59th Annual Report on Research 2014

MAO is one of the most widely used co-catalysts in homogeneous and heterogeneous olefin polymerization with metallocene catalysts. But, even the most basic properties of MAO (such as its structure) are unknown, impeding progress. A better understanding of MAO will enable the optimization of the polymerization process, and decrease the cost associated with the co-catalyst.

Our first-principles calculations showed that dispersion-corrected Density Functional Theory (DFT-D) can be used to obtain reliable thermochemical data for species likely to be present in MAO at a fraction of the cost of MP2 theory, or DFT with meta-hybrid functionals. As a result, we have been able to carry out the most comprehensive computational study of species that may be important components of homogeneous MAO to date. We find that both cage-like, (AlOMe)_n,c, and trimethylaluminum (TMA) capped nanotubes and cages, (AlOMe)_n,c/t ∙ (AlMe₃)_m (n=6-20, m=1-4) are important components of MAO. Their relative abundances are temperature dependent, as illustrated in Figure 1. At 298 K the computed average formula Al_18.07O_16.12Me_22.00, molecular weight of 1077 g/mol, and C:Al:O ratio of 1.22:1:0.89 are in very good agreement with experimental estimates. Oligomers that can interact with the metallocene to yield the species believed to be active in polymerization comprise 69% of the mixture. Higher temperatures favor the formation of smaller species, so at 498 K the average MAO formula becomes Al_16.94O_16.86Me_17.12 and only 2% of the oligomers have structures that are prerequisites for the active species. Our findings explain the high ratio of Al:catalyst necessary to obtain good activities, and the sudden drop in polymerization observed experimentally above 380 K. At 298 K we find the six most important components of the MAO mixture to be, in order of decreasing abundance: (AlOMe)_20,c ∙ (AlMe₃)₂, (AlOMe)_16,c, (AlOMe)_18,c, (AlOMe)_20,c ∙ (AlMe₃), (AlOMe)_10,t ∙ (AlMe₃)₄, and (AlOMe)_20,c. Only one of these, (AlOMe)_18,c, has been studied computationally before. A manuscript has been submitted for publication.

Figure 1: Predicted abundances of the cage-like and nanotubular ‘TMA-free’ structures, (AlOMe)_n,c/t, as well as those terminated with TMA, (AlOMe)_n,c/t ∙ (AlMe₃)_m, at (left) 298 K and (right) 498 K, obtained using rev-PBE+D3/TZP free energies, and assuming a Boltzmann distribution.

2        MAO Supported on the MgCl₂ (110) Surface

DFT-D calculations have been employed to study how various MAO species, and in particular (AlOMe)₆ ∙ (AlMe₃) and (AlOMe)₆, interact with the (110) cut of the MgCl₂ surface. The metallocene catalyst, Cp₂ZrMe₂, and the TMA dimer may adsorb to the (110) MgCl₂ surface, and the strength of both of these interactions is ~37 kcal/mol. In addition, there are many favorable ways that MAO species can bind to this surface; a few are shown in Fig. 2. The interaction energies range from ~30-70 kcal/mol, and the binding motifs include (from the least to the most stable): aluminum bonded to magnesium via a bridging methyl group (Al-mMe-Mg), and O-Mg as well as Al-Cl bonds. The latter, particularly stabilizing motif is illustrated in Fig. 2(b,c) for models of the dormant species, [Cp₂ZrMe][Me(AlOMe)₆], and the active species,  [Cp₂ZrMe]⁺[mMe-AlMe₃(AlOMe)₆]^-, in polymerization. Interestingly, whereas the formation of the dormant species is energetically preferred over the active one in the gas phase (34.1 vs. 29.4 kcal/mol), the opposite is the case on the surface (36.0 vs. 41.2 kcal/mol). This means that the surface may shift the equilibrium towards the formation of the active species, providing one explanation as to why the Al:catalyst ratio required for good activities decreases when MAO is immobilized on MgCl₂. A publication is in preparation.

Figure 2: Optimized geometries (rev-PBE+D3/TZP) of (a) (AlOMe)₆ ∙ (AlMe₃), (b) [Cp₂ZrMe][Me(AlOMe)₆], and (c) [Cp₂ZrMe]⁺[mMe-AlMe₃(AlOMe)₆]^- adsorbed to the MgCl₂ (110) surface. O/Al/H/Cl/Mg atoms are red/grey/white/green/purple.

3        Miscellaneous Projects

In collaborations with experimental researchers we have carried out density functional theory calculations to: (i) study the relative energies and electronic structures of transition states in enantioselective copper-catalyzed carboetherification of unactivated alkenes, (ii) predict the chromatographic retention times of polybrominated diphenyl ethers and several methyl derivatives, (iii) propose likely structural candidates for cobalt substituted Keggin phosphotungstate, [PW₁₁O₃₉Co(X)]^5-, in toluene.

4        Impact

Students and postdocs have been trained in carrying out first-principles computations, structure prediction, calculations of reaction mechanisms, and analysis of electronic structure. One PhD student who has been involved in this project recently started a temporary instructor position teaching chemistry at a Primarily Undergraduate University (PUI). He plans to defend his PhD thesis by the end of 2014. The PI is using the results obtained during this grant period as preliminary data for full proposals to other funding agencies. A number of conference presentations have been given by the postdoctoral scholar and graduate students working on the grant. In this reporting period these include:

1.      “Computational Studies of Methylaluminoxane (MAO) Oligomer Interactions with Magnesium Chloride Surfaces”, 248^th ACS National Meeting, San Francisco, CA, contributing talk, 08/2014.

2.      “DFT study of Methylaluminoxane (MAO) Structures on Support: Interactions with MgCl₂ Crystal Surfaces”, and “Exploring the Dynamic Equilibrium between Methylaluminoxane (MAO) Oligomers via First Principles Calculations”, Gordon Research Conference on “Atomic and Molecular Interactions”, two contributed posters, 07/2014.

3.      “Exploring the Dynamic Equilibrium between Methylaluminoxane (MAO) Oligomers via First Principles Calculations”, Graduate Student Symposium, University at Buffalo, SUNY, contributing talk, 06/2014.