When droplets become stars: charged dielectric droplets beyond the Rayleigh limit
Bibliographic record
Abstract
When a nano-drop comprising a single spherical central ion and dielectric solvent is charged above a well-defined threshold, it acquires a stable star morphology. In contrast, conducting droplets, will undergo fission. Here we report combined atomistic molecular dynamics and continuum modelling study of star formation of droplets that contain a highly charged ion. We assume that in the continuum model the dielectric response is linear. In this linear continuum model, which is an extension of Rayleigh model, the energy of the drop is comprised of terms analogous to those in Rayleigh model, which are surface energy and electrostatic energy of dielectric droplet charged by a central point charge. We present the stability analysis of the continuum model to determine the threshold of instability. Indeed we find that the model accounts well for the onset of the instabilities. Molecular dynamics show that the number of points of the star-shaped nano-drops depends only on the surface tension, dielectric constant and size of the droplet, and on the magnitude of the charge of the central ion, but not on its sign. Intuitively, it is expected that when a spherical dielectric drop becomes unstable it would transform into a non-spherical finite shape of the same volume as the initial spherical shape with the point charge located in the drop interior. To test whether the extended Rayleigh model can account for the observed droplet shapes, we performed numerical simulations of the linear continuum model. Contrary to the expectations, the simulations of the extended Rayleigh model does not reproduce the stable star shapes found in the atomistic simulations, not even when we account for the bending rigidity and spontaneous curvature of the surface. We argue that the assumption that the dielectric response is linear breaks down if the droplet surface approaches the central macro-ion, where the electric field strength is such that dielectric saturation sets in. We envisage that for certain solvents, these stars could be made permanent by cross-linking, opening the way to the production of a novel class of highly-non-convex colloids.
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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 | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.001 |
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".