Simulation of polymerization and long chain branch formation in a semi

batch reactor using two single-site metallocene catalysts

By:Saeid Mehdiabadi

May, 20071

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Outline

1. Introduction (Thermoplastic elastomers)2. Simulation results

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Thermoplastic Elastomers (TPEs)

The idea behind TPEs is the notion of reversible crosslink

There are two types of crosslinks

Chemical cross-link (Cross linking by covalent bond)Physical crosslink

Thermoplastic elastomers (TPEs) are materials with functional properties of conventional thermoset rubbers and processing characteristic of thermoplastics

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Cross linking by covalent bond

• An example of cross-linking is the reaction of natural rubber or poly(isoprene)

• By a process called vulcanization ,sulfurinterconnects the chains by reacting with the double bonds

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Physical CrosslinkingA simple structure is ABA block copolymerA: Short, rigid polystyreneB: long, flexible polybutadiene

Other possibilities includeMultiblock A-B-A-B-A-……..Graft copolymer

Immiscible (incompatible) microdomains within polymer matrix

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Copolymers

Hard segments

graft copolymers

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Graft copolymer (Branch-block)

iPP-g-aPP

Stereoselective catalyst + Propylene

i-PP

LCB catalyst +Propylene

Isotactic macromonomer

=

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Graft Block CopolymersAmorphous Backbones + Crystalline LCBs

iPP

aPP

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Simulation in a Semi batch Reactor

• Assumptions:• Constant monomer concentration• No mass transfer limitations

• Model Predictions

• Molar (n %) and weight (w %) percentages vs. time

• Number (rn) and weight (rw) average chain lengths vs. time

• Average LCB per 1000 C atoms (LCBD) and per chain (LCBF) vs. time

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M1 + Monomer

LCB 1

Cross-product

M2 + Monomer

LCB 2

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Kinetic Mechanism

1,,

iip

i Pk

MC ⎯⎯ →⎯+

Initiation Propagation

1,,

, +⎯⎯ →⎯+ riip

ri Pk

MP

1,,

, +⎯⎯ →⎯+ riip

ri Pk

MP

1,,

, +⎯⎯ →⎯+ riip

ri Pk

MPChain transfer reactions

iriiH

iriiAl

iriiM

irii

ri

CDk

H

CDk

Al

Pk

M

Ck

P

+⎯⎯ →⎯+

+⎯⎯ →⎯+

+⎯⎯ →⎯+

+⎯⎯→⎯

,,

2

,,

1,,,

,,

,µ

µβ

iriiH

iriiAl

iriiM

irii

ri

CDk

H

CDk

Al

Pk

M

Ck

P

+⎯⎯→⎯+

+⎯⎯ →⎯+

+⎯⎯ →⎯+

+⎯⎯→⎯

,,

2

,,

1,,,

,,

,µ

µβ

iriH

iriAl

iriM

iri

ri

CDk

H

CDk

Al

Pk

M

Ck

P

+⎯⎯→⎯+

+⎯⎯ →⎯+

+⎯⎯ →⎯+

+⎯⎯→⎯

,2

,

1,,

,

,µ

µβ

Long chain branch formations

Long chain branches are formed by incorporation of macromonomers of different types:

sriib

s

sriib

sj

sriib

si

sriib

sj

sriib

si

ri

Pk

Pk

Pk

Pk

Pk

P

+

+

+

+

+

⎯⎯→⎯

⎯⎯→⎯

⎯⎯→⎯

⎯⎯→⎯

⎯⎯→⎯

+

,,

,,

,

,,

,

,,

,

,,

,

,

µ

µ

µ

µ

µ

sriib

s

sriib

sj

sriib

si

sriib

sj

sriib

si

ri

Pk

Pk

Pk

Pk

Pk

P

+

+

+

+

+

⎯⎯→⎯

⎯⎯→⎯

⎯⎯→⎯

⎯⎯→⎯

⎯⎯→⎯

+

,,

,,

,

,,

,

,,

,

,,,

,

,

µ

µ

µ

µ

µ

sriib

s

sriib

sj

sriib

si

sriib

sj

sriib

si

ri

Pk

Pk

Pk

Pk

Pk

P

+

+

+

+

+

⎯⎯→⎯

⎯⎯→⎯

⎯⎯→⎯

⎯⎯→⎯

⎯⎯→⎯

+

,,

,,

,

,,

,

,,

,

,,

,

,

µ

µ

µ

µ

µ

iriid

ri CDk

P ˆ,

,, +⎯⎯→⎯ iri

idri CD

kP ˆ,

,, +⎯⎯ →⎯

irid

ri CDk

P ˆ,, +⎯⎯→⎯ i

idi C

kC ˆ,⎯⎯ →⎯

Deactivations

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Case study 1: Effect of kβ+kM[M]C2 Linear

C1LCB Cat.

0.90.9Kβ+KM[M]4 µmole/L

Ctotal

Transfer to Hydrogen

00KH2

Transfer to Al00KAl600tr

Transfer to monomer

11KM0.0Al

Β-hydride elimination

0.40.4kβ0.0H2

Deactivation rate constant

0.005 1/s0.005 1/s

KdMonomer conc.

0.5M

Long chain formationRate constant

0.001400kbInitial conc. ofcatalyst 2

C2

Propagation rate constant

50005000kpInitial conc. of catalyst 1

C1LCB CAT.

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Cross-product weight percent at different values of kβ+KM[M].

X-Product wt% vs. Catalyst ratio (Effect of KB+KM[M])

Kb=.001

0

5

10

15

20

25

30

35

40

45

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

r=C1/Ctotal

X-Pr

oduc

t wt%

(KB+KM[M])cat.2/(KB+KM[M])cat.1=10(KB+KM[M])cat.2/(KB+KM[M])cat.1=6(KB+KM[M])cat.2/(KB+KM[M])cat.1=2(KB+KM[M])cat.2/(KB+KM[M])cat.1=1

Case 1

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Cross-product mole percent at different values of kβ+KM[M].

Cross product mole% vs. Catalyst Ratio (Effect of KB+KM[M])

(Kb=.001)

0.0000

1.0000

2.0000

3.0000

4.0000

5.0000

6.0000

7.0000

8.0000

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

r=C1/(C1+C2)

mol

e%

(KB+KM[M])cat.2/(KB+KM[M])cat.1=10(KB+KM[M])cat.2/(KB+KM[M])cat.1=6(KB+KM[M])cat.2/(KB+KM[M])cat.1=2(KB+KM[M])cat.2/(KB+KM[M])cat.1=1

Case 1

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Effect of kβ+KM[M] on long chain branch density(LCBD)

Long Chain Branch Density vs. Catalyst Ratio( r) (Effect of (KB+KM[M]))

Kb=.001

0.0000

0.0100

0.0200

0.0300

0.0400

0.0500

0.0600

0.0700

0.0800

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

r= catalyst ratio

LCB

D

(KB+KM[M])cat.2/(KB+KM[M])ca.1=10(KB+KM[M])cat.2/(KB+KM[M])cat.1=6(KB+KM[M])cat.2/(KB+KM[M])cat.1=2(KB+KM[M])cat.2/(KB+KM[M])cat.1=1

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Effect of kβ+KM[M] on Polydispersity index (PDI)

Polydispersity index vs. catalyst ratio(Effect of KB+KM[M])

Kb=.001

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

r =catalyst ratio

PDI

(KB+KM[M])cat.2/(KB+KM[M])cat.1=10(KB+KM[M])cat.1/(KB+KM[M])cat.1=6(KB+KM[M])cat.2/(KB+KM[M])cat.1=2(KB+KM[M])cat.2/(KB+KM[M])cat.1=1

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Effect of kβ+KM[M] on weight average molecular weight (rw)

Weight average chain length vs. catalyst ratio (Effect of KB+KM[M]) (Kb=.001)

0.00

1000.00

2000.00

3000.00

4000.00

5000.00

6000.00

7000.00

8000.00

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

r C1/Ctotal

rw

(KB+KM[M])cat.2/(KB+KM[M])cat.1=1(KB+KM[M])cat.2/(KB+KM[M])cat.1=2(KB+KM[M])cat.2/(KB+KM[M])cat.1=6(KB+KM[M])cat.2/(KB+KM[M])cat.1=10

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Effect of kβ+KM[M] on number average molecular weight (rw)

Number average chain length vs. catalyst ratio (r)

0.00

500.00

1000.00

1500.00

2000.00

2500.00

3000.00

3500.00

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

r C1/Ctotal

rn

kb=0.001, a=1kb=0.001, a=2kb=0.001, a=6kb=0.001, a=10kb=400, a=1kb=400, a=2kb=400, a=6kb=400, a=10

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Results: Effect of parameter kβ+KM[M] of linear catalyst

• Increase in kβ+KM[M] :

• will increase cross-product wt% and mole %• Will increase LCBD • Will increase PDI• Will decrease weight average and number average

chain lengths• Weight average chain length is a linear function of

catalyst ratio

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Case study 2: Effect of kb,2

Cross-Product wt% vs. Catalyst ratio(Effect of changing Long chain branching rate constant)

-5.0000

0.0000

5.0000

10.0000

15.0000

20.0000

25.0000

30.0000

35.0000

40.0000

45.0000

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

r=C1/Ctotal

X-Pr

oduc

t wt%

kb=0.001, a=1kb=0.001, a=2kb=0.001, a=6kb=0.001, a=10kb=400, a=1kb=400, a=2kb=400, a=6kb=400, a=10

a=10

X-product wt% vs. catalyst ratio

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Case study 2 Effect of kb,2LongChain Branch Density vs. r=C1/(C1+C2)

Effect of different long chain brabching rate constant

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

r =C1/(C1+C2)

LCB

D

kb=0.001, a=1kb=0.001, a=2kb=0.001, a=6kb=0.001, a=10kb=400, a=1kb=400, a=2kb=400, a=6kb=400, a=10

LCBD vs. catalyst ratio

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PDI vs. catalyst ratio (Effect of different Kb)

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

r= catalyst ratio

PDI

kb=0.001, a=1kb=0.001, a=2kb=.001, a=6kb=0.001, a=10kb=400, a=1kb=400, a=2kb=400, a=6kb=400, a=10

Case study 2 Effect of kb,2 PDI vs. Catalyst ratio

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Case study 2 Effect of kb,2

0.00

1000.00

2000.00

3000.00

4000.00

5000.00

6000.00

7000.00

8000.00

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

r= C1/Ctotal

rw

kb=0.001, a=1kb=0.001, a=2kb=0.001, a=6kb=0.001, a=10kb=400, a=1kb=400, a=2kb=400, a=6kb=400, a=10

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Case 2: Results

1. A linear relationship between LCBD and catalyst ratio is observed

2. If our only objective is to maximize LCBD there is no need for adding catalyst 1.Using only one catalyst with high macromonomer formation rate and high long chain branch incorporating ability is preferred than using combination of two catalysts.

When Kb2=kb1

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Case study 3: Effect of monomer concentration on cross-product wt %

25

X-Product wt% vs. Catalyst Ratio ( Effect of Monomer concentration)

0

5

10

15

20

25

30

35

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Catalyst Ratio (C1/(C1+C2))

X-Pr

oduc

t w

M=0.25M=0.5M=2M=4

Weight % of Cross product vs. catalyst ratio at different monomer concentrations

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PDI vs. catalyst ratio (Effect of Monomer concentration)

0

1

2

3

4

5

6

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

r=C1/(C1+C2)

PD

M=4M=2

M=0.5

M=0.25

Polydispersity index vs. catalyst ratio at different monomer concentrations

Case study 3: Effect of monomer concentration on PDI

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Long Chain Branch Density vs. Catalyst ratio( r=C1/(C1+C2) (Effect of Monomer Concentration)

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

r =C1/(C1+C2)

LCB

D

M=0.25 M=0.5M=2M=4

Case study 3: Effect of monomer concentration on LCBD

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Case study 3: Effect of monomer concentration on weight average molecular weight

Weight average chain length vs. catalyst ratio (Effect of monomer concentration)

0

2000

4000

6000

8000

10000

12000

14000

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

r= C1/Ctotal

rw

M=4M=2M=0.5M=0.25

Increase in monomer conc.

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Result: Effect of monomer concentration

• Increase in monomer Concentration Has no effect on PDI

• Cross-product wt % is independent on monomer concentration

• LCBD decreases with increasing monomer concentration

• Increase in monomer concentration increase both number and weight average chain lengths

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Case study 4: Effect of catalyst deactivation on cross-product wt%

X-Product wt% vs. Catalyst Ratio ( Effect of Deactivation Rate Constant )

0

10

20

30

40

50

60

70

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

r=C1/(C1+C2)

X-Pr

oduc

t wt% Kd=5E-8 1/s

Kd=5E-5 1/sKd=5E-4 1/sKd=5E-3 1/sKd=5E-2 1/s

30

Increase in Kd

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LongChain Branch Density vs. r=C1/C total (Effect of Catalyst Deactivation)

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

catalyst ratio

LCB

D

Kd=5E-8 1/sKd=5E-5 1/sKd=5E-4 1/sKd=5E-3 1/sKd=5E-2 1/s

Case study 4: Effect of catalyst deactivation on LCBD

31

Increase in Kd

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Case study 4: Effect of catalyst deactivation on PDI

PDI vs. catalyst ratio (Effect of Catalyst Deactivation)

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

catalyst ratio

PDI

Kd=5E-8 1/sKd=5E-5 1/sKd=5E-3 1/SKd=5E-2 1/sKd=5E-4 1/s

Increase in kd

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Weight average chain length vs. catalyst ratio (Effect of Deactivation Rate Constant)

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Catalyst ratio

rw

Kd=5E-8 1/sKd=5E-5 1/sKd=5E-4 1/sKd=5E-3 1/sKd=5E-2 1/s

Case study 4: Effect of catalyst deactivation on weight average chain length

Increase in Kd

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Case study 4Results:

Increase in catalyst deactivation

1-Decrease in cross-product wt %

2-Decrease in LCBD

3-Decrease in PDI

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Thank you

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