A statistical mechanical model for the calculation of the permittivity of water in hydrated polymer electrolyte membrane pores
Bibliographic record
Abstract
An equilibrium statistical mechanical model is derived to compute the spatial variation in the permittivity of water within the hydrated pores of ion-containing polymeric membranes. The fixed anionic groups within the pore are modeled as periodic arrays of point charges. The Helmholtz free energy is calculated from a total Hamiltonian of the pore that includes energy from (1) interactions between the fields generated by the fixed charge groups and the dipoles of the water molecules, (2) “hard core” interactions between the water molecules, and (3) dipole–dipole interactions between the water molecules. The free energy is divided into two parts: (a) a reference free energy associated with five water molecules in a cluster interacting with each other through the hard core potentials and with the fixed charge groups and (b) an excess free energy due to the dipolar interactions between the water molecules in two cluster units. In the present work we calculate the polarization and corresponding permittivity from this reference free energy. We first show that our calculations, even at this level of sophistication, go beyond all the traditional approaches. Furthermore, with our model we compute radial profiles of the permittivity in the pores of the sulfonic acid–based Nafion® and 65% sulfonated poly ether ether ketone ketone polymer electrolyte membranes at several different hydration levels. These numerical results and predictions are in agreement with known experimental measurements.
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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) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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; 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".