1. Modeling MAO (Methylalumoxane ) Eva Zurek, Tom Woo, Tim Firman, Tom Ziegler University of Calgary, Department of Chemistry, Alberta, Canada, T2N-1N4

2. Introduction n MAO is one of the most industrially important activators in single-site metallocene catalyst polymerization n Commonly accepted role of MAO in catalysis: (n 5 -C 5 H 5 ) 2 ZrMe 2 + MAO  [(n 5 -C 5 H 5 ) 2 ZrMe] + + [(MAO)Me] - [(n 5 -C 5 H 5 ) 2 ZrMe] + + n[CH 2 =CH 2 ]  [(n 5 -C 5 H 5 ) 2 Zr-[CH 2 -CH 2 ] n -CH 3 ] + n Not possible to isolate crystalline samples of MAO; disproportionation reactions give complicated NMR spectra n Hence, it is not possible to characterize MAO and thus the structure(s) of MAO remain largely unknown n Goal of study is to propose a structural model for MAO

3. Preliminary Structural Investigation n Density Functional Theory Calculations were carried out using the Amsterdam Density Functional (ADF) program version 2.3.3 n Binding Energy Per Monomer = (E[(AlOMe) n ] - E[n(AlOMe)])/n n Preliminary study shows that three-dimensional caged structure have lower BE/monomer, thus are more energetically stable than two- dimensional sheet structures

4. Types of Structures Studied n Three-dimensional cage structures, consisting of square, hexagonal and octagonal faces n Four-coordinate Al centers bridged by three-coordinate O atoms n [MeAlO] n, where n ranges between 4-16 n ADF calculations were performed on 35 different structures

5. Mathematical Relationships n For a given MAO Structure the following mathematical relationships were derived* n SF = OF + 6 [1] n 3(3S) + 2(2S+H) + (2H+S) = 24 [2] n (2S+H) + 2(2H+S) + 3(3H) = 6(HF) [3] n SF is # of square, HF is # of hexagonal, OF is # octagonal faces n (3S) is the # of atoms bonded to three square faces, (2S+H) the number of atoms bonded to two square and one hexagonal face, etcetera. n [1] shows us that minimum number of SF in MAO cage is 6, when OF is zero n [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

6. Formula for Predicting MAO Cage Energies/ Example Shown for (AlOMe) 8 n A least squares fit was performed to derive a formula predicting MAO Energies n 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 n Rms deviation was found as being 4.70kcal/mol for 35 structures

7. Determination of Entropic/Enthalpic Corrections n ADF Frequency calculations on (AlOMe) 4 and (AlOMe) 6 were used to parametrize UFF 2 (Molecular Mechanics Program) n Parametrization gave good values for two different (AlOMe) 8 isomers This parametrized version of UFF2 was then used to calculate entropies and finite temperature enthalpy corrections for the 35 different MAO structures This parametrized version of UFF2 was then used to calculate entropies and finite temperature enthalpy corrections for the 35 different MAO structures

8. Enthalpic Considerations n Equations were found which predict enthalpic values for (AlOMe) n n H 0 = 25n kcal/mol [5] n Vibrational Portion of H temp [6] H vib = H 0 + (0.0028T - 0.3548)n x ln(T) rms deviation of 3.28, 0.78, 1.32 and 3.36kcal/mol at 198.15K, 298.15K, 398.15K, 598.15K n H = E + H 0 + H temp [4] where E is the energy, H 0 the zero- point energy, H temp the finite temperature enthalpy correction

9. Entropic Considerations n S vib = 7.91(3S)+8.30(2S+H)+10.20(2H+S)+8. 49(3H)+10.41(2S+O)+9.50(2O+S)+10. 45(S+O+H)+7.32(2H +O)+0(2O+H) cal/molK [9] rms deviation of 1.78Kcal/mol at 298.15K n Extension to Different Temperatues: n Translational Entropy: [10] S 2 = S 1 + T 2 /T 1 + T 2 (0.014) - 5.47 n Rotational Entropy: [11] S 2 = S 1 + T 2 /T 1 + T 2 (0.007) - 3.28 Vibrational Entropy: [12] S 2 = (T 2 /T 1 -((0.0006T 2 2 - 0.5353T 2 + 108.85) -1 )S 1 rms deviation of 0.27, 1.70 and 4.90kcal/mol at 198.15K, 398.15K, 598.15K S = S vib + S trans + S rot n S trans = (0.35n + 41.17)cal/molK at 298.15K [7] n S rot = (0.57n + 30.57)cal/molK at 298.15K [8]

10. Gibbs Free Energy Per Monomer (AlOMe unit) at Different Temperatures (G/n) n Lowest Gibbs Free Energy per Monomer Unit gives most stable structure n For a given n, the most stable structures composed of SF and HF only. Reason: equation [1] shows that as # OF increases, so does #SF. SF exhibit ring strain therefore destabilizing the structure n Graph shows G/n for structures composed of SF and HF only n Equations [2] and [3] used to construct structures for n > 16. n Equations [4] - [11] used to predict G/n for n =14 & n > 16. n Most Stable structure at all temperatures is (AlOMe) 12 n At low temperatures, (AlOMe) 16 is almost as stable as (AlOMe) 12  G =  E +  H 0 +  H temp -T  S

11. Percentage of Each n at Different Temperatures n Most stable structure is (AlOMe) 12 n Consists of 24 atoms in a (2H+S) environment; 6SF; 8HF n t-butyl analogue sunthesized by Barron and co-workers 1,2 n Graph corresponds to experimental data, which predicts that n ranges between 9 and 30 3 and between 14 and 20 4

12. Investigation of MAO-TMA Interactions n All MAO solutions contain residual TMA (trimethylaluminum) n It has been shown that TMA participates in equilibrium with different MAO oligomers 2 and in disproportionation reactions 5 n The way in which TMA bonds to MAO was determined via studying (AlOMe) 6 n (AlMe) 2 bonds to the oxygen and there is an Me transfer to the Al n The bond which breaks belongs to two square faces and both the Al and O are in a (2S+H) environment

13. Determining the Sites with Greatest Latent Lewis Acidity The bond which gives us the greatest  E value when reacted with TMA has the greatest Latent Lewis Acidity (LLA). Bonds with greatest LLA for structures composed of SF and HF only are shown below The bond which gives us the greatest  E value when reacted with TMA has the greatest Latent Lewis Acidity (LLA). Bonds with greatest LLA for structures composed of SF and HF only are shown below n The figure below shows us that LLA is dependant upon the presence of SF n Equation [1] shows that for a MAO structure composed of SF and HF, there are only six SF present; hence there are few LLA sites n Cp 2 ZrMe 2 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 catalysis to occur.

14. Conclusions n Formulae predicting the energy, entropy and finite temperature enthalpy corrections for a given MAO structure consisting of SF, HF and OF have been found n When pure MAO is considered (AlOMe) 12 is the most stable structure in the temperature range 198.15K-598.15K n The way in which TMA bonds to MAO has been determined n The sites exhibiting greatest LLA for five MAO structures have been found n It has been shown that the presence of LLA is dependant upon the presence of SF n 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])

15. Miscellaneous n Acknowledgements: Dr. Clark Landis, University of Wisconsin for supplying us with UFF2; NSERC n References: 1) Mason, M.R.; Smith, J.M.; Bott, S.G.; Barron, A.R.; J. Am. Chem. Soc. 1993, 115, 4971. 2) Harlan, C.F.; Mason, M.R.; Barron, A.R.; Organomet. 1994, 13, 2957. 3) Babushkin, D.E.; Semikolenova, N.V.; Panchenko, V.N.; Sobolev, A.P.; Zakharov, V.A.; Talsi, E.P.; Macromol. Chem. Phys. 1997, 198, 3845. 4) Talsi, E.P.; Semikolenova, N.V.; Panchenko, V.N.; Sobolev, A.P.; Babushkin, D.E.; Shubin, A.A.; Zakharov, V.A.; J. Molecular Catalysis A: Chemical, 1999, 139, 131. 5) Tritto, I.; Sacchi, M.C.; Locatelli, P.; Macromol. Chem. Phys. 1996, 197, 1537. n Work in Progress: -to study the role which TMA plays in lowering the energeies of different MAO oligomers -to study the metallocene/MAO interaction thereby determining the active species in polymerization