Pressure-Temperature Phase Diagram and $\lambda$-Transition in Liquid Sulfur

TL;DR

This study uses machine-learned molecular dynamics to explore sulfur's phase diagram, revealing the microscopic mechanisms of its lambda transition, polymerization, and melting behaviors under various pressures and temperatures.

Contribution

It provides the first detailed microscopic picture of sulfur's lambda transition and polymerization processes across a range of pressures using advanced simulations.

Findings

Reproduces experimental signatures of the lambda transition, including heat capacity increase.

Reconstructs a phase diagram showing polymerization temperature decreases with pressure.

Provides evidence of polymerization emerging from crystalline sulfur before melting.

Abstract

Using molecular dynamics simulations driven by a machine-learned interatomic potential, we investigate at low to intermediate pressures the $\lambda$-transition of sulfur, a temperature-induced polymerization. At ambient pressure, we capture the melting of crystalline cyclo-octasulfur into a liquid of molecular rings. Within this liquid, the concentration of non-S$_8$ rings increases with temperature; we show that these molecules act as reactive centers, which eventually trigger polymerization. We reproduce key experimental signatures of the $\lambda$-transition, including the sharp increase in heat capacity and the pronounced dependence of the transition temperature on the heating rate. Building on this, we reconstruct a phase diagram of polymerization up to intermediate pressures. Our results reveal a moderate decrease of the polymerization temperature with pressure, culminating with its merging with the melting line at a critical point. Beyond this point, we provide direct evidence of polymerization emerging from the crystalline phase. By analyzing temperature-ramp trajectories, we observe the formation of non-S$_8$ rings, open chains, and extended polymeric structures which retain features of the crystalline arrangement; further heating the system leads to disorder taking over through melting. Polymerization is therefore initiated slightly before melting. Altogether, our findings provide a microscopic picture of the $\lambda$-transition throughout the sulfur phase diagram.