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Chapter 9: Rheological and Mechanical Properties of Polymers AE 447: Polymer Technology, Dr. Cattaleeya Pattamaprom Adapted from the workshop on Fundamentals of Rheology Seminar by Dr. Abel Gaspar-Rosas TA Instruments – Waters, Inc. April, 2004 Thailand Outline 1. Rheology – Introduction 2. Elasticity, Viscosity and Viscoelasticity 3. Rheology tests • • • • Steady-state flow Stress Relaxation Creep Recovery Oscillatory Tests – Dynamic Frequency sweep – Dynamic Temperature ramp 4. Molecular Properties vs. Rheology of Polymers 5. Mechanical Testing Definition of Rheology • Rheology is the science of deformation and flow of matter. ่ าวถึง รีโอโลยี (Rheology): ศาสตร ์ของรีโอโลยี เป็ นศาสตร ์ทีกล่ สมบัตก ิ ารไหลหรือการเสียรูป รีโอโลยีของพอลิเมอร ์ส่วนใหญ่มก ั กล่าวถึงค่าโมดูลสั และค่าความหนื ด Simple Shear Deformation and Shear Flow Shear Deformation x(t) F = t A V y0 q y A z x . g = Dg Dt x(t) Strain, g = y 0 1V d x(t) . Strain Rate, g = yy d t 00 t Viscosity, h = . g t Shear Modulus, G = g Range of Rheological Material Behavior Rheology: The study of deformation and flow of matter. Range of material behavior Elastic solid Solid Like ---------Liquid Like Ideal Solid-------------Ideal Fluid Viscoelastic Classical Extremes Viscous liquid Classical Extremes: Elastic Solid 1678: Robert Hooks develops his “True Theory of Elasticity” “The power of any spring is in the same proportion with the tension thereof.” Hooke’s Law: t =Gg or where G is the RIGIDITY MODULUS . G is constant (Stress = G x Strain) Classical Extremes: Viscosity 1687: Isaac Newton addresses liquids and steady simple shearing flow in his “Principia” “The resistance which arises from the lack of slipperiness of the parts of the liquid, other things being equal, is proportional to the velocity with which the parts of the liquid are separated from one another.” Newton’s Law: t = hg h is constant wherehis the Coefficient of Viscosity Response for Classical Extremes Spring Purely Elastic Response Hookean Solid t = Gg Dashpot Purely Viscous Response Newtonian Liquid t = hg For the classical extremes cases, what only matters are the values of stress, strain and strain rate. The response is independent of the loading. Overview about the different rheological material behavior ilustrated by the use of… Ideal viscous Newton‘s law viscoelastic fluid / solid Ideal elastic Hooke‘s law shear viscosity h [Pas] shear stress t [Pa] shear rate g [1/s] Oil, Solvent shear modulus G [Pa] Apparent Yield Point, Thixotropy, … Coatings, Food, Cosmetics, Polymers Glass, Steel Physica Messtechnik Gmbh Vor dem lauch 6, 70567 Stuttgart, Germany Internet:http://www.physica .de Viscoelasticity Defined Range of Material Behavior Solid Like ---------- Liquid Like Ideal Solid ----- Most Materials ----- Ideal Fluid Purely Elastic ----- Viscoelastic ----- Purely Viscous Viscoelasticity: Having both viscous and elastic properties Realistic polymer material - Materials are in between Elastic solid and Newtonian liquid called “viscoelastic” - Some energy stored, some dissipated. - Some time independent, some time dependent. A typical viscoelastic effect is tackiness (with long strings) which is not occuring with purely viscous liquid (example: water), or purely elastic solid (example: stone) Physica Messtechnik Gmbh Vor dem lauch 6, 70567 Stuttgart, Germany Internet:http://www.physica .de Viscoelastic Fluids Viscoelastic behavior, illustrated by use of a dashpot and a spring Polymers at rest Macromolecules are entangled and have spherical shapes Macromolecules are deformed and disentangled low viscosity under shear high viscosity Physica Messtechnik Gmbh Vor dem lauch 6, 70567 Stuttgart, Germany Internet:http://www.physica .de Newtonian and Non-Newtonian Behavior of Fluids Non-Newtonian Region 1.000E5 Newtonian Region h Independent of g 1.000E5 h = f(g) 10000 Zero-shear viscosity (ho) h t (Pa) h(Pa.s) 1000 100.0 Shear thinning Pseudo-plastic t 10000 1.000E-5 1.000E-4 1.000E-3 10.00 0.01000 shear rate (1/s) g 0.1000 1.000 1.000 Elastic Modulus vs. Temp. 4 E brittle 3 leathery 2 rubbery 1 viscous Temp Area 1: Viscous state: Area 2: Rubbery state Area 3: Leathery state Area 4: Glassy state E = stress = F/A = strain = dL/L E = elastic modulus Linear and Non-Linear Stress-Strain Behavior of Solids Linear Region G is constant Non-Linear Region 100.0 G = f(g) osc. stress (Pa) 1000 100.0 G 10.00 1.000 0.010000 0.10000 1.0000 10.000 % strain 100.00 0.01000 1000.0 Viscosity and Viscoelasticity Viscosity: Definition Viscosity is . . . . synonymous with internal friction. resistance to flow. Variables that Affect Viscosity –for polymer • • • • • Shear Rate - Molecular Weight Time of Shearing Temperature Pressure Surface Tension Characteristic Diagrams for Newtonian Fluids t, Pa hPa.s Ideal Yield Stress (Bingham Yield) gs gs or tPa Viscosity: Temperature dependence v is c o s ity (P a .s ) 10000 1000 100.0 10.00 20.0 30.0 40.0 50.0 60.0 temperature (Deg C) 70.0 80.0 90.0 100.0 Summary of Types of Flow Shear Stress, t Bingham (Newtonian w/yield stress) Bingham Plastic (shear-thinning w/yield stress) Shear Thinning (Pseudoplastic) ty Newtonian Shear Thickening (Dilatent) Shear Rate, g Viscosity vs. Shear Rate Result: Rheological material behaviour Shear stress & viscosity as a function of the shear rate • Newtonian Ideal viscous (e.g.: oil, solvent) • Shear thinning (e.g.: typical food, cosmetics, coatings, polymers, …) • Shear Thickening Shear thickening (e.g.: PVC plastisol & paper coatings under high shear cond.) Newtonian and Non-Newtonian Behavior of Fluids Non-Newtonian Region 1.000E5 Newtonian Region h Independent of g 1.000E5 h = f(g) 10000 h t (Pa) h(Pa.s) 1000 100.0 t 10000 1.000E-5 1.000E-4 1.000E-3 10.00 0.01000 shear rate (1/s) g 0.1000 1.000 1.000 Idealized Flow Curve - Polymers Power Law Region First Newtonian Plateau h0 = Zero Shear Viscosity h0 = K x MW3.4 log h Extend Range with TimeTemperature Superposition (TTS) & Cox-Merz Measure in Flow Mode on AR1000/AR500 Extend Range with Oscillation & Cox-Merz Molecular Structure 1.00E-5 1.00E-4 1.00E-3 Compression Molding 0.0100 0.100 1.00 Extrusion 10.00 shear rate (1/s) 100.00 Second Newtonian Plateau Blow and Injection Molding 1000.00 1.00E4 1.00E5 Comparison of Newtonian & Shear Thinning Samples viscosity (Pa.s) 10000 Standard oil A 1000 100.0 10.00 Xanthan/Gellan Fructose Soln. 1.000 0.1000 Standard oil B 0.01000 1.000E-3 1.000E-6 1.000E-4 0.01000 1.000 shear rate (1/s) 10.00 100.0 1000 Non-Newtonian, Time Dependent Fluids Thixotropy A decrease in apparent viscosity with time under constant shear rate or shear stress, followed by a gradual recovery, when the stress or shear rate is removed. Rheopexy An increase in apparent viscosity with time under constant shear rate or shear stress, followed by a gradual recovery when the stress or shear rate is removed. Also called Anti-thixotropy or negative thixotropy. Reference:Barnes, H.A., Hutton, J.F., and Walters, K., An Introduction to Rheology, Elsevier Science B.V., 1989. ISBN 0-444-87469-0 Non-Newtonian, Time Dependent Fluids Viscosity Rheopectic Shear Rate = Constant Thixotropic time Time-Dependent Viscoelastic Behavior: Solid and Liquid Properties of "Silly Putty" T is short [< 1s] T is long [24 hours] Deborah Number [De] = t/ Storage and Loss of Viscoelastic Material SUPER BALL LOSS X TENNIS BALL STORAGE Rheology Tests Some Types of Rheometers • Typical Rheometer: Low shear rate/Oscillatory • Capillary Rheometer: High shear rate Rheology:Choosing Tests and Conditions Geometries: Typical Rheometer Max. 3° Max. 3° Delta < 1.2 Delta < 1.2 0.25mm < gap < 2mm Ref.: Physica 1. Stepped Ramp or Steady-Shear Flow A series of logarithmic stress steps allowed to reach steady Viscosity state, each one giving a single viscosity data point: Shear Thinning Region Shear Rate Time hg (d dt) Shear Rate, 1/s Typical steady shear flow experiment Polyethylene Rheology @ 150 C 1000000 HDPE 100000 viscosity (Pa.s) LLDPE 10000 LDPE 1000 1.000E-4 1.00E-3 0.01000 0.1000 shear rate (1/s) 1.000 10.00 Idealized Full Flow Curve - Polymers Power Law Region First Newtonian Plateau h0 = Zero Shear Viscosity h0 = K x MWc 3.4 log h Extend Range with TimeTemperature Superposition (TTS) & Cox-Merz Measure in Flow Mode on AR1000/AR500 Extend Range with Oscillation & Cox-Merz Molecular Structure 1.00E-5 1.00E-4 1.00E-3 Compression Molding 0.0100 0.100 1.00 Extrusion 10.00 shear rate (1/s) 100.00 Second Newtonian Plateau Blow and Injection Molding 1000.00 1.00E4 1.00E5 At very high shear rate Melt fracture Higher Shear Rate 2. Stress Relaxation Experiment Strain is applied to sample instantaneously Strain (in principle) and held constant with time. Stress is monitored as a function of time (t). 0 time Stress Relaxation Experiment 0 time Response of Classical Extremes Hookean Solid Newtonian Fluid stress for t>0 is 0 stress for t>0 is constant 0 time 0 time Stress Relaxation Experiment (cont’d) Response of Material Stress decreases with time starting at some high value and decreasing to zero. 0 time For small deformations (strains within the linear region) the ratio of stress to strain is a function of time only. This function is a material property known as the STRESS RELAXATION MODULUS, G(t) G(t) = (t)/g 3. Creep Recovery Experiment Stress is applied to sample instantaneously, t1, and Stress held constant for a specific period of time. The strain is monitored as a function of time g(t). The stress is reduced to zero, t2, and the strain is monitored as a function of timegt. t1 time t2 Creep Recovery Experiment t1 time t2 Response of Classical Extremes Stain for t>t1 is constant – Strain for t >t2 is 0 – t1 time t2 Stain rate for t>t1 is constant – Strain for t>t1 increase with time – Strain rate for t >t2 is 0 – t1 time t2 Creep Recovery Experiment: Response of Viscoelastic Material Creep >0 Recovery = 0 (after steady state) /h Recoverable Strain t 1 Strain rate decreases with time in the creep zone, until finally reaching a steady state. t2 time In the recovery zone, the viscoelastic fluid recoils, eventually reaching a equilibrium at some small total strain relative to the strain at unloading. Reference: Mark, J., et.al., Physical Properties of Polymers ,American Chemical Society, 1984, p. 102. 4.Oscillatory Testing of Polymers (Dynamic Mechanical Tests) Dynamic Mechanical Testing An oscillatory (sinusoidal) Deformation deformation (stress or strain) is applied to a sample. The material response Response (strain or stress) is measured. The phase angle d, or phase shift, between the deformation and response is measured. Phase angle d Dynamic Mechanical Testing Viscoelastic Material Response Phase angle Stress Strain 0° < d < 90° DMA Viscoelastic Parameters: The Complex, Elastic, & Viscous Stress The stress in a dynamic experiment is referred to as the complex stress t* Phase angle d Strain, g Complex Stress, t* t* = t' + it" DMA Viscoelastic Parameters The Complex Modulus: Measure of materials overall resistance to deformation. G* = Stress*/Strain G* = G′ + iG″ The Elastic (Storage) Modulus: Measure of elasticity of material. The ability of the material to store energy. G' = (stress*/strain)cosd The Viscous (loss) Modulus: The ability of the material to dissipate energy. Energy lost as heat. G" = (stress*/strain)sind Tan Delta: Measure of material damping - such as vibration or sound damping. Tan d = G"/G' Storage and Loss of Viscoelastic Material SUPER BALL LOSS X TENNIS BALL STORAGE 4.1 Frequency Sweep Deformation Time USES The material response to increasing frequency (rate of deformation) is monitored at a constant amplitude (stress or strain) and temperature. Information - Zero Shear h, shear thinning Elasticity (reversible deformation) in materials MW & MWD differences Polymer Melts and Polymer solutions. Finding Yield in gelled dispersions High and Low Rate (short and long time) modulus properties. Extend time or frequency range with TTS Viscosity Frequency Sweep: Material Response Terminal Region Rubbery Plateau Region Transition Region Glassy Region 1 2 Storage Modulus (E' or G') Loss Modulus (E" or G") log Frequency (rad/s or Hz) Typical Oscillatory Data PDMS 1.000E6 1.000E5 1.000E6 1.000E5 1.000E5 10000 10000 10.00 1000 |n*| (Pa.s) 100.0 1000 G” G'' (Pa) G' (Pa) 10000 1000 100.0 G’ 10.00 1.000 1.000 0.1000 0.1000 PDMS Extended frequency sweep-0001o, Frequency sweep step 0.01000 100.0 1.000E-5 1.000E-4 1.000E-3 0.010000.1000 1.000 frequency (Hz) 10.00 0.01000 100.0 Time-Dependent Viscoelastic Behavior: Solid and Liquid Properties of "Silly Putty" T is short [< 1s] T is long [24 hours] Deborah Number [De] = t/ Dynamic Moduli of a Polymer Melt vs. Frequency 1000000 1000000 1.00E7 PDMS at 20°C 100000 100000 10000 1000 1000 100.0 100.0 10.00 10.00 h* 100000 10000 G" 1000 1.000 1.000 G' 0.1000 0.1000 1.000E-3 1.000E-4 0.01000 0.1000 1.000 10.00 ang. frequency (rad/sec) 100.0 100.0 1000 h* (Pa.s) 10000 G'' (Pa) G' (Pa) 1000000 Typical steady shear flow experiment Polyethylene Rheology @ 150 C 1000000 HDPE 100000 viscosity (Pa.s) LLDPE 10000 LDPE 1000 1.000E-4 1.00E-3 0.01000 0.1000 shear rate (1/s) 1.000 10.00 Cox-Merz Rule v is c o s ity (P a .s ) 100000 10000 Polydimethylsiloxane Creep or Steady shear Flow Dynamic Frequency Sweep . hg h*w PDMS.05F-Flow step PDMS.08F-Flow step 1000 Dynamic data gives high shear rates unattainable in flow 100.0 1.000E-5 1.000E-3 0.1000 shear rate (1/s) 10.00 1000 4.2 Dynamic Temperature Ramp: Material Response Glassy Region Transition Region Rubbery Plateau Region Storage Modulus (E' or G') Loss Modulus (E" or G") Temperature Terminal Region Time – Temp Superposition: Time – Temp Superposition: can be used for shifting “moduluse” in creep test (E(t)), relaxation test (G(t)), dynamic oscillatory test ( G’, G”) t 1/f “ Time scale (or frequency) of stress applies and temperature has a similar influent on mechanical properties.! “ short time ( high f ) = h/G long time ( low f ) low temp. high temp. works because t and T affect the relaxation time of polymer in same way < Relaxation time determines mechanical properties Relationship between Molecular Properties and Rheology of Polymers Effect of Molecular Properties on Rheology Molecular Structure •MW & MWD •Chain Branching and Cross-linking •Interaction of Fillers with Matrix Polymer •Single or Multi-Phase Structure Viscoelastic Properties As a function of:: •Strain Rate(frequency) •Strain Amplitude •Temperature Processability & Product Performance Molecular Structure - Effect of Molecular Weight Glassy Region Transition Region Rubbery Plateau Region MW has practically no effect on the modulus below Tg Low MW Temperature High Med. MW MW Effect of Molecular Weight on Viscosity and Elasticity MWc = critical MW 3.4 MWc log MW log Joe log ho MWc’ log MW Ref. Graessley, Physical Properties of Polymers, ACS, c 1984. Zero Shear Viscosity ho Sensitive to molecular weight, MW For low MW (no entanglements) ho is proportional to MW For MW > Critical MW, ho is proportional to MW3.4. Effect of Molecular Weight h0 =K x MW3.4 h0 Increasing MW log g Effect of Molecular Weight Distribution on h0 A Polymer with a broad MWD exhibits nonNewtonian flow at a lower rate of shear than a polymer with the same h0 but has a narrow MWD Narrow MWD Broad MWD Log Shear Rate (1/s) IV.8 : Mechanical Tests Tensile – CompressionTest < stress–strainbehavior > Stress Normal Stress ( normal stress) F(t) A0 L(t) F(t) = ForceF/ A ( A = cross-sectionarea) if A = A 0 engineeringstress A = A (t) true stress Strain = L L0 L0 (engineering ) true = ln( 1+ eng ) ( truestrain) ้ (TrueLength) แทนL0 DeriveจากการใชL(t) Shear Stress DUxx A DUyy F Shear stress = Shear strain = Force F surface area DUxx Dy uyx = ระยะทางทีเค่ ลือ่ นทีไปในแ ่ นวแกนX y x Stress (psi * 103) true eng Compressive strength fracture compression fracture Tensile strength tension 30 Strain( %) Stress–straincurvefor anormallybrittlepolymer under tensionandcompression Elastic modulus : slope of stress – strain curve at origin ( indicator of stiffness ) Strength : stress at fracture (normally strength tension < strength compression) Elongation at break : strain at fracture ถามี ้ ค่ามาก ductile นอ้ ย brittle Toughness : area under stress–strain curve [ = ] energy/unit volume desirable material stiff, strong, ductile, and tough Note Test can be performed in tension, compression, flexure, or torsion. Elongationat yield Ultimate strength stress Plastic deformation Yieldstress strain Physical Testing