Dynamic-Mechanical Properties of Polymers
Michael Hess
Department of Physical Chemistry, University Duisburg-Essen, Campus Duisburg, Duisburg, Germany
Department of Polymer Engineering & Science, Chosun University, KwangJu, South Korea
Department of Materials Science, University of North Texas, Denton, Texas, USA
2. EXAMPLES
Most of the examples by courtesy of Kevin Menard (University of North Texas, Department of Materials Science and Perkin
Elmer Corp.)
Tg by DMA and DSC
Kevin P. Menard, Dynamic-Mechanical Analysis, CRC-Press (1999) Boca Raton
Peak Tan = 140.5°C
Tf
Onset E’ = 133.1 °C
Heat
Peak E” = 136.7 °C
Modulus/Pa
J/g)
Tan 
Inflection Point
Onset E” = 127.3 °C
Onset
Onset Tan  = 130.0 °C
Temperature /C
Temperature/C
(a)
(b)
C
Transitions are clearly seen in highly crosslinked
samples
# 1 epoxyresin:afriedli.1
Storage Modulus (Pa x 10
Modulus (Pa x 10
9
)
#2
9
)
1.0
tan
4.5
0.9
4.0
0.8
3.5
0.7
3.0
0.6
2.5
0.5
2.0
0.4
1.5
0.3
1.0
0.2
0.5
0.1
0.0
0.0
50.0
100.0
heavy xlink
TEMP1: 30.0 C
TEMP2: 250.0 C
Temperature (
TIME1:
0.0 min
RATE1:
10.0 C/min
150.0
C)
200.0
tan
Curve 1: DMA
Temp/Time Scan in 3 Point Bending
File info:
afriedli.1
Thu Feb 17 12:14:11 1994
Frequency: 1.00 Hz
Dynamic Stress: 800.0mN
epoxyresin
Static Stress: 1000.0mN
0.0
250.0
km
PERKIN-ELMER
7 Series Thermal
Analysis System
Thu Jun 23 13:45:10 1994
This Tg is normally undetectable in the DSC!!!!!! Because the step in cp is broad
and flat (hindered mobility by crosslinking)
Kevin P. Menard, Dynamic-Mechanical Analysis, CRC-Press (1999) Boca Raton
Blends and Copolymers
Kevin P. Menard, Dynamic-Mechanical Analysis, CRC-Press (1999) Boca Raton
Polymer A
E’
Both Tgs
Block
Graft Copolymers
Immiscible
E’
Temperature/K
Temperature/
+
=
Single Tg
Polymer
E’
E’
Exact T depends on
concentration of A and B
Temperature/K
Temperature/K
Random
Copolymers &
Miscible
It’s not always so simple:
For example, crystal-crystals slips can cause transitions
Curve 1: DMA
Temp/Time Scan in 3 Point Bending
File info:
AMPfrPP.1 Wed Oct 27 13:49:06 1993
Frequency: 1.00 Hz
Dynamic Stress: 950.0mN
LeBrun samples
Static Stress: 1000.0mN
# 1 LeBrun samples:AMPfrPP.1
Storage Modulus (Pa x 10
#2
tan
(x 10
-1
9
)
)
3.0
Tg or
Alpha
1.0
1.0
T*
0.5
0.5
0.0
-150.0
-100.0
-50.0
AMP Flame Retardant Polypropylene
TEMP1: -160.0 C
TEMP2: 300.0 C
TIME1:
0.0 min
RATE1:
0.0
Temperature (
5.0 C/min
-1
(x 10
1.5
1.5
tan
9
)
Modulus (Pa x 10
2.0
2.0
)
2.5
2.5
50.0
C)
100.0
KPM
PERKIN-ELMER
7 Series Thermal
Analysis System
Sun Nov 26 20:58:36 1995
Kevin P. Menard, Dynamic-Mechanical Analysis, CRC-Press (1999) Boca Raton
Cold Crystallization in PET
DMTA
Tm
Tg
DSC
Cold Crystallization
Kevin P. Menard, Dynamic-Mechanical Analysis, CRC-Press (1999) Boca Raton
Left: silicon rubber with a glass transition at –117°C and a melting transition at –40°C. 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 –47°C.
R. Kosfeld, M. Hess, Progr. Colloid & Polymer Sci. 66 (1979) 43-50
Dissipation of mechanical energy:
Higher Order Transitions affect toughness
Curve 1: DMA
Temp/Time Scan in 3 Point Bending
File info:
AMP66gp.1 Tue Oct 26 16:05:29 1993
Frequency: 1.00 Hz
Dynamic Stress: 190.0mN
LeBrun samples
Static Stress: 200.0mN
LeBrun samples
4.0
5.5
5.0
3.5
Good Impact Strength
4.5
3.0
3.0
)
-1
2.5
Transitions
2.0
Tg
2.5
Poor
2.0
1.5
1.5
1.0
1.0
0.5
0.5
0.0
0.0
-150.0
-100.0
-50.0
AMP good part 20% glass filled Nylon 6/6
TEMP1: -160.0 C
TEMP2: 300.0 C
TIME1:
0.0 min
RATE1:
0.0
Temperature (
5.0 C/min
50.0
C)
100.0
150.0
KPM
PERKIN-ELMER
7 Series Thermal
Analysis System
Sat Oct 15 14:32:54 1994
Impact was good if Tg/T was 3 or less.
Kevin P. Menard, Dynamic-Mechanical Analysis, CRC-Press (1999) Boca Raton
(x 10
Modulus (Pa x 10
3.5
tan
9
)
4.0
Operating Range by DMA
in 3 P o in t Ben d in g
Cu rv e 1 : DM A T emp /T ime S can
T h u Ju n 3 0 0 2 :1 7 :2 4 1 9 8 8
g amma_ 1
F ile in fo :
Dy n amic S tress: 1 . 8 6 e+ 0 6 P a
F req u en cy : 7 . 0 0 Hz
S tatic S tress: 1 . 8 6 e+ 0 6 P a
E P OXY P C BOARD AT 7 Hz
# 1 E P OXY P C BOARD AT 7 Hz:g amma_ 1
10
)
S to rag e M o d u lu s (P a x 1 0
1 .1
5 .0
4 .5
Tg
0 .8
10
)
Operating
range
)
4 .0
)
(b)
0 .9
-1
(x 1 0
Beta
1 .0
3 .5
2 .5
Operating
range
0 .5
0 .4
2 .0
1 .5
1 .0
0 .2
0 .5
0 .1
0 .0
0 .0
T emp eratu re (
TEM P1 :
TEM P2 :
in 3 P o in t Ben d in g
Cu rv e 1 : DM A T emp /T ime S can
AM P frP P . 1 W ed Oct 2 7 1 3 :4 9 :0 6 1 9 9 3
F ile in fo :
Dy n amic S tress: 9 5 0 . 0 mN
F req u en cy : 1 . 0 0 Hz
S tatic S tress: 1 0 0 0 . 0 mN
L eBru n samp les
- 180. 0
300. 0
# 1 L eBru n samp les:AM P frP P . 1
S to rag e M o d u lu s (P a x 1 0
#2
t an
(x 10
-1
0. 0
TI M E1 :
C
C
9
m in
RATE1 :
C/ m i n
3 .0
1 .0
1 .5
1 .0
0 .5
0 .5
0 .0
- 160. 0
300. 0
C
C
TI M E1 :
0. 0
m in
RATE1 :
T emp eratu re (
5. 0
C/ m i n
5 0 .0
0 .0
-5 0 . 0
-1 0 0 . 0
-1 5 0 . 0
AM P F lame Retard an t P o ly p ro p y len e
TEM P 1 :
TEM P 2 :
C)
-1
t an
Modul us (P a x 10
Operating
range
1 .5
( x 10
)
2 .0
2 .0
)
2 .5
2 .5
9
10. 0
)
)
1 0 0 .0
KP M
P E RKIN-E L M E R
An aly sis S y stem
7 S eries T h ermal
S u n No v 2 6 2 0 :5 8 :3 6 1 9 9 5
1 0 0 .0
0 .0
-1 0 0 . 0
C)
2 0 0 .0
P E DM A7 R&D L AB
P E RKIN-E L M E R
An aly sis S y stem
7 S eries T h ermal
S u n No v 2 6 2 0 :1 3 :5 3 1 9 9 5
t an
M odul us (P a x 10
3 .0
0 .6
( x 10
0 .7
0 .3
(c)
-1
(a)
-> # 2 t an
Analysis of a Cure by DMA
E’-E” Crossover ~ gelation point
10 8
10 7
Modulus
10 6
106 Pa ~ Solidity
10 5
vitrification point
E”
10 4
Curing
10 3
E’
10 2
Melting
Minimum Viscosity (time, length,
temperature )

10 1
10 0
50.0
70.0
90.0
110.0
130.0
150.0

right figure after J. K. Gillham, Encyclop. Polym. Sci. Technol. (1986) 2nd ed.; J. K. Gillham, Polym. Eng. Sci. (1979) 19, 676
DMA’s advantage is viscosity
information along with Ea and k
8.0
7.0
6.0

5.0
4.0
T=70
3.0
2.0
T=60
T=50
1.0
0.0
0.0
5.0
10.0

15.0
20.0
25.0
From Isothermal Data, you...
log 





 
Plot log  vs. time for each T to
get  and k. Then plotting the
of log of these against 1/T gives
us Ea and E
log 
Slope = Ea
time in sec.
Kevin P. Menard, Dynamic-Mechanical Analysis, CRC-Press (1999) Boca Raton
1/T K
Postcure studies allow process
optimization:
1.0
Postcure time vs... Tg and E’
1 hour
0 hours
2 hours
200
180
3 - 8 hours
160
140
120
tan 
Property
0.5
100
E'@ 50 (e9 Pa)
80
60
E' onset
40
tan d peak
20
0.0
tan d onset
0
150
175 200
Temperature
0
Kevin P. Menard, Dynamic-Mechanical Analysis, CRC-Press (1999) Boca Raton
2
4
Time in H ours
6
8
Kevin P. Menard, Dynamic-Mechanical Analysis, CRC-Press (1999) Boca Raton
Multiplexing…
Instead of just the Tg
Sheet
Film
Fiber
multiple frequencies in one run
Kevin P. Menard, Dynamic-Mechanical Analysis, CRC-Press (1999) Boca Raton
Or you can use the Synthetic Oscillation Mode
Take five frequencies
Sum together
And
apply the
complex
wave
form to
the
sample
Temperature in C
Kevin P. Menard, Dynamic-Mechanical Analysis, CRC-Press (1999) Boca Raton
We can then do further analysis
Activation energy
Master curve
??????0.01?100Hz?
Why?…
Kevin P. Menard, Dynamic-Mechanical Analysis, CRC-Press (1999) Boca Raton
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.
TTS
• After TTS, our range is 1e-7 to 1e9 Hertz (1/sec)
• Then x scale can then be inverted to get time
To Review, DMA ties together...
molecular structure
Molecular weight
MW Distribution
Chain Branching
Cross linking
Entanglements
Phases
Crystallinity
Free Volume
Localized motion
Relaxation Mechanisms
product properties
Material
Behavior
processing conditions
Stress
Strain
Temperature
Heat History
Frequency
Pressure
Heat set
Dimensional Stability
Impact properties
Long term behavior
Environmental resistance
Temperature performance
Adhesion
Tack
Peel