A Statistical Mechanical Model of Proton and Water Transport in a Proton Exchange Membrane
Bibliographic record
Abstract
We present here a mathematical model that focuses on the computation of the effective friction coefficient of an hydronium ion in a water‐filled pore of a proton‐exchange membrane (PEM) with a nonuniform charge distribution on the walls of the pore. The total Hamiltonian is derived for the hydronium ion as it moves through the hydrated pore and is affected by the net potential due to interaction with the solvent molecules and the pendant side chains. The corresponding probability density is derived through solution of the Liouville equation, and this probability density is then used to compute the friction tensor for the hydronium ion. The conventionally derived continuum‐model friction coefficient is then "corrected" with the effective friction coefficient computed in this model, and then the corresponding proton diffusion coefficient is calculated. For a Nation® membrane pore with six water molecules associated with each fixed anionic site (a total of 36 sites) and experimentally estimated pore parameters, the model predicts a proton diffusion coefficient of . A similar calculation for a pore containing 13 water resulted in a diffusion coefficient of . Both of these theoretically calculated values are in good agreement with experimentally measured diffusion coefficients. © 2000 The Electrochemical Society. All rights reserved.
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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) | 0.000 | 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".