Pair Correlation Functions and the Self-Diffusion Coefficient of Lennard-Jones Liquid in the Modified Free Volume Theory of Diffusion
Bibliographic record
Abstract
In this paper, we apply the Matteoli-Mansoori empirical formula for the pair correlation function of simple fluids obeying the Lennard-Jones potential to calculate reduced self-diffusion coefficients on the basis of the modified free volume theory. The self-diffusion coefficient thus computed as functions of temperature and density is compared with the molecular dynamics simulation data and the self-diffusion coefficient obtained by the modified free volume theory implemented with the Monte Carlo simulation method for the pair correlation function. We show that the Matteoli-Mansoori empirical formula yields sufficiently accurate self-diffusion coefficients in the supercritical regime, provided that the minimum free volume activating diffusion is estimated with the classical turning point of binary collision at the mean relative kinetic energy 3k(B)T/2, where k(B) is the Boltzmann constant and T is the temperature. In the subcritical regime, the empirical formula yields qualitatively correct, but lower values for the self-diffusion coefficients compared with computer simulation values and those from the modified free volume theory implemented with the Monte Carlo simulations for the pair correlation function. However, with a slightly modified critical free volume, the results can be made quite acceptable.
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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 | 0.001 | 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".