Modeling MAO Modeling MAO (Methylalumoxane(Methylalumoxane))

Eva Zurek, Tom Woo, Tim Firman, Tom ZieglerEva Zurek, Tom Woo, Tim Firman, Tom Ziegler

University of Calgary, Department of Chemistry, University of Calgary, Department of Chemistry, Alberta, Canada, T2N-1N4Alberta, Canada, T2N-1N4

IntroductionIntroduction

MAO is one of the most industrially important activators in MAO is one of the most industrially important activators in single-site metallocene catalyst polymerizationsingle-site metallocene catalyst polymerization

Commonly accepted role of MAO in catalysis:Commonly accepted role of MAO in catalysis:((nn55-C-C55HH55))22ZrMeZrMe22 + MAO + MAO [( [(nn55-C-C55HH55))22ZrMe]ZrMe]++ + [(MAO)Me] + [(MAO)Me]--

[([(nn55-C-C55HH55))22ZrMe]ZrMe]++ + n[CH + n[CH22=CH=CH22] ] [( [(nn55-C-C55HH55))22Zr-[CHZr-[CH22--

CHCH22]]nn-CH-CH33]]++

Not possible to isolate crystalline samples of MAO; Not possible to isolate crystalline samples of MAO; disproportionation reactions give complicated NMR spectradisproportionation reactions give complicated NMR spectra

Hence, it is not possible to characterize MAO and thus the Hence, it is not possible to characterize MAO and thus the structure(s) of MAO remain largely unknownstructure(s) of MAO remain largely unknown

Goal of study is to propose a structural model for MAOGoal of study is to propose a structural model for MAO

PreliminaryPreliminary Structural Structural InvestigationInvestigation

Density Functional Theory Calculations were carried out using the Density Functional Theory Calculations were carried out using the Amsterdam Density Functional (ADF) program version 2.3.3Amsterdam Density Functional (ADF) program version 2.3.3

Binding Energy Per Monomer = (E[(AlOMe)Binding Energy Per Monomer = (E[(AlOMe)nn] - E[n(AlOMe)])/n] - E[n(AlOMe)])/n

Preliminary study shows that three-dimensional caged structure have Preliminary study shows that three-dimensional caged structure have lower BE/monomer, thus are more energetically stable than two-lower BE/monomer, thus are more energetically stable than two-dimensional sheet structuresdimensional sheet structures

C C

OAl O AlAl

O

C

OAl O Al

OC Al CC

C

C

O Al

Al

C

O

Al O

O Al

O

C

Al

Al O

C

C

Binding Energy per monomer = -79.27kcal/mol Binding Energy per monomer = -95.93kcal/mol

Types of Structures StudiedTypes of Structures Studied Three-dimensional cage Three-dimensional cage

structures, consisting of square, structures, consisting of square, hexagonal and octagonal faceshexagonal and octagonal faces

Four-coordinate Al centers Four-coordinate Al centers bridged by three-coordinate O bridged by three-coordinate O atomsatoms

[MeAlO][MeAlO]nn, where n ranges , where n ranges

between 4-16between 4-16 ADF calculations were ADF calculations were

performed on 35 different performed on 35 different structuresstructures

C

C

O Al

Al O

C

Al O

OAl

C

O Al

Al O

C

C

Example of such a MAO caged structure

MathematicalMathematical RelationshipsRelationships For a given MAO Structure the following For a given MAO Structure the following

mathematical relationships were derived*mathematical relationships were derived* SF = OF + 6SF = OF + 6 [1] [1] 3(3S) + 2(2S+H) + (2H+S) = 243(3S) + 2(2S+H) + (2H+S) = 24 [2] [2] (2S+H) + 2(2H+S) + 3(3H) = 6(HF) [3](2S+H) + 2(2H+S) + 3(3H) = 6(HF) [3] SF is # of square, HF is # of hexagonal, OF is # SF is # of square, HF is # of hexagonal, OF is #

octagonal facesoctagonal faces (3S) is the # of atoms bonded to three square faces, (3S) is the # of atoms bonded to three square faces,

(2S+H) the number of atoms bonded to two square (2S+H) the number of atoms bonded to two square and one hexagonal face, etcetera.and one hexagonal face, etcetera.

[1] shows us that minimum number of SF in MAO [1] shows us that minimum number of SF in MAO cage is 6, when OF is zerocage is 6, when OF is zero

[2] and [3] can be used to construct large MAO cages [2] and [3] can be used to construct large MAO cages with OF zerowith OF zero *using concepts from *using concepts from

Regular PolytopesRegular Polytopes, the branch of Pure Mathematics which studies Polyhedrons in n-dimensions, the branch of Pure Mathematics which studies Polyhedrons in n-dimensions

C

C

Al O

C

O Al

O Al

C Al O

OAl

OAl

C

O Al

C

C

(2H+S)

(2S+H)

(3S)

Diagram showing three different bonding environments for (AlOMe)7

Formula for Predicting MAO Cage Formula for Predicting MAO Cage Energies/ Example Shown for (AlOMe)Energies/ Example Shown for (AlOMe)88

A least squares fit was performed to derive a formula predicting MAO A least squares fit was performed to derive a formula predicting MAO EnergiesEnergies

E = -373.57(3S) -377.49(2S+H) -381.13(2H+S) -381.80(3H) -377.14(2S+O) -E = -373.57(3S) -377.49(2S+H) -381.13(2H+S) -381.80(3H) -377.14(2S+O) -380.59(2O+S) -381.03(S+O+H) -378.86(2H+O) -365.51(2O+H)kcal/mol380.59(2O+S) -381.03(S+O+H) -378.86(2H+O) -365.51(2O+H)kcal/mol

Rms deviation was found as being 4.70kcal/mol for 35 structuresRms deviation was found as being 4.70kcal/mol for 35 structures

C

C

Al O

O

CAl

O

C

Al

Al

O

AlC

O

OO

Al

Al

Al O

C

C

CC

C

O

C

C

Al

AlAl

Al

O

O

O

O

O

O

AlAl

Al

Al

C

C

O

C

C

CAl

C

OC

O

O

Al

Al

C

AlO

Al

C Al

O

C

O O

OAlAl

CC

-2 octagonal faces-8 square faces-16 atoms (2S+O)-Energy: -6037.87kcal/mol-Predicted: -6034.24kcal/mol

-2 octagonal faces-8 square faces-4 atoms (3S)-8 atoms (2S+O)-4 atoms (2O+S)-Energy: -6028.60kcal/mol-Predicted: -6033.76kcal/mol

-4 hexagonal faces-6 square faces-8 atoms (2S+H)-8 atoms (2H+S)-Energy: 6070.48kcal/mol-Predicted: -6068.96kcal/mol

Determination of Determination of Entropic/Enthalpic Corrections Entropic/Enthalpic Corrections

ADF Frequency calculations on (AlOMe)ADF Frequency calculations on (AlOMe)44 and (AlOMe) and (AlOMe)66 were used to were used to

parametrize UFF 2 (Molecular Mechanics Program)parametrize UFF 2 (Molecular Mechanics Program) Parametrization gave good values for two different (AlOMe)Parametrization gave good values for two different (AlOMe)88 isomers isomers

This parametrized version of UFF2 was then used to calculate entropies and This parametrized version of UFF2 was then used to calculate entropies and finite temperature enthalpy corrections for the 35 different MAO structuresfinite temperature enthalpy corrections for the 35 different MAO structures

Enthalpic ConsiderationsEnthalpic Considerations Equations were found which predict Equations were found which predict

enthalpic values for (AlOMe)enthalpic values for (AlOMe)nn

HH00 = 25n kcal/mol = 25n kcal/mol

[5] [5] Vibrational Portion of HVibrational Portion of Htemptemp [6] [6]

H Hvibvib = H = H00 + (0.0028T - + (0.0028T -

0.3548)n x ln(T) 0.3548)n x ln(T) rms rms

deviation of 3.28, 0.78, 1.32 and deviation of 3.28, 0.78, 1.32 and 3.36kcal/mol at 198.15K, 298.15K, 3.36kcal/mol at 198.15K, 298.15K, 398.15K, 598.15K398.15K, 598.15K

H = E + HH = E + H00 + H + Htemptemp [4] [4]

where E is the energy, Hwhere E is the energy, H00 the zero- the zero-

point energy, Hpoint energy, Htemptemp the finite the finite

temperature enthalpy correctiontemperature enthalpy correction

Entropic ConsiderationsEntropic Considerations SSvib vib = 7.91(3S)+8.30(2S+H)+10.20(2H+S)= 7.91(3S)+8.30(2S+H)+10.20(2H+S)

+8.49(3H)+10.41(2S+O)+9.50(2O+S)+8.49(3H)+10.41(2S+O)+9.50(2O+S)+10.45(S+O+H)+7.32(2H +O)+0(2O+H) +10.45(S+O+H)+7.32(2H +O)+0(2O+H) cal/molK [9] cal/molK [9] rms deviation of 1.78Kcal/mol at rms deviation of 1.78Kcal/mol at 298.15K298.15K

Extension to Different Temperatues:Extension to Different Temperatues: Translational Entropy: Translational Entropy: [10] [10]

S S22 = S = S11 + T + T22/T/T11 + T + T22(0.014) - 5.47 (0.014) - 5.47

Rotational Entropy:Rotational Entropy: [11] S [11] S22

= S= S11 + T + T22/T/T11 + T + T22(0.007) - 3.28(0.007) - 3.28

Vibrational Entropy:Vibrational Entropy: [12] S [12] S22

= (T= (T22/T/T11-((0.0006T-((0.0006T2222 - 0.5353T - 0.5353T22 + 108.85) + 108.85)--

11)S)S11 rms deviation of 0.27, 1.70 and rms deviation of 0.27, 1.70 and

4.90kcal/mol at 198.15K, 398.15K, 4.90kcal/mol at 198.15K, 398.15K, 598.15K598.15K

S = SS = Svibvib + S + Stranstrans + S + Srotrot

SStranstrans = (0.35n + 41.17)cal/molK at = (0.35n + 41.17)cal/molK at

298.15K 298.15K [7] [7]

SSrotrot = (0.57n + 30.57)cal/molK at = (0.57n + 30.57)cal/molK at

298.15K 298.15K [8] [8]

Gibbs Free Energy Per Monomer (AlOMe Gibbs Free Energy Per Monomer (AlOMe unit) at Different Temperatures (G/n)unit) at Different Temperatures (G/n)

Lowest Gibbs Free Energy per Monomer Unit Lowest Gibbs Free Energy per Monomer Unit gives most stable structuregives most stable structure

For a given n, the most stable structures For a given n, the most stable structures composed of SF and HF only. Reason: equation composed of SF and HF only. Reason: equation [1] shows that as # OF increases, so does #SF. [1] shows that as # OF increases, so does #SF. SF exhibit ring strain therefore destabilizing the SF exhibit ring strain therefore destabilizing the structurestructure

Graph shows G/n for structures composed of Graph shows G/n for structures composed of SF and HF onlySF and HF only

Equations [2] and [3] used to construct Equations [2] and [3] used to construct structures for n > 16.structures for n > 16.

Equations [4] - [11] used to predict G/n for n Equations [4] - [11] used to predict G/n for n =14 & n > 16.=14 & n > 16.

Most Stable structure at all temperatures is Most Stable structure at all temperatures is (AlOMe)(AlOMe)1212

At low temperatures, (AlOMe)At low temperatures, (AlOMe)1616 is almost as is almost as

stable as (AlOMe)stable as (AlOMe)1212

G = G = E + E + HH00 + + H Htemptemp -T -T S S

Percentage of Each n at Percentage of Each n at Different TemperaturesDifferent Temperatures

Most stable structure is Most stable structure is (AlOMe)(AlOMe)1212

Consists of 24 atoms in a Consists of 24 atoms in a (2H+S) environment; (2H+S) environment; 6SF; 8HF6SF; 8HF

tt-butyl analogue -butyl analogue sunthesized by Barron and sunthesized by Barron and co-workers co-workers 1,21,2

Graph corresponds to Graph corresponds to experimental data, which experimental data, which predicts that n ranges predicts that n ranges between 9 and 30between 9 and 30 3 3 and and between 14 and 20 between 14 and 20 44

Investigation of MAO-TMA Investigation of MAO-TMA InteractionsInteractions

All MAO solutions contain residual All MAO solutions contain residual TMA (trimethylaluminum)TMA (trimethylaluminum)

It has been shown that TMA It has been shown that TMA participates in equilibrium with participates in equilibrium with different MAO oligomersdifferent MAO oligomers22 and in and in disproportionation reactionsdisproportionation reactions55

The way in which TMA bonds to The way in which TMA bonds to MAO was determined via studying MAO was determined via studying (AlOMe)(AlOMe)66

(AlMe)(AlMe)22 bonds to the oxygen and bonds to the oxygen and

there is an Me transfer to the Althere is an Me transfer to the Al The bond which breaks belongs to The bond which breaks belongs to

two square faces and both the Al two square faces and both the Al and O are in a (2S+H) environmentand O are in a (2S+H) environment

H

H

H

CH

C

H

O

H

Al

Al O

H

C

Al

O

H

H

O

Al

C

H

O Al

Al

H

O

H

C

H

C

H

H

H

H

H

H

H

CH

HC

H

O Al

H

H

Al O

H

H

C

C

H

AlO

Al

O

H

H

H

H

C

H

Al C

H

H

H

C

O Al

OAl

H

H

H

CH

H

C

H

H

H

TMA*

*

*

*

*-* bondbreaks

E= -13.06kcal/mol with TMA dimer

Determining the Sites with Determining the Sites with Greatest Latent Lewis AcidityGreatest Latent Lewis Acidity

The bond which gives us the greatest The bond which gives us the greatest E value when reacted with TMA has the greatest E value when reacted with TMA has the greatest Latent Lewis Acidity (LLA). Bonds with greatest LLA for structures composed of SF Latent Lewis Acidity (LLA). Bonds with greatest LLA for structures composed of SF and HF only are shown belowand HF only are shown below

The figure below shows us that LLA is dependant upon the presence of SFThe figure below shows us that LLA is dependant upon the presence of SF Equation [1] shows that for a MAO structure composed of SF and HF, there are only six Equation [1] shows that for a MAO structure composed of SF and HF, there are only six

SF present; hence there are few LLA sitesSF present; hence there are few LLA sites CpCp22ZrMeZrMe22 also coordinates to the LLA sites in MAO, and hence there are a limited also coordinates to the LLA sites in MAO, and hence there are a limited

amount of sites where this could occur. This explains the high Al:Zr ratio needed for amount of sites where this could occur. This explains the high Al:Zr ratio needed for catalysis to occur.catalysis to occur.

ConclusionsConclusions Formulae predicting the energy, entropy and finite temperature enthalpy Formulae predicting the energy, entropy and finite temperature enthalpy

corrections for a given MAO structure consisting of SF, HF and OF have been corrections for a given MAO structure consisting of SF, HF and OF have been foundfound

When pure MAO is considered (AlOMe)When pure MAO is considered (AlOMe)1212 is the most stable structure in the is the most stable structure in the

temperature range 198.15K-598.15Ktemperature range 198.15K-598.15K The way in which TMA bonds to MAO has been determinedThe way in which TMA bonds to MAO has been determined The sites exhibiting greatest LLA for five MAO structures have been foundThe sites exhibiting greatest LLA for five MAO structures have been found It has been shown that the presence of LLA is dependant upon the presence of It has been shown that the presence of LLA is dependant upon the presence of

SFSF The high ratio of Al:Zr which is needed for catalysis to occur is attributed to The high ratio of Al:Zr which is needed for catalysis to occur is attributed to

the limited amount of SF present within a MAO structure (cf. Equation [1])the limited amount of SF present within a MAO structure (cf. Equation [1])

MiscellaneousMiscellaneous

Acknowledgements:Acknowledgements:Dr. Clark Landis, University of Wisconsin for supplying us with UFF2; NSERCDr. Clark Landis, University of Wisconsin for supplying us with UFF2; NSERC

References:References:1) Mason, M.R.; Smith, J.M.; Bott, S.G.; Barron, A.R.; 1) Mason, M.R.; Smith, J.M.; Bott, S.G.; Barron, A.R.; J. Am. Chem. Soc. J. Am. Chem. Soc.

19931993, , 115115, 4971., 4971. 2) Harlan, C.F.; Mason, M.R.; Barron, A.R.; 2) Harlan, C.F.; Mason, M.R.; Barron, A.R.; Organomet.Organomet. 19941994, , 1313, 2957., 2957.3) Babushkin, D.E.; Semikolenova, N.V.; Panchenko, V.N.; 3) Babushkin, D.E.; Semikolenova, N.V.; Panchenko, V.N.;

Sobolev, A.P.; Zakharov, V.A.; Sobolev, A.P.; Zakharov, V.A.; Talsi, E.P.; Talsi, E.P.; Macromol. Chem. Phys. Macromol. Chem. Phys. 19971997, , 198198, 3845., 3845.4) Talsi, E.P.; Semikolenova, N.V.; Panchenko, 4) Talsi, E.P.; Semikolenova, N.V.; Panchenko,

V.N.; Sobolev, A.P.; Babushkin, D.E.; V.N.; Sobolev, A.P.; Babushkin, D.E.; Shubin, A.A.; Zakharov, V.A.; Shubin, A.A.; Zakharov, V.A.; J. J. Molecular Catalysis A: ChemicalMolecular Catalysis A: Chemical , , 19991999, , 139139, 131., 131. 5) Tritto, I.; Sacchi, M.C.; Locatelli, 5) Tritto, I.; Sacchi, M.C.; Locatelli, P.; P.; Macromol. Chem. Phys.Macromol. Chem. Phys. 19961996, , 197197, 1537., 1537.

Work in Progress:Work in Progress:-to study the role which TMA plays in lowering the energeies of different -to study the role which TMA plays in lowering the energeies of different

MAO oligomersMAO oligomers -to study the metallocene/MAO interaction thereby determining the active -to study the metallocene/MAO interaction thereby determining the active species in species in polymerization polymerization