Eva Zurek, Tom Ziegler* Department of Chemistry University of Calgary Calgary, Alberta, Canada

1. A Combined Quantum Mechanical and Statistical Mechanical Study of the Equilibrium of Trimethylaluminum (TMA) and Oligomers of (AlOCH3)n Found in Methylaluminoxane (MAO) Solution Eva Zurek, Tom Ziegler* Department of Chemistry University of Calgary Calgary, Alberta, Canada T2N 1N4 edzurek@ucalgary.ca, ziegler@ucalgary.ca

2. General Introduction • MAO is one of the most industrially important activators in single-site metallocene catalyst polymerization • MAO is formed from controlled hydrolysis of TMA in toluene or other hydrocarbon solvent. This leaves residual TMA present in the MAO solution • TMA exists primarily as the dimer (Al(CH3)3)2, in solution • It is not possible to isolate crystalline samples of MAO; disproportionation reactions give complicated NMR spectra • The equilibrium between different oligomers in ‘pure’ (TMA-free) MAO can be represented by the following: (AlOMe)x (AlOMe)y (AlOMe)z, where x,y,z are integers (1) • 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 (2) • It is difficult to determine how much TMA is coordinated to MAO and how much is ‘free’ in solution. 1H NMR gives a 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 1.51 when free TMA has been removed or corrected for

3. Introduction to ‘Pure’ MAO • We have already investigated the equilibrium shown in (1). Our work on MAO2 indicates that it is composed primarily of three-dimensional caged structures consisting of square and hexagonal faces • ‘Pure’ (TMA-free) 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 • At all temperatures, (AlOMe)12 has the greatest stability • Since there is always TMA present in MAO solution, in this study we aim to investigate the equilibrium shown in (2) and determine the extent of coordination of TMA to MAO. Percentage of (AlOMe)n as a Function of n Present at Different Temperatures in a Solution of ‘Pure’ MAO (AlOMe)12

4. How TMA Binds to MAO +1/2(TMA)2 • We have studied six different ways of binding one TMA to (AlOMe)6 and one way of binding two TMA groups. There were 2 reaction which had a -DE. They are shown on the left • We propose that 1 is an intermediate and TMA binds to MAO as in 2, the fully ring-opened cage • Note that three variables are needed to characterize the broken bond: - The Al was in a (2S+H) environment (it belonged to 2 square and 1 hexagonal face) - The O was in a (2S+H) environment - The bond broken was a s-s (square-square) bond DE=-7.79kcal/mol DE=-13.06kcal/mol 1 2

5. Determining the Sites with Greatest Latent Lewis Acidity • We found DE for the reaction of TMA with our MAO cages • The broken bond with the most negative DE defines the most Lewis Acidic Site • 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 since these structures contain no s-s bonds and atoms in 2H+S or 3H environments. DE for reaction with (AlOMe)12 for the breaking of a s-h bond with Al and O in 2H+S environment was 1.70 kcal/mol confirming the hypothesis.

6. TMA was added to sites in MAO cages which were determined as being acidic. This was done for (AlOMe)nwhere 6n 13 and n12. Depending upon the number of acidic sites present in the parent cage, between 2 and 4 TMA groups could be added. The different ways in which this could be done was also considered. For example 3 TMA groups can be added to (AlOMe)9 in four different ways. In the graph below we give the most negative DE for a given n and m. • This underlines the fact that the addition of TMA is energetically most favorable when two TMA groups are added. If more are added, steric repulsion results in a less negative DE. If n=12 or n14 then adding even one TMA group gives a positive DE. DE(n,m) for reaction of (AlOMe)n With m/2(TMA)2 vs n Two different ways of bonding 2 TMA groups to (AlOMe)7

7. Examples of Structures Studied (AlOMe)10•(TMA)2 (AlOMe)8•(TMA)1 (AlOMe)9•(TMA)1 (AlOMe)9•(TMA)2

8. Fully quantum mechanical frequency calculations are computationally expensive. Hence, UFF2 was parametrized to reproduce frequencies calculated with ADF. • Parametrization was performed on (AlOMe)6•(TMA)1 and checked on (AlOMe)6•(TMA)2 and (AlOMe)8•(TMA)1. In both the case of the finite temperature enthalpy correction (HEC) and the entropy at 298.15K good agreement between ADF and UFF2 was obtained • HEC was calculated at 198.15, 298.15, 398.15 and 598.15K

9. Parametrized UFF2 code was used to calculate entropic contribution to the Gibbs Free Energy at 198, 298, 398 and 598K At 298K the enthalpy for the addition of one TMA to a MAO must be at least -7.77 kcal/mol (on average) in order for the reaction to be favourable In general -TDS(n,m) increases at higher temperatures At higher temperatures smaller structures are more favourable due to entropic effects

10. The free energy change is plotted for the most stable structural alternative only • It suggests that very little TMA is bound to MAO • We calculated DG for this reaction at 198K, 398K and 598K as well • As temperature increases, entropic effects become more important in stabilizing smaller structures. Thus, at 598K there are no negative DG values • However higher temperatures favor smaller structures. Thus the parent structures are in higher abundance At 298.15K only four reactions Have negative DG values. They Are for the addition of 1 and 2 TMA’s To (AlOMe)6 and for the addition of 2 TMA’s to (AlOMe)8 and (AlOMe)10. The parent cages abundance is 0.01%, 0.23% and 0.14%. 10

11. Equilibrium Distributions • For the reaction in (1) if DG0(n,m) is obtained as in (2), Keqfound as in (3) then (4) may be used to find the % abundance of a specific (AlOMe)n•(TMA)m • The % abundance of (AlOMe)n•(TMA)m was calculated for 4 n  30 and 0  m  4, depending upon the topology of the parent MAO cage • The most abundant species at every temperature was (AlOMe)12 as in the ‘pure’ MAO solution • Increasing temperature shifts equilibrium towards slightly smaller structures • Experimentally measured ratio of Me/Al ~1.4 or 1.5 not obtained

12. Analysis of Theoretical and Experimental Results • Our calculated Me:Al ratio of ~1 does not agree with experiment. Here we aim to find out why. • Errors in the Calculations:DG(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. The error margin for an ADF calculation is within  5 kcal/mol. • Solvent Effects:DE for the addition of (TMA)1/2 to (AlOMe)6 changes by 0.76kcal/mol when energies are computed using parameters for the solvent toluene. • Other Possible Bonding Modes:Seems unlikely • Analysis of Experimental Data and Techniques: Experimentally the Me:Al ratio was found via the addition of THF to a MAO solution. Hence, the peaks due to TMA and MAO as seen by proton NMR became resolved. Thus, the amount of Me coordinated to MAO could be determined. This method relies on the assumption that THF does not facilitate the bonding of TMA to MAO.

13. Reactions & Products THF Possible Reactants 1+1/2(2) (AlOMe)6 Inter-action of MAO, TMA and THF 1 TMA DE= -14.17kcal/mol 1+3 3 2 • The negative DE value for the first • reaction shows that when THF is • added to MAO, an adduct between • the TMA and THF is formed. • The low negative DE value for the • second reaction shows that there is • little interaction between THF and • MAO. • The highly negative DE value for the • third reaction shows that THF • facilitates the bonding of TMA groups • to MAO. Hence, it inflates the Me/Al • ratio and decreases the average n value. • Any basic impurity (“Dirty MAO”) • may potentially have this same effect. DE= -6.56kcal/mol 1+1/2(2) +3 DE= -23.15kcal/mol 13

14. Conclusions on TMA Containing MAO • How TMA bonds to MAO has been determined • 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 for a ‘real’ MAO solution • Very little TMA is actually bound to MAO: most exists as the dimer in solution. Within the temp range 198K-598K the Me/Al ratio is ~1 • The most abundant species at all temperatures, (AlOMe)12, has no Lewis Acidic Sites. Few acidic sites are present in a MAO solution • Basic impurities in a MAO solution can change the equilibrium present; specifically by facilitating binding of TMA to MAO and shifting the equilibrium towards the formation of smaller MAO oligomers

15. Computational Details: The density functional theory calculationswere carried out using the Amsterdam Density Functional (ADF) program version 2.3.3. UFF2 was parametrized in order to calculate entropicand finite temperature enthalpy corrections to the Gibbs Free Energy. • Related Work: - a study of the possible candidates for dormant and active species present in a Cp2ZrMe2-MAO solution (J.A.C.S., submitted) • 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, 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) ofCalgary ($$$) - NSERC ($$$) • References: 1) Imhoff, D.W.; Simeral, L.S.; Samngokoys,S.Z.; Peel, J.H. Organometallics1998, 17, 1941 2) Zurek, E.; Woo, T.K.; Firman, T.K.; Ziegler, T. Inorg. Chem. 2001, 40, 361