Nonzero ionic size and charge-correlation forces between fluid membranes
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Bibliographic record
Abstract
We present a theoretical approach to charge-correlation attractions between like-charged membranes with neutralizing counterions assumed to be localized to the membrane surface. In particular, we study the effect of nonzero ionic sizes on the attraction by treating the membrane charges (both backbone charges and localized counterions) as forming a two-dimensional ionic fluid of hard spheres of the same diameter D . Using a two-dimensional Debye-Huckel approach to this system, we examine how ion sizes influence the attraction. We find that the attraction gets stronger as surface charge densities or counterion valency increase, consistent with long-standing observations. Our results also indicate a nontrivial dependence of the attraction on separations h: The attraction is enhanced by ion sizes for intermediate h ranges, while it crosses over to the known D -independent universal behavior as h-->infinity; it remains finite as h-->0, as expected for a system of finite-sized ions.
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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 it