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RHEOLOGY and DYNAMIC MECHANICAL ANALYSIS – What They Are and Why They’Re Important

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RHEOLOGY and DYNAMIC MECHANICAL ANALYSIS – What They Are and Why They’Re Important RHEOLOGY AND DYNAMIC MECHANICAL ANALYSIS – What They Are and Why They’re Important Presented for University of Wisconsin - Madison by Gregory W Kamykowski PhD TA Instruments May 21, 2019 TAINSTRUMENTS.COM Rheology: An Introduction Rheology: The study of the flow and deformation of matter. Rheological behavior affects every aspect of our lives. Dynamic Mechanical Analysis is a subset of Rheology TAINSTRUMENTS.COM Rheology: The study of the flow and deformation of matter Flow: Fluid Behavior; Viscous Nature F F = F(v); F ≠ F(x) Deformation: Solid Behavior F Elastic Nature F = F(x); F ≠ F(v) 0 1 2 3 x Viscoelastic Materials: Force F depends on both Deformation and Rate of Deformation and F vice versa. TAINSTRUMENTS.COM 1. ROTATIONAL RHEOLOGY 2. DYNAMIC MECHANICAL ANALYSIS (LINEAR TESTING) TAINSTRUMENTS.COM Rheological Testing – Rotational - Unidirectional 2 Basic Rheological Methods 10 1 10 0 1. Apply Force (Torque)and 10 -1 measure Deformation and/or 10 -2 (rad/s) Deformation Rate (Angular 10 -3 Displacement, Angular Velocity) - 10 -4 Shear Rate Shear Controlled Force, Controlled 10 3 10 4 10 5 Angular Velocity, Velocity, Angular Stress Torque, (µN.m)Shear Stress 2. Control Deformation and/or 10 5 Displacement, Angular Deformation Rate and measure 10 4 10 3 Force needed (Controlled Strain (Pa) ) Displacement or Rotation, 10 2 ( Controlled Strain or Shear Rate) 10 1 Torque, Stress Torque, 10 -1 10 0 10 1 10 2 10 3 s (s) TAINSTRUMENTS.COM Steady Simple Shear Flow Top Plate Velocity = V0; Area = A; Force = F H y Bottom Plate Velocity = 0 x vx = (y/H)*V0 . -1 γ = dvx/dy = V0/H Shear Rate, sec σ = F/A Shear Stress, Pascals . η = σ/γ Viscosity, Pa-sec These are the fundamental flow parameters. Shear rate is always a change in velocity with respect to distance. TAINSTRUMENTS.COM Representative Flow Curve 1.E+05 Newtonian Pseudoplastic Region Behavior 1.E+04 0 < n < 1 (Newtonian) 1.E+03 η η Transition Power Law = 0 Region Region 1.E+02 Viscosity (Pa-sec) 1.E+01 . η = m*γ (n-1) 1.E+00 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 η ∝ 3.4 0 MW Shear Rate (sec-1) TAINSTRUMENTS.COM Simple Shear Deformation Top Plate Displacement = X0; Area = A; Force = F H y Bottom Plate x Displacement = 0 x = (y/H)*X0 γ = dxx/dy = X0/H Shear Strain, unitless σ = F/A Shear Stress, Pascals G = σ/γ Modulus, Pa These are the fundamental deformation parameters. Shear strain is always a change in displacement with respect to distance. TAINSTRUMENTS.COM Stress Relaxation Stress Relaxation of Soy Flour, Overlay 109 • Instantaneous Strain • Note the decrease in the modulus as a ) function of time. 108 G(t) ( [Pa] F G(t) T=20°C T=30°C T=40°C T=50°C 107 1 2 100 10 10 103 time [s] TAINSTRUMENTS.COM Creep Testing Stress is held constant. Strain is the measured variable. 3x10 -3 HDPE 2x10 -3 Viscoelastic (1/Pa) 1x10 -3 Fluid Compliance Solid 0x10 0 0 5 10 15 20 Step time (min) TAINSTRUMENTS.COM Geometry Options Concentric Cone and Parallel Torsion Cylinders Plate Plate Rectangular Very Low Very Low Very Low Solids to Medium to High Viscosity Viscosity Viscosity to Soft Solids Water to Steel TAINSTRUMENTS.COM Examples for Common Configurations Geometry Examples Coatings Beverages Concentric Cylinder Slurries (vane rotor option) Starch pasting Low viscosity fluids Viscosity standards Cone and Plate Sparse materials Polymer melts in steady shear Widest range of materials Adhesives Polymer melts Parallel Plate Hydrogels Asphalt Curing of thermosetting materials Foods Cosmetics Thermoplastic solids Torsion Rectangular Thermoset solids TAINSTRUMENTS.COM Rheology – Speak Machine Parameter Rheological Parameter Angular Velocity (rad/sec) Shear Rate (1/sec) Angular Displacement (rad) Shear Strain ( - ) Torque (µN-m) Shear Stress (N/m2, Pa) TAINSTRUMENTS.COM Converting Machine to Rheological Parameters in Rotational Rheometry Machine Parameters M x Kσ σ M: Torque = =η Ω : Angular Velocity Ω γ• θ : Angular Displacement xKγ Conversion Factors Kσ : Stress Conversion Factor Kγ : Strain (Rate) Conversion Factor σ Rheological Parameters MxKσ σ : Shear Stress (Pa) = = γ• : Shear Rate (sec-1) G η : Viscosity (Pa-sec) γ : Shear Strain θ xKγ γ G : Shear Modulus (Pa) The conversion factors, Kσ and Kγ, will depend on the following: Geometry of the system – concentric cylinder, cone and plate, parallel plate, and torsion rectangular Dimensions – gap, cone angle, diameter, thickness, etc. TAINSTRUMENTS.COM Shear Rate and Shear Stress Calculations Geometry Couette Cone & Plate Parallel Plates Conversion Factor Kγ Ravg/(Ro-Ri) 1/β R/h 2 3 3 Kσ 1/(2*πRi L) 3/(2πR ) 2/(πR ) TAINSTRUMENTS.COM Cone & Plate and Parallel Plate Geometric Considerations Standard DHR Peltier 20mm 40mm 50mm plate geometry diameters Shear Stress Shear Stress At given torque, Increase in diameter → Decrease in shear stress Shear Rate At given angular velocity Increase in cone angle → Decrease in shear rate Increase in gap (parallel plate) → Decrease in shear rate So, for low viscosity fluids, use the largest diameter cone or plate. For high viscosity fluids, use the smallest diameter cone or plate TAINSTRUMENTS.COM Rheological Methods – Unidirectional Testing . Flow . Stress/Rate Ramp . Stress/Rate Sweep Sweep . Time sweep/Peak Hold . Temperature Ramp . Creep (constant stress) Ramp . Stress Relaxation (constant Stress, Shear Rate strain) Time . Axial Testing TAINSTRUMENTS.COM Thixotropy: Up & Down Flow Curves Toothpaste loop 600 400 (Pa) thixotropy: 600.997 Pa/s Stress 200 The area between the curves is an indication of the thixotropic nature of the material. 0 0 2 4 6 8 10 Shear rate (1/s) TAINSTRUMENTS.COM Flow Stress Ramp on a Yielding Material 500 464 Pa-sec 400 300 319 Pa-sec (Pa) Stress 200 EmulsionSample A (3) A 197 Pa EmulsionSample B (3) B 100 The yield stress was obtained just by visual means. A has a higher yield stress than B 0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Shear rate (1/s) TAINSTRUMENTS.COM Steady State Flow at 25 C - Coatings 10 3 10 2 10 1 (Pa.s) G 10 0 These are rate sweeps. Equilibration occurs at each point. Concentric Cylinder geometry 10 -1 10 -2 10 -1 10 0 10 1 10 2 10 3 S (1/s) TAINSTRUMENTS.COM Polymer Melt Flow Curve 1.E+06 Williamson Model . c η = η0/(1+(σγ) ) 1.E+05 Cone and Plate 1.E+04 Viscosity (Pa-sec) 1.E+03 0.01 0.1 1 10 η 3.4 0 = KMw Shear Rate (1/sec) Steady testing with cone and plate and Mw = 400,000 Mw = 250,000 Mw = 160,000 parallel plate geometries is The shear rate and shear stress are constant throughout the gap with the often limited to cone-and-plate geometry. Parallel plate data can be corrected with the Rabinowitsch correction. low shear rates. TAINSTRUMENTS.COM Normal Force Measurements with Cone & Plate Normal Stress Difference: • In steady flow, polymeric materials can exert a force that tries to separate the cone and the plate. • A parameter to measure this is the Normal Stress Difference, N1, which equals σxx- σyy from the Stress Tensor. • N1 = 2F/(πR2), where F is the measured force. 2 • Ψ1 = N1/ This is the primary normal stress coefficient. TAINSTRUMENTS.COM TAINSTRUMENTS.COM Creep Testing on US and UK Paints Creep and recovery can be done on both DHR and ARES rheometers Creep is a unidirectional way of getting viscoelasticity. It is often followed by creep recovery. Creep answers the question of how much deformation to expect when a material is subjected to a constant stress, such as gravity It is usually easier on a DHR, but the ARES sometimes works better when there are instances of creep ringing. TAINSTRUMENTS.COM Stress Relaxation 10 6 10 5 PDMS 10 4 10 3 (Pa) 10 2 10 1 Stress relaxation is another unidirectional way of Modulus getting viscoelastic properties. 10 0 This works better on the ARES than on the DHR. 10 -1 10 -4 10 -3 10 -2 10 -1 10 0 10 1 Step time (min) TAINSTRUMENTS.COM Flow Temperature Ramp – Printing Inks 1,000 Room Temperature 100 10 Viscosity (Pa-sec) Viscosity Printing Press Temperature 1 20 25 30 35 40 45 50 Temperatue (C) TAINSTRUMENTS.COM Dynamic Testing STRAIN ELASTIC RESPONSE 90o VISCOUS RESPONSE Response, Strain Response, VISCOELASTIC RESPONSE δo Polymers are viscoelastic materials. Time Both components – viscosity and elasticity – are important. TAINSTRUMENTS.COM Dynamic Rheological Parameters Parameter Shear Elongation Units Strain γ = γ0 sin(ωt) ε = ε0 sin(ωt) --- Stress σ = σ0sin(ωt + δ) τ = τ0sin(ωt + δ) Pa Storage Modulus G’ = (σ /γ )cosδ E’ = (τ /ε )cosδ Pa (Elasticity) 0 0 0 0 Loss Modulus G” = (σ /γ )sinδ E” = (τ /ε )sinδ Pa (Viscous Nature) 0 0 0 0 Tan δ G”/G’ E”/E’ --- Complex Modulus G* = (G’2+G”2)0.5 E* = (E’2+E”2)0.5 Pa Complex Viscosity η* = G*/ω ηE* = E*/ω Pa-sec . Cox-Merz Rule for Linear Polymers: η*(ω) = η(γ) @ γ = ω TAINSTRUMENTS.COM Dynamic Testing •Dynamic Stress or Strain Sweep •Dynamic Time Sweep •Dynamic Frequency Sweep •Dynamic Temperature Ramp •Dynamic Temperature Sweep TAINSTRUMENTS.COM Linear Viscoelasticity 10 4 Linear Region: • Osc Stress is linear with Strain. • G’, G” are constant. This is typically the first test done on unknown materials. Non-Linear Region G’ = f(γ) Stress v. Strain End of LVR or (Pa) Critical Strain γc 10 3 0.1 1 10 100 It is preferable to perform testing in the linear region because you are measuring R (%) intrinsic properties of the material, not material that has been altered.
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