Applied Science, Faculty of
Engineering, School of (Okanagan)
DSpace
UBCO
Mirshahidi, Kianasadat
Master of Applied Science - MASc
University of British Columbia
In cold regions, icing is a serious challenge that people face daily. Ice accretion on bridge cables, wind turbines and ship hulls are only a few examples of where icing can have fatal effect. Much research has been done to overcome this problem using various solutions such as producing surfaces that delay ice formation or preventing ice accumulation using coatings exhibiting low adhesion to ice. Among these, elastomeric materials have repeatedly been reported as successful coatings with ultra-low adhesion values to ice, arising from an interfacial instability which was recently proposed as the underlying phenomena. This instability, interfacial cavitation, occurs when tensile forces are indirectly generated at the ice/substrate interface during shear. Most research has focused on studying, measuring, and manipulating ice adhesion of surfaces by shear forces. In this work, a high throughput, low-cost apparatus was designed and benchmarked to measure the tensile ice adhesion strength of various surfaces. The performance and precision of the setup was verified using experimental trials and the effect of various parameters such as temperature, pull-off speed, substrate thickness, and ice/substrate interfacial area were characterized. We then delved deeper in the ice adhesion behavior of polydimethylsiloxane (PDMS), a commonly used elastomeric ice phobic coating, comparing its pure tensile adhesive fracture to its typical shear adhesion behavior. It was found that tensile ice adhesion strength of PDMS is usually higher than the shear ice adhesion strength. Also, all parameters (such as thickness, elastic modulus, and probe speed) affected the tensile ice adhesion strength in the same manner they did with the shear ice adhesion strength, except roughness. When roughness of the PDMS surface was increased to up to an Sq = 32 μm, the shear ice adhesion strength remained almost constant. We also developed a superhydrophobic PDMS that maintained the low tensile and shear ice adhesion value of σice= 11.2 kPa and τice= 8.6 after harsh abrasion periods. This work elucidates tensile ice/elastomer adhesion mechanisms and behavior, which is crucial for designing future elastomeric coatings that facilitate ice removal through interfacial instabilities.
EXPLORING THE TENSILE ICE ADHESION STRENGTH OF SURFACES USING A NEWLY DESIGNED AND VERIFIED MEASUREMENT APPARATUS by Kianasadat Mirshahidi BSc., Golestan University, 2018 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE COLLEGE OF GRADUATE STUDIES (Mechanical Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Okanagan) April 2021 © Kianasadat Mirshahidi, 2021 ii The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, the dissertation entitled: Exploring the Tensile Ice Adhesion Strength of Surfaces Using a Newly Designed and Verified Measurement Apparatus submitted by Kianasadat Mirshahidi in partial fulfillment of the requirements for the degree of Master of Applied Science Dr. Kevin Golovin, School of Engineering, Faculty of Applied Science Supervisor Dr. Abbas Milani, School of Engineering, Faculty of Applied Science Supervisory Committee Member Dr. Mohammad Hossein Zarifi, School of Engineering, Faculty of Applied Science Supervisory Committee Member Dr. Kyle Larson, Department of Earth, Environmental and Geographic Sciences, Irving K. Barber Faculty of Science University Examiner iii Abstract In cold regions, icing is a serious challenge that people face daily. Ice accretion on bridge cables, wind turbines and ship hulls are only a few examples of where icing can have fatal effect. Much research has been done to overcome this problem using various solutions such as producing surfaces that delay ice formation or preventing ice accumulation using coatings exhibiting low adhesion to ice. Among these, elastomeric materials have repeatedly been reported as successful coatings with ultra-low adhesion values to ice, arising from an interfacial instability which was recently proposed as the underlying phenomena. This instability, interfacial cavitation, occurs when tensile forces are indirectly generated at the ice/substrate interface during shear. Most research has focused on studying, measuring, and manipulating ice adhesion of surfaces by shear forces. In this work, a high throughput, low-cost apparatus was designed and benchmarked to measure the tensile ice adhesion strength of various surfaces. The performance and precision of the setup was verified using experimental trials and the effect of various parameters such as temperature, pull-off speed, substrate thickness, and ice/substrate interfacial area were characterized. We then delved deeper in the ice adhesion behavior of polydimethylsiloxane (PDMS), a commonly used elastomeric ice phobic coating, comparing its pure tensile adhesive fracture to its typical shear adhesion behavior. It was found that tensile ice adhesion strength of PDMS is usually higher than the shear ice adhesion strength. Also, all parameters (such as thickness, elastic modulus, and probe speed) affected the tensile ice adhesion strength in the same manner they did with the shear ice adhesion strength, except roughness. When roughness of the PDMS surface was increased to up to an Sq = 32 μm, the shear ice adhesion strength remained almost iv constant. We also developed a superhydrophobic PDMS that maintained the low tensile and shear ice adhesion value of σice= 11.2 kPa and τice= 8.6 after harsh abrasion periods. This work elucidates tensile ice/elastomer adhesion mechanisms and behavior, which is crucial for designing future elastomeric coatings that facilitate ice removal through interfacial instabilities. v Lay Summary Rubbery coatings have proven to be an advantageous choice as ice repellent coatings because of their incredibly low adhesion to ice. This low ice adhesion strength occurs because of the coexistence of both shear and tensile stresses. In this work a high throughput tensile ice adhesion measurement system was designed and benchmarked. Further, the pure tensile adhesion strength of ice to a soft substrate, comparison of ice adhesion behavior of soft substrates under shear and tensile, and various parameters affecting the ice adhesion of rubbers, are comprehensively studied. vi Preface The second Chapter of the thesis is published as a journal paper as follows: [1] K. Mirshahidi, K.A. Zarasvand, W. Luo, K. Golovin, A High Throughput Tensile Ice Adhesion Measurement System, HardwareX, 2020. The author designed and conducted most of the experiments discussed in the thesis in both Chapters 2 and 3 at the Okanagan Polymer Engineering Research and Applications (OPERA) Lab in the School of Engineering, The University of British Columbia. The whole work was supervised by Dr. Kevin Golovin, the principal investigator of OPERA Lab. Mr. Kamran Alasvand Zarasvand, PhD student, at OPERA Lab, build the tensile ice adhesion structure, designed, and analyzed the ice holders that were used in all the experiments, and also helped in the manuscript of Chapter 2, and some of the characterization tests in Chapter 3. The author also contributed to the following: Journal publications: [2] B.D Wiltshire, K. Mirshahidi, A.V. Nadaraja, S. Shabanian, R. Hajiraissi, M.H. Zarifi, K. Golovin, Oleophobic Textiles with Embedded Liquid and Vapor Hazard Detection Using Differential Planar Microwave Resonators, Journal of Hazardous Materials, 2021. Contribution: Preparation and swelling studies of the silicone rubber samples, data analysis [3] X. Zhao, B. Khatir, K. Mirshahidi, K. Yu, J. N. Kizhakkedathu, K. Golovin, Macroscopic Evidence of the Liquid-like Nature of Nano-PDMS Brushes, Science, 2021. (submitted) vii Contribution: Tensile ice adhesion characterizations [4] B.D Wiltshire, K. Mirshahidi, K. Golovin, M.H. Zarifi. Robust and Sensitive Frost and Ice Detection via Planar Microwave Resonator Sensor, Sensors and Actuators B: Chemical, 2019. Contribution: Ice and frost testing and data acquisition Patent: [5] B.D. Wiltshire, K. Mirshahidi, K. Golovin, M.H. Zarifi. Robust and Sensitive Frost and Ice Detection via Planar Microwave Resonator Sensor, U.S. Patent Application 62/877,399 Presentations: [6] B.D Wiltshire, K. Mirshahidi, K. Golovin, M.H. Zarifi. Robust and Sensitive Frost and Ice Detection via Planar Microwave Resonator Sensor, Sensors and Actuators B: Chemical, 2019, presented at 69th Canadian Chemical Engineering Conference, Halifax, NS, (2019). viii Table of Contents Abstract ................................................................................................................................... iii Lay Summary ...........................................................................................................................v Preface ..................................................................................................................................... vi Table of Contents ................................................................................................................. viii List of Tables .......................................................................................................................... xi List of Figures ........................................................................................................................ xii List of Symbols .......................................................................................................................xv List of Abbreviations .......................................................................................................... xvii Acknowledgements ............................................................................................................ xviii Chapter 1: Introduction ..........................................................................................................1 1.1 Background ............................................................................................................... 3 1.1.1 Wettability............................................................................................................. 3 1.1.1.1 Young’s and static contact angles ................................................................. 4 1.1.1.2 Advancing, receding and contact angle hysteresis ....................................... 5 1.1.1.3 Wenzel and Cassie-Baxter states .................................................................. 6 1.1.2 Ice adhesion strength ............................................................................................. 7 1.2 Existing Techniques ................................................................................................ 10 1.2.1 Ice adhesion and wettability ................................................................................ 10 1.2.2 Ice adhesion and elastic modulus ........................................................................ 13 1.2.3 Tensile ice adhesion ............................................................................................ 14 ix 1.3 Motivation ............................................................................................................... 17 1.4 Objectives and outline ............................................................................................. 18 Chapter 2: A High Throughput Tensile Ice Adhesion Measurement System ..................21 2.1 Overview ................................................................................................................. 21 2.2 Description of the System ....................................................................................... 21 2.2.1 Design and Optimization of the Ice Holder ........................................................ 23 2.2.2 Device Structure.................................................................................................. 26 2.2.3 Build instructions ................................................................................................ 28 2.2.3.1 Structural instructions ................................................................................. 28 2.2.3.2 Electronics instructions ............................................................................... 37 2.2.4 Operation Instructions ......................................................................................... 44 2.3 Validation and Characterization ............................................................................. 46 2.3.1 Materials ............................................................................................................. 46 2.3.2 Results ................................................................................................................. 47 Chapter 3: Tensile versus Shear Ice Adhesion Strength of PDMS Elastomers................53 3.1 Overview ................................................................................................................. 53 3.2 Materials and methods ............................................................................................ 54 3.2.1 Materials: ............................................................................................................ 54 3.2.2 Surface fabrication: ............................................................................................. 54 3.2.2.1 Smooth surface ............................................................................................ 54 3.2.2.2 Rough surface ............................................................................................. 54 3.2.2.3 PDMS elastomers of varying moduli .......................................................... 54 3.2.3 Roughness measurement ..................................................................................... 55 x 3.2.4 Contact angle measurements ............................................................................... 55 3.2.5 Tensile strength and moduli ................................................................................ 55 3.2.6 Ice adhesion measurement .................................................................................. 57 3.3 Tensile and shear ice adhesion measurements ........................................................ 58 3.3.1 Substrate thickness .............................................................................................. 58 3.3.2 Probe height ........................................................................................................ 60 3.3.3 Elastic modulus ................................................................................................... 61 3.3.4 Probe speed ......................................................................................................... 64 3.3.1 Roughness ........................................................................................................... 65 Chapter 4: Durable superhydrophobic PDMS with ultra-low ice adhesion ....................69 4.1 Overview ................................................................................................................. 69 4.2 Materials and methods ............................................................................................ 69 4.2.1 Superhydrophobic surface preparation ............................................................... 69 4.2.2 Abrasion .............................................................................................................. 70 4.2.3 Surface characterization ...................................................................................... 70 4.3 Tensile and shear ice adhesion of superhydrophobic PDMS .................................. 71 Chapter 5: Conclusion and future work recommendations ..............................................75 5.1 Summary ................................................................................................................. 76 5.2 Future work recommendations ............................................................................... 78 Bibliography ...........................................................................................................................80 xi List of Tables Table 2.1. Cohesive zone model parameters used in the numerical simulations27. ................ 26 Table 2.2. Building part directory ........................................................................................... 41 Table 2.2. Building part directory ........................................................................................... 42 Table 2.2. Building part directory ........................................................................................... 43 Table 2.3.Tensile ice adhesion strength of different materials using a pull-off speed of 100 µm/s, an interfacial area of 0.785 cm2, and a test temperature of -15 °C. .............................. 52 Table 3.1. Shear modulus of the samples, calculated based on the tensile strength testing ... 57 xii List of Figures Figure 1.1. Ice adhesion measurement devices used, (a) designed tensile ice adhesion measurement apparatus, (b) shear ice adhesion measurement device ...................................... 3 Figure 1.2. Possible liquid/solid configurations, (a) Wenzel state, (b) Cassie-Baxter state ..... 7 Figure 1.3. Schematic illustration of the tensile force generated at the rear edge of an ice cube when a shear force is being applied at a height above its interfacial plane. ........................... 10 Figure 2.1.Tensile adhesion ice holder. (a) Isometric view of the designed ice holder. (b) Sectioning a quarter of the model reveals the cylindrical ice inside the holder. (c) Two-dimensional top view of the ice holder. (d) Drawing of designed ice holder (front view). The dimensions are in mm. (e) Assembly model of the Mode I ice adhesion test ........................ 24 Figure 2.2.Stress distribution within the Al sheet. (a)first increment of analysis. (b) second increment (before separation) of the analysis. ........................................................................ 24 Figure 2.3.Tensile ice adhesion measurement system break-down into four main structures 27 Figure 2.4.Dimensions and specifications of the Al sheets. a, part (13) b, part (26) c, part (9). The dimensions are in mm. ..................................................................................................... 28 Figure 2.5. Movable structure framing completed view and exploded view (numbered parts are specified in Table 2.2). ...................................................................................................... 29 Figure 2.6. Crosshead assembly completed view and exploded view (numbered parts are specified in Table 2.2). ............................................................................................................ 30 Figure 2.7. Crosshead assembly fixed on the movable structure, both completed view and exploded view (numbered parts are specified in Table 2.2). .................................................. 31 xiii Figure 2.8. Crosshead assembly fixed on the movable structure, both completed view and exploded view (numbered parts are specified in Table 2.2). .................................................. 33 Figure 2.9. Installation of the electronics on the stationary structure (numbered parts are specified in Table 2.2). ............................................................................................................ 34 Figure 2.10. Peltier plate stage assembly, both completed view and exploded view. Note that (27) comes with 3 internal screws that are removed and re-attached to fix (27) onto (26) (numbered parts are specified in Table 2.2). ........................................................................... 35 Figure 2.11. The Peltier plate stage and movable structure fixed on the stationary structure 36 Figure 2.12. Closed-loop water circulation system via the measurement stage structure, mini fridge, and chiller (numbered parts are specified in Table 2.2). ............................................. 37 Figure 2.13. Wiring diagram for the electronics of the tensile ice adhesion measurement device. ..................................................................................................................................... 38 Figure 2.14. Tensile ice adhesion of polypropylene and polyethylene as a function of temperature. ............................................................................................................................ 48 Figure 2.15. Tensile ice adhesion of polypropylene and polyethylene as a function of pull-off speed. ...................................................................................................................................... 49 Figure 2.16. Tensile ice adhesion of polypropylene and polyethylene as a function of thickness of the material. ........................................................................................................ 50 Figure 2.17. Critical detachment force for different radii of ice, plotted according to Equation (2.1). ........................................................................................................................................ 51 Figure 2.18. Fifteen individual measurements of the critical force to detach ice from polypropylene at -15 °C. The interfacial area was 1.77 cm2. ................................................. 52 Figure 3.1. The tensile stress-strain curve of prepared PDMS samples ................................. 56 xiv Figure 3.2. Shear and tensile ice adhesion strength of various thickness of soft PDMS ........ 59 Figure 3.3. Critical pull-off force dependence on thickness of thin PDMS surfaces. ............ 59 Figure 3.4. Effect of the probe height on the shear ice adhesion strength of (a) soft PDMS, (b) polypropylene ......................................................................................................................... 61 Figure 3.5. Critical ice pull-off force dependence on the elastic modulus of thick PDMS substrates. ................................................................................................................................ 62 Figure 3.6. Tensile and shear ice adhesion strength plotted against the ratio of shear modulus over thickness on logarithmic axes. ........................................................................................ 64 Figure 3.7. Shear and tensile ice adhesion strength of soft PDMS versus the speed of the applied force............................................................................................................................ 65 Figure 3.8. Shear and tensile ice adhesion strength dependence of soft PDMS on roughness parameters (a) average roughness, (b) root-mean-squared roughness, (c) developed surface area, in the form of the Wenzel roughness, and (d) local crack formation on roughness features .................................................................................................................................... 67 Figure 4.1. 3D scanning laser microscope image of the (a) morphology and (b) topography of the superhydrophobic PDMS and (c) morphology and (d) topography of the initially rough hydrophobic PDMS ................................................................................................................ 72 Figure 4.2. Superhydrophobic PDMS, (a) SEM image of the surface showing the hierarchical structure, (b) a water droplet deposited on the superhydrophobic PDMS. ............................. 73 Figure 4.3. Tensile and shear ice adhesion strength of the initially superhydrophobic PDMS plotted against abrasion time. ................................................................................................. 74 xv List of Symbols τice shear ice adhesion strength σice tensile ice adhesion strength θ Young’s contact angle θs static contact angle θadv advancing contact angle θrec receding contact angle θ * apparent contact angle γsl solid-liquid surface tension γsv, γ solid-vapor or interfacial surface energy γlv liquid-vapor surface tension fs solid surface fraction fv vapor surface fraction Wa thermodynamic work of adhesion Ws work of ice removal xvi µ shear modulus h film thickness E* apparent elastic modulus E elastic modulus lc length of crack Λ non-dimensional constant 2a stud diameter ν Poisson ratio Fc critical pull-off force Sq root-mean-squared roughness Sa average roughness Sdr developed surface area r Wenzel roughness xvii List of Abbreviations PDMS Polydimethylsiloxane CAH Contact angle hysteresis PE Polyethylene PP Polypropylene PLA Polylactic acid Al Aluminum PFC Perfluorinated compounds PTFE Polytetrafluoroethylene PMMA Polymethyl methacrylate PTES 1H,1H,2H,2H-perfluorodecyltriethoxysilane MOF Metal-organic framework CORM Component of relative motion POSS Polyhedral oligomeric silsesquioxane xviii Acknowledgements I wish to thank my fabulous supervisor Prof. Kevin Golovin for his unexampled support throughout my journey as a master’s student at UBCO. He was always open to hearing my ideas and boosted them in the cleverest way. From him I have learned how to think as a scientist and solve problems as an engineer. His brilliance as my supervisor will reflect in my future endeavor, if not yet. I would like to thank my wonderful OPERA lab mates for being such a benevolent, positive, friendly, and encouraging group of people, who I could always count on, and drink coffee with. I also would like to thank my friends at UBC Okanagan for making my wonderful experience of living in Kelowna filled with more love, joy, and laughter. Finally, I want to thank my parents and my sister, for their everlasting support, care, and love, no matter how near or far. They inspired me to be who I am today. xix “To my inspiring parents Elia and Mehdi, and my lovely sister Kimia” 1 Chapter 1: Introduction Ice accumulation on surfaces has always been a challenging problem that brings risk and difficulty both on an industrial level and to people’s everyday lives. Ice buildup on snowy days on the windshield of vehicles is a palpable example of it affecting daily activities during winter. Furthermore, ice accretion on top of bridges1, tall buildings2 and airplane parts3 may cause severe hazards. There were a total of 258 icing and inflight icing accidents reported between 2006 to 2010, in the National Transportation Safety Board and Aviation Safety Reporting System, one of which killed 4 crew members, 45 passengers and 1 person on the ground4. On an industrial level, icing can negatively affect the efficiency of a wind turbine by changing the aerodynamic of the blades5. The government of Canada reported that each year around $113 million dollars was lost between 2010-2016, because of the loss of wind energy production in cold regions as a consequence of icing of blades6. Researchers have come up with several ideas to avoid the difficulties brought by the icing of surfaces. Most common solutions to the problem include preventing or delaying the formation of ice on surfaces, or producing coatings that lower a surface’s adhesion strength to ice. Ice formation happens in two steps: nucleation and growth 7. If at least one of these steps is hindered, the ice formation process either stops or slows down. For example, on surfaces with roughness values less than the critical nucleation radius of ice, ice formation is greatly delayed because of nucleation hinderance. Surfaces with such low roughness values are identified as smooth surfaces 8. Highly structured surfaces however, trap air pockets which delay the heat transfer between a water droplet and the substrate, and can decelerate the growth process 9. 2 A considerable number of studies have focused on producing surfaces with low adhesion to ice utilizing different methods and materials 10–16. The accreted ice on a surface with low adhesion strength to ice can easily be removed by a small amount of force which in some cases may be as low as the weight of the formed ice, which results in passive ice shedding. Among them, elastomers have revealed to possess some of the lowest ice adhesion values 15–18. The low ice adhesion of elastomers is enabled by a surface instability known as interfacial cavitation, which is a tension-driven phenomenon19. However, most ice adhesion measurement devices used in prior studies can only measure the shear ice adhesion strength of surfaces 20,21. Few studies have utilized devices and methods that measure the adhesion of ice by applying a tensile force 22–38 and there is no standard or high throughput system readily available. In this work a reliable and high throughput tensile ice adhesion measurement device was designed, and the performance was investigated. The designed tensile ice adhesion setup (Figure 1.1a) and a conventional shear ice adhesion setup (Figure 1.1b) were then used to carefully study and compare the shear and tensile ice adhesion strength of a polydimethylsiloxane (PDMS) based elastomer. Finally, a PDMS based superhydrophobic surface was developed with lasting low adhesion to ice. Studying surfaces such as elastomers under pure tensile force helps to better understand the underlying fracture phenomena and provides an overview when fabricating elastomeric-based ice phobic coatings, which exhibit low shear ice adhesion strength because of the incorporation of a tensile component. 3 Figure 1.1. Ice adhesion measurement devices used, (a) designed tensile ice adhesion measurement apparatus, (b) shear ice adhesion measurement device 1.1 Background 1.1.1 Wettability Accumulated ice on surfaces forms when liquid water such as rain droplets or melted snow, comes in contact with a solid surface at sub-zero temperatures. Therefore, the way water interacts with the surface may directly affect the ice/substrate interface interactions and conformation. The water/solid surface interaction is comprehended as wettability characteristics of the substrate. 4 1.1.1.1 Young’s and static contact angles Consider a liquid droplet resting on a smooth solid surface. The line where the liquid (l), vapor (v), and solid (s) phase meet is called the triple-phase contact line. The angle that the droplet makes with the surface at any point on the contact line is called the Young’s contact angle (θ). In general, the angle that a liquid makes with a solid surface could be calculated using Young’s equation: 𝑐𝑜𝑠𝜃 =𝛾𝑠𝑣 − 𝛾𝑠𝑙𝛾𝑙𝑣 (1.1) where γsl, γlv, and γsv are solid/liquid free interfacial energy, liquid surface tension, and solid surface free energy, respectively. This equation is a thermodynamic equilibrium and indicates that the angle a liquid makes while resting on a solid surface is the result of a balance between the tendency of the liquid to spread on the solid and keep its spherical shape. Lower surface tension leads to higher tendency to spread and wet a solid surface which results in lower contact angles. However, Young’s equation is based on some assumptions that may not be the case in real scenarios. For example, the surface should be smooth and chemically homogenous without any kind of contaminants. The gas environment around the droplet should be 100% saturated with the vapor of the liquid. The solid surface should be rigid and should not interact with the liquid in any other way such as swelling, etc. In real life with non-ideal surfaces, violation of the assumptions results in inaccurate Young’s contact angle measurements. The contact angle of a static droplet measured on a surface is called the static contact angle (θs). The static contact 5 angle and the Young’s contact angle may or may not be equal, depending on how ideal the surface is and if any of the assumptions are violated. 1.1.1.2 Advancing, receding and contact angle hysteresis One way to determine the wetting properties of a non-ideal surface is by measuring the dynamic contact angles. By steadily adding more water to a static water droplet, the droplet volume and the water contact angle will increase without moving the contact line until the angle is large enough that the droplet moves further out, making a larger contact line with the same static contact angle. The angle observed just before or after the droplet advances along the dry surface is called the advancing contact angle (θadv). By removing water from a static water droplet, on the other hand, the volume and the water contact angle will decrease without moving the contact line until the angle is low enough that water recedes, making a contact line shorter in length. The water contact angle just before or after the droplet de-wets the surface is called the receding contact angle (θrec). The difference between the advancing and receding contact angle is called the contact angle hysteresis. Contact angle hysteresis (CAH) is a measure of surface homogeneity and perfection. High CAH on a surface means lower mobility of the droplet which is pinned on the surface in some parts of the contact line. Two main reasons for high CAH include chemical heterogeneity and surface roughness. Recalling the assumptions in Young’s equation, an ideal surface should have a contact angle hysteresis of 0˚. 𝐶𝐴𝐻 = 𝜃𝑎𝑑𝑣 − 𝜃𝑟𝑒𝑐 (1.2) 6 Surfaces are categorized in a range of superhydrophilic to superhydrophobic based on their water contact angle and contact angle hysteresis. Surfaces with θ < 90˚ are considered hydrophilic surfaces. Surfaces that make contact angles with water as low as 0˚ < θ < 5˚ are considered superhydrophilic surfaces. If θ > 90˚, the surface is considered a hydrophobic surface. Superhydrophobic surfaces make a water contact angle of θ > 150˚ and a CAH < 5˚. 1.1.1.3 Wenzel and Cassie-Baxter states On a rough surface, a water droplet can adopt two configurations. The Wenzel state happens when the droplet completely penetrates the surface texture, wetting the whole surface (Figure 1.1a.) In this case the total water/solid interfacial area, and the triple contact line length, will increase. The contact angle of a liquid on such surface can be calculated using the Wenzel equation (Eq. 1.3): cos 𝜃∗ = 𝑟 cos 𝜃 (1.3) where θ* is the apparent contact angle and r is the surface area of the rough surface, divided by the projected surface area, which is called the Wenzel roughness. Therefore, Wenzel roughness is always r ≥ 1. If the contact angle of a liquid on a smooth surface is below 90˚, by roughening the surface the apparent contact angle will decrease. In contrast, if a droplet exhibits a contact angle higher than 90˚, roughening the surface will result in an increase in the apparent contact angle of the liquid. In other words, by roughening a smooth surface that is chemically hydrophobic, such as silicone, the contact angle will increase. After a certain increase in roughness, wetting the surface is not energetically favorable. In this case the water droplet will 7 rest on air pockets that are trapped in the grooves on the surface, shown in Figure 1.1b. The contact line will partially touch the surface and partially touch air. The apparent contact angle is described by the Cassie-Baxter model (Eq. 1.4): cos 𝜃∗ = 𝑓𝑠 cos 𝜃 + 𝑓𝑣 cos 𝜃𝑣 (1.4) Where 𝑓𝑠 and 𝑓𝑣 are the solid surface fraction and vapor surface fraction, respectively. Because the vapor surrounding a droplet in most cases is air, 𝜃𝑣 is considered as 180˚. The Cassie-Baxter equation shows that the apparent contact angle will increase when the droplet is in contact with more air rather than the solid surface. Figure 1.2. Possible liquid/solid configurations, (a) Wenzel state, (b) Cassie-Baxter state 1.1.2 Ice adhesion strength Consider a water droplet sitting on a surface. The work required to detach the water droplet from the substrate at the interface without deforming the surface is called the thermodynamic work of adhesion (Wa). Here detachment refers to completely eliminating the in-common area of the two materials and producing two new surfaces. In the case of a solid and a liquid, the 8 thermodynamic work of adhesion is 𝑊𝑎 = 𝛾𝑆𝑉 + 𝛾𝐿𝑉 − 𝛾𝑆𝐿 39. The Young-Dupre equation was derived by coupling this formulation with Young’s equation40: 𝑊𝑎 = 𝛾𝐿𝑉(1 + cos 𝜃) (1.5) This equation explains that the thermodynamic work of adhesion depends on the surface tension of the liquid and its Young’s contact angle on the surface. However, the wetted surface area for rough surfaces could be totally different than the wetted area on an ideal surface with the same chemistry. The work of adhesion for a droplet that is in the Wenzel state on a hydrophilic surface is greater than the ideal smooth surface because the droplet is in contact with a greater area of the hydrophilic solid; meaning that more liquid-solid bonds need to be broken for detachment. On the other hand, a droplet on a superhydrophobic surface which is in the Cassie-Baxter state wets a portion of the surface, making smaller liquid-solid interface. Relatively similar chemical interactions exist between ice and substrates because it is the solid form of water. The configuration that a frozen droplet adopts on a surface may or may not be the same as the configuration of the droplet before freezing depending on the environmental conditions such as humidity. However, it is still bound by complete Wenzel or complete Cassie-Baxter state and the laws hold for both41. Ice detachment physically happens when a crack is formed from an applied force and propagates across the interface. Accordingly, characterizing surfaces by the ice adhesion strength, which is the maximum force required to mechanically detach ice from a surface, is preferred 42. The shear stress (τice) required to de-bond ice from an elastomeric film, is given by:15,43 9 𝜏𝑖𝑐𝑒~(𝑊𝑎𝜇ℎ)1/2 (1.6) This equation indicates that the shear ice adhesion strength on a surface depends on the shear modulus (µ) and thickness (h), as well as the wettability characteristics of the material (Wa). If a surface can repel ice with shear stresses τice ≤ 100 kPa, it is called an icephobic surface. Now consider a rigid stud such as ice on an elastomeric film which is being pushed off by applying a distributed shear force at a line above the plane of the interface (Figure 1.3.). An elastic instability at the interface of the rigid/soft materials results in emerging air bubbles at the interface which produce vertical displacement. Before the shear stress is high enough to detach the ice from the surface, the ice will compress the elastomeric film at the front edge of the ice because of the torque generated, as shown in Figure 1.2. Simultaneously, a normal force will be generated at the rear end of the ice, which opens a cavity at the rear end of the interface. In other words, the discrepancy between the elastic modulus of the rigid ice stud and the soft substrate results in the instability of interfacial cavitation. This phenomena can be explained from a fracture mechanics point of view, formulated below:44,45 𝜏𝑖𝑐𝑒 = (𝐸∗𝛾𝑠𝑣𝜋𝑙𝑐Λ)1/2 (1.7) where E* is the apparent elastic modulus, lc is the length of crack and Λ is a non-dimensional constant determined by the geometric configuration of the crack. Based on this equation, a lower ice adhesion strength can be obtained by increasing the maximum crack length, 10 decreasing the elastic modulus, or decreasing the surface energy of the material. Surfaces with lower energy result in weaker bonds with the ice. Also, the number of probable crack initiation sites on a surface with ice in the Cassie-Baxter state is higher than for a smooth surface46. Cracks act as stress concentration sites and increase the efficiency of ice removal 44. However, an exclusive, detailed study on pure tensile ice adhesion of soft substrates has often been neglected and there are only few studies that have reported tensile ice adhesion values or utilized related methods 22–38. This triggered our motivation to dig deeper into the ice adhesion strength of elastomeric coatings under tensile forces. Figure 1.3. Schematic illustration of the tensile force generated at the rear edge of an ice cube when a shear force is being applied at a height above its interfacial plane. 1.2 Existing Techniques 1.2.1 Ice adhesion and wettability Recall that wettability characteristics of a surface, and the icephobicity, are mainly affected by the chemistry and roughness properties of the surface. In other words, the water contact angle 11 in Eq. 1.5, which affects the ice adhesion of the surface, depends on the molecular interactions at the interface and the roughness of the surface. The highest water contact angle on a smooth surface is 120˚ and is observed Perfluorinated compounds (PFC) which exhibit the lowest surface energy due to the high percentage of the -CF3 groups on their surfaces. Therefore, many studies have focused on preparing surfaces with low surface energy chemistries to study the relationship between wettability and ice adhesion and achieve ice-phobic properties. Meuler et al. coated bare steel samples with various polymers to achieve smooth surfaces with a range of wettabilities and measured their shear ice adhesion strength. They found that the ice adhesion strength decreases linearly with increasing the receding contact angle with a scaling parameter of a [1 + cos θrec]. Based on this correlation, they claimed that they have achieved the lowest ice adhesion possible for a smooth surface, by obtaining the highest receding contact angle reachable on a smooth surface of 118.2 ±2.4˚ 47. By adding micro- and nano-textures on hydrophobic chemistries, superhydrophobic surfaces with water contact angles as high as ≈180˚ and contact angle hysteresis less than 5˚ can be achieved. Researchers expected even lower ice adhesion values on superhydrophobic materials compared to the smooth material with the same chemistry, because of the decreased solid-liquid interface due to the initial water droplet being in the Cassie-Baxter state. Ozbay et al. measured the ice adhesion strength of various materials with a range of surface free energies, between 21.8 mN/m for polytetrafluoroethylene (PTFE) and 39.2 mN/m for copper. The ice adhesion strength increased 4.5 fold with increasing surface free energy 48. Arianpour et al. prepared surfaces with varied contact angles and contact angle hysteresis by adding nanoparticles to a silicon rubber matrix. They found that droplets on the superhydrophobic 12 surfaces rolled off easier because of having low CAH. The ones that remained on the surface froze after a longer time because the droplets were resting on air pockets that reduced heat transfer in the Cassie-Baxter state. Also, the shear ice adhesion strength of the surface reduced significantly which was believed to be because of the low CAH. Arianpour et al. reported their surface as an attractive icephobic candidate because of its anti-icing and ice repellency properties49. Kulinich and Farzaneh coated aluminum (Al) substrates with a nanoparticle/fluoropolymer suspension and measured the ice adhesion strength on the samples. Their results revealed that the ice adhesion directly correlates with the contact angle hysteresis of the surface and it is believed to be because of the higher interfacial area on substrates with high CAH50. They argued that previous conclusions, indicating that the ice adhesion strength on rough surfaces depends on the water contact angle51, only holds when the contact angle hysteresis on the surface is low. Many studies argue that superhydrophobicity does not necessarily make a surface capable of repelling ice with low forces. Meuler et al. explain that adding topographical features alone is not enough for achieving low ice adhesion strength values in every environmental condition. They suggest that a superhydrophobic surface that does not hold a droplet on the air pockets after freezing, i.e. does not produce Cassie-Baxter ice, would not be promising as a durable ice phobic surface52. Cui et al. prepared hydrophobic and superhydrophobic surfaces with a variety of roughness, wettability, and surface energy. They showed that on rough superhydrophobic surfaces in rose petal or lotus model, the contest between mechanical interlocking and stress concentration determines the ice adhesion strength on the surface53. Maghsoudi et al. prepared superhydrophobic silicone rubber surfaces by two different methods, resulting in different 13 roughness values, and measured their shear ice adhesion strength. They revealed that on surfaces constructed of micro/nano textures, lower ice adhesion is achieved on surfaces with lower roughness54. 1.2.2 Ice adhesion and elastic modulus In previous sections it was explained how a surface’s ice adhesion strength is related to the work of adhesion, elastic modulus, and thickness, and we particularly focused on work of adhesion. In this section, we reflect on the elastic modulus, specifically soft elastomeric substrates such as PDMS. As explained earlier in Figure 1.2, when a shear force is applied to an ice at a height above the interfacial plane of the ice/soft substrate, a moment will form. A sufficient moment will generate a tensile force at the rear end of the ice that is large enough to separate the ice from the soft substrate, initiating crack formation. The constantly applied shear stress and the low modulus of the substrate all together progress the crack propagation. The addition of a tensile stress to the applied shear stress, results in a lower shear force needed for complete detachment43,55. Beemer et al. prepared PDMS gels and varied their elastic moduli by adding plasticizers and manipulating the cross-link density. They studied the effect of elastic modulus and film thickness on ice adhesion by applying a shear force. They showed that the shear ice adhesion decreased with an increase in the thickness of the film, up to 1.4 mm following Equation (6), and remain constant thereafter. The elastic modulus, on the other hand, had a direct relation with the ice adhesion strength43. In another work, Wang et al. observed that by increasing the height of the applied shear force above the interfacial plane, the critical force of detachment of poly methyl methacrylate (PMMA) decreased because a tensile/shear mode emerged56. Golovin et al. studied the shear ice adhesion dependence on 14 elastic modulus by tailoring the cross-link density of various elastomers. In addition, they facilitated interfacial slippage by adding different oils. They revealed that for soft surfaces, cross-link density and interfacial slippage independently dictate the shear ice adhesion strength, rather than the wettability characteristics of the surface. Their results precisely matched the governing equations15. Zhuo et al. prepared a PDMS coating with slidable crosslinks and investigated the shear ice adhesion. They suggested that besides the hydrophobic nature of PDMS, the slidable crosslinks were responsible for the low ice adhesion not only because of a decreased the elastic modulus, but also enabling interfacial slippage57. He et al. were able to decrease the shear ice adhesion strength of PDMS surfaces by introducing macro-cracks in the form of holes that diminished the stiffness homogeneity. They found that increasing the diameter of the holes decreases the ice adhesion strength by enabling and improving crack initiation and propagation. However, the effect of hole diameter on stiffness inhomogeneity became less distinct with increasing the film thickness44. A year later, they fabricated a sandwich-like PDMS sponge and tuned the elastic modulus by modulating the weight ratio the prepolymer and curing agent. They indicated that the facilitated crack initiation, the low elastic modulus, and the inherent low surface energy of their surfaces resulted in shear ice adhesion values as low as τice = 0.9 kPa58. 1.2.3 Tensile ice adhesion As discussed in the previous section, soft elastomers such as PDMS have been suggested widely to be used as ice-phobic coatings. Interfacial cavitation, one of the governing mechanisms responsible for the low shear ice adhesion strength of rubbers, is a tension-driven phenomenon. However, measurements of pure tensile ice adhesion strengths (σice) of such 15 surfaces, along with a comparison to their shear ice adhesion strengths, are rare. In 2013, Ruan et al. studied the anti-icing behavior of superhydrophobic Al, prepared by etching and chemical methods. In their paper, they briefly explained that they used a dynamometer to pull-off frozen water droplets from the surface via a hairline through the droplet34. Based on the images published in the paper, the hairline begins trapped in the frozen droplet. However, this is not an accurate and repeatable method of tensile adhesion measurement for many reasons. First, there is no control over the wetted/iced area when a droplet is deposited on the surface. Second, the hairline that is used to pull the ice off, is not attached to a fixed position, and passes through the bulk of ice. This would result in inconsistent stress distribution at the interface for different measurements, limiting the repeatability of the method. In 2013, Wang et al. characterized the ice adhesion of etched aluminum (Al) surfaces. They performed the ice adhesion measurements using a pulley-like device. They explain that they had to move frozen samples from a freezer to the test device. The tensile ice adhesion measurement was also done by gradually adding weight to the driving arm36. In 2018, Work et al. reviewed the ice adhesion measurement techniques and pointed out that they could not find any paper on a tension test device that analyses the stress distribution and standardizes the method59. Davis et al. used the blister method to measure the tensile ice adhesion of their rough surfaces. In this method, a tensile force was applied at the ice/substrate interface by pumping pressurized air through the cylindrical cracks at the interface60. Loho et al. introduced a new device measures the tensile ice adhesion of samples by pulling off the samples from a bulk-ice formed beneath61. The devices that Davis et al.60 and Loho et al.61 used had the advantage of in situ ice formation compared to previously explained techniques were the iced surface was 16 transferred to the measurement stage from a freezer. However, only one ice/substrate interface could be prepared and tested at a time. Murase et al. measured the tensile and shear ice adhesion strength of 22 polymers with different works of adhesion, glass transition temperatures, dispersion and hydrogen bond and viscoelastic behavior. They found that work of adhesion is affected by mobility of the chains. Therefore, any physical property that alters the chain mobility will also influence the shear and tensile ice adhesion strength62. Wang et al. characterized the anti/de-icing of their Al substrate using tensile ice adhesion strength measurements. They prepared a superhydrophobic surface by etching Al and then coating it with 1H,1H,2H,2H-perfluorodecyltriethoxysilane (PTES), generating air pockets that lead to a reduction in the tensile ice adhesion63. Zhu et al. measured the tensile and shear ice adhesion of bare, PDMS coated, and silicone oil infused, PDMS coated Al. Their results showed an overall reduction in both tensile and shear adhesion strength with an increase in the oil content38. In a different work, Yang et al. 64 measured the tensile and shear adhesion strength of fluoro-based coatings on Al substrates. The lowest shear and tensile adhesion belonged to the pristine polytetrafluoroethylene (PTFE), a low surface energy, smooth surface. Adding sub-micrometer texture to their surfaces resulted in improving the hydrophobicity but the shear and tensile ice adhesion was increased due to mechanical interlocking. The increase in interfacial chemical interactions also lead to an increase in the tensile ice adhesion on smooth surfaces. In 2019, Gao et al. fabricated metal-organic framework (MOF) coatings with micro-nano texture and infused them with silicone oils in a way that kept the texture of the surface. They investigated the anti-icing as well as the de-icing of their surfaces under a tensile force. The 17 tensile ice adhesion value of the micro-nano textured oil infused MOF was reported to be less than 20 kPa, which was around 10 times lower than that of nano texture MOF surfaces. They also showed that the viscosity and amount of the oil added to the texture did not have a significant effect on the tensile ice adhesion of their surface35. Maeno et al. studied ice-ice friction coefficient dependence on sliding velocity, temperature, and normal stress65. Dan et al. investigated the tensile and shear adhesion of ice to asphalt pavement at different temperatures and roughness. Their results showed that both tensile and shear adhesion increase with decreasing temperature and increasing roughness66. Peng et al. also used hydrophobic coatings on asphalt pavement and measured the tensile and shear ice adhesion strength of their samples67. The above studies are the only ones that have took into consideration the importance of tensile ice adhesion measurements, to the best of our knowledge. Among them, only a few have utilized tensile ice adhesion measurements to characterize the icephobicity of elastomeric surfaces. 1.3 Motivation The advantageous influence of interfacial tensile forces on the shear ice adhesion strength of a soft surface has been strongly supported by theories. However, few experimental studies have focused on or measured the tensile ice adhesion strength of soft surfaces and compared it to the relative shear ice adhesion strength. When it comes to superhydrophobic, ice-phobic surfaces, maintaining the icephobicity and durable ice repellency is a big challenge. Further, comparisons between different surfaces are difficult as there is no standard technique of measurement for tensile ice adhesion. Accordingly, we designed a high throughput tensile ice adhesion measurement system, which: (1) enabled cooling and adhesion measurement on the 18 same stage, (2) provided space for several samples to be tested at a single run. The design and construction of the tensile ice adhesion measurement is presented in Chapter 2, along with the reasoning for the design decisions. The performance of the setup is characterized using experimental trials varying parameters such as temperature, pull-off speed, thickness of the substrate, and ice/substrate interfacial area, to verify the precision of the measurements. We then study the tensile and shear ice adhesion strengths of PDMS surfaces in Chapter 3, varying different parameters such as PDMS film thickness, elastic modulus, roughness, and the speed of the applied force. We further compare the tensile adhesion strength of the PDMS, which is a single value, to shear adhesion values measured by applying the shear force at different heights above the iced interface. Our findings enabled us to fabricate a superhydrophobic, durable icephobic PDMS surface (σice= 4.2 kPa and τice= 7.3) that maintained the low tensile and shear ice adhesion strength after 20 minutes of abrasion (σice= 11.2 kPa and τice= 8.6), even when mechanical interlocking occurred. 1.4 Objectives and outline Objective 1: Designing an accurate and efficient tensile ice adhesion measurement apparatus and verifying the performance of the device by comparing the measurements with known laws of fracture mechanics. Hypothesis: By using well-designed ice holders that uniformly distribute force, a cold stage on which many holders could fit, and an adjustable measurement system we can achieve consistent, repeatable tensile ice adhesion measurements. 19 Tasks: • Design and build the measurement system • Investigate the stress distribution of the ice/substrate interface when using various designs of ice holders • Study the effect of various parameters on tensile ice adhesion of at least two substrates • Validate the performance of the apparatus by comparing the results with literature values and theoretical trends Objective 2: Achieve a comprehensive understanding of the ice adhesion strength of soft elastomeric materials under shear and tensile forces. Hypothesis: Tensile ice adhesion strength of a surface is lower than its shear ice adhesion strength, and by increasing the tensile force component on a surface with mixed shear/tensile mode, the ice adhesion strength will decrease and approach the pure tensile ice adhesion strength. Tensile and shear ice adhesion strengths decrease with decreasing the modulus and force speed, and increasing the thickness. Roughness could either decrease or increase both tensile and shear ice adhesion strength based on the wettability characteristics that it provides. Tasks: • Measure the tensile and shear ice adhesion strength of soft, PDMS-based elastomers while varying different parameters such as modulus, thickness, roughness, and force speed 20 • Compare the tensile ice adhesion strength with shear ice adhesion strength while triggering interfacial cavitation by applying the shear force at different heights 21 Chapter 2: A High Throughput Tensile Ice Adhesion Measurement System 2.1 Overview Herein, the design and construction of a tensile ice adhesion measurement device is discussed which exhibits many advantages over previous measurement systems. The benchtop system has a small footprint (overall dimensions of 26 cm × 33 cm × 70 cm, length × width × height) and is simple to construct and operate. The device mainly consists of a motor, force gauge, cold stage, ice holders, chiller, and Al framing which provides mechanical support to the structure. A thermocouple and a PID controller control the temperature of the Peltier stage where measurement takes place. Various experimental test parameters, such as temperature, speed of applied force, iced area, and thickness of the test material can be varied independently. 2.2 Description of the System Unlike a typical uniaxial tension setup, our tensile ice adhesion setup includes a Peltier stage with an area of 12 cm × 6 cm, which also serves as the measurement stage. Larger Peltier stages could be substituted to allow for a greater number of tested samples per freeze cycle. The temperature of the stage is tunable in the range of 0 °C to -25 °C using a thermocouple and a cold-water circulation system. This makes it possible to measure the tensile adhesion of ice to substrates at different temperatures. The size of the ice holder affects the number of measurements per freeze cycle. For example, the ice holder that was used to verify the operation of the setup under different temperatures, pull-off speeds, and thicknesses had an outer radius of 6 mm, allowing for 6 tensile ice adhesion measurements during each freeze 22 cycle. Making several measurements during a single freeze cycle decreases the risk of errors due to varied testing conditions, resulting in more precise and consistent values. Unlike previous tensile measurement systems 29,30,68, the freezing cycle and the tensile measurement occur on the same stage. This means that the ice/substrate sample does not need to be carried to the measurement stage. Environmental errors such as ice surface melting are avoided. The apparatus allows for three degrees of freedom in the x-, y-, and z-directions. The x- and y- translation enables the operator to freely position the force gauge hook directly above an ice holder. The z-direction translation, which is essential for the tensile force measurement, is enabled by mounting the force gauge on a linear motion stage connected to a motor. The force gauge can be easily and quickly replaced by another with a larger or smaller load cell, such that surfaces with vastly different adhesion values may be investigated. To control the iced area, holders with specific internal surface areas were designed. The geometry and shape of the holders were optimized to achieve a uniform stress distribution at the interface. The ice holders are one the most influential elements that govern the precision of the measurements. Accordingly, the design and optimization of the ice holder is discussed, in detail. This device: • Measures the tensile force needed to detach ice from a substrate • Is an inexpensive and simple setup to build • Can measure several samples during a single freeze cycle • Was verified and the measurements matched known laws of fracture mechanics 23 2.2.1 Design and Optimization of the Ice Holder Unlike shear-based methods, the design of the ice holder was more complex as tension must be applied normal to the interfacial plane. An ice holder was designed and analyzed using finite element modeling (Abaqus) in order to minimize stress concentration and avoid any induced bending moment. In contrast to the push-off shear ice adhesion test method, where uniform compression is applied on the lateral side of the ice cube holder, a pull-off method was simulated in order to investigate ice adhesion in Mode I fracture (tensile detachment). Uniformity in the stress distribution at the interface was considered in the optimized design of the ice holder, along with a methodology for easily and repeatedly applying tension. The deformable solid parts of the ice holder, cylindrical ice, and an Al substrate were modeled. In these simulations, the ice holder (made of polylactic acid, PLA, a common 3D-printing resin) was placed on an Al sheet with dimensions L = 60 mm, W = 60 mm, and t = 0.5 mm. The elastic moduli of Al, PLA, and ice were set to 70, 3.5, and 8.5 GPa, respectively, with Poisson ratios of 0.3, 0.33, and 0.3, respectively. The static analysis step was defined as ‘solver’ for all numerical simulations. After several iterations, the ice holder with the geometry shown in Figure. 2.1 was selected. 24 Figure 2.1.Tensile adhesion ice holder. (a) Isometric view of the designed ice holder. (b) Sectioning a quarter of the model reveals the cylindrical ice inside the holder. (c) Two-dimensional top view of the ice holder. (d) Drawing of designed ice holder (front view). The dimensions are in mm. (e) Assembly model of the Mode I ice adhesion test A concentrated force was applied to the connection points of the beam connectors via a high-strength cord, and the stress was transferred uniformly to the ice holder and ice adhered to the Al sheet as shown in Figure 2.2. Figure 2.2.Stress distribution within the Al sheet. (a)first increment of analysis. (b) second increment (before separation) of the analysis. 25 Interfacial fracture was modeled by applying a cohesive zone model to the ice/ Al interface69. The values of the cohesive zone parameters obtained by Chen et al.27 were utilized (Table 2.1). The interaction between the ice and ice holder was considered as a tie constraint to stipulate deformation continuity at the interfacial plane. The designed ice holder could effectively transfer the concentrated external force uniformly over the top surface of the cylindrical ice due to the chosen geometry (Figure 2.1b). Undeformable beam connector elements were selected for the connection between the ice holder and loading points (Figure 2.1e). These elements transferred the applied force between the components with a constrained component of relative motion (CORM) of the translational and rotational displacements in all three directions. In order to optimize the element size in the numerical simulations, mesh convergence was studied. 14,400, 9,724 and 33,086 elements with type C3D8R, consisting of an 8-node linear brick with reduced integration, were used for the sheet, ice cube, and ice holder models, respectively. No significant variation in the maximum stress was observed in the Al sheet for a larger number of elements, and the optimum element size of 0.5 mm was selected. Overall, the relatively uniform stress distribution at the ice/ Al interface (Figure 2.1a,b) indicated that the designed ice holder should exhibit consistent tensile ice adhesion measurements. 26 Table 2.1. Cohesive zone model parameters used in the numerical simulations27. Parameter Values Normal cohesive stiffness (Kn) 1×106 N/mm3 Shear cohesive stiffness (Kt) 1×106 N/mm3 Normal mode fracture energy (Gcn) 1×10-3 N/mm Shear mode fracture energy (Gct) 1×10-3 N/mm Normal cohesive traction (TnMax) 0.8 MPa Shear cohesive traction (TtMax) 0.8 MPa 2.2.2 Device Structure This device consists of four major components (Figure 2.3): (1) The stationary structure on which the electronics are attached and which provides the mechanical support of the system. (2) The movable structure which is fixed to the stationary structure while having the freedom to move in both x- and y- directions. (3) The crosshead, which is mainly comprised of a motor and a force gauge with a freedom of movement in the z-direction, due to the linear motion stage. The crosshead is held and supported by the movable structure. The attachment of these two parts together enables the whole part to have a freedom of movement in all three directions. (4) The Peltier stage which is fixed on the stationary structure and is responsible for the cooling. Below, step-by-step build 27 instructions are given along with figures with numbers for easy understanding. Table 2.2 includes the number directory of the pieces including all needed dimensions. Figure 2.3.Tensile ice adhesion measurement system break-down into four main structures 28 2.2.3 Build instructions 2.2.3.1 Structural instructions Cut and drill the Al sheets (9), (13), and (26) with respect to the dimensions depicted in Figure 2.4. Figure 2.4.Dimensions and specifications of the Al sheets. a, part (13) b, part (26) c, part (9). The dimensions are in mm. Phase 1 (see Figure 2.5): 1. Slide two T-nuts (5) into a T-slotted profile (2). Do the same for another T-slotted profile (2). 29 2. Use corner concealed brackets (4) to attach the T-slotted profiles (1), (2) and (3) to each other as shown in Figure 2.5. Ensure that the profiles from Step 1 are placed at the back end). Figure 2.5. Movable structure framing completed view and exploded view (numbered parts are specified in Table 2.2). Phase 2 (see Figure 2.6): 3. Attach the motor (6) to the Z axis CNC slide (7) using four steel socket head screws (8). 4. Attach the Z axis CNC slide (7) from Step 3 to the Al sheet (9) using four pairs of steel socket head screws (10) and locknuts (11). 5. Fix the force gauge (12) to the Al sheet (13) using two steel socket head screws (14) 30 6. Attach the Al sheet (13) from Step 5 to the Z axis CNC slide (7) from Step 4 using four pairs of steel socket head screws (10) and locknuts (11). Figure 2.6. Crosshead assembly completed view and exploded view (numbered parts are specified in Table 2.2). Phase 3 (see Figure 2.7): 7. Slide three T-nuts (5) into the outer slot and one into the top slot of two T-slotted profiles (15). 8. Slide one T-nut (5) to each of the vertical T-slotted profiles (1) from Phase 1, as illustrated in Figure 2.7. 31 9. Attach T-slotted profiles (15) from Step 7 to the Phase 1 structure from Step 8 using two corner brackets (16), two 90 degree angled flat plates (17) and twelve Flanged Button Head Socket Cap Screws (FBHSCS) (18). Note: The structure from Phase 1 should be able to slide freely on T-slotted profiles (15) at this point. 10. Use four FBHSCS (18) and the previously inserted T-nuts in Step 1 to attach the final structure from Phase 2 to structure from Step 9. 11. Insert four corner concealed brackets (4) to the bottom slots of the T-slotted profiles (15). Figure 2.7. Crosshead assembly fixed on the movable structure, both completed view and exploded view (numbered parts are specified in Table 2.2). 32 Phase 4 (see Figure 2.8): 12. Begin from the bottom of the structure. 13. Slide T-nuts (5) in the slots of the T-slotted profiles as illustrated in Figure 2.8. 14. Insert all corner concealed brackets (4) as illustrated in Figure 2.8. 15. Use two T-slotted profiles (2) and two T-slotted profiles (15) to form a frame around the MDF Sheet 4 (23). The MDF sheet should be inserted within the slots of the T-slotted profiles. 16. Slide two horizontal T-slotted profiles (2) into the slots of the two vertically standing T-slotted profiles (19) from the bottom (let them be loose). 17. Slide one T-slotted profile (2) horizontally into the two shorter vertically standing T-slotted profiles (2) from the bottom (let them be loose). 18. Use two T-slotted profiles (15) and corner concealed brackets (4) to connect the tall (19) and short (2) T-slotted profiles. 19. Use the corner concealed brackets (4) to fix the vertically standing T-slotted profiles (2) and (19) in the slots of the bottom structure from Step 14. 20. Insert MDF Sheets 3 (22) and 5 (24) into the slots of the vertically standing T-slotted profiles as shown in Fig. 7. 21. Insert the MDF sheets from the top with the horizontal T-slotted profiles inserted in previous steps and fix the structure. 22. Insert the MDF Sheet 2 (21) into the slots of the tall T-slotted profiles (19), but below the second horizontal T-slotted profile (2). 33 23. Fix the second horizontal T-slotted profile (2) on top of the MDF sheet by inserting the sheet into the slots. 24. Slide MDF Sheet 1 (20) into the slots of the tall T-slotted profiles (19). 25. Fix a T-slotted frame (2) on top MDF Sheet 1 using corner concealed brackets (4). 26. Fix the whole structure from two sides using 90 degree angled flat plate (17) and FBHSCS (18). Note: Now all the components of this structure may be strongly tightened and should be without any free movement. Figure 2.8. Crosshead assembly fixed on the movable structure, both completed view and exploded view (numbered parts are specified in Table 2.2). 34 Phase 5 (see Figure 2.9): 27. Use screws (37) and (34) and nuts (39) and (35) to attach the electronics to the MDF sheets of the structure from Phase 4, as illustrated in Figure 2.9. 28. Attach PID controller (30) to MDF Sheet 5 (24). 29. Attach the LCD shield for Arduino (31) to the housing (32). 30. Glue the housing to the MDF Sheet 5. Figure 2.9. Installation of the electronics on the stationary structure (numbered parts are specified in Table 2.2). STOP! At this point the user may want to skip to the Electronics Instructions below, as at this point there is maximum access to all mounted electronics components. Phase 6 (see Figure. 2.10): 31. Attach Nylon single barbed tube adapter (28) to the Peltier plate (27). 35 32. Use eight FBHSCS (18) and the T-nuts inserted in Step 13 to fix Al sheet (26) as shown in Figure 2.10. 33. Remove the 3 internal screws on the bottom of the Peltier plate (27). Fix the Peltier plate (27) on the Al sheet (26) by re-inserting its three internal screws into the 3 central holes of (26). 34. Attach the PVC tubes (29) to the Nylon single barbed tube adapter (28). Figure 2.10. Peltier plate stage assembly, both completed view and exploded view. Note that (27) comes with 3 internal screws that are removed and re-attached to fix (27) onto (26) (numbered parts are specified in Table 2.2). 35. Attach and fix the movable structure to the stationary structure now containing the Peltier assembly, as shown in Figure 2.11. 36 Figure 2.11. The Peltier plate stage and movable structure fixed on the stationary structure Though not necessary, the ends of all T-slotted profiles may be capped with End Caps (55) if there remain any sharp edges from cutting. Phase 7 (see Figure 2.12): 36. Attach PVC tube (41) to (29) using a stainless-steel hose clamp (42). 37. Attach the submersible pump (44) to the stainless-steel bucket (43). 38. Fill the stainless-steel bucket (43) with water and place inside the mini fridge (45). 39. Connect the Peltier plate system, chiller cooling system (46) and submersible pump (44) using the PVC tubes (41) to create a closed-loop water circulation system. 37 Figure 2.12. Closed-loop water circulation system via the measurement stage structure, mini fridge, and chiller (numbered parts are specified in Table 2.2). 2.2.3.2 Electronics instructions The overall wiring diagram is shown in Figure 2.13 below. Individual instructions follow. 38 Figure 2.13. Wiring diagram for the electronics of the tensile ice adhesion measurement device. Power socket • The entire instrument is powered by a Type B power plug (52) connected to a wall power socket that has 110V 60Hz power. Connect the exposed positive, negative, and ground terminals to Terminal Block A (33) on separate ports using fork connectors (50). 39 • Connect the power supply (40) to the power plug through Terminal Block A (positive to positive, neutral to neutral, negative to negative) with fork connectors (50) using the stripped wires emanating from the power supply. Arduino • Carefully mount the Keypad Shield (31) on top of the Arduino UNO (53). The shield uses pins 4-9 for the display, A0 for buttons, and the +5V and GND pins. • Connect ports GND, 13, and 3 of Arduino UNO (53) to ports (ENA-, DIR-, PUL-), DIR+, and PUL+ of the stepper motor controller (6), respectively, using jumper wires (54). Solder these on the back of the Arduino as the Keypad Shield (31) sits on top of Arduino. • Connect the Arduino UNO to the DC-DC step down converter (49), which lowers the +24V from the Power Supply to +5V. Use the USB cable (type A-Male to B-Male) included in the Arduino UNO kit. Insert the USB type B male connector into the Arduino UNO and the type A male into the USB port of the DC-DC converter. • Connect the positive and negative terminals of the DC-DC converter to the positive and negative terminals of the power supply through Terminal Block B (33) with fork connectors (50). Peltier and Temperature Control: • Connect ports 1, 2, and 3 of the PID controller (30) to the positive, neutral, and negative terminals, respectively, of the power plug via Terminal Block A. Reuse the same terminals that the power plug is already using by loosening the clamp screw, adding the additional wire, and then tightening. 40 • Connect ports 9 and 10 of the PID controller to ports 3 and 4 of the solid state relay (36), respectively, with stripped wires (47,48) and fork connectors (50). • Connect the stripped red wire (positive terminal) coming out of the Peltier plate (27) to port 1 of the solid state relay (36) with fork connectors (50). • Connect port 2 of the solid state relay (36) to the positive terminal of the power supply (40) through Terminal Block B using a stripped wire and fork connector. • Connect the negative terminal (black wire) of the Peltier plate (27) to the negative terminal of the power supply through Terminal Block B using a fork connector and stripped wire. • Connect the positive and negative terminals of the Type-K thermal couple (51) to ports 7 and 6 of PID controller, respectively. • Mount the thermal couple on the Peltier plate with a screw (14). Motor and Motor controller • Connect the VCC+ and GND terminals of the stepper motor controller (6) to the positive and negative terminals of the power supply, respectively, through Terminal Block B using stripped wires and fork connectors. Reuse the same terminals that the power supply is already using by loosening the clamp screw, adding the additional wire, and then tightening. • The stepper motor (6) comes with black, green, red, and blues wires emanating from it. Connect the stepper motor controller ports A+ to black, A- to green, B+ to red, and B- to blue of the stepper motor. 41 Table 2.2. Building part directory Part name Number Smooth Surface T-Slotted Profile- 16 in. Long 1 Smooth Surface T-Slotted Profile- 8 in. Long 2 Smooth Surface T-Slotted Profile- 3 in. Long 3 Corner Concealed Brackets 4 1/4-20 Slide-in T-Nut- Centered Thread 5 NEMA 23 425 oz-in Stepper Motor 6 NEMA 23 WIDE Z axis CNC Slide 7 Black-Oxide Alloy Steel Socket Head Screw, 10-32 Thread Size, 1/2" Long 8 Multipurpose 6061 Al Sheet (See Fig. 3c for Dimensions) 9 Black-Oxide Alloy Steel Socket Head Screw, 5/16"-18 Thread Size, 1" Long 10 Medium-Strength Steel Serrated Flange Locknut, Grade 5, Zinc-Plated, 5/16"-18 Thread Size 11 Nextech 500N Force Gauge 12 Multipurpose 6061 Al Sheet (See Fig. 3a for Dimensions) 13 Black-Oxide Alloy Steel Socket Head Screw, M5 × 0.8 mm Thread, 8 mm Long 14 Smooth Surface T-Slotted Profile- 12 in. Long 15 3 Hole – Inside Corner Bracket 16 4 Hole - 90 Degree Angled Flat Plate 17 1/4-20 x .375" Flanged Button Head Socket Cap Screw (FBHSCS) 18 Smooth Surface T-Slotted Profile- 24 in. Long 19 42 Table 2.3. Building part directory MDF sheet 1- 352mm × 205mm × 6.35mm 20 MDF sheet 2- 60mm × 205mm × 6.35mm 21 MDF sheet 3- 100mm × 205mm × 6.35mm 22 MDF sheet 4- 280mm × 205mm × 6.35mm 23 MDF sheet 5- 100mm × 205mm × 6.35mm 24 Smooth Surface T-Slotted Profile- 11 in. Long 25 Multipurpose 6061 Al Sheet (See Fig. 3b for Dimensions) 26 Peltier Plate 27 1/4 in. Barb, 1/4, Nylon Single Barbed Tube Adapter - Black, Male 28 1/4 in. Clear PVC Tubing, NSF 29 PID Controller (AC powered, DC signal) 30 DFRobot DFR0009 LCD Shield for Arduino 31 Housing for Arduino 32 SODIAL(R) 5 Pcs Dual Row 4 Position Covered Screw Terminal Block Strip 600V 15A 33 Black-Oxide Alloy Steel Socket Head Screw, M3 x 0.5 mm Thread, 20 mm Long 34 Black-Oxide Steel Hex Nut, Medium-Strength, Class 8, M3 x 0.5 mm Thread 35 Solid State Relay (DC control, DC output) with Heat Sink 36 Black-Oxide Alloy Steel Socket Head Screw, M4 x 0.7 mm Thread, 15 mm Long 37 43 Table 2.4. Building part directory NEMA 23 425 oz-in Stepper Driver 38 Left-Hand Threaded Medium-Strength Steel Hex Nut, Class 5, Zinc-Plated, M4 x 0.7 mm Thread 39 Mean Well HLG-320H-24 40 3/8 in. Clear PVC Tubing, NSF 41 3/8 in. Stainless Steel Hose Clamps 42 Stainless Steel Flat Side Bucket 43 Submersible Pump 44 Mini Fridge 45 Water Chiller Cooling System 46 Stranded Wire 300V AC, 16 Wire Gauge (black) 47 Stranded Wire 300V AC, 16 Wire Gauge (red) 48 7-24V to 5V (USB) step-down converter (to power Arduino) 49 100x Blue/Red Insulated Spade Fork Connector Electrical Crimp Wire Terminals 50 WTK-10-24 Bolt-On Washer Thermocouple Assemblies 51 3-Wire Appliance and Power Tool Cord 52 Arduino UNO 53 Jumper wires 54 10 SERIES – Black Plastic End Cap w/ Push-Ins 55 Emma kites 70~2000lb Kevlar Kite String Braided 56 44 2.2.4 Operation Instructions Before using the system, the ice holders should be 3D-printed out of a desired resin. PLA printed very well and was sufficiently hydrophobic in order to prevent leakage. For each printed ice holder, thread a ~ 20 cm long piece of kite string through the hole at the top of the ice holder and tie the two ends in a knot so that a loop is formed. • Turn the system on either by plugging the power cord into an outlet, or turning on a surge protector if using one. Set the temperature as preferred using the PID controller. • Set the pull-off speed (Slow Forward/Reverse) using the Arduino. The UNO remembers the last used configuration, so skip this step if not changing the speed from a prior measurement. • Turn off the device to place the test material and the ice holders. It is important to strongly fix the test material on the Peltier stage in order to prevent deflection and bending during tension. When the expected tensile forces are low, substrates can be fixed to the Peltier stage using 3M 9629PC double-sided tape. If higher forces are expected, or if the materials exhibit poor tape adhesion, the materials can be glued to Al foil using an appropriate adhesive (3M scotch-weld adhesive DP604NS recommended) and then the foil taped to the Peltier stage using the 3M 9629PC double-sided tape. • Clean the surface using isopropyl alcohol, acetone, or any solvent suitable for the substrate material. 45 • Place the ice holders on the surface with a clearance of at least 1 mm from each other and the edges of the substrate. • Inject de-ionized water into the ice holders from the openings in its upper surface using a syringe or pipette, until the cylinder is completely full. The 1 cm diameter ice holders require ~ 0.785 mL whereas the 15 cm diameter ice holders require ~ 1.766 mL. Make sure no leaking occurs from the bottom of the holders as it will affect the measured tensile force. • Turn the water circulation system (submersible pump) and the device on at the same time. The temperature of the cold stage will begin to drop to the pre-set temperature. Freezing occurs directionally from the bottom of the holder contacting the cold sample surface. • Wait until the water inside the holders is completely frozen and forms glaze (also known as bulk water ice). To verify that the ice has fully frozen, poke the ice through the opening on the upper side of the ice holders with a syringe tip. • Turn on the force gauge and align the hook manually, exactly above any holder. Place the looped kite string around the force gauge hook. • Use the Fast Forward/Reverse buttons on the LCD shield to position the hook end far enough from the holder such that the kite string is not under tension but there is minimal amount of slack in the cord. • Turn on the force gauge or, if already on, zero any residual measurements. Push the Slow Reverse button to pull the ice holder off of the substrate at the pre-set rate, until complete detachment occurs. Record the measured force. 46 • Repeat the previous 3 steps for all additional ice holders. • In order to remove the material from the stage, detach it while the stage remains at sub-zero temperatures, as the tape comes off much easier. • Clean up the tape residue from the Peltier stage before running a second test. • To turn off the machine simply unplug the power cords. 2.3 Validation and Characterization In order to validate the performance of the system, the tensile ice adhesion, σice, of Al, stainless steel, and brass were first measured. Next, the performance of the device was characterized with respect to different test parameters such as temperature, pull-off speed, ice/substrate interfacial area, and thickness of the substrate. To evaluate these parameters the ice/surface fracture needs to be adhesive (rather than cohesive failure through the ice itself), so polyethylene (PE) and polypropylene (PP) sheets were used as they are known to exhibit lower ice adhesion than metals 69. At least 10 measurements were recorded for each sample to verify the system’s repeatability. 2.3.1 Materials Polypropylene, polyethylene, Al, brass, and stainless-steel sheets were purchased from McMaster-Carr. 47 2.3.2 Results Similar to their adhesion to ice under shear loading 70,71, cohesive rather than adhesive fracture was observed between ice and the three metals tested. The tensile ice adhesion of Al, stainless steel, and brass at -15 °C were σice = 1,400 ± 300 kPa, 1,300 ± 400 kPa, and 1,200 ± 200 kPa, respectively (Table 2.2). The measured value for Al fell within the range of reported literature values23,36,60. Literature values for steel and brass were not available. The measured tensile adhesive fracture of PP and PE, while varying the test parameters, was used to determine the precision and performance of the device. First, the temperature of the stage was varied from -5 °C to -20 °C in 5 °C increments while keeping other test variables constant (pull-off speed = 100 µm/s, area of ice, A = 0.785 cm2, material thickness = 0.84 mm). The tensile ice adhesion of PP and PE were independent of temperature within the range tested, as a T-test over the data did not show a significant change in the measured values (P-value ≥ 0.10) (Figure 2.14), similar to prior studies of tensile ice adhesion on other materials32,61. The reason was that the ice was formed from room-temperature water on a peltier stage with temperature dropping to the set point from ambient temperature, so the structure of the ice that was formed should have been the same for all the samples. 48 Figure 2.14. Tensile ice adhesion of polypropylene and polyethylene as a function of temperature. Next, the rate of the applied tensile force was varied between 10 µm/s – 1000 μm/s at a test temperature of -15 °C and the same interfacial area and thickness of the underlying material. The tensile ice adhesion strengths of PP and PE were also found to be independent of the rate of the applied force within this range of velocity (P-value ≥ 0.06) (Figure 2.15). Speed-dependency is a property of viscoelastic material because of the viscous component, while PP and PE only exhibit an elastic behaviour at the temperatures tested. This is the reason why the tensile ice adhesion strength did not change with changing the rate of applied force. 49 Figure 2.15. Tensile ice adhesion of polypropylene and polyethylene as a function of pull-off speed. The tensile ice adhesion strength of PP and PE sheets of varying thickness was also measured at -15 °C while maintaining a pull-off speed of 100 µm/s and an interfacial area of 0.785 cm2. A decrease in tensile ice adhesion was observed by increasing the substrate thickness to 3.2 mm, followed by an increase, up to a thickness of 6.2 mm (Figure 2.16). The fluctuations in the tensile adhesion values may be an effect of the way the sheets were fixed on the Peltier stage and if they were not fully and strongly confined as aimed to. Also, the modulus of the surface may have been affected by the modulus of the material underneath, which was the Peltier stage), when the thin sheets were used. The results from varying the temperature and pull-off speed statistically equivalent, indicating that the device was quite precise for the ranges of variables evaluated. 50 Figure 2.16. Tensile ice adhesion of polypropylene and polyethylene as a function of thickness of the material. The tensile adhesion of a rigid studs to an incompressible elastic solid has been previously shown to depend on stud size72–74. As such, it was expected that the interfacial area of ice would alter the observed values of σice. From Kendall’s original formulation, the critical load to de-bond a circular stud, Fc, is given by74, 𝐹𝑐 = √𝑋𝐸𝛾(2𝑎)3 (2.1) where E is the elastic modulus, γ is the interfacial surface energy, 2a is the stud diameter, and X = π/(1 – ν2), ν being the Poisson ratio. Accordingly, a plot of Fc against [Eγ(2a)3]1/2 should fall on a straight line. The recorded tensile ice adhesion measurements when varying the iced area for PP and PE strongly followed the above relation, as shown in Figure 2.17. The slope of the fitted line was measured to be 11 ± 0.1. A Chi-squared Goodness of Fit test showed a P-51 value of 0.99 which was higher than the significance level (0.05), showing that the sample data was consistent with the fitted line. More than any other measurements, this dataset indicated the device was working correctly and with high precision, as the adhesion measurements matched known laws of fracture mechanics precisely. Figure 2.17. Critical detachment force for different radii of ice, plotted according to Equation (2.1). The reproducibility of the ice type and repeatability of the interfacial fracture process was studied by monitoring the critical force to detach ice on the 0.84 mm thick PP with an interfacial area of 1.77 cm2 at -15 °C and pull-off speed of 100 µm/s (Figure 2.18). The small scatter of the 15 independent data points (146 ± 13 N) highlights the instrument’s precision, and is on par with other shear69 and tensile61 ice adhesion measurement devices. 52 Figure 2.18. Fifteen individual measurements of the critical force to detach ice from polypropylene at -15 °C. The interfacial area was 1.77 cm2. Table 2.5.Tensile ice adhesion strength of different materials using a pull-off speed of 100 µm/s, an interfacial area of 0.785 cm2, and a test temperature of -15 °C. Material Thickness (mm) σice (kPa) Fracture type Polypropylene (PP) 3.251 460 ± 120 Adhesive Polyethylene (PE) 3.251 270 ± 80 Adhesive Al 0.076 1400 ± 300 Cohesive Brass 0.076 1200 ± 200 Cohesive Stainless Steel 0.076 1300 ± 400 Cohesive 53 Chapter 3: Tensile versus Shear Ice Adhesion Strength of PDMS Elastomers 3.1 Overview The vast majority of ice adhesion studies have focused on the shear ice adhesion strength, in part because ice is typically removed in shear44,55,75. Recently, elastomeric surfaces utilizing interfacial cavitation as a de-bonding fracture mechanism have reported extremely low shear `ice adhesion strengths15,17,18,43. As interfacial cavitation is a tension-driven phenomenon19, it has now become critically important to understand and to measure the tensile adhesive properties between ice and various materials. For ice removal in shear, prior works have systematically characterized the effects of surface energy47, modulus15, surface roughness76, and thickness18 on τice. However, no work has concentrated on standardizing and characterizing the tensile ice adhesion strength or how the above parameters affect σice. This is likely because ice is rarely removed in tension, and interfacial cavitation has only recently been well understood15. In this section, the effect of various parameters including modulus, surface roughness, material thickness, and speed of applied force on σice is characterized using the custom-build apparatus explained in Chapter 2. The observed σice trends are also compared to the measured τice on the same surfaces which followed well-established trends. Further, τice was measured by applying the shear force at different heights from the surface of PDMS (elastomeric surface) and PP (plastic surface) and the values were compared to the σice which has a single value for a given surface. 54 3.2 Materials and methods 3.2.1 Materials: The PDMS elastomers used in the experiments were EcoflexTM 00-30, Mold Max 60 (both purchased from SMOOTH-ON), and SS-3 Stuntman Safe Ice and Glass (purchased from SILICONE SOLUTIONS). The AEROSIL® R 202 (Hydrophobic fumed silica) was obtained from EVONIK. Polypropylene (PP) sheets were purchased from McMaster-Carr. 3.2.2 Surface fabrication: 3.2.2.1 Smooth surface The smooth PDMS surfaces were fabricated by mixing two parts of the Ecoflex 00-30 uncured resin in a 1:1 ratio, per manufacturer instruction. The mixture was then poured into rectangular 3D printed molds on a clean, smooth glass sheet and left at room temperature for 4 hours to cure. The smooth PP sheet was used as received. 3.2.2.2 Rough surface The rough PDMS surfaces were fabricated by casting the same mixture, on sandpaper with various grits, including 180, 800, 1200 and 2500 to achieve a range of roughness on the surface. The 3D roughness and wettability parameters where then measured. 3.2.2.3 PDMS elastomers of varying moduli In order to obtain surfaces with a range of moduli, different weight percentages (0, 30, 50, 70 and 100 wt%) of Ecoflex 00-30 were mixed with Mold Max 60 or SS-3 and left at room 55 temperature for 24 hours to cure. The final moduli were then determined by testing the tensile strength of each sample. Among the samples, E0, E30, E50, E70, and E100 were chosen to represent a specific modulus in the range. The composition and moduli of the samples are listed in Table 3.1. 3.2.3 Roughness measurement Surface roughness was measured using a 3D scanning laser microscope (LEXT OLS5000, Olympus). The root-mean-squared roughness (Sq), average roughness (Sa) and developed interfacial area (Sdr) of the surfaces were measured using a 20X long distance objective lens and repeated on 3 different spots with a scan area of 1935 µm × 1935 µm, for each surface. The Wenzel roughness was calculated using the developed surface area by 𝑟 = 1 +𝑆𝑑𝑟100 . 3.2.4 Contact angle measurements The static, advancing and receding contact angles of water were measured using a Ramé Hart 260 Contact Angle Goniometer. ~ 10 µL droplets of water were carefully deposited on a levelled surface and the liquid volume was slowly increased (advancing) and then decreased (receding). At least 3 independent measurements were recorded for each parameter of the samples. 3.2.5 Tensile strength and moduli To determine the elastic modulus (E) of the cured mixtures, tensile strength tests were conducted using a universal tester (Instron, USA) on dumbbell-shape samples prepared according to ASTIM D412. The grip separation rate was set to 50 mm/min and a 50 kN load 56 cell was used. The elastic modulus of each specimen was calculated by dividing the tensile stress by the strain, 𝐸 =∆𝜎∆𝜀 , at 100% elongation, assuming the data was in the linear region (see Figure 3.1). The tensile strength measurements for both E30 and E50 were repeated twice and the graphs for each almost perfectly overlapped. Accordingly, the remainder of the samples were just tested once. The shear modulus (µ) and bulk modulus (K) of the samples were then calculated using Eq. 3.1 and 3.2, respectively. The Poisson ratio ν = 0.495 was taken for all the PDMS samples. All the values are listed in Table 3.1. The water contact angle on various PDMS surfaces did not vary significantly (less than 10˚), therefore, neither did the cosθ in Eq.1.5, so the work of adhesion was assumed to remain constant. 𝜇 =𝐸2(1 + 𝜈) (3.1) 𝐾 =𝐸3(1 − 2𝜈) (3.2) Figure 3.1. The tensile stress-strain curve of prepared PDMS samples 57 Table 3.1. Shear modulus of the samples, calculated based on the tensile strength testing Sample Composition Young’s modulus E (kPa) Shear modulus µ (kPa) Bulk modulus K (kPa) E100 100% Ecoflex 00-30 21 15 698 E70 70% Ecoflex 00-30/ 30% SS-3 73 55 2455 E50 50% Ecoflex 00-30/ 50% SS-3 122 91 4083 E30 30% Ecoflex 00-30/ 70% Mold Max 60 228 170 7602 E0 100% Mold Max 60 947 708 31578 3.2.6 Ice adhesion measurement Ice adhesion on all surfaces was measured both in shear and tensile modes. The shear ice adhesion values were measured by using a universal push-off test15. The tensile ice adhesion measurement device was a custom-made apparatus that measured the detachment force necessary to remove a piece of ice within the optimized ice holder from a surface in the direction normal to the interfacial plane (details discussed in Chapter 2). 58 3.3 Tensile and shear ice adhesion measurements 3.3.1 Substrate thickness In order to study the dependence of tensile and shear ice adhesion on the substrate thickness, h = 0.2, 0.5, 0.7, 1 and 3 mm thick films were prepared by pouring different amounts of the uncured PDMS resin in the 3D printed molds, while the bulk modulus of the substrate was kept constant at K = 698 kPa. Shear ice adhesion values decreased with an increase in the thickness to up to h = 0.7 mm (P-value ≤ 0.001), and then stayed almost constant for thicker samples up to h = 3 mm (P-value ≥ 0.17), as illustrated in Figure 3.2. This result was in agreement with other reports on the thickness dependence of shear ice adhesion18,43. The tensile ice adhesion strength values, however, dropped more drastically overall (P-value ≤ 0.007). At the same time, the tensile ice adhesion strength was higher than the shear ice adhesion except for the 3 mm thick sample. According to Kendall, the critical pull-off force (Fc) to detach a rigid punch from a thin elastic surface can be calculated by the equation below74: 𝐹𝑐 = 𝑎𝜋(2𝐾𝛾ℎ)1/2 (3.3) Therefore, a plot of critical pull-off force against ℎ−1/2 should follow a linear relationship. As shown in Figure 3.3, obtained critical tensile forces for ice detachment followed a line with a slope of 3 ± 0.6 (N(mm)1/2)a s expected based on Eq. 3.3. The P-value for the linear regression was measured to be 0.99 when a Chi-square Goodness of Fit test was used. 59 Figure 3.2. Shear and tensile ice adhesion strength of various thickness of soft PDMS Figure 3.3. Critical pull-off force dependence on thickness of thin PDMS surfaces. 60 3.3.2 Probe height When a shear force is applied at a distance above the ice/substrate interface, a torque is generated on the ice which imposes a tensile force at the interface. The torque, and therefore the generated tensile force, increases when the shear force is applied at greater heights77. It has been shown that with increasing height of the applied force above the surface of an elastomeric substrate, the shear ice adhesion decreases because of the mixed shear and tensile modes56. Here, the shear and pure tensile adhesion of ice were measured on PDMS (thicknesses of 0.2 and 3 mm of the Ecoflex 00-30) as an elastomer, and PP as a rigid substrate. The shear force was applied at different heights above the interfacial plane. The shear ice adhesion strength of the h = 3 mm PDMS substrates decreased with increasing probe height (P-value ≤ 0.02) as expected. For the h = 0.2 mm PDMS, the means followed an overall decreasing trend, but ANOVA showed that the data statistically remained constant, which may be because of the large error bars in the ice adhesion strength measurements of the thin substrate. The shear ice adhesion strength remained almost constant for the PP sheet (P-value ≥ 0.05) (Figure 3.4). The reason is that on a rigid surface such as PP, the induced torque does not produce interfacial cavitation. The tensile ice adhesion strength of the 0.2 and 3 mm PDMS and the PP sheet were measured to be 57 ± 30, 14 ± 2 and 465 ± 115 kPa, respectively. The pure shear ice adhesion strength of 0.2 mm and 3 mm PDMS and the PP sheet were measured to be 26 ± 4, 13 ± 2, and 367 ± 122 kPa when the force was applied at the height of 0 mm. Comparing the shear ice adhesion strength when the force was applied at the highest height (7 mm) and were measured to be 15 ± 3, 5 ± 0.7, and 248 ± 139 kPa, respectively, with the above values, the presence of the mixed tensile and shear mode fracture that was resulting in such low adhesion strengths, 61 was clearly demonstrated. The adhesion strength of the mixed mode fracture was lower than the pure shear or tensile fracture. Figure 3.4. Effect of the probe height on the shear ice adhesion strength of (a) soft PDMS, (b) polypropylene 3.3.3 Elastic modulus To determine the effect of the elastomer’s elastic modulus on the tensile ice adhesion strength, substrates were prepared by mixing various weight ratios of PDMS with different hardness values. Elastic moduli of the samples ranged between 21 to 950 kPa (Table 3.1), while the thickness was kept constant at h = 2.5 mm. It was observed that the critical pull-off force to detach ice from the surface increased with increasing the elastic modulus of the PDMS, and therefore, decreasing the elastic mismatch at the interface. Elastic mismatch at the interface of two bonded material, results in displacement discrepancy of the material at the interface under an applied force, which facilitates crack formation/propagation78. The critical tensile force 62 necessary to detach ice increased with increasing substrate elastic modulus and the data fell on a line with a slope of 0.11 ± 0.04 (mNm2)1/2 when plotted against the square root of the elastic modulus, in the range that was tested, as shown in Figure 3.5. The P-value of the linear regression was measured to be 0.97 (> 0.05) which indicated that the data met the specified distribution. The relationship strongly followed the equation proposed by Kendall in 1971, on pulling a rigid slab off from an infinitely thick elastic substrate (Eq. 2.1), that demonstrates a Fc ~ E1/2 dependence74. Figure 3.5. Critical ice pull-off force dependence on the elastic modulus of thick PDMS substrates. The tensile and shear ice adhesion of various shear modulus (µ = 21- 950 kPa) and thickness (h = 0.2-2.5 mm) PDMS elastomers were also analyzed. In Figure 3.6, the shear and tensile ice 63 adhesion strength of PDMS surfaces were plotted against µ/h, to combine the effect of modulus and thickness, along with legitimate lines of τice ~ (µ/h)0.5 based on Eq. 1.6. As experimentally observed by other authors, the shear ice adhesion measurements of the PDMS elastomers followed the relationship, as shown in Figure 3.6. The tensile ice adhesion measurement data also followed a similar relation. However, the multivariable regression of the shear and pure tensile strength data indicated a τice ~ (µ/h)0.32 and σice ~ (µ/h)0.33 dependence, with R2 values of 0.41 and 0.35, respectively. The variance between the expected dependence of τice and σice on the ratio of shear modulus to substrate thickness ((µ/h)0.5) and the multivariable regressions of shear and tensile ice adhesion strengths may be because of instrumental, environmental, or human errors in measuring thickness, modulus, or ice adhesion strengths. 64 Figure 3.6. Tensile and shear ice adhesion strength plotted against the ratio of shear modulus over thickness on logarithmic axes. 3.3.4 Probe speed As shown in Figure 3.7, tensile and shear ice adhesion strength of PDMS substrates of 3 mm thickness increased with the speed of the tensile or shear force applied. However, the ice adhesion strengths varied slightly, and even when the speed increased 100X the tensile adhesion strength only increased by a factor of 2. Similar trends have been reported by other authors, where the change in the ice adhesion strength with loading rate was negligible13. On viscoelastic substrates such as PDMS elastomers, the speed dependency may change with 65 material thickness, modulus and test geometry, and some authors have suggested a threshold after which the shear ice adhesion strength will increase with an increase in the shear rate18. Figure 3.7. Shear and tensile ice adhesion strength of soft PDMS versus the speed of the applied force. 3.3.1 Roughness The roughness of the PDMS surfaces was varied and the roughness parameters Sa, Sq and Sdr were measured to investigate their effect on ice adhesion. The rough surfaces exhibited water receding contact angles θrec ≤ 70˚, and contact angle hysteresis values ≥ 25˚, indicating that the water droplet was partially in the Wenzel state. However, very surprisingly, the shear ice adhesion strength remained almost constant (P-value ≥ 0.09) with the variation in surface roughness parameters, as shown in Figure 3.8a-c. The reason is that the ice/PDMS interfacial area is increased by increasing the roughness. But also, a nonuniform surface deformation happens and the tips of the roughness features on the PDMS surface act as stress-concentrated 66 points and streamline crack initiation and propagation under the applied shear force. At the interface of Wenzel ice, rough PDMS features protrude into the ice, making a composite-like interface consisting of two material with different stiffness, as shown in Figure 3.8d. When a shear force is applied to the ice, the force will be transmitted to the PDMS roughness features via the ice, and the mismatch between the moduli of the two materials will facilitate crack formation. Because of the local compressive component of the shear force that is being applied to the PDMS, local bulges can facilitate crack formation, as illustrated in Figure 3.8d. This is in contrast to most studies which have reported an increase in shear ice adhesion strength with increasing surface roughness, due to mechanical interlocking of ice into the roughness features52,79,80 For example, Memon et al. demonstrated that shear ice adhesion strength increased with increasing roughness of surfaces including stainless steel, Al, polyurethane (Ra ≤ 1 µm) and superhydrophobic PDMS (Ra ≤ 2 µm)81. In contrast, the tensile ice adhesion strength linearly increased with increasing average roughness and root-mean-squared roughness of the surface. However, the tensile adhesion strength even on the roughest surface remained σice < 30 kPa. The different behavior of the rough PDMS under shear and tensile stress can be explained by the anisotropy of the microscale rough elastomeric materials under shear stress, as explained by Sahli et al 82. Moreover, the mechanism that facilitates crack formation under shear does not occur under a tensile stress unless the surface is hierarchically structured, which was not the case for these surfaces. The developed anisotropy under shear loading, which is in the form of a change in the shape of roughness micro-features, facilitates crack initiation and further propagation. 67 The above finding reveals that it is possible to employ surface texture and fabricate a rough, and potentially superhydrophobic, surface with low shear ice adhesion strength that maintains its low adhesion strength regardless of the ice being in the Wenzel or Cassie-Baxter state. Figure 3.8. Shear and tensile ice adhesion strength dependence of soft PDMS on roughness parameters (a) average roughness, (b) root-mean-squared roughness, (c) 68 developed surface area, in the form of the Wenzel roughness, and (d) local crack formation on roughness features 69 Chapter 4: Durable superhydrophobic PDMS with ultra-low ice adhesion 4.1 Overview Based on the findings surrounding tensile and shear ice adhesion strength of rough surfaces that were discussed in Chapter 3, the fabrication of a superhydrophobic surface with durable, ultra-low ice adhesion was explored. Fabricating a superhydrophobic surface that can offer durable, ubiquitous icephobicity in any environment has always been a challenge in the field. Nosonovsky et al. argue that superhydrophobic surfaces that contain large voids at the interface, which act as microcracks, can exhibit low shear ice adhesion strength80. Some argue that surfaces with low water contact angle hysteresis exhibit low shear ice adhesion strengths, and others believe that this does not hold when mechanical interlocking occcurs50,81. Here a PDMS-based superhydrophobic surface with micro scale roughness was fabricated that exhibits ultra-low shear and tensile ice adhesion strength (σice= 4.2 kPa and τice= 7.3 kPa) and preserves the low ice adhesion strengths after 20 minutes of abrasion despite the ice forming in the Wenzel state (σice= 11.2 kPa and τice= 8.7 kPa). 4.2 Materials and methods 4.2.1 Superhydrophobic surface preparation To fabricate the superhydrophobic surface, nano/micro-scale roughness was added to the naturally hydrophobic chemistry of PDMS. Micro-scale roughness was fabricated by casting Ecoflex 00-30 on grit 800 sandpaper, with a controlled thickness of h = 2.5 mm. The piece was cured and demolded after 4 hours at room temperature. Uncured PDMS resin was then diluted 70 in toluene to 0.02 wt% and stirred for 5 minutes. 3-4 layers of this solution were then applied on the rough PDMS surface using a brush wider than the width of the PDMS piece, to ensure that the whole surface was uniformly exposed to the solution each brushing round. The wet surface was left at room temperature for 2 hours in order for the solvent to completely evaporate and for the resin to partially cure. A solution of 2g of hydrophobic fumed silica nano particles (AEROSIL® R 202) in 10g of toluene was prepared and mixed using a hotplate stirrer for 2 hours. The homogenized and slightly stable solution was then sprayed on the vertically positioned, partially cured PDMS layer, using a spray gun by moving it in circles from a distance of 35 cm to cover the whole surface. The surface was then left horizontally at room temperature for 2 more hours to dry and cure completely. 4.2.2 Abrasion A RYOBI orbital sander was used to abrade the superhydrophobic surface by varying sanding period from 5 to 20 minutes. A total weight of around 3000 g was put on the samples of 3 x 4 cm2 and kept during each sanding period, resulting in a pressure of around 25 kPa. A grit 240 sandpaper was chosen as it was rougher than the sandpaper that the PDMS was initially casted on, to mimic very harsh abrasive conditions. The sandpaper was fixed on the sander and was not replaced during the whole abrasion period. The sanded surface was wiped with isopropyl alcohol after each abrasion cycle to get rid of all the PDMS that was scraped out. 4.2.3 Surface characterization Surface morphology, topography, and roughness of all PDMS samples were characterized using the 3D laser microscope used in Chapter 3. The surface morphology of the 71 superhydrophobic PDMS was also imaged using a scanning electron microscope (SEM, Tescan Mira 3 XMU). Water contact angles were measured using the Ramé Hart 260 Contact Angle Goniometer and same method used in Chapter 3. 4.3 Tensile and shear ice adhesion of superhydrophobic PDMS The superhydrophobic PDMS surface exhibited a static contact angle of θs = 152˚±2 and CAH of 10˚ (Figure 4.2b). The morphology and topography of the rough PDMS surface before and after coating with the superhydrophobic particles is shown in Figure 4.1a-d. Figures 4.1a and c show the addition of the particles on the micro-scale roughness of the hydrophobic PDMS surface. The increase in the height variation of the surface of the superhydrophobic PDMS can be clearly seen by comparing Figures 4.1b and d. 72 Figure 4.1. 3D scanning laser microscope image of the (a) morphology and (b) topography of the superhydrophobic PDMS and (c) morphology and (d) topography of the initially rough hydrophobic PDMS The tensile and shear ice adhesion strengths of the superhydrophobic PDMS were measured to be σice= 4.2 kPa and τice= 7.3 kPa. Interestingly, the tensile ice adhesion strength of the superhydrophobic PDMS was lower than its shear ice adhesion strength, in opposition to the previous results where the shear ice adhesion strength was always lower or equal to σice. When the surface of the superhydrophobic PDMS was imaged using SEM, it was observed that the particles that were added on the surface as a coating produced a hierarchical structure (Figure 4.2a). This observation supported our hypothesis from Chapter 3, that the composite-like 73 interface and the mismatch in the modulus of the ice and elastomer lowered the ice adhesion strength values. In contrast to the rough surfaces studied in Chapter 3, here, the hierarchical features on the surface produced a composite-like interface in the direction normal to the plane of the surface, enabling crack formation under tensile forces which finally led to a decrease in the tensile ice adhesion strength. Figure 4.2. Superhydrophobic PDMS, (a) SEM image of the surface showing the hierarchical structure, (b) a water droplet deposited on the superhydrophobic PDMS. The superhydrophobic surface was then abraded for a total of 20 minutes. The water contact angles were measured on the abraded sample to evaluate any wettability changes. The static water contact angle and contact angle hysteresis on the abraded sample were measured to be θs = 120˚± 4 and 47˚, respectively, indicating that water atop some parts of the surface was in the Wenzel state. By abrading the superhydrophobic surface and diminishing the hierarchical structures, the tensile ice adhesion strength increased after the first abrasion period and remained constant thereafter (P-value ≥ 0.65), as shown in Figure 4.3. However, the value 74 never exceeded σice = 15 kPa, still quite a low adhesion strength. The surface also maintained an ultra-low shear ice adhesion strength that remained below τice = 10 kPa. Figure 4.3. Tensile and shear ice adhesion strength of the initially superhydrophobic PDMS plotted against abrasion time. 75 Chapter 5: Conclusion and future work recommendations Ice falling from bridge cables and tall structures is an enduring threat to the lives of people passing by. Also, ice accretion on the blades of a wind turbine or ship hull and structures can significantly affect the efficiency and performance of the structures. Preventing ice accretion and accumulation on such surfaces will save lives and money. For this reason, designing and progressing surfaces and coatings with low adhesion values to ice has been an active field of research. Two important parameters that have independently been at the core of many studies in this field, and the key to successful design of ice-phobic surfaces are wettability characteristics and the elastic modulus of the surface. Among the various methods and coatings that have been developed, elastomeric and soft surfaces have gained attention because of the ultra-low ice adhesion strengths they exhibit. The low adhesion strength on these surfaces is due to an interfacial instability, interfacial cavitation, which is a tension-driven phenomenon and typically occurs at the interface of two material with dissimilar stiffnesses. PDMS-based surfaces have shown significant promise among all elastomers, due to their tunable elasticity and the intrinsic hydrophobic chemistry of the material. Accordingly, we started by reviewing the work of other authors that studied icephobicity of surfaces with respect to wettability and elasticity. Literature reviews on the tensile ice adhesion strength of materials indicated that the tensile ice adhesion measurement of soft materials has been widely neglected, even though it has been proved to be the underlying reason responsible for the ultra-low shear adhesion strength of ice on elastomers. Accordingly, we developed and standardized a tensile ice adhesion measurement device including a step-by-step build procedure, and additionally verified its precision. Using this 76 device, we measured and studied the tensile ice adhesion strength of PDMS elastomers by varying different test parameters such as force speed and probe height, as well as material/surface properties such as thickness, modulus, and roughness. Our results then enabled us to fabricate and characterize an ice-phobic and superhydrophobic PDMS surface which exhibits durable low ice adhesion strengths even in the Wenzel state after harsh abrasion. 5.1 Summary In the second chapter of this work, a high throughput, low-cost device was designed to measure the tensile ice adhesion strength of different surfaces. The design and construction of the tensile ice adhesion measurement system was presented, along with the reasoning for the design decisions, such as the optimally designed ice holder. The performance of the setup was characterized using experimental trials varying parameters such as temperature, pull-off speed, thickness of the substrate, and ice/substrate interfacial area, to verify the precision of the measurements. The important points are listed as follows: • The tensile ice adhesion measurements of Al were consistent with values reported in literature • The tensile ice adhesion strengths of PP and PE were found to be independent of temperature, force speed, and material thickness • The tensile ice adhesion strengths of PP and PE were observed to be size-dependent, and this was found to precisely follow the known laws of fracture mechanics • The measurements were shown to be reproducible 77 In Chapter 3, we explored the tensile ice adhesion strength of elastomeric coatings, and various parameters affecting it, such as coating thickness, roughness, modulus, and force speed. To further understand the mechanism of ice detachment when a shear force is applied, the shear ice adhesion strength of all the samples was also measured and compared with the tensile ice adhesion values. PDMS was used as a representative elastomeric coating. Our most important findings are as follows: • The tensile ice adhesion strength (σice) was always greater than or equal to the shear ice adhesion strength (τice) on the same surface. When shear and tensile forces coexisted, the shear ice adhesion strength was decreased by the synergistic effects of mixed-mode fracture. This was observed when the shear force was applied at a height above the interface and was more pronounced with increasing probe height. • By increasing the substrate thickness, σice decreased more substantially than τice, demonstrating that the tensile ice adhesion strength depends on the thickness-more than the shear ice adhesion strength. • Similar to τice, σice increased with the elastic modulus and followed known relationships of fracture mechanics. • Multivariable regression of the tensile and shear strength data showed that the ratio of µ/h affected σice and τice in the exact same manner, and both data sets fitted the ½ power of ratio of shear modulus to thickness. • The speed of the applied force did not significantly affect σice and τice, at least over the range of speeds evaluated. • By increasing the roughness parameters Wenzel ice was formed, but σice increased at most only two times, even for a roughness value of Sq = 32 µm, τice remained 78 statistically unchanged. This result led us to hypothesize that a composite-like interface of materials with dissimilar moduli helps enable crack formation. In Chapter 4, we fabricated a superhydrophobic PDMS surface by coating an initially rough PDMS surface. The surface maintained low tensile and shear ice adhesion strengths even when the ice froze from water in the Wenzel state. We also further supported our hypothesis about the composite-like interface: the tensile ice adhesion strength of the superhydrophobic PDMS decreased in the presence of hierarchical structures that acted as roughness intrusions perpendicular to the direction of the tensile force. These findings open a new door that enables the application of superhydrophobic surfaces as ice-phobic coatings that can maintain low ice adhesion strengths even when the superhydrophobicity is lost and the ice freezes in the Wenzel state. 5.2 Future work recommendations Shear ice adhesion strength values are widely reported in the literature for various materials including elastomers. We recommend the investigation of tensile ice adhesion measurements of other elastomers which may prove to be promising candidates as ice-phobic materials, and overall collecting the data in a tensile ice adhesion strength library. Knowing that an elastomer’s ice adhesion strength may change with thickness, we recommend further exploring that the testing parameters to understand if they alter σice for thin elastomers in the same way they did with the 3 mm thick elastomer. 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Thesis/Dissertation
eng
Mechanical Engineering
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Exploring the tensile ice adhesion strength of surfaces using a newly designed and verified measurement apparatus
Text