Wormlike Polymer Brush: A Self-Consistent Field Treatment
Bibliographic record
Abstract
We investigate a homopolymer brush system on the basis of the wormlike-chain model, incorporating an Onsager-type interaction between polymer segments in the excluded-volume interaction. The model depends on the ratio between the total polymer length and the persistent length and a reduced grafting density as two basic parameters. Our numerical solutions to the self-consistent field theory are compared with scaling properties that can be deduced in various limits. In the limit of long chain and weak-to-moderate grafting density, our numerical results follow the scaling power law predicted by the classical-trajectory theory of a flexible polymer brush. In the limit of long chain and high grafting density, our numerical results show that the brush properties are comparable to the conformational properties of a nematic wormlike solution. In the limit of rod brush, our numerical results are consistent with the solution of a trial-function treatment from a previous mean-field theory.
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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) | 0.002 | 0.001 |
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; both teacher heads agree on what is shown here.
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".