Liquid-liquid critical point mapped in deep neural network

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

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

One of these unusual features has prompted decades of research to understand the unique behavior of water, especially in the supercooled regime.

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

“Water is unique, with properties that scientists have been trying to understand for decades,” explained Prof. Francesco Paesani, of the University of California San Diego.

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

Prof. Francesco Sciortino, co-author of the study, continued: “The point at which these two phases become imperceptible 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.”

Photo Left: snapshot of a molecular dynamics simulation of supercooled water. Right: Phase diagram of supercooled water predicted by molecular dynamics simulations with the DNN@MB-pol potential.

The predicted critical point is indicated as a star at the end of the Widom line (blue), corresponding to the location of maximum fluctuations along the isobars.

Liquid-liquid phase transition

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

In 1992, researchers first proposed that water could 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 postdoctoral fellow at Boston University.

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

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

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

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

A mixture of curiosity and skepticism surrounding the fact that MB-pol could rigorously probe the validity of the two-liquid 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 (DNN@MB-pol) trained on MB-pol data.

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 molecular dynamics simulations.

“These are crucial for studying water in deeply supercooled states because, as the temperature decreases, molecular diffusion slows down dramatically.

This slowdown makes it increasingly difficult for the system to reach a metastable equilibrium, requiring exceptionally long simulations to capture the relevant dynamics,” explained Prof. Paesani.

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

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

Identifying liquid-liquid 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 approximately 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, the clear signature of such transitions.

Taking into account the systematic deviation of the model compared to experimental values, the team estimated the actual critical point in water to be approximately 198 K (-75 °C) and 126.7 MPa.

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

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

“We are very confident in our estimated critical point because it is developed from first-principles quantum chemistry at the coupled theory level – 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 LLPT in water, helping to resolve a scientific question that has persisted for over 30 years.

The researchers believe that water nanodroplets – water droplets just nanometers wide that exist 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 route to probe the LLCP,” said Prof. Paesani.

Prof. Sciortino added: “Neutron and X-ray scattering experiments could be used to detect the structural signatures of the two states in these closed droplets.”

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

The discovery of LLPT has a broad impact on multiple scientific fields.

Understanding the behavior of water in its two states could improve climate modeling and weather prediction, provide insights into oceans on distant moons and planets.

It could also improve understanding of cellular processes driven by phase separation, and advance energy storage and water treatment technologies.

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Source: phys.org, pnas.org, researchgate.net.

Foto: F. Sciortino et al.

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