[Paper Review] Minimal microscopic model for liquid polyamorphism and water-like anomalies

Frédéric Caupin, М. А. Анисимов|arXiv (Cornell University)|Apr 16, 2021

Material Dynamics and Properties59 references40 citations

TL;DR

This paper proposes a minimal two-state lattice model for single-component fluids with water-like anomalies and liquid polyamorphism. By starting from a non-interconverting binary mixture with liquid-liquid demixing and critical azeotropy, and then introducing interconversion between two species with distinct energy and entropy, the model generates a unified framework that reproduces both liquid-liquid transitions with critical points and singularity-free scenarios with thermodynamic anomalies—offering a microscopic foundation for phenomena in supercooled water and other polyamorphic liquids.

ABSTRACT

Liquid polyamorphism is the intriguing possibility for a single component substance to exist in multiple liquid phases. We propose a minimal model for this phenomenon. Starting with a binary lattice model with critical azeotropy and liquid-liquid demixing, we allow interconversion of the two species, turning the system into a single-component fluid with two states differing in energy and entropy. Unveiling the phase diagram of the non-interconverting binary mixture gives unprecedented insight on the phase behaviors accessible to the interconverting fluid, such as a liquid-liquid transition with a critical point, or a singularity-free scenario, exhibiting thermodynamic anomalies without polyamorphism. The model provides a unified theoretical framework to describe supercooled water and a variety of polyamorphic liquids with water-like anomalies.

Motivation & Objective

• To establish a minimal microscopic model for liquid polyamorphism in single-component fluids.
• To connect phenomenological two-state models of water-like anomalies with underlying intermolecular interactions.
• To demonstrate how liquid-liquid transitions and thermodynamic anomalies emerge from a binary mixture with interconversion.
• To provide a unified theoretical framework for diverse polyamorphic systems, including water and sulfur.
• To clarify the role of interconversion equilibrium in shaping phase diagrams and anomalies.

Proposed method

• Uses a compressible binary lattice-gas model with two species (1 and 2) on a lattice, where sites are either empty or occupied.
• Introduces interaction energies −2ω1/z, −2ω2/z, and −2ω12/z for 1–1, 2–2, and 1–2 pairs, respectively.
• Analyzes the non-interconverting binary system to map its 3D T–P–x phase diagram, including liquid-liquid and liquid-vapor coexistence.
• Introduces interconversion between species 1 and 2 via changes in energy (e) and entropy (s), governed by reaction equilibrium at fixed T and P.
• Maps the resulting one-component fluid’s phase behavior as a 2D manifold embedded in the 3D binary phase diagram.
• Uses the model to reproduce both scenarios with and without a liquid-liquid critical point, including cases with opposite dP/dT slopes.

Experimental results

Research questions

• RQ1 How can a minimal microscopic model reproduce both liquid-liquid transitions and water-like anomalies in a single-component fluid?
• RQ2 What is the role of interconversion between two molecular states in enabling liquid polyamorphism?
• RQ3 How does the phase behavior of a non-interconverting binary mixture inform the phase diagram of the interconverting one-component fluid?
• RQ4 Can the model explain both the presence and absence of a liquid-liquid critical point, as seen in water and sulfur?
• RQ5 How do thermodynamic anomalies like density maxima and compressibility extrema emerge from the interconversion mechanism?

Key findings

• The model reproduces a liquid-liquid transition with a critical point (LLCP) for ω12 = 1.04 and 1.12, with the LLCP located at T ≈ 0.69, P ≈ 0.12.
• For ω12 = 1.16, the system exhibits a singularity-free scenario with no LLCP, showing anomalies without polyamorphism.
• The lines of anomalies (density maxima, compressibility maxima) in the model align qualitatively with experimental data for supercooled water, despite using far fewer parameters.
• The spinodal curve for the LL transition shows non-monotonic behavior in pressure for ω12 = 1.04, with a maximum and minimum, indicating complex stability boundaries.
• The model successfully captures the coexistence of liquid-vapor and liquid-liquid equilibria, including a triple point and a LLV triple line.
• The phase diagram of the interconverting fluid is a 2D manifold embedded in the 3D binary phase diagram, providing a geometric framework for understanding polyamorphism.