A QSPR Investigation of Thermal Stability of [Al(CH₃)O]_n Oligomers in Methylaluminoxane Solution: The Identification of a Geometry-Based Descriptor

Abstract

Fifty-six methylaluminoxane (MAO) cage structures with the general formula [AlMeO] n , where n ranges from 6 to 12, have been optimized using density functional theory calculations in order to identify relevant chemical descriptors to reveal the thermodynamic stability of MAO. First, NMR properties were calculated for the most stable optimized structures, showing a good agreement with experimental results and revealing a relationship between the calculated 27 Al NMR shifts and local geometry of the aluminum atoms. Then, different electronic and geometric descriptors of optimized structures have been calculated and compared via a QSPR approach to various thermodynamic functions: internal energy, enthalpy, and Gibbs free enthalpy (ΔG r ), leading to the identification of a relevant descriptor based on the calculation of the distortion of aluminum sites in the [AlMeO] n structures. The identified descriptor was thus applied to predict ΔG r for [AlMeO] n structures with n ranging from 6 to 33. The study of the evolution of ΔG r as a function of temperature and size (n) reveals that there is a window of stable sizes for [AlMO] n depending on the temperature, which is between n = 12 and n = 24. Low temperatures disfavors smaller (n < 12) sized oligomers due to strong distortion of aluminum sites, while at high temperatures [AlMO] n structures with n greater than 18 become destabilized due to entropic effects.

The Dynamic Equilibrium Between (AlOMe)n Cages and (AlOMe)n·(AlMe3)m Nanotubes in Methylaluminoxane (MAO): A First-Principles Investigation

“…60 One of the parameters they considered was the deviation between the angles of the aluminum atoms and the ideal tetrahedral geometry using the equation:…”

“…35,60 In this section, we re-examine the relative energies and free energies of various (AlOMe) n oligomers. Moreover, we present a newly found oligomer, T d -(AlOMe) 16,c , that turns out to be more stable at room temperature than any other structure studied so far.…”

“…45 Out of all of the oligomers studied in ref 35 the T h symmetry (AlOMe) 12,c , whose body resembles a truncated octahedron, was found to have the lowest normalized free energy in a wide temperature range from 198 to 598 K. At 298 K Boudene and co-workers found another structure to be preferred, the (AlOMe) 18,c cage, but by 498 K (AlOMe) 12,c had regained its reign as the most stable oligomer. 60 This shift of the equilibrium toward smaller n can be explained by the increasing importance of the entropy, which favors smaller structures, toward the total free energy at higher temperatures.…”

“…Recent studies by Boudene and co-workers of cage structures using metaGGAtype functionals have illustrated that an (AlOMe) 18 oligomer may be the predominant species in solution at roomtemperature, and identified geometric descriptors that can be employed to calculate thermodynamic parameters of arbitrary cages. 60 Linnolahti and co-workers performed periodic calculations at the Hartree−Fock and B3LYP levels of theory on various armchair, zigzag, and chiral nanotubes. 41 On the basis of a comparison of the energies of some of these systems with the spherical (AlOMe) 12,c structure it was suggested that aluminoxanes may be nanotubular.…”

Metallocene-catalyzed ethylene−α-olefin isomeric copolymerization: A perspective from hydrodynamic boundary layer mass transfer and design of MAO anion

“…The observed common composition distribution broadness demonstrates the presence of strong micromixing/segregation effect [58][59][60]. This phenomenon can be ascribed to the three-dimensional MAO cage structures that feature the following [61][62][63][64][65][66][67][68]:…”