A Theoretical Investigation of the Structure and Function of MAO

(Methylaluminoxane)

Eva Zurek, University of Calgary

AlO

O

OAl

Al

AlO

Al

Al

O

O

O

O

Al

O

Al

Al

Al

AlO

O

OAl

Computational Details• DFT Calculations: performed with ADF 2.3.3 and 2000• Functional: LDA along with gradient corrected exchange functional of Becke;

correlation functional of Perdew• Basis-set: double- STO basis with one polarization function for H, C, Al, O; triple-

STO basis with one polarization function for Zr• Frequencies: single-point numerical differentiation • Molecular Mechanics: UFF2 parameterized to give entropies/enthalpies which agreed

with those obtained from ADF• Solvation: COnductor-like Screening Model (COSMO)• NMR Chemical Shifts: triple- STO basis with two polarization functions for H and C;

Gauge Including Atomic Orbitals (GIAO)• Transition States: geometry optimizations along a fixed reaction coordinate. TS where

gradient less than convergence criteria

Catalysis

• K. Ziegler (1953) & G. Natta (1954); Nobel Prize in 1963

• Annual production of polyolefins is a hundred million tons (2001)

• 1/3 of the polymers made today are by Ziegler/Natta catalysis

• Polyethylene is the most popular plastic in the world

• Grocery bags, shampoo bottles, children’s toys, bullet proof vests (Kevlar), …

• Goal: to control MW, stereochemistry

• Single site catalysts: narrow MW distribution; higher stereoselectivity; higher activity

• Allow detailed structural & mechanistic studies

Single-Site Homogeneous Catalysis

• Catalysts: L1L2MR1R2; L=Cp, NPR3, NCR2; M=Ti, Zr, R=methyl, propyl, etc.

• Co-Catalyst (Anion): B(C6F5)3, MAO (Methylaluminoxane)

• MAO + Cp2Zr(CH3)2 Cp2ZrCH3+ + MAOMe-

Zr+

CH3

Zr+

CH3

Zr+

CH3

Insertion Transition Stateπ-complexSeparated Species

Zr+

CH3

Product

C2H4, olefin

MAODoes not crystallize

Gives complicated NMR

Industrially, one of themost important co-catalysts

MAO is formed from controlled hydrolysis of TMA (trimethylaluminum)

Why is an excess ofMAO necessary for

polymerization? (Al/Zr > 1000)

MAO is a ‘Black Box’

‘Pure MAO’

• presence of different oligomers and multiple equilibria:

(AlOMe)x (AlOMe)y (AlOMe)z

• Experimental data suggests that x,y,z range between 9-30; 14-20

O

Al O

Al

Me

Me

O

Al

O

Al

O

Al

Me

MeMe

O

Al

O Al

O

Al

OAl

Me

Me

Me

Me

Cyclic Structures

Al

Me

OMe2AlO AlMe2

n

Linear Structure

O

Al

O

Al

O

Al

O

Al

O

Al

Al

O

Me

Me Me

MeMe

Fused Ring Structure

AlO

Al

OAl

O

AlO

Al

OAl

O

MeMe

Me

Me

Me

Me

Cage Structures

• Three-dimensional cage structures, consisting of square, hexagonal and octagonal faces

• Four-coordinate Al centers bridged by three-coordinate O atoms

• [MeAlO]n, where n ranges between 4-16

• ADF calculations were performed on 35 different structures

Octagonal Face

Square Face

Hexagonal Face

Four-coordinate Al

Three-coordinate O

Four-coordinate Al

Three-coordinate O

Structural Investigation

Constructing the Cages

Schlegel Diagram 3-D Representation

• The order of stability is, 3H > 2H+S > H+O+S > 2O+S > 2H+O > 2S+H > 2S+O > 3S > 2O+H

• Structures composed of square and hexagonal faces only have the lowest energies for a given n

• SF = OF + 6

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

-2 octagonal; 8 square faces-4 (3S); 8 (2S+O); 4 (2O+S)-Energy -6028.60kcal/mol

-4 hexagonal; 6 square faces-8 (2S+H); 8 (2H+S)-Energy -6070.48kcal/mol

MAO Cage Energies

Entropies & Enthalpies

• UFF2 (Universal Force Field) parametrized for (AlOMe)4 and (AlOMe)6

• Tested on two different (AlOMe)8 oligomers

• ZPE differs by up to 1.27 kcal/mol; entropy by up to 1.39 kcal/mol (298.15K)

-755.00

-750.00

-745.00

-740.00

-735.00

-730.00

-725.00

4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

n

Gibbs Free Energy Per Monomer (kcal/mol)

298.15

598.15

398.15

198.15

Gibbs Free Energy per (AlOMe) Unit

0.00

5.00

10.00

15.00

20.00

4 6 8 10 12 14 16 18 20 22 24 26 28 30

n

Percentage

298.15398.15198.15598.15

Percent Distribution

average unit formula of (AlOMe)18.41, (AlOMe)17.23 , (AlOMe)16.89, (AlOMe)15.72 at 198K, 298K, 398K and 598K

• Free TMA ((AlMe3)2) is always present in a MAO solution

• TMA and ‘pure’ MAO react with each other according to the following equilibrium

(AlOMe)n + m/2(TMA)2 (AlOMe)n•(TMA)m

• Difficult to measure amount of bound TMA. Estimates give Me/Al of 1.4 ~ 1.5

‘Real’ MAO

+1/2(TMA)2

ΔE = -13.06kcal/mol

O: 3S

Al: 2S+H

O: 2S+H

Al: 3S

Variables Characterizing the Most Lewis Acidic

Site for (AlOMe)n

n Al environment O environment Bond Broken

6 2S+H 2S+H s-s

7 2S+H 3S s-s

8 2S+H 2S+H s-s

9 2H+S 2S+H s-h

10 2S+H 2S+H s-s

11 2S+H 2S+H s-s

13 2S+H 2S+H s-s

Reactive Sites in MAO

ΔG(n,m) for Reaction of (AlOMe)n with m2

(TMA)2 at 298.15K

-10

-5

0

5

10

15

20

6 7 8 9 10 11 13

n

Δ ( , ) ( / )G n m kcal mol

1/2 ( )2TMA( )2TMA3/2 ( )2TMA2 ( )2TMA

Temp (K) Me/Al AlTMA/Altot (%) Average Unit

Formula

% (AlOMe)12

198.15 1.00 0.21 (AlOMe)18.08•(TMA)0.04 15.27298.15 1.01 0.62 (AlO )Me 17.04•(TMA)0.11 19.05

398.15 1.02 1.05 (AlO )Me 15.72•(TMA)0.17 18.92

598.15 1.03 1.76 (AlO )Me 14.62•(TMA)0.26 16.56

• Most abundant species at every temperature still (AlOMe)12

• Increasing temperature shifts equilibrium towards slightly smaller structures

• Experimentally obtained ratio of Me/Al ~1.4 or 1.5 not obtained

Equilibrium Including TMA (1mol/L)

+1/2(TMA)2

-14.17kcal/mol

-6.56kcal/mol

+

-23.15kcal/mol

+1/2(TMA)2

+

Interaction Between MAO, TMA and THF

O

Al

O

Al

O

Al

Al

O

Al O

AlO

Al

O

Al

Al

O O

Al

O

AlO

AlO

Al

O

AlO O

Al

Al

O

Al

OO

Al

OAl

O

Al

Al

O

Al

O

Al

O

O Al

OAl

O

Al

OO

Al

Al

O

Al

O

O Al

AlO

Al

Al

OAl

OAl

O

Al

Al

O

Al

O Al

O

O

AlO

AlAl

O

O

Al

Al

O

OAl

Al

AlO

O

O

AlO

Al

OAl

O

AlO

Al

OAl

O

Al

O

Al

O

Al

OAl Al

OO

O

Al Al

O

Al

Al

Al

OO

Al

O O

(AlOMe)6 (AlOMe)7 (AlOMe)8

(AlOMe)9 (AlOMe)10 (AlOMe)11

(AlOMe)13

*

*

*

*

*

*

*

*

*

**

*

*

*

*

*

*

*

0.01%, 0.06% 0.01%, 0.00% 0.22%, 0.81%

1.22%, 2.22% 0.13%, 0.61% 2.36%, 1.17%

2.02%, 1.26%

Reactive MAO Cages

• Species I: a weak complex

• Species II: binuclear complex contact ion-pair

• Species III: heterodinuclear complex contact ion pairs/similar separated ion pairs (possibly active)

• Species IV: unsymmetrically Me-bridged complex (possibly dormant)

ZrMe

MeIV

AlMAO

+

-

ZrMe

MeAl

Me

Me

III

MeMAO

+

-

ZrMe

Me

Zr

Me

II

MeMAO

+

-

ZrMe

MeI

AlMAO

‘Real’ MAO and Cp2ZrMe2

Testing the Method

δexp δcalcΔδ

13C (Cp) 109.11 111.65 2.541H (Cp) 5.64 6.12 0.4813C (Me) 29.26 32.47 3.211H (Me) -0.15 -0.08 0.07

δexp δcalcΔδ

μ-Me 13C -5.34 -5.80 -0.46

μ-Me 1H -0.005 0.53 0.53

terminal 13C -8.025 -9.46 -1.44

terminal 1H -0.535 -0.64 -0.10

Chemical Shifts, ppm

Chemical Shifts, ppm

δexp Integration exp δcalc Integration calc

13C (Cp) 112.0 10 115.83 101H (Cp) 5.7 10 6.67 1013C (Zr-Me) 29.5a) 1 42.33 11H (Zr-Me) - - 0.66 313C (μ-Me) 29.5a) 1 13.41 11H (μ-Me) - - 0.50 313C average* N/A N/A 27.87 2C1H average* N/A N/A 0.58 6Ha) only one band with double intensity revealed

* Corresponds to average chemical shift of Zr-Me and μ-Me for 13C

and 1H

The Weakly Interacting SpeciesChemical Shifts, ppm

δexp Integration exp δcalc Integration calc

13C (Cp) 115.73 10C 113.60 10C1H (Cp) 5.5 10H 6.35 10H13C (Zr-Me) - - 41.7 1C1H (Zr-Me) - - 0.41 3H13C (μ-Me) 38.07 2C 19.38 1C1H (μ-Me) -0.27 6H 0.07 3H13C (Al-Me) -6.00 2C -1.21 2C1H (Al-Me) -0.58 6H -0.47 6H13C average* N/A N/A 30.54 2C1H average* N/A N/A 0.24 6H* Corresponds to average chemical shift of Zr-Me and μ-Me for 13C

and 1H

The ‘Active’ SpeciesChemical Shifts, ppm

δexp Integration exp δcalc Integration calc

13C (Cp) 113.90 10 115.78 101H (Cp) 5.70 10 6.40 1013C (Zr-Me) 42.00 1 46.77 11H (Zr-Me) - - 0.38 313C (μ-Me) 9.00 1 - -1H (μ-Me) - - - -

The ‘Dormant’ SpeciesChemical Shifts, ppm

+ Cp2ZrMe2

+ 1/2(Al2Me6)

-12.32 kcal/mol, t

-16.12 kcal/mol, t

-16.64 kcal/mol, t

0 kcal/mol

-13.06 kcal/mol, g

-16.88 kcal/mol, g

-16.58 kcal/mol, g

*g=gas phase t=toluene solution

+1/2 (Al2Me6)

Formation of ‘Dormant’, ‘Active’ Species

Possible Mechanisms‘Dissociative’ Mechanism

‘Associative’ Mechanism

M+

π-complex

A-

M+

R

A-

M+

R

Insertion Transition State

Uptake TransitionState

Separated Species

A-

R

M+

A-

R

M+

π-complex

A-

RM+

R

A-

M+ R

A-

M+

A-

R

Insertion Transition State

Uptake Transition State

Separated Species

First Insertion: ‘Dormant’ Species

Zr-O: 3.658

Zr-O: 4.539

Cis-Attack

Trans-Attack

Zr-O: 4.209

Zr-O: 3.336

Transition StateΔEgas= 38.80 kcal/molΔEtoluene= 35.55 kcal/mol

π-complexΔEgas= 31.88 kcal/molΔEtoluene= 28.43 kcal/mol

π-complexΔEgas= 34.65 kcal/molΔEtoluene= 26.96 kcal/mol

Transition StateΔEgas= 35.37 kcal/molΔEtoluene= 29.26 kcal/mol

First Insertion: ‘Active’ Species

Cis-Attack

Trans-Attack

Zr-Me: 3.999 Zr-Me: 4.108

π-complexΔEgas= 20.73 kcal/molΔEtoluene= 16.22 kcal/mol

Transition StateΔEgas= 21.87 kcal/molΔEtoluene= 17.00 kcal/mol

Transition StateΔEgas= 16.63 kcal/molΔEtoluene= 18.36 kcal/mol

π-complexΔEgas= 14.97 kcal/molΔEtoluene= 12.32 kcal/mol

Zr-Me: 3.938 Zr-Me: 2.501

Second Insertion: ‘Active’ Species

Transition StateΔEgas= 22.29 kcal/molΔEtoluene= 24.11 kcal/mol

Transition StateΔEgas= 21.26kcal/molΔEtoluene= 16.40 kcal/mol

π-complexΔEgas= 14.77 kcal/molΔEtoluene= 9.13 kcal/mol

Zr-Me: 2.517

Zr-Me:4.658

Second Insertion: ‘Active’ Species

π-complexΔEgas= 18.70 kcal/molΔEtoluene= 13.69 kcal/mol

Zr-Me: 4.161

16.00

16.50

17.00

17.50

18.00

18.50

19.00

19.50

20.00

2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8

Cα-C ethylene ( )Distance Angstroms

(AlOMe)6(TMA)(Cp2ZrMeProp) + C2H4 Trans Attack; - agostic Interactions; Insertion Profile

• In order for polymerization to occur, an excess of MAO is needed (typical conditions Al/Zr 1000 - 10,000)

• Most stable ‘pure’ MAO species do not contain strained acidic bonds and therefore do not react with TMA

• For example, (AlOMe)12, ~19% at 298.15 K

• [Cp2ZrMe]+[MeMAO]- is dormant

• [Cp2ZrMe]+[AlMe3MeMAO]- is active

• The same feature which makes a cage structure less stable is the same that makes it catalytically active!!!

Why is an Excess of MAO Necessary?

Conclusions

• MAO consists of 3D cage structures with square and hexagonal faces

• Very little TMA is bound to ‘pure’ MAO; most exists as the dimer in solution

• Basic impurities in MAO can influence the equilibrium

• Identified most likely structures for ‘dormant’ and ‘active’ species in polymerization

• First insertion: cis-approach has an associated TS; trans-approach has a dissociated TS

• First insertion: trans-approach has lower insertion barrier

• Second insertion: trans-approach, α-agostic interaction has no insertion barrier. An uptake barrier needs to be found

• Future Work: - to finish calculating uptake & insertion barriers for the second insertion; examine

termination barriers. Do the anion & cation associate after insertion?

• Acknowledgements:

- Tim Firman, Tom Woo, Robert Cook, Kumar Vanka, Artur Michalak, Michael Seth, Hans Martin Senn and other members of the Ziegler Research Group for their help and fruitful discussions

- Dr. Clark Landis, University of Wisconsin for giving us UFF2

- Novacor Research and Technology (NRTC) of Calgary ($$$)

- NSERC ($$$)

- Alberta Ingenuity Fund ($$$)

Miscellaneous