Stochastic Simulations of Polymer Growth and

Isomerization in Ethylene/-Olefin Polymerization

Catalyzed by Late Transition Metal Complexes -

- From DFT Calculations to a Macroscopic Modeling

Stochastic Simulations of Polymer Growth and

Isomerization in Ethylene/-Olefin Polymerization

Catalyzed by Late Transition Metal Complexes -

- From DFT Calculations to a Macroscopic Modeling

Artur Michalaka,b and Tom Zieglera

aDepartment of Chemistry,

University of Calgary,

Calgary, Alberta, Canada

bDepartment of Theoretical Chemistry

Jagiellonian University

Cracow, Poland

Artur Michalaka,b and Tom Zieglera

aDepartment of Chemistry,

University of Calgary,

Calgary, Alberta, Canada

bDepartment of Theoretical Chemistry

Jagiellonian University

Cracow, Poland

The controlled design of polymer material with a specific microstructure is an emerging frontier in olefin polymerization. Of special interest are the dendric and hyperbranched structures, usually obtained with special monomers. Recently, the hyperbranched polymers have been obtained with Pd-based diimine catalyst in ethylene polymerization under low pressure (Brookhart et al., Chem.Rev. 2000, 100, 1169; Guan Z. et al. Science 1999, 283, 2059). Rigorous quantum chemical studies on the relationship between the catalyst structure and the microstructure of polymer, as well as the influence of the reaction conditions is beyond the present computational abilities. Here, however, the ‘mesoscopic’ approach can be applied in which the results of the DFT calculations are used as input data for stochastic modeling.

A model for performing stochastic simulations of the polymer growth and isomerization has been developed. Based on the assumption that relative probablilities of the reactive events in the catalytic cycle are equal to the relative (macroscopic) rates of elementary reactions, stochastic simulations allows one to investigate the influence of catalyst structure, as well as of the temperature and olefin pressure on the microstructure of the resulting polymers. This kind of molecular modeling links the microscopic, quantum mechanical approach with the modeling of the macroscopic properties of the polymers.

We present here the results of the simulations for the polymerization of propylene with the set of the Pd-based diimine catalysts, using the barriers for elementary reactions obtained in the recent DFT calculations (Michalak, Ziegler Organometallics 1999, 18, 3998; 2000, 19, 1850). Also presented are the results of a general, model studies on the relationship between the barriers of elementary reactions, temperature, and olefin pressure, and the microstructure of the resulting polyethylenes.

The controlled design of polymer material with a specific microstructure is an emerging frontier in olefin polymerization. Of special interest are the dendric and hyperbranched structures, usually obtained with special monomers. Recently, the hyperbranched polymers have been obtained with Pd-based diimine catalyst in ethylene polymerization under low pressure (Brookhart et al., Chem.Rev. 2000, 100, 1169; Guan Z. et al. Science 1999, 283, 2059). Rigorous quantum chemical studies on the relationship between the catalyst structure and the microstructure of polymer, as well as the influence of the reaction conditions is beyond the present computational abilities. Here, however, the ‘mesoscopic’ approach can be applied in which the results of the DFT calculations are used as input data for stochastic modeling.

A model for performing stochastic simulations of the polymer growth and isomerization has been developed. Based on the assumption that relative probablilities of the reactive events in the catalytic cycle are equal to the relative (macroscopic) rates of elementary reactions, stochastic simulations allows one to investigate the influence of catalyst structure, as well as of the temperature and olefin pressure on the microstructure of the resulting polymers. This kind of molecular modeling links the microscopic, quantum mechanical approach with the modeling of the macroscopic properties of the polymers.

We present here the results of the simulations for the polymerization of propylene with the set of the Pd-based diimine catalysts, using the barriers for elementary reactions obtained in the recent DFT calculations (Michalak, Ziegler Organometallics 1999, 18, 3998; 2000, 19, 1850). Also presented are the results of a general, model studies on the relationship between the barriers of elementary reactions, temperature, and olefin pressure, and the microstructure of the resulting polyethylenes.

IntroductionIntroduction 2

Mechanism of the olefin polymerizationMechanism of the olefin polymerization

• two possible insertion paths, 1,2- and 2,1- (RA and RB);• isomerisation reaction RC, produces additional methyl branch, while the isomerisation reaction RD leads to shortening, and eventually removing branches;• presence of different alkyl species (A-D; with a primary, secondary, or tertiary carbon attached to the metal) in the catalytic cycle; each of them can lead to the next olefin insertion

• two possible insertion paths, 1,2- and 2,1- (RA and RB);• isomerisation reaction RC, produces additional methyl branch, while the isomerisation reaction RD leads to shortening, and eventually removing branches;• presence of different alkyl species (A-D; with a primary, secondary, or tertiary carbon attached to the metal) in the catalytic cycle; each of them can lead to the next olefin insertion

3

It is know from the experimental data that with different catalysts one can obtain the polyolefins with different number of branches. The total number of branches can be independent of the olefin pressure or change dramatically with its changes. Further, even when the number of branches is pressure independent, the microstructure of the polymer can be strongly affected.

It is know from the experimental data that with different catalysts one can obtain the polyolefins with different number of branches. The total number of branches can be independent of the olefin pressure or change dramatically with its changes. Further, even when the number of branches is pressure independent, the microstructure of the polymer can be strongly affected.

Stochastic simulation - how it worksStochastic simulation - how it works

Energetics of elementary reactions

Relative probabilities of the elementary reactions

Choice of a path

Energetics of elementary reactions

Relative probabilities of the elementary reactions

Choice of a path

1 C atom attached to the catalyst:two possible events:

olefin capture followed by 1,2- or 2,1-insertion

Primary C at the catalyst - 4 events:1) 1 possible isomerization 2) olefin capture and 1,2- insertion3) olefin capture and 2,1- insertion4) termination

Secondary C attached to the catalyst:1) isomerization to primary C2) isomerisation to secondary C3) olefin capture and 1,2- insertion4) olefin capture and 2,1- insertion5) termination

1

2

3

4

12

345

Primary C at the catalyst - 4 events:1) 1 possible isomerization 2) olefin capture an`d 1,2- insertion3) olefin capture and 2,1- insertion4) termination

1

3

2

4

e.g., chosen isomerization

e.g., chosen 1,2-ins.

e.g., chosen 1,2- ins.etc.

4

Probablities of the eventsProbablities of the events

Basic assumption:relative probabilities (microscopic)

= relative rates (macroscopic):

e.g. isomerization vs. isomerization:

isomerization vs. insertion:

etc.

Thus, a structure resulting from a simulation represents a model polymer chain (ensemble averaged)

Basic assumption:relative probabilities (microscopic)

= relative rates (macroscopic):

e.g. isomerization vs. isomerization:

isomerization vs. insertion:

etc.

Thus, a structure resulting from a simulation represents a model polymer chain (ensemble averaged)

i

j

ri

rj

iso .1

iso .2

riso .1

riso .2

k iso .1

kiso .2

exp(G1, 2

kT)

i

i 1

iso .1

ins. 1 , 2

riso .1

rins.1 , 2

kiso .1

k ins.1 , 2 Kcompl. polefin

][ 01,1 isokr

][ 02,2 isokr

olefincomplins

insins

pKk

kr

][

][

0..

0..

][ 01,1 isokr

- alkyl -agostic complexes;- olefin complex;

5

main chainprimary branch

secondary branch

tertiary branch

etc.

Results:- Polymer chain;- Total No. of branches;- Classification of branches: no. of branches of a given type, and their length;- Molecular weight;

Results:- Polymer chain;- Total No. of branches;- Classification of branches: no. of branches of a given type, and their length;- Molecular weight;

Stochastic simulations - analysis of resultsStochastic simulations - analysis of results

As a result of a set of simulations, the polymer structures are obtained, the average number of branches is calculated, and a classification and an analysis of the branches is performed: length of the main chain, number and length of primary branches, secondary, tertiary etc. If the termination reactions were taken into account, the molecular weights could also be obtained. Here, however, since we focused on the polymer structure, we assumed no termination, and each simulation was performed until the chain reached a length of 1000 carbon atoms.

As a result of a set of simulations, the polymer structures are obtained, the average number of branches is calculated, and a classification and an analysis of the branches is performed: length of the main chain, number and length of primary branches, secondary, tertiary etc. If the termination reactions were taken into account, the molecular weights could also be obtained. Here, however, since we focused on the polymer structure, we assumed no termination, and each simulation was performed until the chain reached a length of 1000 carbon atoms.

6

I. Propylene polymerization catalyzed by Pd-based diimine catalystI. Propylene polymerization catalyzed by Pd-based diimine catalyst

•Simulations based on the activation barriers from the DFT calculations for a set of model catalysts with different substituents (Michalak, Ziegler Organometallics 1999, 18, 3998; 2000, 19, 1850). • The 1,2- and 2,1- insertion barrirers as well as the -complexation energies were calculated for each catalyst model, while the values of the isomerisation barriers were taken from a generic catalyst. No insertion from the tertiary carbon was allowed.•For each system/reaction conditions 500 simulations were performed; in each of them a chain of 1000 carbon atoms was built.

•Simulations based on the activation barriers from the DFT calculations for a set of model catalysts with different substituents (Michalak, Ziegler Organometallics 1999, 18, 3998; 2000, 19, 1850). • The 1,2- and 2,1- insertion barrirers as well as the -complexation energies were calculated for each catalyst model, while the values of the isomerisation barriers were taken from a generic catalyst. No insertion from the tertiary carbon was allowed.•For each system/reaction conditions 500 simulations were performed; in each of them a chain of 1000 carbon atoms was built.

Models for the catalyst: •R = H; Ar = H •R = H; Ar = Ph• R = H; Ar = Ph (Me)2

• R = H; Ar = Ph (i-Pr)2

•R = Me; Ar = Ph (Me)2

• R = Me; Ar = Ph (i-Pr)2

•R2 = An; Ar = Ph (i-Pr)2

Models for the catalyst: •R = H; Ar = H •R = H; Ar = Ph• R = H; Ar = Ph (Me)2

• R = H; Ar = Ph (i-Pr)2

•R = Me; Ar = Ph (Me)2

• R = Me; Ar = Ph (i-Pr)2

•R2 = An; Ar = Ph (i-Pr)2

CC

NN

Pd

CC

CCCC

CNN CCC

CCC C

Pd

C

CC

C

CCCC

CNN CCC

CCC C

C

Pd

C

CC

C

CC

C

CC

C

CC

C

C

CNN CCC

CC

C

C C

CC

Pd

CC

C

CC

C

C

CC

C

CC

C

CC

C

C

N CNC CC

CC

C

C C

CC

Pd

CC

CC

C

CC

C

CCCC

CNN CCC

CCC C

C

Pd

C

CCC

CC

CC

C

C

CC

C

CC

C

CC

C

C

CC

C

N CNC CC

C

C

CCC C

CC

Pd

CC

7

Propylene polymerization - effect of the catalystPropylene polymerization - effect of the catalyst

R=H; Ar=H: 331.6 br.; 66.7% 33.3%; 0

R=H; Ar=Ph: 122.5 br.; 51.7%; 40.1%; 14.2

R=H; Ar=Ph(CH3)2: 269.6 br.;60.9%; 38.1%; 0.89

R=H; Ar=Ph(i-Pr)2: 269.6 br.; 60.9%; 38.1%; 1.37

R=CH3; Ar=Ph(CH3)2: 251.0 br.; 59.7%; 38.7%; 0.93

R=CH3; Ar=Ph(i-Pr)2: 238.2 br.;61.7%; 36.5%; 2.6

R=An; Ar=Ph(i-Pr)2: 255.6 br.; 59.9%; 38.5%; 1.35

Examples of the polymer structures obtained with different catalysts (T=298K, p=1). The values above the plots denote: the the average number of branches / 1000 C, % of atoms in the main chain and % in primary branches, and the ratio between the isomerization and insertion steps. Colors are used to mark different types of branches (primary, secondary, etc.).

8

220

240

260

280

300

320

0 100 200 300 400 500

T [K]

No.

of b

ranc

hes

Propylene polymerization - temperature effectPropylene polymerization - temperature effect

Effect of temperature on the average No. of branches / 1000 C in the propylene polymerization catalyzed by the catalyst with R=CH3 and Ar=Ph(i-Pr)2.

T=98K

T=198K

T=298K

T=398K

T=498K

9

220

240

260

280

300

320

0.001 0.01 0.1 1

p [ arbitrary units]

No.

of

bra

nch

es

Propylene polymerization - pressure effectPropylene polymerization - pressure effect

0

10

20

30

40

50

60

70

0.001 0.01 0.1 1

% in main% in prim.% in sec.% in tert.

A change in the olefin pressure does not influence the global number of branches, while it strongly affects the microstructure of the resulting polymer. At high pressures the chains are ‘linear’ with relatively short branches, while at low pressures the hyperbranched structures are obtained.

A change in the olefin pressure does not influence the global number of branches, while it strongly affects the microstructure of the resulting polymer. At high pressures the chains are ‘linear’ with relatively short branches, while at low pressures the hyperbranched structures are obtained.

Effect of the olefin pressure on the average no. of branches / 1000 C and the % of atoms in the main chain and the branches of different types in the propylene polymerization catalyzed by the catalyst with R=CH3 and Ar=Ph(i-r)2.[T=298K].

%

10

0

10

20

30

40

50

60

70

80

0.001 0.01 0.1 1

p [arbitrary units]

No.

Of

C in

th

e lo

nge

st b

ran

chPropylene polymerization - pressure effectPropylene polymerization - pressure effect

prim.sec.tert.quatr.

Formation of the hyperbranched structures at low pressure values is reflected by the length of the longest primary, secondary, tertiary and quatrinary branches obtained in the simulations.

Formation of the hyperbranched structures at low pressure values is reflected by the length of the longest primary, secondary, tertiary and quatrinary branches obtained in the simulations.

Effect of the olefin pressure on length of the longest branches and the ratio of the isomerization and insertion steps in the propylene polymerization catalyzed by the catalyst with R=CH3 and Ar=Ph(i-Pr)2.[T=298K].

0

5

10

15

20

25

30

35

40

45

50

0.001 0.01 0.1 1

Av.

No.

of i

som

eris

atio

ns/ i

nser

tion

11

Propylene polymerization - pressure effectPropylene polymerization - pressure effect

Examples of the structures obtained from the simulations with different olefin pressure in the propylene polymerization catalyzed by the catalyst with R=CH3 and Ar=Ph(i-Pr)2.[T=298K]. All the structures are characterized by a similar global number of branches.

p=0.1

p=0.01

p=0.001

p=0.0001

12

II. Ethylene polymerization - model studies on the effects of catalyst (elementary reaction barriers), temperature, and

pressure on the microstructure of polymers

II. Ethylene polymerization - model studies on the effects of catalyst (elementary reaction barriers), temperature, and

pressure on the microstructure of polymers

•The main goal of this study was to understand the relationship between the structure of polyethylenes and the polymerization catalyst (modeled by different reaction barriers) as well as the reaction conditions•Since the ethylene polymerization is characterized by relatively large number of parameters characterizing all possible elementary reactions, for simplicity, the values of the isomerization barriers calculated for Brookhart Pd-diimine catalyst (Michalak, Ziegler Organometallics 1999, 18, 3998) were used in all the calculations, while the insertion barriers (for the primary and secondary carbon) were systematically changed (E1 from 1 to 6 kcal/mol, and E1 from 1 to 9 kcal/mol). •For each system/reaction conditions 500 simulations were performed; in each of them a chain of 1000 carbon atoms was built.

•The main goal of this study was to understand the relationship between the structure of polyethylenes and the polymerization catalyst (modeled by different reaction barriers) as well as the reaction conditions•Since the ethylene polymerization is characterized by relatively large number of parameters characterizing all possible elementary reactions, for simplicity, the values of the isomerization barriers calculated for Brookhart Pd-diimine catalyst (Michalak, Ziegler Organometallics 1999, 18, 3998) were used in all the calculations, while the insertion barriers (for the primary and secondary carbon) were systematically changed (E1 from 1 to 6 kcal/mol, and E1 from 1 to 9 kcal/mol). •For each system/reaction conditions 500 simulations were performed; in each of them a chain of 1000 carbon atoms was built.

13

Ethylene polymerization - pressure / catalyst effectsEthylene polymerization - pressure / catalyst effects

0

50

100

150

200

250

300

350

0.0001 0.001 0.01 0.1 1

E2=1E2=2E2=3E2=4E2=5E2=6E2=7E2=8E2=9N

o. o

f b

ran

ches

/ 10

00 C

p [arbitrary units]

E1=1.0 kcal/mol

pressure independent region

For every combination of E1 and E2 there exist a range of pressures, for which the global number of branches (per 1000 C) does not depend on the olefin pressure (pressure independent region). Depending on the values of the insertion barriers, E1 and E2 the global number of branches varies between 0 and 500. (see also next page). This indicates that by modifications of the catalysts (i.e. reaction barriers) anbd the process conditions one can design a variety of polyethylene materials with different microstructure.

14

0

50

100

150

200

250

300

350

400

450

0.0001 0.001 0.01 0.1 1

E1=2.0 kcal/mol

050

100150200250

300350400450500

0.0001 0.001 0.01 0.1 1

E1=3.0 kcal/mol

0

100

200

300

400

500

600

0.0001 0.001 0.01 0.1 1

E1=4.0 kcal/mol

0

100

200

300

400

500

600

0.0001 0.001 0.01 0.1 1

E1=6.0 kcal/mol

Pressure dependence of the total number of branches for the systems characterized by different insertion barriers (see previous page)

15

0

20

40

60

80

100

0.0001 0.001 0.01 0.1 1

E1E2=2

E1E2=4

E1E2=7

E1E2=9

% a

tom

s in

th

e m

ain

ch

ain

p [arbitrary units]

Ethylene polymerization - from linear to hyperbranched structuresEthylene polymerization - from linear to hyperbranched structures

Even in the ‘pressure independent region’ where the global number of branches does not depend on the olefin pressure, the microstructure of the polymer changes with the change of the pressure and the catalyst (insertion barriers). One can obtain a huge range of materials from linear to hyperbranched structures. Here we characterize the structure of the polymer by % of the atom in the main polymer chain. In the next page - by lengths of the branches.

16

0

20

40

60

80

2 3 4 5 6 7 8

E1=1.0 kcal/molp=0.001

Ave

rage

len

gth

of

bra

nch

es

E2 [kcal/mol]

0

50

100

150

200

250

300

2 3 4 5 6 7 8

No.

of

C in

th

e lo

nge

st b

ran

ches

E2 [kcal/mol]

E1=1.0 kcal/molp=0.001

prim.sec.tert.quatr.

By modifying the E1 and E2

values (i.e. the catalyst structure) one can obtain the hyperbranched structures with different structures of branches. For example, the low values of the barrier for the insertion into the M-C bond involving the secondary carbon, E2 (compared to E1) result in hyprebranched structures with very short higher-order branches. The high values of E2 result in a small probability of the ‘secondary’ insertion, and thus in producing the very long branches. (See also next page).

17

The polyethylene galleryThe polyethylene gallery

E1E2=2 kcal/mol

E1E2=5 kcal/mol

E1E2=7 kcal/mol

E1E2=5 kcal/mol

E1E2=5 kcal/mol

p=0.0001; T=298 K

18

Ethylene polymerization - temperature / catalyst effectsEthylene polymerization - temperature / catalyst effects

0

50100

150

200250

300

350

400450

500

0 100 200 300 400 500

T [K]

No.

of

bra

nch

esE1E2=1 kcal/molE1E2=3 kcal/molE1E2=5 kcal/mol

The values of E1 and E2 strongly affect the temperature-dependence of the polyethylene branching. For the catalysts with E1, E2 below the isomerisation barriers, one observe an increase of the number of branches, while for the systems with E1, E2 above the isomerisation barriers, the global number of branches decreases with an increase of T (However, such catalysts could be inefficient, due to high insertion barriers).

19

Acknowledgements. This work was supported by the National Sciences and Engineering Research Council of Canada (NSERC), Nova Chemical Research and Technology Corporation as well as donors of the Petroleum Research Fund, administered by the American Chemical Society (ACS-PRF No. 36543-AC3). A.M. acknowledges a University of Calgary Postdoctoral Fellowship.

Acknowledgements. This work was supported by the National Sciences and Engineering Research Council of Canada (NSERC), Nova Chemical Research and Technology Corporation as well as donors of the Petroleum Research Fund, administered by the American Chemical Society (ACS-PRF No. 36543-AC3). A.M. acknowledges a University of Calgary Postdoctoral Fellowship.

Conclusions•The stochastic modeling of the polymer growth and isomerisation provides a link between the molecular modeling on the microscopic level (quantum chemical calculations) and the macroscopic modeling of the polymer properties.• Applications to the polymerization of olefins allow one to identify the factors and understand their role in the controlling of the polyolefin branching and their microstructure as well as its dependence on the reaction conditions. • A qualitative agreement with the experimental facts for the polymerization of propylene catalyzed by the Pd-diimine catalyst demonstrates that indeed, the results of the DFT calculations can be used as input data for the stochastic simulations.• A model studies on the ethylene polymerization indicate that by modification of the catalyst (insertion barriers) and the reaction conditions one can potentially design a huge range of polyolefin materials characterized by specific microstructures.• The results of the stochastic modeling of the influence of the specific elementary reaction barriers on the polymer structure/properties can be also useful in interpreting the experimental results.

Conclusions•The stochastic modeling of the polymer growth and isomerisation provides a link between the molecular modeling on the microscopic level (quantum chemical calculations) and the macroscopic modeling of the polymer properties.• Applications to the polymerization of olefins allow one to identify the factors and understand their role in the controlling of the polyolefin branching and their microstructure as well as its dependence on the reaction conditions. • A qualitative agreement with the experimental facts for the polymerization of propylene catalyzed by the Pd-diimine catalyst demonstrates that indeed, the results of the DFT calculations can be used as input data for the stochastic simulations.• A model studies on the ethylene polymerization indicate that by modification of the catalyst (insertion barriers) and the reaction conditions one can potentially design a huge range of polyolefin materials characterized by specific microstructures.• The results of the stochastic modeling of the influence of the specific elementary reaction barriers on the polymer structure/properties can be also useful in interpreting the experimental results.

20