Modeling the Dynamic Equilibrium between Oligomers of (AlOCH<sub>3</sub>)<i><sub>n</sub></i> in Methylaluminoxane (MAO). A Theoretical Study Based on a Combined Quantum Mechanical and Statistical Mechanical Approach
Bibliographic record
Abstract
Density functional theory (DFT) has been used to calculate the energies of 36 different methylaluminoxane (MAO) cage structures with the general formula (MeAlO)n, where n ranges from 4 to 16. A least-squares fit has been used to devise a formula which predicts the total energies of the MAO with different n's giving an rms deviation of 4.70 kcal/mol. These energies in conjunction with frequency calculations based on molecular mechanics have been used to estimate the finite temperature enthalpies, entropies, and free energies for these MAO structures. Furthermore, formulas have been devised which 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 structures 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 calculations give an average n 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 amount of square faces as compared to octagonal and hexagonal ones. It is also suggested that the limited number of square faces with their strained Al-O bonds explain the high molar Al:catalyst ratio required for activation. Moreover, in this study we outline a general methodology which may be used to calculate the percent abundance of an equilibrium mixture of oligomers with the general formula (X)n.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".