Investigation of the kinetics of ethylene polymerization

Investigation of the kinetics of ethylene polymerization

for the bi-component catalyst Cp*2NdCl2Li(OEt2)2/MgR2

Rui Miguel Tinoco Ruivo

Thesis to obtain the Master of Science Degree in

Chemical Engineering

Supervisors:

Prof.a Maria do Rosário Gomes Ribeiro

Dr. Christophe Boisson

Examination Committee

Prof José Manuel Félix Madeira Lopes, Chairperson

Prof.a Maria do Rosário Gomes Ribeiro, Supervisor

Dr. Jorge Alberto Vigário Moniz dos Santos, Member of the Committee

December, 2014

Acknowledgments

First of all, I would like to thank Dr. Jorge Moniz, for accepting to examine this work.

Many thanks also to Prof. Dr. José Madeira Lopes, chairperson of the jury.

I am extremely grateful to Dr. Christophe Boisson for having accepted me in his team,

for providing me with excellent conditions to carry out this research project, and for his

scientific advices. Thanks to your availability and patience especially during the

corrections of this dissertation. Particularly thanks to Dr. Franck D'Agosto for your

constructive remarks and comments you made during all the meetings we had.

I would like also to thank Sebastien Norsic and Benoit Macqueron for their teaching

skills on polymerization practice and their valuable assistance in the implementation of

the experimental setup and manipulations. On that matter I also want to appreciate the

help given by Islem Belaid and Manel Taam.

A big thanks to the LCPP team, from the Laboratory of Chemistry, Catalysis, Polymers

and Processes (C2P2 – UMR 5265), who received me well and that made my stay in

Lyon a great experience, especially to Bárbara Rezende, Anthony Palmeira, Thaíssa

Chaparro, Thiago Guimarães, Eliana Grant, Aarón Sanz and Leila Santos. Not

forgetting the Portuguese coworkers Andreia Nunes and Teresa Pinto from LCOMS

team.

Lastly but not least, I express my gratitude to Professor Rosário Ribeiro for introducing

me to this internship opportunity and for all the guidance given until the finalization of

this thesis.

iv

Abstract

This thesis is a contribution to the comprehension of the mechanism of a metallocene

bi-component, more particularly, the neodymium metallocene catalyst,

Cp*2NdCl2Li(OEt2)2/MgR2.

The first part of this work is dedicated to the acquisition of experimental data. For that,

polymerization reactions were performed, at 80 ºC and 3 bar of ethylene (relative

pressure), in order to obtain reliable data regarding the influence of the catalyst and

cocatalyst concentration on the reaction kinetics. Two types of polymerizations were

performed, one until precipitation of the polymer and the other until a specific molar

mass of polymer was produced. For all reactions apparent rate constant of propagation

reaction was determined, and the polymers with a target molar mass were analyzed by

SEC analysis.

The second part of this work focuses on the investigation of the effect of the addition of

dibutyl ether (Bu2O) as a base on the reaction solvent and of polymerizations

temperature (80, 70, 60 and 50 ºC) on the polymerization behavior. With respect to the

use of Bu2O, it was seen that the base interacts with the MgR2, changing the

equilibrium between the dormant magnesium and polymerization-active transition-

neodymium centers. As for the runs at different temperatures, these ones allowed the

determination of the energy of activation using the Arrhenius equation, obtaining a

value of 15.2 kcal mol-1.

In the third and last part of this work, it was carried out a polymerization reaction with

withdrawal of samples over time. The different polymers were analyzed by SEC

analysis, in order to follow the evolution of molar mass and dispersity ((Đ) over time

and to evaluate the pseudo-living character of these systems.

v

Resumo

Esta tese consiste numa contribuição para uma melhor compreensão de um sistema

bi-componente, mais precisamente, o catalisador metaloceno lantanídeo,

Cp*2NdCl2Li(OEt2)2/MgR2.

A primeira parte deste trabalho foi dedicada à aquisição de dados experimentais. Para

tal, foram feitas reacções de polimerização, a 80 ºC e 3 bars de etileno (pressão

relativa), de modo a obter dados fidedignos da influência da concentração de

catalisador e co-catalisador sobre a cinética da reacção. Foram realizados dois tipos

de polimerizações, uma até a precipitação do polímero e a outra até que uma massa

molar específica de polímero foi produzida. Para todas as reacções de polimerização

foi determinada a constante de velocidade aparente, e os polímeros onde foi obtida

uma específica massa molar, foram analisados por análise de SEC.

A segunda parte deste trabalho incidiu sobre a investigação da adição de éter

dibutílico, como base no solvente reaccional, bem como, outras temperaturas de

polimerização, 70, 60 e 50 ºC, no decorrer da polimerização. Em relação ao uso de

Bu2O verificou-se que a base interage com o MgR2, alterando o equilíbrio entre a

espécie adormecida de magnésio e centros de transição de polimerização com

neodímio-activo. Os ensaios a diferentes temperaturas de polimerização permitiram a

determinação da energia de activação, através da equação de Arrhenius, tendo-se

obtido o valor de 15.2 kcal / mol.

Na terceira e última parte deste trabalho, foi realizada uma reacção de polimerização

com extracção de amostras ao longo do tempo. As diferentes amostras de polímero

foram analisados pela análise SEC, a fim de monitorizar a evolução da massa molar e

a dispersividade (Đ) ao longo do tempo e para avaliar o carácter pseudo-vivo destes

sistemas.

vi

Contents

Abstract ....................................................................................................................... iv

Resumo ........................................................................................................................ v

Contents ...................................................................................................................... vi

List of figures ............................................................................................................... ix

List of tables ............................................................................................................... xii

Nomenclature ............................................................................................................ xiii

Introduction ................................................................................................................. xv

Chapter I - Literature Review ..................................................................................... 1

1. Polyolefins .......................................................................................................... 2

1.1. General aspects .......................................................................................... 2

1.2. Polyolefins Production ................................................................................. 3

1.3. Polymerization Catalysis ............................................................................. 6

1.3.1. Ziegler-Natta Catalysts ......................................................................... 7

1.3.2. Phillips Catalysts .................................................................................. 8

1.3.3. Metallocenes Catalysts ........................................................................ 9

1.3.4. Late Transition Metal .......................................................................... 10

1.3.5. Conclusion ......................................................................................... 10

2. Single-site catalysts.......................................................................................... 11

2.1. Cocatalyst (Activator) ................................................................................ 11

2.2. Catalyzed chain growth ............................................................................. 13

2.3. System Cp*2NdCl2Li(OEt2)2 / MgR2 ............................................................ 15

vii

Chapter II - Experimental Section ............................................................................ 17

1. Materials .......................................................................................................... 18

1.1. Solvents (Toluene, THF, Heptane) ............................................................ 18

1.2. Ethylene .................................................................................................... 19

1.3. Cp*2NdCl2Li(OEt2)2 .................................................................................... 20

1.4. BOMAG, Butyl(octyl)magnesium ............................................................... 20

1.5. Dibutyl ether .............................................................................................. 21

2. Experimental Set up ......................................................................................... 21

3. Inert atmosphere .............................................................................................. 26

4. Ethylene Polymerization ................................................................................... 28

5. Polymer Analysis .............................................................................................. 30

Chapter III - Results and Discussion ....................................................................... 19

1. Calculations Review ......................................................................................... 32

2. Monitoring the consumption of ethylene ........................................................... 34

3. Treatment and Discussion of Results ............................................................... 36

3.1. Investigation of different concentration ratios of bimetallic system ............. 37

3.2. Apparent rate constant of propagation reaction (𝑘𝑝𝑎𝑝𝑝) for different

reactions .............................................................................................................. 41

3.3. Investigation of the addition of bases, Bu2O .............................................. 45

3.4. Investigation of the energy of activation .................................................... 47

3.5. Sample extraction investigation during polymerization trial ........................ 51

3.5.1. Pseudo-living character ...................................................................... 51

viii

Chapter IV - Conclusions and Perspectives ........................................................... 19

Chapter V - References ............................................................................................ 62

Chapter VI - Appendices .......................................................................................... 67

Appendix A.1 – BOMAG Specification Sheet........................................................... 68

Appendix A.2 – Dibutyl ether Specification Sheet .................................................... 69

Appendix A.3 – Experimental polymerization procedure .......................................... 70

Appendix B.1 – Solubility of Ethylene in Toluene ..................................................... 72

Appendix B.2 – Linear regressions .......................................................................... 73

Appendix B.3 – Determination of theoretical molar mass and experimental number of

polyethylene chains per magnesium ....................................................................... 79

Appendix B.4 – Comparison between the productivity values with and without sample

withdrawn ................................................................................................................ 80

ix

List of figures

Figure 1: Processes for Olefin Polymerization .............................................................. 3

Figure 2: Coordination of the monomer ....................................................................... 6

Figure 3: Insertion of the monomer in the metal-carbon bond ..................................... 6

Figure 4: Successive steps of coordination and insertion ............................................. 6

Figure 5: Structure of group 4 metallocene complex Cp2MX2 (M = Ti, Zr, Hf) ............... 9

Figure 6: Activation of the metallocene complex Cp2ZrMe2 with MAO ........................ 11

Figure 7: Lanthanide metallocene general structure .................................................. 12

Figure 8: Basic reaction steps of CCG using MgR2 chain as transfer agent (CTA); M,

metal; L, ligand; P, polymer chain; R, alkyl group; H, hydrogen .................................. 13

Figure 9: Nd catalyzed polyethylene chain growth on magnesium ............................. 14

Figure 10: Termination mechanism, β-H transfer ....................................................... 14

Figure 11: Postulated mechanism for chain growth on dialkylmagnesium [31] ............. 15

Figure 12: Purification system solvent ........................................................................ 18

Figure 13: Gas and solvent flow throughout the system ............................................. 19

Figure 14: Butyloctylmagnesium in heptane ............................................................... 20

Figure 15: Experimental Set up .................................................................................. 21

Figure 16: Reactor ..................................................................................................... 22

Figure 17: Cartridge connected to the reactor ............................................................ 23

Figure 18: Ethylene’s reservoir .................................................................................. 23

Figure 19: Two stage rotary pump and Power Control-Visc Stirrer ............................. 24

Figure 20: SPY RF® Wireless System ....................................................................... 24

Figure 21: Syrius stockage software .......................................................................... 25

x

Figure 22: Air free techniques .................................................................................... 26

Figure 23: Introduction of the catalyst solution ........................................................... 28

Figure 24: Filtration and drying of the polymer ........................................................... 29

Figure 25: GPC system from Viscotek ....................................................................... 30

Figure 26: Temperature and pressure profile obtained using the “Sirius, Stockage”

software. ..................................................................................................................... 34

Figure 27: Activity and Productivities profiles obtained at 50 µM of neodymium and

with various amounts of MgR2 ..................................................................................... 38

Figure 28: Molar mass distribution of the polymer (50 µM Nd and 8 mM of MgR2) ..... 39

Figure 29: Activity and Productivities profiles obtained for 4 and 8 mM of MgR2 for 50,

80 and 100 µM of neodymium..................................................................................... 40

Figure 30: Activity and Productivities profiles obtained at several concentrations of

Bu2O ........................................................................................................................... 45

Figure 31: Activity and Productivities profiles obtained for several temperatures of

polymerization............................................................................................................. 47

Figure 32: Arrhenius plot of ln(k) versus T −1 .............................................................. 49

Figure 33: Activity profile obtained at 50 µM and 8 mM of MgR2 for polymerization

perform with and without withdrawal system ............................................................... 52

Figure 34: Number average molar mass over time theoretical and experimental over

productivity ................................................................................................................. 53

Figure 35: Productivities profiles obtained at 50 µM and 8 mM of MgR2 for both

polymerizations perform with and without withdrawal system ...................................... 54

Figure 36: Molar mass distribution of the several samples extracted during

polymerization............................................................................................................. 56

Figure 37: Number average molar mass over time .................................................... 56

xi

Figure 38: Inverse of the degree of polymerization over the inverse of time plot ........ 57

Figure 39: Linear regression of the productivity over time (50 µM Cp*2NdCl2Li(OEt2)2,

0.4 mM MgR2) ............................................................................................................. 73


0.8 mM MgR2) ............................................................................................................. 73

Figure 41: Linear regression of the productivity over time (50 µM Cp*2NdCl2Li(OEt2)2, 2

mM MgR2)................................................................................................................... 74


mM MgR2)................................................................................................................... 74


mM MgR2)................................................................................................................... 75


16 mM MgR2) .............................................................................................................. 75


mM MgR2)................................................................................................................... 76


mM MgR2)................................................................................................................... 76


4 mM MgR2) ................................................................................................................ 77


4 mM MgR2) ................................................................................................................ 77

Figure 49: Linear regression of the productivity over time for different concentration of

Bu2O ........................................................................................................................... 78

Figure 50: Linear regression of the productivity over time for the different

polymerization’s temperature ...................................................................................... 78

xii

List of tables

Table 1: Characteristics of the different techniques for olefin polymerization ................ 4

Table 2: Conditions of each polymerization process ..................................................... 4

Table 3: Ethylene content specification ...................................................................... 19

Table 4: [MgR2] / [Cp*2NdCl2Li(OEt2)2] ratios investigated ......................................... 37

Table 5: Results for polymerization reactions ............................................................. 42

Table 6: Polymers results obtain on the several polymerization trials ......................... 43

Table 7: Polymerization trials with and without Bu2O .................................................. 46

Table 8: Polymerization trials at different temperatures .............................................. 48

Table 9: Kinetic results for each polymerization .......................................................... 49

Table 10: Results of all the samples extracted during polymerization ......................... 53

Table 11: Sample results taken during the polymerization trial ................................... 55

Table 12: Productivity (mol PE mol Nd-1) data for both polymerizations ...................... 80

xiii

Nomenclature

Acronyms

BOMAG butyl(octyl)magnesium

Bu2O dibutyl ether

CCG catalyzed chain growth

CCTP coordinative chain transfer polymerization

CSTR continuous stirred-tank reactor

CTA chain transfer agent

DEAC diethyl aluminum chloride

FBR fluidized bed reactor

HDPE high density polyethylene

HSBR horizontal stirred bed reactor

LDPE low density polyethylene

LLDPE linear low density polyethylene

MAO methylaluminoxane

MWD molecular weight distribution

PDI polydispersity index

PE polyethylene

PP polypropylene

iPP isotactic polypropylene

sPP syndiotactic polypropylene

aPP atactic polypropylene

SEC size exclusion chromatography

THF tetrahydrofuran

TEA triethyl aluminum

TMA trimethyl aluminum

xiv

Symbols

C catalyst precursor

C∗ active site

[𝐶0] initial concentration of active sites

Đ dispersity

𝐸𝑎 energy of activation

𝑘𝑝 rate constant of propagation reaction

𝑘𝑝𝑎𝑝𝑝

apparent rate constant of propagation

𝑘𝑡 irreversible transfer constant

𝑀 molar mass

M monomer

𝑀n number average molar mass

𝑀𝑤 weight average molar mass

𝑀0 monomer molar mass

n number of long-chain branches per chain

𝑃𝑛 number-average degree of polymerization

R gas constant

𝑟𝑝 propagation rate

t time

T temperature

[Y0] total concentration of active sites or living polymer chains

xv

Introduction Scope & Aim

In the field of olefin polymerization there is a wide variety of catalysts structures that

are able to efficiently polymerize olefins. Among them, lanthanide metallocenes display

an unique behavior towards transfer reactions to main group organometallic

compounds such as AlR3, MgR2, or ZnEt2. Such chain transfer reactions can be very

fast and sometimes reversible. In this particular case and in absence of any other

detectable transfer reaction, the polymerization is then best described as pseudo living

since the polymers produced display a remarkably narrow molar mass distribution and

molar masses increasing linearly with productivity. This technique of polymerization

based on a degenerative chain transfer is based on the formation of a heterobimetallic

intermediate [𝐶𝑝∗

2𝐿𝑛𝑅 − 𝑀𝑔𝑅2] which is a dormant species in equilibrium with the active

propagating species.

Because of the increasing importance of this unique technique for controlled olefin

polymerization, the main objective of this work is to better understand the catalytic

behavior of these lanthanide complexes and what are the main parameters that may

affect the pseudo living character. For that the influence of distinct experimental

parameters, such as catalyst and cocatalyst concentration, polymerization temperature

and addition of bases to polymerization media were investigated.

Outline of the Manuscript

The manuscript comprises five chapters, organized as follows.

Chapter I offers an up-to-date bibliographic review of the aspects of polymerization

most relevant to this work.

Chapter II deals with the experimental part of this work, which goes from techniques of

polymerization, experimental set up, and polymer synthesis to polymer

characterization.

Chapter III contains the results and discussion of the different polymerizations

performed. Different methodologies and treatments were used in order to determine

the kinetic parameters for the bi-component catalyst Cp*2NdCl2Li(OEt2)2/MgR2, such as

apparent rate constant of propagation reaction, and energy of activation as well as to

evaluate its pseudo living character.

Chapter IV reports the conclusions and future prospective of this study, and finally,

Chapter V and VI contain the references and the appendices, respectively, to fully

comprehend this work.

Chapter I - Literature Review

2


1. Polyolefins

1.1. General aspects

Polyolefins are synthetic polymers, produce from simple olefin monomers like ethylene

and propylene, and with a wide range of applications as plastics materials such as

grocery bags, containers, toys, adhesives, automotive parts, among others. The simple

connection between the monomer molecules in the polymer chain defines the

molecular architecture of the polyolefin. By changing how ethylene, propylene, and

higher α-olefins, are bound in the polymer chain, it’s possible to produce different types

of polymers of Polyethylene (PE) and Polypropylene (PP).

In 2013, polyolefins represented near 60 % of the production of plastic materials, with a

production of 75 millions of tonnes for PE and 50 millions of tonnes for PP (mostly

isotactic).[1]

The physical properties of the plastics, such as crystallinity (density), molar mass and

melting temperature, are dependent on the catalysts and polymerization processes

used.

Polyolefins can be divided in two main types, polyethylene and polypropylene. On the

other hand, polyethylene can be divided in three main families, [2]

depending on its

physical properties and the number and type of chain branching:

Low Density Polyethylene (LDPE): PE with numerous long and short

chain branching. Density in the range of 0.910 - 0.940 g cm-3

Linear Low Density Polyethylene (LLDPE): PE with only short chain

branching. Density in the range of 0.915 - 0.940 g cm-3

High Density Polyethylene (HDPE): PE with only few short chain

branching. Density in the range of 0.941 - 0.97 g cm-3

Regarding polypropylene homopolymers, there main types can be defined based on

the orientation of each methyl group relative to the methyl groups on the neighboring

monomer. The different orientation will strongly influence the crystallization ability of the

polymer.

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The different products classes are: [2]

Isotactic Polyproylene (iPP): The methyl groups are consistently on one

side, and consequently the product is highly crystalline and stiff. This

type is the most produced in industry’s.

Syndiotactic PolyPropylene (sPP): The methyl groups are arranged

alternately to one or the other polymer chain side, also giving a quite stiff

material.

Atactic PolyPropylene (aPP): The methyl groups are arranged randomly

along the polymer chain, making the polymer amorphous.

The type of product obtained is directly related to the polymerization process as well to

the catalytic system used in the manufacture. These processes are going to be

described in the following part.

1.2. Polyolefins Production

The main polymerization processes in polyolefins production falls into two categories,

showed in the Figure 1, [4] and described below. [3]

Polymerization Processes

High Pressure Free Radical

Polymerization (LDPE)

Catalytic Polymerization

(LLDPE, HDPE, PP)

Solution

Slurry

Gas

Figure 1: Processes for Olefin Polymerization

4


For industrial applications, the polyethylene is made through the use of radical initiators

and high pressure polymerization, or by coordination catalysts, low pressure

polymerization, while polypropylene is produced only by coordination catalysts.

Coordination catalysts can control more efficiently the polymer microstructure than

radical initiators. The first ones are used to produce polyolefins with wide

microstructures.

In the table 1 are described some characteristics of each polymerization technique. [5]

Table 1: Characteristics of the different techniques for olefin polymerization

High pressure polymerization Low pressure polymerization

Produces LDPE Produces LLDPE and HDPE

Operating pressure ranging from 1000 to

3000 barg

Operating pressure ranging from 10 to 80

barg

Operating temperature from 80 to 300 oC Operating temperature from 70 to 300 oC

Autoclave or tubular reactor FBR, Loop reactor or CSTR

Free radical using initiators (peroxides) 3 types of catalysts can be used:

Ziegler-Natta

Phillips

Metallocene

Ethylene compression to the reaction

pressure through several compression

stages with inter stage cooling is a major

step

Moreover, the catalytic polymerization processes, can be distinguished by the type of

the phase of the continuous medium: solution, slurry or gas phase. Table 2 [3] shows

the main characteristics of each process them. Next will be described this processes.

[6]

Table 2: Conditions of each polymerization process

Polymerization Process Solution Slurry Gas

Temperature (oC) 130 - 300 85 - 110 70 - 120

Pressure (bar) 40-200 10- 45 20 - 30

Catalyst Homogeneous Heterogeneous

Density (g/cm3) 0.86 - 0.96 0.93 - 0.97 0.91 - 0,97

Reactor CSTR CSTR, Loop FBR, CSTR, HSBR

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In the solution process (liquid phase), both catalyst and resulting polymer remain

dissolved in a solvent that must be removed to isolate the polymer. The polymer is

made with a homogeneous catalyst, producing generally low molar mass distribution.

In slurry processes, catalyst and polymer formed during production remains suspended

in the liquid medium undissolved. The solid catalyst and the polymer particles are

dispersed in the continuous phase containing the dissolved monomer.

Slurry reactors are typically equipped with a cooling jacket in order to remove the heat

generated by the reaction. Since, the olefin polymerization is highly exothermic process

and a poor heat removal could lead to formation of hot spots inducing local particle

overheating and even fouling on the reactor wall.

At last, at gas phase processes, the monomer is introduced under pressure into a

reaction vessel containing a polymerization catalyst. Once polymerization begins,

monomer molecules diffuse to the growing polymer chains.

This work will be focused on the catalytic polymerization of ethylene in a solution

process.

6


1.3. Polymerization Catalysis

Polymerization using coordination catalysts involves two main steps: i) coordination of

the monomer, on the active transition metal, followed by ii) insertion of the monomer in

the metal-carbon bond.

The step of coordination is responsible for the versatility of these catalysts, since the

inlet monomer needs to coordinate with the active center of the transition metal, before

the insert takes place.

[M] R

[M] R

n+1

n

R

[M]

R

[M]

Figure 2: Coordination of the monomer

Figure 3: Insertion of the monomer in the metal-carbon bond

Figure 4: Successive steps of coordination and insertion

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The polymerization catalyst can be solid, soluble or colloidal, and can be classified in

supported or unsupported.

While unsupported catalysts are normally very active, supported catalyst requires a

high surface area support to disperse the primary catalyst. The support may also act

as a co-catalyst or secondary catalyst for the reaction.

Also, catalysts can be one of two physical types. Homogeneous, in which catalyst are

dissolved in the reaction mixture, or heterogeneous, where the catalyst consists of a

solid phase separate from and insoluble in the reaction mixture. Both types are

represented on the industrial scene, but the latter are much more common.

Currently four families of catalysts are used in industrial polymerization by insertion:

Ziegler – Natta, Phillips, Metallocene and post-metallocene including late transition

metals catalysts.

Each class of catalysts provides the manufacture of polyolefins with distinct

microstructural characteristics that are adequate for different applications.

Next will be described the different families of catalysts.

1.3.1. Ziegler-Natta Catalysts

Ziegler-Natta catalysts were discovered in the early fifties by Karl Ziegler and Giulo

Natta (Z-N).

These catalysts are composed of a transition metal salt of metals from groups 4 to 8

(pre-catalyst) and a metal alkyl of a base from groups 1, 2 and 13 (cocatalyst). The

most common transition metals used are titanium, zirconium and vanadium. [7]

Regarding the cocatalyst, the most used are organometallic components such as

trimethyl aluminum (TMA), triethyl aluminum (TEA), diethyl aluminum chloride (DEAC),

or TriIsoButylAluminum (TIBA). The nature of the cocatalyst will influence the activity

and also the polymer properties.

8


Ziegler-Natta catalysts can be heterogeneous or homogeneous. Homogeneous

Ziegler-Natta catalysts are generally, but no exclusively, vanadium based and is used

to produce ethylene-propylene-diene (EPDM) elastomers.

Since their discovery, Z-N have undergone several distinct form of “evolution”, and

currently are being used the fifth generation of Z-N catalysts, with typical productivities

of 100 - 130 Kg PP / g catalyst [8]

contrary to the first generation which allowed only 2 -

4 Kg PP / g catalyst.

The most common type of heterogeneous Ziegler-Natta catalyst is TiCl4 supported on

MgCl2 or SiO2/MgCl2. However the insertion of ethylene in this complex is not

energetically favorable, because the M-Cl bond is stronger than the M-C bond. The

solution found was to add a cocatalyst (typically AlEt3), allowing an exchange of one

chlorine, forming TiCl3Et, making it possible the insertion of the ethylene. During the

reaction, different oxidation states can be achieved and consequently different actives

sites can be formed on the surface of a same particle.

1.3.2. Phillips Catalysts

Phillips catalysts were discovered in 1950 by Hogan and Blanks. They are constituted

of either chromium oxide (CrOx) or a vanadium oxide (VOx) impregnated on silica, and

only exists in heterogeneous form. It is mainly used to produce HDPE and can only

insert very small amounts α-olefins. [9]

One of the advantages and particularities of this system is that there is no need of a

cocatalyst because the catalyst is activated by calcination at high temperatures (200 -

900 oC). [10]

HDPE made with Phillips catalysts have a very broad MWD, often with PDIs of 10 or

higher, which can be controlled by support selection and calcination conditions before

the polymerization. Such broad MWDs point to the existence of several types of active

sites on the surface of Phillips catalysts, which mean that the produced polymers will

have a broad molar mass distribution. Despite the simple system, which makes it

economical, the catalyst can be difficult to use because its sensitivity to impurities.

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1.3.3. Metallocenes Catalysts

A metallocene is a compound typically consisting of two cyclopentadienyl anions (Cp =

C5H5, which is C5H5-) bound to a metal center (M) in the oxidation state II, with the

resulting general formula (C5H5)2M.[11]

By extension its used the term of metallocene

for metal complexes supported by two cp ligands, such as, group 4 metallocene

(Cp2MX2), shown in the figure 5.

Figure 5: Structure of group 4 metallocene complex Cp2MX2 (M = Ti, Zr, Hf)

These catalysts were mainly developed in the 1980’s, after the discovery of

methylaluminoxane, which is a fantastic activator. What distinguished metallocenes

from the Ziegler-Natta and Phillips are their well-defined structure, their high activity,

and above all, their control of the polymer properties. [12]

The main difference compared to the others is that during the activation step only one

degree of oxidation can be reached theoretically in these sterically hindered molecules

and consequently only one type of active sites can be formed. This property has

conferred them the designation of “single-site” catalysts. This topic will be discussed

later in this chapter.

All olefin polymerization processes described in the subchapter 1.2 can be operated

commercially with metallocene catalysts. Metallocene can be used directly in solution

processes, but need to be supported to be used in slurry and gas-phase (which

represented 70% of the total industrial polyolefin production). [1]

M

http://en.wikipedia.org/wiki/Cyclopentadiene

http://en.wikipedia.org/wiki/Anion

10


Since slurry and gas-phase reactors require morphologically uniform catalyst particles

that can be continuously fed to the reactor, soluble metallocene complexes must be

fixed onto insoluble carriers before they can be used in these processes. It is crucial

that the characteristics of the catalyst, such as, structure, comonomer reactivity and

stereoselectivity, be maintained after supporting.

1.3.4. Late Transition Metal

Late transition metal catalysts for olefin polymerization were discovered by Brookhart

and researchers from DuPont in the early 1990s. [13]

These complexes are much less

oxophilic than Ziegler-Natta, Phillips, or metallocene catalysts, allowing the

copolymerization of olefins and polar comonomers such as vinyl acetate and methyl

metacrylate.

The literature on late transitional metal catalysts is very large and keeps growing as

new complexes are developed. Several families have been developed such as

Brookhart (Ni and Pd), Gibson-Brookhart (Co and Fe), and Grubbs (neutral Ni)

catalysts.

Despite being much less sensitive to polar compounds and the fact that can be used to

copolymerize olefins with polar monomers, these catalysts have not found commercial

applications.

1.3.5. Conclusion

Of the several families of catalysts discussed above, there are many factors that

oriented the research focus on the metallocene catalyst. Such as high productivity of

the catalyst, narrow molar mass distribution, better comonomer distribution.

These factors are the reasons why in this work, the family of catalyst studied is

metallocene. In the next section will be discussed in detailed the catalyst used, as well

as, details of its activation.

IST December,

11

2. Single-site catalysts

Over the years researchers try to prove that metallocene could be used for the

ethylene polymerization. First attempts pursuing that goal were first made by Breslow

et al. [14]

These authors found that when using small impurities of oxygen present in

ethylene (0,003 to 0.025 mol%), activity increased approximately by ten (2600 g/molTi/h

to 35 000 g/molTi/h). Later on, Reichert and Meyer, [15]

proved that the polymerization

activity could be enhanced by adding a small controlled amount of water. This

observation was totally unexpected because in the case of Ziegler-Natta or Phillips

catalysts, water act as a poison. Despite these new discoveries, the catalysts activity

was still very low, obtaining poor stability during the polymerization, and producing only

low molar mass polymers.

2.1. Cocatalyst (Activator)

It was only in 1976 that, Sinn and Kaminsky,[16]

demonstrated that the metallocene

complex Cp2MMe2 was very active when contacted with trimetylaluminium (TMA) that

had initially been precontacted with water. This relatively high activity was attributed to

the reaction of water and trimethylaluminum to form aluminoxane, in this case

methylaluminoxane (MAO). MAO was shown to react with the metallocene complex

originating the cationic active species depicted in figure 6 (Cp2ZrMe2 + MAO →

Cp2ZrMe+ + MeMAO−). Then, polymerization reaction proceeds according to monomer

coordination and insertion steps already shown in section 1.3, figures 2 to 4.

Zr

Me

Me

MAOZr

Me

MeMAO-

+

Figure 6: Activation of the metallocene complex Cp2ZrMe2 with MAO

12


In the 1980’s, Sinn et al. [17]

successfully synthesized MAO, not in-situ as in 1976, and

used it as a cocatalyst. These new catalyst systems were at least ten times more active

than the best Ziegler-Natta catalysts at equal quantity of metal. The discovery of MAO

allowed obtaining extremely high polymerization activities that enrolled a strong interest

and effort to develop this new catalyst type.

The polyethylene obtained with this catalytic systems show different features than the

one obtained with Ziegler-Natta catalysts. The main one is the very narrow molar mass

distribution (PDI was around 2), which suggests that only one type of active site is

present.

The main disadvantages of this system are the price and the instability of MAO.

Consequently, extensive research has been performed in order to find another

cocatalyst so far with limited successes.

In this work it was used a lanthanide metallocene, from group 3, instead of group 4

metallocenes. The difference between those two is the degree of oxidation, which is +3

for lanthanide metallocene and +4 for metallocene from group 4. Unlike the

metallocenes from group 4 (Cp2ZrMe2, figure 6), lanthanide metallocenes do not need

an activator (such as MAO) to polymerize, because there is already a free coordination

for monomer coordination (figure 7).

Ln

Me

Figure 7: Lanthanide metallocene general structure

In order to fully understand the reactions that occur between the magnesium (MgR2)

and the lanthanide, the concepts of catalytic chain growth as well as chain transfer

reactions occurring during ethylene polymerization, will be explained to depict the

catalyst system used in this study.

IST December,

13

2.2. Catalyzed chain growth

The catalytic polymerization of α-olefins via transition metals is an industrial process

with a broad spectrum of catalysts and monomers in use. Special catalyst systems

have been found to enable a living polymerization process. [18,19]

Living polymerization is desirable because it offers precision and control in

macromolecular synthesis. It consists of chain growth polymerization where the ability

of a growing polymer chain to terminate has been suppressed.[20,21]

The polymer

chains obtained grow at a more constant rate than seen in traditional

chain polymerization and their lengths remain very similar (i.e. they have a very

low polydispersities index).

One class of these systems utilizes the catalyzed chain growth (CCG) mechanism.[22]

The main principle of CCG in the presence of MgR2 is a reversible chain transfer

between the reactive catalyst species (I) and the organometallic compound that serves

as a chain transfer agent (CTA) (figure 8 ).

This CTA constitutes a reversibly deactivated dormant species, which in contrast to the

active species, does not terminate via β-hydride elimination at the applied

temperatures.

The extent of termination is thus reduced drastically, as most of the polymer chains

being present in the system rest in this dormant state.

Figure 8: Basic reaction steps of CCG using MgR2 chain as transfer agent (CTA); M, metal; L, ligand; P,

polymer chain; R, alkyl group; H, hydrogen

kex

kex

CTA CTA

kp

kp

(I)

(II)

(I)

http://en.wikipedia.org/wiki/Polymer_chain

http://en.wikipedia.org/wiki/Chain_termination

http://en.wikipedia.org/wiki/Living_polymerization#cite_note-1

14


The influence of the transfer on the control of polyethylene chain growth is shown in the

figure 9.

Figure 9: Nd catalyzed polyethylene chain growth on magnesium

During polymerization, polymer chains P are frequently shuttling between I and CTA

via the bimetallic complex II, which equilibrates the growth probability of all chains and

results in a uniform growth rate of the polymer ensemble.

Narrow molar mass distributions are obtained, and the macromolecular chains carry a

metal atom at their terminal end and may thus easily be functionalized via subsequent

organometallic reactions. [23-27]

In this catalytic system, the control of the polymerization via degenerative chain

transfer is generally limited to rather low molar mass polyolefins (up to 3000 g/mol).

Since precipitation of polyolefins makes the control of polymerization not possible

anymore. Indeed the chain transfer reaction to the main group metal center is no longer

possible due the dramatic decrease of the chain mobility.

One solution, in order to get high molar mass polyolefins in a controlled way via CCG

consists on keeping the polymer soluble by increasing the polymerization temperature.

Meanwhile, this remains tricky because at higher temperatures, chain transfer to the

CTA is not the only chain transfer reaction. At higher temperatures β-H elimination

reactions become predominant (see figure 10), occurring in the active metal center,

producing vinyl terminated dead chains that cannot be involved in the degenerative

transfer any more. [24]

PL

nM

LnM

H

P

+LnM H P

Figure 10: Termination mechanism, β-H transfer

IST December,

15

2.3. System Cp*2NdCl2Li(OEt2)2 / MgR2

The capacity of well-defined lanthanide (group 3) metallocenes, in this particularly

case, neodymium metallocene, to polymerize ethylene has been demonstrated about

15 years ago. Highly efficient initiators for this purpose include trivalent rare-earth metal

complexes [Cp’2LnR]n (Cp* = substituted cyclopentadienyl ligand, typically C5Me5 =

Cp*; Ln= Nd, Sm, La; R= H, Me, CH2SiMe3; n=1,2). [28]

These organolanthanide complexes, especially the hydride complexes [Cp’LnH]2, are,

however extremely sensitive and their synthesis as well as their handling is tough.[29]

To skip this difficulty, one alternative is in situ alkylation of a readily available chloro

precursor, Cp*2NdCl2Li(OEt2)2, with a dialkylmagnesium. [30]

Figure 11: Postulated mechanism for chain growth on dialkylmagnesium [31]

16


This combination between the chloro precursor and dialylmagnesium forms an active,

stable system for pseudo-living ethylene polymerization in which a chain transfer

reaction between the MgR2 derivatives and the catalytically active lanthanocenes

complexes takes place (see figure 11).[32]

The transfer process was fast and reversible between magnesium and the neodymium.

That means that, in the presence of a large Mg/Nd ratio, the alkyl chains were

essentially located on magnesium, while insertion of ethylene took place on

neodymium.

Each chain can be considered as continuously transferred from one to another metallic

atom, with insertion of ethylene only when it was found on the lanthanide metal. Alkyl

chains were observed inactive for ethylene insertion when located on magnesium, so

they were named “dormant species” in this case, since they were only waiting for a

transfer to lanthanide. [32]

The result of this chain transfer reaction consists on yielding eventually long chain

dialylmagnesium compounds, Mg(PE)2, of narrow molar mass distribution and the

molar masses increase with the ethylene consumption.

However, the pseudo-living behavior is, stopped by the precipitation of Mg(PE)2 that

occurs when the molar mass of the corresponding polyethylene (PE) chains has

reached a limit value (solubility in the toluene, reactional solvent). This limit is

maximum at the optimum polymerization temperature (80 oC). [24]

The precipitation of

Mg(PE)2 deprives the polymerization system of reversible CTA and the control is

rapidly lost.

This present study is focused on the activation of the catalyst precursor during

initialization, by which a chlorinated metal catalyst is alkylated, giving a species that

promotes polymerization. The determination of kinetic constants and the influence of

addition of bases, dibutyl ether (Bu2O) in the reaction solvent, are other subjects

investigated in this study.

IST December,

17

Chapter II - Experimental Section

18


Before starting to perform the reactions, it was first necessary to become familiar with

the experimental set up, and optimize the technique and the procedures of the

polymerization reaction.

In this chapter will be described the materials, apparatus, techniques and the

procedures used in all the manipulations and polymerization reactions. Finally will be

mentioned the analytical techniques used for the characterization of the polymer

samples.

1. Materials

All operations performed in this work were done under dry argon by using standard

Schlenk techniques.

1.1. Solvents (Toluene, THF, Heptane)

The solvents used in the reactions, such as, toluene, THF and heptane, were purified

by a purification system named MB SPS-800 from MBRAUN, [33]

illustrated in the figure

12.

Figure 12: Purification system solvent

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19

The MBRAUN Solvent Purification System operates by way of solvent storage vessels

being pressurized through an inert gas supply (Typically a nitrogen source of 99.99%

purity or better). The solvent rises through the dip tube and flows through a series of

two filter columns that absorb moisture from the solvent (figure 13 [33]

). Ultra-pure

solvents are then dispensed into evacuated collection vessels directly at the system.

Figure 13: Gas and solvent flow throughout the system

1.2. Ethylene

The ethylene used in the trials is supplied by Air Liquid with the specification described

in the table 3. The ethylene was used without further purification.

Table 3: Ethylene content specification

Product specification

CO2 O2 N2 H2O H2 S

PPM < 5 < 10 < 40 < 5 < 10 < 2

20


1.3. Cp*2NdCl2Li(OEt2)2

The synthesis of the neodymium precursor was not made in this study. The precursor

was already prepared. However, the main steps of the synthesis will be described

below. [34]

The compound Cp*2NdCl2Li(OEt2)2 was synthesized by reaction of Lithium

pentamethylcyclopentadienide, LiCp* (5.00 g, 0.035 mol) with NdCl3(THF)3 (5.73 g,

0.018 mol).

The suspension was refluxed for 12 hours at 66 oC. THF was evaporated under

vacuum, and the residue was extracted with diethyl ether, forming a red solution. After

a second washing with ether, ether was slowly evaporated until blue crystals begin to

appear in the Schlenk.

Next, crystallization was done using a cold bath of ethanol (-10, -20 oC). Finally the

large blue prims were collected, wash and dried under vacuum.

1.4. BOMAG, Butyl(octyl)magnesium

The BOMAG used is a 20% solution of butyloctylmagnesium in heptane from Chemtura

[35] (see appendice A.1), illustrated in the figure 14. As a dialkylmagnesium reagent

with both butyl and octyl alkyl ligands, it offers greater solubility than magnesium

reagents with short chain substituents.

Figure 14: Butyloctylmagnesium in heptane

IST December,

21

1.5. Dibutyl ether

Dibutyl ether (anhydrous, 99.3%) from Sigma-Aldrich, was degased by freeze-thaw

cycles (see appendice A.2) and stores on molecular sieves (3 Å).

2. Experimental Set up

The polymerization experimental installation is composed of double layer reactor, an

integral heating/cooling system, one cartridge for the catalyst admission, one reservoir

of ethylene, an agitator and one pump. The figure 15 shows the experimental

installation used for the trials.

Figure II – 4: Experimental installation

Ethylene’s reservoir

Heating system

Reactor

Cartridge Stirrer

SPY sensors

Figure 15: Experimental Set up

22


The reactor, which works under semi batch conditions, consists of a double layer

reactor. The internal layer consists of a glass lined vessel of 0.5 liters, while the

external layer consists of a suspension system in which, when connected with the

glass reactor, allows the water circulation between them (figure 16). The heat/cool

water witch flows through the outside of the double layer ensures a good temperature

control.

Figure 16: Reactor

The heating and cooling thermostats, from LAUDA Ecoline Staredition, Control head E

100, are compliant with the highest precision requirements with a temperature stability

of up to ±0,01 K. The device includes two safety circuits, self-diagnosis, over

temperature. Power is delivered to each element through a thermostat, a switch that

senses the water temperature.

IST December,

23

Regarding the introduction of the metallocene complex in the reactor, this is done

through a cartridge with is connected to the reservoir of ethylene, illustrated in the

figure 17.

Figure 17: Cartridge connected to the reactor

The feed of ethylene is made through a reservoir of 2.13 liters, at temperature and

pressure of 20 °C and 3 bars (4 bars absolute), with a precision of 0.01 Celsius and

0.01 bars, respectively. The reservoir, showed in the figure 18, is equipped with a

sensor that monitories the pressure drops inside it.

Figure 18: Ethylene’s reservoir

24


The vacuum pump used was an two stage Edwards rotary vane pump, [36]

while the

stirrer is a “Power Control-Visc” stirrer with Stand from IKA Werke, Eurostar.[37] Both of

them are illustrated in the figure 19.

Figure 19: Two stage rotary pump and Power Control-Visc Stirrer

Using specific resistances sensors installed in the experimental set up, is possible to

measure values of temperature and pressure at different points, such as, the

temperature of the bath, the temperature inside the reactor, the pressure of the ballast

and the pressure inside the reactor. The sensors used are SPY RF® recorders (figure

20) that transmit their measurements to a server PC at every two seconds, with a radio

frequency in the 868 MHz band. [38]

Figure 20: SPY RF® Wireless System

IST December,

25

The electrical signs sent to a computer, enable the monitoring of the reaction variables

in-line. The measure is done using a software named “Sirius, Stockage”, version

1.5.10. One illustration of this software is shown in the figure 21.

Figure 21: Syrius stockage software

26


3. Inert atmosphere

In organometallic chemistry, most of the complexes must be manipulated in an air-free

environment. It was then necessary to use air free techniques in order to prevent

undesirable chemical reactions like oxidation and hydrolysis. A common characteristic

among these techniques is the use of a high vacuum to remove air, and the use of an

inert gas, preferably argon.

The most common types of air-free techniques are the use of a glovebox and a

Schlenk line, illustrated in the figures 22.

Figure 22: Air free techniques

The glass materials, such as Schlenk tubes, balloons, among other equipment used in

the manipulations and reactions, are normally pre-dried in ovens prior to use. Next, the

vessels are further dried by purge-and-refill, with vacuum and argon. This cycle is

usually repeated three times or the vacuum is applied for an extended period of time.

IST December,

27

The way that the cycles are made differentiates these two techniques. In the glovebox,

the purge-and-refill is applied to an airlock attached to the glovebox, commonly called

“ante-chamber”. In contrast of the glovebox, the Schlenk’s purge-and-refill is applied

directly to the reaction vessel through a hose or gland glass joint that is connected to

the Schlenk.

Both of these techniques were used in this experimental work. The glovebox, to safely

measure the amount of neodymium precursor used in the polymerization reaction and

Schlenk lines to prepare reaction solvent, and other compounds used for the reactions.

28


4. Ethylene Polymerization

The polymerization procedure involves a number of steps that will be described next.

400 mL of toluene are introduced in a 1000 round bottom flask under argon. Then, the

desire amount of cocatalyst, butyl(octyl)magnesium is added in the round bottom lask.

In parallely, cycles of vacuum-argon are performed in the reactor, while the reactor’s

temperature increases until the desire temperature of polymerization (normally 80 oC).

Once the temperature’s reactor is close to the targeted one, the solution is introduced,

into the reactor using a cannula. When all is introduced, the agitation is switch on.

The next step is the introduction of the solution of the neodymium metallocene in the

cartridge, which is shown in the figure 23. The complex Cp*2NdCl2Li(OEt2)2 is

weighed in the glove box, in a small round bottom flask, and 10 mL of toluene are

added, resulting in a clear blue solution. The solution is then introduced by a cannula in

the cartridge.

Figure 23: Introduction of the catalyst solution

IST December,

29

Before the introduction of the solution of the metallocene complex from the cartridge to

the reactor, first the reactor is put under 2.5 bar of ethylene. Then, the reactor is

isolated and the ethylene pressure is set at 3 bar. Finally the admission of the solution

is done with a pulse of ethylene.

The pressure is kept constant at 3 bar (relative pressure) during the polymerization.

After consumption of the desired quantity of ethylene, the polymerization is stopped.

The resulting mixture is poured in 400 mL of methanol. The polymer is collected by

filtration, washed with methanol and dried under vacuum at 90 oC for a couple of hours,

as shown in the figure 24.

Figure 24: Filtration and drying of the polymer

The relation between the ethylene pressure drop and its mass is going to be further

explained in the chapter III.

The complete procedure of the trials can be consulted in the chapter appendices A.3.

30


5. Polymer Analysis

All samples were characterized by Size Exclusion Chromatography (SEC). This

analytical technique is used for the determination of average molar masses (Mn and

MW), dispersities (Đ =Mw/Mn) and molar mass distribution (MMD). The principle of this

technique is to separate a solution of polymer chains according to their size. The

sample passes through three columns packed with porous material (gel) and the

separation of the polymer chains occurs due to their migration times through the

columns. The larger chains migrate faster than the shorter. [39]

High temperature Size Exclusion Chromatography (HT-SEC) analyses were performed

using a Viscotek system (from Malvern Instruments) equipped with three columns (PPS

POLEFIN 1 000 000Å, 100 000Å and 1 000Å). 200 L of sample solutions with

concentration of 5 mg.mL-1 were eluted in 1,2,4-trichlorobenzene using a flow rate of 1

mL.min-1 at 150°C. The mobile phase was stabilized with 2,6-di(tert-butyl)-4-

methylphenol (200 mg.L-1). The OmniSEC software was used for data acquisition and

data analysis. The molar mass distribution were calculated with a calibration curve

based on narrow poly(ethylene) standards (Mp : 338, 507, 750, 1180, 2030, 22000,

73000, 99000, 126000 g mol-1) from Polymer Standard Service (Mainz).

Figure 25: GPC system from Viscotek

In the next chapter will be presented one review of the calculations used to do the

analysis of the results and also how the consumption of ethylene is monitored during

polymerization. Then the results obtain and their treatment will be discussed.

Chapter III - Results and Discussion

32


1. Calculations Review

We can model most olefin polymerization kinetic with relatively simple

expressions that are derived from the general mechanism of polymerization. The most

important reactions are site activation, propagation, and catalyst deactivation.

Since, according to the fundamental model, chain transfer reactions are

assumed to have no effect on the polymerization rate [40]

, we do need to include them

in the present treatment.

Polymerization reactions are generally described by the empirical rate law:

𝑟𝑝 = − 𝑑[𝑀]

𝑑𝑡= 𝑘𝑝[𝑀] ∑ [𝑃𝑟]∞

𝑟=0 = 𝑘𝑝[𝑀]𝛼[𝐶∗] (1)

Where 𝑘𝑝 is the rate constant of propagation reaction, [M] is the monomer

concentration at the active sites and [C*] the concentration of active sites.

Although most polymerizations are first-order in monomer (α = 1), in some instances, a

non-integer dependence on [M] has been found, 0 < α < 2. [41]

In very early reaction stages 𝑅𝑝 is steady within the experimental error.

Therefore, from the observed dependences of reaction yield (Y) and number-average

degree of polymerization of the products (𝑃𝑛) on reaction time (t), can be estimated the

following equations: [42]

𝑌 = 𝑅𝑝 𝑡 = 𝑘𝑝[𝑀]𝛼[𝐶∗] 𝑡 (2)

1/Pn = Mo/Mn = kt / kp[M] + (1/kp [M]) (1/t) (3)

where [C]* is given by the equation 4.

[C]∗ = C∗[Complex] (4)

Where C* represents the fraction of the complex leading to active sites and [Complex]

is the concentration of the pre-catalyst.

IST December,

33

Substituting the equation (4) into equation (2) and admitting α = 1, we obtain the

equation 5 that relates the productivity of polymerization with time.

Y/[Complex] = kpC∗ [M] t (5)

Where Y/[Complex] are given in moles of monomer per moles of complex, kp in moles

of complex per volume per time and [M] in moles of monomer per volume.

When kt (irreversible transfer constant) is low in comparison to kp and/or at

short polymerization time, it is possible to measure the real rate of polymerization kp by

plotting 1/Pn versus 1/t.

However in the case of Coordinative Chain Transfer Polymerization the number of

chain and consequently the polymerization degree does not depend of the

concentration of active metal centers but to the concentration of the chain transfer

agent. In the present case the number of growing polymer chain are equal to 2*MgR2

(two chains per magnesium center). Then equation (6) should be considered:

1/𝑃𝑛 = 𝑀𝑜/𝑀𝑛 = 𝑘𝑡/𝑘𝑝[𝑀] + (𝑅/𝑘𝑝𝐶∗[𝑀])(1/𝑡) (6)

Where, 𝑅 = 2𝑀𝑔/𝑁𝑑

Consequently it appears not possible to get the real kp from the measure of the Pn

versus time in the case of CCTP, since the propagation depends on the number of

active sites (C*) but the number of chains is only related to the concentration of

magnesium (kt>>0). More complex kinetics investigations are required in order to

obtain the real kp value.

34


2. Monitoring the consumption of ethylene

During the polymerization experiment values of temperature (thermostatic bath and the

reactor) and pressure (ethylene’s reservoir and inside the reactor) were recorded over

time. The figure 26 shown one example of the profile obtained for one polymerization.

Figure 26: Temperature and pressure profile obtained using the “Sirius, Stockage” software.

The light green curve represents the temperature inside the reactor, which is first

increased from the room temperature to the temperature reaction.

IST December,

35

Once the temperature of the reactor equals the bath temperature (polymerization

temperature) and the solvent is introduced in the reactor, placed then at 2.5 bar of

ethylene, the neodymium complex is inserted on the reactor and the admission of

ethylene starts (3 bar), starting the polymerization, which corresponds to the drop of

pressure on the reservoir of ethylene (blue curve).

During polymerization, an increase of the temperature in the reactor is observed, which

results from the exothermic nature of the reaction. The end of the polymerization is

accompanied by a decrease in reactor temperature until the temperature value of the

thermostatic bath as well as by an stabilization of the ethylene consumption (pressure

reservoir of ethylene).

In order to further analyze the results obtained for each polymerization, it is first

necessary to relate the pressure drop of the ethylene reservoir with the consumed

mass of ethylene over time. This correlation was studied before [43]

, and the resulting

equation obtained, by adjusting the experimental data to a polynomial equation, is

presented in (appendix B.1).

Once the mass of ethylene of the reservoir at each instant is known it is possible to

determine the activity and productivity for each polymerization run, by using equations

7 and 8.

Activity =mn−mn+1

mcatalyst⁄

tn+1−tn (7)

Productivity =mn−m0

mcatalyst (8)

By knowing these values for each time instant, it is possible to determine some kinetic

parameters that may account for the observed polymerization behavior of the system.

Those calculations are going to be described in the next topic.

The concentration of ethylene is given by equation 9 that relates the ethylene

admission pressure (bar, absolute) and the polymerization temperature (ºC), as follow:

[𝐸𝑡ℎ𝑦𝑙𝑒𝑛𝑒] = 𝑃 × 1,15 × 10−3𝑒(2700/1,98 𝑇) (9)

In the next paragraphs the results obtained during this investigation will be presented

and discussed.

36


3. Treatment and Discussion of Results

Previously to any data treatment, a short explanation on a typical kinetic profile

obtained when Coordinative Chain Transfer Polymerization mechanism is operating,

will be presented.

In the first instants of polymerization the solubilization of ethylene in toluene takes

place as well as the in situ alkylation of the Neodymium chloro precursor, with the di-

alkylmagnesium (see figure 8, section 2.2, chapter I) leading to a heterobimetallic

complex that behaves like an deactivated dormant species. This species may then

dissociate through an equilibrated reaction giving rise to MgR2 derivatives, and to the

catalytically active lanthanocene complex responsible for chain growth (I) (see figure

11, section 2.3, chapter I). This initial activation process should be quite rapid since an

almost instantaneous increase of activity is observed in the kinetic profile.

Then a period of decreasing activity follows, which may indicate that the various

species involved in the aforementioned reactions have not attained equilibrium. Once

equilibrium is attained this is reflected in a period of steady state activity, During this

period, polymer chains P are frequently shuttling between the dormant bimetallic

complex II and the active propagating species, which equilibrates the growth probability

of all chains and results in a uniform growth rate of the polymer. This way long chain

dialylmagnesium compounds, Mg(PE)2, of narrow molar mass distribution. The molar

masses increase with the polymerization time.

However, this pseudo-living behavior is, stopped by the precipitation of Mg(PE)2 that

occurs when the molar mass of the corresponding polyethylene chains reached its limit

of solubility in the solvent at the polymerization temperature. The precipitation of

Mg(PE)2 deprives the polymerization system of reversible chain transfer agent and the

control is rapidly lost.

The period of time before polymer precipitation, is directly related to the concentration

of MgR2 used, increasing for higher concentrations values.

Consecutive to MgPE2 precipitation, all the neodymium species becomes in active form

leading to a rapid and significant increase in activity but the system rapidly deactivates

and a fast decrease in activity is next observed.

IST December,

37

At the end of polymerization, the chains are terminated by a mechanism of b-H

transfer, giving rise to a new family of polyethylene of much higher molar masses. The

chains produced present a Schulz-Flory distribution characteristic of single-site

catalysts (dispersity close to 2).

3.1. Investigation of different concentration ratios of bimetallic system

The first phase of this study was to investigate different concentrations of the system

Cp*2NdCl2Li(OEt2)2/MgR2, at 80 ºC and 3 bar of ethylene (relative pressure). Different

concentrations were investigated, such as 50, 80 and 100 µM. Various concentrations

of MgR2 were also investigated namely, 0.4, 0.8, 2, 4, 8 and 16 mM. The ratio [MgR2] /

[Nd] employed are shown in the table 4.

Table 4: [MgR2] / [Cp*2NdCl2Li(OEt2)2] ratios investigated

[MgR2] / [Nd] 50 80 100

0.4 8 - -

0.8 16 - -

2 40 - -

4 80 50 40

8 160 100 80

16 320 200 160

The profiles obtained for the first set of experiments, using a constant neodymium

complex concentration of 50 µM and various amounts of MgR2, are illustrated in the

figure 27.

38


Figure 27: Activity and Productivities profiles obtained at 50 µM of neodymium and with various amounts

of MgR2

At concentrations equal to 0.4 and 0.8, the precipitation of the polymer occurs very fast,

with only a period of 20 minutes of controlled polymerization (i.e stable activity). Due to

the fact that the controlled polymerization time is very low, investigations of lower

concentrations of MgR2 for the other neodymium complex were not carried out.

The increase of MgR2 augments the proportion of dormant to propagating species and

consequently the rate of growth of PE diminishes and the period of time before polymer

precipitation, is raised.

0,00E+00

2,00E+05

4,00E+05

6,00E+05

8,00E+05

1,00E+06

1,20E+06

1,40E+06

1,60E+06

0 50 100 150 200 250 300 350

Act

ivit

y (g

/mo

l/h

)

0,00E+00

2,00E+05

4,00E+05

6,00E+05

8,00E+05

1,00E+06

1,20E+06

1,40E+06

1,60E+06

1,80E+06

0 50 100 150 200 250 300 350

Pro

du

ctiv

ity

(g/m

ol)

Time (min)

0,4 mM 0,8 mM

2mM 4mM

8mM 16mM

IST December,

39

The stability of the complex is enhanced making the polymerization slower and

allowing a longer period of constant activity until polymer precipitation.

This way, for higher concentrations of MgR2, the limit value of molar mass of the

polymer before precipitation (around 3000 g mol-1 at 80 ºC) is produced in a longer

period of time.

This effect is most noticeable for higher concentrations of MgR2 (8 mM). It appears that

the reactions with higher [MgR2] / [Nd] ratio lead to higher control. The figure 28 shows

the molar mass distribution for the polymerization run using [Nd] = 50 µM and MgR2 = 8

mM.

Figure 28: Molar mass distribution of the polymer (50 µM Nd and 8 mM of MgR2)

The figure 29 shows the profiles obtained for polymerization reactions at different

neodymium complex concentration, 80 and 100 µM and at 4 and 8 mM of MgR2.

0,00E+00

1,00E-01

2,00E-01

3,00E-01

4,00E-01

5,00E-01

3,0 3,5 4,0 4,5 5,0

No

rmal

ize

d W

t Fr

Molar mass (Da)

40


Figure 29: Activity and Productivities profiles obtained for 4 and 8 mM of MgR2 for 50, 80 and 100 µM of

neodymium

Fixing the MgR2 concentration, the reaction control appears better for lower

concentrations of neodymium complex. This corresponds to higher [MgR2] / [Nd] ratios

which probably also favors the stability of the formed bimetallic complex. This effect is

visible for both polymerization series but is more pronounced when using the higher

concentrations of MgR2 (8 mM).

In conclusion, using a concentration of 50 mM of neodymium complex, optimum results

are obtained providing a good control of the reaction and high yields.

0,00E+00

1,00E+05

2,00E+05

3,00E+05

4,00E+05

5,00E+05

6,00E+05

7,00E+05

8,00E+05

9,00E+05

1,00E+06

0 50 100 150 200 250 300

Act

ivit

y (g

/mo

l/h

)

0,00E+00

2,00E+05

4,00E+05

6,00E+05

8,00E+05

1,00E+06

1,20E+06

1,40E+06

1,60E+06

0 50 100 150 200 250 300

Pro

du

ctiv

ity

(g/m

ol)

Time (min)

[Nd] = 50 µM, [MgR2] = 4 mM

[Nd] = 50 µM, [MgR2] = 8 mM

[Nd] = 80 µM, [MgR2] = 4 mM

[Nd] = 80 µM, [MgR2] = 8 mM

[Nd] = 100 µM, [MgR2] = 4 mM

[Nd] = 100 µM, [MgR2] = 8 mM

IST December,

41

Regarding the concentration of MgR2, the combination of 50 µM of neodymium

complex with 8 mM MgR2, offers a good compromise to further study the

Cp*2NdCl2Li(OEt2)2 / MgR2 system.

3.2. Apparent rate constant of propagation reaction (𝒌𝒑𝒂𝒑𝒑

) for different

reactions

The determination of the rate constant of propagation reaction is a very important

parameter that allows calculating the polymerization rate.

The apparent rate constant of propagation (𝑘𝑝𝑎𝑝𝑝

) is determined from equation (5), by

linear regression, of the productivity, in moles of ethylene per moles of neodymium

versus time.

The plots for all polymerization reactions (stopped after precipitation) can be found in

the appendix B.2 and the respective values of apparent rate constant of propagation

(𝑘𝑝𝑎𝑝𝑝) are listed in the table 5. Note that values of 𝑘𝑝

𝑎𝑝𝑝 were determined when the

steady state was reached.

Each polymer sample obtained after precipitation was analyzed by SEC. All the

samples showed a bimodal distribution although with a different shape. At low

concentration of MgR2 a large quantity of polymer is produced after precipitation so, the

bimodal shape is obvious. At higher concentration of MgR2 most of the polymer is

produced before the precipitation and generally we can observe two distributions.

Since the molar masses are obtained via two different polymerization regimes (before

and after precipitation) values of molar masses can be considered only as indicative.

The table 5 only contained information about the polymer obtained after precipitation.

42


Table 5: Results for polymerization reactions

Entry a)

[Nd] (µM)

[MgR2] (mM)

Time (min)

𝒌𝒑𝒂𝒑𝒑

b)

(L mol Nd-1 s-1)

Mn c)

(g/mol) Đ

d)

1

50

0.4 100 5.88E+01 13 650 10.5

2 0.8 110 4.53E+01 10 500 3.5

3 2 160 2.17E+01 8 400 2.4

4 4 210 1.76E+01 6 300 2.2

5 8 320 1.15E+01 4 500 1.6

6 80

4 145 1.73E+01 5 700 1.5

7 8 235 1.15E+01 4 650 1.3

8 100

4 105 1.43E+01 6 200 1.3

9 8 235 9.19E+00 4 700 1.2

a) T = 80 oC; VToluene = 400 mL

b) See appendix II

c) Determined by SEC analysis using PE standards

d) Đ: dispersity = MW / Mn

In order to recover polymer of a targeted molar mass, polymerizations were also

performed under the same conditions (catalyst, cocatalyst concentration, temperature,

and pressure) but stopped before precipitation. The productivity plots, in terms of

ethylene per moles of neodymium with time, can be found in the appendix B.2. For

comparison the same figure also shows the productivity plots obtained for

polymerizations, carried out under the same experimental conditions, but stopped after

precipitation. The figure with both plots shows the reproducibility of the polymerization

experiments.

The SEC analyses of the resulting polymers would provide us molar mass data that

can be introduced in the kinetic modeling of the reaction. Those results are shown in

the table 6.

IST December,

43

Table 6: Polymers results obtain on the several polymerization trials

Entry a)

[Nd] (µM)

[Mg] (mM)

Mg/ Nd

Time

(min)

Et b)

consup.

(g)

PE obtained

(g) Mn

theo v)

Mn d)

Đ c)

nchains/

e)

Mg

kp app

(L.mol Nd

-1 s

-1)

10

50

2 40 15 3.78 4.67 2919 2510 1.39 2.33 3.51E+01

11 4 80 55 7.6 6.70 2094 2100 1.25 1.99 1.51E+01

12 8 160 115 12.85 11.30 1766 1850 1.23 1.91 1.15E+01

13 16 320 145 12.91 11.90 930 950 1.28 1.96 9.00E+00

14

80

4 50 40 7.53 7.28 2275 2333 1.22 1.95 1.28E+01

15 8 100 125 12.78 18.40 2875

2000 f)

2160 1.27

2.66

1.85 f)

7.08E+00

16 100

4 40 40 8.13 8.98 2806 2840 1.18 1.98 1,20E+01

17 8 80 85 12,82 12.71 1986 2194 1.17 1.81 8,46E+00

a) T = 80 oC; VToluene = 400 mL

b) Et consup: Ethylene consumption

c) Mntheo

= mPE / 2*nMg (see appendix B.3)

d) Determined by SEC analysis using PE standards

e) Đ: dispersity = MW / Mn

f) Using the expected PE mass based on ethylene consumption

The dispersities lower than 1.4 suggests the expected pseudo living polymerization

behavior leading to narrow molar mass distributions.

The experimental number of chains of polyethylene per magnesium was also

determined. With the exception of the entries 10 and 15, the obtained values are very

close to the expected value of two, confirming that the depicted transfer of polyethylene

chain.

When analyzing the apparent rate constant of propagation obtained, it is noticed that

the kpapp decreases with the increase in the amount of MgR2 used. That is, increasing

concentration of MgR2, shift the equilibrium (figure 8, section 2.2, chapter I) to the

dormant species. This observation supports the hypothesis that during polymerization,

the equilibrium constant for exchange reaction between active and dormant species,

must be greater than the propagation constant ensuring that the chain growth

probability is equal.

44


A decrease of kpapp is also observed, when increasing the concentration of neodymium

complex. However this effect is less pronounced than when changing MgR2

concentration. By comparing the apparent kpapp values shown in tables 5 and 6 it may

be seen that generally close values are obtained.

This is expectable since the different experiments from table 5 and 6 were made under

the same conditions, the only difference being that, in the second case polymerizations

were stopped before precipitation. However for entries 3 and 10 a big difference

between kpapp values is observed. That can be explained by looking to figures 40 of

appendix B.2.

This figure shows that 15 minutes, still corresponds to a period where no steady state

activity has been reached and polymerization is not controlled (as it may also be

noticed by the higher dispersity value obtained for entry 10). Therefore determination of

kpapp from linear regression in this initial period may not be representative and the

slopes obtained in each case are quite different, accounting for the different values of

the apparent propagation constant. Some reproducibility issues may also account for

other discrepancies detected.

IST December,

45

3.3. Investigation of the addition of bases, Bu2O

The second phase of this study was to analyze the effect of the addition of bases,

dibutyl ether (Bu2O), on the polymerization kinetics. For that polymerization runs, were

carried out at 80 oC and 3 bar of ethylene (relative pressure), fixing neodymium

complex and MgR2 concentrations, respectively at 50 µM and 8 mM. The main goal

was to compare the results with the ones without Bu2O, for the same molar mass target

(2000 g/mol), and then study the effect of the Bu2O on the molar mass distribution.

Two different trials with Bu2O were performed and compared with one without Bu2O

(entry 12). Those profiles are showned in the figure 30.

Figure 30: Activity and Productivities profiles obtained at several concentrations of Bu2O

0,00E+00

2,00E+05

4,00E+05

6,00E+05

8,00E+05

1,00E+06

1,20E+06

1,40E+06

0 10 20 30 40 50 60 70 80 90 100 110

Act

ivit

y (g

/mo

l/h

)

0,00E+00

1,00E+05

2,00E+05

3,00E+05

4,00E+05

5,00E+05

6,00E+05

7,00E+05

0 10 20 30 40 50 60 70 80 90 100 110

Pro

du

ctiv

ity

(g/m

ol)

Time (min)

0 equivalent of Bu2O vs Mg



46


By adding dibutyl ether, the kinetic profile changes and higher activity values and more

stable profiles may be obtained. It is believed that the ether interacts with the BOMAG,

changing the equilibrium between the dormant and polymerization-active transition-

neodymium centers. This results shows an increase of the number of active sites and

thus of the reaction rate.

However the active species are not stable and, probably bimetallic degradation may

occur. In the presence of Bu2O, we have at the same time an efficient control of the

chain growth but also a slight deactivation of the catalyst.

Table 7 shows the polymerization conditions and the amount of polymer produced for

each run and the data obtained by size exclusion chromatography. The productivity

plots in mol PE mol Nd-1 can be found in the appendix B.2, figure 48.

Table 7: Polymerization trials with and without Bu2O

Entry a)

[Bu2O] /MgR2

VBu2O (mL)

Time (min)

Et b)

consup.

(g)

PE obtained

(g) Mn

theo c) Mn

d) Đ

e)

nchains c)

/Mg

kp app

(L.mol Nd

-1 s

-1)

12 0 0 115 12.85 11.3 1 766 1 850 1.23 1.91 1.15E+01

18 1 0.56 50 12.45 13.40 2 094 2 250 1.18 1.86 3.11E+01

19 10 5.6 35 12.77 16.10 2 516 2 570 1.12 1.96 4.64E+01

a) T = 80 oC; VToluene = 400 mL, [Cp*2NdCl2Li(OEt2)2] = 50 µM ; [MgR2] = 8 mM

b) Et consup: Ethylene consumption

c) Mntheo

= mPE / 2*nMg (see appendix B.3)

d) Determined by GPC analysis using PE standards


Regarding the values of dispersities and the number of polymer chains / magnesium, it

can be seen, that the values obtained are very similar and in the expected ranges.

It appears that the increase of dibutyl ether increases the propagation rate, in other

words, increases the ethylene insertion into the metal-carbon bond. The control is

maintained and the rate is higher.

These results are of high interest for the production of MgPE2 which can be further

functionalized. [23-27]

IST December,

47

3.4. Investigation of the energy of activation

The next stage of this study consisted on the investigation of the kinetics of

Cp*2NdCl2Li(OEt2)2/MgR2 catalytic system, at different temperatures in order to

determine the energy of activation for kpapp . For that 4 reactions were performed at 80,

70, 60 and 50 ºC. Temperature was kept under 80 ºC, since at higher temperatures, β-

H elimination occurs readily.

However, working at temperatures lower than 80 ºC brings disadvantages, since the

polymer molar mass possible to obtain, is limited by the solubility of polyethylene at the

polymerization temperature. To try to overcome this obstacle and to get useful results,

it was decided to use 8 mM of MgR2 and use 80 µM of neodymium complex (instead of

50 µM).

Additional polymerization reactions were performed in the same conditions, but

stopped before polymer precipitation. Different molar masses were targeted. The

results obtained are showed in figure 31 and table 8, respectively.

Figure 31: Activity and Productivities profiles obtained for several temperatures of polymerization

0,00E+00

1,00E+05

2,00E+05

3,00E+05

4,00E+05

5,00E+05

6,00E+05

7,00E+05

8,00E+05

0 10 20 30 40 50 60 70

Act

ivit

y (g

/mo

l/h

)

0,00E+00

5,00E+04

1,00E+05

1,50E+05

2,00E+05

2,50E+05

3,00E+05

0 10 20 30 40 50 60 70

Pro

du

ctiv

ity

(g/m

ol)

Time (min)

80 ºC 70 ºC

60 ºC 50 ºC

48


In the table 8 can be found results for each polymerization.

Table 8: Polymerization trials at different temperatures

Entry a)

b)

T (oC)

Polymerization time (min)

Ethylene consuptio

n (g)

PE obtaine

d (g) Mntheo

c) Mn

d) Đ

e)

nchains/Mg

c)

20 80 45 8.4 7.73 1 208 1410 1.23 1.71

21 70 70 8.34 7.81 1 220 1450 1.32 1.68

22 60 20 3.2 1.86 291 1040 1.36 0.56

23 50 15 2.34 0.69 108 1110 1.40 0.19

a) VToluene = 400 mL

b) [Cp*2NdCl2Li(OEt2)2] = 80 µM ; [MgR2] = 8 mM

c) See appendix B.3

d) Determined by GPC analysis


By observation of the profiles shown in the figure 31 and the results listed on table 8, it

can be seen that for temperatures equal or lower than 60 °C, the solubility limit is very

low, giving rise to polymers with molar mass below 300 g/mol. The values of theoretical

and obtained by SEC molar masses appear very different. Since lower temperature

lead to a control less efficient, is not surprising obtained higher molar masses with

respect to the expected ones.

For higher temperatures, the solubility of ethylene in toluene is higher, leading to higher

yields, higher polymerization rates and higher control of the reaction as well as higher

target molar masses.

However, it was observed a big difference between the values of ethylene consumption

and PE obtained for the polymerization performed at 50 ºC. Loss of low molar masses

by precipitation and/or filtration can be one possible explanation for this big difference.

The energy of activation can be determinate using the equation 10, obtained by

linearization of the Arrhenius equation.[44]

ln(𝑘) =−𝐸𝑎

𝑅

1

𝑇+ ln (𝐴) (10)

IST December,

49

The values for kpapp at each polymerization temperature were calculated, as explained

before, from the slope of the linear regression of the productivity (see equation 5), in

mol Ethy mol Nd-1 versus time (see figure 49, appendix B.2). However, since the

concentration of ethylene depends on the polymerization temperature, the values of

apparent rate constant of propagation were determinate using different values of

ethylene concentration.

Table 9 shows the results for each polymerization temperature.

Table 9: Kinetic results for each polymerization

Entry T (oC) Slope [Ethylene]

(mol L-1) kpapp

(L mol Nd-1 s-1) ln(kp)

20 80 167.93 0.219 1.28E+01 2.55

21 70 99.66 0.245 6.78E+00 1.91

22 60 166.55 0.276 1.01E+01 2.31

23 50 133.07 0.313 7.09E+00 1.96

The plot of ln(𝑘𝑝) over 1/T is represented in the figure 32.

Figure 32: Arrhenius plot of ln(k) versus T −1

y = -7683x + 24,304 R² = 1

1,5

2

2,5

3

0,0028 0,0029 0,003 0,0031 0,0032

ln (

kp)

1/T (K-1)

50


Observing the plot, it’s clear that the polymerizations at 60 and 50 ºC are not in

agreement with the ones at 80 and 70 ºC. The figure 31 shows that for 60 and 50 ºC,

the steady state regime was not reached for these two temperatures, that can

explained why the values of kpapp

appear too high. Therefore, rejecting the trials at 60

and 50 ºC, and by linear regression, a slope value of -7683 s-1 is obtained. The slope of

the linear regression is equal to - Ea/R. So, multiplying the slope by -1.987 (universal

gas constants in cal mol-1s-1), is obtained the energy activation value, of 15.2 kcal/mol.

This value is below the expected one for calculations of mechanisms (considering both

the dissociation of the heterobimetallic complex (Nd/Mg) and the insertion of the

ethylene in the alkyl complex, Cp*2Nd-R), which is about 20 kcal/mol.[45]

One of the possibilities for the lower value may be due to changes on the fraction of

active sites with the temperature. The performance of polymerizations at 75 and 65°C

would be a good idea in order increase the precision of the value.

IST December,

51

3.5. Sample extraction investigation during polymerization trial

3.5.1. Pseudo-living character

A very important aspect in this study was to confirm the pseudo-living character for the

Cp*2NdCl2Li(OEt2)2/MgR2 catalytic system.

It is first necessary, to measure, the number average molar mass (�̅�𝑛) at different

polymerization time.[4] That is only possible, if samples are withdrawn during the

polymerization reaction.

The �̅�𝑛 is defined as the average molar mass of individual macromolecules and it is

determined by measuring the molar mass of n polymer molecules, summing the

masses, and dividing by n. [46]

�̅�𝑛 =∑ 𝑛𝑖𝑀𝑖𝑖

∑ 𝑛𝑖𝑖 (11)

Since the reactor used does not have a device to recover samples, the polymerization

reaction was performed in another reactor equipped with the required withdrawal

system. However, using a different reactor has some limitations since it may influence

the kinetic profile of the reaction. The possible influence of the reactor in the results

would be later discussed.

The polymerization performed in this other reactor, where samples were extracted

during the experimental, was carried out with the optimized concentrations obtained in

the first phase of this study, [Cp*2NdCl2Li(OEt2)2] = 50 µM and [MgR2] = 8 mM.

The figure 33 shows the activity profile obtained with this new set up. These data was

compared to a blank polymerization (Entry 12) performed in the same conditions

(temperature, concentration of catalyst and co-catalyst) in the first experimental set up.

52


Figure 33: Activity profile obtained at 50 µM and 8 mM of MgR2 for polymerization perform with and

without withdrawal system

Similar profiles were obtained until about 90 minutes. After 90 minutes of

polymerization however, the control is rapidly lost and the polymer precipitates. This

means that for some reason Mg(PE)2 species have grown faster and attained its

solubility limit earlier than observed in the precedent test. The use of a different

reactor and the extraction of several samples during reaction (in total approximately 75

mL, in a total of 200 mL of solvent), may account for the different behavior observed.

However, since just one experiment was performed further investigations are needed.

During the reaction were taken small samples (10, 20, 40, 60, 90 and 120 minutes)

from the reaction solution, followed by addition of methanol, to break the metal-carbon

bond leading to a methyl chain-end. Then the samples were dried.

To obtained the productivity profile for these experimental using dry-extract content

was necessary determinate the concentration of polyethylene (g PE L-1) of each

sample and dividing by the concentration of the neodymium complex (mol Nd L-1). The

polyethylene concentration of each sample was determined by dividing the mass of

polyethylene obtained, by the volume of solvent (which is determinate by the difference

between the mass of solvent at the beginning, after the sample extraction, and after

drying the polymer).

The table 10 shows the calculations above mentioned.

0,00E+00

1,00E+05

2,00E+05

3,00E+05

4,00E+05

5,00E+05

6,00E+05

7,00E+05

8,00E+05

0 50 100 150 200 250 300 350

Act

ivit

y (g

/mo

l/h

)

Time (min)

Blank Polymerization

Sample Polymerization

IST December,

53

Table 10: Results of all the samples extracted during polymerization

Entry a)

Mass

lost b)

(g)

Volume of

solvent c)

(L)

PE obtained

(g)

[PE] (gPE L-1)

Productivity d)

(gPE mol Nd-1)

Mn Theo e) (g mol-1)

Productivity f)

(mol PE mol Nd-1)

Sample 1 14.72 1.70E-02 0.1575 9.28 1.86E+05 580 6.62E+03

Sample 2 18.98 2.19E-02 0.2864 13.08 2.62E+05 817 9.33E+03

Sample 3 13.87 1.60E-02 0.2741 17.13 3.43E+05 1 070 1.22E+04

Sample 4 16.79 1.94E-02 0.5626 29.04 5.81E+05 1 815 2.07E+04

Sample 5 8.39 9.68E-03 0.3192 32.98 6.60E+05 2 061 2.35E+04

Sample 6 8.61 9.93E-03 0.4057 40.85 8.17E+05 2 553 2.91E+04

a) [Cp*2NdCl2Li(OEt2)2] = 80 µM ; [MgR2] = 8 mM

b) Mass lost by evaporation

c) 𝜌𝑇𝑜𝑙𝑢𝑒𝑛𝑒 = 0,8669 𝑔𝑐𝑚−3

d) Productivity (gPE mol Nd-1) =[PE] (gPE L-1) / 80 µM [Cp*2NdCl2Li(OEt2)2]

e) Mn=Productivity (g PE mol Nd-1

) / 2R ; R = [MgR2] / [Nd] = 160

f) Mo = 28,05 g mol-1

Meanwhile, the theoretical Mn can be obtained by dividing the productivity by the

theoretical number of chains (number of chains = 2 Mg/Nd). That way it’s obtained the

molar mass of the polymer per chain of magnesium.

Figure 34 shows the experimental and theoretical number-average molar masses of

the polymer over the productivity (g PE /mol Nd). A good agreement is observed

between them.

Figure 34: Number average molar mass over time theoretical and experimental over productivity

0

500

1000

1500

2000

2500

3000

3500

0,00E+00 1,50E+05 3,00E+05 4,50E+05 6,00E+05 7,50E+05 9,00E+05

Mn

Productivity (gPE /mol Nd)

Experimental

Theoretical

54


The linear increase of Mn with productivity observed confirms that the equilibrium

between the active and dormant species (figure 8, section 2.2, chapter I) is rapidly

instaured although the dispersity for the first sample is rather high (see below, on table

11).

In the figure 35 is showed the profiles of the productivity (mol PE mol Nd-1) over time

for the polymerization performed for samples recovery during reaction and for the blank

polymerization (polymerization performed in the same conditions, but without a device

of samples recover – Entry 12, see appendix B.4 for the data values).

Figure 35: Productivities profiles obtained at 50 µM and 8 mM of MgR2 for both polymerizations perform

with and without withdrawal system

Observing both profiles it is observed that the productivity obtained from sample

withdrawn from the polymerization medium (kpapp = 1.57E+01 L mol Nd-1 s-1) is higher

than the one the measures considering the pressure drop in the reservoir, Entry 12

(kpapp = 1.20E+01 L mol Nd-1 s-1). The precipitation occurred when it was reached the

same productivity but this event took place earlier in the reactor used for withdrawal of

samples.

The dried samples were then analyzed by size exclusion chromatography technique

and the results obtained can be found in the table 11.

y = 206,08x + 5230,6 R² = 0,968

y = 157,26x + 5247,4 R² = 0,987

0,00E+00

5,00E+03

1,00E+04

1,50E+04

2,00E+04

2,50E+04

3,00E+04

3,50E+04

0 20 40 60 80 100 120 140

Pro

du

ctiv

ity

(mo

l PE

mo

l Nd

-1)

time (min)

SamplePolymerization

IST December,

55

Table 11: Sample results taken during the polymerization trial

Entry a) b)

Polymerization

time (min) PE

obtained (g) Mn

c)

(g mol-1) Đ

d) Pn

e)

Sample 1 10 0.157 780 2.19 27.7

Sample 2 20 0.286 980 1.42 34.9

Sample 3 40 0.274 1320 1.39 47.0

Sample 4 60 0.563 1740 1.34 62.0

Sample 5 90 0.319 2370 1.29 84.5

Sample 6 120 0.406 2870 1.37 102.3

Final Polymer 220 7.28 3400 1.49 121.2

a) T = 80 oC ; VToluene = 200 mL (toluene)

b) [Cp*2NdCl2Li(OEt2)2] = 50 µM ; [MgR2] = 8 mM

c) Determined by SEC analysis

d) Đ: dispersity = MW / Mn

e) Pn = Mn / Mo ; Mo = Ethylene molar mass (28,05 g mol-1

)

The entry corresponding to the characterization of the final polymer should not be

taken into account for the following plots since the polymer was recovered in these

cases after precipitation.

All the samples show a dispersity around 1.4 indicative of an effective polymerization

control, except the one withdrawn at 10 minutes that hasn’t still attained steady-state

activity.

Figure 36, represents the molar mass distribution, obtained by SEC, for the polymer

samples withdrawn along polymerization time.

56


Figure 36: Molar mass distribution of the several samples extracted during polymerization

This figure is of high significance, since shows how the polymerization is controlled.

Finally, the dependence of the number average molar mass with time is shown in figure

37.

Figure 37: Number average molar mass over time

The figure above shows a linear increase of the molar mass with time, demonstrating

the pseudo-living character of the polymerization.

0,0

0,2

0,4

0,6

0,8

1,0

1,2

2,0 2,5 3,0 3,5 4,0 4,5 5,0 5,5 6,0 6,5

No

rmali

zed

Wt

Fr

Molecular Weight (Da)

Final Sample

Sample 1

Sample 2

Sample 3

Sample 4

Sample 5

Sample 6

0

500

1000

1500

2000

2500

3000

3500

0 20 40 60 80 100 120

Mn

Time (min)

IST December,

57

However, it can be seen that this is not happening since the beginning, or else the line

would be linear from the origin. That means that in the first minutes reactions are

occurring in an uncontrolled manner. After 20 minutes, a steady-state is reached, and

from that point, is established a period where the polymer grows in a controlled way.

This situation is also clearly visible from figure 38 where it is plotted 1 / Pn versus 1/t

(equation 6). It may be seen that the first two points, until 20 minutes, are not aligned

with the remaining ones, which means that the system is not under the steady state

conditions yet. More conclusions cannot be obtained at this time.

As mentioned before this representation is a useful way to determine the active site

concentration in the case of Ziegler-Natta or metalllocene catalysts operating by

coordination mechanism and under conditions where transfer reactions are negligible.

However, it may not be applied in the case of the CCTP mechanism.

Figure 38: Inverse of the degree of polymerization over the inverse of time plot

0,000

0,005

0,010

0,015

0,020

0,025

0,030

0,035

0,040

0 0,02 0,04 0,06 0,08 0,1 0,12

1/P

n

1/t (min)-1

Chapter IV - Conclusions and Perspectives

IST December,

59

In this thesis, some key issues related to the use of a lanthanide metallocene catalyst

for ethylene polymerization were studied. The main objective was to investigate and

understand how pseudo living ethylene polymerization can be attained, in order to

allow the effective control of polymer properties from a reaction synthetic point of view.

The first phase of this work was focused on improving the experimental set up of the

polymerization reaction. One of the modifications made in the protocol was to increase

the ethylene pressure in the reactor up to 2.5 bar, before the introduction of the

neodymium complex (at 3 bar). That way, (unlike the initial procedure where the

neodymium complex was admitted to the reactor under vacuum), the saturation of the

solvent with ethylene occurs before the introduction of the catalyst. Therefore the first

instants of polymerization correspond only to polymerization kinetics occurring

(formation of the different species) and not to solubility effects.

Once improved the procedure, the main goal was to investigate the kinetics of a

bimetallic complex system, Cp*2NdCl2Li(OEt2)2/MgR2, for ethylene polymerization

under given experimental conditions such as, catalyst concentration, chain transfer

agent concentration, base’s addition and polymerization temperature. The effect of

these parameters on polymer properties was another key point in study.

It was concluded that, at a given neodymium precursor concentration, and for low

concentrations of MgR2, such as 0.4, 0.8 and even 2 mM, the period of time

corresponding to a controlled polymerizations (i.e. stable activity) was very low. On the

other hand, increased concentrations of MgR2 led to higher control of the

polymerization. The same behavior was observed when using the same concentration

of CTA but decreasing concentrations of neodymium precursor. In other words,

combination of bimetallic concentrations where the ratio [Mg]/[Nd] is high led to longer

periods where a steady-state is achieved and allow a better control of the polymer

properties.

60

Chapter IV - Conclusions and Perspectives

Analysis of the different apparent propagation constants, (𝑘𝑝𝑎𝑝𝑝

) derived from the

kinetic profiles, lead to the conclusion that increasing CTA concentration (for the same

precursor concentration), or decreasing the precursor concentration (for the same

MgR2 concentration) leads to lower rates of propagation. Therefore, the chain transfer

to magnesium is actually faster than ethylene insertion into a metal-carbon bond. The

chain shuttling is made by reversible alkyl-group exchange between dormant

magnesium and polymerization-active transition-neodymium centers, which allows the

tune the properties of the resulting polymers, such as, best reaction control.

By addition of dibutyl ether on the reaction media, a high increase in activity was

observed without affecting the control of the polymerization by CCTP. This result is of

high importance for up-scaling the process of polymerization since targeted molar

masses can be obtained in shorter times.

The kinetic data obtained at different polymerization’s temperatures (from 50 to 80 ºC)

allowed the determination of the activation energy, Ea = 15.2 kcal mol-1. In those

experiments temperature was kept under 80ºC since above this temperature,

irreversible transfer pathways, namely β-H elimination, start to be significant. This way

the control of the polyethylene molar mass is limited to a range up to 3000 - 4000 g

mol-1, which corresponding to the solubility of polyethylene in the solvent media at

these temperatures.

Finally the pseudo-living character of this type of polymerization was checked by

collecting polymer samples during the polymerization and monitoring the evolution of

molar masses, determined by SEC, over time. As expected a linear increase of the

number average molar mass with time was observed (figure 37). This result

demonstrates that CCTP is a unique example of controlled coordination catalysis

polymerization.

IST December,

61

Concerning the plots of productivity over time, of the polymerizations with and without

samples withdrawal, it can be seen that the productivity based on sample withdrawal,

increase faster with time. So polymer precipitation occurred approximatively when was

reached the same productivity but, this event took place earlier in the case of the

polymerization with samples withdrawal.

The reason why this polymerization was first precipitated is not yet fully understood, but

is not fully unexpected since the experimental protocol and the reactor is not the same.

In this thesis some important features in terms of kinetic and polymer properties were

demonstrated. However, some of the aspects studied still need further investigation

namely in order to confirm the value of energy of activation obtained.

Another feature to be taken into account is the investigation of more complex kinetic

modelling in order to experimentally determine the real rate constant of propagation

and the fraction of the complex leading to active sites, which is one important kinetic

result.

The ultimate aim of this study will be, through additional series of ethylene

polymerizations tests using a lanthanide metallocene, develop a complete kinetic

model for modelling the experimental data.

Through a proposed kinetic scheme and using one kinetic simulation program, such as

PREDICI [47] as well as the kinetic parameters determined in this study, it might be

possible to obtained a complete kinetic and mechanistic picture of the reaction steps

for the bi-component catalyst Cp*2NdCl2Li(OEt2)2/MgR2.

This work based on the set of data generated during the respective internship, is under

progressed in collaboration with the group of Prof. P. Vana at the University of

Göttingen (Germany).

62

Chapter V - References

IST December,

63

1. http://www.nexant.com/company/news/nexant-issues-new-global-

polyolefins-technology-review

2. McKenna, T.F. and J.B.P. Soares, Polyolefin Reaction Engineering, First

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3. Severn, J.R;, J.C Chadwick, R Duchateau, and N. Friederichs, “Bound but

not gagged”-Immobilizing single-site α-olefin polymerization catalysis,

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4. http://www.borealisgroup.com

5. http://www.academia.edu/4066905/POLYETHYLENE_PRODUCTION_TEC

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6. Tisse, Virginie., Kinetics and Morphology of Metallocene Catalysts used in

Ethylene Polymerisation, Ph.D. Thesis, LCPP-CNRS/ESCPE-Lyon, p. 6-8

(2006)


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8. Albizzatti, E. And M.Galimberti, Catalysts for olefins polymerization,

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9. Thüne P.C., Loos J., D.Wouters, Lemstra P.J., and Niemantsverdriet J.W.,

A surface science approach to supported olefin polymerization catalysis,

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12. Tisse, Virginie, Kinetics and Morphology of Metallocene Catalysts used in

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14. Breslow, D.S. and N.R. Newburg, Bis-(cyclopentafienyl)-titanium dichloride

– alkylaluminium complexes as catalysts for the polymerization of ethylene,

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17. Sinn, H., W. Kaminsky, H.J. Vollmer, and R. Woldt, Living Polymers on

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28. (a) B. J. Burger, M. E. Thompson, D. W. Cotter, J. E. Bercaw, J. Am.

Chem. Soc. 1990, 112, 1566; (b) P. L. Watson, G. W. Parshall, Acc. Chem.

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Schumann, T. J. Marks, J. Am. Chem. Soc. 1985, 107, 8103; (d) G. Jeske,

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29. N. Swepston, H. Schumann, T. J. Marks, J. Am. Chem. Soc. 1985, 107,

8091; (e) P. L. Watson, T. Herskovitz, ACS Symp. Ser. 1983, 212, 459

30. Polyolefins, K. Soga and M. Terano, Eds., Elsevier, Amsterdam 1994, pp.

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Chem., Int. Ed. Engl. 1996, 35, 1854

31. T. Chenal, M. Visseaux, End-capped Oligomers of Ethylene, Olefins and

Dienes, by means of Coordinative Chain Transfer Polymerization using

Rare Earth Catalysts, ISBN 978-953-51-1617-2, (2014)

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33. http://www.mbraun.com/products/solvent-purification/mbsps-800/

34. T.Don Tilley, and R. Andersen, Pentamethylcyclopentadienyl derivatives of

the trivalent lanthanide elements neodymium, samarium, and ytterbium,

Inorganic Chemical; 1981, 20 (10), pp 3267–3270

35. http://www.chemturaorganometallics.com/corporatev2/v/index.jsp?Vgnextoi

d=40c60aad6c75f310VgnVCM1000000a53810aRCRD&vgnextchannel=d3

3a5f15fa43f310VgnVCM1000000a53810aRCRD

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radiofrequences/spy-rf

39. http://en.wikipedia.org/wiki/Size-exclusion_chromatography

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http://www.edwardsvacuum.com/products/A65509906/View.aspx

http://www.labwrench.com/?equipment.view/equipmentNo/771/IKA/EUROSTAR-digital/

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http://www.jri-maxant.com/index.php/en/nos-produits/enregistreurs-radiofrequences/spy-rf

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40. T.F. McKenna, and J.B.P. Soares, Polyolefin Reaction Engineering, First

Edition, p. 4 – 12 (2012)

41. Fuquan Song,., , Roderick D. Cannonand Manfred Bochmann, ,

Zirconocene-Catalyzed Propene Polymerization: A Quenched-Flow Kinetic

Stud, Journal of the American Chemical Society, 125(25), p. 7641-7653

(2003)

42. Vincenzo Busico, Roberta Cipullo, and Valentina Esposito, , Stopped-flow

polymerizations of ethene and propene in the presence of the catalyst

system rac-Me2Si(2-methyl-4-phenyl-1-indenyl)2ZrCl2/methylaluminoxane,

Macromol. Rapid Commun. 20, p. 116 – 121 (1999)

43. B. Michel-Florin, Copolymers Ethylene Hexane-1:Synthesis,

Characterisation, Etude de qualques proprieties, 1977,Université Claude

Bernard, Lyon 1

44. http://en.wikipedia.org/wiki/Arrhenius_equation

45. Lionel Perrin, University Lyon 1, personal communication

46. http://en.wikipedia.org/wiki/Molar_mass_distribution#Number_average_mol

ar_mass

47. http://www.cit-wulkow.de/predici

http://en.wikipedia.org/wiki/Arrhenius_equation

IST December,

67

Chapter VI - Appendices

68


Appendix A.1 – BOMAG Specification Sheet

IST December,

69

Appendix A.2 – Dibutyl ether Specification Sheet

70


Appendix A.3 – Experimental polymerization procedure

1. Experimental protocol for ethylene polymerization:

1.1. With the reactor already set from the previous reaction, so the installation doesn’t

catch any air, connect the hot water hole in the reactor, and turn on the heating

water.

1.2. Next, do some cycles of vacuum-argon:

1.2.1. Connect the hole of the vacuum, turn on the pump and admit the admission of

vacuum to the reactor;

1.2.2. Between 5 and 10 minutes after, close the admission of vacuum, and admit

argon to the system, until its full of argon;

1.2.3. Do this cycles 3 times.

1.2.4. Wait until the reactor is at the desire temperature;

2. Preparation the solution of support (MgR2 + toluene):

2.1. Fetch the balloon of 1000 mL and its “arms” (big - vacuum; small – argon)

2.2. Do cycles of vacuum-argon (15 min):

2.2.1. Start the admission of vacuum;

2.2.2. Five minutes after, close the admission of vacuum and open the argon

admission. When the argon ampoule’s starts bubbling, close the argon admission

and start the vacuum admission again. Do it three times with 5 min on vacuum

on each time;

2.3. Weigh the balloon with argon;

2.4. Transfer the toluene from the fountain to the balloon, until the mark on the balloon

(± 400 mL):

2.4.1. Put the balloon under argon;

2.4.2. Open the first valve to the N2 position;

2.4.3. Before open the second valve, made a purge in the tap of the purification

system with vacuum;

2.4.4. After the toluene transfer, close both the valves and release the balloon from

argon;

2.4.5. Weigh the balloon with the toluene;

2.5. Transfer of the MgR2 from the Schlenk tube to the balloon:

2.5.1. Put a valve with 2 heads in the balloon (big head) ;

2.5.2. Connect the Schlenk of MgR2, previously placed under argon, in the second head

of the valve;

2.5.3. Using a pipette (under argon previously) transfer the MgR2. Do not forget to do

some purges with the pipette;

3. Turn on the reactor sensors of temperature and pressure;

IST December,

71

4. Add the solution MgR2 + toluene to the reactor:

4.1. Put the balloon under argon; 4.2. Put under argon the reactor and then take out the hole of vacuum and open the

respective valve to introduce the hole for the transfer of the MgR2 and toluene solution.

4.3. Put the hose inside the reactor until you can see the other extremity of it, inside the reactor;

4.4. After the transfer of the solution, let the reactor under argon, and turn on the agitation of the reactor.

5. Injection of the complex:

5.1. Close the red valve to conduct the vacuum to the small chamber of the glove box and

also the valve of argon located near the big chamber;

5.2. Under argon, open the door of the small chamber and put the necessary equipment

inside;

5.3. Leave it under vacuum during 15 min (or do some cycles instead);

5.4. When the cycles are over, open from inside the glove-box and take out the

equipment and then measure the required quantity of complex. In case of precaution

put the small chamber at vacuum.

5.5. After the measure put the equipment inside the small chamber and then take it out

from the outside of the glove-box;

5.6. Under argon, add some toluene to form a solution;

6. Add the solution of the complex to the reactor: 6.1. Put the balloon under argon; 6.2. Using a hose and a cover with a small hole, transfer the solution to the cartridge set in

the experimental installation (see topic 3); 6.3. Close the valve to the admission of argon o the reactor, and open the admission of

the ethylene to the reactor;

7. Open the admission of ethylene to the reactor, that will drag the solution;

8. Go to the pc and open the software and do some alteration (date, hour, etc);

9. When the reaction is over, turn off the heating water, unplug the hot hoses and connect

the cold ones in reactor to cool down the reactor. Wait until the temperature of the

reactor drops around 20 Celsius degree;

10. When the reactor is cold, unplug the holes, to remove the water from the reactor;

11. Take the polymer and with methanol, go to a filtration station, to separate the polymer

from the solution;

12. After that clean the installation with heptane and then set another reactor in the

installation for the next reaction;

13. Go to the pc and turn off the sensors;

14. Leave the polymer for one day in the fume hood;

15. Finally, put the polymer in a recipient and then into “cloche” to dry the polymer.

15.1. Fetch the reactor and put it on the experimental installation, for the next

polymerization.

72


Appendix B.1 – Solubility of Ethylene in Toluene

The solubility of the ethylene in toluene is calculated using the model of Michel-Florin,

where, the molar fraction of ethylene in the heptane (xe) is given by:

𝑥𝑒 = 𝑎0 + 𝑎1. 𝑃 + 𝑎2. 𝑃2 (12)

validated for:

1 bar < P < 10 bar, 20 oC < T < 80 oC

The three parameters a0, a1 and a2 are depending on the temperature.

𝑎0 = 1.256 − 0.004505 𝑇 + 0.0000109 𝑇2 (13)

𝑎1 = 0.0052 − 0,00001495 𝑇 − 0,0000001244 𝑇2 (14)

𝑎2 = 0.0003252 − 0,00000732 𝑇 + 0,00000004195 𝑇2 (15)

From the molar fraction of ethylene in toluene (xe) the mass of ethylene can be

determined.

𝑚𝑎𝑠𝑠𝑒𝑡ℎ𝑦𝑙𝑒𝑛𝑒 = 𝑥𝑒𝑉𝑟𝑒𝑠𝑒𝑟𝑣𝑜𝑖𝑟 𝑃𝑖 (16)

IST December,

73

Appendix B.2 – Linear regressions

Representation of the productivity over time, based on the experimental results of

polymerizations performed until precipitation and until a target molar mass.

Figure 39: Linear regression of the productivity over time (50 µM Cp*2NdCl2Li(OEt2)2, 0.4 mM MgR2)

Figure 40: Linear regression of the productivity over time (50 µM Cp*2NdCl2Li(OEt2)2, 0.8 mM MgR2)

y = 771,49x - 2994,8

0

10000

20000

30000

40000

50000

60000

0 20 40 60 80 100 120

Pro

du

cti

vit

y (

mo

l E

thy/m

ol

Nd

)

time (min)

Precipitation (Entry 1)

y = 593,94x - 1995,8 R² = 0,9941

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

0 20 40 60 80 100

Pro

du

cti

vit

y (

mo

l E

thy/m

ol

Nd

)

time (min)


74


Figure 41: Linear regression of the productivity over time (50 µM Cp*2NdCl2Li(OEt2)2, 2 mM MgR2)


y = 284,58x + 1950,3 R² = 0,9976

y = 460,37x + 866,86 R² = 0,9948

0,00E+00

5,00E+03

1,00E+04

1,50E+04

2,00E+04

2,50E+04

3,00E+04

3,50E+04

4,00E+04

4,50E+04

0 50 100 150 200

Pro

du

cti

vit

y (

mo

l P

E m

ol N

d-1

)

time (min)


Target (Entry 10)

y = 230,28x + 3216,7 R² = 0,9997

y = 198,31x + 3276,6 R² = 0,9972

0,00E+00

5,00E+03

1,00E+04

1,50E+04

2,00E+04

2,50E+04

3,00E+04

3,50E+04

4,00E+04

4,50E+04

5,00E+04

0 50 100 150 200 250

Pro

du

cti

vit

y (

mo

l P

E m

ol N

d-1

)

time (min)


Target (Entry 11)

IST December,

75



y = 150,5x + 4772,8 R² = 0,9997

y = 151,38x + 5996,6 R² = 0,999

0,00E+00

1,00E+04

2,00E+04

3,00E+04

4,00E+04

5,00E+04

6,00E+04

0 50 100 150 200 250 300 350

Pro

du

cti

vit

y (

mo

l P

E m

ol N

d-1

)

time (min)


Target (Entry 12)

y = 118,01x + 6172,4 R² = 0,9969

0

5000

10000

15000

20000

25000

0 20 40 60 80 100 120 140 160

Pro

du

cti

vit

y (

mo

l E

thy /

mo

l N

d-1

)

time (min)

Target (Entry 13)

76




y = 227,07x + 1537 R² = 0,9985

y = 168,56x + 2088,7 R² = 0,9998

0,00E+00

5,00E+03

1,00E+04

1,50E+04

2,00E+04

2,50E+04

3,00E+04

0 20 40 60 80 100 120 140 160

Pro

du

cti

vit

y (

mo

l P

E m

ol N

d-1

)

time (min)


Target (Entry 14)

y = 151,13x + 3749 R² = 0,9992

y = 92,833x + 3066,2 R² = 0,997

0,00E+00

5,00E+03

1,00E+04

1,50E+04

2,00E+04

2,50E+04

3,00E+04

3,50E+04

4,00E+04

0 50 100 150 200 250

Pro

du

cti

vit

y (

mo

l P

E m

ol N

d-1

)

time (min)


Target (Entry 15)

IST December,

77



y = 187,54x + 1369,4 R² = 0,9998

y = 157,86x + 1453,4 R² = 0,9995

0,00E+00

2,00E+03

4,00E+03

6,00E+03

8,00E+03

1,00E+04

1,20E+04

1,40E+04

1,60E+04

1,80E+04

2,00E+04

0 20 40 60 80 100 120

Pro

du

cti

vit

y (

mo

l P

E m

ol N

d-1

)

time (min)


Target (Entry 16)

y = 120,53x + 2588,4 R² = 0,9996

y = 111,04x + 2217,5 R² = 0,9983

0,00E+00

5,00E+03

1,00E+04

1,50E+04

2,00E+04

2,50E+04

3,00E+04

0 50 100 150 200 250

Pro

du

cti

vit

y (

mo

l P

E m

ol N

d-1

)

time (min)


Target (Entry 17)

78


Figure 49: Linear regression of the productivity over time for different concentration of Bu2O

Figure 50: Linear regression of the productivity over time for the different polymerization’s temperature

y = 151,37x + 6002 R² = 0,9989

y = 408x + 2387,5 R² = 0,9997

y = 608x + 3020 R² = 0,9984

0,00E+00

4,00E+03

8,00E+03

1,20E+04

1,60E+04

2,00E+04

2,40E+04

0 20 40 60 80 100 120

Pro

du

cti

vit

y (

mo

l P

E m

ol N

d-1

)

time (min)

Entry 12

Entry 18

Entry 19

y = 167,93x + 2393,4 R² = 0,9984

y = 99,657x + 2732,9 R² = 0,9915

y = 166,55x + 770,56 R² = 0,9901

y = 133,07x + 1062,6 R² = 0,9577

0,00E+00

2,00E+03

4,00E+03

6,00E+03

8,00E+03

1,00E+04

1,20E+04

0 10 20 30 40 50 60 70 80

Pro

du

ctiv

ity

(g P

E m

ol N

d-1

)

time (min)

80 ºC (Entry 20)

70 ºC (Entry 21)

60 ºC (Entry 22

50 ºC (Entry 23)

IST December,

79

Appendix B.3 – Determination of theoretical molar mass and experimental

number of polyethylene chains per magnesium

In order to determine the exact time to stopped the polymerization in order to target a specific

molar mass (Mtarget), it is first necessary to determine, the requested mass of ethylene (mPE)

that must be consumed to get this molar mass. That calculation is made using the equation

below, which relates the mass of polyethylene with the number of moles of each experimental

reaction, the desired molar mass of polymer assuming a transfer to MgR2, 2 oligomer chains

per magnesium (chain number = 2 * nMg).

mPE = Mtarget * 2 nMg (17)

Once determinate the mass of polyethylene supposed to get, which corresponds to the mass

of ethylene consumed, it is possible to determine the final value of pressure drop of the

reservoir of ethylene, which corresponds to the end of polymerization. That relation between

the mass and the pressure of ethylene was already explained in the section 2, chapter III.

With the experimental mass of polyethylene obtained, it is possible to determine the

theoretical molar mass (Mn) supposed to achieve, assuming a transfer to MgR2 on two

oligomer chains per magnesium.

On the other hand, the experimental number of oligomer chains per magnesium can also be

determinate, using the same equation, with the experimental data obtained, mass of

polyethylene, molar mass and number of moles of magnesium.

80

Appendix B.4 – Comparison between the productivity values with and

without sample withdrawn

Table 12: Productivity (mol PE mol Nd-1

) data for both polymerizations

time (min)

Blank a)

Polymerization Sample

b)

Polymerization

10 5.72E+03 6.62E+03

20 8.48E+03 9.33E+03

40 1.22E+04 1.22E+04

60 1.56E+04 2.07E+04

90 1.95E+04 2.35E+04

120 2.35E+04 2,91E+04

a) Values from the initial profile, obtained by the ethylene mass reacted

b) Obtained from the treatment of the experimental Mn by SEC method

Documents

Investigation of the kinetics of ethylene polymerization