Mathematical modelling of enzymatically cross‐linked polymer–phenol conjugates using deterministic and stochastic methods
Bibliographic record
Abstract
Abstract In this study, two different modelling approaches, namely, a deterministic and a stochastic one, are developed to model the enzymatic cross‐linking of polymer–phenol conjugates. A comprehensive kinetic mechanism is postulated to describe the elementary reactions in the cross‐linking of polymer–phenol chains in the presence of the horseradish peroxidase (HRP)–H2O2 initiation system. In the first approach, a moments‐based model is derived to account for the conservation of all molecular species and leading moments of the number chain length distribution (NCLD) in the reactive system. In the second approach, a stochastic Monte Carlo kinetic model is formulated to follow the time evolution of a sample of cross‐linkable polymer chains and calculate the weight chain length distribution (WCLD). From the numerical solutions of both models, the dynamic evolution of the concentrations of all the reactive species, the gelation onset time, the sol and gel mass fractions as well as the number and weight average molecular weights of the cross‐linkable polymer chains are calculated. The two derived models are validated using experimental kinetic measurements on the enzymatic cross‐linking of tyramine‐modified hyaluronic acid and carboxymethyl‐chitin. It is shown that both models can accurately predict the gelation onset time of the two cross‐linkable systems over a wide range of variations in HRP and H2O2 concentrations. Finally, the MC model predictions on the weight average number of polymer chains in the cross‐linked molecules are compared to Flory's analytical solution on the tetrafunctional cross‐linking of polymer chains of uniform length.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".