ON the WETTING STATES of LOW MELTING POINT METAL GALINSTAN and WETTING CHARACTERISTICS of 3-DIMENSIONAL NANOSTRUCTURED FRACTAL SURFACES

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5-2017 On The ettW ing States of Low Melting Point Metal Galinstan and Wetting Characteristics of 3-Dimensional Nanostructured Fractal Surfaces Ethan Allan Davis University of Nebraska-Lincoln, [email protected]

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Ethan Allan Davis

A THESIS

Presented to the Faculty of The Graduate College at the University of Nebraska In Partial Fulfillment of Requirements For the Degree of Master of Science

Major: Mechanical Engineering and Applied Mechanics Under the supervision of Professor Sidy Ndao Lincoln, Nebraska May 2017

ON THE WETTING STATES OF LOW MELTING POINT METAL GALINSTAN and WETTING CHARACTERISTICS OF 3-DIMENSIONAL NANOSTRUCTURED FRACTAL SURFACES

Ethan Allan Davis, M.S. University of Nebraska, 2017

Advisor: Sidy Ndao

Exergy, or the availability of energy for useful work, is a critical issue that must be addressed to accommodate growing energy demands of society. Increasing population and steady advancement of technology necessitates novel approaches to the management, conversion, and storage of energy. Per the Lawrence Livermore National Laboratory, approximately 60 percent of the energy used by the United States in 2015 was rejected as waste [1]; a large quantity of which can be assumed to be in the form of heat. Therefore, novel thermal management methods for waste heat are critical to increasing energy efficiency and sustainability in the future.

The primary goal of this thesis is to measure the wetting characteristics of a low melting point metal to determine the efficacy of this type of material for use in thermal energy storage applications. Galinstan, an alloy consisting of Gallium, Indium, and Tin was subjected to contact angle measurements on various substrates at varying temperatures. Due to the oxidation characteristics of Galinstan, all experiments are conducted in an inert nitrogen environment (< 0.5 ppm oxygen) to maintain fluid-like properties. This work found that although contact angle changed with substrate and surface structure, temperature had minimal effect on the contact angle. Contact angles ranged from

141° on smooth silicon to greater than 160° on silicon micropillars. Although a temperature dependence was not observed, having wetting properties of Galinstan on various surfaces is a step toward better understanding the capabilities of this and similar materials in energy management.

A secondary goal of this research is to measure the wetting characteristics of 3- dimensional nanostructured fractal surfaces (3DNFS) and explore their efficacy in physical and biological science applications. Contact angle measurements were performed on three distinct multiscale fractal surfaces to characterize their wetting properties. Average contact angles ranged from 66.8° for the smooth control surface to 0° for one of the fractal surfaces.

The change in wetting behavior was attributed to modification of the interfacial surface properties due to the inclusion of 3-dimensional hierarchical fractal nanostructures.

However, the wetting behavior exhibited does not exactly obey existing wetting models found in the literature.

ACKNOWLEDGMENTS

Firstly, I would like to thank my family and friends for their continued support throughout all my academic career. Specifically, I would like to thank my Mother, Diana, and Father, Ron, for their unwavering support and instilling in me the desire to learn.

Without them, I would not be where I am today.

I would like to thank my advisor, Dr. Sidy Ndao, for the opportunity to continue my education and gain priceless experience as well as his help and insight. I would like to thank Dr. George Gogos for helping me through not only my undergraduate career, but my graduate studies, as well.

I would like to thank my lab mates, Mahmoud Elzouka, Henry Ems, Ahmed

Hamed, Anton Hassebrook, Corey Kruse, and Sarah Wallis, for their stimulating discussions and moral support. I would like to thank Lyanda Dudley for her help in obtaining data contained within this report.

I would also like to thank Dr. Yongfeng Lu, Ying Liu, and Lijia Jiang of the LANE

Lab for their help with the fabrication and publication of the fractal surfaces.

Finally, I would like to thank Drs. George Gogos and Jefferey Shield for assuming roles in my thesis committee.

Table of Contents ACKNOWLEDGMENTS ...... IV List of Figures ...... VIII List of Tables ...... XIV INTRODUCTION ...... 1 1.1 Motivation: Increasing Energy Efficiency ...... 1 1.2 Literature Review: Wetting ...... 3 1.3 Literature Review: Low Melting Point Metals ...... 8 1.4 Literature Review: Wetting of Fractal Surfaces ...... 13 1.5 Objectives and Goals: To Better Understand Wetting Properties ...... 15 1.5.1. Low Melting Point Liquid Metals ...... 15 1.5.2. 3-Dimensional Fractal Nanostructured Surfaces ...... 16 EXPERIMENTAL METHODS ...... 17 2.1 Development of a Robust Setup for the Study of Low Melting Point Metals ...... 17 2.2 Microcontact Angle Experimental Setup ...... 23 SURFACE FABRICATION ...... 25 3.1 Materials ...... 25 3.1.1 Water ...... 25 3.1.2 Low Melting Point Metal: Galinstan ...... 26 3.1.3 Substrate Material ...... 26 3.1.4 Fractal Surfaces ...... 28 3.2 Smooth Surfaces ...... 30 3.3 Structured Surfaces ...... 33 3.3.1 Copper Microchannel Fabrication ...... 33 3.3.2 Silicon Microstructure Design ...... 34 3.3.3 Cleanroom Nanofabrication ...... 36 3.3.4 Two-Photon Photolithography ...... 42 RESULTS...... 46 4.1 Wetting States of Low Melting Point Galinstan on Silicon Structures ...... 47 4.2 Adverse Effects of Low Melting Point Metal Galinstan on Stainless Steel, Copper, and Polydimethylsiloxane Surfaces ...... 58 4.3 Wetting Characteristics of 3-Dimensional Nanostructure Fractal Surfaces...... 62 CONCLUSIONS ...... 71 VI

5.1. Wetting States of Liquid Metal Galinstan ...... 71 5.2. Wetting Characteristics of Fractal Surfaces ...... 77 APPENDIX A. SUPPLEMENTAL FIGURES ...... 79 Appendix B. CONTACT ANGLE MEASUREMENT IMAGES ...... 81 Silicon Microchannels ...... 81 Pitch 125µm ...... 81 Pitch 225µm ...... 82 Pitch 275µm ...... 83 Pitch 325µm ...... 84 Pitch 425µm ...... 85 Silicon Micropillars ...... 86 Pitch 125µm ...... 86 Pitch 225µm ...... 87 Pitch 275µm ...... 88 Pitch 325µm ...... 89 Pitch 425µm ...... 90 Smooth Stainless Steel 304 ...... 91 Copper Microchannels ...... 92 Smooth Polydimethylsiloxane ...... 93 APPENDIX C. SILICON MICROSTRUCTURE SEM IMAGES ...... 94 Microchannels ...... 94 Pitch 125µm ...... 94 Pitch 225µm ...... 96 Pitch 275µm ...... 98 Pitch 325µm ...... 100 Pitch 425µm ...... 102 Micropillars ...... 104 Pitch 125µm ...... 104 Pitch 225µm ...... 106 Pitch 275µm ...... 108 Pitch 325µm ...... 110 Pitch 425µm ...... 112 VII

Appendix D. Matlab code: Silicon microstructure geometric properties ...... 114 Find Roughness Values for Each Surface ...... 114 Plot Critical Angle and Intrinsic Angle ...... 116 APPENDIX E. MATLAB CODE: FRACTAL DIMENSION ...... 118 REFERENCES ...... 123

VIII

List of Figures Figure 1-1. Schematic of liquid droplet on a solid surface showcasing the interaction between surface energies...... 4

Figure 1-2. (a)Galinstan droplet dispensed from a syringe under ambient conditions.

(b)Galinstan droplet dispensed witha syringe with less than 1 ppm oxygen.[3] ...... 10

Figure 1-3. Demonstration of how oxidation affects contact angle. (a) Oxidized Galinstan

(b) Unoxidized Galinstan...... 11

Figure 2-1. Rame Hart Model 250 goniometer. Source: www.ramehart.com ...... 18

Figure 2-2. Screenshot of contact angle measurement setup. The green lines are inputs for the center of the droplet and the solid-liquid interface...... 19

Figure 2-3. Rame-Hart elevated temperature syringe. Max temperature of 300°C. Source: www.ramehart.com ...... 20

Figure 2-4. Rame-Hart heated stage. Max temperature of 300°C. Source: www.ramehart.com ...... 21

Figure 2-5. Image of the glovebox setup...... 22

Figure 2-6. Goniometer, elevated temperature syringe, and heated substrate setup inside the inert glovebox...... 23

Figure 2-7. Kyowa automatic microcontact angle machine MCA-3 ...... 24

Figure 3-1. Optical microscopy image of a fractal surface. Material is a polymer derived from an acrylic based monomer...... 29

Figure 3-2. Wafer cleaving technique used to obtain smooth silicon surfaces for contact angle measurements...... 31 IX

Figure 3-3. CAD rendering of copper microchannel surface fabricated using traditional machining techniques. A wall thickness and channel width of 203µm and 254µm was used, respectively...... 34

Figure 3-4. Characteristic dimensions of the silicon microstructures...... 35

Figure 3-5. Nanofabrication process flow for silicon microstructures...... 37

Figure 3-6. Silicon microstructure photolithography mask. Both micropillars (left half) and microchannels (right half) were fabricated on the same wafer...... 38

Figure 3-7. General configuration and concept of the isotropic etching step of the Bosch process...... 40

Figure 3-8. Passivation and etching steps in the Bosch process for deep reactive ion etching...... 41

Figure 3-9. Image of the successfully fabricated silicon microstructures...... 42

Figure 3-10. CAD models of each fractal structure and associated surface...... 45

Figure 4-1. Contact angle measurements of Galinstan on silicon microchannels...... 47

Figure 4-2. Contact angle measurement results for Galinstan on silicon micropillars. .... 48

Figure 4-3. Contact angle measurements for Galinstan on smooth silicon at 30°, 100°C,

200°C, and 300°C...... 49

Figure 4-4. Contact angle of Galinstan on silicon microchannels assuming not temperature dependence...... 52

Figure 4-5.. Contact angle of Galinstan on silicon micropillars assuming not temperature dependence ...... 53

Figure 4-6. Galinstan droplet on micropillars with 425µm pitch at 100°C. (A) Droplet after being dispensed (B) Droplet after moving droplet with needle...... 54 X

Figure 4-7. Roughness and solid fraction for silicon microstructures as a function of pitch distance...... 55

Figure 4-8. Critical contact angle for silicon microstructures with varying pitch distance.

The red line represents the intrinsic contact angle. Error bars are standard deviation of contact angles measured...... 56

Figure 4-9. Wetting phase diagram illustrating the transition point between a Cassie-

Baxter state and a Wenzel state...... 57

Figure 4-10. Contact angle results for Galinstan on smooth stainless steel 304, smooth

PDMS, and copper microchannels...... 59

Figure 4-11. Corrosion of copper microchannels and smooth stainless steel after exposure with Galinstan...... 61

Figure 4-12. Molecular structure of polydimethylsiloxane (PDMS)...... 61

Figure 4-13. Oxide residue left behind after taking contact angle measurements of

Galinstan on smooth PDMS surfaces...... 62

Figure 4-14. SEM images of each fractal structure and corresponding surface...... 63

Figure 4-15. Linear fits for determining fractal dimension of (a) simple cube (b) cubic structure (c) romanesco broccoli structure (d) sphereflake structure ...... 66

Figure 4-16. Images of contact angle measurements for (a) flat control surface (b) Cubic fractal surface (c) Romanesco broccoli fractal surface (d) Sphereflake fractal surface ... 67

Figure 4-17. Comparison of experimental contact angles to the theoretical Wenzel model.

...... 69 XI

Figure 4-18. Geometric properties of each fractal surface used to explain contact angle trends. Surfaces are listed in order of decreasing contact angle. Respective contact angles are bracketed next to each surface along the x-axis...... 71

Figure 5-1. Wetting of a water droplet with increasing applied pressure [33]...... 74

Figure 5-2. Concept for thermal storage technology. (Left) A force is applied to cause a

Galinstan drop to transition to a Wenzel state, increasing the amount of heat transfer into the droplet. (Right) The force is removed to cause the droplet to transition back Cassie-

Baxter, reducing the contact area and heat transfer out of the droplet...... 74

Figure A-1. Estimated energy usage in the US for the year 2015 ...... 79

Figure A-2. False color SEM images of a Romanesco (left) and Sphereflake (right) structure...... 80

Figure B-1 Contact angle measurements on 125µm pitch microchannels at various temperatures...... 81

Figure B-2 Contact angle measurements on 225µm pitch microchannels at various temperatures...... 82

Figure B-3 Contact angle measurements on 275µm pitch microchannels at various temperatures...... 83

Figure B-4 Contact angle measurements on 325µm pitch microchannels at various temperatures...... 84

Figure B-5 Contact angle measurements on 425µm pitch microchannels at various temperatures...... 85

Figure B-6 Contact angle measurements on 125µm pitch micropillars at various temperatures...... 86 XII

Figure B-7 Contact angle measurements on 225µm pitch micropillars at various temperatures...... 87

Figure B-8 Contact angle measurements on 275µm pitch micropillars at various temperatures...... 88

Figure B-9 Contact angle measurements on 325µm pitch micropillars at various temperatures...... 89

Figure B-10 Contact angle measurements on 425µm pitch micropillars at various temperatures. Left side of figure is after dispensing the droplet and right side is after moving the dispensed droplet...... 90

Figure B-11 Contact angle measurements on smooth stainless steel 304 at various temperatures...... 91

Figure B-12 Contact angle measurements on copper microchannels at various temperatures...... 92

Figure B-13 Contact angle measurements on smooth polydimethylsiloxane at various temperatures...... 93

Figure C-1. 125µm pitch microchannels top down 100X and 200X magnification...... 94

Figure C-2. 125µm pitch microchannels angled 45° 100X and 200X magnification...... 95

Figure C-3. 225µm pitch microchannels top down 100X and 200X magnification...... 96

Figure C-4. 225µm pitch microchannels angled 45° 100X and 200X magnification...... 97

Figure C-5. 275µm pitch microchannels top down 100X and 200X magnification...... 98

Figure C-6. 275µm pitch microchannels angled 45° 100X and 200X magnification...... 99

Figure C-7. 325µm pitch microchannels top down 100X and 200X magnification...... 100

Figure C-8. 325µm pitch microchannels angled 45° 100X and 200X magnification. ... 101 XIII

Figure C-9. 425µm pitch microchannels top down 100X and 200X magnification...... 102

Figure C-10. 425µm pitch microchannels angled 45° 100X and 200X magnification. . 103

Figure C-11. 125µm pitch micropillars top down 100X and 200X magnification...... 104

Figure C-12. 125µm pitch micropillars angled 45° 100X and 200X magnification...... 105

Figure C-13. 225µm pitch micropillars top down 100X and 200X magnification...... 106

Figure C-14. 225µm pitch micropillars angled 45° 100X and 200X magnification...... 107

Figure C-15. 275µm pitch micropillars top down 100X and 200X magnification...... 108

Figure C-16. 275µm pitch micropillars angled 45° 100X and 200X magnification...... 109

Figure C-17. 325µm pitch micropillars top down 100X and 200X magnification...... 110

Figure C-18. 325µm pitch micropillars angled 45° 100X and 200X magnification...... 111

Figure C-19. 425µm pitch micropillars top down 100X and 200X magnification...... 112

Figure C-20.425µm pitch micropillars angled 45° 100X and 200X magnification...... 113

XIV

List of Tables

Table 1-1. Properties of Galinstan and Mercury ...... 9

Table 3-1. Cure times for various cure temperatures...... 32

Table 3-2. Silicon microstructure pitches used and their corresponding channel width. . 36

Table 3-3. Characteristic dimensions for each fractal structure fabricated ...... 44

Table 4-1. Fractal dimension for each structure with 95% confidence intervals...... 66

Table 4-2. Experimental data for measured contact angle and drop volume for all fractal surfaces...... 68

Table 4-3. Comparison of geometric properties of the fabricated 3DNFS...... 70

INTRODUCTION

1.1 Motivation: Increasing Energy Efficiency

Exergy, or the availability of energy for useful work, is a critical issue that must be addressed to accommodate growing energy demands of society. Increasing population and steady advancement of technology necessitates novel approaches to the management, conversion, and storage of energy. Per the Lawrence Livermore National Laboratory, approximately 60 percent of the energy used by the United States in 2015 was rejected as waste [1] despite recent advances in energy conversion. It is not unrealistic to assume that a large portion of this rejected energy is in the form of heat due to the many thermodynamic processes associated with energy conversion and transmission. Therefore, novel thermal management methods for waste heat are critical to increasing energy efficiency and sustainability for the future. A graphic showing the estimated energy usage in the United

States for the year 2015 is shown in Appendix A.

Applications such as solar energy conversion require a means of energy storage for the long intervals between the periods of thermal energy availability and energy usage (e.g. time between periods of solar energy absorption and periods of usage). Other applications including thermal comfort control and microelectronic device cooling will benefit greatly from enhanced thermal management techniques. Of these enhanced techniques, the use of phase-change materials (PCMs) to store thermal energy is promising. Research into this area of study is deficient and, consequently, no sustainable and efficient thermal energy storage technologies have been developed. State-of-the-art PCMs are often composed of

2 organic and inorganic compounds that suffer from low thermal conductivity, poor stability at elevated temperatures, and a limited range of operating temperatures [2]. To meet the increasingly extreme demands of technology, new options are required for PCMs, and low melting point liquid metals are a promising option due to their superior thermal properties

(i.e. low melting temperature, high boiling point, high thermal conductivity, and large volumetric latent heat of phase change).

Low melting point (LMP) metals have been studied in the past, but interest in these metals has recently re-emerged due to the promising properties that these metals possess.

Many of these materials possess high thermal conductivity, akin to most metals, and a large range of melting temperatures (from well below 0°C up to 300°C). To further their attractiveness in cooling applications, some of these metals have an operating range of -

19°C to greater than 1300°C between melting and boiling point [3] making them ideal candidates for high temperature cooling applications. They also possess a relatively constant volume during phase change, low vapor pressure (essentially zero at 20°C), and large volumetric latent heat of phase change (due to strong metallic bonds) [4]. LMP metals have also garnered attention in other areas because of their good electrical properties. Some researchers have been able to manipulate some metals via electric fields [5–7].

Hierarchical structures have been shown to greatly alter the interactions at liquid- solid interfaces [8–18]. This alteration has been shown to improve the efficiency of engineered systems in heat transfer [19–23], microfluidics [17,24–27], and filtration

[28,29]. Using these types of surfaces to help increase the efficiency of current processes would help to reduce the amount of energy being used. Therefore, fractal surfaces show great promise because of their inherent hierarchical nature and ease of characterization.

The motivation behind the current research is to gain a better understanding of the wetting characteristics of hierarchical surfaces and wetting states of low melting point metals. With a more fundamental grasp on mechanisms associated with interfacial interactions, future research can focus on applying this knowledge in developing more efficient energy management technologies.

1.2 Literature Review: Wetting

The term wetting refers to how a liquid and solid interact at an interface. If liquid spreads completely over a surface, the system is said to be totally wetting. If, instead, liquid beads up on a surface, the system is said to be non-wetting. However, the degree to which a liquid wets a surface depends on a great many criteria, is not discrete, and spans a large spectrum [30–34]. Many different methods have been developed to quantify the degree of wetting for a liquid-solid-gas system. The, simplest and most prominent method is using optical imaging to trace the profile of a droplet using computer programs to discern contact angle.

The study of wetting is of great importance to many industrial and research areas such as heat transfer, inkjet printing, waterproofing of clothing, and anti-icing of airplane wings. The phenomenon of wetting is also taken advantage of in nature by insects that move on the surface of water, self-cleaning plant leaves, and even the human body ensuring the inherently non-wetting eye is wet [34].

Understanding wetting will only allow explanation of why a liquid will wet one surface but not another. Controlling wetting means having the ability to alter a surface to make an inherently wettable surface into a non-wettable surface, or vice versa. The latter is the goal of research in this area of study [30–33,35–37]. The ability to change the wetting

4 properties of a system allows new, more efficient surfaces and, thus, enhanced engineered systems.

The wetting of a surface is governed by a force balance between the interfacial energies of the materials in the system: a solid surface, liquid, and gas are the most common constituents. This force balance dictates whether a liquid will spread over a surface or coalesce with itself. Adhesive forces between the liquid and solid cause a liquid to spread and intramolecular forces within the liquid cause it to avoid contact[38]. An image illustrating this force balance is shown below in Figure 1-1.

Figure 1-1. Schematic of liquid droplet on a solid surface showcasing the interaction between surface energies.

In the above figure, the three surface energies may be seen on the left side of the liquid droplet where 훾푆퐺, 훾푆퐿, 푎푛푑 훾퐿퐺 are the solid-gas surface energy, solid-liquid surface energy, and liquid-gas surface energy (liquid surface tension), respectively. The angle 휃 shown is a result of the force balance, and thus a degree of measure for the wetting of the system. For a liquid that wets a surface readily, the contact angle will be smaller than the contact angle for a liquid that does not wet a surface. When referring to the wetting of

5 water, a surface is said to be hydrophilic when the contact angle is less than 90° and hydrophobic when the contact angle is greater than 90°. For an ideal surface, as shown in

Figure 1-1, the contact angle may be described using Young’s equation which uses the same surface energies as given above and 휃푒 is the Young’s contact angle on a perfect surface [34]:

Equation 1-1

훾퐿퐺푐표푠휃푒 = 훾푆퐺 − 훾푆퐿

From the above equation, it may be noted that the contact angle, and degree of wetting, may be changed depending on the interaction between each phase of the system.

Therefore, contact angle manipulation is often achieved by using some sort of surface treatment to change the surface energy of the solid surface[34]. So far, the solid surface has been assumed to be perfectly smooth, with no defects, and chemically homogeneous.

It is not unreasonable, then, to assume that the contact angle may be manipulated by altering surface morphology.

Wetting on real surfaces is more complicated by considering chemical heterogeneity and roughness. Wetting of liquids on textured surfaces can be described by two models: the Wenzel model [39], for liquids in completely wetting state, and the Cassie-

Baxter model [40], for liquids in a non-wetting state. An image of a droplet in each state is shown below.

Figure 1-4. Wetting on a smooth surface and models for rough surfaces: Wenzel and Cassie-Baxter

Wenzel’s model describes a droplet that completely wets a structured surface which is a function of the roughness of the surface. Wenzel’s model is given below [39].

Equation 1-2

훾푆퐺 − 훾푆퐿 푐표푠휃푊 = 푟 = 푟푐표푠휃푒 훾퐿퐺

Where 푟 is the roughness ratio of the solid surface and equal to the ratio of the actual surface area to the projected surface area. Therefore, if 휃푒 < 90° the apparent contact angle will be less than the intrinsic Young’s contact angle, and if 휃푒 > 90° the apparent contact angle will be greater than the Young’s contact angle. Surface roughness enhances the underlying wetting properties of the system [10,11,22,34,41]. Conversely, Cassie-

Baxter model describes a droplet that is in a nonwetting state and is given below [40].

Equation 1-3

푐표푠휃퐶퐵 = 푟푓푐표푠휃푒 + 푓 − 1

Where 푟 is, again, the roughness ratio of the surface and 푓 is the solid fraction of the surface that is in contact with the droplet. Both variables are geometrically determined from the surface. There exists a transition point between a Wenzel state and Cassie-Baxter state. That point is given by [34]:

Equation 1-4 −(1 − 푓) 푐표푠휃 = 퐶 푟 − 푓

For 휃푒 < 휃푐, a Wenzel state is thermodynamically favored. However, there do exist metastable Cassie-Baxter states where a Wenzel state is favored. This occurs on surfaces where the aspect ratio of the structures is very large, making it harder for a droplet to initiate contact with the bottom of the surface [30–33,35]. However, if enough energy is given to the droplet to encounter the bottom surface, it will transition to a fully wetting Wenzel state.

There have been countless studies performed on tailoring the wettability of a surface for certain applications [10–12,16,17,38,42–45]. Often, surfaces are biomimetic, or inspired by structures found in nature [8,9,13,18,41,46]. Many of these studies are concerned with altering the wettability of a surface for heat transfer applications [47–56] because of the large implications that wettability has on the amount of heat transfer that occurs. A fully wetted surface is able to reach higher heat fluxes than a nonwetting surface

[19,22,50,57–59]. This is a combination of many aspects; however, a simple explanation is that there is more surface area in contact with the heated surface, thus increasing the amount of heat that may be removed from the surface. For this reason, wettability plays a vital role in the heat transfer capabilities of a system.

1.3 Literature Review: Low Melting Point Metals

Research has been performed on the potential for LMP metals in heat transfer applications [60–71], electronic components [72–78], and biological and medical sciences

[79], among other applications. For heat transfer in specific, little research has been done on how the wetting properties are related. Wettability plays a vital role in heat transfer using a liquid cooling mechanism. Therefore, further research into the wettability of low melting point metals is necessary to further their use in heat transfer applications.

In many applications, metals in their liquid state are used because of their superior conductivities and fluidic properties such as mercury, gallium and its alloys, aluminum, bismuth, indium, etc. However, these applications are usually at temperatures higher than room temperature, and, as such, there are few options for room temperature liquid metals.

Mercury comes to mind when thinking of metals that are in a liquid state at room temperature, and is often employed in thermometers and electromechanical relays.

However, mercury is toxic and cannot be used in many applications. Galinstan is a commercially available, non-toxic alloy (developed by Geratherm® Medical AG) that has replaced mercury in thermometers [80]. It is composed of 68 wt% gallium, 22 wt% indium, and 10 wt% tin. Galinstan is liquid far below room temperature and has a large working temperature range, with a melting temperature of -19°C and a boiling temperature above

1300°C, making it ideal for heat transfer applications. The properties of Galinstan and mercury are tabulated below for comparison [3].

Table 1-1. Properties of Galinstan and Mercury

Property Galinstan Mercury

Color Silver Silver

Odor Odorless Odorless

Boiling Point >1300°C 356.62°C

Melting Point -19°C -38.83°C

Vapor Pressure < 10−6 Pa at 0.1713 Pa at 20°C

500°C

Density 6440 kg/m3 13533.6 kg/m3

Solubility Insoluble Insoluble

Viscosity 2.4푥10−3 Pa∙s 1.526푥10−3Pa∙s at

at 20°C 25°C

Thermal 16.5 W/m∙K 8.541 W/m∙K

Conductivity

Electrical 2.30푥106 S/m 1.04푥106 S/m

Conductivity

Recently, liquid metals have been studied for use in thermal management of computer chips [61,63]. This is not the first case of using liquid metals as a coolant for high powered equipment. The first nuclear-powered submarine was launched in 1963 with a liquid alloy of lead and bismuth as the coolant for the exhaust from the nuclear components

[81]. However, this alloy is toxic and generally corrosive to structural materials, and alternative materials need consideration. Liquid metals have also been used in the cooling

10 of high power optical equipment with great success [64,82]. In one study, Smither et al. suggest that higher than normal power densities could be achieved with the use of liquid gallium as a coolant for x-ray beam sources [82].

For all its advantageous properties, Galinstan has one major drawback that has prevented its widespread use in many areas: Galinstan oxidizes instantly under ambient conditions[83,84]. In fact, Galinstan will form a thin oxide layer at the free surface with as little as 20 ppm oxygen where it acts like a gel rather than a liquid. Ensuring that Galinstan behaves like a true liquid, requires that the oxygen content be kept below 1 ppm [3]. An image of the effect of oxidation on the surface properties of Galinstan may be seen below in Figure 1-2.

Figure 1-2. (a)Galinstan droplet dispensed from a syringe under ambient conditions. (b)Galinstan droplet dispensed witha syringe with less than 1 ppm oxygen.[3] Oxidation on the surface of a droplet can give the illusion that Galinstan readily wets surfaces as reported by Liu et al. [3]. Shown below in Figure 1-3 is a graphic illustrating how the oxidation of a Galinstan droplet can skew the apparent wetting.

Figure 1-3. Demonstration of how oxidation affects contact angle. (a) Oxidized Galinstan (b) Unoxidized Galinstan.

Oxidation effects also have adverse effects on the physical properties of Galinstan.

Scharmann et al. studied the effect of oxide on the viscosity of GaInSn eutectic alloys and found that viscosity of the fluid increases as oxygen reacts with the alloys [85]. This study also reported that the gallium is the primary oxidizing component. It was found that 퐺푎2푂3

(the most stable oxide phase) was the most predominant oxide phase, but 퐺푎2푂 was also detected. The oxide layer at high oxygen content was reported to be as large as 25 angstroms.

The effect of oxidation is even more impactful when considering the use of this material in microelectromechanical systems. Due to the high surface area-to-volume ratio, small droplets exposed to oxygen can become almost entirely oxidized except for a small volume in the core. With this high amount of oxide present, the properties of the droplet become almost completely those of the oxide.

Instead of attempting to mitigate the oxidizing effects of gallium alloys, some have embraced the oxide layer for microfluidic applications, room temperature printing methods, and electronic components [73,77,86,87]. Dr. Michael Dickey of North Carolina

State University is particularly interested in the applications for gallium alloys featuring oxide layers. He and his team have fabricated 3D printed structures, microfluidic channels filled with gallium alloys that are stabilized via surface oxide, and flexible, stretchable antennas [73]. In most of these applications, the oxide layer is used as a mechanically stabilizing mechanism.

Metals have also been studied for use as inorganic phase change materials in thermal energy storage systems [88]. Metals and their alloys normally do not have high enough heat of fusion per unit weight, which results in a high weight for systems that use these materials. Therefore, they are not normally used in phase change energy storage.

However, common inorganic phase change materials suffer from low thermal conductivity, considerable supercooling, large volume changes during phase transition, and corrosion.

Metals and their alloys are superior in all of these aspects, except for low energy storage density [88]. Metals also have much better thermal stability at high temperatures, low specific heat, and virtually no vapor pressure.

Most research has been performed on metals with higher melting temperatures like

Cu, Mg, and Zn [89], but recently, low melting point metals have been explored as replacements in thermal energy storage applications, as well [90–93]. Low melting point metals have all the same beneficial properties as higher melting point metals, but have the added benefit of lower melting temperature which makes them attractive for cooling and heat storage for lower temperature range applications.

Gallium-based low melting point metals are an exciting new material that could have wide spread success in many emerging applications. Their good conductivities, large working temperature range, and fluid properties at room temperature make them appealing to many applications. However, their oxidation behavior must be either mitigated or embraced depending on the application. For heat transfer applications, in specific, a thermally insulating oxide layer is unappealing. Therefore, in both macro- and microscale heat transfer applications, oxidation effects must be mitigated to truly explore the capabilities of these materials.

1.4 Literature Review: Wetting of Fractal Surfaces

Modern science relies increasingly on understanding physics at the micro/nanoscale to explain phenomena at the macroscale and increase the efficiency of engineering systems. For example, heat transfer[19–23,94] and fluid transport [28,29] can be better understood. Consequently, surfaces can be functionalized to improve transport by optimizing their interfacial and wetting properties at the micro/nanoscale. The wetting characteristics of a surface is generally a function of surface chemical composition and topographical structure. The inclusion of multiscale structures has been proven to markedly alter the wettability of surfaces [15,16,44,45,95–98]. Inspiration for these types of surfaces often comes from nature with the intent to mimic it structures to achieve similar physical traits (e.g., superhydrophilicity, superhydrophobicity, etc.) [9,13,41]. Biomimetic surfaces have been therefore modeled after plant leaves for their self-cleaning attributes, different aquatic animal skins for reduced drag, and various insect eyes for antireflective properties [46]. The superhydrophobic lotus leaf is a well-known example used for

14 engineering surface functionalization [8,14,18]. An example of a multiscale surface used for enhanced heat transfer is shown below.

Figure 1-5. Multiscale surface fabricated via laser processing for use in boiling heat transfer enhancement.[22]

Going beyond simple multiscale structures, we also find in nature structures with extraordinarily ordered geometrical patterns. The term ‘fractal’ was introduced by Benoit

Mandlebrot in 1975 to describe this type of geometry that exhibits self-similarity on every length scale [99]. Fractal structures have several appealing properties: (1) A fractal structure is inherently hierarchical due to its spanning of multiple length scales and (2) these structures can be easily characterized, as will be shown later in this letter.

Additionally, fractal structures appear throughout all of nature such as in geology[100], human anatomy[101], and river networks[102]. Fractal geometries have been found to be deterministic and inherently optimal, and thus can be used to design engineering systems

[103,104]. Below is an image illustrating several fractal structures found in nature.

Figure 1-6. Fractal structures found in nature. [105]

1.5 Objectives and Goals: To Better Understand Wetting Properties

1.5.1. Low Melting Point Liquid Metals

Reducing the amount of waste heat or, rather, better utilizing the waste heat that is produced will help provide energy security across the globe. The goal of this research was to develop a better understanding of the wetting properties (equilibrium contact angle, wetting state) of low melting point liquid metals on smooth and nanoengineered surfaces as a function of temperature. The literature review presented provided critical information on the state-of-the-art for the low melting point metals. Liquid metal Galinstan was chosen

16 to be studied because of its appealing thermal properties, relatively low cost, and the recent re-emergence of interest in it by the scientific community.

The objective of the current research was to develop a robust setup and experimentally study the wetting characteristics of low melting point metal Galinstan. A multi-component system was placed inside of an inert gas environment to obtain contact angle measurements of Galinstan on various materials with both smooth and structured surfaces as a function of temperature.

1.5.2. 3-Dimensional Fractal Nanostructured Surfaces

In addition to researching novel liquids for increasing the efficiency of various applications, it is necessary, also, to consider more efficient engineered surfaces. In fact, the subject of engineered surfaces is of great interest to the scientific community. Many studies have been performed on functionalized surfaces for application in heat transfer[20,22,23,94], microfluidics[24–27], and biological sciences[106]. With more efficient surfaces, engineered systems can be greatly improved. In this research, the objective is to explore the wetting characteristics (contact angle, wetting state) of 3- dimentional nanostructured fractal surfaces (3DNFS) created using direct laser writing for functionalized surface applications.

EXPERIMENTAL METHODS

2.1 Development of a Robust Setup for the Study of Low Melting Point Metals

The goal of the current research is to obtain contact angle measurements of low melting point metals on various smooth and structured surfaces as a function of temperature. To accomplish this, a robust experimental setup was required to ensure valid measurements. The three major components of the setup are: a goniometer, an elevated temperature syringe, and a heated stage.

The goniometer is an instrument used to measure contact angle of liquids on a surface. The same instrument may also be used to measure surface tension of liquids, however, only contact angle was measured in this study. A goniometer consists of a high definition camera, light diffuser, and sample stage. The sample is placed on the stage, between the diffuser and camera, and a droplet of liquid is placed on top. An image of the goniometer is shown below.

Figure 2-1. Rame Hart Model 250 goniometer. Source: www.ramehart.com

Once brought into focus with good contrast, the camera takes an image of the 2-D profile of the droplet. After designating the center of the droplet and the horizontal interface between the solid and droplet, an included software performs an edge tracing filter routine to detect the outline of the droplet by comparing the intensity of pixels in the image. From the outline of the droplet at the contact point and the horizontal, contact angle is extrapolated. An image of a typical contact angle measurement setup using the software is shown below.

Figure 2-2. Screenshot of contact angle measurement setup. The green lines are inputs for the center of the droplet and

the solid-liquid interface.

Because melting point can be chosen to fit certain heat transfer applications better, the melting temperatures may be greater than room temperature. Therefore, an elevated temperature syringe is used for melting metals with melting points above room temperature. The syringe is capable of dispensing droplets of materials with melting points up to 300°C. The materials are placed in a glass syringe that is housed inside a metal case with a resistive heating element connected to a PID temperature controller. Various sized needles may be used interchangeably depending on the properties of the material being melted. An image of the elevated temperature syringe is show below in Figure 2-3.

However, because of the lack of volume control of the dispensed droplets using the elevated temperature syringe, a common syringe was used to consistently dispense droplets within the range of 5-10 microliters.

Figure 2-3. Rame-Hart elevated temperature syringe. Max temperature of 300°C. Source: www.ramehart.com

Substrate temperature control is vital for the current study. Therefore, a temperature controlled heated stage was fitted on top of the goniometer stage. The heated stage is controlled by a PID temperature controller to hold a set temperature at the surface. The temperature may be controlled to one-tenth of a degree Celsius, however due to the nature of the PID controller, the exact temperature can fluctuate by a few tenths of a degree. Due to limitations in the design of the heated stage, the highest achievable temperature of the heated stage is 300°C. An image of the heated stage is shown below.

Figure 2-4. Rame-Hart heated stage. Max temperature of 300°C. Source: www.ramehart.com

Although Galinstan has many appealing properties, it possesses one major drawback which makes it difficult to work with: Galinstan readily oxidizes under ambient conditions. In fact, according to Liu et al. [3], Galinstan only maintains its fluid property up to 1 part per million (ppm), or 0.0001%, of oxygen. In an ambient environment, a droplet of Galinstan dispensed from a pipette is oxidized instantaneously and adheres to the pipette and the surface it is being dispensed on. When enough force is applied, the droplet will release from the pipette leaving a residue behind. Therefore, a method to negate this behavior is required to perform accurate measurements of wetting properties using the methods outlined in this study

Like other gallium-containing alloys, different methods have been explored to prevent oxidation of Galinstan. Two prominent methods include keeping the liquid metal in an inert environment like nitrogen [3] or keeping the liquid metal in a solution like diluted hydrochloric acid (HCl) [107]. Keeping the liquid metal in an aqueous solution is not a viable option when measuring interfacial properties; in this case contact angle.

Contact angle is a force balance of the capillary forces acting on the triple line. Setting the sum of these forces to zero, as they are in equilibrium, and normalizing to a unit length yields that the contact angle is a function of the interfacial tensions between the three distinct phases [34]. In addition to altering the apparent contact angle, there would be unwarranted heat transfer effects taking place which may introduce error into the measurements. Therefore, the method of keeping and performing measurements in an inert environment was deemed the best solution.

Figure 2-5. Image of the glovebox setup.

Figure 2-6. Goniometer, elevated temperature syringe, and heated substrate setup inside the inert glovebox.

With all three major components and the inert gas environment, the study of low melting point metal wetting properties was possible. The contact angle of Galinstan can be taken on various substrates, both smooth and structured, with varying temperature without oxidation taking place. Therefore, the true wetting characteristics of Galinstan may be studied.

2.2 Microcontact Angle Experimental Setup

Contact angle measurements on each of the fabricated 3DNFS were carried out using a micro contact angle meter (Kyowa Interface Science Co., Lt. MCA-3) shown below. The MCA-3 is specially designed to accurately measure the contact angle at the microscale and consists of a vertically mounted camera above the specimen stage, a horizontally mounted camera next to the specimen stage, and a pneumatic capillary liquid

24 dispensing system. The system can capture up to 100,000 frames per second for particularly volatile liquids or absorbing surfaces.

Figure 2-7. Kyowa automatic microcontact angle machine MCA-3 Four independent contact angle measurements were taken for each fractal pattern.

A single droplet of de-ionized water was dispensed from a 5 µm coated glass capillary tip on each 140x140 µm fractal surface and optically imaged at 2x zoom. Measurement and analysis software (FAMAS) integrated with the micro contact angle measurement system was then used to obtain equilibrium contact angle. Temperature and humidity were constant for all tests (75°F and 41%RH, respectively).

Due to restrictions stemming from the relative size of the dispensed droplets, each

140x140 µm surface was limited to only one contact angle measurement. For this reason, the average contact angle of the 4 tests was taken as the true equilibrium contact angle for each 3DNFS. To compare droplet size to the roughness scale of each surface, the droplet radius was calculated. Volume calculations were undertaken from the pictures obtained during contact angle measurements. At such a small scale, gravity effects on the droplets

25 were considered negligible and it was assumed that each droplet was spherical in shape.

From this information, the droplet radius was calculated for each test.

SURFACE FABRICATION

Both smooth and structured surfaces were studied in this research. Various traditional and non-traditional fabrication methods were used to create the surfaces. The techniques included traditional machining methods, nanofabrication methods, and direct laser writing processes.

3.1 Materials The materials used in this research were selected due to their promising properties and prominence in both research and industrial applications. Water and low melting point metal, Galinstan, were the fluids used in contact angle measurements. Surfaces were created using single-crystalline silicon, stainless steel 304, Polydimethylsiloxane (PDMS), copper, and a polymer derived from an acrylic based monomer photoresist.

3.1.1 Water Water was used for contact angle measurements on the 3-dimensional nanostructured fractal surfaces due to restrictions of the microcontact angle apparatus used in this research. Because this portion of the research was focused on characterizing the surface wetting properties of these fractal surfaces, low melting point metals were not used.

3.1.2 Low Melting Point Metal: Galinstan

Galinstan is a quite unusual material. It is a metallic alloy, but it is a fluid at room temperature. In fact, the melting point of Galinstan is approximately -19°C. Therefore, the material maintains fluidic properties while also maintaining its metallic properties (e.g. thermal conductivity). This is very useful in heat transfer applications. Similar materials are used as thermal interface materials (TIMs), but is those applications, there is only conduction. Galinstan is so interesting because it could be used to replace traditional heat transfer fluids in use today. For this reason, Galinstan was chosen to study its wetting states as a function of temperature, surface energy, and surface morphology.

3.1.3 Substrate Material

Monocrystalline silicon is used in the electronics industry as a base material for virtually all microchips found in electronic equipment. It is also used as a photovoltaic material in solar cells [108], among other applications. It is a unique material in that its crystal lattice is mostly continuous throughout the entire material. Monocrystalline silicon may be prepared consisting of purely silicon atoms or it may be doped, or prepared with very small amounts of other elements to change its properties. It is most often prepared using the Czochralski where a seed crystal is used to grow the crystal from a melt. The crystal orientation of the bulk material is dependent upon the orientation of the seed crystal. The monocrystalline silicon used in the current research is <100> orientation. Because of the repeatability that may be obtained for surfaces, its ability to be processed using nanofabrication techniques, and its wide-spread use in electronic

27 applications, monocrystalline silicon was used in the current research for both smooth and structured surfaces.

Stainless Steel is most notable for its corrosion resistance stemming from the increased amount of chromium present. The chromium in stainless steel helps by forming a passivation layer (chromium oxide) that is inert and does not allow further corrosion. It is used widely in many industrial applications where a harsh environment is present.

Stainless steel comes in many different grades and surface finishes that may be optimized for certain applications. The stainless steel used in the current research was stainless steel

304. This grade of stainless steel is the most commonly used of 300 series. It usually contains 18wt% chromium and 8wt% nickel as the non-iron components. Because of its good corrosion resistance, widespread use in industrial applications, and ease of machinability, stainless steel 304 was used in the current research for smooth surfaces.

Copper is widely-used heat and electricity conductor. It has very high thermal and electrical conductivity and compared to most metals, it is relatively soft, malleable, and ductile making harder to machine in its pure form. Like stainless steel, copper reacts with atmospheric oxygen to form a passivation layer to prevent further corrosion of the material beneath. Copper was used in the current research to make a microchannel surface due to these properties.

Polydimethylsiloxane, or PDMS as it is widely known, is one of the most widely used silicon-based organic polymer. It is optically clear, inert to most materials, nontoxic, and non-flammable. In the scientific community, is most commonly used in the creation of microfluidic devices due to its low cost, optical transparency, and easy

28 fabrication using molding processes. Because of these properties, PDMS was used to make smooth surfaces in the current research.

3.1.4 Fractal Surfaces

The material used in the fabrication of the fractal surfaces is restricted due to the direct laser writing process used to create them. The process will be discussed in detail in a following section. The fabrication process uses an acrylic-based monomer liquid photoresist optimized for multi-photon photolithography applications (IP-DIP, Nanoscribe

GmbH). This photoresist is a resin that is polymerized at the focal point of a laser.

Therefore, the material of the surface is a polymer. Due to proprietary reasons, the exact makeup is unknown. An optical microscopy image is shown below to illustrate the material of the fractal surfaces.

140um

Figure 3-1. Optical microscopy image of a fractal surface. Material is a polymer derived from an acrylic based monomer.

3.2 Smooth Surfaces

The smooth surfaces used in this research were obtained in various ways. Smooth surfaces for contact angle measurements were made using silicon, stainless steel, and

PDMS.

Smooth silicon surfaces were achieved using a cleaving technique on a single- crystalline silicon wafer (<100>). Using a diamond-tipped scribe, a small notch was etched at the edge of the wafer. Taking advantage of the crystal orientation, a moment was applied at the scribed point and the wafer breaks in a straight line along the scribed line. Because of the crystal orientation, the wafer cleaves both parallel and perpendicular to the notch.

This process was repeated to obtain 16 silicon surfaces per wafer. Before their use in contact angle measurements, the surfaces were subjected to an ultrasonic bath using isopropyl alcohol as the cleaning medium. An image illustrating the cleaving method is pictured below in Figure 3-2.

Figure 3-2. Wafer cleaving technique used to obtain smooth silicon surfaces for contact angle measurements.

The smooth stainless steel surfaces were obtained from McMaster-Carr®, an online fulfillment company with an eclectic array of industrial application products. A mirror-like pre-polished stainless steel 304 strip (1”x36”) was ordered. From this strip, 1x1” pieces were cut for use in the contact angle measurements. After the protective covering was removed from the metal, the pieces were cleaned in an ultrasonic bath using isopropyl alcohol as the cleaning medium.

Smooth PDMS surfaces were also created for contact angle measurements using a traditional soft lithography technique. Sylgard® 184, a two-part silicone elastomer kit, was used to create the PDMS surfaces. The kit consists of two liquid components, a polymer

32 and a curing agent, that, when mixed in a 10:1 mass ratio, cure to form an elastomer. The curing process occurs at room temperature over a 48-hour period, or the process may be accelerated via heat. A table with the various cure times is shown below.

Table 3-1. Cure times for various cure temperatures.

Temperature [°C] Cure Time

25 48 hours

100 35 minutes

125 20 minutes

150 10 minutes

After mixing the polymer and curing agent in a 10:1 mass ratio, the solution was subjected to centrifugal mixing in a Thinky AR-100 conditioning mixer for two rounds of

15 seconds. An aluminum weighing dish was used as the mold for the PDMS solution. To ensure the surfaces of the cured PDMS were smooth and flat, glass microscope slides were placed in the bottom of the aluminum weighing dish. The PDMS solution was then poured into the aluminum weighing dish over the glass slides. This was then place in a desiccator for degassing. Once degassed, the PDMS solution was placed in a furnace for curing. For reasons related to the shelf-life of the PDMS components, the cure time and temperature used to create the PDMS surfaces was approximately 75 minutes at 125°C. An image of a fabricated PDMS surface is shown below in

3.3 Structured Surfaces

Structured surfaces were fabricated on single-crystalline silicon, copper, and a polymer derived from an acrylic based monomer photoresist. The processes used to create these surfaces included nanofabrication techniques, traditional machining methods, and two-photon photolithography (TPP). These processes are detailed below.

3.3.1 Copper Microchannel Fabrication

Copper microchannels were fabricated using traditional machining techniques. A single surface was created with a pitch of 457µm. The wall thickness was 203µm and the channel width was 254µm. The dimensions of the copper microchannels were restricted based on the machining techniques used. Copper stock was placed into a CNC machine where a slotting saw (254µm thick) was used to cut the channels. This was the only copper surface created due to adverse effects observed during contact angle measurements. These effects will be discussed in a later section. A rendering of the copper microchannel surfaces is shown below in Figure 3-3.

Figure 3-3. CAD rendering of copper microchannel surface fabricated using traditional machining techniques. A wall thickness and channel width of 203µm and 254µm was used, respectively.

3.3.2 Silicon Microstructure Design

An array of microstructures (microchannels and micropillars) were created to study the wetting states of low melting point metal Galinstan. The pitch of the microchannels and micropillars was varied while both the wall thickness and channel depth were kept constant on all surfaces. Therefore, the width of the channel increased with increasing pitch. A

35 figure showing the characteristic dimensions of the structures is shown below in Error! R eference source not found..

Figure 3-4. Characteristic dimensions of the silicon microstructures.

The pitch values were chosen based on previous work by Kim et al. using cylindrical PDMS micropillars and oxidized Galinstan [109]. This group saw a transition from Cassie-Baxter to Wenzel wetting states at a pitch of approximately 275µm.

Therefore, the current research took pitch values both less than and greater than 275µm, as well as 275µm. Based on the work done by Kim et al., the wall thickness remained a constant 75µm for all microstructures. The main difference between the current research and the previous work done by Kim et al. is that the current research uses square micropillars where the previous research used cylindrical micropillars. Some characteristic dimensions of the microstructures can be found in Table 3-2.

Table 3-2. Silicon microstructure pitches used and their corresponding channel width. Pitch [µm] Channel Width [µm]

125 50

225 150

275 200

325 250

425 350

3.3.3 Cleanroom Nanofabrication

Nanofabrication techniques were used to achieve microscale structured silicon

surfaces in a certified class 10,000 (ISO-7) cleanroom. Processes included laser

lithography, photoresist deposition, optical lithography, photoresist developing, deep

reactive ion etching, and photoresist stripping. An overview of the fabrication methods

is shown below as a process flow in Figure 3-5.

Figure 3-5. Nanofabrication process flow for silicon microstructures.

In the above figure, the process starts with a cleaned <100> silicon wafer shown in

(1) above. A positive photoresist (SPR 220-7) is then spin coated at 500 rpm for 10 seconds and then 3000 rpm for 45s. The wafer with spin coated photoresist is then soft baked at

115°C for 120 seconds to minimize the solvent concentration present. This avoids mask contamination or sticking and improves the adhesion of the resist to the substrate.

Once the wafer has cooled, it was placed in the optical lithography apparatus (SUSS

MJB-4 Mask Aligner) where it was exposed to ultraviolet wavelength light for 35 seconds at a power of 350W. A mask that was patterned with the desired dimensions of the microstructures was used to only allow a portion of the light through. A contact exposure was used to achieve the highest resolution. This step is shown in (3) in the previous figure.

The mask used in the exposure step was created using Layout Editor, a software for the design of microelectromechanical systems and integrated circuits. Essentially, it is a

CAD program optimized for the creation of micro- and nanoscale systems. To take

38 advantage of largest amount of area of the wafer, an angular segmented pattern was used on the mask. Because of the aperture of the mask aligner, the largest diameter that may be exposed is 75mm. Therefore, the mask, and the exposed area of the wafer, is 75 mm in diameter instead of the 100mm diameter of the wafer. An image of the mask in Layout

Editor is shown below in Figure 3-6.

휙 75푚푚

Figure 3-6. Silicon microstructure photolithography mask. Both micropillars (left half) and microchannels (right half) were fabricated on the same wafer.

The pitch of each structure is overlaid on each segment. Both micropillars and microchannels were fabricated on the same wafer. The five angular segments on the left side of the wafer are micropillars and the five angular segments on the right side of the wafer are microchannels.

Because the photoresist used in this research was “positive,” the exposed areas became soluble in a developer. The developer (MF 24A) removed the soluble parts of the photoresist and the unexposed portions were left to act as a barrier to an etchant. Once the wafer was rinsed with deionized water, it was checked with an optical microscope for defects in the photoresist pattern.

After confirming that the pattern was acceptable, the wafer was taken to the deep reactive ion etching (DRIE) machine (Oxford Instruments PlasmaPro® 100 Estrelas). This piece of equipment uses an anisotropic etching process capable of creating high aspect ratio structures and was originally created for MEMS fabrication. The etching process used in the current research was achieved using a Bosch process, coined after the German company, Robert Bosch Gmbh. This process alternates between two modes to achieve the anisotropic traits associated with DRIE:

1. Standard isotropic plasma etching. In this step, the surface is bombarded with

ions contained in the plasma created by applying a strong radio frequency

electromagnetic field. For this research, sulfur hexafluoride (푆퐹6) was used as

the gas to create the plasma. A figure showing the general concept of this setup

is shown below in Figure 3-7.

Figure 3-7. General configuration and concept of the isotropic etching step of the Bosch process.

2. A passivation process. 퐶4퐹8 gas was used to yield an inert, uniform layer of

polymer on the surface of the silicon. This layer is deposited on the bottom of

the etched feature, as well as the side walls. The kinetic energy is still enough

to etch the material that is perpendicular to the electromagnetic field, but the

ions lose enough kinetic energy that they etch the side walls drastically less

once they are reflected. An image illustrating the passivation step is shown

below in Figure 3-8.

Figure 3-8. Passivation and etching steps in the Bosch process for deep reactive ion etching.

An image of the completed microstructure surface is shown below in Figure 3-9 and SEM images of the silicon microstructured surfaces resulting from the nanofabrication process detailed above are shown in Appendix A. The surfaces were fabricated as intended with minimal inconsistencies. The inconsistencies that are present are likely due to the contact exposure used in the ultraviolet exposure step. In this type of exposure, the mask is brought into direct contact with the surface of the wafer. Therefore, any particles present on either the mask or wafer can cause damage to the photoresist which would produce adverse effects.

Figure 3-9. Image of the successfully fabricated silicon microstructures.

3.3.4 Two-Photon Photolithography 3-dimensional nanostructured fractal surfaces were fabricated using two-photon photolithography (TPP) methods. First, a Computer Aided Design (CAD) program was used to design and export the fractal surfaces as STL files to a mesh fixing, slicing, and hatching software. This software (DeScribe) translates the files to .GWL files to be then imported to the 3D laser lithography system (Nanoscribe GmbH, Photonic Professional

GT). Three distinct 3DNFS were fabricated: a cubic fractal surface, a Romanesco broccoli fractal surface, and a sphereflake fractal surface. To quantitatively compare the contact angle measurements for the 3DNFS, a flat control surface was also fabricated. CAD images of the individual fractal structures and corresponding surfaces are shown in Figure 3-10.

Characteristic dimensions for each of the fractal structures are listed in

Table 3-3.

Table 3-3. Characteristic dimensions for each fractal structure fabricated

Fractal Structure Smallest Dimension Largest Dimension [풏풎] (Dimensions from CAD models) [풏풎]

Cubic (Side Length) 12,800 800

Romanesco Broccoli (Base Radius) 15,000 422

Sphereflake (Sphere Radius) 7,500 352

Figure 3-10. CAD models of each fractal structure and associated surface.

An acrylic-based monomer liquid photoresist optimized for TPP applications (IP-

DIP, Nanoscribe GmbH) was used along with our 3D laser lithography system to transfer the 3DNFS to a glass substrate. A femtosecond laser (780 nm wavelength, 80 MHz repetition rate, and 100 fs pulse duration) was directed to an objective lens (63x zoom and

46 numerical aperture of 1.4) that is immersed in the photoresist. The photoresist was drop- casted onto square glass substrates with side length of 2.5 mm. Four (4) duplicates of a single 140x140 µm fractal surface were fabricated on one substrate. Fabrication of three

(3) distinct fractal surfaces and one (1) control sample resulted in a total of sixteen (16) surfaces.

A laser power of 15 mW was used in the TPP process and was controlled by an acousto-optic modulator. The writing speed used in this experiment (10 mm/s) was controlled by a galvo-mirror scanner. After TPP, the samples were removed from the sample holder and developed in propylene glycol monomethyl ether acetate (PGMEA) for

20 min, followed by a cleaning in isopropyl alcohol (IPA) before drying. After completion, each sample was imaged using an optical microscope to detect the presence of major defects. Successful samples were then imaged via field-emission scanning electron microscopy (SEM).

RESULTS

The results obtained from the contact angle measurements for low melting point metal Galinstan on various surfaces, both smooth and structured, are detailed below.

Contact angle results for water on various 3-dimensional nanostructured fractal surfaces are also given. A discussion of both is offered.

4.1 Wetting States of Low Melting Point Galinstan on Silicon Structures

Results for the contact angle measurements of Galinstan as a function of temperature on silicon microchannels and silicon micropillars are shown below in Figure

4-1 and Figure 4-2, respectively.

Contact Angle of Galinstan® on Silicon Microchannels with Respect to Temperature 180

160

140

120

100

80 Contact Angle ContactAngle [deg] 60

0 0 50 100 150 200 250 300 350 Temperature [°C] Smooth Silicon Channels 1 - 125um Pitch Channels 2 - 225um Pitch Channels 3 - 275um Pitch Channels 4 - 325um Pitch Channels 5 - 425um Pitch

Figure 4-1. Contact angle measurements of Galinstan on silicon microchannels.

Contact Angle of Galinstan® on Silicon Micropillars with Respect to Temperature 180

160

140

120

100

Contact Angle ContactAngle [deg] 60

0 0 50 100 150 200 250 300 350 Temperature [°C] Smooth Silicon Pillars 1 - 125um Pitch Pillars 2 - 225um Pitch Pillars 3 - 275um Pitch Pillars 4 - 325um Pitch Pillars 5 - 425um Pitch - Before Pillars 5 - 425um Pitch - After

Figure 4-2. Contact angle measurement results for Galinstan on silicon micropillars.

As seen in the above figures, there does not seem to be any correlation between contact angle and temperature. Prokhorenko et al. performed contact angle measurements as a function of temperature using an Indium-Gallium-Tin alloy on 12Kh18N9T steel.

Their results show similar results to those found in the current study. The contact angle remained relatively constant up to approximately 800°C, where a large drop was observed.

Contact angle images for Galinstan on smooth silicon as a function of temperature are

49 shown below in Figure 4-3. No appreciable change in contact angle was observed.

Additional contact angle measurement images are shown in Appendix B.

Figure 4-3. Contact angle measurements for Galinstan on smooth silicon at 30°, 100°C, 200°C, and 300°C.

Due to constraints in the equipment used in this study, the maximum temperature that could be achieved was 300°C. If the capabilities of the experimental setup were increased, it is thought that a similar trend would be observed. This trend is due to a decrease in surface tension of the liquid at elevated temperatures. Roland Eötvös described that the surface tension of any fluid is linear with respect to temperature and offered a relationship to relate the two values [110]. The Eötvös rule is given below in Equation 4-1

50 where 훾 is the surface tension, 푉 is the molar volume, 푘 is the Eötvös constant

−7 퐽 (2.1푥10 2), and 푇푐 is the critical temperature of the fluid. 퐾 ∗ 푚표푙3

Equation 4-1

푘(푇푐 − 푇) 훾퐿퐺 = 2 푉3

Per the previous equation, as the temperature approaches the critical temperature, the surface tension of the liquid approaches a null value. A null value for the surface tension of a fluid corresponds to a contact angle of zero and a complete wetting of a surface, as shown by the spreading parameter 푆 which determines whether partial wetting or complete wetting will occur [34].

Equation 4-2

푆 = 훾푆퐺 − (훾푆퐿 + 훾퐿퐺)

When 푆 is less than zero, partial wetting occurs and when 푆 is greater than zero, complete wetting occurs. The surface energy of the solid-gas interface is the largest of the three surface energies. Therefore, if the liquid-gas surface energy is approaching zero in the case of a fluid approaching its critical temperature, 푆 will be positive and there will be complete wetting. The same point may be illustrated using the Law of Young-Dupré [34]:

Equation 4-3

훾퐿퐺푐표푠휃푒 = 훾푆퐺 − 훾푆퐿

If the surface energy of the liquid-gas interface goes to zero, the equation becomes

Equation 4-4

−1 훾푆퐺 − 훾푆퐿 휃푒 = cos ( ) 훾퐿퐺 → 0 Which causes the argument of the inverse of the cosine to go to infinity

Equation 4-5

−1 → 휃푒 = lim cos 푥 푥→∞

However, the cosine function is bounded at a value of 1.

Equation 4-6

−1 → θe = cos 1 = 0

Then, the contact angle resulting from a liquid-gas surface energy of zero is zero and the fluid is said to completely wet the surface. Therefore, as the surface tension of the fluid decreases with increasing temperature, the contact angle may be expected to decrease.

Galinstan was, however, found to be nonwetting on all silicon surfaces, including smooth silicon. The contact angle of Galinstan on both microchannels and micropillars increases with respect to pitch distance. This agrees with the Cassie-Baxter model for a two-component surface (silicon and air) shown below in Equation 4-7 [111]. In the equation, 훾푆퐺, 훾푆퐿, and 훾퐿퐺 are the surface tensions among the three solid, liquid, and gas phases, and 푓 is the fraction of the surface that is contacted by the droplet.

Equation 4-7

훾퐿퐺푐표푠휃퐶퐵 = 푓(훾푆퐺 − 훾푆퐿) − (1 − 푓)훾퐿퐺

This equation is a force balance of the intermolecular forces at the interfaces of the three phases. This form of the equation is acceptable for use when the droplet sits on top of a structured surface so there is a combination of the surface and air in contact with the droplet. This is the case for the Galinstan droplets on both the silicon microchannels and micropillars. Therefore, as the pitch of the microstructures increases, the solid fraction in contact with the droplet, 푓, decreases. Consequently, the contact line moves in response to the change in the forces to reach an equilibrium causing an increase in contact angle.

If it is assumed that the contact angle of Galinstan on the silicon surfaces is not a function of temperature over the studied temperature range, the contact angle results may be summarized as a function of pitch distance, alone. The results using this assumption are shown below in Figure 4-4 and Figure 4-5.

Contact angle of Galinstan on Silicon Microchannels with Varying Pitch 180

160

140

120

100

60 Contact Angle [deg] 40

0 0 50 100 150 200 250 300 350 400 450 Pitch Distance [um]

Figure 4-4. Contact angle of Galinstan on silicon microchannels assuming not temperature dependence.

Contact Angle of Galinstan on Silicon Micropillars with Varying Pitch 180

160

140 After Moving

120 Before Moving 100

60 Contact Angle [deg] 40

0 0 50 100 150 200 250 300 350 400 450 Pitch Distance [um]

Figure 4-5.. Contact angle of Galinstan on silicon micropillars assuming not temperature dependence

For each pitch, a composite contact angle was taken as the average of the contact angles over the temperature range. For the silicon microchannels, the contact angle increased for the pitches studied. However, the contact angle increases with pitch until some value for pitch distance and there appears to be a transition in wetting behavior for the micropillar structures. For the largest pitch distance (425µm), when the Galinstan droplets are dispensed, they completely wet the surface. A fully wetting state is described by the Wenzel model where 푟 is the roughness, the ratio of the actual area of the rough surface to the projected area on the horizontal plan, and 휃푒 is the intrinsic contact angle on a smooth surface of the same material [111]:

Equation 4-8

푟(훾푆퐺 − 훾푆퐿) 푐표푠휃푊 = = 푟푐표푠휃푒 훾퐿퐺

However, if a force is applied to the droplet in a horizontal direction, the droplet will transition to sitting on top of the pillars, causing the contact angle to increase by almost

20°. Images showing a droplet on the 425µm pitch micropillars before and after being moved are shown below illustrating the transitioning of a Galinstan droplet.

Figure 4-6. Galinstan droplet on micropillars with 425µm pitch at 100°C. (A) Droplet after being dispensed (B) Droplet after moving droplet with needle.

The droplets on structured surfaces in the Cassie-Baxter regime can be a metastable state. If enough energy is applied to the droplet it can overcome an energy barrier and transition to a different wetting state. When the Galinstan droplets dispensed, the velocity may have been large enough that the force of the impact was enough to transition to a completely wetting Wenzel state. Then, when energy was added to the droplet (pushing it with the syringe needle) it transitioned back to a Cassie-Baxter state.

For a favorable Cassie-Baxter state, 휃푒 much be should be greater than a critical angle 휃푐 that is given by [30]

Equation 4-9 −(1 − 푓) 푐표푠휃 = 푐 (푟 − 푓)

When 휃푒 < 휃푐, a Wenzel state is favored over a Cassie-Baxter state. The values for

푟 and 푓 are shown below for each pitch on both the microchannels and micropillars in

Figure 4-7.

Figure 4-7. Roughness and solid fraction for silicon microstructures as a function of pitch distance.

Both roughness and solid fraction decrease with respect to pitch distance. This corresponds with the decreasing amount of material that is present as the channel width increases for each pitch. These values were then used to solve for the critical contact angle for each pitch, shown in Figure 4-8.

Figure 4-8. Critical contact angle for silicon microstructures with varying pitch distance. The red line represents the intrinsic contact angle. Error bars are standard deviation of contact angles measured.

For the silicon microchannels, the intrinsic contact angle is always much larger than the critical angle for its corresponding pitch distance. However, the critical angle for the silicon micropillars approaches the intrinsic contact angle as pitch increases. For a pitch

57 distance of 425µm, the critical angle and intrinsic angle are 135° and 141°, respectively.

The two values may be even closer due to fabrication inconsistencies.

If the critical angle and intrinsic angle are close, the droplet is at a transition point between Wenzel and Cassie-Baxter. This may explain why the droplets behavior strangely on the 425µm pitch micropillar surface. The droplet may contact the bottom surface below the pillars where it becomes pinned in a Wenzel state when it is dispensed at a certain height. However, when energy is added to the droplet, it transitions to a Cassie-Baxter state. This pitch, and others close to it, could allow a droplet to alternate between Wenzel and Cassie-Baxter states because it is so close to the transition contact angle. A wetting phase diagram illustrating this transition point is shown below. The red circle shows where the transition occurs for a given surface. The dashed line illustrates where a metastable

Cassie-Baxter state may exist. The 425µm pitch micropillars would be just to the left of this transition point.

Figure 4-9. Wetting phase diagram illustrating the transition point between a Cassie-Baxter state and a Wenzel state.

A similar phenomenon was observed by Lafuma and Quéré [33]. In their study, they focused on the pressure required to cause a transition between Cassie-Baxter and

Wenzel states of a water drop on a square lattice of triangular spikes. A drop was deposited on a surface and a pressure was applied to the drop to observe a change in wetting state.

With a large enough applied pressure, the drop was forced down into the structures to transition from a Cassie-Baxter state to a Wenzel state. When the pressure was removed, the drops would stay pinned in a Wenzel state. Another study observed similar results using water on micropillar arrays[32].

It is hypothesized, then, that when the Galinstan drops were dispensed from a given height above the surface, the droplet was forced down between pillars and contacted the bottom material. This caused the droplet to become pinned in a Wenzel state. However, because the surface tension of Galinstan is large (approximately 10 times larger than water), it is easier for the droplet to become unpinned and transition to a Cassie-Baxter state.

For pitches above 425µm, this transition may still occur until a critical value where the critical contact angle 휃푐 is greater than the intrinsic contact angle 휃푒 and the

Wenzel state becomes the more favorable state. This critical contact angle for the

Galinstan-silicon system should happen for a microchannel pitch of 500-525µm.

4.2 Adverse Effects of Low Melting Point Metal Galinstan on Stainless Steel, Copper, and Polydimethylsiloxane Surfaces

Contact angle measurements were also recorded on smooth stainless steel 304, smooth PDMS, and copper microchannels. However, these surfaces exhibited adverse

59 effects when in contact with Galinstan, so the results cannot be assumed to be accurate.

The contact angle results are shown below in Figure 4-10. Again, there does not seem to be any correlation between temperature and contact angle for the temperature range studied.

Liquid Metal Galinstan Contact Angle as a Function of Temperature on Various Surfaces 180

160

140

120

100

60 Contact Angle [deg]

0 0 25 50 75 100 125 150 175 200 225 250 275 300 Temperature [°C]

Flat SS304 Flat PDMS Cu MC

Figure 4-10. Contact angle results for Galinstan on smooth stainless steel 304, smooth PDMS, and copper microchannels.

Copper microchannels exhibited the highest contact angle, which is to be expected given they are a structured surface like the silicon microchannels discussed above. There was no smooth copper surface studied to compare to the microchannel surface. Given the results achieved with the silicon microstructures, it is assumed that

Galinstan would be non-wetting on smooth copper with a lower contact angle than that on the copper microchannels due to microstructure.

An interesting observation can be noted about the contact angle of Galinstan on smooth stainless steel and smooth polydimethylsiloxane (PDMS). Contact angles on

PDMS were only taken up to 190°C due to the decomposition of the material above

200°C, but they are very similar to those taken on stainless steel. This is interesting because these two substrate materials have very different surface energies. Stainless steel

(훾 =700-1100 mN/m) is a metal which are high-energy surfaces and PDMS (훾 = 20 mN/m) is a polymer which are low-energy surfaces.

This interesting, however, the contact angles cannot be assumed to be accurate due to the corrosion behavior of Gallium-containing alloys. Gallium is a reactive material and reacts with many common metals including both stainless steel and copper [112–

117]. While taking contact angles on copper and stainless steel, tarnishing of the metal was observed. At elevated temperatures, this occurs at a higher rate since the corrosion is diffusion-base process. Images of the tarnishing of the substrate materials are shown below in Figure 4-11.

Figure 4-11. Corrosion of copper microchannels and smooth stainless steel after exposure with Galinstan.

The Galinstan also reacted with the PDMS during contact angle measurements.

Droplets dispensed on the surface left residue behind indicating some sort of oxidation process occurring. PDMS is composed of polymer chain (−푂 − 푆푖 − 푂−) with each Si atom also bonded to two methyl (−퐶퐻3) groups. The polymer is capped with

(퐶퐻3)3푆푖 − groups. An image of the molecular structure is given below.

Figure 4-12. Molecular structure of polydimethylsiloxane (PDMS).

Since Galinstan reacts readily with oxygen to form a thin oxide layer, it is believed that the Galinstan droplets were reacting with the oxygen atoms at the surface of

the PDMS substrate to form 퐺푎2푂3. This oxidation would leave residue behind when the droplet was removed from the surface. An image of this residue is shown below.

Figure 4-13. Oxide residue left behind after taking contact angle measurements of Galinstan on smooth PDMS surfaces. Due to the reactive behavior of Galinstan with copper, stainless steel, and PDMS, the contact angles taken on these surfaces cannot be taken as an accurate representation of the wetting behavior.

4.3 Wetting Characteristics of 3-Dimensional Nanostructure Fractal Surfaces Scanning electron microscopy images in Figure 4-14 show the final 3DNFS created via the TPP fabrication process. These images show successful creation of controllable and complex hierarchical surfaces at the micro- and nanoscales. Seen in this figure, the features of each structure and surface match closely the CAD models shown in

Figure 3-10. Discrepancies between the CAD models and fabricated surfaces are attributed to process resolution limitations from a combination of the laser lithography system and the photoresist used in the fabrication process.

Figure 4-14. SEM images of each fractal structure and corresponding surface.

The fractal dimension is a convenient way to characterize a geometry that exhibits self-similarity [118]. There are many different fractal dimensions or methods that can be used to describe such a geometry. These methods include, but are not limited to,

64 triangulation algorithm, the variogram, and the box counting method [119]. Generally, there exists a difference in the fractal dimension depending on which method is used to describe the geometry. However, for many classical fractal geometries, all methods result in the same fractal dimensions.

For the current work, fractal dimensions were calculated using the box counting method. The aim of the box counting method is to quantify the fractal scaling of a structure.

Realistically, that would entail knowing the scaling beforehand. In other words, one must know the correct size of box that encapsulates the structure that is repeated at each scale.

Box counting algorithms are then used to find an ideal way to partition a structure for calculating the fractal dimension. Using the box counting method, the fractal dimension of a structure is defined as.

Equation 4-10

log(푁푟) 퐷 = lim 푟→0 1 log ( ) 푟

Where 푁푟 is the number of repeated features and 푟 is the scaling factor. For instance, if, at each iteration, the structure being repeated were reduced by a factor of 2, 푟 would equal 2.

In the present study, modified MATLAB codes [120,121] were used to import and voxelize the .STL files and calculate the box counting dimensions. The box counting program gives the number of cubes, 푛, of size 푟 that it took to completely cover the fractal structure. The log of 푛 was then plotted against the log of 푟 and a linear curve fitting was applied. The slope of the resulting curve fit is the negative of the fractal dimension for each structure.

To validate the procedure used to approximate the fractal dimensions of our structures, the process was performed on a simple cube. Exhibiting no fractal behavior, the fractal dimension of a cube should be close to that of its Euclidean dimension. From the procedure, the cube was found to have a box counting dimension of 3 with a 95% confidence interval of (3, 3). The results agree with the expected fractal dimension of a cube. It should be noted that even though the process works for a simple cube, the box counting method is an approximation limited by the number of iterations performed.

The plots that resulted from the box counting method can be seen in Figure 4-15 and the calculated fractal dimensions from this method are tabulated in Table 4-1. Each linear curve fitting can be written in the form:

Equation 4-11

푦 = 푚푥 + 푏

Where 푏 is the y-intercept and 푚 is the slope of the line given by

Equation 4-12

log(푛) 푚 = = −퐷 log(푟)

and is equal to the negative of the box counting dimension, 퐷, as shown in Equation

4-10.

Figure 4-15. Linear fits for determining fractal dimension of (a) simple cube (b) cubic structure (c) romanesco broccoli

structure (d) sphereflake structure

Table 4-1. Fractal dimension for each structure with 95% confidence intervals.

Romanesco Cube (Control) Cubic Sphereflake Fractal Structure Broccoli Fractal Dimension 3 ± 0.0 2.657 ± 0.082 2.794 ± 0.054 2.688 ± 0.06

Figure 4-16. Images of contact angle measurements for (a) flat control surface (b) Cubic fractal surface (c) Romanesco

broccoli fractal surface (d) Sphereflake fractal surface

Photos from distinct tests for each surface are shown in Figure 4-16. Average contact angle of the flat control surface was found to be 66.8°, suggesting that the acrylic-based monomer material used to fabricate these structures is intrinsically hydrophilic (θ < 90°) with a moderate surface energy. Inclusion of each 3DNFS lowered the contact angle even further. Contact angle measurements for each of the surfaces are tabulated below in Table

4-2.

Table 4-2. Experimental data for measured contact angle and drop volume for all fractal

surfaces.

Romanesco Flat (Control) Cubic Sphereflake Broccoli Test Drop Drop Drop Drop Contact Contact Contact Contact Volume Volume Volume Volume Angle Angle Angle Angle [pL] [pL] [pL] [pL] 1 69.3 88.3 22.4 115.1 36.5 136.4 0.0 N/A 2 66.4 54.1 18.6 94.1 37.1 144.3 0.0 N/A 3 64.8 50.3 17.2 79.4 37.0 141.0 0.0 N/A 4 66.8 82.1 16.6 71.2 36.6 131.6 0.0 N/A Average 66.8 68.7 18.7 90.0 36.8 138.3 0.0 N/A Standard 1.9 19.3 2.6 19.3 0.3 5.5 0.0 N/A Dev.

When concerned with the wetting of rough surfaces, there are two standard wetting

models used to describe the observed phenomenon: Wenzel’s model or the Cassie-Baxter

model [34]. In the Wenzel model, the droplet completely wets the surface. This model is

given by [39]

Equation 4-13

∗ 푐표푠휃W = 푟푐표푠휃푒

∗ 휃푊 is the apparent Wenzel contact angle and 푟 is the roughness ratio of the surface,

calculated as the ratio of the total surface area to the projected area of the surface. In the

Cassie-Baxter model, the droplet sits on top of the structured surface. The model can be

formulated as [122]

Equation 4-14

∗ 푐표푠휃CB = r푓푓푐표푠휃푒 + 푓 − 1

∗ 휃퐶퐵 is the apparent Cassie-Baxter contact angle, 푓 is the fraction of the projected area that

is in contact with the droplet, and 푟푓 is the roughness ratio of the wetted portion. In both

Equation 4-13 and Equation 4-14, 휃푒 is the intrinsic, or Young, contact angle on a flat surface.

From the optical images seen in Figure 4-16 it appears that the droplets completely wet the surfaces. Therefore, it is assumed they are in a Wenzel state. Using Equation 4-13, a plot of the theoretical Wenzel model and the experimental contact angles was constructed to determine the effectiveness of this model to characterize the 3DNFS. Figure 4-17 shows that the cubic and sphereflake surfaces do not follow the Wenzel model. However, the experimental contact angle and theoretical model of the Romanesco broccoli surface are within the bounds of measurement error.

Figure 4-17. Comparison of experimental contact angles to the theoretical Wenzel model.

To rationalize the trends seen in the measured contact angles, geometric properties of each surface were obtained from the CAD drawings. Surface area and surface area to volume ratio were calculated for each individual fractal structure. In addition to these values, the roughness of each surface is also tabulated and can be found in

Table 4-3. A bar graph of these tabulated values can be found in Figure 4-17. Comparison of experimental contact angles to the theoretical Wenzel model.; the contact angle of each surface is located next to its label along the x-axis.

Table 4-3. Comparison of geometric properties of the fabricated 3DNFS.

Surface Average Contact Angle Surface Area Volume SA:V Roughness [deg] [μm2] [μm3] [μm-1] [ ]

Cubic 18.7 5332.5 5022.2 1.06 7.25

Romanesco 36.8 2597.2 4628.6 0.56 2.03 Broccoli Sphereflake 0.0 3311.4 3231.7 1.02 3.89

CONCLUSIONS 5.1. Wetting States of Liquid Metal Galinstan

The wetting behavior of low melting point metal Galinstan was explored by taking contact angle measurements on smooth and structured surfaces fabricated using various substrate materials. Smooth surfaces included monocrystalline silicon, stainless steel 304, and polydimethylsiloxane (PDMS). Structured surfaces included microchannels on

72 monocrystalline silicon and copper, and micropillars on monocrystalline silicon. Contact angle was taken on these surfaces with varying substrate temperature.

Contact angle on all the surfaces studied in the current research did not show a dependence on temperature. However, temperature was restricted to a maximum of restricted to a maximum of 300°C due to the limitations of the experimental equipment. If the maximum achievable temperature was greater than 800°C, it is hypothesized that the contact angle would decrease on all surfaces due to a decrease in surface tension of the

Galinstan. Similar trends have been observed before [110,123–125]. Future work would entail upgrading the experimental setup to achieve higher temperatures to test the temperature dependence of contact angle at temperatures closer to the critical temperature.

A dependence on microstructure pitch distance was observed for contact angle on monocrystalline silicon microstructures. Contact angle increased on both microchannels and micropillars with increasing pitch. Results for the microchannels studied suggest that the contact angle increases with pitch distance without bound. However, calculations for the critical angle 휃푐 show that at a pitch of approximately 1000-1100µm, there should be a transition to a fully wetted Wenzel state, which was not observed for the pitches studied. Until that point, the droplet should be in a Cassie-Baxter state.

Contact angle for Galinstan on the silicon micropillars increased until the largest pitch distance where droplets were observed to transition between the two wetting states.

When the droplet was dispensed, it would completely wet the surface. However, adding energy to the system by pushing the droplet with a needle causes the droplet to pop up on top of the structures into a Cassie-Baxter state. The cause behind this is that the geometry for this pitch of micropillars is such that the critical contact angle 휃푐 is very close to the

transition point between Wenzel and Cassie-Baxter states. When 휃푐 is less that the intrinsic

Young’s contact angle 휃푒, it is more favorable to be in the Cassie-Baxter state. 휃푐 for the

425µm pitch micropillar surface is approximately 135.28° and 휃푒 for the system is

141.02° ± 1.18° and with fabrication inconsistencies, 휃푐 may be closer. Therefore, it is reasonable to assume that the Galinstan droplets for this pitch can transition between wetting states with the addition of a certain amount of energy.

Future work pertaining to the study of wetting state of low melting point metal

Galinstan on silicon microstructured surfaces would include creating microstructures with pitches at and near the transition point to study the transition between Cassie-Baxter and

Wenzel wetting states. Calculations show that this transition should be most prevalent near

500-525µm pitch distance. In addition, it would be beneficial to study the effect of vibration and temperature at the transition point. To make the study of the effect of temperature worthwhile, the experimental setup should be expanded to include a heater with a greater temperature range.

An interesting experiment to consider for the future would be to study the effect of pressure on the wetting states of Galinstan, especially close to the transition point between

Wenzel and Cassie-Baxter. Lafuma and Quéré performed this experiment with water and structured surfaces made from a complex mixture of perfluoroacrylates and non- fluoronated acrylates [33]. In the study, they placed a drop of water on a structured surface where the drop was in a non-wetting Cassie-Baxter state. They then used both smooth and identical surfaces to apply a pressure from the top of the droplet until the droplet was forced into a Wenzel state. The pressure was then removed to study if a transition back to a Cassie-

Baxter state occurred. An image of the experimental setup is shown below in Figure 5-1.

Figure 5-1. Wetting of a water droplet with increasing applied pressure [33]. By controlling the pressure applied to a Galinstan droplet, the wetting state may be controlled. If this effect is found to be reversible, this could have a tremendous effect on the ability to control the heat flow in a similar system. When the pressure is increased, causing a fully wetting state, the heat transfer would be greater than when the pressure was decreased because of a transition back to a non-wetting state. The ability to control the amount of heat transfer in this manner could have great implications in thermal energy storage technology. Below is a very preliminary concept of how this would work.

Figure 5-2. Concept for thermal storage technology. (Left) A force is applied to cause a Galinstan drop to transition to a Wenzel state, increasing the amount of heat transfer into the droplet. (Right) The force is removed to cause the droplet to transition back Cassie-Baxter, reducing the contact area and heat transfer out of the droplet. Wetting of Galinstan on copper, stainless steel, and PDMS surfaces resulted in adverse effects making these surfaces impractical to use for further experiments with gallium-containing alloys. The gallium in the Galinstan alloy tarnished both copper and

75 stainless steel surfaces, and reacted with the PDMS to form an oxide layer. These effects are accelerated at higher temperatures due to the diffusion processes that govern them

[112–114,117]. Therefore, these surfaces are unsuitable applications with gallium- containing alloys, and especially for heat transfer applications. Future work in this area should include determination of wetting states on tungsten metal due to its high corrosion resistance. Work has also been done on the effect of including graphene as a diffusion barrier between Galinstan and metal surfaces [126]. They found that adding graphene at the interface between Galinstan and aluminum blocked the formation of aluminum oxides.

A similar experiment could be performed to help prevent the adverse effects that Galinstan has on the stainless steel, copper, and PDMS surfaces studied in this research.

Galinstan and other low melting point metals are certainly very interesting materials that could be used to further scientific research and applications. Due to their appealing properties (e.g. low melting point, high boiling point, high thermal conductivity, high electrical conductivity, low vapor pressure, etc.) they are of great interest to the scientific and industrial community. This recent reemergence of interest in these materials has produced many great studies on their properties and applications. Such studies have included liquid metal manipulation through electromagnetic fields [5,127–134], their application in biological and medical sciences [79,135], flexible electronics [76,77,136–

140], and energy management, conversion, and storage [60,61,63,67,70,71,73,91,93,141–

144].

Because wetting characteristics play a vital role in many applications, it is the believed that the results obtained in the current research should prove to be beneficial for future research into the use of low melting point metals as a new class of thermal

76 management material. However, to fully report the efficacy of Galinstan for use in a thermal management device, the experiments detailed in this report should be completed again at temperatures higher than 800°C where surface tension effects are assumed to become important. It would also be beneficial to repeat the experiments at pitch distances at and near the critical transition values (~1000µm microchannels and ~500µm micropillars). If these experiments are carried out, a much better understanding of the possibilities for these materials to be used in many applications could be achieved.

5.2. Wetting Characteristics of Fractal Surfaces

As seen in the plots from Figure 4-18, there appears to be no discernable trend based on the geometrical properties of the three structures. One could attempt to correlate these geometric properties to the reduction seen in the contact angle from the Romanesco broccoli surface to the cubic surface, but the sphereflake surface does not follow the same tendency. Additionally, there seems to be no clear correlation between fractal dimension and contact angle between the three distinct surfaces. It is important to note that only four samples of each surface were tested and further experimentation may be needed.

Nevertheless, we learned that 3DNFS are as fascinating in their interfacial physics as they are in their appearance. Because of their hierarchical nature and ability to be mathematically characterized, 3DNFS are an excellent platform for understanding interfacial transport in nanostructured surfaces while having great potential in many engineering applications.

For example, 3DNFS that exhibit multiscale roughness may have interesting applications in increasing heat transfer in the two-phase regime such as in condensation and boiling

[19,20,22,23]. Another important area where 3DNFS can play a transformative role is in microfluidics. Similar structures have been used to decrease the drag on a surface, manipulate droplets, control adsorption of biomolecules, and promote cell adhesion [24–

27]. Recently, flexible organic light-emitting diodes were fabricated with a nanoimprinting process to increase the efficiency for wearable electronics [145]. Similar structures to those discussed above could be fabricated to act as a mold for this nanoimprinting procedure and

78 help increase the efficiency of components in the rapidly growing field of electronics integration.

APPENDIX A. SUPPLEMENTAL FIGURES

Figure A-1. Estimated energy usage in the US for the year 2015

Figure A-2. False color SEM images of a Romanesco (left) and Sphereflake (right) structure

APPENDIX B. CONTACT ANGLE MEASUREMENT IMAGES Silicon Microchannels Pitch 125µm

Figure B-1 Contact angle measurements on 125µm pitch microchannels at various temperatures.

Pitch 225µm

Figure B-2 Contact angle measurements on 225µm pitch microchannels at various temperatures.

Pitch 275µm

Figure B-3 Contact angle measurements on 275µm pitch microchannels at various temperatures.

Pitch 325µm

Figure B-4 Contact angle measurements on 325µm pitch microchannels at various temperatures.

Pitch 425µm

Figure B-5 Contact angle measurements on 425µm pitch microchannels at various temperatures.

Silicon Micropillars Pitch 125µm

Figure B-6 Contact angle measurements on 125µm pitch micropillars at various temperatures.

Pitch 225µm

Figure B-7 Contact angle measurements on 225µm pitch micropillars at various temperatures.

Pitch 275µm

Figure B-8 Contact angle measurements on 275µm pitch micropillars at various temperatures.

Pitch 325µm

Figure B-9 Contact angle measurements on 325µm pitch micropillars at various temperatures.

Pitch 425µm

Figure B-10 Contact angle measurements on 425µm pitch micropillars at various temperatures. Left side of figure is after dispensing the droplet and right side is after moving the dispensed droplet.

Smooth Stainless Steel 304

Figure B-11 Contact angle measurements on smooth stainless steel 304 at various temperatures.

Copper Microchannels

Figure B-12 Contact angle measurements on copper microchannels at various temperatures.

Smooth Polydimethylsiloxane

Figure B-13 Contact angle measurements on smooth polydimethylsiloxane at various temperatures.

APPENDIX C. SILICON MICROSTRUCTURE SEM IMAGES Microchannels Pitch 125µm

Figure C-1. 125µm pitch microchannels top down 100X and 200X magnification.

Figure C-2. 125µm pitch microchannels angled 45° 100X and 200X magnification.

Pitch 225µm

Figure C-3. 225µm pitch microchannels top down 100X and 200X magnification.

Figure C-4. 225µm pitch microchannels angled 45° 100X and 200X magnification.

Pitch 275µm

Figure C-5. 275µm pitch microchannels top down 100X and 200X magnification.

Figure C-6. 275µm pitch microchannels angled 45° 100X and 200X magnification.

100

Pitch 325µm

Figure C-7. 325µm pitch microchannels top down 100X and 200X magnification.

101

Figure C-8. 325µm pitch microchannels angled 45° 100X and 200X magnification.

102

Pitch 425µm

Figure C-9. 425µm pitch microchannels top down 100X and 200X magnification.

103

Figure C-10. 425µm pitch microchannels angled 45° 100X and 200X magnification.

104

Micropillars Pitch 125µm

Figure C-11. 125µm pitch micropillars top down 100X and 200X magnification.

105

Figure C-12. 125µm pitch micropillars angled 45° 100X and 200X magnification.

106

Pitch 225µm

Figure C-13. 225µm pitch micropillars top down 100X and 200X magnification.

107

Figure C-14. 225µm pitch micropillars angled 45° 100X and 200X magnification.

108

Pitch 275µm

Figure C-15. 275µm pitch micropillars top down 100X and 200X magnification.

109

Figure C-16. 275µm pitch micropillars angled 45° 100X and 200X magnification.

110

Pitch 325µm

Figure C-17. 325µm pitch micropillars top down 100X and 200X magnification.

111

Figure C-18. 325µm pitch micropillars angled 45° 100X and 200X magnification.

112

Pitch 425µm

Figure C-19. 425µm pitch micropillars top down 100X and 200X magnification.

113

Figure C-20.425µm pitch micropillars angled 45° 100X and 200X magnification.

114

APPENDIX D. MATLAB CODE: SILICON MICROSTRUCTURE GEOMETRIC PROPERTIES

% Measured contact angle c = [151.79 152.74 157.30 159.42 162.01]; p = [157.31 160.90 164.35 165.16 138.66 156.56];

% cos(theta) cstar = cosd(c); pstar = cosd(p);

% Error (Standard Deviation) cerr = [1.45 1.24 1.64 1.62 1.04]; perr = [1.47 .39 .53 1.55 1.18 .72]; Find Roughness Values for Each Surface

Lp = 10000; %Projected Length [µm] Ap = Lp^2; %Projected Area [µm^2] w = 75; %Wall Thickness [µm] h = 150; %Channel Height [µm]

%P = [125 225 275 325 425]; %Pitch Distance [µm] P = 100:25:500; c = P-w; %Channel Width [µm]

% Microchannels nc = Lp./P; %Number of channels in projected area [ ] cLa = nc.*(w+2*h+c); %Actual Length [µm] cAa = Lp.*cLa; %Actual Area [µm^2] rc = cAa./Ap; %Channels Roughness Ratio [ ] fc = (nc.*w*Lp)./Ap; %Fraction of the projected area wet by the droplet thetacc = acosd(-(1-fc(:))./(rc(:)-fc(:))); %Critical contact angle

% Micropillars np =(Lp./P).^2; %Number of pillars in projected area [ ] Apil = np.*(w^2+4*h*w+c*w); %Area of pillars in projected area [µm^2] pAa = Apil + (Ap - np.*(w^2)); %Actual area [µm^2] rp = pAa./Ap; fp = (np.*(w^2))./Ap; %Fraction of the projected area wet by the droplet

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thetacp = acosd(-(1-fp(:))./(rp(:)-fp(:))); %Critical contact angle

% Plot Roughness and Solid Fraction p = [rc;rp]; p = p'; f = [fc;fp]; f = f'; figure subplot(2,1,1); b1 = bar(P,p); title('Roughness for Silicon Microstructures') legend('Microchannels','Micropillars') xlabel('Pitch [µm]') ylabel('Roughness [ ]') % ax = gca; % ax.XTick = [125 225 275 325 425]; % ax.XLim = [100 450]; subplot(2,1,2); b2 = bar(P,f); title('Solid Fraction for Silicon Microstructures') legend('Microchannels','Micropillars') xlabel('Pitch [µm]') ylabel('Solid Fraction [ ]') % ax = gca; % ax.XTick = [125 225 275 325 425]; % ax.XLim = [100 450];

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Plot Critical Angle and Intrinsic Angle

% Flat Contact Angle thetae = 141.02; thetae = thetae*ones(size(P)); stdev = 1.18; err = stdev*ones(size(P)); figure subplot(2,1,1); hold on bar(P,thetacc); plot(P, thetae); errorbar(P,thetae,err) title('Critical Angle for Silicon Microchannels') xlabel('Pitch [µm]') ylabel('Contact Angle [deg]') % ax = gca; % ax.XTick = [125 225 275 325 425]; % ax.XLim = [100 450]; hold off

subplot(2,1,2);

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hold on bar(P,thetacp); plot(P,thetae); errorbar(P,thetae,err) title('Critical Angle for Silicon Micropillars') xlabel('Pitch [µm]') ylabel('Contact Angle [deg]') % ax = gca; % ax.XTick = [125 225 275 325 425]; % ax.XLim = [100 450]; hold off

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APPENDIX E. MATLAB CODE: FRACTAL DIMENSION

% %Plot the original STL mesh: % figure [stlcoords] = READ_stl('800nm.stl'); xco = squeeze( stlcoords(:,1,:) )'; yco = squeeze( stlcoords(:,2,:) )'; zco = squeeze( stlcoords(:,3,:) )'; [hpat] = patch(xco,yco,zco,'b'); axis equal

%Voxelise the STL: [cubes] = VOXELISE(512,512,512,'800nm.stl','xyz');

% %Show the voxelised result: figure subplot(1,3,1); imagesc(squeeze(sum(cubes,1))); colormap(gray(256)); xlabel('Z-direction'); ylabel('Y-direction'); axis equal tight subplot(1,3,2); imagesc(squeeze(sum(cubes,2))); colormap(gray(256)); xlabel('Z-direction'); ylabel('X-direction'); axis equal tight subplot(1,3,3); imagesc(squeeze(sum(cubes,3))); colormap(gray(256)); xlabel('Y-direction'); ylabel('X-direction'); axis equal tight

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figure

[nc, rc] = boxcount(cubes,'slope'); figure boxcount(cubes); sc=-gradient(log(nc))./gradient(log(rc)); lnc = log(nc); lrc = log(rc);

function [n,r] = boxcount(c,varargin) %BOXCOUNT Box-Counting of a D-dimensional array (with D=1,2,3). % [N, R] = BOXCOUNT(C), where C is a D-dimensional array (with D=1,2,3), % counts the number N of D-dimensional boxes of size R needed to cover % the nonzero elements of C. The box sizes are powers of two, i.e., % R = 1, 2, 4 ... 2^P, where P is the smallest integer such that % MAX(SIZE(C)) <= 2^P. If the sizes of C over each dimension are smaller % than 2^P, C is padded with zeros to size 2^P over each dimension (e.g., % a 320-by-200 image is padded to 512-by-512). The output vectors N and R % are of size P+1. For a RGB color image (m-by-n-by-3 array), a summation % over the 3 RGB planes is done first. % % The Box-counting method is useful to determine fractal properties of a % 1D segment, a 2D image or a 3D array. If C is a fractal set, with % fractal dimension DF < D, then N scales as R^(-DF). DF is known as the % Minkowski-Bouligand dimension, or Kolmogorov capacity, or Kolmogorov % dimension, or simply box-counting dimension. % % BOXCOUNT(C,'plot') also shows the log-log plot of N as a function of R % (if no output argument, this option is selected by default). % % BOXCOUNT(C,'slope') also shows the semi-log plot of the local slope % DF = - dlnN/dlnR as a function of R. If DF is contant in a certain % range of R, then DF is the fractal dimension of the set C. The % derivative is computed as a 2nd order finite difference (see GRADIENT). % % The execution time depends on the sizes of C. It is fastest for powers % of two over each dimension. % % Examples: % % % Plots the box-count of a vector containing randomly-distributed % % 0 and 1. This set is not fractal: one has N = R^-2 at large R, % % and N = cste at small R. % c = (rand(1,2048)<0.2); % boxcount(c); %

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% % Plots the box-count and the fractal dimension of a 2D fractal set % % of size 512^2 (obtained by RANDCANTOR), with fractal dimension % % DF = 2 + log(P) / log(2) = 1.68 (with P=0.8). % c = randcantor(0.8, 512, 2); % boxcount(c); % figure, boxcount(c, 'slope'); % % F. Moisy % Revision: 2.10, Date: 2008/07/09

% History: % 2006/11/22: v2.00, joined into a single file boxcountn (n=1,2,3). % 2008/07/09: v2.10, minor improvements

% control input argument error(nargchk(1,2,nargin));

% check for true color image (m-by-n-by-3 array) if ndims(c)==3 if size(c,3)==3 && size(c,1)>=8 && size(c,2)>=8 c = sum(c,3); end end warning off c = logical(squeeze(c)); warning on dim = ndims(c); % dim is 2 for a vector or a matrix, 3 for a cube if dim>3 error('Maximum dimension is 3.'); end

% transpose the vector to a 1-by-n vector if length(c)==numel(c) dim=1; if size(c,1)~=1 c = c'; end end width = max(size(c)); % largest size of the box p = log(width)/log(2); % nbre of generations

% remap the array if the sizes are not all equal, % or if they are not power of two % (this slows down the computation!) if p~=round(p) || any(size(c)~=width) p = ceil(p); width = 2^p;

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switch dim case 1 mz = zeros(1,width); mz(1:length(c)) = c; c = mz; case 2 mz = zeros(width, width); mz(1:size(c,1), 1:size(c,2)) = c; c = mz; case 3 mz = zeros(width, width, width); mz(1:size(c,1), 1:size(c,2), 1:size(c,3)) = c; c = mz; end end n=zeros(1,p+1); % pre-allocate the number of box of size r switch dim

case 1 %------1D boxcount ------%

n(p+1) = sum(c); for g=(p-1):-1:0 siz = 2^(p-g); siz2 = round(siz/2); for i=1:siz:(width-siz+1) c(i) = ( c(i) || c(i+siz2)); end n(g+1) = sum(c(1:siz:(width-siz+1))); end

case 2 %------2D boxcount ------%

n(p+1) = sum(c(:)); for g=(p-1):-1:0 siz = 2^(p-g); siz2 = round(siz/2); for i=1:siz:(width-siz+1) for j=1:siz:(width-siz+1) c(i,j) = ( c(i,j) || c(i+siz2,j) || c(i,j+siz2) || c(i+siz2,j+siz2) ); end end n(g+1) = sum(sum(c(1:siz:(width-siz+1),1:siz:(width-siz+1)))); end

case 3 %------3D boxcount ------%

n(p+1) = sum(c(:)); for g=(p-1):-1:0

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siz = 2^(p-g); siz2 = round(siz/2); for i=1:siz:(width-siz+1), for j=1:siz:(width-siz+1), for k=1:siz:(width-siz+1), c(i,j,k)=( c(i,j,k) || c(i+siz2,j,k) || c(i,j+siz2,k) ... || c(i+siz2,j+siz2,k) || c(i,j,k+siz2) || c(i+siz2,j,k+siz2) ... || c(i,j+siz2,k+siz2) || c(i+siz2,j+siz2,k+siz2)); end end end n(g+1) = sum(sum(sum(c(1:siz:(width-siz+1),1:siz:(width- siz+1),1:siz:(width-siz+1))))); end end n = n(end:-1:1); r = 2.^(0:p); % box size (1, 2, 4, 8...) if any(strncmpi(varargin,'slope',1)) s=-gradient(log(n))./gradient(log(r)); semilogx(r, s, 's-'); ylim([0 dim]); xlabel('r, box size'); ylabel('- d ln n / d ln r, local dimension'); title([num2str(dim) 'D box-count']); elseif nargout==0 || any(strncmpi(varargin,'plot',1)) loglog(1./r,n,'s-'); xlabel('r, box size'); ylabel('n(r), number of boxes'); title([num2str(dim) 'D box-count']); end if nargout==0 clear r n end

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