Glassy Arrest Behind the Apparent Second Liquid in Water

Abstract

The origin of water's anomalous behavior remains a central open problem in the physical sciences and is often attributed to a liquid-liquid transition (LLT) between high- and low-density liquid states deep in the supercooled regime. Experimental access to this region has been challenging due to rapid crystallization, leaving atomistic simulations as a major source of supporting evidence. Using extensive machine-learning-accelerated first-principles simulations in direct comparison with spectroscopic, structural, and dynamical experimental measurements, we show that features commonly interpreted as signatures of two-liquid behavior emerge at the onset of dynamical arrest. Specifically, we find that two-state fluctuations previously associated with an LLT reflect a transformation from a high-density liquid to a kinetically arrested low-density glass. By mapping equilibrium dynamics across pressure and temperature, our results suggest a reassessment of water's metastable landscape, in which apparent two-state behavior may reflect a relatively high glass-transition temperature of ambient-pressure low-density water, 189$\pm$8 K -- remarkably close to the temperature previously associated with the LLT.

Figures (11)

• Figure 1: Apparent liquid--liquid fluctuations arise from intermittent kinetic arrest. Trajectories from the literature gartner2022liquidsciortino2025constraintsdebenedetti2020second obtained with two neural-network water models (DNN@SCAN, DNN@MB-pol) and the classical TIP4P/2005 potential show alternating intervals of high potential energy (in kJ/mol per molecule) with strong molecular diffusion and low potential energy with vanishing mobility. The latter corresponds to a dynamically arrested, low-density amorphous state, while the former reflects a mobile high-density liquid. A zoom into the arrested regime reveals negligible diffusion on $\sim$100 ns timescales for DNN@MB-pol and TIP4P/2005, and only limited motion for DNN@SCAN. Since crystallization is excluded, the low-density state is glassy, demonstrating that the reported fluctuations do not involve two liquids but transitions between a liquid and a glass. Temperatures indicated for the DNN models are corrected for their melting point mismatch with respect to experiment.
• Figure 2: Pressure- and cooling-driven vitrification. (A) Potential energy (in kJ/mol per molecule) during depressurization of equilibrated high-density liquid (HDL) configurations at 195 K using different pressure-ramp rates. Slower ramps produce progressively lower-energy states, characteristic of pressure-induced glass formation upon depressurization. Inset: physical aging after rapid depressurization reflects slow relaxation toward equilibrium. (B,C) Comparison to laser-heating X-ray experiments kim2020experimental. Simulated structure factors before and after depressurization reproduce the experimentally observed low-$q$ shift. The experimental signal is consistent with a mixture of HDL and a low-density amorphous state. (D) Cooling at ambient pressure shows rate-dependent trapping in lower-energy glassy states; inset: aging after fast cooling matches the energy scale of the apparent phase fluctuations. (E) Heat capacity during cooling evolves from a step-like glass-transition signature at fast rates to an additional peak at slower rates, approaching experimental droplet data. (F) Translational dynamics show that kinetic arrest coincides with the $C_p$ maximum, indicating that vitrification cuts off the divergence of $C_p$ on accessible timescales. For the dynamic arrest during depressurizing see Fig. \ref{['fig:dynArrest']}.
• Figure 3: Pressure- and temperature-dependent structural relaxation (A) Dielectric-loss peak positions from simulations at 1 bar and 5000 bar separate upon cooling, revealing much faster slowing of structural relaxation at ambient pressure. (B) Corresponding relaxation times show a pronounced minimum between 3000 and 5000 bar, with rapid growth for lower pressures at low temperatures. Open symbol is an extrapolation and black line a guide to the eye, see SM, Fig. \ref{['fig:extrapol']} for details. (C) Comparison to experimental relaxation times from dielectric spectroscopy fischer2020supercooled and NMR steinrucken2024complex (vertically shifted by a factor of 2, see SM, Fig. \ref{['fig:total_self']}) demonstrates close agreement with nanoconfined water at 1 bar. At 5000 bar, simulated relaxation times match those of a 14.8 mol% LiCl solution lunkenheimer2025exploring and yield a glass-transition temperature near 136 K. At 1 bar, relaxation slows much more steeply, leading to $T_g \approx 189\pm8$ K, depending on the model, placing kinetic arrest in the same temperature range where a liquid--liquid transition has been proposed.
• Figure 4: "Phase diagram" of the DNN@SCAN model. Circles connected by lines are isochrones, i.e., lines of equal structural relaxation time $\tau$, with values as indicated on the right side. Solid circles denote time scales covered by the simulations, while open circles are extrapolations with the VFT equation, see Fig. \ref{['fig:dyn']}. Solid blue line is the melting temperature taken from zhang2021phase. Squares connected by lines is the first-order–like transition between the two amorphous phases, taken as the average of the pressure up- and down-ramps reported in szukalo2025computational. The purported LLCP is taken from gartner2022liquid. The temperature at which the pressure dependence of the relaxation time is maximal is indicated as a dashed line.
• Figure S1: Influence of barostat settings on two-state fluctuations. Simulations performed with the DNN@SCAN model and 192 water molecules. Left: All setting according to the original work gartner2022liquid, where two-state fluctuations were observed (see Fig. \ref{['fig:MSD']}). Right: Damping times of barostat and thermostat increased by a factor of 10, all other settings identical.