POLYCHAR 22 - Short Course DYNAMIC-MECHANICAL and CALORIMETRIC PROPERTIES OF POLYMERS hanks to Dr. Kevin Menard, University of North Texas and Perkin Elmer for some of the examples Michael Hess
POLYCHAR 22 - Short Course DYNAMIC-MECHANICAL and CALORIMETRIC PROPERTIES OF POLYMERS Thanks to Dr. Kevin Menard, University of North Texas and Perkin.
Dec 31, 2015
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POLYCHAR 22 - Short Course
DYNAMIC-MECHANICAL and CALORIMETRICPROPERTIES OF POLYMERSThanks to Dr. Kevin Menard, University of North Texas and Perkin Elmer for some of the examplesMichael Hess
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Calorimetric Analysis of Polymers
course of polymerizationtransreactionschain scissionradiation induced degradationthermal degradationchain stripping leaving carbonaceous residuecuring of thermosets...phase behaviour (estimation of a phase diagram)mesophase behaviour(processing) history(themoreversible) gelationthermal transitions (Tg, Tm, Tcr...)bound water in hydrogelscrystallization and ordering...
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Dynamic-Mechanical Analysis
mechanical properties of (polymeric) materials under the influence of dynamic load and temperaturemechanical modulus as a function of load, temperature, timetransitions, relaxations, service range (temperature), service time
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Thermal Transitionstransition temperatures, transition enthalpieglass transitioncold crystallizationrecrystallizationcrystallizationmeltingbrittle/viscousmiscibilitythermal historypolymorphismmesophasesphase diagramkineticsdegree of crystallizationpurity
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DTA DSCDT Wel (DT=0)
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heat fluxorcppoly(dimethyl siloxane) (PDMS)TgTm (onset)Tm (end)Tm (rate max)cold crystallizationmeltingenthalpy relaxation
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the modern machines can rapidly change the measuring device so that solid and fluid samples can be measured and many different modes can be appliedThermomechanical AnalysisStress-Strain CurvesCreep RecoveryStress RelaxationDynamic Mechanical AnalysisSolvent Immersed testingDynamic-mechanical analysis - rheology
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simple extensionsimple shear deformation(also in liquids possible)simple deformations in a solid
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simple stress in a shear deformationThe total stress ij is a second rank tensor composed of normal andshear components222123323331111213123
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(ideal) energy elasticitycaused by deformation of bond angles and bond length at small deformationsthe energy is stored and completely released after the load is removedthere is no (internal) friction = strain; = uniaxial deformation ratio; = shear (angle); F = force [N]; A0 = initial areaE = Young modulus [Pa]; G = shear modulus [Pa]; J = compliance [Pa-1]
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elongation The stress [Pa = N/m2] refers to the initial cross sectionStress and strain are principally time-dependent
stress can relax (at constant strain) elongation can creep (at constant stress)
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Stress Causes Strain
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in theSlope: elastic (Young-) modulus Eideal stress-strain diagram
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The elastic limit: Hookes Law
=
Strain increases with increasing Stress
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extension Young modulus Eshear shear modulus Gcompression bulk modulus B bending* bending modulus Eb*three-point bending, 4 point bending
The lateral strain elat is the strain normal to the uniaxial deformation.the major types of modulithe different moduli can be converted into one another, see D. Ferry
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so that for elastomers: The volume change on deformation is for most elastomers negligible so that m=0.5 (isotropic, incompressible materials).
In a sample under small uniaxial deformation!!
The lateral strain elat is the strain normal to the uniaxial deformation.
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shear in an ideal (Newtonian) liquid= shear rate ideal liquid betweentwo parallel platesan ideal liquid shows no elasticity = dynamic viscosity [Pa s]; 1 centipoise = 1 mPa s
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plate-plate cone-plate Couetteconstant shear ratealong the radiustorqueimportant rheometer types for viscous samples
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visco-elastic behaviourJames Clerk Maxwell, Phil. Trans. Roy. Soc. London 157 (1867) 52single relaxation time spectrum of relaxation times iThere is mater that shows elastic and viscous behaviour (e.g. pitch):fast deformation rather elastic, slow deformation rather viscous responsea combination of both:
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major response types on deformational stress
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dissipated energysaved energydamping (factor)storage and loss of energy
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Youngs modulus is designed for elastic materials. Real materials consist of both elastic and viscous response.
E lost to friction and rearrangement - the Loss Modulus
E stored and released the Storage Modulus (conceptually like Youngs Modulus)
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stress strain 'simple' static stress-strain experimentyield strengthtensile strengthtensile strengthtensile strengthelongation at breakelongation at breakbrittleness B*):*) according to Brostow et al., J. Mater. Sci 21 (2006) 2422 not to be confused with the bulk modulus B (compression modulus)
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frequency dependence of damping
temperature depending properties (elasticity, flow)
long term prediction, fatigueTTStimetemperaturesuperposition
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frequency range and applied technique
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DMA relates:
molecular structure
processing conditions
product properties
MaterialBehavior
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Free damping experiment amplitudelogarithmic decrementshear (storage) modulus G'(f, T)loss modulus G''(f, T)loss factor D (tangent)
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stress strainstress and strain are in phase in an ideal energy-elastic material, phase angle = 0stress and strain are out of phase in an ideal viscous material, phase angle = 90
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storeddissipated (loss)The modulus of a visco-elastic material is a complex physical entity
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Because Youngs Modulus isnt enough
Youngs modulus is designed for elastic materials. Real materials consist of both elastic and viscous response.
E lost to friction and rearrangement - the Loss Modulus
E stored and released the Storage Modulus (conceptually like Youngs Modulus)
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in the Gaussian plane of complex numbers thecomplex shear modulus G*, the Young modulus E*and the complex viscosity * can be visualized asthe damping factor D is then given by the tan ofthe loss angle D shows a behaviour similar to Correlation between moduli and phase angle (damping)
-
or tan or tan Modulus, damping and their correlation with molecular motions(rubber)
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There is not onlyone glass.The type of glassdepends on the thermal history.slowly heating can causeannealinga thermodynamic view at the 'glass transition'
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glassy visco-elastic rubbery TG'G''tanThe glass transition in a dynamic experiment
-
DMA and different molecular parameters
-
Tg are easily seen, as in PET Film
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Tg by DMA and DSCTemperature/CModulus/PaTan dOnset E = 133.1 CPeak Tan d = 140.5COnset Tan d = 130.0 COnset E = 127.3 CPeak E = 136.7 C(a)(b)differential scanning calorimetry
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Operating Range by DMABetaTg(b)(c)(a)Operatingrangeleather-like statetoughness is okmodulus is ok
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amorphous semicrystalline thermoplaststemperature of use'leather'vacuumformingblowformingextrusioninjection mouldingrigidrubberviscoustemperature of usecold formingvacuum formingblowformingextrusioninjection mouldingshear modulusshear modulus
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Cold Crystallization in PET seen by DMA and DSCTgCold CrystallizationTmDSC
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b TransitionsTgGood Impact StrengthPoorHigher Order Transitions affect toughness Impact was good if Tg/Tb was 3 or less.
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Tg
Cold Crystallization
DMTA
DSC
Left: silicon rubber with a glass transition at 117C and a melting transition at 40C. Beyond the melting temperature this crosslinked (vulcanised) material shows rubber-elasticity with modulus that increases with the temperature.Right: also a silicone rubber that contains silicone oil as diluent, as plasticizer. The oil causes a stress-relaxation at the beginning of the melting transition around 47C.
stress-relaxation in a silicone rubber
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Blends and CopolymersTemperature/K Temperature/K
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Temperature dependency of E' and tan of PVC at different frequencies, afterBecker, Kolloid-Z.140 (1955) 1The frequency-dependence of dynamic experiments
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Time-Temperature-Superposition Principle(TTS)experimentalwindow
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empirical WLF equationTg+50K Arrhenius-typeWilliams-Landel-Ferry (WLF) equationTemperature-dependence of the viscosityof PMMA (M=63.000 g/mol) after Buechelg The glass transition temperature seen by viscosity
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TTS gives the frequency-dependence of the glass transition temperature:An increase of the measuring frequency (heating rate) by a factor 10 (or a decrease of the time frame by a factor of 10) near Tg the glass-transition temperature is found about 3 K higher.
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Master Curves*) extend the rangeWe can collect data from 0.01 to 100 Hz.If we do this at many temperatures, we can superposition the data.
After TTS, our range is 1e-7 to 1e9 Hertz (1/sec)Then x scale (frequency) can then be inverted to get time TTS*) modulus or compliance; compliance = (modulus)-1
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BUT...TTS assumes that:all relaxation times are equally affected by temperature.
THIS IS KNOWN TO OFTEN BE INVALID.J. Dealy
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Failure of TTSLog J*compliance J = 1/E
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time-temperature-transition diagramafter Gillhamexperiment at a constant heating rate
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Analysis of a Cure by DMA
E
E
Modulus
T
h*
E-E Crossover ~ gelation point
vitrification point
Minimum Viscosity (time, length, temperature )
106 Pa ~ Solidity
Melting
Curing
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Activation Energy tells us about the moleculeFor example, are these 2 Tgs or a Tg and a Tb?
Because we can calculate the Eact for the peaks, we can determine if both are glass transitions.
Elastomer Sample
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351.7 kJ/mol146.5 kJ/molDetermination of the apparent energy of activationHow can we do this experimentally??MULTIPLEXING
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MultiplexingInstead of just the Tg
FilmSheetFibermultiple frequencies in one run
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Or you can use the Synthetic Oscillation ModeTake five frequenciesSum togetherAnd apply the complex wave form to the sampleTemperature in C
Sheet: Sheet1
Sheet: Sheet2
Sheet: Sheet3
Sheet: Sheet4
Sheet: Sheet5
Sheet: Sheet6
Sheet: Sheet7
Sheet: Sheet8
Sheet: Sheet9
Sheet: Sheet10
Sheet: Sheet11
Sheet: Sheet12
Sheet: Sheet13
Sheet: Sheet14
Sheet: Sheet15
Sheet: Sheet16
0.0
0.0
0.0
0.0
0.0
0.0
0.05
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0.15
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0.25
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0.3
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0.7
0.644217687237691
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0.75
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1.25
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1.3
0.963558185417193
0.5155013718214642
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1.7783303888247475
1.35
0.9757233578266591
0.4273798802338298
0.803784426551621
0.956375928404503
2.3904991054606257
1.4
0.9854497299884601
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1.45
0.9927129910375885
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1.5
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1.55
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1.6
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1.65
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2.3
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2.35
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2.4
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2.55
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2.6
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2.65
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2.7
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2.75
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2.8
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2.85
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2.9
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2.95
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3.0
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3.1
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3.2
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3.25
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3.3
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3.35
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3.4
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3.45
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3.5
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3.55
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3.6
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0.5788497064224987
3.65
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3.7
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0.8987080958116269
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3.75
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0.43114606314361936
3.8
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0.2963685787093853
0.5661076368981803
1.7049366855501327
3.85
-0.6506251370651673
0.9881682338770004
0.7179745927716441
0.9995201585807313
2.3581562049099105
3.9
-0.6877661591839738
0.998543345374605
0.9637953862840878
0.5139784559875352
1.8963046807616983
3.95
-0.7231881240865121
0.998941341839772
0.9736454556949781
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0.7133791545130481
4.0
-0.7568024953079282
0.9893582466233818
0.7451131604793488
-0.9938886539233752
-0.3041230587936381
4.05
-0.788525254426195
0.9698898108450863
0.33415117684842055
-0.6298879942744539
-0.5867942474056083
4.1
-0.8182771110644103
0.9407305566797731
-0.158622668804709
0.31322878243308516
-0.3610471231042084
4.15
-0.8459837010754465
0.9021718337562933
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0.9683644611001854
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4.2
-0.8715757724135882
0.8545989080882804
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0.7331903200732922
-1.0878751257491537
4.25
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0.7984871126234903
-0.996086503119594
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-2.2300618605528313
4.3
-0.9161659367494549
0.7343970978741133
-0.8317747426285983
-0.9234584470040598
-2.9339020945495955
4.35
-0.9350525775584491
0.6629692300821833
-0.46381551598382736
-0.8218178366308225
-2.5503760805615485
4.4
-0.951602073889516
0.5849171928917617
0.017701925105413577
0.03539830273366068
-1.2624291510768042
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