Investigations on the Structures Present in a Solution of (1) 'Pure', (2) TMA

(Trimethylaluminum) Containing and (3) Dimethylzirconocene (Cp2ZrMe2)

Containing MAO (Methylaluminoxane)

Eva ZurekUniversity of Calgary

AlO

O

OAl

Al

AlO

Al

Al

O

O

O

O

Al

O

Al

Al

Al

AlO

O

OAl

General Introduction• MAO is formed from controlled hydrolysis of TMA• MAO is one of the most industrially important activators in single-site

metallocene catalyst polymerization

• Commonly accepted role of MAO in catalysis: (n5-C5H5)2ZrMe2 + MAO [(n5-C5H5)2ZrMe]+ + [(MAO)Me]-

[(n5-C5H5)2ZrMe]+ + n[CH2=CH2] [(n5-C5H5)2Zr-[CH2-CH2]n-CH3]+

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

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

• Questions about MAO: why do we need such a high Al/Zr ratio to be present in order for polymerization to occur? (Catalytic conditions have Al/Zr 200)

• Goal of study is to propose a structural model for MAO along with the active and dormant species present in polymerization

Introduction to ‘Pure MAO’• It is not possible to characterize MAO experimentally due to the 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

Al

R

OR2AlO AlR2

n

Linear Structure

O

Al O

Al O

AlO

Al

OAl

O

AlO Al

O

AlOAlR

R

R

RR

R

R

RR

Cyclic Structures

O

AlO

Al

OAl

OAl

OAl

Al

O

Me

Me Me

MeMe

Fused Ring Structure Caged Structure

Preliminary Structural Investigation

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

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

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

BE/n = -79.27 kcal/mol BE/n = -95.93 kcal/mol

Types of Structures Studied

• 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

Mathematical Relationships• For a given MAO structure the following relationships were derived:*• SF = OF + 6 [1]• 3(3S) + 2(2S+H) + (2H+S) = 24 [2]• (2S+H) + 2(2H+S) + 3(3H) = 6(HF) [3]• [1] shows us that minimum number of SF in MAO cage is 6, when OF is zero• [2] and [3] can be used to construct large MAO cages with OF zero

*using concepts from Regular Polytopes, the branch of Pure Mathematics which studies Polyhedrons in n-dimensions

0 octagonal faces; 3 hexagonal faces; 6 square faces

# atoms in a 3S environment = 2# atoms in a 2S+H environment = 6

# atoms in a 2H+S environment = 6

3S

2S+H

2H+S

Calculating % Distributions

ΔG0(n,m,p) =GT0(n,m,p)−nGT

0(AlOMe)−m2GT

0(TMA)2 −pGT0(Cp2ZrMe2)

n(AlOMe)+m2

(TMA)2 +p(Cp2ZrMe2)→ (AlOMe)n(TMA)m(Cp2ZrMe2)p

In this case, m=p=0

Keq(n,m,p) =exp(−ΔG0(n,m,p) /nRT)

%(AlOMe)n(TMA)m(Cp2ZrMe2)p =Keq(n,m,p)

Keq(i)i∑

⎛

⎝

⎜ ⎜

⎞

⎠

⎟ ⎟ ×100

GT0(n,m,p)=HT (n,m,p)−TST(n,m,p)

HT (n,m,p) =E(n,m,p) +HEC (n,m,p)

Formula for Predicting MAO Cage Energies

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

• 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/mol

• 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

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

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

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

Energy per Monomer (AlOMe) Unit

-763

-761

-759

-757

-755

-753

-751

-749

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

Energy per Monomer (kcal/mol)

Reaches a plateau as n increases

Presence of local Maxima at n=7,10,13

Finite Temperature (HEC) Correction per Monomer

24

26

28

30

32

34

36

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

H (OK)H (198.15K)

H (298.15K)H (398.15K)

H (598.15K)

HEC(n)/nKcal/mol

Enthalpy correction per monomer unitIs almost the same for all oligomers atA given temp; HEC(n) ~ 0

Entropic Contribution per Monomer (-TST(n))

-30

-25

-20

-15

-10

-5

0

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

-TS

T(n) /n (kcal/mol)

198.15K298.15K398.15K598.15K

At high temp differences between adjacent points become greater; thus entropic contributions become more important in stabilizing smaller structures

Gibbs Free Energy per Monomer

-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

At all temp (AlOMe)12 is most stableAt high temperaturesThe difference increases:Entropic effects

At low temp (AlOMe)16 is almost as Stable as (AlOMe)12

Local maxima at n =7,10,13Due to energetic effects

Percentage of Each n at Different Temperatures

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

Conclusions on ‘Pure’ MAO

• At all temperatures, (AlOMe)12 has the greatest stability

• Three dimensional caged compounds are more stable than two-dimensional sheet structures

• SF = OF + 6; since SF exhibit high ring strain structures composed of only SF and HF are most stable

• Pure MAO gives an average unit formula of (AlOMe)18.41, (AlOMe)17.23 , (AlOMe)16.89 and (AlOMe)15.72 at 198K, 298K, 398K and 598K, respectively

Introduction to TMA Containing MAO

• Controlled hydrolysis of TMA in toluene or other hydrocarbon solvent leaves residual TMA present in the MAO solution

• TMA exists primarily as the dimer (Al(CH3)3)2 in solution

• It is generally accepted that the TMA exists as free and bound species according to the following equilibrium:

(AlOMe)n + m/2(TMA)2 (AlOMe)n•(TMA)m

• 1H NMR gives spectrum where peaks from MAO and TMA overlap; removal of volatiles produces more free TMA upon standing; titration with Lewis bases is unreliable since they react with TMA and MAO

• Some experimental methods claim to have overcome these problems giving a Me:Al ratio of 1.4 or 1.5 when free TMA has been removed or corrected for

How TMA Binds to MAO

+1/2(TMA)2

E = -7.79kcal/mol

E = -13.06kcal/mol

Determining the Sites with Greatest Latent Lewis Acidity

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

• In all cases but one the bond broken was a s-s bond.

• In all cases but one the Al was in a 2S+H environment

• The oxygen was at least in a 2S+H environment

• The exception exists due to less steric congestion in the ring-opened product

• This suggests that TMA will not react with (AlOMe)n where n=12 and n≥14

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

(TMA)2

-25

-20

-15

-10

-5

0

6 7 8 9 10 11 13n

( , ) ( / )E n m kcal mol

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

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

(TMA)2 at 298.15K

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

6 7 8 9 10 11 13n

HEC( , ) ( / )n m kcal mol

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

−TΔS(n,m) for Reaction of (AlOMe)n with m2

(TMA)2 at 298.15K

0

5

10

15

20

25

6 7 8 9 10 11 13n

-T( , ) ( / )S n m kcal mol

1/2 ( )2TMA

( )2TMA

3/2 ( )2TMA

2 ( )2TMA

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

( , ) ( / )G n m kcal mol

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

Equilibrium DistributionsTemp (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

Analysis of Theoretical and Experimental Results

• Errors in the Calculations: G(n,m) needs to be decreased by 25kcal/mol for each (TMA)2 present in the solution to achieve a ratio of Al:Me 1.4; decreased by 32kcal/mol to achieve a ratio of 1.5

• Solvent Effects: E(6,1)changed by 0.76kcal/mol when solvation in toluene

• Other Possible Bonding Modes: Seems unlikely

• Analysis of Experimental Data and Techniques: Addition of THF to a MAO solution resolved the peaks due to TMA and MAO by proton NMR. Relies on the assumption that THF does not facilitate the bonding of TMA to MAO

Interaction of MAO, TMA and THF

+1/2(TMA)2 E= -14.17kcal/mol

E= -6.56kcal/mol+

E= -23.15kcal/mol+1/2(TMA)2

+

Conclusions on TMA Containing MAO

• Basic impurities in MAO solution can change the equilibrium present; specifically by facilitating binding of TMA to MAO and formation of smaller MAO oligomers

• Very little TMA is actually bound to MAO: most exists as the dimer in solution

• The most abundant species at all temperatures, (AlOMe)12, has no Lewis Acidic Sites. Few acidic sites are present in a MAO solution

• Average unit formulae of (AlOMe)18.08•(TMA)0.04, (AlOMe)17.04•(TMA)0.11, (AlOMe)15.72•(TMA)0.17 and (AlOMe)14.62•(TMA)0.26 are obtained at 198K, 298K, 398K and 598K respectively

Introduction to Cp2ZrMe2 Containing MAO

• Proposed role of MAO in polymerization:

Cp2ZrMe2 + MAO [Cp2ZrMe]+[MAOMe]-

[Cp2ZrMe]+ + n[CH2=CH2] [Cp2Zr-[CH2-CH2]n-CH3]+

• Dormant species: the [Cp2ZrMe]+[MAOMe]- bond is so strong so that formation of the catalyst, [Cp2ZrMe]+ cannot occur

• Traditionally this has been thought of as an ‘oxygen-bound’ species, since a Zr-O bond is quite strong

• Active species: the [Cp2ZrMe]+[MAOMe]- bond is weak enough so that that formation of the catalyst, [Cp2ZrMe]+ can occur and polymerization can proceed as in Step 2 above

Structural NMR Determination • 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

Structural Alternatives for III

AB

• A does not correspond to a minimum on the potential energy surface;-Me bond breaks during optimization procedure yielding B

Structural Alternatives for III

• In gas phase this structure is 46.80 kcal/mol less stable than best structural alternative (B)

• In toluene solution this structure is 30.90kcal/mol less stable than best structural alternative (B)

C

Energetically Possible Structural Alternatives for III

• 6.05 kcal/mol less stable than the best structural alternative (B) in gas phase• 6.30 kcal/mol less stable than the best structural alternative (B) in toluene solution

• The structural alternative with lowest energy in gas phase and toluene solution

D

B

Possible Mechanisms of Bond Breaking and Reformation for B

1

2

Bond 2’ forms

Bond 2 breaks

Bond 1 breaks

Free rotation About bondBond 1’ forms

Calculated and Experimental Chemical Shifts (ppm) for Cp2ZrMe2

δexpa) δcalc

Δδ

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 0.07a) Reference 1.

1) Babushkin, D.E.; Semikolenova, N.V.; Zakharov, V.A.; Talsi, E.P. Macromol.

Chem. Phys. 2000, 201, 558.

Calculated and Experimental Chemical Shifts (ppm) for B and III

δexpa) Integration exp

a) 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 6Ha) Reference 1.

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

and 1H

Structural Alternatives for IV

• E does not correspond to a minimum on the potential energy surface;-Me bond breaks during optimization procedure yielding F

E F

Structural Alternatives for IV

• E = 0.02kcal/mol (gas phase)• E = -1.63kcal/mol (toluene solution)• This structure corresponds to a weakly bound species

• E = -16.58kcal/mol (gas phase)• E = -16.12kcal/mol (toluene solution)• This structure corresponds to a tight ion pair

G F

Calculated and Experimental Chemical Shifts (ppm) for G and I

δexpa) Integration exp

a) δcalc Integration calc

13C (Cp) 112.0 10 115.83 101H (Cp) 5.7 10 6.67 1013C (Zr-Me) 29.5b) 1 42.33 11H (Zr-Me) - - 0.66 313C (μ-Me) 29.5b) 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) Reference 1.b) only one band with double intensity revealed

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

and 1H

Calculated and Experimental Chemical Shifts (ppm) for F and IV

δexpa) Integration exp

a) 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) - - - -

a) Reference 1.

+ 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)

Energetic Relationships

Eipd = 62.60 kcal/mol (toluene)

Eipd = 34.61 kcal/mol (toluene)

The MAO/TMA/Cp2ZrMe2 Mixture

n(AlOMe)+m2

(TMA)2 +p(Cp2ZrMe2)→ (AlOMe)n(TMA)m(Cp2ZrMe2)p

ΔG0(n,m,p) =GT0(n,m,p)−nGT

0(AlOMe)−m2GT

0(TMA)2 −pGT0(Cp2ZrMe2)

ΔE(6,1,0) =−13.06kcal/mol≈ΔE(6,0,1) =−16.68kcal/mol

Thus we will assume that: ΔG0(n,0,1) =ΔG0(n,1,0) at

298.15K and that p≤1

ΔE for the addition of Cp2ZrMe2 to (AlOMe)6(TMA) is−3.82kcal/mol

thus we will assume that ΔG is ~2kcal/mol or that:

ΔG0(n,m,1) =ΔG0(n,m,0)+2kcal/mol at 298.15K and that p≤1

The MAO/TMA/Cp2ZrMe2 Mixture

• At 298.15K the ratio of ‘F-like’ to ‘B-like’ structures is 1.76

• Experimentally, it was found that at high Al/Zr ratios the molar ratio of IV/III varied between 1-4 depending upon the TMA content of the solution [1]

• If there is no free TMA present the mixture has an Al/Zr ratio of 177:1

• Assuming 30% of the total Al is due to free TMA the Al/Zr ratio becomes 248:1

• This implies that an Al/Zr ratio of ~250:1 is necessary in order for free Cp2ZrMe2, I and II to disappear from a MAO/TMA/ Cp2ZrMe2 Mixture

• Experimentally NMR signals due to I, II are still seen at Al/Zr ratios of 100, however the ratio at which they completely disappear is not given [1]

Conclusions on Cp2ZrMe2 Containing MAO

BF

• Most likely candidate for the dormant species is F

• A high Al/Zr ratio is necessary in order for all of the Cp2ZrMe2 to bind to MAO as the dormant and active species (I, II and free Cp2ZrMe2 to disappear from the solution)

• Most likely candidate for the active species is B

• The most abundant species in a MAO solution within the temperature range of 198K-598K is (AlOMe)12

• MAO is composed of caged structures consisting mainly of square and hexagonal faces

• Very little TMA is bound to MAO within the temperature range of 198K-598K

• An average unit formula of (AlOMe)17.04•(TMA)0.11 at 298K is obtained for ‘real’ (TMA containing) MAO

• The most likely structural candidates for the dormant and active species in polymerization are F and B, respectively

• A large Al/Zr ratio is necessary in order for all of the dimethylzirconocene to bind to MAO as F and B

Conclusions(i)i=1

3

∑

Miscellaneous

• Future Work: - to study the insertion process of an ethylene molecule into the Zr--Me

bond of B and F via static ADF and dynamic PAW calculations

• Acknowledgements:

- Tim Firman, Tom Woo, Robert Cook, Kumar Vanka 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 ($$$)

- God and my parents