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POLYMERIZATION KINETICS AND MODELING OF SLURRYETHYLENE POLYMERIZATION PROCESS WITH METALLOCENE/MAOCATALYSTSMu-Jen Younga; Chen-Chi M. Maaa Department of Chemical Engineering, National Tsing Hwa University, Hsinchu, Taiwan
Online publication date: 20 August 2002
To cite this Article Young, Mu-Jen and Ma, Chen-Chi M.(2002) 'POLYMERIZATION KINETICS AND MODELING OFSLURRY ETHYLENE POLYMERIZATION PROCESS WITH METALLOCENE/MAO CATALYSTS', Polymer-PlasticsTechnology and Engineering, 41: 4, 601 618
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POLYMERIZATION KINETICS AND
MODELING OF SLURRY ETHYLENE
POLYMERIZATION PROCESS WITH
METALLOCENE/MAO CATALYSTS
Mu-Jen Young1,2
and Chen-Chi M. Ma1,*
1Department of Chemical Engineering, National Tsing Hwa
University, Hsinchu 30043, Taiwan2Union Chemical Laboratories, Industrial Technology
Research Institute, Hsinchu 30043, Taiwan
ABSTRACT
Polymerization methods of ethylene include the slurry, solution,
and gas-phase processes. This study investigates polymerizationconditions and kinetics under slurry process. Typical metallocene
catalyst/cocatalyst Cp2ZrCl2/MAO system was used for ethylene
polymerization. Two kinds of polymerization kinetics were
compared in this study, multiple active-site model and transfer-
effect model. The kinetic studies used metallocene-type
polymerization kinetics, including catalyst activation, initiation,
chain propagation, chain transfer, and termination steps. In
addition, kinetic constants of polymerization reaction model were
calculated. Calculation results of catalyst activity and molecular
weight were compared with experimental results, indicating their
good correlation. Moreover, the conventional polymerization was
modified to accurately predict the molecular weight behaviors
601
Copyright q 2002 by Marcel Dekker, Inc. www.dekker.com
*Corresponding author. E-mail: [email protected]
POLYM.PLAST. TECHNOL. ENG., 41(4), 601618 (2002)
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under various reaction conditions with the proposed transfer-
effect model. Exactly, how reaction time, pressure, catalyst
concentration, and cocatalyst ratio affect catalyst activity and
molecular weight of the polymer were also discussed.
Key Words: Metallocene; Polymerization kinetics; Polyolefin;
Slurry PE
INTRODUCTION
Coordination polymerization was first used in the ZieglerNatta catalyst forolefin polymerization. This technology allows the geometry of the catalyst around
the metal center to control the polymer structure. In homogeneous polymerization,
the ligand of a catalyst largely controls the geometry of an active metal center in
which the polymerization reaction occurs. The metallocene catalyst discovered by
Kaminsky[1] has proven to be a major breakthrough for the polyolefin industry. The
major difference between metallocene and conventional-type ZieglerNatta
catalyst is the coordination environments. As a type of heterogeneous catalyst, the
environments of active metal center of ZieglerNatta catalyst are varied based on
the shape of support materials; however, the metallocene catalyst has uniform
environments of active metal center. The result of this difference is due to the fact
that the polydispersity indices of metallocene catalysts are smaller than those of
ZieglerNatta catalysts. Thus the physical properties of polymer products can be
modified by changing the catalyst structure.The slurry process of polyethylene (PE) was the typical polymerization
process for the operation at lower temperatures. Sarker et al.[2] used a multigrain
model to explain the broad molecular weight distribution of propylene obtained
from a slurry reactor using ZieglerNatta catalysts. Estrada et al. [3] carried out
the slurry PE process in a semi-batch reactor and proposed a multiple active-site
model to explain the experimental results. The effect of mass transfer on the
heterogeneous Ziegler Natta catalysts polymerization has been extensively
studied. Bhagwat et al.[4] proposed a mathematical model for isothermal, slurry
polymerization of ethylene using ZieglerNatta catalysts, which explains how
gas liquid mass-transfer limitations affect the overall rates and polymer
properties. McKenna et al.[5] studied the heat, mass-transfer effect with particle-
growth model, indicating that the conductive heat and mass transfer might play
an important role in the early stage of polymerization. McKenna et al.[6] also
studied the reaction conditions limited by mass transfer, indicating that the
critical length scale for mass transfer is much smaller than the particle radius, and
convection is not the dominant heat-transfer mechanism during the critical stages
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of the reaction. Choi et al.[7] studied how different chain-transfer constants
affect the molecular weight and polydispersity by simulating the system of
ZieglerNatta catalysts ethylene polymerization. Marques et al.[8,9] also studied
the homogeneous ZieglerNatta catalyst polymerization system and, by doing
so, they proposed steady-state and transient-state kinetics models for such a
system.
The characteristic of the molecular weight behavior has a certain mode in
the addition polymerization. Once the polymerization reaction proceeds, the
molecularweight buildsup in a short time, andthen maintains a stablevalueduring
the entire polymerization process. Unfortunately, the molecular weight of the
polymerization product varies with conditions and reaction time of the process,
which is not explained adequately with the conventional polymerization reaction
kinetic models.This study investigates the polymerization kinetic behaviors under various
reaction conditions. A mathematical model for polymerization is also proposed to
explain the reaction phenomena, thereby providing a valuable reference for
further engineering studies.
EXPERIMENTS
Slurry polymerization of ethylene was conducted in an autoclave reactor as
shown in Fig. 1. A check valve was used to maintain the ethylene pressure. The
solvent used in this study wasisopar-E, a mixture of C7 andC8 alkanes. Thecatalyst
used for polymerization, a typical metallocene catalyst and the co-catalyst, was
methylalumoxane (MAO). No support material was used in this study.The experimental procedure was as follows. The catalyst used in this study
was the commercialized Cp2ZrCl2 catalyst. Owing to its ability to react easily with
water and oxygen in air, this catalyst must be dissolved in toluene to form a
2 1023M solution in the dry box. Once it was set up, the reactor was heated to
908C and purged with N2. The solvent was injected into the reactor, the reactor
temperaturewas elevatedto the reaction temperature, and then the co-catalyst MAO
was injected into the reactor and stirred.After the co-catalyst was thoroughly stirred,
the catalyst solution was injected into the reactor and continuously stirred while the
ethylene gas was induced into the reactor. When the reaction was completed, the
polymer product was dried in a vacuum oven and the Mw and molecular weight
distribution (MWD) were analyzed by gel permeation chromatography (GPC).
The calibration standard of GPC was polystyrene (PS); solvent was
trichlorobenzene; and the operation temperature was 1308C. The GPC model
used in this study was the Waters GPV2000 (Waters Asia Ltd., Taiwan).
Table 1 lists the typical operating conditions, while Table 2 summarizes the
experimental results. Table 2 reveals that the molecular weight of polymer
POLYMERIZATION METHODS OF ETHYLENE 603
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products formed by polymerization reaction varied with the operation conditions.In accordance to the traditional mechanism of additional polymerization, the
molecular weight is roughly the same. Molecular weight and polydispersity index
are defined by probability of propagation p
p Rp
Ri Rp Rtrm1
Figure 1. Experimental apparatus.
Table 1. Typical Operating Conditions
Reaction phase volume 500 mL
Temperature 908C
Al/Ti ratio 1000Catalyst concentration 6.67 10
26mol/L
Ethylene pressure 10 psig
Reaction time 30 min
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Table2.
Exper
imentalResultsofEthylenePolymerizatio
n
Temperature
(8C)
Pressure(psig)
Time(min)
[CAT](mol/L)
Al/Zr
Mn
(g/m
ol)
Mw
(g/mol)
Act(g-PE/g-Cat)
90
10
30
6.6
7
1026
500
46,82
0
125,1
19
100,0
00
90
10
30
6.6
7
1026
1,0
00
40,96
7
101,3
98
188,0
00
90
10
30
6.6
7
1026
1,5
00
33,45
6
68,0
21
204,0
00
90
10
30
6.6
7
1026
2,0
00
33,39
1
73,0
57
210,0
00
90
10
30
6.6
7
1026
2,5
00
29,03
7
59,5
86
213,0
00
90
10
30
6.6
7
1026
1,0
00
40,96
7
101,3
98
188,0
00
90
20
30
6.6
7
1026
1,0
00
31,42
4
123,7
18
212,0
00
90
30
30
6.6
7
1026
1,0
00
50,07
5
125,9
06
247,0
00
90
40
30
6.6
7
1026
1,0
00
42,96
2
158,2
00
259,0
00
90
10
30
6.6
7
1026
1,0
00
40,96
7
101,3
98
188,0
00
90
10
30
0.0
0001
1,0
00
22,62
8
59,3
19
207,0
00
90
10
30
1.3
3
1025
1,0
00
24,74
0
53,7
85
216,0
00
90
10
30
1.6
7
1025
1,0
00
21,57
2
53,3
34
225,0
00
90
10
10
6.6
7
1026
326.7
974
47,12
9
122,7
86
55,0
00
90
10
15
6.6
7
1026
326.7
974
37,96
0
85,8
36
92,0
00
90
10
25
6.6
7
1026
326.7
974
41,31
8
90,4
47
122,0
00
90
10
30
6.6
7
1026
326.7
974
47,98
4
104,9
01
145,0
00
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Mn 1
1 2 p2
Mw
Mn 1 p 3
whereRp is the rate of chain propagation;Ri the rate of chain initiation;Rtrm the rate
of chain transfer by monomer. Therefore, as long as the monomer concentration
remains unchanged during the reaction process, the molecular weight and
polydispersity index of polymer product do not change significantly. The change of
molecular weight during the change of reaction conditions implies that the effect of
monomer concentration do change as the reaction condition changes.
POLYMERIZATION KINETICS
The slurry polymerization of ethylene uses a two active-site model to
explain the broadened polydispersity index. Where the first-type active can
transform to second-type active site, chain-initiation reaction only produce first
active site, and chain-deactivation reaction preformed only on second type active
site. The typical kinetic scheme includes the following kinetic equations;[3] the
notations of the following equations are summarized in the Appendix.
Instantaneous formation of C*1
Cat MAOka! C* 4
Instantaneous initiation of C*1 ; first-type active site
C* Mki! Pi 5
Site transformation
Prktran! Qr 6
Propagation of active species
Pr Mkp1! Pr1 7
Qr Mkp2! Qr1 8
Spontaneous chain transfer by b-hydride eliminationPr
ktrm1! Rr P1 9
Qrktrm2! Rr Q1 10
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Spontaneous deactivation of active species
Qrkd! Rr 11
According to the above kinetic equations, a set of differential equations that
describe the mass balance can be written as follows:
dMAO
dt 2kaMAOCat 12
dCat
dt 2kaMAOCat 13
dCat*
dt 2kaMAOCat 2 kiCat* CyC 14
dCyC
dt 2kiCat* CyC 2 kp1Cat* CyC 2 kp2Cat* CyC 15
dPEA*
dt kiCat* CyC 2 ktrmPEA* 16
dPEB*
dt ktrmPEA* 2 kdPEB* 17
dPE
dt ktrn1PEA* ktrn2PEB* kdPEB* 18
where [CyC] is the ethylene concentration in the solution; [MAO] the cocatalyst
methylalumonxane concentration; [Cat] the catalyst concentration; [Cat]* the
activated catalyst concentration; [PEA]* the concentration of living polymer
chains with first kind of active site; [PEB]* the concentration of living polymer
chains with second kind active site; [PE] the concentration of dead polymer
chains; ka the kinetic constant of catalyst activation by cocatalyst; ki the chain
initiation kinetic constant; kp the chain propagation kinetic constant; ktrm the
chain transfer by monomer kinetic constant; ktrn the chain transfer by monomer
rate constant; and kd the spontaneous chain termination kinetic constant.
Despite its merits, the above model is limited in that its molecular weight is
nearly the same at the same temperature despite different reaction conditions.
Importantly, the model must be modified to accurately determine the molecularweight change according to different reaction conditions.
When the molecular weight varies with the weight fraction of polymer in
the reaction slurry, a gel-effect parameter that accounts for molecular weight
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change can be introduced into the kinetic constant of the chain propagation
reaction. This observation implies that the chain propagation reaction slows
down with an increasing weight fraction of polymer in the reaction slurry.
The kinetic constant of chain-transfer reaction can be modified by gel-
effect parameter G, where the value ofG lies between zero and unity. The defined
gel-effect parameter must be proportional to the weight fraction of solvent in the
reaction slurry.
G Wsolvent
Wsolution
a19
The above equation describes the gel effect in the slurry polymerization of
ethylene by metallocene catalyst. The kinetic constant of polymerization was
solved in both cases, with and without the gel-effect parameter. In the case in
which the polymerization kinetics were solved with gel-effect parameter, the
single-site model was employed because the molecular weight and polydispersity
index can be adjusted by gel-effect parameter, and hence the two active-site
assumption was no longer needed.
Figure 2 shows the relationship between weight fraction of polymer in the
reaction slurry and molecular weight of polymers. The number average molecular
weight in this figure is roughly disproportional to the weight fraction of the polymer
in the reaction slurry. This finding suggests that the diffusion effect of a monomer
through a polymer particle in the reaction slurry inhibits the chain-transfer reaction.
Thus, the chain-transfer reaction by a monomer can be modified as
ktrn;new Gktrn 20
Figure 2. Relationship between number averaged molecular weights and weight fraction
of polymer in the reaction slurry.
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Hence, the molecular weight should be decreased with an increase in the
weight fraction of polymer in the reaction slurry.
Since the gel-effect model has been proposed, reaction in the
polymerization kinetic network that is affected by mass transfer must be
determined. The simplest means is to verify the relationship between molecular
weight and weight fraction of polymer in the reaction slurry. Polymerization
kinetics of ethylene with gel-effect parameter are as follows:
Cat MAOka! C* 21
C* Mki! P1 22
Pr Mkp! Pr1 23
Prk*rm! Qr P0 24
Prkd! Qr 25
The differential equations of mass balance can thus be written similarly.
dMAO
dt 2kaMAOCat 26
dCat
dt 2kaMAOCat 27
dCat*
dt kaMAOCat 2 kiCat* CyC 28
dCyC
dt 2kiCat* CyC 2 kpPE* CyC 29
dPE*
dt kiCat* CyC 2 kdPE* 30
dPE
dt ktrPE* kdPE* 31
where [PE] in the above equations is the molar concentration of the living
polymer chain. The number of undetermined kinetic constants of the gel-effect
model is also less than two active-site model, and thus accelerates the parameter
finding and equation solution procedure.
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COMPUTATIONAL METHODS
Predicting the solubility of ethylene in a solvent is crucial in simulating the
slurry process of ethylene polymerization. Herein, the ChaoSeader model [11] is
used to calculate the phase equilibrium and obtain the ethylene concentration in a
solvent in the polymerization reactor.
Owing to the inter-relation and coupling of polymerization kinetics, the
nature of differential equations of the polymerization reaction kinetics is a stiff set
equation. Single-step explicit integration methods such as RungeKutta often
diverge in the integration process. To ensure the convergence of integration
process, this study used Adams finite difference formula of the Predictor
Corrector method.[10] Evaluation of the best-fit kinetic constants of polymerization
reaction involves the definition of an object function to calculate the differencebetween the calculated and experimental results. The object function is defined as
follows:
Fk1; k2; k3; k4. . . w1X Mwexp 2 Mwcalc
Mwexp
2w2
X Mnexp 2 MncalcMnexp
2
w3X Actexp 2 Actcalc
Actexp
232
where wi is the weight of each term in the function. For each set of kinetic
constants, there is a value of object function. An optimization scheme is then used
for the set of best-fit polymerization reaction constants.
This study adopts the Powell method[10]
for the optimization procedure.The Powell method, also known as the method of successive variation of
parameters, optimizes the parameter one after another to obtain the optimized
parameter set. Although the Powell method is a less efficient optimization
method for stability, this method was used to estimate the parameters of
polymerization kinetic constants.
RESULTS AND DISCUSSION
Both sets of kinetic parameters, with and without gel effect modification,
were calculated according to the proposed model and experimental data. Table 2
summarizes the experimental results of the polymerization reaction. Table 3 lists
the kinetic constants of polymerization reaction that was obtained from the
optimization process. Table 4 summarizes the calculation results by the set of
kinetic constants, where the abbreviation expt represents experimental data, 2
site represents the two active-site polymerization kinetic model as described in
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section Computational methods, and gel represents the novel gel-effect model
with the gel-effect parameter.
Figures 3 and 4 show how ethylene pressure affects the reaction results,
indicating that the ethylene concentration increases with an increase in the
ethylene pressure. According to these figures, the catalyst reactivity also
increases with an increase in monomer concentration. In addition, increasing the
monomer concentration in the reaction slurry by increasing ethylene pressure can
ultimately decrease the molecular weight. The gel-effect model not only predicts
the correct trend in yield of PE product, but the conventional model cannot
calculate the trend of molecular weight with the change in monomer
Table 3. Kinetic Constants
Two-Site Model k (1/sec) Gel Model k (1/sec)
ka 10300 ka 88.68108
ki 1.007 ki 30.25945
kp1 0.0742 kp 525.3284
kp2 33,290 ktr 0.3732
ktr 2.611 kd 0.000881
kd 0.1181 a 17.69337
trem1 14.153
ktrm2 5.299
Figure 3. Effect of ethylene pressure on the catalyst activity of PE. (Exp: experimental
results, Gel: gel-effect model results, 2 Sites: 2-sites model results.)
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Table
4.
CalculationResults(Exp:Experimen
talResults,2-Sites:2-SitesModelResults
,Gel:Gel-EffectModelResults)
Mn
(g/mole)
Act
(g-PE/g-Cat)
Temperature
(8C)
Pressure
(psig)
Time
(min)
[CAT]
(mol/L)
Al/Zr
Expt
2-Site
Gel
Expt
2-Site
Gel
90
10
30
6.6
7
1026
500
46,8
20
33,2
29
46,896
100,0
00
168,6
63
107,2
68
90
10
30
6.6
7
1026
1,0
00
40,9
67
33,2
30
37,416
188,0
00
171,0
09
171,1
69
90
10
30
6.6
7
1026
1,5
00
33,4
56
33,2
30
32,787
204,0
00
175,0
23
224,9
97
90
10
30
6.6
7
1026
2,0
00
33,3
91
33,2
31
29,855
210,0
00
193,1
49
273,1
64
90
10
30
6.6
7
1026
2,5
00
29,0
37
33,2
31
27,763
213,0
00
241,4
42
317,5
28
90
10
30
6.6
7
1026
1,0
00
40,9
67
33,2
30
37,416
188,0
00
171,0
09
171,1
69
90
20
30
6.6
7
1026
1,0
00
31,4
24
32,8
79
34,816
212,0
00
219,3
68
197,5
13
90
30
30
6.6
7
1026
1,0
00
50,0
75
32,4
35
32,807
247,0
00
249,0
18
222,6
74
90
40
30
6.6
7
1026
1,0
00
42,9
62
31,9
35
31,185
259,0
00
266,0
32
246,9
14
90
10
30
6.6
7
1026
1,0
00
40,9
67
33,2
30
37,416
188,0
00
171,0
09
171,1
69
90
10
30
0.0
0001
1,0
00
22,6
28
33,2
30
28,732
207,0
00
170,8
20
197,1
66
90
10
30
1.3
3
1026
1,0
00
24,7
40
33,2
31
23,824
216,0
00
193,1
49
217,9
79
90
10
30
1.6
7
1026
1,0
00
21,5
72
33,2
31
20,602
225,0
00
241,4
42
235,6
35
90
10
10
6.6
7
1026
326.8
47,1
29
30,1
65
62,363
55,0
00
56,2
98
57,2
77
90
10
15
6.6
7
1026
326.8
37,9
60
31,7
66
59,714
92,0
00
91,1
07
63,4
51
90
10
25
6.6
7
1026
326.8
41,3
18
32,9
60
55,548
122,0
00
146,9
99
75,0
39
90
10
30
6.6
7
1026
326.8
47,9
84
33,2
29
53,862
145,0
00
168,6
00
80,5
26
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concentration. This finding suggests that the gel-effect modification can yield
much better results that correlate better with the experimental results.
Figures 5 and 6 show how the reaction time affects the polymerization
reaction. Although the yield from both the models corresponds to the
experimental data, the trend of molecular weight is unclear. However, the
change in molecular weight of the polymer product with an increase in reaction
time has no specific trend.
Figure 4. Effect of ethylene pressure on the Mn of PE. (Exp: experimental results, Gel:
gel-effect model results, 2 Sites: 2-sites model results.)
Figure 5. Effect of reaction time on the PE catalyst activity. (Exp: experimental results,
Gel: gel-effect model results, 2 Sites: 2-sites model results.)
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Figures 7 and 8 show the effect of catalyst concentration on the reaction
results. According to these figures, the amount of polymer product increases with
an increase in the catalyst concentration; this can also be calculated from both the
models. Only the gel-effect model can represent the declining effect of molecular
weight with an increase in the concentration of the catalyst. This effect can
contribute to the competition of active sites in the site-activation reaction that
causes the decrease in molecular weight.
Figure 6. Effect of reaction time on the Mn of PE. (Exp: experimental results, Gel: gel-
effect model results, 2 Sites: 2-sites model results.)
Figure 7. Effect of catalyst concentration on the PE catalyst activity. (Exp: experimental
results, Gel: gel-effect model results, 2 Sites: 2-sites model results.)
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Figures 9 and 10 summarize the effect of cocatalyst ratio (Al/Zr ratio) on
the polymerization reaction, again although both models can predict the catalyst
activity according to different cocatalyst ratio, the two-site model failed to
predict the site competition effect mentioned above.
The above comparisons, show that there is a good correlation between the
calculated and experimental results in the polymer yield for both models. While
Figure 8. Effect of catalyst concentration on the Mn of PE. (Exp: experimental results,
Gel: gel-effect model results, 2 Sites: 2-sites model results.)
Figure 9. Effect of Al/Ti ratio on the PE catalyst activity. (Exp: experimental results,
Gel: gel-effect model results, 2 Sites: 2-sites model results.)
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calculating the molecular weights, only the gel-effect modification can accurately
represent the relationship between the molecular weight and the solution
conditions of the polymerization reaction.
CONCLUSIONS
This work has investigated the reaction conditions and kinetic parameters
of slurry process for the metallocene PE process. How various reactionparameters affect the catalyst activity and the molecular weight is also exactly
studied. A gel-effect modification on the polymerization kinetic model is also
proposed to explain the variation of molecular weight during the polymerization
reaction.
Experimental results indicate that the yield of polymerization product
increases with ethylene pressure, reaction time, and catalyst concentration, and
the Al/Ti ratio. Moreover, the molecular weight of a polymer product decreases
with an increase in the weight fraction of polymer in the reaction slurry, possibly
owing to the gel-effect parameter of a chain-propagation reaction.
The polymerization kinetic scheme used in this study is highly promising
for attempts to simulate the catalyst activity under various operating conditions.
Kinetic simulation is highly effective for optimizing process design and scaling
up reactors.
Figure 10. Effect of Al/Ti ratio on the Mn of PE. (Exp: experimental results, Gel: gel-
effect model results, 2 Sites: 2-sites model results.)
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NOTATION
Act catalyst activity (g-polymer/g-Cat.)
C* activated catalyst conc. (mol/L)
Cat catalyst conc. (mol/L)
ka kinetic constant of catalyst activation (1/mol/sec)
ki kinetic constant chain initiation (1/mol/sec)
kp kinetic constant of propagation (1/mol/sec)
ktrm kinetic constant chain transfer (1/mol/sec)
kd kinetic constant catalyst deactivation (1/mol/sec)
M monomer conc. (mol/L)
MAO methylalumonxane conc. (mol/L)
MWD molecular weight distributionMn number averaged molecular weight (g/mol)
Mw weight averaged molecular weight (g/mol)
P living polymer chain conc. (mol/L)
p probability of propagation
R dead polymer chain conc. (mol/L)
Q dead polymer chain conc. (mol/L)
Rtrm rate of chain initiation (1/sec)
Rp rate of chain transfer (1/sec)
Rp rate of propagation (1/sec)
wi weight of object function
wi weight or object function
ACKNOWLEDGMENTS
The authors would like to thank the Ministry of Economic Affairs, Taiwan,
and R.O.C. for financially supporting this research.
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