A <i>β</i>-NMR study of the depth, temperature, and molecular-weight dependence of secondary dynamics in polystyrene: Entropy–enthalpy compensation and dynamic gradients near the free surface
Bibliographic record
Abstract
We investigated the depth, temperature, and molecular-weight (MW) dependence of the γ-relaxation in polystyrene glasses using implanted 8Li+ and β-detected nuclear magnetic resonance. Measurements were performed on thin films with MW ranging from 1.1 to 641 kg/mol. The temperature dependence of the average 8Li spin–lattice relaxation time (T1avg) was measured near the free surface and in the bulk. Spin–lattice relaxation is caused by phenyl ring flips, which involve transitions between local minima over free-energy barriers with enthalpic and entropic contributions. We used transition state theory to model the temperature dependence of the γ-relaxation, and hence T1avg. There is no clear correlation of the average entropy of activation (Δ‡S̄) and enthalpy of activation (Δ‡H̄) with MW, but there is a clear correlation between Δ‡S̄ and Δ‡H̄, i.e., entropy–enthalpy compensation. This results in the average Gibbs energy of activation, Δ‡Ḡ, being approximately independent of MW. Measurements of the temperature dependence of T1avg as a function of depth below the free surface indicate the inherent entropic barrier, i.e., the entropy of activation corresponding to Δ‡H̄ = 0, has an exponential dependence on the distance from the free surface before reaching the bulk value. This results in Δ‡Ḡ near the free surface being lower than the bulk. Combining these observations results in a model where the average fluctuation rate of the γ-relaxation has a “double-exponential” depth dependence. This model can explain the depth dependence of 1/T1avg in polystyrene films. The characteristic length of enhanced dynamics is ∼6 nm and approximately independent of MW near room temperature.
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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 | 0.001 |
| 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".