certain geometrical confinement, for instance, inside a capillary tube (capillary rise ( ) or depression ( )) or on a rough surface (cf. section 2.2.2.3).

Thermodynamically, the three-phase system can be described by the Gibbs energy that is minimized when a system reaches equilibrium. It can be calculated for a liquid droplet for all possible contact angles in consideration of , the replaced solid–gas interface by the solid–liquid one, due to the boundary condition of a constant liquid volume (Figure 2.5a):[82]

( ) . (2.9)

The equilibrium condition is characterized by a minimum of the energy function:

. (2.10)

In case of a smooth, rigid, and chemically homogeneous surface, there exist only a single minimum, which gives directly an access to the intrinsic contact angle, thus, represents the equilibrium state on an ideal solid surface (Figure 2.5b).

2.2.2.2 Pinning effects As explained above, an ideal solid surface exhibits only one contact angle that can be precisely determined by Young’s law (Eq. 2.8). This is also true for the moving three- phase contact line of such a sessile droplet, which is inflated or deflated by continuously adding or reducing the liquid volume, respectively. However, ideal solid surfaces rarely exist in real applications. Most of the real solids exhibit surface roughness or chemically contaminations. Due to such heterogeneities, a moving triple line across the surface is pinned and immobile not only for , but for a certain range around the Young contact angle . The lowest feasible contact angles is referred to as

19 Chapter 2

Figure 2.6. Illustrations that show the pinning of an advancing contact line: (a) At a phase boundary where the intrinsic contact angle varies and, thus, the apparent contact angle at the solid 2 is not equal to . (b) At a convex edge that is defined by the geometrical angle, . receding contact angle and the highest obtained contact angle is referred to as advancing contact angle. The difference between both angles is defined as contact angle hysteresis. On an ideal solid surface the propagation of the triple line is continuously. However, local changes of the surface chemistry lead to pinning of the three-phase contact line even on a perfectly flat surface. (Figure 2.6a). Local changes in the spatial orientation (edges or wedges)[85] on a rough solid surface can also cause pinning of the contact line. Such an edge or wedge can be described by the geometrical edge angle. As an example, when the contact line of a droplet advances across an edge, it is pinned until the Young equation (Eq. 2.8) on the other side of the edge is fulfilled (Figure 2.6b).[86,87]

Thus, one obtains a maximal apparent contact angle, , regarding the horizontal plane can be calculated by:[86,87]

( ). (2.11)

The phenomenon is referred to as canthotaxis and affects wetting on real surfaces (section 2.2.2.3) and in microfluidic systems.[88]

2.2.2.3 Wetting on real surfaces Depending on the local position of the triple line, the local microscopic actual contact angle (in a close view to the contact line) has to fulfil the Young-equation (Eq. 2.8) as explained above (Figure 2.7a), which, of course, has an influence to the whole fluid interface that tries to minimize its area driven by the surface tension. Hence, the macroscopic apparent contact angle, which is determined by inspection of the whole droplet, may vary from the intrinsic one.

Thermodynamically, the calculations of the Gibbs energy (Figure 2.7b) result in an energy landscape that now exhibits multiple minima in comparison to the energy function of a smooth, rigid, and chemically homogeneous surface. For each minimum

20 Fundamentals

Figure 2.7. Illustration of the equilibrium conditions of the three-phase contact line at a rough surface: (a) The macroscopic apparent contact angle, , which is determined by inspection of the whole droplet, vary from the intrinsic contact angle, , due to roughness that is not macroscopically visible. (b) The Gibbs energy versus the contact angle for a droplet on a rough solid surface. Each minimum represents a metastable state attendant on a possible macroscopic contact angle. The global minimum is the most stable one. The lowest and highest possible contact angles are referred to as receding (RCA) and advancing contact angle (ACA), respectively. Adapted from ref. [83], Copyright 2009, with permission from Annual Reviews. the equilibrium conditions are fulfilled. However, only the global minimum gives the most stable state and refers to the most stable apparent contact angle, whereas all other minima are metastable states.[89]

2.2.2.4 Homogeneous and heterogeneous wetting As described in section 2.2.2.3, roughness impacts the macroscopic shape of a liquid droplet, which can be measured by the macroscopic apparent contact angle. This was first considered by R. Wenzel in 1936, who evolved a geometrical model based on the roughness factor, , the ratio between the actual surface area and the projected surface area of a rough solid surface.[90] In this model, the liquid completely wets the whole surface (Figure 2.8). This homogeneous wetting state is referred to as Wenzel state. The apparent Wenzel contact angle, , can be calculated by:[90]

. (2.12)

21 Chapter 2

Figure 2.8. Illustration showing the homogeneous wetting on a rough surface by Wenzel model. is the apparent Wenzel contact angle and is the projected surface area that is utilized for the calculation of the roughness factor of Eq. 2.12.

Figure 2.9. Illustration showing the heterogeneous wetting state on a rough surface by Cassie- Baxter model. is the apparent Cassie-Baxter contact angle, is the fraction of the projected area of the solid surface that is wet by the liquid, and is the roughness ratio of the wet area.

Consequently, surface roughness enhances ( ) or decreases ( ) the wettability. Although these tendencies are generally observed, the Wenzel model does not include pinning effects or boundary conditions concerning the size of the surface features compared to the droplet diameter. Furthermore, the model is physically not valid for very rough hygrophobic surfaces ( ) predicting a total drying of the surface due to .

On intrinsically hygrophobic solids, the attraction of the liquid to the solid is much lower than to intrinsically hygrophilic one. Hence, the surface tension may dominate the system, which forces the droplet formation of the liquid. Thus, the liquid does not conform anymore to the solid surface and is sustained at the top of the surface features, while air pockets are simultaneously formed underneath the liquid.[91] This heterogeneous wetting state is referred to as Cassie or fakir state (Figure 2.9).[92] The apparent Cassie-Baxter contact angle, , for a flat-topped surface can be calculate by:[89]

, (2.13)

22 Fundamentals

Figure 2.10. Relationship between the intrinsic contact angle and the apparent contact angle regarding the two models of wetting on textured surfaces (Eqs. 2.12 and 2.13). At the point of intersection ( ) a transition from the heterogeneous to the homogeneous wetting state takes place. in which is the fraction of the projected area of the solid surface that is wetted by the liquid, and is the roughness ratio of the wetted area.

In sum, both models describe the influence of the surface roughness concerning the wetting characteristics. The complete, homogeneous wetting is described by the Wenzel model where the liquid wets the entire asperities of the rough surface and forms a continuous and homogeneous liquid-solid interface. In turn, a heterogeneous wetting is described by the Cassie model where the liquid is sitting atop the asperities, trapping air below inside the grooves.

As seen above, there are two possible states when a liquid contacts a rough surface, i.e. the homogeneous and the heterogeneous wetting state. The relationship between the intrinsic contact angle and the apparent contact angle for these two states is plotted in Figure 2.10 according to the Eqs. 2.12 and 2.13 (the utilized surface texture corresponds to a pillar array exhibiting flat tops as depicted in Figure 2.8 and 2.9). The two curves intersect at the cosine of the critical angle where the transition from the heterogeneous to the homogeneous wetting state takes place. The transition criterion can be calculated by two dimensionless parameters, namely and (for ), which describes the surface topography:[93]

, (2.14)

23 Chapter 2

Figure 2.11. Droplets ( ) of (a) water ( ) in heterogeneous wetting state and (b) hexadecane ( ) in homogeneous wetting state onto (c) a fluorinated low-energy and textured surface ( ). Scale bar: . where with respect to the considered textured surface due to and . Thus, a heterogeneous wetting state is only achievable by means of a sufficient hydrophobic material ( ) and an appropriately chosen roughness, which was also experimentally proven by the Kao experiment.[94] Liquids with lower surface tensions than water have an intrinsic contact angle that is typically lower than even on low energy surfaces such as Teflon. Thus, low-surface-tension liquids usually wet a rough surface homogeneously that is demonstrated in Figure 2.11. For water on a fluorinated and textured surface one obtain a high apparent contact angle accompanied by a heterogeneous wetting state, while for hexadecane a low apparent contact angle was observed that correlates to the homogeneous wetting state.

2.2.2.5 Omniphobic surfaces In 2000, Herminghaus suggested a strategy for maintaining a heterogeneous wetting state also for low-surface tension liquids by implementation of surface features exhibiting overhangs, which inhibit the liquid penetration into the grooves of the surface roughness.[28] Thermodynamic analysis, have already confirmed that surface features with overhanging cross-sectional profiles can maintain a heterogeneous state even for

, which is referred to as omniphobicity.[95-99] Furthermore, experimental studies supports the geometrical concept of omniphobic surfaces and several types of engineered rough surfaces such as porous gold surfaces,[100] certain polymer[101] or silicon oxide[102] structures, fiber mats,[30,103,104] fabrics,[105,106] pillar structures,[29,30,107-111] or hierarchical structures[42,96] could be realized.

However, omniphobicity in natural surfaces is rare, but some attention should be drawn to springtails (Collembola) (Figure 2.12a). The skin of these animals exhibits omniphobicity that enables the formation of stable air layer (called physical gill or

24 Fundamentals

Figure 2.12. (a) Springtail colony of O. stachianus. (b,c) Plastron surrounding the entire animal upon immersion into (b) water and (c) olive oil. Scale bars: 1mm. Adapted with permission from ref. [146], Copyright 2013, American Chemical Society. plastron),[15,112,113] upon immersion into water (Figure 2.12b) and even into many low-surface-tension liquids such as oil (Figure 2.12c) or ethanol.[32] The plastron formation protects these skin breathing animals against suffocation in their often rain- flooded habitat. Furthermore, it was found that these plastrons show a high resistance against collapse at elevated hydrostatic pressures.[32] The origin of this exceptional wetting resistance is based on the hierarchically aligned micro- and nanostructures of the skin surface, although a quantitative theoretical elaboration is still missing.

2.2.2.6 Stability of the heterogeneous wetting state – The wetting resistance By definition, the wetting transition is an abrupt change, spontaneous or induced by external stimulus, in the wetting properties of a flat or rough solid surface.[114] Concerning rough surfaces, it was found that the heterogeneous wetting state is a metastable state, which can be irreversible transferred to the homogeneous wetting state.[92,115] Thus, beyond predicting the existence of the heterogeneous wetting state, [89] the stability against an enforced wetting transition and the dynamics of this process are of great interest, in particular, in technological applications.

In principle, there exist two distinctive transition scenarios: (i) the sag transition and (ii) the depinning of the triple line (Figure 2.13).[116] Both scenarios can be induced by external stimuli such as droplet gravity, applied hydrostatic pressure, droplet impact, droplet evaporation, electrical fields, and vibration of droplets.[117] The sag transition occurs, if the liquid-air interface sags between the asperities and touches the bottom of the grooves. The triple line remained pinned at the top edge of the asperities; while the fluid interface exhibits an increasing convex curvature (pressure inside the liquid is higher than the pressure of the surrounding air). When this distance between apex and baseline becomes greater than the height of the roughness features, the liquid touches

25 Chapter 2

Figure 2.13. Transition from heterogeneous to homogeneous wetting state due to (a) sagging of the fluid interface or (b) depinning of the triple line and advancing inside a cavity along the side walls. the bottom (Figure 2.13a). This described transition process can be inhibited by raising the height of the asperities, so that the sagged interface cannot reach the bottom of the rough surface. However, the transition then may occur due to depinning of the triple line that leads to a liquid invasion into the grooves and simultaneously the collapse of the air cushion (Figure 2.13b). The transition due to depinning can be viewed as a process in which the work done by external forces is greater than the energy barrier between the Cassie and the Wenzel state.[116]

However, the Cassie-Wenzel transition, in particular, the transition dynamics is not completely understood and several aspects for future investigations aroused:[117]

- Impact exerted by the surface topography, in particular, cross-sectional profiles of the asperities and hierarchical assembled surfaces. - Impact of the surface chemistry: intrinsically hygrophilic or hygrophobic surfaces. - Experimental studies of the triple line dynamics during the wetting transition. - Study of wetting transition for various organic liquids. - Development of a theoretical threshold criterion of the Cassie-Wenzel transition. - Development of surfaces exhibiting highly stable Cassie states.

2.3 Imprint lithography – Patterning by molds

Rapid advancements in micro- and nanomanufacturing have enabled scientists and engineers to fabricate biomimetic functional surfaces using a broad spectrum of synthetic materials. In particular, imprint lithography is one of the emerging lithography techniques of the last decades and, since 2003, it is permanently part of the International

26 Fundamentals

Figure 2.14. Scheme of the imprint process flow: (a) imprint, (b) de-molding, and (c) residual layer etch.

Technology Roadmap for Semiconductors (ITRS).[118] Differing from well-established optical or electron beam lithography, imprint lithography is a mechanical patterning technique, transferring the texture of a pre-patterned mold to the precursor of a solid material such as mono-/oligomers, melted polymers or sol-gels (Figure 2.14).[119-122] Therefore, imprint lithography as a direct patterning technique that offers a number of advantages with respect to the optical and electron beam lithography:

- Direct patterning of a wide range of organic and inorganic materials by printing, embossing or molding with low cost and simplicity.[121,123] - The high resolution is not restricted by diffraction (optical lithography) or scattering effects (electron beam lithography).[120-122,124] - Beside binary patterns, 2.5D-patterns with multiple height levels and complex 3D-patterns can be directly replicated.[125,126] - High aspect (height-to-width) ratios are feasible.[121,127] - Hybrid techniques combining imprint lithography with optical or electron beam lithography are possible.[128,129] - Several substrate materials such as planar, curved, flexible and soft are feasible.[122,123]

However, one of the common problems of this technique is the residual layer, a thin film which connects the surface features, that requires optimization procedures of the imprint process to avoid undesired effects or post treatments such as residual layer etching

27 Chapter 2

(Figure 2.14c).[121] Further failures during the imprint process can be caused by incomplete filling of the mold cavities due to insufficient material displacement, voids due to entrapped air or shrinkage of the features during the solidification. All these aspects should be considered in order to obtain the best possible results and depend on the properties of the precursor material (viscosity, free surface energy,…), the properties of the mold material (gas permeability, surface free energy, elasticity,…), the process parameters (contact pressure, temperature, gas atmosphere,…), and the pattern itself (feature density, feature size, size variation,…).[121]

2.3.1 Particle replication in non-wetting templates

In 2005, DeSimone and co-workers developed an imprint technique, which is referred to as particle replication in non-wetting templates (PRINT).[130,131] The non-wetting templates are composed of a photochemically cross-linked perfluoropolyether dimethacrylate (PFPEdma) exhibiting a low free surface energy ( ⁄ ).[132] Furthermore, the cross-linked PFPEdma does only swell in fluorinated solvents, has high gas permeability and is optical transparent down to that allows for UV- crosslinking of the precursor material through the mold.[133,134] During the imprint process (Figure 2.15), a liquid precursor solution is placed between the fluorinated templates (mold and substrate), which are subsequently pressed together. The cavities of the pre-patterned mold are filled by the precursor, while the rest of the solution is forced to flow outward to the periphery due to the low surface free energy of the templates (capillary depression) and, thus, do not produce any residual layer. After cross-linking and removal, single particles can be harvested. The achievable resolution of this method was found to be about ,[132] which ensures accurate replication of master structures. Hence, PRINT has high potential for producing particles of different shape and size in a uniform size distribution and can be adapted to roll-to-roll processes for mass production.[135]

2.3.2 3D replication techniques

One of the advantage of imprint lithography is the feasibility to replicate three- dimensional structures, if the mold is flexible enough to enable de-molding of undercuts or overhangs.[136] In particular, the replication of complex shaped features (serially) made by two-photon lithography allows for rapid duplication and the transfer of the

28 Fundamentals

Figure 2.15. Scheme of the PRINT process flow: (a) imprint and (b) de-molding. The low surface energy of the fluorinated mold and substrate (green) confines the liquid precursor solution inside the cavities of the mold that allows for the generation of isolated particles. motifs into several materials. Therefore, the Fourkas lab has developed strategies to replicate such complex structures and even closed loops, for instance, by implementing a thin vertical membrane into the master structures, which allows de-molding and forms a reversible seal.[126] Subsequent infiltration of the mold by precursor fills the cavities of the mold, but excludes the site of the membrane.

A further approach to generate 3D structures was realized by utilization of two pre- patterned molds showing commensurate lattice parameters.[137] Therefore, the PRINT method was improved and expanded to generate a free-floating microarray, which afforded a chemical patterning of fluid interfaces without loss of the lateral arrangement of the entities (Figure 2.16). The developed fabrication process synergistically combined bottom-up (capillary assembly) and top-down (PRINT) microfabrication strategies for a spatially controllable integration of molecular entities into the macroscopic device (Figure 2.17).

29 Chapter 2

Figure 2.16. Scanning electron micrograph of the mesh structure featured by cross-shaped particles, which were modified by incorporation of silica colloids. The insert shows a section of the device. The corresponding EDX elemental (Si-K alpha line) mapping represents the lateral distribution of the incorporated silica particles (right). Reproduced from ref. [137], Copyright 2012, permission by The Royal Society of Chemistry.

Figure 2.17. Schematic illustration of the two-step fabrication process that can be varied

30 Fundamentals between a homogeneous (route A) and a heterogeneous (route B) modification. (a) Pre- patterned perfluoropolyether dimethacrylate (PFPEdma) template I. (b) Capillary assembly set- up. (c) Molecular entities inside the cavities of the pre-patterned template I. (d) Micro-pipette set-up. The grey arrows represent the path of the micro-pipette. (e) Several molecular entities (represented by different colours) addressed to different cavities. (f) Pre-patterned PFPEdma template II that has a commensurate lattice parameter regarding template I. (g) Face-to-face alignment of the pre-treated template I and template II after deposition of a the poly(ethylene glycol) diacrylate (PEGda) oligomer solution (spherical-shaped droplet). (h) Contact of both templates and subsequent cross-linking by exposing to UV-irradiation. (i) De-molding of the cross-linked device. (j) Homogeneously modified device. (k) Individually modified device. Reproduced from ref. [137], Copyright 2012, permission by The Royal Society of Chemistry.

2.3.3 Reverse imprint lithography

A further process scheme of imprint lithography is the reverse imprint lithography approach (Figure 2.18).[119] Here, a thin film of the precursor solution is first deposited onto the pre-patterned site of the mold and fills the cavities. Subsequently, the patterned film can be transferred (before or after cross-linking of the precursor film) to a certain substrate. This process also enables the fabrication of more complex structures by repetitive deposition steps of pre-cured structures.[138,139] Again, fluorinated templates known from PRINT can be utilized for direct patterning of functional devices such as optical planar wave guides by reverse imprint lithography.[125] The formation of a residual layer is inhibited due to de-wetting of the drop-wise deposited pre-polymer solution onto the pre-patterned mold. Thus, only the cavities of the mold were filled before printing without any connecting layer between the features. After (reverse) imprint, post-etching steps were not required. Thus, crucial parameters concerning the efficiency of an optical wave guide: shape, size, and side-wall roughness of the wave guide were not affected.

2.3.4 Imprint lithography in biomimetics

For imprint lithography, not only silicon-based master structures, but also natural templates can be used. Since, such templates are often complexly shaped, hierarchically assembled and fragile one needs certain requirements and optimizations to the replication process.[140] However, the replication of natural surfaces is often the only way to copy one-to-one their morphology into synthetic materials of defined bulk and surface chemistry. Such copies are not designated as biomimetics as explained in section 2.1, but can support the understanding of biological phenomena. Successful

31 Chapter 2 replication of various different hierarchically assembled biological templates such as plant leaves[140-142], insect corneas[143,144], or grasshopper wings[145] was recently demonstrated.

Figure 2.18. Scheme of the reverse imprint process flow: (a) deposition of the liquid precursor inside the cavities of the pre-patterned mold by doctor blade technique, (b) printing to the substrate, and (c) de-molding.

32

Chapter 3

Materials and methods

In this chapter, parts of the text and the figures are reproduced with permission from ref. [146], Copyright 2013, American Chemical Society (http://dx.doi.org/10.1021/la304179b) and with permission; from ref. [147], Copyright 2013, Nature Publishing Group (This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-nd/3.0/); and from ref. [148], Copyright 2014, John Wiley and Sons (http://dx.doi.org/10.1002/adma.201305408).

3.1 Animals

Orthonychiurus stachianus (Bagnall, 1939) and Folsomia candida (Isotomidae) were collected from the tropical greenhouse at the Dresden Botanical Garden. All necessary permits were obtained for the collection and no endangered or protected species were involved. Tetrodontophora bielanensis (Waga 1842) springtails were collected in the wooded mountains of Saxony near Dresden, south-eastern Germany. The animals were kept as laboratory colonies in large petri dishes using soil, litter, decaying wood and moss from their original habitat as food source and substrate. Petri dishes containing the animals were kept at 14°C and sealed with silicon to prevent escape and dehydration during breeding. Dishes were coated with gypsum mixed with chromite powder (20:1) to produce a water reservoir and porous substrate that maintained a convenient microclimate. Dark chromite powder was used to support the observation of the white, non-pigmented animals.[31,32,147]

33 Chapter 3

3.2 Replication of the springtail skin

3.2.1 Mold preparation

Individual animals were freshly prepared by freezing at - for immediately before mold preparation was started. The animal was ventrally dipped into perfluoropolyether dimethacrylate (PFPEdma) precursor solution Fluorolink MD700 ( , Solvay Solexis, Bollate, Italy) containing Irgacure 651 (CIBA, Basel, Switzerland) and mechanically fixed by exposing to UV-irradiation ( ) by DELOLUX 04 (DELOLUX 04, DELO, Windach, Germany) at each side. Next, perfluoropolyether dimethacrylate precursor solution Fomblin MD40 ( , Solvay Solexis) containing Irgacure 651 was applied dorsal onto the animal skin and exposed to vacuum of for to ensure infiltration of the entire skin by the precursor solution. Fomblin MD40 was cross-linked by exposing to UV-irradiation ( ) under nitrogen atmosphere. Subsequently, the cured elastomeric MD40 mold was gently peeled from the springtail skin. Representative SEM images of each step in the replication process flow are summarized in Figure 3.1.

3.2.2 Fabrication of faithful PEGda replicas – Route A

A poly(ethylene glycol) diacrylate (PEGda) precursor solution ( , Sigma–Aldrich, Deisenhofen, Germany) containing Irgacure 651 was cast onto the pre-patterned MD40 mold and exposed to vacuum of for . PEGda was cross-linked by exposing to UV-irradiation ( ) under nitrogen atmosphere. Subsequently, the PEGda polymer replica was gently peeled from the MD40 mold.

3.2.3 Fabrication of PEGda replicas without PGs – Route B

A high-viscous polydimethylsiloxane (PDMS) precursor solution Sylgard 184 (Dow Corning, Wiesbaden, Germany) was freshly mixed with the curing reagent in the ratio , cast onto the pre-patterned MD40 mold and exposed to vacuum of for . The residuary PDMS cross-linking took place at room temperature over two more days. The elastomeric PDMS replica was gently peeled from the MD40 mold and used as template for the preparation of a further MD40 mold that, in turn, was used to made PEGda polymer replicas using the same procedure as described above in route A.

34 Materials and methods

3.2.4 Surface treatment

For Teflon-AF-coating, the PEGda polymer replicas were dipped ( ) into a solution of of amorphous fluoropolymer Teflon (Teflon AF, DuPont, Wilmington, DE, USA) diluted in a fully-fluorinated solvent FC-77 (3M, Haven, Belgium). After withdrawing, the replicas were dried ( ) on a hot plate at .

35 Chapter 3

Figure 3.1. Representative SEM images of each step in the replication process. Starting from the biological template T. bielanensis, the whole skin features were firstly captured by an elastomeric perfluoropolyether dimethacrylate (PFPEdma) mold 1 that, in turn, was the starting point for the fabrication of polymer skin replicas by two different routes. In route A, poly(ethylene glycol) diacrylate (PEGda) was used as a liquid pre-polymer. After cross-linking of the PEGda and subsequent de-molding, the polymer replicas possessed the entire superficial granular surface features but without any hairy structures with respect to the natural skin structure of T. bielanensis. In route B, polydimethylsiloxane (PDMS) was used as a liquid pre- polymer. The PDMS replica did not have nanoscopic primary granules and was used as new templates for making PEGda polymer replicas that also did not have primary granules via a new PFPEdma mold 2. Reprinted with permission from ref.[147], Copyright 2013, Nature Publishing Group (CC BY-NC-ND 3.0).

36 Materials and methods

3.3 Membrane manufacturing

3.3.1 Silicon master fabrication

Silicon master structures exhibiting two height-levels were fabricated using a lithography-etch-lithography-etch approach without any planarization steps for pre- patterned substrates. Wafer-stepper exposure with an PAS 550-250C (ASML, Veldhoven, Netherland) was used to fabricate structures with hole diameters below in a quadratic lattice with an overlay accuracy of the two layers below . The patterned area was for each structure type which was generated by 224 adjacent exposures for each lithographic layer. Contact lithography with a mask aligner 6200 (EVG, St.Florian am Inn, Austria) has been used to fabricate the structures with hole diameters above in a hexagonal lattice with an overlay accuracy of about . Herein, patterned field sizes were due to limited space availability on the used mask. The patterned resist layers served as etch-mask for reactive ion etch processes using an ASE System (STS, Newport, UK). Finally, after resist stripping, a 1H,1H,2H,2H-perfluorododecyltrichlorosilane (Sigma–Aldrich) anti-sticking layer has been applied to the silicon molds by molecular vapour deposition.[127]

3.3.2 Polymer feature replication

The silicon masters were used for casting a PFPEdma daughter mold as a negative of the master using Fomblin MD40 precursor solution containing Irgacure 651. The PFPEdma was crosslinked by exposing to UV-irradiation for under nitrogen atmosphere. For tone inversion, a second PFPEdma mold was cast from the daughter mold. Liquid poly(ethylene glycol) dimethacrylate (PEGdma) pre-polymer solution

( , Sigma–Aldrich) containing Irgacure 651 was applied onto the prepatterned PFPEdma mold. The excessive pre-polymer solution was removed using doctor blade technique. The pre-polymer was cured by exposing to UV-irradiation for under nitrogen atmosphere. The resulting polymer membrane was de-molded in dichloromethane (Merck, Darmstadt, Germany), rinsed in ethanol (absolute, VWR, Darmstadt, Germany), and transferred to a water-air interface. Finally, the membrane was immobilized by dipping a certain solid substrate, which was previously coated by Acronal 500D (BASF, Ludwigshafen, Germany) or a thinned Parafilm layer (Brand, Wertheim, Germany), into the water and carefully withdrawn.

37 Chapter 3

3.4 Contact angle goniometry

Smooth reference polymer films were used for determination of the intrinsic wetting characteristic of the used polymer material. Dynamic contact angle measurements were performed using a contact angle measurement system OCA 30 (DataPhysics Instruments, Filderstadt, Germany). Droplets ( ) of Milli-Q filtered water (Merck Millipore, Billerica, MA, USA) and hexadecane (Sigma-Aldrich) were applied to smooth polymer surfaces. The droplet was inflated and deflated ( ) to monitor the advancing and the receding contact angle, respectively. The static contact angle was estimated as ( ) where is the static contact angle,

is the advancing contact angle, and is the receding contact angle.

For determination of the skin wetting characteristics, small droplets ( ) of water and hexadecane were dorsally applied at the skin of T. bielanensis and its polymer replicas. Dynamic contact angle measurements of the Collembola skin and its polymer replicas were impossible due to the restricted sample area.

3.5 Immersion tests

Plastron collapse experiments were performed using a self-made setup that consisted of an optical microscope, a pump, a processing unit and chamber flooded either by water or hexadecane where the samples were previously placed (Figure 3.2). The liquid reservoir was linearly compressed (animals, animal replicas: - ; polymer membranes: - ) by increasing hydrostatic pressure and images were simultaneously recorded using an optical microscope unit. To minimize the influence of the gas solubility in water, the experiments were carried out at a water-air ratio of 10:1.

In long-term immersion tests, time-lap images were recorded without any increased hydrostatic pressure.

3.6 Rheology

The shear viscosities of the pre-polymers were determined using rotational rheometer ARES-G2 (TA Instruments, New Castle, DE, USA) in parallel plate regime at room temperature. The frequency was varied in the range between .

38 Materials and methods

Figure 3.2. Schematic illustration of the experimental setup for immersion tests that consists of an optical microscope, a water pump, a processing unit and a water-flooded chamber (cross- sectional view) where the samples (green) were previously placed. Insert 1 shows the plastron (air cushion) that was formed around T. bielanensis by a visible shiny appearance. The disappearance of the shine was observed in situ using an optical microscope while at the same time the hydrostatic pressure inside the aqueous phase was linearly increased. Insert 2 shows the animal after final plastron collapse. Scale bars: 1 mm. Adapted with permission from ref.[147], Copyright 2013, Nature Publishing Group (CC BY-NC-ND 3.0).

3.7 Wear testing

The wear tests were performed using a nano tribometer (CSM Instruments, Peseux, Switzerland). A steel ball (100Cr6) with the diameter of was brought in contact to the sample surface and pressed with a normal load that was stepwise increased until the surface features were damaged. Shear stress was generated by lateral oscillation of the probe: 10 cycles with a speed of and a maximal displacement of .

3.8 Electron microscopy imaging and focused ion beam preparation

Scanning electron microscopy studies were performed using a Gemini DSM 982 (Carl Zeiss SMT, Oberkochen, Germany). The animals were prepared by freezing and subsequent air-drying without any fixation. All samples were coated with platinum (BAL-TEC SCD 500, BalTec, Pfäffikon, Switzerland) to eliminate surface charging effects.

39 Chapter 3

Transmission electron microscopy studies were carried out using an EM 912 Omega (Carl Zeiss SMT, Oberkochen, Germany). The samples were fixed, stained and subsequently sliced into ultrathin sections as described in ref. [31,32]. The focused ion beam preparation was performed using a NEON40 Crossbeam (Carl Zeiss SMT, Oberkochen, Germany).

3.9 Numerical FEM-simulations

In addition to the analytical methods, numerical finite element method (FEM) simulations were performed to gain insight into the dynamics of the wetting transition process with respect to all cross-sectional profiles (skin sections and abstracted models), which are analytically discussed in this work.

In contrast to the analytical studies, the numerical simulations were carried out using a two-phase flow model. To remove singularities at the three-phase contact line, a diffuse fluid interface model was employed. It is based on a concentration field/phase field that ranges between in the bulk of the two fluids and varies continuously across the interface with finite thickness, as depicted in Figure 3.3. Thus, the interface is not sharp, but diffuse, which is a realistic assumption in nanoscopic systems.[149]

The concentration field/phase field is coupled to the Navier-Stokes equations for the fluid motion through extra stresses that mimic surface tension and is evolved by an advective Cahn-Hilliard equation that is equipped with boundary conditions that encode contact line information (e.g. equilibrium contact angle).

Figure 3.3. A dynamic contact line in a diffuse-interface framework. The phase-field variable, , represents the two fluid bulks by and the fluid-fluid interface by (solid line). The thickness of this interface is . The advancing of the three-phase contact line is characterized by the surface normal, the velocity and the intrinsic contact angle. Reproduced with permission from ref. [146], Copyright 2013, American Chemical Society.

40 Materials and methods

3.9.1 Sharp solid-fluid interface

Here, the diffuse fluid interface model is described by the phase field variable, , ranging between in the bulk of the two fluids, which was chosen for in the liquid phase and in the air phase. The diffuse interface model for mixtures of two immiscible and incompressible fluids inside a geometrical confinement exhibiting a sharp solid-fluid interface leads to the following Navier-Stokes-Cahn-Hilliard equations that have been considered by several authors:[150-153]

( )( ) ( ) (3.1) (3.2) (3.3) ( ) ( ( ) ) ( ) (3.4) Here , , are the velocity, pressure, chemical potential, respectively. The function

( ) ( ) is a double well potential, ( ), is a mobility constant and a scaled surface tension. Furthermore, the densities were set for the liquid phase ( ) and the air phase ( ) with a linear interpolation across the fluid interface. The viscosity was and the interface thickness . As boundary conditions a pressure difference was imposed between the top and bottom boundary which pushed the fluids downwards for . At the remaining boundaries the no slip condition was implemented. Furthermore, a contact angle condition, ( ), was specified to enforce the prescribed contact angle, where is the surface normal.

The system of equations was solved by an FEM with a semi-implicit Euler time stepping algorithm. The adaptive finite element toolbox AMDiS[154] was used for the discretization. AMDiS is freely available for research and teaching purposes and can be downloaded at http://www.simunova.com. The numerical results were compared to the analytical results using the determined curvature of the fluid interface and the position of the three-phase contact line for each time step. Thereby, the curvature was calculated by integrating across the interface.[155] √

3.9.2 Diffuse solid-fluid interface

The diffuse interface model inside a geometrical confinement exhibiting a diffuse solid- fluid interface afforded the simulation of more complex cross-sectional profiles such as

41 Chapter 3 the skin section of springtails.[156-158] To describe the geometrical confinement, a circumvents mesh generation of complex or curved geometries was utilized by embedding the complex domain in a larger, regular domain and reformulating the equations using an other phase-field function, , that approximates the characteristic function of the complex domain. Note, in this approach the phase-field function describes the diffuse solid-fluid interface. In this way, a cross-sectional profile can be obtained from experimental images (here taken from TEM images) and directly implemented to simulations after a transformation that sets in the domain occupied by the fluids, and at the solid with a smooth transition layer of size at the domain boundary. Consequently, the solid boundary is described by ( ) . In the figures of the numerical simulations the solid phase region ( ) were colored in black.

Now, the diffuse fluid interface is decribed by the concentration field variable, , which was chosen for in the water phase and in the air phase. The phase field varies rapidly but smoothly at the interface, where the transition layer has a finite thickness, . Again, this diffuse interface approach for mixtures of two immiscible, incompressible fluids lead to the Navier-Stokes-Cahn-Hilliard equations that have been considered by several authors, see e.g. refs. [150-153].

The resulting equations are the diffuse domain Navier-Stokes Cahn-Hilliard equations for simulating multiphase flows in complex geometries:[159]

( ) ( ) ( ) (3.5)

( ) (3.6)

( ) ( ) ( ( ) ) (3.7) ( ) ( ) (3.8) in . Here , , are the velocity, pressure, and chemical potential, respectively. The function ( ) ( ) is a double well potential, ( ), is a mobility constant and a scaled surface tension. Furthermore, we set the density , viscosity and the interface thickness of transition layers and

. As boundary conditions we imposed a hydrostatic pressure difference

between the top and bottom boundary, which pushes the fluids downwards for . At the remaining boundaries, we used the no slip condition . Furthermore, we specified a contact angle condition, ( ), to enforce the prescribed contact angle, .

42 Materials and methods

The system of equations was again solved by a finite element method with a semi- implicit Euler time stepping algorithm where the adaptive finite element toolbox AMDiS was used for discretization. For local mesh adaptation, we use an -like error indicator based on a jump residual (e.g. ref. [160] for and to maintain approximately 5 grid points across the transition layers).

43 Chapter 3

44

Chapter 4

Results and discussion

4.1 Replication of springtail skin

In this section, parts of the text and the figures are reproduced with permission from ref.[147], Copyright 2013, Nature Publishing Group (This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-nd/3.0/)

Springtails, wingless arthropods, are obviously well adapted to cutaneous respiration in temporarily rain-flooded habitats due to an unique omniphobic characteristic of the springtail skin (Figure 2.12).[32] The focus of this section was to decipher the origin of the omniphobicity concerning the several impacts of the distinct and hierarchically assembled surface features of the springtail skin. For this purpose, a tuneable nanoimprint replication process was developed to translate the cuticle ornamentation of T. bielanensis into polymer replicas. The obtained replicas could be precisely varied concerning the nanoscopic surface morphology and surface chemistry. To determine the wetting characteristics of the polymer replicas, static contact angle measurements and in situ plastron collapse tests upon complete immersion and at elevated hydrostatic pressures are performed in reference to the skin surface of T. bielanensis.

The representative scale levels of the hierarchically assembled skin of T. bielanensis are depicted in Figure 4.1. The entire body is de facto covered with nanoscopic primary granules that are joined by interconnecting ridges; together forming gas permeable nanocavities (mean diameter of about ), which are arranged in a comb-like pattern. Note that the skin at the bottom of these cavities has to be highly permeable to ensure the respiration through the skin.[72] TEM-sections of the skin revealed that the primary granules protrude above the ridges, thus, the nanocavities exhibit overhangs. At the microscopic scale, T. bielanensis possess papillose secondary granules that are

45 Chapter 4

Figure 4.1. Skin pattern of T. bielanensis (European giant springtail). The inserts represents SEM images of the several skin features of the hierarchically structured skin. The smallest elements are primary granules that are joined by interconnecting ridges and spatially arranged in a rhombic comb-like lattice. Transmission electron micrograph of a section through the skin shows a nanocavity (diameter ) that exhibits overhangs formed by adjacent primary granules. T. bielanensis possess papillose secondary granules and a limited number of thin bristles as secondary and tertiary structures, respectively. The secondary granules are completely decorated by primary granules excluding the smooth domes at the top of these papillae. Reprinted with permission from ref.[147], Copyright 2013, Nature Publishing Group (CC BY-NC-ND 3.0). completely decorated by primary granules excluding the smooth domes at the top of these papillae. Furthermore, the springtail skin possesses a limited number of thin bristles as a tertiary structure.

46 Results and discussion

Figure 4.2. Replication process flow and the contact angle measurements. (a) Schematic illustration of the sample preparation via replication of the natural skin of T. bielanensis. Two routes are feasible albeit distinctive regarding the nanoscopic morphology; Route A generates faithful polymer skin replicas with primary granules (PG), whereas route B leads to polymer replicas without primary granules. The material of the final replicas (in both routes) is poly(ethylene glycol) diacrylate (PEGda) a hydro and lyophilic polymer. In a further step, the surface chemistry is varied between untreated and Teflon-AF-coated polymer replicas. Scale bars: . (b) Determined static contact angles using droplets of water (black bars) as a polar liquid with high surface tension and hexadecane (white bars) as a non-polar liquid with low surface tension. Reprinted with permission from ref.[147], Copyright 2013, Nature Publishing Group (CC BY-NC-ND 3.0).

47 Chapter 4

The developed replication process is schematically depicted in Figure 4.2a (for more SEM images of each replication step, see Figure 3.1). Starting from the biological template, T. bielanensis, the whole skin features were firstly captured by an elastomeric perfluoropolyether dimethacrylate (PFPEdma) mold. The mold material has a high fluorine content ( ) that inhibited chemical cross-reactions with the biological template due to its chemical inertness.[144] The PFPEdma mold as the negative replica of the natural skin was then the starting point for the fabrication of polymer skin replicas by two different routes. In route A, poly(ethylene glycol) diacrylate (PEGda) was used as a liquid pre-polymer. After cross-linking and subsequent de-molding, the PEGda polymer replicas possessed the entire superficial granular surface structure of T. bielanensis but did not contain any bristles (Figure 4.3). In route B, polydimethylsiloxane (PDMS) was used as the liquid pre-polymer, which exhibited a significantly higher shear viscosity. The penetration of the more viscous PDMS pre- polymer into the smallest pores of the mold was nearly inhibited. This could be explained by the Washburn equation, which describes the penetration velocity, , of a liquid into capillary pores:[161]

, (4.1)

where is the atmospheric pressure, is the surface tension, is the Young contact angle, is the pore radius, is the shear viscosity and is the penetration distance. Consequently, larger pores of the mold such as secondary granules were filled faster than smaller pores such as primary granules. Furthermore, pores of the same dimensions

Figure 4.3. SEM images regarding the disappearance of the hairy structures. (a) Cross-sectional view of the perfluoropolyether dimethacrylate (PFPEdma) mold after peeling of the natural template T. bielanensis and fracturing with a thin bristle stuck inside. (b) The poly(ethylene glycol) diacrylate (PEGda) polymer replicas possessed the entire superficial granular surface features but without any bristles. The red arrows indicate the hair lines. Reprinted with permission from ref.[147], Copyright 2013, Nature Publishing Group (CC BY-NC-ND 3.0).

48 Results and discussion were filled faster by low-viscous liquids such as the PEGda pre-polymer ( ) than high-viscous liquids such as the PDMS pre-polymer ( ) due to the significantly higher shear viscosity. Additionally, the viscosity of PDMS has been continuously enhanced upon mixing of the PDMS precursor solution with the curing agent due to an immediate initiation of the cross-linking reaction, even at room temperature, which ultimately led to a down-regulation of the advancing PDMS front before the smallest pores of the PFPEdma mold were completely filled. Thus, the replicas of route B did not contain any nanoscopic primary granules and nanocavities. To finally end up with the same material as described in route A, the PDMS replicas were used as templates for making replicas from PEGda polymer via a second PFPEdma mold, which, of course, did also not contain any primary granules.

The cross-linked PEGda polymer is intrinsically hydrophilic, i.e. wettable by water. A second set of polymer replicas was produced according to route A and route B as described above but additionally coated by amorphous Teflon (Teflon AF). This fluoropolymer is intrinsically hydrophobic due to its low surface energy of about .[162] In sum, polymer skin replicas of similar chemical bulk composition were produced, but showed distinctive surface morphologies regarding the presence of the primary granules and distinctive surface chemistries.

The wetting of the generated polymer skin replicas was studied with contact angle goniometry using the skin of T. bielanensis, and smooth polymer films of the respective replica materials as references. Water was applied as a polar liquid with high surface tension ( ) and hexadecane as a non-polar liquid with low surface tension ( ). The results of the contact angle measurements are depicted in Figure 4.2b. The smooth films were used to determine the intrinsic contact angles, , of the polymer surfaces without any influences of the surface roughness reflecting the moderately hydrophilic ( ) and lyophilic ( ) behaviour of PEGda polymer. Teflon-AF-coated polymer surfaces were intrinsically hydrophobic ( ) and moderately lyophilic ( ). The contact angle data of the replica samples showed a clear correlation with the distinctive surface morphologies: Polymer replica surfaces containing primary granules produced contact angles considerably higher than with values up to for both test liquids, reflecting an omniphobic wetting performance irrespective of the polymer surface chemistry. In contrast, PEGda polymer replicas without replication of the nanoscopic surface morphology of the springtail skin were completely soaked by both test liquids

49 Chapter 4

Figure 4.4. Pressure resistance of the heterogeneous wetting state. (a) Plastron (air cushion) that was formed around T. bielanensis by a visible shiny appearance. Snap shots show the disappearance of the shine that was observed in situ using an optical microscope while at the same time the hydrostatic pressure inside the aqueous phase was linearly increased. Finally, the shine around the animal is disappeared after the plastron collapse at the breakthrough pressure . Scale bars: 1 mm. (b) Determined breakthrough pressures that provide the robustness of the Cassie state a priori of the set of polymer skin replicas in reference to T. bielanensis. Adapted with permission from ref.[147], Copyright 2013, Nature Publishing Group (CC BY-NC-ND 3.0). resulting in macroscopic contact angles of about . Teflon-AF-coating of the latter replicas afforded water repellence, but were soaked by hexadecane.

Thus, T. bielanensis and its faithful polymer replicas exhibited an omniphobic wetting performance irrespective of their surface chemistry based on the Cassie state of the liquid exposed to the surface, i.e. a minimized liquid-solid contact area and a plastron underneath the liquid phase. The presence of such a plastron is obvious from its shiny appearance due to the total internal reflection of light at the liquid-air interface (Figure 4.4a). With elevated pressures the plastron structures gradually disappear, defining a measure for the Cassie-Wenzel transition of the respective surface structure. Plastron collapse tests were performed in situ to explore the robustness of the observed

50 Results and discussion

Cassie state of liquid in contact with T. bielanensis and the derived polymer replicas as described in detail in section 3.5. The pressure at which the plastron finally collapsed was defined as breakthrough pressure and the values are depicted in Figure 4.4b. The plastron formed around T. bielanensis collapsed at pressures of about . Nearly the same value was determined for the untreated, faithful PEGda polymer replicas with pressures of about . The breakthrough pressure values for the Teflon-AF-coated polymer replicas containing nanoscopic granules even exceeded those observed for the animals and were determined to . In contrast, the untreated PEGda polymer skin replicas without primary granules were readily soaked after dipping into the aqueous phase. Teflon-AF-coating of these structures enabled the formation of a plastron but resulted in a significantly lower hydrostatic resistance of about . Thus, the durability of the Cassie state clearly depends on both the nanoscopic morphology and the surface chemistry. The primary granules evolved by the springtail skin were found to afford the Cassie state even for intrinsically hydrophilic surfaces and the resistance against wetting at elevated pressures was enhanced by a factor of four when these replica surfaces were coated with Teflon AF. The barrier against complete wetting can, for example, effectively protect springtails against suffocation in rain, because the dynamic pressure of rain droplets, which is in the range from to ,[24] is smaller than the obtained barrier.

In sum, the experimental approach provides new insights into the structural and chemical origins of the protection of springtail skin against wetting: Contact angle goniometry and enforced wetting of a series of imprinted polymer replicas clearly identified the nanoscopic primary granules of the cuticle to play a decisive role in liquid repellence. Specifically, the overhangs of the nanoscopic granules were concluded to effectively retain air upon wetting, resulting in a solely structural wetting barrier even for liquids with low surface tension.

4.2 Analytical studies of the wetting resistance

In this section, parts of the text and the figures are reproduced with permission from ref. [146], Copyright 2013, American Chemical Society (http://dx.doi.org/10.1021/la304179b)

The objective of the following section is to analytically analyse wetting resistance of the springtail skin, which was experimentally obtained. In order to achieve this aim, an analytical theory was developed in section 4.2.1 to determine the breakthrough pressure, which a priori affords an evidence of the wetting resistance. Furthermore, the

51 Chapter 4 breakthrough phenomena canthotaxis and the Laplace breakthrough are defined. In section 4.2.2, the wetting resistance of real single cavities (based on transmission electron micrographs of O. stachianus) are analytically calculated and discussed. Therefore, polynomial fits are utilized for a detailed representation of the obtained sectional surface profiles. In section 4.2.3, abstracted model profiles with well-defined geometries are introduced and analytically analysed to develop a general design principle for the most robust surface features.

4.2.1 Analytical Theory

Different concepts are currently being used to describe wetting phenomena on solid surfaces. One common approach is referred to as “energy concept” that is mainly used to estimate equilibrium wetting states for certain three-phase (liquid-solid-gas) systems or to predict the existence of heterogeneous wetting states on rough surfaces. The Gibbs energy of the system is therefore analysed for minima in the energy function that correspond to possible heterogeneous and homogeneous wetting states on a certain rough surface.[89,99] Supposing a liquid droplet, these distinctive wetting states are associated to several macroscopic contact angles and contact angle hysteresis.[163,164] This means that the same droplet can have different shapes on the same solid surface regarding both wetting states.

In this work another approach is used, which is referred to as “pressure concept”.[24] This concept, in particular, allows for analytical determination of the wetting resistance, i.e. the robustness of the heterogeneous wetting state. Herein, based on an existing heterogeneous wetting state, the penetration of an expanding fluid into the micro- and nanoscopic grooves of rough surfaces is taken into account, until the homogeneous wetting state is achieved. Note that, both the pressure and the energy approach allow for the estimation of the wetting transition barrier. However, the pressure concept commonly allows for analytical access in cases of solid surfaces with complex shaped geometries; while the energy concept essentially requires numerical models.[165]

Experimentally, the expansion of the liquid front can be initiated by a continuously increasing hydrostatic pressure inside the applied liquid phase. The resistance against a pressure-induced wetting transition can be analytically described by the Laplace’s law (Eq. 2.6) supported by the Young’s law (Eq. 2.8). As mentioned in section 2.2.1.2, the Laplace’s law describes the pressure difference, , across a liquid-gas interface for a

52 Results and discussion

Figure 4.5. Illustration of two distinctive pressure-induced wetting transition phenomena. (a) Liquid phase sustained atop a circular cavity with the radius, , and geometrical edge angle, , of a conical cross-sectional profile with intrinsic contact angle, . (b-e) In both considered phenomena the liquid-air interface sags into the cavity due to continuously increasing hydrostatic pressure, , whereas the air pressure, , is kept constant. (b) In the canthotaxis case the critical pressure difference is achieved when the apparent contact angle, , of the sagging liquid-air interface becomes ( ) (Eq 2.11). (c) The three-phase contact line immediately slides downward the cavity side-wall (symbolized by arrows). (d) The critical pressure difference in the Laplace breakthrough phenomenon is achieved when the sagging liquid-air interface forms a semi-circular profile that corresponds to the minimal curvature radius, , which corresponds to the maximal Laplace pressure across the interface. (e) The liquid front inevitably breaks through (symbolized by arrows) by further increasing hydrostatic pressure. Reproduced with permission from ref. [146], Copyright 2013, American Chemical Society. certain interface curvature radius, , that is also connected to the intrinsic contact angle as will be shown below.

Figure 4.5 illustrates two distinctive pressure-induced wetting transition phenomena. In the initial situation (Figure 4.5a), a liquid phase is applied atop a circular cavity with the radius, , and geometrical edge angle, , of the conical cross-sectional profile.

Immediately after application, the liquid is sustained atop the cavity when . It is

53 Chapter 4 assumed that the volume of the liquid phase is sufficiently large compared to cavity radius. The curvature of the liquid-air interface inside the cavity has to be equal to the curvature of the liquid phase itself, which is very small. Consequently, the initial liquid- air interface inside the cavity is assumed to be planar and can be represented by (Eq. 2.6).

In formulating the wetting transition conditions and the breakthrough pressure, the solid surfaces are considered to be ideal (smooth, rigid, and chemically homogeneous) so that any contact angle hysteresis can be neglected and the intrinsic contact angle is the only independent variable. The edge angle, , is considered on the right hand side of the cavities. Furthermore, deformations of the liquid-air interface due to gravitational forces can be ignored due to considerably small dimensions of the cavity (cf. Figure 4.6) in comparison to the capillary lengths (Eq. 2.3), which are for water and for hexane.

A continuously increasing hydrostatic pressure, , inside the liquid phase induces a sagging of the liquid-air interphase into the cavity due to the sustained pinning of the three-phase contact line at the solid edge. The sagging interface has the shape of a spherical cap with a curvature radius, , that is given by

, (4.2) ( ) where is the distance between the three-phase contact line and the symmetry center of the cavity and is the apparent angle between the fluid interface and the horizon. For further simplicity, we assume that the expanding liquid front does not result in a compressed air reservoir inside the cavity ( ), which can be justified by the highly permeable cuticle of the skin breathing springtails.[72] Due to canthotaxis (section 2.2.2.2), the pinning of the three-phase contact line at the edge is maintained until achieves a maximal value that is described by a geometrical boundary condition (Eq. 2.11).[86,87] A further increase of the hydrostatic pressure results in a downward directed sliding of the three-phase contact line along the cavity side-wall, i.e. the breakthrough scenario that finally results in a homogenous wetting state.

With regard to the critical pressure difference that induces the breakthrough scenario two phenomena have to be distinguished:

The first phenomenon is referred to as canthotaxis breakthrough.[88] Here, the critical pressure difference directly corresponds to the geometrical boundary condition (Eq 2.11)

54 Results and discussion as illustrated in Figure 4.5b and 4.5c. The critical pressure difference can be calculated using Eqs. 2.6,2.11 and 4.2 and is denoted as breakthrough pressure, :

( ) . (4.3)

The other phenomenon is denoted to as Laplace breakthrough and is illustrated in Figure 4.5d and 4.5e. Here, the sagged liquid-air interface forms a semi-circular shape before the geometrical boundary condition (Eq. 2.11) is fulfilled. Thus, the semi-circular shape corresponds to the minimal achievable curvature radius as well as the maximal Laplace pressure across the interface. When the hydrostatic pressure inside the liquid phase still increases, the liquid front inevitably breaks through. The breakthrough pressure is determined by the Laplace law (Eq. 2.6) with :

(4.4)

and consequently depends only on the surface tension of the applied liquid and the cavity radius. In sum, the robustness of a heterogeneous wetting state can be determined either by the canthotaxis breakthrough (Eq. 4.3) or the Laplace breakthrough (Eq. 4.4).

The transition between both phenomena is given by the relation between , the intrinsic contact angle and , the edge angle:[88]

Canthotaxis effect: , (4.5)

Laplace breakthrough: . (4.6)

The previous approach illustrates the wetting transition for a conical-shaped cavity using the edge angle, . This angle further describes the slope of the cavity side-wall, which was constant ( ) in our first considerations. Note, that for more complex shaped cavities, such as discussed in section 4.2.2, the slope along the cavity side-wall may change, so that ( ). In general, the slope is given by the arctangent of the first derivative of the function that describes the side-wall profile.

4.2.2 Springtail skin

In Figure 4.6a the characteristic nanoscopic skin morphology of O. stachianus is depicted. The entire skin of the animal is similar to T. bielanensis covered by a comb structure. The primary granules are located at the intersections of the ridges that finally results in a

55 Chapter 4

Figure 4.6. Skin surface topography of the springtail O. stachianus. (a) Scanning electron micrograph reveals the nanoscopic skin ornamentation with granules at the intersections of the underlying comb structure. (b-e) Different sections through the skin, taken by transmission electron microscopy, show cavities with characteristic overhanging cross-sectional profiles. Scale bars: . Reproduced with permission from ref. [146], Copyright 2013, American Chemical Society. regularly arranged, but complex-shaped surface structure.[31,32,72,147] Cross-sectional images of this surface topography, taken by transmission electron microscopy, show different shapes of cavities probably by different sections through the cavities. However, all cavities exhibit overhangs at their top edges (Figure 4.6b-e). Two distinctive cavity shapes (Figure 4.6b and 4.6e) were analytically studied to get a first impression of their wetting performance, in particular, the pressure resistance against the wetting transition from the heterogeneous to the homogeneous wetting state. To get access to the distinctive shapes, the overhanging part of the side-wall profiles of these cavities were fitted with polynomials ( ) ∑ by measuring points using the open-source software ImageJ, v. 1.43.[166] The polynomial fits with the highest coefficient of correlation have been chosen for further analysis (applied with Origin, OriginLab, v. 8.6). The origin of the coordinate system was set to be at the bottom centre of each cavity. The cavity side-wall, which is depicted in Figure 4.6b, was fitted using a fourth degree

56 Results and discussion

polynomial where , , , and

. The polynomial is displayed as green line in Figure 4.7a and reflects the characteristic overhang of the cavity in the range with a point of inflection at in a height of . The cavity side-wall, which is depicted in Figure 4.6e, was fitted using a third degree polynomial where

, , and . Here, the characteristic overhanging part of the cavity is located in the range with a minimum at

, a maximum at and the point of inflection at in a height of (Figure 4.7d). The local slope along the side-wall of the cavity, , can be determined by the first derivative of the polynomial:

( ). (4.7)

The maximal slope along the fitted profiles are situated in the point of inflections that gives a negative slope ( ) for the first (Figure 4.7a) and a positive slope

( ) for the second profile (Figure 4.7d).

Considering an applied liquid phase atop the cavity, the Laplace pressures, , across the liquid-air interface in a heterogeneous wetting regime can be calculated by Eqs. 2.6, 4.2 and 4.7, which gives:

( ( )) ( ) . (4.8)

The calculations can be visualized by three-dimensional surface plots (Figure 4.7b and 4.7e) depending on the current -value of the three-phase contact point and the intrinsic contact angle, , where the characteristic shape of the plot depends on the profile polynomial. The plots are divided into a bright blue surface area for ( ) and a dark blue surface area for ( ) . The positive and negative Laplace pressures are related to convex and concave interface curvatures with an upward and downward- directed capillary net force, respectively. Between both areas equilibrium states with a planar liquid-air interface can be determined by:

( ( | ))

( ) (4.9)

when the derivative of the pressure is positive:

( ( )) ( ) | ( ( ( ))) (4.10)

( ( ) )

57 Chapter 4

The surface plot of the first considered profile (Figure 4.7b) shows that ( ) is only achievable for intrinsic contact angles higher than due to the maximum slope

( ) along the profile in the inflection point, according to Eq. 4.3. This means that applied liquids with concerning the solid surface immediately soak the cavity without any pinning along the cavity side-wall due to a continuously downward- directed capillary net force. On the other hand, a heterogeneous wetting state is achievable for all . The yellow line in the surface plot represents the maximum Laplace pressures, i.e. the breakthrough pressures, which represent the breakthrough barrier for . The low height of the cavity restricts the maximal achievable breakthrough pressure in such a real system due to the contact of the sagged liquid-air interface with the bottom of the cavity before the theoretical maximum occurs (see scenario A in Figure 4.7a and the red shaded region in Figure 4.7b). The contact with the bottom of the cavity would immediately result in a homogenous wetting state. The condition for a sagged liquid-air interface that does not contact the bottom can be given by ( ) ( ( ( )) ) . This means that the sagging height of the liquid-air interface with the curvature radius, , is smaller than the -value of the three- phase contact point. However, assuming water as applied liquid with a surface tension of about and an intrinsic contact angle of gives a pressure barrier of about (Figure 4.7c).

The surface plot of the second and more pronounced mushroom-like profile in Figure 4.7e shows that a pressure barrier against homogeneous wetting, i.e. a positive Laplace pressure maximum, exists for all intrinsic contact angles. There even exist two positive maxima for , however, the value of the first maximum (that is located before the point of inflection) is always higher than the second maximum (that is located after the point of inflection) due to the higher interface curvature in the first maximum. Therefore, the first Laplace pressure maximum can be considered as the actual breakthrough pressure. In contrast to the first considered profile above, the red shaded area (scenario A in Figure 4.7d), which represents the contact of the sagged liquid-air interface with the bottom of the cavity, does not cut out any values of the maximum Laplace pressure (yellow line in Figure 4.7e). On the other hand, the area that is enclosed by a dashed red line also represents physically invalid values. Here, for considered three-phase contact points the polynomial profile was touched or crossed by the corresponding virtual liquid-air interface more than one time, which typically occurs for a low as shown in scenario B in Figure 4.7d. For explanation, each pressure value

58 Results and discussion

Figure 4.7. Analytical calculations of the Laplace pressure across the liquid-air interface for certain positions of the three-phase contact point. (a,d) Polynomial fits (green line) of two cavity profiles of O. stachianus, taken by transmission electron microscopy ((a) cf. Figure 4.6b; (d) cf. Figure 4.6e). The blue curved lines schematically represent the advancing liquid front with different Laplace pressures, , across the interface. The scenarios A and B illustrate limitations given by the real system, for instance, A contact of the liquid-air interface with the cavity bottom and B physically invalid solutions. (b,e) Surface plot of the calculated Laplace pressure (Eq. 4.8) depending on the -value of the three-phase contact point and the intrinsic contact angle, . The bright blue surface area represents the solutions ( ) and dark blue surface areas the solution ( ) . The yellow and the black line represent the maximal possible Laplace pressure and the position of the polynomial inflection point, respectively. The red shaded areas A and the area that is encased with a dotted red line B represent physically invalid

59 Chapter 4 solutions. (c,f) Curves for different intrinsic contact angles that represent calculated Laplace pressures for hexane and water with surface tensions of and , respectively. The thick solid part of the curves represents the physically valid and relevant positive segments of the solutions. Reproduced with permission from ref. [146], Copyright 2013, American Chemical Society. corresponds to a certain curvature radius that is related with a certain virtual circle

( ) ( ) , with and as the coordinates of the circle center. Therefore, the invalid values can be found numerically in

( ) ( ( ) ( )) ( ( )) , by searching for that solve the equation in the here considered profile range for . The array of curves in

Figure 4.7f represents the calculated for certain values of , in particular, for hexane and water with surface tensions of and , respectively. To give some representative values, for an intrinsic contact angle of about 20° for hexane or 100° for water the maximal Laplace pressures are about and , respectively. Note, that the surface tension scales the value of the Laplace pressure but does not change either the shape of the surface plot nor the zero-crossing line for ( ) in the equilibrium state.

In sum, mushroom-shaped profiles, which were proven on springtail skin by TEM studies, often exhibit positive slopes along the profile as a structural requirement for a heterogeneous wetting state and showed a high-pressure resistance even for low- surface-tension liquids, which are in a good consistency with the experimentally determined pressure values in section 4.1.

4.2.3 Abstracted profiles

Three distinctive model profiles, which are illustrated in Figure 4.8, were studied in order to elucidate the wetting resistance of overhanging structures more clearly. The developed abstracted geometrical models are based on a transition from straight side walls to an abstract mushroom-like serif T-shape cross-sectional profile. This transition enabled a stepwise increase of the profile complexity. The maximum occurring slope (regarding the right part of the cavity) is for straight walls (Figure 4.8b), for T- shaped profiles (Figure 4.8c) and for T-shaped profiles with serifs (Figure 4.8d). The qualitative principles of the abstracted profiles and their increased resistance against wetting are illustrated in Figure 4.9. The values were calculated using surface tension of water, but the general trend is qualitatively similar for all liquids. A heterogeneous -

60 Results and discussion

Figure 4.8. Geometrical models based on nanoscopic surfaces structures of O. stachianus. (a) Simplified model surface: a comb structure consisting of hexagonally arranged cavities that is based on a scanning electron micrograph showing the nanoscopic springtail skin morphology (cf. Figure 4.6a); scale bar: . In the sectional view, a complex shaped profile with overhangs at the top edges suggests the shape of small granules. The maximum slope of the profile is depicted by that is higher than . The current diameter of the applied liquid front inside the cavity is given by . (b-d) Geometrical abstraction of the complex shaped profile into cavities with (b) straight walls where and the diameter is , (c) T-shaped profiles where and the diameter is and (d) T-shaped profiles with serifs where , the diameter is and the width of the serif is . Reproduced with permission from ref. [146], Copyright 2013, American Chemical Society. wetting state in the case of straight walls is only achievable for intrinsic contact angles higher than (Figure 4.9a). T-shape profiles with a maximal slope of can already resist a full wetting against liquids that adopt intrinsic contact angles close to

(Figure 4.9b). There exists a transition at between the canthotaxis and the

Laplace breakthrough according to Eq. 4.5 and 4.6. For the breakthrough pressure scales only with the surface tension, , of the applied liquid and inversely proportional with the cavity radius, , regardless of the intrinsic contact angle. On the other hand, the pressure resistance sinks for with decreasing . In a real system, which exhibits a maximal slope of , it may occur that for very small intrinsic contact angles the breakthrough barrier is small enough to be overcome by pressure fluctuations such as acoustical or mechanical vibrations, which would result in an insufficient resistance against wetting. Consequently, the resistance of T-shaped profiles is less robust for very small intrinsic contact angles. A further extension of pressure resistant sectional profiles are serif T structures (cf. Figure 4.8d) that exhibit a maximal slope of . In a first consideration, we assume that the width of the serif, , is rather small compared to the radius of the cavity, , that gives . The breakthrough pressure has the same value for all due to the effect that the maximum Laplace pressure will always occur when the liquid-interface forms a semicircular shape corresponding to the Laplace breakthrough (Figure 4.9c). Thus, the T-shaped profiles

61 Chapter 4

Figure 4.9. Contour plot of calculated breakthrough pressures, , displaying the resistance against wetting transition for three distinctive types of model structures (cf. Figure 4.8b-d). Calculations were performed for water ( ) and depend on cavity diameter, , and intrinsic contact angle, . (a) Cavity with straight side-walls. The wetting transition occurs as canthotaxis breakthrough (Eq. 4.3 and 4.5). (b) Cavity with T-shaped sectional profile. The wetting transition occurs for as canthotaxis breakthrough (Eq. 4.3 and 4.5) and for as Laplace breakthrough (Eq. 4.4 and 4.6). (c) Cavity with serif T-shaped sectional profile under consideration that the serif width is much smaller than the diameter of the cavity. The wetting transition occurs as Laplace breakthrough (Eq. 4.4 and 4.6). Reproduced with permission from ref. [146], Copyright 2013, American Chemical Society. with serifs provide a stable heterogeneous wetting state irrespective of the solid and liquid chemistries for small cavity dimensions.

Further analysis were performed to gain a closer look into this type of profile. We chose spatial dimension of such a T-shaped profile with serifs similar to what has been found on the springtail skin. Thus, the distance was chosen to be (Figure 4.10a). The height of the serif inside the cavity is considered to be higher than to inhibit the contact between the sagged liquid-air interface and the bottom of the cavity before the maximal Laplace pressure occurs. The surface plot in Figure 4.10b does not display any negative values of the Laplace pressure that indicate a pressure barrier against homogeneous wetting for all , according to the displayed results in Figure 4.9c. However, the surface plot exhibits a discontinuity along the profile at the first and the second pinning position of the three-phase contact line, i.e. the front and rear edge of the serif, respectively. After depinning at the front edge, the three-phase contact line is sliding between both edges with decreasing liquid-air interface curvature. Consequently, the maximal Laplace pressure for each is located either on the front or on the rear edge. The array of curves in Figure 4.10c for certain shows that the maximal Laplace pressure for , and is already achieved at the front edge whereas for the

62 Results and discussion

Figure 4.10. Analytical calculations of the Laplace pressure across liquid-air interface for a serif T- shaped profile with ⁄ ratio of . (a) Sectional profile of the serif T-shaped structure. The blue curved lines schematically represent the advancing liquid front with different Laplace pressures, , across the interface. The scenario C illustrates a physical limitation given by the contact of the liquid-air interface with the inner cavity side wall. (b) Surface plot of the calculated Laplace pressure (Eq. 4.8) depending on -value of the three-phase contact point and the intrinsic contact angle. The yellow and the black line represent the breakthrough pressure and the position of the rear edge of the serif, respectively. (c) Curves for different intrinsic contact angles that represent calculated Laplace pressures for hexane and water with surface tensions of and , respectively. Reproduced with permission from ref. [146], Copyright 2013, American Chemical Society. maximal Laplace pressure is achieved in the second pinning position on the rear edge. The condition (Figure 4.11) that defines the position of the global pressure barrier for each depends on the ratio of serif width, , and cavity radius, , and can be calculated

63 Chapter 4

Figure 4.11. The ratio of serif width to cavity radius that determines at which serif edge the breakthrough for different intrinsic contact angles occurs. For contact angles higher than 90° the breakthrough occurs always on the front edge. Reproduced with permission from ref. [146], Copyright 2013, American Chemical Society.

⁄ by ( ⁄ ) ( ( )). This condition evolves for from the comparison of the minimal curvature radius on the front edge, which is

⁄ , and on the rear edge, which is . For the maximum pressure ( ) occurs always on the front edge. Consequently, for the maximal Laplace pressure occurs at the front edge for and at the rear edge for . In sum, T- shaped profiles with serifs enable a heterogeneous wetting state irrespective of the solid surface chemistry and even of the liquid surface tension. Varying lateral dimensions of the serif structure, represented by different ratios ⁄ , will not change its overall behavior due to the remaining qualitative shape of the surface plot in Figure 4.10b. For instance, a T-shaped profile that is given in Figure 4.10a can resist a homogeneous wetting up to for hexane ( ) and an arbitrary chosen intrinsic contact angle of only .

Taken together, it was found that the Laplace breakthrough (in contrast to the canthotaxis breakthrough) is irrespective to the intrinsic contact angle, i.e. the solid material parameter, and depends only on the lateral cavity dimensions and the surface tension of the applied liquid. In particular, the T-shaped profile with slim serifs exhibited a more robust wetting resistance for intrinsic contact angles smaller than , contrary to often discussed T-shaped profiles.[29,30,99,107,108] There is no sense to increase the maximal slope higher than , which may lead to a snail profile at the cavity edge, due to the already obtained robust heterogeneous wetting state of serif T structures for all intrinsic contact angles that can be only overcome by Laplace breakthrough. Consequently from the topographical point of view, a further improvement of the profile shape for a higher wetting resistance may not be achievable.

64 Results and discussion

4.3 FEM-simulation of the enforced wetting dynamics

In this section, parts of the text and the figures are reproduced with permission from ref. [146], Copyright 2013, American Chemical Society (http://dx.doi.org/10.1021/la304179b) and with permission from ref.[147], Copyright 2013, Nature Publishing Group (CC BY- NC-ND 3.0, http://creativecommons.org/licenses/by-nc-nd/3.0/).

The numerical simulations were performed to consolidate the experimental (section 4.1) and analytical (section 4.2) data obtained from the enforced wetting transition. To simulate the dynamics of the observed transition, a diffuse interface approach for two phase flows in complex geometric confinements is utilized. As boundary conditions, a hydrostatic pressure difference between the top and bottom boundary was imposed, which pushed the fluids downwards for , similar to the experimental setup. Furthermore, the considered solid phase fields were kept open at the bottom to focus on the impact of the geometric parameters of the solid surface by neglecting the effects of trapped air inside a closed cavity.

4.3.1 Single cavities

Figure 4.12 illustrates the dynamics of the pressure-induced wetting transition inside single cavities with different cross-sectional profiles and an intrinsic contact angle of by certain characteristic intermediate steps, which do not necessarily correspond to the same time steps in the different simulations. Step 1 is characterized by a concave fluid interface with a downward-directed capillary net force that leads to an initial partial filling of the cavities by the applied liquid. Step 2 shows the planar interface in equilibrium state inside the cavity. Step 3 represents the maximal achievable curvature of the fluid interface corresponding to the maximal Laplace pressure, i.e. the breakthrough pressure. Step 4 shows the advanced wetting that would finally result in a filled cavity, i.e. the homogeneous wetting state. Obviously, all previously considered profiles with overhangs can sustain a heterogeneous wetting state on hydrophilic solid surfaces. Only the cavity with straight walls without any overhang was immediately soaked by the applied liquid phase. Furthermore, the dynamics for intrinsic contact angles in the range of 10° to 120° in steps of 10° were computed concerning the presented profiles. The breakthrough scenario was again defined as the moment where the highest positive curvature of the sagged fluid interface was achieved. Thereby, the curvature

65 Chapter 4

Figure 4.12. Numerical simulations displaying the pressure-induced wetting transition dynamics inside cavities with different cross-sectional profiles and an intrinsic contact angle of . Each panel consists of a scheme on the left hand side, which illustrates the advancing of the sagging liquid-air interface, and certain characteristic intermediate steps (that do not necessarily correspond to the same time steps in the simulations) on the right hand side. Step 1 shows the initial partial filling of the cavities by the applied liquid. Step 2 reveals the planar interface in equilibrium state inside the cavity. Step 3 represents the maximal achievable curvature of the fluid interface corresponding to the maximal Laplace pressure, i.e. the breakthrough pressure. Step 4 shows the advanced wetting that finally results in a filled cavity. (a) Natural mushroom profile that corresponds to polynomial in Figure 4.7d. (b) Cavity with straight side-wall profile that was immediately wetted without any applied pressure. (c) Cavity with T-shaped sectional profile. (d) Cavity with serif T-shaped sectional profile with ratio of serif width to cavity radius of 0.5. Reproduced with permission from ref. [146], Copyright 2013, American Chemical Society.

was calculated by integrating across the interface.[155] The determined √ normalized curvatures are plotted along with the analytical results in Figure 4.13. The pressure-induced resistance against a wetting transition significantly depends on the

66 Results and discussion

Figure 4.13. Maximally determined interface curvature (normalized) by numerical simulations (scatters) and analytical calculations (lines) for different cross-sectional profiles (cf. Figure 4.12) depending on the intrinsic contact angle. These curvatures directly correspond to the maximal achievable Laplace pressure, i.e. the breakthrough pressure. Reproduced with permission from ref. [146], Copyright 2013, American Chemical Society. type of profile. The highest resistance, particularly in case of a low , is achievable using T-shaped profiles featuring serifs, which is in line with our analytical results. Structures with straight walls afford a heterogeneous wetting state for intrinsic contact angles higher than . The robustness of such type of structure increases with increasing , but is always lower than the robustness of structures with overhangs such as the mushroom structures and the sans-serif and the serif T structures. In particular, sans- serif and serif T structures exhibit the same robustness for , which is determined by the Laplace breakthrough. The overall trend is similar for both the numerical and the analytical approach with the exception of some minor differences due to distinctive assumptions of the fluid interface dimensions. Considering a sharp water-air interface with a thickness approaching zero, the three-phase contact line is sustained at the edge until Eq. 2.11 is fulfilled. However, the interface in the numerical approach is not sharp, but has a certain thickness in contrast to the analytical approach. This suggests that the pinning of the three-phase contact point is not located at a certain point of the edge on the profile but is rather advancing around the edge during the “pinning event”: A diffuse interface (Figure 3.3) between two phase fields, , with bulk values of that has a finite thickness, , and a phase field gradient, , does not stay in a certain point during pinning at the edges, but is rather advancing around this edge while the phase field gradient passes by the edge. In other words, the pinning of such an interface starts when the front side of the interface reaches the edge and comes to an end when the backside of the interface leaves the edge. Consequently, the spatial position of the fluid-

67 Chapter 4

Figure 4.14. Advancement of diffuse interface around sharp edge. (a) In the diffuse interface model the advancing fluid interface with the finite thickness, , is moving around a sharp edge. In the breakthrough scenario the base diameter of the sagged fluid interface is broadened by the term compared to the diameter at the edge. The intermediate step 1 and 2 represent the start of the pinning and the minimal interface curvature, respectively. (b,c) The contour plots of the interface (range of : -0.95, -0.75, -0.5, -0.25, 0 (blue solid line), 0.25, 0.5, 0.75, 0.95) are given for both intermediate steps in the numerical simulations and the intrinsic contact angles, , of (b) and (c) . (d) The diffuse interface model in combination with sharp edges behaves like a sharp interface model advancing along a rounded edge. Reproduced with permission from ref. [146], Copyright 2013, American Chemical Society. fluid interface ( ) varies during the pinning and depends on the interface curvature and the interface thickness (Figure 4.14a-c). In particular, this results in a broadening of

68 Results and discussion the bases diameter of the maximal sagging interface before breakthrough by the term

:

⁄ , and from to , (4.11)

with the finite thickness of the interface, √ ,[155] and the intrinsic contact angle, . Thus, the broadening effect has a direct influence on the maximal achievable interface curvature that leads to lower pressure resistance compared to the analytically determined values (Figure 4.13). Consequently, the local position of the three-phase contact point varies close to the edge and has a direct influence on the maximal achievable interface curvature. This effect becomes, in a qualitative manner, realistic for real nano- and microscopic structures that do not have ideally sharp edges (Figure 4.14d).[88]

4.3.2 Hierarchically patterned surfaces

In the previous sections of this chapter, it was discussed that the wetting characteristics of the springtail skin is strongly influenced by its particular nanotopography, which forms an effective barrier against homogenous wetting due to their mushroom-shaped cross-sections. Nevertheless, the springtail cuticle is hierarchically assembled, as obvious from Figure 4.1. The aim of this section is to clarify the influences of the secondary granules, which are completely covered by the nanotopography, with respect to the dynamic of the enforced wetting transition. Therefore, the nanoscopic patterned groove between two adjacent secondary granules was particularly considered. Furthermore, the two-dimensional numerical simulations were based on a complete diffuse interface approach (diffuse fluid and solid-liquid interface; see section 3.9.2) that affords simulations of more complex cross-sectional profiles. Similar to the experimental setup in section 4.1, both hydrophilic ( ) and hydrophobic ( ) surfaces were considered in the simulations. Figure 4.15 illustrates the initial situation and the Cassie- Wenzel dynamics with a few transition states. Neglecting gravity and assuming that the length scale of the surface roughness remains below the capillary length of the applied aqueous phase, the fluid interface between the water and the plastron can be considered as approximately planar in the equilibrium state ( ). Starting the experiment by continuously increasing the hydrostatic pressure, the three-phase contact line was found to propagate downwards until the edges of the first overhangs were

69 Chapter 4

Figure 4.15. Numerical FEM simulations to explore the dynamics of the Cassie-Wenzel transition. On the left hand side, a sectional view through secondary granules that are either decorated by primary granules or not and the initial position of the fluid interface is schematically represented. On the right hand side, numerical results are presented by snap shots from left to right that display the advancing liquid front (blue) displacing the plastron (white) inside certain complex shaped solid phase fields (black). Both hydrophilic ( ) and hydrophobic ( ) surfaces were considered. The hydrostatic pressure difference between the top and bottom boundary was imposed as boundary conditions, which pushes the fluids downwards for . Adapted with permission from ref.[147], Copyright 2013, Nature Publishing Group (CC BY-NC-ND 3.0). reached. At these edges, the three-phase contact line became pinned due to canthotaxis.[86,88] Further elevated hydrostatic pressures resulted in sagging of the water-air interface into the groove between the secondary granules due to the sustained pinning of the three-phase contact line at the edges. When the expanding water-air interface approached the next adjacent primary granules the fluid front jumped over without soaking the nanocavities in between the primary granules. The liquid front discontinuously penetrated the microscopic groove between the secondary granules in discrete slip-stick steps that resulted from pinning and sag-transition phenomena. The observed dynamics was similar for hydrophilic and hydrophobic surfaces. In both cases, nanoplastrons remained stuck inside the nanocavities. The remaining nanoplastrons formed the last barrier against complete wetting of the solid surface. The dynamics of the

70 Results and discussion

Figure 4.16. Recovery effect in Cassie-Wenzel transition. (a) Numerical FEM-simulations exploring the dynamics of the recovery effect in Cassie-Wenzel transition. On the left side, a cross-sectional view through secondary granules that are decorated by primary granules and the initial position of the fluid interface is depicted. On the right hand side, numerical results are presented by snap shots from left to right that display the advancing liquid front (blue) displacing the plastron (white) inside the complex shaped solid phase fields (black). Both hydrophilic ( ) and hydrophobic ( ) surfaces were considered in the simulations. As boundary conditions, the hydrostatic pressure difference between the top and bottom boundary was imposed, which pushed the fluids downwards for and upwards for . (b) In situ plastrons collapse tests were performed for a certain sample in consecutive cycles. For each cycle displayed in individual rows, the final hydrostatic pressures were increased. The left hand column represents an optical micrograph of the initial skin tint of T. bielanensis. In the middle column the left hand optical micrograph of each row shows the plastron (air cushion) by a visible shiny appearance that is immediately formed around T. bielanensis after immersion in water. The right hand optical micrograph shows the residual plastron at the highest hydrostatic pressure for certain cycle. The right hand column represents optical micrograph of the typical skin tint after release from the sample chamber. Scale bars: . Adapted with permission from ref.[147], Copyright 2013, Nature Publishing Group (CC BY-NC-ND 3.0). final transition step was considered in detail in section 4.3.1. In sum, the evolved hierarchical topography of springtail skin caused wetting to occur as a two-stage Cassie-

71 Chapter 4

Wenzel transition process, where the advancing liquid front penetrated the microscopic grooves between adjacent secondary granules before the remaining plastrons inside the nanocavities collapsed. In the absence of overhangs the Cassie-Wenzel transition was found to occur in one step without remaining nanoplastrons (see lower panel in Figure 4.15) and occurred - as observed experimentally in section 4.1 - immediately for hydrophilic surfaces and at an elevated pressure for hydrophobic surfaces.

Furthermore, in the simulations it was found that the described disappearance of the plastron inside the microscopic grooves was reversible also for both hydrophilic

( ) and hydrophobic ( ) surfaces. The numerical results are displaced in

Figure 4.16a. In the first regime, the hydrostatic pressure was greater than zero ( ) and the upper fluid phase penetrated the groove between adjacent secondary granules as described above. In the second regime, the hydrostatic pressure was varied to negative values ( ). Consequently, the penetration of the grooves stopped and the fluid flowed in reverse until the grooves were completely de-wetted. The nanocavities formed by adjacent primary granules were not soaked by either the advancing or receding fluid front for the considered set of contact angles in both regimes.

Experiments were considered to prove the reversibility of the denoted first transition step before the final transition leads to the entire wetting of the surface. The experimental results are displaced in Figure 4.16b. The in situ plastrons collapse tests were performed for a certain sample in consecutive cycles. The final hydrostatic pressures were increased for each cycle. Between the cycles, the samples were always released from the water-flooded chamber and characterized by optical microscopy. It was found that at elevated pressures, up to values of about the enforced wetting of the natural skin of T. bielanensis is reversible by a fully de-wetted state upon pressure reduction. After release, the skin regained the same greyish colour as prior to the plastron collapse test. Increasing the pressure in the second cycle up to values of about induced a partial wetted surface distinguished by a brownish colour and a few confined areas where plastrons remained. After release, the plastron regions were still spanned by an aqueous film and did not de-wet, so that the shiny appearance of the plastron due to light reflection was still observable. In third and last cycle, the hydrostatic pressure was increased until the final remaining plastrons collapsed and the natural skin surface was completely soaked. After release, the skin had a uniform brownish colour shade.

72 Results and discussion

In sum, the enforced wetting transition from heterogeneous to homogeneous wetting state at elevated pressures was observed to occur as a stepwise process, enabling a reversible partial wetting due to nanoplastrons remaining entrapped inside the skin nanocavities, which facilitates recovery of the de-wetted state upon pressure reduction. The barrier, before an irreversible transition takes place, was found to be higher than , which can, for example, effectively protect springtails against suffocation in rain due to a lower dynamic pressure in the range from to of falling rain droplets.[24]

4.4 Bio-inspired omniphobic polymer membranes

In this section, parts of the text and the figures are reproduced with permission from ref. [148], Copyright 2014, John Wiley and Sons (http://dx.doi.org/10.1002/adma.201305408).

Mimicking the effectively liquid-repellent and mechanically stable springtail skin morphology in engineered materials may offer exciting opportunities for numerous emerging applications. In particular, surface features exhibiting overhanging cross- sections and are arranged in self-supporting comb-like patterns may offer an unprecedented level of control over wetting phenomena. Thus, this section is focused on a top-down manufacturing method to develop a polymer membrane that resembles the springtail skin morphology (Figure 4.17). The omniphobic performance of the polymer membranes is demonstrated by in situ plastron collapse and long-term immersion tests. The mechanical durability of the membranes is shown by wear tests in comparison to a pillar surface by using a nanotribometer approach.

Polymer membranes were produced from a two-tier silicon master structure that serves as template for the feature replication, as schematically shown in Figure 4.17b. Two-tier silicon master structures that consisted of small pillars centered atop larger pillars were fabricated by optical overlay lithography using a mask-aligner setup with manual wafer positioning for feature dimensions larger than or a wafer-stepper setup with automatic marker alignment for smaller features down to . The wafer-stepper setup allowed for miniaturization of the surface features due to a better overlay accuracy and higher resolution (Figure 4.17c). The subsequent feature replication is based on a reverse imprint lithography approach using perfluoropolyether dimethacrylate (PFPEdma) templates cast from the silicon master.[130,137] The cavities of this working mold were filled with a poly(ethylene glycol) dimethacrylate (PEGdma) pre-polymer

73 Chapter 4

Figure 4.17. Springtail skin morphology and process scheme for manufacturing polymer membranes with similar structural features. (a) Habitus image of F. candida. Inserts show scanning electron micrographs of the characteristically contained bristles, granules and ridges. The nanoscopic granules and interconnecting ridges form cavities, are arranged in a comb-like pattern and provide a template for the developed polymer membranes. (b) Process scheme for membrane fabrication: Firstly, a two-tier silicon master structure is fabricated by optical lithography. Secondly, the master structure serves as template for reverse imprint lithography. (c) SEM image of the two-tier silicon master structure (insert: detailed view of a small pillar centred atop a larger pillar; scale bar: ). (d) SEM image (insert: cross-section after focused ion beam preparation; scale bar: ) and (e) photograph of the springtail skin-inspired polymer membrane. (f) Water droplet (coloured by red dye) deposited on the membrane, which was transferred to a diameter glass rod. Reproduced with permission from ref. [148], Copyright 2014, John Wiley and Sons. solution by doctor-blade technique without a residual layer on the small pillar structures. After subsequent cross-linking, no further post-etching steps were required to obtain a perforated membrane. Each cavity of the membrane had a narrow opening at the top, which provided an overhang inside the cavity (Figure 4.17d). Finally after de- molding, the flexible membrane is free-standing (Figure 4.17e) and, thus, transferable to various even non-flat substrate materials, e.g., a glass rod (Figure 4.17f). With this methodology, a set of membranes with different opening diameters, , of the cavities in a square (wafer-stepper setup, ) or hexagonal (mask-aligner setup, ) lattice was fabricated.

74 Results and discussion

Figure 4.18. Contact angle goniometry. (a) Dynamic contact angle measurements at polymer membranes with varying opening diameter in reference to intrinsic contact angles obtained at flat polymer films. Brownish circles and green triangles represent the water and hexadecane contact angles, respectively (filled = advancing contact angle, blank = receding contact angle). (b) Pinning of the receding liquid front at the cavity openings and capillary bridge formation. Reproduced with permission from ref. [148], Copyright 2014, John Wiley and Sons.

To evaluate the wetting of membrane-coated surfaces, long term plastron collapse tests upon complete immersion of the membranes were carried out. In addition, dynamic contact angle goniometry was performed. PEGdma polymer membranes were used without any further chemical surface modification as they are intrinsically hydrophilic and lyophilic, showing advancing contact angles of and

of the related planar reference surfaces, respectively (Figure 4.18a). Membranes were placed in a liquid-flooded chamber mounted on an optical microscope for facilitating in situ observations upon hydrostatic pressure manipulation, as schematically illustrated in Figure 4.19a and described in detail previously.[147] The polymer membranes showed a clearly omniphobic behavior as is obvious from the plastron formation immediately upon immersion into water or hexadecane (surface tensions ⁄ and

⁄ , respectively). The stability of the membrane-entrapped plastrons was followed in situ under linearly increasing hydrostatic pressure. The pressure value at which the plastron collapsed was defined as the breakthrough pressure, . Expanding liquid fronts remained inside the narrow opening of the cavities until the three-phase contact line was depinned and the overhang was wetted (Figure 4.19b). For both liquids, the resistance clearly depends on the opening diameter of the cavity, . For , the breakthrough pressure significantly raises up to values of about for water and about for hexadecane (Figure 4.19d), in accordance with the previously reported pressure resistance of the springtail skin.[32,146,147]

75 Chapter 4

Concluding, structure miniaturization allows fabrication of robust omniphobic polymer membranes. The obtained data are in line with recent studies of pillar arrays[25] and calculated values (Figure 4.19d) that were determined by using Eq. 4.3, where is set equal to the advancing contact angle, , and is the maximal slope inside the cavity:

( ) . (4.12)

Besides enforced depinning of the triple phase line, plastron collapse may result from liquid condensation inside the cavities or diffusion of the entrapped air into the liquid phase. Figure 4.19c depicts the nucleation and growth of water droplets inside the cavities. Nucleation was observed to be energetically favourable at the edges of the overhang or the bottom of the cavity.[167] Initially, condensates grew and partially merged by fusion. However, most condensates became stable and did not grow any further after approximately . This steady state persisted for more than seven days, while only a few plastrons collapsed. The examined longevity of the polymer membranes is similar to that found on natural surfaces[57,168] and exceeds the values previously reported on any engineered surfaces.[169,170] Hexadecane did not condensate inside the cavities due to its much lower saturation vapour pressure. Thus, the plastron was stable over time periods of at least seven days.

In sum, the springtail skin-inspired polymer membranes are characterized by persistence against enforced wetting and long-term plastron stability in water as well as in hexadecane. Wetting transitions occurring within individual cavities did not affect adjacent cavities as the cavities are separated by impermeable walls. This separation is clearly advantageous compared to commonly used pillar structures, where locally initialized wetting is often followed by immediate sideward propagation of the fluid front.[171] The overhanging cross-sections of the membrane cavities allow omniphobicity, i.e., resistance even against wetting of low-surface-tension liquids, without any surface modification. In fact, the hydrophilic characteristics of the polymer membrane results in an enhanced adhesion of the liquid-solid interface in comparison to low energy surfaces:[168] The interface sticks to the membrane more tightly and the loss of the plastron due to vibrations or turbulent flow can be avoided (Salvinia effect).[168]

In addition to the immersion tests, the polymer membranes were further characterized by dynamic contact angle goniometry (Figure 4.18). For both liquids, the obtained advancing contact angles at the polymer membranes were higher than the intrinsic one,

76 Results and discussion

Figure 4.19. Immersion experiments. (a) Schematic cross-sectional view of the experimental setup consisting of a liquid-flooded chamber containing the membranes, an optical microscope and a piston for hydrostatic pressure manipulation. (b) Schematic side view and optical micrograph series (top view, bright field) of the pressure-dependent collapse of the plastrons by an expanding water front inside the cavities (scale bars: ). (c) Schematic side view and optical micrograph series (top view, bright field) representing the time-dependent partial filling of the membrane cavities by condensation (scale bars: ). (d) Breakthrough pressures at polymer membranes with varying opening diameter demonstrating the robustness of the Cassie state for water (brown circles) and hexadecane (green dots). Circles and dots represent the experimental data, lines the calculated values (cf. Eq. 4.12). Reproduced with permission from ref. [148], Copyright 2014, John Wiley and Sons.

77 Chapter 4 which indicates the Cassie state of the applied liquids (Figure 4.18a). The advancing contact angles increased with larger opening diameters due to the reduced fraction of the projected solid-liquid contact area, , which simultaneously enhanced the fraction of the liquid-air interface ( ). The arrangement of the array of cavities inside the membranes was kept constant for the contact angle measurements and, therefore, the projected wetted solid area ranges between and depending on the cavity diameter. The apparent contact angle varies only slightly in comparison to the intrinsic contact angles due to the high solid area fractions, which is in line to the model of Cassie and Baxter (Eq. 2.13). The liquids could penetrate inside the narrow cavity openings due to the hydrophilic and lyophilic nature of the polymer membrane. As a consequence, the contact line is pinned by the formation of capillary bridges (Figure 4.18b) in accordance with the model of Dufour et al.[172] The adhesive characteristic of the membrane is further reproduced by the receding contact angle data, which decreases with larger opening diameters due to more pronounced capillary bridges.

To evaluate the mechanical durability of the polymer membranes, wear tests were performed in comparison to pillar structures commonly used for mimicking superhydrophobic surfaces.[115] PEGdma polymer material was used for both the membranes and the pillar arrays to ensure comparability of the intrinsic mechanical properties. Furthermore, the height of the surface features and the lattice parameter of the tested arrays were adjusted to be similar. Shear forces were applied by an oscillating steel ball in combination with a load (Figure 4.20). Load dissipation and failure mode of surface structures clearly differed between the membranes, which were plastically deformed and delaminated from the substrate, and the pillar array, which broke at the bottom where the highest bending stress occurred. The membranes provided a continuous, self-supporting surface that resisted loads of to depending on the comb wall width (Figure 4.20a). In contrast, the mechanical stability of the pillar structures was much lower and ranged from to depending on the pillar diameter (Figure 4.20b). Thus, membrane-coated surfaces showed a significantly higher mechanical stability compared to surfaces covered with pillar arrays.

Taken together, a novel and promising strategy for the fabrication of omniphobic polymer coatings was introduced. Mechanical durability and pronounced, long-term resistance against wetting upon complete immersion, the most striking features of the springtail skin, were effectively reproduced in polymer membranes that mimic the

78 Results and discussion

Figure 4.20. Wear tests of (a) polymer membranes in comparison to (b) pillar arrays: Schematic representation of the experimental setup consisting of an oscillating steel ball, pressed onto the structured surfaces. Experimental data of maximal normal loads the surfaces can resist without destruction and SEM images after failure. Reproduced with permission from ref. [148], Copyright 2014, John Wiley and Sons. contained comb-like patterned cavities with overhangs. Miniaturization of the surface features was found to allow for a particularly high pressure resistance. Omniphobicity of the produced polymer membranes was solely achieved through control over structural features, namely, the presence of overhanging cross-sections of the membrane cavities, independent of the surface chemistry. The produced membranes can be precisely adjusted with respect to morphological and compositional characteristics, and applied to various different, even non-flat bulk materials. Accordingly, a broad spectrum of emerging applications may benefit, particularly when the membranes are utilized under conditions of complete immersion, including examples as different as liquid handling in microfluidics and biofouling prevention on ship hulls and pipes. Upscaling of the utilized reverse imprint lithography technique may be achieved by adaptation of roll-to- roll processing schemes.[130]

79 Chapter 4

80

Chapter 5

Conclusions

In this work a novel surface modification strategy was developed, inspired by the cuticle integuments of springtails. The framework of this thesis was organized in accordance with a classical biomimetic approach (Figure 5.1): Starting from observed phenomena: omniphobicity, high pressure resistance, and mechanical robustness; a set of experimental, analytical and numerical analyses were performed to decipher their physicochemical origin before an abstracted model was constructed. This model provided the basis for translation into a synthetic polymer-based surface coating, which mimics springtail skin and its pronounced characteristics.

Springtails are soil-dwelling arthropods, exhibiting water- and oil-repellent (omniphobic) wetting characteristics and a high resistance against abrasion, which are an evolutionary adaptation to maintain their cutaneous respiration in temporary rain- flooded soil habitats.[32] The characteristic skin morphology of T. bielanensis, O. stachianus, and F. candida were intensively investigated in this work. Microscopic studies revealed a hierarchically arranged and highly textured skin of springtails. The entire body of each species is de facto covered with nanoscopic primary granules and interconnecting ridges; together forming gas permeable nanocavities that are arranged in comb-like patterns. Electron microscopy revealed that the primary granules protrude above the ridges, thus, the nanocavities exhibit overhangs. Furthermore, the three species possess thin bristles and, in addition, T. bielanensis and O. stachianus possess microscopic papillose-shaped secondary granules, according to refs. [31,32].

In order to find the impact of the individual structure elements on the omniphobic characteristics of the springtail skin, an adaptive replication process was developed. Perfluoropolyether dimethacrylate (PFPEdma) was used as elastomeric mold material that ensures high accuracy of the replicated polymer structures.[125,137,173,174] The produced polymer skin replicas exhibited distinctive surface morphologies regarding the

81 Chapter 5

Figure 5.1. Summary of the biomimetic approach, which is presented within this thesis. presence of the nanoscopic granules and different surface chemistries. The obtained contact angle data correlated with the particular surface morphologies irrespective to the surface chemistries. This means that the polymer replica surfaces containing nanoscopic granules reflected an omniphobic wetting performance. In contrast, the polymer replicas without the nanoscopic surface morphology of the springtail skin were completely soaked by water and hexadecane. Thus, the presented tuneable replication approach proved that the protective design principle of springtail skin critically depends on the nanotopography of the cuticle as recently suggested in ref. [32]. In particular, the overhangs of the nanoscopic granules were concluded to effectively retain air upon wetting, resulting in a solely structural wetting barrier even for liquids with low surface tension.

In summary, the experimental approach provides new insights into the physicochemical origins of the protection of springtail skin against wetting:

 It was found that the protective design principle of springtail skin critically depends on the nanotopography of the cuticle, irrespective of the surface chemistry.  It was shown that even intrinsically hydrophilic materials could resist wetting by low-surface-tension liquids when structured according to this principle.

Furthermore, the replicas were analysed by in situ plastron collapse tests, which allowed for exploring of the hydrostatic robustness of the observed plastrons (air cushion), which are immediately formed upon immersion. The transition from a heterogeneous to a completely wetted skin could be described by a (hydrostatic) pressure based model that could be further distinguished by two transition phenomena: The canthotaxis and the Laplace breakthrough. A clear depiction of the origin of the wetting resistance has been

82 Conclusions given in detail by analytical calculations and numerical finite element computations. First, the mushroom-shaped profiles of the nanoscopic primary granules were described by polynomials to get access for the breakthrough pressure calculations. The obtained results showed good consistency with experimentally determined pressure values and are in line with the recently proposed geometrical control over wetting of omniphobic surfaces.[29,30,110] In a next step, three abstracted cross-sectional profiles were utilized to set the evolved analytical model into a more general context by step-wise increased complexity of the cavity side walls. In particular, T-shaped profiles with slim serifs were found to exhibit the most robust wetting resistance even for low intrinsic contact angles in comparison to the other abstracted profiles. Furthermore, the wetting transition takes place only by the Laplace breakthrough, which is irrespective to the intrinsic contact angle, i.e. a characteristic solid material parameter. Thus, the wetting transition for serif T structures depends only on the cavity dimensions and the surface tension of the applied liquid. This new finding allows for the manufacturing of robust omniphobic surfaces that can be chemically modified without any restriction to the stability of the heterogeneous wetting state. This differs from other man-made superhydrophobic surfaces that are restricted to low energetic non-polar coatings, such as fluorine or alkane hydrocarbons that inconveniently narrow the range of applications. The impact concerning the hierarchical assembly of the nanoscopic and microscopic granules occurring on the skin of T. bielanensis and O. stachianus was analysed by numerical computations, which allowed for exploring of the high-pressure resistance of the observed heterogeneous wetting state and, in particular, the dynamics of the transition process. It was found that the transition occurs in a step-wise process due to the spatial arrangement of the nanoscopic granules, which cover the microscopic papillose-shaped granules.

83 Chapter 5

Taken together, the combined approach of experimental, analytical and numerical analyses provided new insights into the origins of the protection mechanisms of springtails against wetting. Our studies revealed that the (pressure) barrier against an enforced wetting upon immersion critically depends on the cross-sectional profile of the surface features:

 It was found that mushroom-shaped profiles, which were demonstrated on springtail skin, often exhibit positive slopes along the profile as a structural requirement for high-pressure resistance, even for low intrinsic contact angles.  The resulting barrier against complete wetting can, for example, effectively protect springtails against suffocation in rain (rain droplets have a dynamic pressure in the range from to .)  The abstraction of mushroom-shaped profile into serif T structures revealed a pressure barrier irrespective of the surface chemistry, which paves the way for a free choice of surface modifications without losing the wetting resistance.  The wetting transition on hierarchically assembled surfaces occurs as a stepwise process. In the first step, the macroscopic plastron collapses while air is still entrapped inside the nanocavities that facilitates recovery of the de- wetted state upon pressure reduction.

The combined approach of experimental, analytical and numerical analyses provided new insights into the origins of the protection mechanisms of springtails against wetting.

Finally, in a proof of principle, these findings were translated into polymer membranes, which combine superb omniphobicity, wetting resistance and mechanical stability. A reverse imprint lithography approach was developed to fabricate polymer membranes, which are flexible, free-standing, and adaptable to various substrate materials and shapes. The produced membranes could be precisely adjusted with respect to morphological characteristics due to the utilized top-down approach. Miniaturization of the surface features was found to allow for a particularly high pressure resistance which is a prerequisite for outdoor applications or large immersion depth.

84 Conclusions

In summary, the obtained polymer membranes effectively mimicked the springtail skin characteristics regarding the omniphobicity, wetting resistance, and mechanical stability:

 It was found that the presence of overhanging cross-sections of the membrane cavities allowed for omniphobicity, despite the intrinsically hydro- and lyophilic polymer material.  A high pressure resistance could be obtained by miniaturization of the surface features.  The wetting transitions occurring within individual cavities did not affect adjacent cavities, because they are separated by impermeable walls. Thus, defects in the membrane do not necessarily lead to a complete collapse of the heterogeneous wetting state.  It was shown that the mechanical stability of the membranes is much higher in comparison to a pillar array made of the same material, due to the mechanically self-supporting design of the membrane.

Conclusively, a novel and promising strategy for the fabrication of omniphobic polymer coatings was introduced. Starting from observed natural phenomena and preliminary suggestions concerning their origin, the presented work follows the biomimetic path: (i) experimental, analytical, and numerical analyses to understand the phenomena, (ii) abstraction, and (iii) first prototypes in a proof of principle. The utilized reverse imprint lithography technique has the potential ability to be up-scaled by adaptation of roll-to- roll processing schemes.[130] Accordingly, a broad spectrum of emerging applications may benefit from the obtained results, including liquid handling in microfluidics and biofouling prevention on ship hulls and pipes.

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Selbstständigkeitserklärung

Hiermit versichere ich, dass ich die vorliegende Arbeit ohne unzulässige Hilfe Dritter und ohne Benutzung anderer als der angegebenen Hilfsmittel angefertigt habe; die aus fremden Quellen direkt oder indirekt übernommenen Gedanken sind als solche kenntlich gemacht. Die Arbeit wurde bisher weder im Inland noch im Ausland in gleicher oder ähnlicher Form einer anderen Prüfungsbehörde vorgelegt.

Die vorliegende Arbeit wurde am Leibniz-Institut für Polymerforschung Dresden e.V. im Teilinstitut Biofunktionelle Polymermaterialien am Max-Bergmann-Zentrum für Biomaterialien unter der Betreuung von Herrn Prof. Dr. Carsten Werner angefertigt.

Die Promotionsordnung der Fakultät Mathematik und Naturwissenschaften der Technischen Universität Dresden vom 23.02.2011 erkenne ich hiermit an.

Bisherige erfolglose Promotionsverfahren haben nicht stattgefunden.

Dresden, den

René Hensel