A QSPR Investigation of Thermal Stability of [Al(CH₃)O]_<i>n</i> Oligomers in Methylaluminoxane Solution: The Identification of a Geometry-Based Descriptor

Abstract

Fifty-six methylaluminoxane (MAO) cage structures with the general formula [AlMeO]_<i>n</i>, where <i>n</i> 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 ²⁷Al 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 (Δ<i>G</i>_r), leading to the identification of a relevant descriptor based on the calculation of the distortion of aluminum sites in the [AlMeO]_<i>n</i> structures. The identified descriptor was thus applied to predict Δ<i>G</i>_r for [AlMeO]_<i>n</i> structures with <i>n</i> ranging from 6 to 33. The study of the evolution of Δ<i>G</i>_r as a function of temperature and size (<i>n</i>) reveals that there is a window of stable sizes for [AlMO]_<i>n</i> depending on the temperature, which is between <i>n</i> = 12 and <i>n</i> = 24. Low temperatures disfavors smaller (<i>n</i> < 12) sized oligomers due to strong distortion of aluminum sites, while at high temperatures [AlMO]_<i>n</i> structures with <i>n</i> greater than 18 become destabilized due to entropic effects