Which liquids have liquid-liquid transitions, and why?
In plain words
Besides water, a few substances such as phosphorus and sulfur show a jump between two liquid forms, while for others the claim is disputed. There is no rule that says which liquids should have such a transition.
Precise statement
First-order liquid-liquid transitions are reported in phosphorus and sulfur at high pressure and temperature and are debated in Si, $\mathrm{SiO_2}$, triphenyl phosphite and some metallic glass formers. Find a criterion based on interaction potential and local structure (tetrahedral order, two competing local structures, softness of the repulsion) that predicts which single-component liquids show a liquid-liquid transition in the stable or metastable range, and test it across these systems.
What would settle it
A criterion that correctly classifies a set of model liquids in simulation and the established experimental cases, with predictions for untested substances later confirmed.
Status in the literature
Unverified note: it names recent work and was partly written without a live literature search; it awaits a check by an editor.
A liquid-liquid transition ending at a critical point was reported in sulfur in 2020 (Henry et al., Nature, https://doi.org/10.1038/s41586-020-2593-1); no general criterion exists (2026).
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