Modeling MAO (Methylalumoxane)

1
Modeling MAO (Methylalumoxane)

• Eva Zurek, Tom Woo, Tim Firman, Tom Ziegler
• University of Calgary, Department of Chemistry,
  Alberta, Canada, T2N-1N4

2
Introduction

• 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 nCH2CH2 ?
  (n5-C5H5)2Zr-CH2-CH2n-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
• Goal of study is to propose a structural model
  for MAO

3
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 (E(AlOMe)n -
  En(AlOMe))/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

• Three-dimensional cage structures, consisting of
  square, hexagonal and octagonal faces
• Four-coordinate Al centers bridged by
  three-coordinate O atoms
• MeAlOn, where n ranges between 4-16
• ADF calculations were performed on 35 different
  structures

5
Mathematical Relationships

• For a given MAO Structure the following
  mathematical relationships were derived
• SF OF 6 1
• 3(3S) 2(2SH) (2HS) 24 2
• (2SH) 2(2HS) 3(3H) 6(HF) 3
• SF is of square, HF is of hexagonal, OF is
  octagonal faces
• (3S) is the of atoms bonded to three square
  faces, (2SH) the number of atoms bonded to two
  square and one hexagonal face, etcetera.
• 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
  
  

6
Formula for Predicting MAO Cage Energies/ Example
Shown for (AlOMe)8

• A least squares fit was performed to derive a
  formula predicting MAO Energies
• E -373.57(3S) -377.49(2SH) -381.13(2HS)
  -381.80(3H) -377.14(2SO) -380.59(2OS)
  -381.03(SOH) -378.86(2HO) -365.51(2OH)kcal/mol
  
• Rms deviation was found as being 4.70kcal/mol for
  35 structures

7
Determination of Entropic/Enthalpic Corrections

• ADF Frequency calculations on (AlOMe)4 and
  (AlOMe)6 were used to parametrize UFF 2
  (Molecular Mechanics Program)
• 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

8
Enthalpic Considerations

• Equations were found which predict enthalpic
  values for (AlOMe)n
• H0 25n kcal/mol 5
• Vibrational Portion of Htemp 6 Hvib
  H0 (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

• H E H0 Htemp 4 where E
  is the energy, H0 the zero-point energy, Htemp
  the finite temperature enthalpy correction

9
Entropic Considerations

• Svib 7.91(3S)8.30(2SH)10.20(2HS)8.49(3H)10
  .41(2SO)9.50(2OS)10.45(SOH)7.32(2H
  O)0(2OH) cal/molK
  9 rms deviation of
  1.78Kcal/mol at 298.15K
• Extension to Different Temperatues
• Translational Entropy 10
  S2 S1 T2/T1 T2(0.014) - 5.47
• Rotational Entropy 11 S2
  S1 T2/T1 T2(0.007) - 3.28
• Vibrational Entropy 12 S2
  (T2/T1-((0.0006T22 - 0.5353T2 108.85)-1)S1
  rms deviation of 0.27, 1.70 and
  4.90kcal/mol at 198.15K, 398.15K, 598.15K

• Strans (0.35n 41.17)cal/molK at 298.15K
  7
• Srot (0.57n 30.57)cal/molK at 298.15K
  8

S Svib Strans Srot
10
Gibbs Free Energy Per Monomer (AlOMe unit) at
Different Temperatures (G/n)

• Lowest Gibbs Free Energy per Monomer Unit gives
  most stable structure
• 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
• Graph shows G/n for structures composed of SF and
  HF only
• Equations 2 and 3 used to construct
  structures for n gt 16.
• Equations 4 - 11 used to predict G/n for n
  14 n gt 16.
• Most Stable structure at all temperatures is
  (AlOMe)12
• At low temperatures, (AlOMe)16 is almost as
  stable as (AlOMe)12

DG DE DH0 D Htemp -T D S
11
Percentage of Each n at Different Temperatures

• Most stable structure is (AlOMe)12
• Consists of 24 atoms in a (2HS) environment
  6SF 8HF
• t-butyl analogue sunthesized by Barron and
  co-workers 1,2
• 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

• All MAO solutions contain residual TMA
  (trimethylaluminum)
• It has been shown that TMA participates in
  equilibrium with different MAO oligomers2 and in
  disproportionation reactions5
• The way in which TMA bonds to MAO was determined
  via studying (AlOMe)6
• (AlMe)2 bonds to the oxygen and there is an Me
  transfer to the Al
• The bond which breaks belongs to two square faces
  and both the Al and O are in a (2SH) environment

13
Determining the Sites with Greatest Latent Lewis
Acidity

• The bond which gives us the greatest DE 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 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 SF
  present hence there are few LLA sites
• Cp2ZrMe2 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 AlZr ratio needed for catalysis to occur.

14
Conclusions

• Formulae predicting the energy, entropy and
  finite temperature enthalpy corrections for a
  given MAO structure consisting of SF, HF and OF
  have been found
• When pure MAO is considered (AlOMe)12 is the most
  stable structure in the temperature range
  198.15K-598.15K
• The way in which TMA bonds to MAO has been
  determined
• The 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 SF
• The high ratio of AlZr 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

• Acknowledgements Dr. Clark Landis,
  University of Wisconsin for supplying us with
  UFF2 NSERC
• 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.
• 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