Dynamic Mechanical Analysis (DMA) Basics and Beyond
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1 Dynamic Mechanical Analysis (DMA) Basics and Beyond ε ω = Σ(Δε β /1+ιωτ β ) Dr. Lin Li Thermal Analysis PerkinElmer Inc. April 2000
2 The DMA lets you relate: product properties molecular structure Material Behavior processing conditions
3 DMA Structure in general How the DMA works: Constant inputs and outputs function as in the TMA A sine wave current is added to the force coil The resultant sine wave voltage of the LVDT is compared to the sine wave force The amplitude of the LVDT is related to the storage modulus, E' via the spring constant, k. The phase lag, δ, is related to the E" via the damping constant, D. Force Motor Coil Magnet Temperature Enclosure LVDT Core Rod Interchangeable Measuring System Furnace Heat Sink/Cooling System
4 Outstanding Flexibility 1: Multiple Geometries Compressive Cup & Plate Extension Shear Flexure Parallel Plate Cup & Plate Tray & Plate Sintered Plates 3 pt. Bending 4 pt. Bending AST M Flexure Dual Cantilever Single Cantilever Extension Shear Sandwich Coaxial Cylinder Paper Fold
5 Why? Log E mm 1 mm mm 20 mm 3
6 Stress Causes Strain... Cauchy or Engineering Strain ε = ΔL/L o L o L Henchy or True Strain ε = ln (ΔL/L o ) Kinetic Theory of Rubber Strain ε = 1/3{L/L o -(L o /L) 2 } Kirchhoff Strain ε = 1/2{ (L/L o ) 2-1} L-L o = ΔL Murnaghan Strain ε = 1/2{1-(L o /L) 2 } The different definitions of tensile strain become equivalent at very small deformations.
7 The Elastic Limit: Hooke s Law = σ slope = k Strain increases with increasing Stress ε
8 Stress (Pa x 10 7 ) Real vs... Hookean Stress- Curve 1: DMA Creep Recoveryin Parallel Plate File info: Drssr90R.2Thu Apr 14 15:16: Sample Height:3.359 mmcreep Stress: mN Recovery Stress: 1.0mN Dresser 90 Durameter Strain Curves Limiting Modulus Slope Pa/% σ Hookean Behavior Slope Pa/% TEMP1: 20.0 C TIME1: 5.3 min Strain (%) KPM PERKIN-ELMER 7 Series ThermalAnalysis System Thu Apr 14 16:34: Real behavior ε
9 The Viscous Limit: Newtonian Behavior σ slope = η The speed at which the fluid flows through the holes (the strain rate) increases with stress!!!. γ
10 Viscosity Effects τ. γ Newtonian behavior is linear and the viscosity is independent of rate. Pseudoplastic fluids get thinner as shear increases. Dilatant Fluids increase their viscosity as shear rates increase. Plastic Fluids have a yield point with pseudoplastic behavior. Thixotrophic and rheopectic fluids show viscosity-time nonlinear behavior. For example, the former shear thin and then reform its gel structure.
11 Polymers are Non-Newtonian Fluids!!! η Log Zero Shear Plateau ~ η o Infinite Shear Plateau ~ η Log γ. Linear Dependence on Rate At low shear rates, the viscosity is controlled by MW. The material shows Newtonian behavior Viscosity shows a linear dependence on rate above the η o region. At high rates, the material can no longer shear thin and a second plateau is reached.
12 Analyzing a Stress-Strain linear region Curve nonlinear region failure (ε Β,σ Β ) σ yield point (ε y,σ y ) Young s modulus (E) E d σ = = d ε ε σ ε L L The area under the curve to this line is the energy needed to break the material
13 Under Continuos Loads: Creep Applying a constant load for long times and removing it from a sample. Allows one to see the distortion under constant load and also how well it recovers. Recovery
14 Strain (%) Force (mn) Creep is a fundamental engineering test. Creep is used as a basic test for design. By looking at both the creep and recovery parts of the curve, we can begin to examine how polymers relax. Curve 1: DMA Creep Recovery in 3 Point Bending File info: cr_ptfe-5 Wed Jun 29 15:31: Sample Height: 3.300mmCreep Stress: 1.50e+06Pa PTFE - CREEP/RELAXATION # 1 PTFE - CREEP/RELAXATION AT -5C:cr_ptfe-5 Strain (%) TEMP1: C TIME1: 7.0 min Time (minutes) Recovery Stress: 6.25e+02Pa # 2 Force (mn) DMA7 APPLICATIONS LAB PERKIN-ELMER 7 Series ThermalAnalysis System Thu Apr 28 20:32:
15 Dynamic Stress Force (dynamic) Force material response F (static) Time Phase angle = δ Stress =FA Stress Time Amplitude = k Strain =y o /y
16 Why? Let s bounce a ball. E ~ energy loss in internal motion E ~ elastic response
17 All this is calculated from δ and k: From k, we calculate E (storage modulus) From δ, we calculate E (loss modulus) then: Tan δ = E /E E * = E + ie = SQRT(E 2 + E 2 ) G * = E * /2(1+ν) η = 3G * /ω
18 To apply this to materials... Dynamic Stress Scan σ ο σ ε Since each part of the ramp has a sine wave stress associated with it, we get: tan δ E *, E, E η for each data point!! ε ο
19 Dynamic Stress (Pa x 10 6 ) Viscosity (Pa s x 10 7 ) For example, DSS Curves Curve 1: DMAC Stress Scanin Parallel Plate File info: Drssr70DssThu Apr 14 16:44: Frequency: 1.00 Hz Stress Rate: 250.0mN/min Dresser 70 Durameter Tension: % Curve 1: DMAC Stress Scanin Parallel Plate File info: Drssr70DssThu Apr 14 16:44: Frequency: 1.00 Hz Stress Rate: 250.0mN/min Dresser 70 Durameter Tension: % # 1 Dresser 70 Durameter:Drssr70Dss Complex Viscosity (Pa s x 10 7 ) # 2 Dresser 90 Durameter:Drssr90dss 7 Complex Viscosity (Pa s x 10 ) Slope Pa/% 1.5 TEMP1: 10.5 C TIME1: -1.2 min Slope Pa/% Strain (%) KPM PERKIN-ELMER 7 Series ThermalAnalysis System Thu Apr 14 16:59: TEMP1: 10.5 C 1.0 TIME1: -1.2 min Strain (%) KPM PERKIN-ELMER 7 Series ThermalAnalysis System Thu Apr 28 20:28:
20 Now, let s induce temperature as a variable. We can heat the material under minimal load at a calibrated rate. This allows the material to change with temperature. These changes can be described in terms of free volume or relaxation times. Free Volume
21 Penetration (mm) Thermomechanical Analysis as a starting Point. Curve 1: TMA in Penetration File info: Tgflex Tue Oct 10 16:21: Sample Height:4.180 mmdc Force: mn Tg by flex 7.0 # 1 Tg by flex:tgflex Penetration (mm) Onset C TEMP1: 30.0 C TIME1: 0.0 min RATE1: 10.0 C/min TEMP2: C Temperature (C) PERKIN-ELMER 7 Series Thermal Analysis System Sun Nov 26 20:10:
22 Expansion (mm) TMA - It s all free volume. Curve 1: TMA in Expansion File info: cte Tue Oct 10 16:46: Sample Height: mm DC Force: 10.0 mn cte # 1 cte :cte Expansion (mm) Free Volume Cx x 10-2 /C Cx x 10-5 /C Onset C T g Occupied Volume TEMP1: 30.0 C TIME1: 0.0 min RATE1: 10.0 C/min TEMP2: C Temperature ( C) PERKIN-ELMER 7 Series Thermal Analysis System Sun Nov 26 20:08:
23 Extension (mm) And it s not just Tg. Curve 1: TMA in Extension File info: menard005 Tue Feb 21 12:28: Sample Height: mm DC Force: 0.0 mn FIBER E # 1 FIBER E:menard005 Extension (mm) He/20psi/H/Chiller TEMP1: 30.0 C TIME1: 0.0 min RATE1: 5.0 C/min TEMP2: C Temperature ( C) Tech.Support Lab/K.Menard PERKIN-ELMER 7 Series Thermal Analysis System Tue Feb 21 12:29: (the traditional way to do heat set)
24 Time Temperature Scans at a Fixed Frequency hold frequency constant and vary temperature or time at temperature allows detection of transitions in material allows one to study cures most sensitive method for finding Tg can also get changes in dimension (TMA) while collecting DMA data Best probe of polymer relaxations as function of temperature
25 Idealized Multi-Event DMA Scan (6) γ (5) Β (4) Tg - glass transition (3) α E Rubbery Plateau (2) Tm - melting (1) Temperature (6) (5) (4) (3) (2) (1) local bend side gradual large chain motions and groups main scale slippage stretch chain chain
26 In more detail... Deformation Molecular Motion Log Modulus (Pa) F F Secondary Dispersion Localized Motion E Glassy D C Temperature Rubbery B Cross-linked E D C B A Hookean Second Primary Highly Visco Elastic Behavior Transition Transition Flow (gamma) (beta) (alpha) (rubbery) (melt) Bend & Stretch Bonds Side Groups Main Chain Gradual Crystalline Polymer Crystal-crystal slip Main Chain Large Scale Mobility A Chain Slipping Unstrained State Strained State Increasing R. Seymour, 1971
27 Common changes show as: MW MWD Crosslink Density Crystallinity E tan δ
28 tan Modulus (Pa x 10 Tg are easily seen, as in PET Film Curve 1: DMA Temp/Time Scan in Extension File info: demofilm Wed Oct 11 17:06: Frequency: 1.00 Hz Amplitude: u pet film Tension: % 1.6 # 1 pet film:demofilm tan # 2 Storage Modulus (Pa x 10 9 ) ) Onset C Onset C TEMP1: C TIME1: 0.0 min RATE1: 10.0 C/min TEMP2: C Onset C Temperature ( C) PERKIN-ELMER 7 Series Thermal Analysis System Sun Nov 26 21:02:
29 tan (x 10 Modulus (Pa x 10 or in PP fishing line. Curve 1: DMA Temp/Time Scan in Extension File info: Wed Nov 16 13:20: Frequency: 1.00 Hz Dynamic Stress: 200.0mN fishing line Static Stress: 300.0mN # 1 fishing line: tan (x 10 ) # 2 Storage Modulus (Pa x 10 9 ) ) -1 ) TEMP1: C TIME1: 0.0 min RATE1: 10.0 C/min TEMP2: C Temperature ( C) PERKIN-ELMER 7 Series Thermal Analysis System Sun Nov 26 21:24: Sample prep can be minimal if only temperatures are needed.
30 Modulus (Pa x 10 tan Transitions are clearly seen in highly crosslinked samples Curve 1: DMA Temp/Time Scan in 3 Point Bending File info: afriedli.1 Thu Feb 17 12:14: Frequency: 1.00 Hz epoxyresin Dynamic Stress: 800.0mN Static Stress: mN # 1 epoxyresin:afriedli.1 Storage Modulus (Pa x 10 # 2 tan 9 ) ) heavy xlink TEMP1: 30.0 C TIME1: 0.0 min RATE1: 10.0 C/min TEMP2: C Temperature ( C) This T g is undetectable in the DSC!!!!!! km PERKIN-ELMER 7 Series Thermal Analysis System Thu Jun 23 13:45:
31 Modulus (Pa) tan as well as in blends. Curve 1: DMA Temp/Time Scan in 3 Point Bending File info: sbr14 Thu Feb 15 10:45: Frequency: 1.00 Hz Dynamic Stress: 2.00e+05Pa STYRENE BUTADIENE RUBBE Tension: % # 1 STYRENE BUTADIENE RUBBER:sbr14 Storage Modulus (Pa) L # 2 tan K66:22T TEMP1: C TIME1: 0.0 min RATE1: 5.0 C/min TEMP2: C Temperature ( C) APPLICATION LABORATORY PERKIN-ELMER 7 Series Thermal Analysis System Sun Nov 26 20:54:
32 Modulus (Pa x 10 tan (x 10 It s not always so simple: For example, crystal-crystals slips can cause α transitions Curve 1: DMA Temp/Time Scan in 3 Point Bending File info: AMPfrPP.1 Wed Oct 27 13:49: Frequency: 1.00 Hz Dynamic Stress: 950.0mN LeBrun samples Static Stress: mN # 1 LeBrun samples:ampfrpp.1 Storage Modulus (Pa x 10 9 ) # 2 tan (x 10-1 ) ) ) T g or Alpha T α * AMP Flame Retardant Polypropylene TEMP1: C TIME1: 0.0 min RATE1: 5.0 C/min TEMP2: C Temperature ( C) KPM PERKIN-ELMER 7 Series Thermal Analysis System Sun Nov 26 20:58:
33 Modulus (Pa x 10 tan (x 10 Higher Order Transitions affect toughness Curve 1: DMA Temp/Time Scan in 3 Point Bending File info: AMP66gp.1 Tue Oct 26 16:05: Frequency: 1.00 Hz Dynamic Stress: 190.0mN LeBrun samples Static Stress: 200.0mN LeBrun samples ) Good Impact Strength ) β Transitions Poor T g AMP good part 20% glass filled Nylon 6/6 TEMP1: C TIME1: 0.0 min RATE1: 5.0 C/min TEMP2: C Temperature ( C) KPM PERKIN-ELMER 7 Series Thermal Analysis System Sat Oct 15 14:32: Impact was good if T g /T β was 3 or less.
34 Modulus (Pa x 10 tan (x 10...and also define operating range. Curve 1: DMA Temp/Time Scan in 3 Point Bending File info: gamma_1 Thu Jun 30 02:17: Frequency: 7.00 Hz Dynamic Stress: 1.86e+06Pa EPOXY PC BOARD AT 7 Hz Static Stress: 1.86e+06Pa 10 ) Beta # 1 EPOXY PC BOARD AT 7 Hz:gamma_1 10 Storage Modulus (Pa x 10 ) -1 -> # 2 tan (x 10 ) Operating range T g ) TEMP1: C TIME1: 0.0 min RATE1: 10.0 C/min TEMP2: C Temperature ( C) PE DMA7 R&D LAB PERKIN-ELMER 7 Series Thermal Analysis System Sun Nov 26 20:13:
35 Modulus (Pa) tan (x 10 It can get complex... Curve 1: DMA Temp/Time Scan in Extension File info: T2n4ptg Fri Jan 18 18:14: Frequency: 1.00 Hz Dynamic Stress: 1.00e+07Pa NYLON MONOFILAMENT Static Stress: 1.05e+07Pa 2 # 1 NYLON MONOFILAMENT:T2n4ptg Storage Modulus (Pa) L -1 # 2 tan (x 10 ) ) initial RUN TEMP1: C TIME1: 0.0 min RATE1: 4.0 C/min TEMP2: 0.0 C TIME2: 0.0 min RATE2: 2.0 C/min TEMP3: C T γ T β Stress Relief Temperature ( C) T g or T α B.Cassel PERKIN-ELMER 7 Series Thermal Analysis System Sun Nov 26 20:59:
36 Curing of Thermosets can be studied at constant temperature or by a temperature ramp can get minimum viscosity, gelation point (time), vitrification point, and activation energies from DMA curve can adapt instrument to do simultaneous DEA- DMA to follow cure to completion cure studies are not limited to polymeric systems but include food products like cakes and cookies
37 Analysis of a Cure by DMA Modulus Melting E -E Crossover ~ gelation point 10 6 Pa ~ Solidity E E η Τ vitrification point Curing Minimum Viscosity (time, length, temperature )
38 QC can often be done by simply fingerprinting the resin η note the different slopes and the different curve shapes bad 0.5 good
39 Postcure studies allow process optimization: hours 1 hour 2 hours 3-8 hours Postcure time vs... Tg and E tan δ Temperature Property E'@50 (E9 PA ) 60 E' ONSET 40 T AN D PE A K 20 0 T AN D ONSET TIME IN HOURS
40 Frequency Scans hold temperature constant and vary frequency allows one to look at trends in material can estimate changes in MW and MWD looks at both tack-like and peel-like behavior can use data for Time Temperature Superposition to extend frequency range or predict age life.
41 Frequency determines the type of response More Liquid like More solid like Modulus (Pa) s) Viscosity (Pa Flow dominates Elastic dominates Frequency (Hz) 10 3
42 For example, two hot melt adhesives... show affect of rate (peel vs... tack) η bad E good Τ 10 2
43 Strain (%) Force (mn) Creep can look at distortion under load, Curve 1: DMA Creep Recovery in 3 Point Bending File info: cr_ptfe-5 Wed Jun 29 15:31: Sample Height: mm Creep Stress: 1.50e+06Pa Recovery Stress: 6.25e+02Pa PTFE - CREEP/RELAXATION # 1 PTFE - CREEP/RELAXATION AT -5C:cr_ptfe-5 Strain (%) # 2 Force (mn) TEMP1: C TIME1: 7.0 min Time (minutes) DMA7 APPLICATIONS LAB PERKIN-ELMER 7 Series Thermal Analysis System Thu Apr 28 20:32:
44 cyclic application of loads, % Strain Differences can be seen in good and bad samples and get more apparent with several cycles. Here the bad material is not flowing enough to fill the pores and form a mechanical bond Good Bad Time in minutes 6.0
45 Strain (%) Force (mn) and with varying temperatures. Curve 1: DMA Creep Recovery in Parallel Plate File info: DR90D2.1 Fri Jul 23 12:23: Sample Height: mm Creep Stress: mN Recovery Stress: 1.0mN Dresser 90 D # 1 Dresser 90 D:DR90D2.1 Strain (%) # 2 Force (mn) # 3 T P ( C) TEMP1: C TIME1: 11.0 min RATE1: 10.0 C/min TEMP2: 0.0 C TIME2: 15.0 min RATE2: 10.0 C/min TEMP3: 50.0 C TIME3: 15.0 min RATE3: 10.0 C/min TEMP4: C TIME4: 75.0 min Time (minutes) KPM PERKIN-ELMER 7 Series Thermal Analysis System Sun Nov 26 20:41:
46 And you can tabulate this stuff graphically... τ 1/T The time to 1/e percent recovery is the relaxation. This is a measure of how quickly a material recovers. (There is a lot more to this subject.)
47 Stress Relaxation By exploiting the special controls of the DMA-7e, we can run stress relaxation experiments. These look at how the force change for a sample kept at a set distortion as a function of time or temperature. σ Experiment Starts Time Position Sample would be distorted to y length and held.
48 Don t forget the DMA-7e also does Stress Scans can do either static or dynamic ramps static scans calculate Young s modulus and stress-strain curves dynamic scans give material response to increasing oscillatory forces: get complex viscosity and modulus for each data point can look at changes in elasticity (E ) and lag (phase angle) with increasing stress Both methods are fast tests for QC applications after the material has been fully characterized by other DMA modes.
49 Specialized Testing is Possible... The design of the DMA-7e makes it possible to do: Time-Temperature Superposition (TTS) DEA/DMA Tests in Solution Microscopic DMA Photo DMA DMA-?
50 PP fibers in solvent Force in mn xylene air water iso-octane Temperature in C
51 To Review, DMA ties together... m olecular structure Molecular weight MW Distribution Chain Branching Cross linking Entanglements Phases Crystallinity Free Volume Localized motion Relaxation Mechanisms Material Behavior processing conditions Stress Strain Temperature Heat History Frequency Pressure Heat set product properties Dimensional Stability Impact properties Long term behavior Environmental resistance Temperature performance Adhesion Tack Peel
52 Conclusions DMA allows you to preform a wide range of tests from sensitive probes of molecular structure to model studies. the DMA-7e allows operation as six different instruments to maximize flexibility. Data can be overlayed with DSC, TGA, TMA, and DTA for easier analysis.
53 References: Books Menard, DMA: Introduction to the Technique, Its Applications and Theory, CRC Press, Brostow et a., Failure of Plastics, Hanser, Ferry, Viscoelastic Properties of Polymers, Wiley, Gordon et al., Computer Programs for Rheologists, Hanser, Gol'dman, Prediction of Deformation Properties of Polymeric and Composite Materials,, ACS, Mascosko, Rheology, VCH, Matsouka, Relaxation Phenomena in Polymers, Hanser, McCrum et al, Anelastic and Dielectric Properties of Polymeric Solids, Dover, 1992 (reprint of 1967 edition). Nielsen et al., Mechanical Properties of Polymers and Composites, Dekker, Sperling, Introduction to Physical Polymer Science, Academic Press, Ward et al., Introduction to Mechanical Properties of Solid Polymers, Wiley, 1993.
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