Polymerization Kinetics and Modeling of Slurry

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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)


3/19

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

YOUNG AND MA602


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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


5/19

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

YOUNG AND MA604


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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



7/19

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

YOUNG AND MA606


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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



9/19

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.

YOUNG AND MA608


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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.



11/19

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

YOUNG AND MA610


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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.)



13/19

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

YOUNG AND MA612


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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.)



15/19

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.)

YOUNG AND MA614


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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,


Figure 9. Effect of Al/Ti ratio on the PE catalyst activity. (Exp: experimental results,




17/19

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.)

YOUNG AND MA616


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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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Polymerization Kinetics and Modeling of Slurry