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A 2020 study of compressed liquid sulfur reported evidence for a transition between two liquid forms and for the critical point where that transition ends. The team combined density measurements with X-ray diffraction and Raman spectroscopy. Whether the experiment directly observed the critical point itself was debated at the time, and a later simulation offered a different account of the transition’s structure.
What is a liquid–liquid critical point?
A liquid–liquid transition (LLT) is a first-order change between two liquid states of the same substance. In the sulfur study, the states 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.
A liquid–liquid critical point (LLCP) is the endpoint of the boundary separating those two liquid states. The idea is significant because it proposes that a substance can have distinct liquid forms, much as it can have distinct solid phases.
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Laura Henry and colleagues reported their results in Nature on 19 August 2020. Their paper describes combined in situ density, X-ray diffraction, and Raman-scattering measurements as direct evidence for a first-order LLT and an LLCP in sulfur. Read the Nature paper.
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The measurements were used to identify both a sharp density jump and changes in liquid structure. The density result indicated a discontinuous change between the proposed liquid states; X-ray-derived pair-distribution information and Raman scattering supplied structural evidence. Together, the measurements made the case broader than an interpretation based on a pressure anomaly alone.
The authors also reported that the density jump did not simply shrink steadily as temperature moved away from the critical point: it first grew and then diminished. They linked this non-monotonic behavior to competing density and entropy effects. The available reported summary does not establish numerical critical coordinates, absolute densities, or uncertainty estimates, so those values are not given here.
Was the critical point directly observed?
The authors characterized their combined measurements as direct evidence for both the transition and the critical point. A contemporaneous expert comment drew a distinction between the strength of the evidence for the LLT and the evidence for its endpoint.
In a 2020 Chemistry World report, Francesco Sciortino of Sapienza University of Rome said, “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. This was a qualification of the endpoint evidence, not a retraction of the paper’s findings. Read the Chemistry World report.
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The same report described a rough experimental boundary: below about 1,035 K, increasing pressure caused a sudden drop in sample pressure, whereas above that temperature it did not. That is secondary reporting, not an exact critical temperature, and should not be treated as one.
How does later work affect the interpretation?
A 2024 Physical Review B paper used ab initio molecular dynamics to examine the reported first-order transition. Its authors said their calculated pair-correlation functions agreed well with experimental results, but their simulations showed a continuous structural change and no discontinuous density change along the simulated isotherms. This is a simulation result with a different interpretation, not a new experimental measurement or a definitive resolution of the disagreement. Read the 2024 study.
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How this differs from sulfur’s lambda transition
Sulfur is also known for a lambda transition associated with polymerization in liquid sulfur. That is distinct from the high-pressure LDL-to-HDL transition discussed in the 2020 study. A separate 2024 simulation investigated the lambda transition, polymerization, and ring formation; it should not be taken as evidence for or against the compressed-liquid LLT. Read the 2024 Chemical Science study.
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