Modeling the Liquid-Liquid Phase Transition in Polymeric Sulfur

We suggest a simple model to describe the recently observed phase separation in liquid sulfur (Nature, 584, 382, 2020), which polymerizes at high temperatures and pressures. The model contains three types of interactions: i) atoms attract each other by van der Waals forces which produce the liquid-gas phase transition at low pressures, ii) atoms may form covalent bonds which induce polymerization, and iii) polymerized atoms attract each other by van der Waals forces stronger than nonpolymerized atoms. We show that the latter interaction couples polymerization with phase segregation and produces the liquid-liquid phase transition that was recently observed in sulfur. We implement these three conditions using a discrete molecular dynamics approach. The phase diagram and structure factor demonstrate a qualitative agreement with the behavior of real sulfur. Introduction Above 160 °C, at ambient pressure, sulfur polymerizes with a sharp increase in viscosity, which has been interpreted as a “lambda transition” to a polymerized state [1–3]. However, with further increase of temperature, as the system approaches the liquid-gas phase transition (LGPT), the polymer chains gradually dissociate and the viscosity decreases. Previous studies of sulfur have predicted a liquid-liquid phase transition (LLPT) at very high pressures, based on its electronic properties [4]. Contrarily, more recent ab initio molecular dynamics simulations predicted a continuously decreasing average polymer chain length upon heating at 10 GPa, not associated with a change in density [5]. Recently, it was discovered that high-density sulfur, well above the liquid-gas critical pressure (in the range from 0.5 to 2.0 GPa), exhibits a LLPT indicated by a discontinuity in density from a low-density liquid (LDL) to a high-density liquid (HDL) [6]. This LLPT in polymerizing substances has also been observed in phosphorous [7] and liquid carbon [8], while being proposed to exist in selenium and tellurium [4,5]. The coexistence of two alternative liquid phases in a single component substance, like sulfur, is known as “liquid polyamorphism” [9, 10], which was first observed by molecular dynamics simulations of classical all-atom models of supercooled water [11–14]. This phenomenon can be understood via two-state thermodynamics [15, 16], in which two alternative molecular or supramolecular states may interconvert via a reversible reaction [16, 17]. In spite of the significant recent progress [18], no definitive experimental confirmation of a liquid-liquid transition in water has been found yet [10]. Computationally, a LLPT has also been observed in single-component systems with core soften potentials [19–24], e.g. a spherically symmetric potential consisting of a wide attractive well and a repulsive shoulder. In such models, the particles may acquire alternative local structures, forming high-density and low-density phases, which can be understood through the two-state idea. In this work, using this approach, we propose a maximum-valence model [25–27] where atoms may form covalent bonds via a reversible reaction, changing their state according to the number of bonds they have with other atoms. We assume that the atoms form linear polymers with a maximum of two bonds per atom, mimicking the valence structure and bond formation similar to sulfur. We consider the scenario where polymerized atoms (with two bonds) attract each other stronger than the other unbonded atoms and single-bonded atoms in the system. Our molecular dynamics (MD) simulations demonstrate that this model is able to qualitatively reproduce the LLPT observed in sulfur, and demonstrates that the polymerization reaction is the cause of this liquid-liquid phase separation. 1 ar X iv :2 11 1. 08 10 9v 1 [ co nd -m at . s of t] 1 5 N ov 2 02 1