56
Pergamon Prog. Polym. Sci., Vol. 21, 651-706, 1996 Copyright 0 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved. 0079-6700196 $32.00 PII:SOO79-6700(96)00001-9 POLYMERIZATION REACTION ENGINEERING - METALLOCENE CATALYSTS ARCHIE. E. HAMIELEC’* and JOAO B. P. SOARESb ‘McMaster Institute for Polymer Production Technology, Department of Chemical Engineering, McMaster University, Hamilton, Ontario, Canada, LBS 4L7 bDepartment of Chemical Engineering, University of Waterloo, Waterloo, Ontario, Canada, N2L 3Gl Abstract - Metallocene catalysts are operative in all existing industrial plants that are presently used for polyolefin manufacture and have the potential to revolutionize the technology for the production of these polymers. A review of metallocene catalysis and its effects on polymer process engineering for the manufacture of polyolefins is provided. This review concentrates on the aspects of polymer reactor engineering, mathematical modelling of polymerization processes, and the characterization of polyolefins made with these novel catalysts. CONTENTS 1. Introduction 1.1. Industrial Ziegler-Natta catalysts 1.2. Historical review of metallocenes 1.2.1. Synthesis and characterization of ferrocene 1.2.2. Metallocene/aluminum catalyst systems for olefin polymerization 1.2.3. Discovery of methylaluminoxane as a cocatalyst for metallocene catalysis 1.2.4. Catalysts for long chain branching 2. Metallocene catalyst systems 2.1. Metallocene/aluminoxane catalysts 2.1.1. The role of the aluminoxane cocatalyst 2.1.2. Non-stereospecitic catalysts 2.1.3. Stereospecific catalysts 2.2. MAO-free catalyst systems 2.3. Supported metallocene catalysts 2.4. Catalysts for long chain branching formation 3. Mechanisms and chain growth kinetics of polymerization using metallocene catalysts 3.1. Introduction 3.2. Mechanisms 3.2.1. Linear chains 3.2.2. Chains with long branches 4. General dynamic modelling of metallocene-catalyzed polymerization 4.1. Introduction 652 653 655 655 655 657 657 657 658 658 659 661 665 666 668 671 671 672 672 674 676 676 *To whom all correspondence should be addressed 651

Review João Soares

Embed Size (px)

Citation preview

Page 1: Review João Soares

Pergamon Prog. Polym. Sci., Vol. 21, 651-706, 1996

Copyright 0 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved.

0079-6700196 $32.00

PII:SOO79-6700(96)00001-9

POLYMERIZATION REACTION ENGINEERING - METALLOCENE CATALYSTS

ARCHIE. E. HAMIELEC’* and JOAO B. P. SOARESb

‘McMaster Institute for Polymer Production Technology, Department of Chemical Engineering, McMaster University, Hamilton, Ontario, Canada, LBS 4L7

bDepartment of Chemical Engineering, University of Waterloo, Waterloo, Ontario, Canada, N2L 3Gl

Abstract - Metallocene catalysts are operative in all existing industrial plants that are presently used for polyolefin manufacture and have the potential to revolutionize the technology for the production of these polymers. A review of metallocene catalysis and its effects on polymer process engineering for the manufacture of polyolefins is provided. This review concentrates on the aspects of polymer reactor engineering, mathematical modelling of polymerization processes, and the characterization of polyolefins made with these novel catalysts.

CONTENTS

1. Introduction 1.1. Industrial Ziegler-Natta catalysts 1.2. Historical review of metallocenes

1.2.1. Synthesis and characterization of ferrocene 1.2.2. Metallocene/aluminum catalyst systems for olefin polymerization 1.2.3. Discovery of methylaluminoxane as a cocatalyst for metallocene catalysis 1.2.4. Catalysts for long chain branching

2. Metallocene catalyst systems 2.1. Metallocene/aluminoxane catalysts

2.1.1. The role of the aluminoxane cocatalyst 2.1.2. Non-stereospecitic catalysts 2.1.3. Stereospecific catalysts

2.2. MAO-free catalyst systems 2.3. Supported metallocene catalysts 2.4. Catalysts for long chain branching formation

3. Mechanisms and chain growth kinetics of polymerization using metallocene catalysts 3.1. Introduction 3.2. Mechanisms

3.2.1. Linear chains 3.2.2. Chains with long branches

4. General dynamic modelling of metallocene-catalyzed polymerization 4.1. Introduction

652 653 655 655 655 657 657 657 658 658 659 661 665 666 668 671 671 672 672 674 676 676

*To whom all correspondence should be addressed

651

Page 2: Review João Soares

A. E. HAMIELEC and J. B. P. SOARES 652

4.2.

4.3.

4.4. 4.5.

4.6.

Calculation of the molecular weight distribution of homopolymers 4.2.1. Linear chains and Flory’s most singular probable distribution 4.2.2. Polymer chains with long branches Calculation of the distribution of molecular weight, composition, and long chain branching frequency of copolymers 4.3.1. Linear binary copolymer chains and Stockmayer’s bivariate distribution 4.3.2. Copolymer chains with long chain branches 4.3.3. Multicomponent copolymers Mass and heat transfer resistances during polymerization with supported metallocene catalysts Calculation of polymer particle size distribution 45.1. Introduction 4.52. Supported catalysts 4.5.3. Unsupported catalysts Designing multi-site type catalyst systems

676 677 678

681 682 684 684 685 690 690 691 693 694

5. Active site type identification using polymer characterization techniques - TREF/GPC/NMR 694 5.1. Deconvolution of molecular weight distributions - GPC detector responses and Flory’s most

probable distribution 694 5.2. Deconvolution of chemical composition distributions - TREF/NMR detector responses and

Stockmayer’s bivariate distribution 695 6. Synthesis of polyolefins with long chain branches with metallocene catalysts 699

6.1. Polymerization processes 699 6.1.1. Slurry polymerization 699 6.1.2. Gas-phase polymerization 700 6.1.3. Solution polymerization 700

6.2. Reactor operation conditions 700 6.2.1. Batch operation 700 6.2.2. Semi-batch operation 701 6.2.3. Continuous operation 701

7. Adaptation of metallocene catalysis to existing olefin polymerization processes 701 7.1. Gas-phase processes 702 7.2. Liquid-bulk or diluent slurry processes 703 7.3. Solution processes 703

8. Summary 703 References 704

1. INTRODUCTION

Metallocene catalysts are organometallic coordination compounds in which one or two cyclopentadienyl rings or substituted cyclopentadienyl rings are bonded to a central transi- tion metal atom (Fig. 1). The cyclopentadienyl ring of a metallocene is singly bonded to the central metal atom by a n-bond. Consequently, the formal valence of the ring-metal bond is not centered on any one of the five carbon atoms in the ring but equally on all of them. ’ The nature and number of the rings and substituents (S); the type of transition metal (M) and its substituents (R); the type of the bridge, if present, and the cocatalyst type determine the catalytic behavior of these organometallic compounds towards the polymerization of linear and cyclic olefins and diolefins. These novel polymerization catalysts have been used for the production of polymers with entirely novel properties.

The importance of these new catalytic systems is revealed by the more than 600 patents issued in this field since 1980. Currently, there are four review articles published in the

Page 3: Review João Soares

METALLOCENE CATALYSTS 653

M : transition metal of groups 4b, 5b or 6b

R : hydrocarbyl, alkylidene, halogen radicals

9 hydrogen, hydrocarbyl radicals

B: alkylene, alkyl radicals, heteroatom groups

Fig. 1. Generic structure of a metallocene catalyst.

literature on metallocene catalysts. 2-5 These review papers cover different aspects of metallocene catalyst synthesis, nature of active sites, polymerization conditions and mechanisms, and metallocene catalyst patents. In the current review article we will focus on aspects of polymerization reaction engineering using these catalytic systems.

1.1. Industrial Ziegler-Natta catalysts

Polyolefins are among the most important modern commodity polymers. Polyethylene and polypropylene are today the major tonnage plastic materials worldwide. These two resins accounted for 44% of all U.S. plastic sales in 1988. The industrial capacity for the production of polyethylene and polypropylene in 1990 was approximately 45 million tons. 6,7

Polyolefins are commercially produced using free-radical initiators, Phillips type catalysts, Ziegler-Natta catalysts and, more recently, metallocene catalysts. Industrial processes that use Ziegler-Natta catalysts are the most important ones because of the very broad range of applications of their products.

Ziegler-Natta catalysts have evolved considerably since their discovery by K. Ziegler and G. Natta in the early fifties. These catalysts have been used in homogeneous, heterogeneous and colloidal forms to synthesize various types of polymers and copoly- mers. In its broadest definition, Ziegler-Natta catalysts are composed of a transition metal salt of metals from groups IV to VIII (known as the catalyst) and a metal alkyl of a base metal from groups I to III (known as the cocatalyst or activator). However, not all

Page 4: Review João Soares

654 A. E. HAMIELEC and J. B. P. SOARES

Table 1. Industrial processes for the production of polyethylene and polypropylene using Ziegler-Natta catalysts

Industrial processes

Polyethylene

Reactor type Licenser

Polypropylene

Reactor type Licenser

Gas phase Fluidized-bed

Slurry (diluent suspension Slurry (liquid monomer

Autoclave Autoclave

Solution Autoclave Autoclave Autoclave

Union Carbide

Hoescht Mitsubishi

DuPont Dow Chemical Mitsui

Fluidized-bed Vertical stirred-bed Horizontal stirred-bed Autoclave Autoclave Loop reactor Autoclave Autoclave Autoclave

Union Carbide/Shell BASF

Mitsubishi Montedison Himont Amoco Mitsui Eastman-Kodak

combinations are equally efficient nor can all monomer types be used. For industrial use, most Ziegler-Natta catalysts are based on titanium salts and aluminum alkyls.’

The industrial importance of Ziegler-Natta catalysts is truly remarkable. Several indus- trial processes using a variety of reactor types exist today for the production of polyolefins using these catalysts (Table 1). Before the discovery of Ziegler-Natta catalysts, polyethy- lene was produced commercially only with free-radical initiators at high polymerization temperatures and pressures. As a consequence of the mechanism of polymerization, the polymer chains obtained with free-radical processes contain both short and long chain branches. These branches significantly decrease the density of the polymer and affect important rheological and mechanical properties. The resin produced via free-radical poly- merization is generally known as high-pressure low-density polyethylene (HP-LDPE). HP-LDPE is used predominantly for making films because of its limp feel, transparency and toughness. The high levels of chain branching give excellent processability and high melt tension suitable for the manufacture of thin films.

The most important innovations introduced in the manufacture of polyolefins with Ziegler-Natta catalysts are the synthesis of linear high-density polyethylene (HDPE), the copolymerization of ethylene and cu-olefins to produce linear low-density polyethylene (LLDPE), and the production of highly isotactic and syndiotactic polypropylene.

HDPE has few or no short chain branches and no long chain branches. HDPE is used in structural applications because of its greater rigidity. Copolymerization of ethylene with (Y- olefins disrupts the order of the linear polyethylene chain by introducing comonomer units that contain short chain branches. As a consequence, the density, crystallinity and rigidity of the polymer is decreased. By varying the amount and type of cr-olefin, the type of catalyst and the polymerization conditions, one can produce several grades of copolymers to meet specific market demands. LLDPE shares the market with HP-LDPE made by free- radical processes. Both HP-LDPE and LLDPE are used predominantly for the manufac- ture of films.

Several types of Ziegler-Natta catalysts are stereospecific, i.e. the insertion of

Page 5: Review João Soares

METALLOCENE CATALYSTS 655

asymmetric monomers into the growing polymer chain in a given orientation is favored over all other possible orientations. This characteristic of Ziegler-Natta catalysts permitted for the first time the production of highly isotactic and syndiotactic polypropylene. Isotactic polypropylene is used in several injection molding and extrusion processes due to its excellent rigidity, toughness and temperature resistance. Only atactic polypropylene of low molecular weight, which has little commercial value, is obtained in free-radical poly- merization.

Most industrial processes today utilize heterogeneous Ziegler-Natta catalysts. Conven- tional soluble Ziegler-Natta catalysts have not found widespread industrial applications, mainly because of insufficient catalytic stability and stereochemical control. Important exceptions include some vanadium-based systems for the production of ethylene-propylene copolymers and ethylene-propylene-diene terpolymers9’10 and syndiotactic polypropy- lene. l1

1.2. Historical review of metallocenes

There are three general categories of cyclopentadienyl transition-metal complexes: (a) symmetric molecules with parallel cyclopentadienyl rings (Fig. 2a); (b) bent metallocenes, in which the number of ligands L can vary from one to three (Fig. 2b); and (c) complexes containing only one cyclopentadienyl ring, in which the number of ligands L can vary from one to four (Fig. 2~). Because of their characteristic structures, metallocenes have been called “sandwich compounds” or “half-sandwich compounds”. l2

1.2.1. Synthesis and characterization of ferrocene

The discovery and elucidation of the structure of metallocene compounds is considered a landmark in the history of organometallic chemistry. Bis(cyclopentadienyl)iron or ferro- cene was first synthesized independently in the early fifties by Kealy and Pauson13 and Miller et al. l4 The correct a-bond structure of ferrocene was elucidated in 1952 by Wilkinson et al. l5 These discoveries greatly stimulated research in organometallic chem- istry, notably the work developed by Wilkinson and Fischer. Wilkinson and Fischer were awarded the Nobel Prize in 1973 for their scientific contribution to organometallic chemistry. l2

1.2.2. Metallocenelaluminum catalyst systems for olefin polymerization

Breslow and Newburg were among the first researchers to apply metallocene catalysts for polymerization. 16J7 They used soluble bis(cyclopentadienyl)titanium derivatives and alkylaluminums for ethylene polymerization. Several other researchers followed this ori- ginal work, using the same catalytic system or modifications of that system, including Natta. l8 However, these catalytic systems had low activities and stabilities for the poly- merization of ethylene and produced only low molecular weight polymers. Additionally, they were not active for propylene polymerization. l9

Page 6: Review João Soares

656 A. E. HAMIELEC and J. B. P. SOARES

Ph Ph

Ph

Ni (11)

4B I OCf.~O

oc”

,Mo -

ClO’CO &

Fig. 2. (a) Metallocenes with parallel cyclopentadienyl rings, (bJ bent metallocenes, (c) mono- cyclopentadienyl metallocenes.

Page 7: Review João Soares

METALLOCENE CATALYSTS 657

1.2.3. Discovery of methylaluminoxane as a cocatalyst for metallocene catalysis

It was noted that the activity of metallocene/alkylaluminum catalysts could be signifi- cantly increased by the controlled addition of water to the polymerization reactor. 20,21 This enhanced activity was attributed to the reaction between water and alkylaluminum to form alkylaluminoxane. This single discovery led to the development of an entirely new class of soluble catalytic systems that are today the most promising branch of Ziegler-Natta catalysis.

Experimental evidence seems to indicate that beside acting as an alkylating agent, aluminoxanes are involved in the formation of active sites and in the prevention of their deactivation by bimolecular processes, by stabilization of the active species and by scavenging impurities. More recently, due to the discovery of aluminoxane-free cationic metallocene complexes, 22*23 it has been proposed that the aluminoxane may be involved in the production of cationic active sites and in the stabilization of the anion.

1.2.4. Catalysts for long chain branching

Prior to the publications by Lai et al.24225 and Swogger and Kao26 there was no unam- biguous experimental evidence in the literature that ionic catalyst systems, such as Phillips chromium oxide, Ziegler-Natta and metallocene catalyst systems, could be used to synthe- size homopolyethylene or ethylene-a-olefin copolymers with long chain branches. Lai et al. 24 synthesized these branched polyolefins, and considered them to be substantially linear polyolefins, using a particular type of metallocene catalyst (constrained geometry catalyst). Substantially linear polyolefins have a frequency of long chain branching in the range of 0.01-3 long chain branches per 1000 carbon atoms. The polymerization is done in a continuous stirred-tank reactor (CSTR) operating at steady-state and high temperatures. An aliphatic solvent is used in the reactor and all of the polymer chains are in solution. In the example provided in their patent, the homopolyethylene synthesized under the recom- mended polymerization conditions had a long chain branching frequency of 0.34 long chain branches per 1000 carbon atoms, as measured by carbon-13 nuclear magnetic resonance (13C NMR) using the methodology proposed by Randall.27

2. METALLOCENE CATALYST SYSTEMS

Metallocene catalyst systems can be conveniently divided into two categories. In the first an aluminoxane, an alkylaluminum, or a combination of aluminoxanes and alkylalumi- nums, are used to activate the metallocene catalyst. In general, these metallocenes have poor or no activity when used alone. In the second category, an ion exchange compound is combined with the metallocene catalyst, forming what is generally called a cationic metallocene catalyst. It is now generally accepted that the catalytic active species for metallocene/aluminoxane/alkylaluminum systems is also cationic.

General aspects of metallocene catalysts and applications will be covered in the next sections. This review does not intend to be exhaustive, since good reviews have been published recently, 2-5 including a patent review.5

Page 8: Review João Soares

658 A. E. HAh4IELEC and J. B. P. SOARBS

2.1. Metullocenelaluminoxane catalysts

2.1.1. The role of the aluminoxane cocatalyst

Ethylene was the first olefin to be polymerized using metallocene/aluminoxane catalysts. The activity of dicyclopentadienyl and tricyclopentadienyl zirconium derivatives could be greatly enhanced by the addition of small amounts of water.21 This increased activity is related to the formation of aluminoxanes in the reaction between alkylaluminum and water.

The type of aluminoxane has a marked influence on the efficiency of the metallocene/ aluminoxane catalytic system. Methylaluminoxane (MAO) seems to be more effective as a cocatalyst than other aluminoxanes such as ethylaluminoxane (EAO) and isobutylalumi- noxane (IBA0).28 More remarkably, the catalytic activity of the metallocene complex is directly proportional to the degree of oligomerization of the aluminoxane.21 For most homogeneous metallocene catalysts, a large excess of aluminoxane is required for the polymerization to reach its optimum value. Aluminum/transition metal ratios varying from 1,000 to 50,000 are commonly reported in the literature.

Despite its marked influence in catalytic performance, the exact role of the aluminoxane component is not known precisely. Experimental evidence seems to indicate that besides acting as an alkylation agent and an impurity scavenger, aluminoxanes are involved in the formation of active sites and the prevention of their deactivation by bimolecular processes. Chien and Wang29 unequivocally demonstrated that the functions of the aluminoxane component go beyond alkylation of the metallocene. When 99% of MAO is substituted by trimethylaluminum (TMA), which also acts as an effective alkylation agent, polymer- ization rates are reduced by one third to one fourth of the value obtained when pure MAO is used. The molecular weight of the polymer is also lowered by 40% when the TMA/MAO ratio equals 10, but remains unaffected when the TMA/MAO ratio equals 2.

Aluminoxanes are obtained by the reaction of an alkylaluminum with water. Water should be present in a dilute or a less accessible form such as in wet solvents or hydrated salts, since the reaction between water and alkylaluminums is extremely fast and highly exothermic. Several methods for synthesizing aluminoxanes have been published in the literature. 19,30-32 Reddy and Sivaram4 recently published an extensive review of techniques for the synthesis of aluminoxanes.

The exact structure of aluminoxanes is still a matter of controversy. They supposedly exist as a mixture of different cyclic or linear oligomers with degrees of oligomerization commonly varying from 6 to 20. MAO, the most commonly used aluminoxane, may have the structures shown in Fig. 3. Some recent experimental studies have suggested that MAO can also have a three-dimensional open cage structure.33

The synthesis of aluminoxanes is associated with several serious limitations such as long reaction times to obtain a controlled exotherm, low yields, the risk of explosion and the formation of solid by-products. Recently some alternate methods have been applied to produce aluminoxanes. 34-37

New forms of aluminoxanes for use as cocatalysts have also been proposed. Resconi et al. 38 suggested the use of an aluminoxane obtained by the reaction of alkylaluminum and water vapor at low temperature (O’C). Crapo and Malpass39 synthesized a modified form of methylaluminoxane (MMAO) by reacting TMA, a polyalkyldialuminoxane containing

Page 9: Review João Soares

METALLOCENE CATALYSTS 659

Al 0 ~ Al

/ \ CH 3 CH 3

CH 3

/

CH 3

O- 0 ___ Al

Linear

Cyclic

Fig. 3. Linear and cyclic structures for methylaluminoxane.

alkyl groups (ethyl or higher), and water. MMAO contains alkyl substituents unlike con- ventional MAO. According to Crap0 and Malpass, this process does not have the draw- backs of the conventional MAO synthesis and MMAO/metallocene and MAO/metallocene systems have comparable polymerization rates.

2.1.2. Non-stereospecific catalysts

Achiral cyclopentadienyl catalysts can be used to produce polyethylenes at high produc- tivities and with narrow molecular weight and chemical composition distributions. The most commonly used catalysts for polyethylene production are achiral cyclopentadienyl derivatives of zirconium, titanium and hafnium. Titanium and hafnium catalysts show smaller activity and are less stable at temperatures above 50°C than the zirconocenes.28P40 One of the most striking features of these catalysts is their elevated polymerization rates. Kaminsky41 reported polymerization activities as high as 40,000 kg of polyethylene (g Zr h)-’ for bis(cyclopentadienyl)zirconium dichloride/MAO (Cp2ZrC12/MAO) at a poly- merization temperature of 95°C and an ethylene pressure of 8 bars.

Catalytic activity is strongly related to the aluminum/transition metal ratio.42 The catalytic activity of Cp2ZrClJMAO for ethylene polymerization increases steadily from

Page 10: Review João Soares

660 A. E. HAMIELEC and .I. B. P. SOARES

25,000 kg polyethylene (g Zr h atm)-’ to 480,000 kg polyethylene (g Zr h atm)- ’ by vary- ing the aluminum/zirconium ratio from 1070 to 460,000.29 The molecular weight of poly- mer made with Cp2ZrC12/MA0 is very sensitive to temperature, ranging from l,OOO,OOO at 0°C to 1000 at 100”C.21 Most soluble metallocene catalysts show a similar relationship between molecular weight and polymerization temperature, presumably due to an intensi- fication of P-hydride elimination with increasing temperature. At polymerization tempera- tures below -20°C transfer reactions are so reduced that the molecular weight becomes only a function of polymerization time, thus behaving as in a living polymerization system.43

Hydrogen is an efficient chain transfer agent when used with metallocene catalysts. However, contrary to what is observed with conventional Ziegler-Natta catalysts, only traces of hydrogen are necessary to significantly reduce the molecular weight of the poly- mer. The presence of hydrogen also lowers the activity of the Cp2ZrC1JMA0 system,44 but this effect is reversible; removal of hydrogen results in an increase of the polymerization rate back to its original value. This behavior is also observed with conventional Ziegler- Natta catalysts.45

By altering the chemical environment around the central transition metal atom, it is possible to change considerably the behavior of the metallocene catalysts. Kaminsky et al. 46 used bis(pentamethy1 cyclopentadienyl)zirconium dichloride ((Me5Cp)2ZrC12) and MAO to catalyze ethylene polymerization. The catalyst was S-10 times less active than Cp2ZrC&/MA0, but it produced polymer with higher molecular weight averages and much broader molecular weight distributions under the same polymerization conditions. This behavior was attributed to the presence of two active site types formed sequentially during the contact of metallocene and aluminoxane.

Chien and Razavi42 used bis(neomenthy1 cyclopentadienyl)zirconium dichloride ((NMCp)2ZrC12) and MAO to catalyze ethylene polymerization. The catalytic activity was not as high as for Cp2ZrC1JMA0 and the melting point of the produced polyethylene was low, indicating the presence of structural defects or low molecular weights. Poly- hexene was also synthesized using Cp2ZrC12/MA0.43 The polymer was amorphous and the molecular weight was very low.

The metallocenes commonly used for ethylene polymerization, such as nonchiral cyclo- pentadienyl derivatives, are also able to polymerize propylene with high productivities, but only atactic chains are produced. Achiral metallocene catalysts have also been used to produce olefin copolymers. The most remarkable property of these catalysts is their ability to produce copolymers with narrower chemical composition distributions than those pro- duced with heterogeneous Ziegler-Natta catalysts. This not only permits an improved control of copolymer composition but is also essential for the production of elastomers free of crystallinity. Additionally, metallocene catalysts can produce copolymers with an almost random incorporation of comonomers which results in a maximum decrease in polymer crystallinity for a given amount of comonomer incorporation. Bis(cyclopentadienyl)titanium dimethyl (CP2TiMe2) and MAO can produce random copolymers of ethylene with propylene, butene-1 or hexene-Lm This catalyst can also be used for the copolymerization of ethylene and 1,3-butadiene47 and for the terpolymer- ization of ethylene-propylene-ethylidene norbornene.43

Page 11: Review João Soares

METALLOCENE CATALYSTS 661

Kaminsky and Scholobohm 47 copolymerized ethylene and butene-1 using Cp2ZrC12/ MAO. For the same degree of butene-1 incorporation, the melting point of the copolymer made with the zirconocene catalyst was lower than for a similar copolymer made with the heterogeneous catalyst TiCl&riethylaluminum (TEA). This indicates that the comonomer is more regularly distributed in the copolymer chain when the zirconocene catalyst is used.

The copolymerization of ethylene and propylene with Cp2ZrC12/MA0, MgC1JI’iC14 and VOC& was compared by Koivumaki and Sepa11a.48 It was shown that the metallocene catalyst produced copolymers with the most random distributions, as measured by 13C NMR. Dynamic mechanical properties, such as tan 6,,,, which correlates with rubber fraction and impact resistance, increase faster with decreasing ethylene content for the copolymer made with the metallocene catalyst. Copolymers made with the metallocene catalyst are also denser for the same content of ethylene. The molecular weight distribu- tions of copolymers made with the metallocene catalysts are the narrowest (with polydis- persity indexes of 2.3-2.7). Polymers produced with the other two types of catalysts have much higher polydispersities, even for the soluble VOC& and diethylaluminum (DEAC) system. This experimental evidence supports the hypothesis of a single-site type catalyst for the Cp2ZrC12/MA0 system.

Cp2ZrC12/MA0 has also been used for the binary and ternary copolymerization of ethylene/l-butenell-decene. 49 The rate of polymerization was enhanced by adding the cr-olefin comonomer. In the case of terpolymerization, the polymerization rate was also enhanced by keeping the concentrations of ethylene and 1-butene constant and increasing the concentration of 1-decene. These results cannot be related to mass transfer resistance

‘effects, since both catalyst and copolymers were soluble in the solvents employed. The oligomerization of olefins with metallocenes is also very attractive, because oligo-

mers of high regioregularity can be synthesized and the mechanisms of chain termination are highly specific. 5o Depending on the catalyst type, almost 100% of the chains terminate in vinyl or vinylidene groups that can be used for functionalization reactions (Fig. 4). In making waxes, metallocenes are advantageous because polymer molecular weight can be decreased by increasing polymerization temperature, leading to chains with terminal double-bonds formed via P-hydride elimination. For conventional Ziegler-Natta catalysts, a large excess of hydrogen is required to produce oligomers, therefore the dead polymer chain-ends are fully saturated.

2.1.3. Stereospecific catalysts

By the appropriate selection of metallocene catalysts, it is possible to produce poly- propylene with different chain microstructures. Polypropylene with atactic, isotactic, iso- tactic-stereoblock, atactic-stereoblock and hemi-isotactic configurations have been produced with metallocene catalysts (Fig. 5). More remarkably, it is also possible to synthesize polypropylene chains that have optical activity by using only one of the enantiomeric forms of the catalyst.43 For the synthesis of stereospecific metallocene catalysts for propylene polymerization, C, symmetric precursors are necessary to obtain a catalyst for isospecific polymerization, and C, symmetric precursors to produce a catalyst for syndiospecific polymerization. Asymmetric precursors can be used to synthesize

Page 12: Review João Soares

662 A. E. HAh4IELEC and J. B. P. SOARES

/ 3 r 7

additives for fuel lacquers, paper and

additives leatherindustry \ , L ,

R-NH2 R-OH

i

fiagfances

Fig. 4. Functionalization reactions for polyolefins containing a terminal double-bond.”

Designation Fisher Projection Bovey’s NMR Nomenclature

atactic --tip

.mmmmrmmmlnfmmlr...

isotactic

syndiotactic -1171-

.JfIlllW~...

isotactic-

stereoblock --ii

. ..mmmmmrmmmmmmmmmmmmnnmm...

isotactic

atactic- . ..mrnfllllllnmlmmInmm”mlrnmT.. stereoblock ---

hemiisotactic I , I I I I / / , I ( I / I I I , I I I 1 I

Fig. 5. Types of polypropylene chains produced with metallocene catalysts.

Page 13: Review João Soares

METALLOCENECATALYSTS 663

metallocene catalysts that produce hemi-isotactic and isotactic-stereoblock polypro- pylene. 51

Ewen52 was the first to report the synthesis of isotactic polypropylene with bis(cyclo- pentadienyl)titanium diphenyl (Cp2TiPh2) and MAO, and ethylenebis(indenyl)titanium dichloride (Et(Ind)zTiCl;?) and MAO. The first catalyst produced isotactic polypropylene with helix inversions at low temperatures, according to a chain-end control mechan- ism.52-54 Et(Ind)2TiC12 was produced as a mixture of 56% racemic and 44% meso forms. Of the total polypropylene produced, 63% was isotactic and the mechanism of monomer insertion was site-controlled. The meso form of the catalyst produced the 37% atactic polymer fraction.

A bridge extending between the two indenyl rings imparts stereorigidity to the metallo- cene complex, preventing the rotation of the rings about their coordination axes. The spatial arrangement of the chiral racemic isomeric form favors the coordination of propylene molecules in such a way as to produce mainly isotactic chains. For the meso form, both monomer orientations are equally favored and therefore only atactic chains are formed. Chiral metallocenes such as ethylenebis(tetrahydroindenyl)zirconium dichloride (Et(HJnd)zZrCl$ and ethylenebis(indenyl)zirconium dichloride (Et(Ind)2ZrC12) can pro- duce polypropylene with a high degree of stereoregularity. These zirconocenes are obtained as racemic mixtures of the d- and l-forms. The concentration of the meso form is very low.55

Highly isotactic polypropylene was first produced by Kaminsky et ~1.~~ using Et(H41nd)2ZrC12/MA0. The polymer had a narrow molecular weight distribution (with a polydispersity around the theoretical value of 2 for the isotactic fraction) and 95% mm triads, as measured by 13C NMR. Unfortunately, these catalysts produce polymer with low molecular weight averages (only 12,000 for the number average molecular weight at 60°C) and although the dominating propagation mechanism is l,Zinsertion, a small amount of 2,1- and 1,3-insertions also take place.56 Consequently, they produce polymer that has a melting temperature that is lower than for isotactic polypropylene obtained with hetero- geneous Ziegler-Natta catalysts. 57 Some researchers have proposed that this low melting temperature could be caused by an inversion of the polypropylene helix configuration,58,59 which is supported by the tendency of these polymers to crystallize in the y-form which is unstable for high molecular weight, isotactic polypropylene. 60,61

The performances of Et(H41nd)2ZrC12 and its non-hydrogenated equivalent Et(Ind)2ZrC12 were compared by several researchers. 43,46p58,59Y62 Et(Ind)2ZrC12 was found to be more active than Et(H41nd)2ZrC12. The rates of polymerization with both catalysts depended linearly on monomer and catalyst concentrations. Molecular weights and stereoregularities were very sensitive to polymerization temperature because of the flexibility of the ligands; more atactic polymer was formed and the rate of P-hydride elimination increased at higher temperatures. The activity of both catalysts depended strongly on the aluminum/zirconium ratio, but showed distinct behavior. It was proposed58359 that MAO could coordinate in a weaker way with Et(H,Jnd)zZrC12 than with Et(Ind)2ZrC12. More than one type of active site appeared to be present since the polymer could be fractionated by extraction with different solvents. Metallocene complexes with different coordination states with MAO were assumed to be responsible for the formation of different types of active sites.

Page 14: Review João Soares

664 A. E. HAhlIELEC and J. B. P. SOARES

The effect of reaction conditions on the polymerization of propylene with Et(Ind),ZrCld MAO was extensively studied by Rieger et aL6’ The polymerization rate increased with temperature in the range -55 to 80°C. The Arrhenius plot was linear over this range of temperature, with estimates of activation energies of 10 kcal/mol for propagation and 15 kcal/mol for chain transfer. Increasing the polymerization temperature broadened the DSC melting curve and decreased the melting point temperature of the polymer. Decreas- ing the polymerization temperature increased the molecular weight averages and narrowed the molecular weight distribution considerably: the polydispersity index was equal to 2.69 at 80°C 1.3 at 0°C and 1.5 at -20°C. Higher aluminum/zirconium ratios caused an increase in the catalytic activity and molecular weight, but a decrease in the polydispersity index.

Tsutsui et aZ.63,64 fractionated polypropylene made with Et(Ind)2ZrC1JMA0 and the conventional heterogeneous Ziegler-Natta catalyst MgClfliClJIEA by successive extractions with boiling pentane, hexane, heptane and trichloroethylene. Most of the poly- propylene made with the metallocene catalyst was soluble in boiling heptane or trichlor- oethylene, indicating good homogeneity of the polymer samples in terms of stereo- and regioregularity, as well as molecular weight (polydispersity indexes varied from 1.8 to 2.9). The characteristics of the polypropylene made with the heterogeneous Ziegler-Natta catalyst were markedly different: polymer fractions were obtained in all solvents and the polydispersity index was 5.53. The 13C NMR data were particularly revealing. For the polypropylene made with the metallocene catalyst, the mmmm pentads ranged from 86.3 to 95.4 for the fractions soluble in boiling heptane or trichloroethylene. On the other hand, for polypropylene produced with the heterogeneous Ziegler-Natta catalyst, the mmmm pentad was 23.4 for the fraction soluble in boiling pentane and 93.5 for the fraction insoluble in boiling trichloroethylene.

Syndiotactic polypropylene with high molecular weight, narrow molecular weight dis- tribution and high productivity can be synthesized with isopropyl(fluorenyl)(cyclopenta- dienyl)hafnium dichloride (iPr(Flu)(Cp)HfClz) and MAO and the equivalent zirconium derivative. As a consequence, the industrial production of syndiotactic polypropylene is planned by Fina and Mitsui Toatsu. Since syndiotactic polypropylene is more resistant to ultra-violet radiation than isotactic polypropylene, it can be used for medical applications which require sterilization. 65,66 The rrrr pentads determined with 13C NMR varied from 0.74 to 0.86.65 MezPr(Cp)(Flu)ZrClz and Ph2Me(Cp)(Flu)ZrClz can also be used for syndio- tactic polymerization with both MAO or cation forming agents.@

Stereoblock polypropylene, with sequence lengths between 2 and 7 and a narrow molecular weight distribution, can be produced with (NMCp)2ZrC1JMA0.28Y62 Poly- propylene having the properties of a thermoplastic elastomer can be synthesized with the asymmetric metallocenes Et(Me4Cp)(Ind)TiC1,MA0 and Et(Me&p)(Ind)TiEtJ MAO. 67&s This is the first example of a thermoplastic elastomer consisting of only one monomer type. To account for the properties of these new polypropylenes, it is supposed that the active sites can exist in two different states, one stereospecific and the other non- stereospecific. Since they can change states during the lifetime of a growing polymer molecule, the chain consists of alternating blocks of atactic and isotactic polypropylene. The isotactic domains act as physical cross-links and give the polymer its elastomeric properties.

Page 15: Review João Soares

METALLOCENE CATALYSTS 665

One remarkable feature of some chiral metallocene catalysts is that they can polymerize cycloalkenes to isotactic polycycloalkenes without ring opening. Although some conven- tional Ziegler-Natta catalysts are also able to polymerize cycloalkenes, 20-30% of the rings are opened during the polymerization, providing the polymer with elastomeric prop- erties, 28 in contrast to highly crystalline polycycloalkenes made with chiral metallocene catalysts. Cyclopentene,28*69 cyclobutene and norbomene41’70 can be polymerized with Et(Ind)2ZrC12/MA0 to produce crystalline, high melting polycycloalkenes.

Chiral metallocene catalysts are also effective for the copolymerization of ethylene, propylene and higher cr-olefins. Et(Ind)2ZrC12/MA0 can be used to copolymerize ethylene and propylene, producing a copolymer richer in propylene than the one produced with the achiral CpzTiMe2/MA0 or Cp2ZrMe2/MA0 under the same polymerization conditions.71 The presence of ethylene seems to favour 2,1-insertions of propylene units in the copoly- mer: 2,1-insertions increase from 0.58% in the absence of ethylene to 0.88% when the ethylene content in the copolymer is 22%.63 The stereorigid systems iPr(Flu)(Cp)ZrCl2/ MAO and Me2Si(Ind)2ZrC1m0 can copolymerize ethylene/l-dodecene and ethylene/ 1-octadecene. 72

Et(Ind)2ZrC12/MA0 and Et(H41nd)*ZrC12/MA0 are also effective for the copolymeriza- tion of ethylene and 4-methyl-l-pentene,69 ethylene and norbornene,70 and ethylene and dimethanooctahydronaphthalene. 73 Remarkably, for the copolymerization of ethylene and norbomene, the reactivity ratio of ethylene is only 1.5-3.2 for the hydrogenated catalyst which means that copolymers containing more than 50% norbomene can be synthesized.

Several monocyclopentadienyl derivatives of titanium (such as CpTiCl&lAO) can be used to synthesize syndiotactic polystyrene and substituted-polystyrene.74’75 Since the equivalent biscyclopentadienyl derivatives cannot produce syndiotactic polystyrene with good yield, one can assume that the two cyclopentadienyl rings hinder the active sites from the bulky styrene molecules.

CpTiC13/MA0 can also be used to copolymerize ethylene and styrene76 and styrene and isoprene.77 Longo and Grassi claim that by varying the ratio MAO/Ti from 1000 to 100, they were able to synthesize block and alternating copolymers, respectively.76 On the other hand, Aaltonen and SeppalB:78979 reported that the same catalytic system produced only polyethylene and polystyrene as homopolymers. This catalytic system has also been applied for the copolymerization of styrene and isoprene, butadiene and 4-methyl-1,3- pentadiene. 8o

2.2. MAO-free catalyst systems

Cationic metallocenes are catalysts in which the transition metal atom is positively charged. The metallocene complex is therefore a cation associated with a stable anion. There is now enough experimental evidence to support the hypothesis that all active center types operative with metallocenes are cationic.

Cationic metallocenes are prepared by combining at least two components. The first is a metallocene and the second is an ion exchange compound comprising a cation and a non-coordinating anion. The cation reacts irreversibly with at least one of the first com- ponent’s ligands. The anion must be capable of stabilizing the transition metal cation complex and must be labile enough to be displaced by the polymerizing monomer. The

Page 16: Review João Soares

666 A. E. HAMIELEC and .I. B. P. SOARES

relationship of the counterion to the bridged structure controls monomer insertion and isomerization. 81

Jordan et al.22>23 used a cationic metallocene catalyst, Cp2Zr(CH3)(THF)’ , to produce polyethylene in the absence of an aluminum cocatalyst. Even though the rate of polymer- ization was low, the activity of this catalyst supported the hypothesis that a cationic complex was the active species in metallocene catalysts and that the aluminum cocatalyst acted mainly as an alkylation agent and an activator. This idea has been further supported by observing that copolymers of ethylene and propylene, and copolymers of ethylene, propylene and ethylidene norbornene, made in the presence of Et(Ind)~ZrCl~O or [Et(Ind)*ZrEt]’ [B(C6F&]- have similar microstructures. 82 The same cationic catalyst can be used to produce highly isotactic polypropylene at a temperature of -55”Cs3

The hypothesis that the catalyst center is polar or ionic is further supported by the electronic effects observed in some metallocenes of the type (X2C9H&ZrC12/MA0, where X can be a chlorine, a hydrogen, or a fluorine atom, or a CH3 or a OCH3 group.84,85 It was observed that, for ethylene polymerization, electron withdrawing atoms such as fluorine significantly lowered the catalytic activity and molecular weight of the produced polymer, while electron donors such as CH3 had little influence over the polymerization. For the case of polypropylene production, electron withdrawing groups reduced considerably the stereochemical control of the catalysts. This has been related to changes in the degree of association of the metallocene and the MAO counterion or to the increase in the strength of the metal-carbon bond between the metallocene and the ligands.

Zambelli et al. 86 prepared a MAO-free isotactic specific homogeneous catalyst based on group 4 metallocenes and a mixture of trimethylaluminum and dimethylaluminum fluoride (TMA-DMF). Polymers made in the presence of one particular group-4 metallocene and either MAO or TMA-DMF had similar stereochemical structures. The ability of MAO to activate group 4 metallocenes towards propylene polymerization has been tentatively attributed to the formation, in the presence of MAO, of cationic complexes such as [M(IV)bR]’ , where M is a group 4 transition metal, L is a ligand and R is an alkyl ligand (CH3 or growing polymer chain), which would be the actual active species.

It has been suggested that the use of TMA-DMF leads to the same cationic active species obtained when MAO is used as cocatalyst.

2.3. Supported metallocene catalysts

Since most of the conventional Ziegler-Natta polyolefin industrial plants are designed to use heterogeneous catalysts (with the exception of EPDM plants which use soluble vanadium-based catalysts), the commercial application of soluble metallocene catalysts would require the design of new plants or the adaptation of existing ones to operate with soluble catalysts. One way of overcoming this problem is by supporting the metallocene catalyst on an “inert” carrier, hopefully without the loss of catalytic activity, stereoche- mica1 control and ability to make polymer with narrow molecular weight and chemical composition distributions and, when desired, long chain branches.

Metallocenes can be effectively supported on several inorganic oxides, the most com- monly used being SiOz, MgC12, Al2O3, MgF2 and CaF2. Janiak et al. 87 suggested the use of polymeric MAO as a support. Polymeric MAO is produced as a three-dimensional lattice in

Page 17: Review João Soares

METALLOCENECATALYSTS 667

the reaction between MAO and l,lO-dodecanodiol or 1,6-dodecanodiol. Polyolefin parti- cles and natural polymers such as cellulose have also been used to support metallocene catalysts.

The type of support as well as the technique used for supporting the metallocene and MAO have a crucial influence on catalyst behavior. Several techniques for supporting metallocenes and MAO have been proposed:88 (1) Adsorption of MAO onto the support followed by addition of the metallocene; (2) immobilization of the metallocene on the support, followed by contact with MAO in the polymerization reactor; (3) immobilization of the metallocene on the support, followed by treatment with MAO, producing a catalyst which does not require MAO during polymerization, but generally requires alkyl- aluminums. 89

By the appropriate choice of supporting conditions, stereo- and regioselectivity can be improved and transfer reactions can be minimized with the ultimate production of polymers with improved stereoregularities and higher molecular weights. Additionally, supported metallocenes usually require smaller aluminum to transition metal ratios than the equiva- lent soluble systems and some systems can be activated in the absence of aluminoxanes by common alkylaluminums. 90-93 This reduced dependence on the presence of aluminoxanes and on high ratios of aluminum to transition metal may be related to a reduction in catalyst deactivation by bimolecular processes due to the immobility of the active sites on the surface of the support.

Several patents have been issued regarding supporting technology for metallocene catalysts.5 Aluminoxanes can be either synthesized separately and then supported on the carrier or they can be produced in situ by reacting an alkylaluminum directly with the water adsorbed on the support.

For the in situ production of aluminoxanes, the order of the addition of the wet support and the alkylaluminum is important. It is known that the activity of metallocene- aluminoxane catalysts is proportional to the degree of oligomerization of the aluminoxane. Therefore, the slow addition of the wet support to a solution of alkylaluminum forces the reaction to take place under water deficient conditions and produces an aluminoxane with a higher degree of oligomerization (usually between 6 and 20). If the reverse order of addition is chosen, the catalyst generally has low polymerization activity.

Soga et al. 94 and Soga and Kaminaka95 proposed a technique to produce MAO-free, Si02-, A1203- and MgClz-supported metallocene catalysts, which are active for polymer- ization even in the absence of MAO, using only common trialkylaluminums. The silica surface is modified by a reaction with C1$Si(CH3)2 and NaHCO&O according to the schematic shown in Fig. 6. Four different techniques for producing silica-supported metallocenes for propylene polymerization were compared: 96 (1) direct immobilization of the metallocene on SiOz; (2) immobilization of MAO on SiO2, followed by supporting the metallocene; (3) immobilization of the metallocene on SiOz followed by MAO treat- ment; (4) immobilization of a metallocene ligand on SiOz, followed by the addition of zirconium compounds. For MezSi(Ind)2ZrC12, the use of C12Si(CH3)2 treated-Si02 caused a marked increase in polymerization activity. Method (4) was the best for increasing isospecificity and molecular weight. The DSC curves of polypropylene products were bimodal suggesting the existence of at least two active site types. For Et(H41nd)ZZrClz

Page 18: Review João Soares

668 A. E. HAMIELEC and J. B. P. SOARES

I Si-OH + ClzSi(CH3)z e

CH3

Si- 0-Si-Ci+NaHCOs/HzO I

CH3

CH3

3i- 0-Si-OH

CHZ

Fig. 6. Mechanism for the modification of a silica gel surface using NaHC03/H20.94

the isospecificity was found to be a strong function of the supporting technique: the isotactic index increased in the order of soluble catalyst < (2) < (l), (3) < (4). For iPr(Flu)(Cp)ZrC12, method (1) produced polypropylene with low melting temperatures but method (4) produced isotactic polypropylene. This was highly unexpected since soluble iPr(Flu)(Cp)ZrClz produces syndiotactic polypropylene. The calcination temperature of SiOz was found to have an important effect on the stereochemical control of the catalyst. Calcination temperatures of 200 and 400°C lead to strongly attached metallocenes on the surface, but at 900°C the metallocene will be loosely attached to the support surface due to a lesser amount of dual silanol groups. Polypropylene and copolymers of ethylene and propylene made with these supported catalysts show frequent monomer inversions.97

Janiak and Rieger98 proposed a supporting technique consisting of the following steps: (1) supporting MAO; (2) supporting metallocene; (3) supporting MAO. The authors claim that step (3) increases the catalytic activity. They also show very interesting scanning electron microscopy results for the polymer particles. Apparently, the silica particles are not broken by the polymer which leads to a sponge-like, low density polymer particle.

Supported multiple-site type catalysts can also be designed to produce polyolefins with broad molecular weight distributions. In a series of patents, Welborn’ claims that it is possible to produce LLDPE and HDPE with polydispersity indexes between 2.5 and 100 by combining at least one metallocene, at least one non-metallocene transition metal com- pound, an aluminoxane and an organometallic compound on a support.

The catalytic activity of supported metallocenes is usually inferior to that of the equiva- lent soluble catalyst, probably due to a deactivation of catalytic sites or an inefficient production of active sites during the supporting process. A broadening of the molecular weight distribution for supported catalysts can also occur under certain supporting conditions. 91,93

2.4. Catalysts for long chain branching form&ion

When considering ethylene-a-olefin copolymers containing long chain branches, one should, for practical reasons, consider that a long branch is longer than the short branch resulting from the incorporation of the cw-olefin comonomer in the copolymer chains. From the point of view of the effect of long chain branching on rheological properties, the length of the long branch should be greater than the entanglement chain length. For polyethylene melts, the entanglement length is approximately equal to 136, which is equivalent to 272 carbon atoms in the chain and to a molecular weight of 3800.

Page 19: Review João Soares

METALLOCENE CATALYSTS 669

The most suitable catalyst types appear to be those with an “open” metal active center, such as the Dow Chemical constrained geometry catalysts. The active center of these catalysts is based on group IV transition metals that are covalently bonded to a mono- cyclopentadienyl ring and bridged with a heteroatom, forming a constrained cyclic struc- ture with the titanium center. The bond angle between the monocyclopentadienyl ring, the titanium atom center and the heteroatom is less then 115”. 99 Strong Lewis acid systems are used to activate the catalyst to a highly effective cationic form. This geometry allows the titanium center to be more “open” to the addition of ethylene and higher cr-olefins, but also for the addition of vinyl-terminated polymer molecules.100 A second and very important requirement for the efficient production of polyolefins containing long chain branches by these catalytic systems is that a high level of dead polymer chains with terminal unsatura- tion be produced continuously during the polymerization.

Swogger and Kao26 presented further evidence for long chain branch formation using the synthesis conditions recommended by Lai et al2 Four homopolyethylenes were syn- thesized with one constrained geometry catalyst in a CSTR under different operation conditions. These polyethylenes had long chain branching frequencies of 0.2, 0.44, 0.53 and 0.66 long chain branches per polymer molecule as measured by 13C NMR and gel permeation chromatography (GPC). The authors presented a mathematical model for a CSTR which apparently predicted with good accuracy long chain branching frequencies, the density of ethylene-octene-1 copolymers over the range 0.87-0.94 g/cm3, the melt index and finally the 110/12 ratios over the range 7-10.5 (Jrdl, is the melt index ratio using 10 and 2.16 kg weights). Unfortunately, very little detail was given about the mathematical model.

Lai et al. 24 also presented some remarkable data on the effect of polydispersity on 1r& for polyolefins synthesized using classical heterogeneous titanium-based Ziegler-Natta catalysts and produced with constrained geometry catalysts. It is generally accepted that classical Ziegler-Natta catalysts have multiple active center types and consequently pro- duce polyolefins with broad molecular weight distributions. lo1 Shear thinning, as expected, increases as the molecular weight distribution broadens for polyolefins produced with these catalysts. On the other hand, polyolefins synthesized with constrained geometry catalysts have narrow molecular weight distributions, with polydispersities near the theoretical value of two for the single-site type catalyst.lo2 However, the 1ro/12 ratio can be increased at almost constant polydispersity by increasing the long chain branching frequency. Figure ‘7 illustrates these remarkable results. In fact, these authors have shown how to synthesize polyolefins with narrow molecular weight distribution and sufficient degree of long chain branching that combines the excellent mechanical properties of polyolefins with narrow molecular weight distributions (impact properties, tear resistance, environmental stress cracking resistance and tensile properties) with the good shear thinning of linear poly- olefins with broad molecular weight distribution. 3 Polyolefins with narrow molecular weight distributions and containing no long chain branches generally have poor rheological properties.

Sugawara lo3 synthesized two ethylene-a-olefin copolymers (with densities of 0.906 and 0.912 g/cm3) using the recommended procedure of Lai et aZ.25 Sugawara constructed the calibration curve shown in Fig. 8 for a CSTR using data available in the patent application

Page 20: Review João Soares

670 A. E. HAMIELEC and J. B. P. SOARES

ll- + Heterogeneous +

10 - 9- x CGCT

8 - 0 Homogeneous

% 7

$ 5”- 4-

3- 2-

1 I I I I I I I I I 4 5 6 I 8 9 10 11 12 13

IlOiI2

Fig. 7. Relationship between the polydispersity index and the Z1dZ2 ratio for polyolefins produced with heterogeneous and homogeneous Ziegltl-Natta catalysts and a constrained

geometry catalyst.

by Lai et al. The melt index ratio Iroll, versus the ratio of polymer concentration to ethylene concentration on a weight basis is plotted in Fig. 8. This ratio should correlate with long chain branching frequency (the higher the ratio, the higher the long chain branching frequency). Sugawara used this calibration curve to find CSTR operation conditions to produce a polymer with a very low level of long chain branching (polymer A) and a polymer with a moderate level of long chain branching (polymer B). Sugawara then compared polymers A and B with a linear LLDPE sample and with a HP-LDPE sample in terms of impact strength, processability, blown film processability, stability and MD/TD balance of tear strength. Polymers A and B were superior in impact strength. Polymer B was superior to LLDPE but inferior to HP-LDPE in processability. Polymer B was sig- nificantly inferior to HP-LDPE in bubble stability. This superiority of HP-LDPE over polymer B was very likely due to the much higher levels of long chain branching in HP- LDPE polymers. Polymers A and B were inferior to both LLDPE and HP-LDPE in MD but superior to HP-LDPE in TD. Sugawara provided an interesting summary of property

“0 5 10 15

Polymer/ethylene concentration ratio in solution (wt)

Fig. 8. Calibration curve for the Z1dZ2 ratio as a function of the polymer/ethylene concentration ratio in the polymerization reactor. lo3

Page 21: Review João Soares

METALLOCENE! CATALYSTS

MWD = 6-10

Processability, Moldability -

Fig. 9. Balance of strength versus processability and moldability for polyolefins synthesized using different polymerization processes. lo3

balances and the position of metallocene copolymers of ethylene-a-olefins in the balance of strength versus processability and moldability (Fig. 9).

A suitable cocatalyst specified by Lai et al. 24 is tris(pentafluorophenyl)borane. There is no evidence in the literature that methylaluminoxane cocatalysts are suitable for the syn- thesis of polyolefins containing long chain branches. It can be speculated that the presence of methylaluminoxane will promote transfer to aluminum and therefore produce dead polymer chains with saturated chain-ends which are unavailable for long chain branch formation.

Although there is not a great deal of information in the literature concerning optimal solvents for long chain branch formation, it appears that paraffinic solvents are preferable to aromatics. Lai et aZ.24 recommend the use of aliphatic solvents for long chain branch synthesis. This choice was also supported by Brant et al. lo4 for the catalytic system bis(cyclopentadienyl)zirconium dimethyl/pertIuorotriphenyl boron. They found that this catalyst system gave high levels of vinyl ends during polymerization in hexane and few or no vinyl ends in toluene.

It seems that the target for polymers made with these catalytic systems is to produce polymer chains having narrow molecular weight distributions but with high levels of long chain branching to further improve processability.

3. MECHANISMS AND CHAIN GROWTH KINETICS OF POLYMERIZATION USING METALLOCENE CATALYSTS

3.1. Introduction

Despite intense research activity, no definite, unequivocal polymerization mechanism has yet been defined to describe the behavior of metallocene and Ziegler-Natta catalysts. This is hardly surprising, given the complex nature of the catalytic systems considered. The catalyst may be soluble or insoluble in the reaction medium; a cocatalyst is generally

Page 22: Review João Soares

672 A. E. HAMIELEC and J. B. P. SOARES

I/” (1) I/“,, 2

X-Ti--0 + CH ,=CH 2 __) X-Ti

X” X

(2)

\ R--H 2

I I X--Ti-cH 2

/I CH 2 CH 2 R

( /x (4)

x’ i

X-Ti-0 w X-Ti-CH ,CH 2 R

X” X X” X

Fig. 10. Cossee’s mechanism.

required but some catalysts are able to polymerize olefins alone; the monomers may be liquid or gaseous; electron donors may be present or not; and the polymerization can take place in the gas phase, in liquid monomer or suspended in a diluent with various residence- time distributions.

As part of an effort to unify the knowledge in this field, several attempts have been made to propose a mechanism that could be applied to all Ziegler-Natta-catalyzed polymeriza- tions. Several good reviews on the polymerization mechanisms of Ziegler-Natta catalysts have been published recently. 117105~106

3.2. Mechanisms

3.2.1. Linear chains

It is well established now that the two key steps in Ziegler-Natta and metallocene- catalyzed polymerizations are the complexation between the monomer and the active center, followed by insertion into the growing polymer chain. In this mechanism, the cocatalyst acts as an alkylating and reducing agent, and polymer growth takes place via insertion of monomer into the transition metal-carbon bond.

One model having a significant impact on the further development of monometallic polymerization mechanisms was proposed by Cossee107*108 and is shown in Fig. 10. In Fig. 10, X is a halogen ligand, R is a growing polymer chain or alkyl group, and the open squares indicate a ligand vacancy. In Cossee’s model, the active site is composed of a transition metal atom having an octahedral configuration, with four chlorine ligands from the crystal lattice, an alkyl group introduced by the cocatalyst and a coordination vacancy. According to Arlman, lo9 coordination vacancies are required to ensure the electroneutrality of the crystal. Step 4 is probably the weakest assumption of Cossee’s model. In order to explain isotacticity, the polymer chain has to flip back to the position occupied before the monomer insertion step. Moreover, several important phenomena, such as monomer reac- tion orders higher than one and copolymerization rates higher than homopolymerization rates of both comonomers, cannot be explained by Cossee’s mode1.r”

Several alternative monometallic models have been proposed based on Cossee’s

Page 23: Review João Soares

METALLOCENE CATALYSTS

R P v C

Fig. 11. Trigger mechanism. ‘lo

model. 11~105~106 There is no agreement about the general validity of these models, but it is generally accepted that Cossee’s model provides the best representation to date for the mechanisms governing Ziegler-Natta polymerization. ‘11

Recently a new mechanism was proposed which overcomes some of the deficiencies of Cossee’s mechanism. ‘lo This model was called the trigger mechanism and involves a two- monomer transition state, where the insertion of a complexed monomer is triggered by another monomer unit. The trigger mechanism is illustrated in Fig. 11. The main assump- tions of this model are: (1) the monomer site is never free since a new monomer will enter the site when the monomer that previously occupied this site is inserted in the growing chain; (2) the insertion step will not proceed, or will proceed very slowly, in the absence of another monomer unit; (3) in the transition state, two monomer units interact with each other and with the transition metal atom. The trigger mechanism is able to predict poly- merization rate dependency upon monomer concentration from first to second order, and increase in polymerization rate of ethylene upon adding propylene.

Farina et al. ‘12 presented a general mechanism for polymerization with metallocene catalysts. They pointed out that metallocene catalysts differ from conventional hetero- geneous Ziegler-Natta catalysts because they have two active sites bound to the same metal atom allowing the growing chain to shift from one site to the other. Two mechanisms

Page 24: Review João Soares

674 A. E. HAMIELEC and J. B. P. SOARES

Table 2. Stereochemical analysis of the five classes of metallocene catalysts”2

Catalyst type

I II III IV V

Symmetry of the bMtX2 complex Chirotopicity of atom Mt in bMtX, Chirotopicity of atoms X in LMtX, Relationship between atoms X in LMtX2 Chirotopicity of atom Mt in ILMtMP/+ Stereogenicity of atom Mt in lbMtMPl+ Polymer structure predicted for catalyst control and alternating mechanism

czv

No

CS

No

c2

Yes

CS

No

Cl

Yes

No No Yes Yes Yes

Equal

No

Different

No

Homotopic

Yes

Enantiotopic

Yes

Diastereotopic

Yes

No Yes No Yes Yes

Atactic Atactic Isotactic Syndiotactic No simple prediction

Mt - group IV transition metal; b - cyclopentadienyl ligand; X - halogen atom or organic group such as CH3 and C6H5; M - monomer molecule.

have been proposed for monomer insertion: in the alternating mechanism the chain shifts positions between monomer insertions; in the retention mechanism, the chain always occupies the same position in the active site. Metallocene catalysts are classified according to their symmetry (Table 2) and four statistical insertion models are proposed: (1) alter- nating mechanism combined with site control; (2) alternating mechanism combined with site and chain-end control; (3) alternating and retention mechanisms combined with site control; (4) alternating and retention mechanisms combined with site and chain-end control. Unfortunately no simulation results were presented.

3.2.2. Chains with long branches

The most likely long chain branch formation mechanism with metallocene catalyst systems is terminal branching, a mechanism which has been known in the free-radical polymerization literature for many years. ‘I3 In free-radical polymerization, macromono- mers (a long chain molecule with a reactive carbon-carbon double-bond at its end) are generated via termination by disproportionation and via chain transfer to monomer. With metallocene catalyst systems, the facile P-hydride elimination reaction appears to be responsible for in situ macromonomer formation. Other reaction types, such as P-methyl elimination and trans ‘14 may also generate dead polymer chains with terminal unsaturation. This may actually be the most important transfer mechanism in propylene polymerization when (Me$p)2Ti, (Me=,Cp)zZr and (Me&p)zHf complexes are used.3 Therefore, these catalytic systems have the potential of producing polypropylene with long chain branches. To our knowledge, this possibility has not been explored to date. These and other chain transfer mechanisms are summarized in Table 3.

It is generally accepted that the most effective macromonomer for addition to the active center with the generation of a long trifunctional branch is the one with terminal vinyl unsaturation, probably due to steric effects.

Page 25: Review João Soares

METALLOCENE CATALYSTS 6’75

Table 3. Source of unsaturation and mechanisms of formation of dead polymer with terminal double- bon&“7,158

R-CHZ-CHZ-Cat + R-CH=CHz + H-Cat

(vinyl)

R-Cat + F

H=CHz -+ I-Y

R- - C-Cat

F I

CY H

+ R-C=CHz + H-Cat

I

CY

(vhylidene)

R- C - C-Cat + R-CH=CH2 + CH3-Cat I I

CH3 H (vinyl)

R-Cat + CHz= H +

H H

I I -+ R-C=

F + H-Cat

C,

(tram)

R - polymer chain; Cat - catalytic site; C, - short chain branch containing y carbon atoms.

Page 26: Review João Soares

676 A. E. HAMIELEC and J. B. P. SOARES

Macroscale Microscale

Monomer

Fig. 12. Levels of mathematical modelling for olefin polymerization.

4. GENERAL DYNAMIC MODELLING OF METALLOCENE-CATALYZED POLYMERIZATION

4.1. Introduction

It is convenient to classify mathematical models for polymerization processes in three levels: microscale, mesoscale and macroscale. 1’S Microscale models define the kinetics of polymerization and the number of active site types on the catalyst. Mesoscale models define interparticle and intraparticle mass and heat transfer resistances in the polymer particle. Macroscale models describe the macroscopic behavior of the polymerization reactor, such as imperfect mixing, residence-time distribution, gas-liquid mass transfer and the removal of the heat of polymerization. The final application of the model determines the degree of complexity required in each modelling level. Figure 12 shows schematically these three levels of mathematical modelling.

Mathematical models that can predict molecular weight distribution and chemical composition distribution will be reviewed in the following sections.

4.2. Calculation of the molecular weight distribution of homopolymers

Molecular weight averages are conventionally estimated using the method of moments. The number average chain length is expressed as the ratio of the first moment to the zeroth moment of the molecular weight distribution. Similarly, the mass average chain length is expressed as the ratio of the second moment to the first moment of the distribution. Higher

Page 27: Review João Soares

METALLOCENECATALYSTS 677

averages (z, z+l,...) are obtained in a similar way. Therefore:

(1)

pdi = Mf n

where iii, is the number average molecular weight, n;i, is the weight average molecular weight, Mw is the molecular weight of monomer, pdi is the polydispersity index, r is the polymer chain length, and P, is the concentration of live or dead polymer molecules with chain length r.

Population balances can be derived for the living and dead polymer chains and solved for the moments of the distribution. In this way, one does not need to solve the population balances directly, which, for most cases, requires enormous computational effort. For steady-state operations, analytical solutions can be easily derived for these population balances. This approach should be used whenever possible, because it permits the calcu- lation of the whole distribution of molecular weights. It is known that several rheological and mechanical properties of polymers depend upon the whole distribution of molecular weight. This approach will become increasingly more important as our knowledge of property-structure relationships increases.

42.1. Linear chains and Flory’s most singular probable distribution

Flory’s most probable distributionl’* is simply expressed as:

w(r) = T2r exp( - v-) (4)

where 7 is the ratio of transfer to propagation rates. This well-known expression can be used to calculate the chain length distribution of linear homopolymers produced with single-site type metallocene or Ziegler-Natta catalysts and predicts a theoretical value of 2 for the polydispersity index.

For the case of multiple-site type catalysts, Flory’s distribution can be applied to predict the chain length distribution of polymer molecules made on each site type (and therefore having different values of 7). The instantaneous chain length distribution of the total polymer produced with the catalyst will be a weighted average of the individual Flory most probable distributions for each site type:

C(r) = J$ miWi(r) (5)

where mi is the weight fraction of polymer made on each site type i.

Page 28: Review João Soares

678 A. E. HAMIELEC and J. B. P. SOARES

0.8

lo9 (0

Fig. 13. Instantaneous chain length distribution of a polyolefm made with a multiple-site type catalyst as a superposition of four individual Flory most probable chain length distributions (solid lines indicate the chain length distribution of the accumulated polymer and the dotted

lines represent the chain length distributions of polymer made on distinct active sites). lo1

Figure 13 illustrates the predicted chain length distribution of a polymer made with a multiple-site type catalyst as a superposition of individual Flory most probable chain length distributions. This model can be used to analyze actual molecular weight distributions, as obtained by gel permeation chromatography, and to derive information about the nature of the active sites present in the catalyst.101’116

4.2.2. Polymer chains with long branches

Soares and Hamielec’17 derived a phenomenological model for the chain length distri- bution of polymers produced with metallocene catalysts that allow long chain branching formation via terminal double-bond mechanisms, such as Dow’s constrained geometry catalysts. They obtained an analytical solution for the chain length distribution of the populations containing different numbers of long chain branches per polymer molecule. The polymerization kinetic model involves steps of propagation, long chain branch formation via reaction with dead polymer chains containing terminal vinyl double-bonds, transfer to chain transfer agent and P-hydride elimination, as follows:

pr,i +o, + Pr+q,i+j+l kpLCB

Page 29: Review João Soares

METALLOCENECATALYSTS 6'79

where, Pr,i is a living polymer molecule of chain length r containing i long chain branches, DL is a dead polymer molecule of chain length 9 containing j long chain branches and having terminal vinyl unsaturation, D, is a dead polymer molecule of chain length 4 containing j long chain branches and a saturated chain-end, M is the monomer, CTA is a chain transfer agent, kP is the propagation rate constant for monomer, kpLCB is the propaga- tion rate constant for dead polymer with terminal vinyl unsaturation, kaA is the rate constant for transfer to chain transfer agent, and kp is the rate constant for P-hydride elimination.

Dead polymer chains having terminal vinyl unsaturation, Ds, can coordinate to the catalytic active site and insert in the growing chain, forming a trifunctional long chain branch. Dead polymer chains with saturated chain ends, D+ cannot polymerize again. Observe that, by examining the mechanism of chain formation, one can conclude that the instantaneous molecular weight distributions of live polymer, dead polymer with vinyl chain-end unsaturation and dead polymer with saturated chain-ends will be the same:. However, the relative amount of dead polymer with and without terminal vinyl unsatur- ation is proportional to the rates of P-hydride elimination (producing dead polymer chains with terminal vinyl unsaturation), and transfer to chain transfer agent (commonly to hydro- gen, producing dead polymer chains with saturated chain ends).

Soares and Hamielec ‘17 showed that the frequency distribution of chain length for polymer populations with 12 long chain branches per chain was given by:

1 f(r, n) = (2n)!r 2n r 2n + r exp( - 7 r)

where, r represents chain length and r is given by:

Rp &TA RLCB ~=--+-+-

% % % (7:)

where RP is the rate of P-hydride elimination, R, is the rate of monomer propagation, RaA is the rate of transfer to chain transfer agent and RLCB is the rate of macromonomer propagation or long chain branch formation.

It is interesting to note that the chain length averages of the polymer populations with different numbers of long chain branches per chain are related by the simple relationships:

F,,i=(1+2i)T-,,o (81

Fw,i’ (1 +ih,0 (9)

(10)

pdii = (11)

Page 30: Review João Soares

680 A. E. HAMIELEC and J. B. P. SOARES

fraction

number weight

liaear 0.8843 0.6792

1 LCB 0.0905 0.2095

2 LCB 0.0185 0.0715

3LCB 0.0048 0.0256

4 LCB 0.0014 0.0094

5 LCB 0.0004 0.0035 6 LCB 0.0001 0.0013

3.COE-06

2.5oE-06

s 8 2.OOE-06

g ‘g

1 lSOE-C@

S.OOE-07

O.OOE+M)

3Ooo 4000 YJOO KrJo

chain length (r)

2cQo 3ooo 4ooo 5MxJ eeQO

chain length (I)

Fig. 14. Chain length for polymer populations containing different numbers of long chain branches per polymer chain: (a) weight chain length distributions normalized for each individual population; (b) weight chain length distributions normalized with respect to the total weight of the whole polymer. The global distribution (over all polymer populations) is indicated by the bold line. The table in the top right comer indicates number and weight

fractions of each population. ‘17

Page 31: Review João Soares

METALLOCENECATALYSTS 681

Table 4. Comparison of chain length averages and degree of long chain branching calculated by direct solution of population balances, Monte-Carlo model and analytical solution “’

7, FW Fz pdi & (long chain branches per polymer chain)

Population balance Monte-Carlo

289 289 661 664 1110 1117 2.29 2.30 0.15 0.15

Analytical solution -

288 662 1110 2.30 0.15

F, - number average chain length; 7, - weight average chain length; pdi - polydispersity index.

where, i indicates the number of long chain branches per chain, and r,,i, T,,,i, FZ,i and pdii are the number, weight and z-average chain lengths, and polydispersity, respectively.

Average values for long chain branching frequency can also be easily obtained by noticing that:

(12)

where BN is the average number of long chain branches per polymer chain, and Qt is the zeroth moment of the distribution of dead polymer with terminal vinyl unsaturation, or in other words, the concentration of these chains.

It is also easy to calculate the number of long chain branches per 1000 carbon atoms,&

AN ,500Rp, $LCBQ~ P w

(13)

Figure 14a and b shows the predicted chain length distributions for a polyolefin produced in a CSTR for a given value of r. Table 4 shows the chain length averages and average degree of long chain branching predicted with the model. Figure 15 and Table 5 show the effect of varying the rate of long chain branch incorporation in the chain length distribution. As expected, the chain length distribution becomes broader as the long chain branching level increases.

It is clear that the analytical solution shown in eqn (6) can also predict the instantaneous chain length distribution of polymer produced during non-steady-state operation of a CSTR or in other reactor types. This analytical solution was also compared with the numerical solution of the population balances and with chain length distributions generated with a Monte-Carlo simulation. The agreement with the analytical solution was excellent (Table 4).

4.3. Calculation of the distribution of molecular weight, composition and long chain branching frequency of copolymers

Molecular weight averages of copolymers can be easily calculated with the method of moments by using pseudo-kinetic rate constants, and average copolymer compositions can be obtained from the relative rate of comonomer polymerization. 1’3~118 However, as for

Page 32: Review João Soares

682 A. E. HAMIELEC and .J. B. P. SOARES

-. -. t = 0.004267, B = 27.7879

-. . . . t = 0.004507, B = 5 1.93875

~ t = 0.004905, B = 91.85493

-t = 0.005476, B = 149.1786

0 1000 mw 3cm 4ccm 5Goo moo

chain length (r)

Fig. 15. Effect of varying macromonomer addition rate on weight chain length distribution. “’

homopolymerization, whenever possible it is advantageous to predict the whole distribu- tion of molecular weight and chemical composition for copolymerization. For the case of linear chains and binary copolymerization, this instantaneous bivariate distribution is given by Stockmayer’s distribution. ‘I9

4.3.1. Linear binary copolymer chains and Stockmayer’s bivariate distribution

Stockmayer ‘19 used the general copolymerization theory proposed by Simha and Bran- son 120 to derive a simple expression for the bivariate distribution of chain length and composition valid for linear binary copolymers with long chains. Tacxr21 introduced a minor correction term to Stockmayer’s distribution to account for comonomers with dis- tinct molecular weights.

Table 5. Chain length averages and degree of long chain branching as a function of long chain branching incorporationl”

B&ong chain branches per chain)

pdi

0.075 268 580 928 2.16 0.150 288 662 1110 2.30 0.290 320 806 1378 2.51 0.500 363 952 1556 2.62

7, - number average chain length; f, - weight average chain length; pdi - polydispersity index.

Page 33: Review João Soares

METALLOCENE CATALYSTS 683

llO-

100 -

90-

80 -

70 -

60 - 2

Y 50-

40 -

30-

20 -

10 -

-8.05 -0.03 -0.01 0.01 0.03 0.05 I

Deviation from average composition (y)

Fig. 16. Stockmayer’s bivariate distribution for chemical composition as a function of chain

Stockmayer’s bivariate distribution is given by the expression:

rv(r,y)drdy=(l +y@r% exp( (14)

where,

@=E,(l -E,)K (15)

K=[1+4P,(l -E&IQ - 1)]“.5 (16)

(l-2) 6=Mwz _ ibfwz

-+&(l- -) Ml Ml

(17)

where y is the deviation from the average mol fraction of monomer 1 in the copolymer, Et is the average mol fraction of monomer 1 in the copolymer, rl and r2 are the reactivity ratios, and MIVi and A4TV2 are the molecular weights of monomers 1 and 2, respectively. Figure 16 presents the composition distribution as a function of chain length. Longer chains (smaller 7) have narrower chemical composition distributions. This is a consequence of the statistical nature of polymerization: chains of infinite chain length will, evidently, have a mol fraction of comonomer 1 equal to El, while smaller chains can have values of El varying from 0 to 1.

For the case of multiple-site type catalysts, one can assume that each active site instan- taneously produces copolymer chains that follow the Stockmayer bivariate distribution. In this way, the bivariate distribution of chain length and chemical composition for the product copolymer can be obtained as a weighted average of individual Stockmayer distributions over all site types:

Page 34: Review João Soares

684 A. E. HAMIELEC and J. B. P. SOARES

260

240

220

200

180

160

140

120

s I 100

80

60

40

20

0 0.84 1 0.86 1 0.88 1 0.9 / 0.92 / 0.94 1 0.96 1 0.98

0.85 0.87 0.89 0.91 0.93 0.95 0.97

Mole fraction of ethylene (y)

Fig. 17. Predicted chemical composition distribution of a LLDPE made with a multiple-site type catalyst. 122

Figure 17 shows the predicted chemical composition distribution for a LLDPE made with a multiple-site type catalyst. Stockmayer’s bivariate distribution can also be used as a mathematical model for temperature rising elution fractionation detector response for polymers made with multiple-site type catalysts. 122

4.3.2. Copolymer chains with long chain branches

The analytical solution for the chain length distribution of homopolymers with long chain branches, eqn (6), is also valid for copolymerization when appropriate pseudo-kinetic rate constants are used to calculate 7. Additionally, for the case of binary copolymerization, Stockmayer’s distribution can be used to obtain the chemical composition distribution of the copolymer. This is possible because the branched chains are formed by linear copoly- mer chains which follow Stockmayer’s bivariate distribution.

4.3.3. Multicomponent copolymers

For copolymerizations involving three or more monomer types, Stockmayer’s bivariate distribution is no longer valid. However, Flory’s most probable distribution is valid, providing a working analytical expression for the molecular weight distribution for

Page 35: Review João Soares

METALLOCENE CATALYSTS 685

Potymer

Particle size

Fig. 18. Fragmentation of heterogeneous Ziegler-Natta or supported metallocene catalyst (secondary) particles during polymerization.

multicomponent polymerization. The dimensionless parameter r in Flory’s equation is defined in the same general way in terms of ratios of rates. To evaluate r for a multi- component polymerization, one must evaluate these rates in the appropriate manner using pseudo-kinetic constants in the context of the terminal model for copolymerization or for any other copolymerization model which is applicable (e.g. the penultimate model). 123

With a lack of any analytical expression for the chemical composition distribution for a terpolymerization or higher, one can make the reasonable assumption that, for long copolymer chains, all of the chains have the same composition at an average value (Fr, E2, etc.). In this manner, one can construct a multi-dimensional distribution of chain lengths and mole frac- tions for the different monomer types, for single-site and multiple-site type catalysts.

4.4. Mass and heat transfer resistances during polymerization with supported metallocene catalysts

Heterogeneous Ziegler-Natta and supported metallocene catalysts consist of porous secondary particles, formed by loosely aggregated primary particles. 124 During polymer- ization, the growing polymer chains fragment these secondary particles, forming an expanding particle containing primary particles and living and dead polymer chains (Fig. 18). This catalyst fragmentation mechanism has been documented for several types of Ziegler-Natta catalysts. 124~125 One of its consequences is the well-known replication phenomenon: the particle size distribution of the polymer particles at the end of batch or semi-batch polymerization closely approximates the particle size distribution of the

Page 36: Review João Soares

686 A. E. HAMIELEC and J. B. P. SOARES

catalyst at the beginning of polymerization. For the case of continuous reactors, the residence-time distribution can significantly broaden this particle size distribution. 126~127

Based on this experimental evidence, some researchers advocate that, due to diffusion resistances, catalyst fragments at different radial positions in the polymer particle are exposed to different concentrations of monomer and chain transfer agent, and consequently produce polymers with chain length averages that differ radially inside the polymer par- ticle. For copolymerization, monomers with different effective diffusivities and reactivities may be responsible for radial composition heterogeneity in the polymer particle. In addition, if there are appreciable heat transfer resistances, hot spots can occur inside the polymer particle, altering reaction rates and further broadening molecular weight and chemical composition distributions. Some strong experimental support for these hypoth- eses has been recently presented. 128-130 Models based on this approach are generally called physical models. Several of these models have been published in the literature, especially for modelling conventional heterogeneous Ziegler-Natta catalysts. The polymeric flow model, 13’ the multigrain model, ‘15 and modifications of these models have been applied extensively for different polymerization conditions. For a comprehensive review on physical models and mathematical modelling of olefin polymerization in general see Dub6 et al. 132 and Soares and Hamielec1t8. Only a few of these models have been used to simulate polymerization with supported metallocene catalysts. It is clear, however, that most of these mathematical models can be readily modified to simulate these new catalytic systems.

Soares and Hamielec ‘18 applied a polymeric multilayer model for supported metallocene catalysts as well as for conventional heterogeneous Ziegler-Natta catalysts. In the case of supported metallocene catalysts with only one active site type, the only factor responsible for broadening of the molecular weight and chemical composition distributions would be intraparticle mass and heat transfer resistances. In these calculations, the polymeric particle is divided into concentric spherical layers. Initially all layers have the same concentration of active sites as the whole catalyst particle, i.e. there is no radial profile of active sites. This assumption is supported by some recent electron microscopy studies of heterogeneous Ziegler-Natta catalysts. 124 Population balances for each active species are calculated inside each layer. The volume of each concentric layer is updated using average monomer concentrations and average temperature after a given time interval. Additionally, this polymeric multilayer model calculates not only molecular weight and copolymer com- position averages, but also the complete distributions of molecular weight and chemical composition in each model layer and for the whole polymer particle using Stockmayer’s bivariate distribution (Fig. 19). It is well known that several important mechanical and rheological properties of polyolefins depend on these distributions. 133

For copolymerization, the combined effect of different effective diffusivities and reactivities for the comonomers can generate a radial profile of chemical composition. Figs 20a-d shows that for smaller monomer diffusivities, the mole fraction of propylene (the slower polymerizing monomer) in an ethylene-propylene copolymer increases from the surface to the center of the particle. This behavior can be attributed to the higher reactivity of ethylene. Since ethylene is more reactive than propylene, its consumption will be affected more by mass transfer than propylene consumption. Consequently, the

Page 37: Review João Soares

METALLOCENE CATALYSTS 687

Mole fraction of propylene

In(r) Mole fraction of propylene

Fig. 19. Prediction of chain length and chemical composition distributions of a polyolefin made with a three site-type catalyst using the polymeric multilayer model. Layer numbers ;;; indicated with an “1”; layer 1 is the innermost layer. Site types are indicated with an “s”.

radial profile of ethylene concentration will be steeper than the one for propylene. In this way, the inner layers of the polymer-catalyst particle will produce polymer that is richer in propylene than in ethylene. For smaller diffusivities, the radial profile of copolymer composition becomes more prominent, especially for short polymerization times, in good agreement with the ex- perimental results published by Hoe1 et al. lz9 for the copolymerization of ethylene and propylene using a supported metallocene catalyst. It is important to notice that this effect is less marked for longer polymerization times due to particle expansion.

For single-site type catalysts, the main conclusions of the polymeric multilayer model confirm and complement the conclusions obtained with the polymeric flow model and the multigrain model: (1) mass transfer resistances can reduce the polymerization rate and decrease molecular weight averages; (2) particularly important for supported catalysts, the concentration of highly active catalytic sites can increase the effect of mass transfer resistances and reduce catalyst performance and product quality; (3) mass transfer resis- tances may also be a source of composition heterogeneity for highly active and large catalyst particles if the comonomers have reactivities that differ significantly; (4) tempera- ture gradients in the polymeric particle are not expected to be a significant factor for reactions carried out in slurry reactors.

Hoe1 et al. 129 developed a simplified flow model with no polymer molecular weight

Page 38: Review João Soares

688 A. E. HAMIELEC and J. B. P. SOARES

0.85

0.84

0.83

0.82

0.81

0.8

0.78

0.78

Fi 0.77

0.76

0.75

0.74

0.73

0.72

0.71

0.7

1

I I I I I I I /

0 2 4 6

time (s) x 1000

1

0.8

0.8

0.4

0.3

-I 8

I I I I I / I I ,

1 3 5 7 8

radial poslion

Fig. 20. Effect of monomer diffusivity for a high activity catalyst during copolymerization: (a) mole fraction of propylene in copolymer (Fl) as a function of polymerization time; (b) radial profiles of propylene and ethylene; (c) chemical composition distribution for different Frdel

layers; (d) average chemical composition distribution for whole polymer particle.

Page 39: Review João Soares

METALLOCENE CATALYSTS 689

70

60

50

40

WY) 30

20

10

0 c

layer 9

0.7 0.72 0.74 0.76 0.78

Mole fraction of propylene

0.8 0.82 0.84

28 r\

26

24

22

20

16

0 I / I I 1 I I I -

0.7 0.72 0.74 0.76 0.78 0.8 0.82 0.84

Mole fraction of propylene

Fig. 20. Continued.

Page 40: Review João Soares

690 A. E. HAMIELEC and J. B. P. SOARES

calculations, and used it to interpret their experimental data on ethylene-propylene polymerization using a silica-supported metallocene catalyst in a liquid propylene slurry reactor. Unfortunately, they did not specify the two catalyst types used for the polymeriza- tions. Both catalysts produced polymers with narrow molecular weight distributions at a constant rate of polymerization. However, one catalyst produced polymer with a narrow chemical composition distribution, while the other afforded polymer with a broad chemical composition distribution and a decreasing amount of ethylene in the copolymer as a func- tion of polymerization time. The radial composition was measured by FTIR-microscope analysis for microtomed 250-750 pm particles and it was found to be richer in propylene in the center of the particle than in the exterior layers. Although their model could qualita- tively predict the radial profile of chemical composition, it could not account for the decrease in ethylene content during the polymerization. In reality, their model predicted an increase in ethylene content with polymerization time, and so would any physical model published in the literature, since the concentration of active sites in the polymeric particle decreases during the polymerization, decreasing the effect of intraparticle mass transfer resistances. The decrease in ethylene content in the copolymer was attributed to variations in monomer diffusivity and particle porosity during the polymerization.

Recently, Bonini et al. 134 applied a modified form of the multigrain model to the poly- merization of propylene with silica-supported Me2Si(Ind)2ZrC12/MA0. Their model takes into account the mechanism of catalyst fragmentation by the growing polymer chains to explain the observed induction period when the supported metallocene is used. In their model the catalyst particle is fragmented by the growing polymer in successive concentric shells, from the external surface to the center of the particle, as proposed by Ferrer0 and Chioveta.135 Their model agreed well with experimental rates of polymerization, including the induction period, and number average molecular weight, but could not predict the relatively broad molecular weight distribution (polydispersities from 2.4 to 3.8). The simulated polydispersities were always less than 2.1, surprisingly low values.

These conclusions obtained with single-site type physical models are especially impor- tant for the technology of supported metallocene catalysts, where single site, highly active species, may be subjected to mass and heat transfer resistances.

4.5. Calculation of polymer particle size distribution

4.5.1. Introduction

The replication phenomenon in heterogeneous Ziegler-Natta and metallocene catalysts permits one to readily predict the particle size distribution of the polymer particles from the knowledge of the catalyst’s particle size distribution. The particle size distribution of the polymer is an important variable in designing and operating polymer recovery, treatment and processing units. Good replication is supposed to occur when there is an adequate balance between the mechanical strength of the particle and catalyst activity. If the reactivity is too high and the particle very weak, the fast growing polymer chains can rupture the catalyst particle into smaller, isolated fragments, forming undesirable fine polymer powder. On the other hand, if the particle is too strong, there will be little or no fragmentation and the polymer chains will block the catalyst pores, making the internal

Page 41: Review João Soares

METALLOCENECATALYSTS fl91

active sites inaccessible to monomer. Replication factors of 40-50 (ratio of average polymer particle diameter to average catalyst particle diameter) can be obtained with third generation Ziegler-Natta catalysts. 136

It has been shown with detailed simulation models for the growth of polymer particles produced with heterogeneous Ziegler-Natta catalysts, that the effect of mass transfer resistances on the polymerization rate (and thus on the rate of growth of the polymer particle) is more significant for larger catalyst particles than for smaller ones under the same polymerization conditions. “‘Jo Since commercial catalysts show a distribution of particle sizes, it is reasonable to assume that the growth of the bigger catalyst particles will be more influenced by mass transfer than the growth of the smaller particles. If this effect is significant, it could lead to imperfect replication of the catalyst particle size distribution.

However, a factor frequently overlooked in the simulation models is the effect of the residence-time distribution of polymer particles in industrial continuous reactors used for polymerizing olefins. A necessary condition to obtain a perfect replication of the catalyst particle size distribution is that the residence time of all catalyst particles in the reactor be the same. For the case of continuous operation, this requirement is only possible in plug flow reactors. In a CSTR (commonly used in slurry and mechanically agitated gas-phase processes) and fluidized bed reactors (such as the UNIPOL gas-phase reactor) the catalyst particles experience a distribution of residence times in the reactor which does influence the size distribution of the formed polymer particles. 127

4.5.2. Supported catalysts

Soares and Hamielec 127 developed a model to account for the influence of the reactor residence-time distribution on the particle size distribution of the polymer product. This model considered an average polymerization rate for all catalyst particles and assumed that the active sites were homogeneously distributed on the catalyst particle. Two types of sites were considered: stable sites which did not deactivate, and unstable sites which were allowed to deactivate following an exponential deactivation rate law. A numerical algo- rithm for predicting the polymer particle size distribution from knowledge of the catalyst particle size distribution and from the residence-time distribution of the polymerization reactors was developed, Polymerization reactors could have any residence-time distribu- tion and could be used alone or in series. Numerical solutions were compared with the analytical solution proposed by Kanetakis et al. 137 for the size distribution of polymer particles produced in a series of ideal CSTRs, when all particles entering the first reactor in the series had the same size. The agreement between the general numerical solution and the particular analytical solution was excellent.

The effect of mass transfer resistance on the replication factor as calculated with the polymeric multilayer model was also accounted for. Mass transfer resistance was not found to significantly influence the growth of the polymer particle even for very low effective diffusivities. In reality, the polymeric multilayer model predicted near perfect replication for the studied polymerization conditions. However, the reactor residence-time distribution had a significant influence on polymer particle size distribution (Fig. 21a and b). The conclusions drawn are especially important for the case of ethylene-propylene

Page 42: Review João Soares

692 A. E. HAhIIELEC and J. B. P. SOARES

35

30

25

1

0.8

0.6

0.4

0.2

0

/ \ I

1’

300 400 500 600 700 800 900 1000

DP (w)

-non-ideal CSTR - I” --I ideal CSTR (K)

0 400 500 600 700 800 900 1000

DP (pm) -non-ideal CSTR “. ^- .- ideal CSTR (K) o perfect replication

Fig. 21. Effect of non-ideal residence time distribution on the particle size distributgp of polymer made in a CSTR: (a) frequency distribution; (b) cumulative distribution.

Page 43: Review João Soares

METALLOCENE CATALYSTS 693

plltiele diameter

time

Fig. 22. Mechanism for polymer particle formation for olefin polymerization with soluble metallocene catalysts.‘38

copolymers. With these resins, it is often necessary to produce a copolymer with an optimum ratio of isotactic polypropylene to ethylene-propylene rubber to maximize the impact properties of the product. However, a broad residence-time distribution in the polymerization reactor will produce polymer particles with varying ratios of isotactic polypropylene to ethylene-propylene rubber, consequently decreasing product. Narrow residence-time distributions are clearly beneficial for impact copolymers.

4.5.3. Unsupported catalysts

the quality of the the production of

In most polymerizations using soluble Ziegler-Natta catalysts in general, and metallo- cenes in particular, the polymer is not soluble in the reaction medium and precipitates after a critical chain length is achieved. If, after chain termination, the active site returns to solution, then interparticle mass and heat transfer effects should not influence the poly- merization. However, if the active sites are trapped inside the polymer particles, interpar- title mass and heat transfer resistances can become significant.

A mathematical model for particle growth during ethylene polymerization catalysed with soluble metallocenes was proposed by Hermann and Bijhm138 using the diffusion limited model proposed by Witten and Sander.139 Unfortunately, very little detail about their model was given. They found out that the process of polymer particle formation in a slurry reactor consisted of aggregation by Brownian motion followed by diffusion con- trolled particle growth, leading to the formation of particles with high surface area and low bulk density. Figure 22 shows their proposed mechanism of polymer particle formation.

Koivumaki et al. ‘QJ studied the mechanism of polymer particle formation in a heat

Page 44: Review João Soares

694 A. E. HAMIELEC and J. B. P. SOARES

balance calorimeter for the polymerization of ethylene and 1-hexene with Cp2ZrCl?JMAO. For the homopolymerization of ethylene, the particles formed were five times larger in size and had lower bulky densities than particles formed via copolymerization. This caused a significant increase in the slurry viscosity and decreased the overall heat transfer coeffi- cient. For copolymerization, the presence of comonomer apparently favored the formation of smaller polymer particles, causing no measurable increase in slurry viscosity. Actually, if during a homopolymerization run, comonomer is introduced in the reactor, the viscosity stops increasing after a lag time. This particle size difference can be used to explain polymerization rate enhancement during copolymerization due to a decrease in mass transfer resistances. The authors, however, acknowledge that their model assumed, incor- rectly, Newtonian behavior for the slurry and that this could lead to some data distortion.

4.6. Designing multi-site type catalyst systems

It is possible to combine different types of metallocene catalytic systems to produce polymers for applications which require broad molecular weight and chemical composition distribution. 14’ One way of using metallocene catalysts to produce a polymer with a broad molecular weight and composition distribution is by combining different metallocene compounds in the same support, thus engineering a multiple-site type catalyst. If each site type has distinct ratios of chain transfer to propagation rates as well as different reactivity ratios, copolymers with “tailored” molecular weight distributions and chemical composi- tion distributions can be synthesized by the planned selection of metallocene types and their relative proportions.

There is significant potential for controlling the microstructure of polyolefins via metallocene catalysts. Additionally, the presented mathematical models can predict poly- mer microstructure from the knowledge of the leading polymerization kinetic parameters. Unfortunately, there is considerable lack of information concerning quantitative structure- property relationships for polyolefins. The ability to control the microstructure of such polyolefins will have its usefulness reduced if polyolefin microstructure cannot be related to rheological and mechanical properties.

5. ACTIVE SITE TYPE IDENTICATION USING POLYMER CHARACTERIZATION TECHNIQUES - TREF / GPC / NMR

5.1. Deconvolution of molecular weight distributions - GPC detector responses and Flory ‘s most probable distribution

Polyolefins produced using most heterogeneous and some homogeneous metallocene, and Ziegler-Natta catalysts have chain length distributions that are significantly broader than the Flory most probable distribution expected for ionic chain growth homo- and copolymerization. It is now generally accepted that these broad chain length distributions are caused by the presence of multiple-active site types on the catalyst, although in some instances mass and heat transfer can further broaden these distributions. 118~142~143 Assuming that the polymerization conditions are such that the chain length distribution is equal to the instantaneous chain length distribution, it is possible to obtain information about the

Page 45: Review João Soares

METALLOCENE CATALYSTS 695

number and activity of catalyst sites by decomposing the chain length distribution of the whole polymer into individual most probable chain length distributions of each active site

type. 101,116

Vickroy et al. ‘16 used commercially available software to successfully decompose the chain length distribution of polyethylenes into Flory’s most probable distributions. Soares and Hamielec lo1 developed a decomposition program using two alternate numerical methods: the Levenberg-Marquardt method14 and the Golub-Pereyra method. 145 They used these two methods to decompose the chain length distribution, as measured with gel permeation chromatography, of polypropylene produced with a heterogeneous Ziegler- Natta catalyst. Both methods converged to the same result. However, the Golub-Pereyta method had a faster rate of convergence than the Levenberg-Marquardt method.

Soares and Hamielec also proposed a methodology for the efficient deconvolution of the chain length distributions by plotting the residuals as a function of chain length. It was observed that when the “best” solution was achieved, the residuals were not correlated with chain length. Figure 23a shows the results of one deconvolution and Fig. 23b shows the plot of the residuals as a function of chain length.

This methodology was used to study the effect of hydrogen on the polymerization of propylene using a heterogeneous Ziegler-Natta catalyst.45 It was found that hydrogen increased the polymerization rate of propylene and broadened the molecular weight distribution of polypropylene. Hydrogen apparently activated catalytic sites unavailable in its absence, creating additional site types, and consequently broadening the molecular weight distribution of the resulting polymer.

5.2. Deconvolution of chemical composition distributions - TREF I NMR detector responses and Stockmayer’s bivariate distribution

Temperature rising elution fractionation (TREF) has been used with considerable success for copolymer characterization, especially for polyolefins. Good reviews of this technique have been published recently in the literature. 146-148 This technique is based on the relationship between molecular structure, crystallinity and dissolution temperature of polymer molecules.

When a binary copolymer is made with monomers that form crystalline homopolymers, the crystallinity of the copolymer is lower than that of both homopolymers because the presence of dissimilar molecules disrupts the order of the polymer chains. This decreased crystallinity will be reflected in a lower dissolution temperature of the copolymer. 149 Stereo- and regiochemical defects (such as an atactic placement in a mainly isotactic chain, and a head-to-head placement in a mainly head-to-tail chain) will have similar effects.

Copolymers of olefins (ethylene with comonomers propylene and higher cr-olefins) made with heterogeneous Ziegler-Natta catalysts are particularly well suited for TREF fraction- ation. These copolymers show broad molecular weight and composition distributions arising from several site types on the catalyst. Although metallocene catalysts in general produce polymer with narrow molecular weight and chemical composition distributions, there are several reports in the literature indicating that some catalytic systems produce copolymers with broad chemical composition distributions. Soga et al. 15’ found that copolymers of ethylene and hexene-1 produced with Cp2ZrC12/MAG had a bimodal TREF

Page 46: Review João Soares

696 A. E. HAMIELEC and J. B. P. SOARES

- model

0.Q

0.6

0.7

0.6

0.5

0.4

0.3

0.2

0.1

1.5 2 2.5 3 3.5 4 4.5 5

__ predicted

5

4'

q

q q EP Cl

El q 0

q

-5 I I I I I I I I

1.5 2 2.5 3 3.5 4 4.5 5

log (0

Fig. 23. Deconvolution of a polymer chain length distribution into most probable Flory dis- tributions: (a) solid line indicates chain length distribution for the whole polymer and dotted lines indicate chain length distributions for individual site types; (b&plot of residuals, for actual

distribution and predicted distribution.

Page 47: Review João Soares

METALLOCENE CATALYSTS 697

PPH

Y

I I

40 I I

30 20 PPM

Fig. 24. 13C NMR spectra of a impact ethylene-propylene copolymer made with a hetero- geneous Ziegler-Natta catalyst: (a) rubber fraction, obtained at an elution temperature interval of 60-8O”C; (b) crystalline isotactic polypropylene fraction, obtained at elution temperature

interval of 120-140°C. 14*

curve, although the highly crystalline peak was mainly produced in the beginning of the polymerization. Broad TREF profiles were also obtained when copolymerizing ethylene and hexene-1 with other metallocene catalytic systems. They suggested that at least two site types must be present on the catalyst to account for their experimental results.

When polymer fractions obtained with preparative TREF are analyzed with 13C NMR, it is possible to obtain very detailed information about polymer microstructure and the nature of catalytic active sites. Figure 24a and b show the 13C NMR spectra of two preparative TREF fractions for an impact ethylene-propylene copolymer produced with a hetero- geneous Ziegler-Natta catalyst. 14’ The spectrum for the fraction obtained at the lower

Page 48: Review João Soares

698 A. E. HAMIELEC and J. B. P. SOARES

60 r 50

0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98

Mole fraction of ethylene

Fig. 25. Theoretical temperature rising elution fractionation detector response of a LLDPE made with a five-site-type catalyst. lz2

temperature shows several peaks associated with ethylene-propylene units in the polymer chain, while the spectrum for the fraction obtained at the higher temperature shows only three well-defined peaks for the primary, secondary and tertiary carbons in the polymer chain. 14*

A mathematical model for TREF fractionation using Stockmayer’s bivariate distribution was proposed recently. 122 This model can be used to qualitatively deconvolute TREF profiles for both analytical and preparative TREF and to calculate the molecular weight distribution of fractions obtained with preparative TREF. The model assumes that each site type produces copolymer chains that have an individual Stockmayer bivariate distribution. Having determined the bivariate distribution of each site type, it is possible to derive expressions for the whole polymer and for each TREF fraction. Figure 25 shows the predicted analytical TREF detector response for a LLDPE produced with a catalyst having five different types of active site. The predicted profile is remarkably similar to experi- mental TREF curves of LLDPE produced with multiple-site type catalyst. Table 6 shows the predicted molecular weight averages of the TREF fractions. It is interesting to note that, although the TREF fractions have a smaller polydispersity index than that of the whole polymer, they are not equal to 2, due to incomplete recovery of polymer chains from one site type or to the superposition of polymer chains made on different site types. Notice also that site types that make polymer chains with lower molecular weight averages also make polymer chains with a broader chemical composition distribution and, therefore, these sites

Page 49: Review João Soares

METALLOCENE! CATALYSTS 699

Table 6. Simulated TREF fraction averages for LLDPElz2

Mol fraction of ethylene

f ?I FW pdi Mass fraction

0.84-0.88 97 178 1.8 0.012 0.88-0.90 218 374 1.7 0.051 0.90-0.92 373 894 2.4 0.158 0.92-0.94 905 2615 2.9 0.391 0.94-0.96 1943 12183 6.3 0.384 0.96-0.98 100 597 6.0 0.004

?n - number average chain length; P, - weight average chain length; pdi - polydispersity index.

have a considerable effect on the ability of TREF to fractionate polymer produced on different site types.

A thermodynamic model for TREF, based on an extension of the Flory-Huggins theory has also been published recently.151 These models can be used to help understand TREF profiles of metallocene polymers and the nature of the active sites in these catalysts.

6. SYNTHESIS OF POLYOLEFINS WITH LONG CHAIN BRANCHES WITH METALLOCENE CATALYSTS

6.1. Polymerization processes

6.1.1. Slurry polymerization

In slurry polymerization with soluble metallocene systems, the polymer molecules are insoluble in the solvent (also called the diluent). When polymer chains precipitate from solution, there is the possibility of two-phase polymerization, one occurring in the solvent phase and the other occurring in the polymer phase. Active centers and monomers may partition between these two phases, giving rise to different polymerization rates and forrn- ing polymers with different molecular weight distributions in each of the two phases. In batch and semi-batch operations, phase volume ratios would change with time, giving overall polymerization rates and molecular weight distributions which would change with time. However, the slurry polymerization of ethylene with Cp2ZrC1JMA0 in toluene in a semi-batch reactor152 has a constant rate of polymerization and the polyethylene produced has a polydispersity of two, suggesting that the active centers do not partition between the two phases. Although no conclusive evidence has been presented in the literature, it is generally accepted that the active sites remain in the solvent phase during the polymeriza- tion. For an alternative view, see Hermann and Bohm.138

With supported metallocenes, which are insoluble in the solvent, active centers are encapsulated by polymer and the polymerization occurs almost exclusively in the polymer phase. Long chain branch formation should depend on the mobility of the macromonomers in the monomer/solvent swollen polymer particles. Self-diffusion coefficients of macro- monomers depend on molecular weight and one therefore might expect that the rate of

Page 50: Review João Soares

700 A. E. HAMIELEC and J. B. P. SOARES

addition of a macromonomer to the active center is diffusion-controlled with preferential formation of shorter long chain branches. On the other hand, the steric barrier for addition of a macromonomer also increases with size of the reactant, retarding the addition process of the longer macromonomers and, as a result, diffusion resistances may not be as important for larger macromolecules as one might expect (the controlling step may be the overcoming of the steric barrier at the metal center).

6.1.2. Gas-phase polymerization

In gas-phase reactors, metallocene catalysts have to be supported prior to the polymer- ization. With these processes, active centers are encapsulated in polymer and the limiting factor on long chain branch formation may be low levels of swelling of polymer particles by monomer and low self-diffusion coefficients of highly entangled polymer chains,

6.1.3. Solution polymerization

In solution processes, active centers and polymer chains are soluble in the solvent. These processes are generally carried out at temperatures above the melting temperatures of the polymer chains. 24 Solution processes are preferred for long chain branch synthesis for several reasons. Macromonomers with terminal vinyl unsaturation are formed at higher rates at elevated temperatures. These dissolved polymer chains, with concentrations usually less than 15 wt% in solvent, are mobile and have relatively large self-diffusion coefficients. Most importantly, at these higher temperatures the steric barrier for the addition of a macromonomer to the active center is relatively less important than at lower temperatures,

A potential negative effect of these elevated temperatures is the reduced lifetime of the catalyst active centers. Short residence times can be used with a CSTR to overcome this problem. Shorter reactor residence times would also have the advantage of making product grade transitions more efficient.

6.2. Reactor operation conditions

6.2.1. Batch operation

For batch operation, all of the ingredients (catalyst, cocatalyst, solvent, monomers and chain transfer agents) are added to the reactor at time zero. Polymer concentration increases continuously with time until all of the monomers have been consumed. High polymer concentrations are reached only near the end of the polymerization, requiring long poly- merization times to produce a significant amount of long chain branches. Unfortunately, particularly with solution polymerization at elevated temperatures, severe catalyst deacti- vation may take place during the polymerization and therefore long residence-times would not be practical. To achieve desired long chain branching levels, high polymer concentra- tions in solvent would likely be necessary, giving excessively high viscosities, problems with stirring, heat and mass transfer.

Page 51: Review João Soares

METALLOCENE CATALYSTS 701

6.2.2. Semi-batch operation

For semi-batch operations, all the ingredients, except for ethylene, are added to the reactor at time zero. The polymerization is done at constant temperature and pressure, with ethylene being fed on demand to maintain constant pressure. Semi-batch operation of the polymerization reactor has the same drawbacks as a batch operation. Additionally, the ethylene concentration in the solvent is essentially time-independent. For the same reactor pressure, the ratio of polymer to monomer concentration would be lower for a semi-batch operation than for a batch operation, which is less favorable for long chain branch formation.

6.2.3. Continuous operation

For continuous operation at steady-state, all of the ingredients are fed into the reactor continuously. The polymer product, unreacted monomers and comonomers, and catalytic species leave the reactor continuously, and the temperature and concentrations of all species in the reactor are time-independent.

For continuous operation at steady-state, the residence time distribution plays a very significant role in long chain branch generation. To illustrate this, we will consider the two extremes of a plug flow tubular reactor (PFTR) with a narrow residence-time distribution, and of CSTR with a very broad residence-time distribution. With the PFTR, the polymer concentration increases while the monomer concentration decreases as one moves along the tube (similar to a batch reactor in time). High polymer concentrations are obtained near the exit of the PFl’R, while much of the polymerizing mass in the reactor is at low polymer concentrations. With the CSTR, the entire reacting mass is at the same high polymer and low monomer concentration. Rates of long chain branch reactions are clearly higher at higher polymer concentrations (polymer with terminal vinyl unsaturations) and rates of monomer consumption are clearly lower at the lower monomer concentrations, giving high levels of long chain branching per 1000 carbon atoms. It should also be pointed out that with the CSTR, the concentration of ethylene in the polymerizing mass and exit stream is usually significantly lower than that of equilibrium solubility at the operating temperature and pressure of the reactor. It is perfectly clear, therefore, that the optimal reactor type and operation conditions for maximum long chain branch formation is the steady-state operation of a continuous stirred tank reactor.

7. ADAPTATION OF METALLOCENE CATALYSIS TO EXISTING OLEFIN POLYMERIZATION PROCESSES

Metallocene catalysts have the potential of significantly changing the polyolefin market if production costs (especially those associated with MAO synthesis) can be reduced and if new polymer grades can be implemented without significant processing difficulties.

Although metallocene-produced polyolefins can compete with commodity polyolefins synthesized with conventional Ziegler-Natta catalysts, they will not probably be restricted to the polymer commodity market. Because of the better polymer microstructure control obtained with metallocene catalysts, it will be possible to produce specialty polyolefins to

Page 52: Review João Soares

702 A. E. HAMIELEC and J. B. P. SOARES

Table 7. Worldwide metallocene polyolefins capacity commitments4

Company Region Year of commercialization

Capacity (ton/year)

Polyethylene Dow Exxon Mitsui Mitsubishi Union Carbide

Polypropylene Chisso Exxon Hoeschst Mitsui Toatsu

U.S. U.S. Japan Japan U.S.

Japan U.S. Europe Japan

1993 1995 1995 1994 1995

1996 1995 1994-1995

50,000 100,000 100,000 100,000 300,000

20,000 100,000 100,000 75-100,000

compete with non-olefinic polymers, thus opening a completely new market for polyolefin applications.

The following industrial processes are already in operation using metallocene catalysts: Exxon EXACT processes for polyethylene production; a gas-phase Mitsui process for polyethylene production; and Dow Chemical INSITE technology for substantially linear polyolefins. 153 Table 7 shows the expected production of polyolefins using metallocene catalysts by different polymer companies in North America, Europe and Japan.

7.1. Gas-phase processes

Metallocene catalysts need to be supported to be used in gas-phase reactors, such as Union Carbide’s fluidized-bed UNIPOL process, or BASF’s stirred-bed NOVOLEN pro- cess. For these processes it is necessary to have a free flowing catalyst powder which will form polymer particles with adequate size distribution, avoiding the formation of fine powder or particle agglomerates. In other words, good replication of the catalyst particles is essential for the efficient performance of these reactors.

Langhauser et al. 154 reviewed the industrial production of polypropylene (homopolymer, random copolymer and impact copolymer) using Me$Si(2Melnd)2ZrC1~O-supported catalyst and the NOVOLEN-BASF process. This catalyst can produce polypropylene with a high molecular weight even at elevated temperatures. The polymer particles replicate well the size distribution of the catalyst particles. This catalyst can produce polypropylene with new properties, such as low extractables for food wrapping and medical applications, which is a consequence of the homogeneous microstructure of polymers produced with a single-site type catalyst.

Impact copolymers can also be produced with this catalyst. Impact copolymers made with heterogeneous Ziegler-Natta catalysts show some crystalline domains in the amorphous elastomeric phase, while the elastomeric phase of the metallocene-produced copolymer is entirely amorphous. This new microstructure will likely enable the produc- tion of copolymers with enhanced impact properties.

According to Langhauser et al. this catalytic system can be adapted to their existing gas- phase polymerization process without any significant technical change. Mobil Chemical

Page 53: Review João Soares

METALLOCENE CATALYSTS 703

Co. is also producing LLDPE for film resins using metallocene catalysts in a gas-phase fluidized bed polymerization reactor. Minimal capital investment was necessary to adjust the processes to the new metallocene catalyst and the new resins have superior properties over the corresponding Ziegler-Natta resins.155

7.2. Liquid-bulk or diluent slurry processes

Slurry processes, either using liquid monomer or a diluent, are commonly used for laboratory-scale olefin polymerizations. Supported metallocenes and heterogeneous Ziegler-Natta catalysts will have similar behavior regarding macroscopic phenomena in the reactor, provided that there is no desorption of the active sites during the polymeriza- tion. It is reasonable to assume that most existing slurry polymerization reactor processes can be easily adapted to use supported metallocene catalysts.

For homogeneous catalysts, the process of polymer particle formation generally leads to porous, low-density polymer particles which can cause a significant increase in the slurry viscosity and reactor fouling, leading to inadequate reactor temperature control. Addition- ally, polymer particles with poor powder properties are undesirable for post-reactor poly- mer processing. These problems must be addressed before using soluble metallocene catalysts for the industrial production of polyolefins.

7.3. Solution processes

Solution processes are especially adequate for the production of polyolefins containing long chain branches. Presently, two industrial solution processes are being used to produce polyethylene: Dow Chemical’s INSITE process and Exxon’s EXACT process. These pro- cesses can produce polyolefins with novel properties due to the controlled incorporation of long chain branches in a homo- or copolymer backbone. These processes were discussed at length in Section 6.

8. SUMMARY

A review of metallocene catalysts and their effects on polymer process engineering for the manufacture of polyolefins has been made. It has been stated156 that for a new technol- ogy to have a revolutionary impact, certain criteria must be satisfied. One of the criteria concerns the adaptability of existing manufacturing facilities to the new technology with small capital investment. Metallocene catalysis satisfies this requirement. Metallocene catalyst systems are operative in all existing industrial plants that are presently used for polyolefin manufacture. This includes facilities which use slurry, gas-phase and solution processes, and at polymerization temperatures which cover all catalyst types presently employed, such as heterogeneous titanium-based Ziegler-Natta and chromium oxide catalysts.

The effect of metallocene catalysis on the manufacture of polymers others than poly- olefins will likely be significant, but evolutionary. Most of these polymer types are now manufactured using free-radical polymerization and adaptation of existing production facilities for metallocene catalysis may require significant capital investment. In some cases, the polymerization process, such as emulsion polymerization with water as the

Page 54: Review João Soares

704 A. E. HAMIELEC and J. B. P. SOARES

continuous phase, may not be adaptable because of the adverse effect of water on the metallocene catalyst system. An outstanding example, where metallocene catalysis has permitted the synthesis of new polymers from a non-olefinic monomer for the first time ever, is the synthesis of highly syndiotactic polystyrene. At present, atactic polystyrenes are produced commercially by free-radical polymerization and these polymers are classified as thermoplastics with a glass-transition temperature near 100°C. Syndiotactic polystyrene is classified as a semi-crystalline engineering plastic with a melting temperature of 270°C with high heat resistance and excellent chemical resistance.‘57 This is a good example of the extraordinary ability of designed metallocene catalyst systems to control molecular structure of growing chains. No doubt, in the near future, other important examples of the polymerization of non-olefin monomers to obtain polymer chains with unique molecular structures and outstanding end-use properties will be published.

1. 2. 3. 4. 5. 6.

7.

8. 9.

10. 11.

12.

13. 14. 15. 16. 17. 18.

19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38.

REFERENCES

J. C. Johnson, MetuZlocene Technology, Noys Data Corporation, New Jersey (1973). V. K. Gupta, S. Satish and I. S. Bhardwaj, J.M.S. --Rev. Mucromol. Chem. Phys., C34 (3), 439 (1994). J. Huang and G. L. Rempel, Prog. Polym. Sci., 20,459 (1995). S. S. Reddy and S. Sivaram, Prog. Polym. Sci., 20,309 (1995). J. B. P. Soares and A. E. Hamielec, Polym. React. Engng, 3 (2), 131 (1995). H. G. Elias, Ulmann’s Encyclopediu of Industrial Chemistry (B. Elvers, S. Hawkins and G. Schultz Eds), Vol. A20, p.543, VCH Publishers, New York (1992). K. S. Whiteley, T. G. Heggs, H. Koch, R.-L. Mawer and W. Immel, Ulmann’s Encyclopedia of Industrial Chemistry (B. Elvers, S. Hawkins and G. Schultz Eds), Vol. A21, p.487, VCH Publishers, Weinheim (1992). J. Boor Jr, Ziegler-Natta Catalysts and Polymerization, Academic Press, New York (1979). W. Cooper, Chemical Kinetics (C. H. Bamford and C. F. H. Tipper Eds), Vo1.15, p.133, Elsevier, New York (1976). P. L. T. Tait, Comprehensive Polymer Science (Sir G. Allen Ed.), Vol. 4, p. 1, Pergamon Press, Oxford (1989). P. Corradini, V. Busico and G. Guerra, Comprehensive Polymer Science (Sir G. Allen Ed.), Vol. 4, p. 29, Pergamon Press, Oxford (1989). J. P. Colhnan, L. S. Hegedus, J. R. Norton and R. G. Finke, Principles and Applications of Organotransition Metal Chemistry, University Science Books, Mill Valley, CA (1987). T. J. Kealy and P. J. Pauson, Nature (London), 168, 1039 (1951). S. A. Miller, J. A. Tebboth and J. F. Tremaine, J. Chem. Sot. 632 (1952). G. Wilkinson, M. Rosenblum, M. C. Whiting and R. B. Woodward, J. Am. Chem. Sot., 74, 2125 (1952). D. S. Breslow and N. R. Newburg, J. Am. Chem. SOL, 79,5072 (1957). D. S. Breslow and N. R. Newburg, J. Am. Chem. SOL, 81, 81 (1959). K. H. Reichert, Transition Metal Catalyzed Polymerization (R. P. Quirk Ed.), Vol. 4, p. 465, Harwood, New York (1983). E. Giannetti, G. M. Nicoletti and R. Mazzocchi, J. Polym. Sci.: Polym. Chem. Ed., 23,2117 (1985). K. H. Reichert and K. R. Meyer, Mahromol. Chem., 169,163 (1973). H. Sinn and W. Kaminsky, Adv. Organomet. Chem., l&99 (1980). R. F. Jordan, C. S. Bajgur, R. Willett and B. Scott, J. Am. Chem. Sot., 108,741O (1986). R. F. Jordan, J. Chem. Ed., 65 (4), 285 (1988). S. Y. Lai, J. R. Wilson, G. W. Knight, J. C. Stevens and P. W. S. Chum, U.S. Patent 5,272,236 (1993). S. Y. Lai, J. R. Wilson, G. W. Knight and J. C. Stevens, U.S. Patent Application WO 93108221 (1993). K. W. Swogger and C. I. Kao, Polyolefins VII, SPE RETEC, p. 14, Houston, 22-24 Feb. (1993). J. C. Randall, Polymer Sequence Distribution. Carbon-13 NMR Method, Academic Press, New York (1977). W. Kaminsky and R. Steiger, Polyhedron, 7 (22/W), 2375 (1988). J. C. W. Chien and B. P. Wang, .I. Polym. Sci.: Part A: Polym. Chem., 26,3089 (1988). F. R. W. P. Wild, L. Zsolnai, G. Huttner and H. H. Brintzinger, J. Organomet. Chem., 232,233 (1982). W. Kaminsky, M. Miri, H. Sinn and R. Woldt, Mahromol. Chem. Rapid Commun., 4,417 (1983). W. Kaminsky, K. Kulper, H. H. Brimzinger and F. R. W. P. Wild, Angew. Chem. Int. Ed. Engi., 24 (6), 507 (1985). M. R. Mason, J. M. Smith, S. G. Bolt and A. R. Barron, J. Am. Chem. Sot., 115,497l (1993). M. Chang, Eur. Patent 308,177 (1989). H. Luker, U. S. Patent 5,023,388 (1991). P. M. Stricklen, U.S. Patent 5,064,797 (1991). H. C. Welbom Jr, U.S. Patent 5,001,244 (1991). L. Resconi, U. Giannini and E. Albizzati, U.S. Patent 5,126,303 (1992).

Page 55: Review João Soares

METALLOCENE CATALYSTS 705

39. C. C. Crapo and D. B. Malpass, U.S. Parenr 5,086,024 (1992). 40. W. Kaminsky, CutulyticPolymerizution of Olefins (T. Keii and K. Soga Eds), p. 225, Kodansha-Elsevier, Tokyo (1986). 41. W. Kaminsky, Catalysis Sot. Japan, 33 (S), 536 (1991). 42. J. C. W. Chien and A. Razavi, J. Polym. Sci.: Part A: Polym. Gem., 26,2369 (1988). 43. W. Kaminsky, Cutalytic Polymerization of Olejns (T. Keii and K. Soga Eds), p. 293, Kodansha-Elsevier, Tokyo (1986). 44. W. Kaminsky and H. Luker, Makromol. Chem. Rapid Commun., 5,225 (1984). 45. J. B. P. Soares and A. E. Hamielec, Polymer, in press (1995). 46. W. Kaminsky, K. Kulper and S. Niedoba, Mukromol. Chem., Macromol. Symp., 3, 377 (1986). 47. W. Kaminsky and M. Scholobohm, Mukromol. Chem., Mucromol, Symp., 4, 103 (1986). 48. J. Koivumlki and J. V. Seppala, Eur. Polym. J., 30 (lo), 1111 (1994). 49. J. V. Seppala, J. Koivumlki and X. Liu, J. Polym. Sci.: Part A: Polym. Chem., 31,3447 (1993). 50. K. D. Hungenberger, J. Kerth, F. Langhauser, H. J. Muller and P. Muller, Angew. Mukromol. Chem., 227,159 (1995). 51. R. Fierro, J. C. W. Chien and M. D. Rausch, J. Polym. Sci.: Part A: Polym. Chem., 32,2817 (1994). 52. J. A. Ewen, J. Am. Chem. Sot., 106,6355 (1984). 53. A. Grassi, A. Zambelli, L. Resconi, E. Albizatti and R. Mazzocchi, Macromolecules, 21,617 (1988). 54. A. Zambelli and P. Ammendola, Transition Metals und Orgunometallics us Catalysts for Olefin Polymerization (W.

Kaminsky and H. Sinn Eds), p. 329, Springer-Verlag, Berlin (1988). 55. F. R. W. P. Wild, M. Wasiucionek, G. Huttner and H. H. Brintzinger, J. Orgunomet. Chem., 288,63 (1985). 56. H. N. Cheng and J. A. Ewen, Mukromol. Chem., 190,193l (1989). 57. K. Soga, T. Shiono, S. Takemura and W. Kaminsky, Mukromol. Chem., Rapid Commun., 8, 305 (1987). 58. J. C. W. Chien and R. Sugimoto, J. Polym. Sci.: Part A: Polym. Gem., 29,459 (1991). 59. J. C. W. Chien, Mukromol. Chem., Mucromol. Symp., 63, 209 (1992). 60. B. Rieger, X. Mu, D. T. Mallin, M. D. Rausch and J. C. W. Chien, Macromolecules, 23,3559 (1990). 61. D. Fischer and R. Mulhaupt, Mucromol. Chem. Phys., 195, 1433 (1994). 62. W. Kaminsky and M. Bushermohle, Recent Advances in Mechanistic and Synthetic Aspects of Polymerization (M.

Fontanille and A. Guyot Eds), p. 503, D. Reidel Publishing Company (1987). 63. T. Tsutsui, N. Ishimaru, A. Mizuno, A. Toyota and N. Kashiwa, Polymer, 30, 1350 (I 989). 64. T. Tsutsui, A. Mizuno and N. Kashiwa, Makromol. Chem., 190,1177 (1989). 65. J. A. Ewen, R. L. Jones, A. Razavi and J. D. Ferrara, J. Am. Chem. Sot., 110,6255 (1988). 66. Z. Yu and J. C. W. Chien, J Polym. Sci.: Part A: Polym. Chem., 33, 1085 (1995). 67. D. T. Mallin, M. D. Rausch, Y. G. Lin, S. Dong and J. C. W. Chien, J. Am. Chem. Sot., 112,203O (1990). 68. J. C. W. Chien, G. H. Llinas, M. D. Rausch, G. Y. Lin, H. H. Winter, J. L. Atwood and S. G. Bott, J. Am. Chem. Sot.,

113,8569 (1991). 69. W. Kaminsky, A. Bark, R. Spiehl, N. Moller-Lindenhof and S. Niedoba, Transition Metals und Orgunometullics us

Catalysts for Olefin Polymerization (W. Kaminsky and R. Sinn Eds), p.291, Springer-Verlag, Berlin (1988). 70. W. Kaminsky, A. Bark and M. Amdt, Mukromol. Chem., Mucromol. Symp., 47, 83 (1991). 71. H. Drogemiiller, K. Heiland and W. Kaminsky, Trunsition Metals and Orgunometallics us Catalysts for Olefin Poly-

merization (W. Kaminsky and H. Sinn Eds), p. 303, Springer-Verlag, Berlin (1988). 72. J. Koivumiki, G. Fink and J. V. Seppiila, Macromolecules, 27,6254 (1994). 73. W. Kaminsky and A. Bark, Polym. Int., 28, 251 (1992). 74. N. Ishihara, M. Kuramoto and M. Uoi, Macromolecules, 21,3356 (1988). 75. A. Zambelli, C. Pellecchia, L. Oliva, P. Long0 and A. Grassi, Mukromol. Chem., 192, 223 (1991). 76. P. Longo and A. Grassi, Mukromol. Chem., 191, 2387 (1990). 77. C. Pellecchia, A. Proto and A. Zambelli, Macromolecules, 25, 4450 (1992). 78. P. Aaltonen and J. Seppalill, Eur. Polym. J., 31 (l), 79 (1994). 79. P. Aaltonen and J. Seppalill, J. Eur. Polym., 31 (l), 683 (1994). 80. A. Zambelli, A. Proto, P. Long0 and P. Oliva, Macromol. Chem. Phys., 195,2623 (1994). 81. M. J. Elder, A. Razavi and J. A. Ewen, U.S. Patent 5,155,080 (1992). 82. J. C. W. Chien and B. Xu, Mukromol. Chem. Rapid Commun., 14, 109 (1993). 83. J. C. W. Chien, W. M. Tsai and M. D. Rausch, J. Am. Chem. Sot., 113,857O (1991). 84. P. Piccolrovazzi, P. Pino, G. Consiglio, A. Sironi and M. Moret, Orgunometullics, 9,3098 (1990). 85. I. M. Lee, W. J. Gauthier, J. M. Ball, B. Iyengas and S. Collins, Orgunometullics, 11, 2115 (1992). 86. A. Zambelli, P. Longo and A. Grassi, Macromolecules, 22,2186 (1989). 87. C. Janiak, B. Rieger, R. Voelkel and H. G. Braun, J. Polym. Sci.: PartA: Polym. Chem., 31,2959 (1993). 88. W. Kaminsky and F. Renner, Mukromol. Chem. Rapid Commun., 14,239 (1993). 89. K. Soga and M. Kaminaka, Mukromol. Chem. Rapid Commun., 13,221 (1992). 90. J. C. W. Chien and D. He, J. Polym. Sci.: Part A: Polym. Chem., 29, 1603 (1991). 91. M. Kaminaka and K. Soga, Makromol. Chem. Rapid Commun., 12,367 (1991). 92. M. Kaminaka and K. Soga, Polymer, 33 (5), 1105 (1992). 93. K. Soga and M. Kaminaka, Mukromol. Chem., 194,1745 (1993). 94. K. Soga, T. Shiono and H. J. Kim, Mukromol. Chem., 194,3499 (1993). 95. K. Soga and M. Kaminaka, Mucromol. Chem. Phys., 195, 1369 (1994). 96. K. Soga, H. J. Kim and T. Shiono, Mucromol. Chem. Phys., 195,3347 (1994). 97. K. Soga, T. Uozumi, M. Saito and T. Shiono, Mucromol. Chem. Phys., 195, 1503 (1994).

Page 56: Review João Soares

706 A. E. HAMIELEC and J. B. P. SOARES

98. C. Janiak and B. Rieger, Ang. Makromol. Chem., 215, 45 (1994). 99. Dow European Patent Application 0416815A2, August 30 (1990).

100. T. K. Woo, L. Fan and T. Ziegler, Organometallics, 13,2252 (1994). 101. J. B. P. Soares and A. E. Hamielec, Polymer, 36 (ll), 2257 (1995). 102. P. J. FIory, Principles of Polymer Chemistry, Cornell University Press, Ithaca (1953). 103. M. Sugawara, SPO ‘94, p. 37 (1994). 104. P. Brant, J. A. M. Kanich, D. A. Jay, R. L. Bamberger, G. F. Licciardi and P. M. Henrichs, PM International Patent

Application WO - 94/07930, 14 April, Exxon Chemical Patent Inc. (1994). 105. V. A. Zakharov, G. D. Bukatov and Y. F. Yermakov, Adv. Polym. Sci., 56,61 (1983). 106. P. J. T. Tait and N. D. Watkins, Comprehensive Polymer Science (Sir G. Allen Ed.), Vol. 4, p. 533, Pergamon Press,

Oxford (1989). 107. P. Cossee, Tetrahedron Lett., 17, 12 (1960). 108. P. Cossee, J. Catal., 3, 80 (1961). 109. J. Arlman, Proc. Int. Congr. Catal., 2,957 (1964). 110. M. Ystenes, J. Catal., 129, 383 (1991). 111. J. J. A. Dusseault and C. C. Hsu, J.M.S. -Rev. Macromol. Sci., C33 (2), 103 (1993). 112. M. Farina, G. Di Silvestro and A. Terragni, Macromol. Chem. Phys., 196,353 (1995). 113. A. E. Hamielec, J. F. MacGregor and A. Penlidis, Makromol. Chem., Macromol. Symp. lO/ll, 521 (1987). 114. L. Resconi, F. Piemontesi, G. Franciscono, L. Abis and T. Fiorani, J. Am. Chem. Sot., 114, 1025 (1992). 115. W. H. Ray, Transition Metal Catalyzed Polymerization (R. P. Quirk Ed.), p. 563, Harwood, New York (1988). 116. V. V. Vickroy, H. Schneider and R. F. Abbot, J. Appl. Polym. Sci., 50,551 (1994). 117. J. B. P. Soares and A. E. Hamielec, Macromol. Theory SimuL, 5,547 (1996). 118. J. B. P. Soares and A. E. Hamielec, Polym. React. Engng, 3 (3), 261 (1995). 119. W. H. Stockmayer, J. Chem. Phys., 13, 199 (1945). 120. R. Simha and H. J. Branson, Chem. Phys., 12,253 (1944). 121. J. C. J. F. Tacx, H. N. Linssen and A. L. German, J. Polym. Sci.: PartA: Polym. Chem., 26, 61 (1988). 122. J. B. P. Soares and A. E. Hamielec, Macromol. Theory SimuZ., 4,305 (1995). 123. H. Tobita and A. E. Hamielec, Polymer, 32, 2641 (1991). 124. L. Noristi, E. Marchetti, G. Barruzi and P. Sgarzi, J. Polym. Sci.: Part A: Polym. Chem., 32, 3047 (1994). 125. M. Kakugo, H. Sedatoshi, J. Sakai and M. Yokoyama, Macromolecules, 22,3172 (1989). 126. K. Y. Choi, X. Zhao and S. Tang, J. Appl. Polym. Sci., 53, 1589 (1994). 127. J. B. P. Soares and A. E. Hamielec, Macromol. Theory Simul., 4,108s (1996). 128. K. Soga, H. Yamagihara and D. E. Lee, Makromol. Chem., 190,995 (1989). 129. E. L. Hoel, C. Cozewith and G. D. Byrne, AZChE J., 40 (lo), 1669 (1994). 130. I. A. Jaber and G. Fink, Macromol. Chem. Phys., 195,249l (1994). 131. W. R. Schmeal and J. R. Street, AlChE J., 17, 1188 (1971). 132. M. Dub& J. B. P. Soares, A. Penlidis and A. E. Hamielec, Ind. Eng. Chem. Res., submitted (1996). 133. W. W. Graessley, Physical Properties of Polymers 2nd edition, American Chemical Society, Washington (1993). 134. F. Bonini, V. Fraaije and G. Fink, J. Polym. Sci.: Part A: Polym. Chem., 33,2393 (1995). 135. M. A. Ferrer0 and M. G. Chiovetta, Polym. Engng Sci., 31, 886 (1991). 136. P. GaIli and J. C. Haylock, Macromol. Chem., Macromol. Symp., 63, 19 (1992). 137. J. Kanetakis, F. Y. C. Wong, A. E. Hamielec and J. F. MacGregor, Chem. Engng Commun., 35, 123 (1985). 138. H. F. Hermann and L. L. Bohm, Polym. Commun., 32,58 (1991). 139. T. A. Witten and L. M. Sander, Phys. Rev. Lett., 47, 1400 (1981). 140. J. Koivumaki, M. Lahti and J. V. Sepplla, Angew. Makromol. Chem., 221, 117 (1994). 141. H. C. Wellbom Jr, U.S. Patent 5,183,867 (1993). 142. U. Zucchini and G. Cecchin, Adv. Polym. Sci., 51, 101 (1983). 143. S. Floyd, R. Heiskanen and W. H. Ray, Chem. Engng Prog., 84,56 (1988). 144. D. M. Bates and D. G. Watts, Nonlinear Regression Analysis and Its Application, Wiley, New York (1988). 145. G. H. Golub and V. Pereyra, SJAM J. Num. Anal., 10 (2), 413 (1973). 146. L. Wild, Adv. Polym. Sci., 98, 1 (1990). 147. J. M. Vela-Estrada and A. E. Hamielec, Polym. React. Engng, 1, 171 (1993). 148. J. B. P. Soares and A. E. Hamielec, Polymer, 36 (8), 1639 (1995). 149. P. J. Flory, J. Chem. Phys., 17, 223 (1949). 150. K. Soga, T. Uozumi, T. Arai and S. Nakamura, Macromol. Rapid Commun., 16,379 (1995). 151. J. Borrajo, C. Cordon, J. M. Carella, S. Toro and G. Goizereta, J. Polym. Sci.: Part B:PoZym. Phys., 33, 1627 (1995). 152. J. M. Vela-Estrada and A. E. Hamielec, Polymer, 19, 808 (1994). 153. F. Garbassi, L. Gila and A. Proto, Polymer News, 19,367 (1994). 154. F. Langhauser, J. Kerth, M. Kersting, P. Kolle, D. Lilge and P. Mttller, Makromol. Chem., 223, 155 (1994). 155. Chemical Engineering Progress, 20 July (1995). 156. K. B. Sinclair and R. B. Wilson, Chemistry and Industry, 21, 857 (1994). 157. T. H. Newman, R. E. Campbell and M. T. Malanga, Worldwide Metallocene Conf, Metcon ‘93,26-B May, Houston,

TX (1993). 158. G. W. Knight and S. Lai, Polyolefins VIII, SPE RETEC, p. 28, Houston, 22-24 Feb. (1993).