Classical nucleation theory with a radius-dependent surface tension: A two-dimensional lattice-gas automata model
Bibliographic record
Abstract
The constant surface tension assumption of the Classical Nucleation Theory (CNT) is known to be flawed. In order to probe beyond this limitation, we consider a microscopic, two-dimensional Lattice-Gas Automata (LGA) model of nucleation in a supersaturated system, with model input parameters E(ss) (solid particle-to-solid particle bonding energy), E(sw) (solid particle-to-water bonding energy), η (next-to-nearest-neighbor bonding coefficient in solid phase), and C(in) (initial solute concentration). The LGA method has the advantages of easy implementation, low memory requirements, and fast computation speed. Analytical results for the system's concentration and the crystal radius as functions of time are derived and the former is fit to the simulation data in order to determine the equilibrium concentration. The "Mean First-Passage Time" technique is used to obtain the nucleation rate and critical nucleus size from the simulation data. The nucleation rate and supersaturation data are evaluated using a modification to the CNT that incorporates a two-dimensional radius-dependent surface tension term. The Tolman parameter, δ, which controls the radius dependence of the surface tension, decreases (increases) as a function of the magnitude of E(ss) (E(sw)), at fixed values of η and E(sw) (E(ss)). On the other hand, δ increases as η increases while E(ss) and E(sw) are held constant. The constant surface tension term of the CNT, Σ(0), increases (decreases) with increasing magnitudes of E(ss) (E(sw)) at fixed values of E(sw) (E(ss)) and increases as η is increased. Σ(0) increases linearly as a function of the change in energy during an attachment or detachment reaction, |ΔE|, however, with a slope less than that predicted for a crystal that is uniformly packed at maximum density. These results indicate an increase in the radius-dependent surface tension, Σ, with respect to increasing magnitude of the difference between E(ss) and E(sw).
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".