THE USE OF SURFACE TEXTURING AND MICROSPHERES IN AQUEOUS BASED LUBRICATION

Transcription

1 THE USE OF SURFACE TEXTURING AND MICROSPHERES IN AQUEOUS BASED LUBRICATION AN ABSTRACT SUBMITTED ON THE FIFTH DAY OF April, 2016 TO THE DEPARTMENT OF CHEMICAL AND BIOMOLECULAR ENGINEERING IN PARTIAL FULFILLMENT OF THE REQUIREMENTS OF THE SCHOOL OF SCIENCE AND ENGINEERING OF TULANE UNIVERSITY FOR THE DEGREE OF DOCTOR OF PHILOSOPHY BY: Tushar Khosla APPROVED: Noshir Pesika, Ph.D. Director Lawrence Pratt, Ph.D. Vijay John, Ph.D. Damir Khismatullin, Ph.D.

2 Abstract: Several billion tons of lubricants are consumed yearly to reduce friction and wear. Modern lubricants consist either of base oils that are derived from refining crude oil (i.e., mineral base oil) and/or chemically synthesized oil (synthetic base oil). Lubricants also contain a variety of additives to impart desired characteristics such as anti-oxidation properties, corrosion resistance, etc. It is estimated that over 40% of waste lubricants end up being disposed improperly, which can potentially cause a negative impact on the environment. Hence, there is an emerging interest in formulating biodegradable lubricants or novel low friction surfaces. Aqueous based lubricants provide an eco-friendly alternative. In this thesis, two novel methods relying on (i) surface texturing, and (ii) microspheres are explored to reduce friction under aqueous conditions. Typically, a liquid medium such as oil is used to reduce friction between two surfaces. The latter prevents two shearing surfaces from achieving intimate contact, thereby reducing van der Waals interactions. There has been extensive research in the development of lubricants. However, relatively less research has focused on engineering low friction surfaces. This thesis first describes the engineering, fabrication and implementation of low friction polymer surfaces. These surfaces are inspired by the weeping lubrication mechanism of articular cartilage, which exhibits superior tribological properties (i.e., minimal surface wear and ultra-low friction). We show for the first time, that it is possible to shift the lubrication mechanism from a boundary to a hydrodynamic regime, even at a low shear velocity. This is achieved by creating vertical pores in a compliant polymer, which undergoes the necessary deformation. We hypothesize that the compressed, pressurized liquid in the pores produces a repulsive hydrodynamic force as it extrudes from the pores. The presence of the fluid between two shearing surfaces shifts the lubrication mechanism to the hydrodynamic/mixed regime thereby providing low friction. Tribological properties of these surfaces are studied for a range of applied loads and shear velocities, both relevant parameters in practical applications. Probes made of different materials are used to show that the load induced lubrication mechanism can be observed for a range of materials. The use of a traditional

3 boundary lubricant, when combined with an optimized surface texture, has the potential to provide a novel means to attain unprecedented low friction. The next section of the thesis explores the tribological properties of iron-core hard carbon microspheres (HCS), which act as micro-sized ball bearings in aqueous media. Previous work in the Pesika lab demonstrated that HCS, dispersed in an aqueous medium, are effective lubricants. However, under prolonged shearing, friction forces were found to increase. This was attributed to the squeezing out of the HCS from the contact zone region causing the two shearing surfaces to make direct contact. We hypothesize that the use of a magnetic field and iron-core HCS will maintain the particles between the two shearing surfaces for prolonged times. Iron-core HCS are successfully synthesized and preliminary studies demonstrate that the iron-core HCS are effective at lowering friction. Ongoing research seeks to determine the influence of particle size, particle concentration, and magnetic field strength on the effectiveness of magnetic iron-core HCS. The exploratory work presented in this thesis provides results to provide an initial proof of concept in using surface texturing of soft polymers and microspheres to reduce friction in aqueous medium. By improving the design and material properties of the porous polymers, we can create surfaces with ultra-low friction that can be potentially used as a coating in total joint replacement implants. Through systematic studies on the effect of magnetic field over the tribological properties of HC/Fe microspheres, it is possible to create systems in which friction can be tuned by changing the external magnetic field.

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5 THE USE OF SURFACE TEXTURING AND MICROSPHERES IN AQUEOUS BASED LUBRICATION A DISSERTATION SUBMITTED ON THE FIFTH DAY OF April, 2016 TO THE DEPARTMENT OF CHEMICAL AND BIOMOLECULAR ENGINEERING IN PARTIAL FULFILLMENT OF THE REQUIREMENTS OF THE SCHOOL OF SCIENCE AND ENGINEERING OF TULANE UNIVERSITY FOR THE DEGREE OF DOCTOR OF PHILOSOPHY BY: Tushar Khosla APPROVED: Noshir Pesika, Ph.D., Director Lawrence Pratt, Ph.D. Vijay John, Ph.D. Damir Khismatullin, Ph.D.

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7 Acknowledgements This work is dedicated to my family and my mentors who have supported me throughout my academic career and encouraged me to see learning as a life-long pursuit. I want to thank with sincere gratitude the Chemical and Biomolecular Engineering Department at Tulane University for providing me with a positive and intellectual environment and a wealth of resources and infrastructure to make this work possible. The faculty and staff have been immensely encouraging throughout my program at Tulane University. I would like to send a special acknowledgement to my adviser Dr. Noshir Pesika, whose support and guidance was instrumental in the completion of this project. I would also like to thank Dr. Vijay John, Dr. Lawrence Pratt and Dr. Damir Khismatullin for serving on my committee and providing me with numerous insights and feedbacks. I would also like to acknowledge the National Science Foundation (NSF grant CMMI ) for funding this project. And last, but not least, a special thanks to all the friends, classmates and colleagues who have trained me, advised me and with whom I shared many memorable experiences during my PhD. ii

8 Table of Contents Acknowledgements...ii List of Figures... vii List of Equations... xi List of Tables... xii List of Abbreviations... xii Chapter 1: Friction, Wear and Lubrication Friction and Friction Coefficient Mechanisms of Friction Load Controlled Friction Adhesion-Controlled Friction Elastohydrodynamic Friction Stick Slip Friction Rolling Friction Constancy of the Friction Coefficient Wear Lubrication Lubrication Regimes Dry Friction Boundary Lubrication Mixed Lubrication iii

9 1.6.4 Hydrodynamic Lubrication Motivation and Outline of Thesis Chapter 2: Structure and Tribological Properties of Articular Cartilage Structure of articular cartilage Tribological Properties of articular cartilage Cartilage inspired lubrication systems Artificial Joint Replacement Chapter 3: Load Induced Lubrication of Porous Polymers Summary Tribological Effect of Surface Texture Lubrication Regimes Lubrication Mechanism of Cartilage Biocompatibility of PDMS Load Induced Hydrodynamic Lubrication Fabrication of porous PDMS samples Creating patterned Si wafers Molding PDMS samples from the Si wafers Tribology tests of PDMS samples Friction Coefficient of Flat vs. Patterned PDMS Effect of Shear Velocity Effect of Applied Load Effect of Boundary Lubricant Effect of Pore Diameter and Spacing iv

10 3.14 Conclusion Chapter 4: Factors affecting load induced lubrication of porous polymers Summary Introduction Fabrication of porous PDMS samples Tribological Experiments on porous PDMS samples Measurement of tribological properties of PDMS samples Design of Experiments to explore the factors effecting load induced hydrodynamic lubrication Design of experiments to demonstrate the material and design independence of the proposed lubrication mechanism Effect of curvature of the shearing probe Effect of modulus (ϒ) of the PDMS sample Effect of pore depth (h) Effect of probe material Lubrication properties of PDMS with non-unifromly distributed pores Conclusions Chapter 5: Further reduction in friction through improvements in design and material properties Summary Study the combined effect of pattern and modulus of the polymer Use computer simulations to aid in optimizing the design Use Polyurethane instead of PDMS Use of Lubricin or other biocompatible lubricants instead of SDS v

11 5.6 Design and test a multi-probe prototype Test sample wear over time Conclusion Chapter 6: Synthesis of Hard Carbon/Iron Microspheres and Their Aqueous- Based Tribological Performance Summary Introduction Synthesis of the HC/Fe particles Carbon/Iron microspheres characterization Experimental Setup Tribological properties of the HC/Fe microspheres Influence of particle size on the stability of the lubrication properties Study the effect of strength of magnetic field on lubrication properties of HC/Fe microspheres Conclusion List of References Appendices vi

12 List of Figures Figure 1: Schematic of Load Controlled Friction (As adopted from [1]). The total friction force is independent of the area of contact Figure 2: Schematic of Adhesion Controlled Friction (As adopted from [1]) showing that adhesion controlled friction is dependent on the number of contact points and hence the actual or true area of contact Figure 3: A friction vs. time graph showing stick slip motion Figure 4: Schematic of Stribeck s curve showing the various lubrication regimes as a function of lubrication parameter Figure 5: Various lubrication regimes as described by Stribeck s curve (A) Dry lubrication when the two sliding surfaces make direct contact (B) Boundary lubrication in which a thin layer of boundary lubricant is present between the sliding surfaces that reduces friction (C) Mixed lubrication regime, where there is a thin fluid layer present between the two sliding surfaces but there are still points of direct contact (D) Hydrodynamic lubrication regime, where the two sliding surfaces are separated by a layer of lubricant of thickness d such that the asperities never come in direct contact leading to low friction and wear Figure 6: Model of cartilage porous structure as described by Greene et al. [67]. (A) The cartilage is described as a network of springs. (B) As the load is applied, the synovial fluid is directed out of these pores Figure 7: Schematic illustration of the mechanism by which a thin fluid layer forms between a spherical glass surface and a porous polymer surface under an applied load. The thin film vii

13 remains as the glass probe is sheared over the polymer surface at a constant velocity V Figure 8: (A) Top view SEM image of a porous polymer surface. Scale bar = 200 µm. (B) Cross sectional side view of a porous polymer surface. Scale bar = 50 µm Figure 9 : (A) Plot of a typical friction force vs time while shearing a glass probe on a PDMS surface for various test conditions: PDMS under dry conditions (Red - sample set 1), flat PDMS with water (Blue - sample set 2), textured PDMS under dry conditions (Green - sample set 3) and textured PDMS under water (Light blue - sample set 4) (B) Plot of the average coefficient of friction between a spherical glass probe and the polymer surface under various conditions. The applied load in all cases was 49 mn and the shearing speed was 100 µm/s Figure 10: Plot of the coefficient of friction between a spherical glass probe and a porous PDMS surface as a function of shear velocity Figure 11: Plot of the coefficient of friction between a spherical glass probe and a porous PDMS surface as a function of applied load, using water as the lubricating fluid. The inset in shows the typical measurement of the coefficient of friction (data in red) with increasing applied load (data in blue) Figure 12: (A) to (E), Images taken from underneath the PDMS sample for an applied load of 5, 15, 25, 35 and 45 g respectively. It can be seen that the area of contact increases with the increase in applied load Figure 13: Plot of the coefficient of friction as a function of SDS concentration for a flat surface of PDMS (red line) compared to a textured surface of PDMS (green line). The preload was 45 mn and the shear velocity was maintained at 100 µm/s viii

14 Figure 14: Selection of a unit cell to calculate porous fraction Figure 15: Schematic illustration of the proposed load induced hydrodynamic lubrication mechanism. The radius of curvature (r) of the shearing glass probe, the modulus (ϒ) of the PDMS sample and the depth (h) of the pores are explored in this chapter Figure 16: An optical micrograph (20X, top view) of the PDMS sample fabricated with channels 40 μm wide spaced 20 μm apart Figure 17: Plot of the average friction force (Fx) between spherical glass probe of different radii and the PDMS polymer under aqueous conditions. In each case, 100 g load was applied at a shear speed of 200 μm/s Figure 18: Schematic of the proposed underlying mechanisms. (A) Domain I: pores get completely closed causing boundary lubrication. (B) Domain II: Shows the load induced hydrodynamic lubrication. (C) Domain III: There is always a layer of water present between the relatively flat probe and the patterned PDMS sample Figure 19: Plot of the average friction force (Fx) for patterned PDMS samples of different compressibility made by changing the ratio of polymer to cross linker when sheared against a glass probe at 0.2 mm/s under a normal load of 98 mn Figure 20: (A) to (C) shows the 3-D profilometer characterization of PDMS samples of height 4.4 μm, 15.4 μm and 23.4 μm respectively Figure 21: Plot of the average friction force (Fx) for PDMS samples of different depths (h) when sheared against a glass probe at a speed of 98 mn under an applied load of 98 mn ix

15 Figure 22: Comparison of friction forces (Fx) between a flat and patterned PDMS sample with a steel (grey), ceramic (yellow) and plastic (blue) probe of 0.25 diameter under dry and aqueous conditions. The applied load in each case was 49mN and the shearing speed was 0.2mm/s Figure 23: (A) Optical micrograph of the top view of a section of the non-uniform PDMS sample. (B) Plot of average friction force (Fx) for a non-uniform PDMS sample and a glass probe under dry and aqueous conditions under 49 mn applied load at 0.2 mm/s Figure 24: Setup to measure the Young s modulus of soft polymers using CETR UMT-2. A steel disk is connected directly to the force sensor of UMT and the force required to compress the polymer in small increments of 0.01mm is measured to calculate the Young s modulus Figure 25: Schematic of expected behavior of coefficient of friction by changing the porosity of the sample Figure 26: Simulation of a hard sphere shearing against a porous polymer in a Newtonian liquid Figure 27: 3-D simulation of a hard sphere sheared against a porous polymer having an array of pores in a Newtonian fluid Figure 28: Comparison of friction force between a glass probe and polyurethane samples in various test conditions at an applied load of 50g Figure 29:(A) A schematic of a multi probe prototype. (B) A setup using four glass probes to test the tribological properties of porous polymers when load is applied at multiple points. (C) Plot of friction force (Fx) in dry and aqueous conditions for a porous polymer when a 150 g load is applied across multiple points and sheared at 200 μm/s...80 x

16 Figure 30: (A) and (B) 20X and 50X optical micrographs of PDMS sample showing no signs of wear after over three hundred test cycles Figure 31: SEM images of HC/Fe microspheres (A) to (C) with mean size of 700nm, 2 μm and 2.5μm respectively (D) shows the TEM micrograph of a 700 nm HC/Fe microsphere. (E) Shows the EDS of the 700 nm HC/Fe microspheres confirming the presence of C and Fe with their characteristic peaks at 2.3 KeV and 8, 9 KeV respectively Figure 32: Schematic diagram of the proposed lubrication mechanism. The glass lens is cemented on a magnet pillar as the probe to measure the friction against a Si wafer in a dispersion of HC/Fe microspheres Figure 33: Comparison of friction coefficient (μ) of four different sizes of HC/Fe microsphere suspensions as lubricant between a glass probe and Si wafer shearing at 200 μm/s with loads increasing from 10g to 450g Figure 34: Plot of the coefficient of friction μ versus shear cycles for an extended run at a fixed load of 2 N using a spherical glass lens sheared against a silicon surface, with an aqueous 1 mg ml -1 HC/Fe microsphere 3.5 mm-sds suspension as the lubricant List of Equations Equation 1: The Amontons law... 2 Equation 2: The mechanistic derivation of Amontons law... 2 Equation 3: Derjaguin s modification of Amontons law... 4 Equation 4: Modified Amontons law... 6 xi

17 Equation 5: Force between two parallel surfaces shearing in a Newtonian fluid of viscosity η Equation 6: Calculation of surface porosity Equation 7: Hertz equation of contact between a sphere and elastic half space Equation 8: Calculation of effective modulus for non-adhesive contact between two surfaces Equation 9: Approximation for effective modulus for non-adhesive contact between the surfaces when one surface is significantly less compliant than the other Equation 10: Dependence of depth of indendendation to radius of curvature of the probe according to Hertz theory of contact mechanics List of Tables Table 1: Summary of results of effect of Porous Fraction on coefficient of friction Table 2: Modulus of PDMS of different cross-linker to polymer ratio as measured by the set up described in section List of Abbreviations μ F L v A Coefficient of Friction Friction Force Normal Load Shearing Velocity Area of Contact xii

18 σ η D P PVA PDMS PVA-PVP UHWPE MOM COC SDS DI OTS r ϒ ν SEM TEM HC/Fe Shear Stress Fluid Viscosity Distance between the shearing surfaces Load per unit length Polyvinyl alcohol Poly dimethyl siloxane Polyvinyl pyrrolidone Ultra High Molecular Weight Polyethylene Metal on Metal Ceramic on Ceramic Sodium Dodecyl Sulphate Dionized water Octadecyltrichlorosilane Radius of curvature of the probe Elastic modulus Poisson's ratio Scanning Electron Microscope Transmission Electron Microscope Iron Core Hard Carbon Spheres xiii

19 1 Chapter 1: Friction, Wear and Lubrication 1.1 Friction and Friction Coefficient Friction is the reaction force that resists the motion between shearing surfaces. The shearing surfaces could be solid surfaces, fluid layers or any material elements sliding against each other. In other words friction is an inherent consequence of motion and is often referred to as a non-conservation force because it involves energy loss or dissipation, mechanical (potential or kinetic energy) into heat [1]. Friction has a significant effect on global economy and is directly or indirectly responsible for over 2% of the gross national product in the industrial countries [2]. Tribology is the study of friction, wear and lubrication. The first recorded studies of tribology can be traced back to 1880 BC when the Egyptians used lubricants (oil or water) to reduce the friction between the sleighs that supported statues weighing several tons and the wooden boards on which those sleighs were sliding [3]. Leondardo da Vinci did the first quantitative studies of friction when he measured the force needed to slide wooden and iron blocks over boards of wood and iron [4]. Through his experiments, he was able to observe and conclude that friction force is proportional to the applied load (weight of the blocks) and independent of the area of contact. These observations were later confirmed by Amontons [5] and Coulomb

20 2 [6], who also noticed that the friction force is independent of the velocity of motion between the two objects. The results are summarized in Amontons law (independent of A and V) μ = F L Equation 1: The Amontons law where: is the friction coefficient F is the friction Force L is the applied load A and V are the apparent or the macroscopic area of contact and the speed of shearing between the two sliding elements. A simple geometric or mechanistic explanation was sufficient to describe the observations made in Amontons law. Since each surface was considered to have asperities, in order to shear or move across each other, the asperities of one surface would have to rise above those of the other. The lateral friction force Fi needed to move the i th asperity over the i th junction, equals the applied load Li multiplied by the tan i, where i is the slope of the i th asperity junction. When averaged over all asperities, the space-averaged angle was considered constant, hence <tan i> is constant. The total friction force F can be given by, F = Fi = Li tanθi = <tanθi>l = μl Equation 2: The mechanistic derivation of Amontons law

21 3 With the advancements in the field it is now known that the equation 1 is not valid over a large range of loads and sliding velocities [7]. It is to be noted that all the terms in Amontons law refer to macroscopic or in other words space and time averaged values [8]. Thus, friction can be considered independent of the area of contact A as long as we consider the contact area to be the apparent or the projected geometric area instead of the real contact area at the molecular level. Similarly, the velocity of shear V is also the mean or the average velocity of shear at the macroscopic level and not the actual velocity at the micro junctures at the asperities. These micro junctions can be at considerably different velocities or even in stick-slip motion, characteristic when friction changes from static to kinetic. Also the effect of material elasticity and adhesion are completely ignored in the classical discussion of Amontons law. [9] Bowden and Tabor through their experiments of studying electrical conductivity at a metal interface, showed that the area of contact at the interface was directly proportional to the applied load [10]. This was in contradiction with Hertz theory of contact mechanics that explained the contact between two elastic bodies in non-adhesive contact [9]. His theory predicted the relationship between the area of contact A, for a sphere of radius R and a flat surface at a load L is such that A (RL) 2/3. There were some other contradictory studies such as those from Maugis and Pollock [11] that showed that for metal micro-contacts, the area of contact A R 1/2 L. Greenwood and Williamson provided some reconciliation when they showed through Hertz theory that for two rough, non-adhering surfaces, the area of contact is proportional to the applied load as long as the asperities are distributed in a Gaussian

22 4 manner and are deformed elastically [12]. However, even the Greenwood and Williamson theory is highly dependent on the experimental or theoretical conditions and some assumptions in the model are controversial. To this extent Greenwood along with JJ Wu published another article in 2001 highlighting and discussing the fundamental assumption of assuming the peaks on a rough surface [13]. In that publication, the idea of 3-point peaks (where each point on the surface higher than the neighboring two points was considered as a peak) was reconsidered in determining the surface roughness. To sum up, in the studies discussed so far, the work done to move the asperity of the top surface over those of the bottom surface has been considered as the origin of friction for non-adhering shearing surfaces. So far, we have only considered models that assumed no adhesion between the two sliding surfaces. To complete the discussion, it is important to consider the model proposed by Derjaguin [14]. According to him, in order to account for intermolecular adhesive forces, a constant internal load L0 is added to the internal load L. His model accounted for his experimental observation that showed that there is a friction force F0, even at zero loads for adhering surfaces. F = μ(l0+l) = F0 + μl Equation 3: Derjaguin s modification of Amontons law Although this equation provides some insight into the friction coefficient at no load (or zero load), it s solution gives = at zero load, which is contradictory to common observation and convention in which friction coefficient is defined as the slope of the measured friction force versus applied load, df/dl= =constant.

23 5 1.2 Mechanisms of Friction Load Controlled Friction Amontons law in its classical sense explains the load-controlled friction mechanism (equation 1), in which the friction force is proportional to the applied load and is independent of the area of contact. This is only true for non-adhering surfaces. Figure 1 schematically illustrates this concept of how the load-controlled friction is only dependent on the applied load and is independent of the area of contact and the geometry of the shearing surfaces. L L ⅓ L ⅓ L ⅓ L µl ⅓µL ⅓µL ⅓µL Figure 1: Schematic of Load Controlled Friction (As adopted from [1]). The total friction force is independent of the area of contact Adhesion-Controlled Friction The molecular origin of friction and adhesion can be explained based on the interaction potentials between the molecules of the interacting surfaces [1], such as the Lennard-Jones potential. However, while the adhesion force between two surfaces is independent on the atomic scale (or mathematical) roughness of the two surfaces, friction is not. As described by Derjaguin, friction for adhesive surfaces can

24 6 be considered as having two independent and additive components, an external load dependent and contact area independent component and an additional internal adhesion-dependent contribution. This adhesion contribution is present even at zero loads and even at negative loads as long as the two surfaces have a finite area of contact [15]. Adhesion during shearing of two surfaces can be attributed to the breaking and reforming of the intermolecular bonds during the sliding of surfaces over one another [16]. Since the number of bonds is directly proportional to the density of atoms in the intermolecular space and the area of contact between two perfectly flat surfaces (mathematically speaking), the adhesion component of the friction force can be considered proportional to this real contact area. It should be noted that for rough surfaces (practically all surfaces) the real contact area would be different from the apparent projected contact area. This is particularly important for soft elastic surfaces. This is shown schematically in Figure 2. The modified Amontons law summarizes the load dependent and adhesion dependent components of friction F = μl + σa Equation 4: Modified Amontons law where: F is the Friction force is the coefficient of friction L is the applied normal load

25 7 is the shear stress between the surfaces A is the real area of contact between the surfaces KA KA₁ KA₂ KA₃ µka µka₁ µka₂ µka₃ Figure 2: Schematic of Adhesion Controlled Friction (As adopted from [1]) showing that adhesion controlled friction is dependent on the number of contact points and hence the actual or true area of contact Elastohydrodynamic Friction This arises when there is a fluid film present between two solid surfaces, giving rise to viscous and hydrodynamic forces [17]. It can also arise due to shear induced melting, when a thin layer of solid melts or behaves more like fluid [18]. In the presence of a liquid layer between them, the hydrodynamic repulsive forces (short range solvation, steric-hydration, double-layer repulsion) keeps the two surfaces from making intimate contact (at least at the molecular level). In such a case of a fluid film trapped between the two surfaces, the shear stress as described in the previous segment is now given by =(viscosity of the liquid)*(sliding velocity)/(fluid film thickness). The fluid film thickness is also dependent on the applied load L (A L 2/3 for both Hertzian and JKR contacts.

26 Stick Slip Friction It is a common observation that the force required to initiate sliding motion is higher than the force needed to maintain the sliding. The friction coefficient to initiate sliding is called the static coefficient of friction and the friction coefficient after the sliding starts is called kinetic coefficient of friction [19]. Stick-slip is a form of nonuniform friction and is a direct consequence of static friction being higher than the kinetic friction and the kinetic friction decreasing with an increase in sliding speed [20]. Instead of smooth sliding at a constant speed, during stick-slip motion sliding occurs as a sequence of sticking and slipping or as an oscillation. This effect can be seen as a sawtooth motion when the measured friction force is plotted versus the time as shown in Figure 3. Stick-slip friction is responsible for a number of common phenomena such as creating musical notes from guitars and violins and in the wear of machinery. At the molecular level, stick-slip is a complicated phenomenon and can only be described with complex theoretical analysis [21].

27 Frition Force, F x (g) time (s) Figure 3: A friction vs. time graph showing stick slip motion Rolling Friction Rolling friction occurs when there is a wheel or ball-bearing rolls between two shearing surfaces essentially leading to no slip [22]. Presence of ball or roller bearings provides excellent lubrication properties at high loads and speeds. To minimize the loss of energy and have low rolling friction it is important to have the roller bearings made of materials with high elastic modulus and hardness. 1.3 Constancy of the Friction Coefficient The simple Amontons equation is valid for the majority of shearing surfaces involving ductile, brittle, rough and smooth surfaces (as long as they are non-adhesive

28 10 or not atomically smooth). Section 1.1 describes the conditions and theories for exceptions in Amontons law. It shall however be emphasized that the simple concept of attributing the friction to the work done by the asperities of the top surface to overcome those of the bottom surfaces as described by early researchers (Coulomb, Cobblestone etc) in this field is valid for most practical scenarios. The Bowden-Tabor theory and the Greenwood-Williamson models all lead to the derivation of Amontons law considering the real area of contact. Even the molecular simulations that account for local forces, when integrated point towards a constant friction coefficient [23, 24] for a certain system. Although the value of coefficient of friction is material dependent and varies with external conditions e.g. humidity, surface morphology, it is tabulated in many engineering handbooks and manuals [25] and is widely used in the design of machinery, construction industry and other various practical applications. It is for these reasons that the coefficient of friction will be used widely as a parameter to compare the lubrication properties of the various systems described in this research. 1.4 Wear Wear is the removal or deformation of a substance from the surface of a body as a result of sliding or shearing motion against another body [22]. Wear is a direct consequence of the friction and is responsible for failure of machinery, accidents and economic consequences. Numerous studies have been published to model and describe the mechanism [26-29] of wear. The wear rate is defined as the volume of material lost as a function of sliding distance. Various tests methods have been

29 11 described to measure and quantify the wear rate e.g. ASTM G-2 committee and the Society for Tribology and Lubrication Engineering (STLE) have described a large number of tests to measure wear. It shall however be noted that owing to the complex nature of wear mechanisms all of these tests are system specific and have some inherent limitations [30]. Hence, it is important to consider wear testing in conditions that closely simulate the exact nature and conditions of the actual conditions. This can sometimes be extremely difficult as it is not always possible to recreate the exact field conditions in a lab. Simulations are often used to determine the wear rate and the working life of materials [31, 32]. In this work, we rely on a simple optical microscope comparison of our samples to look for signs of wear. 1.5 Lubrication When dry solid materials such as metals, ceramics and most polymers shear against each other, they often result in high friction and wear [20]. A lubricant is a substance that is introduced between two sliding surfaces with the aim of reducing the friction between two sliding surfaces in mutual contact. The benefits of using liquids and greases as lubricants were discovered long back as some archeological evidence have shown presence of animal fats on wheels and the use of water as lubricants by ancient Egyptians [3]. Today, lubricants play an essential role in the operation of several important technologies such as internal combustion engines, vehicles, gear systems, compressors, turbines, hydraulics etc. Lubricants are also used extensively in various small-scale technologies such as hard disks drives [33], micro-electromechanical systems (MEMs) [34] etc. The main purpose of a lubricant

30 12 is to reduce the intimate contact between the two shearing surfaces, thereby reducing friction and wear. In some cases, it also acts as a coolant and prevents expansion of metals due to heating. 1.6 Lubrication Regimes Thurston in 1870s developed one of the first machines that could directly measure the coefficient of friction [35] to study the friction between steel wheels for railroad purposes. His results were similar to those published later by Stribeck in Stribeck performed systematic experiments to study the effect of liquid lubrication at various conditions in journal bearings [36]. The graphs of friction force as plotted against a dimensionless quantity called the lubrication parameter are commonly known as Stribeck s curve (or Stribeck s plots). The lubrication parameter is defined as V/P, where is the dynamic viscosity of the fluid (Ns/m 2 ), V (m/s) is the shear velocity and P is the applied load per unit length on the bearing surface (N/m). It is considered as an important parameter in identifying suitable lubricants for a given application [37].

31 Friction Coefficient (μ) 13 Dry Friction Boundary Lubrication Mixed Lubrication Hydrodynamic Lubrication Elastohydrodynamic Lubrication Parameter V/P Figure 4: Schematic of Stribeck s curve showing the various lubrication regimes as a function of lubrication parameter Figure 4 shows the various lubrication regimes as described by Stribeck s curve [38]. On the vertical axis is the log of friction coefficient (log ) and on the horizontal axis is the lubrication parameter ( V/P). Moving along the Stribeck curve left to right, the lubrication regimes can be described as follows: Dry Friction The friction between molecularly smooth surfaces is caused by interfacial interaction in the contact zone [39]. These interactions are proportional to the Hamaker constant, which is a material dependent property. When the two solid surfaces are shearing without any lubricant between them, the surfaces are in direct contact and result in high friction and wear rates. This usually occurs at extremely high loads or slow speeds when the lubricant is squeezed out completely from the contact zone. It is represented schematically in Figure 5 (A) when there is no lubricant present between the shearing surfaces.

32 Boundary Lubrication In this regime, a thin layer of lubricant (typically a couple of monolayers thick) e.g. oil exists between the two shearing surfaces. The van der Waals attractive forces are decreased due to a decrease in the Hamaker constant [1]. It should be noted that in order to be effective, the thickness of the lubricating layer should be at least larger than the surface asperities of the shearing surfaces to avoid direct contact and high friction. As the surfaces shear across each other, the boundary lubricant can be squeezed out of the contact zone and thus needs to be continuously replaced. In order to avoid this, some commercial lubricants are blended with small percentage of additives that bind strongly to the shearing surfaces and thus provide boundary lubrication when the machines are starting or coming to a halt (slow speeds and high load conditions). Figure 5 (B) shows the schematic for this lubrication regime Mixed Lubrication Moving further right in the Stribeck s curve, the mixed lubrication regime is observed. In this regime, there is a layer of lubricant present between the two sliding surfaces but the surface roughness still plays an important role [40]. As practical surfaces are not smooth, there are some points of direct contact between the two sliding surfaces in mixed lubrication regime. This regime is characterized by a decrease in friction as the lubrication parameter increases and is represented schematically in Figure 5(C).

33 Hydrodynamic Lubrication In this regime a layer of liquid separates the two shearing surfaces so that they never come in intimate contact. The pressurized fluid film protects surfaces from wear as they are not in contact and also reduces the friction force. The viscous shear force FII between two parallel surfaces of area A, sliding at a relative velocity VII, separated by a distance D by fluid of viscosity is given by FII= ηavii D Equation 5: Force between two parallel surfaces shearing in a Newtonian fluid of viscosity η It can be easily observed that lubrication in this regime does not follow Amontons law and is directly proportional to the shearing velocity and the area of contact. This regime is usually observed at conditions of low load and relatively high velocity. It can also be seen that friction force is inversely proportional to the distance of separation D, between the sliding surfaces. Thus, it is intuitive that at some separation distance D, there will be a minimum in Stribeck s curve. This minima is usually observed in the elastohydrodynamic lubrication regime in which the separation distance D is small enough such that the pressure generated in the fluid layer can elastically deform the surface asperities. Even though the separation distance D, is small, it is still significantly larger than the surface roughness and hence the regime is characterized by low friction and wear. Figure 5 (d) schematically represents the hydrodynamic lubrication regime.

34 16 A B C D d Figure 5: Various lubrication regimes as described by Stribeck s curve (A) Dry lubrication when the two sliding surfaces make direct contact (B) Boundary lubrication in which a thin layer of boundary lubricant is present between the sliding surfaces that reduces friction (C) Mixed lubrication regime, where there is a thin fluid layer present between the two sliding surfaces but there are still points of direct contact (D) Hydrodynamic lubrication regime, where the two sliding surfaces are separated by a layer of lubricant of thickness d such that the asperities never come in direct contact leading to low friction and wear. 1.7 Motivation and Outline of Thesis Over 40 billion tons of lubricants are consumed globally mainly to reduce friction and wear [41]. Lubricants are composed of base oil (or a mixture of base oils) and a variety of additives to impart desired characteristics such as anti-oxidation properties, corrosion resistance etc. Over 40% of the waste lubricants end up being disposed in the environment and as a result, there is an emerging stress on ecofriendly and biodegradable lubricants. One approach to minimize the environmental impact on lubricants and to develop lubricants which are safer for food grade and biocompatible requirements, is to develop aqueous based lubrication systems.

35 17 This thesis demonstrates two ways to reduce friction in aqueous conditions. The first part of this thesis discusses design and fabrication of low friction polymer surfaces inspired by articular cartilage. The second half of this thesis discusses the synthesis and tribological properties of Iron core-carbon microspheres under aqueous conditions. Chapter 2 discusses the weeping lubrication mechanism of cartilage. Chapter 3 presents a novel lubrication method to induce hydrodynamic lubrication even at low speeds by creating pores in compliant polymers. Factors affecting the load induced lubrication mechanism are explored further in Chapter 4. Chapter 5 describes some initial results and provides insights for further reducing the friction by design optimization. In Chapter 6, an initial study describing the synthesis and lubrication properties of iron core carbon microspheres is presented.

36 18 Chapter 2: Structure and Tribological Properties of Articular Cartilage 2.1 Structure of articular cartilage Cartilage is a connective tissue found in many areas of the body including the joints between the bones [42] e.g. knee joint, hip joint etc. Cartilage has unique structural and mechanical properties. It is often considered as a viscoelastic material which is softer and less rigid than bones, but it is stiffer and more flexible than the supporting muscles [43]. It is composed mainly of water (60-80%), collagen and a small volume of cells (chondrocytes) [44]. Typically, cartilage supports the joints and facilitates joint movements throughout the life span of the organism. It acts as a very effective lubrication system, which provides low friction and wears resistance over a range of shear velocities and loads. Cartilage has a coefficient of friction of [45]. Though there is still some debate about the microstructure of cartilage among various species, recent findings from Gwynn et. al. using scanning and transmission electron microscopy suggest that the collagen fibrin are arranged in a honey comb like structure with an array of open and parallel tubular pores that are approximately 1~2 μm in diameter [46, 47]. The structure of articular cartilage is organized into three vertical zones through its depth. The top 10 to 20% of the total thickness is

37 19 called the superficial tangential zone which is rich in collagen fibers nm in diameter woven in planes parallel to the articular surface [48, 49]. The middle zone extending from 40 to 60% of the total thickness consists of fibers that are randomly oriented and homogeneously dispersed. The fibers extending in the remaining 30% of the cartilage depth (also called the deep zone) form larger radially oriented network [50]. Thus, articular cartilage can be considered as an inhomogeneous tissue with composition and structure varying throughout the depth of the tissue. This vertical variation in structure and composition of articular cartilage leads to some very unique and interesting mechanical properties. The tensile stiffness in the top most zone is greater than that in the deep end [51, 52]. Cartilage is also shown to exhibit inhomogeneity in compression stiffness, which contrary to the tensile stiffness, increases as we move away from the articular surface [53, 54]. The compressive modulus of cartilage in the depth direction is also smaller than in a plane perpendicular to it [55]. One functional significance of the depth-dependent inhomogeneity in the articular cartilage is the interstitial fluid pressurization, which is believed to be responsible for the exceptional lubrication properties and low wear rate of the cartilage [56]. 2.2 Tribological Properties of articular cartilage Traditional lubrication theories of boundary lubrication and fluid film lubrication were extended since the 1950s to explain the lubrication properties of the articular cartilage [42]. None of these theories could comprehensively explain the tribological properties of the articular cartilage over a range of physiological conditions. It was established that the unique lubrication properties of cartilage are linked with its microstructure [57]. The cartilage is not connected to the body s

38 20 circulatory system. It is surrounded by extra cellular fluid, called the synovial fluid [58]. Synovial fluid also runs through the pores of the cartilage network. The cells in cartilage get their nutrients by diffusion from the synovial fluid. The porous structure of cartilage works synergistically with the synovial fluid to provide the excellent tribological properties of the cartilage. The synovial fluid contains hyaluronic acid (HLA), surface-active phospholipids (e.g. phosphatidylcholine) and superficial zone proteins (e.g. lubricin) [59, 60]. In the presence of water, it also traps some proteoglycans bounded with glycosaminoglycan side chain e.g.. chondroitin sulphate and keratan suphate [61]. The proteoglycan concentration is highest in the middle zone of the cartilage, followed by the deep zone and is least in the superficial top zone [62]. Though the specific role of these molecules is debated, there is an agreement that they are responsible for providing wear resistance and boundary lubrication at static contact and slow shear velocities [63]. At higher shear velocities, the mechanism shifts to elasto-hydrodynamic or hydrodynamic lubrication. Soltz and Athesian have shown that under a compressive load, the friction in articular cartilage is inversely proportional to the pressure in the interstitial fluid [64, 65]. It is proposed that the load applied on the cartilage is supported by the pressurized interstitial fluid, which prevents the two surfaces to come in contact and reduces wear. The rate and the direction of the interstitial fluid flow depends on the microstructure of the solid porous network within the cartilage [66]. Green et. al. [67] proposed a model of cartilage lubrication based on the tubule pore structure as reported by Gwynn et. al [68]. The model is described schematically in Figure 6.

39 21 A B Figure 6: Model of cartilage porous structure as described by Greene et al. [67]. (A) The cartilage is described as a network of springs. (B) As the load is applied, the synovial fluid is directed out of these pores. According to their model, the cartilage is assumed to be an array of porouswalled capillary channels. These channels determine axial porosity. They are connected by a network of lateral pores made up of counter spiraling fibrils that result in the formation of a lattice structure. Initially, as the load is applied, the interfacial fluid is directed out of the axial pores and becomes pressurized in the confinement between the two shearing surfaces. This pressurized fluid film is expected to bear the bulk of the load. The pore matrix [69] regulates the flow of the interstitial fluid. When load is applied, the collagen deforms non-uniformly, resulting in a significant decrease in lateral porosity while the axial porosity is mostly unchanged. This restricts the flow in lateral direction and most of the fluid flows axially in the confined region between shearing surfaces where it gets pressurized. The interstitial fluid has a high density of immobile charge centers on the proteoglycan complexes that get entangled in the fibril network of the collagen. Proteoglycans are inherently negatively charged and they attract a lot of cations, creating a charge imbalance and an osmotic pressure. The presence of charged proteoglycans also creates electro static repulsion forces when the cartilage is compressed under load. As the cartilage continues to compress under the load, the

40 22 electrostatic repulsion forces and osmotic pressure produced by the charged groups bound to proteoglycans prevent the collagen from collapsing by increasing the effective stiffness of the cartilage. This also results in slowing the rate of flow in the axial direction, thereby prolonging the liquid load support. This mechanism of lubrication is unique to biphasic materials in which one phase is a soft porous material whose pores are filled with a liquid. This mechanism is also referred to as weeping lubrication. The porous material complies under the load and the pressurized fluid film provides the tribological properties. 2.3 Cartilage inspired lubrication systems Due to its excellent tribological properties, some groups have tried to mimic the mechanism of cartilage lubrication using polymers. Hydrogels, such as Polyvinyl alcohol (PVA) [70] or hydrogel composites like PVA-chitosan [71], PVA-PVP (poly vinyl pyrrolidone) [72] have been studied and used as a replacement for cartilage as they have excellent lubrication properties and modulus comparable to articular cartilage. Timothy et. al. studied lubrication properties of PVA functionalized with organic fatty acid derivatives to act as boundary lubricants [73]. Green et. al demonstrated a reconstituted cellulose based system to mimic the porous structure of cartilage. This system was enriched with immobilized polyelectrolytes that served as boundary lubricants [74]. In this project, we mimic the porous structure and the weeping lubrication mechanism of the cartilage by creating pores in a compliant polymer.

41 Artificial Joint Replacement Although cartilage has excellent tribological properties, injury, disease or age can cause damage to the cartilage. Since cartilage is not connected to the body s circulatory system, this results in very limited repair and leads to increased pressure on the bones causing pain while a person is moving [75]. Total joint replacement surgery (TJR) is an established method to replace the natural worn out materials with artificial ones. In knee implants, a ball shaped femoral component is attached to the patella and a flat tray is attached to the tibia [76]. The femoral head is usually made up of a cobalt-chrome alloy and the flat tibia tray is made up of Ultra High Molecular Weight Polyethylene (UHWPE) [77]. One of the leading causes of knee implant failure is delamination of UHWPE because of wear caused by fatigue [78, 79]. Corrosion of the chromium-cobalt alloy also leads to producing sharp metal debris in the vicinity of the knee joint [79]. The debris from the femoral head or the tibial tray can also lead to an immune response causing inflammation and pain. To improve the wear resistance of UHWPE, various methods are tried including irradiation to increase cross-linking and adding additives to prevent oxidation [80]. Another approach is to make the femoral ball with ceramics such as Oxinium. Ceramics offer better scratch resistance, lower coefficient of friction and are much harder than metals, but they are also brittle [79]. Titanium, due to its biocompatibility, lower modulus and enhanced corrosion resistance, is also used as an alternative however its use is limited due to poor shear strength and wear resistance [81]. Some research groups tried coating the metals surface with diamond-like carbon to reduce friction. They have so far achieved limited success as carbon layer comes out exposing the underlying material [82]. It is

42 24 proposed that one of the potential applications of the cartilage inspired low friction polymer surfaces described in this thesis can be used as coatings on the metal (steel) ball in total joint replacement surgeries. Such a coating is expected to provide low friction wear, and enhanced durability. The next two chapters describe this idea and show the proof of concept and discuss the factors affecting the tribological properties of such surfaces from a materials prospective. However, studies to do perennial in vitro durability tests or in vivo testing of such samples are beyond the scope of this research.

43 25 Chapter 3: Load Induced Lubrication of Porous Polymers 3.1 Summary This chapter presents an exploratory study of the tribological properties and mechanisms of porous polymer surfaces under applied loads in aqueous media. It is hypothesized that the compressed, pressurized liquid in the pores produces a repulsive hydrodynamic force as it extrudes from the pores. The presence of the fluid between two shearing surfaces results in low coefficients of friction (μ 0.31). The coefficient of friction is reduced further by using a boundary lubricant. The tribological properties are studied for a range of applied loads and shear velocities to demonstrate the potential applications of such materials in total joint replacement devices. 3.2 Tribological Effect of Surface Texture Surfaces have unique properties and an inherent topography that is often different than the bulk material [83]. Surface engineering is the discipline of creating materials with smart properties by modifying the surface texture or chemistry. Surface engineering has been studied since 1900s and with an enhanced understanding of surface phenomena at the micron and nano scale, it has gained traction in the last few decades [84]. It is currently applied in an array of applications including semiconductor manufacturing [85, 86], biomedical applications [87, 88], dry adhesives design [89, 90],

44 26 micro-fluidics [91, 92], self-cleaning surfaces [93, 94], oil recovery and remediation [95, 96] etc. Although significant advances have been made in developing better and improved lubricants, limited research has been done to create surfaces with reduced friction. Surface texturing can be defined as the introduction of intentional, regular surface asperities such as grooves, dimples or channels to modify the physical or chemical behavior of the surfaces [97]. The effect of surface texturing on the tribological properties of sliding materials was first studied systematically by Hamilton in 1966 [98]. In his experiment he studied the effect of micro-irregularities on the interaction of lubricant and parallel shearing surfaces of a rotary-shaft face seal as a function of speed, viscosity and surface-asperity dimensions. It was seen that the presence of cavities enhanced load support. Anno et al. verified the theory a few years later and established that microasperities were important in enhancing lubrication for load bearing mechanical face seals [99] and parallel rotating thrust bearings [100]. Since then, many groups, through simulations and experimental research have shown that the presence of micrometer scale textures can modify the tribological characteristics of two sliding surfaces. The increased momentum in this area in the last two decades can be attributed to enhancement in computational resources and the improvements in surface texturing techniques such as laser surface texturing, photolithography and micro contact printing. Laser surface texturing has been used extensively to study the effect of microirregularities over hard materials such as metal alloys and ceramics. Effect of surface texturing on sapphire discs [101] was published by Blatter et al, while Pettersson and

45 27 Jacobson studied coated silicon discs [102]. Dumitru et al. studied steel discs [103] with micro-cavities at low speeds. Several other groups have shown similar studies with other materials, Gerbig [104] et al (ceramic plates), Wakuda [105] et al. (silicon nitride plates) etc. All these and many other studies have shown that laser texturing improves the tribological properties of the material by reducing friction and wear [106]. Tribological behavior of softer materials such as polymers have distinguishing features, as it becomes important to consider the true contact area, shear and rupture of rubbing materials and the strength of the interfacial bonds [ ]. These factors are responsible for some unique features in polymer tribology, e.g. it is well known that the coefficient of friction is proportional to applied load (Amontons law). However for polymers, it is inherently true for only a certain range of load (5-100 N) [110]. Outside this range the friction coefficient is no longer proportional to the applied load, in fact for low to moderate loads ( N) friction coefficient actually decreases with increase in load [111]. Temperature [112] [113] also play an important role in the tribological behaviors of polymers. These unique properties of polymers makes the study of effect of surface texturing on polymers more challenging and interesting. With the advances in photolithography and contact lithography some groups have studied the effect of surface texturing on soft materials such as Poly (dimethylsiloxane) [114] and Poly (methylene) [115]. These studies have shown that it is possible to modify the friction coefficient of polymers by changing the surface pattern. It is also seen from these and other studies [116] in literature that the friction coefficient of textured polymers is dependent on the

46 28 velocity of the shearing surface, presence of lubricating material and other experimental settings. The increase in computational abilities and development of more efficient algorithms have led to an increase in the number of theoretical (simulations based) publications that study the impact of pattern on tribological properties of the material [97]. Most of these studies involve solving Navier-Stokes [117] or Reynolds s [118] equations under different boundary conditions and other constraints [97]. It is overall agreed that the textured or rough surfaces act as cavities and micro cavities which act as reservoirs of lubricants. These reservoirs enhance the load bearing capacity by increasing the lubricant film thickness, which leads to lowering the friction compared to un-textured surfaces [119]. Simulations based study have been published to optimize the design [120] and determine the effect of aspect ratio, orientation[121] and packing density [122] of these micrometer scale textures to minimize friction between shearing surfaces. It is considered that in aqueous conditions the micron scale textures enhance load support and film thickness by acting as miro-hydrodynamic bearings, resulting in lower friction compared to a flat surface. 3.3 Lubrication Regimes As discussed earlier in Chapter 1, the Stribeck s curve describes the various lubrication regimes [36] as a function of lubrication parameter ƞv/p where ƞ is the dynamic viscosity of the fluid lubricant, V is the shear velocity between the two sliding

47 29 surfaces and P is the applied load. Considering a Newtonian fluid (a liquid whose viscosity does not change with the rate of shearing) and constant applied load, the lubrication parameter is directly proportional to the shear velocity. At low shearing speeds, and in the absence of a lubricant, the surfaces come into intimate contact leading to large friction forces and high wear rates. In the boundary lubrication zone, a thin layer of lubricant e.g. oil, exists between the two sliding surfaces. As the surface shears, the lubricant gets pushed out of the contact zone and hence, has to be continuously replaced. At high shear velocity, the sliding surfaces enter the hydrodynamic lubrication regime. In this regime a thicker, pressurized layer of liquid exist between the shearing surfaces [123]. This layer of fluid is responsible for supporting the load between the two sliding surfaces. Since the surfaces never come in contact with each other, this lubrication regime is associated with low friction and wears rates. 3.4 Lubrication Mechanism of Cartilage The load that is applied on the cartilage is supported by the extracellular matrix, which due to the charged species present in proteoglycans (found in cartilage) creates an osmotic pressure to hydrate the cartilage. The high water content of the cartilage provides a compliant structure with an effective modulus ranging from MPa [55]. Cartilage supports the joints for the duration of life span unless affected by injury (through direct impact) or diseases (such as osteoporosis). The synovial fluid runs through the pores of cartilage providing nutrition to the cells. As discussed in Chapter 2, the cartilage and synovial fluid works synergistically to

48 30 make joint lubrication efficient, resulting in ultra-low coefficient of friction that ranges from [45]. During movement, at high shear velocities, hydrodynamic lubrication regime dominates. It has been shown that the measured friction forces in the cartilage are inversely proportional to the pressure of the interstitial fluid. The pore matrix regulates the flow of interstitial fluid. It is agreed that a thick pressurized layer of synovial fluid separates the shearing cartilage surface responsible for ultra-low friction. Synovial fluid is rich in boundary lubricants such as hyaluronic acid, surface-active phospholipids and superficial zone proteins. These lubricants act as a sacrificial layer during shear at slow speeds, thus they need to be replaced continuously. Therefore, in order to successfully replicate such a system it is important to consider both; the properties of the lubricant and the surface mechanical and structural properties. 3.5 Biocompatibility of PDMS Several materials are currently used in joint replacement assemblies, including metal on metal (MOM), metal on ultra high molecular weight polyethylene (UHMWPE), ceramic on ceramic (COC) etc. Metal on UHMWPE is the most commonly used design, but shear of metal on polymer surfaces results in debris that can cause pain, inflammation and complete implant failure. In the past MOM suffered from severe debris, but with the latest developments they are the contact of choice especially for younger patients. COC contacts are brittle and have been reported to make a cranking noise on shearing that makes them undesirable.

49 31 Poly-dimethylsiloxane (PDMS) is a polymer consisting of repeating units of dimethylsiloxane that belongs to a group of polymers commonly referred to as silicones. The monomer is available in liquid form, which can be easily polymerized by adding a cross-linker. Once polymerize, PDMS is an elastic solid with a Young s modulus of 0.8~2MPa [124]. Changing the temperature of curing and the ratio of cross linker to monomer can vary the mechanical properties of PDMS [125]. PDMS is stable, non-toxic and is biocompatible [126]. It is currently being used to make shunts, breast implants and heart valves among other biomedical applications. PDMS is used as a material to mimic cartilage porous structure in polymers to study the load induced hydrodynamic lubrication. The ease of processing, mechanical properties close to those of articular cartilage, biocompatibility and stability in aqueous medium makes PDMS a good candidate for this research. 3.6 Load Induced Hydrodynamic Lubrication In this project, we demonstrate that by engineering the design on a compliant polymer surface (i.e. by adding vertical hollow pores), hydrodynamic (or mixed) lubrication can be induced even at relatively low shear velocities, where one would typically expect boundary lubrication for a flat surface. The idea is inspired by the mechanism of hydroplaning in which the presence of a water film between two surfaces can drastically reduce friction between the two surfaces (such as a car tire and asphalt). Typically hydroplaning occurs at high shearing velocities where the water film does not have sufficient time to drain from the confined region of contact. In this project, we purposefully create small pores in a compliant polymer (PDMS) and fill them with a

50 32 lubricant (water). These pores act as reservoirs of lubricant (water). When an external load is applied to the porous, compliant polymer, the water gets extruded from these pores forming a thin pressurized layer between the shearing surfaces. This layer of water supports the applied load and results in reduced friction between the two surfaces. The design is inspired by the weeping lubrication mechanism of cartilage [127] [128] in which the pressurized layer of synovial fluid confined in the region of movement acts as the load bearer, reducing friction and preventing wear on cartilage. The Figure 7 shows a schematic of the proposed load induced lubrication mechanism. Figure 7: Schematic illustration of the mechanism by which a thin fluid layer forms between a spherical glass surface and a porous polymer surface under an applied load. The thin film remains as the glass probe is sheared over the polymer surface at a constant velocity V 3.7 Fabrication of porous PDMS samples Fabrication of PDMS samples was done by (i) Creating patterned Si wafers using photolithography

51 33 (ii) Molding PDMS samples from the Si wafers Creating patterned Si wafers Conventional photolithography was used to create pillars of SU-8 photoresist (MicroChem) in a square lattice on silicon wafers (Test grade, University wafers). Photolithography is a patterning technique used to transfer a micron scale pattern on a light sensitive substrate by using UV radiation as the source of energy [129]. The process is commonly used in the microchip manufacturing and micro fluidic industry to create multiple layers of patterns. The process as applied to the making patterned Si wafers is summarized in the following steps: Cleaning the Si wafers 4 Si wafers (University Wafers, test grade) were cleaned using DI, ethanol and dried under Ultra-Pure Nitrogen to obtain a clean wafer Spin Coating Photoresist SU-8 was spin coated on the clean wafers by following the manufactures recommendations to coat a layer of approximately 40 μm Pre Exposure Baking The wafer was heated at 95C for 60s to facilitate removal of solvent and improve the adhesion of the photoresist on the substrate. This step is also called soft bake Exposure to UV radiation A photomask designed in-house and purchased from Fineline Imaging was aligned on the wafer. The mask has a repeating pattern of micron scale transparent circular patterns on a black background. These circular patterns are placed at a specified distance

52 34 in the X and Y space. An example of a typical mask is included in the appendix. SU-8 is a negative tone photoresist, which implies that areas exposed to UV light undergo preferential cross-linking, while those unexposed are washed off in the developing solution. Since we are only interested in generating a single layer pattern, photomask is manually aligned on the wafer. A clear glass slide 4.5 X4.5 was used to press the mask against the SU-8 coated Si wafer to increase contact, minimizing diffraction of UV light between the mask and the wafer. OAI UV lamp was used to irradiate the SU-8 through the photo mask to initiate cross-linking Post Exposure Bake The coated Si wafer after UV exposure is baked at 65C for one minute followed by baking at 95C for five minutes to complete cross-linking of SU-8 that was exposed to UV radiation Developing After the post exposure baking step, the wafer is developed in the propriety developing solution. The developing solution mainly consists of propylene glycol methyl ether acetate. The photoresist that was not exposed to the UV radiation remains uncrosslinked and is preferentially removed by the developing solution. To facilitate the process and to ensure that the developing solution diffuses through the narrow features the solution is mixed and dispensed on top of the features using a pipette. The wafers are developed for approximately 10 minutes in the developing solution till no more uncrosslinked SU-8 is washed off the wafer using iso-propanol.

53 Cleaning the patterned wafer The patterned wafer is rinsed with dodecane to remove any unpolymerized SU-8. It is then subjected to the final hard baking step at 150C for 30 minutes to remove the volatile solvents. This step also increases the strength of the final SU-8 pillars. The patterned wafer is then washed with ethanol followed by DI before being air-dried in Ultra-Pure Nitrogen. The patterned Si wafers were then used as a mold to obtain the final porous polymer surfaces out of PDMS (Sylgard 184, Dow Corning). In order to facilitate the removal of the PDMS from the mold, the silicon wafers (with Su8 patterns) were treated with Octadecyltrichlorosilane (Sigma Aldrich). OTS treatment was done by immersing the wafers into a 100 μl OTS per 100 ml pentane (HPLC grade, Pharmaco-Aaper) solution for 5 minutes. The wafers were then rinsed with pure pentane, DI water and ethanol to remove excess OTS followed by drying under Nitrogen (UHP, Airgas) Molding PDMS samples from the Si wafers The OTS coated patterned Si wafers were used as molds to fabricate PDMS samples. PDMS (Sylgard 184 from Dow Corning) was mixed in the ratio of 10:1 for base to curing agent as recommended by the manufacturer s guidelines. It was then pored over the OTS coated patterned Si molds and subjected to vacuum to ensure that the PDMS flows inside the micro-channels. The polymer was then allowed to cure for 24 hours at 60C inside an oven on a flat surface. The samples were allowed to reach room temperature before unmolding them from the wafers. Patterned Si wafers were

54 36 recovered, cleaned with ethanol and DI to be re-used as molds. Figure 8 shows the SEM micrographs of the fabricated PDMS patterns. A B Figure 8: (A) Top view SEM image of a porous polymer surface. Scale bar = 200 µm. (B) Cross sectional side view of a porous polymer surface. Scale bar = 50 µm OTS coated flat Si wafers were used as molds to fabricate flat PDMS samples as control samples. To create flat samples PDMS was mixed in the same ratio as patterned samples (10:1) and molded for 24 hours at 60C in an oven. 3.8 Tribology tests of PDMS samples In a typical experiment, a fixed pre-load was applied on the polymer sample using CETR Universal Materials Tester (UMT-2) and the friction force between the polymer sample and a spherical glass probe (Edmund Optics 27420) was measured while shearing a fixed distance at a constant speed. DFM and FL sensors from CETR were used to measure the tribological behavior of the samples. Various samples were tested in both dry and aqueous conditions.

55 37 Prior to measuring their tribological properties, glass probe and all samples were cleaned using air plasma for 60s. Plasma treatment makes PDMS hydrophilic and facilitates water to penetrate the pores of the porous surfaces. To further ensure that the water penetrates the micron scale pores in the samples, the samples were kept in vacuum for approximately 10s, till air bubbles ceased to emit from the surface. The samples were kept in aqueous environment to eliminate any changes due to evaporation that may have caused the drying of the samples. Each test condition was repeated at least five times. 3.9 Friction Coefficient of Flat vs. Patterned PDMS The coefficient of friction of PDMS and a circular glass probe was measured by applying a 49 mn (5 g) load at a constant shearing speed of 100 µm/s under four test conditions (i) Flat PDMS and a glass lens under dry conditions (ii) Flat PDMS and a glass lens under aqueous conditions (iii) Porous PDMS and glass lens under dry conditions (iv) Porous PDMS (with various diameters and pore spacing) and glass lens under aqueous conditions. The average coefficient of friction in each case is shown in Figure 9 (B)

56 Figure 9 : (A) Plot of a typical friction force vs time while shearing a glass probe on a PDMS surface for various test conditions: PDMS under dry conditions (Red - sample set 1), flat PDMS with water (Blue - sample set 2), textured PDMS under dry conditions (Green - sample set 3) and textured PDMS under water (Light blue - sample set 4) (B) Plot of the average coefficient of friction between a spherical glass probe and the polymer surface under various conditions. The applied load in all cases was 49 mn and the shearing speed was 100 µm/s. 38

57 39 The first set of experiments consisted of shearing a spherical silica surface against a flat PDMS surface under dry conditions. The Young s modulus of the PDMS surface is 1~2MPa[130], which allows for relatively large deformations upon application of a small normal load. The resulting large contact area and the fact that both surfaces have a high surface energy (due to plasma treatment) is consistent with the high coefficient of friction of around Under aqueous conditions, water can act as a boundary lubricant. But since PDMS is inherently hydrophobic, water does not act as a good boundary lubricant. This effect is visible in the second sample set as the friction coefficient is reduced slightly from 3.7 to While classical understanding of friction between two shearing surfaces is independent on the area of contact and applied load, the studies at the micro and nanolevels have shown otherwise. As discussed in Chapter 1 friction is dependent on the true or real area of contact, which is also dependent on the applied pressure. The modified Amontons law as described by equation 4 can be used to explain the decrease in the friction coefficient of patterned PDMS in the sample set to Introduction of pores on the surface reduces the actual amount of polymer in contact with the probe thereby reducing the apparent (and true) area of contact between the two sliding surfaces. However, over large regions of shear, the micron scale asperities average out and Amontons law is still widely used.

58 40 The drastic decrease in the coefficient of friction to a value of 0.31 under the aqueous conditions in patterned PDMS cannot be explained solely due to the boundary lubrication contribution of water or modified Amontons law. It is hypothesized that as the silica probe (under an applied load) shears against the porous PDMS surface, water is extruded from the pores, resulting in a repulsive hydrodynamic force as the water drains. The draining water maintains a separation gap between the silica and porous PDMS surfaces, which changes the lubrication mechanism from boundary lubrication to hydrodynamic (or mixed) lubrication. As the probe moves, the pores on the trailing side no longer experience a compressive local stress and therefore elastically regain their original shape and water goes back in the pores. This mechanism ensures that the samples have low friction coefficient for an extended period of time as long as water is present. The effect is similar to the weeping lubrication mechanism of cartilage Effect of Shear Velocity To study the effect of shearing velocity over the proposed load induced lubrication mechanism, a PDMS sample, which had pores that were 40 μm deep, 20 μm in diameter and spaced 20 μm apart (end to end) were tested over a range of shearing speeds. Speeds were varied from 5 μm/s to 1000 μm/s while sample was maintained under aqueous conditions at an applied load of 49 mn. Figure 10 summarizes the results of various experiments.

59 41 Figure 10: Plot of the coefficient of friction between a spherical glass probe and a porous PDMS surface as a function of shear velocity. It can be seen that the load induced hydrodynamic (or mixed) lubrication can be seen over the entire range of test speeds. These results are extremely useful while thinking of potential applications such as those in biomedical implants which may be subjected to a range of shearing velocities Effect of Applied Load Similar PDMS sample (pores 40 μm deep, 20 μm in diameter and spaced 20 μm apart) was used to study the effect of increasing load on the coefficient of friction in aqueous conditions by increasing the load from 49 mn (5 g) to 392 mn (40 g). The shearing speed between the sample and the spherical glass probe was kept constant at 100 μm/s. The figure summarizes the results various tests.

60 42 Figure 11: Plot of the coefficient of friction between a spherical glass probe and a porous PDMS surface as a function of applied load, using water as the lubricating fluid. The inset in shows the typical measurement of the coefficient of friction (data in red) with increasing applied load (data in blue). It can be seen that the friction coefficient is low for the entire range of applied load. It is also seen that the friction coefficient decreases slightly from (0.28 to 0.26) with increasing loads. This decrease in friction is small and is more significant at lower loads. It is proposed that this reduction in friction may be attributed to the fact that PDMS is compliant and therefore more pores can contribute as load is increased due to an increase in contact area. Figure 11, shows the images taken from underneath the sample in which a die was added between the probe and the surface. It can be seen that as proposed (also as expected) the area of contact increases with increasing load.

61 43 A B C D E Figure 12: (A) to (E), Images taken from underneath the PDMS sample for an applied load of 5, 15, 25, 35 and 45 g respectively. It can be seen that the area of contact increases with the increase in applied load. Scale = 200 µm

62 44 This supports our hypothesis, however, more controlled experiments are needed to confirm this trend. Nevertheless these results demonstrate that the system is robust and provides low friction over a wide range applied loads Effect of Boundary Lubricant So far, we have only mimicked the porous structure of cartilage. The coefficient of friction, although lower than a flat sample under similar conditions, is still much higher than cartilage. In order to further reduce friction sodium dodecyl sulfate (SDS) was used as a boundary lubricant. Stock solutions of sodium dodecyl sulfate (Sigma Aldrich) were made at various concentrations to study the effect of adding a boundary lubricant. Figure 13, shows the effects of using various concentrations of SDS for both flat and textured polymer samples.

63 45 Figure 13: Plot of the coefficient of friction as a function of SDS concentration for a flat surface of PDMS (red line) compared to a textured surface of PDMS (green line). The preload was 45 mn and the shear velocity was maintained at 100 µm/s. It can be seen that SDS at a very small concentration of 1 mm acts as a boundary lubricant for a flat surface, but has no significant effect on the textured surface. The latter is not surprising since the flat surface produces a larger contact area and therefore boundary lubricants are expected to exhibit a larger effect. However, by increasing the concentration of SDS we can see the contribution of the boundary lubricant even in the textured samples, presumably reducing friction at regions where the probe still makes contact with the textured PDMS surface, which results in a lower coefficient of friction. On further increasing the concentration of SDS we could further reduce the friction coefficient. However, such measurements were close to the lower limit of the sensor and are hence not included in the results as contribution of noise was significant.

64 Effect of Pore Diameter and Spacing To systematically study the effect of pore diameter and spacing, samples with various surface patterns were tested for their tribological properties. Porous fraction was calculated as the ratio of hollow channels to the PDMS polymer by considering a unit cell such that A square of side a represents the total area of the polymer in the unit cell if there were no pores, where a is the X & Y spacing between the two pores A circle of diameter d represents the hollow (or porous) area of the pattern in the unit cell, where d is the diameter of the pores Porous fraction is calculated as the ratio of the porous area to that of PDMS in a unit cell and is given by Porous Fraction (%) = Πr2 4a Equation 6: Calculation of surface porosity Figure 14, illustrates the selection of a unit cell.

65 47 d a Figure 14: Selection of a unit cell to calculate porous fraction Design of experiments was used to create one set of samples with increasing pore diameter keeping the pore spacing constant. Another set of samples were created keeping the pore spacing constant while systematically increasing the pore diameter. All samples were prepared using the same PDMS mixture to eliminate fluctuations surfacing from variations in the polymer preparation. Results are summarized in Table 1.

66 48 Sample Pore Diameter d (μm) Pore Spacing a (μm) Porous Fraction (%) Coefficient of Friction (dry) Coefficient of Friction (Wet) Table 1: Summary of results of effect of Porous Fraction on coefficient of friction 3.14 Conclusion Overall, these results show that by creating pores in a compliant polymer surfaces one can exploit hydrodynamic (or mixed) lubrication even at low shear speeds. Low friction can be maintained for a wide range of shear velocities and applied load. The addition of a boundary lubricant can further reduce friction for a relatively low applied load and shear velocity and it would be interesting to verify whether this effect persists over a wide range of shear velocities and applied loads. Future studies towards optimization of design parameters such as pore density, aspect ratio, polymer stiffness among other important parameters and moving towards biocompatible boundary lubricants could lead to application of such materials in biomedical implants for joint replacements.

67 49 Chapter 4: Factors affecting load induced lubrication of porous polymers 4.1 Summary In this chapter the factors affecting the previously described load induced hydrodynamic lubrication mechanism are studied in more detail. In particular the effect of radius of curvature (r) of the shearing glass probe, the ratio of cross-linker to polymer in PDMS samples that affects the modulus (ϒ) of the PDMS sample and the effect of depth of pores (h) is discussed in this chapter. It is seen that the observed friction coefficient in the porous polymer samples under aqueous conditions is highly dependent on the dynamic equilibrium between the applied pressure, modulus and the depth of the samples. Systematically exploring the interplay in these factors helps in understanding the underlying mechanisms of the proposed lubrication mechanism. It is also shown that the proposed lubrication mechanism is material independent and that the mechanism can also be exploited on a PDMS sample on which the pores of random diameter are distributed in a non-uniform manner. 4.2 Introduction In the previous chapter, it is demonstrated that creating pores and applying pressure on compliant Polydimethylsiloxane (PDMS) hydrodynamic (or mixed) lubrication

68 50 regime can be induced under aqueous conditions, even at low shearing speeds. Friction force was measured between a curved glass probe and a patterned PDMS sample that was submerged in water using CETR Universal Materials Tester (UMT-2). It is proposed that the pores in PDMS act as tiny reservoirs of lubricant (water). When axial load is applied on these surfaces, the lubricant is extruded from these pores. The confined water forms a pressurized layer between the two sliding surfaces, resulting in the observed low friction coefficient (0.31), which is much lower than that of flat PDMS under similar conditions (3.16). The proposed lubrication mechanism was shown to be effective over a range of shear velocities ( μm/s) and applied load ( mn). However, the discussion about pore fraction and addition of boundary lubricants shows that the design is far from optimum. It was noted that by optimizing the design and by introducing boundary lubricants the already low coefficient of fricttion can be reduced even further. The aim of this chapter is to study the effects of some of the parameters that are important in understanding the underlying mechanisms of the load induced hydrodynamic lubrication of porous polymers. Specifically, the effect of radius (r) of the circular probe sliding against the patterned PDMS sample, modulus (ϒ) of PDMS and the depth (h) of pores are considered. Figure 15, shows a graphical representation of the proposed load induced lubrication mechanism and the various factors considered in this chapter.

69 51 ϒ Figure 15: Schematic illustration of the proposed load induced hydrodynamic lubrication mechanism. The radius of curvature (r) of the shearing glass probe, the modulus (ϒ) of the PDMS sample and the depth (h) of the pores are explored in this chapter. To demonstrate that the lubrication mechanism is material independent, spherical probes, of same radius of curvature, made up of different materials (ceramic, steel and plastic) were used in this study. Finally, a PDMS sample with a non-uniform pattern of pores was also shown to exhibit load induced hydrodynamic lubrication. A systematic study of these factors enhances our understanding of the underlying mechanisms for load induced hydrodynamic lubrication of porous polymers. This is an important step in moving towards optimization of pattern and material properties of the polymer to design surfaces with ultra-low and tunable friction for potential applications in biomedical implants and separation devices.

70 Fabrication of porous PDMS samples PDMS samples were made by molding from patterned silicon wafers. Photolithography was used to create patterns on silicon wafers (test grade, University Wafers) using SU-8 Photoresist (MicroChem). Viscosity of SU-8 (SU , SU and SU ) and spin conditions were selected according to standard protocol provided by MicroChem to produce patterns of different heights on silicon wafers. The various conditions used to make the silicon wafers of different heights are summarized in Appendix 6. The silicon wafers were coated with Octadecyltrichlorosilane (OTS, Sigma- Aldrich) by immersing the wafers in a solution of 100μl OTS per 100ml of pentane (HPLC grade, Pharmaco-Aaper) for 2 minutes. The wafers were then washed with pentane, DI and ethanol to remove excess OTS, and then dried with nitrogen (UHP, airgas). The OTS coating was done to ease the demolding of PDMS from the silicon wafers. Sylgard 184 (Dow Corning) was then poured onto the silicon master mold to create porous PDMS samples. The PDMS was cured in the oven at 60 C for 24 hours. The PDMS samples obtained were characterized using Zygo ZeGate Profilometer. 4.4 Tribological Experiments on porous PDMS samples A CETR Universal Materials Tester (UMT-2, CETR) was used to measure the friction force between the shearing probe and the sample polymer surface under various test conditions. A typical experiment consisted of applying a pre-load and shearing the two surfaces at a constant speed (0.2mm/s or 0.4mm/s). The probe was connected to the force sensor (FL, CETR) through a spring (KFL= 520N/m). Various borosilicate glass lenses

71 53 of different curvature (Edmund Optics), 0.25 diameter steel, ceramic and plastic balls (McMaster-Carr) were used as probes to shear against the PDMS surface. All the probes and PDMS samples were cleaned with air plasma for 60s before starting the experiment. To ensure that the water gets inside the micron length pores in PDMS, the high surface energy plasma cleaned PDMS samples were immediately submerged in water under vacuum for approximately 20s to replace the air from the pores with water. Throughout the experiments samples were submerged in water to compensate for any loss through evaporation. All chemicals and materials were used as received. 4.5 Measurement of tribological properties of PDMS samples This study can be divided into two parts (i) Understanding the factors affecting the load induced hydrodynamic lubrication of porous polymers in aqueous conditions (ii) Showing that the proposed lubrication mechanism is independent of the material of the shearing probe and can also be observed on a sample with nonuniform distribution of pores Design of Experiments to explore the factors effecting load induced hydrodynamic lubrication In a typical experiment, a preload was applied on the patterned PDMS samples using CETR Universal Materials Tester (UMT-2) and the friction force between the glass probe and the polymer samples was measured as they slide against each other under

72 54 aqueous conditions. Throughout the experiments carried in this chapter, the design of the pattern on PDMS samples was kept constant with 40 μm diameter holes separated 20μm in X and Y direction as shown in Figure μm Figure 16: An optical micrograph (20X, top view) of the PDMS sample fabricated with channels 40 μm wide spaced 20 μm apart. The radius (r) of the circular probe, modulus (ϒ) of PDMS and the depth (h) of the pores were varied systematically to explore the load induced lubrication regimes. The shearing speed and the applied load were kept constant at 200 μm/s and 98mN (10g) respectively and each sample was sheared for 5mm in both left and right directions for multiple cycles Design of experiments to demonstrate the material and design independence of the proposed lubrication mechanism

73 55 In order to show that the proposed lubrication mechanism is independent of the material of shearing probe, probes of different materials (stainless steel, plastic and ceramic, McMasterCarr) 0.25 inches in diameter were used instead of the glass probe. Friction was measured between the shearing probe and the PDMS samples (both flat and patterned) under dry and aqueous conditions. The applied load was kept constant at 98mN (10g) while maintaining 100 um/s shearing speed to cover a distance of 5mm on each sample. 4.6 Effect of curvature of the shearing probe Spherical glass lenses obtained from Edmund optics of various radii (1.65, 3.4, 6.05, 7.75, and 18.75mm) were used as shearing probes. A PDMS sample prepared by mixing Sylgard 184 PDMS patterned with 30 μm deep, 40 μm wide (diameter) holes spaced 20 μm apart was used as the test candidate. A constant force of 98mN was applied as the preload and the two surfaces were sheared at a constant speed of 0.2 mm/s (200 μm/s) while being submerged in water. The friction force (Fx) generated was measured and the averages of several experiments is reported in Figure 17. It is seen that the friction force was high for a probe with small radius of curvature (r=1.65 mm). It then follows a somewhat bell shaped curve before it finally flattens out.

74 Frcition Force, F x (mn) Probe Radius (mm) Figure 17: Plot of the average friction force (Fx) between spherical glass probe of different radii and the PDMS polymer under aqueous conditions. In each case, 100 g load was applied at a shear speed of 200 μm/s. This can be explained by exploring the relationship between the applied load, the radius of curvature and the depth of indentation. Since the normal force applied is kept constant throughout each case, the applied pressure and the area of contact changes by changing the radius of curvature of the probe. Hertz equation [1] for non-adhesive contact between a sphere and a flat surface can be used to explain this dynamic relationship between; d (depth of indentation in the compliant flat surface), F (applied normal force), R (radius of sphere of contact) and E (effective modulus) F = 4 3 E R 1 2 d 3 2 Equation 7: Hertz equation of contact between a sphere and elastic half space E is the effective moduli and is calculated from equation 8

75 57 1 E = 1 ν1 E ν22 Equation 8: Calculation of effective modulus for non-adhesive contact between two surfaces E2 where E1, v1 and E2, v2 are the Elastic modulus and Poisson s ratio of the material of the sphere and the flat surface respectively. Since, in our case, the glass probe is significantly rigid (Elastic modulus 75~95 GPa) than the compliant PDMS sample (Elastic modulus 1.5~2.5 MPa) E1>>E2 1 E = 1 ν2 Equation 9: Approximation for effective modulus for non-adhesive contact between the surfaces when one surface is significantly less compliant than the other. E2 2 It should be noted here that E2 (the elastic modulus of the PDMS sample) and v2 (the Poisson s ratio of PDMS sample) are again dependent on the porous fraction, the depth of the channels made in the sample and also the thickness of the samples. Presence of water in these pores also adds to the complexity in determining these values from literature. An in-house approach to measure the modulus using the CETR UMT-2 is discussed in Chapter 5 and is a future direction for the project. Although exact values cannot be calculated, it can be seen that for everything else being constant, d 1 R (1 3 )

76 58 Equation 10: Dependence of depth of indendendation to radius of curvature of the probe according to Hertz theory of contact mechanics. Hence, for a small change in Radius R (in mm) of the probe, one can expect a significant change (10s' of microns) in the indendation made by the probe. Based on the above discussion we explain the change in measured friction forces by changing the radius of the sliding probe as seen in Figure 17 by dividing the curve into three zones. Each of these zones is dominated by a different lubrication mechanism depending on the compression of the polymer, which at a constant applied load is dependent on the radius of the probe. Figure 18 shows schematic representation of each of these regimes.

77 59 (A) Domain I (B) Domain II (C) Domain III Figure 18: Schematic of the proposed underlying mechanisms. (A) Domain I: pores get completely closed causing boundary lubrication. (B) Domain II: Shows the load induced hydrodynamic lubrication. (C) Domain III: There is always a layer of water present between the relatively flat probe and the patterned PDMS sample. In the case of probe with a small radius of curvature (R=1.65mm), it is proposed that the applied pressure is high, causing the pores to close. The fluid is squeezed out of the contact zone. The end result is similar to the probe sliding against the polymer (PDMS), which explains the high friction force. As we increase the curvature of the sliding probe, the pressure decreases and so does the indentation in the polymer. In this regime hydrodynamic (or mixed) lubrication dominates. This regime is characterized by compression of the pores such that the water expels out of them and forms a pressurized layer between the probe and the polymer sample resulting in low friction forces as seen

78 60 previously in Chapter 3. The friction increases slightly as the curvature of the probe increases. This can be attributed to mixed lubrication dominating over pure hydrodynamic lubrication as the increase in radius of the probe results in increased area of contact causing the probe to make contact with the polymer at the edge. This is shown schematically in region 2 of Figure 18 (B) where we can see that although there is a liquid layer present between the shearing surfaces the probe and the polymer comes in direct contact at certain points as observed in mixed lubrication [131]. As we continue to increase the probe radius, the friction force continues to decrease. In this case, it is hypothesized that the probe is now extremely flat and a layer of water is always present between the probe and the PDMS surface since the pressure is not enough to squeeze the lubricant (water) away from the contact zone, especially at the low shearing speeds as in this experiment. This results in low friction throughout this lubrication regime. Figure 18 (C) schematically explains this lubrication regime. These explanations are further supported by exploring the effect of the modulus (ϒ) of PDMS and the depth (h) of the pores in the following sections. 4.7 Effect of modulus (ϒ) of the PDMS sample The elastic modulus of Sylgard 184 PDMS can be varied easily by changing the ratio of polymer to cross-linker [124]. It has been shown in literature that the polymer will become less compliant by increasing the ratio of cross-linker and vice versa. For this part of the study, we created patterned PDMS samples (40 μm wide, 20 μm apart and 30 μm deep channels) and varied the ratios of polymer to cross-linker to change the elastic modulus of the samples. Tribological properties were studied for samples with polymer

79 Friction Force Fx (mn) 61 to cross-linker ratio 5:1, 8:1, 10:1, 12:1, 15:1 and 20:1 with a glass probe of radius 7.75mm (Edmund optics 27420) under aqueous conditions. Figure 19, summarizes the results of friction force measured by shearing the sample and the glass probe at 0.2 mm/s with a pre-load of 98mN :1 8:1 10:1 12:1 15:1 20:1 Polymer to Cross Linker Ratio Figure 19: Plot of the average friction force (Fx) for patterned PDMS samples of different compressibility made by changing the ratio of polymer to cross linker when sheared against a glass probe at 0.2 mm/s under a normal load of 98 mn. It can be seen that the friction force is high in the case of the sample with 5:1 ratio of polymer to cross-linker and follows a bell-shaped curve as we increase this ratio. In the case of a relatively stiff polymer (5:1 polymer to cross-linker ratio) the probe is not able to apply sufficient pressure to squeeze enough lubricant from the pores. Boundary lubrication dominates in this case and water is continuously being pushed out of the contact zone resulting in high friction. These results are similar to that measured for flat

80 62 PDMS in aqueous conditions in Chapter 3. As we increase the compliance by increasing the ratio of polymer to cross-linker load induced hydrodynamic (or mixed) lubrication regime can be observed again. This explains the decrease in friction as we decrease the modulus by changing the ratio of the polymer to cross-linker from 8:1 to 12:1. This trend is expected as under similar conditions, more fluid is pushed out of the pores of a softer material compared to that with a higher modulus. Also as the compliance increases the area of contact increases for the same applied load and hence more pores can contribute, resulting in lower friction force. As we keep decreasing the amount of cross-linker, the friction force increases again as the polymer becomes softer. This can be attributed to some pores getting completely compressed resulting in direct contact of probe with the polymer, resulting in higher friction as the friction mechanism now shifts again from purely hydrodynamic to mixed. To maintain the structural integrity of the polymer it was not possible to keep reducing the ratio of cross-linker, but the observation supports our explanation in section 4.6 that the pores can get closed on applying high pressure (by applying the same force over a smaller contact region) or when testing a sample made up of a softer material. 4.8 Effect of pore depth (h) To corroborate our previous explanations we studied the lubrication properties of pores with the same dimensions (40 μm wide and 20 μm apart), same material properties (10:1 polymer to cross-linker ratio) and by using the same probe (r=7.75 mm). However, this time the depth (h) of the pores (h=4.6 μm, 7.5 μm, 11 μm, 15 μm and 24 μm) is varied. Different pore depths were achieved by creating Si molds of different heights. This was

81 63 done by using SU-8 of various viscosities and by changing the experimental conditions such as spin coating time, exposure time etc. The details to create various samples are provided in Appendix 6. The PDMS samples as fabricated were characterized using the ZeGage Plus Optical Profilometer (Zygo). Figure 20 (A) to (C) shows the 3-D optical profilometer images of three of the various test samples. The results of the tribological properties of the samples of various depths are summarized in Figure 21. A B B C Figure 20: (A) to (C) shows the 3-D profilometer characterization of PDMS samples of height 4.4 μm, 15.4 μm and 23.4 μm respectively

82 Friction Force (mn) Pore Depth (μm) Figure 21: Plot of the average friction force (Fx) for PDMS samples of different depths (h) when sheared against a glass probe at a speed of 98 mn under an applied load of 98 mn. It can be seen from Figure 21 that the friction force is high for extremely shallow pores of 4.6μm. This can be explained on the basis of the pores getting completely compressed as discussed previously in sections 4.6 and 4.7. Once we reach a critical pore depth where the pores are not completely squeezed out, we start seeing the load induced hydrodynamic lubrication taking over the boundary lubrication resulting in significantly low friction over a range of pore depths. This explanation corroborates our previous hypothesis of the pores getting compressed and completely closed when subjected to high pressure (due to high curvature of the probe) or on a softer polymer (due to the decreased cross-linker to polymer ratio). It should be noted that this critical pore depth would be specific to the design, the material properties and the applied external pressure.

83 Effect of probe material So far in this project, we have only tested PDMS samples with glass probes. In order to show that the mechanism of lubrication is material independent probes of different materials (ceramic, plastic and steel) were used to test the lubrication properties of PDMS samples under various conditions. To compare the results, all probes had a diameter of 0.25 inches. Lubrication experiments were carried out at pre-load of 49mN, shearing 5 mm in each direction at a speed of 0.2 mm/s (200 m/s). Similar to the tests performed in Chapter 3, tests were performed under four conditions (1) Flat PDMS in dry conditions; (2) Flat PDMS under water; (3) Patterned PDMS under dry conditions and (4) Patterned PDMS under water for each probe material. Figure 22 summarizes the results of the friction forces measured under various test conditions to when probes of different materials were shearing with PDMS samples.

84 Frcition Force (mn) Steel Ceramic Plastic 20 0 Dry Water Dry Water Flat Flat Pattern Pattern Figure 22: Comparison of friction forces (Fx) between a flat and patterned PDMS sample with a steel (grey), ceramic (yellow) and plastic (blue) probe of 0.25 diameter under dry and aqueous conditions. The applied load in each case was 49mN and the shearing speed was 0.2 mm/s. The friction in dry conditions was higher for flat PDMS samples compared to the patterned PDMS. As discussed in Chapter 3, this can be explained on the bases of modified Amontons law (equation 1). By creating pores in the samples, the true area of contact between the probe and the polymer is decreased. A reduction in true area of contact can explain the decrease in friction between flat and patterned PDMS samples in dry conditions. Water acts as a poor boundary lubricant for flat samples. However, when the patterned samples were tested under water, the reduction in the measured friction forces is very significant and cannot be explained on the bases of modified Amontons law. It was proposed in our previous work and is supported by the results of this study that this drastic decrease in friction can be explained on the basis of load induced

85 67 hydrodynamic (or mixed) lubrication. Since we can observe the same trend over a wide range of materials (glass, steel, ceramic, polymers) we can conclude that the affect is material independent Lubrication properties of PDMS with non-unifromly distributed pores Lubrication properties of PDMS sample with pores of diameter ranging from 10-50μm spaced 10-50μm apart in both X and Y directions were tested in dry and aqueous conditions. The sample had surface porosity of 16.89% as analyzed by using Image J. The surface porosity of this pattern is close to that for the unit cell of the PDMS sample that we tested in the Chapter 3 (20 m diameter, 20 m apart, porosity 19.25%). Figure 6A shows the top view of the non-uniform PDMS sample and Figure 6B summarizes the results of friction forces measured dry and aqueous conditions.

86 Friction Force (mn) Dry Test Condition Water Figure 23: (A) Optical micrograph of the top view of a section of the non-uniform PDMS sample. (B) Plot of average friction force (Fx) for a non-uniform PDMS sample and a glass probe under dry and aqueous conditions under 49 mn applied load at 0.2 mm/s A pre-load of 49mN was applied and the sample was sheared with a 7.75mm glass probe at 0.2 mm/s (200 m/s) under dry and aqueos conditions. It can be seen that the load induced hydrodynamic lubrication is observed even when the pores are distributed in a non-uniform order. The friction forces are somewhat higher than those for the PDMS sample with a higher surface porosity. This matches our expectations that the proposed lubrication mechanism is not restricted to a particular design or geometry of the pores. However, the design can be optimized dependent on the material properties and other constraints to create surfaces with low and tunable friction Conclusions In summary, we have studied some important factors effecting the load induced lubrication of porous polymers under aqueous conditions. These results provide a deeper insight into the novel lubrication mechanism. By changing the radius of curvature of the

87 69 probe and the modulus of the polymer material, it has been shown that the observed friction forces between two shearing surfaces are dependent on the dynamic relationship between the area of contact and the applied pressure. Based on this relationship, the proposed lubrication mechanism was divided into three regimes. It is also shown that for a particular material under given test conditions, there is a critical depth of pores that is required to observe the load induced hydrodynamic lubrication. Finally, we have shownthat the proposed lubrication mechanism can be observed for different materials and can also be seen for non-unifromly distributed pores. Better understanding of the underlying regimes of the load induced hydrodynamic lubrication opens opportunity to design surfaces with ultra-low and tunable friction by modifying design and material properties. Such surfaces can be potentially used as a coating in joint replacement implants.

88 70 Chapter 5: Further reduction in friction through improvements in design and material properties 5.1 Summary In the previous chapters it has been shown that in an aqueous medium and under an applied load, the lubrication regime can be changed from boundary lubrication to mixed or hydrodynamic lubrication by creating pores in compliant polymer such as PDMS. The factors effecting load induced hydrodynamic lubrication were systematically studied which led to deeper understanding of the novel lubrication mechanism. However, there are still a few unanswered questions and the design is far from optimum. This chapter summarizes some initial results and insights that can be used as a reference for future work to further reduce friction and create prototypes for potential applications in total joint replacement devices. 5.2 Study the combined effect of pattern and modulus of the polymer In Chapter 4, it was shown that the compliance and the porosity of the PDMS sample influenced the friction coefficient. It is hence proposed to study the combined effect of changing the cross-linker's ratio and the design on the friction coefficient. The aim of such a study would be to predict and determine the friction coefficient based on a relationship between the cross-linkers ratio (and hence the modulus of

89 71 the polymer) and the porosity. Such a relationship can be useful in designing surfaces with tunable friction where we can control the friction between the sliding surfaces by changing either the modulus (e.g. by changing temperature [132]) or by changing the pattern through the length of shearing surface. One of the challenges in achieving such a relationship is to establish a method to accurately measure the modulus of PDMS. It has been shown in literature that the variation in measuring the modulus of soft materials such as PDMS can be significant depending on the method used [124]. The addition of micron scale pattern on the PDMS samples compounds the limitations of readily available methods such as using the atomic force microscope (AFM). To overcome this hurdle, an in-house setup is designed to measure the modulus of PDMS (or other soft polymers) using the CETR UMT-2. The Figure 24 shows the setup, which comprises of a steel disk of 12 mm diameter used as a probe connected directly to the DFM force sensor. A polymer sample cut using a biopsy probe (6 mm diameter) is fixed on the stage and a pre-load is applied. The sample is compressed in small increments (0.01mm) at the speed of 0.01 mm/s (10 μm/s) and the force sensor measures the force required to do so. Elastic modulus is calculated using the classical formula ϒ=Stress/Strain Appendix 7 shows the details of a worked out example to calculate modulus using the described method.

90 72 Force Sensor Steel disk PDMS Sample Figure 24: Setup to measure the Young s modulus of soft polymers using CETR UMT- 2. A steel disk is connected directly to the force sensor of UMT and the force required to compress the polymer in small increments of 0.01mm is measured to calculate the Young s modulus. Table 2, summarizes the results obtained so far for a flat sample. The modulus values obtained are consistent (within the limits of experimental variation) with those reported in the literature for PDMS with similar cross-linker to polymer ratio [124]. In addition to establishing the relationship between the friction coefficient, modulus of the material and the design, this method of measuring the modulus can also be used as a potential way to screen other candidate materials for similar studies for load induced lubrication.

91 73 Ratio of cross-linker to PDMS Modulus (MPa) Standard deviation (MPa) 1: : : : : : Table 2: Modulus of PDMS of different cross-linker to polymer ratio as measured by the set up described in section Use computer simulations to aid in optimizing the design In section 3.13 it is seen that the friction coefficient changes with the porosity of the PDMS sample. It is further noted from section 4.8 that there is a critical pore depth for a particular design and material properties, which is essential to observe the proposed lubrication mechanism. It is proposed to use computer simulations and modeling to facilitate optimization of the pattern and study the aspect of the aspect ratio. The different design parameters to be studied include the pore diameter, the separation distance between two pores and the channel depth along with material properties such as the elastic modulus of the polymer. The effect of the curvature of the sliding probe can also be studied to validate the various observations and hypothesis made in Chapter 4. It is proposed that by increasing the pore density, more pores can contribute at a given load. This shall result in lower friction. However, we cannot simply keep increasing the porosity due to limitations of photolithography in creating the mold silicon wafers from SU8 and the molding method used to fabricate the polymer samples. Also, increasing the pore density reduces the effective Young s modulus, which can cause the pores to collapse or close completely on applying a

92 74 load. Depth of the channels is another important criteria as it affects the aspect ratio of the pores and the compliance of the polymer under load. It is hypothesized that for a given soft polymer, there must be optimal geometrical parameters that will provide lowest coefficient of friction. It is expected that the coefficient of friction would behave as the shown in Figure 25. Figure 25: Schematic of expected behavior of coefficient of friction by changing the porosity of the sample. The future work shall be guided by computational modelling from Dr. Khismatullin s group. The computational model is based on a fully three-dimensional algorithm for multiphase viscoelastic flow, where the fluid-fluid interface is tracked by the volume-of-fluid (VOF) method [133]. The external fluid is a Newtonian fluid with viscosity ηext = 1 cp (water). The particle is modeled as a drop containing two compartments: Newtonian solvent (described by viscosity ηs) and a polymer matrix. The viscoelasticity of the polymer matrix is captured by the Giesekus model [134]. We assume that the solvent viscosity ηs is equal to the viscosity of the external fluid.

93 75 This algorithm has been successfully applied to model liquid drop deformation under shear stress in a viscoelastic medium [135] and extended to model leukocyte adherence on surfaces [136, 137]. In our case, modeling tools can be applied to the project by simulating the shearing of a solid (mostly incompressible) glass probe against a compliant polymer surface (considered as a high viscosity viscoelastic material), together with a liquid between these materials. These should form three different phases of a multiphase material. The algorithm will test how the pore geometry, shear velocity and applied load would affect the friction between the glass sphere and the PDMS surface. So far we have been able to simulate the process over one row of pores in 2-D as shown in Figure 26. Figure 26: Simulation of a hard sphere shearing against a porous polymer in a Newtonian liquid. The size of the probe used and the high applied load and shearing forces used in our experiments are some of the challenges in creating models that more closely represent the conditions as described in this project. However, there is some

94 76 promising progress and efforts are now being directed to run 3-D simulations with a 2-D array of pores in both X and Y directions, to mimic the test samples as shown in Figure 27. Figure 27: 3-D simulation of a hard sphere sheared against a porous polymer having an array of pores in a Newtonian fluid. As we adopt the model in the simulations to more closely replicate the experimental conditions, we can get some significant insights into design surfaces with low friction. Such designs shall then be verified by designing new masks and samples. 5.4 Use Polyurethane instead of PDMS PDMS is inherently hydrophobic by nature. In order to make sure that the water enters the narrow channels in the sample, it is essential to first plasma clean the sample and then submerge it in water under vacuum. To avoid the extra steps and

95 Friction Force, Fx (g) 77 ensure that water easily enters the pores it is proposed to use a hydrophilic polymer such as polyurethane. Polyurethane is also biocompatible and has improved wear resistance properties over PDMS [138]. This makes it an ideal candidate material for our tests. Initial experiments were tried using polyurethane LS 60 and LS 30 from BJB Enterprises. The results for polyurethane samples made by using LS 30 are summarized in Figure Flat Dry Flat Water Porous Dry Porous Pattern Flat Dry Flat Water Porous Dry Porous Pattern Figure 28: Comparison of friction force between a glass probe and polyurethane samples in various test conditions at an applied load of 50g and shear velocity of 100 μm/s. Although the hydrodynamic lubrication effect cannot be observed for the polyurethane, it provides important insights in choosing other materials for future experiments. It was noted that the shore hardness of the polymer was different that of SYLGARD 184. This can explain why the hydrodynamic lubrication regime was missing for the polyurethane sample. To prove that it was indeed the difference in mechanical properties of the polymers that resulted in different lubrication results, it is proposed to conduct experiments with softer PU such as LS 15 BJB Enterprises,

96 78 which have shore hardness of 15 shore A respectively. Also a softening agent SC-22 from BJB Enterprises can be used during the curing of harder polyurethanes such as LS 60. Using the technique described in section 5.2, it is possible to compare the modulus of polyurethane samples to corresponding PDMS samples. By changing the amount of the softening agent added to the polymer the modulus of the polyurethane could be changed to match closely with SYLGARD 184. This can be a convincing way to determine if polyurethanes can be used as candidate materials for the project and open up new horizons to study other test candidates. 5.5 Use of Lubricin or other biocompatible lubricants instead of SDS In section 3.12 the effect of SDS as a boundary lubricant was discussed in the lubrication properties of flat and patterned PDMS samples. It was observed that due to the synergistic effect of boundary lubrication from SDS and load induced hydrodynamic lubrication by creating the pores in the samples, we could observe a further reduction in friction compared to either of the two mechanisms acting on their own. Initial tests with SDS on patterned PDMS samples showed that the friction coefficient was significantly reduced (0.035~0.004) when 100mM SDS solution was used instead of DI water. Such a low friction coefficient is comparable with that of articular cartilage. Although promising as a lubricant, SDS is not biocompatible. In future experiments, it is proposed to use a biocompatible boundary lubricant such as lubricin instead of SDS. Chang et. al. [139] along with various other groups [140, 141]

97 79 have successfully shown the superior lubrication properties of lubricin. The normal concentration of lubricin in articular joints is around 200 g/ml [141]. It is seen that an injury or a disease (such as osteoporosis) reduces the lubricin concentration in the synovial fluid to as low as 40~50 g/ml [142]. Thus it is important to test the tribological properties of the samples under the reduced lubricin conditions to mimic the biological conditions of those present in the patients who might need a total joint replacement surgery. Another approach could be stamping of phospholipids such as phosphatidylcholine which also acts as an excellent biocompatible lubricant as shown by Goldberg et. al [143]. Compared to lubricin which is an expensive recombinant protein isolate, phosphatidylcholine is relatively cheap and easily available. It is however, insoluble in water as such and thus need to be transferred inside the PDMS channels by smart methods such as stamping. 5.6 Design and test a multi-probe prototype All studies so far in this thesis have been done using a single spherical probe on a small polymer sample. It is proposed to design and create a surface with multiple spherical probes/bumps that can be used to test a polymer around 3 cm in length and 1.5 cm wide to mimic the cartilage in dimensions [144]. A schematic of the design is shown in Figure 29 (A). Figure 29 (B) shows how the four glass lenses of radius of curvature 7.75 mm (Edmund Optics 27420) were attached to the Si wafer to be used as a probe. This should allow an understanding of how the proposed polymer design behaves when load is applied at multiple points. Initial experiments by using four

98 Friction Force, F x (g) 80 glass probes over a 2.5cmX2.5 cm sample with 20 m diameter pores spaced 20 m apart are summarized in Figure 29 (C). A B C Dry Water Dry Water Figure 29:(A) A schematic of a multi probe prototype. (B) A setup using four glass probes to test the tribological properties of porous polymers when load is applied at multiple points. (C) Plot of friction force (Fx) in dry and aqueous conditions for a porous polymer when a 150 g load is applied across multiple points and sheared at 200 μm/s. A load of 1.5 N was applied and a distance of 1cm was sheared at the speed of 0.2 mm/s (200 μm/s). It should be noted that although we can see a reduction in friction forces in the aqueous conditions, this study was not comprehensive. It was

99 81 easily observed that the pattern of the arrangement of the lenses was important, which is intuitive as it will affect the distribution of load on the polymer. A more systematic and in-depth study with lenses of different radii arranged in different patterns is suggested to move towards the fabrication of a prototype. 5.7 Test sample wear over time The wear on the PDMS samples can be determined by visualizing the samples using optical microscope. Figure 30, shows images of a sample that has been subjected to over four hundred test cycles. It can be seen that there is virtually no visible wear on the surface of the samples. To gauge the degradation of the polymer sample, its Young s modulus can be measured by the in-house technique described in section 6.2 and observed over the duration of study. It is hypothesized that the addition of a boundary lubricant will result in excellent wear resistance properties close to that of natural cartilage. However, to perform longevity studies up to the expected life span of the total joint replacement implant (10~20 years) is beyond the scope of this research.

100 82 A B Figure 30: (A) and (B) 20X and 50X optical micrographs of PDMS sample showing no signs of wear after over three hundred test cycles. 5.8 Conclusion Through this project, a novel lubrication mechanism to shift the lubrication regimes by creating pores in a compliant polymer is described. Methods to further reduce friction by optimization of design and material properties were presented in this chapter. To further enhance understanding of the lubrication mechanism and design surfaces with predictable friction, a study of combined influence of modulus and pattern is proposed. An in-house method to measure the modulus of soft polymers using the CETR UMT-2 is described. It is also proposed to use computer simulations to optimize the pattern to create surfaces with ultra-low friction. Load induced hydrodynamic lubrication was not observed in stiff polyurethanes, which support the hypothesis described in previous chapters about the compliance of the materials. It is proposed to add softening agents to reduce the modulus of the polyurethanes closer to that of PDMS and confirm that the proposed lubrication mechanism is independent of material chemistry and is a function of mechanical

101 83 properties of the material. Finally, methods to test viability of such coatings on joint replacement implants were discussed. These include performing lubrication studies using a bio-lubricant such as lubricin and creating prototypes using multiple probes. Some initial results demonstrating the load induced lubrication over multiple probes and negligible wear in over three hundred shear cycles are promising and demonstrate the potential of these surfaces for practical applications.

102 84 Chapter 6: Synthesis of Hard Carbon/Iron Microspheres and Their Aqueous- Based Tribological Performance 6.1 Summary This chapter presents an initial study on the synthesis and tribological properties of Iron Core Hard Carbon microspheres (HC/Fe microspheres) prepared by a hydrothermal reaction. A series of ball on disk tribological tests were carried out on a CETR UMT-2 and the results show that adding aqueous dispersion of HC/Fe microsphere can significantly reduce the friction coefficient by rolling between the two sliding surfaces. The effect of particle size and sliding velocities is also explored. A magnet is used to keep the HC/Fe microspheres in the contact zone during the test. A low stable friction coefficient is observed for a range of applied loads. 6.2 Introduction Carbon-based materials have many unique properties such as low surface energies [145], stable thermal and chemical properties [ ], and high conductivity [149] and can be used in many fields. The tribological performance of carbon-based additives including single-walled carbon nano-horns [150] onion-like carbon [151, 152], carbon nanotubes [153], graphene [154, 155], graphene oxide sheets [156], nano-diamonds [157], carbon black [158], and graphitic nano-particles [159], have been evaluated

103 85 extensively in literature. Due to its lamellar structure, carbon based particles exhibit good tribological properties. From a mechanistic point of view, most nano-particulate lubricant additives can interact with sliding surfaces, just like their liquid counterparts, to form a slick and protective boundary film [160, 161], or by rolling over the surface. Since rolling friction is lower than sliding friction, tribological properties of particles with spherical geometry have been investigated by various groups [ ]. In our group, we have previously shown that surfactant coated hard carbon spheres can be used as ball bearings in aqueous medium to reduce friction [164]. However, under prolonged shearing, friction forces were found to increase. This was attributed to the squeezing out of the HCS from the contact zone region causing the two shearing surfaces to make direct contact. This chapter describes a method of synthesizing HC/Fe microspheres by a simple hydrothermal process and provides an initial report of their tribological properties in an aqueous medium. The microspheres have magnetic iron particles dispersed inside graphitic carbon continuous phase. Since the final pyrolysis step in the synthesis renders the particles hydrophobic, Sodium Dodecyl Sulfate (SDS) was used to disperse the particles in DI water. Using a CETR Universal Materials Tester (UMT), we show that an aqueous dispersion of uniform HC/Fe microspheres exhibits very promising lubrication properties between a glass lens and a silicon wafer. We hypothesize that the use of a magnetic field and iron-core hard carbon spheres will maintain the particles between the two shearing surfaces for prolonged times. The size of the particles used in this study (700 nm to 2.5 μm) is sufficiently larger than the roughness of the shearing surfaces which allows them to easily roll over the surface defects. A magnetic field was applied to confine

104 86 the particles in the contact region thereby improving their properties as a lubricating agent. 6.3 Synthesis of the HC/Fe particles Aqueous precursor solution was prepared by dissolving (+) Glucose (G-7528 Anhydrous > 99.5% HPLC grade, Sigma Aldrich), and FeCl3 (powder, 99.99%, Sigma Aldrich) in DI water. The Glucose/FeCl3 precursor solutions were poured in a 15 ml acid treated glass vial and placed inside a steel pressure autoclave. The autoclave was heated in a furnace with a ramp rate of 4 C/min. The hydrothermal process was carried out at C for 4 hours, and then cooled to room temperature. The black precipitate was collected and washed with acetone and ethanol using the centrifuge for multiple cycles. The collected particles were dried at 80 C for 6 hours in an oven. Pyrolysis [166] was used to carbonize or graphitize the samples. The dried samples were placed in a clean ceramic boat, which was placed at the center of a tube furnace. The furnace was purged with argon at a flow rate of 25 Lt/min for 1 hour and then heated at 800 C for 10 hrs. After cooling to room temperature, the resulting micro-spheres were stored in an airtight glass vial. By changing the parameters of the hydrothermal process, HC/Fe microspheres with four different sizes ranging from 700 nm to 2.5 μm were prepared. 6.4 Carbon/Iron microspheres characterization The morphology and size of hard carbon spheres were characterized by a scanning electron microscopy (SEM, Hitachi S-4800). High-resolution transmission electron

105 87 microscope (HRTEM, FEI Tecnai G2 F30) was also used to identify the iron in the hard carbon spheres. Figure 31 (A) to (C) shows SEM micrographs of the prepared HC/Fe microspheres of mean sizes 700 nm, 2 μm and 2.5 μm respectively. Most of the particles are spherical and uniformly distributed. However, as observed in Figure 30(C) larger microspheres than 2.5 μm, did not have a uniform size distribution, and included some peanut or dumbbell shaped fused-spheres. The black iron particles diffused in the carbon sphere can be seen in the TEM micrograph of the 700 nm particles as shown in Figure 31(D). Figure 31(E) shows the electron diffraction spectrum (EDS) of the HC/Fe microspheres with the peaks appearing at approximately 8 kev and 9 kev, confirming the existence of iron. It is proposed that during the hydrothermal process, the added FeCl3 hydrolyzes to produces Fe(OH)2 or Fe(OH)3, which forms precipitates in an environment rich in molecules produced by simultaneous decomposition of glucose. The hydroxyl (OH - ) group on Fe 2+ (or Fe 3+ ) attracts the decomposition molecules to form the nucleus. In this way, the Fe(OH)2 or Fe(OH)3 gets wrapped by Carbon. The pyrolization step reduces the Fe 2+ /Fe 3+ to Fe that can be attracted by a magnet.

106 88 A B C D E C Count Fe Fe Energy (Kev) Figure 31: SEM images of HC/Fe microspheres (A) to (C) with mean size of 700nm, 2 μm and 2.5μm respectively (D) shows the TEM micrograph of a 700 nm HC/Fe microsphere. (E) Shows the EDS of the 700 nm HC/Fe microspheres confirming the presence of C and Fe with their characteristic peaks at 2.3 KeV and 8, 9 KeV respectively

107 Experimental Setup A ball-on-disk setup (CETR UMT-2) was used to investigate the tribological characteristics of HC/Fe microspheres, as shown schematically in Figure 32. A glass lens (Edmund Optics, 27420) and silicon wafers (test grade, University Wafers) were used as the two sliding surfaces. A magnet pillar of dimensions ( mm) was used as the lens holder to create a magnetic field. It is proposed that the magnetic field plays an important role in keeping these ferrous carbon particles confined within the shearing zone. The assembly was connected to a spring (K= 520 N/m), which was then connected to the DFM Sensor of the CETR UMT-2 that measured the friction force between the two sliding surfaces. Figure 32: Schematic diagram of the proposed lubrication mechanism. The glass lens is cemented on a magnet pillar as the probe to measure the friction against a Si wafer in a dispersion of HC/Fe microspheres. 1 mg of HC/Fe microspheres was ultrasonically dispersed in 1 ml of 3.5 mm SDS-DI water aqueous solution of which 20 μl of the suspension was used as lubricant between the glass lens and the Si wafer. The probe was sheared in a cyclic-lateral motion 20 mm in each direction against the Si wafer. The velocity was fixed at 0.2 mm/s and the friction force was measured. The experiments were conducted under two loading methods; in the

108 90 first case the applied load is increased from 0.1 to 4.7 N ( g) at the increments of 0.98 N (10 g) per cycle and in the second case a constant load of 2 N was applied. The experiments were repeated for four different sizes of HC/Fe microspheres. 6.6 Tribological properties of the HC/Fe microspheres A 3.5mM solution of Sodium dodecyl sulphate (SDS, Sigma Aldrich) was used as a control solution (coefficient of friction 0.25). Figure 33, shows the results of friction measurements between the two sliding surfaces under an increasing load from 0.1 N to 4.7 N using aqueous suspensions of HC/Fe microspheres of different sizes. It can be seen that the friction coefficient decreases with the increasing particles size. This is counterintuitive at first, based on the theory of contact mechanics [163], according to which for a single particle a smaller particle would have less contact area and hence less friction force. It is proposed that in our suspensions with 1 mg particles in 1 ml of 3.5 mm SDS-DI solution, more particles with smaller size will contact the glass lens compared to particles with larger size, which effectively increases their area of contact. This is why the friction coefficient goes down with the increase in particle size. The high coefficient of friction in the case of 2.5 μm particles can be explained on the basis of the previously mentioned polydispersity of these particles in Figure 31 (C). This shows the importance of highly uniform and mono-dispersed particles for effective rolling lubrication.

109 Friction Coefficient (μ) 91 Friction Coefficient nm 2000nm 800nm 700nm Normal Load (g) Figure 33: Comparison of friction coefficient (μ) of four different sizes of HC/Fe microsphere suspensions as lubricant between a glass probe and Si wafer shearing at 200 μm/s with loads increasing from 10g to 450g 6.7 Influence of particle size on the stability of the lubrication properties Load (g) The coefficient of friction between a glass lens and a silicon surface lubricated by a HC/Fe microspheres SDS-DI suspension was monitored at a relative high constant normal load F = 1.96 N (200g). In order to reach equilibrium, the friction tests were carried out 2 minutes after adding the aqueous suspension between the shearing surfaces. All tests were carried for 60 cycles (total shear distance = 0.5 m) and the results are plotted in Figure 34. It was found that the friction coefficient for 700 nm particles was most stable among the four different sizes of particles studied, which was at approximately Although the 2 μm particles showed the lowest friction coefficient, it was unstable. A possible explanation for these results is that larger particles contain more iron particles,

110 Friction Coefficient (μ) 92 and hence experience a larger magnetic force compared with that of smaller particles. Also in the scenario of wear of HC/Fe microspheres, the magnet will prevent removal of iron rich debris and worn out microspheres from the contact zone. However, although the results for larger HC/Fe microspheres fluctuate more than the smaller size particles, it still represents a lower friction coefficient over the entire duration of the experiment. Friction Coefficient nm 800nm 2000nm 2500nm Cycles Cycles Figure 34: Plot of the coefficient of friction μ versus shear cycles for an extended run at a fixed load of 2 N using a spherical glass lens sheared against a silicon surface, with an aqueous 1 mg ml -1 HC/Fe microsphere 3.5 mm-sds suspension as the lubricant. 6.8 Study the effect of strength of magnetic field on lubrication properties of HC/Fe microspheres The initial results so far are promising to show that the HC/Fe particles can be used as additives in aqueous based lubricants. The future studies for this project shall include a detailed investigation of the role of applied magnetic field in the lubrication properties

111 93 of these microspheres. This can be achieved through a systematic study of changing the concentration of iron precursors and by changing the external magnetic field. Such a study could lead to development of aqueous based lubricants with tunable lubrication properties. 6.9 Conclusion HC/Fe microspheres of different sizes were synthesized by a simple hydrothermal method and were characterized by SEM and TEM. The lubrication properties of aqueous suspensions of the prepared HC/Fe microspheres between a glass lens and silicon wafer were investigated using a CETR UMT-2. A magnet of dimensions mm was used as the lens holder to create a magnetic field in order to hold the particles in an effective lubrication placement. It is hypothesized that the magnetic field can confine the particles in the shearing zone. Initial results show that the HC/Fe microspheres suspensions showed promising lubrication properties, with larger particles displaying lower coefficient of friction. Future work in this project should include a systematic study of the role of the applied magnetic field (stronger or weaker magnetic field) on the lubrication properties of the HC/Fe microspheres produced with potential applications in mechanical engineering, mining industry, and bio-lubrication.

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125 107 Appendices Appendix 1: Graphical Representation of major steps in Photolithography Appendix 2: An example of photolithography mask design Appendix 3: Optical micrographs of photolithography masks Appendix 4: Sample script of CETR UMT for tribological testing of the porous polymer samples Appendix 5: Statistical analysis of load vs friction coefficient Appendix 6: Various settings used to create PDMS wafers of different heights Appendix 7: Calculation of modulus of the PDMS

126 108 Appendices Appendix 1: Graphical Representation of major steps in Photolithography Clean Si wafer Uncured Photoresist Spin Coat Photoresist Photomask Cured Photoresist Align mask and expose to UV light Develop in developing solution Pillars of cured photoresist on Si Wafer A1: graphic representation of the major steps in the photolithography process, spincoating, exposure of the photoresist through a mask, development (rinsing off) of the undeveloped photoresist to obtain the desired pattern on the Silicon wafer

127 109 Appendix 2: An example of photolithography mask design A 2.842" square is circumscribed in a circle of radius 4". The square is divided into nine patterned squares each of side 0.942". In each of those nine squares there were repeating clear circles (against a black background) in a matrix. The diameter of the circles should be ranging in a matrix of 15, 20, and 30 µm radius and X, Y spacing: X Three radii at 15, 20, and 30 µm Three spacings (X = Y spacing) at 15, 20, and 30 µm Each of the 9 squares should be to a side Three spacings (X = Y spacing) at 15, 20, and 30 µm Y Each of the 9 squares should be to a side Radius (µm) Spacing (µm) Area: µm radius, 15 µm X,Y spacing µm radius, 20 µm X,Y spacing µm radius, 30 µm X,Y spacing µm radius, 15 µm X,Y spacing µm radius, 20 µm X,Y spacing µm radius, 30 µm X,Y spacing µm radius, 15 µm X,Y spacing µm radius, 20 µm X,Y spacing µm radius, 30 µm X,Y spacing A2: A sample of photolithography mask

128 110 Appendix 3: Optical micrographs of photolithography masks A3: 20X Optical micrograph of a photolithography mask showing 20 μm clear circles on a black background.

129 111 Appendix 4: Sample script of CETR UMT for tribological testing of the porous polymer samples A B

130 112 C A4: (A) to (C) Script to measure the friction force between the sample and a shearing glass probe at 100 μm/s with an applied load of 5g.