Simulation of polymerization and long chain branch ... · • By a process called vulcanization...
Transcript of Simulation of polymerization and long chain branch ... · • By a process called vulcanization...
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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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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Graft copolymer (Branch-block)
iPP-g-aPP
Stereoselective catalyst + Propylene
i-PP
LCB catalyst +Propylene
Isotactic macromonomer
=
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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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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 %
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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
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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
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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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