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46
Yan Rong Wu Yan Rong Wu Supervisor: Dr. Costas Tzoganakis and Dr. Neil McManus Ui it fWt l University of W aterloo May 11, 2010 IPR 2010
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Page 1: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

Yan Rong WuYan Rong Wu Supervisor: Dr. Costas Tzoganakis and Dr. Neil McManus

U i it f W t lUniversity of WaterlooMay 11, 2010

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Page 2: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

BackgroundBackground

Objective

Experimental

CharacterizationCharacterization

Conclusion2

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Page 3: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

Metal – catalyzed reactionRearrange carbon carbon bonds viaRearrange carbon – carbon bonds via cleavage and reassemblyTypes of olefin metathesis:

3

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Page 4: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

Cross Metathesis:

Mechanism:

‐ Y. Chauvin. Angew. Chem. Int. Ed. 2006, 45, 3741 4

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Page 5: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

First GenerationStable in air, well-defined High stability, functional

Second GenerationStable in air, well defined structureHigh functional groups

High stability, functional groups tolerance and selectivityg g p

tolerance and selectivityActive in alcohol, water or

100 times higher reactivityCatalyze formation of tri

carboxylic acids. and tetra-substitutiedolefins

5‐ Robert H. Grubbs. Tetrahedron 2004, 60, 7117  

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Page 6: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

Good thermal and mechanical propertiesExcellent chemical resistanceLow priceLow price

Density (g/ml) 0.902

Number Average MW (g/mol) 5000Number Average MW (g/mol) 5000

Weight Average MW (g/mol) 12,000

Ring and Ball Softening Point (°C) 163

6

Ring and Ball Softening Point ( C) 163

Vinylidene Concentration (mol/g polymer) 8.4*10-5

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Page 7: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

High thermal and chemical stabilityg yLubricant propertiesLow glass transition temperatureLow glass transition temperature

Boiling Point (°C) >205Boiling Point ( C) >205

Melting Point (°C) <-60

M l l W i ht ( / l) 60 000 70 000

7

Molecular Weight (g/mol) 60,000-70,000

Viscosity (cSt) 9000-11,000

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Page 8: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

In 1998, Tzoganakis and Malz proved feasibility of hydrosilylation of terminal double y y ybonds in PP in melt phase, screw extruder

Melt Phase:o Simultaneous extrusion

Solution Phase:o Mild conditions o Simultaneous extrusion

and functionalizationo Save time equipment

o Mild conditionso Good homogenization

E d l b o Save time, equipment, energy and labor

o Energy and laborconsuming

8

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Page 9: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

BackgroundBackground

Objective

Experimental

CharacterizationCharacterization

Conclusion9

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Page 10: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

Mono-vinyl terminated PDMS chemically y y

modified vinyl-terminated PP through CM in

melt phase: PP-PDMS Copolymers

1) Expect change in properties: chemical

reactivity and adhesion

2) Expand its applications in highly profitable

i i d i d t iareas: engineering and aerospace industries10

‐ Hauke Malz and Costas Tzoganakis. Polymer Engineering and Science 1998, 38(2), 7117  

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Page 11: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

Characterize chemical, physical and

viscoelastic properties of synthesized

copolymers

Detect and quantify relationship among

experimental factors through factorial

design analysisdesign analysis

11

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Page 12: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

+ 333 3

Grubbs 2nd33 3

Generation Catalyst

Melt phasep

CM Product12

CM ProductIP

R 2010

Page 13: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

++

R1 : R2 CM Product Selectivity

1 : 1

2 : 1

50%

66%

4 : 1

10 : 1

80%

91%

13- Arnab K. C.; Tee L.C.; Daniel P.S.; Robert H.G. J.Am. Chem. Soc. 2003, 125, 11360

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Page 14: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

BackgroundBackground

Objective

Experimental

CharacterizationCharacterization

Conclusion14

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Page 15: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

PP and PDMS react in batch mixerin batch mixerPurified copolymersp y

15

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Page 16: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

3 3

2

3

2 2 2

16

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Page 17: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

F t T C MFactors High Low

Temperature 175 165

Factor T C M

Run 1 175 140 200(T, °C) 175 165

Catalyst Amount 140 60

2 175 140 100

3 175 60 200(C, mg) 140 60

PP/PDMS (M l ti ) 100:1 200:1

4 175 60 100

5 165 140 200(M, mole ratio) 100:1 200:1

6 165 140 100

7 165 60 200

8 165 60 100

17

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Page 18: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

BackgroundBackground

Objective

Experimental

CharacterizationCharacterization

Conclusion18

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Page 19: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

158°C147°C -47°C

-126°C -38°C

-86°C

19

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Page 20: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

8 165°C, 60 mg, PP/PDMS=100 165°C, 60 mg, PP/PDMS=200

6

W/g

) Tm-pp2

En4

t Flo

w (W Tm-pp1

ndotherm

2Heat

mic-140 -100 -60 -20

Temperature (°C)

0-140 -90 -40 10 60 110 160140 90 40 10 60 110 160

Temperature (°C)

Confirm: (1) Presence of PDMSConfirm: (1) Presence of PDMS (2) Feasibility of CM in melt phase

20

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Page 21: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

Tm-pp1 ∆Hm-pp1 Tm-pp2 ∆Hm-pp2Run m pp1

(°C)m pp1

(J/g)m pp2

(°C)m pp2

(J/g)

165°C 60mg PP/PDMS =200 156 1005 146 870165°C, 60mg, PP/PDMS =200 156 1005 146 870

165°C, 60mg, PP/PDMS =100 157 646 149 772

Pure PP wax 158 1547 147 1116

In copolymers, PP crystalline proportion

i i fl d b PDMS tis influenced by PDMS component

21

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Page 22: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

100 PP wax165°C, 60 mg, PP/PDMS=100 165°C, 60 mg, PP/PDMS=200

60

80

t (%

)

40

60

ng W

eigh

t

Air

20

40

Rem

aini

n

050 200 350 500

Temperature (°C)

Thermal degradation beginning at :Thermal degradation beginning at : 309°C (PP); 368°C and 327°C (Copolymer) 22

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Page 23: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

Remaining Remaining

Run

Remaining

Weight % at

Remaining

Weight % at

350 °C 450 °C

165°C, 60mg, PP/PDMS =200 61.06 8.09165 C, 60mg, PP/PDMS 200 61.06 8.09

165°C, 60 mg, PP/PDMS =100 79.16 7.83

Higher thermal stabilit is obser ed in copol mers

Pure PP Wax 24.49 1.49

Higher thermal stability is observed in copolymers

PDMS concentration Thermal stabilityPDMS concentration Thermal stability 23

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Page 24: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

30003000

Pa)

a)

20002000

us, G

" (P

us, G

´(Pa

10001000 ss M

odul

ge M

odul

Los

Stor

ag

000 200 400 600

Angular Frequency ω (rad/s)Angular Frequency, ω (rad/s)

Viscous Component is dominant over elastic counterpartcounterpartImproved G′; Decreased G″ 24

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Page 25: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

6 PP wax165°C, 60 mg, PP/PDMS=100

5ty,

165°C, 60 mg, PP/PDMS=200

Visc

osi

Pa·s

)

4

mpl

ex V

|ŋ*|

(P

3

Com

0 200 400 600

Angular Frequency, ω (rad/s)

At high frequency: |ŋ*| (Copolymers) < |ŋ*| (PP)25

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Page 26: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

Source of Variance p valueSource of Variance p-value

Main Effects: Temperature (T) 0.00741

Catalyst (C) 0.22161

Mole Ratio (M) 0.00974

Interaction Effects: TxC 0.00004

TxM 0.25319

CxM 0.73920

TxCxM 0.52531

100

150

orqu

e

Torque was significantly affected by T, M and TxC

0

50

0 10 20 30 40 50

To

Time (min)

26

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Page 27: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

45T t Eff t45M l R ti Eff t 45 C t l t C t ti Eff t

g)

Temperature Effect

*g)

Mole Ratio Effect 45

m*g

)

Catalyst Concentration Effect

40

que

(m*g

40

rqu

e (m

*

40

Torq

ue (

m

35

Torq

35T

or35

T

35160 165 170 175 180

Temperature (°C)

3550 100 150 200 250

Mole Ratio

3550 90 130

Catalyst Amount (mg)

27

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Page 28: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

60

g)

Low catalyst amountHigh catalyst amount

50

60

)

Low TemperatureHigh Temperature60

)

Low PP/PDMSHigh PP/PDMS

40rque

(m*g

40

que

(m*g

)

40

que

(m*

g)

20

To

20

30

Torq

20

Torq

20160 170 180

Temperature (°)80 120 160 200

PP/PDMS Mole Ratio

2040 80 120 160

Catalyst Amount (mg)

TQ = 39.3375-3.3375xT+0.9625xC-3.0875xM-13.4625xTxC

28

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Page 29: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

BackgroundBackground

Objective

Experimental and Results

CharacterizationCharacterization

Conclusion29

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Page 30: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

Successfully syntheszied PP-PDMS

copolymers through CM, in melt phase

Characterization of copolymers:

Thermal stability Elasticity Viscosity

Factorial design: statistical analysis for torque

response

30

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Page 31: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

Repeat all experiments: fully replicated

factorial designfactorial design

Perform same polymerizations in extruder:Perform same polymerizations in extruder:

better mixing, shorter reaction timebetter mixing, shorter reaction time

Investigate other types of PDMS or g yp

polymers (PE, PB)

31

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Page 32: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

Supervisor: Dr. Costas TzoganakisSupervisor: Dr. Costas Tzoganakis

Dr. Neil McManus

Dr Ralph DickhoutDr. Ralph Dickhout

Colleagues in the Tzoganakis Lab

32

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Page 33: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

33

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Page 34: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

Factor T C MFactor T C M

Run 1 175 140 200

2 175 140 100

3 175 60 200

4 175 60 100

5 165 140 200

6 165 140 100

7 165 60 200

8 165 60 100

CP 1 and 2 170 100 150

BM 1 2 d 3 175 100 150

34

BM 1, 2 and 3 175 100 150

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Page 35: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

Run T

(°C)

Catalyst

( )

Initial

ti

5 min

ti

30 min

ti(°C) (mg) mass ratio mass ratio mass ratio

1 175 140 329 488 408

2 175 140 329 348 3622 175 140 329 348 362

3 175 60 329 514 447

4 175 60 329 647 3574 175 60 329 647 357

5-2 165 140 329 601 315

6 165 140 329 353 3276 165 140 329 353 327

7 165 60 329 1264 350

8 165 60 329 468 854

35

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Page 36: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

175°C

170°C

36

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Page 37: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

Tg-1 Tg-2 Tm-PDMS2 Tm-PDMS1Run g 1

(°C)g 2

(°C)m PDMS2

(°C)m PDMS1

(°C)

1 -126 -99 -50 -38

2 -126 -111 -50 -38

3 -126 -110 -46 -38

4 127 89 50 374 -127 -89 -50 -37

5-2 -126 -95 -51 -38

6 -129 -98 -50 -38

7 -130 -88 -51 -38

8 ― -92 -51 -38

CP1 -123 ― -51 -38

CP2 ― -115 -51 -38

PDMS 126 86 (T ) 47 38PDMS -126 -86 (Tc) -47 -38

37

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Page 38: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

NAir

N2

165°C

Td in air: 309°C (PP), 368°C ( ) and 327°C ( )

Td in N2: 419 °C (PP), 423°C ( ) and 420°C ( ) 38

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Page 39: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

RW at RW at Run #

350 °C (%) 450 °C (%)

1 52.41 3.14

2 61.93 8.36

3 40.90 5.50

4 55.96 7.04

5-2 43.06 5.37

6 62.33 7.78

7 61.06 8.09

8 79.16 7.83

CP1 40.37 5.90

39

CP2 47.10 5.78

PP 24.49 1.49

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Page 40: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

4 PP wax60 PP/PDMS 100

4

2

3

(Pa)

60 mg, PP/PDMS=10060 mg, PP/PDMS=200

165°C

2

3

) (Pa

)

165°C 1

Log

(G´)

1

Log

(G´´

)

-1

0

L

-1

0

L

0 0.5 1 1.5 2 2.5 3Log (ω) (rad/s)

0 0.5 1 1.5 2 2.5 3

Log (ω) (rad/s)

Improved elasticity: fiber spinning&thermoformingEffect of PDMS into PP on viscous modulus is lessEffect of PDMS into PP on viscous modulus is less than elastic modulus

40

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Page 41: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

1.2PP wax60 PP/PDMS 100

(Pa)

60 mg, PP/PDMS=10060 mg, PP/PDMS=200

165°C

0.7

(|ŋ*

|) (

Log

0.20 0.5 1 1.5 2 2.5 3

Log (ω) (rad/s)

|ŋ*| of copolymers < |ŋ*| of virgin PP at |ŋ | p y |ŋ | ghigher frequency

41

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Page 42: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

• Rheology is defined as “ the study of the deformation and

flow of matter” and the fundamental relations between forceflow of matter and the fundamental relations between force

and deformation in materials is called constitutive relations.

• Most materials studied in rheology exhibit both liquid-like and

solid-like properties Hookean Solidsolid-like properties. Hookean Solid

Newtonian Liquid

Silly Putty behaves like a solid (a and b) and a liquid (c)solid (a and b) and a liquid (c)

42Macosko, C.W. Rheology: Principles, Measurements, and Applications; VCH Publisher, Inc.:New York, 1994

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Page 43: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

• Rheometers are instruments that measure

both “stress and deformation history” on a

material for which the constitutive relation is

kunknown.

Rh t b t i d i t t• Rheometers can be categorized into two

major classes by kinematics: Shearmajor classes by kinematics: Shear

Rheometers and Extension Rheometers.

43Malkin, A.Y.; Isayev, A.I. Rheology: Concepts, Methods, and Applications; Chem Tec Publishing: Toronto, 1994.

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Page 44: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

Rotational Measurement: a defined speed (shear rate) is

used and the resultant torque (stress) is measured.

Oscillatory Measurement:

• Applied a sinusoidal oscillating stress wave and• Applied a sinusoidal oscillating stress wave and measure the resulting strain wave.

• Measurements are made over a range of frequencies.

• Complex viscosity ( *) Phase angle ( and Storage• Complex viscosity ( *), Phase angle ( and Storage and Loss modulus (G‘ & G“) as a function of frequency

44are determined. Bird, R.Byron; Armstrong, Robert C.; Hassager, Ole. Dynamics of Polymeric Liquids V1: Fluid Mechanics; John Wiley & Sons Inc.:

Toronto, 1977. 

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Page 45: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

Hook solid response with phase angle = 0phase angle = 0  . 

Newtonian fluid response with phase angle = 90 °. 

Viscoelastic materials response with phase angle in between 0 ° and 90 °

45Rheology Advantage Data Analysis Manual. TA instruments, 2007. 

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Page 46: 2010 IPR - University of Waterloo...3000 3000 P a) a) us, G´(P 2000 2000 us, G" (1000 1000 s s Modul g e Modul Stora Lo 0 0 0 200 400 600 Angular FrequencyAngular Frequency, ω(rad/s)

Source of

VarianceEffect SS DF MS F p

Temperature (T) -6.6750 89.1112 1 89.1112 25.1539 0.00741

Catalyst (C) 1.9250 7.4112 1 7.4112 2.0920 0.22161

Mole Ratio (M) -6.1750 76.2612 1 76.2612 21.5267 0.00974

TxC -26.9250 1449.9113 1 1449.9113 409.2745 0.00004

TxM 1.7750 6.3012 1 6.3012 1.7787 0.25319

CxM 0.4750 0.4513 1 0.4513 0.1274 0.73920

TxCxM 0.9250 1.7112 1 1.7112 0.4830 0.52531

Error 4 3.5426

Total 1631.1588 11

46

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