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Super-hydrophobic nanopatterned interfaces : optimization and manufacturing Moradi, Sona 2014

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Super-hydrophobic Nanopatterned Interfaces:Optimization and ManufacturingbySona MoradiM.Sc., Sharif University of Technology, Iran, 2008B.Sc., Sharif University of Technology, Iran, 2006A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES(Chemical and Biological Engineering)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)April 2014© Sona Moradi, 2014iiAbstractThis work studies in detail the effect of femtosecond laser irradiation processparameters (fluence, scanning speed and scanning overlap) on the wettability of theresulted micro/nano-patterned morphologies on stainless steel. Depending on the laserparameters, four distinctly different nano-patterns were produced, namely nano-rippled,parabolic-pillared, elongated sinusoidal-pillared and triple roughness nanostructures. Allof the produced structures were classified according to a newly defined parameter, theLaser Intensity Factor (LIF) that is a function of scanning speed and fluence of laser. Byincreasing LIF, the ablation rate and the periodicity of the asperities increase. In order todecrease the surface energy, all of the surfaces were coated with a fluorinated alkylsilaneagent. Analysis of the wettability in terms of contact angle (CA) and contact anglehysteresis (CAH) revealed enhanced superhydrophobicity for most of these structures,particularly that possessing triple roughness pattern. This also exhibited a low CAH. Thehigh permanent superhydrophobicity of this pattern is due to the special micro-nanostructure of the surface that facilitates the Cassie-Baxter state.A new two-dimensional (2D) thermodynamic model is developed to predict thecontact angle (CA) and contact angle hysteresis (CAH) of all types of surface geometries,particularly those with asperities having non-flattened tops. The model is evaluated bymicro/nano sinusoidal and parabolic patterns fabricated by laser ablation. Thesemicrostructures are analyzed thermodynamically through the use of the Gibbs freeenergy to obtain the equilibrium CA and CAH. The effects of the geometrical details onmaximizing the superhydrophobicity of the nano-patterned surface are also discussed inan attempt to design surfaces with desired and/or optimum wetting characteristics. Theanalysis of the various surfaces reveals the important geometrical parameters, which maylead to lotus effect (high CA>150o and low CAH<10o) or petal effect (high CA>150o andhigh CAH>>10o).iiiPrefaceThis thesis is original, independent work by the author, Sona Moradi. This work wassupported by The University of British Columbia through the Four Year Fellowshipprogram (4YF).The following journal papers have been published from the research work presentedin this dissertation. I am the primary author and Professor Savvas G. Hatzikiriakos,Professor Peter Englezos and Dr. Saeid Kamal extensively helped with all aspects of theresearch work.Journal Papers1. Moradi, S., Englezos, P. & Hatzikiriakos, S. G. (2012). Contact anglehysteresis: surface morphology effects. Colloid and Polymer Science291(2), p. 317.( The material of this paper ispart of chapter 6 and Appendix of thisthesis)2. Moradi, S., Englezos, P., Kamal, S.& Hatzikiriakos, S. G. ( 2013)Femtosecond laser irradiation of metallic surfaces: effects of laserparameters on superhydrophobicity. Nanotechnology, 24(41), p. 415302.( The material of this paper ispart of chapter 5 of this thesis)3. Moradi, S., Englezos, P.& Hatzikiriakos, S. G. (2014) Contact AngleHysteresis of non-Flattened Top Micro/Nano-Structures. Langmuir, 2014,30 (11), p. 3274–3284.( The material of this paper is part of  chapter 6 of this thesis)ivTable of ContentsAbstract .............................................................................................................................. iiPreface............................................................................................................................... iiiTable of Contents .............................................................................................................. ivList of Tables..................................................................................................................... viList of Figures .................................................................................................................. viiList of Symbols ............................................................................................................... xiiiAcknowledgements .......................................................................................................... xvDedication ....................................................................................................................... xviCHAPTER 1: INTRODUCTION ...................................................................................... 1CHAPTER 2: LITERATURE REVIEW ........................................................................... 42.1. Wettability............................................................................................................... 42.2. Theory of Contact Angleand Wettability ................................................................ 52.3. Contact Angle Hysteresis ........................................................................................ 92.4. Lotus Effect ........................................................................................................... 112.5.  Artificial Superhydrophobic Surfaces.................................................................. 132.5.1. Common Methods to Create Roughness ........................................................ 142.5.2. Surface Chemistry Modification .................................................................... 152.5.3. Laser Ablation Method .................................................................................. 162.6. Thermodynamic Analysisof Wettability ............................................................... 18CHAPTER 3: THESIS OBJECTIVES AND ORGANIZATION ................................... 223.1. Thesis Objectives .................................................................................................. 223.2. Thesis Organization .............................................................................................. 22CHAPTER 4: EXPERIMENTAL METHODS AND MATERIALS.............................. 244.1. Materials................................................................................................................ 244.2. Surface Laser Irradiation....................................................................................... 24v4.3. Surface Silanization .............................................................................................. 264.4. Surface Analysis.................................................................................................... 284.4.1. Contact Angle (CA) and Contact Angle Hysteresis (CAH)........................... 284.4.2. Surface Patterning/Geometric Details ............................................................ 29CHAPTER 5:EXPERIMENTAL RESULTS .................................................................. 315.1. Surface Morphology.............................................................................................. 315.2. Effect of Laser Parameters on Micro/Nano-Patterning......................................... 355.3. Surface Hydrophobicity and Contact Angles........................................................ 425.4. The Effect of Overlap on Surface Wettability ...................................................... 475.5. Summary ............................................................................................................... 49CHAPTER 6:THERMODYNAMIC ANALYSIS AND RESULTS............................... 516.1. Introduction ........................................................................................................... 516.2. Surface Geometry.................................................................................................. 546.3. Thermodynamic Analysis of Surfaces .................................................................. 556.4. Gibbs Free Energy Analysis For the Non-Composite Case of The SinusoidalPattern .......................................................................................................................... 596.5. Gibbs Free Energy Analysis For the Composite Case of the Sinusoidal Pattern.. 616.6. Results and Discussion.......................................................................................... 646-6-1. Model Evaluations......................................................................................... 656.6.2. Parametric Analysis of the CA....................................................................... 696.6.3. Parametric Analysis of the CAH.................................................................... 726.6.4. Concluding Comments on the CAH Calculations ......................................... 756.7. Conclusions ........................................................................................................... 79CHAPTER 7: CONCLUSIONS AND FUTURE WORKS............................................. 817.1. Conclusion............................................................................................................. 817.1.1. Experimental Work ........................................................................................ 817.1.2. Modeling Work .............................................................................................. 827.2. Future Work .......................................................................................................... 83BIBLIOGRAPHY ............................................................................................................ 84APPENDIX A .................................................................................................................. 94viList of TablesTable 5-1: The range of the LIF for the various structures. ............................................. 41viiList of FiguresFigure 2-1: A wetting (hydrophilic) and a non-wetting (hydrophobic) system................ 4Figure 2-2: A droplet on a solid interface and the balance of the three interfacialtensions.......................................................................................................... 5Figure 2-3: The actual and apparent contact angle on a rough surface. ........................... 6Figure 2-4: A droplet on surface defining the two distinct wetting states (a). The Wenzelstate and (b). The Cassie-Baxter state ........................................................... 7Figure 2-5: Relationship of with . The black solid, blue solid, red dotted,and red dashed lines correspond to the Wenzel state, the Cassie state, themetastable Cassie state when , and the metastable Cassie state when, respectively. .................................................................................... 9Figure 2-6: Schematic of variations on the sessile-drop method to measure ContactAngle Hysteresis ......................................................................................... 10Figure 2-7: Schematic of advancing and receding contact angles on the tilting plate. .. 11Figure 2-8:  (a). Lotus leaf, (b). SEM image of Lotus leaf (Patankar, 2004), (c). Highermagnification image of part (b) (Eadie and Ghosh, 2011), (d). Schematicillustration of micro/nano structure of a single papilla constituting thesurface of lotus leaf. .................................................................................... 12Figure 2-9: (a). Classical beam-matter interaction; (b). Ultrafast beam-matter interaction(Leitz et al., 2011). ...................................................................................... 17Figure 2-10: Multiple minima of the Gibbs energy of a droplet deposited on a roughsurface. ........................................................................................................ 19Figure 4-1: Schematic diagram of the laser irradiation set-up. ...................................... 25Figure 4-3: A typical droplet image and the measurement of contact angle. ................. 28Figure 4-4: Experimental sequence of advancing and receding images of a droplet todetermine the advancing and receding contact angles. ............................... 29cos Rough cos Y90Y  90Y viiiFigure 4-5: Advancing and receding contact angles for a hydrophobic sample............. 29Figure 4-6: (a). SEM image of a micro-pattern, (b). FFT image of image 4-6(b) in thespatial frequency domain, (c). Inverse FFT of image 4-6(b) in the spacedomain after certain corrections. ................................................................. 30Figure 4-7: Average gray profile of Figure 4-6(c) versus horizontal pixels................... 30Figure 5-1: SEM images of nano-rippled patterns formed with (a). Laser fluence of 1.5and scanning speed of 250 (b). Laser fluence of 10 andscanning speed of 1850 (c). SEM image of sample in Figure 5-1(a) ata higher magnification................................................................................. 32Figure 5-2: SEM images of the parabolic-pillared patterns, formed by the scanningspeed of 930 and laser fluence of  (a). 10 , (b). 16 , (c). 92, (d). SEM image with a higher magnification to show doubleroughness of the sample depicted in Figure 5-2(b). .................................... 33Figure 5-3: Sinusoidal elongated pillared pattern created by using (a). Laser fluence of136 and scanning speed of 930 , (b). Laser fluence of 185and a scanning speed of 1850 , and (c). SEM image with a highermagnification to show double roughness of the sample depicted in Figure 5-3(b). ............................................................................................................. 34Figure 5-4: Triple roughness patterns created by using (a). Laser fluence of 440and scanning speed of 1850 , (b). Laser fluence of 480 and ascanning speed of 1850 , (c). SEM with a higher magnification toshow triple roughness of the sample depicted in Figure 5-4(b). ................. 34Figure 5-5: Formation of four patterns at various laser power and scanning speeds. .... 35Figure 5-6: Gaussian laser beam fluence profile with different laser powers. ............... 38Figure 5-7: Schematic of laser ablation with pulsed Gaussian beam, (a). Laser ablationin one pass, xi is the distance traveled by the sample between two pulseswith speed of V, (b). Observed point on the sample after laser irradiation. 392.J cm 1.m s  2.J cm1.m s 1.m s  2.J cm 2.J cm2.J cm2.J cm 1.m s  2.J cm1.m s 2.J cm1.m s  2.J cm1.m s ixFigure 5-8: Periodicity of microstructures versus Laser Intensity Factor (LIF) with “n”equal to 0.5. ................................................................................................. 40Figure 5-9(a): The Cassie-Baxter contact angle of various samples in the four distinctlydifferent nano/micro-patterns as a function of the LIF parameter. ............. 42Figure 5-9(b): The contact angle hysteresis of various samples in the four distinctlydifferent nano/micro-patterns as a function of the LIF parameter. ............. 42Figure 5-10: SEM images of nano-patterns in Section I of Figure 5-9 (nano-rippledpattern, parabolic-pillared patterns) in increasing order of the LIF parameter(a). LIF of 22, fluence of 1.5 and scanning speed of 250  (b). LIF of 186.5,fluence of 16, and scanning speed of 460,(c). LIF of 591.7, fluence of 38.2and scanning speed of 250, unit of all reported LIFs is unit of fluenceis and scanning speed unit ...................................................... 44Figure 5-11: SEM images of nano-patterns in Section II of Figure 5-9 (elongatedsinusoidal-pillared pattern) in increasing order of the LIF parameter (a).LIF:771, fluence of 135.8, scanning speed of 1850, (b). LIF:1091, fluenceof 135.8, scanning speed of 930, (c). LIF: 1848, fluence of 214, scanningspeed of 1850. Unit of all reported LIFs is , unit of fluence isand scanning speed unit is ................................................................. 44Figure 5-12: SEM images of nanopatterns in Section III in Figure 5-9 (triple roughnessnano-pattern) in increasing order of the LIF parameter (a). LIF: 1849,fluence of 325.4, scanning speed of 1850, (b). LIF: 2331, fluence of 410,scanning speed of 1850. (c). LIF:2730, fluence of 480, scanning speed of1850. Unit of all reported LIFs is , unit of fluence is andscanning speed unit is ........................................................................ 45Figure 5-13: (a). Structure with 8° CAH and CA of 155° created by: (a). LIF of 1091, fluence of 136 , scanning speed of 930 , (b). Tripleroughness structure with 4° CAH and CA of 164° created by LIF of 2730, fluence of 480 , scanning speed of 1850..................... 472.J cm2.J cm 1.m s 2.J cm 2.J cm1.m s 2.J cm 2.J cm1.m s 2.J cm 2.J cm 1.m s 2.J cm 2.J cm 1.m s xFigure 5-14: Structurs created by  using two different overlaps of 0% and 50% (a).Fluence of 18.67 , scanning speed of 930 , (b).  Fluence of16.55 , scanning speed of 460 , (c). Fluence of 480 ,scanning speed of 1860 . .................................................................... 48Figure 5-15: Wettability of patterned surfaces with 50% and 0% scanning overlap forthess sets of fluence and scanning speed parameters(a). Fluence of 16.5and scanning speed of 460 ; (b). Fluence of 38.2 andscanning speed 460 ; (c). Fluence of 480 and scanning speed of1860 . In all cases decrease of overlap from 50 to 0% causes adecrease of contact angle. ........................................................................... 49Figure 6-1:A droplet sitting on a uniform patterned surface. ......................................... 51Figure 6-2:(a) SEM image of sinusoidal structure, (b). SEM image of paraboloidalstructure (c). Idealization (model) of the sinusoidal structure shown inFigure 1(a), (d). Idealization of the paraboloidal structure shown in Figure1(b). ............................................................................................................. 54Figure 6-3: Schematic of the non-composite state of a droplet on a sinusoidalmicrostructure showing the local apparent contact angles and thegeometrical details needed in the numerical analysis. ................................ 57Figure 6-4: The energy profile between two pillars to determine the maximum andminimum Gibbs free energy of the system (a). For the sinusoidal structure(b). For the paraboloidal pattern for the non-composite case. .................... 58Figure 6-5: Schematic diagram of the composite state of a droplet (droplet penetratingthe trough to a certain length H1) on a sinusoidal microstructure showingthe local apparent contact angles and the geometrical details needed in thenumerical analysis. ...................................................................................... 62Figure 6-6: SEM image and CA of sinusoidal structure with (a). Periodicityof25m andheight of 12m, (b). Periodicity of 35 m and height of 45 m................. 662.J cm 1.m s 2.J cm 1.m s  2.J cm1.m s 2.J cm 1.m s  2.J cm1.m s  2.J cm1.m s xiFigure 6-7: Thermodynamic energy analysis for the non-composite state of a sinusoidalstructure with wavelength of 25 m and height of 12 m, (a). Normalizedfree energy variation with apparent contact angle, (b). Energy barrier versuscontact angle to predict contact angle hysteresis. ....................................... 66Figure 6-8: Energy barrier analysis for the composite state of a sinusoidal structure withperiodicity of 35 mand height of 45m . .................................................. 67Figure 6-9: SEM image and CA of paraboloidal structure samples with pitch of 0.5 mand (a). Diameterof 15 m and height of 11m, (b). Diameter of 23 m andheight of 32 m. .......................................................................................... 68Figure 6-10: Energy barrier analysis for the paraboloidal structure (a). Non-compositestate of a pattern with diameter 15 m, height of 11 m and pitch of 0.5 m(b). Composite state of a pattern with diameter 23 m, height of 32 m andpitch of 0.5 m. ........................................................................................... 69Figure 6-11: Contact angles of Cassie-Baxter and Wenzel states for the sinusoidalpattern versus (a). Ratio of and (b). Height, H................................... 70Figure 6-12: Contact angle (CA) of Cassie-Baxter and Wenzel states for theparaboloidal pattern as functions of (a). The ratio and (b). Height, H. 72Figure 6-13: Contact angle hysteresis of composite (Cassie-Baxter) and non-composite(Wenzel) configurations for the sinusoidal pattern as functions of (a). Theratio and (b). Height, H. ..................................................................... 73Figure 6-14: Contact angle hysteresis of the composite (Cassie-Baxter) and non-composite (Wenzel) configurations for the paraboloidal pattern as functionsof (a). The ratio and (b). Height, H (c). 3D plot of CAH of theparaboloidal pattern as a function of pillar base diameter, D and pillarheight H. ...................................................................................................... 74SH DH DSH DH DxiiFigure 6-15: (a).Contact angle (CA) and (b).Contact angle hysteresis of Cassie-Baxterand Wenzel states for the paraboloidal pattern as functions pillar pitch (P)...................................................................................................................... 75Figure 6-16: The liquid-air contact area beneath the droplet for the (a).Sinusoidal(b).Paraboloidal microstructures. ................................................................ 76Figure 6-17: (a). and (b). SEM images of the rose leaf (reprinted(Feng et al., 2008) withpermission from ACS, copyright (2008) American Chemical Society), (c).and (d).: SEM images of the manufactured paraboloidal pattern on stainlesssteel by laser irradiation. ............................................................................. 77Figure 6-18: Variation of CAH versus pillar diameter at different heights for theparaboloidal structure. ................................................................................. 78Figure 6-19: Variation of the penetrated height of the sinusoidal and paraboloidalpatterns versus the pillar height at constant diameters. ............................... 79Figure A-1: Schematic of the non-composite state of a droplet on a parabolicmicrostructure showing the local apparent contact angles and thegeometrical details needed in the numerical analysis. ................................ 94Figure A-2: Schematic diagram of the composite state of a droplet on a paraboloidalmicrostructure showing the local apparent contact angles and thegeometrical details needed in the numerical analysis. ................................ 97xiiiList of SymbolsA Interfacial areaAtot Total area of the solid surfaceAP Side area of a pillar (in 2D system)AV Area of void space between two pillarsD Diameter of a parabolic structureD Diameterof an ablated craterDs Periodicity of sinusoidal structureEP Laser beam pulse energyF Gibbs free energy of systemF* Normalized Gibbs free energyH Pillar heightLiquid penetrating into the troughs between pillarsN Number of laser pulsesNeff Number of pulsesLi Radius of wetted area by droplet at location “i”Ablation depth per pulse in gentle ablationAblation depth per pulse in stronger ablationS Accumulation parameterP1 Power of one pulsePtot Total incident powerR Radius of the spherical dropletV Scanning speedDroplet volumeP Pitch of parabolic patternsAverage roughness valueAir phaseFraction of solid surface area in contact with the liquidLaser frequencyh Depth of liquid penetrationLiquid phaseRatio of wetted area to projected areaRoughness factor of Wenzel stateSolid phaser Distance from the beam centerlineArc length of droplet in contact with airPeriodicity of the asperitiesz0 Half of pillar Height1HLLdropVaRafflrrfslal0xxivGreek LettersGibbs free energy difference between two given statesLaser fluence profileAblation thresholdBeam peak fluenceSingle pulse ablation threshold fluenceMultipulse ablation threshold fluenceAblation fluence threshold of transition to the stronger ablation regimeAblation threshold for gentle ablationSlope angle of the surfaceInterfacial tensionElectron heat diffusion lengthδ Optical penetration depthAct Actual contact angleApp Apparent contact angleCritical intrinsic contact angleCassie-Baxter contact angleWenzel apparent contactYoung contact angle0 Gaussian beam radiusAbbreviationsCA Contact angleCAH Contact angle hysteresisCB Cassie-BaxterFFT Fast Fourier TransformFTS Trichloro (1H,1H,2H,2H-perfluorooctyl) silaneLIF Laser Intensity FactorW WenzelF( )rth0(1)th( )th N,th,thCCBWYxvAcknowledgementsI wish to express my sincere gratitude to my thesis supervisor Prof. Savvas G.Hatzikiriakos for his skillful guidance and constructive criticism throughout this work.He has helped me become a better professional in various ways. I would also like tothank my co-supervisor Prof. Peter Englezos for his valuable suggestions, points andcomments throughout this work. My supervisors have provided me with plenty ofacademic freedom in order to reach my research goals. Their continuous encouragementand support has been a source of motivation during the course of this work.I gratefully acknowledge Dr. Saeid Kamal, the manager of Laboratory for AdvancedSpectroscopy and Imaging Research (LASIR) of Chemistry Department of UBC for hisvaluable suggestions and skillful comments throughout experimental work.Working in the Rheology Laboratory and Hydrate Laboratory has been a privilege and Iwould like to thank all my past and present colleagues for making this lab an inspiringand enjoyable place to work.And finally, my most loving thanks to those who matter to me the most, my parents, mybrother and my sisters...xviDedicationTo my family1CHAPTER 1: INTRODUCTIONThe wettability of a solid surface by a liquid is an important aspect in a variety ofpractical applications in nature and in the fields of daily life, industry, and agriculture.The ability to control surface wettability has recently attracted significant attention in theopen literature from both the academic and industrial sectors. Numerous micro/nanosystems such as Micro Electrochemical Systems (MEMS), lab-on-a-chip or microfluidicsystems require surfaces with low adhesion and friction (Yao et al., 2011). Due to thesmall size of these devices, the surface forces tend to dominate over the volume forces,and therefore control of the adhesion and friction becomes a challenging problem forgood operation of these systems. In order to reduce the surface adhesion for suchapplications, the development of non-wettable and non-adhesive surfaces seems to becrucial.Nature is full of biological organisms that exhibit amazing properties for low-adhesive surfaces such as the self-cleaning property of the surface of lotus leaves(Barthlott et al., 1997; Chen et al., 2009; Feng et al., 2002; Neinhuis and Barthlott,1997) , the ability of a strider to walk on water (Gao and Jiang, 2004; Hu et al., 2003),the antifogging functionality of mosquito eyes (Gao et al., 2007), the water harvesting ofthe Namib Desert beetle for survival (Parker and Lawrence, 2001; Zheng et al., 2010) ,the submarine self-cleaning ability of fish scale(Liu et al., 2009), the low drag surface ofshark skin (Bechert et al., 2000) and the use of plastron property for underwaterbreathing (Mchale et al., 2010; Neil J. Shirtcliffe et al., 2006). The wettability of asurface is measured in terms of the static and the dynamic contact angles of a waterdroplet on that surface. In all these surfaces (superhydrophobic), the static contact angle(CA) well exceeds 150°.The substrates with extremely high water repellency are referred to assuperhydrophobic surfaces and they exhibit a water contact angle of more than 150°. Influid flow, in order to have low friction and for applications that require the self-cleaningfeature (water droplets flow readily at small angles of inclination), in addition to the high2contact angle, superhydrophobic surfaces should also possess a low water contact anglehysteresis (difference of advancing and receding contact angles)typically less than 10°(Lafuma and Quéré, 2003).The surface of the lotus leaf is such an example where water droplets readily rolland remove contaminant particles from the surfaces, leading to a self-cleaning propertyknown as the “Lotus effect” (Solga et al., 2007). Study of the details of the surface of thelotus leaf has revealed that the poor wettability of the surface is attributed to thecombined effects of surface micro/nano asperities and surface chemistry. The surface ofa lotus leaf is made up of a certain dual scale roughness structure, where randomlydistributed asperities of micrometer scale are covered with fine nanometer scale hairs(Cheng et al., 2006).Superhydrophobic surfaces have a number of potential applications such as dustfree and self-cleaning surfaces for solar cells and satellite dishes, corrosion resistantsurfaces for heat transfer devices, transparent and antireflective surfaces, anti-freezingand anti-snow surfaces (Yao et al., 2011). The fact that liquid in contact with suchsurface slides with lowered friction suggests applications such as micro-fluidics andmedical devices. The non-wettable character has been claimed in biomedical applicationsranging from blood vessel replacement to wound management (Wang et al., 2012). Otherunexpected applications are expected to emerge as the technology of making non-wettable surfaces matures.There are several methods to prepare superhydrophobic surfaces particularly onmetals of particular interest in the present thesis. These methods are reviewed in chapter2 (literature review). A new method to surface roughening is ablation with short-pulselaser. Kietzig et al. (2009) investigated the effect of femtosecond laser pulses to createroughness on steels and Fe-containing alloy surfaces. They monitored the contact anglefor 30 days and the results revealed that the surface changes from hydrophilic tohydrophobic over time. This behavior is justified by the presence of carbon and activemagnetite on the laser structured area of the surface. Therefore, laser ablation can changesurface morphology and chemistry.3The preparation of superhydrophobic surfaces in general is still in its initial stateand there is no industrial method for producing such surfaces. Most of the methodsdeveloped are in the academic developmental stage. The procedures are costly and time-consuming with respect to the number of steps and surface treatments. Another importantaspect that needs significant work is an understanding of the factors controllingsuperhydrophobicity and how these factors can be manipulated to develop surfaces ofcontrolled wettability. This requires the development of a robust model that can predictthe contact angle and contact angle hysteresis as a function of geometrical parameters ofthe surface as well as the surface chemistry.The goal of this dissertation is the use of laser femtosecond ablation on metallicsurfaces such as stainless steel, to produce a variety of different micro/nano-patterns as afunction of laser intensity, scanning speed and overlap. Understanding of the influence ofthese parameters will help in the optimization and control of the wettability of themanufactured surfaces. Coating these surfaces with a hydrophobic polymeric materialmay produce self-cleaning biocompatible interfaces, which can find many applications inthe medical sector. Femtosecond laser produces double roughness on the metallicsurfaces. The regular pattern structure created by the laser irradiation on the metal will becoated by low surface energy fluorinated silane to produce surfaces of controlledwettability. Furthermore, another goal of this study is the modeling of the manufacturedsuperhydrophobic surfaces in order to gain a better understanding of the effect of thedifferent geometrical parameters of surface morphology on the nano-patterned surfacewettability. The relationship between surface morphology and wettability/sliding is notwell-understood. By specifying the effect of surface geometry on the surfacehydrophobicity, the optimal surface morphology that would result the highest surfacehydrophobicity can be identified. This modeling can also be used to reveal thehydrodynamics of droplet on a surface, and the mechanism of transition from ametastable to a stable state.4CHAPTER 2: LITERATURE REVIEW2.1. WettabilityControlling the wetting of a surface is important in many areas of technology. Thewettability of materials ranges from total wetting to partial wetting. The contact angle(CA) is a quantitative measure of surface wettability. The contact angle (see Figure 2-1)is defined as the angle between the tangent to the liquid–air interface and the tangent tothe solid interface at the contact line between the three phases (Marmur, 2006). Totalwetting results from the high affinity of the water molecules to a solid surface in whichthe CA approaches zero and causes formation of a liquid film on the surface. In contrast,when the liquid forms a droplet on a surface the affinity of the water molecules tothemselves is higher than their affinity with the solid surface. This causes partial wettingof the surface. The wetting surface with water CA less than 90° is referred as hydrophilic(“hydro” means water in Greek). Non-wetting surface with water CA greater than 90° iscalled hydrophobic. For surface wetting by oil and organic liquids, the term of“oleophilic/phobic” is used.Figure 2-1: A wetting (hydrophilic) and a non-wetting (hydrophobic) system52.2. Theory of Contact Angleand WettabilityThe tendency of liquid to wet the surface is a function of the interaction betweencohesive and adhesive forces. Interfacial tension is a measurement of the cohesiveenergy present at an interface arising from the imbalance of forces between molecules atan interface. The liquid-air interfacial tension called surface tension is defined as theamount of force necessary to expand the surface of a liquid by one unit (Gennes et al.,2004).The wettability is controlled by the interfacial tensions acting at the three interfaces(air-liquid-solid), which are in balance; the formed contact angle is called the equilibriumCA (see Figure 2-2).Figure 2-2: A droplet on a solid interface and the balance of the three interfacial tensionsThe CA on an ideal (flat) surface is determined by Young’s equation, as following(Young, 1805).(2-1)where , is the Young contact angle or flat surface CA, is the interfacial tension andthe superscripts “ ”, “ ” and “ ” stand for liquid, air (or gas) and solid phases,respectively. The focus of Young’s equation is on the physico-chemical property of thethree phases without any dependency on the effect of gravity on the droplet shape(Marmur, 2006).The Young’s ideal solid surface is defined as a smooth, rigid, chemicallyhomogeneous, nonreactive and insoluble surface (Marmur, 1996). However, the problemis not that simple: most of real solid surfaces are rough and chemically heterogeneous toθYγ laγsaγ lscossa slY la  Y l a s6some extent. By addition of roughness to the surface, the CA may change locally fromone point to another. In such cases, the CA between the local direction of the tangent lineto solid-liquid interface and the direction of the tangent to the liquid-vapour interface at agiven point is called the “intrinsic contact angle” or “actual contact angle”, θAct. Theapparent contact angle, θApp is also defined as the angle between the tangent lines of theliquid-vapour interface and the nominal solid-liquid interface (Marmur, 1996). Figure 2-3 schematically illustrates the apparent and actual CAs on a rough surface.Figure 2-3: The actual and apparent contact angle on a rough surface.The most common method to measure the apparent CA is the sessile drop method.In this technique, a small droplet is deposited on the surface, and the image of the dropletis analyzed by image processing methods to determine the liquid CA on the surface.Theoretically, depending on the surface structure and degree of roughness, thereare two different distinct states of wetting discussed below, namely the Wenzel(homogenous) and the Cassie-Baxter (heterogeneous) states. In 1936, Wenzel introducedthe effect of roughness on the CA by multiplying a roughness factor to the Young’sequation according to equation 2-2 (Wenzel, 1936).(2-2)Where is the Wenzel apparent CA and is the roughness factor, which is the ratioof actual solid surface area to the projected area and the roughness factor is alwaysgreater than 1. The Wenzel equation is based on the assumption that liquid fullypenetrates into the grooves of the roughness and this wetting configuration on roughsurface is referred to as “ homogeneous wetting” (see Figure 2-4a). In this wettabilityθAppθActcos .cosW f Yr W fr7regime, the presence of roughness makes an inherently hydrophilic surface ( )more hydrophilic and an inherently hydrophobic surface ( ) more hydrophobic.However, the Wenzel equation can predict non-physical states for surfaces with ahigh roughness i.e. when is greater than 1. In addition, the Wenzel equationpredicts only one apparent CA for a droplet on a rough surface, while on a rough surfacethere exists a range of apparent CAs (Marmur, 1994).Figure 2-4: A droplet on surface defining the two distinct wetting states (a). The Wenzel state and (b).The Cassie-Baxter stateDepending on the surface roughness and surface chemistry, the liquid might notfully penetrate into the grooves to wet the surface entirely. Instead some air pocketstrapped beneath the liquid droplet may lead to “heterogeneous wetting” or “composite”state (see Figure 2-4b). The equation describing this state was developed by Cassie-Baxter in 1944, as following (Cassie and Baxter, 1944):(2-3)Where is the Cassie-Baxter CA, is the ratio of total area of solid under the drop tounit projected area under the droplet with on a flat surface of material 1. Likewise,is defined in an analogous way with material 2 as air. If the liquid-air interface beneaththe droplet is flat (Milne and Amirfazli, 2012), then Eq. (2-3) can be rewritten as:(2-4)90Y  90Y  .cosf Yr 1 2cos .cosCB Yf f  CB 1fY 2fcos . .cos 1CB Yr f f   8where is the ratio of wetted area to projected area and is the fraction of solidsurface area in contact with the liquid. When f=1, the CB equation reduces to the Wenzelequation. As recently realized both equations are correct only if the drop is sufficientlylarge compared with the typical roughness scale at least one or two orders of magnitude(Marmur, 1997).According to the Cassie-Baxter equation creating a hydrophobic surface using anintrinsically hydrophilic surface is possible and roughness can increase surfacehydrophobicity. Depending on the roughness factor and the amount of partial penetrationof liquid into troughs, the predicted Cassie-Baxter CA varies and instead of a single CA,a range of CA is obtained (Wolansky and Marmur, 1999).From a thermodynamic point of view, the equilibrium states are the minima ofGibbs free energy of the droplet lying on a rough surface. The global minimumcorresponds to a stable state, while the other minima correspond to metastable states(Marmur, 2006). Due to the possibility of the existence of either Cassie-Baxter orWenzel state, transition between thermodynamic states may occur depending on thegeometrical details of the roughened surface or the existence of external forces such aspressure, vibration and gravitational (Extrand, 2002; He et al., 2003; Mettu andChaudhury, 2011). The most stable state is determined by comparing the total Gibbsfree energy of the system at the two states. Hence the Cassie-Baxter state is the moststable state if the CA satisfies the condition (Bico et al., 2002):, with (2-5)where is the critical intrinsic CA of the flat surface above which a stable compositestate is possible.It has been proven that by decreasing the CA of the rough surface (Cassie-Baxterof Wenzel), the surface total energy monotonically decreases, so that the state with lessrough CA is more stable as shown in Figure 2-5 (Cao et al., 2007). As it can be seen inthis figure, for materials inherently hydrophilic ( ), always the Wenzel state isalways the most stable state. To have the Cassie-Baxter as a possible state, the surfacer fY C  1cos Cffr f C90Y  9should possess an overhang structure (shown in the lower-right quarter of Figure 2-5).For inherently hydrophobic surfaces ( ), depending on the roughness geometryand surface roughness, and the flat surface CA, , the Cassie-Baxter can be the moststable state (if ).Figure 2-5: Relationship of with . The black solid, blue solid, red dotted, and reddashed lines correspond to the Wenzel state, the Cassie state, the metastable Cassie state when, and the metastable Cassie state when , respectively.2.3. Contact Angle HysteresisThe presence of chemical heterogeneity and roughness on the surface has twoconsequences on the wettability. Firstly, it affects the contact angle (as discussed above);secondly it allows contact line to pin on these imperfections of surface, resulting inmultiple values for contact angle (a range of apparent contact angle instead of singlevalue) (Quéré, 2005). The difference of the upper limit and lower limit values of thisrange is referred to as contact angle hysteresis (CAH) and typically is quantified by twomethods: variations on the sessile-drop approach and the tilting plate method (Strobeland Lyons, 2011). The variation on the sessile-drop approach, as shown in Figure 2-6, is90Y  YY C cos θYcos θCcos θRoughcos Rough cos Y90Y   90Y  10based on the growth/shrinkage of sessile drop. By adding liquid to a sessile drop thevolume of the droplet gradually increases and causes the contact line to advance(advancing CA). On the other hand, reduction of the droplet volume causes the droplet toretract/recede (receding CA). The difference between the minimum receding and themaximum advancing CAs is referred to as CAH (Nosonovsky and Bhushan, 2008).Figure 2-6: Schematic of variations on the sessile-drop method to measure Contact AngleHysteresisIn the tilting plate method, the surface is set at a certain inclination angle in orderto cause rolling of the droplet. The contact angle (CA) of droplet in the moving direction(at the front of droplet) is referred to as the advancing CA and the CA in the oppositedirection (at the back of the droplet) is referred to as the receding CA (see Figure 2-7).Both definitions (sessile drop variation and tilting plate) are equivalent in spite of somedebate in the literature (Krasovitski and Marmur, 2005). The tilting angle of the surfaceat which the droplet starts rolling is called the sliding angle or roll-off angle (α in Figure2-7).Increasing the difference between the advancing and receding CA raises the roll-off angle, which, in turn, increases the adhesion between the liquid and the substrate.11Figure 2-7: Schematic of advancing and receding contact angles on the tilting plate.The value of the static CA always lies between those of the advancing and recedingCAs. It must be mentioned that reported CA and the CAH values in the literature aresensitive to the experimental techniques used for their measurement (Bormashenko et al.,2008; Decker et al., 1999).2.4. Lotus EffectWhen a raindrop falls onto a lotus leaf, by rolling on the surface it carries away anycontaminant particles from the leaf. This self-cleaning property is termed as the “lotuseffect” (Blossey, 2003). In nature, several species such as the leaves of certain plants andparts of the body of some creatures such as insect wings exhibit extreme water repellencysimilar to the lotus leaf. Such surfaces with a water contact angle higher than 150° andlow contact angle hysteresis, typically less than 10°, are defined as “superhydrophobic”surfaces (Guo and Liu, 2007).The wetting behavior of superhydrophobic surfaces found in the nature has beensignificantly studied over the past two decades. Therefore, by mimicking the structureand wetting properties of superhydrophobic creatures in nature, artificialsuperhydrophobic surfaces have been manufactured since 1990s (Celia et al., 2013; Maand Hill, 2006; Subhash Latthe, 2012).The lotus leaf (Nelumbonucifera), shown in Figure 2-8(a), was first investigated in1997 (Barthlott et al., 1997; Neinhuis and Barthlott, 1997). Studies on the structuralmorphology of the lotus leaf revealed that the poor wettability of the surface is attributedSubstrate αMovingθAdvθRec12to the combined effects of surface micro/nano asperities (Figure 2-8 (b)) and chemistry.The surface of a lotus leaf is made up of a certain dual scale roughness structure whererandomly distributed micro-scale papillaes are covered by a dense coating ofagglomerated wax tubules in nano-scale (Figure 8-2(c)-(d)). This dual roughness incombination with the low surface energy waxy layer leads to poor surface wettability onthe lotus leaf (Ensikat et al., 2011). The average diameter of the micro scale bumps onthe lotus leaf surface is about 20μm and the nano-scale waxy chains have an averagediameter of 200 nm (Patankar, 2004). The reported contact angle on the lotus leaf surfaceis about 161° with a sliding angle of only 2° (Feng et al., 2002).Figure 2-8: (a). Lotus leaf, (b). SEM image of Lotus leaf (Patankar, 2004), (c). Highermagnification image of part (b) (Eadie and Ghosh, 2011), (d). Schematic illustration of micro/nanostructure of a single papilla constituting the surface of lotus leaf.When water droplets come into contact with the lotus leaf, air is trapped beneaththe droplet (Cassie-Baxter state). As a result of air bubbles, the droplet rests on the apexof micro/nano structure supported by a composite surface made out of thesolid(leaf)micro/nano structure and air. These air bubbles prevent the liquid to fully13penetrate into the valleys of the surface and consequently, the droplet doesn’t stick to thesurface and easily rolls off the surface carrying away dust particles and othercontaminants. This occurs due to the existence of only weak van der Waals forcesbetween the leaf surface and the particles, whereas stronger capillary forces existbetween the water droplet and the contaminants (Koch et al., 2009).The surface chemistry and roughness are two crucial parameters that significantlyaffect surface wettability. Among all of the chemical materials, the methylated andfluorinated carbons have the lowest surface energy in the following order (Genzer andEfimenko, 2006):−CH2− > −CH3>−CF2−> CF2H >−CF3Hence flat surfaces manufactured by trifluoromethyl (−CF3) groups have CA of119° corresponding to surface energy of ≈ 6.7 (Nakajima et al., 2001). Since themaximum contact angle on the flat surface is 119°, to fabricate superhydrophobicsurfaces, controlled roughness should be added on the surface.2.5.  Artificial Superhydrophobic SurfacesIn recent years, due to a plethora of potential applications of superhydrophobicityin daily life, many efforts have been taken to manufacture artificial superhydrophobicsurfaces. Depending on the application and material, different methods have beenemployed to create a superhydrophobic surface. Most of these methods involve eithercreating a micro/nano-structure on an inherently hydrophobic material (Azimi et al.,2013; Bormashenko et al., 2007) or treating a specific micro/nano-structure with ahydrophobic coating (Groenendijk and Meijer, 2006; Liu and Lange, 2006; Moradi et al.,2013; Nosonovsky and Bhushan, 2009) or finally directly fabricating a sophisticatedsurface design (Cao et al., 2007).2.mJ m142.5.1. Common Methods to Create RoughnessOnda et al. (1996) were the first to report the synthesis of an artificialsuperhydrophobic surface by using alkylketene dimer wax with water contact angle of174°. Their paper was the start of an explosion in the number of published papers in theartificial superhydrophobic surfaces. There have been several attempts to use the naturalsuperhydrophobic species such as plant leaves and insect wings as templates to producethe water repellent structures (Neil J Shirtcliffe et al., 2006; Zhang et al., 2006). Theother methods to create non-wettable surfaces simply can be divided into two categories:Top-down and bottom-up approaches using either intrinsically hydrophobic materials orcoating the hydrophilic rough substrate by low surface energy layers. Note thatroughness is usually a more critical parameter than surface chemistry, since surfaces withdifferent surface energies exhibit the same hydrophobicity after roughening.Top-down approach is referred to the fabrication of materials and devices bymolding, carving or machining bulk materials. To produce superhydrophobic roughsurfaces various methods have been used including, templation (Kim and Hwang, 2010;Li et al., 2006) lithography (Martines et al., 2005; Notsu et al., 2005; Öner andMcCarthy, 2000), plasma treatment (Teare et al., 2002; Woodward et al., 2003, 2006),and laser ablation and micromachining (Yoshimitsu et al., 2002) amongst others. Thesemethods are briefly discussed below:Templation: It involves the use of a master with the desired features, replication of thefeatures of the master on the manufactured substrate by molding and subsequent liftingoff the replica or dissolution of the templates. Templation is useful for the production ofpolymeric superhydrophobic surfaces (Li et al., 2007).Lithography: Light (radiation: X-ray lithography, electrons: e-beam lithography) isirradiated through a mask with desired features to the substrate that is mostly silicon.Subsequent developing and etching steps yield the desired patterned surfaces.Plasma treatment: Plasma etching as a dry etch technique is using the reactive atoms orions (such as oxygen, chlorine, fluorine) generated in a gas discharge. Plasma etchingequipment accelerates the ions in the boundary layer between plasma and substrate withhigh directivity to make them able to create deep grooves with steep walls on thesubstrate.15Laser ablation: In this process, laser energy is applied to remove the materials fromsolid surfaces via melting, evaporating or sublimating. This technique is discussed inmore detail later as it is the technique used in the present work to produce the variouspatterns.Bottom-up approach involves the design of the larger and more complex structuresby integrating the smaller components. The most common methods of this approach tofabricate superhydrophobic surfaces are electrochemical deposition (Han et al., 2005; X.Zhang et al., 2004), chemical vapor deposition (CVD) (Ma et al., 2005; Wu et al., 2005)chemical bath deposition (CBD) (Hosono et al., 2005; Wu et al., 2005), layer-by- layer(LBL) deposition (Han et al., 2005; Zhai et al., 2004) via colloidal assembly,electrostatic assembly, hydrogen bonding, sol gel (Shirtcliffe et al., 2005; Tadanaga etal., 2003) and others. Some of these techniques are briefly discussed below.Chemical Deposition: Chemical deposition takes place in a chemical reaction, wherethe product deposits on a suitable substrate. Chemical deposition is commonly used forgenerating thin films of crystalline inorganic materials. Depending on the depositionconditions, several terms have been used such as chemical bath deposition (CBD),chemical vapor deposition (CVD), and electrochemical deposition.Layer-by-layer (LBL): This deposition technique takes advantages of the electrostaticcharge interactions between the different layers such as poly-anion and poly-cation. TheLBL technique is easy to perform with molecular level control over film thickness andchemistry using electrostatic interaction and hydrogen bonding.Sol gel: A sol is usually prepared by hydrolysis of the corresponding oxide in thepresence of solvent. During the network formation process, a large amount of solvent isalso impregnated in the network and thus a gel is formed.2.5.2. Surface Chemistry ModificationAs stated before, the superhydrophobicity is realized when the low surface energyand high degree of surface roughness (typically dual) are satisfied. The current methodsto produce superhydrophobic surfaces by roughening low surface energy materials are16often one-step processes and have the advantage of simplicity. However, they are limitedto a small set of materials such as PDMS (poly dimethylsiloxane) (Huang et al., 2011),PTFE (poly tetrafluoroethylene) (J. Zhang et al., 2004) and rare earth metal oxides(Azimi et al., 2013). It is believed that by following a totally different strategy, i.e.,making a rough substrate first and then modifying it with a low surface energy material,decouples the surface wettability from the bulk properties of the substance and increasesthe number of potential applications of superhydrophobic surfaces (Ma and Hill, 2006).There are several methods which can be used to modify the chemistry of a surfacesuch as physical binding, dip coating, self-assembly, electrochemical andchemical/physical vapor deposition coating. Due to low surface energy of fluorocarbonsand silanes, the fluoroalkylsilanes (Pellerite et al., 2002) and CF4 (Woodward et al.,2003) are mostly used to decrease the surface energy.2.5.3. Laser Ablation MethodAmong all surface modification techniques, laser patterning using an ultrashortpulse laser source is a unique, noncontact technique that can modify the surfacemorphology to complex patterns with very limited distortion of the bulk material. Laserprocessing has been proven to be an effective technique to create dual scale roughnessstructures in noncontact material processing for industrial applications.According to well-established experimental (Her et al., 1998) and theoretical works(Dolgaev et al., 2001), pulsed lasers, especially ultrashort pulses (pico or femtosecond),can deposit energy into a material in a very short time period, before thermal diffusionoccurs. Thus, the heat-affected zone, where melting and solidification can occur, issignificantly reduced. Therefore decreasing pulse duration below several picoseconds,increase material machining precision and quality. Figure 2-9 compares the heat-affectedzone of short and ultrashort laser pulses. Due to high intensity and short pulse duration,ultrashort laser pulse leads to high accuracy and precise pattern due to evaporationwithout noticeable melting.17Figure 2-9: a). Classical beam-matter interaction; b). Ultrafast beam-matter interaction (Leitzet al., 2011).Ultrashort laser pulses result in the fabrication of a periodic nano-ripple structuresuperimposed onto the more chaotic protuberances that the periodicity of ripples is lessthan laser wavelength (Römer et al., 2009). By controlling the energy density, the lasercan safely process silicon, metals, ceramics, and polymers as well as various othercrystalline structures. The application of femtosecond laser ablation in achievinghydrophobic surface has also attracted attention recently. Baldacchini et al. (2006)initially created superhydrophobic silicon surfaces by coating the laser-structured surfacewith fluoroalkylsilane, while Zorba et al.(2008, 2006) reported the wettability and self-cleaning properties of micro/nano patterned Si surfaces induced by femtosecond laser ingaseous SF6. Yoon et al.(2008) used the femtosecond laser to fabricate a PDMS moldwith dual scale roughness, which exhibits superhydrophobicity for both the negative andpositive replicas of the structure on PDMS. Wu et al. (2009) used low fluencefemtosecond laser to prepare laser-induced periodic surface structures on stainless steelsurfaces with a submicron level to achieve superhydrophobic surface with static contactangle of 166°. Groenendijk et al. (2006) irradiated a stainless steel mold with thefemtosecond laser in order to create a dual scale roughness structure and subsequentlyreplicated this structure on hydrophobic polymers, which became superhydrophobic dueto the dual scale roughness structure. Kietzig et al. (2009; 2011) analyzed the wettingbehavior of different metals and metal alloys irradiated with femtosecond laser atdifferent low laser fluence.  They pointed out that the metals and alloys with initiallysmooth, hydrophilic surfaces could become nearly superhydrophobic by a one-step18femtosecond laser process. This is possible due to catalytic reactions that take placegradually on the surface after the irradiation that creates gradually a carbonaceouscoating on the treated surface.Laser ablation of different materials is a phenomenon depending mainly on thelaser energy released to the target (parameters of laser beam and the physical andchemical properties of the target) (Bauerle, 1996). Laser parameters are the wavelength,intensity, spatial and temporal coherence, polarization, angle of incidence, and the dwelltime (illumination time at a particular site). The increment of the energy released to thetarget generally produces higher atomic, molecular and electron removal and ionisationand photon emission from the plasma generated at the targeted surface. The ablationprocess shows that under a minimum energy, the ablation threshold, no significant atomremoval is possible. In order to understand the effect of different laser processingparameters on the surface morphology, several studies have been performed in recentyears. For instance, the effect of laser fluence (Kuršelis et al., 2010), number of incidentpulses (Raillard et al., 2012), scanning overlap (Kuršelis et al., 2012), focus position(Wang et al., 2008), laser pulse repetition rate (Bruneel et al., 2010) for metallic surfaceshave been investigated. However, all of the manufactured morphologies have beenproduced with low laser fluence (less than 10 ) and low scanning speed (less than250 ). Thus, the manufactured structures are only nano-rippled or small parabolicpillared ones. By increasing the laser fluence or varying laser scanning speed (number oflaser pulses) the type and size of the obtained structure may significantly change as thishas been explored in the present work.2.6. Thermodynamic Analysisof WettabilityTechnically it would be desirable to design surfaces of controlled roughness inorder to control the levels of wettability (superhydrophobicity or hydrophilicity). Thisrequires a fundamental understanding of the thermodynamics of the system and theinfluence of the details of the geometrical parameters of the micro-nanostructures on thewetting properties of the fabricated surfaces. From the thermodynamic point of view, theequilibrium states are the minima of Gibbs free energy of the droplet lying on a rough2.J cm1.m s 19surface. As schematically depicted in Figure 2-10, the global minimum corresponds to astable state, while the other minima correspond to metastable states (Marmur, 1994).Figure 2-10: Multiple minima of the Gibbs energy of a droplet deposited on a rough surface.Transition between thermodynamic states may occur depending on the geometricaldetails of the roughened surface or the existence of external forces such as pressure,vibration and gravitational force and the history of the system (Extrand, 2002; He et al.,2003). This required energy is referred to as free energy barrier.Depending on the droplet formation method, a liquid droplet on a rough surfacecan stay on a metastable point that corresponds to the local energy minimum state. Bicoet al. (2002) and Lafuma and Quéréet (2003) discussed the stability/metastability of thetwo wetting configurations (composite and non-composite). They showed that the Cassiestate is often observed as a metastable state that it has to cross a free energy barrier tocollapse into the grooves. Thus, a suspended drop may form on surfaces, whichthermodynamically prefer the Wenzel regime. The metastability is demonstrated inseveral ways. For instance, by applying small pressure or by moving the metastableCassie droplet, the droplet may slip into the stable Wenzel regime.Similarly, a Cassie droplet recedes into a Wenzel droplet by allowing a smallamount of the liquid to evaporate. Lafuma and Quéréet (2003) also showed that the stateof a droplet depends on the amount of liquid as well as the means of depositing the liquidon the surface. For instance, when the liquid was deposited on the surface at once, itMetastableStateStableStateMetastableStateContact AngleGibbsFreeEnergy20formed a Cassie-like droplet. In contrast, when the liquid was delivered in the form of amist, it wetted the surface instantly as a Wenzel droplet. As a result, one cannot assumeonly Cassie-Baxter or Wenzel state, when designing a superhydrophobic substrate,because a transition from one equilibrium CA to another can cause a significant changein the apparent contact angle. Indeed, both Wenzel and Cassie formulas must beconsidered when designing a superhydrophobic substrate and the surface should berobust. A robust superhydrophobic surface is one for which the apparent CA does notchange when a drop makes a transition from a wetted to a composite state, i.e., when(Patankar, 2003).Due to the possibility of existence of either heterogeneous (composite or Cassie-Baxter state) or homogenous states (non-composite or Wenzel state), the key issue is todesign superhydrophobic surfaces with Cassie-Baxter as the most stable state.An issue closely related to the wetting regime involves adhesion between the liquidand the substrate. While in the Cassie-Baxter regime, the adhesion is small and the dropcan easily be separated from the surface, Wenzel droplets adhere to the substrate morestrongly. A first glance at this behavior can be obtained by exploring the contact anglehysteresis (CAH). CAH is high for the Wenzel regime and low for the Cassie-Baxterregime, as demonstrated experimentally by Bico et al. (1999). Thus, the Cassie-Baxterstate is more desirable for its low CAH and consequently self-cleaning and low frictionproperties.Recently, theoretical aspects of CA of superhydrophobic surfaces have beenwidely investigated (Bico et al., 2002; Choi et al., 2009; Extrand, 2002; He et al., 2003;Im et al., 2010; Johnson Jr. and Dettre, 1964; Kwon et al., 2009; Marmur, 2008, 2004;Nosonovsky and Bhushan, 2005; Patankar, 2004, 2003). However, there are few modelsdeveloped to predict the CAH (Extrand, 2002; Kusumaatmaja and Yeomans, 2007;Marmur, 2003; Quéré, 2002; Roura and Fort, 2002; Yoshimitsu et al., 2002). Due to thecomplexity of CAH, there is no general, simple approach to predict the CAH and most ofthe proposed models are phenomenological in nature (Bico et al., 2002; Extrand, 2002).Moreover, they have not been developed based on thermodynamic principles(Shuttleworth and Bailey, 1948).W CB 21The first thermodynamic analysis to predict the contact angle hysteresis (CAH) ofrough surfaces was performed by Johnson and Dettre (1964). The analysis is based onminimizing the free energy of the system aiming to calculate all the stable and metastablestates. These states are related to local minima calculated from free energy barriers as thedroplet advances and recedes. These barriers refer to the Gibbs free energy differencebetween a local minimum and an adjacent maximum in the direction of the three-phaseline motion (i.e. advancing or receding) (Johnson Jr. and Dettre, 1964; Shuttleworth andBailey, 1948). Their model was developed for a sinusoidal structure and their 3-dimensional numerical analysis of the system was very time-consuming and complicated.Following the Johnson and Dettre (J–D) model, later investigations conducted similarcalculations to understand the surface wettability (Cox, 1983; Huh and Mason, 1977;Shuttleworth and Bailey, 1948). In spite of some improvements, the physical picture ofthe CAH in these studies is obscured by mathematical complexity and hence difficult toapply to what can be produced technologically today.Recently, Li and Amirfazli (2005, 2007, 2008) have proposed a new 2-dimensionalthermodynamic analysis to reduce the complexity of the J-D, 3-dimensional analysis.The weakness of their model which has been illustrated for a square pillared morphology(Li and Amirfazli, 2005) is that the model is perfect just for pillars with flattened tops.For this type of surface geometry, the liquid either completely wets the surface geometry(Wenzel state) or it simply sits on the top of the pillars (Cassie-Baxter state) withoutpartially penetrated to the grooves. However, in reality most of the structures to createsuperhydrophobic surfaces do not possess pillars with flat tops and for structures likesinusoidal or paraboloidal patterns, the liquid penetrates into the trough between pillars.In such a case, the Cassie-Baxter contact angle would depend on the penetrated height ofthe liquid.Theoretical aspects of these thermodynamic models and the methodology by whichthey are developed will be discussed in detail in chapter 6, when these concepts will beapplied on the manufactured nano-patterned substrates of the present work to predicttheir wettability.22CHAPTER 3: THESIS OBJECTIVES AND ORGANIZATION3.1. Thesis ObjectivesThe preparation of superhydrophobic surfaces is still in its initial state and there isno industrial method for producing these surfaces. All of the mentioned methods in theprevious sections are in the academic developmental stage. The procedures are costlyand time-consuming with respect to the number of steps and surface treatments.This thesis is devoted to investigate the femtosecond laser ablation application inthe preparation of metallic superhydrophobic surfaces.The particular objectives of this work can be summarized as follows:1. Investigate the effect of femtosecond laser ablation processing parameters such aslaser fluence and scanning speed on the micro/nano structure of the metallic substratesand in particular stainless steel.2. Examine the wettability of laser-patterned surfaces (different pillaredmorphologies) generated by laser ablation by measuring their contact angle(s) (CA) inthe Wenzel and the Cassie-Baxter states and their corresponding contact angle hysteresis(CAH).3. Develop a simple-appropriate mathematical model to predict the surfacewettability, in particular to predict the CA and the CAH.4. Identify the optimum surface geometry to obtain the Cassie-Baxter state as thestable state on the surface by analyzing the effect of the geometrical parameters on thesurface wettability.3.2. Thesis OrganizationThis thesis is organized as follows. Chapter 1 briefly describes the introduction tothe subject of superhydrophobicity and a quick explanation of the motivation of thisstudy. The literature review on the wettability of surfaces and different methods to createartificial superhydrophobic surfaces, particularly the laser ablation method and others,related to the present study are provided in chapter 2. The objectives and the organizationof this thesis are presented in chapter 3. Chapter 4 describes the material and23methodology used in this study to create and characterize the metallic superhydrophobicsurfaces. Chapter 5 presents experimental work and discusses the different possiblestructures obtained by the laser ablation technique. The details of the surface wettabilityof these patterns are also discussed in detail. A new thermodynamic analysis to calculatethe surface CA and CAH on non-flattened surfaces is presented in chapter 6. Finally,chapter 7 summarizes the concluding remarks of this thesis and recommendations forfuture works.24CHAPTER 4: EXPERIMENTAL METHODS AND MATERIALSIn order to prepare hydrophobic and superhydrophobic surfaces, the metallicsurfaces were patterned by femtosecond laser irradiation; subsequently some of thesubstrates were subjected to silanization in order to reduce their surface energy. In thissection, the materials and the experimental methods used to produce and modify thesuperhydrophobic surfaces are discussed in detail.4.1. MaterialsSheets of stainless steel 316L, 1mm in thickness were used as substrates in thiswork. They were polished using sandpaper to an average roughness value ( ) of 500nm. This is defined as the average length of protrusions above their mean value, ameasure of roughness standard in literature.To modify the surface chemistry in order to render the metallic substrate a lowsurface energy material, trichloro (1H,1H,2H,2H-perfluorooctyl) silane, FTS (97%,Sigma-Aldrich, USA) was applied onto the surface. The other chemicals used in thisstudy are n-Hexane (95%, Sigma-Aldrich), Sulfuric acid, H2SO4 (98%, Sigma-Aldrich),Hydrogen peroxide, H2O2 (30%, Sigma-Aldrich), Ethanol and Acetone. More details onthe laser ablation and the silanization process are discussed below.4.2. Surface Laser IrradiationUltrashort laser pulses to irradiate the various substrates were generated by anamplified all solid-state Ti:Sapphire laser. The laser system includes a Ti:Sapphire seedlaser Coherent Mira HP and an amplifier Coherent Legend to produce amplifiedfemtosecond laser pulses with center wavelength of 800 nm. The repetition rate of laserpulses was 1 kHz with pulse duration of 120 fs and the maximum output power of about2W. The beam profile from this regenerative amplifier system has a Gaussiandistribution with a beam waist of 10mm. A set of neutral density (ND) filters were usedaR25to attenuate and adjust the energy of the laser beam and a lens with 300 mm focal lengthwas used to focus the beam on the sample. The spot size of beam at the focal point ( )was 30μm that has been calculated using the following equation:042 . FD            (4-1)Where λ is laser wavelength, F is the focal length of the lens (300mm in this setup) and D is the beam waist before focal lens (here, 10mm). A schematic diagram of thelaser patterning set up is shown in Figure 4-1.Figure 4-1: Schematic diagram of the laser irradiation set-up.The minimum value of the beam spot size in beam axis is . The laser ablationis a function of the beam spot size to find the laser fluence. Outside of laser focal planethe laser beam is divergent or convergent. In order to have a precise laser patterning, thedistance between focal plane and the target surface should be inside the Rayleigh range.In the Rayleigh range, the spot radius changes slightly and the beam is nearly collimated,while beyond the Rayleigh range, the laser beam becomes convergent or divergent. TheRayleigh range in this set up (2zR) was 1.8 mm found from the following:2022 Rz (4-2)02Ti: SapphireFemtosecondLaserNDFilterMLTargetZYXTSDriverPCGaussian Beam Profileω0 I0/e2I00226In order to move the samples under the laser beam, the stainless steel (SS) sheetswere mounted on a precise, computer-controlled ZABER T-LS80 X-Y translation stagewith step resolution of less than 0.1 μm and a maximum linear speed of 4000 .The power of the incident laser beam was adjusted in the range of 5 to 1700 mW (peakfluence: 1.5 to 480 ) and the scanning speed range varied from 250 to 1850. The samples were irradiated at normal incidence in air and then subjected to anultrasonic bath for 2 min in acetone to remove all the debris off the patterned surface.4.3. Surface SilanizationSince the metallic laser ablated surfaces are hydrophilic after laser irradiation, thefluoroalkylsilane is deposited on the sample surfaces using a chemical reaction bath (dipcoating) in order to decrease their surface energy and obtain hydrophobic samples.Silanization Mechanism. The silanization process occurs mainly by hydrogenbonding when the silane solution subjected to contact with the M (metal) surface formsbonds (Chovelon et al., 1995). The alkylsilane coatings are rather stable andpart of this stability has been attributed to cross-polymerization of alkylsilane chains bycross-links (Sagiv, 1980).A schematic of this silanization mechanism (solution based) is depicted in Figure4-2. The fluoroalkylsilane precursor used in this study is trichloro (1,1,2,2-perfluorooctyl) silane (C6F13CH2CH2 Si Cl3), FTS, 97%. The mechanism of silanizationhas four steps. First, absorbing water hydrolyzes the fluorinated alkyl silane. Second, theacid treatment exposes some hydroxyl groups on the surface. Third, in the main part ofthe coating, hydrogen bonds form between hydroxyl groups on the substrate andhydrolyzed fluorinated alkyl silane groups. Also, cross-links between silane groups formin this part of the mechanism. In the last fourth step, condensation happens and somewater molecules are removed from the coated surface. This step stabilizes the silanizedcoating on the substrate.The procedure of substrate preparation has three experimental steps: pretreatment,silanization and heat curing.1.m s 2.J cm1.m s M O Si Si O Si 27Figure 4-2: Schematic diagram of mechanism of coating a metallic substrate using fluorinatedalkylsilane.Pretreatment step: In order to remove any contamination and expose the hydroxylgroups ( ) on the surface, the stainless samples were pretreated using a Piranhasolution composed of (4:1 v/v) for 1 hour at room temperature. After acidtreatment, the surfaces were rinsed with ethanol, water and acetone respectively for 10minutes in ultrasonic bath. After cleaning followed by blowing nitrogen onto the samplesfor drying, they were subjected to the silanization step.Silanization step: In this step, the surfaces (samples) were immersed in 0.5% wtFTS in n-hexane (0.075 per 10 of n-hexane) for 2 hours at 60°C. Hydrolysis andformation of hydrogen bonding occur in this step. Water for hydrolysis may originate1. Hydrolysis :          CF3(CF2)n (CH2)2 Si(Cl)3 H2O CF3(CF2)n (CH2 )2 Si(OH)32. Acid Treatment:  Substrate H2SO4/H2O2  SubstrateOH OHOH3. Silanization: SubstrateO OSiOH OOSiO OHOH HHHH H SubstrateOSiO O SiOn SubstrateOH OHSiOH OHOHSiOH OHOH4. Condensation: SubstrateO OSiOH OOSiO OHOH HHHH HHeatOH2 4 2 2/H SO H Ogr mL28from several sources. It may be either added or be already present on the substratesurface or may originate from the atmosphere. The degree of polymerization of the silaneis determined by the amount of available water and the organic solvent (Arkles, 1977).Condensation step: Finally in the last step, the samples were heated to 120° C for30 minutes to dry the samples and stabilize the coating.4.4. Surface Analysis4.4.1. Contact Angle (CA) and Contact Angle Hysteresis (CAH)The wetting behavior of the treated/irradiated samples was evaluated by measuringtheir contact angle with distilled, deionized water having a typical resistivity of 18.2at 25°C, a total organic carbon content of less than 10 ppb, and a neutral pHvalue of 7. Droplets of water of volume 5 µL were dispensed on the respective surfaceswith a piston-driven air displacement pipette. Digital images of the water droplet on thesurfaces were taken with a Nikon D90 digital camera. The contact angle (CA) wasdetermined by analyzing droplet images with the image processing methods usingMATLAB (Figure 4-3).Figure 4-3: A typical droplet image and the measurement of contact angle.Contact angle hysteresis (CAH) measurements were performed by measuring theadvancing and receding contact angles of a growing and shrinking droplet on the surface.The camera was set to capture three images per second for advancing and recedingcontact angle analysis. A sample of contact angle hysteresis is shown in Figure 4-4..M cm29Figure 4-4: Experimental sequence of advancing and receding images of a droplet to determine theadvancing and receding contact angles.By analyzing the captured images, the maximum value of CA during the dropletgrowth is defined as the “advancing CA” and the minimum of CA during dropletshrinkage is defined as the “receding CA” (See Figure 4-5).Figure 4-5: Advancing and receding contact angles for a hydrophobic sample.4.4.2. Surface Patterning/Geometric DetailsThe morphology of the surface structures was studied with a variable-pressureScanning Electron Microscopy (Hitachi S-3000N SEM) and a profilometer (Brukr,Dektak XT) in order to map the geometrical characteristics of the patterned surfaces asaccurately as possible. The geometrical characteristics of the patterned surfaces weredetermined by profilometry and the length scale of periodicity of the asperities were30obtained by Fast Fourier Transform (FFT) analysis of the SEM images using ImageJsoftware.The Fast Fourier Transform of the SEM images of the treated areas investigates theevolution of the surface morphologies in detail via the spatial frequency information.Figure 4-6 (a) shows the SEM image of a laser-ablated surface.  The Fourier Transformexpresses an image in terms of the spatial frequencies in the image as depicted in figure4-6(b). A sharply focused image is rich in high spatial frequencies. Large uniform areasare represented by low frequencies. In the next step, the applied method (FD Math ofFFT in ImageJ software) analyses the image in the frequency domain and returns theinverse image of Fast Fourier Transform in the space domain as seen in Figure 4-6(c).Figure 4-6: (a). SEM image of a micro-pattern, (b). FFT image of image 4-6(b) in the spatialfrequency domain, (c). Inverse FFT of image 4-6(b) in the space domain after certain corrections.Figure 4-7 depicts the average gray profile of Figure 4-6(c) and results theperiodicity of the selected area versus image pixel.Figure 4-7: Average gray profile of Figure 4-6(c) versus horizontal pixels.a b c31CHAPTER 5:EXPERIMENTAL RESULTSAs mentioned before there are two important parameters that are required for thefabrication of superhydrophobic surfaces, namely, surface roughness and low surfaceenergy. In order to roughen metallic surfaces in a controlled manner, particularlystainless steel surfaces, the laser ablation method has been used in this work. Thestainless steel substrates were mounted on a precise, computer-controlled translationstage capable of moving in front of a fixed laser beam.The effect of laser parameters such as laser power (fluence), number of laser pulsesinduced to the surface (scanning speed) and laser beam overlap, on the surface structureand wettability are examined. The various manufactured substrates are presented andanalyzed in terms of their geometrical characteristics. After laser irradiation, certainsamples were subjected to silanization in order to reduce their surface energy. Thesesurfaces are also analyzed in terms of their geometrical characteristics in order todetermine the influence of silanization.All of the experiments were done on the stainless steel substrate. Due to thedependency of laser ablation method on the thermo-physical properties of the substrate,the morphology of surface for other metallic surfaces is different.5.1. Surface MorphologySEM images of laser irradiated samples have shown that the geometrical details ofthe morphology of the obtained micro/nano-structures strongly depend on the laserparameters. Namely, they depend on the laser power, the number of laser pulses per spot,the scanning speed and overlap. In this study, the laser power and the scanning speedhave been varied in the range of 5 to 1700 mW (peak fluence: 1.5 to 480 ) and250 to 1850 , respectively. It is noted that we report the fluence values as peakfluence as defined by Equation (5-2) presented below. The scanning overlap was 50% forall the irradiation experiments and set to 15 μm. By changing the effective variableswithin the mentioned ranges, four types of nano and micro-patterns were identified.The first geometrical type of structure is a nano-pattern and forms at very low2.J cm1.m s 32laser fluence with moderate to high scanning speed or at higher laser fluence with highscanning speed. Figure 5-1 shows SEM images of two samples with nano-scale pattern.The sample in Figure 5-1(a) was created by using low laser fluence of 1.5 andscanning speed of 250 , while the one in Figure 5-1(b) was formed using a laserfluence of 10 and a high scanning speed of 1850 . A higher magnifiedimage for sample depicted in Figure 5-1(a) is shown in Figure 5-1(c). This image showsthat the structure of the pattern is a periodic one, possessing regular ripples with acharacteristic diameter in the submicron (nanometer) scale. The magnified SEM imageof the sample depicted in Figure 5-1(b) is very similar to that of Figure 5-1(c), not shownhere. In both cases, the period of ripples (approximately hemi-cylindrical) is around 400-500 nm and their length of about 2-3 μm. The ripples are oriented perpendicularly to thepolarization of the incident light (or electric field vector of incident light). In general, theperiodicity of the ripples depends on the laser beam wavelength and is equal or less thanthe laser wavelength (Bauerle, 1996). The possible explanation for this effect is based onthe interference of incident and scattered laser radiation or excited surface waves(Emmony et al., 1973).Figure 5-1: SEM images of nano-rippled patterns formed with (a). Laser fluence of 1.5 andscanning speed of 250 (b). Laser fluence of 10 and scanning speed of 1850 (c).SEM image of sample in Figure 5-1(a) at a higher magnification.By increasing the laser fluence at a constant scanning speed or decreasing thescanning speed at constant laser fluence, three additional different micro-patterns are2.J cm1.m s 2.J cm 1.m s 2.J cm1.m s  2.J cm 1.m s 33obtained. The first type is a pillared morphology with parabolic shapes (parabolic-pillared pattern). Figure 5-2 shows SEM images of the created parabolic pillared patternsmanufactured with a constant scanning speed of 930 and changing the laserfluence from 10 (Figure 5-2(a)) to 92 (Figure 5-2(c)). Figure 5-2(d) is ahigher magnification of the sample depicted in Figure 5-2(b) (similar images wereobtained for the others) which reveals that the laser induced surface structures areconsisted of micro-paraboloids, which are covered with approximately hemi-cylindricalnano-scaled ripples.Figure 5-2: SEM images of the parabolic-pillared patterns, formed by the scanning speed of 930and laser fluence of  (a). 10 , (b). 16 , (c). 92 , (d). SEM image with ahigher magnification to show double roughness of the sample depicted in Figure 5-2(b).By further increasing the laser power or further decreasing the scanning speed, twoadditional microstructures were observed, which are depicted in Figures 5-3 and 5-4respectively. First, an elongated sinusoidal-pillared pattern covered with dual roughnessis shown in Figure 5-3. Finally, the tripled pattern depicted in Figure 5-4 consists of1.m s 2.J cm 2.J cm1.m s  2.J cm 2.J cm 2.J cm34coarse micro asperities of irregular shape covered by small spheres with characteristicdiameter of 2-3 microns as second degree of roughness. Furthermore on top of thesemicrospheres, there seem to exist smaller nano-scaled ripples. We refer to this structureas triple roughness pattern.Figure 5-3: Sinusoidal elongated pillared pattern created by using (a).Laser fluence of 136and scanning speed of 930 , (b).Laser fluence of 185 and a scanning speed of 1850, and (c). SEM image with a higher magnification to show double roughness of the sampledepicted in Figure 5-3(b).Figure 5-4: Triple roughness patternscreated by using (a).Laser fluence of 440 and scanningspeed of 1850 , (b).Laser fluence of 480 and a scanning speed of 1850 , (c). SEMwith a higher magnification to show triple roughness of the sample depicted in Figure 5-4(b).Figure 5-5 shows representative images of all patterns manufactured in this studyby varying the laser power between 5 to 1700 mW (fluence: 1.5 to 480 ) andscanning speed from 250 to 1850 . In this Figure, colored borders of each imageshow the ranges of laser power and scanning speed, which when used they generate the2.J cm1.m s  2.J cm1.m s 2.J cm1.m s  2.J cm 1.m s 2.J cm1.m s 35specific type of nano/microstructure. Figure 5-5 clearly indicates that a lower laserfluence requires a higher number of laser pulses per spot to form a similar structure thatcan be formed by a higher laser fluence. Decreasing the scanning speed corresponds to ahigher number of laser pulses to create the micro-pattern. Therefore, the effects ofincreasing the laser fluence and decreasing the scanning speed are equivalent as bothincrease the diameter and height of pillars.Figure 5-5: Formation of four patterns at various laser power and scanning speeds.5.2. Effect of Laser Parameters on Micro/Nano-PatterningGenerally, for a Gaussian beam, the fluence profile, , is expressed as:( )r36(5-1)where, referred to as the Gaussian beam radius, is the radius at which the fluence hasdecreased to or 0.135 of its axial, or peak value, r is the distance from the beamcenterline and is the peak fluence of beam, given by:(5-2)Where EP is the laser beam pulse energy, which is ratio of power to repetition rate.At low laser fluence, the energy of induced pulses is absorbed by the surface. Dueto the local temperature increase and consequently, melting, evaporation or sublimationof metallic material by the absorbed energy, nano-structures are formed on the surface.At higher laser fluence the material is converted to plasma. When the metallic atoms onthe surface absorb enough energy, they break their bonds with neighbor atoms. At thispoint, the laser ablation process begins. Certain energy is required to remove every atomduring laser ablation. The minimal energy density required to initiate material removal iscalled the ablation threshold, . Laser ablation just above this ablation threshold iscalled “gentle” ablation. In this regime, the ablation rate is low and depends on theoptical penetration depth given by:(5-3)where, is the ablation depth per pulse, δ is the optical penetration depth and isthe ablation threshold for gentle ablation (Wang et al., 2008). Experimentally, the depthof the removed material in this ablation is of the order of tens of nanometers and theablated area tends to be smooth (Jiang and Tsai, 2003). The nano-rippled structurediscussed above in Figure 5-1 is formed by this type of ablation. The laser ablationthreshold of stainless steel by using femtosecond laser with 150 fs pulse duration andwavelength  of 800 nm is 0.21 (Raciukaitis et al., 2008).The material removal rate grows slowly by increasing the energy density untilsome breakpoint (Mannion et al., 2004). At this point an increase in laser fluence causesa rapid growth of the ablation rate. This enhanced material removal is called “strong”22020( )rr e  021e00 202 pE th,ln othL      L ,th2.J cm37ablation regime, which is dominated by thermal vaporization (Mannion et al., 2004). Theablation depth, in this regime is characterized by the electron heat diffusion length, γ:(5-4)where, is the ablation fluence threshold of transition to the stronger ablation regime.In this region the depth of removed material per pulse is of the order of hundreds ofnanometers and the ablated surface is rough (Jiang and Tsai, 2003; Mannion et al., 2004).For laser ablation with a Gaussian spatial intensity beam profile, a simple relationhas been derived between the diameter of an ablated crater, D, and the “strong” materialsurface ablation threshold  ( ), the laser Gaussian beam radius, , and the peakfluence in the beam, (Jiang and Tsai, 2003):(5-5)which simply implies that by increasing the laser fluence, the diameter of the microcrater increases.Due to the incubation effect of multi-pulse ablation, with the increase of laser pulsenumber, the ablation threshold reduces and the ablation rate increases. According to theincubation model of Jee et al. (1988), the multi-pulse ablation threshold fluence, ,is related to the single pulse ablation threshold fluence, , by a power law:(5-6)where N is the number of laser pulses and S is the accumulation parameter. The value ofS for stainless steel in femtosecond laser system obtained from experiments is 0.86(Raciukaitis et al., 2008). According to Equations (5-4)-(5-6), by increasing the intensityof absorbed energy through the increase of the laser power or processing time andnumber of laser pulses per spot, the structure will be coarser with a higher size ofasperities.Figure 5-6 depicts the profile of Gaussian laser beam fluence for different laserpowers. It can be seen that by using laser beams with peak fluence higher than theablation fluence threshold, for both types of ablation (gentle and stronger), a largerL0,lnthL      ,thth 002 2 002 lnthD      ( )th N(1)th1( ) (1) Sth thN N   38portion of the laser beam can ablate the surface. A larger portion of the laser beam athigher fluence means a larger diameter of the ablated crater (d2>d1) and a deeper ablationdepth per pulse (h2>h1).  Hence, increase of the laser fluence, it causes an increase ofboth the diameter and height of microstructure.Figure 5-6: Gaussian laser beam fluence profile with different laser powers.Due to incubation effect, a higher number of laser pulses results in larger diameter anddepth of ablation. In this work, due to the sample translation in front of laser, instead ofusing the number of laser pulses per spot, the parameter of scanning speed is applied to39find the effective number of laser pulses (Figure 5-7). The maximum received power isequal to the power of Neff number of pulses. By considering the incubation effect on themulti-pulse ablation threshold, then Equation (5-6) can be written/approximated by:(5-7)The effective number of laser pulses incident on one spot with diameter of 4 0 (inwhich the total power of one pulse is covered) for a moving sample with speed of V andlaser repetition rate of f can be found by calculating the total irradiated power on thesample.(5-8)where, P1 is the power of one pulse and Ptot is the total incident power on an area havinga diameter equal to 4ω0.Figure 5-7:Schematic of laser ablation with pulsed Gaussian beam, (a).Laser ablation in one pass,xiisthe distance traveled by the sample between two pulses with speed of V, (b).Observed point on thesample after laser irradiation.The calculated diameter from Equation (5-5) is the diameter of a crater, where thecrater is generated by stationary laser ablation.  To our knowledge, there is no formula inthe literature that can be used to predict the dimensions of pillars and craters as afunction of laser parameters for moving substrates. As mentioned before, S in Equation(5-6) is the accumulation parameter. It is reasonable to hypothesize that the value of S1( ) (1) . Sth eff th effN N   014toteffP fNP V xiDepth of ablated structureof multipulse ablationVa. b.40changes for moving substrates. Using experimental results, for this specific laser set up,the new value of S can be found. From Equations (5-3)-(5-5), it is clear that the ablationrate is a function of .(5-9)The non-constant part of the Equation (5-9) is defined as a new parameter, LaserIntensity Factor (LIF):(5-10)where .Figure 5-8: Periodicity of microstructures versus Laser Intensity Factor (LIF) with “n” equal to 0.5.The modulation period of microstructures (characteristic length of the asperities)was determined by Fast Fourier Transform (FFT) analysis as discussed in detail in0 / th  0 010(1) / 4Sth th V f    00/ 4nLIFV f1n S 41section 4.4.2. By increasing the ablation rate ( ), the periodicity of asperities isalso growing. LIF is equivalent to the ablation rate; therefore the value of modulationperiod should increase with increase of LIF. Plotting the modulation period ofmicrostructures in terms of LIF, the optimum value of “n” that monotonically relates themodulation period with LIF determined is about 0.5, shown in Figure 5-8. This Figuredepicts the different substrates, whose modulation period (characteristic length scale ofpatterns) monotonically correlates well with LIF.Increase of the LIF can be caused by either increase of the laser fluence or decreaseof the scanning speed. It should be noted that all LIF values from the definition givenabove are based on 50% overlap of the laser beam scan lines. The effect of higheroverlap is similar to that of higher laser fluence.If the LIF is less than 75 , independent of the fluence and scanning speedvalues, the pattern will always be nano-rippled. This is the case for the samples shown inFigures 5-1(a) and 5-1(b), where the LIF is 22 and 61 , respectively. By increasingthe LIF from 75 to 150 , there is a region in which the morphology changes fromnano-rippled to parabolic-pillared pattern, similar to the sample depicted in Figure 5-2(a).The range of the LIF parameter and the characteristic dimension of the asperity(approximately or equivalent to a diameter) for the various structures are listed in Table5-1.Table 5-1: The range of the LIF for the various structures.Type of structure Range of LIF( )Typical range ofperiodicity (μm)Nano rippled Below 75 400-500nm, 2-3μmlengthParabolic-pillared 150-750 6-28Elongated sinusoidal-pillared800-1250 30-50Triple structure 1500-3000 45-700 / th 2.J cm2.J cm2.J cm2.J cm425.3. Surface Hydrophobicity and Contact AnglesAfter coating all samples with fluorinated alkylsilane, FTS, the flat surface contactangle is about 105°±3°. The various substrates were analyzed by SEM before and aftersilanization and due to the thin layer coating of fluorinated alkylsilane, the surfacemorphology did not change after the chemical treatment. The Cassie-Baxter CA of thevarious samples is plotted versus the LIF parameter for the four distinct structures inFigure 5-9(a) and the CAH of different micro/nano patterns has been reported in Figure5-9(b). For the first two patterns, namely the nano-rippled and the parabolic-pillaredpatterns, obtained by increasing the LIF parameter, the CA is increasing monotonicallyand CAH is decreasing.Figure 5-9: (a). The Cassie-Baxter contact angle of various samples in the four distinctly differentnano/micro-patterns as a function of the LIF parameter.43Figure 5-9: (b). The contact angle hysteresis of various samples in the four distinctly differentnano/micro-patterns as a function of the LIF parameter.From the parabolic-pillared pattern to the sinusoidal elongated structure, there is areduction in the contact angle and enhancement of contact angle hysteresis, although byincreasing the LIF in this region, the CA of the double roughness sinusoidal-pillaredpattern increases again monotonically, whereas the CAH is decreasing. This is due to areduction of the depth of the dales observed when the morphology changes fromparabolic-pillared to elongated sinusoidal. Finally, the trends of CA and CAH variationin the triple roughness structured regime are similar to that obtained in the elongatedsinusoidal pattern regime. The maximum surface hydrophobicity in each section isobtained at the border of each section. By increasing LIF, the various structures becomecoarser, whereas both the diameter and dale depth increase.44Figure 5-10: SEM images of nano-patterns in Section I of Figure 5-9 (nano-rippled pattern,parabolic-pillared patterns) in increasing order of the LIF parameter  (a). LIF of 22, fluence of 1.5and scanning speed of 250  (b).LIF of 186.5, fluence of 16, and scanning speed of 460,(c). LIF of 591.7,fluence of 38.2 and scanning speed of 250, unit of all reported LIFs is unit of fluence isand scanning speed unit .Figures 5-10, 5-11 and 5-12, present several SEM images of micro/nano-patternsin each of the three sections of Figure 5-9, in increasing order of LIF parameter withsurface CA also shown. Although the patterns become coarser with increase of LIF, theappearance of double roughness on top of micro-pillars increases the level ofhydrophobicity. Moreover, the contact angle hysteresis is decreasing with increase ofLIF.Figure 5-11: SEM images of nano-patterns in Section II of Figure 5-9 (elongated sinusoidal-pillaredpattern) in increasing order of the LIF parameter (a). LIF:771, fluence of 135.8, scanning speed of1850, (b). LIF:1091, fluence of 135.8, scanning speed of 930, (c). LIF: 1848, fluence of 214, scanningspeed of 1850. Unit of all reported LIFs is , unit of fluence is and scanning speed unit is10 μma θ= 112°10 μmb θ= 142°10 μmc θ= 166°2.J cm 2.J cm1.m s 2.J cm 2.J cm1.m s 45Figure 5-11 includes SEM images of the elongated sinusoidal pillared patterns andtheir corresponding contact angles in increasing LIF order. In this region, the contactangle increases with increase of LIF. The pillar diameter and height in this section are inthe range of 30-45μm and 10-40μm respectively.The main reason for contact angle reduction from the parabolic pillared pattern toelongated sinusoidal-pillared one is a rather abrupt decrease of the depth of the lattermicrostructure. For example, according to the SEM images and profilometer results, thediameter and height of the asperities of sample shown in Figure 5-10(d) is 22-24 μm and32 μm respectively, while corresponding values of the sample in Figure 5-11(a) are 27-29 μm and 12μm respectively. Therefore, by decreasing the ratio of height to diameter,the CA decreases.Figure 5-12: SEM images of nanopatterns in Section III in Figure 5-9 (triple roughness nano-pattern) in increasing order of the LIF parameter (a). LIF: 1849, fluence of 325.4, scanning speed of1850, (b). LIF: 2331, fluence of 410, scanning speed of 1850. (c). LIF:2730, fluence of 480, scanningspeed of 1850. Unit of all reported LIFs is , unit of fluence is and scanning speed unit is.Figure 5-12 shows SEM images of triple roughness patterns and their CAs inincreasing LIF order. In this regime, the pillar diameters are larger than 45μm and theheight is also larger than 45μm with the height being always greater than the diameter.The results show that by increasing both of them as a result of the LIF increase, the CAincreases, while the contact angle hysteresis decreases. In summary, besides theindividual values of diameter, D, and depth, H, of the nano-patterning details, the ratio,2.J cm 2.J cm1.m s 46H/D is also important for wettability (discussed further in the modeling chapters below).For a given fluence value, with increase of the number of pulses used to form each crater,the higher amount of the dissipated energy increases the depth of the micro-pattern. TheCAH in the triple structure region is less than 20°. The main reason of low CAH is thespecial micro-nano structure. In triple structure, the large asperities with size in the rangeof 45-60μm, are covered with finer spherical micro-pillars in the range of 2-5μm.Moreover these micro-asperities are covered with fine spherical nano-patterns, which arereferred to as triple roughness (as shown in Figure 5-4). This specific structure is suitableto trap air pockets beneath the water droplet; therefore, it exhibits a high CA and a lowcontact angle hysteresis, rendering this a true superhydrophobic pattern.One of the main objectives of this detailed experimental work was to identify theoptimum pattern that maximizes the hydrophobicity of the surface in other words thatmaximizes the CA and minimizes the CAH. It is noted that the contact angle of a surfaceto qualify as superhydrophobic, should be higher than 150° and its CAH to be less than10°. Figure 5-9 shows that some of microstructures created with high LIF have contactangles of more than 150°. The CAH of the structures with CA higher than 150° are in therange of 8° to 32° for the sinusoidal-pillared pattern and in the range of 4° to 20° for thetriple roughness structure. These values are significantly less than those observed for theparabolic-pillared structures, which are typically more than 20°. Therefore, thesinusoidal-pillared and triple roughness values are more superhydrophobic than theparabolic-pillared ones.The SEM images of two true superhydrophobic surfaces are shown in Figure 5-13.The CA of the sample in Figure 5-13(a) (sinusoidal-pillared pattern) is 155° and its CAH10°. This pattern has been created by laser fluence of 136 and scanning speed of930 . The corresponding values of the CA and CAH of the sample shown inFigure 5-13(b) are 164° and 4°, respectively. This triple structure has been formed bylaser fluence of 480 and scanning speed of 1850 . It seems that overall thetriple roughness nano-structured pattern is the most superhydrophobic compared to theother nano-patterns manufactured in this work.2.J cm1.m s 2.J cm 1.m s 47Figure 5-13: (a). Structure with 8° CAH and CA of 155° created by: (a). LIF of 1091 , fluenceof 136 , scanning speed of 930 , (b). Triple roughness structure with 4° CAH and CA of164° created by LIF of 2730 , fluence of 480 , scanning speed of 1850.It should be mentioned that all CAs reported above refer to Cassie-Baxter state thatis when a droplet is gently laid on the surface. The values of Cassie-Baxter CA, most ofthe times, are more than the corresponding Wenzel ones. The Wenzel CA values weremeasured after measuring the Cassie-Baxter ones by applying pressure or vibrationapplied on the substrate. These cause collapse of the droplet thus filling up the dalesbetween the asperities.5.4. The Effect of Overlap on Surface WettabilityAs discussed above, all patterns presented above were manufactured by 50%overlap of the Gaussian beam diameter ( ). In this section, the effect ofscanning overlap on the surface wettability is investigated. Overlap is defined as the ratioof movement in the perpendicular direction of scanning (Y derection) to the laser beamspot size ( ).2.J cm2.J cm 1.m s 2.J cm 2.J cm 1.m s 02 30 m 0248Figure 5-14: Structurs created by using two different overlaps of 0% and 50% (a). Fluence of 18.67, scanning speed of 930 , (b). Fluence of 16.55 , scanning speed of 460 , (c).Fluence of 480 , scanning speed of 1860 .Increasing the overlap roughly means that more power is applied on the surface.Figure 5-14 depicts the effect of decreasing overlap from 50% to 0% for three differentsets of laser peak fluence and scanning speeds. As it is clear from Figure 5-14a-c, due toreduction of the intensity of incident light at a fixed point, the crater height decreases.The beam of the incident light at a fixed point decreases by decreasing the percentage ofscanning overlap. Decrease of pillar height results into a reduction of surfacehydrophobicity. Thus increasing the scanning overlap decreases the surface wettability asshown in Figure 5-15 from the reported contact angles on the images.2.J cm 1.m s  2.J cm 1.m s 2.J cm 1.m s 49Figure 5-15: Wettability of patterned surfaces with 50% and 0% scanning overlap for thess sets offluence and scanning speed parameters (a). Fluence of 16.5 and scanning speed of 460; (b). Fluence of 38.2 and scanning speed 460 ; (c). Fluence of 480 andscanning speed of 1860 . In all cases decrease of overlap from 50 to 0% causes a decrease ofcontact angle.5.5. SummaryThe effects of laser parameters such as laser fluence, scanning speed and scanningoverlap on the generated micro/nano patterns was examined in detail. First, femtosecondlaser irradiation was applied to Stainless Steel substrates using a wide range of laserenergy density and scanning speeds to manufacture various patterns. Depending on thelaser parameters, four distinctly different nano-patterns were produced, namely nano-rippled, parabolic-pillared, elongated sinusoidal-pillared and triple roughnessnanostructures. These were classified according to a newly defined parameter, the LaserIntensity Factor (LIF) that is related to the laser fluence and the scanning speed.Furthermore, the LIF was found to correlate monotonically with the modulation period(periodicity of microstructures). Consequently, a chemical treatment (silanization) was2.J cm1.m s  2.J cm 1.m s  2.J cm1.m s 50used to reduce the surface energy of all manufactured substrates to the same value andmake them intrinsically hydrophobic with Young contact angle of about 105°. Analysisof the wettability revealed enhanced superhydrophobicity for most of these structures,particularly of the triple roughness pattern (CA in excess of 160o and CAH of less than5o). Finally, the effect of scanning overlap was investigated and results have shown thatdecrease of scanning overlap causes an increase in the wettability of the substrate.51CHAPTER 6:THERMODYNAMIC ANALYSIS AND RESULTS6.1. IntroductionIn general, from a thermodynamic viewpoint, the equilibrium condition of a systemcorresponds to the minimum of Gibbs free energy. Here the system under considerationis a droplet sitting on a uniform patterned surface shown in Figure 6-1.Figure 6-1:A droplet sitting on a uniform patterned surface.The Gibbs free energy of this solid-liquid-air system is expressed as follows:(6-1)where, is the interfacial tension, is the interfacial area and the superscripts , anddenote ‘liquid’, ‘air’ (or gas) and ‘solid’ phases, respectively. The interfacial areas arefunctions of surface roughness and apparent CA locally at each point along theroughened surface (Marmur, 2003, 1994).For simplicity, it is assumed that the effect of gravity is negligible. Under thiscondition, the pressure inside the liquid drop must be uniform. The air pressure is alsouniform and equal to the atmospheric pressure. Another assumption is that the dropradius is much larger than the characteristic length of roughness and that the curvature ofthe liquid-air interface inside the valleys of the roughness is much lower than that of theroughness features. In addition, these interfaces have to adjust their shape in such a waythat the actual CA with the solid surface of the roughness features will be the ideal. . .la la sa sa sl slF A A A     A l as52(Young) contact angle. Based on these assumptions, the interfacial areas and drop radiuscan be calculated as follows (Marmur, 2008). First the liquid-air interfacial area consistsof two parts, the liquid-air interface within the grooves and the area of the liquid exposedinto the atmosphere:(6-2)Where, R is the radius of the spherical droplet, and is the apparent contact angle of thedrop. The solid-liquid interface area is:(6-3)where is roughness factor, the ratio of actual area to projected area, and is thefraction of solid surface area in contact with the liquid.The solid-air interfacial area also consists of two parts, the interface outside thedrop and the solid-air interface within the grooves:(6-4)here, is the total area of the solid surface. The drop radius is related to its volume by:(6-5)Introducing Equations (6-2) to (6-5) into Equation (6-1), the expression for theGibbs free energy can be derived, which can be written in the following dimensionlessform (Marmur, 2003):(6-6)where, and are functions of the independent variable of that is the depth ofliquid penetration beneath the top of the roughness peaks, with and .Thus, the Gibbs free energy of a droplet on a rough surface depends on two independentvariables: the extent of penetration of the droplet into the roughened valleys and theapparent contact angle of the droplet. These two variables must be consideredsimultaneously when determining the minima of the Gibbs free energy; the minima2 2 22 (1 cos ) (1 ) sinlaA R f R      2 2. . .sinsl fA R r f rf f2 2. . .sinsa tot sl tot fA A A A R r f    totA23 22 3 33 (2 3cos cos )VR       1 23 323 23(3 )(2 3cos cos ) 2 2cos sin .(r . .cos 1)laf YFFVf f             fr f h( )f fr r h ( )f f h53correspond to equilibrium states of the system (stable and metastable). Assuming that thefunction of the Gibbs free energy is differentiable, the necessary conditions for localextrema are as follows (Marmur, 2003):(6-7)and(6-8)where, and . .cos 1f Yr f f    .Since (4 >F > 0) for θ >0, equation (6-7) is fulfilled (for θ > 0) when:(6-9)This generalized equation has the same form as the Cassie-Baxter equation.Equation (6-8) is fulfilled when:(6-10)This equation is equivalent to the statement that the actual CA, which the liquidmakes with the solid inside the roughness valleys, must be the Young contact angle(Wolansky and Marmur, 1998). In addition to Equations (6-9) and (6-10), the followingcondition must be met for a local extremum to exist:(6-11)where and and .The nature of the extremum is determined by the sign of and it is a minimumwhen . If Equation (6-11) is not fulfilled, the Gibbs free energy has a saddle pointand the minimum is found at the border value of (Wenzel regime).This thermodynamic analysis results into the determination of the Cassie-Baxterand Wenzel contact angles.  As stated before, besides the high CA, the low contact anglehysteresis is also important to have a truly superhydrophobic surface. In this chapter, anew 2-dimensional thermodynamic analysis is presented that is capable of predicting the 5 232 .sin .( cos )(1 cos ) 0F F           2 23 sin cos 0fY rF fFh h h               3(2 3cos 3cos )F     cos r . .cos 1f Yf f       1cosf Yr hf h    2 0AC B 2 *2FAh 2FBh   22FC  A0A 1f 54surface CA and CAH. The method is applied to the micro/nano-patterns manufacturedpresented in chapter 5.6.2. Surface GeometryAs discussed in the previous chapter, femtosecond laser irradiation on stainlesssteel resulted in at least four distinctly different micro-nanostructures, depending on thelaser parameters. These included nano-rippled, parabolic-pillared, elongated sinusoidal-pillared and triple roughness nanostructures (Figures 5-3,4,5). All microstructures arecovered with nano-ripples as discussed in detail in the chapter 5. In this work, thesinusoidal and parabolic patterns are analyzed numerically. It is worthwhile mentioningthat the geometrical characteristics of the triple roughness were not very well definedfrom the SEM images and therefore impossible to model.Figure 6-2: (a) SEM image of sinusoidal structure, (b). SEM image of paraboloidal structure (c).Idealization (model) of the sinusoidal structure shown in Figure 1(a), (d). Idealization of theparaboloidal structure shown in Figure 1(b).55Figure 6-2(a) is a SEM image of a sinusoidal microstructure with nano-ripplescovering the top and sidewalls of the pillars, which is more evident in the inset of Figure6-2(a) of higher magnification. Figure 6-2(b) shows the SEM image of a paraboloidalstructure covered with nano-ripples. The idealizations of these two selected nano-patterns for theoretical analysis are depicted in Figures6-2(c) and (d) respectively.The sinusoidal structure (Figure 6-2(a)) is defined by the pillar height, H, and theperiodicity, Ds (wavelength) shown in Figure 6-2(c). The nano ripples of the doubleroughness are modeled as semi-cylindrical structures of diameter and length L. On theother hand, the paraboloidal patterns are consisted of micro-paraboloids having a heightequal to H and base diameter of D with a base-to-base distance (pitch) P as shown inFigure 6-2(d).6.3. Thermodynamic Analysis of SurfacesThe Gibbs free energy of a droplet sitting on a rough surface is characterized byseveral minima, where the global minimum is referred to as the stable state; whereas therest are all local minima which are referred to as metastable states characterizing thecorresponding apparent contact angles within the hysteresis range of CAs. The differencebetween the highest contact angle (advancing CA) and lowest contact angle (recedingCA) is known as the CAH. Existence of CAH is associated basically with the chemicalheterogeneity or the roughness of the solid surface (Johnson Jr. and Dettre, 1964;Marmur, 1994). The CAH comes from the barrier of microstructures to the motion of thecontact line. In between two metastable states, there is a local maximum (unstable state)with the height of this maximum referred to as the “energy barrier”, which has to beovercome in order to move from one metastable state to the next one in the direction ofthe three-phase line motion i.e. advancing or receding. The Gibbs free energy differencebetween two given states of the system is expressed by:(6-12)where is the Gibbs free energy difference between two given states. By approachingthe most stable point (global minimum), the magnitude of energy barrier increases. Thed2 2 21 1 1la sa slla sa slA A Ala la sa sa sl slA A AF dA dA dA       F56highest energy barrier of the system is next to the global minimum, whereas the lowestare near to the advancing and receding angles (Marmur, 1994).As mentioned earlier, in this work two-dimensional (2-D) thermodynamic analysisis performed to analyze the CAH using the Gibbs free energy minimization. Thefollowing assumptions are used in the modeling:(i) Gravity is negligible (For drops with radius smaller than capillary length(2.7mm for water), gravity flattening effect is negligible (Bormashenko,2013)),(ii) The Young’s equation is locally valid which means the droplet alwaysmeets the surface with the intrinsic (ideal or Young) contact angle, .(iii) The droplet radius is much greater than the length scale of the asperities(to consider the liquid-air interface beneath the drop as a flat surface).(iv) The droplet profile is similar to a spherical section and always remains assuch during its movement from one position to another.(v) The volume of the droplet is constant.(vi) The kinetic energy of the system is negligible.The modeling starts with a spherical droplet of volume sitting on the surfacehaving a size (radius of projected wet area). The Gibbs free energy is taken zero as areference point. As the droplet is moving forward (advancing) or backward (receding),the apparent CA at each point is obtained by using the geometrical principles and theGibbs free energy of system which depends on the geometrical details of the interfaces.The schematic of the sinusoidal pattern with a fully collapsed droplet (non-composite) isdepicted in Figure 6-3 and the schematic of non-composite state of the parabolic patternis shown in the Appendix A.The magnitude of the energy barrier is nearly independent of the droplet volume.It is noted that the droplet size affects the number of allowed metastable equilibriumstates. The density of metastable states along the apparent contact angle is very sensitiveto the droplet volume. In other words, the larger the droplet, the higher the number ofmetastable states (Marmur, 1994).YViL57In this analysis, when the edge of the droplet is moving from one pillar to the nextone, there are two extremes in the energy curve. These are important to determine theGibbs free energy barrier. The position with the undermost (lower) free energy ismetastable and the one with the uppermost (higher) Gibbs free energy is unstable. Themetastable configuration is always defined with the edge of the drop closest to the top ofthe ridge, which has the minimum Gibbs free energy (Johnson Jr. and Dettre, 1964). InFigure 6-3, the points at the top of the asperities, such as A, D and E define metastableconfigurations.Figure6-3: Schematic of the non-composite state of a droplet on a sinusoidal microstructure showingthe local apparent contact angles and the geometrical details needed in the numerical analysis.Figure 6-4 depicts the typical energy curve of sinusoidal and parabolic structures inmoving from one trough to the next for the non-composite case. According to Figure 6-4(a), the point ‘C’ on the sinusoidal structure has the maximum Gibbs free energy duringthe movement of the droplet edge from one metastable configuration to the next. As theθAθAθEθEθDLDLALCθDAV APDBAECZRERARDDrop ProfileHDS58drop edge moves slightly from ‘A’ towards ‘C’, the interfacial forces balance is suchway as to move the drop back to the metastable point ‘A’. As the drop edge moves from‘C’ to ‘E’, the resultant force vector tends to move the drop edge farther away from ‘C’(Johnson Jr. and Dettre, 1964).Figure 6-4: The energy profile between two pillars to determine the maximum and minimum Gibbsfree energy of the system (a).For the sinusoidal structure (b).For the paraboloidal pattern for thenon-composite case.Figure 6-4(b) indicates that C1 possesses the maximum Gibbs free energy in theparaboloidal structure during movement from one trough to the next. To find the energybarriers during the droplet growth (advancing) and droplet contraction (receding), theGibbs free energy difference between the metastable (such as point ‘A’) and unstablepositions (such as point ‘C1’) should be calculated for all of the troughs in the directionof the movement.In the following section, the detailed procedures for calculating the Gibbs freeenergy at each position and the Gibbs free energy barrier for advancing and receding ofboth the composite and non-composite wetting states of the sinusoidal pattern areexplained.596.4. Gibbs Free Energy Analysis For the Non-Composite Case of TheSinusoidal PatternThe cylindrical coordinate system  , ,x z  is applied to describe the systemdepicted in Figure 6-3 (droplet lying on the sinusoidal structure), where x is the radialdirection. However, due to the symmetry of the system in direction (axisymmetriccase), all of the equations are expressed in the coordinates.For the sinusoidal pattern depicted in Figure 6-3, the profile of the solid wall is:(6-13)where is the periodicity of the asperities (equal to the pillars periodicity, ) andis the height of the pillar, .Consider point A in Figure 6-3, as a randomly chosen position associated with adroplet size of LA and a Gibbs free energy of 0 as the reference point. The apparentcontact angle of A, is calculated by the following equation:(6-14)where is the volume of the droplet. All calculations are performed with respect topoint A as the reference point. In the Gibbs free energy analysis, the difference betweenthe minimum and maximum values of the energy and the relative energy of system atdifferent locations are important, not their absolute values.The constant volume boundary condition in 3D modeling is equivalent to theconstant droplet area in the plane in 2D analysis (Li and Amirfazli, 2005). The dropis supposed to be part of a sphere (circle for 2D modeling) with radius of  “R “ thatchanges during the droplet growth or shrinkage and the droplet radius is assumed to bemuch greater than the characteristic dimension of the asperities. Therefore, when thedroplet advances or recedes from one metastable point to the next (neighborhood), thesolid-liquid contact line length changes infinitesimally compared to the droplet radius.By equating the droplet areas for a given droplet state such as A and its neighborhood( , )x z002(1 cos )xz zx 0x SD 02zHA2 23 32 0 0 00 0 030 0.(cos 3cos 2) 2 2( )cos . sin3sin 2 2A AdropAx z xR R RV z R x z Rx x           dropVx z60point B, for an infinitesimally small drop length change, the geometrical equations tofind the drop length and apparent contact angles can be expressed as:(6-15)where is the radius of wetted area by droplet at the base at location “i”, is the areaof a pillar (in 2D system) and is the area of void space between two pillars. In thepresent case, these areas are given by (see Figure 6-3):(6-16)During receding of the droplet in these calculations (moving backward withdecreasing ), the contact line leads to an increase in the apparent CA since the dropletvolume is constant.The Gibbs free energy per unit length of the contact line for two droplet states atpoints A and B (Figure 6-3) are given by:(6-17)(6-18)where is the free energy of that part of the droplet–surface system which is thesame for A and B positions, is the arc length of droplet in contact with air defined as.lai i il R and and the is equal to the which is the arc length of ABgiven by:(6-19)As stated before, the manufactured superhydrophobic structures by laser irradiationpossess double scale roughness. Nano-ripples cover the sinusoidal/paraboloidalmicrostructures. By considering the hemi-cylindrical structure on top of thesinusoidal/parabolic pattern (depicted in Figure 6-2) the areas of solid/liquid and solid/airincrease significantly. Instead of area in 3D analysis, the arc lengths are affected by thesecond order roughness in the 2D calculations. To account for the influence of the double2 22 22 2cot . cot .sin sinA BA A A A V B B B B PA BL LL n A L n A        iL PAVA.2SP VD HA A iL. . .la la ls lsA A AF l l Const   . . .la la sa saB B BF l l Const   .ConstlalsiniiiLR lsAlsaBl2 2224 21 sinABLoo oLz xArc Length AB dxx x  61scale roughness, the micro-pattern arc length given by equation (6-19) is multiplied by. Thus, the energy barrier of drop during receding is given by:(6-20)The unit of Gibbs free energy per unit length of contact line is J/m and it isnormalized with respect to (J/m2), so the normalized Gibbs free energy, , has unitof length (m).When the droplet advances from A to C (Figure 6-3), the free energy analysis issimilar to the receding free energy analysis presented above:(6-21)and(6-22)The equations for the energy analysis of the paraboloidal micro/nano-structure arereported in Appendix A.6.5. Gibbs Free Energy Analysis For the Composite Case of theSinusoidal PatternConsider the composite case that is depicted in Figure 6-5, where a droplet isplaced on top of the sinusoidal microstructure with liquid penetrating into the troughsbetween pillars by an amount of.In the composite case, the interface under thedroplet consists of both air-liquid and solid-liquid. Since the droplet size is largecompared to the pillar’s wavelength, the liquid-air interface beneath the droplet is flat.The angle with the horizontal is 180°, as shown in the inset of Figure 6-5. As mentionedbefore, the Young contact angle, as the actual contact angle is locally valid. Therefore,the apparent contact angle,app , of each state is the sum of intrinsic CA, Y , plus theslope angle of the surface, , at the point of the local contact, i.e., where. Therefore, the composite state can exist if and only if the slope angle2cossin sin 2A B B AB A YlaB AF L L ArcLength AB       la F222 22 2cot . cot .sin sinCAA A A A V C C C C PA CLL L n A L n A        cossin sin 2A C C AC A YlaC AF L L ArcLength AC       1HYapp Y   1tan ( )dz dx  62of surface at one height of pillar is more than the minimum required slope angle, req(Johnson Jr. and Dettre, 1964):180req Y   (6-23)Thus, the penetrated height for the composite configuration, , depends on theYoung contact angle and the local solid surface slope. To completely define a compositeconfiguration, the critical values of the surface geometrical parameters should bedetermined. For a sinusoidal pattern the critical value of H/Ds to composite stateformation is tan Y  .Figure 6-5: Schematic diagram of the composite state of a droplet (droplet penetrating thetrough to a certain length H1) on a sinusoidal microstructure showing the local apparent contactangles and the geometrical details needed in the numerical analysis.1HθAθAθEθEθDLDLALCθD AV1DB2AEC1ZRERARDDrop ProfileH1DS1AP1θYLiquid SolidAirαB1C263Thus, to calculate the Gibbs free energy of the composite system, the first step is tofind the penetrated height, .  In Figure 6-5, points B1 and B2 define the internal liquid-air interface in the composite case. As the drop recedes from point A, the edge of thedrop follows the solid surface by using external energy, until it reaches B1. At B1 thedroplet no longer follows the solid surface and it jumps from B1 to B2. Then it tracks thesolid surface to reach the equilibrium position at D. Displacement from B2 to D isspontaneous and B2 possesses the maximum Gibbs free energy.Similar to the non-composite configuration, the equivalent equations of the dropletcross-section area are applied in order to determine the apparent contact angle at eachpoint. The apparent contact angle of B2 comes from the following equation:(6-24)where is the area of pillar portion in contact with the liquid (Figure 6-5)6-25)and 1VA is the area of penetrated liquid between the two asperities (Figure 6-5):(6-26)and the contact angle at point D is found by using the information of point A:(6-27)By using a similar approach with that followed for the non-composite state analysis,the energy barrier in the receding droplet in the composite case is determined by:(6-28)and(6-29)When the droplet advances, the equivalent equations for the composite case are asfollows:1H2 22 221 2 2 2 2 12 22cot . cot .sin sinA BA A A A V B B B B PA BL LL n A L n A        1PA11 1 1.sin2 2S SP SH D DHA D HD            11 1 1 1 sin2 S SV S S S SD DHA H D D DD          2 22 212 2cot cot 2sin sinA DA A A D D D VA DL LL L A       2 22 1 12cos .ArcLength ( )sin sin 2A B B AB A Y S SlaB AF L L AB D D         2 22 22cos .ArcLengthsin sin 2B D D BD B YlaD BF L L B D       64(6-30)and(6-31)The Gibbs free energy differences are given by:(6-32)(6-33)By computing the energy barriers and the normalized Gibbs free energy of thesystem at all possible metastable and unstable states during the advancing and thereceding stages of the droplet for both the composite and non-composite cases, theanalysis can be performed to predict the thermodynamic behaviour of the system.As stated earlier, in order to move from one metastable state to the next one, theexternal energy source such as vibration or pressure should be applied to overcome theenergy barrier. The largest energy barriers are close to the global minimum of Gibbsenergy and the lowest are next to the advancing and receding CAs. In this work, thesystem is ideal and in order to find the maximum CAH, external energy source is takento be zero, 0. Then the advancing and receding CAs are determined at the normalizedGibbs free energy barrier of zero. If an external energy is applied to the system duringthe droplet movement, the CAH will decrease and may be eliminated depending on thelevel of applied energy.6.6. Results and DiscussionTo evaluate the capabilities of the model, the predicted wettability (CA and CAH)of the sinusoidal and parabolic micro/nano structured samples are compared withexperimental results. The Young contact angle of a droplet with volume of 5 (withradius of 2mm) on a flat stainless steel surface after silanization is found to be105°± 3°.2 22 212 2cot cot 2sin sinA EA A A E E E VA EL LL L A       222 211 1 1 1 1 12 21cot cotsin sinCAA A A A V C C C C pA CLL L n A L n A        1 11 11cossin sin 2A C C AC A YlaC AF L L ArcLength AC       1 11 2 11cos .ArcLength ( )sin sin 2C E CEE C Y S SlaE CF LL C E D D         L65The droplet initial length in contact with the solid surface (initial iL ) is considered to betwice of the pillar diameter ( ) as the calculations start with an almost sphericaldroplet with a contact angle close to 180o.6-6-1. Model EvaluationsIn the following sections, the presented model is evaluated by comparing itsprediction with experimental data. The reported CAs are static contact angles which weremeasured by the sessile drop method. At first, the droplet was gently placed on thesurface and the CA was measured. Afterwards, vibrations were applied to the surface andthe contact angle was measured again. The minimum value of CA and the value of CAH,were considered to be the stable state.To measure the contact angle hysteresis (as explained in chapter 4) a droplet ofsmall size was placed on the surface and the volume of drop was increased by a constantrate (0.5 ) to reach a volume of 5 . Consequently the droplet volume wasdecreased with the same rate (0.5 ) to complete the CAH measurement.  Themaximum CA during the growth rate corresponds to advancing and the minimum duringthe receding stage corresponds to the receding CA. The difference of these twocorresponds to CAH.Sinusoidal Pattern:Sample 1: Figure 6-6(a) shows the non-composite state of a sinusoidal structure,which has a wavelength of Ds=17m and pillar height of H=12m (see Figure 6-2 for anexplanation of the geometrical characteristics). The experimental static CA of thissurface was found to be 141° and the CAH to be 95°.Sample 2: SEM image depicted in Figure 6-6(b) belongs to a sinusoidal patternwith Ds of 35m and H of 45m. The stable state for this pattern is a Cassie-Baxter statewith a contact angle, of 159° and a CAH of 16°.2 SDLSec LLSecCB66Figure 6-6: SEM image and CA of sinusoidal structure with (a). Periodicityof25m and height of12m, (b). Periodicity of 35 m and height of 45 m.Figure 6-7 plots the Gibbs free energy analysis for the first reported sinusoidal samplewhich has wavelength of Ds=25m and height of H=12m (Figure 6.6(a). Figure 6-7(a)depicts the variation of the normalized Gibbs free energy versus the apparent CA. Theglobal minimum located at 137° is the predicted Wenzel CA, . The inset shows theFigure 6-7: Thermodynamic energy analysis for the non-composite state of a sinusoidal structurewith wavelength of 25m and height of 12m, (a). Normalized free energy variation with apparentcontact angle, (b). Energy barrier versus contact angle to predict contact angle hysteresis.W67metastable (E, A, D) and the most unstable states (B, C) of a small range of apparentcontact angles on the surface.Figure 6-7(b) depicts the advancing and receding energy barrier of a droplet as afunction of apparent CA. As stated before, the external energy in these calculationsassumed to be zero. Thus, the advancing contact angle, θAdv and receding contact angle,θRec are determined at the energy barrier level of 0, resulting values of 163o and 77o forthe advancing and receding CA respectively with their difference of 86° to be the CAH.These values compare well with the experimental ones discussed above.As mentioned above, the second sinusoidal sample analyzed was a rough doublestructured with Ds of 35m and H of 45m (Figure 6.6(b)). The stable state for thispattern is a Cassie-Baxter state with a contact angle, of 159° and a CAH of 16°. Thevariation of the normalized Gibbs energy and energy barrier as a function of the CA isdepicted in Figure 6-8(a) and 6-8(b), respectively. The results indicate that the theoreticalCAH is 23° and the apparent CA of Cassie-Baxter is 171°, both very close to theexperimental ones.Figure 6-8: Energy barrier analysis for the composite state of a sinusoidal structure withperiodicity of 35 mand height of 45m .CB68Paraboloidal PatternSample 1: The first pattern to be analyzed is shown in Figure 6-9(a). This samplehas a diameter of pillar of D=15m, a pillar height H=11m and a pillar pitch ofP=0.5m (see Figure 6-2 for an explanation of the geometrical characteristics). Thestable state for this pattern is non-composite (Wenzel) state and the apparent CA, andCAH are 149° and 98°, respectively.Figure 6-9: SEM image and CA of paraboloidal structure samples with pitch of 0.5m and (a).Diameterof 15 m and height of 11m, (b). Diameter of 23m and height of 32m.Sample 2: Figure 6-9(b) exhibits the second sample to be analyzed which has abase diameter of D=23m, pillar height of H=32m and pillar pitch of P=0.5m.Experimentally, the composite (Cassie Baxter) state is the most stable for this surfaceand the and CAH experimental measurements were found to be 166° and 28°respectively.Figure 6-10 shows the energy barrier for the two examined samples possessingparaboloidal micro/nano-pattern (Figure 6.9). From Figure 6.10(a) the predicted Wenzelcontact angle and CAH are 149° and 107°, respectively, comparable to the experimentalones ( 149W   and CAH=98°).WCB69Figure6-10:Energy barrier analysis for the paraboloidal structure (a).Non-composite state of apattern with diameter 15m, height of 11mand pitch of 0.5m (b).Composite state of a pattern withdiameter 23m, height of 32 m and pitch of 0.5m.The second analyzed paraboloidal sample is depicted in Figure 6.9(b).Experimentally, the composite (Cassie Baxter) state is the most stable for this surfaceand the and CAH experimental measurements were found to be 166° and 28°respectively. The theoretical values predicted and plotted in Figure 8(b) for the CA andCAH are 164° and 34°, respectively, are again close to the experimental ones.6.6.2. Parametric Analysis of the CAAs seen above, all the experimental data were found to compare well with thethermodynamic analysis based on the Gibbs free energy. In this section, the influence ofsurface geometrical characteristics on the surface wettability is examined parametrically.As discussed earlier, the roughness factor, is always more than 1. For highenough values of , the right hand side of Wenzel equation (chapter 2, Equation 2-2),, may become higher than 1. In such cases the Wenzel equation fails to predicta physically acceptable contact angle. This also means that in such a case, there is noCBfrfr.cosf Yr 70minimum value of the Gibbs free energy in the non-composite configuration (theminimum of Gibbs free energy is on the boundary, which means , thatphysically is not possible). In other words, for these cases it is not possible for liquids topenetrate fully into the troughs. Thus, for these cases the composite configuration formsa stable state, where the surface slope should be less than the critical slope, req definedby Equation (6-23). There exist critical values of the surface geometrical parametersrequired for the existence of each state (composite and non-composite). These areanalyzed in the present section.Figure 6-11: Contact angles of Cassie-Baxter and Wenzel states for the sinusoidal patternversus (a). Ratio of and (b). Height, H.For the sinusoidal microstructure covered with elongated nano-ripples (doubleroughness) with flat contact angle of 105°, if the ratio is higher than about 1.8, thenon-composite (Wenzel) configuration cannot be realized (impossible to form) as shownin Figure 6-11(a). On the other hand, in order to form a composite (Cassie-Baxter)configuration, the value of should be higher than about 1.18. Therefore, forsurfaces with sinusoidal patterns having more than 1.8, only composite state mayform, while for those having less than 1.18, simply the non-composite state may180W  SH DH DSH DSH DSH DS71be realized. These results are shown in Figure 6-11 for the sinusoidal pattern of flatcontact angle of 105° as a function of the ratio (Figure 6-11(a)) and height, H(Figure 6-11(b)) for five different pillar wavelengths.More specifically, Figure 6-11(a) shows the variation of Wenzel state (dotted lines)and Cassie-Baxter state contact angle with the ratio. It is clear that by increasing, the contact angle of both configurations gradually increase. The CA of thecomposite state for the sinusoidal pattern is high, within the narrow range between 160°-175°. However, for the non-composite state, the CA varies over a very wide rangebetween 115°-165°. According to Figure 6-11(b), at a given (constant) pillar wavelength,DS, the CA of Wenzel and Cassie-Baxter states are increasing with increase of the pillarheight. On the other hand, at a fixed pillar height, the CA of both states decreases withincrease of the periodicity. Thus, increase of the periodicity and height have oppositeeffects on the CA for the sinusoidal pattern.Figure 6-12 demonstrates that the paraboloidal pattern has similar CA trends forboth the configurations with that of the sinusoidal structure. First, for the paraboloidalmicro/nano structure (double roughness), to obtain Cassie-Baxter state as a possible stateon the surface, the should be higher than about 0.94. For surfaces withgreater than 1.2, the Wenzel state cannot be formed.The small size of pitch and almost high height of pillars, with the large enoughdroplet size compare to the asperities dimensions, provide a condition in which thedroplet size and surface parameters don’t facilitate transition from one state to the otherone (Jung and Bhushan, 2007).In summary, in the non-composite (Wenzel) state where the droplet fully collapseswithin the asperities of the surface, the contact angle is a function of the surfaceroughness. For structures such as sinusoidal and paraboloidal, at a given wavelength (DS)or base diameter (D), increase of the pillar height causes an increase of roughness whichin turn increases the CA (as also implied by Equation 2-2).  A similar effect is obtainedat a given height, H, and a gradual decrease of the diameter, D.Y H DSH DSH DSH D H D72Figure 6-12: Contact angle (CA) of Cassie-Baxter and Wenzel states for the paraboloidalpattern as functions of (a). The ratio and (b). Height, H.For the composite (Cassie-Baxter) state, the water droplet does not wet the surfaceentirely. Instead air pockets are formed between the liquid and the asperities of thesurface. The Cassie-Baxter contact angle, CB, is defined by Equation (2-3) and CB isfunction of , which is the fraction of the droplet surface in contact with the solidsurface.  In this composite case, the penetrated height depends on the surface geometrythrough the surface tangent angle, (Equation (6-23)). Increase of the steepness of theasperities, causes the penetrated height and also the fraction of droplet in contact with thesolid to decrease. Thus by increasing the height of microstructure at a constant diameteror periodicity, increases (Figures 6-11, 12).6.6.3. Parametric Analysis of the CAHSimilar to CA, the CAH is also a function of the ratio instead of the H or D(or DS ) individually. Figure 6-13(a) depicts the CAH of the sinusoidal microstructureand reveals that by increasing the ratio , the CAH of the non-composite stategradually increases, whereas for the composite configuration decreases. For theH DslfCBH DSH DS73composite state, according to Figure 6-13(b), the CAH of the sinusodial structuredecreases with increase of the height of asperities at a given periodicity and increaseswith increase of the periodicity at a given pillar height.Figure 6-13: Contact angle hysteresis of composite (Cassie-Baxter) and non-composite(Wenzel) configurations for the sinusoidal pattern as functions of (a). The ratio and (b).Height, H.Figure 6-14 plots the CAH of the paraboloidal pattern and exhibits CAH valuesmuch higher than those for the composite configurations of the paraboloidal structure,relative to those of the sinusoidial pattern. These high CAH values result in stickycomposite states for the paraboloidal structure (petal effect). Figure 6-14 also shows thatfor paraboloidal pillars with small base diameters, thereis a minimum CAH. Thisminimum increases  with increase of the height, H. Figure 6-14(c) shows a 3D plot ofCAH of paraboloidal pattern as a function of diamater and height. For diameters lessthan 25m, the CAH versus height is descending-ascending. However, fordiametershigher than 25m, the CAH monotonically decreases with height, H.SH D74Figure 6-14: Contact angle hysteresis of the composite (Cassie-Baxter) and non-composite(Wenzel) configurations for the paraboloidal pattern as functions of (a). The ratio and (b).Height, H (c).3D plot of CAH of the paraboloidal pattern as a function of pillar base diameter, D andpillar height H.The last parameter to consider for the paraboloidal structure is pitch (P). Thevariation of CA and CAH are depicted in Figure 6-15. According to Figure 6-15 (a), theCA of the paraboloidal structure increases in the composite state and decrease in the non-composite configuration with pillar pitch. For the noncomposite state, increase of theH D75pitch, decreases roughness and consequently CA. On the other hand, in the compositecase, increasing the pitch decreases the fraction of liquid-solid contact, and enhancesCA. Figure 6-15(b) demonstrates that the CAH in the paraboloidal pattern exhibitssimilar trends for both configurations with the CAH decreasing with pitch. The higherthe pitch, the less the pinning of droplet on the surface and hence the less the CAH.Figure 6-15: (a). Contact angle (CA) and (b). Contact angle hysteresis of Cassie-Baxter andWenzel states for the paraboloidal pattern as functions pillar pitch (P).6.6.4. Concluding Comments on the CAH CalculationsThe ‘contact angle hysteresis’ reflects a fundamental asymmetry of wetting anddewetting and the irreversibility of the wetting/dewetting cycle. A water repellant surfaceshould possess a low CAH to allow water to flow/roll easily along the surface. The pillaredge may pin a moving droplet and increase the CAH. Since the surface roughness isproportional to the density of the edges, the main effect of surface roughness on the CAHcomes from the edges of the pillars (Nosonovsky and Bhushan, 2005). Therefore, thework of adhesion for the non-composite case is proportional to the surface roughness andincreasing the roughness, enhances adhesion and the CAH increases accordingly. Thus,in both the sinusoidal and paraboloidal patterns, by increasing the height of structure atf76constant diameter (or periodicity) or decreasing the diameter at constant height, the CAHis increasing (Figures 6-13, 14).For the composite case, the adhesion is proportional to the solid–liquid contact area.Increase of solid-liquid contact area cause more pinning of the droplet. This results intomore surface adhesion and to a higher CAH.In calculating the CAH, the height of energy barriers associated with themovement of the droplet along a rough surface should be calculated. Looking at theeffective parameters to calculate the energy barrier of composite state of sinusoidal andparaboloidal structures, the main parameter that influences the difference betweenadvancing and receding energy barriers is the liquid-air contact area beneath the droplet,that is for the sinusoidal pattern and for the paraboloidal pattern.Figure 6-16: The liquid-air contact area beneath the droplet for the (a). Sinusoidal (b).Paraboloidal microstructures.Figure 6-16(a) depicts the variation of the liquid-air contact area beneath thedroplet with pillar height and periodicity of sinusoidal structure. It can be seen that at agiven periodicity, increase of the pillar height, the penetrated height, H1, and thepenetrated diameter, DS1, decrease. Thus, by reducing the contact area of solid and liquid,the pining and accordingly the surface adhesion and CAH decrease. The area of liquid-air contact beneath the droplet versus diameter and height of parabolic structure is(DS − DS1)  1P D D 77plotted in Figure 6-16(b). At a given diameter, the contact area of liquid-air under thedroplet increases by increasing of the pillar height. Increase of the liquid-air contact areaand decrease of the liquid-solid contact area, causes a reduction in the surface adhesionand consequently, in the CAH.In the sinusoidal pattern for a fixed pillar height, the periodicity increase resultsinto more liquid penetration and therefore higher CAH (Figure 6-16(a)). On the otherhand, in the paraboloidal pattern, the trend of liquid-air contact area at a fixed pillarheight does not change monotonically as can readily be seen from Figure 6-16(b).The increase of liquid-air interface area enhances the barrier separating theCassie-Baxter and Wenzel states and makes the Cassie-Baxter state more stable(Whyman and Bormashenko, 2011) .Figure 6-17: (a) and (b). SEM images of the rose leaf (reprinted (Feng et al., 2008) withpermission from ACS, copyright (2008) American Chemical Society), (c) and (d): SEM images of themanufactured paraboloidal pattern on stainless steel by laser irradiation.As stated earlier, the range of contact angle hysteresis of the paraboloidal structurefor the composite (Cassie-Baxter) state is relatively high (20°-120°) with contact anglesc2 µm20 µmc d78more than 150°. Therefore, the thermodynamic analysis in this work demonstrated thatfor the paraboloidal structures, the CAH even for the composite state is high and resultsin adhesion of droplet to surface. This effect is called petal (or rose) effect. The SEMimages of rose flower leaf (Feng et al., 2008) reveal that the structure is similar to that ofthe parabolic structures examined in this work (Figure 6-17). According to Figure 6-14and 6-18, there is an optimum value of diameter for each specific height of theparaboloidal pattern to obtain the lotus effect on a rose structure. The value of optimumdiameter is less than 25μm for each specific height, but in total to have a parabolicstructure with lotus effect, besides to the diameter of pillar in this range, the ratiomust be typically more than 2.5 and the ratio must be more than 1 for a surfacewith of 105o.Figure 6-18: Variation of CAH versus pillar diameter at different heights for the paraboloidalstructure.The Figures 6-11 and 6-13 show that unlike to parabolic structure, for sinusoidalstructure, the increasing of ratio increases the lotus effect on the surface.The main reason for the CAH difference of the composite case between theH DPDYH D79sinusoidal and paraboloidal structure is the penetrated height in the two structures. Figure6-19 clearly shows that for the two structures for the same diameter and height, thesurface slope of the sinusoidal pattern grows faster than that of paraboloidal structure andresults indicate that the penetrated height of the liquid in the sinusoidal structure isalmost half of the H1 in the paraboloidal pattern. The more the penetrated height by theliquid, the higher the CAH. Thus, the CAH of the paraboloidal structure is higher thanthat of the sinusoidal pattern at similar geometrical characteristics.Figure 6-19: Variation of the penetrated height of the sinusoidal and paraboloidal patternsversus the pillar height at constant diameters.6.7. ConclusionsSuperhydrophobic surfaces were fabricated by irradiation of stainless steel usingultra-short pulse laser. The manufactured substrates were analyzed in terms of theirthermodynamic behavior by minimizing the Gibbs free energy to calculate possiblecomposite (Cassie-Baxter) and non-composite (Wenzel) states. The effect of the80geometrical characteristics of two specific nano-patterns (sinusoidal and paraboloidal)was also analyzed thermodynamically to obtain the equilibrium CA and CAH. Thepresented thermodynamic analysis was found to be in excellent agreement with theexperimentally measured contact angles and their hysteresis. The geometrical parametersimportant to render these surfaces highly superhydrophobic is the ratio of the height tobase diameter ( ) for the paraboloidal pattern and the ratio of height to wavelength( ) for the sinusoidal pattern. The paraboloidal structures have shown high contactangle hysteresis similar to the rose leaf (petal effect) and the optimum range to obtain thesuperhydrophobic petal structure has been determined. On the other hand, the sinusoidalpattern has shown relatively lower CAH similar to lotus effect.H DH DS81CHAPTER 7: CONCLUSIONS AND FUTURE WORKS7.1. Conclusion7.1.1. Experimental WorkThe laser ablation technique using femtosecond laser pulses on metallicsurfaces, particularly stainless steel was used in this study. The main results from theexperimental work can be summarized as following:1. The effect of laser energy and scanning speed on stainless steel surface structurewere classified according to a newly defined parameter, the Laser Intensity Factor(LIF) that is a combination of scanning speed and laser fluence values. Accordingto this new classification, by increasing the LIF, the structure ranges from smallnano-scale ripples to double and coarse triple-roughness patterns. The patternsare nano-ripples, parabolic micro-nano roughness, sinusoidal micro-nano patternand triple micro-nanostructure. The periodicity of surface increases by increasingthe value of applied LIF.2. The wettability of the surface is a function of the aspect ratio of the pillar heightto periodicity (or diameter) of the patterns ( ). The higher the aspect ratio ofa given structure is the lower surface wettability. In each category of surfacemicrostructure, increasing the LIF causes an increase to the aspect ratio. Besidesthe aspect ratio of height to diameter, the type of nano-structure is also importantfor surface-liquid adhesion. The maximum surface superhydrophobicity wasfound for the triple roughness which possesses a very low contact hysteresis (lessthan 4°) due to spherical small microstructure and nano-ripples which cover therelatively large micro-asperities.3. The wettability of the surface decreases by increasing the scanning beam overlap.Higher overlap provides more energy for a particular site on the surface and thusH D82increases the depth and diameter of the produced crater. As a consequence of this,the surface wettability decreases.7.1.2. Modeling WorkTo predict the surface wettability, especially the contact angle hysteresis ofthe produced microstructures by laser ablation, a new 2-dimensional thermodynamicanalysis was developed and proposed. The main results of modeling are:1. The modeling results were found to be in excellent agreement with experimentaldata. The model can be used to predict the surface contact angle and contactangle hysteresis of non-flattened microstructures.2. The surface wettability (CA and CAH) of the paraboloidal and sinusoidalstructures is a function of aspect ratio of pillar height and diameter of periodicity( ). For both patterns, increasing the aspect ratio increases the Wenzel andCassie-Baxter CAs.  The CAH of Cassie-Baxter configuration on the sinusoidalpattern is also monotonically decreasing with increase of the height to periodicityratio. On the contrary, the CAH of Wenzel state increases with increase of the.3. The CAH of parabolic structures in Cassie-Baxter state is high for most of thediameters and heights of the individual patterns, with high values of CA, similarto the rose leaf effect. The CAH in this structure decreases only by decreasing thepillar diameter to less than 25m with more than about 2.5.H DH DH D837.2. Future WorkTo complete the experimental section of this work, the following suggestionscan be considered for future works in producing the superhydrophobic surfaces bylaser ablation method:1. In addition to laser power and scanning speed to pattern the surface by laserablation, other parameters such as laser wavelength, laser beam overlap andangle of incident light should be varied. These will change the Laser IntensityFactor (LIF) and check its uniqueness in predicting/describing monotonically allpossible microstructures.2. The various micro/nano structures created on SS surface has been manufacturedby varying LIF up to about 3000. By increasing the LIF to higher values, thereare other possible structures. The type of these structures and the wettability ofthem should be studied to gain a better understanding of the superhydrophobicsurfaces manufactured on stainless steel by the laser ablation technique.3. The patterning of the metallic surfaces by local melting of the surface due toultrashort laser pulses is mainly a function of the physical and thermal propertiesof the substance of the substrate. Between all of these properties, the melting andsublimation point are the most important. Surfaces with similar melting pointshave similar structures produced by laser irradiation method (such as Ti andstainless steel). To extend the experimental results of this work and study theapplicability of the LIF parameter for other materials, different metallic surfacesshould be considered in future studies.4. 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A 93, 819–825.94APPENDIX AA.1. Gibbs Free Energy Analysis for the Non-Composite Caseof ParabolicStructureConsider point A in Figure 1, as a randomly chosen position associated with a CAof θA , a droplet size of LA and a Gibbs free energy of 0. All the calculations areperformed with respect to point A as reference point.Figure A-1: Schematic of the non-composite state of a droplet on a parabolic microstructureshowing the local apparent contact angles and the geometrical details needed in the numericalanalysis.The constant volume boundary condition in 3D modeling is equivalent to theconstant droplet area in the x-z plane with 0y  in 2D analysis.  During receding of the95droplet, the contact line leads to an increase in the apparent contact angle since thedroplet volume is constant. The drop is supposed to be similar to a spherical section(circle for 2D modeling) with radius of R which changes during the droplet growth orshrinkage. As mentioned, the drop radius is assumed to be much greater than the pillardiameter (D), pillar height (H) and pitch (P). Therefore, when the droplet advances orrecedes from one pillar to the next (neighborhood), the solid-liquid contact line lengthchanges infinitesimally compared to the droplet radius. By equating the droplet areas inthe plane for a given droplet state such as A and its neighborhood point B, for aninfinitesimally small drop length change, the geometrical equations to find the droplength and apparent contact angles can be expressed as:(A-1)where  is the apparent contact angle at a given state of the drop (A or B in this case),is drop width (solid-liquid contact line length, see Figure A-1), is the surface area of apillar and in the present case can be expressed as:(A-2)and(A-3)The Gibbs free energies per unit length of contact line for two droplet states atpoints A and B are given by:(A-4)(A-5)0y 2 22 222 2 2 22 22cot . cot .sin sinA BA A A A V B B B B PA BL LL n A L n A        LPA2.3PA H D.( )3VDA H P . . .la la ls lsA A AF l l Const   2 2 2. . .la la sa saB B BF l l Const   96where is the free energy of that part of the droplet–surface system which is thesame for A and B positions, is the arc length of droplet in contact with air defined as.lai i il R and and the is equal to the which is the arc length of ABgiven by:(A-6)By considering the hemi-cylindrical structure on top of the paraboloidal pattern(microscale roughness) and to account for the effect of the second scale roughness, themicropattern arc length given by Equation (A-6) is multiplied by .The energy barrier of drop during receding is given by:(A-7)When the droplet advances from A to C1, the free energy analysis is similar to thereceding free energy analysis presented above:(A-8)and(A-9)Where(A-10).ConstlalsiniiiLR lsAlsaBl2 2 22 221 4 16P 16 ln2 4 16D H D HArcLengthAB D HD              22 22 22cos .ArcLengthsin sin 2A B B AB A YlaB AF L L AB       222 211 1 1 12 21cot . cot .sin sinCAA A A A V C C C C PA CLL L n A L n A        1 11 11cos .ArcLengthsin sin 2A C C AC A YlaC AF L L AC       2 2 22 211 4 1616 ln2 4 16D H D HArcLengthAC D HD             97A.2. Gibbs Free Energy Analysis for the Composite CaseConsider now the composite case that is depicted in Figure A-2, where a droplet isplaced on top of the paraboloidal microstructure with liquid penetrating into the troughsbetween paraboloids by an amount of H1.Figure A-2: Schematic diagram of the composite state of a droplet on a paraboloidalmicrostructure showing the local apparent contact angles and the geometrical details needed in thenumerical analysis.98Thus, in order to determine the Gibbs free energy of the composite system, the firststep is to find the penetrated height in order to figure out the composite configuration andthe possibility for its formation.The equivalent equations to determine the relationships between the metastable andunstable configurations when the drop recedes can be written as:(A-11)and(A-12)Where is the area of penetrated liquid between the two paraboloids (see FigureA-2),given by:(A-13)The energy barrier in the receding droplet in the composite case is:(A-14)where(A-15)and(A-16)2 22 212 2cot cot 2.sin sinA DA A A D D D VA DL LL L A       2 22 221 2 2 2 2 12 22cot . cot .sin sinA BA A A A V B B B B PA BL LL n A L n A        1VA311 1 2. .3VDHA P HD 2 22 1 12cos .ArcLength ( )sin sin 2A B B AB A YlaB AF L L AB P D D          2 221 1 12 2 11 1 14 161 16 ln4 16H D HDArcLengthAB D HD            2 22 22cos .ArcLengthsin sin 2B D D BD B YlaD BF L L B D       99When the droplet advances, the equivalent equations and Gibbs energy barrier forthe composite case are as follows:(A-17)and(A-18)The energy barrier in the advancing droplet in the composite case is:(A-19)where(A-20)and(A-21)2 22 212 2cot cot 2.sin sinA EA A A E E E VA EL LL L A       222 211 1 1 1 1 12 21cot . cot .sin sinCAA A A A V C C C C PA CLL L n A L n A        1 11 11cos .ArcLengthsin sin 2A C C AC A YlaC AF L L AC       2 221 1 12 2 11 1 14 161ArcLength 16 ln4 16H D HDAC D HD            1 11 2 11cos .ArcLength ( )sin sin 2C E CEE C YlaE CF LL C E P D D          

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