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Polydimethylsiloxane mechanical properties measured by macroscopic compression and nanoindentation techniques

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Title:
Polydimethylsiloxane mechanical properties measured by macroscopic compression and nanoindentation techniques
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Wang, Zhixin
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University of South Florida
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Subjects / Keywords:
Adhesion Force
Dma
Elastic Modulus
Flat Punch
Soft Material
Dissertations, Academic -- Mechanical Engineering Materials Science -- Masters -- USF   ( lcsh )
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bibliography   ( marcgt )
non-fiction   ( marcgt )

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Summary:
ABSTRACT: In this thesis, the relationship between the elastic modulus of PDMS and the base/agent ratio (the amount of crosslinking) is studied. Reliable macroscopic compression test instrument was developed. Preload method was applied for the nanoindentation flat punch test to develop full contact. In chapter 2, an easy instrument setup for macroscopic compression test is described. A series of PDMS samples with different base/agent ratios were tested using the macroscopic compression method. The relationship between PDMS elastic modulus and its base/agent ratio was established. In chapter 3, PDMS nanoindentation DMA tests provide stable data with different test control models. The storage modulus collected using nanoindenting DMA tests is comparable with elastic modulus collected in PDMS compression test in chapter 2. Nanoindentation experiments with flat punch were also done to test the elastic modulus of PDMS network 5:1. The adhesion force tests with different nanoindentation tips, which are Berkovich tip, conical tip and cube corner tip, show that PDMS's adhesion force is related to the sample's base/agent ratio, the nanoindentating depth and the tip's geometrical shape.
Thesis:
Thesis (M.S.M.E.)--University of South Florida, 2011.
Bibliography:
Includes bibliographical references.
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by Zhixin Wang.
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Title from PDF of title page.
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Document formatted into pages; contains 78 pages.

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Polydimethylsiloxane mechanical properties measured by macroscopic compression and nanoindentation techniques
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ABSTRACT: In this thesis, the relationship between the elastic modulus of PDMS and the base/agent ratio (the amount of crosslinking) is studied. Reliable macroscopic compression test instrument was developed. Preload method was applied for the nanoindentation flat punch test to develop full contact. In chapter 2, an easy instrument setup for macroscopic compression test is described. A series of PDMS samples with different base/agent ratios were tested using the macroscopic compression method. The relationship between PDMS elastic modulus and its base/agent ratio was established. In chapter 3, PDMS nanoindentation DMA tests provide stable data with different test control models. The storage modulus collected using nanoindenting DMA tests is comparable with elastic modulus collected in PDMS compression test in chapter 2. Nanoindentation experiments with flat punch were also done to test the elastic modulus of PDMS network 5:1. The adhesion force tests with different nanoindentation tips, which are Berkovich tip, conical tip and cube corner tip, show that PDMS's adhesion force is related to the sample's base/agent ratio, the nanoindentating depth and the tip's geometrical shape.
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Advisor:
Volinsky Gallant, Alex Nathan A. .
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Elastic Modulus
Flat Punch
Soft Material
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Polydimethylsiloxane Mechanical Properties Measured by Macroscopic Compression and Nanoindentation Techniques b y Zhixin Wang A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Mechanical E ngineering Department of Mechanical Engineering College of Engineering University of South Florida Co Major Professor: Alex. A. Volinsky, Ph.D. Co Major Professor: Nathan Gallant, Ph.D. Delcie Durham, Ph.D. Date of Approval: March 23, 201 1 Keywords : soft material elastic modulus adhesion force flat punch, DMA Copyright 20 11 Zhixin Wang

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Dedication I would like to dedicate this manuscript to my relatives, especially my parents. Thank you for all your support and encouragement throughout the years.

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Acknowledgements I would like to thank my advisor Dr. Volinsky. Without his guidance, this thesis could not be published. I also want to thank my advisor Dr. Gallant for providing valuable suggestions in my research work and thesis writi ng

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i Table of Contents List of Tables ................................ ................................ ................................ ............................ iii List of Figures ................................ ................................ ................................ .......................... iv Abs tract ................................ ................................ ................................ ................................ ... vii Chapter 1. Introduction to PDMS Mechanical Properties ................................ ...................... 1 1.1 Introduction to P olymers M echanical P roperties ................................ .................. 1 1.1.1 Elastic M odulus of P olymers ................................ ................................ .. 1 1.1.2 Viscoelasticity ................................ ................................ .......................... 4 1.2 Introduc tion to PDMS ................................ ................................ ............................. 4 1.2.1 Microstructure of PDMS ................................ ................................ ......... 5 1.2.2 Samples for R esearch ................................ ................................ .............. 6 1.3 The O bjectives and C hallenges for T his R esearch ................................ ................ 7 Chapter 2. Macroscopic C ompression T esting ................................ ................................ ....... 8 2.1 Introduction to T ension and C ompression T ests ................................ ................... 8 2.2 Samples and I nstrumentation ................................ ................................ ................ 10 2.2.1 Samples P reparation ................................ ................................ .............. 10 2.2.2 Instrument D esign ................................ ................................ .................. 12 2.2.3 Analysis M ethod ................................ ................................ .................... 15 2.3 Experiments and D ata for M acroscopic C ompression T esting .......................... 17 2.3.1 PDMS N etwork S ample 5:1 ................................ ................................ 17 2.3.2 PDMS N etwork S ample 7:1 ................................ ................................ 20 2.3.3 PDMS N etwork S ample 10:1 ................................ ............................... 21 2.3.4 PDMS N etwork S ample 16.7:1 ................................ ............................ 22 2.3.5 PDMS N etwork S ample 25:1 ................................ ............................... 23 2.3.6 PDMS N etwork S ample 33:1 ................................ ............................... 24 2.4 Conclusions of Chapter 2 ................................ ................................ ...................... 24 2.4.1 PDMS M odulus D ependence on the B ase/ A gent R atio ..................... 25 2.4.2 PDMS N etwork M odulus D ependence o n the S D iameter/ L ength R atio ................................ ................................ ........ 29 2.4.3 Effect of F riction on PDMS N etwork M odulus ................................ ... 30

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ii Chapter 3. Nanoindentation of PDMS ................................ ................................ ................... 32 3.1 Introduction to Nan oindentation ................................ ................................ ........... 32 3.2 Samples P reparation ................................ ................................ .............................. 34 3.3 Experiments and Data for Nanoindentation Tests ................................ ............... 35 3.3.1 Dynamic Mechanical Analysis ................................ ............................. 35 3.3.2 PDMS N etwork N anoindentation T est with F lat P unch T ip. .............. 41 3.3.3 Adhesion F orce -Berkovich T ip ................................ ......................... 49 3.3.4 Adhesion F orce Conical T ip ................................ ............................... 58 3.3.5 Adhesion F orce Cube C orner T ip ................................ ...................... 59 3.4 Conclusions for Chapter 3 ................................ ................................ .................... 62 Chapter 4. Summary and Future Work ................................ ................................ .................. 63 References ................................ ................................ ................................ ............................... 65

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iii List of Tables Table 1. Mac roscopic compression test of PDMS network 5:1 ................................ .. 17 Table 2. Elastic modulus of PDMS network 5:1. ................................ ......................... 18 Table 3. Macroscopic compression test for PDMS network 7:1. ................................ 20 Table 4. Mac roscopic compression test for PDMS network 10:1. .............................. 21 Table 5. Macroscopic compression test for PDMS network 16.7:1. ........................... 22 Table 6. M acroscopic compression test for PDMS network 25:1. .............................. 23 Table 7. Macroscopic compression test for PDMS network 33:1. .............................. 24 Table 8. E lastic modulus of PDMS network. ................................ ............................... 24 Table 9. Effect of friction on PDMS network modulus ................................ ............... 30

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iv List of Figures Figure 1.a. Stress time behavior of an ideal elastic solid. ................................ .............. 2 Figure 1.b. Strain time behavior of an ideal elastic solid ................................ ............. 2 Figure 2.a. Stress time behavior of an ideal viscous s olid. ................................ ............ 3 Figure 2.b. Strain time behavior of an ideal viscous solid. ................................ ............ 3 Figure 3. PDMS chemical formula [6]. ................................ ................................ ......... 5 Figure 4. Mild ste el tensile test stress strain curve. ................................ ....................... 8 Figure 5. Compression test stress strain curve. ................................ ............................. 9 Figure 6.a. The massive PDMS network sa mple. ................................ ........................ 11 Figure 6.b. Cylindrical PDMS network samples for compression tests. ..................... 12 Figure 7. The instrument setup for macroscopic tests. ................................ ................ 13 Figure 8. Updated instrument setup. ................................ ................................ ............ 14 Figure 9. The final version of the instrument setup. ................................ .................... 14 Figure 10. PDMS network 10:1 macroscopic compression test results. ...................... 16 Figure 11. Compression test of PDMS network 5:1 sample 1. ................................ .... 18 Figure 12. Elastic mo dulus of PDMS network 5:1. ................................ ..................... 19 Figure 13. Elastic modulus of PDMS network 7:1. ................................ ..................... 20 Figure 14. Elastic m odulus of PDMS network 10:1 ................................ ................... 21 Figure 15. Elastic modulus of PDMS network 16.7:1. ................................ ................ 22 Figure 16. Elast ic m odulus of PDMS network 25:1. ................................ ................... 23 Figure 17. Logarithmic curve fitting of PDMS network elastic modulus. .................. 25

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v Figure 18. Polynomial curve fitting of PDMS network e lastic modulus. .................... 26 Figure 19. Exponential curve fitting of PDMS network elastic modulus. ................... 27 Figure 20. 1/x curve fitting of PDMS network elastic mo dulus. ................................ 28 Figure 21. 1/x curve fitting of PDMS network elastic modulus with diameter at 3 and 4 mm. ................................ ................................ ........... 29 Figure 22. Friction does not affect PDMS network elastic modulus ........................... 31 Figure 23. Hysitron Triboindenter. ................................ ................................ ............... 32 Figure 24. Transducer cross section of Hysitron Triboindenter [9]. ............................ 33 Figure 25. Sample for nanoindentation. ................................ ................................ ....... 34 Figure 26. Transducer c alibration. ................................ ................................ ............... 36 Figure 27.a. Storage modulus from the frequency sweep DMA test for PDMS network 5:1 ................................ ................................ ................... 37 Figure 27.b. Loss modulus from the frequency sweep DMA test for PDMS networ k 5:1 ................................ ................................ ............................. 38 Figure 28.a. Storage modulus of PDMS network 5:1 in the force control test. ........... 39 Figure 28.b. Loss modulus of PDMS network 5:1 in the force control test ............. 39 Figure 29. PDMS network 5:1 nanoindentation with flat punch tip. ........................... 42 Figure 30. The initial contact of PDMS network during flat punch nanoindentation test showing partial contact. ................................ ............ 43 Figure 31. The set up of pre load flat punch tip nanoindentation test. ........................ 44 Figure 32. Flat punch nanoindentation of PDMS network 5:1. ................................ ... 45 Figure 33. Linear fitting for upper unloading of nanoindentation curve in Figure 32. ................................ ................................ ................................ ... 45 Figure 34 Two spring model for the transducer and the sample. ................................ 46 Figure 35.a. PDMS network 5:1 nanoindentation recovery behavior. ......................... 47 Figure 35.b. PDMS network 5:1 nanoindentation recovery time relationship ......... 48 Figure 36. PDMS network 16.7:1 nanoindentation recovery time relationship. ......... 49

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vi Figure 37. The Berkovich tip AFM geometry image. ................................ .................. 50 Figure 38. Berkovich tip nanoindentation test of PDMS network 5:1. ....................... 51 Figure 39. Transducer spring vibration. ................................ ................................ ....... 52 Figure 40. PDMS network samples nanoindentation tests for the pull off force s determination. ................................ ................................ .................. 53 Figure 41. PDMS network pull off force based on crosslinking. ................................ 54 Figure 42.a. The pull off forces based on PDMS network nanoindentation displacement. ................................ ................................ ............................. 55 Figure 42.b. The pull off force s data from Figure 42.a. ................................ .............. 56 Figure 42.c. The linear curve fitting f or pull off forces from Figure 42.b. .................. 56 Figure 43.a. PDMS network 10:1 pull off force based on the unloading rate. ............ 57 Figure 43.b. PDMS network 25:1 pull off forces based on the unloading rat e ........ 58 Figure 44. PDMS network nanoindentation adhesion force test with the conical tip. ................................ ................................ ................................ .. 59 Figure 45.a. PDMS network 5:1 nanoindentation adhesion force test with the cube corner tip (L oading time: 2 sec. Unloading time: 5 sec) .................. 60 Figure 45.b. PDMS network 5:1 nanoindentation adhesion force test with the cube corner tip (L oading time: 5 sec. Unloading time: 2 sec) ............. 61

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vii A bstract In this thesis, the relationship between the elastic modulus of PDMS and the base/agent ratio (the amount of crosslinking) is studied. Reliable macroscopic compression test instrument wa s developed Preload method wa s applied for the nanoindentati on flat punch test to develop full contact. In chapter 2, an easy instrument set up for macroscopic compression test is described A series of PDMS samples with different base/agent ratios we re tested using the macroscopic compression method. The relationsh ip between PDMS elastic modulus and its base/agent ratio was established In chapter 3, PDMS nanoindentation DMA tests provide stable data with different test control models. The storage modulus collected using nanoindenting DMA tests is comparable with el astic modulus collected in PDMS compression test in chapter 2. Nanoindentation experiments with flat punch we re also done to test the elastic modulus of PDMS network 5:1. The adhesion force tests with different nanoindentation tips, which are Berkovich tip c onical tip and c ube c orner tip, show that PDMS s adhesion force is related to the sample base/agent ratio the nanoindentating depth and the tip geometrical shape.

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1 Chapter 1. I ntroduction to PDMS Mechanical Properties 1.1 Introduction to P olymers M echanical P roperties P olymers are not as stiff as metals and ceramics, but not as soft as liquids. 1.1.1 Elastic M odulus of P olymers Modulus is one of the most importan ies For an ideal elastic Stress and strain can be either tensile or compressive. From Equation (1), one can get the materia l s stiffness i s i s length change per unit length, L 0 )/L 0 it is easy to understand that for the same strain, the larger the For an ideal viscous liq defined as: (2), where, For simple liquids such as water or toluene, Equation (2) reasonably describes their constant shear stress [ 1 ].

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2 Equation (1) describes the mechanical properties of ideal elastic solids, while Equation (2) is suitable for ideal vis cous liquids. Figure s 1 and 2 show this in more detail and represent the two limiting cases. Figure 1 .a. Stress time behavior of an ideal elastic solid. Figure 1.b. Strain time behavior of an ideal elastic solid.

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3 Figure 2 .a. Stress time behavior of an ideal viscous solid. Figure 2 .b. Strain time behavior of an ideal viscous solid. Equations (1) and (2) neither can accurately describe the mechanical behavior of (3), where E' is the storage modulus and E'' is the loss modulus [ 1 The quantity i represents the square root of minus one. The storage modulus is a measure of the energy stored elastically during deformation, and the loss modulus is a measure of the energy converted to heat. Similar definitions hold f or G* (complex shear modulus) and other mechanical quantities.

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4 Deformed molecules store a portion of the energy elastically and dissipate a portion in the form of heat. The quantity E', storage modulus, is a measure of the energy stored elastically, where as E'', loss modulus, is a measure of the energy lost as heat. 1.1.2 Viscoelasticity As discussed above, complex modulus can describe the mechanical properties of polymers. Also, the comple x modulus describe s viscoelasticity of polymers, which is a basic and specific property of polymers. There are two basic models of v iscoelasticity, namely Maxwell and Kelvin Voigt m odel s [2] Viscoelasticity results in a lot of interesting phenomena in polymers. For example, creep and stress relaxation represent the st atic viscoelasticity, while lag and internal friction can describe the dynamic viscoelasticity [3] Viscoelasticity can be studied with dynamic mechanical analysis (DMA) utilizing Hysitron TriboIndentor. 1.2 Introduction to PDMS The material for research in this thesis is Polydimethylsiloxane (PDMS), which is a silicone based polymer. PDMS is the most widely used silicon based organic polymer and is particularly known for its unusual rheological (or flow) properties. Its applic ations range from contact lenses and medical devices to elastomers. It is also found in shampoos (dimethicone makes hair shiny and slippery), caulking, lubricating oils and heat resistant tiles. PDMS is optically clear, and is generally considered to be in ert, non toxic and non flammable. It is occasionally called dimethicone and is one of several types of silicone oil ( polymerized siloxane ) [ 4 6 ].

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5 Silane precursors with more acid forming groups and fewer methyl groups, such as methyltrichlorosilane, can be used to introduce branches or cross links in the polymer chains. Ideally, each molecule of such a compound becomes a branch point. Thi s can be used to produce hard silicone resins PDMS network can be used as substrate to grow cells. Varying the crosslink density in the polymer network allows one to tune the mechanical properties in a range similar to living tissues. The effect of PDMS network stiffness on the growth and behavior of cells is studied. The main focus of this thesis is to characterize the local surface mechanical properties of a series of PDMS ne twork samples, which are cured to different crosslink densities. Both macroscopic compression and nanoindentation tests were used in this project. 1.2.1 Microstructure of PDMS The chemical formula for PDMS is (H 3 C) 3 SiO[Si(CH 3 ) 2 O]nSi(CH 3 ) 3 where n is the number of repeating monomer [SiO(CH 3 ) 2 ] units. Its brief formula is shown in Figure 3 Industrial synthesi s starts from dimethyl chlorosilane and water following the reaction: n Si(CH 3 ) 2 Cl 2 + n H 2 3 ) 2 O] n + 2n HCl (4). Figure 3 PDMS chemical formula [6].

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6 Network of PDMS polymer is assembled by crosslinking these polymer chains. The long PDMS polymer chains usually have vinyl groups at each end. The short crosslinker is polymethylhydro siloxane, which links the PDMS chains. This reaction can be catalyzed by platinum. 1.2.2 Samples for R esearch PDMS network samples for this research were synthesized with the same composition which are Sylgard 184 silicone elastomer base and S ylgard 184 silicone elastomer curing agent [7] These samples have different base/agent ratios, which mean different degree s of cross link ing T he lower the degree of PDMS s cross link ing the softer PDMS network is. Conversely, the highe r the degree of cross linking, the stiffer the sample will be the ratio of crosslinker to base polymer in this thesis. The most widely used type of PDMS network in research is PDMS 10:1, which means ten mass of Sy lgard 184 silicone elastomer base with 1 mass of S ylgard 184 silicone elastomer curing agent F o r PDMS network different base/agent ratio means different amount of cross linking. For this research, a series of PDMS network samples with different base/agen t ratios are used to explore the relationship between modulus changing and the different amount of PDMS s cross linking, which are PDMS network 5:1, PDMS network 7:1, PDMS network 10:1, PDMS network 16.7:1, PDMS network 25:1 and PDMS network 33:1 [ 7 8]. Different size s of samples are made for different use s O ne part of this research is macroscopic compression test ing the samples for which are cylinders, with length /diameter ratio less than 2. T he other part is nanoindentation based test ing, for wh ich samples are 1 x 1cm 2 squares with the same thickness as samples used in

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7 macroscopic compression testing. Hysitron T riboindenter has DMA system, which is [9]. These two experimental methods will be desc ribe d in the following chapters in more detail s. The samples us ed for this research have different amount s of crosslinking. Varying the crosslink density in the polymer network allows one to tune the mechanical properties in a range similar to living tiss ues. During the tests, one can get the elastic modulus and complex modulus of these samples, compare the data within different test methods and obtain the relationship between PDMS network mechanical properties and its amount of crosslinking. 1.3 T he O bje ctives and C hallenges for T his R esearch Therefore, the goals of this thesis are : meas ur ing mechanical properties of PDMS network of varied crosslinking density and adapting nanoindenter to analyse soft T h e testing of PDMS network mechanical properties is quite novel and there are not many literature references. T he challeng es are mostly about two aspects First, t raditional mechanical propert ies testing machines do not work for these soft PDMS samples. Typical instruments can not provide l ow force control system and can not easily measure the significant displacement during polymer testing [ 10 12 ] To conventional DMA testing, the instrument is complicated to control and the testing process depends too much on the testing te mperature. Second, PDMS network is soft and its elastic modulus is less than 5 MPa. It is not easy to develop full contact in the beginning of the experiment and it is challenging to make standard specimen shape for mechanical propert ies testing [ 13, 14 ]

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8 Chapter 2 Macroscopic C ompression T esting 2 .1 Introduction to T ension and C ompression T est s For almost all metals, one can get their elastic modulus and yield stress with a simple tensile test. Mild steel tensi le test result is shown in Figure 4. Figure 4 Mild steel tensi le test stress strain curve. the sample cross p is t he proportional limit, which is the upper stress limit to the linear relationship. e is the elastic stress, past which material is yielding, and the corresponding deformation is

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9 called plastic deformation. The rise in the curve is called strain hardening, and b is called the ultimate stress. At b the cross sectional area begins to decrease in a localized region of the specimen, instead of over its entire length called necking [1 5 ] k is called fracture stress, which happens when the specimen breaks. T he tensi le test curve is different for different materials. For example, for more ductile materials, proportional li mit is lower while for brittle materials, there will be no necking. Figure 5 Compression test stress strain cu rve. C ompression testing is the opposite of tensile testing, but can describe the same properties of materials. In F igure 5, the p, e s and b have the same engineering meanings as in F igure 4.

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10 In this thesis research c ompression testing is applied for experiments because it is more suitable for soft PDMS network samples. T process is much closer to that shown in F igure 5 2.2 S amples and I nstrumentation 2.2.1 Samples P reparation Sylgard 184 silicone elastomer base and Sylgard 184 silicone elastomer curing agent were used to make PDMS. In F igure 6.a., a massive PDMS network sample is made using a flat Petri dish whose thickness is around 3 mm. A ccording to popular PDMS network curing procedure [1 6 ], PDMS network is cured as following: 1. Material s and equipment used : Sylgard 184 silicone elastomer base Sylgard 184 silicone elastomer curing agent p etri dishes, wood spoons, plastic cups, vacuum desiccator, scale, hot plate, gloves. 2. Place the plastic cup onto the scale and tare. 3. Pour 27 g of the Sylard 184 silicone elastomer base into the cup T are Slowl y pour 2.7 g of the Sylard 184 silicone elastome r curing agent into the same mix with the spoon ( about 10 min, until mixture is milky due to air bubbles). 4. Put the PDMS mixture (in the cup) into the desiccator and turn the vacuum back on. De gas the mixture under vacuum until no bubbles appear (20~30 min ). Make sure the PDMS mixture does not foam out of the container. When large bubbles form at the surface, vent vacuum to pop bubbles. 5. Carefully pour PDMS over a Petri dish (t ry to minimize introduction of bubbles ). 6. P lace the Petri dish onto a hot plate ( ke ep horizontally ) set the hot plate at 65 C let PDMS network cure for 12 hours

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11 After PDMS network mold cures, the sample is sta b le and can be stored for month s. The ratio between the initial length L 0 and the diameter D of the sample is a pertinent par ameter. [17] In reference of ASM handbook -Mechanical Testing and Evaluation, the length/diamater ratio for soft material compression sample should be less than 2. [18] So p unches with 3 mm or 4 mm diameter we re used to cut cylindrical PDMS network sampl e s. In F igure 6.b., the different sizes of cylinder PDMS network samples are shown with clear details. With micrometer calipers the length and diameter of cylinder ical samples we re measured accurately Figure 6 .a. The massive PD MS network sample

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12 Figure 6.b. C ylind rical PDMS network samples for compression tests 2.2.2 I nstrument D esign Different kinds of compression testing machines can be used to measure materials mechanical properties : SANS range of compression testing ma chines (Austr a lia), Universal Compression Testing Machine (SYE 2000) (China), etc. For PDMS, it is not realistic to place samples in heavy load machines. Thus a more suitable instrument was designed for PDMS network compression testing based on the scale a nd displacement gauge [1 9, 20].

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13 Figure 7 The instrument set up for macroscopic tests In F igure 7, the force is measured by the scale under the sample, while displacement is measured by the gauge above the sample. Weights are used to apply force to samples. The data shown in the scale is almost the same with the weight, which means the scale can be removed from this instrument set. ( Shown in Figure 8 ) To reduce the error, the gauge shall be straight all the time during the expe riment. In experiments, calibration is made due to the spring in the gauge. After the spring wa s removed, the weight added on the gauge is exactly the force yield ing on the sample. T he instrument set was update d again shown in Figure 8.

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14 Figure 8 Updated instrument set up. Another calibration is made due to the movable metal connection, which hold s the gauge in F igure 8. The movable joint connection caused 5 percent of the load deviation, so the instrument was simplified further shown in F igure 9. Figure 9 The final version of the instrument set up.

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15 In F igure 9, the weight above the gauge applied the force to the sample in the compression testing. T he sample is fully contacted with the metal stage, so the gauge can measure the displacement of the sample during compression A lso, because the sample is soft, it is not easy to develop full contract between the gauge and the sample. To avoid this problem, the testing force of this experiment always start e d at 50 g [21]. 2.2.3 Analysis M ethod With the designed instrument setup, one can get the stress and strain of the sample: Stress 2 ) (5) Strain = dL/L 0 (6) w h ere, m is the mass above the gauge, wh ich applies the force to the sample. D is the force From Equation (1), it is easy to see the slope of stress strain curve is the elastic modulus of the sample. More details are shown in figure 10

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16 Figure 10 PDMS network 10:1 m acroscopic compression test results. Figure 10 is the data of comp re ssion test for standard PDMS network 10 : 1, after linearly fitting the data the s lope of the straight line is 2.63 E +06 Pa which means th at elastic modulus of 10 : 1 PDMS network sample is 2.63 MPa.

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17 2.3 E xperiments and D ata for M acroscopic C ompression T esting With the designed instrument set up and cylinder ical PDMS network samples, com pression tests were performed on a series of PDMS network samples. 2.3.1 PDMS N etwork S ample 5:1 PDMS network 5:1 is made of 17 g Sylgard 184 silicone elastomer base and 3.4 g Sylgard 184 silicone elastomer curing agent After the sample cured completely, it was carefully cut and removed out of the Petri dish. Punches with 3 mm and 4 mm diameters were used to cut cylindrical sample. The most uniform cylinders we re picked from all the samples. More details about the cylinder samples used in this macroscopic compression testing are shown in Table 1. Table 1 Macroscopic compression test o f PDMS network 5:1 S ample 1 S ample 2 S ample 3 S ample 4 Thickness, mm 2.808 2.834 2.853 2.825 D iameter, mm 3.849 3.82 2.848 2.828 Diameter/Thickn ess Ratio 1.37 1 1.34 8 0.998 1.001 Using the same testing method as described in section 2.2.3, the compression testing curve for PDMS network 5:1 sample 1 is shown in F igure 11.

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18 Figure 11 Compression tes t of PDMS network 5:1 sample 1. In F igure 11, after linearly fitting the data the slope of the straight line is 3.584 E+6 Pa which means the elastic modulus of PDMS network 5:1 sample 1 is 3.584 MPa. In the same way, e lastic modulus of sample 2, sample 3 and sample 4 we re obtained : 3.728 MPa, 3.458 MPa and 3.582 MPa. Elastic modulus measurement results of PDMS network 5:1 are summarized in T able 2 and F igure 12. Table 2 Elastic modulus of PDMS network 5:1. S ample 1 S ample 2 S am ple 3 S ample 4 Elastic Modulus, MPa 3.584 3.728 3.458 3.582 Thus, E average =(E 1 + E 2 + E 3 + E 4 )/4=3.588 Mpa (7 )

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19 : = (8) O ne can get the s tandard d eviation of PDMS network 5 : 1 s e lastic m odulus of 0.11 MPa. Figure 12 Elastic modulus of PDMS network 5 :1 From F igure 12, the elastic modulus of PDMS network 5:1 is 3.5 9 MPa (SD 0.1 1 MPa )

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20 2.3.2 PDMS N etwork S ample 7:1 PDMS network 7:1 sample is made of 18.2 g Sylgard 184 silicone elastomer base and 2.7 g Sylgard 184 silicone elastomer curing agent Sim ilar to compression testing procedure of PDMS network 5:1 cylinder samples, the same procedure for PDMS network 7:1 samples was performed and the details are listed in T able 3. Table 3 Macroscopic compression test for PDMS network 7:1. S ample 1 S ample 2 S ample 3 S ample 4 Thickness, mm 3.01 2.991 2.996 2.941 D iameter, mm 3.855 3.856 2.885 2.875 Diameter/Thickness Ratio 1.28 1 1.289 0.96 3 0.97 8 Elastic Modulus, MPa 2.950 2.924 2.867 2.894 The data of PDMS network 7:1 elastic mo dulus is quite repeatable. The elastic modulus of PDMS network 7:1 data are summarized in F igure 13. Figure 13 Elastic modulus of PDMS network 7:1

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21 F rom T able 3 and F igure 13, the elastic modulus of PDM S network 7:1 is 2.9 1 MPa (SD 0.0 36 MPa ) 2.3. 3 PDMS N etwork S ample 10:1 PDMS network 10:1 is made of 18 g Sylgard 184 silicone elastomer base and 1.8 g Sylgard 184 silicone elastomer curing agent Following the compression testing procedure of PDMS netwo rk 5:1 cylinder ical samples, PDMS network 10:1 sample results are listed in T able 4. Table 4 Macroscopic compression test for PDMS network 10:1. S ample 1 S ample 2 S ample 3 S ample 4 Thickness, mm 2.822 2.786 2.64 2.62 D iameter, mm 3.851 3.851 2.831 2.831 Diameter/Thickness Ratio 1.36 5 1.382 1.072 1.08 1 Elastic Modulus, MPa 2.605 2.633 2.780 2.630 Figure 14 Elastic m odulus of PDMS network 10 : 1

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22 F rom T able 4 and F igure 14, the elastic modulus of PDMS network 10:1 is 2.6 6 MPa (SD 0. 0797 MPa ) 2.3. 4 PDMS N etwork S ample 16.7 :1 PDMS network 16.7:1 is made of 20 g Sylgard 184 silicone elastomer base and 1.2 g Sylgard 184 silicone elastomer curing agent PDMS network 16.7:1 sample te sting results are listed in T able 5. Table 5 Macroscopic compression test for PDMS network 16.7:1. S ample 1 S ample 2 S ample 3 S ample 4 Thickness, mm 2.515 2.493 2.502 2.517 D iameter, mm 3.803 3.8 2.666 2.708 Diameter/Thicknes s Ratio 1.512 1.524 1.065 1.07 6 Elastic Modulus, MPa 1.109 1.234 1.265 1.227 Figure 15 Elastic modulus of PDMS network 16.7 : 1

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23 F rom T able 5 and F igure 15, elastic modulus of PDMS network 16.7:1 is 1.2 1 MPa (SD 0. 06 9 MPa ) 2.3. 5 PDMS N etwork S ample 25 :1 PDMS network 25:1 is made by 30.5 g Sylgard 184 silicone elastomer base and 1.2 g Sylgard 184 silicone elastomer curing agent PDMS network 25:1 sample macroscopic compression testing results are listed in T able 6. Table 6 Macroscopic compression test for PDMS network 25:1. S ample 1 S ample 2 Thickness, mm 2.428 2.403 D iameter, mm 3.652 2.665 Diameter/Thickness Ratio 1. 5 0 4 1. 1 0 9 Elastic Modulus, MPa 0.954 1.006 Figure 16 Elastic m odulus of PDMS network 25:1

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24 F rom T able 6 and F igure 16, the elastic modulus of PDMS network 25:1 is 0.98 MPa (SD 0.0 368 MPa ) 2.3.6 PDMS N etwork S ample 3 3:1 PDMS network 33:1 is made of 19.5 g S ylgard 184 silicone elastomer base and 0.59 g Sylgard 184 silicone elastomer curing agent PDMS network 33:1 sample testing results are listed in T able 7. PDMS network 33:1 elastic modulus is 0. 56 MPa (SD 0.021 MPa ) Table 7 Macro scopic compression test for PDMS network 33:1. S ample 1 S ample 2 Thickness, mm 2. 435 2. 435 D iameter, mm 3. 380 3. 380 Diameter/Thickness Ratio 1.388 1.388 Elastic Modulus, MPa 0. 548 0. 577 2.4 C onclusions of C hapter 2 The elastic modulus results (Tabl e 8) based on the macroscopic compression tests show that PDMS s elastic modulus is related to the samples base/agent ratio (the degrees of crosslink ing ) The relationship between PDMS network elastic modulus and its base/agent ratio is studied in the fol lowing. [22 26] Table 8 Elastic modulus of PDMS network E 1 MPa E 2 MPa E 3 MPa E 4 MPa E ave MPa Diameter around 4mm Diameter around 3mm PDMS 5:1 3.584 3.728 3.458 3.582 3.59 PDMS 7:1 2.950 2.924 2.867 2.894 2.9 1 PDMS 10 :1 2.605 2.633 2.780 2.630 2.66 PDMS 16.7:1 1.109 1.234 1.265 1.227 1.2 1 PDMS 25:1 0.954 1.006 0.98 PDMS 33:1 0.548 0.577 0.56

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25 2.4.1 PDMS M odulus D ependence on the B ase/ A gent R atio Different curve fittings are done to describe the relationship between the modulus of PDMS network and its base/agent ratio. 1 Logarithmic C urve F itting Exponential curve fit ting is also done to describe the relationship between Elastic Modulus and PDMS network base/agent ratio, which is shown in figure 1 7 and writ ten as: E=6.214 3.8034log(n), R=0.98286. ( 9 ) E is PDMS s elastic modulus, and n is PDMS network b ase/ a gent ratio. Figure 17 Logarithmic curve fitting of PDMS network e lastic modulus

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26 2. Polynomial C urve F itting Polynomial curve fit ting is done to describe the relationship between Elastic Modulus and PDMS network Base/Agent ratio, which is shown in figure 18 and written as: E=4.7345 0.26896*n+0.0044*n 2 R=0.98455. ( 10 ) E is PDMS s elastic modulus, and n is PDMS network base/agent ratio. Figure 18 Polynomial curve fitting of PDMS network e lastic modulus.

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27 3. Exponential C urve F itting Exponential curve fit ting is also done t o describe the relationship between Elastic Modulus and PDMS network Base/Agent ratio, which is shown in F igure 19 and written as: E=4.699e 0.066326n R=0.98372. (11) E is PDMS s elastic modulus, and n is PDMS network b ase/ a gent ratio. Figure 19 Exponential curve fitting of PDMS network elastic modulus.

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28 4 1/x C urve F itting I n Figure 17, reverse function curve fit ting is done to describe the relationship between PDMS network elastic m odulus and its base/agent ratios, which can be written as: E=19.981/n, R=0.95266 ( 12 ) where, E is PDMS s elastic modulus, and n is PDMS network base/agent ratio. Figure 20 1/x curve fitting of PDMS network e lastic modulus. In equation 12 it is easy to see 1/n is agent/base ratio, which is also the amount of crosslinker in PDMS network sample. S o it means the PDMS network elastic modulus is linear with its amount of crosslinker. Ov erall, comparing with R values of these curve fitting s they are all very close to each other. The p olynomial curve fitting maybe a better fit according to its R value: E=4.7345 0.26896*n+0.0044*n 2

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29 However, the reverse founction curve fitting has physical meaning. Except for the amount of crosslinker(PDMS network cure agent), all other experiment conditions are the same for each PDMS network sample test. Therefore, the PDMS network elastic modulus is linear with its percent of crosslinker. 2.4. 2 PDMS N et work M odulus D ependence on the S amples D iameter / L ength R atio The ratio between the initial length L 0 and the diameter D of the sample is a pertinent parameter. I n this macroscopic compression test, all the cylindrical samples lengths are around 3mm, but the diameters are varying with two sizes: 3mm and 4mm. The affect of sample s diameter for its elastic modulus are shown in Figure 21. Figure 21 1/x curve fitting of PDMS network e lastic modulus with di ameter at 3 and 4 mm.

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30 I n Figure 21, elastic modul i of samples with diameter at 4mm are plotted in red and elastic modul i of samples with diameter at 3mm are plotted in blue. It shows the diameter of sample does not really affect the PDMS s elastic modul us. 2.4. 3 Effect of F riction on PDMS N etwork M odulus There are different deformation modes in compression testing, for example: buckling, shearing, barreling, homogenous compression. When barreling happens, friction is present at the contact surface. [27 ] In this compression test, the deformation mode is barreling, so additional compression experiments with oil are done to discuss the friction effect on PDMS network modulus. The data are shown in Table 9. Table 9 E ffect of frict ion on PDMS network modulus E 1 MPa E 2 MPa E 3 MPa E 4 MPa W ithout oil Oil test PDMS 5:1 3.584 3.728 3.54 3.57 PDMS 7:1 2.950 2.924 2.87 2.91 PDMS 10:1 2.605 2.633 2.48 2.55 PDMS 16.7:1 1.109 1.234 1.36 1 1.2 76 PDMS 25:1 0.954 0.88 3 0.88 1 PDMS 33:1 0. 548 0.577 0. 489

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31 Figure 22 Friction does not affect PDMS network elastic modulus In Table 9 and Figure 22, it is clear that the elastic modulus of PDMS network reduces in compression testing wit h oil, which means there is friction happening during the test. But comparing with the stress applied on sample during the test, the friction is not a big effect of the compression test. A lso, the reverse function curve fitting does not change much no matt er whether there is friction. O ne may notice that the elastic modulus of PDMS network 16.7:1 in compression oil test is bigger than the data in compression without oil test. That is because the initial force in PDMS network 16.7:1 compression without oil t est is 20 g, but the compression test, the elastic modulus of sample will be smaller than its true value. This is another example of the necessary of pre loading method in th is research.

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32 Chapter 3. Nanoindentation of PDMS 3.1 Introduction to Nan o indentation Anothe r method used to characterize materials mechanical properties is the nanoindentation test. Nanoindentation technology is widely and efficiently used to test sensitive surface forces and mechanical properties of thin films and MEMS devices [27 30]. Hysitron Triboindenter is one of the commonly used nanoindentation machines which is shown in F igure 23 Figure 23 Hysitron T riboindente r.

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33 The main part s of Hysitron Triboindenter consist of a tandem piezoelectric ceramic scanning tube and a transducer. The piezoelectric ceramic tube can provide very fine positioning of the indenter tip during testing. The transducer is the heart of the na noindenter which records force/displacement data [9]. Figure 24 shows the cross section of a center plate capacitor transducer. When a voltage is applied to the drive plates, it produces an electrostatic attraction between the spring loaded center plate an d the bottom plate, and causes the center plate to move making an indent [9]. Figure 24 Transducer cross section of Hysitron Triboindenter [9]. In nanoindentation test, a tip penetrates into the sample and the load displacement curve is recorded. In this process, the compliances of the machine, the inde nter tip and the sample are also recorded. T he relationship can be described as in [9] : C=C m +C 1 (13), where C is the measured compliance, C m is the machine compliance and C 1 is the response of indenter and sample. From this relati onship C 1 is then used to derive the reduced modulus. The accuracy of the reduced modulus is highly dependent on the value of C m and therefore it is advised that machine compliance is tested before data are collected. The machine compliance calibration is d one by tes ting several indents on quartz whose h ardness and r educed modulus are constant at large indentation

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34 depths and graph ing of 1/measured stiffness vs. 1/P max 1/2 for the indentations If it is calibrated, this should yield a straight line where y intercept s defined as the machine compliance [30]. Since PDMS network is quite soft, machine compliance effects do not affect the modulus measurements as much as for stiffer materials. 3.2 S amples P reparation PDMS network was polymerized by the same met hod discussed in chapter 2 but the sample preparation was altered to accommodate the nanoindention workspace. In this instance samples wer e prepared as 1 cm 2 pads of approximately 3 mm thickness, rather than using cylindrical punches, and a re shown in F igu re 25. Figure 25 Sample for n anoindentation.

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35 3 .3 E xperiments and Data for N anoindentation Tests For nanoindentaion tests, different models are used to test different materials. Quasi static test can be used to study the mecha nical properties of metallic thin films. DMA system can be used to test the complex modulus of soft polymer s A lso, different experiment al conditions and different methods are used to achieve the valuable results. 3.3.1 Dynamic Mechanical Analysis T he dy namic mechanical analysis (DMA) system is used for the test. DMA nanoindentati o n is a well developed procedure of Hysitron Triboindenter. It is convenient to get the complex modulus of PDMS network with DMA nanoindentation test [9], which is different from conventional DMA test. To conventional DMA testing, the instrument is complicated to control and the testing process depends too much on the testing temperature. There are different control models in DMA systems, specifically frequency control, dynamic f orce control and static force control. For time dependent behavior, dynamic viscoelastic testing offers the advantage of significantly decreased testing time by examining properties over a range of frequencies rather than extended time. [31 33] T he equatio ns for DMA method calculation are: (14) where k s is the storage stiffness of the sample, C s is the loss stiffness of the sample, A is the contact area. T ransducer is calibrated before the data are collected, shown in the Figure 26.

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36 Figure 26 Transducer c alibration. After proper calibration, transducer mass was determined at 260.23 mg the center plate s pring constant k i is 166. 73 N/m d amping C i is 0.0141 kg/sec and t he transducer resonance frequency is 126 Hz.

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37 Figure 27 .a. Storage modulus from the frequency sweep DMA test for PDMS network 5:1. With the test data file, one can get storage and loss stiffness of the sample, and using equations 14 to calculate the storage modulus and loss modulus. Figure 27.a shows the storage modulus of PDMS network 5:1 in DMA frequency control test. PDMS s storage modulus is increasing when t he frequency. Also, at low frequency, th e DMA result is similar to the flat punch qua si static test. In Figure 27.a, it is easy to see PDMS network 5:1 s storage modulus is around 3.5 MPa when the frequency is at 10 Hz with the nanoindentation depth at 380 nm, which is comparable to the PDMS 5:1 compression test data. The PDMS network 5:1 s storage modulus is around 4.4 MPa when the frequency is at 100 Hz and with the nanoindentation depth at 1140 nm.

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38 Figure 27 .b. Loss modulus fro m the frequency sweep DMA test for PDMS network 5:1. Figure 27.b shows the loss modulus of PDMS network 5:1 in DMA frequency control test. PDMS s loss modulus is changing with test frequency. I n figure 27.b, one can see the loss modulus reaches the peak when the test frequency gets close to the transducer s resonance frequency.

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39 Figure 28 .a. Storage modulus of PDMS network 5:1 in the force control test. Figure 28 .b. Loss modulus of PDMS network 5:1 in the force control test.

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40 Figure 28.a shows the storage modulus of PDMS network 5:1 in DMA static force control test. S tatic force is set from 2 mN to 8 mN, dynamic force is set at 50 N, frequency is set at 10 Hz and 10 0 Hz, respect ively. T he difference between PDMS network loading and unloading test s is due to the viscoelastic properties of PDMS. I n Figure 28.a, storage modulus of PDMS network 5:1 at 1140 nm nanoindent at i o n depth is around 4.5 MPa, which is comparable to the data sh own in Figure 27.a. Also, storage modulus of PDMS network 5:1 at 380 nm nanoindent at i o n depth with 10 Hz test frequency is around 3.5 MPa, which is the same with the data shown in Figure 27.a and the PDMS network 5:1 elastic modulus from compression test. Figure 28.b shows the loss modulus of PDMS network 5:1 in DMA static force control test, which is similar to experiments shown in Figure 27.b. The loss modulus of PDMS network is stable whether in loading or unloading test s T he loss modulus of PDMS netwo rk 5:1 in Figure 28.a at 1140 nanoindent at i o n depth and with 100 Hz test frequency is similar with the data collected at the same experiment al condition s as in Figure 27.a. Thus, PDMS network nono DMA test provide s stable data with different test control m odels. A lso the elastic modulus collected in nano DMA test is comparable with the data collected in PDMS network compression test for PDMS network 5:1 sample

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41 3.3. 2 PDMS N etwork N anoindentation T est with F lat P unch T ip A flat punch tip (MS02091001) wa s used in PDMS s nanoindentation tests. It has a cylindri c al shape a nd the diameter is 100 2 .19 Because soft material like PDMS network is not as stiff as metal s several hundred times bigger depth of PDMS network nanoindentation will be produced with the same load. However, this problem will be avoided when a flat punch tip is used in experimen ts [34, 35]. The commonly used method for calculating mechanical properties of materials is the Oliver Pharr method and it is also appropriate for flat punch nanoindentation test In this continuous stiffness method, the upper unloading curve is used [9, 3 0]: ( 15 ), ( 16 ), w here S is the slope of upper unloading curve, q and m are the fitting parameters, P is the maximum load in an indentation test from the unloading curve. The contact depth is written by: ( 17 ), where h t is the total indentation depth, w is a n indenter geometry factor. The reduced modulus can be c alculated from: ( 18 ), where A C With known t he reduced modulus of the sample in equation 18 thus can be c hang ed as:

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42 ( 19 ), For the perfect Berkovich tip, the tip area A=24.5 depth 2 but for the flat punch used in this research, the diameter of the tip is known at 1002.19 m, therefore, the equation 19 can be simplified as, (20), From the upper part of the unloading curve one can get S (slope) in equation 20 t hen the reduced modulus can be calculated accordingly. PDMS network 5:1 sample 1.65 mm thick wa s used for the flat punch experiments. The sample wa s placed on the ste el substrate to avoid any air bubbles between the sample and substrate. Figure 29 PDMS network 5:1 nanoindentation with flat punch tip. Based on equation 20, since the elastic modulus of PDMS network is c onstant, the slope of nanoindentation load displacement curve should also be constant, but the slope in Figure 29 is changing. T his happens due to incomplete contact between the

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43 cylinder tip and the sample misalignment. Th e flat punch tip has a large diame ter of 100 2 .19 m, and when it touches the sample, the initial contact does not involve the whole surface area of the flat tip as shown schematically in Figure 30. Figure 30 The initial contact of PDMS network during flat punch nanoindentation test showing partial contact To solve this problem, preload method wa s used to perfrom th e flat punch nanoindentation test. In the imagin g window of the Hysitron software the sample was moved into the tip in 5 m increments, for the 40 m total displace ment. More details are shown in Figure 31.

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44 Figure 31 The set up of pre load flat punch tip nan o indentation test. After 40 m total displacement into the sample the load changes linearly, which means that the tip and the sampl e developed full contact. After this pre loading procedure one can start an indent. T he preload flat punch tip nanoindentation test is shown in Figure 32. Different experiments with different load functions and different drift monitor time s are also done i n this section.

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45 Figure 32 Flat punch nanoindentation of PDMS network 5:1. Figure 33 L inear fitting for upper unloading of nanoindentation curve in Fig ure 3 2

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46 T ypical nanoindentation curve is shown in Figure 32. Linear fitting is made for the upper unloading curve, which is shown in Figure 33. According to equation 20, the elastic modulus of PDMS network 5:1 is 2.2 MPa. This value of PDMS network 5:1 ela stic modulus in flat punch Quasi test is lower than the data from DMA test and compression test. The reason is because pre loading 40 m maybe not enough. There is no volt age applied to the transducer i n th is pre loading process, so the transducer spring w ill move backwards due to the pushing back force yielded when the tip is pushing the sample. To PDMS network, its elastic property can be described using spring model. In this case, the pre loading procedure can be explained with two spring model, which is shown in Figure 3 4 Figure 34 Two spring model for the transducer and the sample. In DMA nanoindentation, one can get the transducer spring constant is 167 N/m ess is 3.5 N/nm. It is easy to see the stiffness of the sample is around 20 times of the stiffness of tran s when 40m displacement happens during pre loading process in Figure 3 4 the Transducer with spring constant 167 N/m Sample with spring constant y 3500 N/m 40 m displacement, 1 mm diameter flat punch

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47 displacement of flat punch moving towards the sample is 2 m. In the case the flat 19 m, the misalignment angle of the flat punch is 0.12. Therefore, to this flat punch Quasi test, the elastic modulus of PDMS network 5:1 is 2 times different from the data in DMA nanoindentation and macroscopic compression test, it is possible the test is still not developing full contact. The same experiments performed with different unloading rates are shown in Figure 3 5 .a and Figure 36 Figure 35 .a. PDMS network 5:1 nanoindentation recovery behavior.

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48 Figure 3 5 .b. PDMS network 5:1 nanoindentation recovery time relationship. procedure, the creep recovered when unloading process rate [1, 20]. Figure 3 5 .b shows the quantitative relationship between PDMS network nanoindentation recovery and the unload ing rate. [1, 39 41] One can see that the

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49 Figure 36 PDMS network 16.7:1 nanoindentation recovery time relationship. 3.3.3 Adhesion F orce -Berkovich T ip The Berkovich tip has three sides with a total included angle of 142 .35 and is one of the most commonly used tips [ 9, 42 4 4]. It is also the standard tip used in nanoindentation tests [9] Berkovich tips are made of diamond with a modulus of 1140 GPa.

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50 Figure 37 The Berkovich t ip AFM g eometry image Because of the versatility of the Berkovich tip it seems it is a natural candidate for testing the properties of PDMS. However, the testing process has some interesting phenomena which have never been seen in other materials tests. T he Berkovich PDMS net work nanoindentation test is shown in Figure 38. PDMS network is soft (E < 5 MPa), so when the sharp Berkovich tip is approaching the surface of the sample, it is difficult for the transducer to determine the initial contact point. Conversely, when the tip 5 4 6 ]. The transducer is calibrated before the experiments. The surface is detected by approaching the sample and touching its surface with 2 N force This method does not work for PDMS network because even at 2 N force the tip is already indenting the sample. An alternative method was used where the Berkovich tip is brought close to the surface (~1.5 m) before the test is started. This is d one becau se the initial

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51 contact will be shown clearly when the tip is contacting the sample. The resulting data curve may be found in Figure 3 8 below. Figure 38 Berkovich tip nanoindentation test of PDM S network 5:1. In Figure 3 8 the tip touche s surface after traveling the last 1.5m in air The pull in negative force is present at 500 nm depth, which will a ffect the elastic modulus calculation using equation 19 In Berkovich tip nanoinden tation test, Oliver Pharr method is commonly used to generate the equation 19 which shows th at elastic modulus of the sample is related to the contact area, while the contact area for the perfect Berkovich tip is A=24.5 depth 2 So because of the 500 nm de pth associate with the pull in phenomenon, Berkovich tip is not a good choice for PDMS network nanoindentation test without accounting for the pull in effect After the pull in

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52 phenomenon t he nanoindentation load starts to increase as the tip pushes a gainst the sample surface. After the indentation process is done, the tip withdraws from the sample s surface. When the tip is leaving the sample surface transducer vibration occurs. F igure 39 graphs nanoindentation load and depth over time, and the tran sducer s vibration can be clearly seen in more detail. O ne can easily see that the transducer s vibration frequency is 125 Hz, which is similar to the transducer resonance frequency of 126 Hz shown in Figure 2 6. Figure 39 Transducer spring vibration. Alt hough the Berkovich tip nanoindentation test is not suitable for PDMS network mechanical properties research, it is functional to find the relationship between the adhesion force and the PDMS network stiff ness and to study the PDMS network

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53 samples surface energy. More PDMS network samples with different base/agent ratios we re tested with Berkovich tip to collect the adhesion forces and details are shown in Figure 40. Pull off forces are present in all samp les, but for these PDMS network samples with different base/agent ratios, the pull off forces are different. The pull off force increas es with PDMS network base/agent ratio. However, the pull off force magnitude is not as large as in F igure 38. The possibl e reason s why the pull off force in F igure 40 is several times smaller than in F igure 38 is because the samples surface in Figure 40 is not clean or the Berkovich tip used in the tests in Figure 40 is worn Figure 40 PDMS network samples nanoindentation tests for the pull off force s determination.

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54 Pull off force of PDMS network samples determined from load displacement curves in F igure 40 is pl otted in F igure 41. The pull off force is related to the geo metr ic shape of the Berkovich tip, its contact area, and adhesion of PDMS network samples [ 4 7]. Figure 41 PDMS network pull off force based on crosslinking. Based to the JKR contact theory for spherical indentation : (21) where P is pull off force, E* is the reduced modulus a is the contact radius and R is the tip radius is a general term that encompasses the work of adhesion [ 4 8] S o the adhesion force is r elated to the tip s geometric shape.

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55 Also, the work of adhesion force is the integral of adhesion force on a certain depth interval. In Figure 38 and 40, the work of adhesion is also the area of pull off force region. F or example : the area of pull off for ce region in Figure 38 is 35 N* m, so the work of adhesion in Figure 38 is 3 5E 12 J. Figure 42 a. The pull off force s based on PDMS network nanoindentation displacement. Figure 42.a shows the relationship between PDMS network pull of f force and the samples nanoindentati o n displacement. The pull off force increases with the indentation depth. The same data is reorganized and shown in F igure 42.b. It is clear that the relationship between PDMS network pull off forces and the samples n anoindentati o n displacements is linear. This relationship can be described as: Y =0.96533+0.00017201x, R=0.99975 (22) Y is the pull off force, x is nanoindentation depth. Both are shown in F igure 42.c.

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56 Figure 42 .b. The pull off force s data from Figure 42.a Figure 42 .c. The linear curve fitting for pull off forces from Figure 42.b

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57 A dditional research wa s done for the relationship between the pull off force and the nanoindentati o n unloading rate shown in F igure 43.a and F igure 43.b. Regardless of whether the uploading time is 5 seconds or 10 seconds, the pull off force doesn't change with the unloading rate. Figure 43 .a. PDMS network 10:1 pull o ff force based on the unloading rate.

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58 Figure 43 .b. PDMS network 25:1 pull off force s based on the unloading rate. 3.3.4 Adhesion F orce Conical T ip The pull off force is related to the geometry shape of the nanoindentation tip. [47] So additional na noindentation experiments on adhesion force we re done using the same procedure, but with a c onical tip instead of a B er k o vich tip. Conical tip is a spherical tip, which is different from the three surfaces Berkovich tip. Open loop control wa s used to do th e test. R esulting data is shown in F igure 4 4.

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59 Figure 44 PDMS network nanoindentati o n adhesion force with the c onical tip. In F igure 44, PDMS network sample with base/agent ratio 5:1 wa s used for the expe riment. T here is no visible initial contact phenomenon, but one can see the pull off force yielding when the tip leaves the sample surface T he pull off force in Figure 44 is around 3 N while the pull off force for PDMS network 5:1 in Figure 38 is around 35 N The difference between the pull off force with the conical tip and the pull off force with the Berkovich tip is due to the geometric shape of nanoindent ation tips [ 4 7 49]. 3 .3. 5 Adhesion F orce C ube C orner T ip Nanoindentation experiments on adhesion force we re also done with a cube corner tip. The same open lop control wa s used to do the test. Collected data is shown in Figure 45.

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60 In F igure 45, PDMS network sample with 5:1 base/agent ratio wa s used for experiments. T here is no visible initial contact phenomenon, but one can see the pull off force. T he pull off force is around 2 N. Figure 45 .a. PDMS network 5:1 nanoindentation adhesion force test with the cube corner tip (L oading time: 2 sec. Unloading time: 5 sec )

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61 Figure 45.b. PDMS network 5:1 nanoin dentation adhesion force test with the c ube corner tip (L oading time: 5 sec. Unloading time: 2 sec) The differences between the experiment in Figure 45.a and the experiment in Figure 45.b are the loading time and the unloading time. I n the tests using a cube corner tip, the loading and unloading ratios do not affect the adhesion force. In equation (2 1), E* is the same due to the same sample, so pull off force P will depend on the contact radius a and the tip radius R which are all related to the tip s g eometric shape. Also, comparing with the pull off force (35 N) in PDMS network 5:1 Berkovich tip test and the pull off force (3 N) in PDMS network 5:1 conical tip test, one can see the tip s geometric shape does influence the adhesion force [ 50 ].

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62 3.4 C onclusions for C hapter 3 PDMS network nano DMA tests provide stable data with different test models. The storage modulus is increasing when the test frequency. T he loss modulus reaches a peak when the DMA test frequency is around the transducer s natural frequency. A lso the data collected in nano DMA test is comparable with the data collected in PDMS network compression test. Nanoindentation experiments with flat punch we re also done to test the elastic modulus of PDMS network 5:1 and yield similar results Adhesion force experiments are done with different tips, which are Berkovich tip, c ornical tip and c ube corner tip. The adhesion forces are related to the PDMS network samples base/agent ratios and the tips geometrical shapes.

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63 Chapter 4. Summar y and F uture W ork This research was done to explore the effect of substrate stiffness on the growth and behavior of cells attached to PDMS network substrates. In this thesis, the relationship between the elastic modulus of PDMS network and the base/agent ratio (the amount of crosslinking) is studied. Most c hallenges of this research have been overcome. Reliable macroscopic compression test instrument wa s created. Preload method was applied for the nanoindentation flat punch test to develop full contact. I n chapter 2, a series of PDMS network samples with different base/agent ratios we re tested with the macroscopic compression test. T he elastic modulus of PDMS network 5:1 is 3.5 9 MPa, the elastic modulus of PDMS network 7:1 is 2.9 1 MPa, the elastic modulus of PDMS network 10:1 is 2.66 MPa, the elastic modulus of PDMS network 16.7:1 is 1.2 1 MPa, the elastic modulus of PDMS network 25:1 is 0.98 MPa, and the elastic modulus of PDMS network 33:1 is 0.78 MPa. The relationship between PDMS network elastic modulus and its base/agent ratio n, is: E= 20 /n. In chapter 3, PDMS network nano DMA tests provide stable data with different test models. The storage modulus collected in nano DMA tests is comparable with elastic modulus collected in PDMS network compression test in chapter 2. Elastic modulus of PDMS network 5:1 wa s also measured using flat punch q uasi static test. The adhesion force tests with different nanoindentation tips, re spectively Berkovich tip, conical tip, cube corner tip, show that PDMS s adhesion forc e is related to the

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64 samples base/agent ratios and the tips geometrical shapes. Different properties and phenomena were studied with different systems of Hysitron Triboindentor. The elastic modulus in chapter 2 with compression test and in chapter 3 with flat punch nanoindentation test and nano DMA test are comparable. In future, DMA as a novel technique for soft polymer materials need to be better developed based on more research. Also, more base/agent ratios of the PDMS network samples need to be tested with both compression method and flat punch nanoindentation method to obtain more accurate PDMS network mechanical properties.

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