The gradual transition from mass-controlled to diffusion-controlled kinetics during melt polymerization
Bibliographic record
Abstract
For most chemical reactions, the rate coefficient, k, is independent of the extent of reaction, α, and varies with the temperature, T, according to the Arrhenius equation, but, for melt polymerization at a fixed T, the diffusion coefficient, D, of the reactant pairs decreases as α increases, and for viscous liquids in general D varies with T according to the Vogel–Fulcher–Tammann equation. We propose that a change in the mass-controlled to diffusion-controlled reaction kinetics during a melt’s polymerization would be seen first as k begins to decrease with increase in α, and second as the temperature dependence of k for a fixed α deviates from the Arrhenius to the Vogel–Fulcher–Tammann type. The range of α and T over which this change occurs may be determined by calorimetry or related experiments. Polymerization of a liquid mixture to a random network structure has been studied by calorimetry. It is shown that, (i) the ln(k) against α plot at a fixed T bends downwards progressively more as α increases, and (ii) over a given range of T, the ln(k) against 1/T plot at a fixed α is a straight line when α is low, and bends downwards when α is high. The onset temperature of this bend increases as α is increased. Thus the gradual onset of diffusion control varies with both α and T. The simulated dα/dt for mass-controlled kinetics is higher than that for diffusion-controlled kinetics up to a certain time and lower thereafter. The ratio of dα/dt for the two kinetics shows a local maximum at a certain time. The procedure developed here would be useful for studying diffusion control in biological processes.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| 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 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".