Modeling the dynamic equilibrium between oligomers of (AlOCH3)(n) in methylaluminoxane (MAO). A theoretical study based on a combined quantum mechanical and statistical mechanical approach

Density functional theory (DFT) has been used to calculate the energies of 36 different methylaluminoxane (MAO) cage structures with the general formu la (MeAlO)(n), where n ranges from 4 to 16; A;least-squares fit has been us ed to devise a formula which predicts the total energies of the MAO with di fferent n's giving an rms deviation of 4.70 kcal/mol, These energies in con junction with frequency calculations based;on molecular mechanics have been used to estimate the finite temperature enthalpies, entropies, and free en ergies for these MAO structures. Furthermore, formulas have been devised wh ich predict finite temperature enthalpies and entropies for MAO structures of any n for a temperature range of 198.15-598.15 K, Using these formulas, the free energies at different temperatures have been predicted for MAO str uctures where n ranges from 17 to 30. The free energy values were then used to predict the percentage of each n found at a given temperature. Our calc ulations give an average II value of 18.41, 17.23, 16.89, and 15.72 at 198. 15, 298.15, 398.15, and 598.15 K, respectively, Topological arguments have also been used to show that the MAO cage structure contains a limited amoun t pf square faces as compared to octagonal and hexagonal ones, it is alsb s uggested that the limited number of square faces with their strained Al-O b onds explain the high molar Al:catalyst ratio required for activation; More over, in this study we outline a general methodology which may be used to c alculate the percent abundance of an equilibrium mixture of oligomers with the general formula (X)(n).