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.

However, determining the optimum elemental components and composition is challenging because of the different physical behaviors and chemical activities of the metal elements in catalytic reactions. Furthermore, it is difficult to determine the metal combination that must be investigated as it is difficult to exactly determine which metal element will affect the catalytic performance within the alloy. Before the introduction of computational techniques, researchers have mainly investigated binary and ternary alloys, with the focus on searching for high-performance multi-metallic catalysts by experimental trial and error. [8][9][10] For example, noble and non-noble metals, for example, platinum (Pt), [11][12][13] ruthenium (Ru), [14,15] iridium (Ir), [16,17] palladium (Pd), [18,19] and nickel (Ni), [20] iron (Fe), [21] cobalt (Co), [22] molybdenum (Mo), [23] as well as their alloys, are typically used in the hydrogen evolution reaction (HER), rendering the dimensionality of the space of alloy composition candidates far beyond human intuition or brute-force search by trial and error. However, it was almost impossible to search for the optimal component and composition for high-performance catalysts as the determination of the catalyst performance is a timeconsuming and expensive process due to the enormous number of candidate combinations and compositions.Searching for an optimal component and composition of multi-metallic alloy catalysts, comprising two or more elements, is one of the key issues in catalysis research. Due to the exhaustive data requirement of conventional machine-learning (ML) models and the high cost of experimental trials, current approaches rely mainly on the combination of density functional theory and ML techniques. In this study, a significant step is taken toward overcoming limitations by the interplay of experiment and active learning to effectively search for an optimal component and composition of multi-metallic alloy catalysts. The active-learning model is iteratively updated using by examining electrocatalytic performance of fabricated solid-solution nanoparticles for the hydrogen evolution reaction (HER). An optimal metal precursor composition of Pt 0.65 Ru 0.30 Ni 0.05 exhibits an HER overpotential of 54.2 mV, which is superior to that of the pure Pt catalyst. This result indicates the successful construction of the model by only utilizing the precursor mixture composition as input data, thereby improving the overpotential by searching for an optimal catalyst. This method appears to be widely applicable since it is able to determine an optimal component and composition of electrocatalyst without obvious restriction to the types of catalysts to which it can be applied.

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.

Small-molecule acceptor (SMA)-based organic solar cells (OSCs) have achieved high power conversion efficiencies (PCEs), while their long-term stabilities remain to be improved to meet the requirements for real applications. Herein, we demonstrate the use of donor−acceptor alternating copolymer-type compatibilizers (DACCs) in high-performance SMA-based OSCs, enhancing their PCE, thermal stability, and mechanical robustness simultaneously. Detailed experimental and computational studies reveal that the addition of DACCs to polymer donor (P D )− SMA blends effectively reduces P D −SMA interfacial tensions and stabilizes the interfaces, preventing the coalescence of the phase-separated domains. As a result, desired morphologies with exceptional thermal stability and mechanical robustness are obtained for the P D −SMA blends. The addition of 20 wt % DACCs affords OSCs with a PCE of 17.1% and a cohesive fracture energy (G c ) of 0.89 J m −2 , higher than those (PCE = 13.6% and G c = 0.35 J m −2 ) for the control OSCs without DACCs. Moreover, at an elevated temperature of 120 °C, the OSCs with 20 wt % DACC exhibit excellent morphological stability, retaining over 95% of the initial PCE after 300 h. In contrast, the control OSCs without the DACC rapidly degraded to below 60% of the initial PCE after 144 h.