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1. Thermodynamic analysis of anomalous region, critical point, and transition from subcritical to supercritical states: Application to van der Waals and five real fluids

   https://doi.org/10.1063/5.0179651  

   Wang, Guo-Xiang; Almara, Laura M; Prasad, Vish (February 2024, Physics of Fluids)

   All fluids exhibit large property-variations near the critical point in a region identified as the anomalous state. The anomaly starts in the liquid and extends well into the supercritical state, which can be identified thermodynamically using the Gibbs free energy (g). The specific heat, isobaric expansion, and isothermal compressibility parameters governing the transitions are: (cp/T), (vβ), and (vκ), rather cp, β, and κ. They are essentially the second-order derivatives of g and have two extrema (minimum, maximum); only maxima reported ever. When applied to the van der Waals fluid, these extrema exhibit closed loops on the phase-diagram to satisfy d3g = 0 and map the anomalous region. The predicted liquid-like to gas-like transitions are related to the ridges reported earlier, and the Widom delta falls between these loops. Evidently, in the anomalous region, both the liquid and the supercritical fluid need to be treated differently. Beyond the anomalous states, the supercritical fluids show monotonic, gradual changes in their properties. The analysis for argon, methane, nitrogen, carbon dioxide, and water validates the thermodynamic model, supports the stated observations, and identifies their delimiting pressures and temperatures for the anomalous states. It also demonstrates the applicability of the law of corresponding states. Notably, the critical point is a state where d3g = 0, the anomaly in the fluid's properties/behavior is maximal, and the governing parameters approach infinity. Also the following are presented: (a) the trajectory of the liquid–vapor line toward the melt-solid boundary and (b) a modified phase diagram (for water) exhibiting the anomalous region. 

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2. Dynamic compression of water to conditions in ice giant interiors

   https://doi.org/10.1038/s41598-021-04687-6  

   Gleason, A. E.; Rittman, D. R.; Bolme, C. A.; Galtier, E.; Lee, H. J.; Granados, E.; Ali, S.; Lazicki, A.; Swift, D.; Celliers, P.; et al (December 2022, Scientific Reports)

   Abstract Recent discoveries of water-rich Neptune-like exoplanets require a more detailed understanding of the phase diagram of H 2 O at pressure–temperature conditions relevant to their planetary interiors. The unusual non-dipolar magnetic fields of ice giant planets, produced by convecting liquid ionic water, are influenced by exotic high-pressure states of H 2 O—yet the structure of ice in this state is challenging to determine experimentally. Here we present X-ray diffraction evidence of a body-centered cubic (BCC) structured H 2 O ice at 200 GPa and ~ 5000 K, deemed ice XIX, using the X-ray Free Electron Laser of the Linac Coherent Light Source to probe the structure of the oxygen sub-lattice during dynamic compression. Although several cubic or orthorhombic structures have been predicted to be the stable structure at these conditions, we show this BCC ice phase is stable to multi-Mbar pressures and temperatures near the melt boundary. This suggests variable and increased electrical conductivity to greater depths in ice giant planets that may promote the generation of multipolar magnetic fields. 

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3. Purification and Fractionation of Lignin via ALPHA: Liquid–Liquid Equilibrium for the Lignin–Acetic Acid–Water System

   https://doi.org/10.1002/cssc.202300989  

   Agede, Oreoluwa; Thies, Mark_C (October 2023, ChemSusChem)

   Abstract In order to effectively practice the Aqueous Lignin Purification with Hot Agents (ALPHA) process for lignin purification and fractionation, the temperatures and feed compositions where regions of liquid–liquid equilibrium (LLE) exist must be identified. To this end, pseudo‐ternary phase diagrams for the lignin–acetic acid–water system were mapped out at 45–95 °C and various solvent: feed lignin mass ratios (S : F). For a given temperature, the accompanying SL (solid–liquid), SLL (solid–liquid–liquid), and one‐phase regions were also located. For the first time, ALPHA using acetic acid (AcOH)–water solution was applied to a lignin recovered via the commercial LignoBoost process. In addition to determining tie‐line compositions for the two regions of LLE that were discovered, the distribution of lignin and key impurities (the latter can negatively impact lignin performance for materials applications) between the two liquid phases was also measured. As a representative example, lignin isolated in the lignin‐rich phase was reduced 7x in metals and 4x in polysaccharides by using ALPHA with a feed solvent composition of 50–55 % AcOH and an S : F of 6 : 1, with said lignin being obtained at a yield of 50–70 % of the feed lignin and having a molecular weight triple that of the feed. 

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4. Computational investigation of water glasses using machine-learning potentials

   https://doi.org/10.1073/pnas.2509609122  

   Szukalo, Ryan J; Giovambattista, Nicolas; Debenedetti, Pablo G (August 2025, Proceedings of the National Academy of Sciences)

   The molecular origins of water’s anomalous properties have long been a subject of scientific inquiry. The liquid–liquid phase transition hypothesis, which posits the existence of distinct low-density and high-density liquid states separated by a first-order phase transition terminating at a critical point, has gained increasing experimental and computational support and offers a thermodynamically consistent framework for many of water’s anomalies. However, experimental challenges in avoiding crystallization near the postulated liquid–liquid critical point have focused attention to water’s canonical glassy states: low-density and high-density amorphous ice. Here, we use two Deep Potential machine-learning models, trained on the Strongly Constrained and Appropriately Normed density functional and the highly accurate Many-Body Polarizable potential, to conduct an investigation of water’s glassy phenomenology based on quantum mechanical calculations. Despite not being explicitly trained on amorphous ices, both models accurately capture the structure and transformation of the water glasses, including their interconversion along different thermodynamic paths. Isobaric quenching of liquid water at various pressures generates a continuum of intermediate amorphous ices and density fluctuations increase near the liquid–liquid critical pressure. The glass transition temperatures of the amorphous ices produced at different pressures exhibit two distinct branches, corresponding to low-density and high-density amorphous ice behaviors, consistent with experiment and the liquid–liquid transition hypothesis. Extrapolating transformation pressures from isothermal compressions to experimental compression rates brings our simulations into excellent agreement with data. Our findings demonstrate that machine-learning potentials trained on equilibrium phases can effectively model nonequilibrium glassy behavior and pave the way for studying long-timescale, out-of-equilibrium processes with quantum mechanical accuracy. 

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5. Manifestations of metastable criticality in the long-range structure of model water glasses

   https://doi.org/10.1038/s41467-021-23639-2  

   Gartner, III, Thomas E.; Torquato, Salvatore; Car, Roberto; Debenedetti, Pablo G. (June 2021, Nature Communications)

   Abstract Much attention has been devoted to water’s metastable phase behavior, including polyamorphism (multiple amorphous solid phases), and the hypothesized liquid-liquid transition and associated critical point. However, the possible relationship between these phenomena remains incompletely understood. Using molecular dynamics simulations of the realistic TIP4P/2005 model, we found a striking signature of the liquid-liquid critical point in the structure of water glasses, manifested as a pronounced increase in long-range density fluctuations at pressures proximate to the critical pressure. By contrast, these signatures were absent in glasses of two model systems that lack a critical point. We also characterized the departure from equilibrium upon vitrification via the non-equilibrium index; water-like systems exhibited a strong pressure dependence in this metric, whereas simple liquids did not. These results reflect a surprising relationship between the metastable equilibrium phenomenon of liquid-liquid criticality and the non-equilibrium structure of glassy water, with implications for our understanding of water phase behavior and glass physics. Our calculations suggest a possible experimental route to probing the existence of the liquid-liquid transition in water and other fluids. 

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