Binary hard-sphere solute-solvent radial distribution function in the colloidal limit: exact calculation from an equation of state
Bibliographic record
Abstract
An exact formula is derived relating the contact value of the solute-solvent radial distribution function for an additive binary hard-sphere (HS) mixture at infinite dilution, g ∞ 12(d 12), to the mixture equation of state (EOS) (1 denotes the solvent and 2 denotes the solute). This result can also be considered to be a consistency condition involving approximations for g ∞ 12(d 12) and for the mixture EOS. Employing three approximate HS mixture equations of state from the literature, we use our formula to derive corresponding analytical approximations for g ∞ 12(d 12) In addition, new computer simulations were performed to obtain accurate results for g ∞ 12(d 12) and for g ∞ 12(r 12) at the solute-solvent diameter ratios {1, 3, 5, 7, 10, 20} and the reduced solvent density ρ∗ = 0.8. We compare our results for g ∞ 12(d 12) with the simulation results and with the results of approximate analytical expressions for g ∞ 12(d 12) proposed by several workers. The results obtained from our formula in conjunction with two of the EOS expressions considered are more accurate than all previously proposed approximations, with the exception of the approximation of Matyushov and Ladanyi [1997, J. chem. Phys., 107, 5815], which is of comparable accuracy.
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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".