polychar 22 - short course dynamic-mechanical and calorimetric properties of polymers thanks to dr....
TRANSCRIPT
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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)
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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
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DMA and different molecular parameters
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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
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4.0
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4.05
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4.1
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4.15
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4.45
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4.5
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4.55
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