A Molecular Weight Distribution Polydispersity Equation for the ATRP System: Quantifying the Effect of Radical Termination
Bibliographic record
Abstract
Polydispersity quantifies the breadth of polymer molecular weight distribution, making it an important and frequently quoted chain microstructural property for characterization. An explicit expression of such an important variable is desirable for ease of calculation, correlation with experiment data, and/or parameter estimation. A review of published literatures shows that great efforts have been put forth by many researchers to derive these equations for various polymerization mechanisms. In atom transfer radical polymerization (ATRP), polydispersity depends on three factors: monomer conversion, number of monomer addition per activation/deactivation cycle, and amount of dead chains. The existing expressions available in the literature only account for, at most, two of these three factors, with the contribution from dead chains commonly neglected. This assumption results in polydispersity monotonically decreasing with conversion, which is often not observed in experiments. In this work, a new equation for polydispersity, which accounts for contributions of all the three aforementioned factors, is proposed. The validity of assumptions involved in the derivation is evaluated by comparing the polydispersity profiles to those simulated by the method of moments. In addition, this new equation is used to correlate several experiment data sets for verification, namely from ATRP of 2-hydroxyethyl methacrylate, methyl methacrylate, and N -isopropylacrylamide, showing better agreement than the existing equation. Although the equation derived here is strictly applicable to homogeneous (bulk and solution) normal ATRP, with further effort it may be extended to other types of ATRP as well as NMP and RAFT systems.
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.002 |
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".