1 SOFT HYDRATED SURFACES ENGINEER ED FOR LUBRICITY By ALISON C. DUNN A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOS OPHY UNIVERSITY OF FLORIDA 2013
2 2013 Alison C. Dunn
3 To the courageous women who have gone before
4 ACKNOWLEDG E MENTS God's works are so great, worth a lifetime of study endless enjoyment! Psalm 111:2 (The Message) I am grateful to all who have led me, helped me, taught me, and told me when I needed to get back in the game. It began with my wonderful parents Robb and Pat, and their parents as well. A plethora of teachers and family friends encour aged me to be kind as well as diligent. I appreciate the motley community of Tribology Lab colleagues from 2004 to 2013, as well as my faith community at Camp us Church of Christ My lovely siblings Jill and Russell have taught me muc h about integrity and a dventure My daughter Cora continues to remind me to play early and often. My greatest teacher has been my husband Nick, who thinks much too highly of me. I thank my graduate advisory committee, who have always had an open door and enjoyed discussing the most interesting problems I strive to live up to their examples of teaching and learning: Dr. Scott Perry, Dr. Malisa Sarntinoranont, and Dr. Tommy Angelini. And to my committee chair Dr. Greg Sawyer, who took a chance on me on many, many instances over the past 9 years. He believes in friendship as well as science, in honesty as well as inquiry May this work d o justice to his investment.
5 TABLE OF CONTENTS page ACKNOWLEDGEMENTS ................................ ................................ ............................... 4 LIST OF FIGURES ................................ ................................ ................................ .......... 7 ABSTRACT ................................ ................................ ................................ ................... 10 CHAPTER 1 ROBUST BIOLOGICAL LUBRICITY ................................ ................................ ...... 12 Moving Toward Softer Materials ................................ ................................ ............. 12 The Eye as a Model System ................................ ................................ ................... 12 Hydrogel Materials ................................ ................................ ................................ .. 14 2 CONTACT LENS SURFACES, QUASI STATIC MECHANICS, AND EXPERIMENTAL PLAN ................................ ................................ .......................... 20 Contact Lens Lubricity in Boundary Sliding Conditions ................................ ........... 20 Strategies for Lubricity Interrogatio n ................................ ................................ ....... 23 Normal Force Changes ................................ ................................ .................... 24 Pressure Effects on Hydrogel Water Content ................................ ................... 25 Sliding Speed Changes ................................ ................................ .................... 26 Lubricity Experimental Configuration ................................ ................................ 28 Material Composition ................................ ................................ ........................ 29 Theory of Experiments ................................ ................................ ............................ 30 3 AQUEOUS LUBRICATION OF HIGH WATER CONTENT POLYACRYLAMIDE HYDROGELS ................................ ................................ ................................ ......... 37 Sli ding Conditions and Hypothesized Lubrication Results ................................ ...... 37 Experimental Configurations and Conditions ................................ .......................... 38 Polyacrylamide Lubricity Aga inst Hard Impermeable Counterfaces: Friction Traces ................................ ................................ ................................ .................. 39 Time at Pressure Mediated Polyacrylamide Lubricity ................................ ............. 40 Discussion ................................ ................................ ................................ .............. 42 Friction Traces ................................ ................................ ................................ .. 42 Contact Area Size Considerations ................................ ................................ .... 44 Fluid Load Support ................................ ................................ ........................... 45 Lubrication Regimes ................................ ................................ ......................... 47 Countersurface Wettability ................................ ................................ ............... 47 4 LIMITS OF AQUEOUS LUBRICATION OF THIN HYDROGEL LAYERS AND BRUSHES ................................ ................................ ................................ .............. 59
6 Pressure Dictated Lubricity Extremes of Thin Surface Hydrogel Layers ................. 60 Fabrication and Substrate Deformation ................................ ................................ .. 61 Friction Response and Brush Pre Stress ................................ ................................ 64 Discussion ................................ ................................ ................................ .............. 65 5 CONCLUSIONS AND FURTHER THOUGHTS ................................ ...................... 73 Lubricity of High Water Content Polyacrylamide ................................ ..................... 73 Lubricity of Hydrogel Brushes Grafted onto a Hydrogel Substrate .......................... 74 Summary ................................ ................................ ................................ ................ 75 APPENDIX A SMALL ANGLE APPROXIMATION CONTACT MECHANICS ............................... 77 B MICROTRIBOLOGICAL INSTRUMENTATION ................................ ...................... 78 C HYDROGEL FABRICATION CONDITIONS ................................ ........................... 80 D INSIGHTS FROM BIOLOGICAL SYSTEMS ................................ ........................... 81 LIST OF REFERENCES ................................ ................................ ............................... 87 BIOGRAPHICAL SKETCH ................................ ................................ ............................ 91
7 LIST OF FIGURES Figure page 1 1 Tribological problems can be identified in many human systems, from dental materials to tactility to cartilage load support and large orthopedic join ts. .......... 16 1 2 Schematic of the human eye including pertinent mechanical properties and mechanical components to blinking (excluding the musculature) ....................... 17 1 3 A simulation of sliding speeds of the eyelid wiper over a contact lens produced these film thicknesses and resultant pressures. ................................ 1 8 1 4 Friction coefficients of hydrogel surfaces sliding against various counterfaces as a function of sliding speed for sel ected recent publications, as delineated by author. ................................ ................................ ................................ ........... 19 2 1 A simple and usefu l model for the mechanics of a thin soft film is the Winkler bed of springs model. Contact mechanics can predict the interaction volume between a glass probe and soft thin membrane. ................................ ................ 31 2 2 Using a probe of radius 3.1 mm means that normal forces of ~100 N must be applied t o reach physiological blinking pressures on soft contact lenses of effective modulus ranging 0.5 1.5 MPa. ................................ ............................ 32 2 3 Contact lens surfaces exhibit characteristic shear stresses over normal for ces from 5 mN to 80 mN. ................................ ................................ ................ 33 2 4 Indentation curves of normal force versus indentation depth ca n be fitted using the Winkler model to approximate the effective elastic modulus of commercial contact lenses at loads up to 30 mN. ................................ .............. 34 2 5 If plane strain is evenly distributed through a vertical section of the bed of springs model, the water can be squeezed out. ................................ ................. 34 2 6 A lubrication curve can be built using shea r stress values obtained from contact lenses, the natural eye environment, and simulations of elastohydrodynamic behavior between an eyelid wiper and corneal surface. .... 35 2 7 Contact area motion can be changed in lubricity measurements of contact lenses by switching the frictional probe from a radiused lens to a flat plate. ...... 36 3 1 The mesh size of poly(N,N dimethylaminoethyl methacrylate) (DMAEMA) hydrogels can be controlled by the polymer content. ................................ .......... 50 3 2 Contacting configurations fabricated in order to examine lubricity of stationary, migrating, and self mated conditions. ................................ ................ 50
8 3 3 Friction traces for cycle 1 and 30 of sliding experiments at normal force F n =300 N. Migrating traces clearly show a breakloose region, while stationary contact does not. ................................ ................................ ................ 51 3 4 The middle 20% of each free sliding friction trace is used to calculate the friction coefficient for that sliding cycle. ................................ .............................. 52 3 5 The middle 20% of each free slidin g friction trace is used to calculate the friction coefficient for that sliding cycle. ................................ .............................. 53 3 6 The middle 20% of each free sliding friction trace is used to calculate the friction coefficient for that sliding cycle. ................................ ............................. 54 3 7 As the flat sheet hydrogel is slid under a polished probe, the pass frequency at half the stroke length is a given value, in this example case f =0.5Hz. ............ 55 3 8 A) The friction trace from the migrating contact condition showing breakloose friction features. B) When the friction coefficient is plotted versus the time since the last pass, ................................ ................................ ............................. 55 3 9 The lubrication behavior of these surfaces changes according to the countersurface. ................................ ................................ ................................ ... 56 3 10 The friction coefficients that were measured in this work are plotted on the same axes as the literature review presented in Figure 1 4. .............................. 57 3 11 Indentation curves showing the applied normal force as a function of the indentation depth can be fit using the well known Hertzian contact model to estimate the elastic modulus of the hydroge l sample. ................................ ........ 58 4 1 The surface hydrogel layer aims to mimic the lubrication mechanism of the natu ral tear film and tissues. A) The natural tear film. B) A schematic represe ntation of a surface gel layer ................................ ................................ .. 66 4 2 Critical pressure causes the surface gel to dehydrate enough to stick to the probe and elicit an unstable friction response. ................................ .................... 67 4 3 The polyacrylamide (PAAm) brush fabrication process involved 3 steps: first, fabricating the polyHEMA substrates, polymerizing brushes by floating the substrate in a bath ................................ ................................ ............................. 68 4 4 Surface brush fabrication resulted in steady s tate bending of the substrates due to a surface pressure within the brush. ................................ ....................... 69 4 5 Plots of bending curvature and stress in surface brushes ................................ .. 70
9 4 6 Stick slip friction was observed following each turnaround point. For similar applied pressures of 650 700 Pa, the free sliding friction coefficient over the central 30% of the track for sample cured for 150 seconds was =0.013 ......... 71 4 7 Polyacrylamide brushes polymerized for longer times, having thicker brushes, appear to be more lubricious than those with thinner brushes. ............ 71 4 8 Composite image of a polymer brush grown on a pHEMA substrate. Green 1 m beads highlight the pHEMA substrate and red 100 nm beads appear to be trapped i n the surface PAAm brush. ................................ ............................. 72 A 1 Comparison of the nomenclature and mechanics of deformation of a sphere on flat model (left) and the approach of two spheres of equal radius (right). ...... 77 B 1 Low forces down to 25 N can be used to probe the lubricity of soft hydrated materials using this cust om microtribometer with a heated fluid cell. ................. 79 D 1 Insights from the native eye environment: compare to an experimental solution environment of simple saline, boundary lubricant solutions reduce the friction coefficient ................................ ................................ .......................... 83 D 2 A custom open platform micr otribometer was used to measure the friction coefficient of a murine cornea in situ against a smooth glass probe. .................. 84 D 3 The friction coefficient b etween a glass probe and murine cornea in situ under an applied load of Fn~4.5 mN, sliding at 250 /s was =0.06. ................. 85 D 4 The lubricity of an epithelial cell monolayer as tested against a soft contact lens probe was on the order of =0.04, though the integrity of the cell monol ayer was compromised after about 10 reciprocating cycles. ..................... 86
10 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy SOFT HYDRATED SURFACES ENGINEERED FOR LUBRICITY By Alison C. Dunn August 2013 Chair: W. Gregory Sawyer Co chair: Malisa Sarntinoranont Major: Mechanical Engineering Hydrogel materials are emerging as biological mimics, es pecially in biomedical applications such as contact lenses that rely on lubricity for success. An integral part of the hydrogel is water, which provides for excellent lubricity in the human body. Taking the eye as a model system to study, the friction resp onse of hydrogel soft contact lenses against glass was found to be low, and dependent upon the experimental conditions. The experimental configuration and sliding speed were varied on custom high water content polyacrylamide gels, resulting in identificati on of distinct behavior when a hydrogel is sliding against itself versus a hard impermeable surface such as glass. At a range of sliding speeds spanning an order of magnitude, the friction coefficient of self mated polyacrylamide never rose above =0.06. The limits of excellent lubricity were probed by synthesizing polyacrylamide brushes onto the surface of a polyhydroxyethyl methacrylate (polyHEMA), Polyacrylamide hydrogel brush films show a reduced friction coefficient with increasing brush layer thickne ss, confirming that the presence of water dictates a lubricious environment. When the surface cannot maintain a high enough water concentration, such as under high pressures, the lubricity of the surface is lost. This thesis provides
1 1 unique and simple ways to interrogate the fundamental mechanisms of hydrogel lubricity, and discusses the limitations to such findings.
12 CHAPTER 1 ROBUST BIOLOGICAL LUBRICITY Moving Toward Softer Materials The human body is composed of approximately 60% water, based on age, se x, health, and lifestyle factors This water is located in every organ, from a minimum of 22% in bone and up to 90% in lung tissue. The human body is constantly in motion, and as such includes many articulating surfaces, from the eyelids to the spine, to t he epithelial membranes lining the gastric system (Figure 1 1). These surfaces in relative motion must maintain a lubricious environment through specialized extracellular matrix deposit ion and hydrophilic components. If they do not, tissues can become unco mfortable and eventually diseased. The Eye as a Model System The human eye is an exquisite mechanical system from which to base biological lubricity studies (Figure 1 2 ). During waking hour s, the eyes are rarely at rest, moving to provide vision, with the eyelid blinking up to 15,000 times per day. Healthy pressure between the eyelid and cornea or sclera when the eye is not blinking is approximately 1 kPa, while blink pressure is o n average 5 kPa [ 1 2 ] These light pr essures are supplied through contractions in the musculature, and are observed between the cornea and eyelid wiper, each having an elastic modulus of about 1 MPa or less, depending upon the scale over which the modulus is measured The blink motion is unique in that the eyelid wiper begins at rest, accelerates up to a maximum speed of 100 mm/s, approaches the lower eyelid, then retracts back. In sweeping fro m near ze ro velocity up to 100 mm/s, the eyelid wiper and cornea contact during blinking span s boundary lubrication to elasto hydrodynamic lubrication T he contacting components include not
13 only the eyelid wiper and cornea, but also the biological gel at th e co rneal surface provided by mucin and mucinous glycoproteins. Load support is spread over these tissues and tear film components, comprising a robust system that can operate through millions of cycles in a lifetime wit hout appreciable degradation, depend ing upon nutrition, lifestyle and aging This thesis features custom instrumentation to apply and measure micro forces on soft materials at pressures seen in the eye (Figure 1 3) Due to the low pressure, it would be difficult to build an instrument with controlled motions that could provide speeds up to 100 mm/s under pressures < 5 kPa As such, the majority of the experimentation in this work takes place at slower sliding speeds, placing the lubrication in the boundary regime. Most eye movements outside of blinking experience boundary lubrication, and as such it is a highly relevant condition. Soft contact lenses worn in the eye become a part of this system when inserted. As such, they are designed to mimic the wettable surface of the cornea such that c omfortable vision correction is achieved. However, soft contact lenses disrupt the thickness and breakup time of the natural tear film. They lack a mucinous surface gel, and must be permeable enough for oxygen and ion transport while in the eye. They must also withstand the v igorous blink pressures and motions up to 15,000 times per day without becoming too fouled by tear film proteins, lipids, or inflammatory response cells. Thus the lubricity of these lenses is very important; people simply do not wear t hem if they are not comfortable. Though contact lenses are not medically necessary for a large portion of the population, other medical devices such as catheters, arterial stents, and orthopedic implants are required for health maintenance and survival.
14 S oft surface lubricity is of great importance to advances in health procedures. A handful of t ribology groups are interested in the lubricity of hydrogels both for fundamental mechanics studies and targeted biomedical applications like contact lenses In 20 05, two works report the friction coefficient between soft hydrogel contact lenses and glass. Ross et al reported a range of friction coefficient of =0.01 0.07 between glass and 7 different commercial contact lenses, though the sliding speeds and applied normal forces were omitted [ 3 ] Rennie et al reported a range of =0.024 0.074 for a single poly(HEMA) based soft contact lens (Acuvue2) under a variety of sliding speeds and normal loads [ 4 ] Also in 2005, Kurokawa et al studied the lubrication beh avior of polyacrylamide (PAAm) hydrogels swollen with water or ethylene glycol [ 5 ] More recently, Roba et al took a step toward physiological conditions by measuring the friction coefficient between contact lenses and mucinized glass [ 6 ] Zhou et al characterized a single silicone based soft contact lens (Acuvue Oasys) under a variety of loading and speed conditions [ 7 ] And Mamada et al studied the lubrication behavior of polyvinyl alcohol (PVA) based hydrogels of different degrees of polymerization under a wide variety of conditions [ 8 ] These studies all present the friction coefficient as a function of the sliding speed, and they are plotted on the same axes in Figure 1 4. Clearly there are both increasing and decreasing trends, even over the same range of sliding speeds. Hydrogel Materials Modern biomedical devices and implants make use of polymeric materials due to their mechanical flexibility ease of fabrication, and biocompatibility [ 9 ] In fact, hydrogel materials which include water as an integral part of the structure appear to be the most
15 biomimetic materials invented due to their mechanical properties hydrophilicity, and water content [ 10 ] Hydrogel materials are characterized by the extent to which hydration affects their structure. Most hydrogels are polymer backbones connected by crosslinking molecules, though physical crosslinking i s also possible. Poly merization or crosslinking can be initiated by light, heat, or chemical catalysts. The result is essentially a mesh of polymer components with a characteristic size; if the mesh size or ag gregate polymer size is greater than ~100 nm, t he hydrogels may show signs of turbidity [ 11 ] Polyacrylamide hydrogels (PAAm) are commonly used for gel electrophoresis, or the filtering of proteins through the gel based on size/molecula r weight [ 12 ]
16 Figure 1 1 Tribological problems can be identified in many human systems, from dental materials to tactility to cartilage load support and large orthopedic joints.
17 Figure 1 2. Schematic of the human eye including pertinent mechanical properties and mechanical components to blinking (excluding the musculature)
18 Figure 1 3. A simulation of sliding speeds of the eyelid wiper over a contact lens produced these film thicknesses and resultant pressures [ A dapted from Dunn A.C. 2013. Lubrication Regimes in contact lens wear during a blink. Tribology International ( Volume 63, Page 46, Figure 1) .]
19 Figure 1 4. Friction coefficients of hydrogel surfaces sliding against various counterfaces as a function of sliding speed for selected recent publications, as delineated by author. Traditional lubrication curves would suggest that increasing friction coefficient with increasing sliding speed (related by a power law of one h alf or one third) indicates some fluid pressurization. Note that in papers with a series of results, these results represent those at minimum applied normal load. [ Adapted from Rennie, A.C. 2005. Friction coefficient of soft contact lenses: measurements an d modeling Tribology Letters (Volume 18 Number 4, Page 503 Figure 5 ) ; a dapted from Kurokawa T. 2005. Elastic Hydrodynamic Transition of Gel Friction. Langmuir (Volume 21, Page 8646, Figure 3); a dapted from Roba M. 2011. Friction Measurements on Contact Lenses in Their Operating Environment. Tribology Letters (Volume 44, Page 393, Figure 7); a dapted from Zhou B. 2011. A study of the frictional properties of senofilcon A contact lenses. Journal of the Mechanical Behavior of Biomedical Materials (Volume 4, Page 1338, Figure 3); adapted from Mamada, K. 2011. Friction Properties of Poly(vinyl alcohol) Hydrogel: Effects of Degree of Polymerization and Saponification Value. Tribology Letters (Volume 42, Page 244, Figure 4). ]
20 CHAPTER 2 CONTACT LENS SURFACES, Q UASI STATIC MECHANICS AND EXPERIMENTAL PLAN Contact Lens Lubricity in Boundary Sliding Conditions When contact lenses slide against glass in relative motion, a question arises ce Lubrication theory tells us that the most intimate type of contact in the presence of sliding is called boundary conditions [ 13 ] The material asperities contact each other at their boundar ies, and elastic or plastic deformation takes place to react the energy of sliding and produce a friction force that opposes the motion. For a hydrogel surface, the contact is completely conformal when pressed against an infinitely stiff countersurface, as any surface features will deform readily [ 14 ] If sliding speed is slow enough and normal force applied is high enough, the apparent contact area can be take n t o be the real contact area This condition is very appropriate for measuring the friction response of a variety of materials that may vary in water content or wettability because they interrogate the intimate contact between the surfaces. Under those cond itions, the contact lens can be modeled as a bed of springs under vertical plane strain [ 15 16 ] The springs are linearly elastic and non interacting. Geometry describes the volume of interaction between a hard spherical countersurface of identical radius as shown in Figure 2 1 Taking a linear elastic spring stress is equal to the strain times an effective modulus (Equation 2 1) a relationship can be found between the normal force applied and the vertical deflection measured First, nomenclature is altered to refer to P as pressure, t to the thickness of the bed of springs (in this case the soft hydrogel contact l ens thickness), and d to be the depth of interaction (in this case the depth of
21 indentation); see Equation 2 2. Integrating this equation over the area of contact of a single spring, A provides a relationship between the applied normal force, F n and the interaction volume, Vol (Equation 2 3). (2 1) (2 2) (2 3) The hemispherical probe in this thesis work is borosilicate glass, so it is considered to be infinitely stiff as com pared to the hydrogel materials being interrogated; therefore, the deformation of the linear bed of springs hydrogel model is the full deformation. Because commercial contact lenses are quite thin ( t ~100 m) as compared to the radius of the probe (radius R ~3,100 m), the contact area and indentation depths are also small, and thus the small angle approximations can be used to relate the indentation depth d the contact radius a and the radius of the probe R The details of those calculations can be found in Appendix A. Substituting the contact radius and probe radius into the equation for the interaction volume (Equation 2 4) gives a relationship from which to calculate what the applied normal forces must be in order to reach the appropriate contact pressu res in the given instrument setup. (2 4) A typical glass probe with radius of 3 .1 mm in contact with a soft material of modulus 1 MPa would require a normal force of 1 00 N in order to apply a typical blink pressure of 6 kPa. Co ntact lens material moduli range from 255 kPa up to nearly 1.5
22 MPa. T hough a normal load of only 1 00 N would be needed to reach blink pressures less than 5 N would be required for the eyelid at rest (a pressure of 1 kPa) Figure 2 2 shows a curve of the relationship between the modulus of the soft sample the normal force applied, and the pressures achieved. Resolving force s less than 100 N approaches the noise limits o f micro sized tribometers, but in this case it can be reached using high precision ca pacitive probes measuring the displacement of a flexure of known stiffness (see Appendix B for details regarding the instrumental setup). Figure 2 2 (B) shows a schematic to scale of the smooth glass probe, the soft, broad radius counterface, and typical st roke length and sliding speed. The data recorded from a sliding experiment takes the form of the normal forces applied F n the stage motion applied and the friction forces F t in that contact. In historical block on plane friction measurements, the app lied normal force is determined by the mass of the object whose surface is being measured [ 17 ] The static and kinetic friction forces are si ngle values, and the friction coefficient is simply the ratio of the friction force to normal force ( Equation 2 5 ) In this case, a normal force is prescribed with piezoelectric stages, and constantly monitored over the length of the experiment. (2 5) Hydrogels differ from other compliant materials due to their hydrated nature as described in the first chapter of this work. As such, applied pressure causes fluid displacement not only from the surface, but a lso within the material in the pressurized zone. This, along with contact area and surface energy considerations, may alter the friction response as the normal force is increased. For this reason, normal forces are
23 applied at discrete levels, each of whic h is allowed to equilibrate before advancing to the next. In this way the lubricity of various material or stress states can be assessed in a single experiment. F igure 2 3A is a plot of the friction force as a function of applied normal load for a variety of contact lenses with silicone and poly( hydroxyethyl methacrylate) (polyHEMA) materials. For a silicone based hydrogel with internal wetting agent (Acuvue Oasys ), the friction coefficient is approximately =0.02 while for a silicone based lens with plasm a surface treatment (PureVision), the friction coefficient is >0. 06 Using the geometry considerations above, the contact area for each lens can be approximated after a simple indentation experiment showing the normal force versus indentation depth into the material ( Figure 2 4 ) [ 18 19 ] Next the shear stress exerted on the contact lens surface under relativ e sliding can be calculated and plotted versus the normal force (Figure 2 3B ). The shear stress on the surface of these contact lenses appears remain fairly constant over contact stresses ranging 20 35 kPa. S trategies for Lubricity Interrogation The resp onse of a hydrogel under applied shear may include elastic deformation, water transport through the hydrogel mesh, viscoelastic deformation, hydrodynamic characteristics, and surface interaction. The competitive rates of these phenomena during a lubricity experiment have yet to be explored. As such, the lubricity of hydrogel systems should be systematically interrogated by altering not only normal fo rce, but also the sliding speed, experimental setup and hydrogel composition This section provides context, limits, and discussion regarding the each strategy for lubricity interrogation, as well as justification for the methods used in this work.
24 Normal F orce C hanges A clear first method of interrogating the lubricity of a sliding pair is to change the normal force to produce a curve of friction force versus normal force, as introduced in the previous section. Th is allows for curve fitting to obtain the overall friction coefficient. In addition, the uncertainty of the overall friction coefficient can be mode led by Monte Carlo simulations [ 20 ] Applying various normal force levels during a lubricity experiment is limited on the lower end by the noise floor of the instrumental setup. For example in the microtribometer used in this work, the capacitive probes 1 are cal ibrated to 5 m/V and the typical stiffness of a medium load flexure in the normal direction is 1000 N/m. The minimum voltage resolution is 0.3 mV, though the capacitive probe error band is 5 nm, which corresponds to a voltage of 1 mV. Propagating this thr ough the known flexure stiffness, the minimum force that could be detected is approximately 5 N. The uncertainty in the flexure stiffness as observed through multiple calibrations is less than 5 N/m. In practice using a system with a very long mechanical path to ground has a noise level of 10 N Though soft hydrated materials may help to damp out noise, the minimum repeatable normal force on a curved gel surface is about 25 N. The higher end of force that can be applied while maintaining free sliding is dependent upon the friction between the interacting surfaces and the yield stress of the material being tested. If the material fails or the probe sticks t o the material over the maximum friction direction stage stroke, friction coefficient cannot be repo rted Contact lens materials and other softer gels have other practical limits such as their physiological ly relevant 1 Capacitive probes used are from Lion Precision, and they function by measuring the changes in capacitance between a conductive surface and th e conductive target, which we mount on to the dual flexure.
25 operating range. For contact lenses this is between 1 k P a and 8 kPa of normal pressure H igher measurement uncertainty in the friction co efficient of commercial contact lenses at higher applied loads is shown in Figure 2 3 which may be related to the applied pressure approaching 5 times those experienced in normal operation, and the subsequent effects on the hydrogel material. Recent work by Angelini et al identifies a rough scaling between the elastic modulus and water content of hydrogel materials [ 21 ] I n hydrogels with 2 magnitude, while at high water content >90% it can change 3 orders o f magnitude with a few percent change in water content Pressure Effects on Hydrogel Water Content Th e commercial lenses in Figure 2 3 have reported equilibrium water content s of 3 6% (PureVision) to 58% (Acuvue2) [ 22 23 ] placing them in the range where modu lus does not change appreciably. However, i t is worthwhile to calculate the change in water content assuming equilibrium change in dimension due to the applied stresses in lubricity experiments. For Acuvue2, the maximum stress is 28 kPa, which corresponds to an indentation depth of 32 m, or approx imately 26% strain at the apex of the lens Theoretically, the water content of the hydrogel in a vertical element under that strain would be [H 2 O ] 1 =43% down from initial water content of 58% if the plane strain condition is upheld (Figure 2 4) This drop in water content of 15% could increase the modulus by a factor of 2 For PureVision, the maximum stress is 33 kPa, corresponding to an indentation depth of 13.5 m, or 14% strain at the apex of the lens According to plane strain, the minimum water conten t would be [H 2 O] 1 =26%, down from initial water content of 36%. This drop in water content of 15% could increase the modulus by a
26 factor of 1.3 T he lubricity, inasmuch as it is a fun ction of the stiffness of the hydrogel and the water available to the con tact zone, may be affected by this One limitation of this very brief analysis is that the lubricity of the commercial lenses was measured in a migrating contact condition, where the probe was continually moved across the surface, and did not dwell at any location. That could prevent reaching the maximum indentation depths reported here due to the viscoelasticity of the biphasic hydrogel material. In addition, the constraint of plane strain in the vertical direction has not been confirmed in this work; in s itu optical tracking techniques may be useful to assess that The lubricity response of a high water con tent polyacrylamide hydrogel where these effects may be magnified, is discussed in detail in Chapter 3. Sliding Speed Changes The next type of sliding condition that can be altered is the speed of relative sliding. The rate at which the probe or countersurface slides in relation to the hydrogel sample being tested will compete with the rate at which fluid is pressurized and expressed from the surface and affected zone. The sliding speed is typically limited by the mechanism of the i nstrument providing the motion. For the custom microtribometer the speed is limited to approximately 1500 m/s over an 800 m stroke length due to the data acquisition speed. If there are few points that can easily be distinguished in the free sliding zone, no friction coefficient can be determined from the sliding cycles. The minimum speed is a speed at which the time it takes to complete a stroke begins to approach the time n eeded to see difference in applied normal force due to evaporation and drift (evaporation causes changes in the capillary forces of the fluid bath around the frictional probe) This is approximately in the single micrometer s per second range. In our experi ence, quasi static conditions are achieved at speeds up to about v = 200 m/s,
27 or when the dwell time on any given location on the hydrogel countersurface sample is less than a few seconds (a ssuming a hydrogel modulus of 1MPa, a probe size of R =3mm, and an a pplied normal force of 1 mN). This quasi static sliding is typically regarded to be in an elastic boundary lubrication regime, where the surfaces have some character of intimate contact and conformation to surface features Shear stress is somewhat constan t based on the surface roughness A schematic of these lubrication regimes is presented in Figure 2 5A As sliding speed increases, the fluid entrained in the contact becomes pressurized because it cannot be squeezed out in the contacting time, and as such it begins to support some of the load. As some load is supported by the fluid, the lubrication regime is called mixed and s hear stress drops. When the surfaces can no longer be said to be in intimate contact but are still somewhat conformal, the regime is elastohydrodynamic. Hamrock and Dowson characterized the shear stress as proportional to the sliding velocity to the one third power and subsequently Jin and Dowson wrote a r eview of elastohydrodynamic lubrication in biological systems [ 24 25 ] Full hydrodynamic lubrication is characterized by separation of the surfaces with no necessary conformation and shear str ess is proportional to the sliding velocity to the one half power, as originally characterized by Reynolds, and more formally by Sommerfeld [ 26 27 ] Using measured and simulated shear stresses as a function of sliding speed, a lubrication curve for the soft hydrated contact in the eye was assembled, as shown in Figure 2 5B Even though the lubrication curve for the soft hydrated contact in the eye shares general characteristics with traditional lubrication curves for oil lubrication of metals [ 28 ] the pressurization of the lubricating fluid takes on added features because it can be
28 pressurized not only between the surfaces but inside the surface materials themselves. In essence, the lubricant/surface distinction is uncl ear; the lubricant is structural ly incorporated into the surfaces. In the case of pressurization, there is fluid load support before the surfaces are separated, and the transitions between lubrication regimes would be highly dependent upon water content of one or both surfaces. Lubricity Experimental Configuration Stepping back before conditions of normal force or sliding speed are considered, the geometry of the sample setup will also affect the local surface response and the friction measured. Recent hyd rogel lubricity publications detail the response of hydrogel surfaces under various environment al and geometrical configurations. In particular, whole contact lenses have been tested against a flat glass interface and a radiused probe (see Figure 2 6 A for a schematic) [ 4 29 ] Unde r a radius probe, a reciprocating contact lens will not always contact the probe at the s ame location, that is, the contact between the surfaces migrates along the hydrogel. The pressure as seen from an observer at the glass probe will follow the surface geometry, in this case a thin gel with a radius of curvature of about 8 mm. The pressure profile is a repeated semispherical pattern that is symmetric in forward and reverse sliding directions of the contact lens (Figure 2 7 B ). If the observer is moved to a particular location on the contact lens surface (blue trace in Figure 2 7 B the pressu re profile takes on a different character, that of intermittent contact. As the contact lens reciprocates, the flexure responds to the local friction force, but the contact lens continuously moved in and out of contact. There is some time between passes f or local area rehydration of the contact lens surface if any fluid was displaced by the previous pass. If the frictional probe is ex changed for a flat
29 glass plate, the character of the interaction is changed to one of stationary contact. Though the contact lens continues to reciprocate, there is no vertical translation of the frictional probe; it is always in contact with the apex of the contact lens. The material being measured in this case is a single location on the hydrogel, which remains un der pressure If any fluid is pumped out of that local contact, it has no chance to return or locally rehydrate the material. This may in fact alter the contact lens material in terms of water content and permeability. The permeability of a hydrogel surface of, for ex ample Acuvue2 (material Etafilcon A) has been measured to be in the range of 1 5 x 10 15 m 4 N 1 s 1 at the initial equilibrium water content of 58% [ 29 ] At a blink co ndition of average pressure P =6 kPa, there would be a quasi static strain of 5.5% and a decrease in water content down to 56%. Even a difference in water content of 2% may alter the material performance to such an extent that as manufactured contact lens p roperties are no longer relevant to on eye conditions This concept is followed in Chapter 3 by reversing the hydrogel sample from the flat to the probe in order to capture migrating and stationary contacting pressures on the same instrument under nearly i dentical conditions. Material Composition Additional factors which will change the mechanical response are degree of crosslinking, impurity concentration, curing solvent, curing method, cha rged groups and hydrophobicity [ 30 31 ] All of those polymer processing variables will change the water content and/or effective mesh size of the material [ 32 ] These parameters are the direction to take further studies for targeted lubricity biomedical applications, but are not explored in the scope of this work.
30 Theory of Experiments The background descriptions and motivations given above give rise to the following hypotheses for a mechanistic des cription of the robust lubricity of hydrogels, as well as the limits on that lubricity. The hypotheses in more detail are as follows: 1. Robust lubricity is possible over more than a single lubrication regime, as they are historically understood. Very low fri ction < 0.05 can be found when testing against surfaces under boundary conditions and under conditions of fluid pressurization. 2. A hydrogel surface provides the best lubricity when water is able to be retained locally in the surface and between the sliding surfaces, that is, the water content of the gel is locally maintained. 3. Hydrogel thin films and brush films are limited in their ability to provide robust lubricity when they are under high applied pressures as exhibited by unstable friction behavior; thin ner brush layers become dehydrated at lower pressures. The experimental plan for this thesis begins with changes to the normal force, moves to changes in sliding speed and finally combines velocity differences with three distinct experimental configurati ons (stationa ry, migrating, and self mated). In choosing those parameters, the shear stre ss response and associated trends will illustrate the lubricity of the material itself in terms of traditional lubrication behaviors. The ability for the contact to ma intain water, even as it may be present inside a surface, is proposed to be one of the reasons for the robust lubricity of high water content surfaces. New insight into the lubricant as an integral part of the soft materials will be discussed
31 Figur e 2 1. A simple and useful model for the mechanics of a thin soft film is the Winkler bed of springs model. Contact mechanics can predict the interaction volume between a glass probe and soft thin membrane. [Adapted from Rennie, A.C. 2005 Friction coeffic ient of soft contact lenses: measurements and modeling. Tribology Letters (Volume 18, Number 4, Page 500, Figure 2).]
32 Figure 2 2. Using a probe of radius 3.1 mm means that normal forces of ~100 N must be applied to reach physiological blinking pre ssures on soft contact lenses of effective modulus ranging 0.5 1.5 MPa. A) A plot of the resulting average pressure applied as a function of the applied normal load for materials with effective elastic moduli between 0.5 MPa and 1.5 MPa. B) A schematic of the rounded glass probe on the contact lens apex, roughly to scale.
33 Figure 2 3. Contact lens surfaces exhibit characteristic shear stresses over normal forces from 5 mN to 80 mN. A) Four popular commercial contact lens brands can be differentiated by m icrotribological measurements. B) If the shear stress is plotted versus the normal stress, a characteristic stress for the contact between glass and soft contact lens surfaces can be identified it runs from about =0.5 kPa for Acuvue Oasys up to =2.5 kPa for PureVision.
34 Figure 2 4. Indentation curves of normal force versus indentation depth can be fitted using the Winkler model to approximate the effective elastic modulus of commercial contact lenses at loads up to 30 mN. Results are listed, and range from 220 kPa up to 710 kPa. Figure 2 5. If plane strain is evenly distributed through a vertical section of the bed of springs model, the water can be squeezed out. Therefore the new equilibrium water conten t can be estimated for a thin film of hydrogel material under applied stress, as a function of the initial water content and the vertical strain. The water and polymer concentrations are indicated by brackets.
35 Figure 2 6. A lubrication curve can be bui lt using shear stress values obtained from contact lenses, the natural eye environment, and simulations of elastohydrodynamic behavior between an eyelid wiper and corneal surface A) The lubrication regimes between soft materials are shown in schematic for m. B) The lubrication curve is assembled from literature and simulations. [ Adapted from Dunn, A.C. 2013. Lubrication Regimes in contact lens wear during a blink. Tribology International ( Volume 63 Page 49, Figure 4) ]
36 Figure 2 7. Contact area motio n can be changed in lubricity measurements of contact lenses by switching the frictional probe from a radiused lens to a flat plate. A) Migrating contact allows for an intermittent pressure and the opportunity for the surface ( s) to rehydrate between passes as shown using observers placed on an arbitrary location on the contact lens surface (blue) and on the radiused probe (black). S tationary contact applies continuous pressure a gainst a hydrogel sample, shown by an observer at the red dot B) A plot of the maximum normal pressure shows the differences in pressures experienced by observers at the locations shown in (A).
37 CHAPTER 3 AQUEOUS LUBRICATION OF HIGH WATER CONTENT POLYACRYLAMIDE HYDROGELS In general, the stiffness of a hydrogel will be dependent up on the water content as described in Chapter 2. Entropic elasticity theory predicts that the elastic modulus will be inversely propo rtional to the mesh size cubed [ 21 ] Hydrogels with low water content <40% by definition will be more difficult to compress under sliding conditions because the mesh size will be smaller, leading to more restriction of flow. However, that ind icates that the trap ped fluid will be more easily pr essurized because its flow rate is restricted. By contrast, high water content hydrogels (>80%) will be more easily deformed as there is less restriction of fluid flow, and overall larger mesh size (Figur e 3 1 ) Going back to the traditional lubrication curve (Figure 2 5 ) a lower viscosity lubricant will require faster sliding speed to provide fluid load support than a higher viscosity lubricant In the same way, the viscoelastic response of a hydrogel su rface will depend largely on the water content. Greater volume of water will lower the effective elastic modulus of the interface, and faster sliding speed will be needed to encourage fluid load support and hydrodynamic conditions. To summarize a hydroge l surface engineered for lubricity would have a structure with small enough mesh size to encourage pressurization, but enough water present to provide aqueous lubrication. Sliding Conditions and Hypothesized Lubrication Results In this case a high water content gel was chosen due to the dynamic range of sliding speed capability of the instrument, and the hydrodynamic lift achieved at those speeds. Appendix C details the material composition and sample fabrication methods. In the case of migrating contact, the integrated hydrogel water content under the probe is unchanged because the contact pressure is applied and relieved in a cyclic fashion at
38 each location the hydrogel. Even if the surface is deformed, the sliding speed and reciprocation track length de termine the time tha t any location i s under pressure. In this testing setup, the sliding track was 3 mm and the contact area estimated to be a maximum of 0.125 m m 2 (diameter of ~ 4 00 m) ; therefore the ratio of time in contact versus out of contact for the free sliding portion of the track is ~ 1/ 8 The second major hypothesis of this work is that the hydrogel surface provides the best lubricity when water is able to be retained locally in the surface and between the sliding surfaces either in boundary lub rication or hydrodynamic lubrication regimes Therefore, stationary contact would have poor lubricity, migrating contact would improve lubricity and the case of two hydrogel surfaces in relative motion would provide the best lubricity, i.e. the lowest me asured friction coefficients. Experimental Configurations and Conditions Migrating contact is provided by placing the flat sheet of polyacrylamide hydrogel on the reciprocating stage, and sliding it with respect to a polished sapphire probe at a given ap plied normal force (Figure 3 2A ) The normal force in this case was chosen to be 400 N in order to apply pressures that typically exist between the eyelid and cornea/sclera in normal physiological function (1 6 kPa). Stationary contact is provided by rep lacing the polished sapphire probe with the polyacrylamide hydrogel probe, and replacing the flat sheet with a simple microscope slide (Figure 3 2B) The sapphire and glass components were cleaned before each experiment using isopropyl alcohol on a fiber f ree wipe. Self mated contact was achieved by combining these setups to include both the hydrogel flat sheet and the soft probe (Figure 3 2C) The initial sliding speed for these experiments was chosen to be 300 m/s due to repeatable friction coefficient measurements with commercia l contact lenses at that
39 speed [ 4 ] The behavior of commercial silicone contact lens surfaces sliding against polished borosilicate glass at low speeds has been identified as boundary lubrication, in which there is no measureable fl uid load support, but rather aqueous boundary lubrication between a wettable hydrogel and the glass [ 7 ] The Stribeck curve predicts that sliding contacts begin to e xperience fluid load support at decreased normal loads, increased sliding speeds, or both. In this case, the friction forces measured were very close to the noise floor of measurements, so the sliding speed was increased to the following levels: 100, 200, 300, 400, 500, 800, and 1,500 m/s. Each experiment was run for 30 reciprocating sliding cycles; for the slowest speed of 100 m/s the experiment lasted 30 minutes, and for the fastest speed of 1,500 m/s the experiment lasted only 2 minutes. Data acquisit ion was ~530 Hz, so more than 400 data points were used to calculate the friction coefficient, even at the fastest sliding speeds. In addition to changing the normal load and sliding speed, increased viscosity of the lubricating fluid has been shown to in crease fluid load support. In this case changing the lubricating fluid viscosity would not only alter the interaction between the surfaces, but also alter the hydrogel material samples themselves because they are permeable. Thus, the complexities of that c hange are not introduced here, but left for future inquiry. Polyacrylamide Lubricity Against Hard Impermeable Counterfaces: Friction Traces The most straightforward data to compare from this experimental set are the ient as a function of the reciprocating track location Figure 3 3 presents the friction traces in both stationary and migrating conditions at a sliding speed of v=300 m/s.
40 The friction trace for cycles 1 and 30 in migrating contact show a distinctly hig her breakloose friction coefficient of up to ~0.7. Free sliding friction coe fficient was a fraction of that: =0.2 and =0.1 for cycles 1 and 30, respectively. In contrast, the friction trace for stationary contact shows no breakloose features. T he same l ocation on the hydrogel sample is continuously in contact, so there are no spans of time between dwell, and therefore no features that reflect that phenomenon Though the surface was very smooth over the 3 millimeters of sliding, the microscope slide count ersurface was likely misaligned very slightly to the vertical axis of force measurement, which is manifested by the right side of the friction loop being wider. The additive effect of normal force into the friction force causes this or ientation dependent h ysteresis [ 20 ] However, the average normal forces and friction forces are calculated from the middle 20% of the stage position for every cycle, so the friction coefficient still scales in the same way. Time at Pressure Mediated Polya crylamide Lubricity Given the distinct configurations and presence or absence of a permeable countersurface, one would expect a characteristic friction response for each configuration Each friction experiment was run for 30 reciprocating sliding cycles at the prescribed speed, un der a normal load of F n =300 N controlled using servo feedback after each sliding cycle. The middle 20% of each friction trace (forward sliding friction force F f,f and reverse sliding friction force F f,r ) was averaged and divided by the average normal forc e over the same 20% to give the friction coefficient for each reciprocating cycle (Equation 3 1). The friction response over time was monitored over all 30 sliding cycles. ( 3 1)
41 The response of the migrating contact condition i s presented in Figure 3 4. Plot A shows the friction coefficient evolution versus sliding cycle for 7 different sliding speeds, with the measurement uncertainty shown at the right. At the slowest sliding speed of 100 m/s, the friction coefficient was hi ghest, at =0.3660.03, and did not vary much over the course of the experiment (30 minutes). As the sliding speed was increased, the friction coefficient response decreased down to very low values of <0.02 though the noise introduced by the motorized st age caused the uncertainty to increase 2 Overall, the decrease in friction coefficient was significant. The same friction coefficient results are plotted again in Figure 3 4B, though the abscissa axis has been changed to the time of the experiment in secon ds. At slow sliding speeds, the relationship between friction coefficient and time in contact (as approximated by a power law fit) is slight. As the sliding speed increases, this strength of the relationship increases, as shown by the increased slopes of t he plots for sliding speeds between 200 m/s and 400 m/s. Beyond that the data is simply too noisy to make any statements and further experiments over more sliding cycles may tease out trends In the stationary condition, the plots take on a different c haracter (Figure 3 5). At all sliding speeds, with the exception of the fastest, 1,500 m/s, the friction coefficient increases over the course of the experiment. At the slowest speed of 100 m/s, it starts at =0.085 and increases in 9 sliding cycles (~54 millimeters of travel over 9 minutes) up to =0.241 for the remainder of the experiment. When this data is presented as a 2 The force resolution of the instrument in the lateral direction is approximately 10 N, though the uncertainty reported here is the result of a Monte Carlo simulation (N>200,000 iterations) per formed on the friction coefficient measured in sliding cycle number 30. Though it is specific to one sliding cycle, it represents the uncertainty of any other cycle 1 29 because the noise and instrument capabilities remained constant.
42 function of time as shown in Figure 3 5B, the power relationship between time and friction response appears to be slightly more unifo rm, leveling off in the general vicinity of experiment time t ~500 seconds. The friction coefficient measured in stationary contact never decreases down to the levels seen in migrating contact cond i tions. hydrated. The friction coefficient response shown in Figure 3 6 is remarkable in that it does not appear to be a super position of the previous respo nses; rather the friction coefficient never rises above =0.058 at any sliding speed. Within the measurement uncertainty, the friction coefficient is the same. This robust lubricity over sliding speeds spanning more than an order of magnitude indicates that either the lubricity mechanisms in play apply at multiple lubrication conditions, or that a specific lubrication mode is maintained over this range (as it is not in the previous 2 configurations). Discussion The dramatically different measured fricti on coefficients for a high water content polyacrylamide hydrogel in 3 distinct experimental configurations occasions the following 5 points of discussion : Friction traces Contact area size over time Estimation of the fra ction of load support by fluid H ow they relate to the Stribeck lubrication curve described in Chapter 2 W ettability of the countersurface Friction Traces The friction traces as shown previously in Figure 3 3 do not share similar breakloose friction characteristics due to the time of local dwell on the hydrogel sample
43 surface. If in fact applied pressure causes water sq u eeze out in a migrating contact the extent of rehydration between passes should manifest itself in the measured friction coefficient. Given the reciprocating stroke length, s and the sliding speed v one can calculate the elapsed time since the last pass for every location along that path. This can be clearly observed by referring back to Figure 2 6 with the blue colored observer at a specific location on the hydrogel surfac e. For every location (with the exception of the center and endpoints of the stroke), the time since last pass will be shorter or longer based on its proximity to the end of the stroke (see Figure 3 7 ). Each location will have a higher and lower pass frequ ency based on the direction of approach, but these are easily distinguished in the data acquisition because all data is recorded as a function of time. The time since the last pass can be used as an axis from which to plot the migrating friction trace res ponse, as showing in Figure 3 8 The characteristic breakloose feature from both sliding directions are now juxta posed. The stage position at which this breakloose force drops off is an indication of the contact radius because the local contact area at th e end of the sliding track is under constant pressure as the probe approaches, dwells, and then departs (in this case approximately 4 seconds). As we follow the time since the last pass, there is a noticeable and possibly significant decrease in the fricti on coefficient from an average of =0.22 at time t =3 seconds down to =0.18 at time t =10 seconds. The ability to measure a difference in friction coefficient is based on the kinetics of the contact, that is, the competition between the permeability of the hydrogel surface and the sliding speed. In this case the permeability of the hydrogel is maximized due to the very high water content, though the sliding speed was
44 only 300m/s (reciprocating frequency of f =0.05). Faster sliding speeds should show a more pronounced effect because the time between passes would approach the estimate of the time for water to be squeezed locally from the contact. Slower sliding speeds could be used to investigate this effect in lower water content hydrogels. Contact Area Size Considerations At a constant force, the contact area continues to increase at a rate of determined by the permeability of the hydrogel surface and the applied pressure In general, as the hydrogel probe remains in contact over the course of the experiment from the surface, causing a polymeric concentration and increase in elastic modulus. This continues over time with an effective increase in contact area and stiffen ing of the material surface until some equilibrium is reached and the contact area can grow no larger. This trend may explain the friction coefficient increase under stationary contacting conditions (as shown in Figure 3 5B) be cause it increases to saturat ion in a timeframe of approximately 500 seconds (8.3 minutes) as directly read from the plot If a very high water content (>90% water) hydrogel under 300 N of normal force takes 8.3 minutes to squeeze water out down to some effective saturation, then th e effects on commercial contact lenses as discussed in Chapter 2 will take a much longer time or higher pressure to be able to see these fluid squeeze out effects over the course of minutes. transport through a porous medium, given a measured value for the permeability [ 33 34 ] The curved geometry prov ides a volume over which to integrate, which would also change over time with continuous applied pressure. Direct measurement of permeability and reconciliation of measured time constants with theory is reserved for future work.
45 Fluid Load Support When th e hydrogel is pressurized, the applied pr essure overcome s the fluid transport within the hydrogel surface; we push on the surface faster than water can flow through the mesh This pressurization gives rise to fluid load support, in which a portion of the normal force is supported by the viscous fluid shear in addition to intimate contact with the polymeric mesh This fluid pressure can be estimated using classical fluid dynamics scaling laws which relate the hydrodynamic fluid film thickness to the slidi ng conditions (Equation 3 2) [ 35 ] After that, an assumption of Couette flo w, that is, laminar viscous shear between plates, can provide a clear relationship between the fluid film thickness and the load partitioning (Equation 3 3). The form of this equation used to calculate a liftoff force is given in Equation 3 4. (3 2) (3 3) (3 4) Couette flow typically describes impermeable plates, though porous plates have recently garnered some interest [ 36 ] Eleg ant solutions exist for Poiseuille flow through many differ ent porous pipe cross sections though in that case the pipe walls are taken to be stationary [ 37 ] The general finding that the pressure drop between the pipe wall and center of the pipe is less in porous pipes aligns with the notion that the fluid pressure extends into some su bsurface region along with any fluid gap between sliding surfaces.
46 In this case the fraction of the normal load supported by viscous shear was estimated using Equation 3 2 and Equation 3 4, given an approximate effective modulus of 37.2 kPa as observed in force displacement measurements (Figure 3 9). For both the migrating and stationary contacting conditions sliding at velocities v <300 m/s, the fluid load support fraction remained low, at less than 3%. As the speed increased up to a maximum of 1,500 m/s, the migrating contact condition provided a better ability to support load, up to 30%. Stationary contact rose to ~10%, and this could be due to the inverse relationship of fluid load support and friction coefficient. Self mated contact over the entire spe ed range showed a fairly consistent fluid load fraction, at 9.13.1%. The curve not showing an increasing trend suggests that a different mechanism of lubrication is dominating the contact when both surfaces are highly permeable. A parameter used by the c artilage community to estimate fluid load support fraction is the P clet Number, a ratio of the fluid transport through a p orous medium to that of the driving forces on that medium. It was proposed initially by Ateshian and Wang [ 38 ] and is currently being expanded by Burris et al [ 39 ] The parameter is defined as the product of sliding velocity and contact h alf width divided by the product of aggregate modulus and permeability. Fluid load support occurs when the deformation rate of the porous media reaches the characteristic flow rate of the fluid. In this work with a PAAm of over 90% water, the changes durin g sliding appear to couple together. For example, the portion of load not supported by viscous shear depends on sliding speed, but that deformation also decreases the local permeability. Thus that analysis is not included in this thesis, but is reserved fo r future explorations.
47 Lubrication Regimes A trend of increasing or decreasing coefficient of friction with respect to sliding speed does not automatically place an experiment into a particular category of lubrication regime; rather, it gives an indication as to the mechanism and requires complementary techniques of film thickness characterization or in situ techniques to get a better idea of the true lubricating phenomena in action. That said, if a contact has some fluid load support, i.e. some character o f hydrodynamic lubrication, the friction coefficient should increase as sliding speed is increased. Figure 3 10 presents a plot of friction coefficient of the three experiments performed here overlaid on the plot of friction coefficient versus sliding spee d as initially presented in Figure 1 4 [ 5 8 6 7 4 ] It is of note that at the same sliding speeds, one could see increasing or decreasing trends of friction coefficient based on the materials and sliding conditions. Important factors not reflected in this plot are the applied pressure and percent strain experienced by the hydrogel surface or layer, as well as the start ing and working water content. Therefore, the study or target of particular regime must include slidi ng speed, applied pressure, and water content of the gel. P olyacrylamide is not known to be a charged gel; it is used extensively in Sodium dodecyl sulfate polyacrylamide gel electrophoresis (SDS PAGE), where highly charged negative proteins are drawn thr ough and trapped solely based on molecular weight. Therefore aqueous interactions during the contact between the polyacrylamide surface regions can be said to dominate over acrylamide chain interactions Countersurface Wettability Polished sapphire was ch osen due to its smooth surface and red color for imaging of the contact area using a special tribometer with interferometric capabilities.
48 Though it is a glass, it differs from microscope slide glass in elastic modulus and surface energy. Even so, the expe riments are run in a submerged environment of ultrapure water, effectively minimizing the contributions of surface interactions of the materials themselves in light of the dominating effects of aqueous lubrication and fluid transport within the contact. A consideration of the surface energies between the materials and the work done during sliding will be briefly considered here to support this assertion. In order to discuss the energies, there must be an estimate of the contact areas under the normal force s applied in the lubricity experiments. Figure 3 1 1 shows the indentation curves for both the flat and probe samples, along with a basic Hertzian fit and the resulting modulus of the 7.5% polyacrylamide gel. The value has already been adjusted for the mat erial properties of the countersurface and an assumed Poisson ratio for the hydrogel of =0.499 (essentially incompressible) The wetting angles of water on microscope glass and sapphire have been reported to be =345 and = 78 4 , respectively [ 40 41 ] A brief calculation of the interfacial tension between, for example, the sapphire probe and water, ca n be found by at the intersection of a solid, liquid, and gas or two fluids and a solid (Equation 3 5). (3 5) The surface tension of sapphire is reported to be s =53.0 mJ/m 2 the surface tension of water at 25C is l = 7 3.0 mJ/m 2 and the contact angle of water on sapphire (an average of all crystallographic planes) is = 78 4 This leads to an interfacial tension between sapphire and water of sl = 38 mJ/m 2
49 The fr iction forces measured in this case range 4 109 N, so the work of friction during a single pass of length 3 mm would be 12 330 nJ. The approximate contact are a under an applied load of F n =300 N would be 190,000 m 2 using the indentation curve in Figure 3 11 and the geometrical relationships in Appendix A. Thus, the work done over the contact area due to shear stress in contact is 64 1700 mJ/m 2 This is approximately 2 50 times the interfacial tension between sapphire and water. That means in our range of measurements, the mechanical interactions dominate the interaction, and the choice of sapphire or glass does not confound measurements.
50 Figure 3 1. The mesh size of poly(N,N dimethylaminoethyl methacrylate ) (DMAEMA) hydrogels can be controlled by the polymer content In this work, h igh water content hydrogels > 90% were used for speed studies in order to magnify pressure effects and associated fluid transport and lubrication properties. [ Adapted from Sen, M. 2007. Controlling of pore size and dist ribution of PDMAEMA hy drogels prepared by gamma rays Radiation Physics and Chemistry ( Volume 76 Page 1344, Table 1) ] Figure 3 2. Contacting configurations fabricated in order to examine lubricity of stationary, migrating, and self mated conditions. A) A sapphire probe of radius 3 mm against the hydrogel flat. B) A hydrogel probe of radius 2.6 mm against microscope glass. C) Combined self mated condition of the hydrogel probe and flat.
51 Figure 3 3. Friction traces for cycle 1 and 30 of sliding ex periments at normal force F n =300 N. Migrating traces clearly show a breakloose region, while stationary contact does not.
52 Figure 3 4. The middle 20% of each free sliding friction trace is used to calculate the friction coeff icient for that sliding cy cle. A) The friction coefficient versus sliding cycle over all 30 sliding cycles for the migrating contact setup shows that the friction coefficient is fairly con sistent at each sliding speed. B) The friction coefficient over time plotted on a log log scal e indicates that the relationship between the friction response and experiment time strengthens as the sliding speed increases.
53 Figure 3 5. The middle 20% of each free sliding friction trace is used to calculate the friction coeff icient for that slidin g cycle. A) The friction coefficient versus sliding cycle over all 30 sliding cycles for the stationary contact setup shows that the friction coefficient increases over time for most sliding speed conditions. B) The friction coefficient over time plotted o n a log log scale confirms plot (A).
54 Figure 3 6. The middle 20% of each free sliding friction trace is used to calculate the friction coefficient for tha t sliding cycle. A) The friction coefficient versus sliding cycle over all 30 sliding cycles for th e self mated contact setup shows that the friction coefficient is fairly consistent at each sliding speed, and remains low, below =0.06. B) The friction coefficient over time plotted on a log log scale indicates that the relationship between the friction response and experiment time is similar for any sliding speed greater than v =100 m/s.
55 Figure 3 7. As the flat sheet hydrogel is slid under a polished probe, the pass frequency at half the stroke length is a given value, in this example case f =0.5Hz. As we observe positions on the stroke length toward either end, the passing frequency splits into higher and lower values based on the approach direction to that position (i.e. the near end or the far end). Figure 3 8. A) The friction trace from the m igrating contact condition showing breakloose friction features. B) When the friction coefficient is plotted versus the ti m e since the last pass, i.e. maximum applied pressure, the characteristic breakloose curves overlap. For the portion of the curve alwa ys in free sliding (time t ~3 10 seconds), the friction coefficient appears to decrease slightly as a f unction of time since last pass. If that is the case, this data confirms that higher water content in the contact decreases the friction coefficient.
56 Figure 3 9. The lubrication behavior of these surfaces changes according to the countersurface. In mi grating or intermittent contact using glass probe against PAAm, fluid load support increases to over 30% of the total normal force at 1,500 m/s sliding s peed In stationary contact, the effect is less, with the fluid supporting a maximum of 10%. In self mated contact, the fluid load support appear to be constant over all sliding speeds, at an average of 9%
57 Figure 3 10. The friction coefficients that were measured in this work are plotted on the same axes as the literature review presented in Figure 1 4.
58 Figure 3 11. Indentation curves showing the applied normal force as a function of the indentation depth can be fit using the well known Hertzi an contact model to estimate the elastic modulus of the hydrogel sample. In this case the modulus of the flat and probe were 52.2 kPa and 45.1 kPa, respectively.
59 CHAPTER 4 LIMITS OF AQUEOUS LUBRICATION OF THIN HYDRO GEL LAYERS AND BRUSHES The human e yeblink surfaces, the eyelid wiper and the cornea, provide a unique lubricating film relying on the gel like mucin and mucinous glycoproteins to protect the epithelia from direct contact [ 42 44 ] The mucin layer itself is much softer than the substrate of, for example, the corneal epithelium, though both surfaces exhibit gradient characteristics ( Figure 4 1 A ) [ 45 ] This renewable graded surface is typically able to sustain up to 14,400 comfortable blinks per day (~0.25 Hz) at speeds of 0.01 10 cm/s. This robust biological system has served as a basis for more recent lubric ation studies of thin hydrogel layers and thin grafted polymer layers. This chapter discusses the ability of those biological mimics to provide aqueous lubrication and the measured limits of those surfaces. P olymer brushes are known to be lubricious unde r favorable solvation conditions [ 46 47 ] However, as solvation is changed and the brushes change conformation, this lubricity is diminished or entirely removed, suggest ing that thin films of hydrated polymers have limits of performance based in part on the fluid present in the surface Recently, a new contact lens material was introduced to the market which is com prised of a thin, water gradient surface hydrogel layer anchored to a silicone based core. Thickness measurements of this gel layer and careful assessment of the surface modulus characterize the layer to have an approximate thickness of 3 5 m (Figure 4 1 B ). The design of this layer mimics the structure of the mucinous gel layer of the corneal epithelium in an effort to provide excellent lubricity during contact lens wear. Given the limits of lubricity for these surface hydrogel layers, polyacrylamide surf ace
60 hydrogels were synthesized in order to explore the performance of thin hydrogel layers that are much softer than their substrate. This chapter will present the feasibility of growing polyacrylamide (PAAm) brush layers from a polyhydroxyethyl methacryla te ( polyHEMA ) substrate, characterizing the grafted polymer and then measuring the friction response of the surfaces. The measured friction coefficient appears to be related to grafted layer thickness. Pressure Dictated Lubricity Extremes of Thin Surfac e Hydrog el Layers On the commercial delefilcon water gradient hydrogel surface, t he very low modulus of <25 kPa was determined from a measurement of the force response during controlled indentation using atomic force microscopy (AFM) es the modulus can be a scaling factor (Equation 4 1 ). When the applied normal pressure, E the strain approaches unity, 1. (4 1) Strain is a ratio of the deformation to the initial state; if these are equivalent, then the material has been completely compressed. Because of this, it was predicted that hydrogel layer and change in the lubricity Authors reported not only a friction increase, but frictional instability (stick slip friction behavior) as wel l. This shift to instability happened as applied pressures approached the measured modulus value. Figure 4 2 details the friction traces over 400 m of sliding at two different pressures of P~ 6 kPa (Figure 4 2 A and Figure 4 2 C ) and P~15 kPa (Figure 4 2 B a nd Figure 4 2 D )
61 Thus for a thin, soft hydrogel layer anchored to a harder substrate, the friction coefficient remains low and the hydrogel layer intact at pressures below the effective modulus. Fabrication and Substrate Deformation In order to explore t his phenomenon further, polyacrylamide chains were grafted onto the surface of harder p oly HEMA coating (process shown in Figure 4 3 ) and then the friction response of the grafted layer was assessed using micro tribology. Substrates were first synthesized by polymerizing flat sheets of 65% polyHEMA between two microscope slides, using two additional microscope slides as shims which determined the thickness of the substrates. Polymerization was done using a free radical donor ammonium persulfate ( APS) at 0.1 tetramethylethylenediamine (TEMED) at 0.1 % (all components added by mass). The methylenebisacrylamide (MBAm) at 0.1 %. Green fluorescent polystyrene beads of diam eter 1 micrometer were added to the solution in order to provide traceable features in microscopy. Polymerization completed in approximately 30 minutes, and substrates were removed from the molds to dishes to equilibrate in ultrapure water for >24 hours N o swelling was observed. Resulting substrate dimensions measured approximately 20 mm by 30 mm. Multiple sets of substrates were formed at different substrate thicknesses ranging from 150 m (1 cover slip thickness) to 1 mm (1 microscope slide thickness). The polyacrylamide chains were anc hored to the polyHEMA substrate by initiating polymerization at or below the substrate surface as the concentration of the catalyst was depleted over time. More specifically, th e substrates were soaked in 10%
62 TEMED solutio n for >30 minutes. The grafted surface layer was grown by placing the prepared substrates afloat on the surface of a solution comprised of 7.5% acrylamide and 2.5% APS for a given amount of time: 1, 4, 13, 49, and 150 seconds Polymerization was limited to chain extension by the omission of the crosslinking agent. The solution also contained a small concentration of 100 nm diameter red fluorescent beads in an effort to locate the grafted layer in fluorescent microscopy. Finished samples were washed in ult rapure water and placed in ultrapure water for >30 minute s for the surfaces to equilibrate In order to assess the samples in various ways, they were cut into 5 mm wide strips. An immediate observation showed each sample to have uniform bending of the subs trates, wit h the grafted layer on the convex side. The substrates were flat upon equilibration, so the bending was a direct result of the grafting polymerization, which introduced a surface stress, bending the substrate from its neutral position. Polyacryl amide brushes are the most likely conformation of the grafted layer due to the substrate bending; the interaction of water shells maintained by the hydrophilic chains could cause the positive strain to such an extent as to bend the substrate. These bending curvatures were assessed by high resolution photography and substrate thickness by fluorescence microscopy (Figure 4 4 A and Figure4 4B ) The longer each surface was left to polymerize, the more curvature was induced. Figure 4 4 C shows the range of curvatu res induced; if curvature was not detectable, the sample curvature is not reported.
63 For each photograph, Microphotonics Image J software 3 was used to draw a circle over the curved sample, and the circle was measured according to image calibration in order to fit the curvature. The stress in the film is equal to the stress in the curved substrate The strain in at the outer surface of the substrate gel can be estimated using Equation 4 2 ; it is the 1 dimensional expansion of the surface based on the neutra l axis Thus, the stress at the outer surface of the substrate is the strain times the elastic modulus (Equation 4 3 ). (4 2 ) (4 3 ) A plot of the resulting curvature as a function of the measured substr ate thickness can found in Figure 4 5 A Thinner substrates are able to curl tighter. 500 kPa, the stresses increase according to a power law relationship as the time to cure is in creased (Figure 4 5 B ). This indicates that the stress cause d by the polymer brush is less a function of the substrate thickness and much more a function of the brush feature that increases as time of polymerization increases As polymerization time incre ased, I suspect that the brush length increased, as opposed to brush graft density because all samples began the brush synthesis with the same concentration of TEMED at the surface, 10%. As the TEMED continued to leach out of the substrate to diffuse into the acrylamide bath, the available monomers would 3 ImageJ is a public domain Java image processing program that can be downloaded from http://rsbweb.nih.gov/ij/index.html
64 exist at the free ends of the brush because all available acrylamide monomer at the substrate surface would have been polymerized first, and consumed. Parallel studies by Krick and Pitenis used a single sam ple with a graded brush structure; the measured friction coefficient against a sapphire probe decreased as the brush thickness increased [ 48 ] One source of error when fabric ating the brushes and measuring the resulting surface stress is that these substrates were floated atop the same bath with acrylamide polymer, and as such there may be have been some depletion of the stock solution as it was consumed by each subsequent sam ple. An increase in th e bath viscosity was noted, as small concentrations of TEMED catalyst were leached from the substrate before brush formation. Friction Response and Brush Pre Stress The high water content brushes anchored to the polyHEMA substrates w ere synthesized in a bath of 7.5% acrylamide, so they likely house more water than the 65% polyHEMA substrates. Based on previous descriptions of the hydrogel surface layers, one could hypothesize that the brush configuration which is able to keep a high w ater concentration during sliding would provide the best lubricity, or lowest friction coefficient. In this case the hypothesis is that the brushes polymerized for the longest time will maintain a higher water content at the surface due to a thicker, more robust layer. The friction response was assessed under a 3.1 mm radius polished borosilicate glass probe applying load levels from 20 N up to 1,000 N corresponding to range of pressures of 200 900 Pa The sample hydrogels were slid at 200 m/s over a tr ack length of 800 m. Comparing the friction traces in forward and reverse directions as shown in Figure 4 6 at a similar applied pressure, the friction coefficient for the sample
65 cured for t =1 second is =0.047, 3.6 times higher than the friction coeffi cient for the sample cured for t =150 seconds, at =0.013. The measured friction coefficient for brushes polymerized for a longer time indicates that the thicker brushes pertain to more robust lubricity. In order to see if that was the case, friction coeff icient was plotted as a function of cure time. Figure 4 7 presents the measured friction coefficient over all applied pressures as a function of the surface brush polymerization time. For both the 300 m and 600 m thick polyHEMA substrates, the friction c oefficient decreased as a function of cure time, which concurs with recent work done b y colleagues Krick and Pitenis where they synthesized a single sample with increasing brush thickness along one edge [ 48 ] Friction coefficient dropped as the brush thickness increased. Discussion In this study, a measurable strain was observed in the pHEMA substrate beams. The associated stress in the surface polyacrylamide hydrogel brush wa s calculated using an effective polyHEMA elastic modulus. This pre stress gave an indication of the thickness of the polyacrylamide brush due to its hydrophilic nature. The longer the polymerization reaction time, the thicker the brush layer became. The c haracteristic size of polyacrylamide monomers is ~0.3 nm, but the composite image in Figure 4 8 indicates some entrapment of 100 nm beads in a brush polymerized over 4 seconds. Thus, the length of the polymers in the brush must be greater than hundreds of nm. Even though the brush does not appear to evenly cover the surface of the substrate, the contact areas are estimated to be large (radius R>200 m) and the integrated friction response was measured.
66 Figure 4 1. The surface hydrogel layer aims to mim ic the lubrication mechanism of the natural tear film and tissues. A) The natural tear film. B) A schematic representation of a surface gel layer that is integrated into and onto a silicone hydrogel core material. The entire graded gel layer is estimated to be on the order of 6 m in thickness based on AFM mapping and fluorescence microsco py. The water content of the surface gel layer is greater than 80%, while the core material is only 33%. [ Adapted from Dunn A.C. 2013. Lubricity of Surface Hydrogel Laye rs. Tribology Letters (Volume 49, Page 373, Figure 1).]
67 Figure 4 2. Critical pressure causes the surface gel to dehydrate enough to stick to the probe and elicit an unstable friction response A) Low, smooth friction at low pressures B) Unstable stick slip behavior C) Schematic of a hydrated gel supporting a load D) Schematic of a collapsed gel under pressure. [ Reprinted with permission from Dunn, A.C. 2013. Lubricity of Surface Hydrogel Layers. Tribology Letters (Volume 49, Page 375, Figure 4) ]
68 F igure 4 3. The polyacrylamide (PAAm) brush fabrication process involved 3 steps: first, fabricating the polyHEMA substrates, polymerizing brushes by floating the substrate in a bath containing the acrylamide monomer, and then equilibrating the entire sampl e in ultrapure water for at least 30 minutes.
69 Figure 4 4 Surface brush fabrication resulted in steady state bending of the substrates due to a surface pressure within the brush. A) Sample image used to calibrate bending curvature B) Sample green flu orescent image of 1 m beads and substrate thickness measurements C) The range of curvatures induced by surface polyacrylamide grafted layers.
70 Figure 4 5 Plots of bending curvature and stress in surface brushes A) Surface brush fabrication resulted i n steady state bending of the substrates due to a surface pressure within the brush. B) Longer polymerization times resulted in a more curved substrate. Stresses range from 800 Pa up to nearly 45 kPa.
71 Figure 4 6. Stick slip friction was observed fol lowing each turnaround point. For similar applied pressures of 650 700 Pa, the free sliding friction coefficient over the central 30% of the track for sample cured for 150 seconds was =0.013, while for the sample cured for only 1 second, it was =0.047 (a n increase of 3.6 times). In this case the polyHEMA substrate was 600m thick. Figure 4 7. Polyacrylamide brushes polymerized for longer times, having thicker brushes, appear to be more lubricious than those with thinner brushes. A) A linear plot of t he measured friction coefficient as a function of the cure time of the polyacrylamide brush. B) On a log log plot, there is a reasonable power relationship between this parameter and the friction response.
72 Figure 4 8 Composite image of a polymer brush grown on a pHEMA substrate Green 1 m beads highlight the pHEMA substrate and red 100 nm beads appear to be trapped in the surface PAAm brush. This PAAm brush was polymerized over 4 seconds on a substrate ~300m thick.
73 CHAPTER 5 CONCLUSIONS AND FURTHE R THOUGHTS The robust physiological system of the eye provides a challenging basis from which to understand and mimic robust excellent lubricity. Soft hydrogel materials are increasingly being considered for many biomedical devices and implants, especially those in relative motion and sliding such as heart valve leaflets. The lubricity of hydrogel materials is just beginning to be understood and the aim of this thesis is to present methods by which to interrogate hydrogel lubricity, and to present prelimin ary results in the context of traditional friction measurements, fluid flow considerations, and both hydrated polymeric gel and brush structures. Lubricity of H igh W ater C ontent P olyacrylamide High water content polyacrylamide was molded into both a flat sheet and hemispherical frictional probe in order to interrogate the hydrogel surfaces with respect to the motion of the contact area and the relative sliding speeds. Contact area motion proved to be critical as to how the contact pressures are accommoda ted through the hydrogel surface. In order of high to low lubricity, as well as increasing physiological relevance are the following: stationary contact, migrating contact, and self mated contact. A wide range of sliding speeds applied to those experimenta l configurations opened the discussion of the conditions under which the water in those contacts can be pressurized to take on a portion of the load support. Future work in this area will focus on estimations of the kinetics of aqueous fluid flow based on a local control volume and sliding conditions. A hydrogel surface engineered for lubricity would have a structure with enough flow restriction to encourage pressurization, but enough water present to provide aqueous lubrication. If more clearly defined, sc aling laws in this area could lead
74 to hydrogel materials designed to provide robust lubricity for a wide variety of applications, applied pressures, and other demands. Open theoretical questions remain, such as how to understand a lubrication curve for b iphasic, porous materials into which the lubricant is integrated. Preliminary results suggest that stationary contacts of hydrogel against non porous countersurfaces behave similarly to soft viscoelastic solids due to local dehydration and intimate materia l contact, even at high sliding speeds. Migrating contacts of hydrogel against non porous counterfaces more closely mimic physiological conditions, say, at the front surface of a contact lens, and feature fluid cycles of dehydration and rehydration as a fu nction of the sliding conditions and water content of the hydrogel sample. Self mated hydrogel contact is very lubricious, but at the same time very difficult to pressurize according to traditional analyses due to the low modulus of both materials. In fact there must be pressurization taking place within the surface. In addition, m any figures in Chapter 3 represent a single measurement or single experiment. In order to determine statistical significance, with for example, the plots of friction coefficient versus time since last pass each of the 30 cycles from each experiment should be analyzed, as well as the larger experiment set at varying speeds. Lubricity of H ydrogel B rushes G rafted onto a H ydrogel S ubstrate The hypothesis that water maintenance in t he contact area lowers the resistance to motion was tested in a model of polyacrylamide hydrogel brushes. The longer the polymerization time in a bath of monomer, the longer the chain extension and the thickness of the brush. Because polyacrylamide is hydr ophilic, it was assumed that thicker brush layers had a propensity to retain a larger volume of water under applied pressures, and therefore provide better lubricity. Experiments measured the friction
75 coefficient between these polyacrylamide brushes and a sooth glass probe, and friction did indeed drop with longer polymerization times. In surface hydrogel layers such as those present on commercial contact lenses made from delefilcon A, the limit of lubricity occurs when the gel is collapsed, and the applie d pressure approaches the effective compressive modulus of the material. This limit was not discovered in the hydrogel brushes synthesized for this thesis; perhaps the layers were much thicker than those on the delefilcon A contact lens surface (>5 m), o r the mismatch between the moduli of the surface and the bulk was not as disparate (and thus presented more of a graded half space rather than a distinct surface layer). Future directions for this work include a clarified model of the exclusion volume of polyacrylamide brushes, and how that directly relates to the resulting curvatures in the polyHEMA substrates, as well as the stress in the brush. Further mapping of the phase space between an oriented hydrogel brush layer and an isotropic crosslinked hydro gel layer, along with lubricity assessments and exclusion v olume modeling would be of value in quantitative understandings of mechanics of soft hydrated materials. Immediate future work (a collaborative effort with other students) is the correlation of hy dration state of a hydrogel surface (or bulk material) and the mechanics in both simple compression and in sliding against permeable and impermeable countersurfaces. Summary The major fin dings of this work are as follows: 1. Very low friction coefficients we re measured in both a migrating and self mated hydrogel contact, under sliding speeds which did and did not induce fluid pressurization within the hydrogel surface or between the contacting surfaces.
76 2. The self mated hydrogel contact was able to maintain lo cally hydrated surfaces because no impermeable counterfaces were used; this resulted in friction coefficients never rising above =0.06 for any sliding speeds used. 3. Polyacrylamide hydrogel brush films show a reduced friction coefficient with increasing bru sh layer thickness, confirming that the presence of water dictates a lubricious environment.
77 APPENDIX A SMALL ANGLE APPROXIMATION CONTACT MECHANICS Figure A 1 Comparison of the nomenclature and mechanics of deformation of a sphere on flat model (left ) and the approach of two spheres of equal radius (right).
78 APPENDIX B MICROTRIBOLO G ICAL INSTRUMENTATION Friction coefficient measurements are only reliable and meaningful within the measurement uncertainty of the instrumentation. Figu re A 1 shows a sch ematic of the microtribometer use d for all of the experiments in this thesis work, along with brief descriptions of the capabilities and force resolution. A brief description of the experimental protocol is as follows: 1. All components that touch the fluid b ath or hydrogel sample are sonica lly cleaned in ethanol for 5 minutes. 2. The contact lens or hydrogel is fixed in place using either adhesive (if using a hydrogel probe) or a clamp (if using a contact lens or hydrogel flat). 3. A solution bath of ultrapure wat er is added using a single use pipette. 4. The samples are coarsely aligned to the experiment location, and the probe is lowered to within ~ 1mm of the countersample. 5. The operator initiates the software and approaches the probe toward the counterface carefull y while monitoring the normal force for a sharp increase, indicating contact. 6. The operator sets a normal load using the vertical piezoelectric stage, and initiates the reciprocating stage (x stage) to start the measurement. 7. The operator makes sure sliding is occurring by monitoring the friction traces in both directions and sets the vertical piezoelectric stage to servo after each cycle to remain at a set average normal force. The force resolution in this instrument arises from the mode of measurement: the deflection of a known stiffness dual cantilever flexure in both normal and friction directions. In this case, the flexure calibration was measured to be 1228 N/m in the normal direction, and the capacitive probes are calibrated to be 5 micrometers per volt And for experiments where the stroke is 3,000 m long, the piezoelectric stage is exchanged for a long stroke servo motor stage driven with a lead screw.
79 Figure B 1 Low forces down to 25 N can be used to probe the lubricity of soft hydrated materia ls using this custom microtribometer with a heated fluid cell. Force resolution is achieved by using a capacitive probe to measure the distance translated by a calibrated dual flexure, which sits between the articulating surfaces and the force application.
80 APPENDIX C HYDROGEL FABRICATION CONDITIONS Hydrogels can be synthesized in a variety of ways, including different solvents, thickening agents, crosslinking method s, and polymerization methods. One of the goals in the synthesis of the hydrogel materials (polyacrylamide, polyHEMA) used in this thesis was prevention of dimensional chang es between cure and equilibrium in ultrapure water the test solution This was accomplished by careful restriction of the constituent concentrations to well documented level s in literature, as well as using ultrapure water as the solvent. Molds for Homogeneous Hydrogel Samples The molds for the hydrogel flats were microscope slides assembled using shims at the sides to control the sample thickness; thinner slides used singl e or multiple glass cover slips, and thicker samples used microscope slides themselves as shims. All glass was cleaned using isopropyl alcohol before use, as the gels would not release from the molds otherwise. Samples were allowed to cure for up to about an hour, then soaked in ultrapure water before popping from the molds. The molds for the hydrogel probes were custom drilled from polytetrafluoroethylene (PTFE) using a 4 mm ball endmill, and a threaded rod was threaded into a mold cover. The mold was asse mbled and the polyacrylamide pipetted in and allowed to cure for up to an hour. Similar to the flat gels, the frictional probes were also equilibrated in ultrapure water.
81 APPENDIX D INSIGHTS FROM BIOLOGICAL SYSTEMS The lubricating mechanisms of synthetic hydrated materials are the focus of this work, but measurements of actual biological systems can provide quantification of the frictional forces experienced by eye tissues, a referece for and the difference between a cell mon olayer and a bulk tissue in situ. At a first pass, one might think that the lubricious tear film components found in the human eye would operate when a contact lens is inserted, and possibly even transfer over to the contact lens surface. A commercial con tact lens Acuvue Oasys, trade named senofilcon A, was used in a study to assess the ex vivo friction coefficient after 15 minutes of wear in the eye. Figure C 1 shows the effect on the friction coefficient (taken to be the slope of the plot of normal force versus friction force) due to wearing, as well as in a solution with added boundary lubricants like block copolymers and surfactants. After only 15 minutes in the eye, the friction coefficient between a glass probe and the silicone based contact lens incr eased slightly, which shows that lubricious tear film components, when removed from their native environment, do not operate in a similar fashion, at least not when measured against glass. However, in a contact lens that has never been worn, but tested in the presence of a block copolymer solution of poly(ethylene oxide) poly(butylene oxide) has better lubricity. Simple saline solution and the contact lens packing solution are also included on the plot for reference. If the lubricious tear film components d o not transfer to a contact lens placed in the eye, perhaps it is better to measure the friction coefficient of glass sliding against living eye tissue. For this reason an open platform microtribometer with the sliding
82 motions provided by an instrumented h ead was designed and built In collaboration with the Perez group at Bascom Palmer, a mouse eye was positioned vertically using a stereotactic holder with continuous inhalational anesthetic underneath the frictional probe (Figure D 2). The probe was recipr ocated across the mouse eye under an applied normal force of 4.5 mN at a sliding speed of 250m/s for up to 10 sliding cycles. Figure D 3 shows the friction trace in forward and reverse sliding directions including the measurement uncertainty indicated by e rror bars. The friction coefficient for smooth flame formed capillary glass sliding against a living mouse cornea is =0.064. The mouse eye did not sustain injury from this measurement, as the cornea did not show immediate or prolonged inflammation, and th e mouse returned to normal activity in less than 10 minutes time from removal of the anesthesia. In addition to living, complete tissue with the natural tear film, the friction coefficient between cell monolayer and a hydrogel material can be measured. Th is setup removes the complexities of animal testing, but is limited by the gene expression of the particular cell line, and does not provide a tear film. Figure D 4 shows the friction trace long with the setup for the measurement. The resulting friction co efficient between a soft contact lens and monolayer of corneal epithelia cells was =0.04. The low values of friction coefficient between smooth glass and living mouse cornea, or between hydrogel contact lens material and a corneal epithelial cell monolay er are very close in value. In addition, they are considered low, especially in comparison with the range of friction coefficients measured in this work on polyacrylamide and polyHEMA hydrogel materials.
83 Figure D 1. Insights from the native eye enviro nment: compare to an experimental solution environment of simple saline, boundary lubricant solutions reduce the friction coefficient. On a plot of the friction force versus normal force, the friction coefficient is the slope of the line as the normal forc e is increased. In contrast, the same contact lens that has been worn in the eye for only 15 minutes showed an increase in friction coefficient. Therefore, the lubricious tear film components of the eye do not appear to transfer to a contact lens during we ar; if they do, it is to the detriment of lubricity.
84 Figure D 2. A custom open platform microtribometer was used to measure the friction coefficient of a murine cornea in situ against a smooth glass probe. The mouse was positioning such that the left e ye was oriented vertically for frictional contact and microscopy in the same position. The mouse was sustained by continuous inhalational anesthetic and a warmer under the abdomen. Following experimentation, the mice recovered to normal activity.
85 Fig ure D 3. The friction coefficient between a glass probe and murine cornea in situ under an applied load of Fn~4.5 mN, sliding at 250 /s was =0.06. [Reprinted with permission from Dunn, A.C. 2013. Friction Coefficient Measurement of an In Vivo Murine Corn ea. Tribology Letters (Volume 49, Page 147, Figure 3).]
86 Figure D 4. The lubricity of an epithelial cell monolayer as tested against a soft contact lens probe was on the order of =0.04, though the integrity of the cell monolayer was compromised after about 10 reciprocating cycles. Though the friction coefficient was low, a cell monolayer may be too delicate a sample to assess robust lubricity. [ Adapted from Dunn A.C 2008 Friction Coefficient Measurement of Hydrogel Materials on Living Epithelial Cel ls Tribolo gy Letters (Volume 30, Page 16, Figure 4).]
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91 BIOGRAPHICAL SKETCH Alison C. Dunn (ne Alison C. Rennie) grew up in 10 U.S. states from Nevada to North Dakota to Virginia. She attended the University of Florida, earning b achelor s and m aster s degrees in mechanical engineering. When wanderlust took hold, she traveled to China with her husband to teach English for two years as a Peace Corps Volunteer. She discovered a love for teaching which she brought back to the Unive rsity of Florida, graduating with her Ph.D. in 2013. She plans to stay on as a postdoc in the Tribology Laboratory and teach the Mechanics of Materia ls Lab lecture sections in the f all after graduation. Her research interests continue to be hydrated materi als in motion, specifically for biological applications. She especially loves building in situ instrumentation.