kinetic modeling and simulation of metallocene catalyzed...

Kinetic Modeling and Simulation of Metallocene

Catalyzed Olefin Polymerization

THESIS

Submitted in the partial fulfillment of the

requirements for the degree of

DOCTOR OF PHILOSOPHY

by

NIKHIL PRAKASH

Under the Supervision of

Dr Arvind Kumar Sharma

and

Dr Sushil Kumar

BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE (BITS), PILANI

Pilani Campus, Rajasthan, India

2013

DEDICATED

To

My Parents, Wife & Daughter

iv

ACKNOWLEDGEMENTS

It gives me a deep sense of gratitude and an immense pleasure to sincerely thank my

supervisor Dr Arvind Kumar Sharma Assistant Professor, Chemical Engineering

Department (BITS-Pilani, Pilani campus) and co-supervisor Dr Sushil Kumar, Assistant

Professor, Chemical Engineering Department (MNNIT, Allahabad) for their constant

encouragement, constructive and valuable suggestions, and moral support throughout the

period of this research work. It has been a privilege for me to work under their valuable

guidance.

I thank the members of Doctoral Advisory Committee, Dr Pratik N. Sheth, Assistant

Professor, Chemical Engineering Department, and Dr Smita Raghuvanshi, Assistant

Professor, Chemical Engineering Department (BITS-Pilani, Pilani campus) for their

support and suggestions to carry out this work effectively.

My sincere thanks go to Prof B N Jain, Vice-Chancellor, BITS-Pilani for giving me the

opportunity to carry out the PhD work in BITS-Pilani. I am thankful to Prof G

Raghurama, Director (Pilani Campus), Prof. Sanjeev K Aggarwal, Director (Goa

Campus), Prof V S Rao, Director (Hyderabad Campus), Prof R K Mittal, Director, (Dubai

Campus), Prof R N Saha, Deputy Director (Pilani Campus), Prof S K Verma, Dean,

Academic Research Division (PhD Programme), Dr H R Jadhav, Professor-in-charge,

Academic Research Division (PhD Programme) for providing the necessary facilities and

infrastructure to carry out this work.

I extend my sincere thanks to Prof R P Vaid, Prof T N S Mathur, Prof B R Natrajan, Prof

B V Babu, Prof A K Sarkar and Prof B B Gulyani for their motivation with affectionate

enquiries about the status of my PhD work.

I extend my special thanks to Dr Suresh Gupta, Head (Chemical Engineering

Department), Dr Harekrishna Mohanta, Convener (Departmental Research Comittee), Dr

Pradipta Chattopadhaya, Mr Amit Jain, Mr Ajaya K Pani, Ms Priya C Sande, Mr Utkarsh

Maheshwari, Mr Subhajit Majumder, Dr Banasri Roy and Dr Sonal Majumder of

v

Chemical Engineering Department for their valuable advice and moral support throughout

the work.

I would like to express the earnest appreciation to Dr Ashish M Gujrathi, Dr Saptarshi

Chatopadyay and Mr Basheer Ahmed for their contribution in stimulating suggestions

and encouragement.

I would also take this opportunity to thank Mr Babu Lal Saini, Mr Jangvir, Mr Ashok

Saini, Mr Jeevan Verma and Mr Subodh Kumar Azad for their good wishes and

cooperation during my PhD work.

I would also like to convey my special thanks to all my students, for extending their

constant support in various ways.

This work could not have been completed without the moral support I got from my loving

parents Mr Dhwaj Prakash Saxena and Mrs Madhvi Saxena, in-laws Dr Subhash Chand

Jauhari and Mrs Neerja Jauhari, my dear sister Mrs Tulika Saxena and my loving wife

Dr Shikha Jauhari. Their unconditional love, constant encouragement, moral support and

immense confidence in me made this work possible. I would like to express my love and

affections to my daughter Vedanshi Saxena for being cheerful all the way and

surprisingly understanding at such a little age.

Thanks are due, to my computing machines (Laptop and Desktop) for being incessant

companion of mine till today and for running day and night during simulation studies

without a single failure or crash.

Last but not the least, I pray and thank to almighty God for showering His blessings and

giving me the inner strength and patience.

NIKHIL PRAKASH

vi

ABSTRACT

Metallocene catalyst system refers to the combination of bis(cyclopentadienyl)metal

complexes of Group 4 (IVB) or cyclopentadienyl-substituted derivatives thereof, and a

cocatalyst, typically methylalumoxane (MAO). Metallocene catalysts have in general

demonstrated high productivity, narrow molecular weight distribution (MWD), greater

efficiency in using comonomer to reduce the density, capability of producing polymer

with varying molecular weights and controlled stereoregularity.

Metallocene based catalyst technology is expected to revolutionize the polyolefin

industry immensely, particularly in polyethylene and polypropylene markets. Metallocene

polyolefins are projected to penetrate a broad array of polymer markets. First with the

higher priced specialty markets, followed by the high volume and commodity markets.

New markets are also expected to be created with the development of new classes of

polymer those are not possible with conventional Ziegler-Natta technologies.

In the present work, the mechanistic aspects of Ziegler-Natta and metallocene

catalyst systems have been studied in detail and used in building up mathematical models

for α-olefin polymerization using metallocene catalysts. Based on the interpretations of

mechanisms for metallocene-catalyzed polymerization, an ecumenical reaction set for

ethylene and propylene polymerization that includes reactions corresponding to all types

of metallocenes is proposed. Thereafter, mathematical models for ethylene and α-olefin

polymerization in a batch/semi-batch/constant-stirred-tank reactor are built up. The

models developed are capable of predicting polymerization kinetics and polymer

properties (viz. number-average- & weight-average molecular weights and polydispersity

index) in general. In addition, mole fraction of dead polymer chains with terminal double

bond and density of long-chain branches & short-chain branches may be determined with

ethylene polymerization model. Fraction of vinyl-terminated chains, butenyl-terminated

chains, isobutyl-terminated chains and vinylidene-terminated chains relative to the total

unsaturated termination may be determined with propylene polymerization model.

Model equations developed include a set of coupled, nonlinear and stiff ordinary

differential equations (ODEs) for the dynamic polymerization. To estimate the kinetic

parameters and to study the effect of parameters, model ODEs are solved with ODE-15s

function provided MATLAB™

7.0.1 software.

In this study, a novel natural logarithmic differential evolution (NLDE) approach

of optimization, a remediated edition of original differential evolution algorithm is

proposed and used to solve parameter estimation problem. Proposed NLDE algorithm is

capable of handing multiple objective functions simultaneously, providing room to admit

objective functions based on polymerization rate, molecular weights, PDI, fraction of

dead polymer chains with terminal double bond, fraction of vinyl-terminated chains,

butenyl-terminated chains, isobutyl-terminated chains and vinylidene-terminated chains

etc. if experimental data are available.

vii

Ethylene polymerization model is applied to gas phase polymerization with silica

supported, bridged Me2Si[Ind]2ZrCl2 catalyst and to solution phase polymerization with

in-situ-silica supported, bridged Et[Ind]2ZrCl2 catalyst and MAO. Propylene

polymerization model is applied to the solution phase production of polypropylene

catalyzed with Me2Si[Ind]2ZrCl2, Et(Ind)2ZrCl2, Me2Si(Ind)2HfCl2, Et(Ind)2HfCl2, (2,4,6-

Me3Ind)2ZrCl2, (2,4,7-Me3Ind)2ZrCl2 and Me2Si[2,4,6-Me3Ind]2ZrCl2 catalyst and MAO.

Models are validated with experimental data available in open literature and

model kinetic parameters are estimated for each catalytic system. Further, parametric

study is carried out for all the polymerization systems in order to examine the effect of

variation in monomer pressure (concentration), polymerization temperature, initial

amount of catalyst and cocatalyst to catalyst mole ratio on polymerization kinetics and

macro- and microstructural properties of polymer.

Set of kinetic parameters determined is catalyst dependent and unique. In general,

it was found that chain initiation, propagation and spontaneous catalyst deactivation are

the essential reactions in olefin polymerization and strongly affect the polymerization

kinetics. Various termination reactions are dependent on actual polymerization process

employed and reaction conditions. Termination reactions are found to affect molecular

weight distribution and microstructural properties of the final product in different ways.

Keywords:

Modeling and simulation; Mechanism; Metallocene; Polymerization; Gas phase;

Solution phase; Ethylene; Propylene; Natural logarithmic differential evolution;

Optimization; Estimation; Kinetic parameters; Kinetics; Microstructural properties.

viii

TABLE OF CONTENTS

Certificate iii

Acknowledgements iv

Abstract vi

Table of Contents viii

List of Figures xi

List of Tables xvi

Nomenclature xvii

1. Introduction 1

1.1 Motivation 1

1.1.1 Metallocene catalyst systems 3

1.1.2 Evolution of the metallocenes 4

1.1.3 Mathematical modeling and simulation 6

1.2 Objectives of research 8

1.3 Organization of thesis 9

2. Literature Review 10 2.1 Ziegler-Natta polymerization 10

2.1.1 Ziegler-Natta catalysts 11

2.1.2 Mechanism of Ziegler-Natta polymerization 11

2.2 Metallocene polymerization 15

2.2.1 Metallocenes catalyst system 16

Metallocenes in ethylene polymerization 20

Metallocenes in propylene polymerization 20

2.2.2 Mechanism of metallocene polymerization 24

Mechanism for activation 24

Mechanisms for propagation 26

Mechanisms for termination 30

2.3 Experimental studies 33

2.4 Mechanistic, modeling & simulation studies 49

2.5 Gaps in research 59

2.6 Scope of the work 59

3. Mathematical Model Development and Simulation 61

3.1 Metallocene polymerization kinetics and model development 62

3.1.1 Mathematical treatment of polymerization kinetics 62

3.2 Modeling of ethylene polymerization 65

3.2.1 Kinetics 65

3.2.2 Model development for ethylene polymerization 70

3.3 Modeling of propylene polymerization 75

3.3.1 Kinetics 75

3.3.2 Model development for propylene polymerization 81

3.4 Simulation methodology 86

3.4.1 Numerical solution procedure 87

3.4.2 Objective function formulation 88

3.4.3 Optimization approach 91

3.4.3.1 Differential evolution 92

Natural logarithmic differential evolution 93

ix

Summary of the chapter 97

4. Results and Discussion 98 4.1 Ethylene polymerization 101

4.1.1 Ethylene polymerization with Me2Si[Ind]2ZrCl2/MAO 101 Estimated parameters and effect of temperature 103

Effect of ethylene pressure 105 Effect of catalyst amount 110

4.1.2 Ethylene polymerization with in-situ-supported Et[Ind]2ZrCl2/MAO 112 Estimated parameters and effect of temperature 113

Effect of ethylene pressure 117 Effect of catalyst amount 117

Effect of cocatalyst to catalyst mole ratio 117

Polyethylene properties 121

4.2 Propylene polymerization 124

4.2.1 Propylene polymerization with Me2Si[Ind]2ZrCl2/MAO 126 Estimated parameters and effect of temperature 126

Effect of pressure 135

Effect of catalyst concentration 138

4.2.2 Propylene polymerization with Et[Ind]2ZrCl2/MAO 140 Estimated parameters and effect of temperature 140 Effect of pressure 147


4.2.3 Propylene polymerization with Me2Si[Ind]2HfCl2/MAO 153 Estimated parameters and effect of temperature 153 Effect of pressure 160


4.2.4 Propylene polymerization with Et[Ind]2HfCl2/MAO 166 Estimated parameters and effect of temperature 166 Effect of pressure 174


4.2.5 Propylene polymerization with [2,4,6-Me3Ind]2ZrCl2/MAO 179 Estimated parameters and effect of temperature 179



4.2.6 Propylene polymerization with [2,4,7-Me3Ind]2ZrCl2/MAO 188

Estimated parameters and effect of Al/Zr mole ratio 188



4.2.7 Propylene polymerization with Me2Si[2,4,6-Me3Ind]2ZrCl2/MAO 197

Estimated parameters and effect of temperature 197



Summary of the chapter 208

5. Concluding Remarks 209

5.1 Summary 209

5.1.1 Introduction 209

5.1.2 Gaps in research 211

5.1.3 Scope of the work 211

5.1.4 Model development and simulation 212

5.1.5 Results and discussion 214

x

5.2 Conclusions 228

5.3 Major contributions 234

5.4 Future scope of research 235

References 236

List of Publications 251

Appendix I: Code in MATLAB to Estimate the Kinetic Parameters

in Ethylene Polymerization with Me2Si[Ind]2ZrCl2/MAO 255

Appendix II: Code in MATLAB to Estimate the Kinetic Parameters

in Ethylene Polymerization in-situ-supported-

Et[Ind]2ZrCl2/MAO 264

Appendix III: Code in MATLAB to Estimate the Kinetic Parameters

in Propylene Polymerization with Me2Si[Ind]2ZrCl2/MAO 275

Biographies 287

xi

LIST OF FIGURES

Figure

No.

Title

Page

No.

1.1 Generic structure of metallocene catalyst. 5

1.2 Various ligands of metallocene. 5

2.1 Bimetallic mechanism of Z-N polymerization by Natta. 12

2.2 Bimetallic mechanism of Z-N polymerization by Patat and Sinn. 12

2.3 Monometallic mechanism of Z-N polymerization by Cossee. 13

2.4 Trigger mechanism of Z-N polymerization by Ystenes. 13

2.5 Chain termination by β-H transfer to monomer (β-H elimination). 14

2.6 Chain termination by spontaneous intramolecular β-H transfer. 14

2.7 Chain termination by molecular hydrogen. 14

2.8 Chain termination to the Group I-III metal alkyl. 14

2.9 Partial hydrolysis of trimethylaluminum to form MAO. 17

2.10 (a) Linear and (b) cyclic structures of MAO

(c) two-dimensional ladder and (d) three-dimensional cage structures

of MAO oligomers.

17

2.11 (a) Chain-end and (b) enantiomorphic site mechanisms of

stereocontrol.

18

2.12 Unbridged (a) and bridged (b) catalysts used in ethylene

polymerization.

22

2.13 General symmetry classifications. 23

2.14 General metallocene symmetry classifications. 23

2.15 Activation of a metallocene complex by methylaluminoxane (MAO).

M = transition metal atom and □ = vacant coordination site

25

2.16 Cossee-Arlman mechanism of propagation with a metallocene

catalyst.

28

2.17 Green-Rooney mechanism of propagation with a metallocene catalyst. 28

2.18 Modified Green-Rooney mechanism of propagation with a

metallocene catalyst.

29

2.19 Transition state α-agostic mechanism of propagation with a

metallocene catalyst

29

2.20 β-Hydrogen transfer to monomer. 32

2.21 β-hydrogen elimination (Spontaneous chain transfer). 32

2.22 β-methyl elimination (Spontaneous chain transfer). 32

2.23 Chain transfer to cocatalyst. 32

3.1 Determination of population for sequent generation in DE. 94

3.2 Flow sheet: Differential evolution optimization procedure. 95

4.1 Ethylene polymerization rate vs. time with Me2Si[Ind]2ZrCl2

(E1)/MAO.

[Catalyst (E1) = 0.2 g; P = 5 bar; Al/Zr = 386]

104

4.2 Polymerization rate vs. time: Effect of pressure.

[Catalyst (E1) = 0.2 g, Al/Zr = 386, T = (a) 50 °C, (b) 60 °C,

(c) 70 °C]

108

4.3 Effect of pressure on average molecular weights.

[Catalyst (E1) = 0.2 g, Al/Zr = 386, T = (a) 50 °C, (b) 60 °C,

(c) 70 °C]

110

xii

4.4 Polymerization rate vs. time: Effect of catalyst amount.

[P = 5 bar, Al/Zr = 386, T = (a) 50 °C, (b) 60 °C, (c) 70 °C]

112

4.5 Effect of temperature on ethylene polymerization rate with in-situ-

supported Et[Ind]2ZrCl2 (E2)/MAO.

[Catalyst (E2) = 6 μmol, Al/Zr = 500 and P = 80 psig]

116

4.6 Active catalyst sites vs. reaction time.


116

4.7 Effect of pressure on ethylene polymerization rate.

[Catalyst (E2) = 6 μmol, Al/Zr = 500 and 60 °C]

118

4.8 Active catalyst sites vs. reaction time


118

4.9 Effect of catalyst amount on ethylene polymerization rate.

[Al/Zr = 500, 60 °C, and 80 psig]

119

4.10 Active catalyst sites vs. reaction time.

[Al/Zr = 500, 60 °C and 80 psig]

119

4.11 Effect of Al/Zr mole ratio on ethylene polymerization rate.

[Catalyst (E2) = 6 μmol, 60 °C and 80 psig]

120

4.12 Active catalyst sites vs. reaction time

[Catalyst (E2) = 6 μmol, 60 °C and 80 psig]

120

4.13 Effect of Al/Zr mole ratio on propylene polymerization rate.

[Catalyst (P1) = 10 μM, T = 25 °C and P = 30 psi]

128



128

4.15 Effect of temperature on propylene polymerization rate.

[Catalyst (P1) = 10 μM, Al/Zr = 500 and P = 30 psi]

129

4.16 Active catalyst site concentration vs. time.

[Catalyst (P1) = 10 μM, Al/Zr = 500, 75 °C and 30 psi]

131

4.17 Hydride actived complex concentration vs. time.

[Catalyst (P1) = 10 μM, Al/Zr = 500, T = 25 °C and P = 30 psi]

132

4.18 Hydride activated complex concentration vs. time.


132

4.19 Methyl activated complex concentration vs. time.


133


[Catalyst (P1) = 10 μM, Al/Zr = 500, and T = 25 °C]

136


[Catalyst (P1) = 10 μM, Al/Zr = 500 and T = 75 °C]

136



137

4.23 Effect of pressure on average molecular weights


137

4.24 Polymerization rate vs. time: Effect of catalyst concentration.

[Al/Zr = 500, T = 25 °C and P = 30 psi]

138


[Al/Zr = 500, T = 75 °C and P = 30 psi]

139

4.26 Effect of catalyst concentration on average molecular weights.

[Al/Zr = 500, T = 25 °C and P = 30 psi]

139


[Al/Zr = 500, T = 75 °C and P = 30 psi]

140

4.28 Polymerization rate vs. time.


142

xiii

4.29 Polymerization rate vs. time.


142



144



145



145

4.33 Methyl actived complex concentration vs. time.


146



148


[Catalyst (P2) = 10 μM, Al/Zr = 500 and 75 °C]

149



149



150


[Al/Zr = 2000, T = 25 °C and P = 30 psi]

151


[Al/Zr = 500, T = 75 °C and P = 30 psi]

151


[Al/Zr = 2000, T = 25 °C and P = 30 psi]

152


[Al/Zr = 500, T = 75 °C and P = 30 psi]

152

4.42 Effect of Al/Hf mole ratio on propylene polymerization rate.


155



156


[Catalyst (P3) = 10 μM, Al/Hf = 2000 and P = 30 psi]

156



157


[Catalyst (P3) = 10 μM, Al/Hf = 2000, T = 40 °C and P = 30 psi]

158



159


[Catalyst (P3) = 10 μM, Al/Hf = 2000 and T = 40 °C]

161



161



162



162


[Al/Hf = 2000, T = 40 °C and P = 30 psi]

164


[Al/Hf = 2000, T = 80 °C and P = 30 psi]

164


[Al/Hf = 2000, T = 40 °C and P = 30 psi]

165

xiv


[Al/Hf = 2000, T = 80 °C and P = 30 psi]

165



167



167



170



170



171



172



172



175



175



176



176


[Al/Hf = 500, T = 40 °C and P = 30 psi]

177


[Al/Hf = 500, T = 80 °C and P = 30 psi]

178


[Al/Hf = 500, T = 40 °C and P = 30 psi]

178


[Al/Hf = 500, T = 80 °C and P = 30 psi]

179


[Catalyst (P5) = 20 μM, T = 0 °C and P = 0.98 atm]

180


[Catalyst (P5) = 20 μM, Al/Zr = 2000, T = 0 °C and P = 0.98 atm]

182



183



183



185



186


[Al/Zr = 2000, T = 0 °C and P = 0.98 atm]

187


[Al/Zr = 2000, T = 0 °C and P = 0.98 atm]

187



189



192

xv



192



193



195



195


[Al/Zr = 2000, T = 0 °C and P = 0.98 atm]

196


[Al/Zr = 2000, T = 0 °C and P = 0.98 atm]

197

4.87 Effect of temperature on propylene polymerization rate.

[Catalyst (P7) = 20 μM, Al/Zr = 2000 and P = 0.98 atm]

199



201

4.89 Hydride actived complex concentration vs. time. (a) 30 °C, (b) 70 °C


202



204



204



205



205


[Al/Zr = 2000, T = 30 °C and P = 0.98 atm]

206


[Al/Zr = 2000, T = 70 °C and P = 0.98 atm]

207


[Al/Zr = 2000, T = 30 °C and P = 0.98 atm]

207


[Al/Zr = 2000, T = 70 °C and P = 0.98 atm]

208

xvi

LIST OF TABLES

Table

No.

Title

Page

No.

1.1 World Commodity Polymers Consumption Estimate 2

1.2 Scales of Modeling Polyolefin Processes 7

2.1 Generations of Ziegler-Natta Catalyst 11

2.2 Representative Examples of Metallocenes 19

2.3 Metallocene Catalyst Systems 20

2.4 Metallocene Catalyzed Ethylene Polymerization, Experimental Studies 40

2.5 Metallocene Catalyzed Propylene Polymerization, Experimental

Studies

45

2.6 Metallocene Catalyzed Olefin Polymerization, Mechanistic, Modeling

& Simulation Studies

55

3.1 Reactions Conceived in Ethylene Polymerization 69

3.2 Reactions Conceived in Propylene Polymerization 80

4.1 Sections discussing results of ethylene polymerization 100

4.2 Sections discussing results of propylene polymerization 100

4.3 Reactions Considered in Ethylene Polymerization 102

4.4 Estimated Parameters for Me2Si[Ind]2ZrCl2 (E1)/MAO 106

4.5 Predicted Molecular Weights & PDI with Me2Si[Ind]2ZrCl2 (E1)/MAO 106

4.6 Reactions Considered in Ethylene Polymerization 114

4.7 Estimated Parameters for Et[Ind]2ZrCl2 (E2)/MAO 115

4.8 Polyethylene Properties with Et[Ind]2ZrCl2 (E2)/MAO 122

4.9 Reactions Considered in Propylene Polymerization 125

4.10 Estimated Parameters for Me2Si[Ind]2ZrCl2 (P1)/MAO 130

4.11 Predicted Properties with Me2Si[Ind]2ZrCl2 (P1)/MAO 130

4.12 Estimated Parameters for Et(Ind)2ZrCl2 (P2)/MAO 143

4.13 Predicted Polypropylene Properties with Et(Ind)2ZrCl2 (P2)/MAO 143

4.14 Estimated Parameters for Me2Si (Ind)2HfCl2 (P3)/MAO 154

4.15 Predicted Properties with Me2Si (Ind)2HfCl2 (P3)/MAO 155

4.16 Estimated Parameters for Et(Ind)2HfCl2 (P4)/MAO 169

4.17 Predicted Properties with Et(Ind)2HfCl2 (P4)/MAO 169

4.18 Estimated Parameters for [2,4,6-Me3Ind]2ZrCl2 (P5)/MAO 181

4.19 Predicted Properties with [2,4,6-Me3Ind]2ZrCl2 (P5)/MAO 181

4.20 Estimated Parameters for [2,4,7-Me3Ind]2ZrCl2) (P6)/MAO 190

4.21 Predicted Properties with [2,4,7-Me3Ind]2ZrCl2) (P6)/MAO 190

4.22 Estimated Parameters for Me2Si[2,4,6-Me3Ind]2ZrCl2) (P7)/MAO 200

4.23 Predicted Properties with Me2Si[2,4,6-Me3Ind]2ZrCl2) (P7)/MAO 200

xvii

NOMENCLATURE

Cat Catalyst (-)

Cocat Cocatalyst (-)

Cp Cyclopentadienyl (-)

CR Cross over frequency in DE (-)

)(iD Dead polymer chain containing i segments (-)

)(iD

Dead polymer chain detached from the catalyst (-)

nDP Number average degree of polymerization (-)

wDP Weight average of degree of polymerization (-)

f Mole fraction of dead polymer chains with terminal double bond (-)

F Weighing factor (-)

)(kF Rate based objective function (-)

)(kG Molecular weight based objective function (-)

)(kH Microstructure based objective function (-)

ka Rate constant for catalyst activation (L.mol-1

.s-1

)

kin Rate constant for chain initiation (L.mol-1

.s-1

)

kp Rate constant for chain propagation (L.mol-1

.s-1

)

kd Rate constant for spontaneous catalyst deactivation (s-1

)

ktH Rate constant for chain transfer to hydrogen (L.mol-1

.s-1

)

ktCo Rate constant for chain transfer to cocatalyst (L.mol-1

.s-1

)

kβ Rate constant for β-hydride elimination (s-1

)

klcb Rate constant for incorporation of polymer chains with terminal

double bonds

(L.mol-1

.s-1

)

ktM Rate constant for chain transfer to monomer (L.mol-1

.s-1

)

kscb Rate constant for short chain branching (s-1

)

kβ,H Rate constant for spontaneous chain transfer to catalyst (s-1

)

rk

Rate constant for reinitiation after chain transfer to catalyst (L.mol-1

.s-1

)

kβ,Me Rate constant for β-methyl elimination (s-1

)

ks Rate constant for secondary insertion (L.mol-1

.s-1

)

ksp Rate constant for propagation after secondary insertion (L.mol-1

.s-1

)

ksM Rate constant for transfer to monomer after secondary insertion (L.mol-1

.s-1

)

ktAl Rate constant for transfer to cocatalyst (L.mol-1

.s-1

)

krAl Rate constant for reactivation after transfer to cocatalyst (L.mol-1

.s-1

)

Em Molar mass of ethylene (g/mol)

SRUm

Molecular weight of the structural repeat unit (g/mol)

M Monomer (-)

nM Number average molecular weight (g/mol)

wM Weight average molecular weight (g/mol)

NP Number of population in DE (-)

P Pressure (atm, bar)

0P Active catalyst site capable of polymerization (-)

xviii

iP Polymer chain attached to a catalyst site containing i monomer

segment

(-)

0*

HP Hydride activated complex (-)

0*

MeP Methyl activated complex (-)

0dP

Deactivated catalyst (-)

A

nP

Active site of type A with a growing polymer chain of length n (-)

)(iR Secondary inserted chains (-)

Rp,max Maximum polymerization rate (mol/L/s)

t Time (sec, min)

T Temperature (°C)

rV

reactor volume (m3)

X Halogen (-)

Greek Symbols l

n n

th moment of the molecular weight distribution of live chains

attached to catalyst site

n n

th moment of the molecular weight distribution of dead chains

n n

th moment of the molecular weight distribution of dead chains

with terminal double bond

m

n n

th moment of the molecular weight distribution of secondary

inserted chains

v0 Zeroth moment for vinylidene-terminated dead chains

'0 v

Zeroth moment for vinyl-terminated dead chains

b0 Zeroth moment for butenyl-terminated dead chains

i0 Zeroth moment for isobutyl-terminated dead chains

E Density of ethylene

Abbreviations

ACO Ant colony optimization

ADM Advection dispersion model

ANN Artificial neural network

a-PP Atactic polypropylene

CAGR Compound annual growth rate

CGC Constrained geometry catalyst

CLD Chain length distribution

CSTR Constant stirred tank reactor

DE Differential evolution

DGM Dusty gas model

Et Ethyl

Flu Fluxional

GA Genetic algorithm

Ind Indenyl

i-PP Isotactic polypropylene

LCB Long chain branching

MAO Methyl aluminoxane

Me Methyl

xix

MGM Multi grain model

mPE Metallocene polyethylene

MW Molecular weight

MWD Molecular weight distribution

NLDE Natural logarithmic differential evolution

PDI Poly dispersity index

PE Polyethylene

PFFDM Polymeric flow Fick's diffusion model

PFM Polymeric flow model

PP Polypropylene

PSO Particle swarm optimization

SA Simulated annealing

SANS Small angle neutron scattering

SCB Short chain branching

TIBA Tri-isobutyl-aluminium

TMA Triethylaluminium

Y Yield

Z-N Ziegler Natta

1

CHAPTER – 1

INTRODUCTION

1.1 Motivation

Polyolefins are the largest group of thermoplastics, often referred to as commodity

thermoplastics, these are polymers of olefins such as ethylene, propylene, butenes, isoprene, and

pentenes, and their copolymers. Polyolefins consist only of carbon and hydrogen atoms and are

non-aromatic. Two most important commodity polyolefins are polyethylene and polypropylene

and they are very popular due to their low cost and wide range of applications.

The term polyethylene (PE) describes a huge family of resins obtained by polymerizing

ethylene gas, CH2=CH2, and it is by far the largest volume commercial polymer. This

thermoplastic is available in a range of flexibilities and other properties depending on the

production process, with high density materials being the most rigid. Polyethylene can be formed

by a wide variety of thermoplastic processing methods and is particularly useful where moisture

resistance at low cost is required. Low density polyethylene typically has a density value ranging

from 0.91 to 0.925 g/cm³, linear low density polyethylene is in the range of 0.918 to 0.94 g/cm³,

while high density polyethylene ranges from 0.935 to 0.96 g/cm³ and above (Odian, 2004).

Polyethylene finds variety of applications in aerospace and automotive applications, batteries,

bearings, building materials, blending, bags, containers, coating, compounding, cosmetics,

membrane, medical/healthcare applications, prosthetics, packaging and irrigation etc.

Polypropylene (PP) is produced by polymerizing propylene with suitable catalysts.

Polypropylene has demonstrated certain advantages in improved strength, stiffness and higher

temperature capability over polyethylene. Polypropylene has been successfully applied to the

2

forming of fibers due to its good specific strength and is one of the lightest plastics available

with a density of 0.905 g/cm3. Polypropylene is used in aerospace and automotive applications,

bags, batteries, bottles, coating, computer components and data storage, microwave cookware,

cosmetics, eyeglasses, films, fibers, fuel tanks, insulation, medical applications, membrane,

food/medical/pharmaceutical packaging, solar panels, tapes, tableware/disposables, sealants etc

(http://www.ides.com; 26_Dec_2012).

Polyethylene and polypropylene are increasingly replacing other materials because of

their versatile properties, low cost, reduced environmental impact, and easy recycling.

World commodity polymers consumption is estimated to reach 214 million tonnes by

2015, with polyethylene and polypropylene accounting for the largest share. An estimate of

compound annual growth rate (CAGR) of commodity polymers during 2011-2015 is given in

Table 1.1 (http://www.icis.com; 27/Dec/2012).

Table 1.1 World Commodity Polymers Consumption Estimate

Compound Annual Growth Rate (CAGR) [% / year]

2011 - 2015

Polyethylene

4.5

Polypropylene

5.8

Polyvinyl chloride

4.2

Polystyrene

2.9

Metallocene catalyzed olefin polymerization has recently attracted research interest since

these catalysts allow the production of tailored macromolecules with properties those can be

accurately designed. A broad spectrum of properties and applications of the polyolefins can be

3

attained with metallocenes due to their single types of sites. Kinetic studies of catalytic

polymerization provide considerable insight into the mechanism of the reactions and scale-up or

commercialization of a polymerization process staggeringly depends on the understanding of the

kinetic behavior of the system under various operating conditions.

1.1.1 Metallocene catalyst systems

Metallocenes belong to a relatively old class of organometallic complexes, with ferrocene being

the first discovered in 1951 (Kauffman, 1983). At that time the term metallocene was used to

describe a complex with a metal sandwiched between two η5-cyclopentadienyl (Cp) ligands.

Since the discovery of ferrocene, a large number of metallocenes have been prepared and the

term has evolved to include a wide variety of organometallic structures including those with

substituted Cp rings, those with bent sandwich structures, and even the half-sandwich or mono-

Cp complexes. Metallocene catalyst system refers to the combination of

bis(cyclopentadienyl)metal complexes of Group 4 (IVB) [especially zirconium, titanium and

hafnium], or cyclopentadienyl-substituted derivatives thereof, and a cocatalyst, typically

methylalumoxane (MAO). Titanocene and zirconocene dichlorides were the first metallocenes

studied (Natta et al. 1957(a), Breslow and Newburg, 1957).

A generic structure of metallocene catalyst is shown in Figure 1.1. Where M is the

transition metal of group IV, normally Zr, Ti and Hf, A is the optional bridging atom usually Si

or C. R is a σ – homoleptic (a metal compound with all ligands identical) hydrocarbyl such as H,

alkyl or other hydro groups and X is chlorine or other halogen from group VII A or an alkyl

group. The simplest metallocene precursor has the formula Cp2MX2.

4

Many variants of metallocenes are also available with different ligands. The most studied ligands

are η5-cyclopentadienyl (Cp) and various substituted cyclopentadienyls, including alkyl-

substituted η5-cyclopentadienyls, 1-indenyl (Ind), 4,5,6,7-tetrahydro-1-indenyl (H4Ind), and 9-

fluorenyl (Flu) ligands as shown in Figure 1.2 (Odian, 2004).

MAO is an oligomeric compound described by the formula (CH3AlO)n, structure of

which is not yet fully understood. MAO plays several roles: it alkylates the metallocene

precursor by replacing halogen atoms with methyl groups; it produces the catalytic active ion

pair Cp2MCH3+/MAO

−, where the cationic moiety is considered responsible for polymerization

and MAO− acts as weakly coordinating anion.

1.1.2 Evolution of the metallocenes

The first step towards controlled polyolefin polymerization was taken by Karl Ziegler and his

group in 1953 (Ziegler, 1963). While investigating ethylene oligomerization in the presence of

aluminium alkyls, they discovered that transition metal compounds were efficient catalysts. In

the presence of aluminium alkyl activators, zirconium and titanium halides catalyzed the

polyinsertion process, which yielded high molecular weight and high density linear polyethylene.

One year later Natta introduced the process of stereoselective α-olefin and diene polymerization.

The discovery of Ziegler-Natta catalysts together with Phillips-type (activator-alkyl-free

SiO2/CrO3) catalysts initiated a rapid growth of polyolefin technology and the production of

polyolefin materials exhibiting a broad range of properties. In 1963, Ziegler and Natta were

awarded the Nobel prize in chemistry (Tynys, 2007).

The polymerization of ethylene with a single-site, metallocene-type catalyst was reported

for the first time in 1957. Initially, these catalysts showed very low polymerization activity due

5

to the cocatalyst employed [Et2AlCl or Et3Al] (Natta et al., 1957(b), Breslow and Newburg,

1957).

AR

R

R

R

RR

X

X

M

M

X

X

Figure 1.1 Generic structure of metallocene catalyst.

CH•

Indenyl

CH•

tetrahydroIndenyl

H•C

fluorenyl

Figure 1.2 Various ligands of metallocene.

In 1973, Reichert and Meyer reported that small amount of water, remarkably improved

the activity of the catalyst system Cp2TiEtCl/EtAlCl2. They proposed a stabilized catalyst

complex resulting from an increase in Lewis acidity (Reichert and Meyer, 1973). Prior to this

water was considered to be a catalyst poison. Next important step was made using racemic

ethylene-bis(4,5,6,7-tetrahydro-l-indenyl)titanium dichloride synthesized by Wild et al. in 1982

for stereospecific polymerization of propene.

6

Ewen et al. in 1988 synthesized a Cs-symmetric zirconocene ([Me2C(Flu)(Cp)]ZrCl2)

capable of producing crystalline syndiotactic polypropylene in high yields at conventional

polymerization conditions.

Since late 1980s, a worldwide, industrial and academic research & development in the

field of metallocene catalysts has been continued.

1.1.3 Mathematical modeling and simulation

Many problems encountered in industrial polymerization processes are associated with inherent

complexities in polymerization kinetics and mechanisms, physical changes and transport effects

(e.g., viscosity increase, particle formation, precipitation, interfacial mass and heat transfer

limitations), non-ideal mixing and conveying, and strong process nonlinearity (potential thermal

runaway, limit cycles, multiple steady states).

Models in polymer reaction engineering involve phenomena at different scales, which

can be classified as macro-; meso- and microscale (Ray, 1988; McKenna and Soares, 2001). The

features of various scales of modeling are presented in Table 1.2.

In the recent yesteryears, modeling of polymerization processes has become more

demanding. Success of meso- and macro-level models greatly relies upon the understandings at

micro-level. Detailed physical properties and thermodynamic data on the partitioning of species

among phases are required to quantify the concentrations of reactants at the loci of

polymerization and valid kinetic rate constants are required for calculating rates and polymer

properties. Rate constants are related to the structure of reactants used in polymerization which

render the effective use of process models in state estimation and control.

7

Table 1.2 Scales of Modeling Polyolefin Processes

Scale Feature

Macroscale (> 1 m) Detailed description of reactor hydrodynamics in order to model

mixing and reactor stability, reactor and particle size distributions,

particle entrainment, etc.

Mesoscale (> 10−3–10−

2 m) Modeling of interparticle, intraparticle, and particle–wall

interactions, especially in terms of heat and mass transfer. This in

turn requires models for particle morphology evolution, and

monomer adsorption. This is also the interface between the

continuum approach used at the macroscale and the discrete

approach needed at the microscale.

Microscale (< 10-3

m) Modeling of polymerization kinetics, the nature of active sites,

diffusion of monomer in the polymer and crystallization of

polymer molecules.

Mathematical modeling is a powerful tool not only for the development of process

understanding, but also for the design of advanced process technology. In particular, a kinetic

model plays an important role in designing polymerization conditions to tailor a polymer’s

molecular architecture. A comprehensive kinetic study of polymerization process helps

developing effective models at meso- and macro-levels, so this study has been focused on the

estimation of kinetic parameters and prediction of polymer properties through modeling at

micro-level.

8

The two most representative objectives in modeling polymerization reactions are to compute (1)

polymerization rate and (2) polymer properties (molecular level and microscopic level) for

various reaction conditions.

In general, polymerization models are derived from the fundamental chemistry and

physics of the polymerization processes to calculate reaction rates and polymer architectural

parameters. Such models are called the first principles models. For certain polymerization

systems, complex molecular structures are not appropriate for the first-principles modeling and

hence empirical or semi-empirical models are the practical alternatives (Yoon et al., 2004).

Determining the parameters of a kinetic model by using laboratory, pilot plant, or plant

data is the most critical step for the successful development of a process model. Practically, it is

not always possible to design experiments to determine all the relevant kinetic parameters.

Therefore, in modern kinetic modeling, pseudo-rate constant methods and computer aided

parameter estimation techniques are widely used.

In transition metal catalyzed olefin polymerizations, the kinetic parameters are catalyst

dependent. Therefore, whenever a new catalyst is employed, a new set of kinetic parameters

must be determined. Considering the fact that the properties of polyolefins are mostly dictated by

the nature of catalyst being used and that a large number of different types of catalysts is used for

different polymer grades, it becomes very important to have a well-established parameter

estimation procedure that can be applied to any catalyst systems.

1.2 Objectives of research

The objectives of the present research are to

1. Study the mechanistic aspects of Ziegler-Natta and metallocene catalyst systems and

various polymerization mechanisms of olefins using metallocene catalysts.

9

2. Develop kinetic models for the polyolefin synthesis using metallocene catalysts.

3. Validate the developed models with available experimental data in literature and to

estimate the kinetic model parameters.

4. Study the effects of various parameters like polymerization time, temperature, monomer

pressure (concentration), catalyst concentration, co-catalyst to catalyst mole ratio and

concentration of transfer agents etc.

1.3 Organization of thesis

The thesis is presented in five chapters. An exhaustive review of literature on olefin

polymerization using various metallocene catalysts is given in Chapter 2. Mathematical models

developed for ethylene and propylene polymerization with metallocene catalysts and simulation

methodology are discoursed in Chapter 3. The obtained simulation results are discussed in detail

in Chapter 4. In Section 4.1, results obtained from simulations of ethylene polymerization model

with different metallocene catalysts are discussed. Model simulation results of solution phase

propylene homopolymerization with various metallocene catalysts are presented and discussed in

Section 4.2. Chapter 5 deals with the summary of the work and important conclusions drawn

from the present study.

10

CHAPTER – 2

LITERATURE REVIEW

Over the past two decades new catalyst technologies have reinvigorated polyolefin industry by

rapidly expanding new polyolefin materials and technology. Catalysts based on group 4 metals

exhibit the most attractive combination of activity, selectivity and generality to a wide variety of

α-olefins. In all polymerization reactions, the phases of chain growth include initiation,

propagation, and termination and the corresponding elementary rate laws and kinetic constants

completely describe the catalytic kinetics and the distribution of polymer products. In this

chapter, the literature on olefin polymerization catalyzed by transition metal catalysts is

summarized and the existing literature on metallocene catalyzed polymerization is discussed

mainly with regard to ethylene and propylene.

Olefin polymerization with Ziegler-Natta and metallocene catalysts and important

mechanisms available in literature are presented in Sections 2.1 and 2.2 respectively. Various

studies reported in the literature on ethylene and propylene polymerization using metallocene

catalysts are discussed in detail in Sections 2.3 (experimental) and 2.4 (theoretical and modeling)

of this chapter.

2.1 Ziegler-Natta polymerization

Ziegler–Natta catalysts have been used in the commercial manufacture of various polyolefins

since 1956 (Heinen, 2012). Usually Ziegler catalysts refer to Ti-based systems for

polymerization of ethylene and Ziegler–Natta catalysts refer to systems for polymerization of

propylene (Cerruti, 1999).

11

2.1.1 Ziegler-Natta catalysts

The Ziegler-Natta catalyst is the combination of a transition-metal salt whose metal is from

groups IV to VII of the Periodic Table, and a metal alkyl whose metal is from groups I to III of

the Table. Different generations of Z-N catalyst are shown in Table 2.1 (Suba et al., 2007).

Table 2.1 Generations of Ziegler-Natta Catalyst

Generation Catalyst composition Productivity

(kg/g)

Isotactic

Index

I. δ-TiCl3, 0.33AlCl3 + (Et)2AlCl 1.5 90-94

II. γ-TiCl3 + (Et)2AlCl 4.0 94-97

III. TiCl4/monoester (ID)/MgCl2 + (Et)3Al/ester (ED) < 20 90-95

IV. TiCl4/diester (ID)/MgCl2 + (Et)3Al /silane (ED) > 25 95-99

V. TiCl4/diether, succinate (ID)/MgCl2 + (Et)3Al > 50 95-99

ID: internal (electron) donor; ED: external (electron) donor

2.1.2 Mechanism of Ziegler-Natta polymerization

Various mechanisms have been proposed to explain the olefin polymerization catalyzed by

Ziegler-Natta initiators and several good reviews are available in literature (Fontana and

Osborne, 1960; Boor, 1979; Corradini et al., 1982; Cavallo et al., 1998). As part of an effort to

unite the cognition in this field, several attempts have been made to propose a mechanism that

could be applied to all Ziegler-Natta catalyzed polymerizations but the mechanism of

polymerization through Z-N catalyst is still not absolutely clear. Out of several proposed

mechanisms, the most recognized ones are summarized in Figure 2.1 through Figure 2.8

(Goodman, 1967; Boor, 1979; Ystenes, 1991; Castonguay and Rappe, 1992; Hamielec and

Soares, 1996; Margl et al., 1999).

12

Ti

H2C

R

H3C

Al

CH2 CHR

Ti

H2C

R

H3C

Al

Ti

H2

C

R

CH3

Al

CH2 CHR

Ti

H2C

R

RHC

Al

CH2 CH3

Figure 2.1 Bimetallic mechanism of Z-N polymerization by Natta.

Ti

H2C

R

H3C

Al

CH2 CHR

Ti

H2C

R

H3C

Al

Ti

CH2

R

CH3

Al

H2C

RHC CH2

HRC

Ti

H2C

R

CH3

Al

H2C

HRC

Ti

H2C

R

RHC

Al

CH2CH3

Figure 2.2 Bimetallic mechanism of Z-N polymerization by Patat and Sinn.

13

M

P

+ CH3 M

P

CH3

M

P

CH3

M

CH3

P

Vacant coordination site P Growing polymer chain

Figure 2.3 Monometallic mechanism of Z-N polymerization by Cossee.

Figure 2.4 Trigger mechanism of Z-N polymerization by Ystenes.

14

M

H2C CH

R

H

CH2H2C

M

H2C CH

R

CH3H2C

+

Figure 2.5 Chain termination by β-H transfer to monomer (β-H elimination).

M

H2

C

CH R

HM

H2C CH

R

H

+

Figure 2.6 Chain termination by spontaneous intramolecular β-H transfer.

M

H2

C CH2

R

HM

H3C CH2

R

H

+H

Figure 2.7 Chain termination by molecular hydrogen.

M

H2

C CH2

R

MH2

C CH2

RCH2CH3 ++ Al(C2H5)3 (C2H5)2Al

Figure 2.8 Chain termination to the Group I-III metal alkyl.

15

The comparative extents of these reactions depend on various factors such as monomer, the

initiator components, temperature, concentrations and other reaction conditions. Under normal

conditions of polymerization, intramolecular hydride transfer is negligible and termination

occurs mainly by transfer reactions (Chanda, 2013).

2.2 Metallocene polymerization

There are three different commercial olefin polymerization processes where metallocene

catalysts can be used viz solution, gas phase and slurry process. Homogeneous catalysts are used

in the solution process. The first commercial metallocene polyethylene (mPE) was introduced to

the market as differentiated or specialty product for applications like food packaging and impact

modifiers, available with the densities ranging from 0.86 to 0.91 g/cm3. Typical examples are

ExactTM

plastomers by Exxon commercialized in 1991 and the AffinityTM

and EngageTM

products by Dow in 1993. In 1995 the first commodity mPE products were commercialized by

Exxon as ExceedTM

polyethylene with densities ranging from 0.915 to 0.930 g/cm3 (Lue, 1999).

Metallocene catalysts are inherently soluble (homogeneous) catalysts, therefore, the

solution process was the first commercial process to use metallocene catalyst to produce

polyethylenes. Gas phase and Slurry process require heterogeneous catalyst. Metallocene

catalysts need to be supported so that they can be employed in gas phase or slurry phase olefin

polymerization processes. They can be supported in three different ways: 1) The metallocene

compound is reacted with supported MAO to produce a supported catalyst. 2) A cross-linked

MAO, which is insoluble in hydrocarbon, is reacted with a metallocene compound to produce a

supported catalyst. The cross-linked MAO may or may not contain inert supports. 3) To support

the metallocene compound first and then react it with soluble MAO.

16

2.2.1 Metallocene catalyst system

Generic structure and features of metallocene catalyst are discussed in Section 1.1.1. Neutral

metallocene compound is inactive without an activator and requires a strong Lewis acid to form

a cationic metal center, which is active in α-olefin polymerization. The predominating cocatalyst

for metallocene activation is methylaluminoxane (MAO). The aluminoxane is understood to be

involved in site activation by alkylation of the metallocene, prevention of site deactivation, and

impurity scavenging (Hamielec and Soares, 1996). The cocatalyst concentration affects the

productivity of the polymerization and the molecular weight of the polymer. MAO is prepared

by controlled hydrolysis of trimethylaluminum (TMA) as shown in Figure 2.9. The structure of

the MAO is not known with certainty, Figure 2.10 unveils various structural suggestions of

MAO in literature (Zohuri et al., 2012).

A number of other activators have been developed as of late. Some organic boron

compounds, such as trisphenylmethyltetrakis-(pentafluorophenyl)borate [Ph3C]+ [B(C6F5)4]

-,

especially fulfill a role as noncoordinating, non-nucleophilic counter anion to the active cationic

species (Chen and Marks, 2000).

Both, the ligand set of a single-site catalyst and the growing polymer chain are found to

influence the stereochemistry. In a chain-growth polymerization reaction a polymer chain

remains bound to the active metal center during monomer enchainment and the stereogenic

center from the last enchained monomer unit influences the stereochemistry of monomer

addition; if this influence is significant, the mode of stereochemical regulation is referred to as

“polymer chain-end control”, whereas if the ligand set is chiral and overrides the influence of the

polymer chain end, the mechanism of stereochemical direction is termed “enantiomorphic-site

control” as shown in Figure 2.11 (Coates, 2000).

17

nH2O + (n+1) AlMe

Me

Me

Al

Me

Me

O Al

Me

Men

+ 2n CH4

Figure 2.9 Partial hydrolysis of trimethylaluminum to form MAO.

Al

Me

Me

O Al

Me

On

Al

Me

Me(a)

Al

Me

O Al

Me

On

Al

Me

(b)

O

Al

O

Me

O

Al

Me

Al

O

Me

O

Al

O

Al

Me

O

Al

MeMe

(c)

Al

OO

Al Al

O

Al

O O

O

AlAl

O

Al Al

O

Al Al

(d)

Figure 2.10 (a) Linear and (b) cyclic structures of MAO.,

(c) Two-dimensional ladder and (d) three-dimensional cage structures of MAO oligomers.

18

MP

MP

LnM

m mm mmmr

End controls stereochemistry

isotacticStereoerror

Pm

m

MP

MP

LnM

m mm mmmr

End controls stereochemistry


Pr

r

(a)

M P MP

LnMP

r mmmr

Ligand controls stereochemistry


mm

(b)

Figure 2.11 (a) Chain-end and (b) Enantiomorphic site mechanisms of stereocontrol

19

The number of known metallocene complexes is very large. Various types of

metallocenes are generally categorized as nonstereorigid, nonstereorigid ring substituted,

stereorigid, cationic and supported metallocenes. Representative examples of each

category are shown in Table 2.2 (Gupta et al. 1994).

Table 2.2 Representative Examples of Metallocenes

[a] Nonstereorigid metallocenes:

(i) Cp2MCl2 (M = Zr, Ti, Hf)

(ii) Cp2ZrR2 (R = CH3, Ph, CH2Ph, CH2SiMe3)

(iii) (Ind)2ZrMe2

[b] Nonstereorigid ring substituted metallocenes:

(i) (Me5C5)2MCl2 (M = Zr, Ti, Hf)

(ii) (Me3SiCp)2ZrCl2

[c] Stereorigid metallocenes:

(i) Et(Ind)2ZrCl2

(ii) Et(Ind)2ZrMe2

(iii) Et(IndH4)2ZrCl2

[d] Cationic metallocenes:

(i) Cp2MR(L)+[BPh4]

- (M = Zr, Ti)

(ii) [Et(Ind)2ZrMe]+[B(C6F5)4]

-

(iii) [Cp2ZrMe]+[C2B9H11)2M]

- (M = Co)

[e] Supported metallocenes:

(i) Al2O3-Et[IndH4]2ZrCl2

(ii) MgCl2.Cp2ZrCl2

(iii) SiO2.Et[Ind]2ZrCl2

Many metallocene systems are found to be active for both ethylene and propylene

polymerization. Activities may vary from high to moderate depending upon the structure

of the catalyst, moreover stereorigid catalysts are found to be stereo- and regiospecific

towards propylene polymerization. Different metallocene systems used in ethylene and

propylene polymerization are summarized in Table 2.3.

20

Table 2.3 Metallocene Catalyst Systems

Catalyst Cocatalyst Remarks

[a] Chlorocyclopentadienyl

derivatives of Ti,

e.g. Cp2TiCl2

Dialkyl aluminium

chloride

Active for ethylene; inactive

for propylene

polymerization.

[b] Nonstereorigid,

e.g. Cp2MX2

MAO Highly active for ethylene;

active for propylene

(atactic).

Stereorigid,

e.g. Et(Ind)2MCl2

MAO Active for stereo- and

regiospecific propylene

polymerization.

Supported,

e.g. SiO2.Et[Ind]2MCl2

MAO /

Alkylaluminium

Active for ethylene and

propylene polymerization.

[c] Ionic Metallocenes

e.g. Cp2MR(L)+[BPh4]

-

- Active for ethylene and

propylene polymerization.

Metallocenes in ethylene polymerization

The metallocenes generally used for ethylene polymerization are unbridged, bridged,

substituted and half-sandwich complexes. Polyethylene is most commonly polymerized

with cyclopentadiene metallocenes of Ti, Zr, and Hf, with zirconocene preferred for their

stability. The metallocenes generally used for ethylene polymerization are achiral.

Examples of unbridged and bridged catalysts are shown in Figure 2.12.

Metallocenes in propylene polymerization

Examination of the outcomes of many separate investigations reveals a predictable

relationship between metallocene complex symmetry and polypropylene tacticity (Leek et

al., 1997; Ewen, 1998). Achiral metallocenes yield atactic polypropylene. Stereoregular

polypropylene requires the use of chiral metallocene catalysts. Metallocene catalyst

21

symmetries are usually either oblique (C1, C2) or rectangular (Cs, C2v) as shown in Figure

2.13. Single-site polymerization catalysts, based on ligand geometries of catalysts and

their stereoselectivities for polyolefin synthesis, can be divided into four main symmetry

categories viz C2v, Cs, C2, C1 as shown in Figure 2.14.

Catalysts exhibiting C2v symmetry typically produce atactic polymers or

moderately stereoregular polymers by chain-end control mechanisms. Cs-symmetric

catalysts that have mirror planes containing the two diastereotopic coordination sites

behave similarly. Cs-symmetric catalysts that have a mirror plane reflecting two

enantiotopic coordination sites frequently produce syndiotactic polymers. C2-symmetric

complexes, both racemic mixtures and enantiomerically pure ones, typically produce

isotactic polymers via a site-control mechanism. Stereoselectivities of asymmetric (C1)

complexes are unpredictable and have been reported to produce polymer architectures

ranging from highly isotactic, to atactic, including isotactic-atactic stereoblock and

hemiisotactic (Razavi et al., 2006; Chen, 2009).

Supported metallocene catalyst systems are preferred to soluble versions in

conventional polyolefin plants, which were designed to use supported Ziegler- Natta or

Cr2O3-based catalysts. Metallocenes can be supported on a number of substrates, such as

SiO2, MgCl2 or Al2O3. Supported catalysts also provide polypropylene with fewer

stereochemical defects (Rudin, 1999).

22

R1 R2

R3

R4

R5M

XR1

R5

R4

R3

R2X

Zr

ClCl

X

M

ClCl

X

Zr

ClCl

X

R1

R2

R2

R1

M

ClCl

X

R

Zr

ClCl

X

Figure 2.12 Unbridged (a) and bridged (b) catalysts used in ethylene polymerization.

M: Zr, Ti, Hf

X: Cl, CH3

R: H, CH3

X: C2H4, (CH3)2Si; R1: CH3; R2: CH3

X: (CH3)2Si; R1: Ph, Naph; R2: H

M: Zr, Hf;

X: C2H4, (CH3)2Si X: C2H4, (CH3)2Si M: Zr; X: (CH3)2C, Ph2C; R: H, CH3,

tBu

M: Hf; X: (CH3)2C; R: H

X: (CH3)2Si, C2H4

(b)

(a)

23

C1 C2Cs C2vOblique Rectangular

Figure 2.13 General symmetry classifications.

MP

C2v

MP MP MP MP

meso-Cs C2 C1Cs

Figure 2.14 General metallocene symmetry classifications.

24

2.2.2 Mechanism of metallocene polymerization

Understanding the mechanisms and kinetics involved in the polymerization process enables to

predict the structure of the polymer formed. Propagation and termination rates determine

molecular weight, molecular weight distribution while catalyst initiation and deactivation

processes have an influence on the kinetics, and the cocatalyst may have an effect on the extent

of the prevailing mechanisms (Alt and Köppl, 2000; Resconi et al., 2000; Imanishi and Naga,

2001). Various mechanisms of olefin polymerization with metallocene catalyst are discussed in

this section.

Mechanisms for activation

Studies reveal that besides acting as a scavenger for impurities in the reaction medium and

alkylating agent, methylaluminoxane (MAO) is involved in the formation of a cationic Group 4

metal center with a vacant coordination site (Brintzinger et al., 1995; Ystenes et al., 2000;

Estenoz and Chiovetta, 2001; Takeuchi, 2010). MAO is considered to act as a Lewis acid,

abstracting chloride/methyl groups from metallocene, and thus enabling the formation of active

species (Pѐdeutour et al., 2001).

The formation of the metallocenium center, which contains a vacant coordination site,

takes place during a fast ligand exchange between methyl groups of MAO and chlorine in the

metallocene catalyst. After methylating the catalyst, MAO abstracts a methide ligand with active

metallocenium catalyst formation as shown in Figure 2.15.

25

M

Cl

ClMAO

M

Cl

Me MAOM

Me

M

Me

Me

MAO MAO

Open coordination

site

MAO

Figure 2.15 Activation of a metallocene complex by methylaluminoxane (MAO).

M = transition metal atom and □ = vacant coordination site.

26

Mechanisms for propagation

Several mechanisms have been proposed for propagation in olefin polymerization with

metallocenes. This has been generally accepted that propagation proceeds by α-olefin

coordination and insertion via a transition state (Resconi et al., 2000). Important mechanisms

are discussed in the following subsections.

Cossee Arlman mechanism

Cossee-Arlman mechanism for propagation in metallocene catalyzed polymerization of α-olefins

is inspired by and quite so similar to the one proposed by Cossee for Ziegler-Natta olefin

polymerization. Figure 2.16 explains the mechanism schematically.

Green-Rooney mechanism

The mechanism proposed by Rooney and Green, involves an oxidative 1,2-hydrogen shift from

the α-carbon of the polymer chain, generating a metal-alkylidene hydride. This species then

reacts with an olefin to generate a metallacyclobutane, and reductive elimination completes the

propagation sequence as schematized in Figure 2.17 (Grubbs and Coates, 1996). Green-Rooney

mechanism, involving metathesis like step was not accepted and refuted convincingly by

Clawson and coworkers (Clawson et al., 1985).

Modified Green-Rooney Mechanism

Modified Green-Rooney mechanism, proposed by Green, Rooney and Brookhart is an

intermediate version to the Cossee-Arlman and Green-Rooney mechanisms, where a hydrogen

atom on the α-carbon of the growing polymer chain interacts with the metal center all over the

catalytic cycle. This three-center, two-electron covalent bond, termed as 'agostic interaction',

27

occurs when the hydrogen atom is simultaneously bonded to both a carbon and a metal atom as

shown in Figure 2.18.

Transition State α-agostic Mechanism

This mechanism is a hybrid of the Cossee-Arlman and modified Green-Rooney mechanisms.

This meshanism suggests the olefin insertion, where an α-hydrogen interacts with the metal

center only during the transition state of the C-C bond formation (shown in Figure 2.19).

The presence of α-agostic interaction in the transition state has been observed

experimentally in mechanistic studies (Leclerc and Brintzinger, 1995, 1996) and is consistent

with the proposed conformation adopted by the growing polymer chains as a means of affecting

enentiaoselective propylene insertion. These experimental results support the modified Green-

Rooney mechanism as the most likely mechanism for propylene insertion.

28

M

Me

M

Me

M

Me

n

M

Men

Figure 2.16 Cossee-Arlman mechanism of propagation with a metallocene catalyst.

M

CH2P

M

CHP

H

M

CHP

H

R

M

PHC

H

R

M

PH2C R

Figure 2.17 Green-Rooney mechanism of propagation with a metallocene catalyst.

29

M

H

P

H

M

H

P

H

M

H

P

H

M

H

P

H

M

H

H

P

Figure 2.18 Modified Green-Rooney mechanism of propagation with a metallocene

catalyst.

M

H

P

H

M

H

P

H

M

H

P

H

M

H

P

H

M

H H

P

Figure 2.19 Transition state α-agostic mechanism of propagation with a metallocene

catalyst.

30

Mechanisms for termination

Termination usually occurs via transfer mechanisms. Each chain transfer reaction results in

dissociation of the chemical bond between the metal atom in a metallocene active center and the

last monomer unit in the growing polymer chain. A number of chain termination modes are

possible, some of the accomplished mechanisms are described below:

β-Hydrogen transfer to monomer

In this mechanism, β-hydrogen is transferred from the growing polymer chain to an incoming

monomer as depicted in Figure 2.20. This is the prevalent chain termination mechanism under

the common experimental conditions (Margl et al., 1999).

This reaction results in the formation of polymer molecules with the terminal -vinyl

group in ethylene polymerization and vinylidene group in homo- and co-polymerization of α-

olefins.

β-Hydrogen elimination (Spontaneous chain transfer)

Chain termination may also take place via spontaneous β-hydrogen transfer to the transition

metal atom of metallocene as shown in Figure 2.21.

The preference for a β-hydrogen transfer to monomer vs. transition metal is often

determined by spacial conditions in the vicinage of the transition metal atom in the active center.

Since the transfer to monomer is preceded by coordination of a monomer molecule at the metal

atom, it is favoured when the active center is more open sterically. For example, β-hydrogen

transfer to monomer is preferred chain transfer reaction in propylene polymerization with the

metallocene catalyst based on the meso-isomer of Me2Si(3-Me-Ind)(Ind)ZrCl2 (one of its lateral

31

side is open). On the other hand, the active center based on the racemic isomer of the same

complex has both its coordination positions sterically crowded, so spontaneous chain transfer is

more preferred in this case (Kissin, 2008).

β-Methyl elimination

Chain termination via β-methyl elimination occurs only in special cases like at high

polymerization temperatures with hafnocenes (Figure 2.22). The mechanism of transfer is

similar to the β-hydrogen elimination. A polymer chain coordinated to the sterically more

hindered site predominantly undergoes a unimolecular β-methyl elimination reaction and leads to

ethenyl (allylic) end groups (Hajela and Bercaw, 1994; Guo et al., 1994; Resconi et al., 1996;

Schöbel et al., 2013).

Chain transfer to aluminium

MAO usually contains leftover Al(CH3)3, which may also render the chain termination via

transfer to aluminium as shown in Figure 2.23. Chain transfer to Al is more commonly observed

at lower propylene concentration (Resconi et al., 1990; Naga and Mizunuma, 1998).

32

M

CH2

H

P

H

MM

CH2

H

P

HM

CH2

H

P

HM

H

P

H2C

H

H

H

Figure 2.20 β-Hydrogen transfer to monomer.

M

CH2

H

P

H

MM

H

PHM

CH2

H

P

H

Figure 2.21 β-hydrogen elimination (Spontaneous chain transfer).

M

CH2

H

Me

P

MM

Me

P MeM

CH2

Me

P

H

M

CH2

Me

P

H

Figure 2.22 β-methyl elimination (Spontaneous chain transfer).

M

CH2

H

P

Me

M RM Al

CH2

R

R

R

+ Al

R

R

R

CHMeP

+ Al

R

CH2

R

CHMeP

Figure 2.23 Chain transfer to cocatalyst (aluminium).

33

2.3 Experimental studies

Ethylene polymerization studies on nonstereorigid, stereorigid and supported metallocene

catalysts are generally carried out to evaluate the activity of the catalysts and product

properties. Tacticity has been the additional interest of investigation in propylene

polymerization apart from kinetic studies. Among many metallocene catalysts, zirconium

based catalysts have been extensively studied in both ethylene and propylene

polymerization. Salient features of some of the experimental studies reported in the

literature on metallocene catalyzed ethylene and propylene polymerization are presented

below.

Several researchers (Rieger and Jainik, 1994; Charpentier et al., 1997; Chakravarti

and Ray (2001); Young and Ma, 2002; Marques and Alcantara, 2004; Zohuri et al., 2005;

Sarzotti et al., 2007) have studied experimental aspects of ethylene polymerization with

zirconocene dichloride/methylalumoxane/trimethylaluminum (Cp2ZrCl2/MAO/TMA)

catalyst systems. In their work, the investigators have examined the effects of variation

of the monomer concentration, catalyst concentration, Al/Zr ratio, polymerization

temperature on the catalyst activity and polymer properties.

Agnillo et al. (1998) in addition to Cp2ZrCl2, investigated its titanium and

hafnium analogues (Cp2TiCl2 and Cp2HfCl2), as well as rac-

ethylenebis(indenyl)zirconium dichloride (Et(Ind)2ZrCl2) and rac-ethylenebis(4,5,6,7-

tetrahydroindenyl)zirconium dichloride (Et(H4Ind)2ZrCl2) for ethylene polymerization.

Reactors with different reaction environments like solution phase (Charpentier et

al., 1997; Zohuri et al., 2005; Sarzotti et al., 2007), slurry process (Chakravarti and Ray

(2000); Young and Ma, 2002) and alumina as support to catalysts (Marques and

Alcantara, 2004) were used.

34

Chu et al. (2000 a) carried out ethylene polymerization with a novel in-situ-

supported metallocene catalyst that eliminated the need for a supporting step before

polymerization. In their sequential study Chu et al. (2000 b) proposed a polymerization

mechanism for the in situ supported Et[Ind]2ZrCl2 catalyst suggesting that during

polymerization, the in situ supported metallocene catalysts may deactivate, but

homogeneous metallocene species present in the reactor may form new active sites and

compensate for deactivated sites.

Mehdiabadi and Soares (2009) studied the solution polymerization of ethylene

using rac-Et(Ind)2ZrCl2/MAO and dimethylsilyl(tert-butylamido)(tetramethyl-

cyclopentadienyl)titanium Dichloride (CGC-Ti)/MAO in a semi-batch reactor and

investigated how polymerization conditions affect the polymerization kinetics with two

metallocene catalysts.

ethylenebis(indenyl)zirconium dichloride (EtInd2ZrCl2) with silica support (Tissea

et al., 2010 a) and the role of morphological properties of different silica used as supports

(Tissea et al., 2010 b) were investigated to infer the effects of monomer concentration,

temperature and alkyl aluminium concentration, upon the reaction rate and the

polyethylene properties.

Firme et al. (2005) carried out ethylene and propylene polymerization using

Ind2ZrCl2 and Ind2Zr(CH3)2/MAO catalytic systems modified by the sterically demanding

bridged alicyclic alcohols, adamantan-1-ol, adamantan-2-ol, 2-methyladamantan-2-ol,

and fenchyl alcohol. Polymers with higher molecular weights were obtained with

modifiers as compared to the non modified systems, but no structural changes in the

polyethylenes were observed.

The initial stages of gas-phase polymerizations of ethylene and propylene were

analyzed by Machado et al. (2011) using a fixed bed stopped flow reactor. The very early

35

development of particle morphology and polymer properties were analyzed for three

different commercial catalyst systems: MgCl2- and SiO2-supported Ziegler–Natta and

SiO2-supported metallocene.

Bridged metallocene catalysts have attracted extensive research interest due to

their high activity towards ethylene polymerization and control over chain branching.

Roos et al. (1997) carried out ethylene polymerization in a stirred powder bed reactor

with silica supported rac-Me2Si[Ind]2ZrC12/methylaluminoxane (MAO) with the

objective to study the influence of temperature on the gas phase polymerization of

ethylene. Authors also modeled deactivation as a first order dependence with respect to

the polymerization rate.

Wang et al. (1998) used high-temperature and high-pressure continuous stirred-

tank reactor (CSTR) for the polymerization of ethylene with the constrained geometry

metallocene system, [C5-Me4(SiMe2NtBu)]TiMe2(CGC-Ti)/tris(pentafluorophenyl)boron

(TPFPB)/ modified methylaluminoxane (MMAO) and synthesized polyethylenes with

long chain branching (LCB) densities up to 0.44 carbons/10000 carbons, and narrow

polydispersity indices about 2.

Studies on ethylene polymerization with cycloalkylidenebridged cyclopentadienyl

metallocene (Wang et al. 2005), 4,4 -bis(methylene)biphenylene bridged homodinuclear

titanocene and zirconocene (Sun et al., 2006), Ph2C(Cp)(Flu)ZrCl2 (Freitas et al., 2011),

N,N-ethylenebis(3-methoxysalicylideneiminato)titanium dichloride (Pietruszka et al.,

2012) and bridged cyclopentadienyl indenyl (fluorenyl) zirconocene complexes (Huang et

al., 2010) activated by MAO were focused to investigate the effects of various reaction

conditions on polymerization rate and polyethylene properties.

Petitjean et al. (1999) through density functional calculations described possible

mechanisms of ethylene polymerization in the presence of zirconocene catalysts.

36

Ramachandran et al. (2009) employed small-angle neutron scattering (SANS) to

investigate the structure and long chain branch (LCB) content of metallocene-catalyzed

polyethylene and applied a scaling approach to SANS data to determine the mole fraction

branch content of LCBs in PE.

Literature on propylene polymerization shows a huge concern on tacticity aspects in

addition to the other research interests. A great attention has been given to the isospecific

polymerization of propylene.

The kinetics of propylene polymerization initiated by rac-(EBI)Zr(NMe2)2) /

MAO (Kim and Hwang, 1998), rac-Me2Si(1-C5H2-2-Me-4-tBu)2Zr(NMe2)2 / MAO (Kim

et al., 1999), rac-(EBI)Zr(NC4H8)2) / MAO (Kim, 1999) were studied by changing

various experimental parameters. The molecular weight of isotactic polymer produced

was, in general, found to decrease with an increase in [Al]/[Zr] ratio, polymerization

temperature, and catalyst concentration, whereas a reverse trend was observed for catalyst

activity.

Resconi et al. (1999) analyzed the chemical structures of end groups of medium-

low molecular weight atactic and isotactic polypropylenes (a-PP and i-PP), produced with

zirconocene/MAO catalysts and used to infer the chain-transfer reaction mechanisms,

which were subsequently correlated with the zirconocene ligand structure and the

polymerization conditions. For the chiral, isospecific ansa-zirconocenes such as rac-

[ethylenebis(1-indenyl)]ZrCl2 / MAO and rac-[ethylenebis(4,7-dimethyl-1-indenyl)]ZrCl2

/ MAO catalysts, i-PP molecular weight was observed dependent on the regiospecificity

of the catalyst.

Lin et al. (2000) investigated the kinetics of propylene polymerization in toluene

solution by bis(2-phenylindenyl)zirconium dichloride, (2-PhInd)2ZrCl2/MAO at 20 °C.

37

Polymerization rates were found to be increasing with increase in monomer and

zirconium concentrations and the activity decreased faster at higher monomer

concentrations.

A good deal of experimental studies on various isospecific metallocene catalysts

for propylene polymerization has been carried out and is available in literature (Schmidt

and Alt, 2001; Meier et al., 2001; Belelli et al., 2001; Marques et al., 2002; Marques et

al., 2003; Song et al., 2003; Song et al., 2004; Palza et al., 2006).

The kinetic behaviour of propene polymerization in heptane using

bis(cyclopentadienyl)zirconium dichloride / MAO as catalyst system was studied by

Ochoteco et al. (2001). Investigations were made for both homogeneous and

heterogeneous systems and the effect of the process variables such as temperature,

pressure, Al/Zr ratio and catalyst concentration on the catalytic performance (activity and

polymer properties) were investigated.

Marques et al. (2002) investigated the effect of temperatures and Al/Mt on the

catalyst activity and the polymer characteristics. Higher catalyst activity for the

zirconocenes was observed, while the hafnocenes produced polypropylene with higher

molecular weight. The complexes with dimethylsilane bridge produced polypropylene

with higher molecular weight, stereoregularity and higher melting temperature in

comparison with the corresponding polymers using the ethylidene bridge.

Yasin et al. (2004) synthesized an unbridged metallocene catalyst bis(2,4,6-

trimethylindenyl)zirconium dichloride. They carried out propylene polymerization with

this catalyst and compared the results with bis(2,4,7-trimethylindenyl) zirconium

dichloride to investigate the steric effects of substituents on the catalytic activity and

microstructure of the resulting polymer. In their subsequent study, Yasin et al. (2005)

synthesized a chiral ansa-metallocene catalyst, namely rac-dimethylsilyl-bis(2,4,6-

38

trimethyl-1-indenyl)zirconium dichloride and used for isospecific polymerization of

propylene, with methyl aluminoxane (MAO) as the cocatalyst. The influences of

polymerization temperature on the polymerization activity, polypropylene microstructure

and polymer properties were investigated, and the results were compared with rac-

dimethylsilyl-bis(indenyl)zirconium dichloride under identical conditions.

Syndiospecific polymerization of propylene has attracted relatively little attention

by researchers. Such studies were generally channeled to understand the kinetics and

effect of reaction parameters on catalyst activity and stereoregularity.

Ko and Woo (2003) performed kinetic studies on the syndiospecific

polymerizations of propylene with iPr(Cp)(Flu)ZrCl2 / MAO at 20, 40 and 70 0C and at 5

atm with various Al/Zr molar ratios. It was concluded that active site isomerization was

dominant source for stereoirregularity and that was strongly dependent on the

polymerization temperature.

Marques and Conte (2006) produced syndiotactic and isotactic polypropylene

using the metallocene compounds Ph2C(Flu)(Cp)ZrCl2 and SiMe2(2-Me,4-Ph-Ind)2ZrCl2

in homogeneous system and supported on silica/MAO. These catalysts were evaluated

either isolated or as a binary system. They observed that at all the studied polymerization

temperatures, the binary catalyst produced polypropylenes with lower melting

temperatures in comparison with those obtained when the mixture of isolated supported

syndio- and isospecific catalysts was employed.

Sanginov et al. (2006) reported a marked rise in the efficiency for syndiospecific

Ph2CCpFluHfMe2 and isospecific rac-Me2SiInd2ZrMe2, upon introduction of Lewis bases

into a reaction medium.

Use of a mixture of racemic metallocenes and Ziegler–Natta catalysts (Lisovskii

et al., 1998), heterogeneous metallocene catalysts on clay minerals (Weiss et al., 2002)

39

and effects of various trialkylaluminiums with tBuNSiMe2C5Me4TiMe2/MAO (Dare et

al., 2004) are some examples of the various dimensions of studies being carried out in

propylene polymerization. A summary of the experimental studies on ethylene and

propylene polymerization is presented in Table 2.4 and Table 2.5 respectively.

40

Table 2.4 Metallocene Catalyzed Ethylene Polymerization, Experimental Studies

SL

No.

Catalyst Cocatalyst(s) Parameters studied

Important Findings References

1.

Cp2ZrCl2

MAO/TMA Effect of [Zr], Al/Zr ratio

and addition of TMA Catalyst productivity (CP) increased (↑)

and molecular weight (MW) decreased

(↓) with small additions of TMA (up to

AlTMA:AlMAO = 1.4)

Rieger and Jainik,

1994

2. MMAO/TMA Effect of [Zr] and

temperature (T) With ↑ in [Zr], MW ↓ and the catalyst

activity (CA) ↑. With ↑ in T between 140

and 200 °C, MW ↓ and polydispersity ↑.

Charpentier et al.,

1997

3. MAO Reaction time (t), [C2H4],

[Zr], and Al/Zr ratio Yield (Y) ↑ with ↑ in [C2H4], t, [Zr], and

the Al/Zr ratio.

Young and Ma, 2002

4. MAO/TMA Comparison of

homogeneous & alumina

supported systems

MW with supported catalysts was higher

than that obtained with the homogeneous

system

Marques and

Alcantara, 2004

5. MAO [C2H4], T, Al/Zr ratio and

H2 as a chain transfer

agent

Y ↑ with ↑ in Al/Zr ratio to a limiting

value. CA ↑ with T to 60 °C and slightly

↓ with more ↑ in T. CP ↑ with ↑ in

[C2H4]. MW ↓ with ↑ in Al/Zr ratio, T

and [H2].

Zohuri et al., 2005

6. MAO, MMAO

and poly(MAO)

Cocatalyst type and

Al/Zr ratio

Existence of two or more active site

types. Proposed a model to explain broad

MWDs

Sarzotti et al., 2007

41

Table 2.4 Metallocene Catalyzed Ethylene Polymerization, Experimental Studies (continued...)

SL

No.

Catalyst Cocatalyst(s) Parameters studied Important Findings References

7. Et[Ind]2ZrCl2 TMA, MAO, silica

treated with MAO

(SMAO)

t, [Zr], T, Al/Zr

ratio, TMA/MAO

ratio, TMA/SMAO

ratio

In-situ-supported catalyst did not show rate

decay with t. With ↑ in Al/Zr ratio CA ↑ and

MW and PDIs were unaffected. With ↑ in T,

MW ↓. Proposed a polymerization mechanism

for the in-situ supported catalyst

Chu et al.,

2000 a, b

8. Et[Ind]2ZrCl2

and CGC-Ti

MAO [C2H4], [Zr]

and [Ti]

First order kinetics with rac-Et(Ind)2ZrCl2 for

polymerization and catalyst deactivation.

Mehdiabadi

and Soares,

2009

9. Et[Ind]2ZrCl2 SMAO [C2H4], T, [Al] and

silica properties

[C2H4] has positive but T has negative effect on

MW. Influence of the physical nature of the

silica support on polymerization.

Tisse et al.

2010 a, b

10. [Ind]2ZrCl2

and

[Ind]2Zr(CH3)2

MAO modified

with bridged

alicyclic alcohols

Modifiers Addition of modifiers to catalyst did not alter

the structure of the polyethylenes but slightly ↑ MW.

Firme et al.,

2005

11. SiO2-supported

Et(Ind)2ZrCl2

- [C2H4], T Development of the morphology of the

polymer particles was analyzed.

Machado et

al. 2011

42


SL

No.


12. Me2Si[Ind]2ZrC12 MAO T Polymerization and

deactivation rate ↑ with ↑ in T.

Roos et al.

1997

13. [C5-Me4(SiMe2NtBu)]TiMe2

and CGC-Ti

tris(pentafluoroph

enyl)boron

(TPFPB) and

MMAO

[C2H4], T;

kinetics of LCB Branching ↑ with [C2H4]. Low

LCB density at elevated T.

Kinetic rate constants were

estimated graphically.

Wang et al.

1998

14. (CH2)nC(C5H4)2MCl2; M =

Ti, Zr, Hf; n = 4,5,6

MAO structure-activity

relationship

much higher activities with

cycloalkylidene-bridged

titanocene catalystst than the

corresponding zirconocene and

hafnocene analogues.

Wang et al.

2005

15 (CpTiCl2)2[C5H4CH2C6H4-p-

C6H4CH2C5H4] and

(CpZrCl2)2[C5H4CH2C6H4-p-

C6H4CH2C5H4]

MAO [Ti], [Zr], T, Al/Zr

ratio CAs were compared. MW ↑

with t.

Sun et al.

2006

16. Ph2C(Cp)(Flu)ZrCl2 MAO Compared

homogeneous and

heterogeneous

systems; T

Homogeneous polymerizations

were more active. CA ↓

significantly with ↑ in T under

homogeneous conditions

Freitas et al.

2011

43


SL

No.


17. N,N-ethylenebis(3-

methoxysalicylideneiminato)titan

ium dichloride immobilized on

Mg support

Me3Al and

MAO

T, [C2H4], and t CA ↑ with ↑ in T and [C2H4].

Bulk density ↑ with T and t.

Broad MWD was obtained.

Pietruszka et

al. 2012

18. [(p-CH3-

Ph)2C(C5H4)(C9H6)]ZrCl2,

{(p-CH3-Ph)[p-C(CH3)3-

Ph]C(C5H4)(C9

H6)}ZrCl2,

[(p-CH3-

Ph)2C(C5H4)(C13H8)]ZrCl2,

{(p-CH3-Ph)[p-C(CH3)3-

Ph]C(C5H4)(C13H8)}ZrCl2

MAO Various catalysts Effect on CA and MW was

discussed.

Huang et al.

2010

19. Cp2ZrCl2, Cp2TiCl2, Cp2HfCl2,

Et(Ind)2ZrCl2 and

Et(H4Ind)2ZrCl2

MAO, TMA Various catalysts, T,

[Zr], [Ti], [Hf],

[MAO], chain

transfer agent (CTA),

and substitution of

MAO with TMA

↑ in T and [catalyst] or [MAO]

caused a ↓ in MW.

Replacement of TMA with

MAO or addition of H2 (CTA)

induced a drastic ↓ in MW. For

the Zr catalysts, transfer to

C2H4 was the main chain

transfer mechanism.

Agnillo et al.

1998

44


SL

No.


20. Zirconocene MAO Mechanisms of

polymerization through

density functional calculations

and energetics were

discussed.

- Petitjean et al.

1998

21. Unbridged supported

zirconocene

MAO T and [C2H4] ↑ in CA and decay with ↑

in T. Polymerization

rates were first order in

ethylene.

Chakravarti

and Ray 2001

22. Metallocene - - Structure and LCB

content of Dow HDB

samples were determined

using small-angle

neutron scattering

(SANS)

Ramachandran

et al. 2009

45

Table 2.5 Metallocene Catalyzed Propylene Polymerization, Experimental Studies

SL

No.


1. rac-(EBI)Zr(NMe2)2 MAO [Zr], T and Al/Zr ratio ↓ in MW with ↑ in Al/Zr ratio, T

and [Zr]. Maximum CA found

at Al/Zr = 2000, [Zr] = 137.1

μM and T = 30 °C

Kim and

Hwang, 1998

2. rac-Me2Si(1-C5H2-2-Me-4-tBu)2Zr(NMe2)2,

rac-Me2Si(1-C5H2-2-Me-4-tBu)2ZrMe2

MAO [Zr] and T ↑ in polymerization rate (Rp)

and ↓ in stereoregularity, Tm,

MW, and MWD with ↑ in T.

Linear ↑ in Rp with ↑ in [Zr]

Kim et al. 1999

3. rac-(EBI)Zr(NC4H8)2) MAO [Zr] and Al/Zr ratio CA ↑ with ↑ in Al/Zr ratio. MW

↓ and PDI insensitive with ↑ in

Al/Zr ratio and [Zr]. iPP with a

meso pentad value of 94.7%

produced.

Kim, 1999

4. rac-(EBI)ZrCl2, rac-[EB(4,7-

dimethyl-1-indenyl)]ZrCl2

MAO Analyzed chemical

structures of end

groups of aPP and iPP

Proposed chain transfer reaction

mechanism

Resconi et al.,

1999

5. (2-PhInd)2ZrCl2 MAO [C3H6] and [Zr] ↑ of the isotactic dyads and

pentads and Rp with ↑ in [C3H6],

β-hydride elimination dominant.

PDI = 2.0-2.6

Lin et al., 2000

46

Table 2.5 Metallocene Catalyzed Propylene Polymerization, Experimental Studies (continued...)

SL

No.


6. Ind'2ZrCl2 (Ind' = 2-alkyl- or

arylalkyl-substituted indenyl)

MAO Catalyst structure and T Productivity, MW and

isotacticity ↓ with ↑ in T

Schmidt and

Alt, 2001

7. Me2Si[Ind]2ZrCl2 MAO/SiO2 [C3H6], T,

Compared gas and

liquid phase

polymerization

Lower reaction rates were

found in the gas phase

compared to liquid phase.

Rp,max ↑ linearly with

[C3H6]. Deactivation rate ↑

with ↑ in T.

Meier et al.

2001

8. SiMe2(Ind)2ZrCl2,

Et(Ind)2ZrCl2,

SiMe2(Ind)2HfCl2,

Et(Ind)2HfCl2

MAO Catalyst type, T, and

Al/Mt ratio MW ↓ with ↑ in Al/Zr ratio

or T. CA, MW and tacticity

were compared for different

catalysts.

Marques et

al., 2002

9. Cp2ZrCl2 and

SiMe2(Ind)2ZrCl2

MAO, different

immobilization

methods

Homogeneous vs.

heterogeneous systems

High CA and low MW with

homogeneous systems

Marques et

al., 2003

10. rac-Me2Si(1-Indenyl)2ZrMe2

and rac-Me2Si(1-

Indenyl)2ZrCl2

AliBu3/[Ph3C] and

MAO

Initial [C3H6], [Zr];

Quenched-flow kinetic

study

First-order dependence of

yield (Y) on [M] and [Zr].

Song et al.,

2003

47

Table 2.5 Metallocene Catalyzed Propylene Polymerization, Experimental Studies (continued...)

SL

No.


11. rac-Me2Si(1-Ind)2ZrCl2 CPh3[B(C6F5)4]/TIBA

and MAO

Comparison of activators

through quenched-flow

kinetic study

CA with MAO was 20

times less than borate

activators

Song et al.,

2004

12. (2,4,6-Me3Ind)2ZrCl2

and (2,4,7-Me3)2ZrCl2

MAO, TIBA T, [Zr], Al/Zr ratio and

[MAO], [TIBA] MW ↑ with ↑ in T and ↓ in

Al/Zr ratio. CA ↓ with ↑ in

[Zr]; High CA obtained

with addition of TIBA in

MAO. Isotacticity ↑ with ↓

in T

Yasin et al.

2004

13. rac- Me2Si(2,4,6-

Me3Ind)2ZrCl2 and rac-

Me2Si(Ind)2ZrCl2

MAO T and catalyst type Very high CA at T = 50 -

70 °C and P = 1 atm. rac-

Me2Si(2,4,6-Me3Ind)2ZrCl2

more isospecific.

Yasin et al.

2005

14. Cp2ZrCl2 MAO P, T, [MAO], Al/Zr ratio

and [Zr] CA ↑ with ↑ in P, T and

[MAO]. MW ↑ with ↑ in P

and ↓ in Al/Zr ratio.

Ochoteco et

al. 2001

15. Me2Si(2-Me-Ind)2ZrCl2 MAO P, T, Al/Zr ratio and [Zr] Linear relationship of Y

with [Zr] and P. With ↑ in

T or Al/Zr ratio, Y ↑ to a

maximum, then ↓.

Palza et al.

2006

48

Table 2.5 Metallocene Catalyzed Olefin Polymerization, Experimental Studies (continued...)

SL

No.


16. iPr(Cp)(Flu)ZrCl2 MAO T and Al/Zr ratio Syndiotactic PP. CA ↓ with

↑ in Al/Zr ratio.

Stereoerrors were

influenced by T and not by

Al/Zr ratio.

Ko and Woo,

2003

17. Ph2C(Flu)(Cp)ZrCl2 and

SiMe2(2-Me,4-Ph-

Ind)2ZrCl2

MAO T and type of catalyst CA ↑ with ↑ in T. CA of

supported catalyst 50% less

than homogeneous.

Marques and

Conte, 2006

18. Ph2CCpFluHfMe2 and

rac-Me2SiInd2ZrMe2

AliBu

3, CPh3B(C6F5)4 Influence of the external

Lewis base as

modifying reagents.

10 times ↑ in CA for

syndiospecific and 15-30

times ↑ in CA for isospecific

catalyst.

Sanginov et

al. 2006

19. tBuNSiMe2C5Me4TiMe2 MAO, Oct3Al, Me3Al,

Et3Al, iBu3Al

Effect of various alkyl

aluminiums CA ↑ with Oct3Al and iBu3Al (possesing more

bulky groups) and CA ↓

with Me3Al, Et3Al.

Dare et al.

2004

20. C2H4(Ind)2ZrCl2,

Me2Si(Ind)2ZrCl2, ZN

catalysts (Ti on MgCl2)

MAO Mixed catalysts MW, Tm and melt flow

index (MFI) were

determined for one step and

two step polymerization.

Lisovskii et

al. 1998

49

2.4 Mechanistic, modeling & simulation studies

Information on mechanistic aspects for olefin polymerization is essential to develop

realistic kinetic models. The mechanisms with special focus on stereochemical control,

homo- and copolymerization of α-olefins with variety of metallocene catalysts have been

extensively studied and published in literature.

Brintzinger et al. (1995) reviewed stereospecific α-olefin polymerization with

chiral metallocene catalysts encompassing correlations between catalyst structures &

stereoselectivities and mechanisms of stereochemical control.

Chien (1999) presented a comprehensive and comparative review on applications

of inorganic support materials, MAO-free supported catalysts, modified silica support and

polymeric support to metallocene catalyst for olefin polymerization.

Mechanism of alkene polymerization reactions with metallocene catalysts has

been discussed by Kissin and Goldman (2009). In their study, ethylene was

homopolymerized and copolymerized with four 1-alkenes—propene, hex-1-ene, hept-1-

ene, and 3,3-dimethylbut-1-ene using (n-Bu-Cp)2ZrCl2 and (Me-Cp)2ZrCl2 complexes

activated with MAO.

Petoff et al. (1998) used bis(2-arylindenyl)zirconium dichlorides and rac- &

meso-dimethylsilyl(bis(2-phenylindenyl))zirconium dichloride activated by

methylaluminoxane (MAO) produce elastomeric polypropylene and provided mechanistic

insight of polymerization.

Several reviews have been published on mechanisms of polymerization via

metallocene catalysts (Busico, 1998; Kaminsky and Strübel, 1998; Kleinschmidt et al.,

1999; Chen and Marks, 2000; Jongsomjit et al., 2005; Bochmann, 2006). Very recently

Kaminsky (2009) and Takeuchi (2010) have presented state of the art mechanistic

50

reviews on a number of transition metal catalysts including early and late transition

metals applied in olefin polymerization.

Modeling studies have been carried out to study the kinetics and mechanism of

polymerizations and the structure of polymer chains, such as the distribution of molecular

weight, branching, stereoregularity and chain topology in different polymer systems.

Kinetics and transport effects were studied and modeled (Bhagwat et al., 1994;

Zarand and Mortazavi, 2005; Kanellopoulos et al., 2007) for slurry polymerization of

ethylene with Ziegler-Natta Catalysts.

Sarzotti et al. (2007) proposed a model for ethylene polymerization with

homogeneous Cp2ZrCl2/aluminoxane catalysts to fit the experimental rate data of as a

function of polymerization time and [Al]/[Zr] ratio. They considered the existence of two

types of active sites and assumed that the active complex formed when the metallocene

precursor is activated, PA, is reversibly transformed to an intermediate species, P*, and

irreversibly to a second active site type, PB.

xAPP n

A

n * (2.1)

B

nn PP * (2.2)

where A

nP is an active site of type A with a growing polymer chain of length n, *

nP an

intermediate catalyst complex with a polymer chain of length n.

The rate constant for initiation and propagation of active site type A were assumed to be

same to reduce the number of parameters. Catalyst deactivation was also not considered.

Instantaneous rate of polymerization was determined by the following expression:

rEE

B

pB

A

pAP VmMPkPkR1

(2.3)

where E : density of ethylene, Em : molar mass of ethylene and rV : reactor volume

51

Iedema (2012) described a semi-analytical approach to model simultaneous chain

scission and branching that assumes the separation of the scission and the branching

problem.

Yiannoulakis et al. (2000) developed a dynamic model for the calculation of the

molecular weight and long chain branching distributions in a continuous solution

metallocene-catalyzed ethylene polymerization reactor.

Roos et al. (1997) studied ethylene polymerization in a stirred powder bed reactor

with silica supported rac-Me2Si[Ind]2ZrC12/methylaluminoxane (MAO) and modeled

deactivation as a first order dependence with respect to the polymerization rate as given

by Equation 2.5.

*CCkR mpP (2.4)

Pd Rkdt

dC

*

(2.5)

Where mC : monomer concentration, *C : concentration of active sites.

Chakravarti and Ray (2001) developed a slurry reactor model to predict the

polymerization behaviour under various reaction conditions. They considered simple

kinetic scheme in their model including activation, propagation and deactivation only as

below:

*

0 Activation CMCpot (2.6)

*

1

* n Propagatio nn CMC (2.7)

ndn DCC * on Deactivati (2.8)

Mehdiabadi and Soares (2009) suggested that kinetics of ethylene polymerization

with rac-Et(Ind)2ZrCl2/MAO can be described with first order reactions for

polymerization and catalyst deactivation. Focusing on catalyst deactivation studies they

52

only considered initiation, propagation and deactivation steps in their kinetic model and

also simplified it by assuming same values of the initiation and propagation constants.

Zeigler-Natta catalysts remained democratic in various modeling studies for both

ethylene and propylene polymerization. Various researchers (Neto and Pinto, 2001; Pater

et al., 2003; Veera, 2003; Reginato, 2003; Luo, 2008), through their modeling efforts,

have enriched the literature to understand propylene polymerization with Z-N catalysts. In

their studies, morphological or transport models like Polymeric flow (PF) model,

multigrain (MG) model, polymeric flow Fick’s diffusion model (PF FDM), Multigrain

Fick’s diffusion model (MG FDM), advection-dispersion model (ADM) and the dusty gas

model (DGM) were generally developed and improved.

Kinetic modeling studies on propylene polymerization with metallocene catalysts were

rare till recent past. Few studies available in literature are discussed hereunder.

Nele et al. (2001) proposed a two state kinetic model to describe the propylene

polymerization behavior of ansa-metallocene catalysts. They applied the model to

describe the polymerization behavior of some simple symmetrical [Me2C(Cp)(Flu)MCl2;

M = Zr, Hf] and unsymmetrical [Me2Y(Cp)(Ind)MCl2; M = Zr, Hf; Y = C, Si] catalysts,

activated with MAO.

A kinetic model was proposed by Ochoteco et al. (2001) to explain the

experimental evolution of catalyst activity at different Al/Zr ratios and catalyst

concentrations for the homogeneous system. In their model they considered catalyst

activation, chain initiation, chain propagation and a reversible second order catalyst

deactivation step followed by an irreversible deactivation process forming inactive

species.

53

*

0 Activation CMAOC ik (2.9)

*

1

*

01 Initiation CMC pk

(2.10)

*

1

* 2 n Propagatio n

k

n CMC p (2.11)

inactivedormant

inactive

k

CC

CC

,2,2

*

n

,2

*

0

2C

2 on Deactivati'1

(2.12)

Belelli et al. (2001) proposed a mathematical model for a semibatch laboratory

polymerization reactor using ethylenbisindenylzirconium dichloride (EtInd2ZrCl2) / MAO

that predicted reactor productivity and the molecular properties of the product. SRK

equation of state was employed to estimate the equilibrium concentration of propylene in

toluene (solvent) at the gas-liquid interface for different pressures at polymerization

temperature which was fixed. In their model they considered the existence of different

types of catalyst sites with reactions quoted below:

kkk PMPki

10 Initiation (2.13)

k

j

kk

j PMPkp

1n Propagatio (2.14)

k

j

kkk

j DPHPk

H- sfer toChain tran (2.15)

kkk PMPHkr

1on Reactivati (2.16)

k

jd

kk

j DCPkd 1

ondeactivatiorder First (2.17)

k

m

k

jd

kk

m

k

j DDCPPkd 2

ondeactivatiorder Second

2

(2.18)

54

Lahelin et al. (2003) prepared polypropylene with rac-SiMe2(2-Me-4-

PhInd)2ZrMe2/MAO (rac-dimethylsilylbis(2-methyl-4-phenylindenyl)dimethylzirconium/

methylaluminoxane) in heptane solution at temperatures from 50 °C to 80 °C with

varying concentrations of monomer, hydrogen, triisobutylaluminium (TIBA) and MAO.

Authors developed kinetic model for low propylene concentrations on the basis of

polymerization data.

Nele et al. (2005) modeled stereospecific polymerization of propylene with C1-

symmetric Me2Si(Ind)(Flu)ZrCl2 complex, activated with methyl aluminoxane. They

proposed the existence of asymmetric ansa and fluxional metallocene catalysts in (at

least) two different states during the lifetime of the growing polymer chain. Authors

employed the Coleman–Fox model in their study, which incorporates the benefits of both

kinetic and probabilistic modeling approaches.

Palza et al. (2006) developed a mathematical model for Me2Si(2-Me-Ind)2ZrCl2

catalyzed propylene polymerization based on the method of the moments. Authors

observed a special effect with respect to the co-catalyst (MAO) on productivity and

improved their model incorporating deactivation-reactivation mechanisms associated with

MAO.

A brief review of the mechanistic and modeling studies on ethylene and propylene

polymerization is summarized in Table 2.6.

55

Table 2.6 Metallocene Catalyzed Olefin Polymerization, Mechanistic, Modeling & Simulation Studies

SL

No.

Monomer Catalyst Cocatalyst(s) Study / Model Remarks References

1. α-Olefin Chiral Metallocene MAO Reviewed kinetics and

mechanism

- Brintzinger et

al. 1995

2. α-Olefin Metallocene MAO Reviewed applications of

inorganic support materials,

MAO-free supported catalysts,

modified silica and polymeric

support.

- Chien, 1999

3. Ethylene (n-Bu-Cp)2ZrCl2 and (Me-

Cp)2ZrCl2

MAO Mechanism and kinetics of

chain growth and chain

transfer reactions were

discussed.

- Kissin and

Goldman,

2009

4. Propylene bis(2-arylindenyl)zirconium

dichlorides and

rac- & meso-dimethylsilyl(bis(2-

phenylindenyl))zirconium

dichloride

MAO Proposed mechanism for the

production of elastomeric

polypropylene.

- Petoff et al.,

1998

5. Ethylene Z-N - Modeling for isothermal slurry

polymerization

Rp and Polymer

properties

Bhagwat et

al., 1994

6. Ethylene Z-N - Combined polymeric

multigrain (PMGM) and

polymeric multilayer (PMLM)

models

Simulation with

parameters taken

from literature.

Zarand and

Mortazavi,

2005

56

Table 2.6 Metallocene Catalyzed Olefin Polymerization, Modeling Studies (continued...)

SL

No.


7. Olefin Z-N - Unsteady-state diffusion

model

Pore size distribution

and crystallinity

Kanellopoulos

et al. 2007

8. Ethylene Cp2ZrCl2 MAO / MMAO Kinetic modeling Rate data prediction Sarzotti et al.,

2007

9. Ethylene Metallocene - Semi-Analytical Model for

simultaneous chain scission

and branching

Comparison of semi-

analytical model with

Monte Carlo simulations

Idema, 2012

10. Ethylene Metallocene

- Dynamic modeling,

continuous reactor

MW and long chain

branching (LCB)

distributions

Yiannoulakis

et al. 2000

11. Ethylene rac- Me2Si[Ind]2ZrC12 MAO Modeling of deactivation Rate data prediction Roos et al.,

1997

12. Propylene Z-N TEA Kinetic modeling Kinetic parameter

estimation

Pater et al.

2003

13. Propylene Z-N TEA Kinetic modeling for slurry

and bulk polymerization

Prediction of MWD,

chain composition

distribution (CCD),

particle size distribution

(PSD)

Netoa and

Pinto, 2001

57


SL

No.


14. Propylene Z-N - Modeling for liquid-phase

polymerization in loop

reactor

Polymer properties Reginato et

al., 2003

15. Olefin Z-N - Advection-dispersion model

(ADM) and the dusty gas

model (DGM)

Comparison with

Polymeric flow (PF)

Fick’s diffusion (FDM),

multigrain FDM (MG

FDM) has been made.

Veera, 2003

16. Propylene Me2Si(Ind)(Flu)ZrCl2 MAO Applied Extended

Coleman–Fox Model

T effects on the

microstructure of

polymer

Nele et al.,

2005

17. Propylene SiO2 supported Cp2ZrCl2 MAO Kinetic model for catalyst

activity at different Al/Zr

ratios and [Zr]

Explanation of their

experimental evolution

Ochoteco et

al., 2001

18. Propylene EtInd2ZrCl2 MAO Modeling for homogeneous

polymerization in semibatch

reactor

Prediction of

productivity

Belelli et al.,

2001

19. Propylene Me2Si(2-Me-Ind)2ZrCl2 MAO Modeling for homogeneous

polymerization in semibatch

reactor

Prediction of Y Palza et al.,

2006

58


SL

No.


20. Propylene Silica supported

metallocene and Z-N

MAO / MgCl2 Modeling for liquid-phase

polymerization in stirred

tank reactor using Monte

Carlo simulation.

Prediction of Y and MW Luo et al.,

2008

21. Propylene Me2C(Cp)(Flu)MCl2, M

= Zr; Hf and

Me2Y(Cp)(Ind)MCl2, M

= Zr, Hf, Y = C, Si

MAO Two state kinetic model for

liquid-phase polymerization

in semibatch reactor.

Stereosequence

distributions

Nele et al.,

2001

22. Propylene rac-SiMe2(2-Me-4-

PhInd)2ZrMe2

MAO / TIBA Polymer characterization,

mechanisms and kinetic

models.

Prediction of MW and

end groups

Lahelin et al.,

2003

59

2.5 Gaps in research

The existing literature on polymerization with metallocene catalyst systems suggests that

efforts have been made in understanding the mechanisms and work performance of

metallocene based catalyst systems with different co-catalysts. These systems allow tailor

making of polymers and offer other process advantages such as ease of handling of

metallocene systems and favourable conditions for polymerization from a commercial

point of view, which has evoked the examen of the commercial potential of such catalyst

systems. The commercial exploitation of such systems has, however, started in a limited

way due to prohibitive cost of the catalyst and the ambiguity associated with the

aluminoxanes (co-catalysts).

Various homo- and copolymers have been synthesized using metallocene catalyst

systems and most of the work is of experimental nature at either laboratory scale or the

pilot scale with more or less common objectives like investigating catalyst activity,

product properties and effect of parameters thereon.

Very little attempts have been made in modeling and simulation related studies for the

polymerization process. Majorly Z-N catalyzed polymerization of olefins was on focus

for modeling the morphological and transport related phenomena. Modeling efforts on

olefin polymerization with metallocene catalysts are as less as negligible when compared

to the other catalyst systems. Further, kinetic modeling and simulation of metallocene

catalyzed olefin polymerization is in its dissilient stage and provides a huge opportunity

to address the understanding of kinetics comprehensively.

2.6 Scope of the work

Significant development in the synthesis of new metallocenes and co-catalysts is

anticipated in near future leading to tailor-made polymers, including functionalized

60

polyolefins with predictable properties. In view of this, it is imperative to model the

polymerization of olefins involving different metallocene catalyst systems. A lot of scope

exists for theoretical as well as computation studies on metallocene catalyzed olefin

polymerization and hence developing a kinetic model and simulation of the same

unquestionably is a task not only for research but also of industrial importance.

In this work, the mechanistic aspects of Ziegler-Natta and metallocene catalyst

systems have been studied in detail and used in building up mathematical models for

ethylene and propylene polymerization using metallocene catalysts. Developed models

are validated with the experimental data available in literature and kinetic parameters are

estimated using differential evolution (DE) approach of optimization. Study on the effects

of various parameters like monomer concentration, polymerization temperature, catalyst

concentrations, and cocatalyst to catalyst molar ratio etc. upon rate of polymerization,

molecular weights and poly dispersity index and stereoregularity is carried out.

The outcomes of this study will help in better understanding of the chemistry and

process of the olefinic polymerization with these revolutionary catalyst systems.

61

CHAPTER – 3

MATHEMATICAL MODEL DEVELOPMENT

AND

SIMULATION

Understanding the fundamentals of reactions that are at the heart of industrial catalytic olefin

polymerization processes yields information that is important for achieving improvements in

these processes, and can also pioneer pathways to new processes and materials. Mathematical

modeling is a mighty tool for the development of process understanding and advanced reactor

technology in the polymer industry. Recent advances in theory, computational software, and

hardware have made it possible to complement experiments and empiricism with sound

mathematical models. These mathematical models, which are constructed on a first principles

basis and have been validated with experimental data, may be used as a surrogate of the real

process for a variety of applications where it may be costly, inconvenient, impractical, or unsafe

to use the actual process.

A kinetic model consists of mass and population balance equations, which are derived

based on elementary reactions proposed in the reaction mechanism. This usually yields a system

of differential and/or algebraic equations that can be solved using various numerical methods

e.g., numerical discretization.

The aim of this chapter is to discuss the development of mathematical models for

metallocene catalyzed ethylene & propylene polymerization and kinetic parameter estimation

methodology used in this work.

62

3.1 Metallocene polymerization kinetics & model development

It is apparent that a kinetic model capable of predicting the molecular development in a

polymerization reactor in terms of the process operating conditions should include appropriate

representations of all chemical and physical phenomena occurring at micro-scale. Kinetic models

vary in their complexity but in general following issues should be addressed while modeling a

polymerization reaction (inferred from Kiparissides, 1996).

(i) Identification of the elementary reactions from the polymerization kinetic mechanism.

(ii) Derivation of polymerization rate functions for all reacting species [e.g. monomer(s),

catalyst, chain transfer agent(s), "live" polymer chains and "dead" polymer chains].

(iii) Specification of the number of phases in the reactor. Homogeneous vs. heterogeneous

kinetics.

(iv) Necessary thermodynamic models for the: (a) calculation of monomer(s) concentration(s)

in the different phases, (b) calculation of enthalpies of the different reacting species, etc.

(v) Selection of reactor configuration. (e.g. batch, semi-batch, continuous, etc).

(vi) Derivation of all necessary reactor design equation for: (a) reaction mixture and (b)

coolant/heating fluids.

(vii) Choosing numerical method for solving the model equations. Estimation of unknown

model parameters. Performing sensitivity studies. Investigation of dynamic model

behavior, etc.

3.1.1 Mathematical treatment of polymerization kinetics

Population balance approach is used to rescript the kinetic equations for each polymerization

step in terms of the leading moments of the molecular-weight distribution of the polymer. This

63

treatment is a statistical technique that enables us to track various polymer chain properties

without the need to include the very large number of equations and unknowns required to

account for chains of every possible length. Characterization of polymer properties is modeled

using the population balances and method of moments. Construction of moment balances allows

the tracking of average polymer properties like number and weight average molecular weights,

chain-length distributions, type and frequency of chain branching, and content of terminal double

bonds etc.

Leading moments of the molecular weight distribution

The moments are averages of the concentrations of polymer molecules that are weighted by their

chain lengths. The moment expression for live polymer chains is given by Equation 3.1.

1

)(i

nl

n iPi (3.1)

where l

n is the nth

moment of the molecular weight distribution of live chains attached to

catalyst site and , )(iP is the molar concentration of the corresponding live polymer chains.

Similar expression for dead chains can be written as Equation 3.2.

2

)(i

n

n iDi (3.2)

where n is the nth

moment of the molecular weight distribution of dead chains and )(iD is the

molar concentration of the corresponding dead chains.

The three leading moments, namely, the zeroth, first, and second, are adequate for depicting the

molecular weight distribution of most commercial polymers.

64

Polymer properties in terms of moment expressions

A variety of common polymer properties those can be deduced using the moment expressions are

given below.

The number-average degree of polymerization is given by Equation 3.3.

00

11

l

l

nDP (3.3)

The weight-average degree of polymerization is given by Equation 3.4.

11

22

l

l

wDP (3.4)

The number-average and weight average molecular weights can be calculated from Equations

3.5 & 3.6.

00

11

l

l

SRUn mM (3.5)

11

22

l

l

SRUw mM (3.6)

where SRUm is the molecular weight of the structural repeat unit.

The polydispersity index is defined as the ratio of weight average to number average molecular

weight and can be computed using Equation 3.7.

211

0022

l

ll

n

w

M

MPDI (3.7)

65

3.2 Modeling of ethylene polymerization

3.2.1 Kinetics

Several authors have recently presented kinetic schemes for metallocene-catalyzed ethylene

polymerization (Wang et al., 1998; Yiannoulakis et al., 2000; Jongsomjit et al., 2005; Bochmann

et al., 2006; Kaminsky et al., 2009). Based on the understanding of mechanisms for metallocene-

catalyzed polymerization developed, a general reaction set for ethylene polymerization that

includes reactions corresponding to all types of metallocenes is proposed in this section. All of

them may not be applicable to every system, e.g. in absence of hydrogen as a chain transfer

agent, chain transfer to hydrogen is not possible and hence should not be considered in scheme.

Catalyst activation by cocatalyst

The catalyst is activated by the cocatalyst.

)0(PCocatCat ak (3.8)

where Cat is the catalyst, Cocat is the cocatalyst species, 0P represents an active catalyst site

that is capable of polymerization, and ka is the rate constant for catalyst activation. MAO is used,

often as cocatalyst species for many metallocene catalysts.

Chain initiation

The active sites react with monomer to initiate chain growth.

10 PMP ink (3.9)

66

where M is the monomer, 1P is a polymer chain attached to catalyst containing one monomer

segment, and kin is the rate constant for chain initiation.

Chain propagation

This step is the addition of monomer species to the growing chains. The addition of monomer

species involves a complexation of the double-bond of the monomer at the catalyst site.

1 iPMiP pk (3.10)

where iP is a polymer chain attached to a catalyst site and kp is the rate constant for chain

propagation. This reaction controls the monomer conversion in the reactor.

Spontaneous catalyst deactivation

A propagating chain converts into a dead polymer chain due to spontaneous deactivation of

active site.

iDPiP d

kd 0

00 d

k PP d

(3.11)

(3.12)

where 0dP is deactivated catalyst, and kd is the rate constant for spontaneous catalyst

deactivation.

Chain transfer to hydrogen

Hydrogen acts as a strong chain transfer agent for metallocene catalysts. Chain transfer to an

external chain transfer agent, such as hydrogen results in a saturated chain end.

67

0)(2 PiDHiP tHk (3.13)

where )(iD is a dead chain containing i segments, and ktH is the rate constant for chain transfer to

hydrogen.

Chain transfer to monomer

Monomer acts as a chain-transfer agent as well.

1)( PiDMiP tMk

(3.14)

where )(iDis a dead polymer chain detached from the catalyst, and contains a terminal double

bond and ktM is the rate constant for chain transfer to monomer. Chain transfer to the ethylene

leads to the formation of vinyl (CH2=CH−) end group.

Chain transfer to cocatalyst

In some cases, cocatalyst also acts as a chain-transfer agent. Chain transfer to the aluminum

(cocatalyst) is usually of minor importance in ethylene polymerization but comes out to be more

important in propene polymerization (Naga and Mizunuma, 1998).

0)( PiDCocatiP tCok (3.15)

where ktCo is the rate constant for chain transfer to cocatalyst.

β-Hydride elimination (Spontaneous chain transfer to the metal)

In β-hydride elimination, a polymer chain can detach from the active site, leaving it with a

terminal double bond. The catalyst site remains active for reinitiation and polymerization. This

68

reaction is important for the incorporation of long chain branches, which requires chains with

terminal double bonds. β-H elimination (chain transfer to the metal) leads to the formation of

vinyl (CH2=CH−) end group in ethylene polymerization.

0)( PiDiPk

(3.16)

where kβ is the rate constant for β-hydride elimination.

Long-chain branching (Transfer to polymer)

A live chain can react with a dead chain containing a terminal double bond to form a single chain

with a long branch.

jiPjDiP lcbk )( (3.17)

where klcb is the rate constant for incorporation of polymer chains with terminal double bonds.

Constrained geometry metallocene catalysts are able to utilize this reaction to produce polymer

with long-chain branches at moderate reactor conditions.

Short-chain branching (Backbiting or intramolecular H-abstraction)

Short chain branching is not applicable to ethylene homopolymerization but important for

copolymerization with α-olefins.

iPiP scbk ' (3.18)

where kscb is the rate constant for short chain branching.

69

Comonomers are normally used to produce HDPE products of varying densities. The

introduction of α-olefins, such as propylene, 1-butene, and 1- hexene, creates short-chain

branching along the polymer backbone, lowering the crystallinity of the polymer.

Table 3.1 summarizes the reactions considered in the kinetic mechanism.

Table 3.1 Reactions Conceived in Ethylene Polymerization

Reaction Stoichiometry Description

1. )0(PCocatCat ak Catalyst activation

2. 10 PMP ink Chain initiation

3. 1 iPMiP pk Chain propagation

4. iDPiP d

kd 0 {chain}

Spontaneous catalyst deactivation 5. 00 d

k PP d {site}

6. 0)(2 PiDHiP tHk Chain transfer to hydrogen

7. 1)( PiDMiP tMk


8. 0)( PiDCocatiP tCok


9. 0)( PiDiPk

β-hydride elimination

10. jiPjDiP lcbk )( Long-chain branching

11. iPiP scbk ' Short-chain branching

70

3.2.2 Model development for ethylene polymerization

Mathematical model building based on the reactions considered in Table 3.1 for ethylene

polymerization is discussed in this section. Semi-batch reactor has been commonly used for

kinetic studies of polymerization by various researchers.

Material balances

In order to obtain the model equations in terms of various moments, material balance has been

written on different species available in the reactor, which is described in the following sections.

Unactivated catalyst, 'Cat'

CocatCatkr aCat (3.19)

Vacant activated catalyst sites, 'P(0)'

ll

tCo

l

tHdinaP kCocatkHkPkPMkCocatCatkr 0002)0( )0()0( (3.20)

Deactivated catalyst sites, 'Pd(0)'

l

dP Pkrd 0)0( )0( (3.21)

Cocatalyst, 'Cocat'

l

tCoaCocat CocatkCocatCatkr 0 (3.22)

71

Monomer, 'M'

l

tM

l

pinM MkMkPMkr 00)0( (3.23)

Hydrogen, 'H2'

l

tHH Hkr 022 (3.24)

Active chains, 'P(i)'

)1()1()1()1(

)1()1()1()1()0(

0

02)1(

PkPkPkPCocatk

MkPMkPHkPkPMkPMkr

scblcbtCo

l

tMtMtHdpinP

(3.25)

)()()()(

)()()()1()(

0

2)(

iPkiPkiPkiPCocatk

iPMkiPHkiPkiPMkiPMkr

scblcbtCo

tMtHdppiP

(3.26)

where

n is the nth

moment of the molecular weight distribution of dead chains with terminal

double bond, given by Equation 3.25.

2

)(i

n

n iDi (3.27)

)(iD is the molar concentration of dead chains with terminal double bond.

Dead chains, 'D(i)'

)()( 2)( iPHkiPkr tHdiD (3.28)

72

Dead chains with terminal double bond, 'D=(i)'

0)()()()()( iPkiPCocatkiPkiPMkr lcbtCotMiD

(3.29)

Live chains with long chain branches, 'P(i+j)'

0)( )( iPkr lcbjiP (3.30)

Live chains with short chain branches, 'P'(i)'

)()('

iPkr scbiP (3.31)

Moments of chain length distribution (CLD) of living polymer chains

Zeroth moment, ' l

0 '

l

tHdin kHkkPMkr l 02)0(0

(3.32)

First moment, 'l

1 '

l

scblcbptCotM

l

tCotHdtMin

kkMkCocatkMk

kCocatkHkkMkPMkr l

01

12)0(1

(3.33)

Second moment, 'l

2 '

l

scbtCotHdtM

l

lcbp

l

lcbptCotMin

kkCocatkHkkMk

kMkkMkCocatkMkPMkr l

22

1102 2)0(2

(3.34)

73

Moments of CLD of dead polymer chains

Zeroth moment, ' 0 '

l

tHd Hkkr 020

(3.35)

First moment, ' 1 '

l

tHd Hkkr 121

(3.36)

second moment, ' 2 '

l

tHd Hkkr 222

(3.37)

Moments of CLD of dead polymer chains with terminal double bond

Zeorth moment, '

0 '

l

lcbtCotM kkCocatkMkr 000

(3.38)

First moment, '

1 '

l

lcb

l

tCotM kkCocatkMkr 0111

(3.39)

Second moment, '

2 '

l

lcb

l

tCotM kkCocatkMkr 0222

(3.40)


A variety of common polymer properties can be deduced using the moment expressions. The

number-average degree of polymerization is given by Equation 3.41.

74

000

111

l

l

nDP (3.41)


111

222

l

l

wDP (3.42)

The MWD of the polymer chains is characterized by number-average, weight-average molecular

weights and PDI calculated from Equations 3.43, 3.44 and 3.45.

000

11105.28

l

l

nM (3.43)

111

22205.28

l

l

wM (3.44)

2111

000222

l

ll

n

w

M

MPDI

(3.45)

Mole fraction of dead polymer chains with terminal double bond can be computed by Equation

3.46.

00

0

f

(3.46)

Number of long-chain branches and short-chain branches per 103 carbon atoms can be calculated

using Equations 3.47 and 3.48 respectively (Pladis and Kiparissides, 1998).

111

5001000/l

LCBCLCB

(3.47)

75

111

5001000/l

SCBCSCB

(3.48)

3.3 Modeling of propylene polymerization

3.3.1 Kinetics

A general reaction set for propylene polymerization that includes reactions corresponding to all

types of metallocenes is proposed in this section. As in the case of ethylene polymerization

kinetics all of them may not be relevant to every system.

Catalyst activation by cocatalyst

The catalyst gets activated by the cocatalyst.

)0(PCocatCat ak (3.49)

where Cat is the catalyst, Cocat is the cocatalyst species, 0P represents an active catalyst site

that is capable of polymerization, and ka is the rate constant for catalyst activation. MAO is used

as cocatalyst species for many metallocene catalysts.

Chain initiation

The active sites react with monomer to initiate chain growth.

10 PMP ink (3.50)

where M is the monomer, 1P is a polymer chain attached to catalyst containing one monomer

segment, and kin is the rate constant for chain initiation.

76

Chain propagation

This step is the addition of monomer species to the growing chains. The addition of monomer

species involves a complexation of the double-bond of the monomer at the catalyst site.

1 iPMiP pk (3.51)

where iP is a polymer chain attached to a catalyst site and kp is the rate constant for chain

propagation. This reaction controls the monomer conversion in the reactor.

Spontaneous catalyst deactivation

A propagating chain converts into a dead polymer chain due to spontaneous deactivation of

active site.

iDPiP d

kd 0

00 d

k PP d

(3.52)

(3.53)

where 0dP is deactivated catalyst, and kd is the rate constant for spontaneous catalyst

deactivation. Spontaneous deactivation leads to the formation of vinylidene (CH2=C<) end group

in propylene polymerization.

Chain transfer to monomer (β hydrogen transfer)

Monomer also acts as a chain-transfer agent.

1)( PiDMiP tMk (3.54)

77

where )(iD is a dead polymer chain detached from the catalyst, and ktM is the rate constant for

chain transfer to monomer. Chain transfer to the monomer leads to the formation of vinylidene

(CH2=C<) end group in propylene polymerization.

β-Hydride elimination (Spontaneous chain transfer to the catalyst)

A propagating chain may terminate by transferring its β-H to the catalyst, carrying unsaturation

at its end. The catalyst site remains active for reinitiation and polymerization.

0)( *,

H

kPiDiP H (3.55)

where 0*

HP is a hydride activated complex, and kβ,H is the rate constant for spontaneous chain

transfer to catalyst. Chain transfer to catalyst also contributes to the formation of vinylidene

(CH2=C<) end group in propylene polymerization.

Reinitiation after β-Hydride elimination

Hydride catalyst activated complex 0*

HP reinitiates a new chain with monomer

)1(0* PMP rk

H (3.56)

where rk is the rate constant for reinitiation after chain transfer to catalyst.

β-Methyl elimination (Spontaneous chain transfer to the metal)

A propagating chain may also terminate by transferring its β-CH3 to the catalyst. This

mechanism of termination is very unusual and applies to special cases where highly substituted

Cp rings are involved (Resconi et al., 1992, Ethuis et al.,1992, Lin and Tsai, 2008).

78

0)( *,

Me

kPiDiP Me (3.57)

where 0*

MeP is a regenerated methyl complex, and kβ,Me is the rate constant for β-methyl

elimination. Chain transfer to catalyst by this mechanism leads to the formation of vinyl

(CH2=CH—) end group in propylene polymerization.

Secondary (2, 1) insertion

In propylene polymerization, a monomer can insert either by primary (1, 2) or secondary (2, 1)

fashion. With early transition metal complexes, insertion generally occurs in a (1, 2) - fashion

resulting in less bulky group on the metal (Makio and Fujita, 2008). A secondary (2, 1) insertion

is unusual for Group 4 transition metal mediated polymerization but can have a significant

influence on polymerization kinetics. Secondary insertion gives a dormant site which has a low

activity for further propene insertion and leads to regioirregularities in the chain.

)1( iRMiP sk (3.58)

where )1( iR is a living polymer chain with (2, 1) insertion, and ks is the rate constant for

secondary insertion.

Propagation after secondary (2, 1) insertion

Chain continues propagating after a secondary insertion occurs.

)1( iPMiR spk (3.59)

where ksp is the rate constant for propagation after secondary insertion.

79

Chain transfer to monomer after secondary (2, 1) insertion

β-hydrogen transfer is a considerable path of termination for living chains after (2, 1) insertion.

)1()( PiDMiR sMk (3.60)

where ksM is the rate constant for transfer to monomer after secondary insertion.

Chain transfer to cocatalyst MAO

MAO usually contains leftover Al(CH3)3. Chain transfer to Al is more common at lower propene

concentration. (Resconi et al., 1990; Naga and Mizunuma, 1998). Chain transfer to Al is

included to describe the influence of cocatalyst on molecular weight and the percentage of

different end groups.

0)( *,

Me

kPiDCocatiP Alt (3.61)

A methylated catalyst activated complex 0*

MeP is formed after chain transfer to cocatalyst. kt,Al

is the rate constant for transfer to cocatalyst.

Reactivation after chain transfer to cocatalyst MAO

The reactivation of methylated catalyst complex is treated as an elementary reaction different

from normal catalyst activation because the two activated complexes are raised in dissimilar

chemical environments.

10* PMP rAlk

Me (3.62)

krAl is the rate constant for reactivation after transfer to cocatalyst.

80

Table 3.2 summarizes the reactions considered in the kinetic mechanism of propylene

polymerization.

Table 3.2 Reactions Conceived in Propylene Polymerization


1. )0(PCocatCat ak Catalyst activation



4. iDPiP d

kd 0 {chain}


k PP d {site}

6. 1)( PiDMiP tMk Chain transfer to monomer

7. 0)( *,

H

kPiDiP H β-Hydride elimination

8. )1(0* PMP rk

H Reinitiation after β-H elimination

9. 0)( *,

Me

kPiDiP Me β-Methyl Elimination

10. )1( iRMiP sk Secondary (2, 1) insertion

11. )1( iPMiR spk Propagation after (2, 1) insertion

12. )1()( PiDMiR sMk Chain transfer after (2, 1) insertion

13. 0)( *,

Me

kPiDCocatiP Alt Chain transfer to cocatalyst

14. 10* PMP rAlk

Me Reactivation transfer to cocatalyst

81

3.3.2 Model development for propylene polymerization

In this section, mathematical model development based on the reactions considered in Table 3.2

for propylene polymerization has been discussed. The model developed is applicable for a batch,

semi-batch or constant stirred tank reactor.

Material balances

Model equations in terms of various moments are obtained for which material balance has been

written on different species present in the reactor. Description follows, in forthcoming sections.

Unactivated catalyst, 'Cat'

CocatCatkr aCat (3.63)

Vacant activated catalyst sites, ' 0P , 0*

HP , 0*

MeP '

)0()0()0( PkPMkCocatCatkr dinaP (3.64)

)]0(][[ *

0,)0(* Hr

l

HPPMkkr

H (3.65)

)]0(][[ *

,0,0,)0(* MeAlr

l

Alt

l

MePPMkCocatkkr

Me

(3.66)

Deactivated catalyst sites, 'Pd(0)'

l

dP Pkrd 0)0( )0( (3.67)

82

Cocatalyst, 'Cocat'

l

AltaCocat CocatkCocatCatkr 0, (3.68)

Monomer, 'M'

)]0(][[][

][][)]0(][[)0(

*

,0

00

*

00

MeAlr

m

sM

m

sp

l

sHr

l

tM

l

pinM

PMkMk

MkMkPMkMkMkPMkr

(3.69)

where m

n is the nth

moment of the molecular weight distribution of secondary (2,1) inserted

chains given by Equation 3.59.

1

)(i

nm

n iRi (3.70)

)(iR is the molar concentration of secondary (2,1) inserted chains.

Active chains, 'P(i)'

)0()1()1()1(

)0()1()1()1()1()0(

*

,,0,

*

,)1(

MeAlrAlt

m

sMsMe

HrHtMdpinP

PMkCocatPkMkPMkPk

PMkPkPMkPkPMkPMkr

(3.71)

CocatPkPMk

PkPkPMkPkPPMkr

Alts

MeHtMdpP

)2()2(

)2()2()2()2()2()1(

,

,,)2(

(3.72)

)()1()(

)()()()()()1(

,

,,)(

iPCocatkiRMkiPMk

iPkiPkiPMkiPkiPiPMkr

Altsps

MeHtMdpiP

(3.73)

Dead chains, 'D(i)'

CocatiPk

iRMkiPkiPkiPMkiPkr

Alt

sMMeHtMdiD

)(

)()()()()(

,

,,)(

(3.74)

83

Secondary (2,1) inserted chains, 'R(i)'

)()()1()( iRMkiRMkiPMkr sMspsiR (3.75)

Moments of chain length distribution (CLD) of living polymer chains

Zeroth moment, ' l

0 '

)0(

)0()0(

*

,0

*

0,,,0

MeAlr

m

sMsp

Hr

l

AltsMeHdin

PMkMkk

PMkCocatkMkkkkPMkr l

(3.76)

First moment, 'l

1 '

)0()0(

)0(

*

,

*

010

101,,,01

MeAlrHr

m

sM

mm

sp

ll

tM

l

AltsMeHd

l

pin

PMkPMkMkMk

MkCocatkMkkkkMkPMkr l

(3.77)

Second moment, 'l

2 '

)0()0(2

2)0(

*

,

*

021020

2,,,102

MeAlrHr

m

sM

mmm

sp

ll

tM

l

AltsMeHd

ll

pin

PMkPMkMkMkMk

CocatkMkkkkMkPMkr l

(3.78)

Moments of CLD of dead polymer chains

Zeroth moment, ' 0 '

In order to reckon the percentage chain termination by different routes, the zeroth moment for

dead chains is dissevered into:

(i) vinylidene-terminated chains ( 0 )v, due to termination via spontaneous deactivation, chain

transfer to monomer (β-H transfer) and chain transfer to catalysts (β-H elimination);

(ii) vinyl-terminated chains ( 0 )v', due to chain transfer to catalysts via β-CH3 elimination);

84

(iii) butenyl-terminated chains ( 0 )b due to chain transfer after secondary (2,1) insertion and

(iv) isobutyl-terminated chains ( 0 )i due to chain transfer to cocatalyst.

l

HtMd kMkkrv

0,)( 0

(3.79)

l

Mekrv

0,)( '0

(3.80)

m

sM Mkrb

0)( 0

(3.81)

l

Alt Cocatkri

0,)( 0

(3.82)

ibvvrrrrr

)()(')()( 00000 (3.83)

First moment, ' 1 '

m

sM

l

AlttMMeHd MkCocatkMkkkkr 11,,,1

(3.84)

Second moment, ' 2 '

m

sM

l

AlttMMeHd MkCocatkMkkkkr 22,,,2

(3.85)

Moments of CLD of secondary (2,1) inserted chains

Zeorth moment, ' m

0 '

m

sMsp

l

s MkkMkr m 000

(3.86)

First moment, 'm

1 '

m

sMsp

ll

s MkkMkr m 1101

(3.87)

85

Second moment, 'm

2 '

m

sMsp

lll

s MkkMkr m 2210 22

(3.88)


The number-average degree of polymerization is given by Equation 3.89.

ml

ml

nDP000

111

(3.89)


ml

ml

wDP111

222

(3.90)

The MWD of the polymer chains is characterized by number-average and weight-average

molecular weights calculated from Equations 3.91 and 3.92 respectively.

Number average molecular weight, ' nM '

ml

ml

nM000

11108.42

(3.91)

Weight average molecular weight, ' wM '

ml

ml

wM111

22208.42

(3.92)

The polydispersity index (PDI) is calculated from Equation 3.93.

2111

000222

ml

mlml

PDI

(3.93)

86

Micro-structural properties of polypropylene in terms of moment expressions

The developed model is capable of predicting the fractions of end groups generated by various

modes of chain transfer. Fraction of vinyl-terminated chains, butenyl-terminated chains,

isobutyl-terminated chains and vinylidene-terminated chains relative to the total unsaturated

termination is calculated from Equations 3.94, 3.95, 3.96 and 3.97 respectively.

i0b0v'0v0

v'0'

) () () () (

) (

vf

(3.94)

i0b0v'0v0

b0

) () () () (

) (

bf

(3.95)

i0b0v'0v0

i0

) () () () (

) (

if

(3.96)

ibvv ffff '1 (3.97)

3.4 Simulation methodology

The proper estimation of kinetic parameters is a cardinal step in the modeling. Model validation

is associated with the determination of a set of kinetic parameters for which the model

predictions match with the experimental behavior of different catalysts in polymerization. Unlike

in other polymerization systems such as free-radical polymerizations, the kinetic parameters in

catalytic olefin polymerization are strongly dependent on the nature of the catalyst. For a kinetic

model developed, relevant kinetic parameters must be determined for each catalyst system (Choi

et al., 1997).

Parameter estimation is a crucial yet difficult task, it is uncommon to find models with

parameters that have been estimated using experimental data. Most modelers obtain approximate

87

values of model parameters from the literature (Xie et al., 1995; Soares and Hamielec, 1996;

Park et al., 2003; Iedema, 2004; Lo and Ray, 2005; Park et al., 2005; Luo et al., 2007; Luo et al.,

2010). These models allowed only qualitative explanations of important phenomena during

olefin polymerization and qualitative previsions of the relationships between operating

conditions and polymer properties, no experiments have been used to verify these explanations

and predictions.

The models developed in this study are grounded on kinetics of ethylene and propylene

polymerization with various metallocene catalysts. For the validation of these models, the

experimental data have been taken from literature (Roos et al., 1997; Chakravarti, et al., 2001;

Marques et al., 2002;Yasin et al., 2004; Yasin et al., 2005).

The previously applied procedures of manual, graphical or trial and error based

estimation of kinetics parameters require significant time and efforts (Huang and Rempel, 1997;

Ochoteco et al., 2001; Nele et al., 2001; Matos et al., 2001; Khare et al., 2002; Lo and Ray,

2005; Neto et al., 2005; Kou et al., 2005; Hagen, 2006; Mehdiabadi and Soares, 2013).

Moreover these techniques are only reliable for small number of parameters.

This section presents the methodology for estimation of kinetic parameters that is based

on a systematic optimization strategy known as differential evolution (DE).

3.4.1 Numerical solution procedure

Model equations developed in previous chapter include a set of coupled, nonlinear and stiff

ordinary differential equations for the dynamic polymerization. These ordinary differential

equations (ODEs) were solved with MATLAB™

7.0.1 software (MATLAB version 7.0.1, 2004).

88

For numerically solving stiff differential equations, certain implicit methods, in particular

backward differentiation methods, perform much better than explicit ones. Explicit numerical

methods usually experience instability on a stiff equations.

The MATLAB ODE suite contains two implicit methods for stiff systems:

The implicit Runge–Kutta pair ode23s of orders 2 and 3,

The implicit numerical differentiation formulas ode15s of orders 1 to 5.

Both the methods have a built-in local error estimate to control the step size. Moreover

ode15s is a variable-order packages which use higher order methods and smaller step size when

the solution varies rapidly. The code ode15s for stiff systems is a quasi-constant step size

implementation of the numerical differentiation formulas of order 1 to 5 in terms of backward

differences. In this study, the model equations were worked out with ODE-15s function provided

in MATLAB™

7.0 software.

3.4.2 Objective function formulation

The goal of the optimization process is to find the parameter values that result in a maximum or

minimum of a function called the objective function. Objective function is a mathematical

expression describing a relationship of the optimization parameters or the result of an operation,

such as simulation that uses the optimization parameters as inputs. In this section, the

development of expression for objective functions on different basis is discussed.

89

Polymerization rate

Overall rate of polymerization is governed by the kinetic rates of monomer trapping and

monomer insertion. The models assume that the intrinsic rates of monomer trapping and

insertion are independent of active site location on the polymer chain. Experimental evidences

justify this assumption for monomer trapping (Simon et al., 1999; Roos et al., 1997; Chakravarti,

et al., 2001; Marques et al., 2002; Yasin et al., 2004; Yasin et al., 2005). Thus the rate of

polymerization can be viewed as the rate of disappearance of the monomer in ethylene (Equation

3.23) and propylene (Equation 3.69) polymerization under steady as well as transient states.

Further, since there is a negligible consumption of monomer in initiation and chain transfer

reactions as compared to the propagation reaction (long chain assumption), the rate of

polymerization can be calculated by Equation 3.98 for both ethylene and propylene

polymerization.

l

pMp Mkrr 0 (3.98)

The values of rate of polymerization calculated from Equation 3.98 are compared with

experimental ones at each measured point. All deviations between experimental and calculated

values (errors) are squared and summed up to form an objective function given in Equation 3.99.

n

j jp

jpjp

r

rrkF

1

2

exp,,

mod,,exp,,)(

(3.99)

90

Molecular weights

If the experimental, end of the run values, of number average and weight average molecular

weights are available, additional objective function can be formulated as given by Equation

3.100.

2

exp,

mod,exp,

2

exp,

mod,exp,)(

w

ww

n

nn

M

MM

M

MMkG

(3.100)

where mod,nM and mod,wM are the values calculated from Equations 3.43 & 3.44 for ethylene and

Equations 3.91 & 3.92 for propylene polymerization respectively.

Microstructural data

In propylene polymerization, when experimental microstructural (methyl pentad distribution

etc.) data are available, fractions of vinyl-terminated chains, butenyl-terminated chains, isobutyl-

terminated chains calculated from model (Equations 3.94 through 3.96) facilitate formulating yet

another objective function as shown in Equation 3.101.

2

exp,

mod,exp,

2

exp,

mod,exp,

2

exp,'

mod,'exp,')(

i

ii

b

bb

v

vv

f

ff

f

ff

f

ffkH

(3.101)

The parameter vector k, sought to be estimated involves the kinetic rate constants for the

reactions asserted in the model. These parameters have been determined by minimizing the

above-mentioned objective function equation(s). Let alone that the model equations are the

constraints to this optimization problem. Inclusion of multiple objective functions render more

appropriate estimation of kinetic parameters as they are large in number, interrelated and pose

different magnitudes of effect on polymerization rate and polymer properties.

91

3.4.3 Optimization approach

Minimization of the objective function in parameter estimation problems, particularly in the field

of polymer engineering, may lead to difficult numerical problems related to the large number of

model parameters, high correlativity among model parameters and multimodal nature of the

objective function. In order to overcome these difficulties, the use of heuristic optimization

method, differential evolution (DE) is proposed and worked out in this study.

Various established methods are being used as parameter estimation techniques, such as

the graphical method and the gradient-based non-linear optimization method (Kenny, 1994; Klar

et al., 2002; Di et al., 2008). The graphical method is limited and it does not have precision to

calculate the parameters. The graphical method can only take on those problems that can be

converted to linear regression problems, while the gradient-based nonlinear optimization method

is easy to trap into local optima.

Recent studies on optimization technique have developed an attractive class of

algorithms, viz. evolutionary algorithms. Evolutionary algorithms deal simultaneously with a set

of possible solutions (the so-called population) and have been received increasing attention due

to their powerful capability for global search. Some popular evolutionary algorithms are genetic

algorithm (GA), ant colony optimization (ACO), particle swarm optimization (PSO) and

differential evolution (DE). Differential evolution has been successfully applied to solve a wide

range of optimization problems such as optimization of non-linear functions (Angira and Babu,

2003), optimal design of shell and tube heat exchangers (Babu and Munawar, 2007),

optimization of process synthesis and design problems (Angira and Babu, 2006), optimization of

non-linear chemical processes (Babu and Angira, 2006) and Estimation of heat transfer

parameters in a trickle-bed reactor (Babu and Sastry, 1999).

92

3.4.3.1 Differential evolution (DE)

DE is a stochastic, population-based optimization algorithm introduced by Storn and Price in

1996 developed to optimize real parameter, real valued functions. Genetic algorithms (GA),

artificial neural networks (ANN), simulated annealing (SA) and differential evolution (DE)

algorithms are among the most famous nontraditional optimization methods used in the

combinatorial optimization field.

DE belongs to the class of genetic algorithms (GAs) which use biology-inspired

operations of crossover, mutation, and selection on a population in order to minimize an

objective function over the course of successive generations. Differential Evolution is a parallel

direct search method which utilizes NP, D-dimensional parameter vectors xi,G (i = 1; 2; . . .; NP)

as a population for each generation G. NP does not change during the minimization process. The

initial vector population is chosen randomly and in such a way that it should cover the entire

parameter space. DE generates new parameter vectors by adding the weighted difference

between two population vectors to a third vector. This operation is called mutation. The mutated

vector’s parameters are then mixed with the parameters of another predetermined vector, the

target vector, to yield the trial vector. Parameter mixing is referred to as crossover (Storn and

Price, 1997). The cost (in case of minimization) of the objective function is evaluated with target

and trial vectors and compared. The vector giving smaller cost secures a place in the population

of next generation. Same procedure is repeated NP times to decide the next generation of vectors

(Figure 3.1) and continues from one generation to another till some convergence criterion is met

as described in a flow sheet in Figure 3.2.

The key parameters of control in DE are: NP- population size, CR- cross over constant,

and F - weight applied to random differential (scaling factor). The details of DE algorithm and

93

pseudo code are available in the literature (Goldberg, 1989; Price and Storn, 1997; Onwubolu

and Babu, 2004; Babu and Angira, 2006; Angira and Babu, 2006). These key parameters of DE

are problem dependent. However, certain guidelines and heuristics are available in literature for

the choice of these parameters.

Natural logarithmic differential evolution (NLDE)

Differential evolution is a floating-point encoding evolutionary algorithm for global optimization

over continuous spaces, which also works well with discrete variables (Price et al., 2005;

Feoktistov, 2006). Since inception, algorithm has been modified and extended several times with

new versions being proposed (Fan and Lampinen, 2003; Ali and Törn, 2004; Rakesh and

Santosh, 2007; Ali, 2007; Liu and Wang, 2009; Pham, 2012).

In simple DE, linear mapping rule applies, in the initialization of normalized population

according to Equation 3.102 and in the mutation operation according to Equation 3.103.

New variable = Min value of the variable +

Random number (max value of the variable - Min value of the

variable)

(3.102)

Mutant vector = Base vector + F (Difference of two randomly chosen vectors) (3.103)

For a very wide range of variable values, linear rule of mapping may not be able to

exploit the entire search domain to generate the initial population which poses a problem of

improper population distribution. Similar trouble also arises across the generations due to

mutation operator (Sheth and Babu, 2008).

94

Figure 3.1 Determination of population for sequent generation in DE.

95

Figure 3.2 Flow sheet: Differential evolution optimization procedure.

96

In order to avert the problem of improper population distribution, natural logarithmic

mapping rule is proposed for initialization of normalized population and mutation as given by

Equation 3.104 and Equation 3.105 respectively.

New variable = exp {loge(Min value)+Random no. [loge(Max value)-loge(Min

value)]} (3.104)

Mutant vector = exp {loge(variable x3) + F [ loge (variable x1)- loge (variable x2)]} (3.105)

Natural logarithmic transformation of variables provide additional advantage by ensuring

that all kinetic parameter estimates are positive (since negative values do not make physical

sense). Natural logarithmic differential evolution (NLDE), an amended version of simple DE, is

used by incorporating natural log initialization and natural log mutation to take care of wide

ranges of variable values. This approach of optimization is applied by taking Equation(s) 3.99

through 3.101 as objective function to be minimized to find the globally optimum set of kinetic

parameters. Theoretical values were calculated from model equations for the objective function

and latter was minimized iteratively till convergence. Based on heuristics the values of DE key

parameters in this study were set as follows:

The population size (NP) was taken as fifty times the size of parameter vector,

Weighing factor (F) = 0.7 and

Cross over constant (CR) = 0.9

The ranges of the kinetic parameters for simulation were chosen based on the reported values in

the literature.

97

Summary of the chapter: Comprehensive mathematical models developed for ethylene and

propylene polymerization catalyzed with metallocene catalyst are discussed in detail. Developed

models are able to capture essential polymer properties, including number- and weight average

molecular weights, polydispersity index (PDI); fraction of polymer chains with terminal double

bond and frequency of long chain branching in ethylene polymerization; fraction of vinyl-

terminated chains, butenyl-terminated chains, isobutyl-terminated chains and vinylidene-

terminated chains in propylene polymerization.

Numerical solution procedure of the modeling equations and objective function

formulation are discussed in the later sections. Subsequently, a detailed overview of optimization

techniques used for kinetic parameter estimation is provided with special attention to differential

evolution approach. A remediated version of simple DE, viz. natural logarithmic differential

evolution (NLDE) is proposed, which is applied in parameter estimation in this study.

Methodology presented was applied to simulate the developed models with data reported in

literature. Obtained results are discussed in the next chapter.

98

CHAPTER – 4

RESULTS AND DISCUSSION

In this chapter, the simulation results obtained for the ethylene and propylene polymerization

using different metallocene catalyst systems are presented in sections 4.1 and 4.2 respectively.

Sections 4.1.1 and 4.1.2 detail the results obtained for ethylene polymerization in gas phase

with silica supported and in solution phase with in-situ-supported zirconocene catalysts

respectively. Results of solution phase propylene homopolymerization with various

metallocene catalysts are presented and discussed in Sections 4.2.1 through 4.2.7. Models

developed in Chapter 3 are simulated for validation and study of effects of reaction

parameters with data reported in open literature. Experimental conditions and corresponding

references are briefed in Table 4.1 and Table 4.2. All polymerizations in referenced works

were carried out in a stirred, semi-batch autoclave reactor with a flowmeter unit.

In all ethylene and propylene polymerization studies carried out in this work, model

equations are first solved analytically. To obtain analytical solution, the reactions of chain

propagation, spontaneous deactivation and chain transfer to monomer are considered. It was

possible to solve the model equations analytically since the concentration of monomer was

held constant (by maintaining its pressure). Differential equations describing moments of

living and dead polymer chain length distribution were analytically solved yielding Equation

4.1 through Equation 4.6.

tkP d

l exp).0(0 (4.1)

tMkktk

k

PkktMdd

tM

tMpl

expexp)0(

1 (4.2)

99

tMkkt

k

MkPkk

tMkktkkkk

Pkk

tMd

tM

ptMp

tMddtMp

tM

tMpl

exp.)0(2

expexp2)0(

22

(4.3)

tk

k

PMkkd

d

tMd

exp1)0(

0

(4.4)

dtMdd

d

tMd

tMd

tM

tMdtMp

kMkkk

tk

Mkk

tMkk

k

PMkkkk

11exp

exp

)0(1

(4.5)

tMkkt

MkkMkk

tMkk

k

MkPkk

kMkk

k

tk

Mkk

tMkk

k

kkPMkkkk

trd

tMdtMd

tMd

tM

ptMp

dtMd

d

d

tMd

tMd

tM

tMptMdtMp

exp.

1exp)0(2

11

expexp

2)0(22

(4.6)

Analytical solution described above is only possible for semibatch reactor with

invariable monomer concentration throughout the polymerization. For the parameters

estimation in all the subsequent studies in this work, this approach is utilized along with

NLDE to determine the coarse values of kinetic parameters in order to judge the range of

parameters those were required in fine optimization.

100

Table 4.1 Sections discussing results of ethylene polymerization

Sec. Catalyst system Reaction conditions Solvent Reference

4.1.1 E1: Silica supported (Me2Si[Ind]2ZrCl2) / MAO P =5 bar; Catalyst: 0.2 g; Al/Zr = 386;

T = 40 °C, 50

°C, 60

°C and 70

°C

- Roos et al. (1997)

4.1.2 E2: In-situ-supported (Et[Ind]2ZrCl2) / MAO P = 80 psig; Catalyst: 6 μmol; Al/Zr = 500;

T = 40 °C, 60

°C, 80

°C, 100

°C, 120

°C.

Hexane Chu et al. (2000)

* For the sake of brevity, above two catalysts shall be denoted as E1 and E2 respectively from here onwards.

Table 4.2 Sections discussing results of propylene polymerization

Sec. Catalyst Reaction conditions Solvent Reference

4.2.1 P1: (Me2Si[Ind]2ZrCl2) / MAO P = 2 bar; [Zr] = 10 μmol/L; T = 25 °C and 75

°C;

Al/Zr 500 and 2000

Toluene Marques et al.

(2002)

4.2.2 P2: (Et(Ind)2ZrCl2) / MAO - Do - - Do -

4.2.3 P3: (Me2Si(Ind)2HfCl2) / MAO P = 2 bar; [Hf] = 10 μmol/L; T = 40 °C and 80

°C;

Al/Hf 500 and 2000

- Do -

4.2.4 P4: (Et(Ind)2HfCl2) / MAO - Do - - Do -

4.2.5 P5: ([2,4,6-Me3Ind]2ZrCl2) / MAO P = 0.98 atm; [Zr] = 20 μmol/L; T = 0 °C;

Al/Zr = 2000 and 4000

- Do - Yasin et al.

(2004)

4.2.6 P6: ([2,4,7-Me3Ind]2ZrCl2) / MAO P = 0.98 atm; [Zr] = 20 μmol/L; T = 0 °C;

Al/Zr = 1000, 2000 and 4000

- Do -

4.2.7 P7: (Me2Si[2,4,6-Me3Ind]2ZrCl2) / MAO P = 0.98 atm; [Zr] = 20 μmol/L; Al/Zr = 2000;

T = 30 °C, 50

°C and 70

°C

- Do - Yasin et al.

(2005)

* For the sake of brevity, above seven catalysts shall be denoted as P1, P2, P3, P4, P6 and P7 respectively from here onwards.

101

4.1 Ethylene polymerization

Ethylene polymerization model is applied to gas phase polymerization with silica supported,

bridged Me2Si[Ind]2ZrCl2 catalyst and to solution phase polymerization with in-situ-silica

supported, bridged Et[Ind]2ZrCl2 catalyst. Based on experimental conditions, suitable

assumptions are made and a truncated form of comprehensive model is applied to both the

cases. The set of reactions considered are described in corresponding sections ahead.

4.1.1 Ethylene polymerization with Me2Si[Ind]2ZrCl2 (E1)/MAO

Ethylene polymerization model (EPM), discussed in Section 3.2.2, is applied to gas phase

polymerization of ethylene with silica- supported Me2Si[Ind]2ZrCl2 catalyst and kinetic

parameters are obtained. Experimental data for model validation are taken from Roos et al.

(1997). Simulations are carried out (with ODE-15s function provided in MATLAB™ 7.0

software) using natural logarithmic differential evolution approach of optimization to estimate

the kinetic parameters.

Model description

The gas phase production of polyethylene by silica supported Me2Si[Ind]2ZrCl2 catalyst is a

multistep process that necessarily includes initiation, propagation, and termination. Following

assumptions are made while employing the comprehensive ethylene polymerization model:

Assumptions

(i) Instantaneous formation of active sites (reaction between catalyst and cocatalyst).

(ii) First-order propagation with respect to monomer and the active site is assumed, and

the reactivity of the complex species does not depend on the length of the polymeric

chain.

102

(iii) Chain transfer takes place to monomer only and follows first order kinetics. This

assumption is induced, as the reactor was flushed with ethylene several times after

scavenging and catalyst introduction. This precludes the possibility of chain transfer to

anything but ethylene.

(iv) The same type of site generates after transfer as is primitively formed by activation of

catalyst with cocatalyst. So chain transfer step does not change the number of active

sites.

(v) Monomer consumption in initiation and chain transfer reactions is negligible as

compared to the propagation reaction (long chain assumption).

(vi) First-order deactivation of active sites.

Ethylene polymerization reactions considered based on above assumptions are

described in Table 4.3.

Table 4.3 Reactions Considered in Ethylene Polymerization


1. )0(PCocatCat Instantaneous catalyst activation



4. iDPiP d

kd 0 {chain} Spontaneous catalyst

deactivation 5. 00 d

k PP d {site}

6. 1)( PiDMiP tMk


103

Estimated parameters and effect of temperature

Figure 4.1 shows the polymerization rates predicted by the model proposed by Roos et al.

(Section 2.4; Page 51) and ethylene polymerization model (Section 3.2.2) developed in this

study. Roos et al. modeled the polymerization rate assuming that deactivation of the catalyst

increases with increasing polymerization rate under isothermal conditions. Since they did not

consider initiation or any chain transfer reaction, the rate profiles are obtained exponentially

decreasing from a maximum value. For the same reason, polymerization rates are under

predicted at low temperatures (50 °C and 60

°C) and over predicted at 70

°C.

On the other hand, polymerization rates predicted by EPM exhibit a good agreement

with experimental data, at all the temperatures (40 °C, 50

°C, 60

°C and 70

°C). Estimated

kinetic parameters and objective function values F(k) are shown in Table 4.4. Close range of

objective function values (from 0.29934 to 0.6735) obtained, shows good fit with

experimental observations. Rates of initiation and propagation are increasing with increase in

temperature, as inferred from the estimated rate constants for these reactions. At the beginning

of polymerization, also referred to as induction period, the monomer is mainly consumed in

initiation followed by propagation reaction. During this period, the slope of polymerization

rate vs. time curve is indicative of the rate of initiation. In Figure 4.1, both, the initial

experimental polymerization rates and corresponding EPM predictions, clearly evince that

initiation and propagation rates are increasing with increase in temperature. Frequency of

spontaneous deactivation and chain transfer to monomer are also increasing with increase in

temperature, moreover the latter termination mechanism dominates over the former.

Increasing rates of deactivation and transfer to monomer at 50 °C, 60 °C and 70 °C are

responsible for a steeper decay in polymerization rate after reaching a maximum value.

104

0 100 200

0.0

8.0x10-3

1.6x10-2

40 0C

50 0C

60 0C

70 0C

Po

lym

eri

za

tio

n r

ate

(m

ole

s/L

/s)

Time (minutes)

Figure 4.1 Ethylene polymerization rate vs. time with Me2Si[Ind]2ZrCl2 (E1)/MAO;

Symbols: Exp data; Lines: Model Prediction ‐‐‐ (Roos et al.), — (EPM; Section 3.2.2).

[Catalyst (E1) = 0.2 g; P = 5 bar; Al/Zr = 386]

105

Model proposed by Roos et al. is not capable to predict average molecular weights and PDIs.

Molecular weight distribution obtained with EPM is shown in Table 4.5. Average molecular

weights are decreasing with increase in temperature. For an increase of 10 °C, from 40 °C to

70 °C, the weight average molecular weight ( wM ) is found to decrease by 67.40 %, 70.47 %

and 81.67 % respectively. This inverse trend is normal in chain growth polymerization and is

usually ascribed to the high activation energies for chain transfer reactions as compared to the

propagation reaction (Rudin, 1999). With increase in temperature, the rate of chain

termination to monomer increases rapidly as compared to the rate of propagation, which

results in decreasing molecular weights. Polymers prepared with metallocene catalysts

possess narrow molecular weight distribution, with polydispersities ranging from 2.0 to 2.5,

which is a consequence of the single-site feature of the metallocenes (Stevens; 1999).

Polydispersity indices of polyethylene prepared with Me2Si[Ind]2ZrCl2/MAO catalyst system

are found to be 1.999 irrespective of temperature.

Simulations are carried out further, to study the effects of ethylene pressure and

catalyst amount on polymerization rate and average molecular weights.

Effect of ethylene pressure

Polymerization rate is linearly increasing with ethylene pressure at all the temperatures as

shown in Figures 4.2. Low pressures (1-3 bar), i.e., low concentrations of monomer, reasons

low rates that are steady and maintained (due to negligible transfer reaction). At higher

pressures (5-7 bar), higher polymerization rates are obtained, but at the same time, transfer to

monomer also increases with high monomer concentrations resulting in steeper decay in

polymerization rates.

106

Table 4.4 Estimated Parameters for Me2Si[Ind]2ZrCl2 (E1)/MAO

T (°C) 40 50 60 70

ink ×10-5

(M-1

.s-1

) 8.4474 26.975 35.832 44.951

pk ×10-3

(M-1

.s-1

) 4.3141 7.2207 42.568 195.420

dk ×10-3

(s-1

) 42.032 45.265 54.526 94.095

tMk (M-1.s

-1) 4.9690 5.5374 6.4339 7.0468

F(k) (-) 0.29934 0.56928 0.67350 0.45939

Table 4.5 Predicted Molecular Weights & PDI with Me2Si[Ind]2ZrCl2 (E1)/MAO

T (°C)

nM (g/mol) wM (g/mol) PDI

40 9.628938 × 105 1.925759 × 10

6 1.999970

50 3.139822 × 105 6.276838 × 10

5 1.999106

60 9.268304 × 104 1.853654 × 10

5 1.999990

70 1.698616 × 104 3.397203 × 10

4 1.999982

107

0 50 100 150 200

0.0

3.0x10-3

6.0x10-3

9.0x10-3

1.2x10-2

1.5x10-2

7 bar

5 bar

3 bar

Po

lym

eri

za

tio

n r

ate

(m

ole

s/L

/s)

Time (minutes)

1 bar

(a)

0 50 100 150 200

0.0

4.0x10-3

8.0x10-3

1.2x10-2

1.6x10-2

2.0x10-2

Po

lym

eri

za

tio

n r

ate

(m

ole

s/L

/s)

Time (minutes)

7 bar

5 bar

3 bar

1 bar

(b)

108

0 50 100 150 200

0.0

6.0x10-3

1.2x10-2

1.8x10-2

2.4x10-2

Po

lym

eri

za

tio

n r

ate

(m

ole

s/L

/s)

Time (minutes)

7 bar

5 bar

3 bar

1 bar

(c)

Figure 4.2 Polymerization rate vs. time: Effect of pressure.

[Catalyst (E1) = 0.2 g, Al/Zr = 386, T = (a) 50 °C, (b) 60 °C (c) 70 °C]

As shown in Figures 4.3(a), at 50 °C, average molecular weights are increasing

slightly and not affected much with a change in ethylene pressure. A similar trend is obtained

at 60 °C as shown in Figure 4.3(b). However, at 70 °C [Figure 4.3(c)], an increase in wM from

2.03457 × 104 to 3.0561 × 10

4 is obtained for a change in pressure from 1 bar to 3 bar. With

further increase in pressure till 7 bar, a slight increase in average molecular weights are

observed. These results come along to be consistent with the assumption that the chain

transfer to monomer reaction is bimolecular giving a unvarying wM with respect to ethylene

concentration (pressure).

109

0 2 4 6 8

2.0x105

4.0x105

6.0x105

A

ve

rag

e m

ole

cu

lar

we

igh

t (g

.mo

l-1)

Pressure (bar)

Mn

Mw

T = 50 0C

(a)

1 2 3 4 5 6 7

0.00

7.50x104

1.50x105

2.25x105

T = 60 0C

Ave

rag

e M

ole

cu

lar

we

igh

t g

.mo

l-1

Pressure (bar)

Mn

Mw

(b)

110

1 2 3 4 5 6 7

0.0

2.0x104

4.0x104

T = 70 0C

Ave

rag

e M

ole

cu

lar

we

igh

t (g

.mo

l-1)

Pressure (bar)

Mn

Mw

(c)

Figure 4.3 Effect of pressure on average molecular weights.

[Catalyst (E1) = 0.2 g, Al/Zr = 386, T = (a) 50 °C, (b) 60 °C (c) 70 °C]

Effect of catalyst Amount

A steady increase in polymerization rate with increase in catalyst amount at constant

temperature and pressure is observed as shown in Figures 4.4. At higher temperatures, the rate

reaches to a maximum within no time and then decreases steeply, suggesting that both, the

initiation and the termination rates increase staggeringly with catalyst amount. With variation

in initial catalyst amount, average molecular weights and PDIs are not affected and the values

are upheld to those given in Table 4.5. In literature, for metallocene catalysts average

molecular weights are reported to be decreasing with increase in catalyst concentration

[Estrada and Hamielec (1994); Rieger and Janiak (1994); Kaminsky (1996); Zohuri et al.

(2005); Cheng and Tang (2010)]. This phenomenon is commonly explicated by the fact that

there is an increase in rate of chain transfer reactions which are dependent on the active site

concentration i.e. chain transfer to monomer, chain transfer to cocatalyst and β-hydride

111

elimination. The model applied to the present case is based on the assumption that the chain

transfer takes place to monomer only. Increase in catalyst amount seems to affect both, the

propagation rate and chain transfer rate equivalently at a given temperature and ethylene

pressure, due to which an invariant MWD is obtained.

0 50 100 150 200

0.0

4.0x10-3

8.0x10-3

1.2x10-2

1.6x10-2

2.0x10-2

0.5 g

0.4 g

0.3 g

0.2 gPo

lym

eri

za

tio

n r

ate

(m

ole

s/L

/s)

Time (minutes)

0.1 g

Zr

(a)

0 50 100 150 200

0.0

5.0x10-3

1.0x10-2

1.5x10-2

2.0x10-2

2.5x10-2

Po

lym

eri

za

tio

n r

ate

(m

ole

s/L

/s)

Time (minutes)

0.5 g

0.4 g

0.3 g

0.2 g

0.1 g

Zr

(b)

112

0 50 100 150 200

0.0

6.0x10-3

1.2x10-2

1.8x10-2

2.4x10-2

3.0x10-2

3.6x10-2

Po

lym

eri

za

tio

n r

ate

(m

ole

s/L

/s)

Time (minutes)

0.5 g

0.4 g

0.3 g

0.2 g

0.1 g

Zr

(c)

Figure 4.4 Polymerization rate vs. time: Effect of catalyst amount.

[P = 5 bar, Al/Zr = 386, T = (a) 50 °C, (b) 60 °C (c) 70 °C]

4.1.2 Ethylene polymerization with in-situ-supported Et[Ind]2ZrCl2 (E2)/MAO

Ethylene polymerization model is applied to solution phase polymerization of ethylene with

in-situ-silica supported Et[Ind]2ZrCl2 catalyst and kinetic parameters are obtained. Data for

the model validation are taken from Chu et al. (2000).

Model description

Some rudimentary assumptions made while employing the model are described hereunder:

Assumptions

(i) Constant and uniform temperature and ethylene concentration inside the reactor.

(ii) Instantaneous vapor-liquid equilibrium. In solution polymerization, the concentration

of monomer in the liquid phase is dependent upon the solubility of the gas in the

solvent. Atiqullah et al. (1998), compared various equations of state for predicting

113

ethylene solubility in toluene under similar reaction conditions and observed that

Peng-Robinson (PR) and Soave–Redlich–Kwong (SRK) equations of state are equally

good for the purpose. Here, Peng-Robinson equation of state (PR-EOS) is used to

determine the concentration of ethylene in solvent at different temperatures and

monomer pressures.

(iii) Negligible polymer volume as compared to the total volume of the reactor, i.e.

constant gas-phase volume in the reactor.

(iv) Instantaneous activation of catalyst sites.

(v) First-order propagation with respect to monomer and the active site, and the reactivity

of the activated complex species does not devolve on the length of the polymer chain.

(vi) First-order deactivation of active sites. Spontaneous catalyst deactivation in a

propagating chain produces dead chain without terminal double bond.

(vii) Chain transfer to monomer, catalyst and cocatalyst produce dead chains with terminal

double bond.

(viii) Chain transfer to a dead polymer with terminal double bond produces long chain

branching.

Ethylene polymerization reactions considered based on above assumptions are

described in Table 4.6.


Model is simulated in order to estimate the kinetic parameters at different temperatures using

ethylene flow rate as a measure of polymerization rate. A very large population size (120

times the dimension) is used to make certain of receiving optimized estimates of parameters.

Table 4.7 summarizes the parameters estimates at 40 °C, 60 °C, 80 °C, 100 °C and 120° C at

fixed catalyst amount 6μmols, Al/Zr = 500 and ethylene pressure 80 psig. Figure 4.5 shows

114

the model predictions of polymerization rate at different temperatures, which are very close to

the experimental values.

Table 4.6 Reactions Considered in Ethylene Polymerization





4. iDPiP d

kd 0 {chain} Spontaneous catalyst

deactivation 5. 00 d

k PP d {site}

6. 1)( PiDMiP tMk


7. 0)( PiDCocatiP tCok


8. 0)( PiDiPk

β-hydride elimination

9. jiPjDiP lcbk )( Long-chain branching

As defined in Equation 3.99 and reported in Table 4.7, the values of objective function

indicate that the model is capable of predicting kinetic behaviour for all the temperatures

expeditiously. Function values obtained are ranging closely, with a least value of 1.1186 at

80 °C representing the best fit to experimental observations as compared to highest value of

1.6063 at 120 °C. Significantly lower values of propagation rate constants at 40

°C and 60

°C

are obtained relating to very low polymerization rate and catalyst activity with respect to those

at higher temperatures. At 80 °C, high propagation rate as compared to those at lower

temperatures trace higher polymerization rate with highest activity of the catalyst.

Polymerization rates are increasing with increase in temperature from 40 °C to 120 °C.

115

Declining rate profiles at 100 °C and 120

°C can be explained by serious catalyst deactivation,

transfers to monomer and β-hydride elimination at higher temperatures as pointed out by the

values of these parameters obtained.

Figure 4.6 shows the predicted decrease in concentration of active catalyst sites with

time at different temperatures. At 40 °C, 60 °C and 80 °C, all the active catalyst sites are

occupied within initial 15 minutes, whereas at higher temperatures (100 °C and 120 °C)

certain fraction of those could not attach a monomer to initiate the chain.

Experimental kinetic data at different operating conditions, like different catalyst

amount, ethylene pressure and cocatalyst to catalyst mole ratio, are utilized to validate the

model at fixed temperature of 60 °C. Parameters estimated at 60 °C, 80 psig and 6 μmol

catalyst amount with Al/Zr = 500 are used to verify the model responses at various conditions.

Table 4.7 Estimated Parameters for Et[Ind]2ZrCl2 (E2)/MAO

T

(°C)

ink ×103

(M-1

.s-1

)

pk

(M-1

.s-1

)

dk ×105

(s-1

)

tMk ×103

(M-1

.s-1

)

tCok ×106

(M-1

.s-1

)

k ×106

(s-1

)

lcbk ×105

(M-1

.s-1

)

F(k)

(-)

40 7.9660 17.1863 1.5377 3.3232 78.1863 1.3426 1.6298 1.3832

60 12.2164 44.9804 2.4541 19.5830 43.1982 7.9277 5.6526 1.1674

80 14.8433 188.9502 4.2504 35.4385 4.1940 8.6007 14.1722 1.1186

100 21.4832 529.4216 8.5169 56.6386 1.6294 1107.979 16.3020 1.3586

120 63.7560 938.188 74.0553 86.9489 1.4610 1307.70 30.3491 1.6063

116

0 10 20 30 40 50 60

0.0

1.0x10-3

2.0x10-3

3.0x10-3

40 0C

60 0C

T 80 0C

100 0C

120 0C

Po

lym

eri

za

tio

n r

ate

(m

ole

s/L

/s)

Time (minutes)

Figure 4.5 Effect of temperature on ethylene polymerization rate with in-situ-supported

Et[Ind]2ZrCl2 (E2)/MAO; solid lines are model predictions.


0 10 20 30 40 50 60

0

2

4

6

40 0C

60 0C

80 0C

100 0C

120 0C

Active

ca

taly

st site

s (m

ol)

Time (minutes)

Figure 4.6 Active catalyst sites vs. reaction time.


117

Effect of ethylene pressure

The model also predicted the proportional changes in polymerization rate at different ethylene

pressures as shown in Figure 4.7. The trend vindicates the first order dependence of rate on

ethylene concentration as no declining regions are seen. Figure 4.8 shows that, at 40 psig

pressure active catalyst sites stayed available for all the polymerization time suggesting the

non-initiation of some active site. At 80 psig pressure, active site were occupied within 10

minutes and for higher pressures within 20 minutes.

Effect of catalyst amount

Figure 4.9 shows a good match between experimental observations and model predictions at

3, 12 and 18 μmol of initial catalyst amount taken. The model adequately captures the features

of polymerization with in-situ-supported metallocene catalyst by following the sustained

polymerization rate with time and increase in the same with the increase in catalyst amount.

Figure 4.10 portrays that all the active catalyst sites were occupied within 10 minutes,

irrespective of initial amount of catalyst used.

Effect of cocatalyst to catalyst mole ratio

Effect of cocatalyst to catalyst mole ratio on the model predictions of polymerization rate are

shown in Figure 4.11. Use of high Al/Zr ratio brings in higher polymerization rate and for the

entire range of ratios, the maximum rate was reached within 10 minutes. Figure 4.12 depicts

that for lower ratios (250 and 500), active catalyst sites disappeared within first 10 minutes,

whereas for higher ratios (above 500) these decreased with time but remained available for

entire polymerization time. This is possible for high amount of cocatalyst delays the

spontaneous catalyst deactivation and also facilitates the regeneration of deactivated catalyst.

118

0 10 20 30 40 50 60

0.0

6.0x10-4

1.2x10-3

1.8x10-3

2.4x10-3

3.0x10-3

40 psig

80 psig

120 psig

160 psig

Time (minutes)

Po

lym

eri

za

tio

m r

ate

(m

ole

s/L

/s)

Figure 4.7 Effect of pressure on ethylene polymerization rate; solid lines are model

predictions.


0 10 20 30 40 50 60

0.0

1.5

3.0

4.5

6.0

7.5

40 psig

80 psig

120 psig

160 psig

Activa

red

ca

taly

st site

s (m

ol)

Time (minutes)



119

0 10 20 30 40 50 60

0.0

4.0x10-4

8.0x10-4

1.2x10-3

1.6x10-3

2.0x10-3

18 mol

12 mol

6 mol

3 mol

Initial catalyst amount

Po

lym

eri

za

tio

n r

ate

(m

ole

s/L

/s)

Time (minutes)

Figure 4.9 Effect of catalyst amount on ethylene polymerization rate; solid lines are

model predictions.

[Al/Zr = 500, 60 °C, and 80 psig]

0 10 20 30 40 50 60

0

5

10

15

20

Active

ca

taly

sts

site

s (m

ol)

Time (minutes)

3 mol

6 mol

12 mol

18 mol

Initial catalyst amount


[Al/Zr = 500, 60 °C and 80 psig]

120

0 10 20 30 40 50 60

0.0

5.0x10-4

1.0x10-3

1.5x10-3

2.0x10-3

2.5x10-3

3.0x10-3

Al / Zr

250

500

1000

2000

4000P

oly

me

riza

tio

n r

ate

(m

ole

s/L

/s)

Time (minutes)

Figure 4.11 Effect of Al/Zr mole ratio on ethylene polymerization rate; solid lines are

model predictions.

[Catalyst (E2) = 6 μmol, T = 60 °C and P = 80 psig]

0 10 20 30 40 50 60

0.0

1.5

3.0

4.5

6.0

Al / Zr

Active

ca

taly

st site

s (m

ol)

Time (minutes)

250

500

1000

2000

4000


[Catalyst (E2) = 6 μmol, T = 60 °C and P = 80 psig]

121

Polyethylene properties

Table 4.8 presents model cyphered properties of polyethylene at different sets of operating

conditions. Following experimental observations, average molecular weights of polyethylene

obtained from the model are found to be decreasing with increase in temperature, whereas the

change in catalyst amount, cocatalyst to catalyst mole ratio or ethylene pressure brought

insignificant effect.

The calculated number average molecular weight values of polyethylene are ranging

from 35127.01 to 38166.63 for varation in catalyst amount, from 35127.01 to 39089.35, for

varation in cocatlyst to catalyst mole ratio and from 35127.01 to 37860.78 for varation in

ethylene pressure, which advises that change in catalyst amount, cocatalyst to catalyst mole

ratio or ethylene pressure have insignificant effect on molecular weight and its distribution of

the polymer produced by in-situ supported Et[Ind]2ZrCl2 catalyst.

For homogeneous and otherwise supported metallocene catalysts, average molecular

weights have been reported to be decreasing with increase in catalyst concentration or

cocatalyst to catalyst mole ratio by many researchers [Estrada and Hamielec (1994); Rieger

and Janiak (1994); Kaminsky (1996); Zohuri et al. (2005); Cheng and Tang (2010)]. This

phenomenon is usually explained by the fact that there is an increase in rate of chain transfer

reactions which are dependent on the active site concentration. It is worth noticing that, the

rate of propagation is also dependent on the active site concentration and when the active site

concentration is maintained during polymerization (as for in-situ supported catalyst),

propagation rate increases proportionally, resulting effectively no change in average

molecular weight.

122

Table 4.8 Polyethylene Properties with Et[Ind]2ZrCl2 (E2)/MAO

S. No. T

(°C)

Zr

(μmoles)

Al/Zr

(-)

P

(psig) nM

(Model)

wM

(Exp)

wM

(Model)

PDI

(Exp)

PDI

(Model)

f (=)

(Model)

lcb/1000C

(Model)

1. 60 3 500 80 38166.63 74038.10 76256.93 2.50 1.998 0.870 4.633 × 10-9

2. 60 6 500 80 35127.01 74234.10 70211.57 2.59 1.998 0.986 7.238 × 10-10

3. 60 12 500 80 35127.08 67110.50 70211.94 2.22 1.998 0.986 1.447 × 10-9

4. 60 18 500 80 35135.82 70916.20 70230.15 2.26 1.998 0.986 2.168 × 10-9

5. 60 6 250 80 38143.88 78666.70 76211.49 2.60 1.998 0.986 5.428 × 10-10

6. 60 6 500 80 35127.01 74234.10 70211.57 2.59 1.998 0.986 7.238 × 10-10

7. 60 6 1000 80 39089.35 80000.00 78022.34 2.13 1.996 0.987 2.501 × 10-14

8. 60 6 2000 80 38969.59 72000.00 77783.32 2.40 1.996 0.864 2.244 × 10-15

9. 60 6 4000 80 36296.29 69333.30 72483.69 2.20 1.997 0.781 9.308 × 10-16

10. 40 6 500 80 56975.08 - 112696.71 - 1.978 0.909 1.439 × 10-7

11. 60 6 500 80 35140.93 74234.10 70211.57 2.59 1.998 0.986 7.238 × 10-10

12. 80 6 500 80 29273.46 - 53102.05 - 1.814 0.972 1.265 × 10-11

13. 100 6 500 80 19669.60 - 39299.87 - 1.998 0.985 3.034 × 10-12

14. 120 6 500 80 13965.66 - 27931.31 - 2.000 0.992 5.615 × 10-12

15. 60 6 500 40 36419.99 59165.70 69598.61 2.44 1.911 0.887 8.061 × 10-12

16. 60 6 500 80 35127.01 74234.10 70211.57 2.59 1.998 0.986 7.238 × 10-10

17. 60 6 500 120 37412.19 75418.70 72579.66 2.61 1.940 0.845 3.105 × 10-8

18. 60 6 500 160 37860.78 73472.40 75607.98 2.62 1.997 0.965 5.798 × 10-9

123

As monomer is also acting as a chain transfer agent, the insight of the effect of ethylene pressure

on molecular weight may be gained by probing Equation 4.7 for number average degree of

polymerization. Estimated parameters (Table 4.7) indicate that chain transfer to monomer is

dominating over other transfer reactions, for which the contribution of other transfer reactions

may be neglected in the denominator of Equation 4.7. For such a situation, degree of

polymerization and so the molecular weight show up to be independent of monomer

concentration.

0 lcbtCotM

pn

kkCocatkMk

MkDP (4.7)

The effect of temperature is widely acknowledged with the reason that the activation

energy for chain transfer is greater than that for propagation. Consequently, early termination of

the chains results in lower average moelcular weight. Polydispersity in all the cases is obtained

very close to 2.

As inferred from calculated fraction of dead chains with double bond at the end, major

modes of chain termination, nearly for all sets of conditions, are believed to be chain transfer to

monomer, chain transfer to cocatalyst and β-hydride elimination. Relative magnitude of different

transfer reactions is evident from estimated parameters at various temperatures. Long chain

branching frequency is detected to be negligibly low, except only for low (40 °C) temperature

and high (120 and 160 psig) ethylene pressures, suggesting that the product is comprising of

linear chains and posseses high density.

124

4.2 Propylene polymerization

Model description

Propylene polymerization model with some elementary assumptions is applied to the solution

phase production of polypropylene catalyzed with various zirconium and hafnium based catalyst

systems. In all the studies hereinafter, simulations are carried out using 'natural logarithmic

differential evolution' approach of optimization.

Assumptions

(i) Instantaneous formation of active sites.

(ii) First-order propagation with respect to monomer and the active site, and the reactivity of

the activated complex species does not devolve on the length of the polymer chain.

(iii) First-order deactivation of active sites.

(iv) Chain transfer following a propagation by primary (1, 2) insertion takes place by β-

hydride transfer to the monomer, producing a vinylidene-terminated dead chain and

liberating an active center.

(v) Chain transfer to catalyst (Zr) takes place by β-hydride elimination, producing a dead

chain and a hydride activated complex which reinitiates and follows the features of a

primitive propagating chain.

(vi) A secondary (2, 1) insertion brings about a mis-inserted chain, which can undergo

propagation and terminate by β-hydride transfer to the monomer to produce a dead chain

with butenyl-end group.

(vii) Monomer consumption in the initiation, secondary (2, 1) insertion and all chain transfer

reactions is negligible as compared to the propagation reaction via primary (1, 2)

insertion.

125

(viii) Chain transfer to cocatalyst (MAO) occurs, producing a dead chain and a methyl

activated complex which reinitiates a new chain.

Polymerization reactions considered based on the above assumptions are described in

Table 4.9.

Table 4.9 Reactions Considered in Propylene Polymerization





4. iDPiP d

kd 0 {chain}


k PP d {site}

6. 1)( PiDMiP tMk Chain transfer to monomer

7. 0)( *,

H

kPiDiP H

β-Hydride elimination

8. )1(0* PMP rk

H Reinitiation after β-H elimination

9. )1( iRMiP sk Secondary (2, 1) insertion

10. )1( iPMiR spk Propagation after (2, 1) insertion

11. )1()( PiDMiR sMk Chain transfer after (2, 1) insertion

12. 0)( *,

Me

kPiDCocatiP Alt Chain transfer to cocatalyst

13. 10* PMP rAlk

Me Reinitiation after transfer to

cocatalyst

126

4.2.1 Propylene polymerization with Me2Si[Ind]2ZrCl2 (P1)/MAO

Propylene polymerization model is applied to solution phase polymerization of propylene with

Me2Si[Ind]2ZrCl2/MAO catalyst system and kinetic parameters are obtained. Data for the model

validation are taken from Marques et al. (2002).

Propylene concentration in toluene is calculated from Equation 4.8 for a specific temperature

(in °C) and pressure. [Bravakis et al. (1998) referred and used in Marques et al. (2002)].

psi 45at 1049.5 1001.1536.0

psi 30at 1066.3 1075.6354.0

psi 15at 1083.1 1037.3179.0

252

253

253

63

TT

TT

TT

X HC (4.8)


Kinetic parameters for Me2Si[Ind]2ZrCl2 (P1)/MAO catalyst system are estimated by simulating

the model with experimental data at 25 °C and 75 °C with Al/Zr molar ratio of 500.

Experimental data for Al/Zr ratio of 2000 are used to validate the model at both temperatures.

Figure 4.13 and Figure 4.14 present experimental and model predicted propylene polymerization

rates at 25 °C and 75 °C respectively. Experimental observations reveal that both, the

temperature and MAO to catalyst molar ratio have a significant effect on polymerization rate.

Model predictions are in very close agreement with experimental observations at both the

temperatures and Al/Zr molar ratios of 500 & 2000.

Figure 4.13 and Figure 4.14 show that with an increase in Al/Zr molar ratio,

polymerization rate increases at both the temperatures considered. Larger Al/Zr ratio gives rise to

higher concentration of activated complex at the beginning of the reaction which increases the

rate of initiation and consequently the rate of propagation. At very high Al/Zr ratio, the

127

decreasing polymerization rate after reaching a maximum may be explained by large rate of

chain transfer to cocatalyst.

Figure 4.15 explains that the temperature has a profound effect on polymerization rate.

Maximum rate is seen to increase four folds at 75 °C when compared with that at 25 °C, at fixed

catalyst concentration, Al/Zr ratio and pressure. Increase in propagation rate constant pk with

temperature is also in coherence with this observed fact. As understood by dk and tMk values

obtained, spontaneous deactivation and chain transfer to monomer are activated hugely with

increase in temperature. Ascribing to which, the polymerization rate is decreasing steeply at 75

°C after reaching a maximum.

Kinetic parameters and objective function [F(k)] values which indicate the extent of fit of

experimental data with model prediction are given in Table 4.10.

Active catalyst site concentration drops to near zero within 5 minutes and 10 minutes at

25 °C and 75 °C respectively as shown in Figure 4.16. Solubility of propylene in solvent

decreases with increase in temperature at fixed pressure (Equation 4.8), thereby reducing the

concentration of monomer in the reaction mixture. Further, the fact, ].[Mk in = 2.2388×10-3

s-1

at

25 °C vs. ].[Mk in = 0.2753×10-3

s-1

at 75 °C explains that chain initiation rate is slower at 75

°C. Active sites are deactivated spontaneously as well, frequency of which is obtained higher (cf.

dk , Table 4.10) at 75 °C.

128

0 10 20 30 40 50 60

0.0

0.5

1.0

1.5

2.0

2.5

Po

lym

eri

za

tio

n r

ate

(m

ol/L

/s)

Time (minutes)

1:500

1:2000

Zr:Al

Figure 4.13 Effect of Al/Zr mole ratio on propylene polymerization rate; solid lines are

model predictions.


0 10 20 30 40 50 60

0

2

4

6

Po

lym

eri

za

tio

n r

ate

(mo

les / L

/ s

)

Time (minutes)

1:500

1:2000

Zr:MAO


model predictions.


129

0 10 20 30 40 50 60

0.0

1.5

3.0

4.5

6.0

Po

lym

eri

za

tio

n r

ate

(m

ol/L

/s)

Time (minutes)

T

25 °C

75 °C

Figure 4.15 Effect of temperature on propylene polymerization rate; solid lines are model

predictions.


The overall rate of disappearance of active sites is higher at 25 °C due to which these are

exhausted little early. Fractional disappearance of active sites by spontaneous deactivation may

be determined by ].[/ Mkkk indd . This fraction is found less at lower temperatures and as per

calculations 10.28% active sites at 25 °C whereas, 53.1% active sites at 75 °C are figured to be

deactivated spontaneously.

Maximum concentration of hydride activated complex 0*

HP is noted to be

3.5409×10-9

μM (in 7 minutes) at 25 °C and 4.0866×10-7

μM (in 14 minutes) at 75 °C as shown

in Figure 4.17 and Figure 4.18 respectively.

130

Table 4.10 Estimated Parameters for Me2Si[Ind]2ZrCl2

(P1)/MAO

T (°C) 25 75

ink ×103

(M-1

.s-1

) 5.1845 10.7586

pk × 10-4

(M-1

.s-1

) 8.566 39.4588

dk × 104

(s-1

) 2.5665 3.1176

tMk (M-1

.s-1

) 2.5699 10.2576

Hk , ×106

(s-1

) 1.55277 11.7565

rk ×10-2

(M-1

.s-1

) 1.5294 152.700

sk ×107

(M-1

.s-1

) 1.3249 11.6351

spk ×104

(M-1

.s-1

) 1.4583 118.967

sMk (M-1

.s-1

) 0.047 1.0394

Altk , (M-1

.s-1

) 426.688 141.243

rAlk (M-1

.s-1

) 8.574 13.0285

F(k) (-) 0.272 0.03713

Table 4.11 Predicted Properties with Me2Si[Ind]2ZrCl2

(P1)/MAO

T (°C) 25 75

Exp Model Exp Model

nM ×10-4

(g/mol)

- 13.549 - 0.9925

wM ×10-4

(g/mol)

12.3 27.257 1.5 1.9984

PDI 1.8 2.011 2.8 2.013

vf (%) - 74.1 - 86.3

bf (%) - 5.2 - 3.4

if (%) - 20.7 - 10.3

131

0 10 20 30 40 50 60

0

5

10

A

ctive

ca

taly

st site

s (m

ole

s/L

)

Time (minutes)

T

25 °C

75 °C

Figure 4.16 Active catalyst site concentration vs. time.


With P1/MAO catalyst system, β-H elimination is observed to occur negligibly ( Hk , of

the order of 10-6

) as compared to all other modes of chain termination. Increase in temperature

enhances the frequency of β-H elimination. Due to higher concentration of monomer at 25 °C

than that at 75 °C, reinitiation rate after β-H elimination is higher, which is reflected by the

falling concentration of hydride activated complex after reaching a maximum. At 75 °C, due to

lower reinitiation rate, 0*

HP is almost steady beyond maximum.

Concentration of methyl activated complex 0*

MeP is found to reach a maximum of

0.8142 μM (1.8 min) followed by a steep decrease at 25 °C as compared to a maximum of

0.2329 μM (3.58 min) at 75 °C followed by slow decrease as shown in Figure 4.19.

132

0 10 20 30 40 50 60

0.0

1.0x10-9

2.0x10-9

3.0x10-9

4.0x10-9

Hyd

rid

e a

ctiva

ted

co

mp

lex (m

ole

s/L

)

Time (minutes)

Figure 4.17 Hydride actived complex concentration vs. time.


0 10 20 30 40 50 60

0.0

2.0x10-7

4.0x10-7

Hyd

rid

e a

ctiva

ted

co

mp

lex (m

ole

s/L

)

Time (minutes)

Figure 4.18 Hydride activated complex concentration vs. time.


133

Chain transfer to cocatalyst is decreasing with increase in temperature. This trend is also

observed with the subsequent cases studied in this work. MAO is an oligomer and consists

mainly of units of the basic structure [Al4O3Me6], which contains four aluminium, three oxygen

atoms and six methyl groups. As the aluminium atoms in this structure are co-ordinatively

unsaturated, the basic units join together and give rise to different structures as described in

Figure 2.10. The observed trend of decrease in chain transfer to MAO with increase in

temperature suggests the existence of different molecular structures of MAO at different

temperatures. It seems that MAO changes its structure from simple (linear or cyclic) at low

temperatures to a congested one (ladder or cage) at high temperatures and thereby offering a

steric hindrance for chain transfer. At 75 °C, the rectivation rate, after transfer to cocatalyst is

slow due to low concentrations of monomer and methyl activated complex, for which the

concentration of 0*

MeP is seen decreasing slowly opposite to that at 25 °C.

0 10 20 30 40 50 60

0.0

0.3

0.6

0.9

Me

thyl a

ctiva

ted

co

mp

lex (m

ole

s/L

)

Time (minutes)

T

25 °C

75 °C

Figure 4.19 Methyl activated complex concentration vs. time.


134

Average molecular weights, PDI and percentage of butenyl- & isobutyl-terminated chains

predicted by the model are given in Table 4.11. Degree of polymerization depends upon relative

rate of propagation against various termination rates as given by Equation 4.9.

MkkkCocatkMk

MkDP

sdHAlttM

pn

,,

(4.9)

Agreement between experimental observations and predicted results for MWD is shown

in Table 4.9. Low molecular weights obtained at higher (75 °C) temperature, may be attributed to

the relatively high frequency of termination via transfer to monomer, spontaneous deactivation

and β-H transfer. The model predicts Schulz-Flory distribution with a polydispersity index very

around 2 for all reaction conditions.

For P1/MAO, chain termination is understood to take place majorly via spontaneous

catalyst deactivation, transfer to monomer and β-Hydride transfer because vf values in Table

4.11 point the dominant presence of chains with vinylidene end group. Low bf values suggest

that the fraction of chains with butenyl end group which are produced by termination after

secondary insertion is miserable, which is expected for highly isotactic polypropylene. However,

with increase in temperature, bf is observed to decrease. This is due to relatively higher increase

in pk than the increase in sk values with increase in temperature. Further, it has been noted that

increased regioirregular (2,l) insertions slow down chain propagation and inhibit chain transfer to

the monomer. This effect is consistent with previous results reported in the literature for the

studied catalyst system [Busico et al. (1998)].

135

if value (Table 4.11) shows, 20.7% terminated chains bear isobutyl end group at 25 °C, which

represent a significant chain transfer to cocatalyst. Further, increase in temperature results in a

decreased rate of chain transfer to cocatalyst which is indicated by the decrease in if (10.3% at

75 °C). This chain transfer dominates at lower temperature, due to depressed, competing β-H

elimination rates [Amin (2007)].

Effect of Pressure

Figure 4.20 shows that an increase in monomer pressure results in a steady increase in

polymerization rate up to a maximum ranging in between 0.685 moles/L/s (15 psi) to 2.056

moles/L/s (45 psi) at 25 °C and fixed Zr = 10 μM, Al/Zr = 500. Increase in pressure seems to

increase the monomer concentration at reaction site and thereby increasing the propagation rate

proportionally as expected and obtained from simulation results. At 75 °C, higher polymerization

rates are observed {2.489 moles/L/s (15 psi) to 8.487 moles/L/s (45 psi)}, which do not continue

maintained due to high rates of termination at this temperature (Figure 4.21).

A marginal increase of 2.22 % (15-30 psi) and 0.87 % (30-45 psi) in weight average

molecular weight wM is observed with increase in pressure at 25 °C (Figure 4.22). Similarly,

at 75 °C, a maximum increment of 10.31 % in wM is seen (Figure 4.23). Therefore, an increase

in monomer pressure is believed to increase the polymerization rate appreciably with an incresed

intake of monomer but brings negligible effect on polymer molecular weights.

136

0 10 20 30 40 50 60

0.0

0.5

1.0

1.5

2.0

2.5

45 psi

30 psiP

oly

me

riza

tio

n r

ate

(m

ole

s/L

/s)

Time (minutes)

15 psi


[Catalyst (P1) = 10 μM, Al/Zr = 500, and T = 25 °C]

0 10 20 30 40 50 60

0

2

4

6

8

45 psi

30 psi

Po

lym

eri

za

tio

n r

ate

(m

ole

s/L

/s)

Time (minutes)

15 psi



137

15 30 45

1x105

2x105

3x105

Mo

lecu

lar

we

igh

t (g

/mo

l)

Pressure (psi)

Mn

Mw



15 30 45

5.0x103

1.0x104

1.5x104

2.0x104

2.5x104

Mo

lecu

lar

we

igh

t (g

/mo

l)

Pressure (psi)

Mn

Mw



138

Effect of catalyst concentration

Polymerization rates at various catalyst concentrations (10, 20, 40 and 80 μM) at 25 °C and 75

°C are shown in Figure 4.24 and Figure 4.25 respectively. On doubling the catalyst

concentration, maximum polymerization rate is almost doubled, showing a linear proportional

dependence. Higher polymerization rates with decreasing trend after reaching a maximum are

obtained at 75 °C, which can be explained with the fact that along with propagation, termination

rates also increase profusely at high temperatures. Average molecular weights are found to be

insensitive to catalyst concentration as shown in Figure 4.26 and Figure 4.27. Catalysts

concentration may affect the degree of polymerization via β-H transfer only. Significantly low

values of Hk , (Table 4.10), as compared to other transfer rate constants, warrant that change in

catalyst concentration has no effect on molecular weights.

0 10 20 30 40 50 60

0

2

4

6

8

10

12

[Zr] = 80M

[Zr] = 40M

[Zr] = 20M

Po

lym

eri

za

tio

n r

ate

(m

ole

s/L

/s)

Time (minutes)

[Zr] = 10M

Figure 4.24 Polymerization rate vs. time: Effect of catalyst concentration.

[Al/Zr = 500, T = 25 °C and P = 30 psi]

139

0 10 20 30 40 50 60

0

10

20

30

40

50

[Zr] = 80M

[Zr] = 40M

[Zr] = 20M

Po

lym

eri

za

tio

n r

ate

(m

ole

s/L

/s)

Time (minutes)

[Zr] = 10M


[Al/Zr = 500, T = 75 °C and P = 30 psi]

0 20 40 60 80

1x105

2x105

3x105

Mo

lecu

lar

we

igh

t (g

/mo

l)

[Zr] (M)

Mn

Mw

Figure 4.26 Effect of catalyst concentration on average molecular weights.

[Al/Zr = 500, T = 25 °C and P = 30 psi]

140

0 20 40 60 80

5.0x103

1.0x104

1.5x104

2.0x104

2.5x104

Mo

lecu

lar

we

igh

t (g

/mo

l)

[Zr] (M)

Mn

Mw


[Al/Zr = 500, T = 75 °C and P = 30 psi]

4.2.2 Propylene polymerization with Et(Ind)2ZrCl2 (P2)/MAO


Et(Ind)2ZrCl2/MAO catalyst system and kinetic parameters are obtained. Simulations are carried

out numerically using 'natural logarithmic differential evolution' approach of optimization. Data

for the model validation are taken from Marques et al. (2002).


Model predictions of reaction rate captures the typical behavior of experimental rate profiles for

propylene polymerization with Et(Ind)2ZrCl2/MAO catalyst system as shown in Figures. 4.28

and 4.29. Estimated kinetic parameters and objective function values are given in Table 4.12. At

75 °C, parameters are evaluated at an Al/Zr molar ratio of 500 and the experimental data at a

141

ratio of 2000 are used to verify the model prediction for polymerization rate. Excellent

predictions are obtained as shown in Figures. 4.28 and 4.29.

Figure 4.30 presents the concentration profiles of active catalyst site at 25 °C and 75 °C.

Active sites are found to decrease exponentially from 10 μM to almost nil in 27 minutes at 25 °C

and within 15 minutes at 75 °C at fixed pressure 30 psi and Al/Zr = 2000. ].[Mk in = 3.61×10-4

at 25 °C vs. ].[Mk in = 9.39×10-4

at 75 °C suggest that chain initiation rate is faster at 75 °C and

therefore active catalyst sites take lesser time to exhaust than that at 25 °C. Spontaneous

deactivation of catalyst site is also increased staggeringly at 75 °C with aids to lower

concentration of active sites observed. As low as 0.35% active catalyst sites at 25 °C against

23.9% at 75 °C are disappearing by spontaneous deactivation.

142

0 10 20 30 40 50 60

0

1

2

Po

lym

eri

za

tio

n r

ate

(m

ol/L

/s)

Time (minutes)

Figure 4.28 Polymerization rate vs. time; solid lines are model predictions.


0 10 20 30 40 50 60

0

1

2

3

Zr:MAO

Po

lym

eri

za

tio

n r

ate

(m

ole

s/L

/s)

Time (minutes)

1:500

1:2000

Figure 4.29 Polymerization rate vs. time; solid lines are model predictions.


143

Table 4.12 Estimated Parameters for Et(Ind)2ZrCl2 (P2)/MAO

T (°C) 25 75

ink ×103

(M-1

.s-1

) 1.7348 1.7686

pk ×10-5

(M-1

.s-1

) 1.1175 2.0135

dk ×106

(s-1

) 1.2638 294.8404

tMk ×104

(M-1

.s-1

) 9.4135 536.7625

Hk , ×106

(s-1

) 6.9652 9.6698

rk ×10-2

(M-1

.s-1

) 2.8886 3.4166

sk ×105

(M-1

.s-1

) 9.9996 11.6170

spk (M-1

.s-1

) 4.5639 68.0812

sMk ×104

(M-1

.s-1

) 4.2017 46.3481

Altk , ×10-4

(M-1

.s-1

) 6.4558 1.5515

rAlk (M-1

.s-1

) 12.9809 93.7468

F(k) (-) 0.2995 0.3615

Table 4.13 Predicted Polypropylene Properties with Et(Ind)2ZrCl2 (P2)/MAO

T (°C) 25 75

Al/Zr 2000 500 2000

Exp Model Exp Model Exp Model

nM ×10-4

(g/mol) - 2.5785 - 0.49795 - 0.3316

wM ×10-4

(g/mol) 5.4 5.3249 1.2 1.0353 0.8 0.7434

PDI (-) 2.2 2.065 2.1 2.079 1.9 2.242

vf (%) - 51.2 - 71.2 - 64.9

bf (%) - 4.6 - 4.1 - 3.8

if (%) - 44.2 - 24.7 - 31.3

144

0 10 20 30 40 50 60

0

4

8

12

Active

ca

taly

st site

s (m

ole

s/L

)

Time (minutes)

T

25 °C

75 °C



Like P1/MAO catalyst system, with Et(Ind)2ZrCl2 (P2)/MAO also, β-H elimination is not

observed significant at both the temperatures considered. Maximum concentration of hydride

activated complex 0*

HP is got to be at 2.2354×10-8 μM (in 14 minutes) at 25 °C and

1.7542×10-7 μM (in 27 minutes) at 75 °C as shown in Figure 4.31 and Figure 4.32 respectively.

Hk , values (Table 4.10) suggest that the rate of β-H elimination is low at 25 °C, for which the

concentration of 0*

HP is low at 25 °C as compared to that at 75 °C. Higher reinitiation rate after

β-H elimination at 25 °C is obtained due to which 0*

HP decreases after reaching the maxima.

145

0 10 20 30 40 50 60

0.00

7.50x10-9

1.50x10-8

2.25x10-8

Hyd

rid

e a

ctiva

ted

co

mp

lex (m

ole

s/L

)

Time (minutes)



0 10 20 30 40 50 60

0.0

6.0x10-8

1.2x10-7

1.8x10-7

Hyd

rid

e a

ctiva

ted

co

mp

lex (m

ole

s/L

)

Time (minutes)



146

Chain transfer to cocatalyst is found to be very high at Al/Zr = 2000 at both the temperatures. At

25 °C, concentration of methyl activated complex is found to reach a maximum of 5.484 μM

(3.37 min) as compared to 3.932 μM (4 min) at 75 °C as shown in Figure 4.33. Methyl activated

complex concentration after reaching the maximum is decreasing steeply to a negligible value at

6.2 min (25 °C) and 7.63 min (75 °C). The rectivation rate constant, after transfer to cocatalyst

is high but monomer concentration is less at 75 °C. Consequently, the reactivation rates are

comparable and high at both the temperatures ( 7013.2MkrAl at 25 °C, 9779.4MkrAl at

75 °C), which clarifies the quick decrease in concentration of 0*

MeP with time.

0 10 20 30 40 50 60

0

2

4

6

Me

thyl a

ctiva

ted

co

mp

lex (m

ole

s/L

)

Time (minutes)

T

25 °C

75 °C

Figure 4.33 Methyl actived complex concentration vs. time.


147

Average molecular weights, PDI and percentage of vinylidene-, butenyl- & isobutyl-terminated

chains predicted by the model for Et(Ind)2ZrCl2/MAO catalyst system are presented in Table

4.13. Model predictions are in very close correspondence with the experimental values. Effect of

temperature on MWD is obtained similar to that discussed for P1/MAO system in Section

4.2.1.1, however P2 yields low molecular weight product at matched reaction conditions. PDIs

at all reaction conditions are obtained near 2.0.

For P2/MAO, vf values in Table 4.13 indicate that chain termination takes place mainly

via spontaneous catalyst deactivation, transfer to monomer and β-Hydride and increasing with an

increase in temperature. With an increase in Al/Zr ratio, vf decreases due to enhanced chain

transfer to cocatalyst. Low bf values obtained advise that the fraction of chains with butenyl

end group is very less as compared to others. bf is noted to decrease with increase in

temperature as well as Al/Zr mole ratio. 44.2 % chains at 25 °C and 31.3 % chains at 75 °C are

found to terminate via chain transfer to cocatalyst as indicated by if values (Table 4.13, Al/Zr =

2000). This trend of decreasing rate of chain transfer to cocatalyst with increase in temperature is

consistent with that obtained with P1/MAO system. The rate of chain transfer to cocatalyst is

proportional to the catalyst concentration. if value is found to increase from 23.6 % to 43.2 %

with increase in Al/Zr mole ratio from 500 to 2000 respectively at 75 °C.

Effect of Pressure

With increase in monomer pressure an increase in polymerization rate up to a stabilized

maximum of 0.8808 moles/L/s (15 psi) and 2.678 moles/L/s (45 psi) at 25 °C and fixed Zr = 10

μM, Al/Zr = 2000 is observed as shown in Figure 4.34. At 75 °C, little higher polymerization

148

rates {Rpmax: 1.083 moles/L/s (15 psi) and 3.96 moles/L/s (45 psi)} with decreasing trend are

observed (Figure 4.35). The changes in average molecular weights with variation in pressures at

25 °C (Figure 4.36) and at 75 °C (Figure 4.37) are trifling. The discussion on the trends of

resultant rate profiles and average molecular weights at varied pressures given in Section 4.2.1.1

adjudges equivalently appropriate for the results obtained for Et(Ind)2ZrCl2/MAO catalyst

system.

0 10 20 30 40 50 60

0

1

2

3

45 psi

30 psi

Po

lym

eri

za

tio

n r

ate

(m

ole

s/L

/s)

Time (minutes)

15 psi



149

0 10 20 30 40 50 60

0

1

2

3

4

45 psi

30 psi

Po

lym

eri

za

tio

n r

ate

(m

ole

s/L

/s)

Time (minutes)

15 psi



15 30 45

1.5x104

3.0x104

4.5x104

6.0x104

Mo

lecu

lar

we

igh

t (g

/mo

l)

Pressure (psi)

Mn

Mw



150

15 30 45

3.0x103

6.0x103

9.0x103

1.2x104

Mo

lecu

lar

we

igh

t (g

/mo

l)

Pressure (psi)

Mn

Mw




Polymerization rates at different catalyst (Et(Ind)2ZrCl2) concentrations at 25 °C and 75 °C are

shown in Figure 4.38 and Figure 4.39 respectively. Like Me2Si[Ind]2ZrCl2 (P1), with this catalyst

system also, polymerization rate is found to be linearly dependent on the catalyst concentration.

However P2 offers a lower polymerization rates than P1 under similar reaction conditions. To

compare, at Zr = 10 μM and 75 °C, a maximum rate of 2.45 moles/L/s with P2 is obtained

against 8.475 mole/L/s with P1. Additionally, average molecular weights are observed to be

unaffected by catalyst concentration as shown in Figure 4.40 and Figure 4.41, which can be

attributed to very low values of Hk , (Table 4.11), as compared to other transfer rate constants.

This has been predicted that catlyst P2 produces lower molecular weight polypropylene when

compared to P1 for alike reaction conditions (Table 4.9 and Table 4.11). The effect of catalyst

151

concentration upon rate and molecular weights are qualitatively similar to that discussed for

catalyst P1 in Section 4.2.1.1.

0 10 20 30 40 50 60

0

4

8

12

16

[Zr] = 80M

[Zr] = 40M

[Zr] = 20M

Po

lym

eri

za

tio

n r

ate

(m

ole

s/L

/s)

Time (minutes)

[Zr] = 10M


[Al/Zr = 2000, T = 25 °C and P = 30 psi]

0 10 20 30 40 50 60

0

5

10

15

20

[Zr] = 80M

[Zr] = 40M

[Zr] = 20MPo

lym

eri

za

tio

n r

ate

(m

ole

s/L

/s)

Time (minutes)

[Zr] = 10M


[Al/Zr = 500, T = 75 °C and P = 30 psi]

152

0 20 40 60 80

2.0x104

3.0x104

4.0x104

5.0x104

6.0x104

Mo

lecu

lar

we

igh

t (g

/mo

l)

[Zr] (M)

Mn

Mw


[Al/Zr = 2000, T = 25 °C and P = 30 psi]

0 20 40 60 80

6.0x103

9.0x103

1.2x104

Mo

lecu

lar

we

igh

t (g

/mo

l)

[Zr] (M)

Mn

Mw


[Al/Zr = 500, T = 75 °C and P = 30 psi]

153

4.2.3 Propylene polymerization with Me2Si(Ind)2HfCl2 (P3)/MAO

Simulation results obtained with propylene polymerization model applied to solution phase

polymerization of propylene with Me2Si(Ind)2HfCl2/MAO catalyst system are presented and

discussed in this section. Data for the model validation were taken from Marques et al. (2002).


Experimental rate data at Al/Hf = 2000 are regressed with the model to determine kinetic

parameters. Further, the model is simulated to predict the polymerization rate at Al/Hf = 500.

Estimated kinetic parameters and objective function [F(k)] values are provided in Table 4.14.

Figures. 4.42 and 4.43 depict a good agreement between the experimental data and model

predictions of polymerization rate with Me2Si(Ind)2HfCl2 (P3)/MAO catalyst system at 40 °C

[F(k) = 1.5175] and 80 °C [F(k) = 0.3161] respectively. Experimental observations reveal that at

40 °C, polymerization rate is weakly affected by a change in Al/Hf ratio as shown in Figure 4.42.

Whereas at 80 °C, polymerization rate increases with increase in cocatalyst to catalyst mole ratio

(Figure 4.43).

Polymerization rate is observed to increase with increase in temperature. At fixed catalyst

concentration, Al/Hf ratio (2000) and monomer pressure, maximum rate is found to be 0.4068

moles/L/s (29 minutes) at 40 °C against 0.9378 moles/L/s (7 minutes) at 80 °C. A rapid gain in

propagation rate at 80 °C is evident from lower frequency of spontaneous catalyst deactivation

(Table 4.12) and a higher initiation rate at this temperature, which provides high concentration of

initiated chains during initial period. Hafnium based metallocene catalysts are known for

producing high molecular weight polymers in comparison to their zirconium analogues, but at

154

the expense of substantially reduced catalytic activity [Ewen et al. (1987); Nakayama and Shiono

(2005)].

Figure 4.44 lays out the concentration profiles of active catalyst site at 40 °C and 80 °C.

Active sites are found to decrease slowly from 10 μM to 1.37 μM in entire polymerization time

at 40 °C and from 10 μM to 0.0124 μM within 19.6 minutes at 80 °C at fixed pressure 30 psi

and Al/Zr = 2000. Chain initiation rate is faster at 80 °C ( ].[Mk in = 1.0898×10-4

s-1

vs. 4.34×10-

5 s

-1 at 40 °C, Table 4.14) and the frequency of spontaneous deactivation of catalyst sites is also

found increasing with temperature (cf. dk , Table 4.14). Therefore active catalyst sites are

consumed in very less time at 80 °C than that at 40 °C.

Table 4.14 Estimated Parameters for Me2Si(Ind)2HfCl2 (P3)/MAO

T (°C) 40 80

ink ×103 (M

-1.s

-1) 0.3045 2.2591

pk ×10-4

(M-1

.s-1

) 4.0398 5.5376

dk ×104 (s

-1) 1.8879 5.3001

tMk ×102 (M

-1.s

-1) 0.2771 8.7269

Hk , ×106

(s-1

) 9.2795 188.81

rk ×10-3

(M-1

.s-1

) 1.4199 22.8680

sk ×108 (M

-1.s

-1) 0.2002 1.4798

spk ×105

(M-1

.s-1

) 1.1091 684.3200

sMk ×108 (M

-1.s

-1) 1.2084 102.4800

Altk , (M-1

.s-1

) 183.5400 99.5750

rAlk ×10-3

(M-1

.s-1

) 1.0293 2.4608

F(k) (-) 1.5175 0.3161

155

Table 4.15 Predicted Properties with Me2Si(Ind)2HfCl2 (P3)/MAO

T (°C) 40 80

Al/Zr 500 2000 500 2000

Exp Model Exp Model Exp Model Exp Model

nM ×10-4

(g/mol) - 10.7115 - 12.1355 - 2.4346 - 1.6478

wM ×10-4

(g/mol) 34.6 30.0459 27.1 24.3074 6.2 4.8698 3.9 3.2919

PDI 2.9 2.8050 2.8 2.003 1.9 2.0002 1.9 1.9977

vf (%) - 86.6 - 87.2 - 90.2 - 90.7

bf (%) - 4.2 - 3.1 - 3.5 - 2.4

if (%) - 9.2 - 9.7 - 6.3 - 6.9

0 10 20 30 40 50 60

0.0

0.2

0.4

Po

lym

eri

za

tio

n r

ate

(m

ole

s/L

/s)

Time (minutes)

Hf:MAO

1:500

1:2000

Figure 4.42 Effect of Al/Hf mole ratio on propylene polymerization rate; solid lines are

model predictions.


156

0 10 20 30 40 50 60

0.0

0.2

0.4

0.6

0.8

1.0

Po

lym

eri

za

tio

n r

ate

(m

ole

s/L

/s)

Time (minutes)

Hf:MAO

1:500

1:2000


model predictions.


0 10 20 30 40 50 60

0

5

10

Active

ca

taly

st site

s (m

ole

s/L

)

Time (minutes)

T

40 °C

80 °C



157

Spontaneous deactivation rate of active catalyst sites is high with comparison to the rate of

initiation at both temperatures. 81.3% active sites at 40 °C and 82.9% at 80 °C are calculated to

disappear due to spontaneous deactivation.

With Me2Si(Ind)2HfCl2 (P3)/MAO system, frequency of β-H elimination is found to increase

from 9.2795×10-6

s-1

at 40 °C to 1.8881×10-4

s-1

at 80 °C (Table 4.14).

At 40 °C, concentration of hydride activated complex reaches a maximum of 1.906×10-7

μM (in 28 minutes) and decreases with a slower rate, on the other hand, at 80 °C it reaches a

maximum of 2.327×10-6 μM (in 8.85 minutes) and decreases appreciably as shown in Figure

4.45. Reinitiation rate after β-H elimination is high ( rk >103) at both the temperatures, so

considerable decrease in 0*

HP is seen at higher concentration.

0 10 20 30 40 50 60

0.0

5.0x10-7

1.0x10-6

1.5x10-6

2.0x10-6

2.5x10-6

3.0x10-6

T

40 °C

80 °C

Hyd

rid

e a

ctiva

ted

co

mp

lex (m

ole

s/L

)

Time (minutes)



158

Chain transfer to cocatalyst is seen significant at Al/Hf = 2000 at both the temperatures. At 40

°C, concentration of methyl activated complex is observed to reach a maximum of 6.96×10-4

μM

(26.8 min) as compared to 1.836×10-5

μM (26.4 min) at 80 °C as shown in Figure 4.46 and

Figure 4.47 respectively. Reactivation rates are high and comparable at both the temperatures

hence methyl activated complex concentration after reaching the maximum is decreasing

appreciably.

Molecular weight distribution and percentage of vinylidene-, butenyl- & isobutyl-

terminated chains predicted by the model for Me2Si(Ind)2HfCl2 (P3)/MAO system are given in

Table 4.15.

0 10 20 30 40 50 60

0.0

2.0x10-4

4.0x10-4

6.0x10-4

8.0x10-4

Me

thyl a

ctiva

ted

co

mp

lex (m

ole

s/L

)

Time (minutes)



159

0 10 20 30 40 50 60

0.0

4.0x10-6

8.0x10-6

1.2x10-5

1.6x10-5

2.0x10-5

Me

thyl a

ctiva

ted

co

mp

lex (m

ole

s/L

)

Time (minutes)



Model predictions are in good agreement with the experimental values. Effect of

temperature on MWD is obtained qualitatively similar to that observed for P1/MAO and

P2/MAO systems (Sections 4.2.1.1 and 4.2.2.1). It is worth noting that Me2Si(Ind)2HfCl2

(P3)/MAO system yields a way higher molecular weight polypropylene when compared to its Zr

analogue i.e. P1/MAO. Model predicted value of PDI at 40 °C with Al/Hf molar ratio is 2.8 (exp.

value = 2.9) and for all other reaction conditions is about 2.0.

Like other catalyst systems discussed so far, with P3/MAO also, the major pathway of

chain termination is via spontaneous catalyst deactivation, transfer to monomer and β-Hydride

elimination. Among these β-Hydride elimination is found increasing dominantly whereas

spontaneous deactivation and transfer to monomer are seen to decrease a bit, with an increase in

160

temperature. vf values are increasing with increase in temperature at a constant Al/Hf molar ratio

as shown in Table 4.15, but there is negligible increase with an increase in Al/Hf ratio at a given

temperature. Fraction of chains with butenyl end group is very less as compared to others as

inferred by low bf values obtained, which are also noticed to decrease with increase in

temperature as well as Al/Hf mole ratio.

9.2 % chains at 40 °C and 6.3 % chains at 80 °C ( if values at Al/Hf = 500) are found to

terminate via chain transfer to cocatalyst which increases with increase in Al/Hf molar ratio. The

trend of decreasing rate of chain transfer to cocatalyst with increase in temperature is similar to

that obtained with its Zr analogue (P1/MAO system) but the amount of this termination is quite

less with P3/MAO system.

Effect of Pressure

Polymerization rates up to a maximum of 0.131 moles/L/s (15 psi), 0.38 moles/L/s (30 psi) and

0.693 moles/L/s (45 psi) at 40 °C and fixed Zr = 10 μM, Al/Hf = 2000 are obtained as shown in

Figure 4.48. At 80 °C, maximum rates of 0.382 moles/L/s at 15 psi, 0.855 moles/L/s at 30 psi

and 1.350 moles/L/s at 45 psi are obtained (Figure 4.49). A steady increase in polymerization

rate with an increase in monomer pressure is seen at both the temperatures. Higher initiation rate

at 80 °C, provide larger concentration of live chains which in turn alleviate to reach high

polymerization rate in less time.

Effect of monomer pressure on molecular weight is found potential at lower temperature.

A significant increase of 71.6 % (15-30 psi) and 30.72 % (30-45 psi) in weight average

molecular weight wM is observed with increase in pressure at 40 °C (Figure 4.50). At 80 °C,

161

relatively lower increase of 18.8 % (15-30 psi) and 6.73 % (30-45 psi) in wM is observed with

increase in pressure (Figure 4.51).

0 10 20 30 40 50 60

0.00

0.25

0.50

0.75

45 psi

30 psi

Po

lym

eri

za

tio

n r

ate

(m

ole

s/L

/s)

Time (minutes)

15 psi



0 10 20 30 40 50 60

0.00

0.25

0.50

0.75

1.00

1.25

1.50

45 psi

30 psi

Po

lym

eri

za

tio

n r

ate

(m

ole

s/L

/s)

Time (minutes)

15 psi



162

15 30 45

7.0x104

1.4x105

2.1x105

2.8x105

3.5x105

Mo

lecu

lar

we

igh

t (g

/mo

l)

Pressure (psi)

Mn

Mw



15 30 45

1.0x104

2.0x104

3.0x104

4.0x104

Mo

lecu

lar

we

igh

t (g

/mo

l)

Pressure (psi)

Mn

Mw



163


Polymerization rates at different catalyst concentrations (10, 20, 30, 40 and 50 μM) at 40 °C and

80 °C are shown in Figure 4.52 and Figure 4.53 respectively. With increase in catalyst

concentration, more number of active catalyst sites are rendered, which increase the rate of

initiation even if monomer concentration is invariant. Propagation rate is also dependent of

concentration of live chains. On this account, a higher polymerization rate is expected with

increase in catalyst concentration, which is correctly predicted by the model at both the

temperatures. Due to higher initiation rate at 80 °C, maximum polymerization rate is achieved

earlier than that at 40 °C at corresponding catalyst concentrations. Since high catalyst

concentration promotes β-H elimination, polymerization rate diminishes at a faster rate as seen in

Figure 4.52 and Figure 4.53 respectively. This effect is particularly pronounced at 80 °C due to

very high Hk , value. Further, the model predicts a proportional dependence of propagation rate

on catalyst concentration.

With P3/MAO catalyst system, average molecular weights are noticed to be decreasing

with increase in catalyst concentration as shown in Figure 4.54 and Figure 4.55. An inverse

relationship between polymer molecular weight and catalyst (Z-N/metallocene) concentration

have been obtained and reported in literature [Breslow and Newburg (1959), Chien (1959),

Brintzinger (1995)]. With P3/MAO, this effect is more influencing at 40 °C, where higher

molecular weights are obtained. A decrease of 35.1% (Hf = 10-20 μM), 21.5% (Hf = 20-30

μM), 14% (Hf = 30-40 μM) and 9.1% (Hf = 40-50 μM) in wM at 40 °C (Figure 4.54), whereas

at 80 °C, 2.1 - 2.3% (Figure 4.55) decrease is obtained.

164

0 10 20 30 40 50 60

0.0

0.5

1.0

1.5

2.0

[Zr]

50M

10MPo

lym

eri

za

tio

n r

ate

(m

ole

s/L

/s)

Time (minutes)

40M

30M

20M


[Al/Hf = 2000, T = 40 °C and P = 30 psi]

0 10 20 30 40 50 60

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

[Zr]

50M

10MPo

lym

eri

za

tio

n r

ate

(m

ole

s/L

/s)

Time (minutes)

40M

30M

20M


[Al/Hf = 2000, T = 80 °C and P = 30 psi]

165

0 10 20 30 40 50

0.0

7.0x104

1.4x105

2.1x105

2.8x105

Mn

Mw

Mo

lecu

lar

we

igh

t (g

/mo

l)

[Hf] (M)


[Al/Hf = 2000, T = 40 °C and P = 30 psi]

0 10 20 30 40 50

1.0x104

2.0x104

3.0x104

4.0x104

Mn

Mw

Mo

lecu

lar

we

igh

t (g

/mo

l)

[Hf] (M)


[Al/Hf = 2000, T = 80 °C and P = 30 psi]

166

4.2.4 Propylene polymerization with Et(Ind)2HfCl2 (P4)/MAO


Et(Ind)2HfCl2 catalyst and kinetic parameters are obtained. Data for the model validation were

taken from Marques et al. (2002).


Kinetic parameters for Et(Ind)2HfCl2 (P4)/MAO catalyst system are estimated by simulating the

model with experimental data at 40 °C and 80 °C with Al/Hf molar ratio of 500. The model

predictions are affirmed with experimental data for Al/Hf ratio of 2000 at both temperatures.

Kinetic parameters and objective function [F(k)] values obtained for P4/MAO system are given

in Table 4.16. Figure 4.56 and Figure 4.57 present experimental and model predicted propylene

polymerization rates at 40 °C and 80 °C respectively. Model predictions are in conformation

with experimental observations at both the temperatures and Al/Hf molar ratios of 500 & 2000.

Figure 4.56 and Figure 4.57 show that with an increase in Al/Hf molar ratio,

polymerization rate increases at both the temperatures. The trend observed is coherent with the

previously discussed studies. At high Al/Hf ratio, large rate of chain transfer to cocatalyst

induces the decrease in polymerization rate after reaching a maximum. In general, increase in

temperature is found to upshoot in higher polymerization rate.

With P4/MAO system, Rp,max is found to increase from 0.5216 moles/L/s at 40 °C to

1.092 moles/L/s at 80 °C at Al/Hf molar ratio of 2000, following the general trend. But with this

catalyst system at Al/Hf ratio of 500, Rp,max is found to decrease meagerly from 0.1952 moles/L/s

at 40 °C to 0.1148 moles/L/s at 80 °C.

167

0 10 20 30 40 50 60

0.0

0.2

0.4

0.6

Po

lym

eri

za

tio

n r

ate

(m

ole

s/L

/s)

Time (minutes)

Hf:MAO

1:500

1:2000


model predictions.


0 10 20 30 40 50 60

0.0

0.5

1.0

Po

lym

eri

za

tio

n r

ate

(m

ole

s/L

/s)

Time (minutes)

Hf:MAO

1:500

1:2000


model predictions.


168

This surprising drift indicates that Al/Hf ratio of 500 is too low to efficiently activate this catalyst

at 80 °C. Owing to this fact a lower value of propagation rate constant ( pk ) is obtained at 80 °C

than that at 40 °C. The model is able to capture the experimental rate profile adequately well at

Al/Hf mole ratio of 2000 with the kinetic parameters determined at a ratio of 500.

Figure 4.58 shows that active catalyst site concentration decreases to negligible value

within 2 minutes at 80 °C, on the contrary, at 40 °C, active catalyst site concentration decreases

slowly. This fact is also evident from very high ink value at 80 °C (Table 4.16). Despite a

decrease in spontaneous deactivation frequency of active catalyst with temperature, extremely

high initiation rate at 80 °C ( ].[Mkin = 1.018×10-3 vs. 4.08×10

-5 at 40 °C ) copiously contribute

for overall rapid decrease in active catalyst site concentration. For the same reasons, fractional

disappearance of active sites by spontaneous deactivation is found to be 93.8% at 40 °C and 16.4

% at 80 °C.

Maximum concentration of hydride activated complex 0*

HP is obtained to be

7.0652×10-3

μM (in 33.5 minutes) at 40 °C and 1.9034 μM (in 17 minutes) at 80 °C as shown in

Figure 4.59 and Figure 4.60 respectively. With P4/MAO catalyst system, β-H elimination is

observed to occur at a higher frequency when compared to other catalyst systems discussed so

far and following the previous trends, increases with increase in temperature.

Reinitiation rate after β-H elimination is higher at 40 °C, which is evident from the

falling concentration of hydride activated complex after reaching a maximum. At 80 °C, due to

lower reinitiation rate, 0*

HP is almost stabilized after maximum.

169

Table 4.16 Estimated Parameters for Et(Ind)2HfCl2 (P4)/MAO

T (°C) 40 80

ink ×104 (M

-1.s

-1) 2.8629 211.0300

pk ×10-3

(M-1

.s-1

) 3.4717 28.5890

dk ×104 (s

-1) 2.0049 6.1684

tMk ×104 (M

-1.s

-1) 3.4470 5.3048

Hk , ×105 (s

-1) 3.0296 127.7600

rk ×103 (M

-1.s

-1) 1.6685 7.7346

sk ×109 (M

-1.s

-1) 1.2524 37.0180

spk ×105 (M

-1.s

-1) 5.6388 17.9600

sMk ×103 (M

-1.s

-1) 5.6042 10.6520

Altk , (M-1

.s-1

) 177.79 34.7210

rAlk ×10-3

(M-1

.s-1

) 2.4626 3.3866

F(k) (-) 1.3866 0.5143

Table 4.17 Predicted Properties with Et(Ind)2HfCl2 (P4)/MAO

T (°C) 40 80

Al/Zr 500 2000 500 2000

Exp Model Exp Model Exp Model Exp Model

nM ×10-8

(g/mol) - 8.2808 - 8.0613 - 1.3440 - 0.5421

wM ×10-8

(g/mol) 22.1 20.8312 17.7 16.1219 2.9 2.6891 2.0 1.0805

PDI 1.83 2.5156 1.85 1.9999 2.78 2.0008 2.18 1.9931

vf (%) - 81.20 - 80.50 - 86.10 - 83.90

bf (%) - 6.30 - 5.40 - 4.60 - 3.90

if (%) - 12.50 - 14.10 - 9.30 - 12.2

170

0 10 20 30 40 50 60

0

3

6

9

12

Active

ca

taly

st site

s (m

ole

s/L

)

Time (minutes)

T

40 °C

80 °C



0 10 20 30 40 50 60

0.0

2.0x10-3

4.0x10-3

6.0x10-3

8.0x10-3

Hyd

rid

e a

ctiva

ted

co

mp

lex (m

ole

s/L

)

Time (minutes)



171

0 10 20 30 40 50 60

0.0

0.5

1.0

1.5

2.0

Hyd

rid

e a

ctiva

ted

co

mp

lex (m

ole

s/L

)

Time (minutes)



With P4/MAO system, chain transfer to cocatalyst is obtained very high at 40 °C than

that at 80 °C. Concentration of methyl activated complex 0*

MeP is found to reach a maximum

of 0.4011 μM (17.3 min) followed by a steep decrease at 40 °C as compared to a maximum of

1.8862×10-5

μM (1.4 min) at 80 °C followed by slow decrease as shown in Figure 4.61 and

Figure 4.62 respectively. Due to low concentrations of monomer and methyl activated complex

at 80 °C, the rectivation rate, after transfer to cocatalyst is slow and therefore the concentration

of 0*

MeP is decreasing slowly. At 40 °C, high concentration of methyl activated complex

enhances the reactivation rate for which a rapid decrease in 0*

MeP is observed after reaching a

maximum.

172

0 10 20 30 40 50 60

0.0

0.2

0.4

Me

thyl a

ctiva

ted

co

mp

lex (m

ole

s/L

)

Time (minutes)



0 10 20 30 40 50 60

0.0

5.0x10-6

1.0x10-5

1.5x10-5

2.0x10-5

Me

thyl a

ctiva

ted

co

mp

lex (m

ole

s/L

)

Time (minutes)



173

For P4/MAO system, model predicted molecular weight distribution and percentage of vinyl-,

butenyl- and isobutyl-terminated chains are given in Table 4.17. A good match between

experimental and predicted results for MWD is obtained.

Polymerization rates obtained with this catalyst system are comparable with P3/MAO but

very less when compared with P1/MAO and P2/MAO. P4/MAO yielded very high molecular

weights (~ 108 g/mol) of polypropylene as compared to its zirconium analogue (P2) as well as

other catalysts (P1 and P3) discussed heretofore.

Molecular weight is found to decrease with increase in temperature (from 40 °C to 80 °C)

and also with increase in Al/Hf molar ratio (from 500 to 2000). At 80 °C, chain termination via

β-H elimination is highly dominating followed by the transfer to monomer, than that at 40 °C,

which causes a significant drop in molecular weight at higher temperature. Polydispersity index

predicted by the model for Al/Hf ratio of 500 at 40 °C is 2.5156, whereas for all other reaction

conditions it is around 2.0.

At all the temperatures and Al/Hf ratios considered, the highest percentage of terminated

chains hold vinylidene end group ( vf > 80%), followed by isobutyl end group (9.3 < if < 14.1)

and butenyl end group (3.9 < bf < 6.3) as shown in Table 4.17. At a fixed Al/Hf molar ratio,

with increase in temperature, vf is increasing whilst bf and if are found decreasing. Increase in

Al/Hf ratio increases the rate of chain transfer to cocatalyst and thereby if increases at a given

temperature.

Though these trends for P4/MAO are consistent with those catalyst systems discussed

earlier but all the termination rates are notably less, due to which high molecular weight product

is raised.

174

Effect of Pressure

Figure 4.63 and Figure 4.64 show the effect of monomer pressure on polymerization rate at 40

°C and 80 °C respectively with P4/MAO system at fixed Zr = 10 μM, Al/Zr = 500. For a change

in monomer pressure of 30 psi to 45 psi, at 40 °C, Rp,max increases from 0.1720 mol/L/s to 0.3186

mol/L/s and at 80 °C, Rp,max increases from 0.07838 mol/L/s to 0.1176 mol/L/s. This indicates

that an increase in monomer pressure results in linear increase in polymerization rate. As

observed experimentally and discussed earlier, this catalyst system affords lower polymerization

rates at 80 °C with an Al/Hf molar ratio of 500.

With increase in pressure, molecular weights are found to increase. 2.92 fold increase in

wM for a change in pressure from 15 to 30 psi and 1.86 fold increase for a change from 30 to 45

psi is found at 40 °C (Figure 4.65). Similarly, at 80 °C, 1.94 fold increase in wM for a change in

pressure from 15 to 30 psi and 2.82 fold increase for a change from 30 to 45 psi is observed

(Figure 4.66).


Polymerization rates at different catalyst concentrations (10, 20, 30, 40 and 50 μM) at 40 °C and

80 °C with P4/MAO system are shown in Figure 4.67 and Figure 4.68 respectively.

Polymerization rate is linearly increasing with increase in catalyst concentration at both the

temperatures and in tune with the discussion for P3/MAO system.

With P4/MAO catalyst system also, an inverse relationship between polymer molecular

weight and catalyst concentration is obtained as shown in Figure 4.69 and Figure 4.70.

175

0 10 20 30 40 50 60

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

45 psi

30 psi

Po

lym

eri

za

tio

n r

ate

(m

ole

s/L

/s)

Time (minutes)

15 psi



0 10 20 30 40 50 60

0.00

0.05

0.10

0.15

45 psi

30 psi

Po

lym

eri

za

tio

n r

ate

(m

ole

s/L

/s)

Time (minutes)

15 psi



176

15 30 45

0.0

1.5x109

3.0x109

4.5x109

Mo

lecu

lar

we

igh

t (g

/mo

l)

Pressure (psi)

Mn

Mw



15 30 45

0.0

1.5x108

3.0x108

4.5x108

Mo

lecu

lar

we

igh

t (g

/mo

l)

Pressure (psi)

Mn

Mw



177

At 40 °C, wM is decreasing from 2.0831 × 109

to 1.757 × 109

(15.6%) for a change in catalyst

concentration from 10 μM to 20 μM. On further increase in catalyst concentration (30, 40 and 50

μM), wM is not observed to decrease much. This outcome again emphasizes that at this

temperature, Al/Hf ratio of 500 is not sufficient to activate catalyst efficaciously and therfore

increase in catalyst concentration does not really increase the number of active chains. On the

contrary, at 80 °C wM is found to decrease with each increment in catalyst concentration. As

shown in Figure 4.70, for every 10 μM increase in catalyst concentration, 44% (10-20 μM),

28.1% (20-30 μM), 19.95% (30-40 μM) and 17.94% (40-50 μM) decrease in wM is obtained.

0 10 20 30 40 50 60

0.00

0.25

0.50

0.75

1.00

[Zr]

50M

10MPo

lym

eri

za

tio

n r

ate

(m

ole

s/L

/s)

Time (minutes)

40M

30M

20M


[Al/Hf = 500, T = 40 °C and P = 30 psi]

178

0 10 20 30 40 50 60

0.0

0.1

0.2

0.3

0.4

Po

lym

eri

za

tio

n r

ate

(m

ole

s/L

/s)

Time (minutes)

[Zr]

50M

10M

40M

30M

20M


[Al/Hf = 500, T = 80 °C and P = 30 psi]

0 10 20 30 40 50

0.0

5.0x108

1.0x109

1.5x109

2.0x109

2.5x109

Mo

lecu

lar

we

igh

t (g

/mo

l)

[Hf] (M)

Mnbar

Mwbar


[Al/Hf = 500, T = 40 °C and P = 30 psi]

179

0 10 20 30 40 50

0.0

1.0x108

2.0x108

3.0x108

Mo

lecu

lar

we

igh

t (g

/mo

l)

[Hf] (M)

Mnbar

Mwbar


[Al/Hf = 500, T = 80 °C and P = 30 psi]

4.2.5 Propylene polymerization with (2,4,6-Me3Ind)2ZrCl2 (P5)/MAO


an ansa-metallocene catalyst and kinetic parameters are obtained. Data for the model validation

were taken from Yasin et al. (2004).

Estimated parameters and effect of Al/Zr mole ratio

Model predicted and experimental polymerization rate profiles for propylene polymerization

with [2,4,6-Me3Ind]2ZrCl2(P5)/MAO catalyst system at Al/Zr molar ratios of 2000 and 4000 are

presented in Figure 4.71. Kinetic parameters are estimated at 0 °C with experimental rate data at

0.98 atm pressure, 20 μM catalyst and Al/Zr molar ratio of 2000. Experimental rate data at Al/Zr

mole ratio of 4000 are employed to verify the model prediction for polymerization rate. Model

180

predictions of polymerization rate are in good agreement with the experimental polymerization

rate at both the cocatalyst to catalyst mole ratios considered. Values of estimated kinetic

parameters and objective function F(k) are given in Table 4.18.

When compared with P1-P4/MAO systems, polymerization rates with P5/MAO system are

found very less, so is the pk value estimated by the model. At 0 °C, Low polymerization rates

(Rp,max = 2.593 × 10-3

moles/L/s) at Al/Zr mole ratio of 2000 and high rates (Rp,max = 4.921× 10-3

moles/L/s) at Al/Zr mole ratio of 4000 are echoing the trend obtained with other catalyst

systems. Also a sharp decrease in polymerization rate after reaching a maximum is seen at high

Al/Zr ratio implying a larger frequency of chain transfer to cocatalyst.

0 10 20 30 40 50 60

0.0

2.0x10-3

4.0x10-3

6.0x10-3

Zr:MAO

1:2000

1:4000

Po

lym

eri

za

tio

n r

ate

(m

ole

s/L

/s)

Time (minutes)


model predictions.


181

Table 4.18 Estimated Parameters for [2,4,6-Me3Ind]2ZrCl2 (P5)/MAO

T 0 °C

ink (M-1

.s-1

) 7.3213 × 10-3

pk (M-1

.s-1

) 71.2665

dk (s-1

) 3.8988 × 10-4

tMk (M-1

.s-1

) 2.6484

Hk , (s-1

) 8.2268 × 10-3

rk (M-1

.s-1

) 628.343

sk (M-1

.s-1

) 8.8514 × 10-4

spk (M-1

.s-1

) 1.6957 × 10-4

sMk (M-1

.s-1

) 0.12125

Altk , (M-1

.s-1

) 7.9402 × 103

rAlk (M-1

.s-1

) 32.4558

F(k) (-) 0.27301

Table 4.19 Predicted Properties with [2,4,6-Me3Ind]2ZrCl2 (P5)/MAO

T (°C) 0

Al/Zr 2000 4000

Exp Model Exp Model

nM (g/mol) 3.02 × 104 2.6715 × 10

4 2.71 × 10

4 2.3537 × 10

4

wM (g/mol) 7.7 × 104 6.2516 × 10

4 6.77 × 10

4 5.4211 × 10

4

PDI 2.55 2.34 2.50 2.30

vf (%) - 81.2671 - 76.4243

bf (%) - 4.4303 - 4.8034

if (%) - 14.3026 - 18.7723

182

Active catalyst site concentration decreases to 0.03 μM from 20 μM in 8.6 minutes as shown in

Figure 4.72. Further, the values, ].[Mk in = 1.2792×10-2

s-1

vs. dk = 3.8988 × 10-4

s-1

suggest

that 2.96 % active sites are deactivating spontaneously and rest are utilized to initiate the chains.

With [2,4,6-Me3Ind]2ZrCl2 (P5)/MAO system, frequency of β-H elimination is found to

be 8.2268 × 10-3

(Table 4.16). Concentration of hydride activated complex reaches a maximum

of 1.4165×10-4 μM rapidly (in 4.6 minutes) and decrease thereafter as shown in Figure 4.73.

Fast reinitiation rate after β-H elimination ( rk = 628.343) causes the decrease in 0*

HP .

Figure 4.74 shows that the concentration of methyl activated complex reaches a

maximum of 8.5575 μM within 1.37 minutes followed by a sharp decrease to a negligible value.

The rate of chain transfer to cocatalyst and reactivation after transfer both are quite high with this

catalyst system at 0 °C.

0 10 20 30 40 50 60

0

5

10

15

20

25

Active

ca

taly

st co

nce

ntr

atio

n (m

ole

s/L

)

Time (minutes)



183

0 10 20 30 40 50 60

0.0

5.0x10-5

1.0x10-4

1.5x10-4

Hyd

rid

e a

ctive

d c

ata

lyst co

nce

ntr

atio

n (m

ole

s/L

)

Time (minutes)



0 10 20 30 40 50 60

0

3

6

9

Me

thyl a

ctive

d c

ata

lyst co

nce

ntr

atio

n

(m

ole

s/L

)

Time (minutes)



184

Table 4.19 presents the molecular weights of polypropylene and percentage of variously

terminated chains predicted by the model for [2,4,6-Me3Ind]2ZrCl2 (P5)/MAO system at 0 °C. At

Al/Zr mole ratio of 2000, wM is found to be 6.2516 × 104

which is decreased by 13.3% on

raising the ratio to 4000. Model predicted molecular weights and PDIs closely match with the

experimentally determined values. Predicted value of PDI is almost unchanged with an increase

in Al/Zr mole ratio, and is found to be 2.34 and 2.30 at an Al/Zr molar ratio of 2000 and 4000

respectively.

Chain termination is via spontaneous catalyst deactivation, transfer to monomer and β-Hydride

elimination remain in force followed by chain transfer to cocatalyst as inferred by vf and if

values obtained (Table 4.19). With increase in Al/Zr ratio, if is found to increase while vf

decreases, showing higher transfer to cocatalyst at higher ratio. Secondary insertions are found to

be less with this catalyst system and unresponsive to Al/Zr ratio as evident from small

percentage (4.43 - 4.8 %) of butenyl end groups obtained (Table 4.19).

Effect of Pressure

Monomer pressure is doubled and tripled from 0.98 atm (experimental) and polymerization rates

are prognosticated with the model as given in Figure 4.75. The maximum rate observed at 0.98

atm, 1.97 atm and 2.96 atm are 0.0022 moles/L/s, 0.0061 moles/L/s and 0.0133 moles/L/s

respectively at 0 °C and fixed Zr = 20 μM, Al/Zr = 2000. With increase in monomer pressure, a

higher initiation and polymerization rates are noted, which is consistent with trend observed

earlier with any catalyst system.

Figure 4.76 depicts that no appreciable increase in molecular weight is obtained with increase in

monomer pressure with this catalyst system. 0.9% and 0.4% increase in weight average

185

molecular weight is recorded for a change of 0.98 to 1.97 atm and from 1.97 to 2.96 atm in

monomer pressure. High monomer concentration not only increases the initiation and

propagation rates but also raises various chain termination rates in which monomer is involved.

Therefore eventually for this catalyst system, despite high polymerization rate no considerable

change in molecular weight is observed.

0 10 20 30 40 50 60

0.0

5.0x10-3

1.0x10-2

1.5x10-2

2.96 atm

1.97 atm

Po

lym

eri

za

tio

n r

ate

(m

ole

s/L

/s)

Time (minutes)

0.98 atm



186

1 2 3

0

3x104

6x104

8x104

Mo

lecu

lar

we

igh

t (g

/mo

l)

Pressure (atm)

Mn

Mw




Polymerization rates at different catalyst concentrations (10, 20, 40 and 80 μM) at 0 °C are

shown in Figure 4.77. Increase in catalyst concentration is resulting in increasead polymerization

rate which reaches to a maximum and decreases afterwards due to elevated termination rates. On

doubling the catalyst concentration, maximum polymerization rate is found to be doubled,

showing a linear proportional dependence. The trend is similar to those obtained with other

catalyst systems discussed earlier.

187

0 10 20 30 40 50 60

0.00

2.50x10-3

5.00x10-3

7.50x10-3

1.00x10-2

Po

lym

eri

za

tio

n r

ate

(m

ole

s/L

/s)

Time (minutes)

[Zr]

10M

80M

40M

20M


[Al/Zr = 2000, T = 0 °C and P = 0.98 atm]

0 20 40 60 80

2x104

4x104

7x104

Mo

lecu

lar

we

igh

t (g

/mo

l)

[Zr] (M)

Mn

Mw


[Al/Zr = 2000, T = 0 °C and P = 0.98 atm]

188

With P5/MAO catalyst system, average molecular weights are noticed to be unaltered with

increase in catalyst concentration as shown in Figure 4.78. An inverse relationship between

polymer molecular weight and catalyst concentration is obtained with hafnium based

metallocenes (P3 and P4), whereas Zr based metallocenes (P1 and P2) have shown a similar

trend as obtained for P5.

4.2.6 Propylene polymerization with [2,4,7-Me3Ind]2ZrCl2) (P6)/MAO


an ansa-metallocene catalyst and kinetic parameters are obtained. Data for the model validation

were taken from Yasin et al. (2004).

Estimated parameters and effect of Al/Zr mole ratio

Figure 4.79 shows the model prediction for the experimental behaviour of [2,4,7-Me3Ind]2ZrCl2

catalyst in propylene polymerization for different Zr/MAO ratios. Experimental polymerization

rate data at Al/Zr molar ratio of 2000 are regressed to determine the kinetic parameters at 0 °C

and other sets of rate data are used to verify the simulation results. A good match between the

model predicted and experimental rate is obtained at all the Al/Zr ratios studied. Values of

estimated kinetic parameters and objective function [F(k)] are given in Table 4.20.

189

0 10 20 30 40 50 60

0.0

1.0x10-3

2.0x10-3

3.0x10-3

Zr:MAO

1:1000

1:2000

1:4000

Po

lym

eri

za

tio

n r

ate

(m

ole

s/L

/s)

Time (minutes)


model predictions.


Polymerization rates with P6/MAO are observed very less when compared with P1-

P4/MAO systems, but comparable with P5/MAO system at identical reaction conditions. The

pk value estimated by the model is slightly higher (106.06 M-1

.s-1

vs. 71.27 M-1

.s-1

) than

P5/MAO system. At Al/Zr mole ratio of 1000, polymerization rate is all less (Rp,max = 1.24 × 10-3

moles/L/s) than those observed at higher ratios. At Al/Zr ratio of 2000, polymerization rate is

found to reach a maximum of 2.9389 × 10-3

moles/L/s, but with further increase in Al/Zr ratio to

4000 polymerization rate is not observed to increase and yields a maximum rate of 2.6332 × 10-3

moles/L/s. This suggests that Al/Zr ratio as high as 4000 is sufficient to activate this catalyst and

higher ratios would bring no further increase in polymerization rate.

190

Table 4.20 Estimated Parameters for [2,4,7-Me3Ind]2ZrCl2) (P6)/MAO

T 0 °C

ink (M-1

.s-1

) 6.2848 × 10-3

pk (M-1

.s-1

) 1.0606 × 102

dk (s-1

) 3.4959 × 10-4

tMk (M-1

.s-1

) 1.0114

Hk , (s-1

) 9.8943 × 10-4

rk (M-1

.s-1

) 3.1658 × 102

sk (M-1

.s-1

) 1.0107 × 10-3

spk (M-1

.s-1

) 2.0210 × 10-5

sMk (M-1

.s-1

) 0.2694

Altk , (M-1

.s-1

) 5.4686 × 102

rAlk (M-1

.s-1

) 4.2644

F(k) (-) 0.92561

Table 4.21 Predicted Properties with [2,4,7-Me3Ind]2ZrCl2) (P6)/MAO

T 0 °C

Al/Zr 1000 2000 4000

Exp Model Exp Model Exp Model

nM (g/mol) - 4.9605 × 104 - 2.8396 × 10

4 - 2.9229 × 10

4

wM (g/mol) - 1.2994 × 105 - 7.8196 × 10

4 - 6.1089 × 10

4

PDI - 2.62 - 2.75 - 2.09

vf (%) - 86.4288 - 83.4627 - 77.8977

bf (%) - 6.2102 - 6.3333 - 6.4323

if (%) - 7.361 - 10.204 - 15.670

191

Active catalyst site concentration decreases from 20 μM to 0.0522 μM in 9.3 minutes as shown

in Figure 4.80. Further, the values, ].[Mk in = 2.1687×10-3

s-1

vs. dk = 3.4959 × 10-4

s-1

suggest

that 13.88 % active sites are deactivating spontaneously while rest are utilized to initiate the

chains.

With [2,4,7-Me3Ind]2ZrCl2 (P6)/MAO system, frequency of β-H elimination is found to

be 9.8943 × 10-4

(Table 4.18). Concentration of hydride activated complex reaches a maximum

of 3.0554×10-5 μM in 13 minutes and decrease thenceforth as shown in Figure 4.81. Due to

rapid reinitiation rate after β-H elimination ( rk =316.58 M-1

.s-1

), 0*

HP decreases after

reaching the maximum.

The rate of chain transfer to cocatalyst and reactivation after transfer both are quite high

with P6/MAO catalyst system at 0 °C. Altk , and rAlk values with this catalyst system are much

higher than those obtained with (P1-P4)/MAO but less than that obtained with P5/MAO system.

Figure 4.82 points that the concentration of methyl activated complex reaches a maximum of

11.84 μM within 3.58 minutes followed by a sharp decrease to a negligible value.

Table 4.21 gives the molecular weights of polypropylene and percentage of variously

terminated chains predicted by the model for [2,4,7-Me3Ind]2ZrCl2 (P6)/MAO system at 0 °C

and different Al/Zr ratios.

192

0 10 20 30 40 50 60

0

5

10

15

20

Active

ca

taly

st co

nce

ntr

atio

n

(m

ole

s/L

)

Time (minutes)



0 10 20 30 40 50 60

0.0

1.0x10-5

2.0x10-5

3.0x10-5

Hyd

rid

e a

ctiva

ted

co

mp

lex c

on

ce

ntr

atio

n

(m

ole

s/L

)

Time (minutes)



193

0 10 20 30 40 50 60

0

3

6

9

12

Me

thyl a

ctiva

ted

co

mp

lex c

on

ce

ntr

atio

n

(m

ol/L

)

Time (minutes)



Increase in Al/Zr molar ratio is resulting in decrease in molecular weights. At Al/Zr mole

ratio of 1000, wM is found to be 1.2994 × 105

which is decreased by 39.82% on raising the ratio

to 2000. On increasing Al/Zr ratio from 2000 to 4000, wM is further decreased by 21.88%.

Weight average molecular weights obtained with P6/MAO are very close to those obtained with

P5/MAO catalyst system at identical conditions, however, polydispersity indices are little high

with P6/MAO evincing broader molecular weight distribution.

vf values in Table 4.21 indicate that chain termination is majorly via spontaneous

catalyst deactivation, transfer to monomer and β-Hydride elimination. With increase in Al/Zr

ratio, if is found increasing while vf decreasing, exhibiting the trends similar to that discovered

with P5/MAO. Secondary insertions with P6/MAO catalyst system are higher than those with

194

P5/MAO but less in comparison with (P1-P4)/MAO systems. Percentage of butenyl end groups

are almost unchanged with variation in Al/Zr ratio.

Effect of Pressure

Like P5/MAO and other catalysts studied up to now, P6/MAO also evidences a higher initiation

rate and increased polymerization rate with increase in monomer pressure. Polymerization rates

are predicted with the model at 0.98, 1.97 and 2.96 atm monomer pressures as shown in Figure

4.83. The maximum rates observed at 0.98 atm, 1.97 atm and 2.96 atm are 0.0030 moles/L/s,

0.0081 moles/L/s and 0.0179 moles/L/s respectively at 0 °C and fixed Zr = 20 μM, Al/Zr = 2000.

Polymerization rates at studied monomer pressures are very comparable with those obtained with

P1/MAO system.

Figure 4.84 shows that a little increase in molecular weight is obtained with increase in monomer

pressure with P6/MAO catalyst system. In weight average molecular weight, a 5.18% and 2.97%

increase is seen respectively for a change of 0.98 to 1.97 atm and from 1.97 to 2.96 atm in

monomer pressure. The small increase in wM conforms to the effect of pressure discussed for

P5/MAO system.

195

0 10 20 30 40 50 60

0.0

6.0x10-3

1.2x10-2

1.8x10-2

2.96 atm

1.97 atmPo

lym

eri

za

tio

n r

ate

(m

ole

s/L

/s)

Time (minutes)

0.98 atm



1 2 3

0

3x104

5x104

8x104

1x105

Mo

lecu

lar

we

igh

t (g

/mo

l)

Pressure (atm)

Mn

Mw



196


With P6/MAO also, polymerization rates are increasing linearly with increase in catalyst

concentration. Figure 4.85 shows polymerization rates at different catalyst concentrations (10,

20, 40 and 80 μM) at 0 °C. Since high initiation rates prevail at high catalyst concentrations,

maximum rate is achieved shortly at higher catalyst concentration.

Like P5/MAO catalyst system, average molecular weights with P6/MAO are also not changing

with increase in catalyst concentration as shown in Figure 4.86.

0 10 20 30 40 50 60

0.0

5.0x10-3

1.0x10-2

1.5x10-2

Zr

80M

40M

20M

Po

lym

eri

za

tio

n r

ate

(m

ole

s/L

/s)

Time (minutes)

10 M


[Al/Zr = 2000, T = 0 °C and P = 0.98 atm]

197

0 20 40 60 80

2x104

4x104

6x104

8x104

1x105

Mo

lecu

lar

we

igh

t (g

/mo

l)

[Zr] (M)

Mn

Mw


[Al/Zr = 2000, T = 0 °C and P = 0.98 atm]

4.2.7 Propylene polymerization with Me2Si[2,4,6-Me3Ind]2ZrCl2) (P7)/MAO


an ansa-metallocene catalyst and kinetic parameters are obtained. Simulations are carried out

using natural logarithmic differential evolution and the experimental data for the model

validation are taken from Yasin et al. (2005).


Experimental and model predicted polymerization rate profiles for propylene polymerization

with Me2Si[2,4,6-Me3Ind]2ZrCl2(P7)/MAO catalyst system at 30 °C, 50 °C and 70 °C are

presented in Figure 4.87. Kinetic parameters are estimated at different temperatures with

198

experimental rate data at 0.98 atm pressure, 20 μM catalyst and Al/Zr molar ratio of 2000.

Estimated kinetic parameters and objective function F(k) values are given in Table 4.22.

A decent agreement between experimental and model predicted polymerization rates is

received at 30 °C and 70 °C. At 50 °C from 2.75 minutes to 12 minutes, very few experimental

data points are available and a large number of data is available for regression only after 12

minutes. For this reason, model is found to under predict the polymerization rate in this time

range which includes the peak corresponding to maximum polymerization rate. Due to possible

unreliableness, model outputs at 50 °C are excluded in further discussion.

Figure 4.87 shows that model predicted maximum polymerization rates at 30 °C and 70

°C are 7.103 × 10-3

(experimental: 8.38 × 10-3

) and 8.747.103 × 10-3

(experimental: 8.95 × 10-3

)

respectively which explicates that polymerization rate with P7/MAO catalyst system is increased

to a little extent with increase in temperature. Despite an increase in pk value with increase in

temperature, the low increase in polymerization rate may be explained with the decreased

solubility of propylene in toluene at higher temperature at fixed monomer pressure. Temperature

is rather found to affect initiation rates, which are increasing with increase in temperature and

thereby achieve maximum rate earlier. Chain termination rates via different routes are

sufficiently high at all the temperatures to induce a descending polymerization rate profile after a

maximum.

Both initiation rate ( ].[Mkin = 2.441×10-2

s-1

vs. 4.849×10-3

s-1

at 30 °C) and frequency of

spontaneous catalyst deactivation ( dk = 4.0949×10-4

s-1

vs. 6.1255×10-5

s-1

at 30 °C) are high at

70 °C. That's why active catalyst site concentration decreases to a negligible value within 3.5

minutes at 70 °C, whereas at 30 °C, it takes 19.8 minutes as shown in Figure 4.88.

199

0 10 20 30 40 50 60

0.0

2.0x10-3

4.0x10-3

6.0x10-3

8.0x10-3

1.0x10-2

30 0C

50 0C

70 0C

Po

lym

eri

za

tio

n r

ate

(m

ole

s/L

/s)

Time (minutes)

Figure 4.87 Effect of temperature on propylene polymerization rate; solid lines are model

predictions.


200

Table 4.22 Estimated Parameters for Me2Si[2,4,6-Me3Ind]2ZrCl2) (P7)/MAO

T (°C) 30 70

ink (M-1

.s-1

) 8.075708 × 10-3

9.985286 × 10-2

pk (M-1

.s-1

) 9.361976 × 102 2.211042 × 10

3

dk (s-1

) 6.125482 × 10-5

4.094922 × 10-4

tMk (M-1

.s-1

) 0.2562587 12.5457

Hk , (s-1

) 1.955819 × 10-4

2.307301 × 10-3

rk (M-1

.s-1

) 101.5226 407.3533

sk (M-1

.s-1

) 1.747163 × 10-3

1.255236 × 10-2

spk (M-1

.s-1

) 1.264525 × 10-4

1.523233 × 10-2

sMk (M-1

.s-1

) 1.33222 × 10-3

1.001232 × 103

F(k) (-) 0.5969 1.0339

Table 4.23 Predicted Properties with Me2Si[2,4,6-Me3Ind]2ZrCl2) (P7)/MAO

T (°C) 30 70

Exp Model Exp Model

nM (g/mol) - 3.9672 × 104 - 7.9313 × 10

3

wM (g/mol) - 7.9344 × 104 - 1.5823 × 10

4

PDI (-) - 2.000 - 1.995

vf (%) - 99.8648 - 99.9097

bf (%) 0.37 0.1352 0.10 0.0903

201

Fractional disappearance of active sites by spontaneous deactivation is as low as 1.24% at 30 °C

and 1.6% at 70 °C.

0 10 20 30 40 50 60

0

5

10

15

20

Active

ca

taly

st site

s (m

ole

s/L

)

Time (minutes)

T

30 0C

70 0C



Concentration of hydride activated complex 0*

HP is found to increase to a maximum

followed by a decrease. Maximum 0*

HP achieved is 4.112×10-5

μM (in 6.4 minutes) at 30 °C

and 3.367 μM (in 5.85 minutes) at 70 °C as shown in Figure 4.89 (a) and (b) respectively. With

P7/MAO catalyst system, frequency of β-H elimination is substantial and increases with increase

in temperature from 30 °C to 70 °C. Reinitiation rate after β-H elimination is much lower at 70

°C than that at 30 °C due to which a high value of maximum concentration of hydride activated

complex is obtained.

202

0 10 20 30 40 50 60

0.0

2.0x10-5

4.0x10-5

Hyd

rid

e a

ctiva

ted

ca

taly

st site

s

(m

ole

s/L

)

Time (minutes)

(a)

0 10 20 30 40 50 60

0

1

2

3

Hyd

rid

e a

ctiva

ted

ca

taly

st site

s

(m

ole

s/L

)

Time (minutes)

(b)

Figure 4.89 Hydride actived complex concentration vs. time. (a) 30 °C, (b) 70 °C


203

Model predicted properties of polypropylene synthesized with Me2Si[2,4,6-Me3Ind]2ZrCl2)

(P7)/MAO are given in Table 4.23. Molecular weights are found to decrease with increase in

temperature. wM estimated at 30 °C is 7.9344 × 104 which is decreased by 80% at 70 °C.

PDIs

at all reaction conditions are obtained almost 2.0 representing standard molecular weight

distribution.

Polypropylene synthesized using P7/MAO system is highly isotactic. Experimental

values of bf , which are closely predicted by the model also (Table 4.23) suggest that the fraction

of dead chains with butenyl end group is very less (< 0.5%) speculating high isotacticity. Since

transfer to cocatalyst is not considered in the model applied here, high vf values account for all

other types of chain termination i.e. via spontaneous catalyst deactivation, transfer to monomer

and β-Hydride elimination.

Effect of Pressure

Monomer pressure is varied from 0.98 atm to 1.97 atm and 2.96 atm to study the effect on

polymerization rate and polymer molecular weight at fixed Zr = 20 μM, Al/Zr = 2000. Figure

4.90 and Figure 4.91 depict the rate profiles at 30 °C and 70 °C respectively. Following the

earlier trends, polymerization rate is found increasing with increase in monomer pressure.

With increase in monomer pressure a linear increase in polymerization rate with a

maximum of 8.61142 × 10-3

moles/L/s (0.98 atm), 1.9996 × 10-2

moles/L/s (1.97 atm) and

3.3598 × 10-2

moles/L/s (2.96 atm) at 30 °C is observed as shown in Figure 4.90. At 70 °C also

a linear relationship between rate and monomer pressure is seen, with a maximum rate of 9.0595

× 10-3

moles/L/s (0.98 atm), 2.4396 × 10-2 moles/L/s (1.97 atm) and 4.0954 × 10

-2 moles/L/s

(2.96 atm). Higher rates are predicted at 70 °C at corresponding monomer pressures.

204

No appreciable change in average molecular weights with variation in monomer pressures is

observed at both 30 °C (Figure 4.92) and 70 °C (Figure 4.93) temperature.

0 10 20 30 40 50 60

0.0

1.0x10-2

2.0x10-2

3.0x10-2

2.96 atm

1.97 atm

Po

lym

eri

za

tio

n r

ate

(m

ole

s/L

/s)

Time (minutes)

0.98 atm



0 10 20 30 40 50 60

0.0

1.0x10-2

2.0x10-2

3.0x10-2

4.0x10-2

2.96 atm

1.97 atm

Po

lym

eri

za

tio

n r

ate

(m

ole

s/L

/s)

Time (minutes)

0.98 atm



205

1 2 3

4.0x104

6.0x104

8.0x104

Mn

Mw

Mo

lecu

lar

we

igh

t (g

/mo

l)

Pressure (atm)



1 2 3

5x103

1x104

2x104

2x104

Mo

lecu

lar

we

igh

t (g

/mo

l)

Pressure (atm)

Mn

Mw



206


Polymerization rates at different catalyst (P7) concentrations at 30 °C and 70 °C are shown in

Figure 4.94 and Figure 4.95 respectively. On doubling the catalyst concentration, predicted

maximum polymerization rate is found to be doubled showing a linear dependence at 30 °C as

well as at 70 °C. However at 70 °C, polymerization rate is noted to be 23% higher than that at 30

°C at corresponding catalyst concentration. All the termination reactions are highly activated at

70 °C, therefore polymerization rate is decreasing steeply after reaching a maximum at all

catalyst concentrations.

Frequency of β-H elimination is calculated to be negligibly low as compared to the chain transfer

to monomer ( Hk , vs. MktM in Table 4.22) at both the temperatures considered. For this

reason, average molecular weights are unchanged with increase in catalyst concentration as

shown in Figure 96 and Figure 97.

0 10 20 30 40 50 60

0.0

1.0x10-2

2.0x10-2

3.0x10-2

[Zr]

80M

40M

20M

Po

lym

eri

za

tio

n r

ate

(m

ole

s/L

/s)

Time (minutes)

10M


[Al/Zr = 2000, T = 30 °C and P = 0.98 atm]

207

0 10 20 30 40 50 60

0.0

1.0x10-2

2.0x10-2

3.0x10-2

4.0x10-2

[Zr]

80M

40M

20MPo

lym

eri

za

tio

n r

ate

(m

ole

s/L

/s)

Time (minutes)

10M


[Al/Zr = 2000, T = 70 °C and P = 0.98 atm]

0 20 40 60 80

4.0x104

6.0x104

8.0x104

Mo

lecu

lar

we

igh

t (g

/mo

l)

[Zr] (M)

Mn

Mw


[Al/Zr = 2000, T = 30 °C and P = 0.98 atm]

208

0 30 60 90

5x103

1x104

2x104

2x104

Mo

lecu

lar

we

igh

t (g

/mo

l)

[Zr] (M)

Mn

Mw


[Al/Zr = 2000, T = 70 °C and P = 0.98 atm]

Summary of the chapter: Models developed for ethylene and propylene polymerization in

previous chapter have simulated and results were discussed in this chapter. Gas phase and

solution phase ethylene polymerization with silica-supported, bridged zirconocene catalysts were

discussed first. Solution phase propylene polymerization with various bridged/unbridged

zirconocene and hafnocene catalysts were discussed in ulterior sections. Kinetic parameters were

determined for each catalyst system with 'natural logarithmic differential evolution' approach of

optimization.

209

CHAPTER – 5

CONCLUDING REMARKS

Kinetic models for olefin polymerization with metallocene catalysts were developed and

validated with experimental data. Kinetic model parameters were estimated using novel

natural logarithmic differential evolution approach of optimization. Parametric studies

were carried out to investigate the effect of various reaction conditions on polymerization

kinetics and polymer properties. This chapter presents a brief summary of the work

followed by conclusions, major contributions and future scope for research in this area.

5.1 Summary

5.1.1 Introduction

Polyolefins are the largest group of thermoplastics, often referred to as commodity

thermoplastics. Two most important and common polyolefins are polyethylene and

polypropylene and they are very popular due to their low cost and wide range of

applications. Metallocene catalyzed olefin polymerization has recently attracted research

interest since these catalysts allow the production of tailored macromolecules with

properties that can be accurately designed due to their single types of sites. Kinetic

studies of catalytic polymerization provide considerable insight into the mechanism of the

reactions and scale-up or commercialization of a polymerization process staggeringly

depends on the understanding of the kinetic behavior of the system under various

operating conditions.

Many problems encountered in industrial polymerization processes are associated

with inherent complexities in polymerization kinetics and mechanisms, physical changes

and transport effects, non-ideal mixing and conveying, and strong process nonlinearity.

210

Mathematical modeling is a powerful tool not only for the development of process

understanding, but also for the design of advanced process technology. In particular, a

kinetic model plays an important role in designing polymerization conditions to tailor a

polymer’s molecular architecture. Valid kinetic rate constants are required for calculating

polymerization rates and polymer properties. A comprehensive kinetic study of

polymerization process helps developing effective models at meso- and macro-levels.

Therefore, this study is focused on the estimation of kinetic parameters and prediction of

polymer properties through modeling at micro-level. The two most representative

objectives in modeling polymerization reactions are to compute polymerization rate and

polymer properties (molecular level and microscopic level) for various reaction

conditions.

Determining the parameters of a kinetic model by using laboratory, pilot plant, or

plant data is the most critical step for the successful development of a process model. It is

not always possible to design experiments to determine all the relevant kinetic

parameters. Therefore, in modern kinetic modeling, pseudo-rate constant methods and

computer aided parameter estimation techniques are widely used.

In transition metal catalyzed olefin polymerizations, the kinetic parameters are

catalyst dependent. Therefore, whenever a new catalyst is employed, a new set of kinetic

parameters must be determined. Considering the fact that the properties of polyolefins are

mostly dictated by the nature of catalyst being used and that a large number of different

types of catalysts are used for different polymer grades, it becomes very important to

have a well-established parameter estimation procedure that can be applied to any catalyst

systems.

211

5.1.2 Gaps in research

The existing literature on polymerization with metallocene catalyst systems suggests that

efforts have been made in understanding the mechanisms and work performance of

metallocene based catalyst systems. These systems allow tailor making of polymers and

offer other process advantages such as ease of handling of metallocene systems and

favourable conditions for polymerization from a commercial point of view, which has

evoked the examination of the commercial potential of such catalyst systems. The

commercial exploitation of such systems has, however, started in a limited way due to

prohibitive cost of the catalyst and the ambiguity associated with the aluminoxanes (co-

catalysts).

Various homo- and copolymers have been synthesized using metallocene catalyst

systems and most of the work is of experimental nature at either laboratory scale or the

pilot scale with more or less common objectives like investigating catalyst activity,

product properties and effect of parameters thereon.

Very little attempts have been made in modeling and simulation related studies for the

polymerization process. Majorly Z-N catalyzed polymerization of olefins was on focus

for modeling the morphological and transport related phenomena. Modeling efforts on

olefin polymerization with metallocene catalysts are as less as negligible when compared

to the other catalyst systems. Further, kinetic modeling and simulation of metallocene

catalyzed olefin polymerization is in its dissilient stage and provides a huge opportunity

to address the understanding of kinetics comprehensively.

5.1.3. Scope of the work

Significant development in the synthesis of new metallocenes and co-catalysts is

anticipated in near future leading to tailor-made polymers, including functionalized

polyolefins with predictable properties. In view of this, it is imperative to model the

212

polymerization of olefins involving different metallocene catalyst systems. A lot of scope

exists for theoretical as well as computation studies on metallocene catalyzed olefin

polymerization and hence developing a kinetic model and simulation of the same

unquestionably is a task not only for research but also of industrial importance.

In this work, the mechanistic aspects of Ziegler-Natta and metallocene catalyst

systems have been studied in detail and used in building up mathematical models for

ethylene and propylene polymerization using metallocene catalysts. Developed models

are validated with the experimental data available in literature and kinetic parameters are

estimated using differential evolution (DE) approach of optimization. Study on the effects

of various parameters like monomer concentration, polymerization temperature, catalyst

concentrations, and cocatalyst to catalyst molar ratio etc. upon rate of polymerization,

molecular weights and poly dispersity index and stereoregularity is carried out.

The outcomes of this study will help in better understanding of the chemistry and

process of the olefinic polymerization with these revolutionary catalyst systems.

5.1.4. Model development and simulation

In this study, mathematical models for metallocene catalyzed ethylene and propylene

polymerization are developed on a first principles basis and have been validated with

experimental data. These models may be used as a surrogate of the real olefin

polymerization process where the use of actual process may be costly or inopportune.

Comprehensive kinetic models consisting of mass and population balance equations, are

developed based on elementary reactions proposed in the reaction mechanism.

Founded on the interpretations of mechanisms for metallocene-catalyzed

polymerization, an ecumenical reaction set for ethylene and propylene polymerization

that includes reactions corresponding to all types of metallocenes, is proposed. Thereafter,

mathematical models for ethylene and propylene polymerization in a batch/semi-

213

batch/constant stirred tank reactor are built up based on the reactions considered. The

models are capable of predicting polymerization rate, and polymer properties (viz.

number-average- & weight-average molecular weight and PDI) in general. In addition,

mole fraction of dead polymer chains with terminal double bond and number of long-

chain branches & short-chain branches per 103 carbon atoms may be determined with

ethylene polymerization model. And fraction of vinyl-terminated chains, butenyl-

terminated chains, isobutyl-terminated chains and vinylidene-terminated chains relative to

the total unsaturated termination may be ascertained with propylene polymerization

model.

Model equations developed include a set of coupled, nonlinear and stiff ordinary

differential equations (ODEs) for the dynamic polymerization. To estimate the kinetic

parameters and to study the effect of parameters, these ODEs are solved with ODE-15s

function provided MATLAB™

7.0.1 software (MATLAB version 7.0.1, 2004).

Various established methods that are being used as parameter estimation

techniques, such as the graphical method and the gradient-based non-linear optimization

method either do not have precision to calculate the parameters or are easily get trapped

into local optima. In this study, a novel natural logarithmic differential evolution (NLDE)

approach of optimization, a remediated version of differential evolution algorithm (Price

and Storn, 1997) is proposed and used to solve parameter estimation problem. Proposed

NLDE algorithm is capable of handing multiple objectives simultaneously, providing

room to admit objective functions based on polymerization rate, molecular weights, PDI,

fraction of dead polymer chains with terminal double bond, fraction of vinyl-terminated

chains, butenyl-terminated chains, isobutyl-terminated chains and vinylidene-terminated

chains etc. if experimental data are available.

214

5.1.5 Results and discussion

In the following sections, the simulation results obtained for the ethylene and propylene

polymerization using different metallocene catalyst systems are summarized.

5.1.5.1 Ethylene polymerization

A. Silica supported (Me2Si[Ind]2ZrCl2)/MAO

Ethylene polymerization model is applied to gas phase polymerization of ethylene with

silica-supported Me2Si[Ind]2ZrCl2 catalyst and kinetic parameters are obtained.

Simulations are carried out analytically as well as numerically (with ODE-15s function

provided in MATLAB™ 7.0 software) using natural logarithmic differential evolution

approach of optimization to estimate the kinetic parameters. Predicted polymerization

rates exhibit a good agreement with experimental data, at all the temperatures (40 °C, 50

°C, 60

°C and 70

°C). Estimated kinetic parameters and objective function values F(k) are

shown in Table 4.4. Close range of objective function values (from 0.29934 to 0.6735)

obtained, shows good fit with experimental observations. Rates of initiation and

propagation are increasing with increase in temperature, as inferred from the estimated

rate constants for these reactions. For an increase of 10 °C, from 40 °C to 70 °C, the

weight average molecular weight ( wM ) is found to decrease by 67.40 %, 70.47 % and

81.67 % respectively. Polydispersity indices of polyethylene prepared with

Me2Si[Ind]2ZrCl2/MAO catalyst system are found to be 1.999 irrespective of temperature.

Polymerization rate is linearly increasing with ethylene pressure at all the

temperatures as shown in Figures 4.2. Low pressures (1-3 bar), i.e., low concentrations of

monomer, reasons low rates that are steady and maintained (due to negligible transfer

reaction). At higher pressures (5-7 bar), higher polymerization rates are obtained, but at

215

the same time, transfer to monomer also increases with high monomer concentrations

resulting in steeper decay in polymerization rates.

A steady increase in polymerization rate with increase in catalyst amount at

constant temperature and pressure is observed. At higher temperatures, the initiation and

termination rates also increase staggeringly with catalyst amount. Molecular weights and

PDI are not appreciably affected by changing catalyst amount.

B. In-situ-supported Et[Ind]2ZrCl2 (E2)/MAO

Ethylene polymerization model is applied to solution phase polymerization of ethylene

with in-situ-silica supported Et[Ind]2ZrCl2 catalyst and kinetic parameters are obtained. A

very large population size (120 times the dimension) is used to make certain of receiving

optimized estimates of parameters. Table 4.7 summarizes the parameters estimates at 40°,

60°, 80

°, 100

° and 120

° C with F(k) values. The model predictions of polymerization rate

obtained at different temperatures, are real close to the experimental values. F(k) values

obtained are ranging closely, with a least value of 1.1186 at 80 °C representing the best fit

to experimental observations as compared to highest value of 1.6063 at 120 °C.

Significantly lower values of propagation rate constants at 40 °C and 60

°C are obtained

relating to very low polymerization rate and catalyst activity with respect to those at

higher temperatures. At 80 °C, high propagation rate but lower deactivation and touching

transfer rates as compared to those at lower temperatures trace higher polymerization rate

with highest activity of the catalyst. At 40 °C, 60

°C and 80

°C, all the active catalyst sites

were occupied within initial 15 minutes, whereas at higher temperatures certain fraction

of those could not attach a monomer to initiate the chain.

Experimental kinetic data at different operating conditions, like different catalyst

amount, ethylene pressure and cocatalyst to catalyst mole ratio, were utilized to validate

216

the model at fixed temperature of 60 °C. Parameters estimated at 60

°C, 80 psig and

6 μmol catalyst amount with Al/Zr = 500 were used to verify the model responses at

various conditions.

The model predicts a proportional change in polymerization rate at different

ethylene pressures vindicating first order dependence of rate on ethylene concentration.

At 40 psig pressure, active catalyst sites stayed available for all the polymerization time

suggesting the non-initiation of some active site. At 80 psig pressure, active site were

occupied within 10 minutes and for higher pressures within 20 minutes.

A good match between experimental rate observations and model predictions at 3,

12 and 18 μmol of initial catalyst amount taken is obtained. The model adequately

captured the features of polymerization with in-situ-supported metallocene catalyst by

following the sustained polymerization rate with time and increase in the same with the

increase in catalyst amount. All the active catalyst sites were occupied within 10 minutes,

irrespective of initial amount of catalyst used.

Use of high Al/Zr ratio brings in higher polymerization rate and for the entire

range of ratios. For lower ratios (250 and 500), active catalyst sites disappeared within

first 10 minutes, whereas for higher ratios (above 500) these decreased with time but

remained available for entire polymerization time.

Average molecular weights of polyethylene obtained from the model are found to

be decreasing with increase in temperature, whereas the change in catalyst amount,

cocatalyst to catalyst mole ratio or ethylene pressure brought insignificant effect.

Estimated parameters indicate that chain transfer to monomer is dominating over

other transfer reactions, for which degree of polymerization and so the molecular weight

show up to be independent of monomer concentration. Polydispersity in all the cases are

obtained very close to 2. As inferred from calculated fraction of dead chains with double

bond at the end, major modes of chain termination, nearly for all sets of conditions, are

217

believed to be chain transfer to monomer, chain transfer to cocatalyst and β-hydride

elimination. Long chain branching frequency is detected to be negligibly low, except only

for low (40 °C) temperature and high (120 and 160 psig) ethylene pressures, suggesting

that the product is comprising of linear chains and posseses high density.

5.1.5.2 Propylene polymerization

A. Me2Si[Ind]2ZrCl2 (P1)/MAO

Propylene polymerization model is applied to solution phase polymerization of propylene

with Me2Si[Ind]2ZrCl2/MAO catalyst system and kinetic parameters are obtained.

Kinetic parameters are estimated by simulating the model with experimental data

at 25 °C and 75 °C with Al/Zr molar ratio of 500. Experimental data for Al/Zr ratio of

2000 are used to validate the model at both temperatures. Kinetic parameters and F(k)

values are given in Table 4.10.

Experimental observations reveal that both, the temperature and MAO to catalyst

molar ratio have a significant effect on polymerization rate. Model predictions are in very

close agreement with experimental observations at both the temperatures (25 °C and 75

°C) and Al/Zr molar ratios of 500 & 2000. With an increase in Al/Zr molar ratio,

polymerization rate increases at both the temperatures considered. At very high Al/Zr

ratio, the decreasing polymerization rate after reaching a maximum is observed.

Maximum polymerization rate is seen to increase four folds at 75 °C when

compared with that at 25 °C, at fixed catalyst concentration, Al/Zr ratio and pressure.

Increase in propagation rate constant pk with temperature is also in coherence with this

observed fact. As understood by dk and tMk values obtained, spontaneous deactivation

and chain transfer to monomer are activated hugely with increase in temperature.

218

Ascribing to which, the polymerization rate is decreasing steeply at 75 °C after reaching a

maximum.

With P1/MAO catalyst system, β-H elimination is observed to occur negligibly

(Hk ,

of the order of 10-6

) as compared to all other modes of chain termination. Increase in

temperature enhances the frequency of β-H elimination.

Chain transfer to cocatalyst is found to be very high at 25 °C than that at 75 °C. At

75 °C, the rectivation rate, after transfer to cocatalyst is slow due to low concentrations of

monomer and methyl activated complex.

A good agreement between experimental observations and predicted results for

MWD is obtained The model predicts Schulz-Flory distribution with a polydispersity

index around 2 for all reaction conditions. The dominant presence of chains with

vinylidene end group over the chains with butenyl end group is predicted by the model

suggesting highly isotactic polypropylene. A significant chain transfer to cocatalyst is

predicted at 25 °C. Increase in temperature (75 °C) results in a decreased rate of chain

transfer to cocatalyst.

An increase in monomer pressure results in a steady increase in polymerization

rate up to a maximum ranging in between 0.685 moles/L/s (15 psi) to 2.056 moles/L/s (45

psi) at 25 °C and fixed Zr = 10 μM, Al/Zr = 500. At 75 °C, higher polymerization rates

are observed {2.489 moles/L/s (15 psi) to 8.487 moles/L/s (45 psi)}, which decline after

reaching a maximum. Polymer molecular weights are negligibly increased with pressure.

Polymerization rates at various catalyst concentrations (10, 20, 40 and 80 μM) at

25 °C and 75 °C show that on doubling the catalyst concentration, maximum

polymerization rate is almost doubled, expressing a linear proportional dependence.

Average molecular weights are found to be insensitive to catalyst concentration.

219

B. Et(Ind)2ZrCl2 (P2)/MAO


with Et(Ind)2ZrCl2/MAO catalyst system and kinetic parameters are obtained.

Model predictions of reaction rate capture the typical behavior of experimental

rate profiles for propylene polymerization with Et(Ind)2ZrCl2/MAO catalyst system.

Estimated kinetic parameters and F(k) values are given in Table 4.12.

Like P1/MAO catalyst system, with Et(Ind)2ZrCl2 (P2)/MAO also, β-H

elimination is not observed significant at both the temperatures considered. Chain transfer

to cocatalyst is found to be very high at Al/Zr = 2000 at both the temperatures (25 °C and

75 °C).

Model predictions are in very close correspondence with the experimental values

of weight average molecular weight and PDI. Effect of temperature on MWD is obtained

similar to that obtained for P1/MAO system, however P2 yields low molecular weight

product at matched reaction conditions. PDIs at all reaction conditions are obtained near

2.0.

For P2/MAO, chain termination takes place mainly via spontaneous catalyst

deactivation, transfer to monomer and β-Hydride and increasing with an increase in

temperature. With an increase in Al/Zr ratio chain transfer to cocatalyst is enhanced. Low

bf values obtained advise that the fraction of chains with butenyl end group is very less

as compared to others. bf is noted to decrease with increase in temperature as well as

Al/Zr mole ratio. A trend of decreasing rate of chain transfer to cocatalyst with increase

in temperature is observed consistent with that obtained with P1/MAO system.

With increase in monomer pressure an increase in polymerization rate up to a

stabilized maximum of 0.8808 moles/L/s (15 psi) and 2.678 moles/L/s (45 psi) at 25 °C

and fixed Zr = 10 μM, Al/Zr = 2000 is observed. At 75 °C, little higher polymerization

rates {Rpmax: 1.083 moles/L/s (15 psi) and 3.96 moles/L/s (45 psi)} with decreasing trend

220

are observed. The changes in average molecular weights with variation in pressures at 25

°C and at 75 °C are trifling.

Like Me2Si[Ind]2ZrCl2 (P1), with this catalyst system also, polymerization rate is

found to be linearly dependent on the catalyst concentration. However P2 offers a lower

polymerization rates than P1 under similar reaction conditions. Additionally, average

molecular weights are observed to be unaffected by catalyst concentration, which is to be

attributed to very low values of Hk ,

, as compared to other transfer rate constants. Model

prediction suggests that catlyst P2 produces lower molecular weight polypropylene when

compared to P1 for alike reaction conditions. The effect of catalyst concentration upon

rate and molecular weights is qualitatively similar to that obtained for catalyst P1.

C. Me2Si(Ind)2HfCl2 (P3)/MAO

Simulation results obtained with propylene polymerization model applied to solution

phase polymerization of propylene with Me2Si(Ind)2HfCl2/MAO catalyst system are

summarized here. Estimated kinetic parameters and objective function [F(k)] values are

provided in Table 4.14. A good agreement between the experimental data and model

predictions of polymerization rate with (P3)/MAO catalyst system at 40 °C (F = 1.5175)

and 80 °C (F = 0.3161) is found. Polymerization rate is observed to increase with increase

in temperature. At fixed catalyst concentration, Al/Hf ratio (2000) and monomer pressure,

maximum rate is found to be 0.4068 moles/L/s (29 minutes) at 40 °C against 0.9378

moles/L/s (7 minutes) at 80 °C. Hafnium based metallocene catalysts are known for

producing high molecular weight polymers in comparison to their zirconium analogues,

but at the expense of substantially reduced catalytic activity [Ewen et al. (1987);

Nakayama and Shiono (2005)].

221

With (P3)/MAO system, frequency of β-H elimination is found to increase from

9.2795×10-6

s-1

at 40 °C to 1.8881×10-4

s-1

at 80 °C. Chain transfer to cocatalyst is seen

significant at Al/Hf = 2000 at both the temperatures.

Model predictions for molecular weight distribution are in good agreement with

the experimental values. Effect of temperature on MWD is obtained qualitatively similar

to that observed for P1/MAO and P2/MAO systems. It is worth noting that (P3)/MAO

system yields a way higher molecular weight polypropylene when compared to its Zr

analogue i.e. P1/MAO.

Like other catalyst systems discussed so far, with P3/MAO also, the major

pathway of chain termination is via spontaneous catalyst deactivation, transfer to

monomer and β-Hydride elimination. Among these β-Hydride elimination is found

increasing dominantly whereas spontaneous deactivation and transfer to monomer are

seen to decrease a bit, with an increase in temperature. vf values are increased with

increase in temperature at a constant Al/Hf molar ratio, but there is a negligible increase

with an increase in Al/Hf ratio at a given temperature. Fraction of chains with butenyl end

group is very less as compared to others and is noticed to decrease with increase in

temperature as well as Al/Hf mole ratio. The trend of decreasing rate of chain transfer to

cocatalyst with increase in temperature is similar to that obtained with its Zr analogue

(P1/MAO system) but the amount of this termination is quite less with P3/MAO system.

Polymerization rate up to a maximum of 0.131 moles/L/s (15 psi),

0.380 moles/L/s (30 psi) and 0.693 moles/L/s (45 psi) at 40 °C and fixed Zr = 10 μM,

Al/Hf = 2000 is obtained. At 80 °C, maximum rate of 0.382 moles/L/s at 15 psi, 0.855

moles/L/s at 30 psi and 1.350 moles/L/s at 45 psi is obtained. A steady increase in

polymerization rate with an increase in monomer pressure is seen at both the

temperatures.

222

Effect of monomer pressure on molecular weight is found potential at lower temperature.

A significant increase of 71.6 % (15-30 psi) and 30.72 % (30-45 psi) in weight average

molecular weight wM is observed with increase in pressure at 40 °C. At 80 °C,

relatively lower increase of 18.8 % (15-30 psi) and 6.73 % (30-45 psi) in wM is observed

with increase in pressure.

Polymerization rates predicted at different catalyst concentrations (10, 20, 30, 40

and 50 μM) at 40 °C and 80 °C show that polymerization rate increases with increase in

catalyst concentration. Since high catalyst concentration promotes β-H elimination,

polymerization rate diminishes at a faster rate. This effect is found particularly loud at 80

°C due to very high Hk ,

value.

With P3/MAO catalyst system, average molecular weights are noticed to be

decreasing with increase in catalyst concentration and this effect is more influencing at 40

°C, where higher molecular weights are obtained. A decrease of 35.1% (Hf = 10-20 μM),

21.5% (Hf = 20-30 μM), 14% (Hf = 30-40 μM) and 9.1% (Hf = 40-50 μM) in wM at 40

°C is observed.

D. Et(Ind)2HfCl2 (P4)/MAO


with Et(Ind)2HfCl2 catalyst and kinetic parameters are obtained.

Kinetic parameters and objective function [F(k)] values obtained for P4/MAO system are

given in Table 4.16. Model predictions are in conformation with experimental

observations showing an increase in polymerization rate at both the temperatures (40 °C

and 80 °C) and Al/Hf molar ratios of 500 & 2000. With P4/MAO system, Rp,max is found

to increase from 0.5216 moles/L/s at 40 °C to 1.092 moles/L/s at 80 °C at Al/Hf molar

ratio of 2000, following the general trend. But at an Al/Hf ratio of 500, Rp,max is

discovered to decrease meagerly from 0.1952 moles/L/s at 40 °C to 0.1148 moles/L/s at

223

80 °C. This surprising drift indicates that Al/Hf ratio of 500 is too low to efficiently

activate this catalyst at 80 °C. Owing to this fact a lower value of propagation rate

constant (pk ) is obtained at 80 °C than that at 40 °C. Chain transfer to cocatalyst is

obtained much higher at 40 °C than that at 80 °C. A good match in experimental and

predicted results for MWD is obtained. Polymerization rates obtained with this catalyst

system are comparable with P3/MAO but very less when compared with P1/MAO and

P2/MAO.

P4/MAO yielded very high molecular weights (~ 108 g/mol) of polypropylene as

compared to its zirconium analogue (P2) as well as other catalysts (P1 and P3) discussed

heretofore. Molecular weight is found to decrease with increase in temperature (from 40

°C to 80 °C) and also with increase in Al/Hf molar ratio (from 500 to 2000). At 80 °C,

chain termination via β-H elimination is highly dominating followed by the transfer to

monomer, than that at 40 °C, which causes a significant drop in molecular weight at

higher temperature. Polydispersity index predicted by the model for Al/Hf ratio of 500 at

40 °C is 2.5156, whereas for all other reaction conditions it is about 2.0. At all the

temperatures and Al/Hf ratios considered, the highest percentage of terminated chains

hold vinylidene end group ( vf > 80%), followed by isobutyl end group (9.3 < if < 14.1)

and butenyl end group (3.9 < bf < 6.3). At a fixed Al/Hf molar ratio, with increase in

temperature, vf is increasing whilst bf and if are found decreasing. Increase in Al/Hf

ratio increases the rate of chain transfer to cocatalyst and thereby if increases at a given

temperature. Though these trends for P4/MAO are consistent with those catalyst systems

discussed earlier but all the termination rates are notably less, due to which high

molecular weight product is raised.

224

For a change in monomer pressure of 30 psi to 45 psi, at 40 °C, Rp,max increases from

0.1720 mol/L/s to 0.3186 mol/L/s and at 80 °C, Rp,max increases from 0.07838 mol/L/s to

0.1176 mol/L/s. This indicates that an increase in monomer pressure results in linear

increase in polymerization rate.

With increase in pressure, molecular weights are found to increase. 2.92 fold

increase in wM for a change in pressure from 15 to 30 psi and 1.86 fold increase for a

change from 30 to 45 psi is found at 40 °C. Similarly at 80 °C, 1.94 fold increase in wM

for a change in pressure from 15 to 30 psi and 2.82 fold increase for a change from 30 to

45 psi is observed.

Polymerization rate is linearly increasing with increase in catalyst concentration at

both the temperatures and in tune with the discussion for P3/MAO system.

With P4/MAO catalyst system also, an inverse relationship between polymer molecular

weight and catalyst concentration is obtained.

E. [2,4,6-Me3Ind]2ZrCl2 (P5)/MAO


with an ansa-metallocene catalyst and kinetic parameters are obtained.

Model predictions of polymerization rate are in good agreement with the experimental

polymerization rate at both the cocatalyst to catalyst mole ratios (2000 and 4000)

considered. Values of estimated kinetic parameters and objective function F(k) are given

in Table 4.18.

When compared with P1-P4/MAO systems, polymerization rates with P5/MAO

system are found very less, so is the pk value estimated by the model. At 0 °C, Low

polymerization rates (Rp,max = 2.593 × 10-3

moles/L/s) at Al/Zr mole ratio of 2000 and

high rates (Rp,max = 4.921× 10-3

moles/L/s) at Al/Zr mole ratio of 4000 are echoing the

trend obtained with other catalyst systems. Also a sharp decrease in polymerization rate

225

after reaching a maximum is seen at high Al/Zr ratio implying a larger frequency of chain

transfer to cocatalyst.

At Al/Zr mole ratio of 2000, wM is found to be 6.2516 × 104

which is decreased

by 13.3% on raising the ratio to 4000. Model predicted molecular weights and PDIs

closely match with the experimentally determined values. Predicted value of PDI is

almost unchanged with an increase in Al/Zr mole ratio, and is found to be 2.34 and 2.30

at an Al/Zr molar ratio of 2000 and 4000 respectively.

Chain termination is via spontaneous catalyst deactivation, transfer to monomer

and β-Hydride elimination remain in force followed by chain transfer to cocatalyst as

inferred by vf and if values obtained. With increase in Al/Zr ratio, if is found increasing

while vf decreasing. Secondary insertions are found to be less with this catalyst system

and unresponsive to Al/Zr ratio.

With increase in monomer pressure, a higher initiation rate and increased

polymerization rate is noted, which is consistent with trend observed earlier with any

catalyst system. No appreciable increase in molecular weight is obtained with increase in

monomer pressure with this catalyst system.

Increase in catalyst concentration results in linearly increasing polymerization rate

which reaches to a maximum and decreases afterwards due to elevated termination rates.

With P5/MAO catalyst system, average molecular weights are noticed to be unaltered

with increase in catalyst concentration. An inverse relationship between polymer

molecular weight and catalyst concentration are obtained with hafnium based

metallocenes (P3 and P4), whereas Zr based metallocenes (P1 and P2) have shown a

similar trend as obtained for P5.

226

F. [2,4,7-Me3Ind]2ZrCl2) (P6)/MAO


with an ansa-P6 catalyst and kinetic parameters are obtained.

A good match between the model predicted and experimental rate is obtained at

all the Al/Zr ratios (1000, 2000 and 4000) studied. Values of estimated kinetic parameters

and objective function [F(k)] are given in Table 4.20.

Polymerization rates with P6/MAO are observed really less when compared with

P1-P4/MAO systems, but comparable with P5/MAO system at identical reaction

conditions. The pk value estimated by the model is slightly higher (106.06 M

-1.s

-1 vs.

71.27 M-1

.s-1

) than P5/MAO system. It is found that Al/Zr ratio as high as 4000 is

sufficient to activate this catalyst and higher ratios bring no further increase in

polymerization rate.

With (P6)/MAO system, frequency of β-H elimination is found to be

9.8943 × 10-4

. The rate of chain transfer to cocatalyst and reactivation after transfer both

are quite high with P6/MAO catalyst system at 0 °C. Altk ,

and rAlk values with this

catalyst system are much higher than those obtained with (P1-P4)/MAO but less than that

obtained with P5/MAO system.

Increase in Al/Zr molar ratio is resulting in decrease in molecular weights. At

Al/Zr mole ratio of 1000, wM is found to be 1.2994 × 105

which is decreased by 39.82%

on raising the ratio to 2000. On increasing Al/Zr ratio from 2000 to 4000, wM is further

decreased by 21.88%. Weight average molecular weights obtained with P6/MAO are very

close to those obtained with P5/MAO catalyst system at identical conditions, however,

polydispersity indices are little high with P6/MAO evincing broader molecular weight

distribution.

227

Chain termination is majorly taking place via spontaneous catalyst deactivation, transfer

to monomer and β-Hydride elimination. Secondary insertions with P6/MAO catalyst

system are higher than P5/MAO but less in comparison with (P1-P4)/MAO systems.

Like P5/MAO and other catalysts studied up to now, P6/MAO also evidences a higher

initiation rate and increased polymerization rate with increase in monomer pressure.

Polymerization rates at studied monomer pressures are very comparable with those

obtained with P1/MAO system.

A little increase in molecular weight is obtained with increase in monomer

pressure with P6/MAO catalyst system similar to as obtained with P5/MAO system.

With P6/MAO also, polymerization rates are increasing linearly with increase in catalyst

concentration. Like P5/MAO catalyst system, average molecular weights with P6/MAO

are also not changing with increase in catalyst concentration.

G. Me2Si[2,4,6-Me3Ind]2ZrCl2) (P7)/MAO


with an ansa-metallocene catalyst and kinetic parameters are obtained.

Estimated kinetic parameters and objective function F(k) values are given in Table 4.22.

A decent agreement between experimental and model predicted polymerization rates is

received at 30 °C and 70 °C.

With P7/MAO catalyst system, frequency of β-H elimination is substantial and

increases with increase in temperature from 30 °C to 70 °C. Reinitiation rate after β-H

elimination is much lower at 70 °C than that at 30 °C.

Molecular weights are found to decrease with increase in temperature. wM

estimated at 30 °C is 7.9344 × 104 which is decreased by 80% at 70 °C.

PDIs at all

reaction conditions are obtained almost 2.0 representing standard molecular weight

distribution. Polypropylene synthesized using P7/MAO system is highly isotactic.

228

Following the earlier trends, polymerization rate is found increasing linearly with increase

in monomer pressure. No appreciable change in average molecular weights with variation

in monomer pressures is observed at both 30 °C and 70 °C temperature.

Polymerization rates at different catalyst (P7) concentrations are showing a linear

dependence at 30 °C as well as at 70 °C. However at 70 °C polymerization rate is noted to

be 23% higher than that at 30 °C at corresponding catalyst concentration. Frequency of β-

H elimination is found to be negligibly low as compared to the chain transfer to monomer

and therefore, average molecular weights are unchanged with increase in catalyst

concentration.

5.2 Conclusions

Based on the results obtained in the present study, the following conclusions are drawn:

1. A comprehensive kinetic model is developed for metallocene catalyzed ethylene

polymerization which accurately predicts the polymerization rate, polymer

molecular weight distribution, mole fraction of dead polymer chains with terminal

double bond and density of long-chain branches and short-chain branches.

2. A comprehensive kinetic model is developed for propylene polymerization with

metallocene catalysts, which efficaciously predicts the polymerization rate,

polymer molecular weight distribution, the fractions of end groups generated by

various modes of chain transfer i.e. fraction of vinyl-terminated chains, butenyl-

terminated chains, isobutyl-terminated chains and vinylidene-terminated chains,

with different catalysts.

3. A novel 'natural logarithmic differential evolution (NLDE), algorithm of

optimization is proposed and applied successfully for estimating optimum kinetic

parameters.

229

4. Polymerization rates and polymer properties are calculated with population

balance approach and method of moments. Combination of population balance

approach and NLDE optimization approach is found to be extremely effective and

robust for parameter estimation.

5. A large value of initial population (NP) in NLDE should be used to ensure a

globally optimum set of parameters. In this work, NP is taken as high as fifty

times or more the size of parameter vector.

6. For semibatch reactor with constant monomer concentration throughout the course

of polymerization, analytical solution of model equations (to determine pk , dk

and tMk only) is presented and applied in simulations with all catalyst systems.

7. Simple models are solved analytically or numerically to obtain the coarse values

of kinetic parameters which are used in judging the range of parameters those are

required in the estimation of full set of parameters.

In case of gas phase ethylene polymerization with silica-supported

Me2Si[Ind]2ZrCl2 (E1)/MAO:

8. Rate of initiation increases with increase in temperature, ethylene pressure and

initial catalyst amount.

9. Rate of propagation increases with increase in temperature, ethylene pressure and

initial catalyst amount. At high temperatures (40 °C - 60 °C), propagation rate

decreases rapidly after reaching a maximum value. Propagation rate linearly

depends on ethylene pressure (concentration). At low pressures (1-3 bar),

propagation rates are low and maintained, but at high pressures (5-7 bar), high

propagation rates are obtained which decrease after reaching a maximum.

230

10. Rate of spontaneous deactivation increases with increase in temperature and initial

catalyst amount.

11. Rate of chain transfer to monomer increases with increase in temperature and

ethylene pressure. Chain termination dominantly takes place by chain transfer to

monomer.

12. Average molecular weights decrease with increase in temperature. Average

molecular weights increase slightly with increase in ethylene pressure. Increase in

initial amount of catalyst does not change the average molecular weight of

polyethylene.

13. A polydispersity index of 1.9999 is obtained which indicates an ideal molecular

weight distribution. PDI is not affected by change in temperature, ethylene

pressure and initial catalyst amount.

In case of solution phase ethylene polymerization with in-situ-silica supported

Et[Ind]2ZrCl2(E2)/MAO:

14. Rate of initiation increases with increase in temperature, ethylene pressure and

initial catalyst amount.

15. Propagation rate increases with increase in temperature. At 40 °C and 60

°C,

propagation rates are very low, but at 80 °C, 100 °C and 120 °C, rate increases

significantly. Propagation rate linearly increases with increase in ethylene pressure

and initial catalyst amount. Till 80 °C, maximum polymerization rate is

maintained with in-situ-supported catalyst system. Propagation rate also increases

with increase in cocatalyst to catalyst mole ratio. For a ratio of more than 500, rate

decreases after reaching a maximum.

16. Rate of spontaneous deactivation increases rapidly with increase in temperature

from 80 °C to 120 °C. Unlike E1/MAO, a change in initial catalyst amount and

231

cocatalyst to catalyst mole ratio do not affect the rate of spontaneous deactivation

of catalyst due to in-situ arrangement.

17. Rate of chain transfer to monomer increases with increase in temperature. Chain

termination dominantly takes place by chain transfer to monomer.

18. β-hydride elimination increases with increase in temperature. Frequency of β-

hydride elimination increases aggressively beyond 100 °C. Increase in initial

catalyst amount and cocatalyst to catalyst mole ratio do not affect the rate of β-

hydride elimination.

19. Rate of chain transfer to cocatalyst decreases with increase in temperature and

increases with increase in cocatalyst to catalyst mole ratio.

20. Average molecular weights decrease with increase in temperature and slightly

increase with increase in ethylene pressure. Increase in initial amount of catalyst

and cocatalyst to catalyst mole ration do not appreciably change the average

molecular weights of polyethylene.

21. Molecular weight distribution is close to ideal with PDIs ranging in between 1.814

and 2.0 for different polymerization conditions.

22. Fraction of dead chains with terminal double bond is very high (0.781 - 0.992),

which indicates that most chains are terminated via chain transfer to monomer, β-

hydride elimination and chain transfer to cocatalyst.

23. Polyethylene produced with E2/MAO catalysts, comprises of linear chains and

posseses high density since long chain branching frequency is found to be

negligibly low.

24. Gas phase ethylene polymerization with E1/MAO catalysts produces polyethylene

of high molecular weights as compared to that in solution phase polymerization

with in-situ-supported E2/MAO system.

232

In cases of solution phase propylene polymerization with various catalyst systems

(P1 through P7):

25. Rate of initiation increases with increase in temperature, propylene pressure

(concentration), initial catalyst concentration and cocatalyst to catalyst mole ratio.

26. Rate of propagation increases with increase in temperature, propylene pressure,

initial catalyst concentration and cocatalyst to catalyst mole ratio. At high

temperatures (75 °C in P1 and P2, 80 °C in P3 and P4, 70 °C in P7), propagation

rate decreases after reaching a maximum with increase in pressure and initial

catalyst concentration. Under similar reaction conditions, catalyst P1offers highest

propagation rate, followed by P2 through P7.

27. Rate of spontaneous deactivation increases with increase in temperature in all

cases of propylene polymerization.

28. Rate of chain transfer to monomer increases with increase in temperature and

propylene pressure. Highest rate of chain transfer (ktM = 10.2576 M-1

.s-1

at 75 °C)

is observed with P1/MAO, whereas lowest rate (ktM = 5.3048×10-4

M-1

.s-1

at

80 °C) is found with P4/MAO system.

29. Frequency of β-hydride elimination increases with increase in temperature and

initial catalyst concentration. The magnitude of specific rate constant for the

systems studied lies in the order of 10-6

s-1

to 10-3

s-1

. specific rate of reactivation

after β-hydride elimination also increases with increase in temperature.

30. All the catalyst systems studied, yield highly isotactic polypropylene as the rates

of secondary (2, 1) insertion obtained are very less. The rates are extremely low

(ks ~10-5

- 10-9

) with P1-P4/MAO system. However, the rates of secondary

insertion, propagation after secondary insertion and chain transfer after secondary

insertion increase, with increase in temperature.

233

31. Chain transfer to cocatalyst is sensitive to temperature and the rate decreases with

increase in temperature. The inverse trend is possibly due to change in structure of

MAO from simple (linear or cyclic) at low temperatures to a congested one

(ladder or cage) at high temperatures. Rate of reactivation after transfer to

cocatalyst is very high as compared to rate of initiation in each case and increases

with increase in temperature.

32. Average molecular weights of polypropylene decrease with increase in

temperature. With increase in propylene pressure, average molecular weights

increase slightly with zirconium based catalyst systems and increase significantly

with hafnium based systems. With increase in catalyst concentration, molecular

weights do not change with zirconium based catalyst systems but decrease

significantly with hafnium based catalyst systems. P4/MAO gives highest

molecular weight polypropylene (of the order of 108) followed by P3/MAO (of the

order of 105), all other catalysts yield polypropylene with relatively lower

molecular weights (of the order of 104).

33. The model predicts Schulz-Flory distribution with a polydispersity index around

2.0 with all the catalyst systems, which evidences an existence of single site types

in catalyst.

34. Fraction of dead chains with vinyl end group (fv) increases with increase in

temperature but decreases with increase in cocatalyst to catalyst mole ratio.

Fraction of dead chains with butenyl end group (fb) decreases with increase in

temperature and cocatalyst to catalyst mole ratio. Fraction of dead chains with

isobutyl end group (fi) decreases with increase in temperature but increases with

increase in cocatalyst to catalyst mole ratio.

234

5.3 Major contributions

1. A comprehensive kinetic model is developed for metallocene catalyzed ethylene

polymerization capable of predicting polymerization rate, polymer molecular

weight distribution, mole fraction of dead polymer chains with terminal double

bond and density of long-chain branches and short-chain branches.

2. Developed ethylene polymerization model is validated with experimental data

available in open literature, for two different catalyst systems with dissimilar

reaction phase and conditions.

3. A comprehensive kinetic model is developed for metallocene catalyzed propylene

polymerization capable of predicting polymerization rate, polymer molecular

weight distribution, the fractions of end groups generated by various modes of

chain transfer i.e. fraction of vinyl-terminated chains, butenyl-terminated chains,

isobutyl-terminated chains and vinylidene-terminated chains.

4. Developed propylene polymerization model is validated with experimental data

available in open literature, for seven different catalyst systems with dissimilar

reaction conditions in solution phase.

5. The natural logarithmic initialization of normalized population and mutation

operations are included in original differential evolution algorithm (an

evolutionary search based algorithm) and natural logarithmic differential

evolution is proposed.

6. Natural logarithmic differential evolution approach of optimization, which is

capable of handling multiple objective functions simultaneously, is used to

estimate the kinetic model parameters for each catalytic polymerization process

studied.

7. Parametric study is carried out for all the polymerization systems in order to

examine the effect of variation in monomer pressure (concentration),

235

polymerization temperature, initial amount of catalyst and cocatalyst to catalyst

mole ratio on polymerization kinetics and macro- and microstructural properties

of polymer.

8. A systematic approach for, translating mechanistic insight of olefin

polymerization with metallocene catalyst systems into kinetic model and

estimation of model parameters is developed and presented, which is well

applicable to the polymerization of any terminal alkene.

5.4 Future scope of research

The future scope of this work is enumerated below:

1. The models developed are extendable to different metallocene catalyst systems.

Simulation studies can be carried out with various catalyst systems used for

polymerization of ethylene and propylene.

2. Kinetic models for metallocene catalyzed homo- and copolymerization of other

terminal alkenes may be developed and simulated by utilizing the systematic and

comprehensive approach developed in this work.

3. Kinetic models developed in this work may be integrated with transport models to

study the behaviour of metallocene polymerization at macroscopic level

effectively.

236

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LIST OF PUBLICATIONS

International Journals (Referred)

1. Nikhil Prakash and Arvind Kumar Sharma, Modeling of Ethylene

Polymerization with Zirconocene Catalyst and Estimation of Kinetic Parameters

using Differential Evolution Algorithm, International Journal of Chemical

Modeling, 2012, 4 (4), 499-514.

2. Nikhil Prakash and Arvind Kumar Sharma, Kinetic Modeling of Gas Phase

Ethylene Polymerization with Silica Supported Metallocene Catalyst and

Determination of Kinetic Parameters using Differential Evolution Algorithm,

International Journal of Polymers and Technologies, 2011, 3 (2), 109-115.

3. Nikhil Prakash, Sushil Kumar and Arvind Kumar Sharma, Ethylene

Polymerization with Supported Metallocene Catalyst: Modeling and Simulation

with Natural Logarithmic Differential Evolution, International Journal of

Chemical Kinetics, (Communicated).

4. Nikhil Prakash, Sushil Kumar and Arvind Kumar Sharma, Modeling and

Simulation of isospecific propylene polymerization catalyzed by rac-

dimethylsilylbis(2,4,6-trimethyl-1-indenyl)zirconium-dichloride/MAO (To be

communicated).

5. Nikhil Prakash, Sushil Kumar and Arvind Kumar Sharma, Modeling of steric

effects of substituents on the microstructure of polypropylene prepared by with

bis(2,4,6-trimethylindenyl)zirconium dichloride and bis(2,4,7-

trimethylindenyl)zirconium dichloride (To be communicated).

International Conference Proceedings (in India)

1. Nikhil Prakash, Sushil Kumar and Arvind Kumar Sharma, Metallocene

Catalyzed Propylene Polymerization: Modeling, simulation and parameter

estimation using differential evolution approach, International Symposium & 66th

Annual Session of IIChE in association with International Partners (CHEMCON-

2013), Depertment of Chemical Engineering, Institute of Chemical Technology,

Mumbai, India, December 27-30, 2013. (Accepted).

2. Saket Anil Ingle, and Nikhil Prakash, Constrained Geometry Catalysts for Olefin

Polymerization, International Conference on Recent Advances in Chemical

Sciences (ICRACS -2013), Department of Chemistry, Arya P. G. College, Panipat,

India, February 24-26, 2013.

3. Saket Anil Ingle, and Nikhil Prakash, Modeling and Simulation of Slurry

Ethylene Polymerization with Supported Unbridged Zirconocene Catalyst using

Logarithmic Differential Evolution Approach, International Conference on

Polymers on the frontiers of Science and Technology, (APA-2013), University

252

Institute of Chemical Engineering and Technology, Punjab University,

Chandigarh, India, Feb 21-23, 2013.

4. Krunal Amin, Purva Goel and Nikhil Prakash, Kinetic Modeling and Simulation

of Ethylene Polymerization with Cp2ZrCl2/MAO Catalyst using Genetic

Algorithm Approach, International Conference on Polymers on the frontiers of

Science and Technology, (APA-2013), University Institute of Chemical

Engineering and Technology, Punjab University, Chandigarh, India, Feb 21-23,

2013.

5. Nikhil Prakash, Sushil Kumar and Arvind Kumar Sharma, Modeling and

Simulation of Metallocene Catalyzed α-Olefin Polymerization: A Logarithmic

Differential Evolution Approach, Proceedings of International Symposium & 65th


2012), Depertment of Chemical Engineering, National Institute of Technology,

Jalandhar, Punjab, India, December 27-30, 2012.

6. Anshu Yadav, Nikhil Prakash and Arvind Kumar Sharma, Kinetic Modeling of

Propene Polymerization with Silica Supported Zirconocene Catalyst and

Estimation of Kinetic Parameters using Differential Evolution Algorithm,

Proceedings of APA International Congress (HEALTH CARE INDIA 2012) on

Advances in Human Healthcare Systems, India Habitat Centre, New Delhi, India,

February 20-23, 2012.

7. Nikhil Prakash and Arvind Kumar Sharma, Modeling and Kinetic Parameter

Estimation of Ethylene Polymerization with Cp2ZrCl2–MAO Catalytic System

using Differential Evolution, Proceedings of International Symposium & 64th


2011), Department of Chemical Engineering, M. S. Ramaiah Institute of

Technology, Bangalore, India, December 27-29, 2011.

8. Nikhil Prakash and Arvind Kumar Sharma, Modeling and simulation of

constrained geometry titanocene catalyzed ethylene/norbornene copolymerization,

Proceedings of International Symposium and 62nd

Annual Session of IIChE in

association with International Partners (CHEMCON-2009), Department of

Chemical Engineering, Andhra University, Visakhapatnam, India, December 27-

30, 2009.

9. Nikhil Prakash and Arvind Kumar Sharma, Modeling and Simulation of High

Performance Polyolefin Production: Applications of homogeneous and supported

(nBuCp)2ZrCl2 in ethylene polymerization, Proceedings of APA International

Conference (Poly–2009) on Advances in Polymer Science & Technology: Vision

& Scenario, India Habitat Centre, New Delhi, India, December 17-20, 2009.

10. Nikhil Prakash and Arvind Kumar Sharma, Modeling and Simulation of Metal

Catalyzed Gas Phase Propylene Polymerization using Aspen Polymer Plus,

Proceedings of International Symposium and 61st Annual Session of IIChE in

association with International Partners (CHEMCON-2008), University Institute

of Chemical Engineering and Technology, Punjab University, Chandigarh, India,

December 27-30, 2008.

253

11. Nikhil Prakash and Arvind Kumar Sharma, Metallocene Catalysts in Olefin

Polymerization: Present State of the Art, Proceedings of APA International

Conference (Poly–2008) on Advances in Polymer Science & Technology, India

Habitat Centre, New Delhi, India, January 28 – 31 2008.

12. Nikhil Prakash and Arvind Kumar Sharma, Mathematical Modeling in

Metallocene Catalyzed Olefin Polymerization, Proceedings of APA International

Conference (Poly–2008) on Advances in Polymer Science & Technology, India

Habitat Centre, New Delhi, India, January 28 – 31 2008.

International Conference Proceedings (Abroad)

1. Nikhil Prakash, Sushil Kumar and Arvind Kumar Sharma, Modeling and Kinetic

Parameter Estimation of Ethylene Polymerization with Silica Supported

dimethylsilylene bis(η5 –inden-1–ylidene)zirconium dichloride Catalyst using

Differential Evolution approach, Proceedings of AIChE Annual meeting 2012,

Pittsburgh Convention Center, Pittsburgh, PA, USA, October 28-November 2,

2012.

National Conference Proceedings

1. Utsav Bhargav, J. Nitin and Nikhil Prakash, Advances in Conducting Polymers,

Proceedings of 8th

Annual Session of Students’ Chemical Engineering Congress

(SCHEMCON-2012), Department of Chemical Engineering, Birla Institute of

Technology and Science, Pilani, Rajasthan, September 21-22, 2012.

2. Nikhil Prakash, Sushil Kumar and Arvind Kumar Sharma, Effect of Reaction

Parameters on Propylene Polymerization with the Me2Si(2-Me-Ind)2ZrCl2

Catalyst: An Artificial Neural Network Approach, Proceedings of Conference on

Technological Advancements in Chemical and Environmental Engineering

(TACEE – 2012), Department of Chemical Engineering, Birla Institute of

Technology and Science, Pilani, Rajasthan, March 23-24, 2012.

3. Poornima Narayanan, Nikhil Prakash and Arvind Kumar Sharma, Reaction

Mechanisms and Kinetics of Olefin Polymerization catalyzed by Metallocenes: A

Review, Proceedings of Conference on Technological Advancements in Chemical

and Environmental Engineering (TACEE – 2012), Department of Chemical

Engineering, Birla Institute of Technology and Science, Pilani, Rajasthan, March

23-24, 2012.

4. Saket Anil Ingle, Nikhil Prakash and Arvind Kumar Sharma, Effects of

Operating Conditions on Ethylene-Norbornene Co-polymerization Catalyzed by

cyclopentadienyl-phenoxytitanium Catalysts: An Artificial Neural Network

Approach, Proceedings of Conference on Technological Advancements in

Chemical and Environmental Engineering (TACEE – 2012), Department of

Chemical Engineering, Birla Institute of Technology and Science, Pilani,

Rajasthan, March 23-24, 2012.

254

5. Nikhil Prakash and Arvind Kumar Sharma, Studies on Ethylene Polymerization

with Metallocene/Methylaluminoxane Catalysts: Mechanism and effects of

reaction conditions, Proceedings of APA National Conference on Advances in

Polymer Science & Engineering (PSE – 2010): Emerging Dimensions, University

Institute of Chemical Engineering and Technology, Punjab University,

Chandigarh, India, November 26-27, 2010.

6. Nikhil Prakash and Arvind Kumar Sharma, Recent Advances in Olefin

Polymerization: Applications of Constrained Geometry Single Site Catalysts,

Proceedings of National Seminar on Recent Advances in Chemical Engineering

Operations and Process in Chemical and Allied Industries, Institute of

Technology, Guru Ghasidas University, Bilaspur, India, February 5 - 6, 2008.

7. Nikhil Prakash and Arvind Kumar Sharma, Modeling and Simulation Trends in

Polymer Processing”, Proceedings of National Seminar on Recent Advances in

Chemical Engineering Operations and Process in Chemical and Allied Industries,

Institute of Technology, Guru Ghasidas University, Bilaspur, India, February 5 -

6, 2008.

Book Chapters

1. Nikhil Prakash, Commodity Thermoplastics with Bespoken Properties using

Metallocene Catalyst Systems in Responsive Materials and Methods: State-of-the-

Art Stimuli-Responsive Materials and Their Applications, Edited by: Ashutosh

Tiwari and Hisatoshi Kobayashi, WILEY-Scrivener Publishing LLC, USA, ISBN:

978-1-118-68622-5, (October 2013).

2. Sushil Kumar, Nikhil Prakash and Dipaloy Datta, Biopolymers Based-on

Carboxylic Acids Derived from Renewable Resources in Biopolymers:

Biomedical and Environmental Applications, Edited by: Susheel Kalia & Luc

Averous, Wiley-Scrivener Imprint, USA, ISBN: 978-0-470-63923-8, (October

2011).

255

APPENDIX - I

Code in MATLAB to Estimate the Kinetic Parameters in Ethylene

Polymerization with Me2Si[Ind]2ZrCl2 (E1)/MAO

------------------------------------------------------------------------------------------------------------

Main Program

------------------------------------------------------------------------------------------------------------

% Gas phase polymerization of ethylene with a silica supported

% metallocene catalyst: influence of temperature on deactivation

% Macromol. Rapid Commun. 18,319-324 (1997) by ROOS et al.

% Author: Nikhil Prakash / Dated 17/July/2012

clear

clc

%%%% ALL NEW THETA %%%%%%%%%

% Theta Set of optimization using kin, kp, kd, ktM values

%%%%%%%% P = 5 bar, V = 1L

%%%%%%%% T = 50 oC

% PARA corresponds to lower and upper bounds to 'k' values, named as pass globally

% Natural lagarithmic values will be used in searching 'k' values, which will be properly

corrected in the function with DEqs.

format long g

% PARA = [kin kp kd ktM]

PARAmin = log([1e-5 1e+1 1e-4 1e-4]); % log (k)min

PARAmax = log([1e-2 1e+5 1e-1 1e+1]); % log (k)max

F = 0.7;

CR = 0.9;

refresh = 1;

VTR = 0;

function_eval_limit = Inf;

Iteration_limit = 31;

% P = 4.9346; % atm

% V = 1; % L

% T = 273.16 + 50; % K

% R = 0.0821;

% Molecular weight of catalyst = 448.57

% weight of catalyst = 0.2 g

% Zr = 0.2/448.57

global MPE

MPE = 0.18599;

Zr = 4.4586e-4; % [Zr] <mol/L>

256

D = length (PARAmin);

NP = 500 * D;

fid = fopen('ALL_NEW_ROOS_50.txt', 'a+');

fprintf (fid,'\n\n\n\n\t\t ALL NEW THETA RUN number = [01]\n Volume 1 L\n\n');

% spacing out data output in file

fclose(fid);


fprintf (fid,datestr(now));

fclose(fid);


fprintf (fid, '\n PARA = [ki kp kd ktM] \n\n PARAmin = [%d %d %d %d] \t and \n

PARAmax = [%d %d %d %d]\n\n F = [%f]\t CR = [%f]\t NP = [%f]\n\n',

exp(PARAmin), exp(PARAmax), F, CR, NP);

fclose(fid);

if (length(PARAmin) ~= length(PARAmax))

error('Length of upper and lower bounds does not match.')

end

if (NP < 5)

error('Populationulation size NP must be bigger than 5.')

end

if ((F <= 0) || (F > 2))

error('Difference Factor F out of range (0,2].')

end

if ((CR < 0) || (CR > 1))

error('CR value out of range [0,1].')

end

if (Iteration_limit <= 0)

error('Iteration_limit must be positive.')

end

if (function_eval_limit <= 0)

error('function_eval_limit must be positive.')

end

refresh = floor(abs(refresh));

population = zeros(NP,D);

for i = 1:NP

population(i,:) = PARAmin + rand (1,D).* (PARAmax - PARAmin);

end

w = rand (NP,1);

wi = w;

population_old = zeros (size (population));

value = zeros (1, NP);

best_member = zeros (1, D);

best_member_iteration = zeros (1 ,D);

number_function_evlauation = 0;

257

ibest = 1;

global pass

pass = population(ibest,:) ;

time = 60*[2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52

54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 100 102 104 106

108 110 112 114 116 118 120 122 124 126 128 130 132 134 136 138 140 142 144 146

148 150 152 154 156 158 160 162 164 166 168 170 172 174 176 178 180 182 184 186

188 190 192 194 196 198 200]; % in seconds

expRp = [3.2 2.5 2.3 2.4 3 3.2 3.3 3.2 3.2 3.3 3.4 3.4 3.3 3.3 3.4 3.3 3.3 3.3 3.3

3.3 3.3 3.3 3.3 3.3 3.2 3.3 3.2 3.2 3.2 3.2 3.2 3.2 3.1 3.2 3.1 3 3 3.1 3.1 3 3 3

3 3 3.1 3 3 2.9 2.9 2.9 2.9 2.9 2.8 2.8 2.8 2.8 2.7 2.8 2.7 2.6 2.6 2.6 2.6 2.6

2.5 2.5 2.5 2.5 2.4 2.4 2.4 2.4 2.4 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.2 2.2 2.2

2.2 2.2 2.2 2.1 2.2 2.1 2.1 2.1 2.1 2.1 2.1 2.1 2 2 2 2]; % in kg/g/h

tspan= 0:time(length(time)); % <sec>

y0 = [1e-78 1e-77 1e-86 1e-94 1e-73 1e-86 Zr];

[t, y] = ode15s(@FUNroos,tspan,y0);

last = tspan(length(tspan));

LIVE_MOM_0 = y(:,1);



DEAD_MOM_0 = y(:,4);



Rp = (28.05e-3*3600/0.2)*exp(pass(2))*MPE*LIVE_MOM_0; % kg (ethylene)/h/gZr,

Reactor volume is 1 L

modRp = [Rp(121) Rp(241) Rp(361) Rp(481) Rp(601) Rp(721) Rp(841) Rp(961)

Rp(1081) Rp(1201) Rp(1321) Rp(1441) Rp(1561) Rp(1681) Rp(1801) Rp(1921)










Rp(10681) Rp(10801) Rp(10921) Rp(11041) Rp(11161) Rp(11281) Rp(11401)

Rp(11521) Rp(11641) Rp(11761) Rp(11881) Rp(12001)];

M1 = (1 - (modRp./expRp));

%-------------------------

zero = LIVE_MOM_0 + DEAD_MOM_0;

first = LIVE_MOM_1 + DEAD_MOM_1;

258

second = LIVE_MOM_2 + DEAD_MOM_2;

% molecular weights

Mnbar = 28.05*(first./zero);

Mwbar = 28.05*(second./first);

PDI = Mwbar ./ Mnbar;

modPDI = PDI(last);

expPDI = 2;

M2 = (1 - (modPDI/expPDI));

%---------------------------------

value(1) = sumsqr([M1 M2]);

value_best = value(1);

weight_best = w(1);

number_function_evlauation = number_function_evlauation + 1;

for i = 2 : NP

pass = population(i,:);


y0 = [1e-78 1e-77 1e-86 1e-94 1e-73 1e-86 Zr];






















Rp(10681) Rp(10801) Rp(10921) Rp(11041) Rp(11161) Rp(11281) Rp(11401)

Rp(11521) Rp(11641) Rp(11761) Rp(11881) Rp(12001)];


259

%-------------------------




% molecular weights




modPDI = PDI(last);

expPDI = 2;


value(i) = sumsqr([M1 M2]);


if (value(i) < value_best)

ibest = i;

value_best = value(i);

weight_best = w(i);

end

end

best_member_iteration = population(ibest,:);

value_bestit = value_best;

best_member = best_member_iteration;

pm1 = zeros (NP, D);





bm = zeros (NP, D);

ui = zeros (NP, D);

mui = zeros (NP, D);

mpo = zeros (NP, D);

rot = 0:1:NP-1;

rotd= 0:1:D-1;

rt = zeros (NP);

rtd = zeros (D);

a1 = zeros (NP);

a2 = zeros (NP);

a3 = zeros (NP);

a4 = zeros (NP);

a5 = zeros (NP);

ind = zeros (4);

iter = 1;

while (iter < Iteration_limit) && (value_best > VTR) % &&

(number_function_evlauation < function_eval_limit)

260

fprintf('\n\n\n Iteration No.[%d] \t of \t [%d]\n Going Well', iter, Iteration_limit);

population_old = population;

wold = w;

ind = randperm (4);

a1 = randperm (NP);

rt = rem (rot + ind(1), NP);

a2 = a1(rt+1);


a3 = a2(rt+1);

rt = rem (rot +ind(3), NP);

a4 = a3(rt+1);


a5 = a4(rt+1);

pm1 = population_old(a1,:);





w1 = wold(a1);

w2 = wold(a2);

bm = repmat (best_member_iteration, NP, 1);

bw = repmat(weight_best, NP, 1);

mui = rand (NP, D) < CR;

mui = sort (mui');

for i = 1:NP

n = floor (rand * D);

if n > 0

rtd = rem (rotd + n, D);

mui(:,i) = mui(rtd+1,i);

end

end

mui = mui';

mpo = mui < 0.5;

ui = pm3 + F*(pm1 - pm2);

ui = population_old.*mpo + ui.*mui;

for i = 1:NP

ui(i,:) = max (ui(i,:), PARAmin);

ui(i,:) = min (ui(i,:), PARAmax);

end

for i = 1:NP

261

pass = ui(i,:);


y0 = [1e-78 1e-77 1e-86 1e-94 1e-73 1e-86 Zr];






















Rp(10681) Rp(10801) Rp(10921) Rp(11041) Rp(11161) Rp(11281) Rp(11401)

Rp(11521) Rp(11641) Rp(11761) Rp(11881) Rp(12001)];


%-------------------------




% molecular weights




modPDI = PDI(last);

expPDI = 2;


value_temporary = sumsqr([M1 M2]);

if (value_temporary <= value(i))

population(i,:) = ui(i,:);

262

value(i) = value_temporary;

w(i) = wi(i);

if (value_temporary < value_best)

value_best = value_temporary;

best_member = ui(i,:);

weight_best = w(i);

end

end

end

number_function_evlauation = number_function_evlauation + NP;

best_member_iteration = best_member;

if (refresh > 0)

if (rem (iter, refresh) == 0)


fprintf (fid, 'Iteration: %d, Best: %8.4e, Worst: %8.4e\n', iter, value_best,

max(value));

fclose(fid);

for n = 1:D


fprintf(fid, '\n k(%d) = %e\n', n, exp(best_member(n)));

fprintf('\n k(%d) = %e\n', n, exp(best_member(n)));

fclose(fid);

end

end

end

iter = iter + 1;

end


fprintf (fid, 'Mnbar: %d,\t Mwbar: %d,\t PDI: %d\n\n', Mnbar(last), Mwbar(last),

PDI(last));

fclose(fid);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

pass = best_member;


y0 = [1e-78 1e-77 1e-86 1e-94 1e-73 1e-86 Zr];





Reactor volume is 1 L; y(1) = Lo

plot(time, expRp, 'k^', tspan, Rp, '-k');

if (iter >= Iteration_limit)

263

warning('max. number of iterations reached (Iteration_limit)') %#ok<WNTAG>

end

if (number_function_evlauation >= function_eval_limit)

warning('max. number of function evaluations reached (function_eval_limit)')

%#ok<WNTAG>

end

if (value_best < VTR)

warning('best value has been obtained') %#ok<WNTAG>

end

------------------------------------------------------------------------------------------------------------

Function

------------------------------------------------------------------------------------------------------------

function dy = FUNroos(t,y)

global MPE

global pass

kin = exp(pass(1));

kp = exp(pass(2));

kd = exp(pass(3));

ktM = exp(pass(4));

%%%%%%% Variables used in DEs corresponds to

%y(1): LIVE_MOM_0 Zeroth Moment of Living Polymer Chain Length Distribution

%y(2): LIVE_MOM_1 First Moment of Living Polymer Chain Length Distribution

%y(3): LIVE_MOM_2 Second Moment of Living Polymer Chain Length Distribution

%y(4): DEAD_MOM_0 Zeroth Moment of Dead Polymer Chain Length Distribution

%y(5): DEAD_MOM_1 First Moment of Dead Polymer Chain Length Distribution

%y(6): DEAD_MOM_2 Second Moment of Dead Polymer Chain Length Distribution

%y(7): Cstar Catalyst activated complex concentration

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% LISTED HERE ARE THE ODEs TO BE SOLVED

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

dy(1) = kin*MPE*y(7)-(kd)*y(1);

dy(2) = kin*MPE*y(7)+kp*MPE*y(1)-kd*y(2)+ktM*MPE*(y(1)-y(2));

dy(3) = kin*MPE*y(7)+kp*MPE*(y(1)+2*y(2))-kd*y(3)+ktM*MPE*(y(1)-y(3));

dy(4) = (kd+(ktM*MPE))*y(1);

dy(5) = (kd+(ktM*MPE))*y(2);

dy(6) = (kd+(ktM*MPE))*y(3);

dy(7) = -kin*MPE*y(7);

dy = dy';

264

APPENDIX - II

Code in MATLAB to Estimate the Kinetic Parameters in Ethylene

Polymerization in-situ-supported Et[Ind]2ZrCl2 (E2)/MAO

------------------------------------------------------------------------------------------------------------

Main Program

------------------------------------------------------------------------------------------------------------

% Modeling and Simulation of

%% "Effect of Experimental Conditions on Ethylene Polymerization with In-Situ-

Supported Metallocene Catalyst"

%%%using Logarithmic Differential Evolution Approach

%%%%%%%%%%%%% TEMP = 60 oC

%%%%%%%%% Experimental values for 60 oC and 80 psig pressure

%%%%%%%%%%% Reactor volume = 500 ml; Solvent hexane = 300 ml

% Author: Nikhil Prakash / Dated 19/June/2013

clear

clc

% optimization using kin, kp, kd, ktM, ktCo, kbeta, klcb values

%%%%%%%%%% MAO/Zr = 500 %%%%%%%%%%%


% Lagarithmic values will be used in searching 'k' values, which will be properly


format long g

% PARA = [kin kp kd ktM ktCo kbeta klcb]

PARAmin = log([1e-5 1e+1 1e-5 1e-5 1e-6 1e-6 1e-6]); % log (k)min

PARAmax = log([1e-1 1e+6 1e-1 1e-1 1e+3 1e+3 1e+3]); % log (k)max

F = 0.7;

CR = 0.9;

refresh = 1;

VTR = 0;


Iteration_limit =201;

global MEE

MEE = 0.5755; %% <mol/L>

molZr = 3e-6; % moles in 300 ml solvent, hexane

Zr = molZr*1000/300; % [Zr] <mol/L>

MAO = 500*Zr;


NP = 120*D;

fid = fopen('ET_90_60_T.txt', 'a+');

fprintf (fid,'\n\n\n\n\t\t RUN number = [01]\n\n\n'); % spacing out data output in file

fclose(fid);

265


fprintf (fid,datestr(now));

fclose(fid);


fprintf (fid, '\n PARA = [kin kp kd ktM ktCo kbeta klcb ] \n\n PARAmin = [%d %d

%d %d %d %d %d] \t and \n PARAmax = [%d %d %d %d %d %d %d ]\n\n F = [%f]\t

CR = [%f]\t NP = [%f]\n\n', exp(PARAmin), exp(PARAmax), F, CR, NP);

fclose(fid);



end

if (NP < 5)


end

if ((F <= 0) || (F > 2))


end

if ((CR < 0) || (CR > 1))


end



end



end


population = zeros(NP,D); % initialize population

for i = 1:NP


end

w = rand (NP,1);

wi = w;






ibest = 1;

global pass


266

time = 60*[0 1 2 4 5 7 8 9 11 12 14 15 17 18 20 21 23 25 26 28 29 31

32 34 35 36 37 38 39 40 41 42 43 44 46 47 48 49 50 51 52 54 55 57 58 59

60];

actexpRp=[10.9372 27.2702 43.676 54.3952 65.1143 70.3649 75.6154 80.866 75.0704

74.7797 74.489 74.2347 73.944 73.6896 73.3989 73.1446 72.8539 72.5632 77.7774

77.4868 82.701 65.8955 76.651 70.8554 70.6011 70.4194 70.3104 70.0197 69.8743

69.729 63.9697 69.3293 63.679 68.9296 68.6752 73.8895 73.7441 68.0939 67.8759

67.7668 78.5223 72.7267 72.436 72.1453 71.891 71.7093 71.6003]; % in cc/min

expRp = (3.42728e-6)*actexpRp; % in moles / s


y0 = [1e-89 1e-77 1e-94 1e-82 1e-73 1e-75 1e-85 1e-95 1e-65 Zr MAO];

[t, y] = ode15s(@FUNE2,tspan,y0);








LIVE_MOM_0 = y(:,7); % Zeroth Moment of Dead Polymer Chain Length Distribution

with terimnal '='

LIVE_MOM_1 = y(:,8);% First Moment of Dead Polymer Chain Length Distribution

with terimnal '='

LIVE_MOM_2 = y(:,9);% Second Moment of Dead Polymer Chain Length Distribution

with terimnal '='

P0 = y(:,10); % P(0) Catalyst activated complex concentration

CCocat = y(:,11); % Cocat Cocatalyst concentration

Rp = exp(pass(2))*MEE*LIVE_MOM_0; % mol(ethylene)/s/L, y(1) = Lo

modRp = [Rp(1) Rp(61) Rp(121) Rp(241) Rp(301) Rp(421) Rp(481) Rp(541) Rp(661)

Rp(721) Rp(841) Rp(901) Rp(1021) Rp(1081) Rp(1201) Rp(1261) Rp(1381) Rp(1501)




Rp(3301) Rp(3421) Rp(3481) Rp(3541) Rp(3601)];


%-------------------------

zero = LIVE_MOM_0 + DEAD_MOM_0 + LIVE_MOM_0;

first = LIVE_MOM_1 + DEAD_MOM_1 + LIVE_MOM_1;

second = LIVE_MOM_2 + DEAD_MOM_2 + LIVE_MOM_2;

% molecular weights



modMnbar = Mnbar(last);

267

modMwbar = Mwbar(last);


modPDI = PDI(last);

expPDI = 2;


value(1) = sumsqr([M1 M2]);


weight_best = w(1);


for i = 2 : NP














P0 = y(:,10);

CCocat = y(:,11);







Rp(3301) Rp(3421) Rp(3481) Rp(3541) Rp(3601)];





% molecular weights





268


modPDI = PDI(last);

expPDI = 2;


value(i) = sumsqr([M1 M2]);



ibest = i;


weight_best = w(i);

end

end









bm = zeros (NP, D);

ui = zeros (NP, D);



rot = 0:1:NP-1;

rotd= 0:1:D-1;

rt = zeros (NP);

rtd = zeros (D);

a1 = zeros (NP);

a2 = zeros (NP);

a3 = zeros (NP);

a4 = zeros (NP);

a5 = zeros (NP);

ind = zeros (4);

fprintf('going well');

iter = 1;

while (iter < Iteration_limit) && (value_best > VTR) && (number_function_evlauation

< function_eval_limit)



269

wold = w;

ind = randperm (4);

a1 = randperm (NP);


a2 = a1(rt+1);


a3 = a2(rt+1);


a4 = a3(rt+1);


a5 = a4(rt+1);






w1 = wold(a1);

w2 = wold(a2);




mui = sort (mui');

for i = 1:NP


if n > 0



end

end

mui = mui';

mpo = mui < 0.5;

ui = pm3 + F*(pm1 - pm2);


for i = 1:NP



end

for i = 1:NP

pass = ui(i,:);




270







LIVE_MOM_0 = y(:,7); % Zeroth Moment of Dead Polymer Chain Length Distribution

with terimnal '='

LIVE_MOM_1 = y(:,8);% First Moment of Dead Polymer Chain Length Distribution

with terimnal '='

LIVE_MOM_2 = y(:,9);% Second Moment of Dead Polymer Chain Length Distribution

with terimnal '='

P0 = y(:,10); % P(0) Catalyst activated complex concentration

CCocat = y(:,11); % Cocat Cocatalyst concentration







Rp(3301) Rp(3421) Rp(3481) Rp(3541) Rp(3601)];





% molecular weights






modPDI = PDI(last);

expPDI = 2;



% value_temporary = sumsqr([M1 M2 M3]);




w(i) = wi(i);



271


weight_best = w(i);

end

end

end



if (refresh > 0)




max(value));

fclose(fid);

for n = 1:D




fclose(fid);

end

end

end

iter = iter + 1;

end


fprintf (fid, 'Mnbar: %d,\t Mwbar: %d,\t PDI: %d, \n\n', Mnbar(last), Mwbar(last),

PDI(last));

fclose(fid);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

pass = best_member;












272



P0 = y(:,10);

CCocat = y(:,11);







Rp(3301) Rp(3421) Rp(3481) Rp(3541) Rp(3601)];

%-------------------------




% molecular weights






modPDI = PDI(last);

expPDI = 2;


fprintf (fid, '\n\n');

fclose(fid);


fprintf (fid, 'P0= %d,\n\n', P0);

fclose(fid);



fclose(fid);


fprintf (fid, 'Cocat= %d,\n\n', CCocat);

fclose(fid);



fclose(fid);


273

fprintf (fid, 'fraction with tdb f(=) = %d,\n\n',

LIVE_MOM_0/(LIVE_MOM_0+LIVE_MOM_0));

fclose(fid);

lcb = exp(pass(7))*LIVE_MOM_0*LIVE_MOM_0;

lcb = lcb(last);

lcb1000C = (500*lcd)/first;


fprintf (fid, 'lcb/1000C = %d,\n\n', lcb1000C);

fclose(fid);

plot(time, expRp, 'k^', tspan, Rp, '-k', time, modRp, '>g');



end



%#ok<WNTAG>

end



end

------------------------------------------------------------------------------------------------------------

Function

------------------------------------------------------------------------------------------------------------

function dy = FUNE2(t,y) global MEE pass % TEMP = 60 oC and Pressure = 80 psig % kin = exp(pass(1)); kp = exp(pass(2)); kd = exp(pass(3)); ktM = exp(pass(4)); ktCo = exp(pass(5)); kbeta = exp(pass(6)); klcb = exp(pass(7)); %%%%%%% Variables used in DEs corresponds to %y(1): LIVE_MOM_0 Zeroth Moment of Living Polymer Chain Length Distribution %y(2): LIVE_MOM_1 First Moment of Living Polymer Chain Length Distribution %y(3): LIVE_MOM_2 Second Moment of Living Polymer Chain Length Distribution %y(4): DEAD_MOM_0 Zeroth Moment of Dead Polymer Chain Length Distribution %y(5): DEAD_MOM_1 First Moment of Dead Polymer Chain Length Distribution %y(6): DEAD_MOM_2 Second Moment of Dead Polymer Chain Length Distribution %y(7): LIVE_MOM_0 Zeroth Moment of Dead Polymer Chain Length Distribution

with terimnal '='

274

%y(8): LIVE_MOM_1 First Moment of Dead Polymer Chain Length Distribution with

terimnal '=' %y(9): LIVE_MOM_2 Second Moment of Dead Polymer Chain Length Distribution

with terimnal '=' %y(10): P(0) Catalyst activated complex concentration %y(11): Cocat Cocatalyst concentration dy(1) = kin*MEE*y(10)-(kd+kbeta)*y(1); dy(2) = kin*MEE*y(10)-

(ktM*MEE+kd+ktCo*y(11)+kbeta)*y(2)+(ktM*MEE+ktCo*y(11)+kp*MEE+klcb*y(8))

*y(1); dy(3) =

kin*MEE*y(10)+(ktM*MEE+ktCo*y(11)+kp*MEE+klcb*y(9))*y(1)+2*(kp*MEE+klcb

*y(8))*y(2)-(ktM*MEE+kd+ktCo*y(11)+kbeta)*y(3); dy(4) = kd*y(1); dy(5) = kd*y(2); dy(6) = kd*y(3); dy(7) = (ktM*MEE+ktCo*y(11)+kbeta-klcb*y(7))*y(1); dy(8) = (ktM*MEE+ktCo*y(11)+kbeta)*y(2)-klcb*y(8)*y(1); dy(9) = (ktM*MEE+ktCo*y(11)+kbeta)*y(3)-klcb*y(9)*y(1); dy(10) = -kin*MEE*y(10)+ktCo*y(11)*y(1)+kbeta*y(1); dy(11) = -ktCo*y(11)*y(1); dy = dy';

275

APPENDIX - III

Code in MATLAB to Estimate the Kinetic Parameters in Propylene

Polymerization with Me2Si[Ind]2ZrCl2 (P1)/MAO

------------------------------------------------------------------------------------------------------------

Main Program

This script is representative one, and is used (with modifications) for kinetic parameter

estimation in propylene polymerization with all catalysts studied in this work.

------------------------------------------------------------------------------------------------------------

% Estudo Comparativo de "Polimerização de Propileno com Diferentes Catalisadores

Metalocênicos

% Através de um Planejamento de Experimentos"

% by Maria et al.

% % % % % % Polímeros: Ciência e Tecnologia, vol. 12, nº 1, p. 48-59, 2002.

%%%%%%%%%%%%% TEMP = 75 oC TEMP = 75 oC TEMP = 75 oC

%%%%%%%%%%%%%%

% Author: Nikhil Prakash / Dated 20/Aug/2012

clear all

clear

clc

%%%% ALL NEW THETA %%%%%%%%%

% Theta Set of optimization using kin, kp, kd, ktM, kH, krH, ks, ksp, ksM, kAl, krAl

values

%%%%%%%%%% MAO/Zr = 500 %%%%%%%%%%%


% Lagarithmic values will be used in searching 'k' values, which will be properly


format long g

% PARA = [kin kp kd ktM kH krH ks ksp ksM kAl krAl]

PARAmin = log([1e-4 1e+4 1e-5 1e-2 1e-6 1e-2 1e-7 1e-4 1e-3 1e-3 1e+1]); % log

(k)min

PARAmax = log([1e-2 1e+6 1e-3 1e+0 1e-3 1e+3 1e-2 1e+0 1e+3 1e+3 1e+5]); % log

(k)max

F = 0.7;

CR = 0.9;

refresh = 1;

VTR = 0;


Iteration_limit = 81;

global MPP

% P = 2; % <bar>

276

% x = 0.0002*P^6 - 0.0015*P^5 + 0.0048*P^4 - 0.0069*P^3 + 0.007*P^2 + 0.1529*P -

0.0012; %% P-x relation at T = 0.0 0C

% moltol = 100*0.8669/92.1381;

% molpro = (x/(1-x))*moltol;

T = 25+273;

MPP = 0.354-(6.75e-3)*T+(3.66e-5)*T^2; %<mol/l>

% MPP = molpro*10; %per liter

Zr = 10e-6; % [Zr] <mol/L>

MAO = 500*Zr;


NP = 200*D;

fid = fopen('P3C1_75_500.txt', 'a+');

fprintf (fid,'\n\n\n\n\t\t RUN number = [00002]\n\n\n');

fclose(fid);

fid = fopen('P3C1_75_500.txt', 'a+');

fprintf (fid,datestr(now)); % writing date and time in file

fclose(fid);

fid = fopen('P3C1_75_500.txt', 'a+');

fprintf (fid, '\n PARA = [kin kp kd ktM kH krH ks ksp ksM kAl krAl] \n\n PARAmin

= [%d %d %d %d %d %d %d %d %d %d %d] \t and \n PARAmax = [%d %d %d %d

%d %d %d %d %d %d %d]\n\n F = [%f]\t CR = [%f]\t NP = [%f]\n\n', exp(PARAmin),

exp(PARAmax), F, CR, NP);

fclose(fid);



end

if (NP < 5)


end

if ((F <= 0) || (F > 2))


end

if ((CR < 0) || (CR > 1))


end



end



end


population = zeros(NP,D); % initialize population

277

for i = 1:NP


end

w = rand (NP,1);

wi = w;






ibest = 1;

global pass


time = [117 175 233 292 358 417 483 533 600 650 700 775 842 892 958 1008 1075 1142

1192 1258 1317 1383 1442 1492 1558 1617 1675 1733 1800 1858 1917 1967 2033 2100

2150 2217 2267 2333 2400 2450 2525 2583 2633 2700 2758 2817 2883 2933 2992 3050

3108 3175 3225 3300 3358 3425 3492 3533 3600]; %% (seconds)

expRp = [3.48168 4.94764 5.16754 5.46073 5.31414 5.38743 5.35079 5.24084 5.27749

5.16754 5.09424 5.05759 4.94764 4.80105 4.72775 4.6911 4.6178 4.5445 4.43455

4.43455 4.32461 4.21466 4.25131 4.10471 3.99476 3.95812 3.92147 3.81152 3.77487

3.73822 3.66492 3.62827 3.55497 3.40838 3.48168 3.33508 3.33508 3.33508 3.29843

3.15183 3.11518 2.96859 2.89529 2.82199 2.74869 2.71204 2.71204 2.63874 2.5288

2.4555 2.4555 2.41885 2.34555 2.34555 2.34555 2.1623 2.2356 2.12565 2.08901];


y0 = [1e-50 1e-52 1e-55 1e-49 1e-48 1e-52 1e-49 1e-66 1e-59 1e-56 Zr 1e-57 MAO 1e-

77 1e-87];

[t, y] = ode15s(@FUNPROP,tspan,y0);





MIS_MOM_0 = y(:,4);

MIS_MOM_1 = y(:,5);

MIS_MOM_2 = y(:,6);

DEAD_MOM_0v = y(:,7);

DEAD_MOM_0B = y(:,8);


DEAD_MOM_2 = y(:,10);

DEAD_MOM_0I = y(:,15);

Rp = exp(pass(2))*MPP*LIVE_MOM_0;



278






Rp(3534) Rp(3601)];


zero = LIVE_MOM_0 + MIS_MOM_0 + DEAD_MOM_0v + DEAD_MOM_0B +

DEAD_MOM_0I;

first = LIVE_MOM_1 + MIS_MOM_1 + DEAD_MOM_1;

second = LIVE_MOM_2 + MIS_MOM_2 + DEAD_MOM_2;

% molecular weights





% expMnbar = ;

% expMwbar = ;

% M2 = (1 - (modMnbar/expMnbar));

% M3 = (1 - (modMwbar/expMwbar));


modPDI = PDI(last);

% expPDI = ;

% M2 = (1 - (modPDI/expPDI));

%---------------------------------

modB =

(DEAD_MOM_0B(last)*100)/(DEAD_MOM_0B(last)+DEAD_MOM_0v(last)+DEAD_

MOM_0I(last));

% expB = ;

% M3 = (1 - (modB/expB));

%----------------------------------

modI =

(DEAD_MOM_0I(last)*100)/(DEAD_MOM_0B(last)+DEAD_MOM_0v(last)+DEAD_

MOM_0I(last));

% expI = ;

% M4 = (1 - (modI/expI));

%-----------------------------

value(1) = sumsqr([M1]);

% value(1) = sumsqr([M1 M2 M3 M4]);


weight_best = w(1);


279

for i = 2 : NP




77 1e-87];






MIS_MOM_0 = y(:,4);

MIS_MOM_1 = y(:,5);

MIS_MOM_2 = y(:,6);




DEAD_MOM_2 = y(:,10);










Rp(3534) Rp(3601)];



DEAD_MOM_0I;



% molecular weights





% expMnbar = ;

% expMwbar = ;




modPDI = PDI(last);

280

% expPDI = ;


%---------------------------------

modB =


MOM_0I(last));

% expB = ;

% M3 = (1 - (modB/expB));

%----------------------------------

modI =


MOM_0I(last));

% expI = ;

% M4 = (1 - (modI/expI));

%-----------------------------

value(i) = sumsqr([M1]);

% value(i) = sumsqr([M1 M2 M3 M4]);



ibest = i;


weight_best = w(i);

end

end









bm = zeros (NP, D);

ui = zeros (NP, D);



rot = 0:1:NP-1;

rotd= 0:1:D-1;

rt = zeros (NP);

rtd = zeros (D);

a1 = zeros (NP);

a2 = zeros (NP);

a3 = zeros (NP);

a4 = zeros (NP);

a5 = zeros (NP);

281

ind = zeros (4);

iter = 1;

while (iter < Iteration_limit) && (value_best > VTR) % &&

(number_function_evlauation < function_eval_limit)



wold = w;

ind = randperm (4);

a1 = randperm (NP);


a2 = a1(rt+1);


a3 = a2(rt+1);


a4 = a3(rt+1);


a5 = a4(rt+1);






w1 = wold(a1);

w2 = wold(a2);




mui = sort (mui');

for i = 1:NP


if n > 0



end

end

mui = mui';

mpo = mui < 0.5;

ui = pm3 + F*(pm1 - pm2);


282

for i = 1:NP



end

for i = 1:NP

pass = ui(i,:);



77 1e-87];






MIS_MOM_0 = y(:,4);

MIS_MOM_1 = y(:,5);

MIS_MOM_2 = y(:,6);




DEAD_MOM_2 = y(:,10);










Rp(3534) Rp(3601)];



DEAD_MOM_0I;



% molecular weights





% expMnbar = ;

283

% expMwbar = ;




modPDI = PDI(last);

% expPDI = ;


%---------------------------------

modB =


MOM_0I(last));

% expB = ;

% M3 = (1 - (modB/expB));

%----------------------------------

modI =


MOM_0I(last));

% expI = ;

% M4 = (1 - (modI/expI));

%-----------------------------


% value_temporary = sumsqr([M1 M2 M3 M4]);




w(i) = wi(i);




weight_best = w(i);

end

end

end



if (refresh > 0)


fid = fopen('P3C1_75_500.txt', 'a+');


max(value));

fclose(fid);

for n = 1:D

fid = fopen('P3C1_75_500.txt', 'a+');

284



fclose(fid);

end

end

end

iter = iter + 1;

end

fid = fopen('P3C1_75_500.txt', 'a+');

fprintf (fid, 'Mnbar: %d,\t Mwbar: %d,\t PDI: %d, \t B: %d,\t I: %d, \n\n',

Mnbar(last), Mwbar(last), PDI(last), modB, modI);

fclose(fid);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

pass = best_member;



77 1e-87];












Rp(3534) Rp(3601)];

plot(time, expRp, 'k^', tspan, Rp, '-k', time, modRp, '>g');



end



%#ok<WNTAG>

end



end

------------------------------------------------------------------------------------------------------------

285

Function

------------------------------------------------------------------------------------------------------------

function dy = FUNPROP(t,y)

% This function contains all ODEs for Estudo Comparativo de

% "Polimerização de Propileno com Diferentes Catalisadores Metalocênicos

% Através de um Planejamento de Experimentos"

% by Maria etal.

% % % % % % Polímeros: Ciência e Tecnologia, vol. 12, nº 1, p. 48-59, 2002.

%%%%%%%%%%%%% TEMP = 75 oC %%%%%%%%%%%%%%

global MPP

global pass

kin = exp(pass(1));

kp = exp(pass(2));

kd = exp(pass(3));

ktM = exp(pass(4));

kH = exp(pass(5));

krH = exp(pass(6));

ks = exp(pass(7));

ksp = exp(pass(8));

ksM = exp(pass(9));

kAl = exp(pass(10));

krAl = exp(pass(11));

%%%%%%% Variables used in DEs corresponds to

%y(1): Lo Zeroth Moment of Living Polymer Chain Length Distribution

%y(2): LIVE_MOM_1 First Moment of Living Polymer Chain Length Distribution

%y(3): LIVE_MOM_2 Second Moment of Living Polymer Chain Length Distribution

%y(4): MIS_MOM_0 Zeroth Moment of (2,1) inserted Polymer Chain Length

Distribution

%y(5): MIS_MOM_1 First Moment of (2,1) inserted Polymer Chain Length

Distribution

%y(6): MIS_MOM_2 Second Moment of (2,1) inserted Polymer Chain Length

Distribution

%y(7): DEAD_MOM_0v Zeroth Moment of Dead Polymer Chain Length Distribution

(vinylidene end group)

%y(8): DEAD_MOM_0B Zeroth Moment of Dead Polymer Chain Length

Distribution(Butentl end group)

%y(9): DEAD_MOM_1 First Moment of Dead Polymer Chain Length Distribution

%y(10): DEAD_MOM_2 Second Moment of Dead Polymer Chain Length Distribution

%y(11): Cstar Catalyst activated complex concentration

%y(12): CHstar Hydride catalyst activated complex concentration

%y(13): MAO Cocatalyst concentration

%y(14): CMestar Methyl catalyst activated complex concentration

%y(15): DEAD_MOM_0I Zeroth Moment of Dead Polymer Chain Length

Distribution(I end group)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

286

% LISTED HERE ARE THE ODEs TO BE SOLVED

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

dy(1) = kin*MPP*y(11)-

(kd+kH+(ks*MPP)+(kAl*y(13)))*y(1)+(ksp+ksM)*MPP*y(4)+krH*MPP*y(12)+krAl*

MPP*y(14);

dy(2) = kin*MPP*y(11)+kp*MPP*y(1)-

(kd+kH+(ks*MPP)+(kAl*y(13)))*y(2)+ktM*MPP*(y(1)-y(2))+ksp*MPP*(y(4)+

y(5))+ksM*MPP*y(4)+krH*MPP*y(12)+krAl*MPP*y(14);

dy(3) = kin*MPP*y(11)+kp*MPP*(y(1)+2*y(2))-

(kd+kH+ks*MPP+kAl*y(13))*y(3)+ktM*MPP*(y(1)-

y(3))+ksp*MPP*(y(4)+2*y(5)+y(6))+ksM*MPP*y(4)+krH*MPP*y(12)+krAl*MPP*y(1

4);

dy(4) = ks*MPP*y(1)-(ksp+ksM)*MPP*y(4);

dy(5) = ks*MPP*(y(1)+y(2))-(ksp+ksM)*MPP*y(5);

dy(6) = ks*MPP*(y(1)+2*y(2)+y(3))-(ksp+ksM)*MPP*y(6);

dy(7) = (kd+kH+(ktM*MPP))*y(1);

dy(8) = ksM*MPP*y(4);

dy(9) = (kd+kH+(ktM*MPP)+kAl*y(13))*y(2)+ksM*MPP*y(5);

dy(10) = (kd+kH+(ktM*MPP)+kAl*y(13))*y(3)+ksM*MPP*y(6);

dy(11) = -kin*MPP*y(11);

dy(12) = kH*y(1)-krH*MPP*y(12);

dy(13) = -kAl*y(13)*y(1);

dy(14) = kAl*y(13)*y(1)-krAl*MPP*y(14);

dy(15) = kAl*y(13)*y(1);

dy = dy';

287

BIOGRAPHIES

Biography of the Candidate

Mr Nikhil Prakash is serving as a Lecturer (since August 2005) in Department of Chemical

Engineering at BITS-Pilani, Pilani Campus, and pursuing his PhD under the supervision of

Dr Arvind Kumar Sharma and Dr Sushil Kumar. He earned his B Tech degree in Chemical

Engineering from Bundelkhand Institute of Engineering & Technology (BIET)-Jhansi in

2001 and M E (Chemical Engg.) from BITS-Pilani in 2003.

Mr Prakash has 10 years of experience in teaching undergraduate and post graduation

students in the field of Chemical Engineering, Polymer Engineering & Petroleum

Engineering and his areas of Research are Polymer Science and Engineering; Process

Engineering; Modeling, Simulation and Optimization; Reaction Engineering; Process

Dynamics and Control; Artificial Neural Networks and Catalysis.

He has guided 1 ME Dissertation, 2 BE Thesis and 260+ Projects (Study oriented

projects; Computer projects; Design projects; Special projects; Professional Practice;

Research Practice and Course projects of ME). He has published 21 research papers in

national & international journals and conferences, 2 book chapters and participated in 25

seminars/conferences/symposia/workshops.

He is the reviewer of 4 International Journals (American Journal of Polymer Science;

International Journal of Materials Engineering; Nanoscience and Nanotechnology; Science

and Technology). He is awarded Minor Research Project by University Grant Commission

(UGC), New Delhi India (2013-15) and Travel Grant by Department of Science &

Technology (DST), New Delhi, India to attend 2012-AIChE Annual Meeting held at

Pittsburgh PA, USA.

He has been a Organizing Committee Member & Resource Faculty for Workshop on

Analytical Instruments for Chemical and Environmental Engineers (WAICEE - 2013), BITS

Pilani, March 22-23, 2013, Organizing Committee Member for 8th Annual Session of

Students' Chemical Engineering Congress (SCHEMCON-2012), BITS Pilani, Sept. 21-22,

2012; Conference on Technological Advancements in Chemical and Environmental

Engineering (TACEE-2012), BITS Pilani, March 23-24, 2012; Conference on Photonic

Polymers: Materials, Devices and Applications (PPMDA-2008), BITS Pilani, April 3-4,

2008; National Conference on Environmental Conservation (NCEC-06), BITS Pilani, Sept.

1-3, 2006 and Organizing Faculty Member for Intensive Teaching Workshop (ITW), BITS

Pilani, April, 2006.

Mr Prakash is the Life associate member of Indian Institute of Chemical Engineers

(IIChE); Life member of Asian Polymer Association (APA), International Association of

Engineers (IAENG), Asia-Pacific Chemical, Biological & Environmental Engineering

Society (APCBEES); Member of AIChE from 2012, and Honorary Treasurer of Indian

Institute of Chemical Engineers (IIChE), Pilani Regional Centre, Pilani.

288

Biography of the Supervisor

Dr Arvind Kumar Sharma graduated (B Tech) from Harcourt Butler Technological

Institute (HBTI) Kanpur in 1986, did Masters (MS) in 1992 and PhD in 2005, both from

Indian Institute of Technology (IIT) Madras.

He worked as a Junior Research Fellow in the Department of Post Harvest Process

and Food Engineering, College of Technology, Govind Ballabh Pant University of

Agriculture and Technology, Pantnagar, during 1986-87. Later at IIT Madras, during 1990-

92, he also worked as a Senior Project Officer for a project on Biogas Generation from

Tannery Effluents funded by the Department of Nonconventional Energy Sources of

Ministry of Energy and as a Research Associate for a project on Colour Removal of

Industrial Effluents using Fluidized Bed funded by Council of Scientific and Industrial

Research (CSIR) during 1997–2002.

Presently he is an Assistant Professor (since June 2006) in the Department of

Chemical Engineering at Birla Institute of Technology and Science (BITS) Pilani – Pilani

Campus, which he joined in December 2004 as a Lecturer.

He also served as Head of the Department (Jan 2007 to August 2012). During this

period, department was granted three major development funds: Departmental Research

Support (DRS) – Special Assistance Programme (SAP) of University Grant Commission

(UGC) [Rs. 48 Lakhs (2011 - 16)], UGC-Infrastructure Support [Rs. 20 Lakhs (2011-12)

and Fund for Improvement of S & T Infrastructure (FIST) of Department of Science and

Technology (DST) [Rs. 80.5 Lakhs (2011-16)]. Five (5) UGC-BSR research fellowships

were also granted to the department. The department also conducted two prominent

conferences: Technological Advancements in Chemical and Environmental Engineering

(TACEE-2012, March 23-24, 2012) and 8th

Annual Session of Students’ Chemical

Engineering Congress (SCHEMCON-2012, September 21-22, 2012), an annual event of

Indian Institute of Chemical Engineers (IIChE).

Dr. Sharma teaches in the field of Chemical Engineering, Environmental Engineering

& Biochemical Engineering and his areas of Research are Environmental Engineering

(Water and Wastewater Treatment), Adsorption, Fluidization, Fluid Dynamics, Biochemical

Engineering (Bioreactor Analysis and Design), Reaction Mechanism & Kinetics and

Modeling & Simulation. He has guided 2 ME Dissertations, around 20 Professional and

Research Practice students, 2 BE Theses and around 50+ BE Projects. He has published

around 30+ research papers in national & international journals and conferences, 5 chapters

in lecture notes and participated in 15+ short term

courses/seminars/conferences/symposiums/workshops/conventions.

He has reviewed research papers submitted for CURIE Journal (Journal of

Cooperation among University, Research and Industrial Enterprises); paper/proposal for 2nd

National Convention on “Energizing Entrepreneurship through Innovation”, Nov. 2-3,

2007, Pilani, India and coordinated the proof reading of 25 review/research papers for the

special issues of Journal of Energy, Heat and Mass Transfer – Dec. 1996 and March 1997

issues, viz., FESTSCHRIFT ISSUES in honour of Prof. Y B G VARMA, on his retirement

from the Department of Chemical Engineering, IIT Madras.

He delivered an Expert Lecture in Workshop on Analytical Instruments for Chemical

and Environmental Engineers (WAICEE 2013), March 22-23, 2013, Pilani, India; Co-

judged a Session in SCHEMCON – 2012, Sept. 21-22, 2012, Pilani, India and Chaired a

Session on Green Chemistry in International Conference on Sustainable Manufacturing :

Issues, Trends and Practices (ICSM 2011), Nov. 10-12, 2011, Pilani, India.

He has been a Member of Organizing Committee for Workshop on Analytical

Instruments for Chemical and Environmental Engineers (WAICEE 2013), March 22-23,

2013, Pilani, India; Member of Local Advisory Committee for National Conference on

Green and Sustainable Chemistry, Feb. 19-21, 2010, Pilani, India; Member of Local

Organizing Committee (Registration) for National Conference on Environmental

289

Conservation (NCEC-06), Sept. 1-3, 2006, Pilani, India; Member of Registration

Committee for Indian Chemical Engineering Congress (CHEMCON) – 2001, Dec. 19–22,

2001, Chennai, India and Student Member of Technical Programme Committee for

International Conference on Advances in Chemical Engineering, ICAChE – 96, Dec. 11–13,

1996, Chennai, India.

He has been an examiner for MTech Project at HBTI Kanpur (April 2013); BTech

(Industry) Projects at Banasthali University, Banasthali (Jan 2013 & Jan 2012); PhD Thesis,

ME Dissertations, Professional and Research Practice, BE Theses, Practice School (PS)

Project Reports and BE Projects at BITS Pilani.

At BITS Pilani, he is/has been a member of Senate, Research Board, Doctoral

Counseling Committee, Doctoral Advisory Committee, Departmental Research Committee,

IIChE - Pilani Regional Centre, Academic Counseling Cell and Library Committee.

He is a Member of Board of Management for Krishna Vidya Niketan, Muradnagar

(Gaziabad), India and Life Member of IIChE. For more details, please visit:

http://universe.bits-pilani.ac.in/pilani/arvinds/profile.

290

Biography of the Co-Supervisor

Dr Sushil Kumar, Assistant Professor, Department of Chemical Engineering at Motilal

Nehru National Institute of Technology (MNNIT), Allahabad has over 10 years of industrial,

teaching, and research experience. Prior to MNNIT, Allahabad, he served as an Assistant

Professor in Department of Chemical Engineering at BITS-Pilani, Pilani Campus. He also

worked with Central Institute of Plastic Engineering and Technology (CIPET), Lucknow for

one and half years as Technical Officer and Graduate Engineer Trainee. He did his B Tech

from Harcourt Butler Technological Institute (HBTI) - Kanpur, M Tech from Indian Institute

of Technology (IIT) - Kanpur and PhD from BITS - Pilani.

His current research interests include Process Intensification, Polymer Science &

Technology, Biochemical Engineering, Green Technology, Chemical Thermodynamics, and

Renewable Energy Sources. He has around 68 research publications (21 refereed journals,

45 conferences and 2 book chapters) to his credit which have been published over the years

in various International and National Journals and Conference Proceedings. Dr Kumar

guided one PhD in the area of Process Intensification (Reactive Extraction) and currently, he

is supervising 3 scholars for their doctoral research. Besides this, he has guided 5 ME

Dissertations and around 20 BE Project students under his supervision.

He is the referee and expert reviewer of 14 International Journals of repute (Journal

of Chemical and Engineering Data, Industrial and Engineering Chemistry Research,

Separation and Purification Technology, Fluid Phase Equilibria, Biotechnology and

Bioprocess Engineering, Desalination etc.). He also reviewed three books of Tata McGraw

Hill publisher. He is awarded Research Project by Department of Science and Technology

(DST), New Delhi, India under Fast Track Scheme for Young Scientists, 2012-2014.

Dr Kumar is the Life member of Indian Institute of Chemical Engineers (IIChE),

Fellow member of International Congress of Chemistry and Environment (ICCE), member

of AIChE for the year - 2010 to 2013, and Executive Committee Member, Lucknow

Regional Centre of IIChE chapter. He organized a national conference on “Technological

Advancements in Chemical and Environmental Engineering (TACEE - 2012)” held at BITS-

Pilani during March 23-24, 2012, and also worked as a Treasurer for SCHEMCON 2012

held during September 27-28, 2012 at BITS-Pilani.

kinetic modeling and simulation of metallocene catalyzed...

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