DYNAMIC-MECHANICAL PROPERTIES OF POLYMERSbeaucag/Classes/Characterization... · DYNAMIC-MECHANICAL...

Laboratorium für Makromolekulare Chemie

UniversitätSiegen

POLYCHAR 18 - Short CourseDYNAMIC-MECHANICAL PROPERTIES OF

POLYMERS

MECHANICAL PROPERTIES OF (POLYMERIC) MATERIALS UNDER THE INFLUENCE OF

DYNAMIC LOAD AND TEMPERATURE

mechanical modulus as a function of load, temperature, time

A project of the IUPAC Division IV (POLYMER DIVISION)

transitions, relaxations


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simple extension simple shear deformation(also in liquids possible)

simple deformations in a solid


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simple stress in a shear deformation

The total stress σij is a second rank tensor composed of normal andshear components

σ22

τ21

τ23τ32

σ33

τ31

σ11

τ12

τ13

1

2

3

ii ijnormal stress; shear stress! "= =


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(ideal) energy elasticity

•caused by deformation of bond angles and bond length at small deformations•the energy is stored and completely released after the load is removed•there is no (internal) friction

normal

0

0

0 0

1

FA

L L LE

L L

!

! " " #

=

$ %= & = = = $

in plane

0

FA

G

!

! "

=

= #

1J

E! " "= # = #

ε = strain; λ = uniaxial deformation ratio; γ = shear (angle); F = force [N]; A0 = initial areaE = Young modulus [Pa]; G = shear modulus [Pa]; J = compliance [Pa-1]


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Lo L

Cauchy orEngineering Strain

L-Lo = !L

Hencky or True Strain " = ln (!L/Lo)

" = !L/Lo

Kinetic Theoryof Rubber Strain " = 1/3{L/L o-(Lo/L)2}

Kirchhoff Strain

Murnaghan Strain

" = 1/2{ (L/L o)2-1}

" = 1/2{1-(Lo/L)2}

The different definitions of tensile strainbecome equivalent at very small deformations.

elongation

The stress [Pa = N/m2] refers to the initial cross section

Stress and strain are principally time-dependent stress can “relax” (at constant strain)

elongation can “creep” (at constant stress)


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The elastic limit: Hooke’s Law

=

Strain increaseswith increasing

Stress

!

"

slope = k

in the

Slope: elastic (Young-) modulus E

ideal stress-strain diagram


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extension → Young modulus Eshear → shear modulus Gcompression → bulk modulus B bending* → bending modulus Eb*three-point bending, 4 point bending

( ) ( )µµ 21312 !=+= BGE

!!"

#$$%

&'=

long

lat

((µ

The lateral strain εlat is the strain normal to the uniaxial deformation.

the major types of moduli

the different moduli can be converted into one another, see D. Ferry


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GE !"#" 35.0µThe volume change on deformation is for most elastomers negligible so thatµ=0.5 (isotropic, incompressible materials).

In a sample under small uniaxial deformation!!

The lateral strain εlat is the strain normal to the uniaxial deformation.


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!•

= shear rate

ideal liquid betweentwo parallel plates

an ideal liquid shows no elasticity

2

grad v

dvgrad v

dx

!

! " " " #•

= $ = $ = $

!σ

γ .

slope = η

dilatant

structuralviscous

η = dynamic viscosity [Pa s]; 1 centipoise = 1 mPa s


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plate-plate cone-plate Couette

constant shear ratealong the radius

torque

important rheometer types for viscous samples


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visco-elastic behaviour

James Clerk Maxwell, Phil. Trans. Roy. Soc. London 157 (1867) 52

single relaxation time τ spectrum of relaxation times τi

There is mater that shows elastic and viscous behaviour (e.g. pitch):fast deformation rather elastic, slow deformation rather viscous response


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major response types on deformational stress


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Young’s 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 Young’s Modulus)

E”

E’

'' 20

' 20

12

rev

rev

Q E

w E

! "

"

=

=

dissipated energy

saved energy

''tan

'EE

! = damping (factor)

storage and loss of energy


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stress σ

strain ε

( )( )Ttf

Tf,,

==

!"#

'simple' static stress-strain experiment

yield strength

tensile strength

tensile strength

tensile strength

elongation at break

elongation at breakbrittleness B*):

1'b

BE!

="

*) according to Brostow et al., J. Mater. Sci 21 (2006) 2422 not to be confused with the bulk modulus B (compression modulus)

b!

b!

b!


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frequency dependence of damping

temperature depending properties (elasticity, flow…)

long term prediction, fatigue…

TTS

time

temperature

superposition


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frequency range and applied technique


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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 applied

Thermomechanical AnalysisStress-Strain CurvesCreep RecoveryStress RelaxationDynamic Mechanical AnalysisSolvent Immersed testing


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molecular structure

processing conditions

product properties

MaterialBehavior

DMA relates:


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Free damping experiment

am

plitu

de

1

ln n

n

AA +

! "# = $ %& '

logarithmic decrement


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st

ress

st

rain

stress and strain are in phase in an ideal energy-elastic material, phase angle δ = 0°

stress and strain are out of phase in an ideal viscous material, phase angle δ = 90°


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( )0 0 0 0

0 0 0 0

' ''

Theory shows that the modulus is complex and can be split into

a real part ' and an imaginary part with '':

* cos sin cos sin

* ' ''

i

E E

E E

E e i i

E E iE

= = = + = +

! = +

!"#"$ !"#"$

"# # # ##" " " "

$ $ $ $ $

' 20

'' 20

12rev

rev

w E

Q E

=

=

!

" !

stored

dissipated (loss) Because Young’s Modulus isn’t enough…

Young’s 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 Young’s Modulus)

E”

E’

The modulus of a visco-elastic material is a complex physical entity


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in the Gaussian plane of complex numbers thecomplex shear modulus G*, the Young modulus E*and the complex viscosity η* can be visualized as

the damping factor D is then given by the tan ofthe loss angle δ

tanD= !D shows a behaviour similar to Λ

* ; * ; *E G! ! "

#$ % %

•= = =

Correlation between moduli and phase angle (damping)


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Λ or tan δ

Λ or tan δ

Modulus, damping and their correlation with molecular motions


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There is not onlyone glass.The type of glassdepends on the thermal history.

slowly heating can causeannealing

a thermodynamic view at the 'glass transition'


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glassy visco-elastic rubbery T

G'

G''

tanδ

The glass transition in a dynamic experiment


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DMA and different molecular parameters


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0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

-100.0 0.0 100.0 200.0 300.0

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

Sun Nov 26 21:02:11 1995

Mod

ulus

(Pa

x 10

9 )

# 2 Storage Modulus (Pa x 10 9)

Onset 83.29 Ctan

Temperature ( C)

# 1 pet film:demofilmtan

Onset 107.82 C

Onset 79.35 C

Curve 1: DMA Temp/Time Scan in ExtensionFile info: demofilm Wed Oct 11 17:06:48 1995Frequency: 1.00 Hz Amplitude: 21.949u

Tension: 110.000% pet film

PERKIN-ELMER7 Series Thermal Analysis System

TEMP1: -100.0 C TIME1: 0.0 min RATE1: 10.0 C/minTEMP2: 250.0 C

Tg are easily seen, as in PET Film


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Tg by DMA and DSCΔΗ

/(J/g)

Hea

t flo

w/m

WTemperature /C

Inflection Point ! ΔCp

Tf

Onset

Temperature/C

Mod

ulus

/Pa Tan δ

Onset E’ = 133.1 °C

Peak Tan δ = 140.5°C

Onset Tan δ = 130.0 °C

Onset E” = 127.3 °C

Peak E” = 136.7 °C

(a) (b)

differential scanning calorimetry


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Operating Range by DMA

-100.0 0.0 100.0 200.00.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

Sun Nov 26 20:13:53 1995

Modu

lus (P

a x 10

10)

PE DMA7 R&D LABTemperature ( C)

# 1 EPOXY PC BOARD AT 7 Hz:gamma_1Storage Modulus (Pa x 10 10)

Curve 1: DMA Temp/Time Scan in 3 Point BendingFile info: gamma_1 Thu Jun 30 02:17:24 1988Frequency: 7.00 Hz Dynamic Stress: 1.86e+06Pa

Static Stress: 1.86e+06Pa EPOXY PC BOARD AT 7 Hz



tan

(x 10

-1)

-> # 2 tan (x 10 -1 )

BetaTg

Operatingrange

(b)

-150.0 -100.0 -50.0 0.0 50.0 100.0

0.5

1.0

1.5

2.0

2.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Sun Nov 26 20:58:36 1995

Modu

lus (P

a x 10

9 )

AMP Flame Retardant Polypropylene KPMTemperature ( C)

# 1 LeBrun samples:AMPfrPP.1Storage Modulus (Pa x 10 9)

Curve 1: DMA Temp/Time Scan in 3 Point BendingFile info: AMPfrPP.1 Wed Oct 27 13:49:06 1993Frequency: 1.00 Hz Dynamic Stress: 950.0mN

Static Stress: 1000.0mN LeBrun samples



tan

(x 10

-1)

# 2 tan (x 10 -1 )

(c)Operating

range

(a)Operating

range

leather-like state

toughness is okmodulus is ok


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amorphous semicrystalline thermoplasts

temperature of use'leather' vacuum

forming

blowforming extrusion

injection mouldingrigid

rubberviscous

temperature of usecold forming

vacuum forming

blowforming

extrusioninjection moulding

shea

r mod

ulus

shea

r mod

ulus


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Cold Crystallization in PET seen by DMA and DSC

Tg

Cold Crystallization

Tm

DSC


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0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

-150.0 -100.0 -50.0 0.0 50.0 100.0 150.00.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

Sat Oct 15 14:32:54 1994

LeBrun samples

tan

(x 10

-1)

Modu

lus (P

a x 10

9 )

AMP good part 20% glass filled Nylon 6/6 KPMTemperature ( C)

Curve 1: DMA Temp/Time Scan in 3 Point BendingFile info: AMP66gp.1 Tue Oct 26 16:05:29 1993Frequency: 1.00 Hz Dynamic Stress: 190.0mN

Static Stress: 200.0mN LeBrun samples



β Transitions

Tg

Good Impact Strength

Poor

Higher Order Transitions affect toughness

Impact was good if Tg/Tβ was 3 or less.


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Tg

Cold Crystallization

DMTA

DSC

Left: silicon rubber with a glass transition at –117°C and a melting transition at –40°C. Beyond the meltingtemperature this crosslinked (vulcanised) material shows rubber-elasticity with modulus that increases with thetemperature.Right: also a silicone rubber that contains silicone oil as diluent, as plasticizer. The oil causes a stress-relaxation atthe beginning of the melting transition around –47°C.

stress-relaxation in a silicone rubber


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Temperature/K Temperature/K

Polymer A

Temperature/K

E’E’

Polymer B+ =

E’

Temperature/K

Both Tgs

Block CopolymersGraft CopolymersImmiscible Blends

Random Copolymers &

Miscible Blends

E’

Single Tg

Exact T depends on concentration of A and B


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Temperature dependency of E' and tanδ of PVC at different frequencies, afterBecker, Kolloid-Z.140 (1955) 1

The frequency-dependence of dynamic experiments


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Time-Temperature-Superposition Principle

experimentalwindow

experimentalwindow

NBS-poly(isobutylene, after A. Tobolski


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( )( )

( ) ( )20,4

ln ln ; 50102

s sT s g

s

T T Ta T T K

T T T!

= = = ++ !

""

empirical WLF equation≈Tg+50K

Arrhenius-type

Williams-Landel-Ferry (WLF) equation

Temperature-dependence of the viscosityof PMMA (M=63.000 g/mol) after Bueche

lg η

The glass transition temperature seen by viscosity


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( )( )

338.0

lg

lglglg338.0

338.0lg

lim

!!"

#$$%

&

'=(

!!"

#$$%

&=!!"

#$$%

&==''

'=')

**

**

g

g

gT

T

ttATgT

TgTTA

TgT

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 range

• We 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 BEINVALID.

J. Dealy


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Failure of TTSLo

g J*

compliance J = 1/E


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Analysis of a Cure by DMA

50.0 70.0 90.0 110.0 130.0 150.010 0

10 1

10 2

10 3

10 4

10 5

10 6

10 7

10 8

E’

E”

Mod

ulus

!

"#

E’-E” Crossover ~ gelation point

vitrification point

Minimum Viscosity (time, length,temperature )

106 Pa ~ Solidity

Melting

Curing

time-temperature-transition diagramafter Gillham

experiment at a constant heating rate


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Activation Energy tells us about the molecule

• For example, are these 2 Tgs or a Tg and a Tβ?

• Because we can calculate the Eact for the peaks, we candetermine if both are glass transitions.

ElastomerSample


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351.7 kJ/mol

146.5 kJ/mol

.1log constTR

Ef a +!=

Determination of the apparent energy of activation

How can we do this experimentally??

MULTIPLEXING


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Multiplexing…

Instead of just the Tg

Film

Sheet

Fiber

multiple frequencies in one run


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Or you can use the Synthetic Oscillation Mode

Take five frequencies

Sum together

And applythecomplexwave formto thesample

Temperature in C


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Gelation Point by Multiplexing


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ＰＭＭＡ　（0.01～100Hz）

Master curve

Activation energy

We can then do further analysis

Why?…


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To Review, DMA ties together...

molecular structure

processing conditions

product propertiesMolecular weightMW DistributionChain BranchingCross linkingEntanglementsPhasesCrystallinityFree VolumeLocalized motionRelaxation Mechanisms Stress

StrainTemperatureHeat HistoryFrequencyPressureHeat set

MaterialBehavior

Dimensional StabilityImpact properties

Long term behaviorEnvironmental resistance

Temperature performanceAdhesion

TackPeel


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Kevin P. Menard, Dynamic-Mechanical Analysis, CRC-Press (1999) Boca Raton W. Brostow, Performance of Plastics, Carl Hanser Verlag (2000) Munich I. M. Ward, Mechanical Properties of Solid Polymers, Wiley (1983) New YorkJ. J. Aklonis, W. J. McKnight, Introduction to Polymer Viscoelasticity, Wiley-Interscience (1983) New YorkN. W. Tschloegl, The Theory of Viscoelastic Behaviour, Acad. Press (1981) New YorkD. Ferry, Viscoelastic Properties of Polymers, Wiley (1980) New YorkB. E. Read, G. D. Dean, The Determination of Dynamic Properties of Polymers and Composites, Hilger (1978) BristolL. E. Nielsen, Polymer Rheology, Dekker (1977) New YorkL. E. Nielsen, Mechanical Properties of Polymers, Dekker (1974) New YorkL. E. Nielsen, Mechanical Properties of Polymers and Composites Vol. I & II, Dekker (1974) New YorkA. V. Tobolsky, Properties and Structure of Polymers, Wiley (1960) New York

Further Readíng

Many examples by courtesy of Kevin Menard(University of North Texas, Department of Materials Scienceand Perkin Elmer Corp.)

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