A Statistical Mechanical Model of Polymer Brushes: Equilibrium and Growth
Bibliographic record
Abstract
Abstract We construct a statistical mechanical model for a polymer brush in θ -solvent. The model is exactly solvable for realistic polymer models ( e.g. the freely rotating chain and the rotational isomeric state models) and it readily accounts for inhomogeneities of the brush with respect to the plane parallel to the grafting surface. The interactions between neighboring chains is mimicked by the presence of a confinement potential centered on the grafting point of each chain. We explore the model to calculate the equilibrium and kinetic properties of the polymer brush. We find that the variations of the brush free energy and height with the coverage depend strongly on the stiffness of the polymer chain (bond angle) and on the severity of the chain confinement. The results for the growth kinetics of the brush are compared with recent measurements on the formation of a PEG2000 brush from solution.
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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) | 0.001 | 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".