Lignin nanoparticles of uniform, small quasi-spherical shape with a relatively high BET surface area (nearly 92 m2 g−1) were synthesized using a facile, one pot technology of a compressed CO2 antisolvent.

Density fluctuations and the Widom line are of great importance in understanding the critical phenomena and the behaviors of supercritical fluids (SCFs). We report on the direct classification of liquid-like and gas-like molecules coexisting in the SCF, identified by machine learning analysis on simulation data. The deltoid coexistence region encloses the Widom line and may therefore be termed the Widom delta. Number fractions of gas-like and liquid-like particles are found to undergo continuous transition across the delta, following a simplified two-state model. These fractions are closely related to the magnitude of supercritical anomaly, which originates from the fluctuation between the two types. This suggests a microscopic view of the SCF as a mixture of liquid-like and gas-like structures, providing an integrative explanation to the anomalous behaviors near the critical point and the Widom line.

The dynamics of supercritical fluids, a state of matter beyond the gas–liquid critical point, changes from diffusive to oscillatory motions at high pressure. This transition is believed to occur across a locus of thermodynamic states called the Frenkel line. The Frenkel line has been extensively investigated from the viewpoint of the dynamics, but its structural meaning is still not well-understood. This Letter interprets the mesoscopic picture of the Frenkel line entirely based on a topological and geometrical framework. This discovery makes it possible to understand the mechanism of rigid–nonrigid transition based not on the dynamics of individual atoms but on their instantaneous configurations. The topological classification method reveals that the percolation of solid-like structures occurs above the rigid–nonrigid crossover densities.

The Frenkel line, a crossover line between rigid and nonrigid dynamics of fluid particles, has recently been the subject of intense debate regarding its relevance as a partitioning line of the supercritical phase, where the main criticism comes from the theoretical treatment of collective particle dynamics. From an independent point of view, this Letter suggests that the two-phase thermodynamics model may alleviate this contentious situation. The model offers new criteria for defining the Frenkel line in the supercritical region and builds a robust connection among the preexisting, seemingly inconsistent definitions. In addition, one of the dynamic criteria locates the rigid-nonrigid transition of the soft-sphere and the hard-sphere models. Hence, we suggest the Frenkel line be considered as a dynamic rigid-nonrigid fluid boundary, without any relation to gas-liquid transition. These findings provide an integrative viewpoint combining fragmentized definitions of the Frenkel line, allowing future studies to be carried out in a more reliable manner.

Supercritical fluid (SCF) is known to exhibit salient dynamic and thermodynamic crossovers and an inhomogeneous molecular distribution. However, the question as to what basic physics underlies these microscopic and macroscopic anomalies remains open. Here, using an order parameter extracted by machine learning, the fraction of gas-like (or liquid-like) molecules, we find simplicity and universality in SCF: First, all isotherms of a given fluid collapse onto a single master curve described by a scaling relation. The observed power law holds from the high-temperature and -pressure regime down to the critical point where it diverges. Second, phase diagrams of different compounds collapse onto their master curves by the same scaling exponent, thereby demonstrating a putative law of corresponding supercritical states in simple fluids. The reported results support a model of the SCF as a mixture of two interchangeable microstates, whose spatiotemporal dynamics gives rise to unique macroscopic properties.