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A 2020 study reported evidence that compressed liquid sulfur can exist in two distinct liquid states, with a first-order transition between them and a possible critical endpoint. The authors combined density, X-ray diffraction and Raman measurements; the strength of the evidence for the transition and for the critical point itself has since drawn different assessments.
What a liquid–liquid critical point means
A liquid–liquid transition (LLT) is a change between two liquid forms of the same substance. In the sulfur study, those forms were described as low-density liquid (LDL) and high-density liquid (HDL). This is not melting, which changes a solid into a liquid, or boiling, which changes a liquid into a gas.
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A liquid–liquid critical point (LLCP) is the endpoint of the boundary separating the two liquid states. Near such an endpoint, the distinction between the states disappears. The idea has also been proposed for other liquids, including water, but the sulfur paper focused on measurements in compressed liquid sulfur.
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What the sulfur experiment measured
Laura Henry and colleagues reported their findings in Nature on 19 August 2020. They combined three kinds of in situ measurement: density, X-ray diffraction and Raman scattering. The paper described the combination as direct evidence for a first-order LLT and an LLCP in sulfur. Read the Nature paper.
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- Density: The authors reported a sharp jump between the low- and high-density liquid states, a key signature of a first-order transition.
- X-ray diffraction: The measurements provided structural information, including distinct features in the pair distribution function.
- Raman scattering: This supplied another structural probe, complementing the density and diffraction evidence.
Considering these measurements together matters: the claim was not based only on an unexplained pressure anomaly. The authors also reported that the size of the density jump changes non-monotonically with temperature: it grows and then shrinks as conditions move away from the critical point. They linked this behavior to competing density and entropy effects. PubMed’s record of the paper summarizes that reported trend.
How strong is the evidence for the critical point?
The 2020 authors presented evidence for both a first-order transition and its critical endpoint. A contemporaneous expert assessment drew a distinction between those claims. Francesco Sciortino of Sapienza University of Rome told Chemistry World: “The liquid–liquid transition is there. The liquid–liquid critical point is 99.9% there. I wouldn’t say they’ve seen it because they didn’t do the experiment to see it.” He said small-angle diffraction measurements showing critical opalescence would be needed to establish the critical point conclusively. That was a qualification of the endpoint evidence, not a retraction of the paper’s findings. Read the Chemistry World report.
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Accordingly, “first experimental proof” reflects the 2020 paper’s framing. A careful reading separates its reported evidence for a first-order liquid transition from the contemporaneous view that the critical endpoint had not been observed conclusively.
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A 2024 Physical Review B ab initio molecular dynamics study revisited the reported first-order transition. Its abstract says the calculated pair-correlation functions agreed well with experimental results, but the simulations found a continuous structural change and no discontinuous density change along the simulated isotherms. This is a simulation result with a different interpretation, not a later experiment or a definitive resolution of the disagreement. Read the 2024 study.
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Do not confuse this with sulfur’s lambda transition
Sulfur also has a familiar lambda transition associated with polymerization at ambient pressure. That is a separate phenomenon from the compressed-liquid LLT in the 2020 study. A 2024 Chemical Science simulation paper examined the lambda transition, polymerization and ring formation; it provides context for sulfur’s complex liquid structure but does not test the same high-pressure transition. Read the 2024 Chemical Science study.
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