Scientists map elusive liquid-liquid transition point using deep neural network

A new Nature Physics study has shed light on the long-hypothesized liquid-liquid critical point where water simultaneously exists in two distinct liquid forms, opening new possibilities for experimental validation.

Water is known for its anomalous properties—unlike most substances, water is densest in its liquid state, not solid. This leads to unique behaviors such as ice floating on water.

One of several such unusual characteristics has prompted decades of research to understand water’s unique behavior, particularly in the supercooled regime.

However, studying the liquid-liquid phase transition (LLPT), which is hypothesized to occur in the supercooled regime, has faced challenges that the researchers wanted to address.

Phys.org spoke to co-authors of the study, Prof. Francesco Sciortino from Sapienza University of Rome and Prof. Francesco Paesani from the University of California San Diego, about their work.

“Water is a unique liquid with properties that scientists have been trying to understand for decades,” explained Prof. Paesani.

“One long-standing hypothesis suggests that under extreme conditions—specifically at very low temperatures and high pressures—water can exist in two distinct liquid phases: a high-density liquid and a low-density liquid.”

Prof. Sciortino continued, “The point at which these two phases become indistinguishable is known as the liquid-liquid critical point. However, its experimental confirmation has remained elusive due to the challenge of preventing water from freezing before reaching these conditions.”

The liquid-liquid phase transition

When pure water is cooled to -38°C, it remains in liquid form despite passing its freezing point at 0°C. This is known as a supercooled state.

In 1992, researchers first proposed that water may have a liquid-liquid phase transition (LLPT) below the supercooled point of -38°C, where it exists in two distinct liquid states or phases.

Prof. Sciortino worked on this problem in 1992 as a postdoc at Boston University.

The difficulty stems from what researchers call “no man’s” land, a region in water’s phase diagram where liquid water typically crystallizes instantly into ice before measurements can be made. This happens below the -38°C supercooled critical point.

The inability to conduct measurements in real-time has forced researchers to rely heavily on computer simulations to predict water’s behavior.

Previous studies have yielded widely varying predictions for the location of the proposed liquid-liquid critical point (LLCP), with estimated critical pressures ranging from 36 to 270 MPa and critical temperatures from -123°C to -23°C (or 150 to 250 K).

The solution came in the form of a conversation between Prof. Sciortino and Prof. Paesani about a data-driven many-body potential developed by Prof. Paesani’s team, MB-pol.

A mixture of curiosity and skepticism surrounding whether MB-pol could rigorously probe the validity of the two-liquids scenario in deeply supercooled water led them to pursue this research.

Using deep neural networks

“Despite its accuracy, MB-pol is computationally more demanding than empirical models. To overcome this limitation, Sigbjørn Bore, the third author of this paper, developed a deep neural network potential (DNN@MB-pol) trained on MB-pol data,” said Prof. Paesani, explaining the involvement of neural networks in their research.

Unlike previous water models, this approach is derived from first-principles quantum chemistry at the coupled-cluster level, which is considered the gold standard for molecular interactions.

Using the DNN@MB-pol model, the researchers performed microsecond-long molecular dynamics simulations.

“These are crucial for studying water in deeply supercooled states because, as the temperature decreases, molecular diffusion slows dramatically. This slowdown makes it increasingly difficult for the system to reach metastable equilibrium, requiring exceptionally long simulations to capture the relevant dynamics,” explained Prof. Paesani.

The simulations were conducted at 280 different state points ranging across 20 temperatures (188 to 368 K or -85°C to 95°C) and 14 pressures (0.1–131.7 MPa).

All the simulations were conducted with a system of 256 water molecules under periodic boundary conditions.

Identifying phase transitions

The simulations revealed direct evidence for two distinct liquid states with different densities and structures.

When studying water at -85°C (188 K), the researchers observed dramatic density fluctuations occurring on microsecond timescales, with water spontaneously switching between high-density and low-density states at around 101.3 MPa.

These observations confirmed the existence of a first-order phase transition between two liquid forms of water, with free-energy barriers that increase upon cooling, a clear signature of such transitions.

Accounting for the model’s systematic deviation compared to experimental values, the team estimated the actual critical point in water at approximately 198 K (-75°C) and 126.7 MPa.

Perhaps most significantly, the critical point identified in this research appears at a lower pressure than many previous predictions, suggesting it may be experimentally accessible.

The researchers were also able to construct a comprehensive phase diagram showing the liquid-liquid coexistence curve.

“We are highly confident in our estimated liquid-liquid critical point as it is developed from first-principles quantum chemistry at the coupled-cluster level of theory—the gold standard for electronic structure calculations,” said Prof. Sciortino.

Nanodroplets for validation

The results provide the strongest computational evidence yet for the existence of the LLPT in water, helping to resolve a scientific question that has persisted for over 30 years.

Researchers believe that water nanodroplets—water droplets nanometers wide existing in confined spaces or suspended in a medium—could experimentally validate the LLPT results.

“For nanodroplets just a few nanometers in diameter, the internal pressure could reach values comparable to the liquid-liquid critical pressure (~1,250 atm). This suggests that carefully controlled nanodroplets could provide an experimental pathway to probe the LLCP,” said Prof. Paesani.

Prof. Sciortino added, “Neutron and X-ray scattering experiments could be used to detect structural signatures of the two liquid states within these confined droplets.”

“Specifically, scattering techniques could reveal density fluctuations and correlations characteristic of critical phenomena. Additionally, time-resolved spectroscopy could help capture the interconversion dynamics between the two liquid phases.”

The discovery of LLPT has broad impacts on multiple scientific fields.

Understanding water’s dual-state behavior could improve climate modeling and weather prediction, provide insights into oceans on distant moons and planets, enhance our understanding of cellular processes driven by phase separation, and advance technologies in energy storage and water treatment.

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