Artur Michalak a,b and Tom Ziegler a a Department of Chemistry, University of Calgary,

DFT and stochastic studies on the influence

of the catalyst structure and the reaction conditions

on the polyolefin microstructure

DFT and stochastic studies on the influence

of the catalyst structure and the reaction conditions

on the polyolefin microstructure

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

April 21, 2023April 21, 2023

Ethylene polymerization mechanismEthylene polymerization mechanism

-agostic

-complex

+ ethylene

-agostic

-agosticinsertion

n

Propylene:

n

Etylene:

333 methyl branches / 1000 C atoms

Linear chain

-olefin polymerization mechanism-olefin polymerization mechanism


n

Propylene:

n

Etylene:


Linear chain

Observed: up to 130 branches / 1000 C

Observed: 210 - 333 branches / 1000 C

Chain isomerization


Diimine catalystsDiimine catalysts

n

Propylene:

n

Etylene:


Linear chain



n

Propylene:

n

Propylene:

n

Etylene:

n

Etylene:


Linear chain



CCC

CC

CC

C

C

CC

C

CC

C

CC

C

C

CC

C

N CNC CC

C

C

CCC C

CC

Pd

CC

Diimine catalystsDiimine catalysts

Influence of olefin pressure on the polymer structurehigh p - linear structureslow p - hyperbranched structures

Pd – No. of branches independent of pNi – No. of braches influenced by p

n

Propylene:

n

Etylene:


Linear chain



n

Propylene:

n

Propylene:

n

Etylene:

n

Etylene:


Linear chain




Models for the catalyst:Models for the catalyst:

1) generic system: R = H; Ar = H1) generic system: R = H; Ar = H

2) a variety of systems with different substituents:

• R = H; Ar = Ph• R = H; Ar = Ph (Me)2

• R = H; Ar = Ph (i-Pr)2

• R = Me; Ar = H• R = Me; Ar = Ph (Me)2

• R = Me; Ar = Ph (i-Pr)2

• R2 = An; Ar = H• R2 = An; Ar = Ph (i-Pr)2


• R = H; Ar = Ph• R = H; Ar = Ph (Me)2

• R = H; Ar = Ph (i-Pr)2




CC

NN

Pd

R R

Ar Ar

+

CC

NN

Pd

R R

Ar Ar

+

CC

NN

Pd




• R = H; Ar = Ph• R = H; Ar = Ph (Me)2

• R = H; Ar = Ph (i-Pr)2





• R = H; Ar = Ph• R = H; Ar = Ph (Me)2

• R = H; Ar = Ph (i-Pr)2




CC

NN

Pd

R R

Ar Ar

+

CC

NN

Pd

R R

Ar Ar

+

CC

CCCC

CNN CCC

CCC C

Pd




• R = H; Ar = Ph• R = H; Ar = Ph (Me)2

• R = H; Ar = Ph (i-Pr)2





• R = H; Ar = Ph• R = H; Ar = Ph (Me)2

• R = H; Ar = Ph (i-Pr)2




CC

NN

Pd

R R

Ar Ar

+

CC

NN

Pd

R R

Ar Ar

+

C

CC

C

CCCC

CNN CCC

CCC C

C

Pd

C




• R = H; Ar = Ph• R = H; Ar = Ph (Me)2

• R = H; Ar = Ph (i-Pr)2





• R = H; Ar = Ph• R = H; Ar = Ph (Me)2

• R = H; Ar = Ph (i-Pr)2




CC

NN

Pd

R R

Ar Ar

+

CC

NN

Pd

R R

Ar Ar

+

CC

C

CC

C

CC

C

CC

C

C

CNN CCC

CC

C

C C

CC

Pd

CC




• R = H; Ar = Ph• R = H; Ar = Ph (Me)2

• R = H; Ar = Ph (i-Pr)2





• R = H; Ar = Ph• R = H; Ar = Ph (Me)2

• R = H; Ar = Ph (i-Pr)2




CC

NN

Pd

R R

Ar Ar

+

CC

NN

Pd

R R

Ar Ar

+

CC

CC

NN

Pd




• R = H; Ar = Ph• R = H; Ar = Ph (Me)2

• R = H; Ar = Ph (i-Pr)2





• R = H; Ar = Ph• R = H; Ar = Ph (Me)2

• R = H; Ar = Ph (i-Pr)2




CC

NN

Pd

R R

Ar Ar

+

CC

NN

Pd

R R

Ar Ar

+

CC

C

CC

C

CCCC

CNN CCC

CCC C

C

Pd

C




• R = H; Ar = Ph• R = H; Ar = Ph (Me)2

• R = H; Ar = Ph (i-Pr)2





• R = H; Ar = Ph• R = H; Ar = Ph (Me)2

• R = H; Ar = Ph (i-Pr)2




CC

NN

Pd

R R

Ar Ar

+

CC

NN

Pd

R R

Ar Ar

+

C

CC

C

C

CC

C

CC

C

CC

C

C

N CNC CC

CC

C

C C

CC

Pd

CC




• R = H; Ar = Ph• R = H; Ar = Ph (Me)2

• R = H; Ar = Ph (i-Pr)2





• R = H; Ar = Ph• R = H; Ar = Ph (Me)2

• R = H; Ar = Ph (i-Pr)2




CC

NN

Pd

R R

Ar Ar

+

CC

NN

Pd

R R

Ar Ar

+

CC

CC

C

CC

C

CC

CC

NN

Pd




• R = H; Ar = Ph• R = H; Ar = Ph (Me)2

• R = H; Ar = Ph (i-Pr)2





• R = H; Ar = Ph• R = H; Ar = Ph (Me)2

• R = H; Ar = Ph (i-Pr)2




CC

NN

Pd

R R

Ar Ar

+

CC

NN

Pd

R R

Ar Ar

+

CCC

CC

CC

C

C

CC

C

CC

C

CC

C

C

CC

C

N CNC CC

C

C

CCC C

CC

Pd

CC

DFT calculations:DFT calculations:Chain growth:

Chain isomerization:

DFT calculations:DFT calculations:

A. Michalak, T. Ziegler, "Pd-catalyzed Polymerization of Propene - DFT Model Studies", Organometallics, 18, 1999, 3998-4004.

A. Michalak, T. Ziegler, "DFT studies on substituent effects in Pd-catalyzed olefin polymerization", Organometallics, 19, 2000, 1850-1858.

Examples of results:

Ethylene insertion barrier:DFT: 16.7 kcal/molexp.: 17.4 kcal/mol

Isomerization barrier:DFT: 5.8 (6.8) kcal/molexp: 7.2 kcal/mol

C

CC

C

C

CC

C

CC

C

CC

C

C

N CNC CC

CC

C

C C

CC

Pd

CC

Substituent effect in real systemsSubstituent effect in real systems

Electronic preference Steric effect(generic system) (real systems)

alkyl complexes iso-propyl iso-propyl

olefin -complexes iso-propyl alkyl n-propyl alkyl

olefin -complexes propene ethene

propene insertion 2,1- 1,2-

Electronic preference Steric effect(generic system) (real systems)

alkyl complexes iso-propyl iso-propyl

olefin -complexes iso-propyl alkyl n-propyl alkyl

olefin -complexes propene ethene

propene insertion 2,1- 1,2-

Isomerization reactionsIsomerization reactions

0.000.00

+4.56+4.56

-3.42-3.42

0.000.00+5.84+5.84

+1.59+1.59

following1,2-insertion



0.000.00

+4.56+4.56

-3.42-3.42

0.000.00+5.84+5.84

+1.59+1.59




0.000.00

+4.56+4.56

-3.42-3.42

0.000.00+5.84+5.84

+1.59+1.59



1 C atom attached to the catalyst:olefin capture

followed by 1,2- or 2,1-

insertion

Stochastic simulation - how it worksStochastic simulation - how it works

1 C atom attached to the catalyst:olefin capture

followed by 1,2- or 2,1-

insertion


Primary C attached to the catalyst:1) 1 possible isomerization 2) olefin capture and 1,2- insertion3) olefin capture and 2,1- insertion4) termination


1

2

3

4

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


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


Primary C attached to the catalyst:1) isomerization to secondary C2) olefin capture and 1,2- insertion3) olefin capture and 2,1- insertion4) termination


Primary C attached to the catalyst:1) isomerization to tertiary C2) olefin capture and 1,2- insertion3) olefin capture and 2,1- insertion4) termination






Probablities of the eventsProbablities of the events

Basic assumption:relative probabilities (microscopic)

= relative rates (macroscopic):



i

π j

=ri

rj

i

i∑ = 1

36

Macroscopic kinetic expressions with microscopic barriers for elementary reactions(calculated or experimental)

Macroscopic kinetic expressions with microscopic barriers for elementary reactions(calculated or experimental)

Use of macroscopic kinetic expressions allows us to discuss the effects of the reaction conditions (temperature and olefin pressure)

Use of macroscopic kinetic expressions allows us to discuss the effects of the reaction conditions (temperature and olefin pressure)

Probablities of the eventsProbablities of the events



e.g. isomerization vs. isomerization:

isomerization vs. insertion:

etc.



e.g. isomerization vs. isomerization:

isomerization vs. insertion:

etc.

i

π j

=ri

rj

iso.1

π iso.2

=riso.1

riso.2

=k iso.1

kiso.2

≈ exp(ΔΔG1, 2

kT)

i

i∑ = 1

iso.1

π 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;

37

Simulations of polymer growth and isomerizationSimulations of polymer growth and isomerization

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;

Propylene polymerization (theoretical data)Propylene polymerization (theoretical data)

R = H; Ar = H

CC

NN

Pd

A. Michalak, T. Ziegler, „Stochastic modelling of the propylene polymerization catalyzed by the Pd-based diimine catalyst: influence of the catalyst structure and the reaction conditions on the polymer microstructure”, J. Am. Chem. Soc, 2002, in press.

R=H; Ar= Ph

CC

CCCC

CNN CCC

CCC C

Pd


R=An; Ar= Ph(i-Pr)2

CCC

CC

CC

C

C

CC

C

CC

C

CC

C

C

CC

C

N CNC CC

C

C

CCC C

CC

Pd

CC


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

The values above the plots denote: 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.).

42

220

240

260

280

300

320

0 100 200 300 400 500

T [K]

No. of branches / 1000 C

Propylene polymerization - temperature effectPropylene polymerization - temperature effect

T=98K

T=198K

T=298K

T=398K

T=498K

43

C

CC

C

C

CC

C

CC

C

CC

C

C

N CNC CC

CC

C

C C

CC

Pd

CC

220

240

260

280

300

320

0 100 200 300 400 500

T [K]

No. of branches / 1000 C

Propylene polymerization - temperature effectPropylene polymerization - temperature effect

T=98K

T=198K

T=298K

T=398K

T=498K

44

C

CC

C

C

CC

C

CC

C

CC

C

C

N CNC CC

CC

C

C C

CC

Pd

CC

• Two insertion pathways: 1,2- i 2,1-

• Chain straightening follows 2,1-insertion only

•Lower barrier for the 1,2-insertion (by c.a. 0.6 kcal/mol)

• Practically each 2,1-insertion is followed by chain straighening

220

240

260

280

300

320

0.001 0.01 0.1 1

p [ arbitrary units]

No. of branches

Propylene polymerization - pressure effectPropylene polymerization - pressure effect45

C

CC

C

C

CC

C

CC

C

CC

C

C

N CNC CC

CC

C

C C

CC

Pd

CC

220

240

260

280

300

320

0.001 0.01 0.1 1


No. of branches

Propylene polymerization - pressure effectPropylene polymerization - pressure effect46

C

CC

C

C

CC

C

CC

C

CC

C

C

N CNC CC

CC

C

C C

CC

Pd

CC

Exp.: 213br. / 1000 C

„Ideal” – no chain straighening333.3

Propylene polymerization - pressure effectPropylene polymerization - pressure effect

p=0.1

p=0.01

p=0.001

p=0.0001

47

C

CC

C

C

CC

C

CC

C

CC

C

C

N CNC CC

CC

C

C C

CC

Pd

CC

Ethylene polymerization by Pd-based diimine catalyst Simulations from experimental data (G)


48

CCC

CC

CC

C

C

CC

C

CC

C

CC

C

C

CC

C

N CNC CC

C

C

CCC C

CC

Pd

CC

0

30

60

90

120

150

0.001 0.01 0.1 1


No. of branches

Ethylene polymerization by Pd-based diimine catalyst Simulations from experimental data


49

CCC

CC

CC

C

C

CC

C

CC

C

CC

C

C

CC

C

N CNC CC

C

C

CCC C

CC

Pd

CC

0

30

60

90

120

150

0.001 0.01 0.1 1


No. of branches



50

CCC

CC

CC

C

C

CC

C

CC

C

CC

C

C

CC

C

N CNC CC

C

C

CCC C

CC

Pd

CC

Exp.



51

p



52

p

0

30

60

90

120

150

180

0 100 200 300 400 500

T [K]

No. of branches



53

CCC

CC

CC

C

C

CC

C

CC

C

CC

C

C

CC

C

N CNC CC

C

C

CCC C

CC

Pd

CC

0

30

60

90

120

150

180

0 100 200 300 400 500

T [K]

No. of branches



54

CCC

CC

CC

C

C

CC

C

CC

C

CC

C

C

CC

C

N CNC CC

C

C

CCC C

CC

Pd

CC



55

CCC

CC

CC

C

C

CC

C

CC

C

CC

C

C

CC

C

N CNC CC

C

C

CCC C

CC

Pd

CC

A. Michalak, T. Ziegler, „DFT and stochastic studies on the factors controlling branching and microstructure of polyethylenes in the polymerization processes catalyzed by the late-transition metal complexes”, in preparation

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

microstructure of polymers

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

microstructure of polymers

56

Ethylene 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

57



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

58

pressure independent region

0

50

100

150

200

250

300

350

400

450

0.0001 0.001 0.01 0.1 1

E1=2.0 kcal/mol

0

50100

150200

250

300350

400450

500

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

59

The faster is the isomerisation (compared to insertions), the more extended is the pressure independent region.

The faster is the isomerisation (compared to insertions), the more extended is the pressure independent region.For Ni-diimine catalyst the isomerisation is slower then for Pdi.e. for Pd the pressure independent region is more extended toward higher values of the pressure

For Ni-diimine catalyst the isomerisation is slower then for Pdi.e. for Pd the pressure independent region is more extended toward higher values of the pressure

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

60

Ethylene polymerization with the Ethylene polymerization with the neutral anilinotropone Ni-based neutral anilinotropone Ni-based

catalystcatalyst


catalystcatalyst

Experimental data:

Hiks, F.A., Brookhart M.

Organometallics 2001, 20, 3217.

Experimental data:




catalystcatalyst


catalystcatalyst

Experimental data:



Experimental data:



0

20

40

60

80

100

120

0 100 200 300 400 500 600 700

p [psig]

br./1000C

0

10

20

30

40

50

60

70

80

20 40 60 80 100 120

T [C]

br./1000C

Ni-anilinotropone catalyst - cis/trans isomers

Alkyl complexes:

Ethylene -complexes:

0

5

10

-5

-10

-15

-20N-isomers

O-isomers

Alkyl

AlkylAlkyl

Alkyl

-

-

- -

ins. TS

ins. TS ins. TS

ins. TS

iso. TS

iso. TS

1.9

-12.9

-17.9

0.01.9

9.5

5.8

1.33.4

-17.5-17.1

5.7

1.7

Secondary alkyl Primary alkyl

Ni-anilinotropone catalyst – results for real catalyst

0

5

10

-5

-10

-15

-20N-isomers

O-isomers

Alkyl

AlkylAlkyl

Alkyl

-

-

- -

ins. TS

ins. TS ins. TS

ins. TS

iso. TS

iso. TS

1.9

-12.9

-17.9

0.01.9

9.5

5.8

1.33.4

-17.5-17.1

5.7

1.7

Secondary alkyl Primary alkyl

Ni-anilinotropone catalyst – stochastic simulations

020

4060

80

100120

140160

0 0.02 0.04 0.06 0.08 0.1

p [arb.u.]

br./1000C

14 - 600 psig


0

20

40

60

80

100

120

140

160

0 0.0038 0.0076 0.0114 0.0152 0.019 0.0228

p [arb.u.]

br./1000C

14 50 100 200 400 600p [psig]


Theoret.

Exp.

0102030405060708090

100

40 50 60 70 80 90 100

T [C]

br./1000C

p = 0.011 arb.u. / p = 400 psig

Theoret.

Exp.


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 NATO Fellowship. Important parts of the calculations was performed using the UofC MACI cluster.

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 NATO Fellowship. Important parts of the calculations was performed using the UofC MACI cluster.

ConclusionsConclusions

DFT:• energetics of elementary reactions in a reasonable agreement with experimental data • understanding of the electronic and steric influence of the catalysts substituents

Stochastic modelling:• provides a link between the molecular modeling on the microscopic and macroscopic level •identifies the factors controlling of the polyolefin branching and their microstructure •demonstrates that a huge range of polyolefin materials with specific microstructures can be rationally designed by modification of the catalysts• can be also useful for interpretation of the experimental results

DFT:• energetics of elementary reactions in a reasonable agreement with experimental data • understanding of the electronic and steric influence of the catalysts substituents

Stochastic modelling:• provides a link between the molecular modeling on the microscopic and macroscopic level •identifies the factors controlling of the polyolefin branching and their microstructure •demonstrates that a huge range of polyolefin materials with specific microstructures can be rationally designed by modification of the catalysts• can be also useful for interpretation of the experimental results

DFT:• energetics of elementary reactions in excellent agreement with experimental data • understanding of the electronic and steric influence of the catalysts substituents

Stochastic modelling:• provides a link between the molecular modeling on the microscopic and macroscopic level • allows one to identify the factors controlling of the polyolefin branching and their microstructure as well as its dependence on the reaction conditions• demonstrates that a huge range of polyolefin materials with specific microstructures can be rationally designed by modification of the catalysts• can be also useful for interpretation of the experimental results.`

DFT:• energetics of elementary reactions in excellent agreement with experimental data • understanding of the electronic and steric influence of the catalysts substituents

Stochastic modelling:• provides a link between the molecular modeling on the microscopic and macroscopic level • allows one to identify the factors controlling of the polyolefin branching and their microstructure as well as its dependence on the reaction conditions• demonstrates that a huge range of polyolefin materials with specific microstructures can be rationally designed by modification of the catalysts• can be also useful for interpretation of the experimental results.`

Documents

Artur Michalak a,b and Tom Ziegler a a Department of Chemistry, University of Calgary,